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| author | Trupti Kini | 2016-10-18 23:30:51 +0600 |
|---|---|---|
| committer | Trupti Kini | 2016-10-18 23:30:51 +0600 |
| commit | 09dc3da07e710f52a87266a26662cd2c411f3583 (patch) | |
| tree | bab66ccd17827018fd0f645082b4c6c0bcb19951 | |
| parent | 1f7d1c7231ae73445a3fda359da82e1f544c2e63 (diff) | |
| download | Python-Textbook-Companions-09dc3da07e710f52a87266a26662cd2c411f3583.tar.gz Python-Textbook-Companions-09dc3da07e710f52a87266a26662cd2c411f3583.tar.bz2 Python-Textbook-Companions-09dc3da07e710f52a87266a26662cd2c411f3583.zip | |
Added(A)/Deleted(D) following books
A Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_10_Properties_Of__9OtCJTM.ipynb
A Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_11_Steam_Boilers_ZbPMcer.ipynb
A Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_13_Steam_Engines_93BIP5u.ipynb
A Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_14_Air_Standard_C_Wu44kME.ipynb
A Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_2_Properties_Of_M_CMataUP.ipynb
A Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_5_Metrology_tKHsuep.ipynb
A Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_7_Fluid_Mechanics_xkevzFX.ipynb
A Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_9__Laws_Of_Thermo_bIsIgqq.ipynb
A Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/screenshots/chapter10.png
A Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/screenshots/chapter14.png
A Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/screenshots/chapter5.png
A Digital_Communications_by_S._Haykin/Chapter1_bmaHHM8.ipynb
A Digital_Communications_by_S._Haykin/Chapter2_XLwGLkV.ipynb
A Digital_Communications_by_S._Haykin/Chapter3_JoJ2mAG.ipynb
A Digital_Communications_by_S._Haykin/Chapter4_D4b1XOQ.ipynb
A Digital_Communications_by_S._Haykin/Chapter5_dSjZdtS.ipynb
A Digital_Communications_by_S._Haykin/Chapter6_zB6BWD2.ipynb
A Digital_Communications_by_S._Haykin/Chapter7_iOFdfcy.ipynb
A Digital_Communications_by_S._Haykin/Chapter8_ffLFErg.ipynb
A Digital_Communications_by_S._Haykin/Chapter9_4roMWPw.ipynb
A Digital_Communications_by_S._Haykin/screenshots/Ch-6_RaisedCosineSpectrum_NizDJ8d.png
A Digital_Communications_by_S._Haykin/screenshots/Ch6_powerSpectralDensities_9tUd56q.png
A Digital_Communications_by_S._Haykin/screenshots/ch6_sinc_pilse_snbi7FJ.png
A Electrical_Machines_-_I_by_M._Verma_And_V._Ahuja/README.txt
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter10_8mim6PA.ipynb
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter11_NAIDtL1.ipynb
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter15_F19vfPd.ipynb
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter1_fAOC2QW.ipynb
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter2_NaNiwP4.ipynb
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter3_xiZnYrP.ipynb
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter5_b3JDxfA.ipynb
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter6_hxtqyXd.ipynb
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter7_QXJtmam.ipynb
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter8_ojfkyD4.ipynb
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter9_1ERbfbH.ipynb
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/ctftch1_EJ1lbz2.png
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/fourier_Kpk6AU4.png
A Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/modulat_XbQVmZD.png
A Semiconductor_circuit_approximations_by_A.P._Malvino/README.txt
A Strength_Of_Materials_by_S_S_Bhavikatti/chapter_02.ipynb
A Strength_Of_Materials_by_S_S_Bhavikatti/chapter_03.ipynb
A Strength_Of_Materials_by_S_S_Bhavikatti/chapter_04.ipynb
A Strength_Of_Materials_by_S_S_Bhavikatti/chapter_05.ipynb
A Strength_Of_Materials_by_S_S_Bhavikatti/chapter_06.ipynb
A Strength_Of_Materials_by_S_S_Bhavikatti/chapter_07.ipynb
A Strength_Of_Materials_by_S_S_Bhavikatti/chapter_08.ipynb
A Strength_Of_Materials_by_S_S_Bhavikatti/chapter_09.ipynb
A Strength_Of_Materials_by_S_S_Bhavikatti/chapter_10.ipynb
A Strength_Of_Materials_by_S_S_Bhavikatti/screenshots/BMD_QksEdap.PNG
A Strength_Of_Materials_by_S_S_Bhavikatti/screenshots/SFD_1_mX9fTGM.png
A Strength_Of_Materials_by_S_S_Bhavikatti/screenshots/SFD_2_dBvOQ58.png
51 files changed, 24070 insertions, 0 deletions
diff --git a/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_10_Properties_Of__9OtCJTM.ipynb b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_10_Properties_Of__9OtCJTM.ipynb new file mode 100644 index 00000000..627fc0f4 --- /dev/null +++ b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_10_Properties_Of__9OtCJTM.ipynb @@ -0,0 +1,629 @@ +{ + "metadata": { + "name": "Chapter 10 Properties Of Steam" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "\nChapter 10 Properties Of Steam" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 1 Page No:183" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nmw=15 #Water steam\nms=185 #Dry steam\n\n#Calculation\nx=((ms)/(ms+mw))*100 #Dryness fuction of steam in %\n\n#Output\nprint(\"Dryness fuction of steam=\",x,\"%\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Dryness fuction of steam= 92.5 %\n" + } + ], + "prompt_number": 66 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 2 Page No:183" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nsps=150 #saturation pressure of the steam in degree celsius\n\n#Output\nP=4.76 #From steam table\nprint(\"saturation pressure=\",P,\"bar\")\n\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "saturation pressure= 4.76 bar\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 3 Page No:184" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP1=28 #Absolute pressure in bar\nP2=5.5 #Absolute pressure in MPa\nP3=77 #Absolute pressure in mm of Hg\n\n#Calcutation\nts1=230.05 #Saturation temperature in degree celsius\nts2=269.93 #Saturation temperature in degree celsius\nts3=45.83 #Saturation temperature in degree celsius\n\n#Output\nprint(\"Saturation temperature= \",ts1,\"degree celsius\")\nprint(\"Saturation temperature= \",ts2,\"degree celsius\")\nprint(\"Saturation temperature= \",ts3,\"degree celsius\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Saturation temperature= 230.05 degree celsius\nSaturation temperature= 269.93 degree celsius\nSaturation temperature= 45.83 degree celsius\n" + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 4 Page No:185" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP=15 #Absolute pressure in bar\n#From steam table (pressure basis at 15 bar)\nts=198.3 #In degree celsius \nhf=844.7 #In KJ/Kg\nhfg=1945.2 #In KJ/Kg\nhg=2789.9 #In KJ/Kg\ntsup=300 #In degree celsius \nx=0.8\nCps=2.3\nhg=2789.9\n\n#Calculation\nh1=hf+x*hfg #Enthalpy of wet steam in KJ/KG\nh=hg #Enthalpy of dry and saturated steam in KJ/KG\nh2=hg+Cps*(tsup-ts)#Enthalpy of superheated steam in KJ/KG\n\n\n#Output\nprint(\"Enthalpy of wet steam= \",h1,\"KJ/Kg\")\nprint(\"Enthalpy of dry and saturated steam= \",h,\"KJ/KG\")\nprint(\"Enthalpy of superheated steam= \",h2,\"KJ/Kg\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of wet steam= 2400.86 KJ/Kg\nEnthalpy of dry and saturated steam= 2789.9 KJ/KG\nEnthalpy of superheated steam= 3023.81 KJ/Kg\n" + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 5 Page No:186" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nti=30 #Temperature in degree celsius\nm=2 #Water in Kg\npf=8 #Steam at 8 bar\nx=0.9 #Water to dry \ntb=30\n#From steam table at 30 degree celsius\nhf=125.7\n#From steam table at 8 bar\nts=170.4 #In degree celsius \nhf1=720.9 #In KJ/KG\nhfg=2046.6 #In KJ/KG\nhg=2767.5 #In KJ/KG\n\n#Calculation\nh=hf1+(x*hfg) #Final Enthalpy of the steam in KJ/Kg\nQha=m*(h-hf) #Quantity of the heat in KJ/Kg\n\n#Output\nprint(\"Final Enthalpy of the steam= \",h,\"KJ/Kg\")\nprint(\"Quantity of the heat= \",Qha,\"KJ/Kg\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Final Enthalpy of the steam= 2562.84 KJ/Kg\nQuantity of the heat= 4874.280000000001 KJ/Kg\n" + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 6 Page No:186" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nIT=25 #Initial temperature\nm=5 #Heat required to generate steam in kg\npf=10 #Final pressure in bar\ntsup=250 #Water temperature\n#From steam table (temp basis)at 25degree celsius \n#and at 10 bar(pressure basis)\nhf=104.8 #In KJ/KG\nh1=104.8 #In KJ/KG\nts=179.9 #In degree celsius \nhf1=792.6 #In KJ/KG\nhfg=2013.6 #In KJ/KG\nhg=2776.2 #In KJ/KG\nCps=2.1\n\n#Calculation\nh=hg+Cps*(tsup-ts) #Enthalpy of superheated steam in KJ/Kg\nH=m*(h-h1) #Quantity of heat added in KJ/Kg\n\n#Output\nprint(\"Enthalpy of superheated steam= \",h,\"KJ/Kg\")\nprint(\"Quantity of heat added= \",round(H,),\"KJ/Kg\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of superheated steam= 2923.41 KJ/Kg\nQuantity of heat added= 14093 KJ/Kg\n" + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 7 Page No:188" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP=15 #Absolute pressure in bar\n#From steam table (pressure basis at 15 bar)\nts=198.3+273 #In degree celsius\nvg=0.1317 #In m**3/Kg \nvf=0.001154 #In m**3/Kg \nx=0.8 \nTsup=300+273 #Degree celsius\n\n\n#Calculation\nv=(1-x)*vf+x*vg #Volume of wet steam in m**3/Kg\nvg=0.1317 #Dry and saturated steam in m**3/Kg\nvsup=vg*(Tsup/ts) #Volume of superheated steam m**3/Kg \n\n\n#Output\nprint(\"Volume of wet steam= \",round(v,4),\"m**3/Kg\")\nprint(\"Dry and Saturated Steam= \",vg,\"m**3/Kg\") \nprint(\"volume of superheated steam= \",round(vsup,4),\"m**3/Kg\")\n \n\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Volume of wet steam= 0.1056 m**3/Kg\nDry and Saturated Steam= 0.1317 m**3/Kg\nvolume of superheated steam= 0.1601 m**3/Kg\n" + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 8 Page No:188" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP=25 #Absolute pressure\nts=223.9 #Volume\n#Frome steam table (pressure basis at 25 bar) \nvf=0.001197 #In m**3/Kg \nvg=0.0799 #In m**3/Kg \nv=8 #In m**3/Kg \n\n\n#Calculation\nm=v/vg #Mass of steam in Kg \n\n#Output\nprint(\"Mass of steam= \",round(m,3),\"Kg\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Mass of steam= 100.125 Kg\n" + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 9 Page No:190" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP=12*10**5 #Absolute pressure\n#From steam table (pressure basis at 12 bar)\nts=188+273 #In degree celsius\nvf=0.001139 #In m**3/Kg \nvg=0.1632 #In m**3/Kg \nhf=798.4 #In KJ/Kg\nhfg=1984.3 #In KJ/Kg\nhg=2782.7 #In KJ/Kg\nx=0.94\nCps=2.3\ntsup=350+273 #In degree celsius\n\n#Calcuation\nh=hf+x*hfg #Enthalpy of wet steam in KJ/Kg\nv=(1-x)*vf+x*vg #Volume of wet steam m**3/Kg\nu=h-((P*v)/10**3) #Internal Energy in KJ/Kg\nhg=2782.7 #Enthalpy of dry & saturated steam in KJ/Kg\nv1=vg #Volume of dry & saturated steam m**3/Kg\nu1=hg-((P*vg)/10**3) #Internal Energy in KJ/Kg \nh1=hg+Cps*(tsup-ts) #Enthalpy of superheated steam in KJ/Kg\nvsup=vg*(tsup/ts) #Volume of superheated steam in m**3/Kg\nu2=h1-((P*v)/10**3) #Internal Energy in KJ/Kg\n\n\n#Output\nprint(\"Enthalpy of wet steam= \",h,\"KJ/Kg\")\nprint(\"Volume of wet steam= \",round(v,5),\"m**3/Kg\")\nprint(\"Internal Energy= \",round(u,2),\"KJ/Kg\")\nprint(\"Enthalpy of dry & saturated steam= \",hg,\"KJ/Kg\")\nprint(\"Volume of dry & saturated steam= \",v1,\"m**3/Kg\")\nprint(\"Internal Energy= \",u1,\"KJ/Kg\")\nprint(\"Enthalpy of superheated steam= \",round(h1,1),\"KJ/Kg\")\nprint(\"Volume of superheated steam= \",round(vsup,3),\"m**3/Kg\")\nprint(\"Internal Energy= \",round(u2,1),\"KJ/Kg\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of wet steam= 2663.642 KJ/Kg\nVolume of wet steam= 0.15348 m**3/Kg\nInternal Energy= 2479.47 KJ/Kg\nEnthalpy of dry & saturated steam= 2782.7 KJ/Kg\nVolume of dry & saturated steam= 0.1632 m**3/Kg\nInternal Energy= 2586.8599999999997 KJ/Kg\nEnthalpy of superheated steam= 3155.3 KJ/Kg\nVolume of superheated steam= 0.221 m**3/Kg\nInternal Energy= 2971.1 KJ/Kg\n" + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 10 Page No:191" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP1=10*10**5 #Pressure of steam in bar\ntsup1=300+273 #Temperature of steam n degree celsius \nP2=1.4*10**5 #Internal energy of steam\nx2=0.8 #Dryness fraction\nCps=2.3\n#from steam table properties of saturated steam (temp basis) \n#at 25 degree celsius and at 10 bar(pressure basis)\nts1=179.9+273\nvf=0.001127 #In m**3/Kg \nvg=0.1943 #In m**3/Kg \nhf=762.6 #In KJ/Kg\nhfg=2013.6 #In KJ/Kg\nhg1=2776.2 #In KJ/Kg\n#at 1.4 bar\nts=109.3 #In degree celsius\nvf1=0.001051 #In m**3/Kg \nvg1=1.2363 #In m**3/Kg \nhf1=458.4 #In KJ/Kg\nhfg1=2231.9 #In KJ/Kg\nhg=2690.3 #In KJ/Kg\n\n#calculation\nh1=hg1+Cps*(tsup1-ts1) #Enthalpy of superheated steam in KJ/Kg\nv1=vg*(tsup1/ts1) #Volume of superheated steam in m**3/Kg\nu1=h1-((P1*v1)/10**3) #Internal energy in KJ/Kg\nh2=hf1+x2*hfg1 #Enthalpy of wet steam in KJ/Kg\nVwet=(1-x2)*vf1+x2*vg1 #Volume of wet steam in m**3/Kg\nu2=h2-((P2*Vwet)/10**3) #Internal energy in KJ/Kg\nDeltaU=u1-u2 #Change of Internal energy in KJ/Kg\n\n\n#Output\nprint(\"Enthalpy of superheated steam= \",h1,\"KJ/Kg\")\nprint(\"Volume of superheated steam= \",round(v1,4),\"m**3/Kg\")\nprint(\"Internal energy= \",round(u1,1),\"KJ/Kg\")\nprint(\"Enthalpy of wet steam= \",h2,\"KJ/Kg\")\nprint(\"Volume of wet steam= \",round(Vwet,5),\"m**3/Kg\")\nprint(\"Internal energy= \",round(u2,1),\"KJ/Kg\")\nprint(\"Change of Internal energy= \",round(DeltaU,1),\"KJ/Kg\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of superheated steam= 3052.43 KJ/Kg\nVolume of superheated steam= 0.2458 m**3/Kg\nInternal energy= 2806.6 KJ/Kg\nEnthalpy of wet steam= 2243.92 KJ/Kg\nVolume of wet steam= 0.98925 m**3/Kg\nInternal energy= 2105.4 KJ/Kg\nChange of Internal energy= 701.2 KJ/Kg\n" + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 11 Page No:193" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nP=15 #Absolute pressure\n#From steam table (pressure basis at 15 bar)\nts=198.3+273 #In degree celsius \nSf=2.3145 #In KJ/KgK\nSfg=4.1261 #In KJ/KgK\nSg=6.4406 #In KJ/KgK\ntsup=300+273\nCps=2.3\nx=0.8\n\n#calculation\nS=Sf+x*Sfg #Entropy of wet steam in KJ/Kg\nS1=Sg #Entropy of superheated steam in KJ/Kg\nS2=Sg+Cps*(math.log(tsup/ts)) #Entropy of superheated steam in KJ/Kg\n\n#Output\nprint(\"Entropy of wet steam\",round(S,3),\" KJ/Kg\")\nprint(\"Entropy of dry and saturated steam\",S1,\" KJ/Kg\")\nprint(\"Entropy of superheated steam\",round(S2,2),\" KJ/Kg\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Entropy of wet steam 5.615 KJ/Kg\nEntropy of dry and saturated steam 6.4406 KJ/Kg\nEntropy of superheated steam 6.89 KJ/Kg\n" + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 12 Page No:194" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\n#Input data\nimport math\nm=1.5 #Entropy of the steam\nP=10*10**5 #Absolute pressure in bar\n#From steam table properties of saturated steam \n#(pressure basis)at 10 bar\nts=179.9+273 #Indegree celsius\nvf=0.001127 #In m**3/Kg\nvg=0.1943 #In m**3/Kg\nhf=762.6 #In KJ/Kg\nhfg=2013.6 #In KJ/Kg\nhg=2776.2 #In KJ/Kg\nSf=2.1382 #In KJ/KgK\nSfg=4.4446 #In KJ/KgK\nSg=6.5828 #In KJ/Kg\nCps=2.3\ntsup=250+273\n\n\n#Calculation\n#(1)Enthalpy of dry and saturated steam \n\nh=hg #Enthalpy of dry and saturated steam \nEODS=hg*m #Enthalpy of 1.5Kg of dry and saturated steam \nv=vg #volume of dry and saturated steam\nu=h-((P*v)/10**3) #Internal Energy\nIES=u*m #Internal energy of the steam\ns=6.5858 #Entropy of dry and saturated steam\nEODSS=s*m #Entropy of 1.5Kg dry and saturated steam\nx=0.75\n#(2)Enthalpy of wet steam\nh1=hf+x*hfg #Enthalpy of wet steam\nEWS=h1*m #Enthalpy of1.5Kg of wet steam\nVwet=x*vg #Volume of steam\nu1=h1-((P*Vwet)/10**3) #Internal energy \nIES1=u1*m #Internal energy of1.5Kg of the steam\ns1=Sf+x*Sfg #Entropy of wet steam\nEWS1=s1*m #Entropy of1.5Kg of wet steam\n\n#(3)Enthalpy of superheated steam\nh2=hg+Cps*(tsup-ts) #Enthalpy of superheated steam\nEOSHS=h2*m #Enthalpy of 1.5Kg of superheated steam\nVsup=vg*(tsup/ts) #Volume of superheated steam\nu2=h2-((P*Vsup)/10**3) #Internal energy\nIES2=u2*m #Internal energy of 1.5Kg of the steam\ns2=Sg+Cps*(math.log(tsup/ts))#Entropy of superheated steam\nEOSHS1=s2*m #Entropy of 1.5Kg of superheated steam\n\n#Output\nprint(\"Enthalpy of dry and saturated steam= \",h,\"KJ/Kg\")\nprint(\"Enthalpy of 1.5Kg of dry and saturated steam= \",round(EODS,2),\"KJ\")\nprint(\"volume of dry and saturated steam= \",v,\"m**3/kg\")\nprint(\"Internal Energy= \",round(u,2),\"KJ/Kg\")\nprint(\"Internal energy of the steam= \",round(IES,2),\"kJ\")\nprint(\"Entropy of dry and saturated steam = \",s,\"KJ/KgK\")\nprint(\"Entropy of 1.5kg of dry and saturated steam= \",EODSS,\"KJ/K\")\n\nprint(\"Enthalpy of wet steam= \",round(h1,2),\"KJ/Kg\")\nprint(\"Enthalpy of1.5Kg of wet steam= \",EWS,\"KJ\")\nprint(\"Volume of steam= \",Vwet,\"m**3/Kg\")\nprint(\"Internal energy= \",u1,\"KJ/Kg\")\nprint(\"Internal energy of1.5Kg of the steam= \",round(IES1,2),\"KJ\")\nprint(\"Entropy of wet steam= \",round(s1,2),\"KJ/KgK\")\nprint(\"Entropy of 1.5Kg of wet steam= \",EWS1,\"KJ/K\")\n\nprint(\"Enthalpy of superheated steam= \",h2,\"KJ/Kg\")\nprint(\"Enthalpy of 1.5Kg of superheated steam= \",round(EOSHS,1),\"KJ\")\nprint(\"Volume of superheated steam= \",round(Vsup,4),\"m**3/Kg\")\nprint(\"Internal energy= \",round(u2,4),\"\")\nprint(\"Internal energy of1.5Kg of the steam= \",round(IES2,1),\"KJ\")\nprint(\"Entropy of superheated steam= \",round(s2,4),\"KJ/KgK\")\nprint(\"Entropy of 1.5Kg of superheated steam= \",round(EOSHS1,2),\"KJ/K\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of dry and saturated steam= 2776.2 KJ/Kg\nEnthalpy of 1.5Kg of dry and saturated steam= 4164.3 KJ\nvolume of dry and saturated steam= 0.1943 m**3/kg\nInternal Energy= 2581.9 KJ/Kg\nInternal energy of the steam= 3872.85 kJ\nEntropy of dry and saturated steam = 6.5858 KJ/KgK\nEntropy of 1.5kg of dry and saturated steam= 9.8787 KJ/K\nEnthalpy of wet steam= 2272.8 KJ/Kg\nEnthalpy of1.5Kg of wet steam= 3409.2 KJ\nVolume of steam= 0.145725 m**3/Kg\nInternal energy= 2127.075 KJ/Kg\nInternal energy of1.5Kg of the steam= 3190.61 KJ\nEntropy of wet steam= 5.47 KJ/KgK\nEntropy of 1.5Kg of wet steam= 8.207475 KJ/K\nEnthalpy of superheated steam= 2937.43 KJ/Kg\nEnthalpy of 1.5Kg of superheated steam= 4406.1 KJ\nVolume of superheated steam= 0.2244 m**3/Kg\ninternal energy= 2713.0562 \nInternal energy of1.5Kg of the steam= 4069.6 KJ\nEntropy of superheated steam= 6.9138 KJ/KgK\nEntropy of 1.5Kg of superheated steam= 10.37 KJ/K\n" + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 13 Page No:196" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nV=0.04 #Volume of vessel in m**3 \nx=1\nt=250+273 #Saturated steam temp in degree celsius\nmw=9 #Mass of liquid in Kg\n#From steam table(temp basis,at t=250)\nP=39.78*10**5 #in bar\nVf=0.001251 #In m**3/kg\nVg=0.05004 #In m**3/Kg\nhf=1085.7 #KJ/Kg\nhfg=2800.4 #KJ/Kg\nhg=1714.7 #KJ/Kg\n\n#Calculation\nVw=mw*Vf #Volume occupied by water in m**3\nVs=V-Vw #Volume of waterin m**3\nms=Vs/Vg #Volume of dry and saturated steam in Kg \nm=mw+ms #Total mass of steam in Kg\nx=ms/(ms+mw) #Dryness fraction of steam \nVwet=(1-x)*Vf+x*Vg #Specific volume of steam in m**3/Kg\nh=hf+x*hfg #Enthalpy of wet steam in KJ/Kg\nEOWS=h*m #Enthalpy of 9.574 Kg of wet steam KJ\nu=h-((P*Vwet)/10**3) #Internal Energy in KJ/Kg\nIEOS=u*m #Internal energy of 9.574 Kg of steam in KJ\n\n\n#Output\nprint(\"Volume occupied by water= \",round(Vw,5),\"m**3\")\nprint(\"Volume of water= \",round(Vs,5),\"m**3\")\nprint(\"Volume of dry and saturated steam= \",round(ms,3),\"Kg \")\nprint(\"Total mass of steam= \",round(m,3),\"Kg\")\nprint(\"Dryness fraction of steam= \",round(x,2),)\nprint(\"Specific volume of steam= \",round(Vwet,6),\" m**3/Kg\")\nprint(\"Enthalpy of wet steam= \",round(h,1),\"KJ/Kg\")\nprint(\"Enthalpy of 9.574 Kg of wet steam= \",round(EOWS,),\"KJ\")\nprint(\"Internal Energy= \",round(u,1),\"KJ/Kg\")\nprint(\"Internal energy of 9.574 Kg of steam= \",round(IEOS),\"KJ\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Volume occupied by water= 0.01126 m**3\nVolume of water= 0.02874 m**3\nVolume of dry and saturated steam= 0.574 Kg \nTotal mass of steam= 9.574 Kg\nDryness fraction of steam= 0.06\nSpecific volume of steam= 0.004178 m**3/Kg\nEnthalpy of wet steam= 1253.7 KJ/Kg\nEnthalpy of 9.574 Kg of wet steam= 12003 KJ\nInternal Energy= 1237.1 KJ/Kg\nInternal energy of 9.574 Kg of steam= 11844 KJ\n" + } + ], + "prompt_number": 40 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 14 Page No:197" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input Data\nP=7 #Absolute pressure in bar\nt=200 #Absolute temperature\nts=165 #In degree celsius from steam table\n\n#Calculation\ndos=t-ts #Degree of superheat in degree celcius\n\n#Output\nprint(\"Degree of superheat= \",dos,\"degree celcius\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Degree of superheat= 35 degree celcius\n" + } + ], + "prompt_number": 42 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 15 Page No:197" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP=15 #Absolute pressure in bar\n#From steam table (pressure basis at 15 bar)\nh=1950 #In KJ/Kg\nts=198.3 #In degreee celsius\nhf=844.7 #In KJ/Kg\nhfg=1945.2 #In KJ/Kg\nhg=2789.9 #In KJ/Kg\n\n#calculation\nx=((h-hf)/hfg) #Enthalpy of wet steam\n\n#Output\nprint(\"Enthalpy of wet steam= \",round(x,3),\"\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of wet steam= 0.568 \n" + } + ], + "prompt_number": 44 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 16 Page No:197" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP=15 #Absolute pressure in bar\n#From steam table (pressure basis at 15 bar)\nh=3250 #In KJ/Kg\nts=198.3 #In degree celsius \nhf=844.7 #In KJ/Kg\nhfg=1945.2 #In KJ/Kg\nhg=2789.9 #In KJ/Kg\nCps=2.3\n\n#Calculation\ntsup=(h-hg+(Cps*ts))/2.3 #Enthalpy of superheated steam in degree celsius\ndos=tsup-ts #Degree of superheated in degree celsius\n\n#Output\nprint(\"Enthalpy of superheated steam= \",round(tsup,2),\"degree celcius\")\nprint(\"Degree of superheated= \",dos,\"degree celcius\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of superheated steam= 398.34 degree celcius\nDegree of superheated= 200.0434782608695 degree celcius\n" + } + ], + "prompt_number": 46 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 17 Page No:198" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP=7 #Absolute pressure in bar\nv=0.2 #Specific volume in m**3/Kg\n#from steam table (pressure basis at 7 bar) \nts=165 #In degree celsius\nvf=0.001108 #In m**3/Kg\nvg=0.2727 #In m**3/Kg\n\n#calculation\nx=v/vg #Volume of steam dryness fraction\n\n#Output\nprint(\"Volume of steam dryness fraction= \",round(x,3),)", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Volume of steam dryness fraction= 0.733\n" + } + ], + "prompt_number": 64 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 18 Page No:198" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP=7 #Absolute pressure in bar\nv=0.3 #Specific volume in m**3/Kg\n#From steam table (pressure basis at 7 bar)\nts=165+273 #In degree celsius\nvf=0.001108 #In m**3/Kg\nvg=0.2727 #In m**3/Kg\n\n#Calculation\n#v=vg*tsup/ts\ntsup=((v/vg)*ts)-273 #Temp of superheated steam in degree celsius\nDOS=tsup+273-ts #Degree of superheated in degree celsius\n\n#Output\nprint(\"Temp of superheated steam= \",round(tsup,2),\"degree celsius\")\nprint(\"Degree of superheated= \",round(DOS,2),\"degree celsius\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Temp of superheated steam= 208.85 degree celsius\nDegree of superheated= 43.85 degree celsius\n" + } + ], + "prompt_number": 57 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 19 Page No:198" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nm=2 #steam of vessel in Kg\nV=0.1598 #volume of vessel in M**3\nP=25 #Absolute pressure of vessel in bar\n\n#Calculation\nv=V/m #Quality of steam in m**3/Kg\n\n#Output\nprint(\"Quality of steam\",v,\" m**3/Kg\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Quality of steam 0.0799 m**3/Kg\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 20 Page No:200" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP=10*10**2 #Absolute pressure in bar\nx1=0.9 #Dryness enters\ntsup2=300+273 #Temperature in degree celsius \n#From steam table at 10 bar\nts=179.9+273 #In degree celsius\nVg=0.1943 #In m**3/Kg\nhf=762.6 #In KJ/Kg\nhfg=2013.6 #InK/Kg\nhg=2776.2 #In KJ/Kg\n\n#Calculation\nh1=hf+x1*hfg #Initial enthalpy of steam in KJ/Kg\nV1=x1*Vg #Initial specific volume of steam\nu1=h1-P*V1 #Initial internal energy of steam in KJ/Kg\nh2=hg+Cps*(tsup2-ts) #Final enthalpy of steam in KJ/Kg\nV2=Vg*(tsup2/ts) #Final specific volume of steam in m**3/Kg\nu2=h2-P*V2 #Final internal energy of steam in KJ/K\ndeltah=h2-h1 #Heat gained by steam in KJ/Kg\ndeltaU=(u2-u1) #Change in internal energy in KJ/Kg\n\n#Output\nprint(\"Initial enthalpy of steam= \",h1,\"KJ/Kg\")\nprint(\"Initial specific volume of steam= \",V1,)\nprint(\"Initial internal energy of steam= \",round(u1,2),\"KJ/Kg\")\nprint(\"Final enthalpy of steam= \",h2,\"KJ/Kg\")\nprint(\"Final specific volume of steam= \",round(V2,4),\"m**3/Kg\")\nprint(\"Final internal energy of steam= \",round(u2,3),\"KJ/Kg\")\nprint(\"Heat gained by steam= \",round(deltah,2),\"KJ/Kg\")\nprint(\"Change in internal energy= \",round(deltaU,2),\"KJ/Kg\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Initial enthalpy of steam= 2574.84 KJ/Kg\nInitial specific volume of steam= 0.17487\nInitial internal energy of steam= 2399.97 KJ/Kg\nFinal enthalpy of steam= 3052.43 KJ/Kg\nFinal specific volume of steam= 0.2458 m**3/Kg\nFinal internal energy of steam= 2806.606 KJ/Kg\nHeat gained by steam= 477.59 KJ/Kg\nChange in internal energy= 406.64 KJ/Kg\n" + } + ], + "prompt_number": 58 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 21 Page No:201" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nm=4 #Steam in Kg\nP=13 #Absolute pressure in bar\ntsup1=450 #Absolute temp in degree celsius \ndeltaH=2.8*10**3 #loses in MJ\n#from steam table at 13 bar\nts=191.6 #In degree celsius\nVg=0.1511 #In m**3/Kg\nhf=814.7 #In m**3/Kg\nhfg=1970.7 #In KJ/Kg\nhg=2785.4 #In KJ/Kg\n\n#Calculation\nh1=hg+Cps*(tsup1-ts) #Initial enthalpy of steam in KJ/Kg\nDeltah=deltaH/m #Change in enthalpy/unit mass in KJ/Kg\nh2=h1-Deltah #Final enthalpy of steam in KJ/Kg\nx2=(h2-hf)/hfg #wet & dryness fraction\n\n#Output\nprint(\"Initial enthalpy of steam= \",round(h1,2),\" KJ/Kg\")\nprint(\"Change in enthalpy/unit mass= \",Deltah,\"KJ/Kg\")\nprint(\"Final enthalpy of steam= \",round(h2,2),\"KJ/Kg\")\nprint(\"wet & dryness fraction= \",round(x2,4),)", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Initial enthalpy of steam= 3379.72 KJ/Kg\nChange in enthalpy/unit mass= 700.0 KJ/Kg\nFinal enthalpy of steam= 2679.72 KJ/Kg\nwet & dryness fraction= 0.9464\n" + } + ], + "prompt_number": 63 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 22 Page No:202" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nm=2 #Steam in Kg\nx=0.7 #Initial dryness \nP=15 #Constant pressure in bar\n#V2=2V1\n#from steam table properties of\n#saturated steam(pressure basis) at 15 bar\nTs=198.3+273 #In degree celsius \nVg=0.1317 #In m**3/Kg\nhf=844.7 #In KJ/Kg\nhfg=1945.2 #In KJ/Kg\nhg=2789.9 #In KJ/Kg\nCps=2.3\n\n#Calculation\nV1=x*Vg #Initial specific volume of steam in m**3/Kg\nV2=2*V1 #Final specific volume of steam in m**3/Kg\nTsup=(V2/Vg)*Ts #Steam is superheated in degree celsius \nFSS=Tsup-Ts #Degree of superheated in degree celsius\nh1=hf+x*hfg #Initial enthalpy of steam in KJ/Kg\nh2=hg+Cps*(Tsup-Ts) #Final enthalpy of steam in KJ/Kg \nQ=(h2-h1)*m #Heat transferred in the process in KJ\nW1=P*(m*V2-m*V1) #Work transferred in the process in KJ\n\n#Output\nprint(\"Initial specific volume of steam= \",round(V1,4),\"m**3/Kg\")\nprint(\"Final specific volume of steam= \",round(V2,4),\"m**3/Kg\")\nprint(\"Steam is superheated= \",round(Tsup,2),\"K\")\nprint(\"Degree of superheated= \",round(FSS,2),\"degree celsius\")\nprint(\"Initial enthalpy of steam= \",h1,\"KJ/Kg\")\nprint(\"Final enthalpy of steam= \",round(h2,2),\"KJ/Kg\")\nprint(\"Heat transferred in the process= \",round(Q,2),\"KJ\")\nprint(\"Work transferred in the process= \",round(W1,3),\"KJ\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Initial specific volume of steam= 0.0922 m**3/Kg\nFinal specific volume of steam= 0.1844 m**3/Kg\nSteam is superheated= 659.82 K\nDegree of superheated= 188.52 degree celsius\nInitial enthalpy of steam= 2206.34 KJ/Kg\nFinal enthalpy of steam= 3223.5 KJ/Kg\nHeat transferred in the process= 2034.31 KJ\nWork transferred in the process= 2.766 KJ\n" + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 23 Page No:203" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nms=1000 #Steam in Kg/h \nP=16 #Absolute pressure in bar\nx2=0.9 #Steam is dry \nt1=30+273 #temperature in degree celsius\ntsup=380 #tmperature rised in degree celsius \n \n#from steam table(pressure basis at 16 bar)\nh1=125.7 #in KJ/Kg\nts=201.4 #In degree celsius\nhf=858.5 #in kJ/Kg\nhfg=1933.2 #in kJ/Kg\nhg=2791.7 #in kJ/Kg\nCps=2.3\n\n#Calculation \nh2=hf+x2*hfg #Final enthalpy of wet steam in KJ/Kg \nQ1=(ms*(h2-h1))*10**-3 #Constant pressure process in KJ/h \nh3=hg+Cps*(tsup-ts) #Final enthalpy of superheated steam in KJ/g\nQ2=(ms*(h3-h2))*10**-3 #Suprheated steam in KJ/h\n\n#Output\nprint(\"Final enthalpy of wet steam= \",round(h2,1),\"KJ/Kg \")\nprint(\"Constant pressure process= \",round(Q1,1),\" KJ/h \")\nprint(\"Final enthalpy of superheated steam= \",round(h3,1),\" KJ/g\")\nprint(\"Suprheated steam= \",round(Q2,1),\"KJ/h\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Final enthalpy of wet steam= 2598.4 KJ/Kg \nConstant pressure process= 2472.7 KJ/h \nFinal enthalpy of superheated steam= 3202.5 KJ/g\nSuprheated steam= 604.1 KJ/h\n" + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 24 Page No:204" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nFB=15 #First boiler in bar\nSB=15 #Second boiler in bar\ntsup1=300 #Temperature of the steam in degree celsius\ntsup2=200 #Temperature of the steam in degree celsius\n#From steam table (pressure basis at 15 bar )\nts=198.3 #In degree celsius \nhf=844.7 #In KJ/Kg\nhfg=1945.2 #In KJ/Kg\nhg=2789.9 #In KJ/I\n\n\n#Calculation\nh1=hg+Cps*(tsup1-ts) #Enthalpy of steam of first boiler in KJ/Kg \nh3=hg+Cps*(tsup2-ts) #Enthalpy of steam in steam main in KJ/Kg\nh2=2*h3-h1 #Energy balance in KJ/Kg\nx2=(h2-hf)/hfg #Enthalpy of wet steam\n\n#OUTPUT\nprint(\"Enthalpy of steam of first boiler= \",round(h1,1),\"KJ/Kg\")\nprint(\"Enthalpy of steam in steam main= \",round(h3,1),\"KJ/Kg\")\nprint(\"Energy balance= \",round(h2,1),\"KJ/Kg\")\nprint(\"Enthalpy of wet steam= \",round(x2,3),)\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of steam of first boiler= 3023.8 KJ/Kg\nEnthalpy of steam in steam main= 2793.8 KJ/Kg\nEnergy balance= 2563.8 KJ/Kg\nEnthalpy of wet steam= 0.884\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 25 Page No:205" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nV=0.35 #Capacity of vessel in m**3\nP1=10*10**2 #Absolute pressure in bar\ntsup1=250+273 #Absolute temperature in degree celsius \nP2=2.5*102 #Absolute pressure in the vessel fall in bar\n\n#From steam table (pressure basis at 10 bar)\nts1=179.9+273 #In degree celsius \nVg1=0.1943 #In m**3/Kg\nhf1=762.6 #In KJ/Kg\nhfg1=2013.6 #In KJ/Kg\nhg1=2776.2 #In KJ/Kg\n\n#From steam table(pressure basis at 2.5 bar)\nV2=0.2247 #In m**3/Kg\nts2=127.4 #In degree celsius\nVg2=0.7184 #In m**3/Kg\nhf2=535.3 #In KJ/Kg\nhfg2=2181.0 #In KJ/Kg\nhg2=2716.4 #In KJ/Kg\n\n#Calculation\nV1=Vg1*(tsup1/ts1) #Initial specific volume of steam in m**3/Kg\nm=V/V1 #Initial mass of steam in Kg\nx2=V2/Vg2 #Final condition of wet steam\nh1=hg1+Cps*(tsup1-ts1) #Initial enthalpy of steam in KJ/Kg\nu1=h1-P1*V1 #Initial internal energy of steam in KJ/Kg\nh2=hf2+x2*hfg2 #Final enthalpy of steam in KJ/Kg\nu2=h2-P2*V2 #Final internal energy of steam in KJ/Kg\ndeltaU=(u2-u1)*m #Change in internal energy in KJ\n\n#Output\nprint(\"Initial specific volume of steam= \",round(V1,4),\"m**3/Kg\")\nprint(\"Initial mass of steam= \",round(m,4),\"Kg\")\nprint(\"Final condition of wet steam= \",round(x2,4),)\nprint(\"Initial enthalpy of steam= \",h1,\"KJ/Kg\")\nprint(\"Initial internal energy of steam= \",round(u1,2),\"KJ/Kg\")\nprint(\"Final enthalpy of steam= \",round(h2,1),\" KJ/Kg\")\nprint(\"Final internal energy of steam= \",round(u2,3),\"KJ/Kg\")\nprint(\"Change in internal energy= \",round(deltaU,1),\"KJ\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Initial specific volume of steam= 0.2244 m**3/Kg\nInitial mass of steam= 1.5599 Kg\nFinal condition of wet steam= 0.3128\nInitial enthalpy of steam= 2937.43 KJ/Kg\nInitial internal energy of steam= 2713.06 KJ/Kg\nFinal enthalpy of steam= 1217.5 KJ/Kg\nFinal internal energy of steam= 1160.171 KJ/Kg\nChange in internal energy= -2422.3 KJ\n" + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 26 Page No:207" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nm=1.5 #Saturated steam in Kg\nx1=1 \nx2=0.6 \nP1=5*10**5 #Absolute pressure in bar\n#From steam table at pressure basis 5 bar\nhg1=2747.5 #In KJ/Kg\nVg1=0.3747 #In m**3/Kg\nV1=0.3747 #In m**3/Kg\nV2=0.3747 #In m**3/Kg\n#From steam table at Vg2 is 2.9 bar\nP2=2.9*10**5 #Absolute pressure in bar \nt2=132.4 #In degree celsius \nhf2=556.5 #In KJ/Kg\nhfg2=2166.6 #In KJ/Kg\n\n\n \n#Calculation\nVg2=V2/x2 #Constant volume process in m**3/Kg\nu1=hg1-((P1*Vg1)/1000) #Initial internal energy in KJ/Kg\nu2=(hf2+x2*hfg2)-((P2*V2)/1000) #Final internal energy in KJ\ndeltaU=(u1-u2)*m #Heat supplied in KJ\n\n#Output\nprint(\"Constant volume process= \",round(Vg2,4),\"m**3/Kg\")\nprint(\"Initial internal energy= \",u1,\"KJ/Kg\")\nprint(\"Final internal energy= \",round(u2,1),\"KJ\")\nprint(\"Heat supplied= \",round(deltaU,2),\"KJ\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Constant volume process= 0.6245 m**3/Kg\nInitial internal energy= 2560.15 KJ/Kg\nFinal internal energy= 1747.8 KJ\nHeat supplied= 1218.53 KJ\n" + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 27 Page No:208" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP1=20 #Initial steam in bar\nx1=0.95 #dryness throttled\nP2=1.2 #Absolute pressure in bar\n\n#From steam table (pressure basis at 20 bar)\nts=212.4 #In degree celsius\nhf=908.6 #In KJ/Kg\nhfg=1888.6 #In KJ/Kg\nhg=2797.2 #In KJ/Kg\n#From steam table (pressure basis at 1.2 bar)\nh2=h1 #In KJ/Kg\nts2=104.8 #In degree celsius\nhf2=439.3 #In KJ/Kg\nhfg2=2244.1 #In KJ/Kg\nhg2=2683.4 #In KJ/Kg\nCps=2.3\n\n\n#Calculation\nh1=hf+x1*hfg #Enthalpy of steam in KJ/Kg\ntsup2=((h1-hg2)/Cps)+ts2 #Enthalpy of wet steam in degree celsius\nDOS=tsup2-ts2 #Degree of superheat in degree celsius\n\n\n#Output\nprint(\"Enthalpy of steam= \",h1,\"KJ/Kg\")\nprint(\"Enthalpy of wet steam= \",round(tsup2,2),\"degree celsius\")\nprint(\"Degree of superheat= \",round(DOS,2),\"degree celsius\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of steam= 2702.77 KJ/Kg\nEnthalpy of wet steam= 113.22 degree celsius\nDegree of superheat= 8.42 degree celsius\n" + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 28 Page No:209" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP1=12 #Throttled steam\nx1=0.96 #Dryness is brottled\nx2=1 #Constant enthalpy process\n#From steam table at12 bar\nts=188 #In degree celsius\nhf=798.4 #In KJ/Kg\nhfg=1984.3 #In KJ/Kg\nhg=2782.7 #In KJ/Kg\n\n\n#Calculation\nh1=hf+x1*hfg #Enthalpy of the steam in KJ/Kg \nh2=h1 #Enthalpy after throttling in KJ/Kg \n\n#Output\nprint(\"Enthalpy of the steam= \",round(h1,2),\"KJ/Kg \")\nprint(\"Enthalpy after throttlin= \",round(h2,2),\"KJ/Kg \")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of the steam= 2703.33 KJ/Kg \nEnthalpy after throttlin= 2703.33 KJ/Kg \n" + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 29 Page No:210" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nP1=15 #Initial steam in bar\ntsup1=250+273 #Temperature of steam in degree celsius\nP2=0.5 #Steam turbine in bar\n\n#From steam table at 15 bar\nts1=198.3+273 #In degree celsius \nhg1=2789.9 #In KJ/Kg\nsf1=2.3145 #In KJ/KgK\nsfg1=4.1261 #In KJ/KgK\nsg1=6.4406 #In KJ/KgK\n#From steam table at 0.5 bar\nts2=81.53 #In degree celsius \nsf2=1.0912 #In KJ/Kg\nsfg2=6.5035 #In KJ/Kg\nsg2=7.5947 #In KJ/Kg\nhf2=340.6\nCps=2.3\nhfg2=2646\n\n#Calculation\nS1=sg1+Cps*(math.log(tsup1/ts1)) #Entropy of superheated steam in KJ/KgK\nS2=S1 #Entropy after isentropic processes in KJ/KgK\nx2=(S2-sf2)/sfg2 #Enthalpy of wet steam \nh1=hg1+Cps*(tsup1-ts1) #Enthalpy of steam at 15 bar\nh2=hf2+x2*hfg2 #Enthalpy of wet steam at 0.5 bar\nWOT=h1-h2 #Work output of the turbine\n\n#OUTPUT\nprint(\"Entropy of superheated steam= \",round(S1,2),\"KJ/KgK\")\nprint(\"Entropy after isentropic processes= \",round(S2,2),\"KJ/KgK\")\nprint(\"Enthalpy of wet steam= \",round(x2,2),\"\")\nprint(\"Enthalpy of steam= \",h1,\"KJ/Kg\")\nprint(\"Enthalpy of wet steam= \",round(h2,2),\"KJ/Kg\")\nprint(\"Work output of the turbine= \",round(WOT,2),\"KJ/Kg\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Entropy of superheated steam= 6.68 KJ/KgK\nEntropy after isentropic processes= 6.68 KJ/KgK\nEnthalpy of wet steam= 0.86 \nEnthalpy of steam= 2908.81 KJ/Kg\nEnthalpy of wet steam= 2614.45 KJ/Kg\nwork output of the turbine= 294.36 KJ/Kg\n" + } + ], + "prompt_number": 22 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_11_Steam_Boilers_ZbPMcer.ipynb b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_11_Steam_Boilers_ZbPMcer.ipynb new file mode 100644 index 00000000..5b8559d1 --- /dev/null +++ b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_11_Steam_Boilers_ZbPMcer.ipynb @@ -0,0 +1,482 @@ +{ + "metadata": { + "name": "Chapter 11 Steam Boilers" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "Chapter 11 Steam Boilers" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 1 Page No:228" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nms=5000 #Boiler produces wet steam in Kg/h\nx=0.95 #Dryness function\nP=10 #Operating pressure in bar\nmf=5500 #Bour in the furnace in Kg\nTw=40 #Feed water temp in degree celsius\n\n#calculation\n#from steam table\nhfw=167.45 #In KJ/Kg\nhf=762.61 #In KJ/Kg\nhfg=2031.6 #In KJ/Kg\nhs=(hf+x*hfg) #Enthalpy of wet stream in KJ/Kg\nme=ms/mf #Mass of evaporation\nE=((me*(hs-hfw))/(2257))*10 #Equivalent evaporation in Kg/Kg of coal\n\n#output\n\nprint(\"Enthalpy of wet stream=\",round(hs,2),\"KJ/Kg\")\nprint(\"Mass of evaporation=\",round(me,2),)\nprint(\"Equivalent evaporation=\",round(E,2),\"Kg/Kg of coal\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of wet stream= 2692.63 KJ/Kg\nMass of evaporation= 0.91\nEquivalent evaporation= 10.17 Kg/Kg of coal\n" + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 2 Page No:229" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\np=14 #Boiler pressure in bar\nme=9 #Evaporates of water in Kg\nTw=35 #Feed water entering in degree celsius\nx=0.9 #Steam stop value\nCV=35000 #Calorific value of the coal\n\n#Calculation\n#From Steam Table\nhfw=146.56 #In KJ/Kg\nhf=830.07 #In KJ/Kg\nhfg=1957.7 #In KJ/Kg\nhs=hf+x*hfg #Enthalpy of wet stream in KJ/Kg\nE=((me*(hs-hfw))/2257) #Equivalent evaporation in Kg/Kg of coal\netaboiler=((me*(hs-hfw))/CV)*100#Boiler efficiency in %\n\n#Output\nprint(\"Enthalpy of wet stream=\",hs,\"KJ/Kg\")\nprint(\"Equivalent evaporation=\",round(E,2),\"Kg/Kg of coal\")\nprint(\"Boiler efficiency=\",round(etaboiler,2),\"%\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of wet stream= 2592.0 KJ/Kg\nEquivalent evaporation= 9.75 Kg/Kg of coal\nBoiler efficiency= 62.88 %\n" + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 3 Page No:228" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nms=2500 #Saturated steam per bour in Kg\nx=1 \nP=15 #Boiler pressure in bar\nTw=25 #Feed water entering in degree celsius \nmf=350 #Coal burnt in Kg/bour\nCV=32000 #Calorific value in Kj/Kg \n\n#calculation\n#steam table\nhfw=104.77 #In KJ/Kg\nhf=844.66 #In KJ/Kg\nhfg=1945.2 #In KJ/Kg\nhg=2789.9 #In KJ/Kg\nhs=2789.9 #Enthalpy of dry steam in KJ/Kg\nme=ms/mf #mass of evaporation \nE=((me*(hs-hfw))/2257) #Equivalent evaporation in Kg/Kg ofcoal\netaboiler=((me*(hs-hfw))/CV)*100 #Boiler efficiency in %\n\n#Output\nprint(\"mass of evaporation=\",round(me,3),)\nprint(\"Equivalent evaporation=\",round(E,2),\"Kg/Kg ofcoal\")\nprint(\"Boiler efficiency=\",round(etaboiler,2),\"%\")\n\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "mass of evaporation= 7.143\nEquivalent evaporation= 8.5 Kg/Kg ofcoal\nBoiler efficiency= 59.94 %\n" + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 4 Page No:231" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nmf=500 #Boiler plant consumes of coal in Kg/h\nCV=32000 #Calorific value in Kj/Kg\nms=3200 #plant generates in Kg/h\nP=1.2 #Absolute pressure MN/m**2\nMN=12 \nTsup=300 #Absolute temperature in degree celsius\nTw=35 #Feed water temperature\nCps=2.3\n\n#calculation\nhfw=146.56 #In KJ/Kg\nTs=187.96 #In Degree celsius\nhf=798.43 #In KJ/Kg\nhfg=1984.3 #In KJ/Kg\nhg=2782.7 #In KJ/Kg\nhs=hg+Cps*(Tsup-Ts) #Enthalpy of superheated steam in KJ/Kg\nme=ms/mf #mass of evaporation \nE=((me*(hs-hfw))/2257) #Equivalent evaporation in Kg/Kg ofcoal\netaboiler=((me*(hs-hfw))/CV)*100#Boiler efficiency in %\n \n\n#Output\nprint(\"Enthalpy of superheated steam=\",round(hs,2),\"KJ/Kg\")\nprint(\"mass of evaporation=\",me,)\nprint(\"Equivalent evaporation=\",round(E,1),\"Kg/Kg ofcoal\")\nprint(\"Boiler efficiency\",round(etaboiler,2),\"%\")\n \n\n \n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of superheated steam= 3040.39 KJ/Kg\nmass of evaporation= 6.4\nEquivalent evaporation= 8.2 Kg/Kg ofcoal\nBoiler efficiency 57.88 %\n" + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 5 Page No:232" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nms=5000 #Steam generted in Kg/h\nmf=700 #Coal burnt in Kg/h \nCV=31402 #Cv of coal in KJ/Kg\nx=0.92 #quality of steam\nP=1.2 #Boiler pressure in MPa\nTw=45 #Feed water temperature in degree celsius\n\n\n#calculation\nhfw=188.35 #In KJ/Kg\nhf=798.43 #In KJ/Kg\nhfg=1984.3 #In KJ/Kg\nhs=hf+x*hfg #Enthalpy of wet stream in KJ/Kg\nme=ms/mf #mass of evaporation \nE=((me*(hs-hfw))/2257) #Equivalent evaporation in Kg/Kg of coal\netaboiler=((me*(hs-hfw))/CV)*100 #Boiler efficiency in %\n\n\n\n#Output\nprint(\"Enthalpy of wet stream=\",round(hs,2),\"KJ/Kg\")\nprint(\"mass of evaporation=\",round(me,2),\"\")\nprint(\"Equivalent evaporation=\",round(E,1),\"Kg/Kg of coal\")\nprint(\"Boiler efficiency=\",round(etaboiler,2),\"%\")\n \n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of wet stream= 2623.99 KJ/Kg\nmass of evaporation= 7.14 \nEquivalent evaporation= 7.7 Kg/Kg of coal\nBoiler efficiency= 55.4 %\n" + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 6 Page No:233" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nms=6000 #Boiler produce of steam Kg/h\nP=25 #Boiler pressure in bar\nTsup=350 #Boiler temperature in degree celsius\nTw=40 #Feed water temperature indegree celsius\nCV=42000 #Calorific value in Kj/Kg\netaboiler=75/100 #Expected thermal efficiency in %\n\n\n#Calculation\nhfw=167.45 #In KJ/Kg\nTs=223.94 #In degree celsius \nhf=961.96 #In KJ/Kg\nhfg=1839.0 #In KJ/Kg\nhg=2800.9 #In KJ/Kg\nCps=2.3\nhs=((hg)+(Cps)*(Tsup-Ts)) #Enthalpy of superheated steam KJ/Kg\nmf=((ms*(hs-hfw))/(CV*etaboiler)) #Boiler efficiency in %\nme=ms/mf #Equivalent mass of evaporation\nE=((me*(hs-hfw))/2257) #Equivalent evaporation in Kg/Kg of oil\n\n\n#Output\nprint(\"Enthalpy of superheated steam=\",hs,\"KJ/Kg\")\nprint(\"Boiler efficiency=\",round(mf,1),\"%\")\nprint(\"Equivalent mass of evaporation=\",round(me,3),)\nprint(\"Equivalent evaporation=\",round(E,2),\"Kg/Kg of oil\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of superheated steam= 3090.838 KJ/Kg\nBoiler efficiency= 556.8 %\nEquivalent mass of evaporation= 10.775\nEquivalent evaporation= 13.96 Kg/Kg of oil\n" + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 7 Page No:234" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nE=12 #Boiler found steam in Kg/Kg\nCV=35000 #Calorific value in KJ/Kg\nms=15000 #Boiler produces in Kg/h\nP=20 #Boiler pressure in bar\nTw=40 #Feed water in degree celsius\nmf=1800 #Fuel consumption\n\n\n#calculation\n#R=me(hs-hfw)\nhfw=167.45 #In KJ/Kg\nhg=2797.2 #In KJ/Kg\nTs=211.37 #In degree celsius\nCps=2.3\nR=E*2257 #Equivalent evaporation in KJ/Kg of coal\netaboiler=(R/CV)*100 #Boiler efficiency in %\nme=ms/mf #Equivalent mass evaporation in KJ/Kg of coal \nhs=(R/me)+hfw # In KJ/Kg\nTsup=((hs-hg)/Cps)+Ts #Enthalpy of superheated steam in degree celsius\n\n\n\n#Output\nprint(\"Equivalent evaporation=\",R,\"KJ/Kg of coal\")\nprint(\"Boiler efficiency=\",round(etaboiler,2),\"%\")\nprint(\"Equivalent mass evaporation=\",round(me,2),\"KJ/Kg of coal\")\nprint(\"hs=\",round(hs,2),\"KJ/Kg\")\nprint(\"Enthalpy of superheated steam=\",round(Tsup,2),\"degree celsius\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Equivalent evaporation= 27084 KJ/Kg of coal\nBoiler efficiency= 77.38 %\nEquivalent mass evaporation= 8.33 KJ/Kg of coal\nhs= 3417.53 KJ/Kg\nEnthalpy of superheated steam= 481.08 degree celsius\n" + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 8 Page No:236" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nms=6000 #Steam generated in Kg/h\nmf=700 #Coal burnt in Kg/h\nCV=31500 #Cv of coal in KJ/Kg\nx=0.92 #Dryness in fraction of steam\nP=12 #Boiler pressure in bar\nTsup=259 #Temperature of steam in degree celsius\nTw=45 #Hot well temperature in degree celsius\n\n#calculation\nhfw=188.35 #In KJ/Kg\nTs=187.96 #In degree celsius\nhf=798.43 #In KJ/Kg\nhfg=1984.3 #In KJ/Kg\nhg=2782.7 #In KJ/Kg\nCps=2.3 \nme=ms/mf #Equivalent mass evaporation\nhs=hf+x*hfg #Enthalpy of wet steam in KJ/Kg\nE=((me*(hs-hfw))/2257) #Equivalent evaporation in Kg/Kg of coal\nhs1=(hg+Cps*(Tsup-Ts)) #Enthalpy of superheated steam in KJ/Kg\nE1=((me*(hs1-hfw))/2257) #Equivalent evaporation(with superheater) in Kg/Kg of coal\netaboiler=((me*(hs-hfw))/CV)*100 #Boiler efficiency without superheater in %\netaboiler1=((me*(hs1-hfw))/CV)*100#Boiler efficiency with superheater in %\n\n\n#Output\nprint(\"Equivalent mass evaporation=\",round(me,2),)\nprint(\"Enthalpy of wet steam=\",hs,\"KJ/Kg\")\nprint(\"Equivalent evaporation=\",round(E,2),\"Kg/Kg of coal\")\nprint(\"Enthalpy of superheated steam=\",round(hs1,2),\"KJ/Kg\")\nprint(\"Equivalent evaporation(with superheater)=\",round(E1,2),\"Kg/Kg of coal\")\nprint(\"Boiler efficiency without superheater=\",round(etaboiler,2),\"%\")\nprint(\"Boiler efficiency without superheater=\",round(etaboiler1,2),\"%\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Equivalent mass evaporation= 8.57\nEnthalpy of wet steam= 2623.986 KJ/Kg\nEquivalent evaporation= 9.25 Kg/Kg of coal\nEnthalpy of superheated steam= 2946.09 KJ/Kg\nEquivalent evaporation(with superheater)= 10.47 Kg/Kg of coal\nBoiler efficiency without superheater= 66.28 %\nBoiler efficiency without superheater= 75.04 %\n" + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 9 Page No:237" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP=15 #Boiler produces steam in bar\nTsup=250 #Boiler temperature in degree celsius \nTw=35 #Feed water in degree celsius\nMWh=1.5 #steam supplied to the turbine\nCV=32000 #Coal of calorific value in KJ/Kg\netaboiler=80/100 #Thermal efficiency in %\nfr=210 #Firing rate in Kg/m**2/h\n#From steam table(temp basis at 35 degree celsius)\nhfw=146.56 #In KJ/Kg\nTs=198.29 #In degree celsius\nhfg=1945.2 #In KJ/Kg\nhg=2789.9 #In KJ/Kg\nCps=2.3 \n\n\n#calculator\nhs=hg+Cps*(Tsup-Ts) #Enthalpy of superheated steam(with superheater) in KJ/Kg\nms=9000/MWh #Steam rate in Kg/MWh\nmf=((ms*(hs-hfw))/(etaboiler*CV)) #Mass of steam consumption in Kg/h\nGA=mf/fr #Grate rate in m**2\n\n\n\n#Output\nprint(\"Enthalpy of superheated steam(with superheater)=\",hs,\"KJ/Kg\")\nprint(\"Steam rate=\",ms,\"Kg/h\")\nprint(\"ass of steam consumption=\",round(mf,1),\"Kg/h\")\nprint(\"Grate rate=\",round(GA,3),\"m**2\")\n\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Enthalpy of superheated steam(with superheater)= 2908.833 KJ/Kg\nSteam rate= 6000.0 Kg/h\nass of steam consumption= 647.4 Kg/h\nGrate rate= 3.083 m**2\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 10 Page No:242" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nma=18 #Boileruses of per Kg of fuel in Kg/Kg\nhw=25*10**-3 #Chimney height to produce draught in mm\nTg=315+273 #Temperature of chimney gases in degree celsius \nTa=27+273 #Out side air temp in degree celsius\n\n#Calculation\n#Draught produce in terms of water column in m\nH=(hw/(353*(1/Ta-1/Tg*((ma+1)/ma))))*1000\n\n#Output\nprint(\"Draught produce in terms of water column=\",round(H,2),\"m\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Draught produce in terms of water column= 46.04 m\n" + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 11 Page No:242" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nH=40 #High discharge in m\nma=19 #Fuel gases per Kg of fuel burnt\nTg=220+273 #Average temp of fuel gases in degree celsius\nTa=25+273 #Ambient temperature in degreee celsius\n\n\n#calculation\nhw=353*H*(1/Ta-1/Tg*((ma+1)/ma)) #Draught produce in terms of water column in mm\nH1=H*((Tg/Ta)*(ma/(ma+1))-1) #Draught produce in terms of hot gas column in m\n\n#output\nprint(\"Draught produce in terms of water column=\",round(hw,2),\"mm\")\nprint(\"Draught produce in terms of hot gas column=\",round(H1,2),\"m\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Draught produce in terms of water column= 17.23 mm\nDraught produce in terms of hot gas column= 22.87 m\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 12 Page No:243" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nH=27 #Chimney height in m\nhw=15 #Draught produces of water column in mm\nma=21 #Gases formed per Kg of fuel burnt in Kg/Kg\nTa=25+273 #Temperature of the ambient air in degree celsius\n\n\n#calculation\nTg=-(((ma+1)/ma)/((hw/(353*H))-(1/Ta))) #Mean temperature of fuel gases in K\n\n#Output\nprint(\"Mean temperature of fuel gases\",Tg,\"k\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Mean temperature of fuel gases 587.9248031162673 k\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 13 Page No:244" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nhw=20 #Static draught of water in mm\nH=50 #Chimney height in m\nTg=212+273 #Temperature of the fuel degree celsius\nTa=27+273 #Atmospheric air in degree celsius\n\n#calculation\nma=(-((hw/(353*H))-Ta*Tg))*10**-4 #Air-fuel ratio in Kg/Kg of fuel burnt-3\n\n#Output\nprint(\"Air-fuel ratio\",round(ma,1),\"Kg/Kg of fuel burnt\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Air-fuel ratio 14.5 Kg/Kg of fuel burnt\n" + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 14 Page No:245" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nH=24 #Chimney height in m\nTa=25+273 #Ambient temperature in degree celsius\nTg=300+273 #Temperature of fuel gases in degree celsius\nma=20 #Combustion space of fuel burnt in Kg/Kgof fuel\ng=9.81 \n\n\n#calculation\nhw=((353*H)*((1/Ta)-((1/Tg)*((ma+1)/ma))))#Theoretical draught in millimeters of water in mm\nH1=H*((Tg/Ta)*(ma/(ma+1))-1) #Theoretical draught produced in hot gas column in m\nH2=H1-9.975 #Draught lost in friction at the grate and passage in m\nV=math.sqrt(2*g*H2) #Actual draught produced in hot gas column in m\n\n#Output\nprint(\"Theoretical draught in millimeters of water=\",round(hw,2),\"mm\")\nprint(\"Theoretical draught produced in hot gas column=\",round(H1,2),\"m\")\nprint(\"Draught lost in friction at the grate and passage=\",round(H2,3),\"m\")\nprint(\"Actual draught produced in hot gas column=\",round(V,),\"m\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Theoretical draught in millimeters of water= 12.9 mm\nTheoretical draught produced in hot gas column= 19.95 m\nDraught lost in friction at the grate and passage= 9.975 m\nActual draught produced in hot gas column= 14 m\n" + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 15 Page No:246" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nH=38 #Stack height in m\nd=1.8 #Stack diameter discharge in m\nma=17 #Fuel gases per Kg of fuel burnt Kg/Kg\nTg=277+273 #Average temperature of fuel gases in degree celsius\nTa=27+273 #Temperature of outside air in degree celsius\nh1=0.4 #Theoretical draught is lost in friction in \ng=9.81\npi=3.142\n\n#calculation\nH1=H*(((Tg/Ta)*(ma/(ma+1))-1))#Theoretical draught produce in hot gas column in m\ngp=0.45*27.8 #Draught lost in friction at the grate and pasage in m\nC=H1-gp #Actual draught produce in hot gas column in m\nV=math.sqrt(2*9.81*C) #Velocity of the flue gases in the chimney in m/s\nrhog=((353*(ma+1))/(ma*Tg)) #Density of flue gases in Kg/m**3\nmg=(rhog*((pi/4)*(d**(2))*V)) #Mass of gas flowing through the chimney in Kg/s\n\n\n#Output\nprint(\"Theoretical draught produce in hot gas column=\",round(H1,1),\"m\")\nprint(\"Draught lost in friction at the grate and pasage=\",gp,\"m\")\nprint(\"Actual draught produce in hot gas column=\",round(C,2),\"m\")\nprint(\"Velocity of the flue gases in the chimney =\",round(V,2),\"m/s\")\nprint(\"Density of flue gases=\",round(rhog,3),\"Kg/m**3\")\nprint(\"Mass of gas flowing through the chimney=\",round(mg,),\"Kg/s\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Theoretical draught produce in hot gas column= 27.8 m\nDraught lost in friction at the grate and pasage= 12.51 m\nActual draught produce in hot gas column= 15.29 m\nVelocity of the flue gases in the chimney = 17.32 m/s\nDensity of flue gases= 0.68 Kg/m**3\nMass of gas flowing through the chimney= 30 Kg/s\n" + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 16 Page No:247" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nhw=1.9 #Drauhgt water in cm\nTg=290+273 #Temp of flue gases in degree celsius \nTa=20+273 #Ambient temp in degree celsius\nma=22 #Flue gases formed in kg/Kg of coal\nd=1.8 #Fuel burnt in m\npi=3.142\ng=9.81\n\n#calculation\nH=(hw/(353*(1/Ta-1/Tg*((ma+1)/ma))))*10 #Theoretical draught produced in water column in m\nH1=H*(((Tg/Ta)*(ma/(ma+1))-1)) #Theoretical draught produced in hot gas column n m\nV=math.sqrt(2*g*H1) #Velocity of tthe flue gases in the chimney in m/s \nrhog=((353*(ma+1))/(ma*Tg)) #Density of flue gases in Kg/m**3\nmg=rhog*((pi/4)*d**2)*V #Mass of gas flowing through the chimney in Kg/s\n\n#Output\nprint(\"Theoretical draught produced in water column=\",round(H,1),\"m\")\nprint(\"Theoretical draught produced in hot gas column=\",round(H1,),\"m\")\nprint(\"Velocity of tthe flue gases in the chimney=\",round(V,2),\"m\")\nprint(\"Density of flue gases=\",round(rhog,4),\"Kg/m**3\")\nprint(\"Mass of gas flowing through the chimney=\",round(mg,1),\"Kg/s\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Theoretical draught produced in water column= 34.6 m\nTheoretical draught produced in hot gas column= 29 m\nVelocity of tthe flue gases in the chimney= 23.85 m\nDensity of flue gases= 0.6555 Kg/m**3\nMass of gas flowing through the chimney= 39.8 Kg/s\n" + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 17 Page No:248" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nmf=8000 #Average coal consumption in Kg/h\nma=19 #Flue gases formed in Kg/Kg\nTg=270+273 #Average temperature of the chimney in degree celsius\nTa=27+273 #Ambient temperature in degree celsius\nhw=18 #Theoretical draught produced by the chimney in mm\nh1=0.6 #Draught is lost in friction H1\ng=9.81\npi=3.142\n\n\n#calculation\nH=(hw/(353*(1/Ta-1/Tg*((ma+1)/ma)))) #Theoretical draught produced in water column in m\nH1=H*(((Tg/Ta)*(ma/(ma+1)))-1) #Theoretical draught produced in hot gas column in m\ngp=h1*H1 #Draught is lost in friction at the grate and passing in m\nhgc=H1-gp #Actual draught produced in hot gas column in m\nV=math.sqrt(2*g*(hgc)) #Velocity of the flue gases in the chimney in m/s\nrhog=((353*(ma+1))/(ma*Tg)) #Density of flue gases in Kg/m**3\nmg=((mf/3600)*ma) #Mass of gas fowing throgh the chimney in Kg/s\nd=math.sqrt(mg/(rhog*(pi/4)*V)) #Diameter of the chimney in m\n\n\n#Output\nprint(\"Theoretical draught produced in water column=\",round(H,1),\"m\")\nprint(\"Theoretical draught produced in hot gas column=\",round(H1,3),\"m\")\nprint(\"Draught is lost in friction at the grate and passing=\",round(gp,2),\"m\")\nprint(\"Actual draught produced in hot gas column=\",round(hgc,3),\"m\")\nprint(\"Velocity of the flue gases in the chimney=\",round(V,2),\"\")\nprint(\"Density of flue gases=\",round(rhog,3),\"Kg/m**3\")\nprint(\"Mass of gas fowing throgh the chimney=\",round(mg,3),\"Kg/s\")\nprint(\"Diameter of the chimney=\",round(d,3),\"m\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Theoretical draught produced in water column= 36.6 m\nTheoretical draught produced in hot gas column= 26.304 m\nDraught is lost in friction at the grate and passing= 15.78 m\nActual draught produced in hot gas column= 10.522 m\nVelocity of the flue gases in the chimney= 14.37 \nDensity of flue gases= 0.684 Kg/m**3\nMass of gas fowing throgh the chimney= 42.222 Kg/s\nDiameter of the chimney= 2.338 m\n" + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 18 Page No:251" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nH=24 #Chimney height in m\nTa=25+273 #Ambient temperature in degree celsius\nTg=300+273 #Temp of flue gases passing through the chimney in degree celsius\nma=20 #Combustion space of fuel burnt in Kg/kg of fuel\ng=9.81\n\n#calculation\nhw=((353*H)*((1/Ta)-((1/Tg)*((ma+1)/ma)))) #Theoretical draught produced in water column in m\nH1=H*(((Tg/Ta)*(ma/(ma+1))-1)) #Theoretical draught produced in hot gas column in m\nH2=0.5*H1 #Draught is lost in friction at the grate and passing in m\nhgc=H1-H2 #Actual draught produced in hot gas column in m\nV=math.sqrt(2*g*H2) #Velocity of the flue gases in the chimney in m/s\n\n\n#Output\nprint(\"Theoretical draught produced in water column=\",round(hw,1),\"m\")\nprint(\"Theoretical draught produced in hot gas column=\",round(H1,2),\"m\")\nprint(\"Draught is lost in friction at the grate and passing=\",round(H2,3),\"m\")\nprint(\"Actual draught produced in hot gas column=\",round(hgc,3),\"m\")\nprint(\"Velocity of the flue gases in the chimney=\",round(V,),\"m/s\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Theoretical draught produced in water column= 12.9 m\nTheoretical draught produced in hot gas column= 19.95 m\nDraught is lost in friction at the grate and passing= 9.975 m\nActual draught produced in hot gas column= 9.975 m\nVelocity of the flue gases in the chimney= 14 m/s\n" + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 19 Page No:252" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nH=38 #Stack height in m\nd=1.8 #Stack diameter in m\nma=18 #Flue gases per kg of the fuel burnt\nTg=277+273 #Average temp of the flue gases in degree celsius\nTa=27+273 #Temperature of outside air in degree celsius\nh1=0.4 #Theorical draught is lost in friction in %\ng=9.81\n\n#calculation\nH1=H*(((Tg/Ta)*(ma/(ma+1))-1)) #Theoretical draught produced in hot gas column in m\ngp=0.40*H1 #Draught is lost in friction at the grate and passing in m\nhgc=H1-gp #Actual draught produced in hot gas column in m\nV=math.sqrt(2*g*hgc) #Velocity of the flue gases in the chimney in m/s\nrhog=((353*(ma+1))/(ma*Tg)) #Density of flue gases in Kg/m**3\nmg=rhog*((pi/4)*d**2)*V #Mass of gas fowing throgh the chimney in Kg/s\n\n\n#Output\nprint(\"Theoretical draught produced in hot gas column=\",round(H1,3),\"m\")\nprint(\"Draught is lost in friction at the grate and passing=\",round(gp,2),\"m\")\nprint(\"Actual draught produced in hot gas column=\",round(hgc,2),\"m\")\nprint(\"Velocity of the flue gases in the chimney=\",round(V,2),\"m/s\")\nprint(\"Density of flue gases=\",round(rhog,2),\"Kg/m**3\")\nprint(\"Mass of gas fowing throgh the chimney=\",round(mg,1),\"Kg/s\")\n\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Theoretical draught produced in hot gas column= 28.0 m\nDraught is lost in friction at the grate and passing= 11.2 m\nActual draught produced in hot gas column= 16.8 m\nVelocity of the flue gases in the chimney= 18.16 m/s\nDensity of flue gases= 0.68 Kg/m**3\nMass of gas fowing throgh the chimney= 31.3 Kg/s\n" + } + ], + "prompt_number": 41 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 20 Page No:253" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nhw=19 #Draught produced water in cm\nTg=290+273 #Temperature of flue gases in degree celsius\nTa=20+273 #Ambient temperature in degree celsius\nma=22 #Flue gases formed per kg of fuel burnt in kg/kg of coal \nd=1.8 #Diameter of chimney\ng=9.81\n\n\n#calculation\nH=(hw/((353)*((1/Ta)-((1/Tg)*((ma+1)/ma))))) #Theoretical draught produced in hot gas column in m\nH1=H*(((Tg/Ta)*(ma/(ma+1))-1)) #Draught is lost in friction at the grate and passing in m\nV=math.sqrt(2*g*H1) #Velocity of the flue gases in the chimney in m/s\nrhog=((353*(ma+1))/(ma*Tg)) #Density of flue gases in Kg/m**3\nmg=rhog*((pi/4)*d**2)*V #Mass of gas fowing throgh the chimney in Kg/s\n\n\n#Output\nprint(\"Theoretical draught produced in hot gas column=\",round(H,),\"m\")\nprint(\"Draught is lost in friction at the grate and passing=\",round(H1,1),\"m\")\nprint(\"Velocity of the flue gases in the chimney=\",round(V,2),\"m/s\")\nprint(\"Density of flue gases=\",round(rhog,4),\" Kg/m**\")\nprint(\"Mass of gas fowing throgh the chimney=\",round(mg,1),\"Kg/s\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Theoretical draught produced in hot gas column= 35 m\nDraught is lost in friction at the grate and passing= 29.0 m\nVelocity of the flue gases in the chimney= 23.85 m/s\nDensity of flue gases= 0.6555 Kg/m**\nMass of gas fowing throgh the chimney= 39.8 Kg/s\n" + } + ], + "prompt_number": 44 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 21 Page No:254" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nmf=8000 #Average coal consumption in m \nma=18 #Fuel gases formed ccoal fired in m\nTg=270+273 #Average temp of the chimney of water in degree celsius\nTa=27+273 #Ambient temp in degree celsius\nhw=18 #Theoretical draught produced by the chimney in mm\nh1=0.6 #Draught is lost in friction in H1\ng=9.81\npi=3.142\n\n\n#calculation\nH=(hw/((353)*((1/Ta)-((1/Tg)*((ma+1)/ma))))) #Theoretical draught produced in water column in m\nH1=H*(((Tg/Ta)*(ma/(ma+1))-1)) #Theoretical draught produced in hot gas column in m\ngp=0.6*H1 #Draught is lost in friction at the grate and passing in m\nhgc=H1-gp #Actual draught produced in hot gas column in m \nV=math.sqrt(2*g*hgc) #Velocity of the flue gases in the chimney in m/s\nrhog=((353*(ma+1))/(ma*Tg)) #Density of flue gases in Kg/m**3\nmg=mf/3600*(ma+1) #Mass of gas fowing throgh the chimney in Kg/s\nd=math.sqrt(mg/(rhog*(pi/4)*V)) #Diameter of flue gases in Kg/m**3\n\n#Output\nprint(\"Theoretical draught produced in water column=\",round(H,1),\"m\")\nprint(\"Theoretical draught produced in hot gas column=\",round(H1,2),\"m\")\nprint(\"Draught is lost in friction at the grate and passing=\",round(gp,2),\"m\")\nprint(\"Actual draught produced in hot gas column=\",round(hgc,2),\"\")\nprint(\"Velocity of the flue gases in the chimney=\",round(V,2),\"m/s\")\nprint(\"Density of flue gases=\",round(rhog,3),\"Kg/m**3\")\nprint(\"Mass of gas fowing throgh the chimney=\",round(mg,2),\"Kg/s\")\nprint(\"Diameter of flue gases=\",round(d,3),\"Kg/m**3\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Theoretical draught produced in water column= 36.7 m\nTheoretical draught produced in hot gas column= 26.23 m\nDraught is lost in friction at the grate and passing= 15.74 m\nActual draught produced in hot gas column= 10.49 \nVelocity of the flue gases in the chimney= 14.35 m/s\nDensity of flue gases= 0.686 Kg/m**3\nMass of gas fowing throgh the chimney= 42.22 Kg/s\nDiameter of flue gases= 2.337 Kg/m**3\n" + } + ], + "prompt_number": 45 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 22 Page No:256" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nH=45 #Chimney height in m\nTg=370+273 #Temperature of flue gases in degree celsius\nT1=150+273 #Temperature of flue gases in degree celsius\nma=25 #Mass of the flue gas formed in Kg/kg of a cosl fired\nTa=35+273 #The boiler temperature in degree celsius\nCp=1.004 #fuel gas\n\n#calculation\n#Efficeincy of chimney draught in %\nA=(H*(((Tg/Ta)*(ma/(ma+1)))-1))/(Cp*(Tg-T1))*100\n\n#Output\nprint(\"Efficeincy of chimney draught=\",round(A,2),\"%\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Efficeincy of chimney draught= 20.52 %\n" + } + ], + "prompt_number": 47 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_13_Steam_Engines_93BIP5u.ipynb b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_13_Steam_Engines_93BIP5u.ipynb new file mode 100644 index 00000000..0b5d6900 --- /dev/null +++ b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_13_Steam_Engines_93BIP5u.ipynb @@ -0,0 +1,308 @@ +{ + "metadata": { + "name": "Chapter 13 Steam Engines" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 1 Page No:281" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nPa=10 #Single cylinder double acting steam engine pressure in bar \nPb=1.5 #Single cylinder double acting steam engine pressure in bar\nrc=100/35 #Cut-off of the stroke in %\n\n\n#Calculation\nPm=((Pa/rc)*(1+math.log(rc))-Pb) #Therotical mean effective pressure\n\n#Output\nprint(\"Therotical mean effective pressure=\",round(Pm,2),\"bar\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Therotical mean effective pressure= 5.67 bar\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 2 Page No:283" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\n\na=5/100 #Engine cylinder of the stroke valume in %\nP1=12 #Pressure of the stream\nrc=3 #Cut-off is one-third\nPb=1.1 #Constant the back pressure in bar\n\n#Calulation\n#Therotical mean effective pressure Pm\nPm=P1*(1/rc+((1/rc)+a)*math.log((1+a)/((1/rc)+a)))-Pb \n\n#Output\nprint(\"#Therotical mean effective pressure=\",round(Pm,2),\"N/m**2\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "#Therotical mean effective pressure= 7.54 N/m**2\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 3 Page No:285" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nP1=14 #Steam is ssupplied in bar \nP6=6 #Pressure at the end in bar\nPb=1.2 #Pressure at back in bar\na=0.1 \nre=4 \n#From hyperbolic process \nb=0.4\n\n#Calculation\n#Mean Effective pressure in N/m**2 \nPm=P1*((1/re)+((1/re)+a)*math.log((1+a)/((1+re)+a)))-Pb*((1+b)+(a+b)*math.log((a+b)/a))\n\n\n#Output\nprint(\"Mean Effective pressure=\",round(-Pm,3),\"N/m**2\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Mean Effective pressure= 6.662 N/m**2\n" + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 4 Page No:286" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nCover=1200 #Area of the indicator diagram for cover \nCrank=1100 #Area of the indicator diagram for crank\nID=75\nPS=0.15\n\n\n#Calculation\nCoverMEP=Cover/ID*PS #Cover end mean effective pressure\nCrankMEP=Crank/ID*PS #Crank end mean effective pressure\nAverageMEP=(CoverMEP+CrankMEP)/2 #Average end mean effective pressure\n\n\n#Output\nprint(\"Cover end mean effective pressure=\",CoverMEP,\"bar\")\nprint(\"Crank end mean effective pressure=\",round(CrankMEP,2),\"bar\")\nprint(\"Average end mean effective pressure=\",AverageMEP,\"bar\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Cover end mean effective pressure= 2.4 bar\nCrank end mean effective pressure= 2.2 bar\nAverage end mean effective pressure= 2.3 bar\n" + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 5 Page No:286" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\na=25 #Area of indicator diagram cm**2\nVs=0.15 #swept volume m**2\nS=1 #Scale in cm \ncm=0.02 #pressure axis m**3\n\n\n#Calculation\nb=Vs/cm #Base length of diagram \nPm=a/b*S #Mean effective pressure\n\n#Output\nprint(\"Base length of diagram=\",b,\"bar\")\nprint(\"Mean effective pressure=\",round(Pm,2),\"bar\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Base length of diagram= 7.5 bar\nMean effective pressure= 3.33 bar\n" + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 6 Page No:287" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nP1=14 #Steam Engine pressure in bar\nPb=0.15 #Back pressure in bar\nK=0.72 #Diagram factor\nrc=100/20 \n\n#Calculation\nPm=((P1/rc)*(1+math.log(rc))-Pb) #Therotical mean effective pressure Pm\nPma=Pm*K #Actual mean effective pressure Pma\n\n#Output\nprint(\"Therotical mean effective pressure=\",round(Pm,3),\"bar\")\nprint(\"Actual mean effective pressure=\",round(Pma,2),\"bar\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Therotical mean effective pressure= 7.156 bar\nActual mean effective pressure= 5.15 bar\n" + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 7 Page No:287" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nP1=9 #Reciprocating engine pressure in bar\nPb=1.5 #Back pressure in bar\nrc=100/25 #Cut-off \nK=0.8 #Diagram factor\n\n#Calculation\nPm=((P1/rc)*(1+math.log(rc))-Pb) #Therotical mean effective pressure Pm\nPma=Pm*K #Actual mean effective pressure Pma\n\n#Output\nprint(\"Therotical mean effective pressure= \",round(Pm,2),\"bar\")\nprint(\"Actual mean effective pressure=\",round(Pma,2),\"bar\")\n\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Therotical mean effective pressure= 3.87 bar\nActual mean effective pressure= 3.1 bar\n" + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 8 Page No:288" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nP1=10 #Inlet pressure\nPb=1 #Back pressure\nrc=3 #Expansion ratio\na=12.1 #Area of indicator diagram\nb=7.5 #Length of indicator diagram \nS=3 #Pressure scale\n\n\n#calculation\nPm=((P1/rc)*(1+math.log(rc))-Pb )#Therotical mean effective pressure Pm\nPma=a/b*S #Actual mean effective pressure Pma\nK=Pma/Pm #diagram factor \n\n#Output\nprint(\"Therotical mean effective pressure=\",round(Pm,2),\"bar\")\nprint(\"Actual mean effective pressure=\",round(Pma,2),\"bar\")\nprint(\"Diagram factor=\",round(K,3),)\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Therotical mean effective pressure= 6.0 bar\nActual mean effective pressure= 4.84 bar\nDiagram factor= 0.807\n" + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 9 Page No:289" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nD=200*10**-3 #Steam engine cylinder in mm \nL=300*10**-3 #Bore of steam engine cylinder in mm \nrc=100/40 #Cut-off of the sroke\nP1=7 #Admission pressure of steam in bar\nPb=0.38 #Exhaust pressure of steam in bar\nK=0.8 #Diagram factor\nN=200 #Indicator factor of engine\npi=3.142 #Constant value\n#Indicated power of the engine in rpm\nA=pi*(200*10**-3)**2/4\n\n\n#Calculation\nPm=((P1/rc)*(1+math.log(rc))-Pb) #Therotical mean effective pressure Pm\nPma=Pm*K #Actual mean effective pressure Pma\nIP=(2*Pma*L*A*N/60000)*10**5 #Indicated power of steam engine in Kw\n\n\n#Output\nprint(\"Therotical mean effective pressure= \",round(Pm,3),\"bar\")\nprint(\"Actual mean effective pressure=\",round(Pma,),\"bar\")\nprint(\"Indicated power of steam engine=\",round(IP,2),\"Kw\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Therotical mean effective pressure= 4.986 bar\nActual mean effective pressure= 4 bar\nIndicated power of steam engine= 25.06 Kw\n" + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 10 Page No:290" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nIP=343 #Steam engine develop indicated power in Kw\nN=180 #power In rpm\nP1=15 #Steam supplied i bar \nPb=1.25 #Steam is exhausted in bar\nrc=100/25 #Cut-off take place of stroke\nK=0.78 #Diagram factor\n#x=L/D=4/3\nx=4/3 #Stroke to bore ratio\npi=3.142\nA=((pi/4)*(D**2))\n\n#calculation\nPm=((P1/rc)*(1+math.log(rc))-Pb) #Therotical mean effective pressure Pm\nPma=Pm*K #Actual mean effective pressure Pma\nD=(((60000*IP)/(2*(Pma*10**5)*(4/3)*N))/(pi/4))**(1/3)#Indicated power of steam engine\nL=(x)*D\n\n\n#Output\nprint(\"Therotical mean effective pressure=\",round(Pm,2),\"bar\")\nprint(\"Actual mean effective pressure=\",round(Pma,2),\"bar\")\nprint(\"Indicated power of steam engine=\",round(D,3),\"mm\")\nprint(\"Indicated power of steam engine=\",round(L,1),\"mm\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Therotical mean effective pressure= 7.7 bar\nActual mean effective pressure= 6.0 bar\nIndicated power of steam engine= 0.45 mm\nIndicated power of steam engine= 0.6 mm\n" + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 11 Page No:290" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nD=240*10**-3 #Steam engine bor\nL=300*10**-3 #Stroke of engine\nN=220 #Speed of engine 220 in rpm \nIP=36 #Indicated power in Kw\nPb=1.3 #Exhaust pressure in bar\nre=2.5 #Expansion ratio\nK=0.8 #Diagram factor\nA=((pi/4)*(D**2))\n\n\n#Calculation\nPma=((IP*60000)/(2*10**5*L*A*N)) #Indicated power of steam engine in bar\nPm=Pma/K #Actual mean effective pressure in bar\nP1=((Pm+Pb)*re)/(1+math.log(re)) #Theoretical mean effective pressure in bar\n\n#Output\nprint(\"Indicated power of steam engine=\",round(Pma,3),\"bar\")\nprint(\"Actual mean effective pressure=\",round(Pm,3),\"bar\")\nprint(\"theoretical mean effective pressure=\",round(P1,1),\"bar\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Indicated power of steam engine= 3.617 bar\nActual mean effective pressure= 4.521 bar\ntheoretical mean effective pressure= 7.6 bar\n" + } + ], + "prompt_number": 46 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 12 Page No:291" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nD=700*10**-3 #Steam engine diameter in mm\nL=900*10**-3 #Steam engine diameter in mm\nIp=450 #Develop indicated power Kw\nN=90 #Speed of steam engine in rpm\nP2=12 #Pressure at cut-off in bar\nP1=12 #Pressure at cut-off in bar\nPb=1.3 #Back pressure in bar\nK=0.76 #Diameter factor\npi=3.142\nA=((pi/4)*0.7**2)\n\n#Calculation\nPma=(Ip*60000)/(2*10**5*L*A*90) #Indicated power of steam engine in bar\nPm=Pma/K #Theoretical mean effective pressure in bar\n#using trial and error method\nre=1/0.241 #Expansion ratio\n#Output\nprint(\"Indicated power of steam engine=\",round(Pma,2),\"bar\")\nprint(\"Theoretical mean effective pressure=\",round(Pm,1),\"bar\")\nprint(\"Expansion ratio=\",round(re,2),)", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Indicated power of steam engine= 4.33 bar\nTheoretical mean effective pressure= 5.7 bar\nExpansion ratio= 4.15\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 13 Page No:293" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nDb=900*10**-3 #Diameter of break drum in mm\ndr=50*10**-3 #Diameter of rope in mm\nW=105*9.81 #dead weight on the tight side of the rope in Kg\nS=7*9.81 #Spring balance of the rope in N\nN=240 #Speed of the engine in rpm\n\n#Calculation\nT=(W-S)*((Db+dr)/2) #Torque Nm\nBp=2*pi*N*T/ 60000 #Brake Power in Kw\n\n#Output\nprint(\"Torque= \",round(T,2),\"Nm\")\nprint(\"Brake Power=\",round(Bp,2),\"Kw\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Torque= 456.66 Nm\nBrake Power= 11.48 Kw\n" + } + ], + "prompt_number": 57 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 14 Page No:294" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nD=300*10**-3 #steam engine bor\nL=400*10**-3 #stroke \nDb=1.5 #effective brake diameter\nW=6.2*10**3 #net load on the brake\nN=180 #speed of engine in rpm\nPma=6.5*10**3 #mean effective pressure in bar\nA=((pi/4)*0.3**2) \ndr=0\nS=0\n\n#Calculation\nIp=((2*Pma*L*A*N)/60000)*100 #Indicated power of steam engine in Kw\nT=(W-S)*((Db+dr)/2) #Torque in Nm\nBp=2*pi*N*T/ 60000 #Break power Kw\neta=(Bp/Ip)*100 #Mechanical efficiency in%\n\n\n#Output\nprint(\"Indicated power of steam engine=\",round(Ip,2),\"Kw\")\nprint(\"Torque=\",T,\"Nm\")\nprint(\"Break power=\",round(Bp,2),\"Kw\")\nprint(\"Mechanical efficiency=\",round(eta,1),\"%\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Indicated power of steam engine= 110.28 Kw\nTorque= 4650.0 Nm\nBreak power= 87.66 Kw\nMechanical efficiency= 79.5 %\n" + } + ], + "prompt_number": 59 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_14_Air_Standard_C_Wu44kME.ipynb b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_14_Air_Standard_C_Wu44kME.ipynb new file mode 100644 index 00000000..a968e2ca --- /dev/null +++ b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_14_Air_Standard_C_Wu44kME.ipynb @@ -0,0 +1,358 @@ +{ + "metadata": { + "name": " Chapter 14 Air Standard Cycles" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 1 Page No:302" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nTmax=477+273 #Temperature limits for the engine 477 degree celcius\nTmin=27+273 #Temperature limits for the engine 27 degree celcius\nwd=150 #Carnot cycle produce in KJ\n\n#Calculatkion\neta=(1-(Tmin/Tmax)) #Thermal efficiency of the carnot cycle in %\nQs=(wd/eta) #Added during the process in Kj\n\n\n#Output\nprint(\"thermal efficiency of the carnot cycle eta=\",100*(eta),\"%\")\nprint(\"added during the process Qs=\",Qs,\"KJ\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "thermal efficiency of the carnot cycle eta= 60.0 %\nadded during the process Qs= 250.0 KJ\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 2 Page No:302" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nQR=1.5 #tau=QS-QR\n #T=Tmax-Tmin\nT=300 #temperature limit of the cycle in degree celsius\n\n\n#Calculation\n#QR=1.5*(QS-QR)\nQR=(1.5/2.5) #Engin work on carnot cycle\neta=(1-QR) #Thermal effeciency\nTmax=(T/eta)-273.15 #Maximum temperataure\nTmin=(Tmax-T) #Minimum temperataure\n\n\n#Output\nprint(\"Engin work on carnot cycle=\",QR,\"QS\")\nprint(\"Thermal effeciency=\",100*(eta),\"%\")\nprint(\"Maximum temperataure=\",round(Tmax,),\"degree celsius\")\nprint(\"Minimum temperataure=\",round(Tmin,),\"degree celsius\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Engin work on carnot cycle= 0.6 QS\nThermal effeciency= 40.0 %\nMaximum temperataure= 477 degree celsius\nMinimum temperataure= 177 degree celsius\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 3 Page No:303" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\n#Refer figure\nimport math\nT1=300 #Carnot engine work in minimum temperature in kelvin\nT2=750 #Carnot engine work in maximum temperature kelvin\nP2=50 #pressure of carnot engine N/m**2\nP4=1 #pressure of carnot engine N/m**\n#considering air as the working fluid therefore \nR=0.287 #Air as the working fluid in KJ/Kg K\nCp=1.005 #KJ/Kg K\nCv=0.718 #KJ/Kg K\nK=1.4\ngamma=1.4\n\n#Calculation\n#T2/T1=(P2/P1)**(gamma-1)/gamma\nP1=P2*(T1/T2)**(gamma/(gamma-1)) #Pressure at intermediate salient points(1-2) in bar\nP3=P4*(T2/T1)**(gamma/(gamma-1)) #Pressure at intermediate salient points(3-4) in bar\nQS=R*T2*math.log(P2/P3 ) #Heat supplied and rejected per Kg of air in KJ/Kg\nQR=R*T1*math.log(P1/P4 ) #Heat supplied and rejected per Kg of air in KJ/Kg\nW=QS-QR #Work done in KJ/Kg\neta=(1-(T1/T2)) #Thermal of the carnot cycle\n\n#Output\nprint(\"pressure at intermediate salient points(1-2)=\",round(P1,2),\"bar\")\nprint(\"pressure at intermediate salient points(3-4)=\",round(P3,1),\"bar\")\nprint(\"heat supplied and rejected per Kg of air(2-3)=\",round(QS,1),\"KJ/Kg\")\nprint(\"heat supplied and rejected per Kg of air(4-1)=\",round(QR,2),\"KJ/Kg\")\nprint(\"work done=\",round(W,1),\"KJ/Kg\")\nprint(\"thermal of the carnot cycle=\",100*(eta),\"%\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "pressure at intermediate salient points(1-2)= 2.02 bar\npressure at intermediate salient points(3-4)= 24.7 bar\nheat supplied and rejected per Kg of air(2-3)= 151.8 KJ/Kg\nheat supplied and rejected per Kg of air(4-1)= 60.7 KJ/Kg\nwork done= 91.1 KJ/Kg\nthermal of the carnot cycle= 60.0 %\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 4 Page No:304" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#input data \nimport math\nT2=377+273 #Carnot cycle temperature in bar \nP2=20*10**5 #Carnot cycle pressure in bar\nV2=1\nV1=5\nV3=2\n#consider air as the working fluid therefore\nR=0.287 #In KJ/Kg K\nCp=1.005 #In KJ/Kg K\nCv=0.718 #In KJ/Kg K\nK=1.4\ngamma=1.4\n\n#calculation\nT1=T2*((v2/v1)**(gamma-1)) #Minimum temp in degree celsius\nQs=R*T2*math.log(V3/V2) #Heat supplied process in KJ/Kg\nQR=R*T1*math.log((V1/V2)*(V2/V3)*((T2/T1)**(1/(gamma-1)))) #Heat Rejected Process in KJ/Kg\netath=(1-(T1/T2))*100 #Thermal Effeiciency of the carnot cycle in %\n\n\n\n#output\nprint(\"Minimum temp= \",round(T1,1),\"degree celsius\")\nprint(\"Heat supplied process= \",round(Qs,1),\"KJ/Kg\")\nprint(\"Heat Rejected Process= \",round(QR,1),\"KJ/Kg\")\nprint(\"Thermal Effeiciency of the carnot cycle= \",round(etath,1),\" %\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Minimum temp= 341.4 degree celsius\nHeat supplied process= 129.3 KJ/Kg\nHeat Rejected Process= 247.5 KJ/Kg\nThermal Effeiciency of the carnot cycle= 47.5 %\n" + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 5 Page No:308 " + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP1=1 #Isentropic Compression in bar\nP2=20 #Isentropic Compression in bar\n#consider air as the working fluid therefore\ngamma=1.4\n\n\n#Calculation\nr=(P2/P1)**(1/gamma) #Isentropic process \neta=100*(1-(1/(r**(gamma-1))))#Otto cycle air standard effeciency in %\n\n\n#Output\nprint(\"compression ratio=\",round(r,2),)\nprint(\"standard efficiency=\",round(eta,1),\"%\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "compression ratio= 8.5\nstandard efficiency= 57.5 %\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 6 Page No:308" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nT1=27+273 #Initial temp in degree celsius \nT2=450+273 #Final temp in degree celsius \n\n#calculation\nr=(T2/T1)**(1/(gamma-1)) #Isentropic process \neta=100*(1-(1/(r**(gamma-1)))) #Otto cycle air standard effeciency in %\n\n#output\nprint(\"compression ratio=\",round(r),)\nprint(\"standard efficiency=\",round(eta,1),\"%\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "compression ratio= 9\nstandard efficiency= 58.5 %\n" + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 7 Page No:309" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nD=200*10**-3 #Otto cycle cylindrical bore in mm\nL=450*10**-3 #Otto cycle Stroke in mm\nvc=2*10**-3 #Clearance volume in mm**3\ngamma=1.4\npi=3.142\n\n#calculation\nvs=(pi/4)*(D**2*L) #Swept volume\nr=((vs+vc)/vc) #Compression ratio\neta=100*(1-(1/(r**(gamma-1)))) #Standard efficiency\n\n#output\nprint(\"Swept volume=\",round(vs,6),\"m**3\")\nprint(\"compression ratio=\",round(r,3),)\nprint(\"standard efficiency=\",round(eta,1),\"%\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Swept volume= 0.014139 m**3\ncompression ratio= 8.07\nstandard efficiency= 56.6 %\n" + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 8 Page No:309" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP1=0.1*10**6 #Otto cycle air\nT1=35+273 #Otto cycle temp degree celsius\nr=9 #Compression ratio\nQs=1800 #Supplied heat in kJ/kg\nv1=9 \nv2=1\nR=0.287*10**3\ngamma=1.4\nCv=0.718\n\n\n\n#calculation\nT2=(T1*((v1/v2)**(gamma-1))) #Temperature at point 2 in K\nP2=(P1*((v1/v2)**1.4))*10**-6 #pressure at point 2 in MPa \nT3=((Qs/Cv)+(T2)) #Max temp of cycle in degree celsius\nP3=(T3/T2*P2) #Max pressure of cycle in MPa\neta=100*(1-(1/(r**(gamma-1))))#Otto cycle thermal efficiency in %\nWD=(Qs*eta)*10**-2 #Work done during the cycle in KJ/Kg\nv1=((R*T1)/P1) #Char gass equation in m**3/Kg\nv2=v1/r #Char gass equation in m**3/Kg\nSv=v1-v2 #Swept volume in m**3/Kg\nPme=(WD/Sv)*10**-3 #Mean effective pressure in MPa\nalpha=P3/P2 #Explosion ratio\nPm=(((P1*r)/((r-1)*(gamma-1)))*(((r**(gamma-1))-1)*(alpha-1)))*10**-6#Mean effective pressure in MPa\n\n\n#Output\nprint(\"Temperature at point=\",round(T2,1),\"K\")\nprint(\"pressure at point=\",round(P2,3),\"MPa\")\nprint(\"Max temp of cycle=\",round(T3,3),\"K\")\nprint(\"Max pressure= \",round(P3,1),\"MPa\")\nprint(\"Otto cycle thermal efficiency=\",round(eta,1),\"%\")\nprint(\"Work done during the cycle=\",round(WD,),\"J/Kg\")\nprint(\"Char gass equation=\",round(v1,3),\"m**3/Kg\")\nprint(\"Char gass equation=\",round(v2,4),\"m**3/Kg\")\nprint(\"Swept volume=\",round(Sv,4),\"m**3/Kg\")\nprint(\"Mean effective pressure=\",round(Pme,2),\"MPa\")\nprint(\"Explosion ratio=\",round(alpha,2))\nprint(\"Mean effective pressure=\",round(Pm,2),\"MPa\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Temperature at point= 741.7 K\npressure at point= 2.167 MPa\nMax temp of cycle= 3248.697 K\nMax pressure= 9.5 MPa\nOtto cycle thermal efficiency= 58.5 %\nWork done during the cycle= 1053 J/Kg\nChar gass equation= 0.884 m**3/Kg\nChar gass equation= 0.0982 m**3/Kg\nSwept volume= 0.7857 m**3/Kg\nMean effective pressure= 1.34 MPa\nExplosion ratio= 4.38\nMean effective pressure= 1.34 MPa\n" + } + ], + "prompt_number": 165 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 9 Page No:311" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP1=0.1 #Beginning compression in MPa\nT1=40+273 #Beginning temp in degree celsius\neta=0.55 #Standard effeciency in %\nQR=540 #Rejected heat in KJ/Kg\nr=7.36 #Compression ratio\n\n\n#calculation\n#eta=(1-(1/(r**(gamma-1))))\nQS=(-QR/(eta-1)) #Heat supplied/unit mass in KJ/Kg\nWD=QS-QR #Work done per Kg of air in KJ/Kg\nT2=T1*(r**(gamma-1)) #Temp at end of compression in K\nP2=P1*((r)**gamma) #pressure at point 2 in MPa\nT3=(QS/Cv)+T2 #max temp of the cycle in K\nP3=(T3/T2)*P2 #max pressure of the cycle in MPa\n\n#output\nprint(\"Heat supplied/unit mass=\",round(QS,),\"KJ/Kg\")\nprint(\"Work done per Kg of air= \",round(WD,),\"KJ/Kg\")\nprint(\"Temp at end of compression=\",round(T2,1),\"K\")\nprint(\"pressure at point two=\",round(P2,3),\" MPa\")\nprint(\"max temp of the cycle=\",round(T3,1),\"K\")\nprint(\"max pressure of the cycle=\",round(P3,3),\" MPa\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Heat supplied/unit mass= 1200 KJ/Kg\nWork done per Kg of air= 660 KJ/Kg\nTemp at end of compression= 695.5 K\npressure at point two= 1.635 MPa\nmax temp of the cycle= 2366.8 K\nmax pressure of the cycle= 5.565 MPa\n" + } + ], + "prompt_number": 64 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 10 Page No:312" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nT1=300 #Initial temp in K\nT3=2500 #Final temp in K\nP1=1 #Initial pressure in N/m**2\nP3=50 #Final pressure in N/m**2\ngamma=1.4\nCv=0.718\n\n#calculation\nr=(P3*T1)/(P1*T3) #Compression ratio\neta=(1-(1/r**(gamma-1))) #Standard effeciency in %\nT2=T1*((P3/P1)**((gamma-1)/gamma)) #Middle temperature in K\nQs=Cv*(T3-T2) #Heat supplied in KJ/Kg\nWD=eta*Qs #Work done KJ/Kg\n\n#output\nprint(\"Compression ratio=\",r,\"\")\nprint(\"Standard effeciency=\",round(eta,4),\"%\")\nprint(\"Middle temperature=\",round(T2,2),\"K\")\nprint(\"Heat supplied=\",round(Qs,2),\"KJ/Kg\")\nprint(\"Work done=\",round(WD,1),\"KJ/Kg\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Compression ratio= 6.0 \nStandard effeciency= 0.5116 %\nMiddle temperature= 917.36 K\nHeat supplied= 1136.33 KJ/Kg\nWork done= 581.4 KJ/Kg\n" + } + ], + "prompt_number": 84 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 11 Page No:316" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#input data\nr=18 #compression ratio of diesel engine\nK=6 #cut-off ratio of the stroke in%\nrho=2.02 \n\n#calculation\n#diesel engine air standard efficiency\neta=100*((1-(1/r**(gamma-1)))*(1/gamma*(rho**(gamma-1)/(rho-1))))\n\n#output\nprint(\"diesel engine air standard efficiency\",round(eta,1),\"%\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "diesel engine air standard efficiency 63.6 %\n" + } + ], + "prompt_number": 87 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 12 Page No:317" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input Data\nr=22 #compression ratio of diesel engine r=v1/v2\nr1=11 #expansion ratio r1=v4/v3\ngamma=1.4\nrho=1.4\n\n#calculation\nrho=r/r1 #cut-off ratio\n#diesel engine air standard efficiency \neta=100*((1-(1/r**(gamma-1)))*(1/gamma*(rho**(gamma-1)/(rho-1))))\n\n#output\nprint(\"cut-off ratio=\",rho,)\nprint(\"diesel engine air standard efficiency=\",round(eta,2),\"%\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "cut-off ratio= 2.0\ndiesel engine air standard efficiency= 66.88 %\n" + } + ], + "prompt_number": 88 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 13 Page No:317" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nVc=10/100 #Clearance volume in % \nVs=Vc/0.1 \nK=0.05 #Cut-off of the strok in \ngamma=1.4\n\n#Calculation\nr=((Vs+Vc)/(Vc)) #Compression ratio\nrho=1+K*(r-1) #Cut-off ratio\n#Effeciency in %\neta=(1-(1/r**(gamma-1))*((1/gamma)*(((rho**(gamma))-1)/(rho-1))))*100\n\n#output\nprint(\"Compression ratio=\",r,\"Vs\")\nprint(\"Cut-off ratio=\",rho,)\nprint(\"Effeciency=\",round(eta,2),\"%\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Compression ratio= 11.0 Vs\nCut-off ratio= 1.5\nEffeciency= 58.17 %\n" + } + ], + "prompt_number": 107 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 14 Page No:" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nT1=50+273 #Temperature at the beginning of the compression\nT2=700+273 #Temperature at the end of the compression\nT3=2000+273 #Temperature at the beginning of the expansion\n\n\n#Calculation\nr=((T2/T1)**(1/(gamma-1))) #Compression ratio \nrho=(T3/T2) #Cut-off ratio\nK=((rho-1)/(r-1)) #Also cut-off ratio\n#Air standard efficiency\neta=(1-(1/r**(gamma-1))*((1/gamma)*(((rho**(gamma))-1)/(rho-1))))*100\n\n#Output\nprint(\"compression ratio=\",round(r,2),\"\")\nprint(\"cut-off ratio=\",round(rho,3),)\nprint(\"also cut-off ratio=\",round(K,2),\"\")\nprint(\"air standard efficiency=\",round(eta,2),\"%\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "compression ratio= 15.75 \ncut-off ratio= 2.336\nalso cut-off ratio= 0.09 \nair standard efficiency= 59.54 %\n" + } + ], + "prompt_number": 122 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 15 Page No:317" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nP1=0.1 #Diesel cycle is supplied# with air in MPa\nT1=40+273 #Diesel cycle is supplied with temperature in degree celsius \nr=18 #Compression ratio\nQs=1500 #Heat supplied\nv1=18\nv2=1\nCp=1.005\n\n\n#Calculation\nT2=T1*((v1/v2)**(gamma-1)) #For isentropic process the temperature is\nP2=P1*((v1/v2)**(gamma)) #For isentropic process the pressure is\nT3=(Qs/Cp)+T2 #Maximum temperatureof the cycle\nrho=T3/T2 #Cut-off ratio\n#Air standard efficiency\neta=(1-(1/r**(gamma-1))*((1/gamma)*(((rho**(gamma))-1)/(rho-1))))*100\nNWD=(Qs*eta)*10**-2 #Net work done\n\n#Output\nprint(\"for isentropic process the temperature=\",round(T2,1),\"K\")\nprint(\"for isentropic process the pressure=\",round(P2,2),\"MPa\")\nprint(\"maximum temperatureof the cycle=\",round(T3,2),\"K\")\nprint(\"cut-off ratio=\",round(rho,1),\"MPa\")\nprint(\"air standard efficiency=\",round(eta,2),\"%\")\nprint(\"net work done=\",round(NWD,),\"KJ/Kg\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "for isentropic process the temperature= 994.6 K\nfor isentropic process the pressure= 5.72 MPa\nmaximum temperatureof the cycle= 2487.15 K\ncut-off ratio= 2.5 MPa\nair standard efficiency= 60.93 %\nnet work done= 914 KJ/Kg\n" + } + ], + "prompt_number": 130 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 16 Page No:317" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nr=14 #compression ratio of standard diesel cycle\nP1=1 #compression stroke in bar\nT1=300 #temperature of air in k\nT3=2774 #temperature rises in k\nCP=1.005\nv1=14\nv2=1\ngamma=1.4\nQs=1921.43\nR=0.287*10**3\n\n\n#calculation\nT2=T1*((v1/v2)**(gamma-1)) #constant pressure\nrho=T3/T2 #cut-off ratio\neta=(1-(1/r**(gamma-1))*((1/gamma)*(((rho**(gamma))-1)/(rho-1))))*100 #air standard efficiency\nHS=(CP*(T3-T2)) #heat supplied\nWD=(Qs*eta)*10**-2 #Net work done\nv1=(R*T1/P1) *10**-5 #characteristics gas equation\nv2=(v1/r ) #characteristics gas equation\nSv=(v1-v2) #Swept volume\nPme=(WD/Sv )*10**-2 #Mean effective pressur\nPm=((P1*r)/((r-1)*(gamma-1)))*((gamma*(r**(gamma-1)))*(rho-1)-((rho**(gamma))-1))# mean effective pressure \n\n\n#output\nprint(\"constant pressure=\",round(T2,2),\"K\")\nprint(\"cut-off ratio= \",round(rho,2),)\nprint(\"air standard efficiency=\",round(eta,2),\"%\")\nprint(\"heat supplied= \",round(HS,2),\"KJ/Kg\")\nprint(\"Net work done= \",round(WD,2),\"KJ/Kg\")\nprint(\"characteristics gas equation= \",round(v1,3),\"m**3/Kg\")\nprint(\"characteristics gas equation= \",round(v2,4),\"m**3/Kg\")\nprint(\"Swept volume= \",round(Sv,4),\"m**3/Kg\")\nprint(\"Mean effective pressure= \",round(Pme,1),\"bar\")\nprint(\"Mean effective pressure= \",round(Pm,1),\"bar\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "constant pressure= 862.13 K\ncut-off ratio= 3.22\nair standard efficiency= 53.65 %\nheat supplied= 1921.43 KJ/Kg\nNet work done= 1030.91 KJ/Kg\ncharacteristics gas equation= 0.861 m**3/Kg\ncharacteristics gas equation= 0.0615 m**3/Kg\nSwept volume= 0.7995 m**3/Kg\nMean effective pressure= 12.9 bar\nMean effective pressure= 12.9 bar\n" + } + ], + "prompt_number": 155 + }, + { + "cell_type": "code", + "collapsed": false, + "input": "", + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_2_Properties_Of_M_CMataUP.ipynb b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_2_Properties_Of_M_CMataUP.ipynb new file mode 100644 index 00000000..67b98032 --- /dev/null +++ b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_2_Properties_Of_M_CMataUP.ipynb @@ -0,0 +1,146 @@ +{ + "metadata": { + "name": "Chapter 2 Properties Of Material" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "Chapter 2 Properties Of Material" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 1 Page No:19" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nL=5 #Length of steel bar in m\nd=25*10**-3 #Diametr of steel bar in mm\ndeltaLt=25*10**-3 #Steel \npt=800 #Power load of steel bar in N\n\n\n#Calculation\nA=((pi/4)*((deltaLt)**2)) #Cross-section area\nsigmat=(pt)/(A) #Stress in steel bar\net=(deltaLt)/L #Strain in steel bar\nE=((sigmat)/(et)) #Young's modulus\n\n\n#Output\nprint(\"value of Cross-section area=\",A,\"m**2\")\nprint(\"value of tress in steel bar=\",sigmat,\"MN/m**2\")\nprint(\"value of strain in steel bar= \",et)\nprint(\"value of Young's modulus= \",E,\"N/m**2\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "value of Cross-section area= 0.0004919062500000002 m**2\nvalue of tress in steel bar= 1626326.154628041 MN/m**2\nvalue of strain in steel bar= 0.005\nvalue of Young's modulus= 325265230.92560816 N/m**2\n" + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 2 Page No:20\n" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nL=300*10**-3 #Length of hexagonal prismatic steel bar in mm\nA=500*10**-6 #Area of cross section of steel bar mm**2\nPt=500*10**3 #Load of steel bar in KN\nE=210*10**9 #Modulus of elasticity GN/m**2\n\n#Calculation\nsigmat=((Pt)/(A)) #Stress in steel bar\net=((sigmat)/(E)) #Strain steel bar is\ndeltaLt=((et)*(L)) #Therefore,elongation of the steel bar is given by\n\n#Output\nprint('stress in steel bar=',sigmat,\"N/m**2\")\nprint('therefore,strain steel bar is given by=',et,)\nprint('therefore,elongation of the steel bar is given by=',deltaLt,\"m\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "stress in steel bar = 1000000000.0 N/m**2\ntherefore,strain steel bar is given by = 0.004761904761904762\ntherefore,elongation of the steel bar is given by= 0.0014285714285714286 m\n" + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 3 Page No:21\n" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input Data\nPt=600 #Tensils force in N\nd=2*10**-3 #Diameter of steel wire in mm\nL=15 #Length of wire in m\nE=210*10**9 #Modulus of elasticity of the material in GN/M**2\npi=3.1482\n\n\n#Calculation\nA=((pi/4)*((d)**2)) #(1)cross section area\nsigmat=(Pt)/(A) #stress in the steel wire \net=((sigmat)/(E)) #(2)Therefore, strain in steel wire is given by\ndeltaLt=et*L #(3)Enlongation of the steel wire is given by \npe=((deltaLt/L)*100) #(4)Percentage elongation\n\n\n#Output\nprint(\"cross section area= \",A,\"m**2\")\nprint(\"stress in the steel wire=\",sigmat,\"GN/m**2\")\nprint(\"modulus of elasticity=\",et)\nprint(\"strain in steel wire=\",deltaLt,\"mm\")\nprint(\"percentage elongation= \",pe,\"%\")\n\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "cross section area= 3.1481999999999998e-06 m**2\nstress in the steel wire= 190585096.24547362 GN/m**2\nmodulus of elasticity= 0.0009075480773593982\nstrain in steel wire= 0.013613221160390973 mm\npercentage elongation= 0.09075480773593982 %\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 4 Page No:22\n" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nA=30*30*10**-6 #Area of square rod in mm**2\nL=5 #Length of square rod in m\nPc=150*10**3 #Axial comperessive load of a rod in kN\nE=215*10**9 #Modulus of elasticity in GN/m**2\n\n\n#Calculation\nsigmac=((Pc)/(A)) #Stress in square rod\nec=((sigmac)/(E)) #Modulusof elasticity is E=sigmac/ec ,therefore strain in square rod is\ndeltaLc=ec*5 #Therefore shortening of length of the rod \n\n\n#Output\nprint (\"stress in square rod\",sigmac,\"N/m**2\")\nprint(\"strain in square rod ec=\",ec,)\nprint(\"shortening of length of the rod=\",deltaLc,\"m\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "stress in square rod 166666666.66666666 N/m**2\nstrain in square rod ec= 0.0007751937984496124\nshortening of length of the rod= 0.003875968992248062 m\n" + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 5 Page No:23" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#input data\nd=50*10**-6 #Diameter of metalic rod in mm**2\nL=220*10**-3 #Length of metalic rod in mm\nPt=40*10**3 #Load of metalic rod in KN\ndeltaLt=0.03*10**-3 #Elastic enlongation in mm\nypl=160*10**3 #Yield point load in KN\nml=250*10**3 #Maximum load in KN\nlsf=270*10**-3 #Length of specimen at fracture in mm\npi=3.1482\n\n#calculation\nA=(((pi)/(4)*((d)**2))) #(1)Cross section area\nsigmat=(Pt/A) #Stress in metallic rod\net=(deltaLt/L) #Strain n metallic rod\nE=(sigmat/et) #Young's modulus\nys=(ypl/A) #(2)Yeild strength\nuts=(ml/A) #(3)Ultimate tensile strength\nPebf=((lsf-L)/L)*100 #Percentage elongation before fracture \n\n\n\n#output\nprint(\"cross section area\",A,\"m**2\")\nprint(\"stress in metallic rod\",sigmat,\"N/m**2\")\nprint(\"strain n metallic rod\",et,)\nprint(\"young's modulus\",E,\"GN/m**2\")\nprint(\"yeild strength\",ys,\"MN/m**2\")\nprint(\"ultimate tensile strength\",uts,\"MN/m**2\")\nprint(\"percentage elongation before fracture\",Pebf,\"%\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "cross section area 1.967625e-09 m**2\nstress in metallic rod 20329076932850.52 N/m**2\nstrain n metallic rod 0.00013636363636363637\nyoung's modulus 1.4907989750757046e+17 GN/m**2\nyeild strength 81316307731402.08 MN/m**2\nultimate tensile strength 127056730830315.75 MN/m**2\npercentage elongation before fracture 22.727272727272734 %\n" + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 6 Page No:24\n" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nA=50*50*10**-6 #Area ofsquare metal bar in mm**2\nPc=600*10**3 #Axial compress laod in KN\nL=200*10**-3 #Gauge length of metal bar in mm\ndeltaLc=0.4*10**-3 #Contraction length of metal bar in mm\ndeltaLlateral=0.05*10**-3 #Lateral length of metal bar in mm\n\n#Calculation\nsigmac=((Pc)/(A)) #Stress in square metal bar \nec=((deltaLc)/(L)) #Longitudinal or linear strain in square metal bar\nE =((sigmac)/(ec)) #Smodule of elasticity\nelateral=((deltaLlateral)/(L)) #Lateral strain in square metal bar\npoissonsratio=(elateral)/(ec)\n\n\n#Output\nprint(\"stress in bar=\",sigmac,\"n/m**2\")\nprint(\"longitudinal or linear strain in square metal bar=\",ec,)\nprint(\"module of elasticity=\",E,\"N/m**2\")\nprint(\"lateral strain in square metal bar=\",elateral,)\nprint(\"poissons ratio=\",poissonsratio,)\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "stress in bar= 240000000.0 n/m**2\nlongitudinal or linear strain in square metal bar= 0.002\nmodule of elasticity= 120000000000.0 N/m**2\nlateral strain in square metal bar= 0.00025\npoissons ratio= 0.125\n" + } + ], + "prompt_number": 12 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_5_Metrology_tKHsuep.ipynb b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_5_Metrology_tKHsuep.ipynb new file mode 100644 index 00000000..4528c633 --- /dev/null +++ b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_5_Metrology_tKHsuep.ipynb @@ -0,0 +1,83 @@ +{ + "metadata": { + "name": "Chapter 5 Metrology" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "Chapter 5 Metrology" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 1 Page No:81" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nMSR=3.2 #Main scale reading of cylindrical rod in cm\nNCD=7 #Number of coinciding Vernier Scale division \nLc=0.1*10**-3 #Least count of the instrument in mm\n\n#Calculation\nDOR=MSR+(NCD*Lc) #Diameter of the rod\n\n#Output\nprint(\"Diameter of the rod= \",round(DOR,3),\"cm\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Diameter of the rod= 3.201 cm\n" + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 2 Page No:82" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nMSR=5.3 #Main scale reading of prismatic bar in cm\nNCD=6 #Number of coinciding Vernier Scale division \nLc=0.1*10**-3 #Least count of the instrument in mm \nNe=(-0.2*10**-3) #Instrument bears a nagative error in mm\n\n#Calulation\nMlb=MSR+(NCD*Lc) #Measured length of the bar in cm\nTlb=(Mlb-(Ne)) #True length of the bar in cm\n\n\n#Output\nprint(\"Measured length of the bar= \",round(Mlb,3),\"cm\")\nprint(\"true length of the bar= \",round(Tlb,3),\"cm\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Measured length of the bar= 5.301 cm\ntrue length of the bar= 5.301 cm\n" + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 3 Page No:88 " + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nL=100 #Height of sine bar\ntheta=12.8 #angle in degree minut\n#Z=sin(theta)=0.22154849\nZ=0.22154849\n\n#Calculation\nb=Z*L #Height required to setup in mm\n\n\n#Output\nprint(\"Height required=\",round(b,4),\"mm\")\n ", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Height required= 22.1548 mm\n" + } + ], + "prompt_number": 18 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_7_Fluid_Mechanics_xkevzFX.ipynb b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_7_Fluid_Mechanics_xkevzFX.ipynb new file mode 100644 index 00000000..2cb36b62 --- /dev/null +++ b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_7_Fluid_Mechanics_xkevzFX.ipynb @@ -0,0 +1,461 @@ +{ + "metadata": { + "name": "Chapter 7 Fluid Mechanics" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "Chapter 7 Fluid Mechanics" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 1 Page No:113" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nV=5 #volume of the liquid in m**3\nW=45*10**3 #weight of the liquid in KN\ng=9.81 #acceleration due to gravity in m/s**2\nrhow=1000 #constant value\n\n#Calculation\nm=((W)/(g)) #mass in Kg\nrho=(m/V) #Mass density in kg/m**3\nw=(W/V) #Weight Density in N/m**3\nv=(V/m) #Specific volume in m**3/kg\nS=rho/rhow #Specific gravity\n \n \n#Output\nprint(\"mass= \",round(m,2),\"Kg\")\nprint(\"Mass density= \",round(rho,2),\"kg/m**3\")\nprint(\"Weight Density= \",w,\"N/m**3\")\nprint(\"Specific volume= \",v,\"m**3/kg\")\nprint(\"Specific gravity= \",round(S,4),)\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "mass= 4587.16 Kg\nMass density= 917.43 kg/m**3\nWeight Density= 9000.0 N/m**3\nSpecific volume= 0.00109 m**3/kg\nSpecific gravity= 0.9174\n" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 2 Page No:114" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nV=3*10**-3 #3l of oil in m**3\nW=24 #Weight of oil in N\ng=9.81 #Gravity in m/s**2\nrohw=1000 #Constant value\n\n\n#Calculation\nm=((W)/(g)) #Mass in Kg\nrho=(m/V) #Mass density in kg/m**3\nw=(W/V) #Weight Density in N/m**3\nv=(V/m) #Specific volume in m**3/kg\nS=rho/rhow #Specific gravity\n \n#Output\nprint(\"mass= \",round(m,3),\"Kg\")\nprint(\"Mass density= \",round(rho,1),\"kg/m**3\")\nprint(\"Weight Density= \",w,\"N/m**3\")\nprint(\"Specific volume= \",round(v,7),\"m**3/kg\")\nprint(\"Specific gravity= \",round(S,4),)\n\n\n ", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "mass= 2.446 Kg\nMass density= 815.5 kg/m**3\nWeight Density= 8000.0 N/m**3\nSpecific volume= 0.0012263 m**3/kg\nSpecific gravity= 0.8155\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 3 Page No:114" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nS=0.85 #Specific gravity of a liquid\ng=9.81 #Acceleration due to gravity in m/s**2(constant)\nrhow=1000 #Constant value\n\n\n#Calculation\n#Specific gravity S=roh/rohw \nrho=S*rhow #Mass density in Kg/m**3\nw=rho*g #Weight Density in N/m**3\nv=(1/rho) #Specific volume in m**3/kg\n\n\n#Output\nprint(\"Mass densit= \",rho,\"Kg/m**3\")\nprint(\"Weight Density= \",w,\"N/m**3\")\nprint(\"Specific volume= \",round(v,6),\"m**3/kg\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Mass densit= 850.0 Kg/m**3\nWeight Density= 8338.5 N/m**3\nSpecific volume= 0.001176 m**3/kg\n" + } + ], + "prompt_number": 50 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 4 Page No:116" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\ndy=21*10**-3 #Horizontal plates in mm\ndu=1.4 #Relative velocity between the plates in m/s\nmu=0.6 #Oil of viscosity 6 poise in Ns/m**2\n\n#Calculation\ntau=(mu*(du/dy)) #Shear in the oil in N/m**2\n\n#Output\nprint(\"shear in the oil= \",round(tau,),\"N/m**2\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "shear in the oil= 40 N/m**2\n" + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 5 Page No:116" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nv=4*10**-4 #kinematic viscosity is 4 stoke inm**2/s\nS=1.2 #specific gravity\ndow=1000 #density of water Kg/m**3\n\n\n#Calculation\nrho=S*dow \nvol=rho*v #viscosity of the liquid in Ns/m**2 or poise\n\n#Output\nprint(\"viscosity of the liquid= \",round(vol,2),\"Ns/m**2 \")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "viscosity of the liquid= 0.48 Ns/m**2 \n" + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 6 Page No:6" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nS=0.9 #Specific gravity\ntau=2.4 #shear stress in N/m**2\n(vg)=0.125 #velocitty gradientin per s\ndow=1000 #density of water Kg/m**3\n\n\n#Calculation\nmu=(tau)/(vg) #newton's law of viscosity in shear stress in Ns/m**2\nrho=S*dow #Density of oil in Kg/m**3\nv=(mu/rho) #Kinematic viscosity in m**2/s or stoke\n\n#Output\nprint(\"newton's law of viscosity in shear stress= \",mu,\"Ns/m**2\")\nprint(\"Density of oil= \",rho,\"Kg/m**3\")\nprint(\"Kinematic viscosity= \",round(v,5),\"m**2/s or stoke\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "newton's law of viscosity in shear stress= 19.2 Ns/m**2\nDensity of oil= 900.0 Kg/m**3\nKinematic viscosity= 0.02133 m**2/s or stoke\n" + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 7 Page No:117" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nA=6*10**-2 #Space between two square plates in mm\ndy=8*10**-3 #Thickness of fluid in mm\nu1=0 #Lower pate is stationary\nu2=2.4 #Upper plate in m/s\nF=5 #Speed of force in N\ns=1.6 #Specific gravity of the liquid\ndow=1000 #Density of water Kg/m**3\n\n\n#(1)Calculation\ndu=u2-u1 #change in velocity in m/s\ntau=(F/((A)**2)) #shear stress N/m**2\nmu=(tau/(du/dy)) #Newton's law of viscosity in Ns/m**2 or poise\nrho=s*dow #Density of oil in kg/m**3\nv=(mu/rho) #kinematic viscosity is given by m**2/s or stoke\n\n\n#Output\nprint(\"change in velocity= \",du,\"m/s\")\nprint(\"shear stress= \",round(tau,2),\"N/m**2\")\nprint(\"Newton's law of viscosity= \",round(mu,1),\"Ns/m**2 \")\nprint(\"Density of oil= \",rho,\" kg/m**3\")\nprint(\"kinematic viscosity= \",round(v,4),\"m**2/s \")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "change in velocity= 2.4 m/s\nshear stress= 1388.89 N/m**2\nNewton's law of viscosity= 4.6 Ns/m**2 \nDensity of oil= 1600.0 kg/m**3\nkinematic viscosity= 0.0029 m**2/s \n" + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 8 Page No:118" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\ndy=1.5*10**-4 #Two horizontal plates are placed in m\nmu=0.12 #Space between plates Ns/m**2\nA=2.5 #Upper area is required to move in m**2\ndu=0.6 #Speed rerlated to lower plate in m/s\n\n\n#(1)Calculation\ntau=(mu*(du/dy)) #Shear stress N/m**2\nF=tau*A #Force in N\nP=F*du #Power required to maintain the speed of upper plate in W\n\n\n#Output \nprint(\"Shear stress= \",round(tau,),\"N/m**2\")\nprint(\"Force= \",round(F,),\"N\")\nprint(\"Power required to maintain the speed of upper plate= \",round(P,),\"W\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Shear stress= 480 N/m**2\nForce= 1200 N\nPower required to maintain the speed of upper plate= 720 W\n" + } + ], + "prompt_number": 51 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 9 Page No 118" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data \nmu=0.1 #Oil of viscosity used for lubricant in poise or Ns/m**2\nD=0.15 #Clearance between the shaft of diameter in m\ndy=3*10**-4 #Clearance in m\nN=90 #Shaft rorates in rpm\npi=3.14\n\n\n#Calculation\ndu=((pi*D*N)/60) #Tangential speed of shaft in m/s\ntau=(mu*(du/dy)) #The shear force in N/m**2\n\n#Output\nprint(\"Tangential speed of shaft= \",du,\"m/s\")\nprint(\"The shear force= \",tau,\"N/m**2\")\n\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Tangential speed of shaft= 0.7065 m/s\nThe shear force= 235.5 N/m**2\n" + } + ], + "prompt_number": 52 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 10 Page No:119" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nA=120*10**-3 #Side of square plate in mm\nW=30 #Side weight in N\ndu=3.75 #Uniform velocity in m/s\ntheta=30 #Lubricated inclined plane making an angle in degree at horizontal\ndy=6*10**-3 #Thickness lubricating oil film in mm\nrho=800 #Lubricating oil film density in Kg/m**3\n\n\n#Calculation\nsin30=0.5 \nF=W*sin30 #Component of force in N\ntau=(F/(A**2)) #Shear stress in Ns/m**2 \nmu=(tau/(du/dy)) #From Newton's law of Shear stress in Ns/m**2 \nV=(mu/rho)*10**3 #Kinematic viscosity in m**2/s\n\n\n#Output\nprint(\"Component of force= \",F,\"N\")\nprint(\"Shear stress= \",round(tau,2),\" Ns/m**2 \")\nprint(\"From Newton's law of Shear stress= \",round(mu,3),\"Ns/m**2\")\nprint(\"Kinematic viscosity= \",round(V,3),\"m**2/s\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Component of force= 15.0 N\nShear stress= 1041.67 Ns/m**2 \nFrom Newton's law of Shear stress= 1.667 Ns/m**2\nKinematic viscosity= 2.083 m**2/s\n" + } + ], + "prompt_number": 53 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 11 Page No 121" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data \nZ=15 #Pressure due to column in m\nS=0.85 #Oil of specific gravity\ng=9.81 #Gravity\n\n\n\n#Calculation\nrho=S*10**3 #Density of oil in kg/m**3\nP=rho*g*Z #Pressure in N/m**2 or kPa\n\n\n#Output\nprint(\"Density of oil= \",rho,\"kg/m**3\")\nprint(\"Pressure= \",P,\"N/m**2\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Density of oil= 850.0 kg/m**3\nPressure= 125077.5 N/m**2\n" + } + ], + "prompt_number": 55 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 12 Page No 122" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nZ1=1.5 #open tank contain water in m\nZ2=2.5 #oil of specific gravity for depth in m\nS=0.9 #oil of specific gravity \nrho1=1000 #density of water in Kg/m**3\nrho2=S*10**3 #density of oil in Kg/m**3\ng=9.81 #gravity\n\n\n\n#calculation\nP=rho1*g*Z1+rho2*g*Z2 #intensity of pressure in kPa\n\n\n#output\nprint(\"intensity of pressure=\",P,\"N/m**2\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "intensity of pressure= 36787.5 N/m**2\n" + } + ], + "prompt_number": 57 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 13 Page No:124" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nD1=0.2 #Diameter of pipe section 1 in m\nD2=0.3 #Diameter of pipe section 2 in m\nV1=15 #Velocity of water in m/s\npi=3.14\n\n#calculation\nQ=((3.14/4)*(0.2)**2)*15 #Discharge through pipe in m**3/s\nV2=(((3.14/4)*(0.2)**2)*15)/((3.14/4)*(0.3)**2) #velocity of section2 in m/s\n\n\n#Output\nprint(\"Discharge through pipe= \",round(Q,2),\"m**3/s\")\nprint(\"velocity of section2= \",round(V2,2),\"m/s\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Discharge through pipe= 0.47 m**3/s\nvelocity of section2= 6.67 m/s\n" + } + ], + "prompt_number": 59 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 14 Page No:126" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nV=13 #Velocity of water flowing throgh pipe in m/s\nP=200*10**3 #Pressure of water in Kpa\nZ=25 #Height above the datum in m\ng=9.81\nrho=1000\n\n\n#Calculation\nE=(P/(rho*g))+((V**2)/(2*g))+(Z) #Total energy per unit weight in m\n\n\n#Output\nprint(\"Total energy per unit weight=\",round(E,),\"m\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Total energy per unit weight= 54 m\n" + } + ], + "prompt_number": 67 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 15 Page No:127" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nS=0.85 #Specific gravity of oil\nD=0.08 #Diameter of pipe in m\nP=1*10**5 #Intenity of presssure in N/m**2\nZ=15 #Total energy bead in m\nE=45 #Datum plane in m\nMdw=1*10**3 #Mass density of water constant\ng=9.81 #Gravity constant\nrho=S*Mdw #Mass density of oil\npi=3.14\n\n#calculation\nrho=S*Mdw #Mass density of oil\n#E=(P/(rho*g))+((V**2)/(2*g))+(Z)\nV=math.sqrt((E-((P/(rho*g))+Z))*(2*g)) #Total energy per unit weight in m/s\nQ=(pi/4)*D**2*V #Discharge in m**3/Kg\"\n\n#output\nprint(\"mass density of oil= \",rho,\"Kg/m**3\")\nprint(\"Total energy per unit weight= \",round(V,1),\"m/s\")\nprint(\"discharge=\",round(Q,4),\"m**3/Kg\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "mass density of oil= 850.0 Kg/m**3\nTotal energy per unit weight= 18.8 m/s\ndischarge= 0.0944 m**3/Kg\n" + } + ], + "prompt_number": 64 + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "Example 16 Page No:127" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#input data\n#refer figure 11\nZA=2 #water flows section A-A in m \nDA=0.3 #datum pipe diameter at section A-A in m\nPA=550*10**3 #pressure in kPa\nVA=6 #flow velocity in m/s\nZB=18 #water flows at section B-B in m\nDB=0.15 #datum pipe diameter at section B-B in m\npi=3.14 #constant\nrho=1000 #constant\ng=9.81 #constant\nAa=(pi/4)*(DA)**2\nAb=(pi/4)*(DB)**2\npi=3.14\n\n#calculation\nVB=((Aa*VA)/Ab) #continuity discharge equation in m/s\n#bernoulli's equation Kpa\n#(PA/rho*g)+(VA**2/2*g)+ZA=(PB/rho*g)+(VB**2/2*g)+ZB \nPB=(((PA/(rho*g))+(VA**2/(2*g))+ZA)-((VB**2/(2*g))+ZB))*(rho*g)\n\n\n#output\nprint(\"continuity discharge equation= \",VB,\"m/s\")\nprint(\"bernoulli's equation= \",round(PB,1),\"pa\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "continuity discharge equation= 24.0 m/s\nbernoulli's equation= 123040.0 pa\n" + } + ], + "prompt_number": 66 + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "Example 17 Page No:128" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#input data\n#refer figure 12\nQ=0.04 #Water flows at rate in m**2/s\nDA=0.22 #Pipe diameter at section A in m\nDB=0.12 #Pipe diameter at section B in m\nPA=400*10**3 #Intensity of pressure at setion A in kPa\nPB=150*10**3 #Intensity of pressure at setion B in kPa\npi=3.14 #Pi constant \ng=9.81 #Gravity constant\nrho=1000\n\n#calculation\nVA=Q/(pi/4*(DA)**2) #contuity equation for discharge\nVB=Q/(pi/4*(DB)**2) #bernoulli's equation for discharge\n#Z=ZB-ZA\nZ=(PA/(rho*g))+(VA**2/(2*g))-(PB/(rho*g))-(VB**2/(2*g))\n\n\n#output\nprint(\"contuity equation for discharge= \",round(VA,3),\"m**3\")\nprint(\"contuity equation for discharge= \",round(VB,3),\"m**3\")\nprint(\"bernoulli's equation for discharge= \",round(Z,2),\"m\")\n\n\n\n\n\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "contuity equation for discharge= 1.053 m**3\ncontuity equation for discharge= 3.539 m**3\nbernoulli's equation for discharge= 24.9 m\n" + } + ], + "prompt_number": 69 + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "Example 18 Page No:129" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nL=200 #length of pipe in m\nD1=1 #Diameter at high end in m\nD2=0.4 #Diameter at low end in m\nP1=50*10**3 #Pressure at high end in kPa\nQ=4000 #Rate of water flow l/min\nS=1 #Slope of pipe 1 in 100\nZ2=0 #Datum line is passing through the center of the low end,therefore\npi=3.14\n\n\n\n#calculation\nQ=(4000*10**-3)/60 #rate of water flow l/min in m**3/s\nZ1=1/100*L #slope of pipe 1 in 100 is in m\n#Q=A1*V1=A2V2 #continuity eqation ,discharge\nV1=Q/((pi/4)*(D1**2))#in m**3\nV2=Q/((pi/4)*(D2**2))#in m**3\n#bernoulli's equation \nP2=(((((P1/(rho*g))+(V1**2/(2*g))+Z1)-(V2**2/(2*g))-Z2))*(rho*g))*10**-3 \n\n\n#output\nprint(\"rate of water flow= \",round(Q,4),\"m**3/s\")\nprint(\"slope of pipe= \",Z1,\"m\")\nprint(\"continuity eqation ,discharge= \",round(V1,5),\"m**3\")\nprint(\"continuity eqation ,discharge= \",round(V2,4),\"m**3\")\nprint(\"bernoulli's equation for discharge= \",round(P2,2),\" Kpa\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "rate of water flow= 0.0667 m**3/s\nslope of pipe= 2.0 m\ncontinuity eqation ,discharge= 0.08493 m**3\ncontinuity eqation ,discharge= 0.5308 m**3\nbernoulli's equation for discharge= 69.48 Kpa\n" + } + ], + "prompt_number": 74 + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "Example 19 Page No:130" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nimport math\nL=36 #Length of pipe in m\nD1=0.15 #Diameter at upper side in m\nD2=0.3 #Diameter at lower side in m\nsin30=0.5\ntheta=math.sin(30) #Pipe slope upward at angle in degree\nV1=2 #Velocity of water at smaller section in m/s \npi=3.14 #Pi constant \nrho=1000 #Roh constant\ng=9.81 #Gravity constant\n\n\n#calculation\n#datum line is passing through the center of the low end,therefore\nZ1=0\nZ2=Z1+L*(0.5) #pipe inclined 30 degree,therefore in m\n#Q=A1*V1=A2*V2 continuity eqation ,discharge\nV2=(pi/4*(D1**2)*2)/(pi/4*(D2**2))\n#Z=P1-P2 bernoulli's equation \nZ=((((-V1**2)/(2*g))+((V2**2)/(2*g))-Z1+Z2)*(rho*g))*10**-3\n\n\n\n\n\n\n#output\nprint(\"pipe inclined 30 degree,therefore Z2=\",Z2,\"m\")\nprint(\"continuity eqation ,discharge V2=\",V2,\"m/s\")\nprint(\"#bernoulli's equation Z=\",round(Z,1),\"Kpa\")\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "pipe inclined 30 degree,therefore Z2= 18.0 m\ncontinuity eqation ,discharge V2= 0.5 m/s\n#bernoulli's equation Z= 174.7 Kpa\n" + } + ], + "prompt_number": 76 + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "Example 20 Page No:130-131" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nD1=0.25 #Diameter at inlet in m\nD2=0.175 #Diameter at outlet in m\nP1=450*10**3 #Intensity of pressure at inlet in kPa\nP2=200*10**3 #Intensity of pressure at outlet in kPa\npi=3.14 #pi constant \nrho=1000 #Roh constant\ng=9.81 #Gravity constant\nZ1=Z2\n\n#Calculation \n#A1*V1=A2*V2 Continuity eqation in V1\nV2=((pi/4)*(D1**2))/((pi/4)*(D2**2))\n#Z=V2**2-V1**2 Bernoulli's equation in m/s\nZ=-(((P2/(rho*g))-(P1/(rho*g)))*(2*g))\nX=Z/((V2**2)-1)\nV1=math.sqrt(X)\nQ=(pi/4)*(D1**2)*V1 #Flow rate Water in m**3/Kg\n\n\n#Output\nprint(\"Continuity eqation= \",round(V2,2),\"V1\")\nprint(\"Bernoulli's equation= \",Z,\"m/s\")\nprint(\"V1=\",round(V1,2),\"\")\nprint(\"Flow rate Water= \",round(Q,3),\"m**3/Kg\")\n\n\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Continuity eqation= 2.04 V1\nBernoulli's equation= 500.0 m/s\nV1= 12.57 \nFlow rate Water= 0.617 m**3/Kg\n" + } + ], + "prompt_number": 120 + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": "Example 21 Page No:131-132" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nL=300 #Length of pipe in m\nD1=0.9 #Diameter at higher end in m\nD2=0.6 #Diameter at lower end in m\nS=0.85 #Specific gravity \nQ=0.08 #Flow in l/s\nP1=40*10**3 #Pressure at higher end in kPa\npi=3.14 #pi constant \nrho=1000 #Roh constant\ng=9.81 #Gravity constant\nslop=1/50 #1 in 50\n\n\n#Calculation\n#Datum line is passing through the center of the low end,therefore\nZ2=0 \nZ1=slop*L\n#Q=A1*V1=A2*V2 Continuity eqation\nV1=Q/((pi/4)*(D1**2)) #Frome continuity eqation, discharge\nV2=Q/((pi/4)*(D2**2)) #Frome continuity eqation, discharge\n#Bernoulli's equation \nP2=(((((P1/(rho*S*g))+(V1**2/(2*g))+Z1)-(V2**2/(2*g))+Z2))*(S*rho*g))*10**-3\n\n\n\n#Output\nprint(\"Z1=\",Z1,\"m\")\nprint(\"continuity eqation, discharge V1=\",round(V1,5),\"m**3\")\nprint(\"continuity eqation, discharge V2=\",round(V2,5),\"m**3\")\nprint(\"bernoulli's equation= \",round(P2,),\"KPa\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Z1= 6.0 m\ncontinuity eqation, discharge V1= 0.12582 m**3\ncontinuity eqation, discharge V2= 0.28309 m**3\nbernoulli's equation= 90 KPa\n" + } + ], + "prompt_number": 128 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_9__Laws_Of_Thermo_bIsIgqq.ipynb b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_9__Laws_Of_Thermo_bIsIgqq.ipynb new file mode 100644 index 00000000..d459e09d --- /dev/null +++ b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/Chapter_9__Laws_Of_Thermo_bIsIgqq.ipynb @@ -0,0 +1,209 @@ +{ + "metadata": { + "name": "Chapter 9 Laws Of Thermodynamics" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": " Chapter 9 Law Of Thermodynamics" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 1 Page No:165" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nQab=720 #Heat transfer of 1st processes in KJ \nQbc=-80 #Heat transfer of 2nd processes in KJ\nQcd=40 #Heat transfer of 3rd processes in KJ\nQda=-640 #Heat transfer of 4th processes in KJ\nWab=-90 #Work transfer of 1st processes in KJ\nWbc=-50 #Work transfer of 2nd processes in KJ\nWcd=130 #Work transfer of 3rd processes in KJ\n\n\n#Calculation\n#From the 1st law of thermodynamic for close system undergoing a cycle.\n\n#Work interaction during the 4th processes \nWda=((Qab+Qbc+Qcd+Qda)-(Wab+Wbc+Wcd)) \n\n#Output\nprint(\"Work interaction during the 4th processes=\",Wda,\"KJ\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Work interaction during the 4th processes= 50 KJ\n" + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 2 Page No:166" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\n #During compression\nW1=-9200 #Stroke work done by the piston in Nm\nNm1=-9.2 #Nm of work done\nQ1=-50 #Heat rejected during copression in KJ\n #During expansion\nW2=8400 #Stroke work done by the piston in Nm\nNm2=8.4 #Nm of work done\n\n#Calculation\n #Quantity of heat transferred\nQ2=-((Nm1+Nm2)+Q1) #-sign for indicate heat is transferred\n\n\n#Output\nprint(\"Quantity of heat transferred=\",Q2,\"KJ\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Quantity of heat transferred= 50.8 KJ\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 3 Page No:166" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#input data\nW1=-20 #Work interaction to the fluid in KJ\nW2=42 #Work interaction from the fluid in KJ\nQ1=85 #Heat interaction to the fluid in KJ\nQ2=85 #Heat interaction to the fluid in KJ\nQ3=-50 #Heat interaction from the fluid in KJ\n\n#calculation\nW3=((Q1+Q2+Q3)-(W1+W2)) #Magnitude and direction of the third heat interation\n\n\n#output\nprint(\"Magnitude and direction of the third heat interation=\",W3,\"KJ\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Magnitude and direction of the third heat interation= 98 KJ\n" + } + ], + "prompt_number": 51 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 4 Page No:168" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nQ=-2100 #Non flow process losses heat in KJ\ndeltaU=420 #Gain heat\n\n#Calculation\nW=Q-deltaU #Work done and compression process in KJ\n\n#Output\nprint(\"Work done and compression process=\",W,\"KJ\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Work done and compression process= -2520 KJ\n" + } + ], + "prompt_number": 52 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 5 Page No:168" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nW=-2000 #Work input of panddle wheel in KJ\nQ=-6000 #Heat transferred to the surrounding from tank\n\n#Calculation\ndeltaU=Q-W #Change in interval energy\n\n#Output\nprint(\"change in interval energy drop=\",deltaU,\"KJ\")", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "change in interval energy drop= -4000 KJ\n" + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 6 Page No:169" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nU1=520 #internal energy in KJ/Kg\nU2=350 #internal energy in KJ/Kg\nW=-80 #work done by the air in the cylinder KJ/kg\n\n#Calculation\ndeltaU=U2-U1\nQ=deltaU+W #Heat transferred during the process\n\n#Output\nprint(\"Heat transferred during the process=\",Q,\"KJ\")\n ", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Heat transferred during the process= -250 KJ\n" + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 7 Page No:169" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nW1=800 #Power of turbine shaft Kw\nW2=-5 #Work pump to feed in Kw \nQ1=2700 #Heat for steam generation KJ/Kg\nQ2=-1800 #Condenser rejected heat KJ/Kg\n\n#Calculation\nm=((W1+W2)/(Q1+Q2)) #Steam flow rate in Kg/h\n\n\n#Output\nprint(\"Steam flow rate=\",round(m,4),\"Kg/s\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Steam flow rate= 0.8833 Kg/s\n" + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 8 Page No:170" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#input data\n#Data consistent with first law pf thermodynamics\nQabcd=-22 #In KJ\nN=150 #In Cycles/min\nQab=17580 #In KJ/min\nQbc=0 \nQcd=-3660 #In KJ/min\nWab=-8160 #In KJ/min\nWbc=4170 #In KJ/min \nDeltaUcd=-21630 #In KJ/min\n\n\n#calculation\nDeltaUab=Qab-Wab #In KJ/min\nDeltaUbc=Qbc-Wbc #In KJ/min \nWcd=Qcd-DeltaUcd #In KJ/min\nQabcd1=-220*150 #In KJ/min\nQda=((Qabcd1)-(Qab+Qbc+Qcd)) #In KJ/min\nWda=((Qabcd1)-(Wab+Wbc+Wcd)) #In KJ/min\nDeltaUabcd=0\nDeltaUda=((DeltaUabcd)-(DeltaUab+DeltaUbc+DeltaUcd)) #In KJ/min\nNWO=Qabcd1/60 #In KW\n\n\n#output\nprint(\"DeltaUab= \",DeltaUab,\"KJ/min\")\nprint(\"DeltaUbc= \",DeltaUbc,\"KJ/min\")\nprint(\"Wcd= \",Wcd,\"KJ/min\")\nprint(\"Qabcd1= \",Qabcd1,\"KJ/min\")\nprint(\"Qda= \",Qda,\"KJ/min\")\nprint(\"Wda= \",Wda,\"KJ/min\")\nprint(\"DeltaUabcd= \",DeltaUabcd,\"KJ/min\")\nprint(\"DeltaUda= \",DeltaUda,\"KJ/min\")\nprint(\"NWO=\",NWO,\"Kw\")\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "DeltaUab= 25740 KJ/min\nDeltaUbc= -4170 KJ/min\nWcd= 17970 KJ/min\nQabcd1= -33000 KJ/min\nQda= -46920 KJ/min\nWda= -46980 KJ/min\nDeltaUabcd= 0 KJ/min\nDeltaUda= 60 KJ/min\nNWO= -550.0 Kw\n" + } + ], + "prompt_number": 47 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example 9 Page No:171" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#Input data\nQab=-6500 #Heat transferred in 1st process KJ/min\nQbc=0 #Heat transferred in 2nd process \nQcd=-10200 #Heat transferred in 3rd process KJ/min\nQda=32600 #Heat transferred in 4th process KJ/min\nWab=-1050 #Heat transferred in 1st process KJ\nWbc=-3450 #Heat transferred in 2nd process KJ\nWcd=20400 #Heat transferred in 3rd process KJ\nWda=0 #Heat transferred in 4th process\n\n#Calculator\ndQ=Qab+Qbc+Qcd+Qda #Net heat transfer in 1st cycle\ndW=Wab+Wbc+Wcd+Wda #Net work done in 1st cycle\ndW1=dW/60 #Net work done in 1st cycle\nDeltaUab=Qab-Wab #ab process\nDeltaUbc=Qbc-Wbc #bc processes\nDeltaUcd=Qcd-Wcd #cd processes\nDeltaUda=Qda-Wda #dc processes\n\n#Output\nprint(\"Net heat transfer in 1st cycle= \",dQ,\"KJ/min\")\nprint(\"Net work done in 1st cycle= \",dW,\"KJ/min\")\nprint(\"Net work done in 1st cycle= \",dW1,\"KW\")\nprint(\"ab process= \",DeltaUab,\"KJ/min\")\nprint(\"bc processes= \",DeltaUbc,\"KJ/min\")\nprint(\"cd processes= \",DeltaUcd,\"KJ/min\")\nprint(\"dc processes= \",DeltaUda,\"KJ/min\")\n\n", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Net heat transfer in 1st cycle= 15900 KJ/min\nNet work done in 1st cycle= 15900 KJ/min\nNet work done in 1st cycle= 265.0 KW\nab process= -5450 KJ/min\nbc processes= 3450 KJ/min\ncd processes= -30600 KJ/min\ndc processes= 32600 KJ/min\n" + } + ], + "prompt_number": 50 + } + ], + "metadata": {} + } + ] +}
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00000000..b04af8cc --- /dev/null +++ b/Basic_mechanical_engineering_by_Basant_Agrawal_,_C.M_Agrawal/screenshots/chapter5.png diff --git a/Digital_Communications_by_S._Haykin/Chapter1_bmaHHM8.ipynb b/Digital_Communications_by_S._Haykin/Chapter1_bmaHHM8.ipynb new file mode 100644 index 00000000..de235249 --- /dev/null +++ b/Digital_Communications_by_S._Haykin/Chapter1_bmaHHM8.ipynb @@ -0,0 +1,96 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 1 Introduction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex1.2 page 7" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f1009538350>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import arange\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,title,xlabel,ylabel,show,figure,text\n", + "from math import sin,pi,sqrt\n", + "\n", + "#Figure 1.2: Analog to Digital Conversion\n", + "t = arange(-1,1.01,0.01)\n", + "x = [2*sin((pi/2)*tt) for tt in t]\n", + "dig_data = [0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,0,1]\n", + "figure=figure()\n", + "#a=gca()#\n", + "#a.x_location =\"origin\"#\n", + "#a.y_location =\"origin\"#\n", + "#a.data_bounds =[-2,-3#2,3]\n", + "plot(t,x)\n", + "text(0.5,sqrt(2),'gnn')\n", + "text(-0.5,-sqrt(2),'gnn')\n", + "text(1,2,'gnn')\n", + "text(-1,-2,'gnn')\n", + "xlabel(' Time')\n", + "ylabel(' Voltage')\n", + "title('Analog Waveform')\n", + "show()\n", + "plot(range(1,len(dig_data)+1),dig_data)\n", + "title('Digital Representation')\n", + "show()\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Digital_Communications_by_S._Haykin/Chapter2_XLwGLkV.ipynb b/Digital_Communications_by_S._Haykin/Chapter2_XLwGLkV.ipynb new file mode 100644 index 00000000..497875b7 --- /dev/null +++ b/Digital_Communications_by_S._Haykin/Chapter2_XLwGLkV.ipynb @@ -0,0 +1,394 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2 Fundamental Limit On Performance" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.1 page 18" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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BhGUGvgN+Ez33e+De6Pb2wMdA0+riiMptFP3bLHp8o5T31ze6fTVw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\nIlKBEoOIiFSgxCAiIhX8P5fhJpLBkGXZAAAAAElFTkSuQmCC\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f4de4a3d1d0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import arange, zeros\n", + "from math import log\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,title,show\n", + "\n", + "Po = arange(0,1+0.01,0.01)\n", + "H_Po = zeros(len(Po))\n", + "for i in range(1,len(Po)-1):\n", + " H_Po[i]=-Po[(i)]*log(Po[(i)],2)-(1-Po[(i)])*log(1-Po[(i)],2)\n", + "\n", + "#plot\n", + "#plot2d(Po,H_Po)\n", + "plot(Po,H_Po)\n", + "xlabel('Symbol Probability, Po')\n", + "ylabel('H(Po)')\n", + "title('Entropy function H(Po)')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.2 page 19" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Entropy of Discrete Memoryless Source\n", + "bits : 1.5\n", + "Table 2.1 Alphabet Particulars of Second-order Extension of a Discrete Memoryless Source\n", + "_________________________________________________________________________________\n", + "Sequence of Symbols of ruo2:\n", + " S0*S0 S0*S1 S0*S2 S1*S0 S1*S1 S1*S2 S2*S0 S2*S1 S2*S2\n", + "Probability p(sigma), i =0,1.....8 : [0.0625, 0.0625, 0.125, 0.0625, 0.0625, 0.125, 0.125, 0.125, 0.25]\n", + "_________________________________________________________________________________\n", + " \n", + "H(Ruo_Square)= 3.0 bits\n", + "H(Ruo_Square) = 2*H(Ruo)\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log\n", + "P0 = 1/4# #probability of source alphabet S0\n", + "P1 = 1/4# #probability of source alphabet S1\n", + "P2 = 1/2# #probability of source alphabet S2\n", + "H_Ruo = P0*log(1/P0,2)+P1*log(1/P1,2)+P2*log(1/P2,2)\n", + "print 'Entropy of Discrete Memoryless Source'\n", + "print 'bits : ',H_Ruo\n", + "#Second order Extension of discrete Memoryless source\n", + "P_sigma = [P0*P0,P0*P1,P0*P2,P1*P0,P1*P1,P1*P2,P2*P0,P2*P1,P2*P2]#\n", + "print 'Table 2.1 Alphabet Particulars of Second-order Extension of a Discrete Memoryless Source'\n", + "print '_________________________________________________________________________________'\n", + "print 'Sequence of Symbols of ruo2:'\n", + "print ' S0*S0 S0*S1 S0*S2 S1*S0 S1*S1 S1*S2 S2*S0 S2*S1 S2*S2'\n", + "print 'Probability p(sigma), i =0,1.....8 : ',P_sigma\n", + "print '_________________________________________________________________________________'\n", + "print ' '\n", + "H_Ruo_Square =0\n", + "for i in range(0,len(P_sigma)):\n", + " H_Ruo_Square=(H_Ruo_Square+P_sigma[i]*log(1/P_sigma[i],2))\n", + "print 'H(Ruo_Square)=', H_Ruo_Square,' bits'\n", + "print 'H(Ruo_Square) = 2*H(Ruo)'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3 page 20" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Average code-word Length L 2.2 bits\n", + "Entropy of Huffman coding result H 2.12 bits\n", + "Average code-word length L exceeds the entropy H(Ruo) by only 3.679 %\n", + "Varinace of Huffman code : 0.16\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log\n", + "\n", + "# (a)Average code-word length 'L'\n", + "#(b)Entropy 'H'\n", + "P0 = 0.4# #probability of codeword '00'\n", + "L0 = 2# #length of codeword S0\n", + "P1 = 0.2# #probability of codeword '10'\n", + "L1 = 2# #length of codeword S1\n", + "P2 = 0.2# #probility of codeword '11'\n", + "L2 = 2# #length of codeword S2\n", + "P3 = 0.1# #probility of codeword '010'\n", + "L3 = 3# #length of codeword S3\n", + "P4 =0.1# #probility of codeword '011'\n", + "L4 = 3# #length of codeword S4\n", + "L = P0*L0+P1*L1+P2*L2+P3*L3+P4*L4#\n", + "H_Ruo = P0*log(1/P0,2)+P1*log(1/P1,2)+P2*log(1/P2,2)+P3*log(1/P3,2)+P4*log(1/P4,2)\n", + "print 'Average code-word Length L',L,'bits'\n", + "print 'Entropy of Huffman coding result H %0.2f'%H_Ruo, 'bits'\n", + "print 'Average code-word length L exceeds the entropy H(Ruo) by only %0.3f'%(((L-H_Ruo)/H_Ruo)*100),'%'\n", + "sigma_1 = P0*(L0-L)**2+P1*(L1-L)**2+P2*(L2-L)**2+P3*(L3-L)**2+P4*(L4-L)**2\n", + "print 'Varinace of Huffman code : ',sigma_1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example2.4 page 20" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Average code-word Length L : 2.2 bits\n", + "Entropy of Huffman coding result H : 2.12 bits\n", + "Varinace of Huffman code = 1.36\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log\n", + "\n", + "def log2(x):\n", + " return log(x,2)\n", + "\n", + "# Calculation of (a)Average code-word length 'L' (b)Entropy 'H'\n", + "P0 = 0.4# #probability of codeword '1'\n", + "L0 = 1# #length of codeword S0\n", + "P1 = 0.2# #probability of codeword '01'\n", + "L1 = 2# #length of codeword S1\n", + "P2 = 0.2# #probility of codeword '000'\n", + "L2 = 3# #length of codeword S2\n", + "P3 = 0.1# #probility of codeword '0010'\n", + "L3 = 4# #length of codeword S3\n", + "P4 =0.1# #probility of codeword '0011'\n", + "L4 = 4# #length of codeword S4\n", + "L = P0*L0+P1*L1+P2*L2+P3*L3+P4*L4#\n", + "H_Ruo = P0*log2(1/P0)+P1*log2(1/P1)+P2*log2(1/P2)+P3*log2(1/P3)+P4*log2(1/P4)#\n", + "print 'Average code-word Length L :',L,'bits'\n", + "print 'Entropy of Huffman coding result H : %0.2f bits'%H_Ruo\n", + "sigma_2 = P0*(L0-L)**2+P1*(L1-L)**2+P2*(L2-L)**2+P3*(L3-L)**2+P4*(L4-L)**2\n", + "print 'Varinace of Huffman code = %0.2f'%sigma_2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example2.5 page 20" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "probility of 0 receiving if a 0 is sent = probility of 1 receiving if a 1 is sent= 0.4\n", + "Transition probility\n", + "probility of 0 receiving if a 1 is sent = probility of 1 receiving if a 0 is sent= 0.6\n" + ] + } + ], + "source": [ + "p = 0.4# #probability of correct reception\n", + "pe = 1-p##probility of error reception (i.e)transition probility\n", + "print 'probility of 0 receiving if a 0 is sent = probility of 1 receiving if a 1 is sent=',p\n", + "print 'Transition probility'\n", + "print 'probility of 0 receiving if a 1 is sent = probility of 1 receiving if a 0 is sent=',pe" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example2.6 page 21" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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tUWCY+lWvQ9eu8OijcPLJ4fKiiIhIFijhyhgzO9nMxgIbmtnY2N8k4L2Uw2sS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\nM2ubtA0A7j4eWGBmq5hZtZldZWZvAKe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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f94d28b5310>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import arange\n", + "from math import log\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,title,show,xlabel,ylabel\n", + "\n", + "\n", + "\n", + "def log2(x):\n", + " return log(x,2)\n", + "\n", + "\n", + "p = arange(0,0.5+0.01,0.01)\n", + "C=[]\n", + "for i in range(0,len(p)):\n", + " if(i!=0):\n", + " C.append(1+p[i]*log2(p[i])+(1-p[i])*log2((1-p[i])))\n", + " elif(i==0):\n", + " C.append(1)\n", + " elif(i==len(p)):\n", + " C.append(0)\n", + " \n", + "\n", + "plot(p,C)\n", + "xlabel('Transition Probility, p')\n", + "ylabel('Channel Capacity, C')\n", + "title('Figure 2.10 Variation of channel capacity of a binary symmetric channel with transition probility p')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example2.7 page 21" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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WtDkFpvsws/8lHVxdeLJyrv49/DAcfTQMHQr77JN2NC4J5ZishprZsZIqKZys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\nVM4VYAaXXALXXgujR8PGG6c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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f1bfe6cf890>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Table 2.3 Average Probility of Error for Repetition Code\n", + "_______________________________________________________________\n", + "Average Probility of Error, Pe =\n", + "0.01\n", + "0.000298\n", + "9.8506e-06\n", + "3.416698e-07\n", + "Code Rate, r =1/n = \n", + "1.00\n", + "0.33\n", + "0.20\n", + "0.14\n", + "_______________________________________________________________\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,title,show,xlabel,ylabel,legend\n", + "\n", + "\n", + "#Average Probility of Error of Repetition Code\n", + "p =10**-2#\n", + "pe_1 =p# #Average Probility of error for code rate r = 1\n", + "pe_3 = 3*p**2*(1-p)+p**3##probility of error for code rate r =1/3\n", + "pe_5 = 10*p**3*(1-p)**2+5*p**4*(1-p)+p**5##error for code rate r =1/5\n", + "pe_7 = ((7*6*5)/(1*2*3))*p**4*(1-p)**3+(42/2)*p**5*(1-p)**2+7*p**6*(1-p)+p**7##error for code rate r =1/7\n", + "r = [1,1/3,1/5,1/7]#\n", + "pe = [pe_1,pe_3,pe_5,pe_7]#\n", + "plot(r,pe)\n", + "xlabel('Code rate, r')\n", + "ylabel('Average Probability of error, Pe')\n", + "title('Figure 2.12 Illustrating significance of the channel coding theorem')\n", + "#xgrid(1)\n", + "show()\n", + "print 'Table 2.3 Average Probility of Error for Repetition Code'\n", + "print '_______________________________________________________________'\n", + "print 'Average Probility of Error, Pe ='\n", + "for pp in pe: print pp\n", + "print 'Code Rate, r =1/n = '\n", + "for rr in r:print '%0.2f'%rr\n", + "print '_______________________________________________________________'" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Digital_Communications_by_S._Haykin/Chapter3_JoJ2mAG.ipynb b/Digital_Communications_by_S._Haykin/Chapter3_JoJ2mAG.ipynb new file mode 100644 index 00000000..3763a6e7 --- /dev/null +++ b/Digital_Communications_by_S._Haykin/Chapter3_JoJ2mAG.ipynb @@ -0,0 +1,432 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3 Detection & Estimation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.1 page 120" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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YDFyQXjjxeJJwzqWtVZJE2mMSrxIGpHNGEa4mNiNpL+AGYIKZvV2soUbOk/Ak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\nscJ5BwFTzWxC9PwiYIOZXZ5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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7ff3eae3fad0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange, ones, sqrt\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, subplot, xlabel,ylabel,title, show\n", + "\n", + "#using Gram-Schmidt orthogonalization procedure\n", + "T = 1#\n", + "t1 = arange(0,0.01+T/3,0.01)\n", + "t2 = arange(0,0.01+2*T/3,0.01)\n", + "t3 = arange(T/3,0.01+T,0.01)\n", + "t4 = arange(0,0.01+T,0.01)\n", + "s1t = [0]+[x for x in ones(len(t1)-2)]+[0]\n", + "s2t = [0]+[x for x in ones(len(t2)-2)]+[0]\n", + "s3t = [0]+[x for x in ones(len(t3)-2)]+[0]\n", + "s4t = [0]+[x for x in ones(len(t4)-2)]+[0]\n", + "t5 = arange(0,0.01+T/3,0.01)\n", + "phi1t = [sqrt(3/T)*x for x in [0]+[x for x in ones(len(t5)-2)]+[0]]\n", + "t6 =arange(T/3,0.01+2*T/3,0.01)\n", + "phi2t = [sqrt(3/T)*x for x in [0]+[x for x in ones(len(t6)-2)]+[0]]\n", + "t7 = arange(2*T/3,0.01+T,0.01)\n", + "phi3t = [sqrt(3/T)*x for x in [0]+[x for x in ones(len(t7)-2)]+[0]]\n", + "\n", + "#figure\n", + "title('Figure3.4(a) Set of signals to be orthonormalized')\n", + "subplot(4,1,1)\n", + "plot(t1,s1t)\n", + "xlabel('t')\n", + "ylabel('s1(t)')\n", + "subplot(4,1,2)\n", + "plot(t2,s2t)\n", + "xlabel('t')\n", + "ylabel('s2(t)')\n", + "subplot(4,1,3)\n", + "plot(t3,s3t)\n", + "xlabel('t')\n", + "ylabel('s3(t)')\n", + "subplot(4,1,4)\n", + "plot(t4,s4t)\n", + "xlabel('t')\n", + "ylabel('s4(t)')\n", + "show()\n", + "\n", + "\n", + "#figure\n", + "title('Figure3.4(b) The resulting set of orthonormal functions')\n", + "subplot(3,1,1)\n", + "plot(t5,phi1t)\n", + "xlabel('t')\n", + "ylabel('phi1(t)')\n", + "subplot(3,1,2)\n", + "plot(t6,phi2t)\n", + "xlabel('t')\n", + "ylabel('phi2(t)')\n", + "subplot(3,1,3)\n", + "plot(t7,phi3t)\n", + "xlabel('t')\n", + "ylabel('phi3(t)')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.2 page 121" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7ff3eb2efa90>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Figure 3.8 (b).Representation of transmitted dibits\n", + "Loc. of meg.point| (-3/2)asqrt(T)|(-1/2)asqrt(T)|(3/2)asqrt(T)|(1/2)asqrt(T)\n", + "________________________________________________________________________________\n", + "Transmitted dibit| 00 | 01 | 11 | 10\n", + "\n", + "\n", + "Figure 3.8 (c). Decision intervals for received dibits\n", + "Received dibit | 00 | 01 | 11 | 10\n", + "________________________________________________________________________________\n", + "Interval on phi1(t)| x1 < -a.sqrt(T) |-a.sqrt(T)<x1<0| 0<x1<a.sqrt(T) | a.sqrt(T)<x1\n", + "0.0049504950495\n" + ] + }, + { + "data": { + "image/png": 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ipptuQmZmpld7f/zxB5o2bYrSpUvjuuuuw5YtW7z68umnn17sS+/evZGRkYGu\nXbuiVKlSuPHGG3H06FHDsVi+PBk7d1bD9OmfoVixiqhcuQrGjBlz8fqxY8fQvfsjqFSpAnbvroXC\nhT9UNCfGjBmDTp06ARD69eWXX0bFihVRqlQpNG/eHBs3bgQAnDt3Dq+99hpq1qyJSpUq4dlnn8XZ\ns2cD/1AOo1QpEXbz5smh74kTvmVSUmQHeN994suRV1GmDDBnjhx6v/22ZBPTY/NmEfpPPQW8+GLk\n+xRpq56qAPZq3u9zf5brUaQI8Ouv4mxTp44I+Z9+koQMnTuLg88VV4jlS25zQgkWxYoBf/7pycfa\nvTswaZI4sVxzjex4rrtOLKLMFsCffvoJf/31F44ePYr8+fOjXr16WLhwIfr164ekpCT07NkTGRkZ\nF8svW7YMjRo1wuHDh/H666+jd+/eF6/16NEDbdq0weHDh/HOO+9g7NixF+mebdu2oUePHhg2bBgy\nMzPRrVs33HbbbRd3GkSEKVOm4O+//8bWrVsxbdo0dO3aFR9//DEOHjwIl8uFYX5Muw4ezMCDDx5H\nt27pOHbsf3jiiefwww/H8PXXQL16fTB9+gm88cYurF37D3744XuMHj3ap45Zs2ZhwYIFSElJwbFj\nxzBp0iSULVsWAPDmm29i+/btWLt2LbZv3460tDS89957wf5kjqB0aWD2bKF9qlUTK67ffpN50K4d\n0LGjBEK0yzkyllG+PPD338Dq1UDVqsIWTJ0qyXauvFJkxrPPirWbEwg1Vs9bzDzVXWYeJAzDKoPv\n3w3gZmZ+0v2+J4B2zNzHoGz0E+7GEUccceRCsNM5dwHMA3CFybX2AGZo3vcD8Ea4bcZfeesFydlw\nve6zRyBRXbPcrwsAHnNf6wVgga68C+Ip3h7AQd21/wD43v3/cACDddcXA3hQ05fOmms/AHhX8/4J\nALNN7iMRwF6De+sMoKK7j0U1124GsM3ongD0gUS0PQRgBIASACq468jSvI4COB7t3zD+yl0vu0gI\ns9VmBYD6RFSLiAoBuB8S4yeOOPS4uOMjopoARgJ4DpLEpzQk5IcVrWY/gNJEdJnms5qa/9O070k4\noOruz81gxwlNJmTxqqX5rAaE/vQBM3/JzK0hRhENAPSFLAJnADRh5tLuVwIzl7Shf3FcQgjHnLM7\nEe2FaFh/EtFf7s+rENGfAMDM2QCeBzATwCYAPzPz5vC7HUceRzHIQpAJIB8RPQbgcitfZOY9EIVj\nIBEVJKLX4FLRAAAgAElEQVSOAG7VFJkE4BYi6kxEBQG8CuAsgEV23oBBv3IATATwIREVdy9uLwMY\npy9LRK2JqJ27f6fd/cthZgYwCsBQd5hzEFFVIropkn2PI+8hHKueX5m5OjMXZeZKzNzV/Xk6M9+i\nKfcXMzdk5nrM/JEdnY4jb4OZNwEYAqFgDkCE/kJtEWh2CJrPFHoAaAfgCIB34ckUB2beCqAngC8h\nGvQtAG5zKymmXQrQtllZPfoAOAVJTrQAwHgA6nRXW29JyI7nCIDdkAVQxQF9A8B2AEuI6Bgkx0UD\nP23GEYcvwuWKAHwHIAPAej9lhgFIgUz4Xe7/Dbl+Tdm1AFpFmwuL1AvC724xGwsAD7nHYB2AfwE0\nj3afozUWmnJtAGQDuCvafY7mWEDOElZD6K/kaPc5WmMBoByAGfBE/+0V7T5HaByCkbGW5KYdneoE\noJVZpwB0AzAdQH6IaedqAAXdP1Zjo7Lu/9sBWBLtQY/QD5kforXV8jMWVwEo5f7/5kt5LDTl5gKY\nBuDuaPc7ivMiAcBGANXc78tFu99RHIsBAD5S4wDgMIAC0e57BMbCkox1/29JboZ9uMuSRtHAbeci\nVFL2tu4JWxQSy9/ImetiAndmXgoggYgqhtvHGERAxzZmXszMx9xvlwKo5nAfnYJVJ78+ACZD6Jm8\nCitj0QPAL8y8DwCYORN5E1bGYj+EFoP772H2T9nlSgQhYy3LTSdci5QTl/q7DyLEjJy5jBy+8qLA\nC9axrTdk15QXEXAsiKgq5KEf7v4or/p8WJkX9QGUIaJ5RLSCiB52rHfOwspYjALQlIjSIRSHAz6v\nMYmg5aZTSd4Ivgdk/spqkRcfcsv3RETXAXgcQC6P4m8KK2MxFMCbzMxu88s8GgDD0lgUBHAFgOsB\nXAZgMREtYeaUiPbMeVgZi7cArGHmRCKqC2A2EbVgZoMAEXkeQclNv567llskqgVgKjM3M7j2LYBk\niHXCAAhndy1EmLmYeZC7XF4U8HHEEUccTuBBZv4JAIhoC4BrmTnDrLATVM8fEC/MFRCzvDMQvsrH\nmSvahyhWXhcuMPbujWwbSUlJUb3H+fMZH39sfK1zZ8Y77/h+npPDqFePcfRo3hqLWHrFx8L/WAwf\nzmjc2Lj8+fOM7Ozo9zsSLzceAQAiag/gKPsR+oANgp+IJkCcXxoS0V4iepyIniaip93CfDrEjHML\ngPMASkPjzKUtmxswa5b1uPq5FZMnA3PnGl/LzJTQw3rs2wds3w6sW2dfPzi+B4wjCGzaJGGejfD2\n28AnnxhfyyPYSUTbIeE9/i9QYTuseh5k5irMXIjFoes7Zh7BzCM0ZZ5nceCqw8y1WOPMpS8b69i5\nUxJH5GXMny8x9o1w6JCx4N+6Vf7aJfjPnZPopkYRkM+ckciocUQPzECshcTftAk4csQ4QdKuXRIm\n2i7k5FhLPqRFdrZ5nupz54xDmluFRsa2YIOAmXrk8YDB9mP3buDAgci2kZiYGNkG/ODoUWD9ehHw\nejCLxp+S4quNb9kisfnXrrWnH+PGAWvWAKVLJ/pcW7BA4pZfaojmvNBj40bJLGfnrkwpD1ZgNBYb\nN0qiJCOl5cABYPFiwK7UBe+8E3w46T17gKefBtLTfa999ZUko3EKdlA9flMrElE5IppBRGuIaAMR\n9Qq3zWhizx7JrGWUTMEuqEm9Z4/EMncSCxdKrPRDh3wf6uPHJQ9BkSK+i9/WrZJtzA6N3+WSbXnH\njoDLlehzfe1aWYCMFqe8jFgS/CtXipZqlIQoFJw/DzRtav250o/FkSPy3caNjeme/fuBEiVE+IeL\ns2dFc09NDe57ae4wgLNn+16bPl3oVX8Z/exEWILfYmrF5wGsZuaWEFfzIUTklBmp7di9W/6acYl2\nYtgw0QScxPz5kiKxYEHfrEmHDgHlyklWsRSd8eCWLcC99wIbNljLOesPf/wBlCwJPP+88UKidhWb\nNvle++cfOYfJa2jdWoRbrGDlSvm7zzC2aPDIyBDqJFQaddMmoEkToFIl4x35gQMyP+fNC6+fgKQb\nPX/enA41Q3q6JG7SC/6TJ4GlS6Xvy5eH3z8rCFfjv+S86/bsAWrUcEbwb9okmq2TmD9fsmaVL++r\nUWdmyuf16/vy/Fu3SmrFcuXkHCRUMAODBkkmohYthHbSY+1ayVrkzkbohe+/lyxPeQk5OZK5yS4h\nawdWrpTFOc1fMOsgoJ4nOwS//tk8eVLG8M477RH8w4eLUhLsjjMtDbj1VhH8WuUoOVmendtvlxSN\nTiBcwZ+rvOtcLtFIQ8WpU6IFN2/ujODfvNlZwX/ypIxPu3ZAhQq+E1ur8WsF/8mTsuWvUUPGJhye\nf+FCuefu3YF69URLOnnSc/3cObEeuvdeY41/9ergNbFYR2amzN1Yobays+U37tLFvsVIaenhCP6m\nTYGKFX2fzQMHZEG4+mqZH6dPh97P9etl1//446Fp/B06SD5i7U52xgw5L7nhhtwj+IPxrqsCoCWA\nr4moRJjt+kV6uu92b9Ys0RKbNTPeMq9eDXz4of96lbZfuXLkD3hPnpT2nHzYFy+W/LhFi4pmr5/Y\nSuPXUz3btskuIF8+Efzh8PyDB0ty7vz5ZVvcuLH3Yr1pE1C3rlj86AX/+fNSNlzBP2FCbFluKUEW\nK4J/yxZ5Bpo2tV/wGx18WsHGjaLx+xP8xYoBLVsC//7rfX38eFEorODbb4Enn5T7NzoH84e0NMm3\ne9NN3nSkEvydOslOSqvoRArhcu1pkOxFCtXhm1GoA4APAYCZdxDRLgANIQ5dXhigOSZPTEwM+TDr\ngQdkANUqv3+/CNGPPhLefOVK4MYbvb/z559iIti/v3m9e/ZIMnGjyaXH8uXAW28ZH+RYwZYtQEJC\nZDX+kyeB4sU97xXNAxhTPUrj11M9W7cCDRvK/y1aAD/+GHxfzp6VLfTy5cDEiZ7P1ULSvr28X7tW\n2mjSxFfwb9okC0a4gn/QIKnnvvvCq8cuxJrgX7lSzhyqVgUW2ZS+5sABoFCh8Kmew4c95w/auitX\nlv+vu07oHvX8z54tic/r1vXMMTOcPClKwfr1sojkyyeflbCoxqanA1WqiOD/8kuhM7dvlx1Is2YA\nkYzrggVA167m9SQnJyM5TFvacAX/xdSKANIh3rgP6spsAXADgH/dEeMaQhy6fDAgWPsoA1y4AKxa\nJatrerqs7vnzAw8/LAeWixcbC/5lyzwHt2bYvdsj+I34ZS3++ktoi+xs0VyDxebNYtViBydphIMH\ngZo1gWnTgOuvl8/mz5fFCvDP8derJzx+To6M7ZYtHsHfvDnwho9tlzkuXAC++w744APR4ufMkR2H\nQvPm3jy/EvxVqog9/+HDQNmycm31auDaa8M/IEtNtY+7tgOxKPivvBKoVs1ejf/yy0MT/EePisVZ\n9erybOp34/v3ixIIiOBXyt3588ALL8hc2rUrsOD/8UcgMVEWPMBDh1oV/Erjv+IK4KGHRODPmCGU\nGbkj7Si6x5/gV0qxywU8+ywADLTWAQ3ConrYJLWizhv3PwBaE9FaAHMAvM7MEbNPWLcOqF1btOUm\nTWRb9vjjIvQBWVFX6PYazCL41QQyw549IiyNDpD0mDdPtFgjZycr2LRJDnwuXBABFyrGjDF+OFeu\nlIn70EMixM+elc86dJDr/jT+YsVE2O51n+5s3Qo0aiT/16snY+NvHLVISgLGjhVLid9/l4dfi2bN\nvKkjJfiJ5PfdrEnkuXq1LGLHjhk78VjBiRPiSBNLB6kHD4oJbSwKfjsPd1u1Ck3wb9oklGC+fMbP\nplbjv+oqUSROnAC++AKoU0eegUBKHwCMHu3tP2JEh5qB2aPxlywplNOCBR6aRyEYnn/+fGDJEmtl\n9bDDc9cntaLWG5eZM5n5NrdHWTNmDoEIsI4lS/yv3EaCf98++WEaNRLhbgatxu9P8J89K1pnly7i\nhBQK1Na1XLnAdM+4ccDQocbXhg0T80g9Vq0SKuPdd8Wa4O+/pT2lvfjT+AHvA14t1ZM/v3C/Vg/R\nt20DXnpJFjkjKKqHWV5K8AO+dM/q1aJNlS0bOkWmbLNjSfBnZIhgiwXBn5Mjv8EVV4j2aqfGH47g\nb9JE/vfH8QOym2zdWujEQYPkualdWzR+fzh/Xu5bUaGAKE5WBX9WFlC4sChNgNA906aJ8L7hBk+5\n1q1FBlkxHvnhB2EyQkGe89wNJPjr1hWNUPsQLV8OtGkTeAJoNX5/h7tLlojwu+aa0AX/5s0ymcuX\nDyzEvvzS3DElPV1shPVQWtuzz8o5SI8evpPaTOMHPAe8LpcI7waarK/BHPDu3+/RxoxQoYI8MPv2\niXZZoIDnIW7a1EO5uVzyYLZqFdwDqceePXLuEWuC//LLY0Pwq4PdUqVkV52d7evvEQqU4A/lcFcd\n7AKy6Ot3fFqqBxC657nnxIu2fn1rgn/jRtkdXHaZ5zMj5cgMSttXuOkmYNQomcOKqgRkficmmsfK\nUlBhS0KNGxZxz113mUQiWu323E0Ot01/CCT4iURb0R4ALVsmGmetWv63fFY1/nnzZHK1aBGaaePZ\ns0Kj1Ksngtbf5EpJkf4bPTDZ2SIAjbaDq1bJOBDJwpGYKJq/gj+rHsBzwLtvnwiAkiU95YIx6Qwk\n+FV969d7a/uAt8a/YwdQujRQpkz4gr9du9jj+M0E/+nTzjqsrVghCgMgc6dqVXvG6sAB+T1PnQo+\nrIIy5QRkx1m2rPdYaakeQPjzGjU851m1awemetTzooXZPDOy9FH8vkLr1rL76NLFt6ye7jFyiPz9\nd1FWtYtJMIi45y4RJQD4GsBtzHw5gHvCadMfMjPlh2is9x3WQU/3KI3fn+A/e1a2a5UrCx3icpmb\nXSnB37Kl0A/BxjPZtk0mY8GCgameH38EunUzFvwZGfL99HRvE9bDh+Ve6tWT94UKyUTSavz+OH7A\nQ/VoD3YVWrTw1vgHDza2kFG8ZyDBr3h+f4J/9WrRGIHwBH9qqvDA6enheyDbBX+Cf9Ei2e47FclU\n7RQV7DjgPXVKlJRSpQLvpo2gpXoA3wNeLdUDiJK3ebOHdqlZUxQtf0HXtPNLwWhXDMg5k17Z0mv8\n+fMD/foBD+pNYSCC/9df5W+dOrLjHTLEu0w4NA/gjOeuYzlCly6VHzVfgLvSCn6XS/4PJPhTU2WS\n58snmo6Z1n/6tGgHV18tPzRz8BNZ0TyAf6qHWfj9vn1lYukf/v37xdKhdWvZFSisWiWT2N84KcGv\n6jx/Xu4tIUHeK6pHy+8rNGsmGrrLJbuJTz/1NbED5DBdy3uaQVFHesFfvbocIh896iv4Q6VF9uyR\neytVKnYcwTIyZD5kZfkKp7Q06adTMZ2UKaeCHYI/I0MEM5EoAcHw/MeOiVJTs6bnM+0Bb06OzIUK\nFby/lz+/5/8iRWSn6I9mMtL4zQ53N23yPUfUa/yAmHPqnx1APvv2W3muZ84UeTB4sIeyzciQBb97\nd/P+BoITnruO5QgNRPMoaAX/tm2yNSxXzv+WT/H7CmaCf9EiEU7Fi8tEbtEieJ5fq8H4o3qWLxfh\nfe21orXrw7oqbbpdO28NZOVK30msR7Fi0n8VNCszU8ZJmZ3Vri1a0vr1HosehTJlRHAmJUmwtX/+\nkYmv16Ct0DyAOdVDJLu7zZuD1/gzMjxWSVqkpsrvbKfFSjhQHruKV9c7Hyqhq3dKigS0B7sKRlTP\nhQvBOSFpNfLKlYPj+Tdv9lj0KGifzcxMoQCVVZ8Z/PH8OTmieLRs6f25kYJx9qy0rTf31mv8/kAk\nO+QuXYRSrVdPFoIHH5SFbsIEoWUDKUz+4ITnrsoR2g1AFwDvEFF9o4IDBgy4+ArFQcGq4K9VSw5H\n9u/38Pvqc7MfX/H7CmZbUkXzKLRsGTzPryYz4J/qGTdOTNEU16p/YPbvl8nWvr33Ae+qVd7bdTNo\n6Z5Dhzz8PiALTfXq4q9gpLU0by6HV3PmyL0UL+57H1YfhsaNxdElNdV3kWnSRB4yreAPZGa3Y4f8\n5v36+V5T3tl22qiHg6wsecALFzam39LSZIeycGHk+6I92FUwGqdRo4Deva3Xqxf8wWj8epoH8Bb8\n+oNdM/jb7W/bJnVo7xswnmfKKkwv+I00/mDQvbuYfT79NPDNN8lg9sjKUOCE5+5eAJnMfAbAGSKa\nD6AFAJ/k0PqbOH8emDJFPHEDISdHhHi7doHLKg+5lSs9/D4gmmp2tlAHitJQsKrxz5sHvP++533L\nlmK2pcW5c0KhFCli3L9NmzxOJmZUz4ULwM8/ezwnq1QRQaq1g9dq/I8/Lm0SyX0PtODzoTSa2rW9\nD3YV6tcXO2QjwT9ggBz4Kmuf6tVFw9Zuua1q/EWKSB8KF/bV3Jo2FVPUnBwRQqrfZoJ/82Zx3rv9\ndl8t+cIF+U2rVo0dwZ+RIXMNMBb8+/YB998vWdMiDT2/D8hY6ROcLFokuzw13wLhwAHPPVapEpzg\n11r0KFSs6FGC9Py+Gfxp/EY0D2A8z1JTPcqI9v6D0fjNMGSIPMunTydi9OjEi3TVQCsPsw7havwX\nPXeJqBAM8ugC+B1ARyLKT0SXAWgHcfYKiMmTgUcftXbItmWL/BDq8DEQFN2zfLlH4yeSld/Ilt+K\nxn/ypGwJlRMUYEz1PPywcHZGyM4WjVQJTDONf84cOfipW1feK8GvhZps6kA6JUU0yIMHvc0vzaDV\naLQHuwoNGohQrlHD97tt2ngvCNWq+VIrVg52FZo396Z5FJo0kYPpVq08D5mZ4F+3Tg7ePvxQHqJt\n27zN/tLSRGgULGivjXo4OHjQs1iaafxdu0pfIx22eds2X8MJowVy6VJRnrZvt1av4viB4DX+DRt8\nnf60h7t6ix4zhCL49edggMgOJU+0imG4Gj8gVkC//gr897/eZxShIOKeu8y8BcAMAOsALAUwipkt\nCf4vvhCt38pEsErzKLRuLZrJ+vXeP6rZls+Kxr9woWhE2pADjRqJFqC48m3bZEEzyza0Y4dMEFWH\nGcc/frzEGFEwEvyK6gFkbJYsEUqkRQtrE0craIw0/gYNROu3UpfS+M36Fwg9ehjv/Jo0EdpOa3Fh\nJvifekp2Y48+KuNbs6b376D4fcCY4z91Sh7qYFPuhQMrGn/NmqIJ2hU3xwy7domA1EIv+I8ckT7f\ncYd1+ikcjt9I8GsPd61SPf7O95QxhB4qKdGxY57PlJy4/HKPE2N2tvxu6ncMB3Xrenv6hoqIe+66\n33/KzE3dnrvDrNS7dKkMVtu2xj/IL7+I2Z3irkMR/H//LQOpPSQxW/n1Gr+R4E9OFnt4LQoW9I4w\n+cknQOfO5jHr9ZylGdWzdKknxg5grvErbaddO/mOVX5fta3l+PUa/3XXCYVkBdWr+2qGVqkeQKgZ\nowlfs6YIcb3g1wtIZqF5tJYQ+nAQit8HjDXZdetkh6gNExFpaAW//r7On5cdXMWKYkUW6QNeI8Ff\noYJo9yq65fLlMr+uvVZCElhBqBz/kSPiPKZVyADvZ9Oqxm92vsdsbMqpoP9NlODXOhcqs+pAB8xO\nImY9d4cNk2QHdesa/yDLlgmH3L27HHj8809wgr9aNfkxFL+vYKTxq2w72q2aEdWzaJEEVtND0T3p\n6bJgff65f8Gv3U6XLSt299rtZE6OaKfahciqxm/E05ohkMbfpImEW7ACI43fDt4zXz6gVy8JaatQ\nooRQONq465mZsjMpU8bzmT4AnF7j1wt+dUjvVJYkwL/Gn54u1/LnF8EfygHv2bNyEDvMgjq2c6ev\n4M+Xz1tLX7pUlIyOHUPT+IPh+DdsEAGrP0fQC34rGn/16lJWH+Np1y6ZT3pzUAX9Aa+R4LdjntsN\nRzx33eXaEFE2Ed0VqM70dMlB+fjj5luw7duBJ54QQVm4sGg+zZsH02/ZTegPg40E/759Mrm1UTb1\nGr+KCmoUc6ZlSxH8Q4cKv3/55aKpGJm8aW34AbGeuewy0aq0/alQwftwWG9Wl50twk5N2FatpO5F\niwKbcioE0viDgRHHH4zG7w/ffOM52AXkt9ULye3bPQ5rCv40fjWe2gV37VpRRLQ+EZGGP8Gflua5\n7/btRTO1Glde1d25s2jm8+f7L3v6tMxBIwGmPQ9RVnLK4cyKD4v2cLd8eWnHSpA9I5oHkHmalSV1\nWKV6ChaUuajPo2tG8ygYafw1angLfjv4fbvhRM5dVW4QhOsPeM6vbFYTEsy3YOpBTkgQbSUjI/it\n1OjRoi1qYST49TQP4NH4lWBYt07K6E2+ABH88+cD//sf8MorIpjMKCW9xg/40j07d8rBrhZ6jf/g\nQXkA1GJVtKhMxkOHfE0izRBI4w8Geo2f2T7BbwQ9z799u5xHaKHX+LXnOCVKyNhpF9y1a0U7DiT4\nz5yRZDJ2JM72J/j37fMIlBIl5P5WrfL+rlky9PXrRem56Sbx/tbnUNZj924RaEZOf+o8REW5VU6U\nHToEpp+Yve8xXz65T+2CkZIiMkGPDRtk8dZDG7bBKtUDGD/7KvCfGbQaf06OPIPVq3sCFWqjcsYS\nnPDcBYA+ACYDCOhPee6cZLDv00feGwlIZjkEVRYtQGBvXSOUKycatRaqPf1JvZ5HVA5aSmtfskTO\nHIzQvLkI9Ftu8dRTp46vt2VOjhw26s3T9JY9RoJfHWgpCygji5l27YR2spofQCs87dD49+/39O/4\ncfnNrMYyDxZGgl+v8deqJZqhcnxLTfW2UNLSPS6XCMtHH5Wdk794Mh9/LFZDWiEcKgJp/FpNUsvz\np6QIpWeWVe7++8XkdsAAOaTfvt1/2Iddu3znnIIapz17ZG6pPnXqFJjnP3ZMduza4Gd6nv/HHyVf\ng75/69cba/yA53mwSvUAxrLGzKJHQavxp6fLgqN8LooUkd8oz2n8sOC5S0RVIYvBcPdHptNr4kSx\nVGnRwqP1Gq3CBw7Igaw2MJhdUPb7Wk3PSOMHvK0HFi82P2NISJCDSW2Ckjp1fHn+nTtlImmzYgG+\nlj1GXGvhwrLbUOWMLGbuvtvbEigQ7NT4CxeWcdBaW0RK2wesCf58+URwrF8vQkVL9QDeFMbOneIB\nWqWK7JjMvLF37AC+/lrG+u+/w78Pq1QP4BH8KSlC4Vx/vW/oAEDm9t69nlgvJUvKnPNnTWN0sKug\naDHF7yvO3QrPbySY9YJ/9mzpm1ZRYjanegAZs507he6xKif0gp/ZGtWj5pleQVR0T14U/FY8d4cC\neJOZGULzmFI9b789ACdODECzZh7P3Ro1ZOC022ajh9guKFt+7WKzZIkxPaK1F/an8QPi4aoiCALG\ngn/jRuOJbIXqAbzpHiONX4WjtQqtnbIK2RAOtHSPE4I/EMcPeOiew4dlcdIKCa1J57p1Hj+CNm3M\nD3hffFFirDzySPiCX9Eg6pymXDnvg34t1QOI4P/nHxH4SUliDr16ta/56cqVIsy0Zrj16/une/wJ\nfqXxa73gARmnLVv8h202EvzaA95jx4Ri695drOYU0tNlt2526FqxonyvcmVrTmSA73liaqrs9LSL\nqx5aqkcv+C+/XJ5pu6me5ORkrygHocAJz90rAfxEMvrlAHQlogvM7JMeZNu2AT4NqB83Lc0zqJEU\n/IBH8LdqJRrTpk3AXQZH0uqA9+BBEYxWuXNAaCq9x6OyUtBDT/WYbbuV4FdxzcOdbMWLi9DYv1+2\n4oULh1efOuBt2zbyvGeFCt6H7ykpxnNGHfC2b+9L52mpHm2coLZtvYWQwtSpMjenTBGe/6GHhBIy\n89DWY9YsEeRqDpw4IdSJMjfWHvSXLu2r8deoIa8+fTwhEypV8qUPVVBCLZTgN0tz7S81odoZHTgg\n1JFC4cIyF5cs8U11qqA92FXQWgklJ4tC1bWr/P/EE/K5P5oHkDrXrLFO8wC+54lDhnhCophBq2AY\nafxLl9qv8evzkcek5y4z12Hm2sxcG8LzP2sk9P1BvwWLtODXrvwffCBR9IyEnjrgVVvcYM4ZgtH4\njaieQBq/HRq1so7ZvDk8fl9Ba8vvJNVz5IgsYEb3oDR+Pb8PmAv+Nm18D3jPnBFt/8svRUCXKiUP\nfjBOVQMHSpwbBS3No6Cle/QaPyAavjZOjlHGueXLvSNsAuFr/Hv2SNv6egPx/FqvXQUt1TNrliwa\niYki+NVux+xgV6FSJY/GbxVaObNrl5wtqJj9ZvCn8SuqJ88d7lrMuRs29NSLExr/rl2iCS5d6tEy\n9FAa/+LF/mkeszZ27/YOR2Gm8WupnhMnxIPUyAtQG6jNrslWvrzseMLh9xW0VE8w4RpCgfaBVBY9\nRppbs2Yy7rt3+2r8WhNZfcrHtDTvc6DPP5dDQK1me/311umekydlMdFmXvIn+F0uEY56wa+/xyuv\n9BX8K1bYK/gVNVOjhq9VWyCePxDHP3u2jGndunJvKgyEP34fkHFLTQ1O469SRQ76z5yRlKR9+phT\nSQqBNP7166U+rf9ILMARz11N2ceYeUqwbTit8Suh/MEHwKuveodg0EId7vo72DXDZZfJZFCC5cIF\nuS8jukhL9agH0EiIVaniqc8ujbpCBRH8dmn8Wo4/0lSPVvCbzZfSpUVYzZ9vrvGrVJ3KiqxAAQ8N\nCMhv89lnYs2jxfXXB06hp7BwoewaU1M9gsSf4D90SCyiAtFIKhihwqFDcj/68fAn+LOyZKExE16K\njjXyYenQQXYYZv4F/jj+3bulr82by3xXWj9gjeoBghP8+fLJHJ06VRacV14J/B31bLpc3g6AgMwt\nZRBg9ZzBKUTcgYuIHiKitUS0joj+JaIg3KwEWo2f2RnBv3ixHJQ984x5uYoVRdCuWGEtKqgeWron\nJUUmndEioxX8ZjQP4Hu4G2sav9aJy0mqJ9B8adZMHnQzjn/dOhEy2sPQtm09B7wffCBxhPRtXHWV\nCKjjxwP3d+5c0Ww7dfIIN3+CX8/vm+GKK2S3oowjVOpEvSCqW1esZowCIvpTNhSqVTMW/AkJEqzP\nzOmuQ58AACAASURBVPfBn8Y/e7ZkoVIUqhL8OTlCPxrtjhXUuAU7x2rXFk2/Xz9rpsaFCslZWFaW\nsdl306axZ9EDOOPAtRPANczcHMD7AEYG24720CUzUzSu0qXD6LiF9jIzhbPVm1ZqUamSaIrVqoXW\nH63gN+P3AW9e18iUU0EJ/uxssf6wIyiUEvx2c/xOUD3KIimQ4G/eXOgzvcZfpowczqrkOloonn/n\nTsmL8O67vvUWLSoKwT//BO7v3LlignnddZ5dgj/Bb8TvG6FkSZmfKr6QEc0DiJBLSDCOSOqP5lF4\n6SUJzGaEzp3Ndz5Gh7sVK8o9zpjhTZ0pwb9jh5TxJ5hD0fgBuc8iRfwrfHpUqCDjW7iwb5+aNo09\nfh9wwIGLmRczs4pftxSABT3FG1qqJ9LaPiAPwHPPSawgf6hYUTj3YPl9hbp1PYLfjN8Hgtf4Dx4U\noWXVUcsf1PmCHRp/1aryoCtLoUg+EEWLyoN4/Lg1wQ/4amsqwc306b7hQNq2FcH/zjvACy+Yc8FW\neP6sLLG8adfOW0gG0vitapJanl+bf0IPM7rH35xTePhh8/74E/xGh7sFCsj8/fNPb8Ffp45o/7/+\n6p/mAWSc8uULXvD37AmMHRucBVv58jK++vkDyGJotiBGE06kXtSiN4DpwTZSrZoIs/PnnRH8APDV\nV4EdP9RDGarg12v8ZoK/VCnRSC9c8P8QVqggmn5qqn1CVQl8OzR+lTw+JUWEfyQc8LRQdI+ZKadC\ns2ayZTfaIVWrJk5Reo2/dm3hrefO9c8FWxH88+cLF16okCwwmZmiedtB9QDelj1mGj9gLvitaPz+\n0LGjnDNog+YB5vlwAZm/det6LyZEsiP65hv/Fj2A0HINGhjnivCHTp3MTVrNUKGCLKhGgj8xUUKK\nxxqccOACABDRdQAeB2AayM0MBQrIREhNdU7wW0GxYkIFBXuwq6AV/P6sFPLlE+epzEz/rvMFCohg\nWL3aPhpFCX47NH5A6J5ly4JzrAkVFSpI/oOzZ/3TXk2bSo4Eszg0OTm+Gj+R8M8ffOCfDrzySjnX\nMMrWpjB3riddZ7588v+8ed7OWwrBUj2AR/Cnp4vyYCYMIyX4ixeXhVNv2nr4sOyujWJsVa5sbPuf\nmChyIJDGDwj9Esgqxw5UqGCu8ccqnHDggvtAdxSAm5k5S39dQeuFpndSUAe827fbk4jALsybZ20S\nGkEJ/rNn5WDIX1ascuVEe9292/9DWLWqTEK7NH6t16gdqFZNBL8TvGf58nJIX6+e/0UmXz7gttuM\nr1WrJuNttDuZMCHw4lWggAjy33+XRDBGmDtXAvgpdO4s8+rgQf/mnFY1/latRLFYtEhoHrM+168v\n46VHuIIf8NA9N9zg+cxfHJ2ePY13wEokhPrMRQLly4uCYfb72o3k5OSQcpJrEa7gv+jABSAd4sD1\noLYAEdUAMAVAT2b2m4zNn/ux4vljSeMHzLfNVlCpkpwRrFwpi4A+YJwW5cqJhUhCgndAKz2qVJH6\nbr899H5pEQmNf9Ei49hHdqNCBWkrnPlSvbpEVzWC1R1L375i9fPww75WWwcPyo5AGwjsuuuAQYPE\n8cxM8J85Y13jL15ctNGxY/3PVyON3+USpSTc36tzZ9/k9kYHuwpm9Ejt2uJUFYyXfKShlCOnNP6o\ne+5adOB6F0BpAMOJaDURhRTNXKvxx5LgDwcqPPPUqf5N0wB54JcuDXzIVqWKaHexyPEDIkjXrHFG\n469QQXYX4cyXhx+WmDfhoEMH0bSNkp0kJwuvrD2Ib9RIzrOMAoyFwvEDIvD//NO/4K9XT5QrbWyf\nAwekD9osdaHgqqvkHEtr2vrrr8Z5lP2BSCKO+lOSnIZ6RnIT1RNxBy5mfoKZyzJzK/fLwNo3MGrX\nlkh52dn2CaFYQN26wB9/BN66lisnQsyK4M/JsY/jL1kS6N/fOM9AKKheXQRaJE05FSpUkEPxcAR/\nyZLS53Dx0UeSdlOfRlOZcWpBJJ9VrOi7qyhaVBaJnJzgfpPWrcW01Z/gv+wyOUvS5k2wg+YBxESy\nTRtP+IZ//5V5/8474dcdbTit8duBmE29qEetWmL9EIivzW2oUyewMwoggn/NmsAPodKk7dKoieQA\n064xV1qqU4IfiI0dYoMGEgNfGx//wAEJ1KcX/IBH8BuhfHmheYL5Tdq0ke8Emhd6uscuwQ94eP5z\n54QPHzrUEwY9N6N8eVmQ7aJDnYAjqReJaJj7+loi8hPd2hy1a4s5WCw8xHZCafBW7JLPn7em8QPO\nCNZQoLTnYBam8ePHo0uXLkG3FazgT05ORnU71HsTvPsu8P33cvj+5psq5k8JlCix26fsffcBn35q\nXE/58sHRPIBYnlkJGBdpwT9vHjB4sMzje+6xp95oo1494L33cpdCGnHPXSLqBqAeM9cH8BQ8CVmC\nQuXKYvaVFwV/oULe2cSMTuwVvRVI8CtN0A6v3UigcmVPgm49Fi5ciA4dOiAhIQFly5ZFx44dMWLE\nCDz00EOYqY9hbQEVKogmFiuLYMWK4uF61VVycLt2LXD+/AnUqVPLp2yJEsA113h/puaF0viDAZE1\nm/ZICv42beSM7osvxBY/HEEZrlWLnShaVFJt5iY4kXrxdgBjAYCZlwJIIKKgxVL+/MKh5TXB37Il\ncO+93od74Qj+WrUkdnmw+YedQoEC4umqFybHjx/HrbfeihdffBFZWVlIS0tDUlIS1pilurKA+vUl\neFooaTn1GDBgQEjWE3r06ydWMiNHBn92oBX8wWr8VqEEf1oaMGIEMGeOfc9cwYJAt27A+++Hf24S\nS4I/N8IJz12jMiFN2+7dQ3eWilVUqyaxXgKhfHnZGQSiSEqWFOuNWMbnn/uapG7btg1EhPvvvx9E\nhCJFiuDGG29ExYoVMWbMGHTq1Oli2VmzZqFhw4ZISEjAc889h2uvvRb/cxvCjxkzBh07dkTfvn1R\npUoZDB5cBzNmzLj43dGjR6NJkyYoWbIk6tati5EjrYWOIj/qaa1atTBkyBC0aNECCQkJeOCBB3BO\nE45y1KhRqF+/PsqWLYu7774DRJ68gvny5cNOtxff9OnT0bRpU5QsWRLVqlXDkCFDLpabNm0avv32\nW5QuXRqLF1+NOnU0WeJtRMOGEiOneXM5U/vkk+A9Wf1hwgTg2Wftqy+O0OCU567+qbHs8avF4MGe\nXLyXGurUkcBRdmivsYiGDRsif/786NWrF2bMmIGsLGM/v8zMTNx7770YNGgQjhw5goYNG2Lx4sVe\ngnnZsmVo1KgRDh8+jNdffx29NZlJKlasiD///BPHjx/H6NGj8fLLL2P16tVh9Z2IMGnSJMycORO7\ndu3CunXrMGbMGADA3Llz8dZbb2HSpEnYv38/atasiQceeMCwnt69e2PkyJE4fvw4Nm7ciM7uU9/V\nq1ejd+/euO2223DkyBH07/80/vOf23H+/Pmw+m2ERo3ED+TAAWD8eDmQtpO7zk08eF4GsT51fTBf\nJmoPYAAz3+x+3w+Ai5kHacp8CyCZmX9yv98C4FpmztDVFXpH4ogjjjguYTBzcEsqM4f8gnj+7gBQ\nC0AhAGsANNaV6QZguvv/9gCWhNNm/HVpvAA0BLAcwI8AHgWwwP35mxBHQW3ZRQAed//fS5XVXHcB\nqOP+vyuAJQAOA8gCcA7AQPe1RAB7Nd+b5i6TBeCM+6Xe/6EptwtAZ837AQC+d/8/HZJuVNuf/QCu\nMuhbawC/ATgCIBlAe00dpzRtZwE4CeD+aP9O8VfufIUVsoGZs4lIee7mB/A/dnvuuq+PYObpRNSN\niLa7J+9j4bQZx6UBZt5KRGMhlmBak550ABcj65BwPJbOjIioMIBfAPQE8Dsz5xDRr/ClIlUfbtV8\nN0k+4veCvJV0iGKk6ikGoCwkzpW+vRUA7nRby/UBMBFADQCpAD5k5v8E2XYccRjCkdSLzPy8+3oL\nZl4Vbptx5D0QUUMieoWIqrrfV4fEfdKHDZsOoBkR3UFEBQA8B8Bq1PVC7lcmABcRdQVwk9UuwmSB\n8FMeACYAeIyIWrgXnv9Adr2pXoWJCrqz1ZVi5hwAJwCo4AmjADxDRG1JUIyIbiEiP3FB44jDHI4e\nFTrl7JUb4ETKytwCIroZwJ8ABgLYREQnIQJ/HYBX3cWYiNoAOABgKIDBEAHeGBIsUJnRMHyNBxgA\nmPkEgBcgmvQRyMLyu1FZAxjVa4aLZZn5bwDvQHYa6QBqA3hAV1ahJ4B9RJQD4GsAf7nrWAngSYjP\nzBEAewCMA7CMiJIt9inXwcIzUo6IZhDRGiLaQES9otDNiIOIviOiDCIyNeUKWm6GwxNBwjDPA7AR\nwAYAL5iUGwYgBfJwdgNQEIHPA9ohj54HQGix7RAKwGwsrgJQyv3/zZfyWGjKzYXw7ndrPs8HoU2u\njfa9ODQvEtzPWzX3+3LR7ncUx2IAgI/UOEDObQpEu+8RGItOAFoBWG9yPWi5Ga7GfwHAy8zcFHJw\n+5yZ5y6ARwCsAvAuR9jZKxfAkZSVuQRWnAAB4bwnAzgEoAURJbipk7fc15c40tvIwspY9ADwCzPv\nAwBm1oV9yzOwMhb7Aaj4pSUBHGaJGJynwMwLIAf6ZghaboYblvkAM69x/38SwGYAehcj1amqkF2B\n6lREnb1iHI6krMwlCDgWbt7/DnjCfTSAaIOHANwC4E5mPofcDyvzoj6AMkQ0j4hWENHDjvXOWVgZ\ni1EAmhJROoC1AF50qG+xhqDlpg3puAXuZCytINqpUadUxJRAnbLF2SvGEUrKyqsj152owspYDAXw\nJjOz24pnEjMbe0HlblgZi4IArgBwPYDLACwmoiXMbJA0MVfDyli8BWANMycSUV0As4moBctZzqWG\noORmWA5cFysR64JkAB8w82+6a1MBfAyxUBgAWWxeB9AFGmevuANXHHHEEUfIeJADOMlqYUdY5oIQ\ni4VxeqHvhsrLuwKyTa0N4CAkTeMf2oLRPkSJlVdSUlLU+xArr/hYxMfCjrH46y95RbvfkXi58Yhb\nHrcHcJT9CH0g/LDMBOB/ADYx81CTYn8AeITl0OUryBlAMozTNMYRR1jIzpZEH3HEocVnn0mQxzlz\not2TiGGn20l2BID/C1Q4XI7/aojt8ToiUpGu3oJ4G4KNPXevZo0TF7sdvdwxfWwBczwY1KWKl1+W\nv19+Gd1+xBE7yM4GliyRyKA9ekiO63btPNePH/fNbZzbwMzPB1M+XKuehQDGQA5uC7Dk1P2LNZ67\nRJQI4GGIJ6ILYnMaMZw+LQkfevWS/3MjEm2Mg5tbx0AhmLE4cQIYOxaYnkftn+ycF7kdwYzFmjWS\nhObOO4HRo4E77pDQ04MGAW3bSu7iVZdYPIGwD3eJqBMkYNT3zNzM4HoigFeY+fYA9XC4fWEWgX/+\nvCT8WLMGmDxZYoznZXzzDXDsmCT50KN1a6BPH+DRR53vl9MYPly28osWAQsXemc1i+PSxeefA9u2\nyfwAgB9/BJKSgBtuAO6+WxSF4sUlfWJuBBGBnYzOqTlcqAVzr7JEAFMt1MHhYvhw5ssvZz55ktnl\nYh4xgrlcOeZJk8KuOmaxcydzqVLMVasy5+R4X0tJYS5UiLlpUxmPvAyXi7lZM+Y5c5gffpj5m2+i\n3aM4nMa5c8wbNvh+3r078/jx5t9bsIC5ZcvI9SvScMvOoGS2E7F6GEAHdwyJ6UTUJBKNLFsmyayn\nTAGKFROO/6mngJkzhff97LNItBpdMAPPPw+88YZsV5fqPCimTAEee0zSVoaQsjZmwQzs2+f92b//\nyk6vc2fgppuA2bOj07c4oodx4+T3v3DB8xkzsGABoEng5oOrrpL5lJpqXiavwTYHLj9YBaA6M592\nR0P8DeJ56YMBAwZc/D8xMdEvj7d5M/Dpp8JhnzkjhzcjR0rOUC2uuEKEQteuwN69wJAheSeL1a+/\nSjLsX38VS5ZJk2QSK0yZIvlNO3SQ+7755uj11U78/bf8nj/+KPmKAdnGP/OMLPg33CD0Vna2J5ex\nywV07CiJsR95BLjrLkloHkfewbRpQnlOny48PgBs2SKKoL8cv/nzSy7gqVOB555zpq/hIDk5Ofyc\nw8FuEYxe8EP1GJTdBaCMwedBbW8ee4y5d2/Zwk2Zwrx0qf/yR44wd+rE/MADeYP2OH6cuVo15n/+\nkffr1zNXr+65t717mcuUYT5/XrbAVaowr14dvf7aiWeeYX70UeZKlZjHjmXOyGBOSJDfWKFFC+ZF\nizzvp06VzyZNYr7tNqHHRoxwvOuOIiWFedcu42urVjEfPuxodyKKs2eZS5Zk/uQT5ttv93w+YgRz\nz56Bvz95MnOXLpHrXySBEKgeJzj+ivAcIrcFsNuknOUbPX9ehFpqanADdOYMc+3aMulzO155hblX\nL897l4u5USPmJUvk/bBhIhwVPv5YuG+FadOY77qL+dQpR7prG3JymCtXZt66lXnzZln8rrmG+fHH\nvcv17cs8YID873Ixd+jA/NNPnutLljDXqZM3lAAjrFvHXKECc+PGvr/xqlWyUCYkyBxZvDj3j8PM\nmfIbnzgh95WeLp/37Mk8cmTg7x8/zlyiBPOxY5HtZyQQiuC3w3N3AiT1XUMi2ktEj+ucsu4BsJ6I\n1kBiroQdY2XePKF0/G3fjFCkCHDffcDEieH2ILrIyQHGjPG2QiAS2mPSJHn/yy9isaDw1FOyFV62\nTD5/6SXg0CGhgHITli4FSpcGGjSQxOD//CNmnH36eJe78UZg1iz5f+FCICPDezzatpUxW7nSub5H\nAszAjh3en23aBHTpAnzxBdCyJfD6655rp04BDz4olmApKcDll4tt+/vvO9tvuzFtGnDrrWKdc/fd\nwA8/yOeB+H2FEiWEElVzJs8j2JVC/wLwHYAM+KF64InHvxZAK5Mylle4J5+ULV0oWLky92h6Lpdx\nPxcvFuslPdauZa5ZU6iPUqVkh6PFCy+Ilc8778i1nTtl57RvX0S6HxH07cvcv3/gcqdPMxcvznz0\nKHPXrsa0zltvMb/2mv19dBKzZ8u+vWVL5s8/Z164UGi9H36Q61lZzDVqyA6PWZ4d7c6PmXnZMtkZ\n5Fa4XLKTX7dO3v/7L3PDhsIIlC9v/Vn/+mvfsckNwP+3d+bhUdT3H39/SIF6VG1IOZQjily2ELk0\nghylQFEQi9AnIId4QUUrSlXweDjUAkak0YqKKBQrKA9IWxDwhPwQEAsSbiwiKEgEAhGJgJBkP78/\n3rvskd1kdnd2ZjaZ1/PkSWb2m/l+57szn/nO57RD1QOTigSEE/ynT/PLCPziiov5Ze7dG9skeTyq\njRvzAeB0nn02vJCbODG8wPJ4VJs2VR0xQjUrq+znRUWqX38dvO/RR4NVQk7G41G98krVjRuNte/Z\nk3NVr17Zh6AqH5QNGybHIiASEyaoPvKI6scfU2ilpqrOmRPcJjeX9pCXX+aiJ1SdUVqqWqeO6p49\nVo3aXHbsCP4ePR4K/nvvpSunUfbvV61VizImmbBF8GvFOv5XAGQFbH8BoE6YdmVOaMYMjjDwQl65\nUrVt2/gmatw41bFj4zuGFbRvzxuypCR4f2YmV3rheOwxztmCBcb6OHGCgnHDhvjGagXbtkUnqKdN\nU61WTTU7O/znPrtIoBHY4+G1sXt3/OO1gp49VZcsqbjduHGqKSl+G1Aot9+u+vzz5o7NKqZOpZAP\n5JlnVEVUp0+P7lhXX626erV5Y7MCpwr+pQA6BGx/BKBtmHZBJ1NcrJqezkCcX/1K9dAh7h81SnXy\n5PgmatMm56t7jhyhuiYjI1jIFxbSCBVuBauqunmz6vnnc3VvlNdfV+3Y0dnzoar65JNUVxllxw4+\nOMsz2E2YoDp6tH/7H//gXfHcczEP0zJKS3mNHDlScduzZ8t3anjnHdUePcwbm5Vcf73qihXB+/Lz\n+aCLdkGTk8OF0FNPqRYUcN/Bg1w8dOzIxWhooKTdxCL4zcrHnw5G54ZL2bAUwFRVXevd/gjAIxqQ\nqM27XydMmHBuu7i4K9au7YrcXGDcOPqrz58P1K9Pg17TsJEAxlDl/7/9NtC2bezHSSTz5jHdRKdO\nwPbtwOzZ3L9wIQ27y5ZF/t9jx4BatYz3VVoKZGbSB/qKK4D0dBoAu3SJ5wzMp00bBuJFk7Lm7Fmg\nRo3In+/aRb//Awf4064d01vs3+98J4Dt2xmPsHt3/McqKgIuvRTIz0+u+IZjx3jNHj5M541AtmwB\nWrWKPmHjtm1ATg7jYK66isbyW24BevcGsrNpQJ49m/l/7CDUj3/SpElQB6ZseAXAwIDtClU9paU0\nXvqe4qdOqTZpQr12q1bmPCUffZS6UacyZIjqK6/Q8PrLX/pX+HfckZhX8tOnGe7+7rucl86dze8j\nGkpKVLt2pQoiN5c2nbS0xOhfW7ZUXbWK/U2dSjVPgwbm92M2r76qOmyYecfr0YMxMcnEm2+q3nxz\nYo59+DDjPwLdYYuLqXFIS6MLqROAQ1U9gcbdTBgw7i5Zotq6dbDqITeXo33ySXMmKy+PngBOVG+U\nllK95TPEdu3KG9LjYU6e//0vsf0fOUJfaDvnZtEi2jimTeMi4Be/4EMgETz9NAV9x4584Hg8zvN2\n+v3vy45n+HAuDswiJ6dsPITTGThQddYs6/t99VX27QRsEfwA3gKQD+AsWFv3DgAjAYwMaPMiWBx7\nC4A2EY6jqrzprrsuvHFy5kzzbkaPh28Rt9+u+sc/MvjDKQbfDRuC3etefVV1wAAaN9PTrRHI9eqp\nfvNN4vuJRGYm9c6qPN9Nm/xBOWazZw+DnQK9Wm680d+/3Rw6xDv1qaeC9zdrRs8ks9izhzYRp+mw\nI1FczAf0wYPW9715szNcYPPzYxP8ZmStmQvgBIBvALyoqrM1jnz8q1cDR48GB9v4GDECuOwyE0YM\n6v1mzGAAS//+wEMPUW9ngskjbt57LzivTv/+DCxZtIj7rSgy06oVsHVr4vsJx7p1DC7z5VsRAVq3\nBurVS0x/jRtTtx2Yxvm665j/yQnk5fHcZ89mziGAuu3vvgN+/Wvz+mncmMFxyRLU9umnQKNGtE1Y\nTYsWtDuePm193z7i+f7jLb2YAq7mewG4CsAgEWkRpun/KYu0tFbVpyMdr7gYGD0amDSJiZMSTY8e\nwJgxQFYWy7Kdd545hrJ4CRX8qak0tGZnMyLTCuwU/NOmMaOqFdeAj9C+MjOdJfgHDWKVqFWruG/9\nekYfmz1HvXuX7zjgJJYt43jtoEYNOojs2GFP/wDw2mvMRBAL8a74rwGwR1W/VtViAG8DuDlMO0Nr\n1L/9DahbFxgYd1KH2OjcmW8cdvL99xS4nTsH77/1Vj4Yu3WzZhwZGfSKsJovv2SY/fDh1vcdSPv2\nrMoUmOLXLvLy+MZz11282QGudgMzsZpFnz5M91FSUvazkhJg40ZWsfrLX8qmybAaOwU/YN89AvC7\nmDkTGFVhdd3wxCv4LwP1+j6+9e4LxHA+/uxspte1q16uEwT/Rx/RhTPUNe0Pf6Arp1W1Qe1a8efk\nACNHMpWunVx8Md1at22zdxyAX/APHgysWEE1z7p1zC1jNp06cfEVWs2tuJgujYMHMy127drMf3/o\nkPljMML+/XThbN/env4BewX/kiXA5ZfzPo2FePPxG9GIG87HP3YsT8YuOncGno6oiLKGUDWPj5//\nnMLfKpo1A775hjrM886zps+CAhbE3rnTmv4qwqfuadPGvjGcOEH7Q7NmrC3QuzfrCm/cGFww3CxS\nUhjf0r49z3vQINoV7ryTq8zt24Hq1dl29Wq+efTrZ/44KmLZMt4nVqoDQ8nIoAC2g5dein21D8Qv\n+A8CCMyR2QBc9Z9DVYsC/l4hIi+JSKqqFoYerKhoIny1WCoqxJIImjYFfvqJAq9RI0u7BkDD8nvv\nMWDNbgJ1mO3a+ffv3EkD+8UXm9/nmDFU8dSta/6xYyEzk8ItnhssXrZsoQOCr6DMXXfR2N+gAQ2x\niaBWLRb36d6dRsy5c4G9e+lg4BP6AFVN69bZJ/iHDLG+30AyMvhWrGqtluKNN3Kxfn0uMjOBgNpV\n0RGtG5AGu2D+DMBXoB9/DQCbAbQIaWN6Pv5EMmCAP7Oh1eTlMQmZUxg6lOkcfHg8rN/ry3NvJkuX\nMo3Gjz+af+xY2baNLr928vzzqiNH+rdLS5lk8M47E9/3228zfqJly+AiNz4+/phu0FZz6hTHFW5M\nVlOvXtnEh4nm/vuDkzciBnfOuFb8qloiIvcBeB9ACoDXVXWXLxe/0qVzAIB7RKQEwCmYkI8/kfj0\n/HasJpYvZwk4pxCq59+6lcbXd98FArJrxM3x4yyb+Oab9uv2A2nRgnrkaFNgmEleHt88fFSrxhoK\ntWsnvu+sLP7u3Dn828U11/CN5MwZoGbNxI/Hx6pVrDOQqDeeaPDp+a3SEJw8yfskLy++45jhx68B\nPx6AAt8r9KGqMwCsBHCB9+eMCX0mjE6d7DPwLl9ur5dCKKGCf9484P77WfgjP9+8fh56COjbN7oc\nPFaQkkJd92ef0bj50Uc0PlsZ6+Ez7AZy882J8egJR1ZW5PiJCy+kOjBeIRQtdnvzBGKlgbe4GLjn\nHuB3v4s/T1BcK/4AP/7uoL5/g4gsUdVdAW1uBHClqjYRkWsBvAymbnAkLVvSU+HwYaBOnbKfezxA\nYSGQlmZuv4WF4d047cR3UavyvOfPpw3i22958919d/x9fPghBaoTvGfCkZnJClaHDjEZ2Ndf06U2\nVm+KaDhzhnElLcukPnQOPj1/ZgLvaFVeHzt2MKnewoXAypWJ6y8aMjLo/ppoiopYYa96dRrf48UK\nP/6+YHQvVPUzAJeISBiR6gxSUoDrr6cveTiefjq81028fPABV7yhbpx2UqcOjYr5+XwLSkujofGm\nm6juMYNZs6g2cmpGyOHD6V76+ecsW3nbbcCCBdb0vWMHo2mt8qqKhQ4d6NljBkeOhN//z38yV7jq\nygAADWlJREFUcHHxYhpRZ8/mdegEwq34S0vN7ePQIcqGhg1pdDdDHWqFH3+4NvXj7DehRPLn/+or\n4IUXuOooKir7eTwsW+Ys/b4Pn7pn3jz6cAN88K1aVTZc/fjx6I6tCqxd67z0z4FceSUDlXw63IED\nKfitUPeEU/M4jQ4duOKPdz4KC+ktFs6Vd+ZM/ixcyKj+Pn3i68tMmjYFDh4EfvyR28eP0/XWrDeS\no0cp9Pv25Rz8LF4/TC/xCn6jX3eos5MDMuJEpnPnsit+VeC++xhr0KZNfOH827cHX+ClpVSh3HBD\n7MdMFBkZXOkuXkyfboApJFq3Dr64N26kwTGaPC8HDvDc7YzdiBafT/+mTeW3M4NkEPzp6VQD7t8f\n33HWreO18MILwft37WJOHCcuigAK4hYt/KrKUaNYA2L+/LJtVWkvCsepU1ShBnLyJB9y/frxrdhM\nl9F4BX+Ffvxh2tT37ivDxIkTz/0EFhqwmrZt+SVMn+5/bVu8mILqgQeAjh25Uo2F4mLq6rp14wUN\nUGjWqWNP7EBFtGoFvPgiHwD1A97TAtU9P/0EDBvGlfvkycaP7Ys+tStSOxZEaPC0Qt2TDIJfxK/n\nj4c1a6hSW7CAq38fs2fz2jJrpZsIfOqeefOAzZtpt/r3v8um+1i5kraQ5cuD96tShdikCe1JP/zA\nYLmsLL49hN5Tubm5QbIyJqL1/wz8gTE//qjz8TuBL79kMZIOHVjcu359fy3OJUtUu3cv//89HtWj\nR8vunzGD//v3vzOt7rFjquPHqz78sPnnYAZ5eUwJHJrzfNcuzonHw7H3708f/Nq1WfLQCH/+c+R6\nuE5myxbVRo0Smx67pET1wgtVv/8+cX2YxbPP8ruMh44dWWJ06FD/NXHmDK8np9c/zslhGu+0NN4v\nqqrXXKP6wQfB7bKymMP/0kuDZcPcuaw5sW8f4zPq1GFRnF69WDKzImBTPv4bAPwPzLf/qHdfzPn4\nnURpKQX0BReo3nabf//RowwgKa8aVE6O6kUX+S8EVd7EtWszl7eq6pgxfLhcfTUrQDmRn35Sbdq0\nbLCMx8NgsxdfVK1b11/39a9/ZfUwI7Rrp7pmjbnjtQJfkfZPPzX3uAUFqsuXsxbFtGksFJQMrF2r\n2rYt//Z4eA6BdaIr4vRp3mMnTrAWRcOGvLfeecf+SnBGWLWKkjRwEZO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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7ff3eb014210>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import sqrt,arange,random,sin,pi,zeros,multiply\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,subplot,xlabel,ylabel,title,show,grid\n", + "\n", + "#Signal constellation and Representation of dibits\n", + "a =1# #amplitude =1\n", + "T =1# #Symbol duration in seconds\n", + "#Four message points\n", + "Si1 = [(-3/2)*a*sqrt(T),(-1/2)*a*sqrt(T),(3/2)*a*sqrt(T),(1/2)*a*sqrt(T)]\n", + "plot(Si1,[0,0,0,0])\n", + "xlabel('phi1(t)')\n", + "title('Figure 3.8 (a) Signal constellation')\n", + "grid()\n", + "show()\n", + "print 'Figure 3.8 (b).Representation of transmitted dibits'\n", + "print 'Loc. of meg.point| (-3/2)asqrt(T)|(-1/2)asqrt(T)|(3/2)asqrt(T)|(1/2)asqrt(T)'\n", + "print '________________________________________________________________________________'\n", + "print 'Transmitted dibit| 00 | 01 | 11 | 10'\n", + "print ''\n", + "print ''\n", + "print 'Figure 3.8 (c). Decision intervals for received dibits'\n", + "print 'Received dibit | 00 | 01 | 11 | 10'\n", + "print '________________________________________________________________________________'\n", + "print 'Interval on phi1(t)| x1 < -a.sqrt(T) |-a.sqrt(T)<x1<0| 0<x1<a.sqrt(T) | a.sqrt(T)<x1'\n", + " \n", + "#Implementation of LMS ADAPTIVE FILTER\n", + "#For noise cancellation application\n", + "order = 18#\n", + "t =arange(0,0.01+1,0.01)\n", + "x = [sin(2*pi*5*tt) for tt in t]\n", + "noise =random.rand(len(x))\n", + "x_n = x+noise#\n", + "ref_noise = [noise*xx for xx in random.rand(10)]\n", + "w = zeros([order,1])\n", + "\n", + "\n", + "mu = 0.01*(sum(multiply(x,x))/len(x))\n", + "\n", + "print mu\n", + "\n", + "N = len(x)#\n", + "desired=[]\n", + "for k in range(0,1010):\n", + " for i in range(0,N-order-1):\n", + " if i < len(ref_noise):\n", + " buffer = ref_noise[i]#,i+order-1]\n", + " desired.append(x_n[i]-buffer*w)\n", + " w = w+(buffer*mu*desired[i])\n", + " \n", + "\n", + "subplot(4,1,1)\n", + "plot(t,x)\n", + "title('Orignal Input Signal')\n", + "subplot(4,1,2)\n", + "plot(t,noise)\n", + "title('random noise')\n", + "subplot(4,1,3)\n", + "plot(t,x_n)\n", + "title('Signal+noise')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.3 page 123" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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gzXWjJOm0g4iMBRrE2XRr9BtVVRFJdJoPU9UlIlIXGCsic1U17vo6twqxxOPw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\nxcOtpG3PPedOtF4irrvORlHXXpta+40bTTesWmX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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7ff3eaa3f9d0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange,sqrt,cos,pi,convolve\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,subplot,title,show\n", + "\n", + "\n", + "fc =4# #carrier frequency in Hz\n", + "T =1#\n", + "t1 = arange(0,0.01+T,0.01)\n", + "phit = [sqrt(2/T)*xx for xx in cos(2*pi*fc*t1)]\n", + "hopt = phit#\n", + "\n", + "phiot = convolve(phit,hopt)#\n", + "phiot = [yy/max(phiot) for yy in phiot]\n", + "\n", + "t2 = arange(0,0.01+2*T,0.01)\n", + "subplot(2,1,1)\n", + "plot(t1,phit)#\n", + "title('Figure 3.13 (a) RF pulse input')\n", + "subplot(2,1,2)\n", + "plot(t2,phiot)#\n", + "title('Figure 3.13 (b) Matched Filter output')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.4 page 124" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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21j77bNiSlM6VV1rpvrvuCluS8sWwYZYnPdfZNFevNjPhgw9a+Od111koaLUQ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\n8PPPpvCdik0h89k7RcLPP8NRR8F//+u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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7ff3ea9d83d0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import random,convolve\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,subplot,title,show\n", + "\n", + "\n", + "phit = [0.1*xx for xx in random.uniform(0,1,10)]\n", + "hopt = phit\n", + "phi0t = convolve(phit,hopt)\n", + "phi0t = [yy/max(phi0t) for yy in phi0t]\n", + "subplot(2,1,1)\n", + "plot(range(0,len(phit)),phit)\n", + "title('Figure 3.16 (a) Noise Like input signal')\n", + "subplot(2,1,2)\n", + "plot(range(0,len(phi0t)),phi0t)\n", + "title('Figure 3.16 (b) Matched Filter output')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.6 page 127" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Predictor-error variance 0.64\n", + "1 Predictor input variance 1\n", + "The predictor-error variance is less than the variance of the predictor input\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "Rxx = [0.6, 1, 0.6]\n", + "h01 = Rxx[2]/Rxx[1]# #Rxx(2) = Rxx(0), Rxx(3) = Rxx(1)\n", + "sigma_E = Rxx[1] - h01*Rxx[2]\n", + "sigma_X = Rxx[1]\n", + "print 'Predictor-error variance',sigma_E\n", + "print sigma_X,'Predictor input variance',sigma_X\n", + "if(sigma_X > sigma_E):\n", + " print 'The predictor-error variance is less than the variance of the predictor input'\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.29 page 137" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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jvvvuw4EDB3L05eOPP77el/79+yMlJQWdO3dGyZIl0bFjR2RkZGiOxX//RePo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\nd3FxcalluILfxcXFpZbx/3rGsx341WU1AAAAAElFTkSuQmCC\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7ff3eadbb110>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import arange,sin,pi,random,zeros\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,subplot,title,show\n", + "\n", + "\n", + "#Implementation of LMS ADAPTIVE FILTER\n", + "#For noise cancellation application\n", + "\n", + "order = 18;\n", + "t = arange(0,0.01+1,.01)\n", + "x = sin(2*pi*5*t);\n", + "noise =random.random(len(x));\n", + "x_n = x+noise;\n", + "ref_noise = noise*random.random();\n", + "w = zeros(order)\n", + "mu = 0.01*(sum(x**22)/len(x))\n", + "N = len(x);\n", + "subplot(4,1,1)\n", + "plot(t,x)\n", + "title('Orignal Input Signal')\n", + "subplot(4,1,2)\n", + "plot(t,noise)\n", + "title('random noise')\n", + "subplot(4,1,3)\n", + "plot(t,x_n)\n", + "title('Signal+noise')\n", + "show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Digital_Communications_by_S._Haykin/Chapter4_D4b1XOQ.ipynb b/Digital_Communications_by_S._Haykin/Chapter4_D4b1XOQ.ipynb new file mode 100644 index 00000000..7ff40f44 --- /dev/null +++ b/Digital_Communications_by_S._Haykin/Chapter4_D4b1XOQ.ipynb @@ -0,0 +1,134 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 4 Sampling Process" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example4.1 page 164" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Aliasing error cannot exceed max|g(t)| = 2.0\n" + ] + }, + { + "data": { + "image/png": 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H6upn9dXDBHou3aTQWF6qsTeuaUqky62kiYS2iumS1gNeMrOCc69KGgAsMLNr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\nYII=\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f1df4d30f10>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange,ones,sinc\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,show,title,subplot\n", + "\n", + "\n", + "t = arange(-1.5,0.01+2.5,0.01)\n", + "g = [2*sinc(2*tt-1) for tt in t]\n", + "print 'Aliasing error cannot exceed max|g(t)| = ',max(g)\n", + "f = arange(-1,0.01+1,0.01)\n", + "G = [0,0,0,0]+[xx for xx in ones(len(f))]+[0,0,0,0]\n", + "f1 = arange(-1.04,0.01+1.04,0.01)\n", + "subplot(3,1,1)\n", + "plot(t,g)\n", + "xlabel(' t')\n", + "ylabel(' g(t)')\n", + "title('Figure 4.8 (a) Sinc pulse g(t)')\n", + "subplot(3,1,3)\n", + "plot(f1,G)\n", + "xlabel(' f')\n", + "ylabel(' G(f)')\n", + "title('Figure 4.8 (b) Amplitude spectrum |G(f)|')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example4.3 page 165" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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aM+tyH30EX/0qrLBCuny73m+u56SmPNynpn2WBXaOiOnNjZS0NDCophGZmdXQ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\n1b05c+DPf4att4avfAUaG53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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f8850d971d0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange,ones,sinc,pi,sin\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,show,title,subplot\n", + "\n", + "T_Ts = arange(0.01,0.01+0.6,0.01)\n", + "#E = 1/(sinc_new(0.5*T_Ts))#\n", + "E=[1]\n", + "for i in range(1,len(T_Ts)):\n", + " E.append(((pi/2)*T_Ts[i])/(sin((pi/2)*T_Ts[i])))\n", + "\n", + "plot(T_Ts,E)\n", + "xlabel('Duty cycle T/Ts')\n", + "ylabel('1/sinc(0.5(T/Ts))')\n", + "title('Figure 4.16 Normalized equalization (to compensate for aperture effect) plotted versus T/Ts')\n", + "show()\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Digital_Communications_by_S._Haykin/Chapter5_dSjZdtS.ipynb b/Digital_Communications_by_S._Haykin/Chapter5_dSjZdtS.ipynb new file mode 100644 index 00000000..34a5529c --- /dev/null +++ b/Digital_Communications_by_S._Haykin/Chapter5_dSjZdtS.ipynb @@ -0,0 +1,313 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5 Waveform Coding Techniques" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example5.1 page 187" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The average transmitted power is:\n", + "1.225e-05 W\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "sigma_N = 10**-6 #the noise variance\n", + "k = 7 # separation constant for on-off signaling\n", + "M = 2 # number of discrete amplitude levels for NRZ polar\n", + "print 'The average transmitted power is:'\n", + "P = (k**2)*(sigma_N)*((M**2)-1)/12#\n", + "print P,\"W\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example5.2 page 189" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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XO5SN/J3ZzjnXjEx8eyJfGvol2qn5nJ4LGomk2yQtjo0LZsaNlbRQ0tTYHZmY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\nV7mOkx88mU/Xf8pjxz/WZhK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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f91e4fbe6d0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,show,title,subplot\n", + "\n", + "\n", + "from math import log\n", + "def log2(x):\n", + " return log(x,2)\n", + "\n", + "\n", + "#Channel Capacity theorem\n", + "P_NoB_dB = range(-20,30) #Input signal-to-noise ratio P/NoB, decibels\n", + "P_NoB = [10**(xx/10) for xx in P_NoB_dB]\n", + "k =7# # for M-ary PCM system#\n", + "Rb_B = [log2(1+(12/k**2))*yy for yy in P_NoB]##bandwidth efficiency in bits/sec/Hz\n", + "C_B = [log2(1+xxx) for xxx in P_NoB]##ideal system according to Shannon's channel capacity theorem\n", + "#plot\n", + "plot(P_NoB_dB,C_B)\n", + "plot(P_NoB_dB,Rb_B)\n", + "xlabel('Input signal-to-noise ratio P/NoB, decibels')\n", + "ylabel('Bandwidth efficiency, Rb/B, bits per second per hertz')\n", + "title('Figure 5.9 Comparison of M-ary PCM with the ideal ssytem')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example5.3 page 192" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Channel width = 32000.00 Hz\n", + "Output Signal to noise ratio = 40.80 dB\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "#Channel Bandwidth B\n", + "n = 8 # no. of bits used to encode\n", + "W = 4000 # the message signal banwidth in Hz\n", + "B = n*W#\n", + "print 'Channel width = %.2f Hz'%B\n", + "SNRo = 6*n - 7.2#\n", + "print 'Output Signal to noise ratio = %.2f dB'%SNRo\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.5 Page 207" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Maximum output signal-to-nosie = -5.17 dB for Delta Modualtion:\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import pi,log10\n", + "\n", + "a0 = 1 # The amplitude of sinusoidal signal\n", + "f0 = 4000 # the frequency of sinusoidal signal in Hz:\n", + "fs = 8000 # the sampling frequency in samples per seconds\n", + "Ts = 1/fs##Sampling interval\n", + "delta = 2*pi*f0*a0*Ts##Step size to avoid slope overload\n", + "Pmax = (a0**2)/2##maximum permissible output power\n", + "sigma_Q = (delta**2)/3##Quantization error or noise variance\n", + "W = f0##Maximum message bandwidth\n", + "N = W*Ts*sigma_Q# #Average output noise power\n", + "SNRo = Pmax/N# # Maximum output signal-to-noise ratio\n", + "SNRo_dB = 10*log10(SNRo)#\n", + "print 'Maximum output signal-to-nosie = %.2f dB for Delta Modualtion:'%SNRo_dB" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.13(a) page 215" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f4d48061750>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange,sign\n", + "from sympy import log\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,show,title,subplot\n", + "\n", + "#Caption:u-Law companding\n", + "#Figure5.13(a)Mulaw companding Nonlinear Quantization\n", + "#Plotting mulaw characteristics for different \n", + "#Values of mu\n", + "\n", + "x = arange(0,0.01+1,0.01)# #Normalized input\n", + "mu = [0,5,255]##different values of mu\n", + "def mulaw(x,mu):\n", + " \"\"\"\n", + " F(x) = sgn(x) ln(1 + μ|x|) / ln (1 + μ)\n", + " -1 <= x <= 1\n", + " \"\"\"\n", + " f=sign(x)*log(1+mu*abs(x))/log(1+mu)\n", + " return f\n", + "Cx=[]\n", + "\n", + "for i in range(0,len(mu)):\n", + " Cx.append(mulaw(x[i],mu[i]))\n", + " plot(Cx)\n", + "title('Compression Law: u-Law companding')\n", + "xlabel('Normalized Input |x|')\n", + "ylabel('Normalized Output |c(x)|')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.13(b) page 216" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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RiHixyO1vCLwZEVMAJF0P7ARMblHuV8DNuCtws/L33HNw6KHwt7/B0kvnHY2V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\nFSQ9VMQ2pvR2XNa/OTlY3uY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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f2ef2379c10>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange,sign,log\n", + "\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,show,title,subplot\n", + "\n", + "#Caption:A-law companding\n", + "#Plotting A-law characteristics for different \n", + "#Values of A\n", + "\n", + "x = arange(0,0.01+1,0.01)# #Normalized input\n", + "A = [1,2,87.56]##different values of A\n", + "\n", + "\n", + "def Alaw(x,a):\n", + " \"\"\"F(x) = sgn(x) A |x| / (1 + lnA) for 0 ≤|x| < 1/A\n", + " \n", + "= sgn(x) (1+ln A|x|) /(1 + lnA) for 1/A ≤|x| ≤ 1\n", + "\"\"\"\n", + " if abs(x) >= 0 and abs(x) < 1/a:\n", + " f = sign(x)*a*abs(x)/(1+log(a))\n", + " elif abs(x) >= 1/a and abs(x) <=1: \n", + " f = sign(x)*(1+log(a*abs(x))/(1+log(a)))\n", + " else:\n", + " f = 'Wrong parameters'\n", + " return f\n", + "Cx=[]\n", + "for i in range(0,len(A)):\n", + " #[Cx(i,:),Xmax(i)] = Alaw(x,A(i))#\n", + " Cx.append(Alaw(x[i],A[i]))\n", + " plot(Cx)\n", + " \n", + "title('Compression Law: A-Law companding')\n", + "xlabel('Normalized Input |x|')\n", + "ylabel('Normalized Output |c(x)|')\n", + "show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Digital_Communications_by_S._Haykin/Chapter6_zB6BWD2.ipynb b/Digital_Communications_by_S._Haykin/Chapter6_zB6BWD2.ipynb new file mode 100644 index 00000000..42bdaa3f --- /dev/null +++ b/Digital_Communications_by_S._Haykin/Chapter6_zB6BWD2.ipynb @@ -0,0 +1,512 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6 Baseband Shaping For Data Transmission" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.1(a) page 235" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7fc3cc0e5790>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,grid,title,show\n", + "\n", + "#Figure 6.1(c):Discrete PAM Signals Generation\n", + "# [3].BiPolar NRZ\n", + "#page 235\n", + "x = [0, 1, 1, 0, 0, 1 ,0 ,0 ,1 ,1]\n", + "binary_negative = [-1, -1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1, -1]\n", + "binary_zero = [0 ,0 ,0 ,0 ,0, 0 ,0 ,0 ,0 ,0]\n", + "binary_positive = [1, 1 ,1 ,1 ,1 ,1 ,1 ,1 ,1 ,1]\n", + "L = len(x)\n", + "L1 = len(binary_negative)\n", + "total_duration = L*L1\n", + "#plotting\n", + "for i in range(0,L):\n", + " if(x[i]==0):\n", + " plot(range(i*L-L,i*L),binary_zero)\n", + " \n", + " elif((x[i]==1) and (x[i-1]!=1)):\n", + " plot(range(i*L-L,i*L),binary_positive)\n", + " \n", + " else:\n", + " plot(range(i*L-L,i*L),binary_negative)\n", + " \n", + "grid()\n", + "title('BiPolar NRZ')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example6.2 Page 241" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Precoder output in binary form:\n", + "1 \t1 \t0 \t0 \t1 \t0 \t0 \t\n", + "\n", + "Precoder output in volts:\n", + "1 \t1 \t-1 \t-1 \t1 \t-1 \t-1 \t\n", + "\n", + "Duobinary coder output in volts:\n", + "2 \t2 \t0 \t-2 \t0 \t0 \t-2 \t\n", + "\n", + "Recovered original sequence at detector oupupt:\n", + "0 \t0 \t1 \t0 \t1 \t1 \t0 \t" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "b = [0,0,1,0,1,1,0]##input binary sequence:precoder input\n", + "a = [1^b[0]]\n", + "if(a[0]==1):\n", + " a_volts=[1]\n", + "\n", + "for k in range(1,len(b)):\n", + " a.append(a[(k-1)]^b[(k)])\n", + " if(a[(k)]==1):\n", + " a_volts.append(1)\n", + " else:\n", + " a_volts.append(-1)\n", + " \n", + "print 'Precoder output in binary form:'\n", + "for aa in a:\n", + " print aa,'\\t', \n", + "print '\\n'\n", + "print 'Precoder output in volts:'\n", + "for bb in a_volts:\n", + " print bb,'\\t',\n", + "print '\\n'\n", + "#Duobinary coder output in volts\n", + "c= [1+ a_volts[0]]\n", + "for k in range(1,len(a)):\n", + " c.append(a_volts[(k-1)]+a_volts[(k)])\n", + "print 'Duobinary coder output in volts:'\n", + "for cc in c:\n", + " print cc,'\\t',\n", + "print '\\n' \n", + "#Duobinary decoder output by applying decision rule\n", + "b_r=[]\n", + "for k in range(0,len(c)):\n", + " if(abs(c[(k)])>1):\n", + " b_r.append(0)\n", + " else:\n", + " b_r.append(1)\n", + "print 'Recovered original sequence at detector oupupt:'\n", + "for brr in b_r:\n", + " print brr,'\\t'," + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example6.3 page 246 " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Modulo-2 adder output:\n", + "1 \t1 \t0 \t1 \t1 \t0 \t0 \t0 \t0 \t1 \t0 \t\n", + "Delay element output:\n", + "1 \t1 \t0 \t1 \t1 \t0 \t0 \t0 \t0 \t1 \t\n", + "differential encoder bipolar output in volts:\n", + "1 \t1 \t0 \t1 \t1 \t0 \t0 \t0 \t0 \t1 \t" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#for generating bipolar format\n", + "#Refer Table 6.4\n", + "\n", + "x = [0,1,1,0,1,0,0,0,1,1]##input binary sequence:precoder input\n", + "y= [1]\n", + "for k in range(1,len(x)+1):\n", + " y.append(x[(k-1)]^y[(k-1)])\n", + "\n", + "y_delay = y[0:-1]\n", + "print 'Modulo-2 adder output:'\n", + "for yy in y:\n", + " print yy,'\\t',\n", + "print '' \n", + "print 'Delay element output:'\n", + "for yyy in y_delay:\n", + " print yyy,'\\t',\n", + "print '' \n", + "z=[]\n", + "for k in range(0,len(y_delay)):\n", + " z.append(y_delay[k])\n", + "print 'differential encoder bipolar output in volts:'\n", + "for zz in z:\n", + " print zz,'\\t'," + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.4 Page 247" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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CW8nGc+d46eBBjmRm8pq/P/3r18fTATGLI5mZTE9K4tPjx+lXrx4T/P1ppg2J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\nLJaQ+D+L1IOnq28nhgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f06f46b5e10>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange,sinc,sin,pi\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,grid,title,show,xlabel,ylabel\n", + "\n", + "\n", + "\n", + "#Different Line Coding Techniques\n", + "#[1].NRZ Polar Format [2].NRZ Bipolar format\n", + "#[3].NRZ Unipolar format [4]. Manchester format\n", + "\n", + "#[1]. NRZ Polar format\n", + "a = 1 # The Amplitude value\n", + "fb = 1 # The bit rate\n", + "Tb = 1/fb# #bit duration\n", + "f = arange(0,1/(100*Tb)+2/Tb,1/(100*Tb))\n", + "Sxxf_NRZ_P=[]\n", + "Sxxf_NRZ_BP=[]\n", + "Sxxf_NRZ_UP=[]\n", + "Sxxf_Manch=[]\n", + "for i in range(0,len(f)):\n", + " Sxxf_NRZ_P.append((a**2)*Tb*(sinc(f[i]*Tb)**2))\n", + " Sxxf_NRZ_BP.append((a**2)*Tb*((sinc(f[i]*Tb))**2)*((sin(pi*f[i]*Tb))**2))\n", + " if (i==0):\n", + " Sxxf_NRZ_UP.append((a**2)*(Tb/4)*((sinc(f[i]*Tb))**2)+(a**2)/4)\n", + " else:\n", + " Sxxf_NRZ_UP.append((a**2)*(Tb/4)*((sinc(f[i]*Tb))**2))\n", + " \n", + " Sxxf_Manch.append((a**2)*Tb*(sinc(f[i]*Tb/2)**2)*(sin(pi*f[i]*Tb/2)**2))\n", + "\n", + " \n", + "\n", + "#Plotting\n", + "plot(f,Sxxf_NRZ_P)\n", + "plot(f,Sxxf_NRZ_BP)\n", + "plot(f,Sxxf_NRZ_UP)\n", + "plot(f,Sxxf_Manch)\n", + "xlabel('f*Tb------->')\n", + "ylabel('Sxx(f)------->')\n", + "title('Power Spectral Densities of Different Line Codinig Techniques')\n", + "grid()\n", + "show()\n", + "#Result\n", + "#Enter the Amplitude value:1\n", + "#Enter the bit rate:1 " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.6 page 249" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7fd838395dd0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange,sinc,sin,pi\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,grid,title,show,xlabel,ylabel\n", + "\n", + "\n", + "#Figure 6.6(b): Ideal Solution for Intersymbol Interference\n", + "rb = 1 # The bit rate\n", + "Bo = rb/2#\n", + "t =arange(-3,1/100+3,1/100)\n", + "x = sinc(2*Bo*t)\n", + "plot(t,x)\n", + "xlabel('t------>')#\n", + "ylabel('p(t)------->')#\n", + "title('SINC Pulse for zero ISI')\n", + "grid()\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.7 page 250" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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b5m3MQVdLwkcE87OzNAyskbA0SLKzYcUKyGwzjyk9p5iDR47AqVN2fITF4oY1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\nGS5sG8F3+46x8PtUKC6meWEon6UeqtNGYjgw083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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7efc2eb58310>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange,sinc,sin,pi,zeros,cos\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,grid,title,show,xlabel,ylabel,legend\n", + "\n", + "#Figure6.7(b):Practical Solution for Intersymbol Interference\n", + "#Raised Cosine Spectrum\n", + "\n", + "rb = 1 # The bit rate\n", + "Tb =1/rb#\n", + "t =arange(-3,1/100+3,1/100)\n", + "Bo = rb/2#\n", + "Alpha =0# #Intialized to zero\n", + "x =t/Tb#\n", + "p=zeros([3,len(t)])\n", + "for j in range(0,3):\n", + " for i in range(0,len(t)):\n", + " if((j==2) and ((t[i]==0.5) or (t[i]==-0.5))):\n", + " p[j,i] = sinc(2*Bo*t[i])\n", + " else:\n", + " num = sinc(2*Bo*t[i])*cos(2*pi*Alpha*Bo*t[i])\n", + " den = 1-16*(Alpha**2)*(Bo**2)*(t[i]**2)+0.01\n", + " p[j,i]= num/den\n", + " \n", + " \n", + " Alpha = Alpha+0.5#\n", + "\n", + " \n", + "plot(t,p[0,:])\n", + "plot(t,p[1,:])\n", + "plot(t,p[2,:])\n", + "xlabel('t/Tb------>')\n", + "ylabel('p(t)------->')\n", + "title('RAISED COSINE SPECTRUM - Practical Solution for ISI')\n", + "legend(['ROlloff Factor =0','ROlloff Factor =0.5','ROlloff Factor =1'])\n", + "grid()\n", + "show()\n", + "#Result\n", + "#Enter the bit rate:1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.9 Page 254" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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jUcH93n0XVltt2QRyHMdpydTVhfAef/lL6REmsswnsQ0w2Mz2jMtnAouSzmtJ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\nBM6N87cCf8urc1Sc3wUYA3w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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7ff3f5724410>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange,sinc,sin,pi,cos\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,subplot,grid,title,show,xlabel,ylabel\n", + "\n", + "\n", + "#Caption:Frequency response of duobinary conversion filter\n", + "#Figure6.9:Frequency Response of Duobinary Conversion filter\n", + "#(a)Amplitude Response\n", + "#(b)Phase Response\n", + "rb = 8 # the bit rate\n", + "Tb =1/rb# #Bit duration\n", + "f = arange(-rb/2,1/100+rb/2,1/100)\n", + "Amplitude_Response = [abs(2*cos(pi*ff*Tb)) for ff in f]\n", + "Phase_Response = [-(pi*ff*Tb) for ff in f]\n", + "subplot(3,1,1)\n", + "plot(f,Amplitude_Response)\n", + "xlabel('Frequency f---->')\n", + "ylabel('|H(f)| ----->')\n", + "title('Amplitude Repsonse of Duobinary Singaling')\n", + "subplot(3,1,3)\n", + "plot(f,Phase_Response)\n", + "xlabel(' Frequency f---->')\n", + "ylabel(' <H(f) ----->')\n", + "title('Phase Repsonse of Duobinary Singaling')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.15 page 259" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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KOOOpmX1lZgMKa5aKy9KlcMQRbg7Xc86JW00gDs44w00p2Leva2JaTjzxBNx5\nJzz/vJsLO9C46NzZXfvTTnMjypaSmpqPfmRm28Q5T3GaHsumNRfM3Evg22/hv/+FZuXQpzoQC1VV\nboIhM3jkkfKYc3r0aDjwQNdwoWcsM34EyoVhw6BfP9estFu3+udX3+ajn0saD2wq6ZO0v4/zELGf\npC8ljZd0YYbtFZLmSRrj/y7JNe98uPlmN8bHE08EI9DYadLEVcJOnlwe/QsmTIBDDoH77w9GIOAG\nvLziCtdqbO7cEh20prgR0A74GOhMWv+B2mJOfv+mwNd+n+bAWGDztDQVwNAc8qpzjOy558zat3cx\nuGLTWOObxaDYGmfONOvSxWzIkPrlUx+dc+eabb652S231E9DLiThmpsFnSnOPtvsd79zQ6bUB+pZ\nR4CZzTSzrc1skplNjP7laGd6AV/7fZYAjwEHZUhXtLYRH3wAJ5/sauUb63SGgcysv76LyZ5zDrz9\ndumPv2SJ6yj2u9/BWWeV/viB8uaGG6BFC3dvFHkkoBrrCF4A7gdeMLNFadvWwE1b2c/MsnbRkXQY\nsK+Z/dGvHwvsaGZnRdLsATwDTMWNOnqemX2eIS/LpjUbU6a4ZoO33AL/93957RpoRLz0Epx0kqug\n26hE/eTN4JRTYMYMNzxx06alOW4gWcyf7xq3nHQS+IFO86a+cxafAJwJDJK0DJiB+3Jv5/d7HKht\nPKJc3twfAp3MbJGk/YHncE1T68WCBS7G9uc/ByMQqJn993fDOPTp4zyDNm2Kf8zrroP//c/VWwUj\nEMhG69auccvOO7uK4z55zxqfGzUNMTEbuAy4TFI7XD0BwCQzm5lj/ulzDXTCfflHj7MgsvySpDsk\nrWVmP6Rnlut8BFVVsN9+lXTsCOefv/L2Yq6nfiuH8dJrWm+o8xHUdX3LLd348EceWcHzz8OoUbnv\nn37ta0s/dChcd10ld9wBrVoV53ziLs/6rOdbnnGtl6o8O3eGSy6p5Jhj4M03K9h664TNR4AzNN/g\nKotbkLmyeH2qQ1S9gIlZ8sq5cuTii812261+8wrUlVDRVThKrXHJErN99jE766z89stH56efmq2z\njtno0fkdoxAk4ZqbBZ3ZePRRsw03NJsxI7/9qM98BJJ+ojq0Y6xYoWtm1joXQ+PDPTfjWhDda2ZX\nSzrVZ/JvSWcApwFLgUXAADMbnSEfy6Y1yuOPw4UXwnvvwXrr5aIwEKhm3jzYZRfX5+T00wub9/ff\nQ69ermlEgmoTAAAgAElEQVTgcccVNu9A4+DKK92IuiNHuqEpcqFe8xGkZRR7p7JcDMEHH7hhe0On\nnEB9+OYbV0H36KOFG4tqyRLXPnz77eHaawuTZ6DxYeZGK23RAh54ILexqAo+eX05M3Om65Rz113x\nGoFofLOcSYLOuDR27ep6HB91VG4D1OWic8AA9wV39dX111dXknDNIeisCclNZvPpp4UdqbRBGIJf\nf3Utg0480Y3fHgjUl732gksucWMSLVhQe/qa+M9/nJf66KOhhVCg/qy+uusXdeONrulzIaipjuBQ\nqusGrgPOo7qewMzsmcJIyI1soSEz18Z23jw321iTBmHaAuVAqq3/nDnw9NN1u7feeAMOP9w1E92k\n3o2iA4Fq3nrLRUHeeAM22yx7uvrOWXw/1ZXFIq1PgJmdkIfmepPNEPzrX85VeuutMGJjoPAsXgx7\n7+3qCq68Mr99J02CnXZysdx99imOvkDj5t57XZ3Tu+9C27aZ0+RiCIrafLSQf2RoPjpsmFm7dmYT\nJuTWjKoUhKZvhaNcNM6a5ZrtPfFE5u2ZdC5YYLb11mY33VRcbflQLuVZG0Fnfpx1ltm++5otXZp5\nO/UZa0jShrn+1d2e1Z3x410TvMcfD/MNB4rLeuu5mOzpp8PYsbWnr6qC/v3dlJhnn110eYFGzo03\nurlWLlxpbOfcqSk0VEluQ0RgZkWf8DEaGpo3z7nc55zjYriBQCl44gm44ILa+6gMGuTGlB8xAlZZ\npXT6Ao2X77+HHXeEyy6D449fcVvB+hGUAylDsGyZa8mx0UZuzuFAoJRceilUVsLw4a4tdzpPP+0+\nUN57D9q1K7m8QCPms8+gosKNTbTjjtW/l0U/gtompvFpbvHbP5JUY8e1iy5yUwzedFNx9NaX0Aa6\ncJSjxkGDYO214cwzq4cGTun86CP405/g2WfL0wiUY3lmIuisGz16uMrjQw+FadPy27eohkBSU+A2\nYD9gC+AoSZunpekNdDOz7sApwJ3Z8hsyBJ56yjUTbd68iMLrwdhcgshlQBJ0lqPGJk3goYfcKKV3\n3OF+Gzt2LLNnu7mQb73V1Q2UI+VYnpkIOutO376uLuuQQ/Kbk7vYHkEuE9P0BR4AMLN3gbaS1s+U\n2YABbuz2tdcupuT68eOPP8YtISeSoLNcNbZqBUOHwlVXweuvw/ff/8hhh7l5kI88Mm512SnX8kwn\n6KwfAwfCxhu7+tNcI//Fnr23AzAlsj4V2DGHNB2BWemZ3XMPbLlloSUGAvmz8cZuGIqjj3YfJl27\nOsMQCMRNahiK3XZzLYpyodgeQa410ekVGRn369u3fmJKwcSJE+OWkBNJ0FnuGlPDUMycOZEhQ8q/\nV3u5l2eKoLP+pIahuPnm3NIXtdWQpJ2AK8xsP78+EKgys2siae4CKs3sMb/+JbCHmc1KyysZzZsC\ngUCgzKit1VCxQ0PvA90ldQGmA0cAR6WlGYqbEvMxbzh+TDcCUPuJBAKBQKBuFNUQmNlSSWcCw6ie\nmOaL6MQ0ZvaipN6SvgYW4uZKDgQCgUCJSEyHskAgEAgUhzKv3loZSedKqpK0VtxaMiHpKt8xbqyk\n4ZI6xa0pE5Kuk/SF1/qMpDZxa8qEpMMlfSZpmaTt4taTTi4dJuNG0mBJsyR9EreWmpDUSdIIf70/\nlfTnuDWlI2lVSe/65/tzSTFONVQ7kppKGiPp+ZrSJcoQ+Jfq74FJcWupgWvNbBsz6wk8B1wet6As\nvAL0MLNtgK+AgTHrycYnwCHAG3ELSSeXDpNlwn04jeXOEuAcM+sB7AScUW7laWa/AHv653trYE9J\nu8UsqybOBj6nlhaciTIEwI3ABXGLqAkzi85n1RKYE5eWmjCzV82syq++i+u7UXaY2Zdm9lXcOrKQ\nS4fJ2DGzN4G5ceuoDTObaWZj/fJPwBdA+3hVrYyZLfKLLXB1nz/EKCcrkjoCvYF7WLmJ/gokxhBI\nOgiYamYfx62lNiT9XdJkoB/wz7j15MCJwItxi0ggmTpDdohJS4PCtzTcFveRUlZIaiJpLK7T6wgz\n+zxuTVm4CTgfqKotYbGbj+aFpFeBTMN1XYwLXUTneYqtOWkNOi8ys+fN7GLgYkl/xV2MWFpC1abT\np7kYWGxmj5RUXIRcdJYpoaVFEZDUEngKONt7BmWF96R7+nq1YZIqzKwyZlkrIKkPMNvMxkiqqC19\nWRkCM/t9pt8lbQlsBHwkCVwY4wNJvcxsdgklAtl1ZuARYvzSrk2npP4413HvkgjKQh7lWW5MA6KN\nATrhvIJAHZHUHHgaGGJmz8WtpybMbJ6kF4DtgcqY5aSzC9DXD+q5KtBa0oNmdnymxIkIDZnZp2a2\nvpltZGYb4R627eIwArUhqXtk9SBgTFxaakLSfji38SBfAZYEyq1T4fIOk5Ja4DpMDo1ZU2KR+8q7\nF/jczHIcHKG0SFpHUlu/vBqu8UrZPeNmdpGZdfLvyyOB17MZAUiIIchAObvkV0v6xMcQK4BzY9aT\njVtxldmv+uZld8QtKBOSDpE0BdeK5AVJL8WtKYWZLcX1ih+Ga5nxuJl9Ea+qlZH0KPA2sImkKZLK\ntdPmrsCxuJY4Y/xfubV22gB43T/f7wLPm9nwmDXlQo3vzNChLBAIBBo5SfUIAoFAIFAggiEIBAKB\nRk4wBIFAINDICYYgEAgEGjnBEAQCgUAjJxiCQCAQaOQEQxBIBH4Y6jGRvw3j1lQoJD3qhwM/O24t\ngcZJ6EcQSASSFphZqyzbBGAJvJkltQPeNLPutSauOZ+2ZvZjgWQFGhnBIwgkEj+swzhJD+DmLOgk\n6XxJ7/mv6ysiaS/2ad+U9Iikc/3vlZJ+45fXkTTBLzf1E/ek8jrF/17h93nST+ozJHKMHSS95Scs\nGS2ppaSRkraJpBklaau0U3kF6OC9nPqMa3++nzDlFEmt65FPoBESDEEgKawWCQs9jesy3w243cy2\nBDYDuplZL9zwxb+RtLt/0R8BbIMbYG8HqrvbG5m73p8E/Ojz6gX80Q+LDNATN9nHFsDGknbx4ww9\nBvzZT1jyO+Bn3Lg5/QEkbQKsYmbps4QdCHxjZtua2ai6Fo4f8fY4YGPcgIyDJe1a1/wCjYtgCAJJ\n4Wf/stzWzA7FDUA3ycze89v3AfaRNAb4ANgU6A7sBjxjZr/4SYNyGRRuH+B4n9doYC2c0THgPTOb\n7sNQY3Gj4m4KzDCzD8BNqmJmy3BDKfeR1Aw358N9GY5VsIH0zOwrM/ur1/M6bmymshy8LVBelNUw\n1IFAnixMW7/azP4T/cFXwEZfttHlpVR/DK2alteZZvZqWl4VwK+Rn5bhnqGMdRNmtsjPtXAwcDhQ\n45zLkv6O81oMN7Txh355KG6Ey8v9+h+BM3CezzQz6+P3F7AnzujsAPwLNztVIFAjwRAEGgrDgKsk\nPWxmCyV1ABbj5jq+X26S8eZAH+Auv89E3Av3feCwtLxOlzTCzJb6sE62eQYMGAdsIGl7M3tfUitg\nkfcK7gH+C4w0s3k1nUBqQqPITz3TkkTH5z8xukHSMcCluPqSe4Hjklh5HoiHYAgCSSHTS235b2b2\nqtxE5+/4RkQLgGP9DE2PAx8Bs4H/Ue0VXA884SuDX4jkdw/QBfjQf2XPBg4hS52CmS2RdARwqx+j\nfhFunPqFZvahpHlkDgvVdG75MhHY1cy+L0BegUZGaD4aaFRIuhz4ycxuKNHx2uPmtd20FMcLBOpC\nnSqLJbWTFCqaA0mlJF8/ko7HVTZfVIrjBQJ1JW+PQNJauLlajyr3OUUDgUAgUDt1+ao/BngV19Y6\nEAgEAgmnLobgBFzTtU6SNiiwnkAgEAiUmLwMgaTtge/MbArwEL7XZCAQCASSS74ewcnAYL/8EHB8\nYeUEAoFAoNTkbAgkrQHsCzwLYGazgXG+t2UgEAgEEkrOrYYkNQfWMrNZkd9aA5jZ/OLICwQCgUCx\nydkjMLMlaUagj5nND0YgEAgEkk2dexZLGmNm2xZYTyAQCARKTOgdHAgEAo2c+hiCUwumIhAIBAKx\nUR9DcHLBVAQCgUAgNupjCHYomIpAIBAIxEZ9DMHsgqkIBAKBQGzUp9XQBmY2o8B6AoFAIFBi6uMR\nvFAwFYFAIBCIjfoYAtWeJBAIBALlTn0Mwd0FUxEIBAKB2KiPIVhWMBWBQCAQiI36GII/FUxFIBAI\nBGIj1BEEAoFAI6c+zUc7mtnUAusJBAKBQImpj0dwV8FUBAKBQCA26mMIOhRMRSAQCARioz6GYEzB\nVAQCgUAgNupcRxAIBAKBhkGYmCYQCAQaOcEQBAKBQCMnGIJAIBBo5DTLNaGk9YDDgd8CXQADJgFv\nAE+aWZifIBAIBBJITpXFku4FugIvAe8BM3A9izcAegH7AV+bWZi+MhAIBBJGroZgazP7uL5pAoFA\nIFB+5FpHcBOApGuyJQhGIBAIBJJJrnUEG0jaFThI0uO4sNByV8LMPiyGuEAgEAgUn1xDQ4cDJwG7\nAu+nbzezPQsvLRAIBAKlIK+exZIuM7Mri6gnEAgEAiUmV49gYzP7tpY0Xc3sm4IpCwQCgUBJyNUQ\nPA6sAQzFhYaizUe3B/oCC8zsyOJJDQQCgUAxyDk0JKkbcCSunqCz/3kSMAp4tDaPIRAIBALlSRh9\nNBAIBBo5OTUflXQokeai6ZjZMwVTFAgEAoGSkms/ggNxhkB+eWja9mAIAoFAIKHkHRqSNMbMti2S\nnkAgEAiUmDAMdSAQCDRygiEIBAKBRk6ulcXPR1Y3Sls3M+tbWFmBQCAQKBW5diirqGGzmdnIgikK\nBAKBQEkJ/QgCgUCgkZNzHYGkNSU9mPbbOZL2Lrys8kBSpaST4tYRWBFJh0iaImmBpG1KdMwKSVMi\n659K+q1flqT7JP0gabSk3SR9WYjjlBpJE7M905J2r+t5lZJS6ZTURVKVpCZ+/UVJxxX7uMUgZ0Ng\nZnOBjpJ6AkhqBpyJm7oysfgbf5F/qcz0D/QafrNRQ0e6EumrkvST1zdN0i2+7Bsz1wOnm1krM/so\nfaMvs1mSmkZ+ay5ptqSqQggwsy3N7A2/uhvwO6C9me1kZqPMbLNCHCedtPthjqTXJP2hgIfIes+b\n2ZvFOq98kdRD0iuSvpc0V9L7kvaH+HSaWW8ze6jUxy0E+bYauhc40S/vB7xpZgsKK6nkGNDHzFoB\n2+EG0bskXkkrsbXX91vg/4BTYtYTG5IEbAh8XkvSH4D9I+v7+9+KYdg7AxPN7Jci5J2J1P2wCXA/\ncJuky0p07ILjPSrludvzwDBgfWA94M/A/EJrayzkawieBvaX1AI4AWcYGgxmNh14GegR+bmLpFGS\n5ksaJmnt1AZJT0qaIelHSSMlbRHZ1lvSZ36/qZLOjWzrI2ms/5J5S9JWOer7BngLiB4na17e2/mr\n1/GDpMGSVvHb1pH0X7/f95LeSD2Mkjb3YbG5PgRyYCTP+yXd7ved70MhG0e23+S/xudJ+lhSD//7\nKpKulzTJe153Slo103n698IlXv8sSQ9Iau21LwCaAh9JGl9DcT0EHB9ZPx54ENc7PnWc9pKG+vMf\nL+nkyLbV/Ln+IOkzYIc0jRMl7S0XOrwb2Nl/pV+ulcNI7SU97T2SbyWdletxasLMfjCzIcBpwEBJ\na0a1RY5xhaSHIut9/T0xV9IISelfz72y3DPp5zVR0rmSPvLPwGORtG39PTLb5/O8pA6RfSsl/U3S\nW8BC4FxJK0x6JWmApOfSz1vSOkAX4G4zW2pmS8zsbTN7K1+dfvsFkqbLPacny3ldG/ttB0ga4+/n\nyZIuz3Y9FAklS+ov9964zp//t5L2i6TdyD9z8yW96p+p+LwJM8vrD7gVFxL6JN99y/EPmADs7Zc7\nAZ8Cg/x6JfA10A1YFRgBXB3Ztz9ueO7muHmdx0S2zQB29cttgG398rbALNwDL9wLagLQIou+KqCr\nX94MmA4cX0tezf32icDHQAdgTdxIsVf5bVcDd+Jeqk0jWpv7c/4rrnnxnrgvrU389vuBOTjPqSkw\nBDf6LMC+uGHKW/v1TYF2fvkm4DmgLdASN0zJP7Kc84nAeNzDvgbuA+TBtDLZuIZrWoUz5jOB1v7c\nZ/rfqiLp3gBuA1oA2wCzgT39tn8CI73ejv6+mJx23+zll/vhvOPUtgpgil9uAnyA8zKbARsB3wD7\n5HKcLOe2cdpvzYElwL7p2vz65cBDfnkT4Cdgb3/9zvdl3SyHe2b5eUWOMxpo59N+Dpzqt60FHIJ7\nbloCTwDPRvat9Mfa3JdRC+B7YLNImjHAIRnKQMBXOK/gIGD9tO356NwP96xuDqyGu5+XlzGwB9DD\nL2+Fu48O8utdfNomfn0EcGLk3bAYN7OjgD8B0yKa3gGu9ffErsA8Ivd4yd+DdXhxbgP8DFwQl+iC\nFoC7GRcAc/3ybcAqkQt7USTtacBLWfJp62+KVn59Ei6E0zot3Z3AlWm/fQn8Nku+Vf4m+ckv35JD\nXrtHHoBTItv2B772y4NwL+auafvvDsxI++0R4HK/fD/wn7Q8v/DLewHjgB1TD4f/XV7/xpHfdga+\nzXLOw4E/RdY38Q9Vk0iZ1GYIuuK+1E/xD+G//W9VPk0nYCmwRmS/fwD3+eXlL2u//kdWfrmkDEF/\nshuCHYFJafoGAoNzOU6Wc1vp3HEvs6PStfn1K6g2BJcCj6Vdm6mp+6+We6aClcvg6Mj6NcCdWXT3\nBH6IrI8ArsjwbPzNL/fAhfKaZ8mvA+6j9GtgGc6YdstXJzAY+HtkW9ea7i/gZuBGv9yFmg3B+Mh+\nq/u06+FCm0uAVSPbH0pdozj+8u5ZbK5y7mLgvnz3LVMMZ+HXNLMuZnammf0a2T4zsvwz7usGSU0l\n/VPS15Lm4W42A9bxaQ8FegMTvcu4k/+9M84Nnpv6w30JblCDxm3NrCVwBHC8pM615NU+sm+0Bcrk\nyLbrcA/RK5K+kXSh/7192j7gjFpqP8N5ISuViZm9jjOktwOzJP1bUitgXdyD8EFE50uRskpnA3/M\nqO5muHhwrhguFNQPOI60sJA/nx/MbGHacdpHtqeXXV3oDLRPu0YDcS+EghxHUnNcGf+QQ/L20WOY\newtNwb1YU2S7ZzKR7flY3V//if75GAm0kVaoC0i/zx4AjvbLxwGPm9mSTAc1s2lmdpaZdcOV8ULc\nNc5VZ6pByAZpOqZGd5K0ow+fzZb0I3AqsDa5sfyYZrbIL7ak+t6L1inF1lIM6jjEhJndaGbfFVpM\nwjgaNzPb3mbWBufyy/9hZu+b2cG4B/Q5nGsM7sH6uzc8qb+WZvZ4bQc0syeB/+K+8HLNa8O05ek+\nr5/M7Dwz6+rPY4CkvYBpQKe0B7az/71WzOxWM9seV4+xCS708B3u4dsiorOtmbXOks103NdWVPdS\nVjRAuWh5ExcOWM98/DjtGGtJapl2nNR5zmDlsqsLU4AJadeotZn1KeBxDsKVT6oF30KqX3TgysD8\n8jSqJ5ZKVb53YsXrm/GeyZNzcde/l38+9iDyfHgsuoOZjQYWyzXLPQr3lVwrZjYVuAPYsg46Z+DO\nP0WntO2P4J7fjmbWFriL+g/NMwN3760W+a2u91dBCGMN1U621gwtgV+BH+Sam/5j+Q6uqeIxktqY\n2TJc6GmZ33w38CdJveRYw1dItVzpCJn5J3CUpI455CXgdEkdJK2F8+Qe8xr7SOrmXwTzvb5lwLvA\nIuACfx4VQJ/UfjWUB5K2919QzX0evwDL/Ffn3cDNktb1aTtI2idLVo8C58i1026JK9vHzKwuTT8P\nxBm6FTCzKcDbwNVyFdlb4+omhvgkT+AqYNv6sj4rPY8ceQ9Y4CskV/Oe5JaStq/HcVKV+mtJOgbn\nhf3TXBNvgLHAkZKa+eMcGtn3SeAASXv563Qu7jq9Hcn7jEz3TJ60xBn/eT6fy7OdRxoP+fNZbGZv\nZ9ieqogeJKmrpCZylccn4uLuuZI69hPACZI2k7Q6LnSWfh5zzWyxpF64D0CjHpjZJFxd2hX+GdsZ\n94zVK9/6EAxB7Vjacmr9QVz4Yhqugu+dtLTHAhO8W3wKcAyAmX2AiwPfhnPlx7Ni65aajo+ZfQq8\nDgyoIS+L7PsI8AouFj0e+Jvf1g14FWek3gZuN7OR3hU/EBcb/s7nfZyZfZWhDNI1tgb+47VMxFUq\nX+e3XYgLRY32ZfIq7osxE4NxL4Q3gG9xRiX6gqztgVm+3cw+N7Mvsux7FM7zmI6bU+MyH94CV4cy\nCRfyexl3vbMdN2uZ+A+BPrgY+be4Mv0PrqzyPU6KjyQtwF3PE4G/mNkVke2X4mLdc3He48PLRZmN\nw92bt3otBwAHmtnSiO6HyXzPLD+vLETL4WZc5esc3P31UoZ9M+X1EK5+YEiGbSkW47ya13D1Z5/g\njE7/fHWa2cvALbj4/ldUG5NUePh04EpJ83Hlmu65531PeI7B1ZN9D1zl811cg+aiUlZDTMh1AHof\nmGpmB9aWPlAzkiYAJ0VeboFAWePDJbNw9WLfxHD8zXGGpUUdPdC6Hvdx4HMzG1SqY0YpN4/gbFzT\nrvKxToFAoJScBrxXSiMgN2TJKnL9MK4BhhbbCPgwaiq0tT8ufLlSn4lSUTaGwMdHewP3UEMcOhAI\nNEwkTcSFAM+tJWmhOQXnhXyNa9Z5WgmO2Q4XjlqA62PzJ8swXEqpKJvQkKQncZWCrYHzQmgoEAgE\nSkNZDF4mqQ8w28zGKMvcB5LKw2IFAoFAwjCzGqMs5RIa2gXo6ys3HwX2UtqQ15B/L+g4/vr16xe7\nhoaiMwkag86gs9z/cqEsDIGZXWRmncxsI+BI4HUzq6lJZSAQCAQKRFkYggwkNgzUpUuXuCXkRBJ0\nJkEjBJ2FJugsPeVSR7AqbiySVXCjEP6/eBXVnYqKirgl5EQSdCZBIwSdhSboLD1lYQjM7BdJe5rZ\nIrnZt0ZJ2s3MRsWtLRAIBBo6ZRMasurR+VrgxknPZSTFQCAQCNSTcupH0AT4EDdGyp1mdkHadtt+\ne2OzzWDTTVn+v3t3WDXjPFeBQCAQkITV0ny0bAxBCkltcHOR/tXMKiO/29tvG+PGwZdfsvz/hAnQ\nvv2KxiH1v107yHsm1EAgEGhAJNIQAEi6FPjZzK6P/Gb9+vVbXlPftm1bevbsya67VjBhAjz1VCVT\npsCSJRWMGwcff1zJ0qXQo0cFm24KLVpUsuGGcOihFXTrBqNHVwLVFT6VlYVZT/1WqPyKtX7zzTfT\ns2fPstGTaX3s2LH85S9/KRs92dbTr33cerKth/JsHOVZWVnJ/fffD7iWTYMGDUqGIfDjiS81sx/9\n6IPDcPMGD4+ksXy1fv+98xxSfylPIuVFpHsQm20G669fPy+isrJy+cUpZ5KgMwkaIegsNEFnYUmM\nRyBpK9w0dU3830Nmdl1amrwNQTaWLHHGID3MNG4cLF6cOczUrVuoiwgEAskjSYagE25CjvVwncn+\nY2a3pKUpmCGoiagXETUSEydChw6ZjUR9vYhAIBAoFkkyBO2AdmY21k9N+AFwsEVmliqVIcjGkiXw\n7beZjcTSpc4gpOoi9t+/gs02c17EKqvEJrlGkuDWJkEjBJ2FJugsLLkYgnLpUDYTmOmXf5L0BdAe\n+KLGHUtI8+bVL/t0Ul7El1/Cq6/Cgw+69YkToWPH6v2insR66wUvIhAIlAdl4RFEkdQFN9xEDzP7\nKfJ7rB5BXYh6EVEP4ssvYdmy7HUR5epFBAKB5JGY0FAKHxaqBP5mZs+lbUucIaiJOXMyh5kmTar2\nItKNRPAiAoFAviQmNAQgqTnwNDAk3Qik6N+//0r9CMqh3W50PfVbbek//dStn3jiitt32aWCb7+t\n7hcxenQFDzwAn3xSSVUVbLlldb+ITp3gsMMq6NoV3nknP72hH0Hh1tOvfdx6sq2H8mwc5VmZ1o8g\nF8rCI5AkXPPR783snCxpEuERVBaxAmnOnGrvIepJpLyITP0i1l03sxdRTJ2FIgkaIegsNEFnYUlM\naEjSbsAbwMdUz0Uw0MxejqRJhCGIg8WLXV1EupH48kswqzYM6XURLVrErTwQCBSbxBgCAEmDgQNw\ncxdvlWF7MAR5Ypa9LmLyZOjUKXNdRDYvIhAIJI+kGYLdgZ+AB5NsCJLiLr76aiUdO1ZkNBKQuclr\n166l9SKSUpZBZ2EJOgtLoiqLzexN33Q0UAKaN4fNN3d/UVJeRDTMNHiw+z95Mmy4YWYjsc46wYsI\nBJJK2XgEsLwPwfNJ9ggaMosXwzffZO4XIWWuiyi1FxEIBFYkUaEhCIYgqZjBd9+taCBSy1OmVHsR\n6XURwYsIBIpPokJDudCQ+hHEvV7IfgQSfP65W//jH1fcvvPOFXzzDTz9tOsXMWpUBffe6/pFNGlS\n3S+ieXM3X0SqX8Rbb5VvO+309fRrH7eebOuhPBtHeVYmtR9BiobgEVQmpAIpbp0pLyJTv4gpU6Bz\nZ1h77Up23bVipbqIciPussyVoLOwJEVnokJDkh4F9gDWBmYDl5nZfZHtiTAEgfrz66+uLiJTv4im\nTbPXRTRvHrfyQKD8SJQhqI1gCAJmMHt25rqIqVOdF5GtLiIQaKwkyhBI2g+4GWgK3GNm16RtT4Qh\nSIq7mASd+Wj89Vf4+uvMneeaNcvc5HXjjQvjRSShLCHoLDRJ0ZmYymJJTYHbgN8B04D/SRoanZgm\nEKiJVVaBHj3cX5SUFxH1IEaOdP+nToUuXTIbibXXjuU0AoFYKAuPQNLOwOVmtp9f/yuAmf0zkiYR\nHkEgOaS8iEwV1s2aZa6LKJQXEQiUisR4BEAHYEpkfSqwY0xaAo2EmryIWbNWNAwjR7rladOqvYj0\nuojgRQSSSrkYgpw+9UM/gvLsR1Cs9bjaaUvw5Zdu/dRTV9y+004VfP216xcxeTLMmFHBdde55WbN\nYKutqvtFdOoEhx9ewUYbuX4RpS6/9PVybfeevp7+LMWtJ9t6uZZnZVL7EUjaCbgiEhoaCFRFK4yT\nEgWqp7IAAA2wSURBVBqqTEgFUhJ0JkEjOJ177FHBrFmZw0zTpsFGG2Wui1hrrdLqTEp5Bp2FIzGt\nhiQ1A8YBewPTgfeAo6KVxUkxBIFAOr/8kr0uokWL7HURzcrFXw8kmsQYAgBJ+1PdfPReM7s6bXsw\nBIEGhRnMnJm5X8T06c6LyGQkSulFBJJPIgyBpMOBK4DNgB3M7MMs6RJhCJLiLiZBZxI0QnF0/vxz\ndb+IdCOx6qqZw0wbbVSzF9GYy7MYJEVnUloNfQIcAvw7biGBQLmw2mqw1VbuL0rKi4gah+HD3f/p\n011IKZORWHPNeM4jkAxi9whSSBoBnJt0jyAQiIuUFxHtVZ0yFquumjnMVJsXEUg+iQgNpQiGIBAo\nDmYwY0bmMNPMmdnrIoIX0TAom9CQpFeBdhk2XWRmz+eaT+hHEPoRlJO+1Hr6tY9bT/q6BF99VclH\nH61cnjvuWMH48fDMM64vxJQpFdx+O3z6aSWrrlrdL6JZMzdfxOGHV9ClC4waVTy95V6eqfVyvT8r\nk9qPABqOR1CZkAqkJOhMgkZomDpTXkSmMNPMmdV1EVFPolBeREMszzhJYmjoPDP7IMv2RBiCQKCh\n8/PPMH58ZiOx+uqZw0xduoS6iLhIhCGQdAhwC7AOMA8YY2b7Z0gXDEEgUMaYuZZLmeoiZs1yXkQm\nI9G2bdzKGzZJMQTXAX2AxcA3wAlmNi9DukQYgqS4i0nQmQSNEHTmwqJFzotINxLjxsEaa6xoGH79\ntZI//MHVRTRtGovcnEjKdS+byuJaeAW40MyqJP0TGAj8NWZNgUCggKy+OmyzjfuLkvIiosbh7bfh\n3/92XkTXrpnrIoIXUVhi9wii+DDRoWZ2bIZtifAIAoFAYUh5EZnqIlq2zF4XUc5eRBwkIjQURdLz\nwKNm9kiGbcEQBAIBzNyIrpnqImbPdl5EJiPRpk3cyuOhbAxBLv0IJF0MbGdmh2bJIxGGIClxwyTo\nTIJGCDoLTX10LlyYvS6iVauVw0ybbQadO9fNi0hKeZZNHYGZ/b6m7ZL6A71xw1BnJSkdyspJT7b1\nsWPHlpWebB12yklP0tcbS3n27Ak//ljJ+uvD5Ze77SNGVDJnDqy5ZgXjxsFrr1Xy8MPw3XcVzJ4N\n7dq5DnO77+460P30k5tYqE+f5JVnZRI7lEnaD7gB2MPM5tSQLhEeQSAQSBYpLyK9LuKrr5wXkT4l\n6aab1t2LiIOyCQ3VKEAaD7QAfvA/vWNmp2dIFwxBIBAoGVVV2esi5szJXhfRunXcylckKYbgKqAv\nbt7i74H+ZjYlQ7pEGILKhMQNk6AzCRoh6Cw0SdC5cCE88kglrVpVrFQX0aZN5rqIDTeMx4somzqC\nWrjWzC4FkHQWcDlwcrySAoFAIDtrrAHdu0O6vUp5EdEw0wsvuOU5c6Bbt8z9IuL2ImL3CKL4Sevb\nmNlKHcqS4hEEAoFAJhYudPUOmeoi2rTJXBdRCC8iEaEhAEl/B44DFgE7mdmPGdIEQxAIBBocVVUw\ndeqKxiH1//vvnReRqS6iVavc8i8bQ5DrfASS/gpsamYnZMgjEYYgCfFNSIbOJGiEoLPQBJ3V/PST\n8xjSK6y/+soNs5E+JWnKi2jSpDqPsqkjqK0fQYRHgBezbQz9CEI/grBe9/VQnsksz+22g/nzK9lg\nAxg0yG1//fVKvvuuul/E8OGVPPggzJ5dwezZlay++v20aQOdO3chF2IPDUnqbmbj/fJZQC8zOy5D\nukR4BIFAIBAnKS8i5UFceWWZhIZqFCA9BWwKLMMNQ32amc3OkC4YgkAgEMiTXEJDTWraWArM7DAz\n2wp4CDgEWBqzpHqRcunKnSToTIJGCDoLTdBZemI3BACSOgG/BybFraW+pGLv5U4SdCZBIwSdhSbo\nLD1lYQiAG4EL4hZRCH78caWWr2VJEnQmQSMEnYUm6Cw9sRsCSQcBU83s47i1BAKBQGOkJM1Ha+hH\ncDFuasp9oslLoalYTJw4MW4JOZEEnUnQCEFnoQk6S0+srYYkbQkMx/UoBugITMM1IZ2dljY0GQoE\nAoE6UPbNR6NImgD8xsx+qDVxIBAIBApC7HUEaZSPVQoEAoFGQll5BIFAIBAoPeXmEdSKpHMlVUla\nK24tmZB0laSPJI2VNNz3kSg7JF0n6Quv9RlJbeLWlAlJh0v6TNIySdvFrScdSftJ+lLSeEkXxq0n\nE5IGS5ol6ZO4tdSEpE6SRvjr/amkP8etKR1Jq0p61z/fn0u6Om5NNSGpqaQxkp6vKV2iDEFCOp5d\na2bbmFlP4DncRDvlyCtADzPbBvgK13qrHPkE1+P8jbiFpCOpKXAbsB+wBXCUpM3jVZWR+3Aay50l\nwDlm1gPYCTij3MrTzH4B9vTP99bAnpJ2i1lWTZwNfE4tYfdEGQIS0PHMzBZEVlsCc+LSUhNm9qqZ\nVfnVd3EttsoOM/vSzL6KW0cWegFfm9lEM1sCPAYcFLOmlTCzN4G5ceuoDTObaWZj/fJPwBdA+3hV\nrYyZpVo5tgCaUj3felkhqSPQG7iHWprlJ8YQJKnjmaS/S5oM9AP+GbeeHDiRGob/DmSlAxCdX3uq\n/y1QTyR1AbbFfaSUFZKaSBoLzAJGmNnncWvKwk3A+UBVbQnLYc7i5SSl41ltE+2Y2cXAxX6inZuA\nlSbaKQW5TAgk6WJgsZk9UlJxEXKduKgMCS0tioCklsBTwNneMygrvCfd09erDZNUYWaVMctaAUl9\ngNlmNkZSRW3py8oQZJvAxnc82wj4SBK4MMYHklbqeFYKCjXRzv9v7/5CLSvLOI5/f4hiGWVk9Iek\nJKaRoshm+jdeFAyEFiVZUFjYiHURSpB5EVESUUQJmgwVwoxKBeJAEY1SMTkJ2aCmc7JydIhKkLwp\naLwoqEaeLt736D7jPmf+Nnvveb8fGGbvddZe69kHzvqd993rPO//2+HqTLKFNnTcfFIKWsVRfD/n\nzV+ByZsBzqWNCnSMkpwO/BD4QVX9eNb1rKWqnkpyF7ARuGfG5RxqE/CBJO8FzgRemOR7VXX5tJ0X\nYmqoqv5QVS+rqvOq6jzaD9tbZhECh5Nk3cTTS4ClWdWyliQX0YaNl/QPwBbBvLUfeRBYl+Q1Sc4A\nPgL8ZMY1Lay03/K2A/uq6luzrmeaJOckObs/fh7t5pW5+xmvqi9U1bn9evlRYPdqIQALEgRTzPOQ\n/OtJft/nEN8NfG7G9axmK+3D7F399rLvzLqgaZJ8MMkTtLtI7kry01nXtKyqDgJXAz+n3ZlxR1U9\nOtuqnivJ7cAe4HVJnkgyk6nKI3Ah8HHanThL/d+83e30CmB3//m+H9hZVXfPuKYjseY10z8ok6TB\nLeqIQJJ0ghgEkjQ4g0CSBmcQSNLgDAJJGpxBIEmDMwikBZPktiR/nrjX/upZ13Si9Lbj+5Iswr35\np4y5ajEh6YgUcG1V/WjaF5OcVlVPn+SaTpQrgU9W1Z5jPUCS5wP/7R1hdQQcEUiLaUW7jST3JLkx\nyW+AzyTZ0Lc9mORnSV7e99swsXDS9cuL1STZkmTrxPHuTPKu/vg9SfYkeSjJjiRn9e2PJ/ly3/67\nJOv79hckubVvezjJpUmuSHLjxPE/leSGQ97DdbS/Lr4lyTeP43uzHtjf39/5x3GcYRgE0uIJcH2f\nFtrbmzIWcHpVvZXWPmQr8KGq2khbmOZr/bW3Alf1hVWK1VsPFFBJzqF1/91cVRuAh4BrJvb5W9/+\nXeDavv1LwD+q6k194aPdwA7g/X0xH4AttL5Cz56w6iu0/k2XVdUxrztSVUu0RWMeA7Yl+VUPurOO\n9ZinOqeGpMXznKmh3pX3jv70fOANwC/69tOAJ3vb5BdV1b19v+8DF69xntB6PL0e2NOPdQatb9Gy\n5Rr2Apf2x5tpDfhasVUHeo27aWHwGC20HlnjvMelt6/eDmzvq5xtB24C5nJJ1lkzCKTFNO1i+c+J\nrz1SVZtWvKB3zVzlGAdZOUNw5sTjXVV12Sp1/Lv//zQrryfT6ttGG108CtyyyvGgjUTeBtzcn18H\nvB14Hy0EN9KCp2jdXpd4dknYK6tqLzyzuM0naN03f9uPoykMAunUsXzx3Q+8NMk7quq+3uN/XVXt\nS3IgyYVV9WvgYxOvfRz4dG8F/SraMpwF3Ad8O8lrq+pPfXrllVX1xzXq2AVcBXwWWgBV1YGqeqAv\nn3gB8Ma13khVPdD3W7YT+OLE8zcf8pJn1i7oAbANeAktcDZV1dwv1TlLfkYgLaZpc/sFUFX/AT4M\nfKO3S14C3tn3uYJ2YV/RQ79PF/2F1k77JtpnAVTV32nz+bcneZg2LbR+lXMv1/RV4MWHtGNftgO4\nt6qeOpo3e5QOAp+vqguqaqshcHi2oZYGleTVwJ1VteZv5yf4nDuBG6rqlyfrnDo8RwTSuMJJWuQp\nydlJ9gP/MgTmjyMCSRqcIwJJGpxBIEmDMwgkaXAGgSQNziCQpMEZBJI0OINAkgZnEEjS4AwCSRqc\nQSBJgzMIJGlwBoEkDc4gkKTBGQSSNDiDQJIGZxBI0uAMAkkanEEgSYMzCCRpcAaBJA3OIJCkwRkE\nkjQ4g0CSBmcQSNLgDAJJGpxBIEmDMwgkaXAGgSQNziCQpMEZBJI0OINAkgZnEEjS4AwCSRqcQSBJ\ngzMIJGlwBoEkDc4gkKTBGQSSNDiDQJIGZxBI0uAMAkka3P8A37H38jsTGrUAAAAASUVORK5CYII=\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f88fc7750d0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,grid,title,xlabel,ylabel,show,legend,subplot\n", + "from numpy import arange,cos,pi,sinc,sin\n", + "\n", + "\n", + "#Caption:Frequency response of modified duobinary conversion filter\n", + "#Figure 6.15: Frequency Response of Modified duobinary conversion filter\n", + "#(a)Amplitude Response\n", + "#(b)Phase Response\n", + "rb = 8# the bit rate\n", + "Tb =1/rb# #Bit duration\n", + "f = arange(-rb/2,1/100+rb/2,1/100)\n", + "Amplitude_Response = [abs(2*sin(2*pi*ff*Tb)) for ff in f]\n", + "Phase_Response = [-(2*pi*ff*Tb) for ff in f]\n", + "subplot(3,1,1)\n", + "plot(f,Amplitude_Response)\n", + "xlabel('Frequency f---->')\n", + "ylabel('|H(f)| ----->')\n", + "title('Amplitude Repsonse of Modified Duobinary Singaling')\n", + "grid()\n", + "subplot(3,1,3)\n", + "plot(f,Phase_Response)\n", + "xlabel(' Frequency f---->')\n", + "ylabel(' <H(f) ----->')\n", + "title('Phase Repsonse of Modified Duobinary Singaling')\n", + "grid()\n", + "show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Digital_Communications_by_S._Haykin/Chapter7_iOFdfcy.ipynb b/Digital_Communications_by_S._Haykin/Chapter7_iOFdfcy.ipynb new file mode 100644 index 00000000..3fc2f580 --- /dev/null +++ b/Digital_Communications_by_S._Haykin/Chapter7_iOFdfcy.ipynb @@ -0,0 +1,976 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# Chapter 7 Digital Modulation Techniques" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.01 page 294" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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u/mXcb64werm2Jm6FMRaVUcxrM2qxCBuhTPyuRpU9HTpovBzBsG4dfPqpa41m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\nZ4lLLMrKdGP1oAcdVOrxV4Y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2GAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7fa9141608d0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange, sin, pi,zeros\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,title,grid,show\n", + "#Caption:Waveforms of Different Digital Modulation techniques\n", + "#Figure7.1\n", + "#Digital Modulation Techniques\n", + "#To Plot the ASK, FSK and PSk Waveforms\n", + "f = 2 # the Analog Carrier Frequency in Hz\n", + "t = arange(0,1/512+1,1/512)\n", + "x = [sin(2*pi*f*tt) for tt in t]\n", + "I = [0,1,1,0,1,0,0,1] # the digital binary data\n", + "#Generation of ASK Waveform\n", + "#Xask = []#\n", + "Xask=zeros(len(x))\n", + "for n in range(0,len(I)):\n", + " if((I[n]==1) and (n==0)):\n", + " Xask = [x,Xask]#\n", + " elif((I[n]==0) and (n==0)):\n", + " Xask = [zeros(len(x)),Xask]\n", + " elif((I[n]==1) and (n!=1)):\n", + " Xask = [Xask,x]\n", + " elif((I[n]==0) and (n!=1)): \n", + " Xask = [Xask,zeros(len(x))]\n", + " \n", + "\n", + "#Generation of FSK Waveform\n", + "Xfsk = []#\n", + "x1 = [sin(2*pi*f*tt) for tt in t]\n", + "x2 = [sin(2*pi*(2*f)*tt) for tt in t]\n", + "for n in range(0,len(I)):\n", + " if (I[n]==1):\n", + " Xfsk = [Xfsk,x2]\n", + " elif (I[n]!=1):\n", + " Xfsk = [Xfsk,x1]\n", + " \n", + "\n", + "#Generation of PSK Waveform\n", + "Xpsk = []#\n", + "x1 = [sin(2*pi*f*tt) for tt in t]\n", + "x2 = [-sin(2*pi*f*tt) for tt in t]\n", + "for n in range(0,len(I)):\n", + " if (I[n]==1):\n", + " Xpsk = [Xpsk,x1]\n", + " elif (I[n]!=1):\n", + " Xpsk = [Xpsk,x2]\n", + " \n", + "plot(t,x)\n", + "title('Analog Carrier Signal for Digital Modulation')\n", + "grid()\n", + "show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.1 page 298" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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y+9k+0EdYC3DVohB5w8fe8WHqA0GCeoCylQNdpzHoZ99YmiWNEYbTZXRV4tN0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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7fa55c4e1c50>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import ones,arange,cos,sin,pi\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,subplot,title,xlabel,ylabel,show\n", + "\n", + "M =4#\n", + "i = range(0,M)\n", + "t = arange(0,0.001+1,0.001)\n", + "s1=ones([len(i),len(t)])\n", + "s2=ones([len(i),len(t)])\n", + "for i in range(0,M):\n", + " s1[i,:] = [cos(2*pi*2*tt)*cos((2*i-1)*pi/4) for tt in t]\n", + " s2[i,:] = [-sin(2*pi*2*tt)*sin((2*i-1)*pi/4) for tt in t]\n", + "\n", + "S1 =[]#\n", + "S2 = []#\n", + "S = []#\n", + "Input_Sequence =[0,1,1,0,1,0,0,0]\n", + "m = [3,1,1,2]\n", + "for i in range(0,len(m)):\n", + " S1 = S1+[s1[m[i],:]]\n", + " S2 = S2+[s2[m[i],:]]\n", + "S = S1+S2#\n", + "subplot(3,1,1)\n", + "plot(S1)\n", + "title('Binary PSK wave of Odd-numbered bits of input sequence') \n", + "subplot(3,1,2)\n", + "plot(S2)\n", + "title('Binary PSK wave of Even-numbered bits of input sequence') \n", + "subplot(3,1,3)\n", + "plot(S)\n", + "title('QPSK waveform') \n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.02 page 302" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "coordinates of message points [1.0, -1.0]\n", + "Message points ['0b1', '0b0']\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7fcab6354f10>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import ones,arange,cos,sin,pi\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,subplot,title,xlabel,ylabel,show\n", + "\n", + "M =2#\n", + "i = range(1,M+1)\n", + "y = [cos(2*pi+(ii-1)*pi) for ii in i]\n", + "\n", + "annot = [bin(xx) for xx in arange(len(y)-1,-1,-1)]\n", + "annot = [bin(yy) for yy in arange(len(y)-1,-1,-1)]\n", + "\n", + "print 'coordinates of message points',y\n", + "\n", + "print 'Message points',annot\n", + "plot(y)\n", + "xlabel(' In-Phase')#\n", + "ylabel(' Quadrature')#\n", + "title('Constellation for BPSK')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.2 page 304" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "coordinates of message points\n", + "[1.0, -1.0]\n", + "[-1.0, -1.0]\n", + "[-1.0, 1.0]\n", + "[1.0, 1.0]\n" + ] + }, + { + "data": { + "image/png": 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/XfKGbwAsyPtuaeB0YCzwbN7/ZgFwEvB2jOEKQMnlIBxgZ8b4eiV+Oxo4tsC8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\nHcPfNdbIOhrXUtRStdptgcl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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f2c4eca9c10>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import ones,arange,cos,sin,pi\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,subplot,title,xlabel,ylabel,show,legend,grid,subplot\n", + "#Table 7.2 signal space characterization of MSK\n", + "\n", + "M =2#\n", + "Tb =1#\n", + "t1 = arange(-Tb,0.01+Tb,Tb)\n", + "t2 = arange(0,0.01+2*Tb,2*Tb)\n", + "phi1 = [cos(2*pi*t11)* cos((pi/(2*Tb))*t11) for t11 in t1]\n", + "phi2 = [sin(2*pi*t22)*sin((pi/(2*Tb))*t22) for t22 in t2]\n", + "teta_0 = [0,pi]\n", + "teta_tb = [pi/2,-pi/2]\n", + "S1 = [];s1 = []\n", + "S2 = [];s2 = []\n", + "for i in range(0,M):\n", + " s1.append(cos(teta_0[i]))\n", + " s2.append(-sin(teta_tb[i]))\n", + " S1 = S1+[s1[i]*phi1]\n", + " S2 = S2+[s2[0]*phi2]\n", + "\n", + "for i in arange(M,-1+1,1):\n", + " S1 = S1+[s1[i]*phi1]\n", + " S2 = S2+[s2(1)*phi2]\n", + "\n", + "Input_Sequence =[1,1,0,1,0,0,0]\n", + "S = []\n", + "t = arange(0,0.01+1,1)\n", + "S = S+[cos(0)*cos(2*pi*tt)-sin(pi/2)*sin(2*pi*tt) for tt in t]\n", + "S = S+[cos(0)*cos(2*pi*tt)-sin(pi/2)*sin(2*pi*tt) for tt in t]\n", + "S = S+[cos(pi)*cos(2*pi*tt)-sin(pi/2)*sin(2*pi*tt) for tt in t]\n", + "S = S+[cos(pi)*cos(2*pi*tt)-sin(-pi/2)*sin(2*pi*tt) for tt in t]\n", + "S = S+[cos(0)*cos(2*pi*tt)-sin(-pi/2)*sin(2*pi*tt) for tt in t]\n", + "S = S+[cos(0)*cos(2*pi*tt)-sin(-pi/2)*sin(2*pi*tt) for tt in t]\n", + "S = S+[cos(0)*cos(2*pi*tt)-sin(-pi/2)*sin(2*pi*tt) for tt in t]\n", + "\n", + "y = [[s1[0],s2[0]],[s1[1],s2[0]],[s1[1],s2[1]],[s1[0],s2[1]]]\n", + "print 'coordinates of message points'\n", + "for yy in y:\n", + " print yy\n", + " \n", + "\n", + "subplot(3,1,1)\n", + "plot(S1[0])\n", + "title('Scaled time function s1*phi1(t)')\n", + "#subplot(3,1,2)plot(S2[0])title('Scaled time function s2*phi2(t)')\n", + "subplot(3,1,3)\n", + "plot(S)\n", + "title('Obtained by adding s1*phi1(t)+s2*phi2(t) on a bit-by-bit basis') \n", + "show()\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.3 page 308" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Table 7.3 Illustrating the Generation of DPSK Signal\n", + "_____________________________________________________\n", + "\n", + "(bk) [1, 0, 0, 1, 0, 0, 1, 1]\n", + "\n", + "(bk_not) [0, 1, 1, 0, 1, 1, 0, 0]\n", + "\n", + "Differentially encoded sequence (dk)\n", + "1 \t0 \t1 \t1 \t0 \t1 \t1 \t1 \t\n", + "\n", + "Transmitted phase in radians\n", + "0 \t3.14159265359 \t0 \t0 \t3.14159265359 \t0 \t0 \t0 \t\n", + "\n", + "_____________________________________________________\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import pi\n", + "\n", + "\n", + "bk = [1,0,0,1,0,0,1,1]##input digital sequence\n", + "bk_not=[]\n", + "for i in range(0,len(bk)):\n", + " if(bk[i]==1):\n", + " bk_not.append(0)\n", + " else:\n", + " bk_not.append(1)\n", + " \n", + "dk_1 = [ 1 and bk[0]]# #initial value of differential encoded sequence\n", + "dk_1_not =[ 0 and bk_not[0]]\n", + "dk = [dk_1[0]^dk_1_not[0]] #first bit of dpsk encoder\n", + "for i in range(1,len(bk)):\n", + " dk_1.append(dk[(i-1)])\n", + " if dk[(i-1)]==1:\n", + " xxx=0\n", + " else:\n", + " xxx=1\n", + " dk_1_not.append(xxx)\n", + " dk.append(((dk_1[i] and bk[i])^(dk_1_not[i] and bk_not[i])))\n", + "dk_radians=[]\n", + "for i in range(0,len(dk)):\n", + " if(dk[i]==1):\n", + " dk_radians.append(0)\n", + " elif(dk[i]==0):\n", + " dk_radians.append(pi)\n", + " \n", + "print 'Table 7.3 Illustrating the Generation of DPSK Signal'\n", + "print '_____________________________________________________'\n", + "print '\\n(bk)',bk\n", + "print '\\n(bk_not)',bk_not\n", + "print '\\nDifferentially encoded sequence (dk)'\n", + "for dd in dk:\n", + " print dd,'\\t',\n", + "print '\\n\\nTransmitted phase in radians'\n", + "for ddd in dk_radians:\n", + " print ddd,'\\t',\n", + "print '\\n\\n_____________________________________________________'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.4 page 314" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "coordinates of message points\n", + "[[1, 0], [0, 1]]\n", + "[[1, 0], [0, 1]]\n", + "Message points ['0b1', '0b0']\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7fa400160c50>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import ones,arange,cos,sin,pi\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,subplot,title,xlabel,ylabel,show,legend,grid\n", + "\n", + "M =2#\n", + "y = [[1,0],[0,1]]\n", + "annot = [bin(xx) for xx in (arange(M-1,-1,-1))]\n", + "print 'coordinates of message points'\n", + "for yy in y:\n", + " print y\n", + "\n", + "print 'Message points',annot\n", + "\n", + "plot(y[0])\n", + "plot(y[1])\n", + "xlabel(' In-Phase')#\n", + "ylabel(' Quadrature')#\n", + "title('Constellation for BFSK')\n", + "legend(['message point 1 (binary 1)','message point 2 (binary 0)'])\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.4. page 320" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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xxx8Z4ZdeekkrVKigmzZtyt9KXgY4e74IQC/aXYCCQG6GxZKAGiISLSIFgd7A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\naYPAq666it69e2eylOvQoQO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1ttm2X467p2+Gt28fvPCCr6XJFX7ZngGKacvgxR3DhMeA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\nQfvw9sS8F8Ob698kv7B65j+7+zHuuQe+/VbXWZo0qU7lEhm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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f9fcb8b6d50>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import ones,arange,cos,sin,pi\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,subplot,title,xlabel,ylabel,show,legend,grid\n", + "from scipy.special import erfc\n", + "from math import log10,sqrt,exp\n", + "from __future__ import division\n", + "#Comparison of Symbol Error Probability\n", + "#of Different Digital Transmission System\n", + "#Eb = Energy of the bit No = Noise Spectral Density\n", + "Eb_No =[18,0.3162278]\n", + "x = arange(Eb_No[1],1/100+Eb_No[0],1./100)\n", + "x_dB = [10*log10(xx) for xx in x]\n", + "Pe_BPSK=ones(len(x))\n", + "Pe_BFSK=ones(len(x))\n", + "Pe_DPSK=ones(len(x))\n", + "Pe_NFSK=ones(len(x))\n", + "Pe_QPSK_MSK=ones(len(x))\n", + "for i in range(0,len(x)):\n", + " #Error Probability of Coherent BPSK \n", + " Pe_BPSK[i]= (1/2)*erfc(sqrt(x[i]))#\n", + " #Error Probability of Coherent BFSK\n", + " Pe_BFSK[i]= (1/2)*erfc(sqrt(x[i]/2))#\n", + " #Error Probability Non-Coherent PSK = DPSK \n", + " Pe_DPSK[i]= (1/2)*exp(-x[i])#\n", + " #Error Probability Non-Coherent FSK\n", + " Pe_NFSK[i]= (1/2)*exp(-(x[i]/2))#\n", + " #Error Probability of QPSK & MSK\n", + " Pe_QPSK_MSK[i]= erfc(sqrt(x[i]))-((1/4)*(erfc(sqrt(x[i]))**2))\n", + "\n", + "plot(x_dB,Pe_BPSK)\n", + "plot(x_dB,Pe_BFSK)\n", + "plot(x_dB,Pe_NFSK)\n", + "plot(x_dB,Pe_QPSK_MSK)\n", + "xlabel('Eb/No in dB ---->')\n", + "ylabel('Probability of Error Pe--->')\n", + "title('Comparison of Noise Performance of different PSK & FSK Scheme')\n", + "legend(['BPSK','BFSK','DPSK','Non-Coherent FSK','QPSK & MSK'])\n", + "grid()\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.06 page 324" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Table 7.7 Bandwidth Efficiency of M-ary PSK signals\n", + "______________________________________________________\n", + "M\n", + "[2, 4, 8, 16, 32, 64]\n", + "______________________________________________________\n", + "r in bits/s/Hz\n", + "[0.5, 1.0, 1.5, 2.0, 2.5, 3.0]\n", + "______________________________________________________\n" + ] + } + ], + "source": [ + "from math import log\n", + "\n", + "#Bandwidth Efficiency of M-ary PSK signals\n", + "M = [2,4,8,16,32,64]##M-ary\n", + "Ruo = [log(MM,2)/2 for MM in M]# #Bandwidth efficiency in bits/s/Hz\n", + "print 'Table 7.7 Bandwidth Efficiency of M-ary PSK signals'\n", + "print '______________________________________________________'\n", + "print 'M\\n',M\n", + "print '______________________________________________________'\n", + "print 'r in bits/s/Hz\\n',Ruo\n", + "print '______________________________________________________'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.6 page 326" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "coordinates of message points\n", + "\n", + "(0.707106781187+0.707106781187j)\n", + "(0.707106781187-0.707106781187j)\n", + "(-0.707106781187-0.707106781187j)\n", + "(-0.707106781187+0.707106781187j)\n", + "dibits value ['0', '1', '10', '11']\n" + ] + }, + { + "data": { + "image/png": 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N398v+jHOprLnA2/sxxiB9zacg07px++SosV2afnv8lbgqOHqzAWAERFRyVjt\nqoqIiB5J4oiIiEqSOCIiopIkjoiIqCSJIyIiKkniiIiISpI4ImJYko6X9M8V3zMgaXl5W/FbJb2u\n3P4fkg4bnUijG5I4IqIdG3PBl4Ev2N4H+Dvgq+XV/bl4bIxL4oiISsoWwxfLBz3dOUzrQQC2FwNr\nKK5SBnhp8/slbS3pKkm/LB8kdUi5/X9I+mH5oKFbJR1ebn++pHp559nLJbW6QWaMgr69yWFE9LUd\nbL9Y0h4U9z66eKjCkl4IPG77/rLV0er9fwLeYPtRSdsD15X75gD32D64rGtKeTPLfwZeZ/sBSUdQ\n3KjvxNH5uNEoiSMiqjLlTSZtLxrigVQC3i3pLcCjFDfYG+r9mwCflvS3FPccmyHpacAtwOckfQb4\nge2fSPobYE/gqvIOuZMonrsTXZDEEREb468NywKQ9EmKp0Ta9r48McbxhXbeDxxN0ZW1r+3Hy9t7\nb2F7iYpntB8MfELS1cB3gdtsH9DRTxVtyRhHRLRj2Acl2f6g7X3KpNH2+xpMoXhg2OPlg6SeDlA+\nf+XPLh7C9jmKJzveDjy1vEU9kjaV9JwKx4oRSIsjItphnjwbarDlVu8bbvu65W8Al0q6heI5EovK\n7c8F/knSWmA18L9sr5b0JuBLkrahOJedSfefdzEh5bbqERFRSbqqIiKikiSOiIioJIkjIiIqSeKI\niIhKkjgiIqKSJI6IiKgkiSMiIipJ4oiIiEr+PyuB8xp0ZJw8AAAAAElFTkSuQmCC\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7fb8900e9cd0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.707106781187\n", + "0.707106781187\n" + ] + } + ], + "source": [ + "from numpy import ones,arange,cos,sin,pi\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,subplot,title,xlabel,ylabel,show\n", + "\n", + "\n", + "#Figure7.6 Signal Space Diagram for coherent QPSK system\n", + "M =4#\n", + "i = range(0,M)\n", + "y = [cos((2*ii-1)*pi/4)-sin((2*ii-1)*pi/4)*1J for ii in i]\n", + "annot = [bin(xx)[2:] for xx in range(0,M)]\n", + "print 'coordinates of message points\\n'\n", + "for yyy in y:\n", + " print yyy\n", + "\n", + "print 'dibits value',annot\n", + "plot([y[0].real,y[1].real,y[2].real,y[3].real],[y[0].imag,y[1].imag,y[2].imag,y[3].imag])\n", + "xlabel(' In-Phase')#\n", + "ylabel(' Quadrature')#\n", + "title('Constellation for QPSK')\n", + "show()\n", + "print y[0].imag\n", + "print y[0].real\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.7 page 329" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Table 7.7 Bandwidth Efficiency of M-ary FSK signals\n", + "______________________________________________________\n", + "M = \n", + "[2, 4, 8, 16, 32, 64]\n", + "______________________________________________________\n", + "r in bits/s/Hz=\n", + "[1.0, 1.0, 0.75, 0.5, 0.3125, 0.1875]\n", + "______________________________________________________\n" + ] + } + ], + "source": [ + "from math import log\n", + "# Bandwidth Efficiency of M-ary FSK\n", + "M = [2,4,8,16,32,64]##M-ary\n", + "Ruo = [2*log(MM,2)/MM for MM in M]# #Bandwidth efficiency in bits/s/Hz\n", + "#M = M'#\n", + "#Ruo = Ruo'#\n", + "print 'Table 7.7 Bandwidth Efficiency of M-ary FSK signals'\n", + "print '______________________________________________________'\n", + "print 'M = \\n',M\n", + "print '______________________________________________________'\n", + "print 'r in bits/s/Hz=\\n',Ruo\n", + "print '______________________________________________________'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.12.7.2 page 332" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "coordinates of message points\n", + "\n", + "[1.0, -1.0]\n", + "[-1.0, 1.0]\n", + "[-1.0, 1.0]\n", + "[1.0, 1.0]\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f16dcd88a50>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import pi,sin,cos,arange,ones,sinc\n", + "from math import log\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,title,show,legend,grid\n", + "\n", + "M =2#\n", + "teta_0 = [0,pi]#\n", + "teta_tb = [pi/2,-pi/2]#\n", + "s1=[]\n", + "s2=[]\n", + "for i in range(0,M):\n", + " s1.append(cos(teta_0[i]))\n", + " s2.append(-sin(teta_tb[i]))\n", + "y = [[s1[0],s2[0]],[s1[1],s2[1]],[s1[1],s2[1]],[s1[0],s2[1]]]\n", + "print 'coordinates of message points\\n'\n", + "for xx in y:\n", + " print xx\n", + "plot(y[0])\n", + "plot(y[1])\n", + "plot(y[2])\n", + "plot(y[3])\n", + "xlabel(' In-Phase')#\n", + "ylabel(' Quadrature')#\n", + "title('Constellation for MSK')\n", + "legend(['message point 1 (0, pi/2)','message point 2 (pi, pi/2)','message point 3 (pi, - pi/2)','message point 4(0, - pi/2)'])\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.29 page 334" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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mf//+QMFLhBZGx44dOeeccyKy5GaojqNmzZpMnz6d2bNnc+WVVwJuLeyyZcuy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\nqgDvA3u9w9Zd1TAShP37c7vFTpsGixb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w8GPcPpGyEjgD7iLiCThvDl/X57EYuK/fugE2\nMvO42Y7TRPjZbWkkEbEEjjLzcaTxdoGdzNwbYzxNhz0GaYIi4gKYAdt/nYv+H1cMkqSOPQZJUsfC\nIEnqWBgkSR0LgySpY2GQJHUsDJKkzhcmetvb0a16tgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7fcadd25bb90>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange,ones,sinc,pi,sin,cos\n", + "from math import log\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,title,show,legend,grid\n", + "\n", + "rb = 2 # the bit rate in bits per second\n", + "Eb = 1 # the Energy of bit\n", + "\n", + "f = arange(0,1/100+8/rb,8/rb)\n", + "Tb = 1/rb# #Bit duration\n", + "SB_PSK=ones(len(f))\n", + "SB_FSK=ones(len(f))\n", + "for i in range(0,len(f)):\n", + " if(f[i]==(1/(2*Tb))):\n", + " SB_FSK[i]=Eb/(2*Tb)\n", + " else:\n", + " SB_FSK[i]= (8*Eb*(cos(pi*f[i]*Tb)**2))/((pi**2)*(((4*(Tb**2)*(f[i]**2))-1)**2))\n", + " \n", + " SB_PSK[i]=2*Eb*(sinc(f[i]*Tb)**2)\n", + "\n", + "plot([ff*Tb for ff in f],[yy/(2*Eb) for yy in SB_FSK]) \n", + "plot([ff*Tb for ff in f],[yy/(2*Eb) for yy in SB_PSK]) \n", + "xlabel('Normalized Frequency ---->')\n", + "ylabel('Normalized Power Spectral Density--->')\n", + "title('PSK Vs FSK Power Spectra Comparison')\n", + "legend(['Frequency Shift Keying','Phase Shift Keying'])\n", + "grid() \n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.30 page 336" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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e2wwBcqrq0yJS2N2+iKpeiJeW9uun5M4NkZFQqhSULg1lykDRopDM2OMB9/e/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\nYFBV9rXuY83WDbyxsZztzeUcG1NNckcRc5LLuHp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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7faefe72dc10>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange,ones,sinc,pi,cos\n", + "from math import log\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,title,show,legend,grid\n", + "\n", + "rb = 2 # the bit rate in bits per second\n", + "Eb = 1 # the Energy of bit\n", + "f = arange(0,1/(100*rb)+(4/rb),1/(100*rb))\n", + "Tb = 1/rb# #bit duration in seconds\n", + "SB_MSK=ones(len(f))\n", + "SB_QPSK=ones(len(f))\n", + "for i in range(0,len(f)):\n", + " if(f[i]==0.5):\n", + " SB_MSK[i]= 4*Eb*f[i]\n", + " else:\n", + " SB_MSK[i]=(32*Eb/(pi**2))*(cos(2*pi*Tb*f[i])/((4*Tb*f[i])**2-1))**2\n", + " \n", + " SB_QPSK[i]=4*Eb*sinc((2*Tb*f[i]))**2\n", + "\n", + "plot([ff*Tb for ff in f],[yy/(4*Eb) for yy in SB_MSK])\n", + "plot([ff*Tb for ff in f],[yy/(4*Eb) for yy in SB_QPSK])\n", + "xlabel('Normalized Frequency ---->')\n", + "ylabel('Normalized Power Spectral Density--->')\n", + "title('QPSK Vs MSK Power Spectra Comparison')\n", + "legend(['Minimum Shift Keying','QPSK'])\n", + "grid()\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.31 page 338" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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J5/awYcNo2rRpwsgTy+3U1FRGjhwJQHJyMnkhuyGp2ab4UdWt2R332igGfAxM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\n+OU+2isiZwV10oZArmYjWnT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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f18572c4a10>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange,ones,sinc\n", + "from math import log\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,title,show,legend,grid\n", + "\n", + "rb = 2 # the bit rate\n", + "Eb = 1 # the energy of the bit\n", + "f = arange(0,1.0/100+rb,1./100)\n", + "Tb = 1/rb# #Bit duration\n", + "M = [2,4,8]#\n", + "SB_PSK=ones([len(M),len(f)])\n", + "for j in range(0,len(M)):\n", + " for i in range(0,len(f)):\n", + " SB_PSK[j,i]=2*Eb*(sinc(f[i]*Tb*log(M[j],2))**2)*log(M[j],2)\n", + " \n", + "plot([ff*Tb for ff in f],[xx/(2*Eb) for xx in SB_PSK[0,:]])\n", + "plot([ff*Tb for ff in f],[xx/(2*Eb) for xx in SB_PSK[1,:]])\n", + "plot([ff*Tb for ff in f],[xx/(2*Eb) for xx in SB_PSK[2,:]])\n", + "xlabel('Normalized Frequency ---->')\n", + "ylabel('Normalized Power Spectral Density--->')\n", + "title('Power Spectra of M-ary signals for M =2,4,8')\n", + "legend(['M=2','M=4','M=8'])\n", + "grid()\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.41 page 340" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f8cd98532d0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import ones,convolve as convol\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,title,show\n", + "#Matched Filter Output\n", + "T =4#\n", + "a =2#\n", + "t = range(0,T+1)\n", + "g = [2*xx for xx in ones([1,T+1])][0]\n", + "h =[abs(x) for x in (convol(g,g))]\n", + "for i in range(0,len(h)):\n", + " if(h[i]<0.01):\n", + " h[i]=0\n", + " \n", + "h = [hh-T for hh in h]\n", + "t1 = range(0,len(h))\n", + "plot(t,g)\n", + "xlabel('t--->')\n", + "ylabel('g(t)---->')\n", + "title('Rectangular pulse duration T = 4, a =2')\n", + "show()\n", + "plot(t1,h)\n", + "xlabel('t--->')\n", + "ylabel('Matched Filter output')\n", + "title('Output of filter matched to rectangular pulse g(t)')\n", + "show()\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Digital_Communications_by_S._Haykin/Chapter8_ffLFErg.ipynb b/Digital_Communications_by_S._Haykin/Chapter8_ffLFErg.ipynb new file mode 100644 index 00000000..ad52b4d6 --- /dev/null +++ b/Digital_Communications_by_S._Haykin/Chapter8_ffLFErg.ipynb @@ -0,0 +1,577 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8 Error Control Coding" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.1 page 384" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "generator matrix\n", + "[[ 1. 1. 1. 1. 1.]]\n", + "\n", + "parity-check matrix\n", + "[[ 1. 0. 0. 0. 1.]\n", + " [ 0. 1. 0. 0. 1.]\n", + " [ 0. 0. 1. 0. 1.]\n", + " [ 0. 0. 0. 1. 1.]]\n", + "\n", + "code word for binary one input\n", + "[[ 1. 1. 1. 1. 1.]]\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import ones,zeros,identity,transpose,hstack,mat\n", + "\n", + "n =5# #block of identical 'n' bits\n", + "k =1# #one bit\n", + "m = 1## bit value = 1\n", + "I = identity(n-k) #Identity matrix\n", + "P = ones(n-k)##coefficient matrix\n", + "I=mat(I)\n", + "P=mat(P)\n", + "H = hstack([I,transpose(P)])##parity-check matrix\n", + "G = hstack([P, mat([1])])##generator matrix \n", + "x = m*G# #code word\n", + "print 'generator matrix\\n',G\n", + "print '\\nparity-check matrix\\n',H\n", + "print '\\ncode word for binary one input\\n',x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.2 page 386" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "identity matrix Ik\n", + "[[ 1. 0. 0. 0.]\n", + " [ 0. 1. 0. 0.]\n", + " [ 0. 0. 1. 0.]\n", + " [ 0. 0. 0. 1.]]\n", + "\n", + "coefficient matrix P\n", + "[[1 1 0]\n", + " [0 1 1]\n", + " [1 1 1]\n", + " [1 0 1]]\n", + "generator matrix G\n", + "[[ 1. 1. 0. 1. 0. 0. 0.]\n", + " [ 0. 1. 1. 0. 1. 0. 0.]\n", + " [ 1. 1. 1. 0. 0. 1. 0.]\n", + " [ 1. 0. 1. 0. 0. 0. 1.]]\n", + "parity chechk matrix H\n", + "[[ 1. 0. 0. 1. 0. 1. 1.]\n", + " [ 0. 1. 0. 1. 1. 1. 0.]\n", + " [ 0. 0. 1. 0. 1. 1. 1.]]\n", + "Code words of (7,4) Hamming code\n", + "[[ 0. 0. 0. 0. 0. 0. 0.]\n", + " [ 1. 0. 1. 0. 0. 0. 1.]\n", + " [ 1. 1. 1. 0. 0. 1. 0.]\n", + " [ 0. 1. 0. 0. 0. 1. 1.]\n", + " [ 0. 1. 1. 0. 1. 0. 0.]\n", + " [ 1. 1. 0. 0. 1. 0. 1.]\n", + " [ 1. 0. 0. 0. 1. 1. 0.]\n", + " [ 0. 0. 1. 0. 1. 1. 1.]\n", + " [ 1. 1. 0. 1. 0. 0. 0.]\n", + " [ 0. 1. 1. 1. 0. 0. 1.]\n", + " [ 0. 0. 1. 1. 0. 1. 0.]\n", + " [ 1. 0. 0. 1. 0. 1. 1.]\n", + " [ 1. 0. 1. 1. 1. 0. 0.]\n", + " [ 0. 0. 0. 1. 1. 0. 1.]\n", + " [ 0. 1. 0. 1. 1. 1. 0.]\n", + " [ 1. 1. 1. 1. 1. 1. 1.]]\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import ones,zeros,identity,multiply,mat,concatenate,hstack,transpose\n", + "\n", + "\n", + "k = 4# #message bits length\n", + "n = 7# #block length\n", + "m = n-k##Number of parity bits\n", + "I = identity(k) #identity matrix\n", + "I=mat(I)\n", + "print 'identity matrix Ik\\n',I\n", + "P =[[1,1,0],[0,1,1],[1,1,1],[1,0,1]]##coefficient matrix\n", + "P=mat(P)\n", + "print '\\ncoefficient matrix P\\n',P\n", + "G = hstack([P,I]) #generator matrix\n", + "print 'generator matrix G\\n',G\n", + "\n", + "H = hstack([identity(k-1),transpose(P)])##parity check matrix\n", + "print 'parity chechk matrix H\\n',H\n", + "\n", + "#message bits\n", + "m = [[0,0,0,0],[0,0,0,1],[0,0,1,0],[0,0,1,1],[0,1,0,0],[0,1,0,1],[0,1,1,0],[0,1,1,1],[1,0,0,0],[1,0,0,1],[1,0,1,0],[1,0,1,1],[1,1,0,0],[1,1,0,1],[1,1,1,0],[1,1,1,1]]\n", + "\n", + "C = m*G#\n", + "C = (C%2)#\n", + "print 'Code words of (7,4) Hamming code\\n',C\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.3 page 389" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "remainder in polynomial form: \n", + " 2\n", + "1 x + 1 x\n", + "Parity bits are: [ 1. 1. 0.]\n", + "G:\n", + "[1, 1, 0, 1, 0, 0, 0]\n", + "[0, 1, 1, 0, 1, 0, 0]\n", + "[0, 0, 1, 1, 0, 1, 0]\n", + "[0, 0, 0, 1, 1, 0, 1]\n", + "\n", + "Generator Matrix G =\n", + "[1, 1, 0, 1, 0, 0, 0]\n", + "[0, 1, 1, 0, 1, 0, 0]\n", + "[1, 1, 1, 0, 0, 1, 0]\n", + "[1, 0, 1, 0, 0, 0, 1]\n", + "\n", + "Partiy Check matrix H =\n", + "\n", + "[1, 0, 0, 1, 0, 1, 1]\n", + "[0, 1, 0, 1, 1, 1, 0]\n", + "[0, 0, 1, 0, 1, 1, 1]\n" + ] + } + ], + "source": [ + "from numpy import poly1d, polydiv\n", + "#message sequence = [1,0,0,1]\n", + "g = poly1d([1,0,1,1]) #generator polynomial\n", + "m = poly1d([1,0,0,0])*poly1d([1,0,0,1]) #message sequence\n", + "q = polydiv(m,g)[0]\n", + "r = polydiv(m,g)[1]\n", + "p = r.coeffs\n", + "print 'remainder in polynomial form: \\n',r\n", + "print 'Parity bits are:',p\n", + "\n", + "def rev_coeffs(x):\n", + " X=[]\n", + " for i in reversed(x):\n", + " X.append(i)\n", + " return X\n", + "\n", + "\n", + "G = [rev_coeffs(g.coeffs),rev_coeffs((g*poly1d([1,0])).coeffs),rev_coeffs((g*poly1d([1,0,0])).coeffs),rev_coeffs((g*poly1d([1,0,0,0])).coeffs)]\n", + "M=len(G[-1])\n", + "for gg in G:\n", + " while len(gg)<M:\n", + " gg.append(0)\n", + "print \"G:\" \n", + "for gg in G:\n", + " print gg\n", + "\n", + "def fun1(a,x,y):\n", + " import numpy as np\n", + " z=[]\n", + " for xx,yy in np.nditer([a[x-1],a[y-1]]):\n", + " z.append(xx+yy)\n", + " a[x-1]=z\n", + " return a \n", + "\n", + "def modulo(a,i):\n", + " bb=[]\n", + " for aa in a[i-1]:\n", + " bb.append(aa%2)\n", + " a[i-1]=bb \n", + " return a\n", + "\n", + "G=fun1(G,3,1)#G(3,:) = G(3,:)+G(1,:);\n", + "G=modulo(G,3)#G(3,:) = modulo(G(3,:),2);\n", + "G=fun1(G,4,1)\n", + "G=fun1(G,4,2)#G(4,:) = G(1,:)+G(2,:)+G(4,:);\n", + "G=modulo(G,4)#G(4,:) = modulo(G(4,:),2);\n", + "print '\\nGenerator Matrix G ='\n", + "for ggg in G:\n", + " print ggg\n", + "\n", + "\n", + "#h = 1+D^-1+D^-2+D^-4;\n", + "#H_D = [D^4*h;D^5*h;D^6*h];\n", + "H_D=[poly1d([1,1,1,0,1]),poly1d([1,1,1,0,1,0]),poly1d([1,1,1,0,1,0,0])] \n", + "\n", + "\n", + "#H_num =numer(H_D);\n", + "#H = coeff(H_num);\n", + "H=[rev_coeffs(aa.coeffs) for aa in H_D]\n", + "\n", + "M=len(H[-1])\n", + "for hh in H:\n", + " while len(hh)<M:\n", + " hh.append(0)\n", + "H=fun1(H,1,3)\n", + "H= modulo(H,1) \n", + "print '\\nPartiy Check matrix H =\\n'\n", + "for hh in H:\n", + " print hh" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.4 page 395" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "remainder in polynomial form: \n", + " 2\n", + "1 x + 1 x\n", + "Parity bits are: [ 1. 1. 0.]\n", + "Table 8.3 Contents of the Shift Register in the Encoder of fig8.7 for Message Sequence(1001)\n", + "__________________________________________________________________________________________\n", + "Shift Input Register Contents\n", + "__________________________________________________________________________________________\n", + "1 1 1 1 0\n", + "2 0 0 1 1\n", + "3 0 1 1 1\n", + "4 1 0 1 1\n", + "____________________________________________________________________________________________\n" + ] + } + ], + "source": [ + "from numpy import poly1d,polydiv\n", + "#message sequence = [1,0,0,1]\n", + "g = poly1d([1,0,1,1]) #generator polynomial\n", + "m = poly1d([1,0,0,0])*poly1d([1,0,0,1])# #message sequence\n", + "q= polydiv(m,g)[0]\n", + "r= polydiv(m,g)[1]\n", + "p = r.coeffs\n", + "print 'remainder in polynomial form: \\n',r\n", + "print 'Parity bits are:',p\n", + "print 'Table 8.3 Contents of the Shift Register in the Encoder of fig8.7 for Message Sequence(1001)'\n", + "print '__________________________________________________________________________________________'\n", + "print 'Shift Input Register Contents'\n", + "print '__________________________________________________________________________________________'\n", + "print '1 1 1 1 0'\n", + "print '2 0 0 1 1'\n", + "print '3 0 1 1 1'\n", + "print '4 1 0 1 1'\n", + "print '____________________________________________________________________________________________'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.5 page 396" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "remainder in polynomial form : \n", + " 2\n", + "2 x + 2 x\n", + "Syndrome bits for error free codeword are: [0.0, 0.0, 0.0]\n", + "remainder in polynomial form for errored codeword : \n", + " 2\n", + "2 x + 3 x + 1\n", + "Syndrome bits for errored codeword are: [0.0, 1.0, 1.0]\n" + ] + } + ], + "source": [ + "from numpy import poly1d,polydiv\n", + "\n", + "#message sequence = [0,1,1,1,0,0,1]\n", + "\n", + "g = poly1d([1,0,1,1]) # #generator polynomial\n", + "C1 = poly1d([1,0,0,1,1,1,0]) #error free codeword\n", + "C2 = poly1d([1,0,0,0,1,1,0]) #middle bit is error\n", + "#[r1,q1] = pdiv(C1,g)#\n", + "\n", + "q1 = polydiv(C1,g)[0]\n", + "r1 = polydiv(C1,g)[1]\n", + "\n", + "S1 = (r1).coeffs\n", + "S1 = [xx%2 for xx in S1]\n", + "print 'remainder in polynomial form : \\n',r1\n", + "print 'Syndrome bits for error free codeword are:',S1\n", + "q2 = polydiv(C2,g)[0]\n", + "r2 = polydiv(C2,g)[1]\n", + "S2 = (r2).coeffs\n", + "S2 = [xx%2 for xx in S2]\n", + "print 'remainder in polynomial form for errored codeword : \\n',r2\n", + "print 'Syndrome bits for errored codeword are:',S2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.6 page 399" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "n = 3\n", + "n-k = 2\n", + "Code rate:r = k/n = 0.333\n", + "It can correct any error upto = 2\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#Single-error-correcting RS code with a 2-bit byte\n", + "\n", + "m =2# #m-bit symbol\n", + "k = 1**2# #number of message bits\n", + "t =1# #single bit error correction\n", + "n = 2**m-1# #code word length in 2-bit byte\n", + "p = n-k# #parity bits length in 2-bit byte\n", + "r = k/n# #code rate\n", + "print 'n =',n\n", + "print 'n-k =',p\n", + "print 'Code rate:r = k/n = %.3f'%r\n", + "print 'It can correct any error upto =',(2*t)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.7 page 401" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Result:\n", + "[1.0, 1.0] \n", + "\n", + "[1.0, 0.0] \n", + "\n", + "[1.0, 1.0] \n", + "\n", + "[1.0, 1.0] \n", + "\n", + "[0.0, 1.0] \n", + "\n", + "[0.0, 1.0] \n", + "\n", + "[1.0, 1.0] \n", + "\n" + ] + } + ], + "source": [ + "from numpy import convolve,ones\n", + "g1 = [1,1,1] # The input Top Adder Sequence\n", + "g2 = [1,0,1] #The input Bottom Adder Sequence\n", + "m =[1,1,0,0,1] # The message sequence\n", + "x1 = [round(xx) for xx in convolve(g1,m)]\n", + "x2 = [round(xx) for xx in convolve(g2,m)]\n", + "x1 = [xx%2 for xx in x1]\n", + "x2 = [xx%2 for xx in x2]\n", + "N = len(x1)\n", + "x=[]\n", + "for i in range(0,len(x1)):\n", + " x.append([x1[N-i-1],x2[N-i-1]])\n", + "print 'Result:' \n", + "for xx in x:\n", + " print xx,'\\n'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.8 page 404" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "top output sequence\n", + "1 \t1 \t1 \t1 \t0 \t0 \t1 \t\n", + "bottom output sequence\n", + "1 \t0 \t1 \t1 \t1 \t1 \t1 \t" + ] + } + ], + "source": [ + "from numpy import poly1d\n", + "g1D=poly1d([1,1,1]) #generator polynomial 1\n", + "g2D=poly1d([1,0,1]) #generator polynomial 2\n", + "mD=poly1d([1,1,0,0,1]) #message sequence polynomial representation\n", + "x1D=(g1D*mD) #top output polynomial\n", + "x2D=(g2D*mD) #bottom output polynomial\n", + "x1=x1D.coeffs\n", + "x2=x2D.coeffs\n", + "x1=x1.tolist()\n", + "X1=[]\n", + "for i in reversed(x1):\n", + " X1.append(i)\n", + "X2=[]\n", + "for i in reversed(x2):\n", + " X2.append(i)\n", + "print 'top output sequence'\n", + "for xx in X1:\n", + " print xx%2,'\\t',\n", + "print '\\nbottom output sequence' \n", + "for xx in X2:\n", + " print xx%2,'\\t'," + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.11 page 409" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "branch metric for correct reception : 0.8822\n", + "branch metric for any one correct recption: -3.7027\n", + "branch metric for no correct reception : -8.2877\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log\n", + "\n", + "r = 1/2# #code rate\n", + "n =2# #number of bits\n", + "pe = 0.04# #transition probility \n", + "p = 1-pe## probability of correct reception\n", + "gama_1 = 2*log(p,2)+2*(1-r)# #branch metric for correct reception\n", + "gama_2 = log(pe*p,2)+1# #branch metric for any one correct recption\n", + "gama_3 = 2*log(pe,2)+1# #branch metric for no correct reception\n", + "print 'branch metric for correct reception : %.4f'%gama_1\n", + "print 'branch metric for any one correct recption: %.4f'%gama_2\n", + "print 'branch metric for no correct reception : %.4f'%gama_3" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Digital_Communications_by_S._Haykin/Chapter9_4roMWPw.ipynb b/Digital_Communications_by_S._Haykin/Chapter9_4roMWPw.ipynb new file mode 100644 index 00000000..ca08a40e --- /dev/null +++ b/Digital_Communications_by_S._Haykin/Chapter9_4roMWPw.ipynb @@ -0,0 +1,365 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9 Spread Spectrum Modulation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.1 page 461" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The PN sequence at step: 1\n", + "x= [1, 0, 0]\n", + "The PN sequence at step: 2\n", + "x= [1, 1, 0]\n", + "The PN sequence at step: 3\n", + "x= [1, 1, 1]\n", + "The PN sequence at step: 4\n", + "x= [0, 1, 1]\n", + "The PN sequence at step: 5\n", + "x= [1, 0, 1]\n", + "The PN sequence at step: 6\n", + "x= [0, 1, 0]\n", + "The PN sequence at step: 7\n", + "x= [0, 0, 1]\n", + "Table 9.1 Range of PN Sequence lengths\n", + "_________________________________________________________\n", + "Length of shift register (m) = [7, 8, 9, 10, 11, 12, 13, 17, 19]\n", + "PN sequence Length (N) = [127, 255, 511, 1023, 2047, 4095, 8191, 131071, 524287]\n", + "_________________________________________________________\n" + ] + } + ], + "source": [ + "#Program to generate Maximum Length Pseudo Noise Sequence\n", + "#Period of PN Sequence N = 7\n", + "\n", + "#Assign Initial value for PN generator\n", + "x0= 1#\n", + "x1= 0#\n", + "x2 =0#\n", + "x3 =0#\n", + "N = 7 # the period of the signal\n", + "for i in range(1,N+1):\n", + " x3 =x2\n", + " x2 =x1\n", + " x1 = x0\n", + " x0 =(x1^x3)\n", + " print 'The PN sequence at step:',i\n", + " x = [x1, x2, x3]\n", + " print 'x=',x\n", + "\n", + "m = [7,8,9,10,11,12,13,17,19]#\n", + "N = [2**mm-1 for mm in m]\n", + "print 'Table 9.1 Range of PN Sequence lengths'\n", + "print '_________________________________________________________'\n", + "print 'Length of shift register (m) =',m\n", + "print 'PN sequence Length (N) =',N\n", + "print '_________________________________________________________'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.2 page 462" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The PN sequence at step : 1\n", + "x= [1, 0, 0]\n", + "The PN sequence at step : 2\n", + "x= [1, 1, 0]\n", + "The PN sequence at step : 3\n", + "x= [1, 1, 1]\n", + "The PN sequence at step : 4\n", + "x= [0, 1, 1]\n", + "The PN sequence at step : 5\n", + "x= [1, 0, 1]\n", + "The PN sequence at step : 6\n", + "x= [0, 1, 0]\n", + "The PN sequence at step : 7\n", + "x= [0, 0, 1]\n", + "Output Sequence : [0, 0, 1, 1, 1, 0, 1]\n", + "Output Sequence levels : [-1, -1, 1, 1, 1, -1, 1]\n", + "Number of 1s in the given PN sequence : 4\n", + "Number of 0s in the given PN sequence : 3\n", + "Property 1 (Balance property) is satisified\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f421c158a90>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import corrcoef as corr\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,xlabel,ylabel,title,show\n", + "\n", + "#Period of PN Sequence N = 7\n", + "#Properites of maximum-length sequence\n", + "\n", + "#Assign Initial value for PN generator\n", + "x0= 1#\n", + "x1= 0#\n", + "x2 =0#\n", + "x3 =0#\n", + "N = 7 #the period of the signal\n", + "one_count = 0\n", + "zero_count = 0\n", + "C=[]\n", + "C_level=[]\n", + "t=[]\n", + "for i in range(1,N+1):\n", + " x3 =x2#\n", + " x2 =x1#\n", + " x1 = x0#\n", + " x0 =(x1^x3)\n", + " print 'The PN sequence at step :',i\n", + " x = [x1 ,x2 ,x3]\n", + " print 'x=',x\n", + " C.append(x3)\n", + " if(C[i-1]==1):\n", + " C_level.append(1)\n", + " one_count = one_count+1\n", + " elif(C[i-1]==0):\n", + " C_level.append(-1)\n", + " zero_count = zero_count+1\n", + " \n", + "print 'Output Sequence : ',C #refer equation 9.4\n", + "print 'Output Sequence levels :',C_level#refer equation 9.5\n", + "if(zero_count < one_count):\n", + " print 'Number of 1s in the given PN sequence : ',one_count\n", + " print 'Number of 0s in the given PN sequence :',zero_count\n", + " print 'Property 1 (Balance property) is satisified'\n", + "\n", + "Rc_tuo = corr(C_level,rowvar=N)\n", + "t = range(1,2*len(C_level)+1)\n", + "plot(t,C_level+C_level)\n", + "xlabel(' t')\n", + "title('Waveform of maximum-length sequence [0 0 1 1 1 0 1 0 0 1 1 1 0 1]')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.3 page 468" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The processing gain is: 4095.0\n", + "The required PN sequence is: 4095.0\n", + "The feedback shift register length: 12.0\n", + "Jamming Margin in dB: 26.122539061\n" + ] + } + ], + "source": [ + "from math import log,log10\n", + "def log2(x):\n", + " return log(x,2)\n", + "\n", + "Tb = 4.095*10**-3##Information bit duration\n", + "Tc = 1*10**-6##PN chip duration\n", + "PG = Tb/Tc##Processing gain\n", + "print 'The processing gain is:',PG\n", + "N = PG# #PN sequence length\n", + "m = log2(N+1)##feedback shift register length\n", + "print 'The required PN sequence is:',N\n", + "print 'The feedback shift register length:',m\n", + "Eb_No = 10##Energy to noise density ratio\n", + "J_P = PG/Eb_No##Jamming Margin\n", + "print 'Jamming Margin in dB:',10*log10(J_P)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.4 page 469" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "number of bits per symbol K = 2\n", + "Number of MFSK tones M= 4\n", + "Period of the PN sequence N = 15\n", + "length of PN sequence per hop k = 3\n", + "Total number of frequency hops = 8\n" + ] + } + ], + "source": [ + "#Slow and Fast Frequency Hopping\n", + "K =2# #number of bits per symbol\n", + "M = 2**K# #Number of MFSK tones\n", + "N = 2**M-1##Period of the PN sequence\n", + "k = 3# #length of PN sequence per hop\n", + "print 'number of bits per symbol K =',K\n", + "print 'Number of MFSK tones M=',M\n", + "print 'Period of the PN sequence N =',N\n", + "print 'length of PN sequence per hop k =',k\n", + "print 'Total number of frequency hops =',2**k" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.5 page 470" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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dPC+/7P495pji9FdpC7rZJp+rBk480RXXmTWrfGPGeQHdG/00PP+8u4r37Bm2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\nIGxN+SCpsaQZkh7OswsD+pv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XeP+vwLbLSpUfYavMkkFEBgJlqvpFzpXlcuCAXfzvAF9hh2i/SFLu78AcYBpw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\n/YF8rP1PPslPf6ars359G7zXpAqxGMfSpTbApxr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HD9sWGT5xaR9X0erli621xV0GmVH5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\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f2287962410>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import ones,sin,arange,hstack,nditer,pi\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot,subplot,xlabel,ylabel,title,show\n", + "\n", + "\n", + "#Figure 9.4:Generation of waveforms in DS/BPSK spread spectrum transmitter\n", + "t = range(0,13+1)\n", + "N = 7#\n", + "wt = arange(0,0.01+1,0.01)\n", + "bt = hstack([[1*xx for xx in ones(N)],[-1*yy for yy in ones(N)]])\n", + "ct = [0,0,1,1,1,0,1,0,0,1,1,1,0,1]\n", + "ct_polar = [-1,-1,1,1,1,-1,1,-1,-1,1,1,1,-1,1]\n", + "mt = [a*b for a,b in nditer([bt,ct_polar])]\n", + "Carrier = [2*sin(wtt*2*pi) for wtt in wt]\n", + "\n", + "st = []#\n", + "for i in range(0,len(mt)):\n", + " st = st+[mt[i]*Cr for Cr in Carrier]\n", + "\n", + "subplot(3,1,1)\n", + "plot(t,bt)\n", + "xlabel(' t')\n", + "title('Data b(t)')\n", + "subplot(3,1,2)\n", + "plot(t,ct_polar)\n", + "xlabel(' t')\n", + "title('Spreading code c(t)')\n", + "subplot(3,1,3)\n", + "plot(t,mt)\n", + "xlabel(' t')\n", + "title('Product Signal m(t)')\n", + "show()\n", + "subplot(3,1,1)\n", + "plot(t,mt)\n", + "xlabel(' t')\n", + "title('Product Signal m(t)')\n", + "subplot(3,1,2)\n", + "plot(Carrier)\n", + "xlabel(' t')\n", + "title('Carrier Signal')\n", + "subplot(3,1,3)\n", + "plot(st)\n", + "xlabel(' t')\n", + "title('DS/BPSK signal s(t)')\n", + "show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Digital_Communications_by_S._Haykin/screenshots/Ch-6_RaisedCosineSpectrum_NizDJ8d.png b/Digital_Communications_by_S._Haykin/screenshots/Ch-6_RaisedCosineSpectrum_NizDJ8d.png Binary files differnew file mode 100644 index 00000000..96b74924 --- /dev/null +++ b/Digital_Communications_by_S._Haykin/screenshots/Ch-6_RaisedCosineSpectrum_NizDJ8d.png diff --git a/Digital_Communications_by_S._Haykin/screenshots/Ch6_powerSpectralDensities_9tUd56q.png b/Digital_Communications_by_S._Haykin/screenshots/Ch6_powerSpectralDensities_9tUd56q.png Binary files differnew file mode 100644 index 00000000..505c3998 --- /dev/null +++ b/Digital_Communications_by_S._Haykin/screenshots/Ch6_powerSpectralDensities_9tUd56q.png diff --git a/Digital_Communications_by_S._Haykin/screenshots/ch6_sinc_pilse_snbi7FJ.png b/Digital_Communications_by_S._Haykin/screenshots/ch6_sinc_pilse_snbi7FJ.png Binary files differnew file mode 100644 index 00000000..8f97aed2 --- /dev/null +++ b/Digital_Communications_by_S._Haykin/screenshots/ch6_sinc_pilse_snbi7FJ.png diff --git a/Electrical_Machines_-_I_by_M._Verma_And_V._Ahuja/README.txt b/Electrical_Machines_-_I_by_M._Verma_And_V._Ahuja/README.txt new file mode 100644 index 00000000..21b573c6 --- /dev/null +++ b/Electrical_Machines_-_I_by_M._Verma_And_V._Ahuja/README.txt @@ -0,0 +1,10 @@ +Contributed By: Preeti Rani +Course: btech +College/Institute/Organization: Techwords Institute +Department/Designation: ME +Book Title: Electrical Machines - I +Author: M. Verma And V. Ahuja +Publisher: Vayu Education Of India, New Delhi +Year of publication: 2009 +Isbn: 9788184316957 +Edition: 1
\ No newline at end of file diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter10_8mim6PA.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter10_8mim6PA.ipynb new file mode 100644 index 00000000..0eb7d255 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter10_8mim6PA.ipynb @@ -0,0 +1,165 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter No 10 - Propagation of radio waves" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example10.1 PageNo 412" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Field strength will reduce by 5.23 dBs\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt, log10\n", + "#Given\n", + "Pt1=100#Radiated power\n", + "Pt2=30# Reduced Power \n", + "r=1#assume distance to be unity for easeof calculation\n", + "E1=300*sqrt(100)/r\n", + "E2=300*sqrt(30)/r\n", + "E=20*log10((E2/E1))# Reduction in field strength in dBs\n", + "print 'Field strength will reduce by %0.2f dBs'%(-E)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example10.2 PageNo 413" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The field strength at distance 20km is 190.53 uV/m\n" + ] + } + ], + "source": [ + "#Given\n", + "P=3#Transmitter power\n", + "ht=100# Antenna height\n", + "G=5#Antenna gain\n", + "d=20e3#distance\n", + "lamda=1\n", + "hr=1#assumed\n", + "E=((88*G*ht*hr*P**0.5)/(lamda*d**2))#field strength\n", + "print 'The field strength at distance 20km is %0.2f uV/m'%(E*1e6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example10.3 PageNo 413" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Direct ray coverage is possible over 63.03 km\n" + ] + } + ], + "source": [ + "from math import sqrt\n", + "#Given\n", + "ht=152.5\n", + "hr=9.15 # Antenna height\n", + "d=4100*(sqrt(ht)+sqrt(hr)) #distance\n", + "print 'Direct ray coverage is possible over %0.2f km'%(d*1e-3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example10.4 PageNo 414" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Max possible distance for efective point to point\n", + " communication is 514.48 km\n" + ] + } + ], + "source": [ + "from math import sqrt\n", + "#Given\n", + "#b\n", + "ht=3e3\n", + "hr=5e3 # Antenna height\n", + "d=4100*(sqrt(ht)+sqrt(hr))#distance\n", + "print 'Max possible distance for efective point to point\\n communication is %0.2f km'%(d*1e-3)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter11_NAIDtL1.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter11_NAIDtL1.ipynb new file mode 100644 index 00000000..b8b0be75 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter11_NAIDtL1.ipynb @@ -0,0 +1,68 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter No 11 - Broadband Communication" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example11.1, page no 435" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The total no of samples per second is:\n", + "160000 samples/second\n" + ] + } + ], + "source": [ + "#Given\n", + "c=20# no of signal channels\n", + "s=8e3# Channel sampling rate\n", + "t=1/s# time interval over which ll channels are sampled once\n", + "#b\n", + "g=5e-6# guaed time for each channel sample\n", + "s_duration=t-g# duration of each sample\n", + "#c\n", + "samples_sec=c*s#\n", + "print 'The total no of samples per second is:\\n%d samples/second'%samples_sec" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter15_F19vfPd.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter15_F19vfPd.ipynb new file mode 100644 index 00000000..d45717f4 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter15_F19vfPd.ipynb @@ -0,0 +1,153 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter No 15 - Basic Information theory" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example15.1, page no 533" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The source entropy is: 1.50 bits/symbol\n" + ] + } + ], + "source": [ + "from math import log\n", + "#Given\n", + "P_A=0.5# probability of producing symbol 'A'\n", + "P_B=0.25# probability of producing symbol 'B'\n", + "P_C=0.25# probability of producing symbol 'C'\n", + "def log2(x):\n", + " return log(x,2)\n", + "H=P_A*log2(1/P_A)+P_B*log2(1/P_B)+P_C*log2(1/P_C)# the source entropy\n", + "print 'The source entropy is: %0.2f bits/symbol'%(H)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example15.2, page no 535" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The source entropy is: 1.94 bits/symbol\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log\n", + "def log2(x):\n", + " return log(x,2)\n", + "\n", + "#Given\n", + "P_A=0.5\n", + "P_B=0.25\n", + "P_C=1/32\n", + "P_D=1/8\n", + "P_E=1/16\n", + "P_F=1/32# probabilities of producing respective symbol\n", + "H=(P_A*log2(1/P_A))+(P_B*log2(1/P_B))+(P_C*log2(1/P_C))+(P_D*log2(1/P_D))+(P_E*log2(1/P_E))+(P_F*log2(1/P_F))# Source Entropy\n", + "n=6\n", + "T=1\n", + "print 'The source entropy is: %0.2f bits/symbol'%(round(1000*H)/1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example15.3, page no 536" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a)\n", + " Channel capacity is: 20 Kbits/sec\n", + " Bandwidth: 5 KHz\n", + "b)\n", + " SNR for 3KHz bandwidth: 100.59\n" + ] + } + ], + "source": [ + "from math import log\n", + "def log2(x):\n", + " return log(x,2)\n", + "\n", + "#Given\n", + "#a\n", + "B1=4e3#Channel Bandwidth\n", + "SNR1=31#Channel SNR\n", + "C1=B1*log2(1+SNR1)#Channel Capacity\n", + "SNR2=14#Reduced SNR\n", + "B2=round(C1/log2(1+SNR2))#Bandwidth for reduced SNR with same Channel capacity\n", + "\n", + "#b\n", + "B3=3e3#Reduced Bandwidth\n", + "SNR3=(2**(C1/B3))-1#Signal Power for reduced bandwidth\n", + "print 'a)\\n Channel capacity is: %d Kbits/sec\\n Bandwidth: %d KHz\\nb)\\n SNR for 3KHz bandwidth: %0.2f'%(C1*1e-3,B2*1e-3,SNR3)\n", + "# the Answer in the book is wrong.It is printed as 90.4 for SNR3 but it should be 100.59" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter1_fAOC2QW.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter1_fAOC2QW.ipynb new file mode 100644 index 00000000..0bf8c0e2 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter1_fAOC2QW.ipynb @@ -0,0 +1,1411 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 1 : Signals" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example1,page no12" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The value of the above integral is:C=0\n", + " Since C=0, the two functions: \n", + " f(t)=sin(n*wo*t)\n", + " g(t)=cos(n*wo*t) are Orthogonal\n" + ] + } + ], + "source": [ + "from numpy.random import randint\n", + "from numpy import pi, arange\n", + "from mpmath import quad, sin, cos\n", + "#Given:\n", + "n=round(randint(1000))#any integers\n", + "m=round(randint(1000))#any integers\n", + "wo=2*(n+m)*pi#Angular Freq\n", + "t=arange(0,2*pi/wo,0.01)\n", + "to=0;t1=2*pi/wo\n", + "C= quad(lambda t:sin(n*wo*t)*cos(m*wo*t),[to,t1])# integrating sin(n*wo*t)*cos(m*wo*t) function\n", + "print \"The value of the above integral is:C=%d\\n Since C=%d, the two functions: \\n f(t)=sin(n*wo*t)\\n g(t)=cos(n*wo*t) are Orthogonal\"%(C,C)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example2,page no 12" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The optimum value of C to minimise the mean square error is:\n", + " C= 1.273240\n" + ] + } + ], + "source": [ + "from numpy import arange,pi\n", + "from mpmath import quad, sin, cos\n", + "#Given:\n", + "# Curve on page no 9....fig 1.6\n", + "t=arange(0,2*pi,0.1)\n", + "t0=0\n", + "t1=2*pi\n", + "C=((quad(lambda t: sin(t),[t0,t1/2])-quad(lambda t: sin(t),[t1/2,t1]))/quad(lambda t :(sin(t))**2,[t0,t1]))\n", + "\n", + "print \"The optimum value of C to minimise the mean square error is:\\n C= %f\"%(C)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3,page no12" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a) The value of constants Cn are:\n", + "1.273237 for n= 1\n", + "\n", + "0.000000 for n= 2\n", + "\n", + "0.424406 for n= 3\n", + "\n", + "0.000000 for n= 4\n", + "\n", + "0.254636 for n= 5\n", + "\n", + "0.000000 for n= 6\n", + "\n", + "0.181874 for n= 7\n", + "\n", + "b) Mean Square error is\n", + "epsi(1) = 0.190000\n", + "\n", + "epsi(3) = 0.100000\n", + "\n", + "epsi(5) = 0.070000\n", + "\n", + "epsi(7) = 0.050000\n", + "\n" + ] + } + ], + "source": [ + "from numpy import arange\n", + "from mpmath import quad\n", + "from math import pi,sin\n", + "#Given:\n", + "#a # Referance Figure on page no 9.. (1.6d)\n", + "\n", + "t=range(0,int(2*3.14+1))\n", + "t0=0\n", + "t1=2*3.14\n", + "print 'a) The value of constants Cn are:'\n", + "C=[] \n", + "for i in range(1,8):\n", + " C.append((quad(lambda t:sin(i*t),[t0,t1/2])-quad(lambda t:sin(i*t),[t1/2,t1]))/quad(lambda t:(sin(i*t))**2,[t0,t1]))\n", + " if C[i-1] <= 0.01:\n", + " C[i-1]=0\n", + " \n", + " print '%f for n= %d\\n'%(C[i-1],i)\n", + "\n", + "#b Mean Square error\n", + "\n", + "int1=quad(lambda t:(1)**2,[t0,t1])\n", + "for n in range(1,8):\n", + " if (n%2) == 0:\n", + " C[n-1] = 0\n", + " else:\n", + " C[n-1]=4.0/(n*pi)\n", + "\n", + "\n", + "K=[]\n", + "for n in range(1,8):\n", + " \n", + " K.append(quad(lambda t:(sin(n*t))**2,[t0,t1]))\n", + " \n", + "K[n-1]=pi\n", + "S=[0]\n", + "for n in range(1,8):\n", + " S.append(S[n-1]+(((C[n-1])**2)*K[n-1]))\n", + "#Mean Square error\n", + "epsi=[]\n", + "for n in range(1,8):\n", + " epsi.append((1.0/(t1-t0)*(int1-S[n])))\n", + "\n", + "print 'b) Mean Square error is'\n", + "for n in arange(1,2+7,2):\n", + " print 'epsi(%d) = %f\\n'%(n,round(100*epsi[n-1])/100)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example4,page no12" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "P0 = 1\n", + "P1 = t\n", + "P2 = 1.5*t**2 - 0.5\n", + "P3 = 2.5*t**2 - 1.5\n", + "\n", + "The Constant coeff (Cn) values are :\n", + "C0 = 0.0\n", + "C1 = -1.5\n", + "C2 = 0.0\n", + "C3 = 0.875\n", + "\n", + "f(t)= 0*P0 + -1.500000*P1 + 0*P2 + 0.875000*P3\n" + ] + } + ], + "source": [ + "from sympy import symbols,solve\n", + "from mpmath import quad\n", + "from numpy import arange\n", + "#Given:\n", + "t=arange(-1,1.01,0.01)\n", + "t0=-1\n", + "t1=1\n", + "# Legendre Polynomial\n", + "t=symbols(\"t\")\n", + "P0=1\n", + "P1=t\n", + "P2=-0.5+1.5*t**2\n", + "P3=-1.5+2.5*t**2\n", + "print \"P0 =\",P0\n", + "print \"P1 =\",P1\n", + "print \"P2 =\",P2\n", + "print \"P3 =\",P3\n", + "#The Constant coeff (Cn)\n", + "C0=0.5*(quad(lambda t:1,[-1,0])+quad(lambda t:-1,[0,1]))\n", + "C1=1.5*(quad(lambda t:t,[-1,0])+quad(lambda t:-t,[0,1]))\n", + "C2=2.5*(quad(lambda t:(1.5*t**2)-0.5,[-1,0])+quad(lambda t:-(1.5*t**2)+0.5,[0,1]))\n", + "C3=3.5*(quad(lambda t:(2.5*t**3)-(1.5*t),[-1,0])+quad(lambda t:-(2.5*t**3)+(1.5*t),[0,1]))\n", + "print \"\\nThe Constant coeff (Cn) values are :\"\n", + "print \"C0 =\",C0\n", + "print \"C1 =\",C1\n", + "print \"C2 =\",C2\n", + "print \"C3 =\",C3\n", + "print \"\\nf(t)= %d*%s + %f*%s + %d*%s + %f*%s\"%(C0,\"P0\",C1,\"P1\",C2,\"P2\",C3,\"P3\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5, page no 19" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The value of a0 is: 0.500000\n", + "\n", + "The values of a(n): (upto n=10)\n", + "0\n", + "0\n", + "0\n", + "0\n", + "0\n", + "0\n", + "0\n", + "0\n", + "0\n", + "0\n", + "The values of b(n): (upto n=10)\n", + "-0.318308838986\n", + "-0.159152848691\n", + "-0.106100153783\n", + "-0.0795732827116\n", + "-0.0636567411629\n", + "-0.0530453643632\n", + "-0.0454655102642\n", + "-0.0397803578398\n", + "-0.0353583398512\n", + "-0.0318205159538\n", + "The trigonometric Fourier series for given function\n", + " can be written as:\n", + "\n", + "f(t)=-0.318309-0.159153sin(2*pi*t)-0.106100sin(4*pi*t)\n", + "-0.079573sin(6*pi*t)-0.063657sin(8*pi*t)-0.053045sin(10*pi*t)\n", + "-0.045466sin(12*pi*t)-0.039780sin(14*pi*t).......\n" + ] + } + ], + "source": [ + "from math import pi,cos,sin\n", + "from numpy import arange,trapz\n", + "#given\n", + "T=1\n", + "t0=0\n", + "wo=2*pi\n", + "P=1\n", + "t=arange(0,1.001,0.001)\n", + "f=P*t\n", + "#The trigonometric Fourier series coeff for given function\n", + "a0=(1/T)*trapz(t,f)\n", + "a=[]\n", + "a.append(0)\n", + "for n in range(1,11):\n", + " f1=[]\n", + " for tt in t:\n", + " f1.append((P*tt)*cos(wo*n*tt))\n", + " a.append((2/T)*trapz(t,f1))\n", + " \n", + " if a[(n)]<2.01:\n", + " a[(n)]=0\n", + " \n", + "b=[]\n", + "b.append(0)\n", + "for n in range(1,11):\n", + " f2=[]\n", + " for tt in t:\n", + " f2.append((P*tt)*sin(2*pi*(1/T)*n*tt))\n", + " b.append(-(2/T)*trapz(t,f2))\n", + "\n", + "# Displaying trigonometric Fourier series coeff\n", + "print \"The value of a0 is: %f\\n\"%(a0)\n", + "print \"The values of a(n): (upto n=10)\"\n", + "for n in range(1,11):\n", + " print a[(n)]\n", + "\n", + "print \"The values of b(n): (upto n=10)\"\n", + "for n in range(1,11):\n", + " print b[(n)]\n", + "\n", + "print \"The trigonometric Fourier series for given function\\n can be written as:\\n\"\n", + "print \"f(t)=%f%fsin(2*pi*t)%fsin(4*pi*t)\\n%fsin(6*pi*t)%fsin(8*pi*t)%fsin(10*pi*t)\\n%fsin(12*pi*t)%fsin(14*pi*t).......\"%(b[1],b[2],b[3],b[4],b[5],b[6],b[7],b[8])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6, page no 21" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The Exponential Fourier coeff(Fn) are:for n=-5 to 5\n", + "-0.05j \n", + "\n", + "(1+0j) \n", + "\n", + "-0.0981305252753j \n", + "\n", + "(1+0j) \n", + "\n", + "-0.315687575734j \n", + "\n", + "(0.5+0j) \n", + "\n", + "0j \n", + "\n", + "(1-0.153884176859j) \n", + "\n", + "0j \n", + "\n", + "(1-0.0688190960236j) \n", + "\n", + "0j \n", + "\n", + "\n", + "The given function in Expo Fourier series can be represented as \n", + "\n", + "f(t)= 0.500000+jP/2*pi* ∑1/n *exp(j2*pi*t)\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import nditer,trapz\n", + "#given\n", + "\n", + "t0=1\n", + "T=1\n", + "w0=2*3.14/T\n", + "P=1\n", + "t=arange(0,0.1+1,0.1)\n", + "f=[P*tt for tt in t]# function f(t)=P*t, 0<t<1\n", + "a=1\n", + "print 'The Exponential Fourier coeff(Fn) are:for n=-5 to 5'\n", + "Fr=[];Fi=[]\n", + "for n in range(-5,6): # Calculating the fourier coeff\n", + " fr=[ff*cos(pi*n*tt/T) for ff,tt in nditer([f,t])]\n", + " #Fr(a)=inttrap(t,fr)\n", + " Fr.append(trapz(t,fr))\n", + " fi=[ff*sin(pi*n*tt/T) for ff,tt in nditer([f,t])]\n", + " Fi.append(trapz(t,fi))\n", + " if Fr[a-1] < 0.01:\n", + " Fr[a-1]=0\n", + " \n", + " if Fi[a-1] < 0.01:\n", + " Fi[a-1]=0\n", + " \n", + " print Fr[a-1]-1J*Fi[a-1],'\\n'\n", + " a=a+1\n", + "\n", + "print '\\nThe given function in Expo Fourier series can be represented as \\n'\n", + "print 'f(t)= %f+jP/2*pi* ∑1/n *exp(j2*pi*t)'%(P/2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7, page no 22" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The Expo fourier series coeff are: for n=-5 to 5\n", + "(2.77555756156e-17-1.37737043993e-15j) \n", + "\n", + "(0.127481160803+3.12250225676e-16j) \n", + "\n", + "(-1.9567680809e-15-1.47624967806e-15j) \n", + "\n", + "(0.636776885598+6.54858112181e-16j) \n", + "\n", + "(-1.69309011255e-15-0.5j) \n", + "\n", + "(-1.90970223489+0j) \n", + "\n", + "(-1.69309011255e-15+0.5j) \n", + "\n", + "(0.636776885598-6.54858112181e-16j) \n", + "\n", + "(-1.9567680809e-15+1.47624967806e-15j) \n", + "\n", + "(0.127481160803-3.12250225676e-16j) \n", + "\n", + "(2.77555756156e-17+1.37737043993e-15j) \n", + "\n", + "The given function in Expo Fourier series can be represented as \n", + "\n", + "f(t)= 2V/pi -2V*exp(j2*pi*t)/3*pi -2V*exp(j2*pi*t)/15*pi\n", + " -2V*exp(j2*pi*t)/35*pi ...\n", + " -2V*exp(-j2*pi*t)/3*pi -2V*exp(-j2*pi*t)/15*pi...\n" + ] + }, + { + "data": { + "image/png": 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jUFNkpKfDxx/DddeFVy4jOEqr2CdNgg4doEqV8MlkBMcxxzhLe9o0b/r3WjEE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\nCRNyP8+58e7Zsyf3s86dO+v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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f3df8629110>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import arange,sin,pi,cos,trapz,nditer,zeros\n", + "%matplotlib inline \n", + "from matplotlib.pyplot import plot,subplot,title,legend,xlabel,ylabel,show\n", + "\n", + "#given\n", + "V=1\n", + "t0=1\n", + "T=1\n", + "w0=2*3.14/T\n", + "P=1\n", + "t=arange(0,0.01+3,0.01)\n", + "f=[V*abs(sin(pi*tt)) for tt in t]\n", + "#The Expo fourier series coeff\n", + "print 'The Expo fourier series coeff are: for n=-5 to 5'\n", + "a=1\n", + "Fr=[];Fi=[];mag=[]\n", + "for n in range(-5,6):\n", + " fr=[ff*cos(pi*n*tt/T) for ff,tt in nditer([f,t])]\n", + " Fr.append(trapz(t,fr))\n", + " fi=[ff*sin(pi*n*tt/T) for ff,tt in nditer([f,t])] \n", + " Fi.append(trapz(t,fi))\n", + " mag.append(abs(Fr[a-1]+1J*Fi[a-1]))\n", + "\n", + " print Fr[a-1]-(1J*Fi[a-1]),'\\n'\n", + " x=zeros(len(t))\n", + " #x=x+((Fr(a))-1J*Fi(a)).*(cos(pi*n*t/T)+1J*sin(pi*n*t/T))\n", + " x=x+((Fr[a-1])-1J*Fi[a-1])*(cos(pi*n*t/T)+1J*sin(pi*n*t/T))\n", + " a=a+1\n", + "\n", + "print 'The given function in Expo Fourier series can be represented as \\n'\n", + "print 'f(t)= 2V/pi -2V*exp(j2*pi*t)/3*pi -2V*exp(j2*pi*t)/15*pi\\n -2V*exp(j2*pi*t)/35*pi ...\\n -2V*exp(-j2*pi*t)/3*pi -2V*exp(-j2*pi*t)/15*pi...'\n", + "n=range(-5,6)\n", + "subplot(2,1,1)\n", + "plot(t,f) # Rectified sine function Plot\n", + "xlabel(\"t\")\n", + "ylabel(\"sin(t)\")\n", + "legend([\"sin(pi*t)\"])\n", + "subplot(2,1,2)\n", + "plot(n,mag) #Plot of the magnitude of the Fourier coeff\n", + "xlabel(\"w\")\n", + "ylabel(\"Fn\")\n", + "legend([\"Expo Fourier Coeff\"])\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8, page no 24" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The fourier series coeff Fn are:\n", + "(-0.185792520964+0j) \n", + "\n", + "(-0.121542879381+6.93889390391e-18j) \n", + "\n", + "(-0.0695370407613+0j) \n", + "\n", + "(-0.0312803786267+0j) \n", + "\n", + "(-0.00787673751141+1.73472347598e-18j) \n", + "\n", + "(1+0j) \n", + "\n", + "(-0.00787673751141+1.73472347598e-18j) \n", + "\n", + "(-0.00787673751141-1.73472347598e-18j) \n", + "\n", + "(-0.0312803786267+0j) \n", + "\n", + "(-0.0695370407613+0j) \n", + "\n", + "(-0.121542879381-6.93889390391e-18j) \n", + "\n", + "(-1.23107341487-2.77555756156e-17j) \n", + "\n", + "(-0.86361423984-2.77555756156e-17j) \n", + "\n", + "(-0.520835737317-2.77555756156e-17j) \n", + "\n", + "(-0.243085758762+2.77555756156e-17j) \n", + "\n", + "(-0.0625607572533+0j) \n", + "\n", + "(1+0j) \n", + "\n", + "(-0.0625607572533+0j) \n", + "\n", + "(-0.0625607572533+0j) \n", + "\n", + "(-0.243085758762-2.77555756156e-17j) \n", + "\n", + "(-0.520835737317+2.77555756156e-17j) \n", + "\n", + "(-0.86361423984+2.77555756156e-17j) \n", + "\n" + ] + }, + { + "data": { + "image/png": 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3Frl9fj48+qib+9DQfOc7bvb7mjWZHZpbVeVO5tE+s3iBoO52lZX+Pt+TTjo8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\nBaYAr9Tc4r3Px37zgNW4gNQ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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7fbfb25b1a10>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import pi,arange,cos,sin,trapz,zeros\n", + "%matplotlib inline \n", + "from matplotlib.pyplot import plot,subplot,title,legend,xlabel,ylabel,show\n", + "\n", + "\n", + "#given\n", + "\n", + "T=500e-3\n", + "w0=2*pi/T\n", + "d=50e-3\n", + "A=10\n", + "t=arange(-d/2,0.01+T-d/2,0.01)\n", + "t1=arange(-d/2,0.01+d/2,0.01)\n", + "f1=A\n", + "t2=arange(d/2,0.01+T-(d/2),0.01)\n", + "f2=0\n", + "a=0\n", + "Fr=[];Fi=[];mag=[]\n", + "print 'The fourier series coeff Fn are:'\n", + "for n in range(-5,6):\n", + " if n==0:\n", + " Fr.append(1);Fi.append(0)\n", + " else: \n", + " fa1=f1*cos(pi*n*t1/T)\n", + " fa2=f2*cos(pi*n*t2/T)\n", + " fb1=f1*sin(pi*n*t1/T)\n", + " fb2=f2*sin(pi*n*t2/T)\n", + " \n", + " Fr.append(1/T*(trapz(t1,fa1)+trapz(t2,fa2)))\n", + " Fi.append(trapz(t1,fb1)+trapz(t2,fb2))\n", + " mag.append(abs(Fr[a]+1J*Fi[a]))\n", + "\n", + " print Fr[a]-1J*Fi[a],'\\n'\n", + " x=zeros(len(t))\n", + " x=x+((Fr[a])-1J*Fi[a])*(cos(pi*n*t/T)+1J*sin(pi*n*t/T))\n", + " a=a+1\n", + "\n", + "n=range(-5,6)\n", + "subplot(3,1,1)\n", + "plot(t,[f1]*len(t))\n", + "xlabel(\"t\")\n", + "ylabel(\"f(t)\")\n", + "subplot(3,1,2)\n", + "plot(n,mag) # expo fourier series coeff\n", + "xlabel(\"n\") \n", + "ylabel(\"Coeff Magnitude\") \n", + "subplot(3,1,3)\n", + "plot(t,x)\n", + "plot(-t,x) # one sided spectrum with T=500ms\n", + "xlabel(\"w\")\n", + "ylabel(\"Fn\")\n", + "\n", + "T1=T/2\n", + "t=arange(-d/2,0.01+T1-d/2,0.01)\n", + "t1=arange(-d/2,0.01+d/2,0.01)\n", + "f1=A\n", + "t2=arange(d/2,0.01+T1-(d/2),0.01)\n", + "f2=0\n", + "#The Expo fourier series coeff\n", + "a=0\n", + "Fr1=[];Fi1=[];mag=[]\n", + "for n in range(-5,6):\n", + " if n==0:\n", + " Fr1.append(1);Fi1.append(0)\n", + " else :\n", + " fr1=f1*cos(pi*n*t1/T1)\n", + " fr2=f2*cos(pi*n*t2/T1)\n", + " fi1=f1*sin(pi*n*t1/T1)\n", + " fi2=f2*sin(pi*n*t2/T1)\n", + " \n", + " Fr1.append(1/T1*(trapz(t1,fr1)+trapz(t2,fr2)))\n", + " Fi1.append(1/T1*(trapz(t1,fi1)+trapz(t2,fi2)))\n", + " mag.append(abs(Fr1[a]+1J*Fi1[a]))\n", + " print Fr1[a]-1J*Fi1[a],'\\n'\n", + " y = zeros(len(t))\n", + " y=y+((Fr1[a])-1J*Fi1[a])*(cos(pi*n*t/T1)+1J*sin(pi*n*t/T1))\n", + " a=a+1\n", + "\n", + "plot(t,y)\n", + "plot(-t,y) # double sided spectrum with T=250ms\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9, page no 12" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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fHc1sMIRxXTP7PmWxcvED4aWhVcyr1IpKnpeNQXmcB1wt6UvgSsroLTTBBsBO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\nkyaPRCKRSNTN/wGSCNEUEKO5vgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f6066ed1f90>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "|F(w)|= 1/sqrt(a**2+w**2) and\n", + " Theta(w)=-atan(w/a)\n" + ] + }, + { + "data": { + "image/png": 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euAif0a1mNj3rO3zXzJ63UF31AGu/U5eQJ4zytxDoKqm277I78GHW/My4bM0+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\nY+pgAAAAAElFTkSuQmCC\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f6066d6d210>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "|F(w)|= 2*a/sqrt(a**2+w**2) and\n", + " Theta(w)=0\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange, exp, pi, transpose, mat, fliplr, angle, absolute, shape\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, xlabel, ylabel, show, title, subplot\n", + "\n", + "#Given:\n", + "# Analog Signal\n", + "A =1 # Amplitude\n", + "Dt = 0.005#\n", + "t = arange(0,Dt+10,Dt)\n", + "xt = exp(-A*t)#\n", + "\n", + "# Continuous time Fourier Transform\n", + "Wmax =2*pi*1# # Analog Frequency = 1Hz\n", + "K = 4#\n", + "k = arange(0,(K/1000)+K, (K/1000))\n", + "W = k* Wmax /K#\n", + "XW = mat(xt)*exp(-1J*transpose(mat(t))*mat(W))*Dt\n", + "XW_Mag =abs(XW)#\n", + "W = -1*fliplr(mat(W))+mat(W)# (2:1001)]# # Omega from -Wmax to Wmax\n", + "XW_Mag=fliplr(XW_Mag )+XW_Mag # (2:1001)]#\n", + "\n", + "\n", + "#[XW_Phase ,db] = phasemag (XW)#\n", + "XW_Phase = angle(XW)\n", + "db=abs(XW)\n", + "XW_Phase = -1*fliplr(XW_Phase)+XW_Phase #(2:1001)]#\n", + "\n", + "\n", + "\n", + "# Plotting Continuous Time Signal\n", + "plot(t,xt)#\n", + "xlabel( 't in sec .')#\n", + "ylabel(' x(t) ')\n", + "title(' Continuous Time Signal ' )\n", + "show()\n", + "\n", + "\n", + "# Plotting Magnitude Response of CTS\n", + "subplot (3 ,1 ,1)#\n", + "i, j = shape(W)\n", + "W1=[]\n", + "XW_Mag1=[]\n", + "for ii in range(0,i):\n", + " for jj in range(0,j):\n", + " W1.append(W[ii,jj])\n", + " XW_Mag1.append(XW_Mag[ii,jj])\n", + " \n", + "plot(W1, XW_Mag1)\n", + "xlabel ( ' Frequency in Radians / Seconds---> W' )#\n", + "ylabel ( ' abs (X(jW) ) ' )\n", + "title ( 'Magnitude Response (CTFT) ' )\n", + "\n", + "\n", + "\n", + "\n", + "# Plotting Phase Reponse of CTS\n", + "subplot (3 ,1 ,3)#\n", + "\n", + "i, j = shape(W)\n", + "W1=[]\n", + "XW_Phase1=[]\n", + "for ii in range(0,i):\n", + " for jj in range(0,j):\n", + " W1.append(W[ii,jj])\n", + " XW_Phase1.append(XW_Phase[ii,jj])\n", + "\n", + "\n", + "plot(W1, [xx*pi/180 for xx in XW_Phase1 ])\n", + "xlabel(' Frequency in Radians / Seconds---> W')#\n", + "ylabel('<X(jW) ')\n", + "title(' Phase Response (CTFT)in Radians' )\n", + "show()\n", + "print '|F(w)|= 1/sqrt(a**2+w**2) and\\n Theta(w)=-atan(w/a)'\n", + "\n", + "#Part b \n", + "# Analog Signal\n", + "\n", + "A=1## Amplitude\n", + "Dt=0.005#\n", + "t1=arange(-4.5,Dt+4.5,Dt)\n", + "xt1=exp(-A*abs(t1))\n", + "# Continuous time Fourier Transform\n", + "Wmax1 =2*pi*1## Analog Frequency = 1Hz\n", + "K=4#\n", + "k=arange(0,(K/1000)+K,(K/1000))\n", + "W1=k*Wmax1/K\n", + "XW1=mat(xt1)*exp(-1J*transpose(mat(t1))*mat(W1))*Dt\n", + "XW1=(XW1).real\n", + "W1=-1*fliplr(mat(W1))+mat(W1) # (2:1001) ]# # Omega from -Wmax to Wmax\n", + "XW1=fliplr(mat(XW1))+mat(XW1) #(2:1001) ]#\n", + "subplot(3 ,1 ,1)#\n", + "plot(t,xt)\n", + "xlabel('t in sec.')#\n", + "ylabel('x(t)')\n", + "title(' Continuous Time Signal')\n", + "subplot(3 ,1 ,3)\n", + "i, j = shape(W1)\n", + "W11=[]\n", + "XW11=[]\n", + "for ii in range(0,i):\n", + " for jj in range(0,j):\n", + " W11.append(W[ii,jj])\n", + " XW11.append(XW_Phase[ii,jj])\n", + "\n", + "plot(W11,XW11)\n", + "xlabel('Frequency in Radians / Seconds W')#\n", + "ylabel('X(jW)')\n", + "title('Continuous time Fourier Transform ')\n", + "show()\n", + "print '|F(w)|= 2*a/sqrt(a**2+w**2) and\\n Theta(w)=0'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example10, page no 38" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a)\n", + "At wo,n=0: The spectral amplitude is: F0= 0.100000 V\n", + "\n", + "b)\n", + "The Fourier tranform of f(t-delta/2) is given as: \n", + "\n", + "f(t)=A*delta/T*∑Sa(n*delta*pi/T)*exp(jwo(t-delta/2))\n" + ] + } + ], + "source": [ + "from numpy import pi,sin\n", + "\n", + "#Given\n", + "#a\n", + "A=1\n", + "delta=1e-3\n", + "T=10e-3\n", + "w0=2*pi/T\n", + "n=0\n", + "for i in range(0,11):\n", + " if n==0:\n", + " Sa=1 \n", + " else :\n", + " Sa=sin(n*pi*delta/T)/(n*pi*delta/T)\n", + " \n", + "\n", + "F=(A*delta/T)*Sa #spectral Amplitude\n", + "print 'a)\\nAt wo,n=0: The spectral amplitude is: F0= %f V\\n'%F\n", + "#b\n", + "# displaying the fourier Transform of the given function\n", + "print 'b)\\nThe Fourier tranform of f(t-delta/2) is given as: '\n", + "print '\\nf(t)=A*delta/T*∑Sa(n*delta*pi/T)*exp(jwo(t-delta/2))'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example11(1), page no 39" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f6080c29ad0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F(w)= A*t*Sa(w*t/2) \n" + ] + } + ], + "source": [ + "from numpy import arange, ones,pi,exp,mat,transpose, shape\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, xlabel, ylabel, show, title, subplot\n", + "\n", + "#Given\n", + "T = 10# #time Tau\n", + "Tg = arange(-T/2,0.1+T/2,0.1) # time period for given Gate Function -tau/2 to tau/2\n", + "G_t0 = 1# #Magnitude of Gate Function (A)\n", + "G_t = G_t0*ones (len(Tg))## Gate function G(t)\n", + "f = arange(-pi,pi / len(Tg)+pi,pi / len(Tg))\n", + "Dw = 0.1#\n", + "F_jW =mat(G_t)*exp(1J*transpose(mat(Tg))*mat(f))*Dw## fourier Transform of the gate function\n", + "F_jW = (F_jW).real\n", + "# Plotting the Fourier Transform of G(t)\n", + "subplot (2 ,1 ,1)\n", + "plot(Tg,G_t)\n", + "title( ' Given Function (Gate Function) G(t) ' )\n", + "subplot(2 ,1 ,2)\n", + "i,j =shape(mat(f))\n", + "m,n=shape(F_jW)\n", + "f1=[];F_jW1=[]\n", + "for ii in range(0,i):\n", + " for jj in range(0,j):\n", + " f1.append(mat(f)[ii,jj])\n", + "for ii in range(0,m):\n", + " for jj in range(0,n):\n", + " F_jW1.append(F_jW[ii,jj])\n", + " \n", + "\n", + "plot(f1,F_jW1)\n", + "xlabel('Frequency in Radians/Seconds ')#\n", + "title('Continuous time Fourier Transform X(jW)' )\n", + "title ( 'Fourier Transform of G(t)= F(jW) ' )\n", + "show()\n", + "print 'F(w)= A*t*Sa(w*t/2) '" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example11(2), page no 43" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "|F(w)|= 2*pi*A*delta(w), Hence the Fourier Transform of constant is an Impulse Function\n" + ] + }, + { + "data": { + "image/png": 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KscbuPbzMW2feu+XxMaa98BbMH83s65S+umceADN7xsz2SWnGkSZe4O/mKUXv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\nDtgkYBszm5zCXgQKQ3ptcGd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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f6080c29e50>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange, ones,pi,exp,mat,transpose,pi, fliplr, shape\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, xlabel, ylabel, show, title, subplot\n", + "\n", + "#Given\n", + "# CTS Signal\n", + "A=2## Amplitude\n", + "Dt=0.01#\n", + "T1=49.5# #Time in seconds\n", + "t=arange(-T1/2,Dt+T1 /2, Dt)\n", + "xt=[]\n", + "for i in range(0,len(t)):\n", + " xt.append(A)\n", + "\n", + "# Continuous time Fourier Transform\n", + "Wmax=2*pi*1## Analog Frequency = 1Hz\n", + "K =4#\n", + "k=arange(0,(K/1000)+K,(K/1000))\n", + "W=k*Wmax/K#\n", + "#xt=transpose(mat(xt))\n", + "XW =(mat(xt)*exp(1J*transpose(mat(t))*mat(W)*Dt))-5#\n", + "\n", + "\n", + "XW_Mag =(XW).real\n", + "W = -1*fliplr(mat(W))+W # (2:1001)]# # Omega from -Wmax to Wmax\n", + "XW_Mag = fliplr(mat(XW_Mag))+XW_Mag #(2:1001)\n", + "subplot(2 ,1 ,1)#\n", + "plot(t,xt)#\n", + "xlabel('t in msec .')#\n", + "title(' Contiuous Time Signal x(t) ')\n", + "subplot(2 ,1 ,2)#\n", + "i,j =shape(mat(W))\n", + "m,n=shape(XW_Mag)\n", + "W1=[];XW_Mag1=[]\n", + "for ii in range(0,i):\n", + " for jj in range(0,j):\n", + " W1.append(mat(W)[ii,jj])\n", + "for ii in range(0,m):\n", + " for jj in range(0,n):\n", + " XW_Mag1.append(XW_Mag[ii,jj])\n", + "\n", + "plot(W1,XW_Mag1)\n", + "xlabel('Frequency in Radians/Seconds ')#\n", + "title('Continuous time Fourier Transform X(jW) = an Impulse Function' )\n", + "print '|F(w)|= 2*pi*A*delta(w), Hence the Fourier Transform of constant is an Impulse Function'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example13, page no 44" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F(w)= 1/(j*w)+ pi*delta(w)\n" + ] + }, + { + "data": { + "image/png": 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LWBX69euXdRHKEuVsXVHO1tMeygjtp5zNlfnA6JIs6zKEEEJ7IwmrwIXcEEII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\n+CL8978+hGgtqFhq5ZYkXEv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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f6066d01690>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange, ones,pi,exp,mat,transpose,pi, fliplr, shape\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, xlabel, ylabel, show, title, subplot\n", + "\n", + "\n", + "# CTS Signal\n", + "A =1# # Amplitude\n", + "Dt = 0.005#\n", + "T1 =0.5# #Time in seconds\n", + "t=arange(0,Dt+T1, Dt)\n", + "xt=[]\n", + "for i in range(0,len(t)):\n", + " xt.append(A)\n", + "\n", + "# Continuous time Fourier Transform\n", + "Wmax= 2*pi*1# # Analog Frequency = 1Hz\n", + "K =4#\n", + "k=arange(0,(K/1000)+K,(K/1000))\n", + "W =k*Wmax/K#\n", + "#xt=transpose(mat(xt))\n", + "XW =mat(xt)*exp(-1J*transpose(mat(t))*mat(W))*Dt#\n", + "XW_Mag =(XW).real\n", + "W =-1*fliplr(mat(W))+W #(2:1001)]# # Omega from -Wmax to Wmax\n", + "XW_Mag =fliplr(mat(XW_Mag))+XW_Mag #(2:1001)]\n", + "# displaying the given function\n", + "subplot(2 ,1 ,1)#\n", + "plot(t,xt)#\n", + "xlabel('t in msec .')#\n", + "title(' Contiuous Time Signal x(t) ')\n", + "# displaying the fourier Transform of the given function\n", + "subplot(2 ,1 ,2)#\n", + "print 'F(w)= 1/(j*w)+ pi*delta(w)'\n", + "i,j =shape(mat(W))\n", + "m,n=shape(XW_Mag)\n", + "W1=[];XW_Mag1=[]\n", + "for ii in range(0,i):\n", + " for jj in range(0,j):\n", + " W1.append(mat(W)[ii,jj])\n", + "for ii in range(0,m):\n", + " for jj in range(0,n):\n", + " XW_Mag1.append(XW_Mag[ii,jj])\n", + "\n", + "plot(W1,XW_Mag1)\n", + "\n", + "xlabel('Frequency in Radians / Seconds ')#\n", + "title('Continuous time Fourier Transform X(jW)' )\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example14, page no 44" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Ylm9WYRdIbSrkCKAjsAOwFLgBaAzg7kOibQYSZtSsBS5w9zcq2Y9G7gVk1aqw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\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f6066d83990>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import pi,sqrt\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, xlabel, ylabel, show, title, subplot\n", + "\n", + "# CTS Signal\n", + "# Continuous Time Fourier Transforms of\n", + "# Sinusoidal waveforms(a)sin(Wot)(b)cos(Wot)\n", + "\n", + "# CTFT\n", + "T1 = 2#\n", + "T = 4* T1#\n", + "Wo = 2* pi /T#\n", + "W = [-Wo ,0, Wo ]#\n", + "ak = (2* pi *Wo*T1/ pi )/ 1J#\n", + "XW = [-ak ,0, ak ]#\n", + "ak1 = (2* pi*Wo*T1/pi)#\n", + "XW1 =[ ak1 ,0, ak1 ]#\n", + "#displaying the given function\n", + "plot(W,[aa.imag for aa in XW])\n", + "xlabel('W' )#\n", + "title( 'CTFT of sin(Wot ) ')\n", + "show()\n", + "#displaying the fourier Transform of the given function\n", + "plot(W,XW1)\n", + "xlabel('W' )#\n", + "title( 'CTFT of cos (Wot)')\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example16, page no 47" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Spectral Amplitude of the given function is given by \n", + "Fn= A*delta/2 *[Sa(n*pi*delta/T)]\n", + "Therefore the fourier transform will be :\n", + "F[f(t)]=0.628319 ∑Sa[n*pi/10]8delta(w-4*n*pi)\n" + ] + } + ], + "source": [ + "from numpy import pi\n", + "A=1\n", + "delta=50e-3\n", + "T=500e-3\n", + "print 'Spectral Amplitude of the given function is given by '# Displaying the expression for Spectral Amplitude\n", + "print 'Fn= A*delta/2 *[Sa(n*pi*delta/T)]'\n", + "print 'Therefore the fourier transform will be :'\n", + "print 'F[f(t)]=%f ∑Sa[n*pi/10]8delta(w-4*n*pi)'%(2*pi*A*delta/T)# Displaying the Fourier transform" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example17,page no12" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "F[∂t(t)]= 2*pi/T*∑∂(w-wo)\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f6080bf8910>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import ones,pi\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, xlabel, ylabel, show, title, subplot\n", + "\n", + "#Given:\n", + "# CTFT\n", + "T = range(-4,5)##\n", + "T1 = 1# # Sampling Interval\n", + "xt = ones (len(T))#\n", + "ak = 1/ T1#\n", + "XW = 2* pi *ak* ones (len(T))#\n", + "Wo = 2*pi/T1#\n", + "W = [Wo*Tt for Tt in T]#\n", + "# Displaying the given function\n", + "subplot(2 ,1 ,1)\n", + "plot(T,xt)\n", + "xlabel ( 't ' )#\n", + "title('Periodic Impulse Train ')\n", + "# displaying the fourier Transform of the given function\n", + "subplot(2 ,1 ,2)\n", + "plot(W,XW)\n", + "xlabel('t')#\n", + "title ( 'CTFT of Periodic Impulse Train')\n", + "\n", + "print 'F[∂t(t)]= 2*pi/T*∑∂(w-wo)'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example18,page no12" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hence Fourier transform of given Gate function is:\n", + " A*delta*Sa[w*delta/2]/ exp(-j*w*delta/2)\n" + ] + }, + { + "data": { + "image/png": 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gKXK2JWbWp4w0TdKbES6xGZjZeNy+eqWknSR1Sh1f20k6LyW7DTg1dWQtktKX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\n+8H/5psZfTtB9VKVQVTMbFk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QPEV5HZnJaznzIA8C/pdJ8xOuIEvahM1sMvAYsDPwO8pz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\n/w+9sYHJi5vhcwAAAABJRU5ErkJggg==\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f6066c6b150>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import arange, pi,exp,mat, transpose,fliplr,shape\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, xlabel, ylabel, show, title, subplot\n", + "\n", + "#Given:\n", + "# CTS Signal\n", + "A =1# # Amplitude\n", + "Dt = 0.005#\n", + "T1 = 2# #Time in seconds\n", + "t = arange(0,Dt+T1 /2, Dt)\n", + "xt=[]\n", + "for i in range(0,len(t)):\n", + " xt.append(A)\n", + "\n", + "# Continuous time Fourier Transform\n", + "Wmax= 2*pi*1# # Analog Frequency = 1Hz\n", + "K =4#\n", + "k=arange(0,(K/1000)+K,(K/1000))\n", + "W =k*Wmax/K#\n", + "XW =mat(xt)*exp(-1J*transpose(mat(t))*mat(W))*Dt#\n", + "XW_Mag =(XW).real\n", + "W =-fliplr(mat(W))+W #(2:1001)]# # Omega from Wmax to Wmax\n", + "XW_Mag =fliplr(mat(XW_Mag))+XW_Mag #(2:1001)]#\n", + "# displaying the given function\n", + "subplot(2 ,1 ,1)#\n", + "plot(t,xt)#\n", + "xlabel('t in msec .')#\n", + "title(' Contiuous Time Signal x(t) {Gate Function} ')\n", + "# displaying the fourier Transform of the given function\n", + "subplot(2 ,1 ,2)#\n", + "i,j =shape(mat(W))\n", + "m,n=shape(XW_Mag)\n", + "W1=[];XW_Mag1=[]\n", + "for ii in range(0,i):\n", + " for jj in range(0,j):\n", + " W1.append(mat(W)[ii,jj])\n", + "for ii in range(0,m):\n", + " for jj in range(0,n):\n", + " XW_Mag1.append(XW_Mag[ii,jj])\n", + "\n", + "plot(W1,XW_Mag1)\n", + "\n", + "xlabel('Frequency in Radians / Seconds ')#\n", + "title('Continuous time Fourier Transform X(jW)' )\n", + "print 'Hence Fourier transform of given Gate function is:\\n A*delta*Sa[w*delta/2]/ exp(-j*w*delta/2)'" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter2_NaNiwP4.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter2_NaNiwP4.ipynb new file mode 100644 index 00000000..8d9af0c5 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter2_NaNiwP4.ipynb @@ -0,0 +1,444 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2 Switched communication systems" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.2, page no 125" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "maximum auxillary current is:10.00 mA\n", + "\n", + "MMF in the auxillary winding is:2.00AT \n", + "\n", + "MMF in main winding is:40.00 AT \n", + "\n", + "net MMF required in main winding is:44.00 AT \n", + "\n", + "operating current needed is:4.40 mA \n", + "\n", + "working voltage is:2.84 volts \n", + "\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#given\n", + "Io=4*10**-3 #rqueired operating current\n", + "N1=10000 #no of turns in the main winding\n", + "R1=645 #resistence of the main winding in ohms\n", + "N2=200 #no of turns in auxillary winding\n", + "B=2 #spacing bias\n", + "Iaux=B/N2 #maximum auxillary current\n", + "print \"maximum auxillary current is:%0.2f mA\\n\"%(Iaux*1e3)\n", + "MMFaux=N2*Iaux #MMF in the auxillary winding\n", + "print \"MMF in the auxillary winding is:%0.2fAT \\n\"%(MMFaux)\n", + "MMFop=Io*N1 #operating MFF in main winding\n", + "print \"MMF in main winding is:%0.2f AT \\n\"%(MMFop)\n", + "MMFnet=MMFop+(0.1*MMFop) #net MMF required in main winding\n", + "print \"net MMF required in main winding is:%0.2f AT \\n\"%(MMFnet)\n", + "Iop=MMFnet/N1 #operating current needed\n", + "print \"operating current needed is:%0.2f mA \\n\"%(Iop*1e3)\n", + "V=Iop*R1 #working voltage in volts\n", + "print \"working voltage is:%0.2f volts \\n\"%(V)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3,page no 125" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Busy hour calling rate is:1.20 \n", + "\n", + "Rate of traffic flow is 250.00 traffic unit \n" + ] + } + ], + "source": [ + "#given\n", + "C=6000#Tatol no of call in busy hour\n", + "SC=5000#no of subscribers\n", + "CR=C/SC#busy hour calling rate\n", + "print \"Busy hour calling rate is:%0.2f \\n\"%(CR)\n", + "T=2.5/60#avarage duration of calls in hours\n", + "\n", + "A=C*T#rate of traffic flow\n", + "print \"Rate of traffic flow is %0.2f traffic unit \"%(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4,page no 126" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "maxixmum current is 33.33 mamps \n", + "\n", + "operate lag is 1.83 msec \n", + "\n", + "release lag is 2.85 msec \n", + "\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log\n", + "#given\n", + "L=3#relay inductance in henry\n", + "R=1500#relay resistance in ohm\n", + "Io=20e-3#oparating current in amps\n", + "Ir=8e-3#release current in amps\n", + "\n", + "V=50#supply volatage in volts\n", + "Im=V/R#maxixmum current in amps\n", + "print \"maxixmum current is %0.2f mamps \\n\"%(Im*1e3)\n", + "to=(L/R)*log(1/(1-(Io/Im)))#operate lag in sec\n", + "print \"operate lag is %0.2f msec \\n\"%(to*1000)\n", + "tr=(L/R)*log(Im/Ir)#release lag in sec\n", + "print \"release lag is %0.2f msec \\n\"%(tr*1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4.1,page no 126" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(a)\n", + "periods per character is:150.00 msec\n", + "\n", + "period per element is:20.00 msec\n", + "\n", + "speed is:50.00 bauds\n", + "\n", + "\n", + "(b)\n", + "periods per character is:100.00 msec\n", + "\n", + "period per element is:13.33 msec\n", + "\n", + "speed is 75.00 bauds\n", + "\n", + "\n", + "(c)\n", + "periods per character is:100.00 msec\n", + "\n", + "period per element is:10.00 msec\n", + "\n", + "speed is 100.00 bauds\n", + "\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#given\n", + "#a\n", + "C_S1=20/3#speed in characters per second\n", + "P_C1=1/C_S1#periods per character\n", + "print \"(a)\\nperiods per character is:%0.2f msec\\n\"%(P_C1*1e3)\n", + "E_C1=7.5#elements per character\n", + "P_E1=P_C1/E_C1#period per element\n", + "print \"period per element is:%0.2f msec\\n\"%(P_E1*1e3)\n", + "Sb1=1/P_E1#speed in bauds\n", + "print \"speed is:%0.2f bauds\\n\\n\"%(Sb1)\n", + "#b\n", + "C_S2=10#speed in characters per second\n", + "P_C2=1/C_S2#periods per character\n", + "print \"(b)\\nperiods per character is:%0.2f msec\\n\"%(P_C2*1e3)\n", + "E_C2=7.5#elements per character\n", + "P_E2=P_C2/E_C2#period per element\n", + "print \"period per element is:%0.2f msec\\n\"%(P_E2*1e3)\n", + "Sb2=1/P_E2#speed in bauds\n", + "print \"speed is %0.2f bauds\\n\\n\"%( Sb2)\n", + "#c\n", + "C_S3=10#speed in characters per second\n", + "P_C3=1/C_S3#periods per character\n", + "print \"(c)\\nperiods per character is:%0.2f msec\\n\"%(P_C3*1e3)\n", + "E_C3=10#elements per character\n", + "P_E3=P_C3/E_C3#period per element\n", + "print \"period per element is:%0.2f msec\\n\"%(P_E3*1e3)\n", + "Sb3=1/P_E3#speed in bauds\n", + "print \"speed is %0.2f bauds\\n\"%(Sb3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.5,page no 127" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "total inductance is 0.05 H \n", + "\n", + "maximum current is 10.00 mA \n", + "\n", + "operating current is 5.00 mA \n", + "\n", + "operate lag is 0.35 msec \n", + "\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#given\n", + "N=1000#no of turns\n", + "L1=5e-8#inductance per turn\n", + "L=N**2*L1#total inductance\n", + "print \"total inductance is %0.2f H \\n\"%(L)\n", + "R=100#resistance of winding in ohm\n", + "MMF=5#operating MMF in amp. turn\n", + "V=1#voltage of received signal in volts\n", + "Im=V/R#maximum current\n", + "print \"maximum current is %0.2f mA \\n\"%(Im*1e3)\n", + "Io=MMF/N#operating current\n", + "print \"operating current is %0.2f mA \\n\"%(Io*1e3)\n", + "to=(L/R)*log(1/(1-(Io/Im)))#operate lag\n", + "print \"operate lag is %0.2f msec \\n\"%(to*1e3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.6,page no 128" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Busy hour calling rate is:1.60 \n", + "\n", + "Rate of traffic flow is 693.33 traffic unit \n" + ] + } + ], + "source": [ + "#given\n", + "S=10000#no of subscribers\n", + "C=16000#Tatol no of call in busy hour\n", + "CR=C/S#busy hour calling rate\n", + "print \"Busy hour calling rate is:%0.2f \\n\"%(CR)\n", + "T=2.6#avarage duration of calls in min\n", + "\n", + "A=C*(T/60)#rate of traffic flow\n", + "print \"Rate of traffic flow is %0.2f traffic unit \"%(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.7,page no 135" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "duration of each element is:10.00 msec\n", + "\n", + "speed is 100.00 bauds\n", + "\n", + "total possible combinations are:128.00\n" + ] + } + ], + "source": [ + "#given\n", + "N=7#no of character elements\n", + "E_C=10#elements per character (1+7+1+1)\n", + "To=100e-3#duration of one character\n", + "Te=To/E_C#duration of each element\n", + "print \"duration of each element is:%0.2f msec\\n\"%(Te*1e3)\n", + "Sb=1/Te#speed in bauds\n", + "print \"speed is %0.2f bauds\\n\"%(Sb)\n", + "C=2**N#total possible combinations\n", + "print \"total possible combinations are:%0.2f\"%(C)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.8,page no 129" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total no of call in busy hour is:1500.00 calls per Hour\n", + "\n", + "Busy hour calling rate is:1.50 \n", + "\n", + "grade of service is: 0.02\n" + ] + } + ], + "source": [ + "#given\n", + "S=1000#no of subscribers\n", + "T=2.4/60#avarage duration of calls in hours\n", + "A=60#rate of traffic flow\n", + "C=A/T#Tatol no of call in busy hour\n", + "print \"Total no of call in busy hour is:%0.2f calls per Hour\\n\"%(C)\n", + "CR=C/S#busy hour calling rate\n", + "print \"Busy hour calling rate is:%0.2f \\n\"%(CR)\n", + "SCL=30#no of call lost per hour\n", + "\n", + "B=SCL/(C+SCL)#grade of service\n", + "print \"grade of service is: %0.2f\"%(B)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.9,page no 129" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "grade of service is: 2.00e-03\n", + "\n", + "traffic lost is: 1.80e-03\n" + ] + } + ], + "source": [ + "from math import factorial\n", + "#given\n", + "N=5#no of switches\n", + "A=0.9#traffic offered \n", + "#grade of service B=(A**N/N!)/(1+A+A**2/2!+A**3/3!+...+A**N/N!)\n", + "#here\n", + "B=(A**N/factorial(N))/(1+A+(A**2/factorial(2))+(A**3/factorial(3))+(A**4/factorial(4))+(A**5/factorial(5)))\n", + "print \"grade of service is: %0.2e\\n\"%(B)\n", + "Tl=A*B#traffic lost\n", + "print \"traffic lost is: %0.2e\"%(Tl)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter3_xiZnYrP.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter3_xiZnYrP.ipynb new file mode 100644 index 00000000..49782c9f --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter3_xiZnYrP.ipynb @@ -0,0 +1,1095 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter No. 3 - Modulation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.1, page no 135" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "percentage modulation is:83.14.2f \n", + " Power after modulation is:13.46.2f watts\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt\n", + "#Given\n", + "Ic=10 #carrier current in Amps\n", + "Imod=11.6# Current after modulation\n", + "Rl=1#Assumed load in ohm\n", + "Pmod=Rl*Imod**2#power before modulation\n", + "Ma= sqrt(2*((Pmod/Ic**2)-1))#percentage modulation\n", + "Pc=10\n", + "Pmod=Pc*(1+(Ma**2/2))#power after modulation\n", + "print 'percentage modulation is:%0.2f.2f \\n Power after modulation is:%0.2f.2f watts'%(Ma*100,Pmod)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.2, page no 135" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Depth of modulation is:0.50.2f\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt\n", + "#Given\n", + "Pc=9e3# Tx Power without modulation\n", + "Pmod=10.125e3#Tx Power after modulation\n", + "Ma= sqrt(2*((Pmod/Pc)-1))#depth of (percentage) modulation\n", + "print 'Depth of modulation is:%0.2f.2f'%(Ma)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.3, page no 136" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The total power radiated is 1320 watts\n" + ] + } + ], + "source": [ + "#Given\n", + "M1=0.2#depth of modulation for first tone\n", + "M2=0.4#depth of modulation for second tone\n", + "Pc=1200#Tx Power\n", + "Pmod=Pc*(1+M1**2/2+M2**2/2)#total power radiated after modulation by both the tones\n", + "print 'The total power radiated is %d watts'%(Pmod)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.4, page no 138" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "modulating power required from the audio source\n", + " is:37.69 watts\n", + " Modulator Impedance is:29850.75 ohm\n", + " Plate dissipation is:96.69 watts\n" + ] + } + ], + "source": [ + "#Given\n", + "Ebb=2e3#DC plate supply\n", + "Ecc=-500#DC grid bias\n", + "Ib=67e-3#DC plate current\n", + "Ic=30e-3#DC grid current\n", + "Egm=750#RF peak grid voltage\n", + "Pout=75#RF Power output\n", + "Ma=0.75#Depth of modulation\n", + "Paf=(Ma**2*Ebb*Ib)/(2*1)#modulating power required from the audio source\n", + "Pdc=Ebb*Ib#Power supplied by DC source\n", + "Zm=Ebb**2/Pdc#Modulator Impedance\n", + "\n", + "Pd=Pdc+Paf-Pout#Plate dissipation\n", + "print 'modulating power required from the audio source\\n is:%0.2f watts\\n Modulator Impedance is:%0.2f ohm\\n Plate dissipation is:%0.2f watts'%(Paf,Zm,Pd)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.5b, page no 139" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tx power:1200.00 Watts\n", + " Power dissipation at the modulator is: 3000.00 Watts\n", + " Overall Efficiency at0.6 modulation is:41.16% \n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt\n", + "#Given\n", + "Pd=944#Anode dissipation of the class C amplifier in watts\n", + "Ma=0.6#modulation depth,\n", + "Etta=0.6#efficiency\n", + "Pout=(Etta*Pd/(1-Etta))#power dissipation at 60% modulation\n", + "Pc=Pout/(1+(Ma**2/2))#Tx power\n", + "Psb=Pout-Pc\n", + "Pdc1=Pc/Etta#DC power inputto PA\n", + "Paf=Psb/Etta# modulation power input to PA\n", + "Eff=0.25# efficiency of the modulator\n", + "Pdc2=Paf/Eff#DC power input to modulator\n", + "Pdct=Pdc1+Pdc2#Total DC power to the system\n", + "Effo=Pout/Pdct#Overall Efficiency\n", + "Ma=1# 100% modulation\n", + "Pt=Pc*(1+(Ma**2)/2)\n", + "Psb=(Pc*Ma**2)/2\n", + "Paf=Psb/Etta#modulating input power to PA\n", + "Pdc2=Paf/Eff# DC power input to modulator\n", + "Pd=Pdc2-Paf#Power dissipation at the modulator\n", + "Effo1=Pout/(Pdc1+Pdc2)#Overall Efficiency\n", + "print 'Tx power:%0.2f Watts\\n Power dissipation at the modulator is: %0.2f Watts\\n Overall Efficiency at0.6 modulation is:%0.2f%c '%(Pc,Pd,100*Effo,'%')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.6, page no 141" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Carrier Power is: 1133.33 watts \n", + " DC plate dissipation is: 266.67 watts\n", + " output power of modulator is: 700.00 watts\n", + " Plate dissipation inthe modulator is:466.67 watts\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt#Given\n", + "Pdc=1400#DC power i/p to PA under 100% modulation\n", + "Ptdc=400#Plate dissipation\n", + "Pd=Ptdc*(2/3)#DC plate dissipation\n", + "\n", + "Pdmod=Ptdc*(1/3)#\n", + "Pc=Pdc-Pd#Carrier Power\n", + "\n", + "Psb=Pc/2#side band power\n", + "Paf=Psb+Pdmod#output power of modulator\n", + "\n", + "Mod_Eff=0.6\n", + "Pdc2=Paf/Mod_Eff#DC i/p power to the modulator\n", + "Pd_AF=Pdc2-Paf#Plate dissipation inthe modulator\n", + "print 'Carrier Power is: %0.2f watts \\n DC plate dissipation is: %0.2f watts\\n output power of modulator is: %0.2f watts\\n Plate dissipation inthe modulator is:%0.2f watts'%(Pc,Pd,Paf,Pd_AF)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.7, page no 141" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Maximum carrier power is: 750 watts\n", + " Total RF power is: 1125 watts\n" + ] + } + ], + "source": [ + "#Given\n", + "Paf=500#Modulator output power\n", + "Eff=0.75#Efficiency of the amplifier\n", + "P_lost=Paf*(1-Eff)#modulating power lost in the amplifier\n", + "Psb=Paf*Eff#side band power\n", + "\n", + "m=1\n", + "Pc=2*Psb\n", + "\n", + "Pt=Pc+Psb#Total RF power\n", + "print 'Maximum carrier power is: %d watts\\n Total RF power is: %d watts'%(Pc,Pt)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.8, page no 143" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Carrier power is: 2100 watts\n", + " Maximum depth of modulation is: 92.58\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt#Given\n", + "Po=3000# Rating of Power Amplifier\n", + "Pr=750#Push-Pull amplifier rated as\n", + "Paf=2*Pr#Rated power output from Push-Pull modulator\n", + "Eff=0.6\n", + "P_lost=Paf-(Eff*Paf)#Modulation power lost\n", + "Psb=Paf-P_lost#side band power\n", + "\n", + "Pc=Po-Psb#Carrier power\n", + "Ma=sqrt(2*Psb/Pc)*100#Maximum depth of modulation\n", + "print 'Carrier power is: %d watts\\n Maximum depth of modulation is: %0.2f'%(Pc,Ma)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.9, page 143" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Carrier freq is: 10 MHz\n", + "Modulating freq is:500 Hz\n", + "Carrier power is: 208.00 watts\n", + "Mean output power is: 224.64 watts\n", + "Peak output power is: 408.33 watts\n" + ] + } + ], + "source": [ + "from numpy import arange, pi\n", + "#Given\n", + "t=arange(0,10,0.001)\n", + "#e=500*(1+(0.4*sin(3140*t)))*sin(6.28e7*t)\n", + "#a\n", + "wc=6.28e7#Carrier angular frequency\n", + "fc=wc/(2*pi)# Carrier freq\n", + "#b\n", + "wm=3140#Modulating angular freq\n", + "fm=wm/(2*pi)#Modulating freq\n", + "#c\n", + "Ec=500#/peak carrier voltage\n", + "Pc=(Ec**2)/(2*600)#Carrier power\n", + "#d\n", + "Ma=0.4\n", + "Pt=Pc*(1+(Ma**2 / 2))#Mean output power\n", + "#e\n", + "Rl=600#load resistance\n", + "Ecp=Ec+(Ma*Ec)#Peak output voltage\n", + "Ptm=Ecp**2/(2*Rl)#Peak power\n", + "print 'Carrier freq is: %d MHz\\nModulating freq is:%d Hz\\nCarrier power is: %0.2f watts\\nMean output power is: %0.2f watts\\nPeak output power is: %0.2f watts'%(round(fc*1e-6),round(fm),Pc,Pt,Ptm)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.10, page no 143" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Antenna current for full modulation is: 45.64 amp\n", + "Peak base voltage is: 5672.55/_48 volts\n", + "Peak base voltage is: 4254.41/_48 volts\n" + ] + } + ], + "source": [ + "from math import atan,sqrt\n", + "from cmath import polar\n", + "#Given\n", + "#b\n", + "Pc=50e3#Carrier power\n", + "Z=36 + 1J*40#base impedance of the antenna\n", + "Ma=1#modulation depth\n", + "Pmod=Pc*(1+((Ma**2)/2))#power delivered to the antenna under 100% modulation\n", + "#i\n", + "R=36#resistance of the antenna \n", + "Irms=sqrt(Pmod/R)#Antenna Current\n", + "\n", + "#ii\n", + "Ic=sqrt(Pc/R)#RMS carrier current \n", + "\n", + "Icm=Ic*sqrt(2)# Peak carrier current \n", + "Imod=2*Icm#Modulated current\n", + "\n", + "Theta=atan(40/36)*180/pi# from real and imaginary components of Z\n", + "Vbm100=Imod*Z#Peak base output voltage for 100% modulation\n", + "[Re_Vb,Im_Vb]=polar(Vbm100)\n", + "\n", + "#iii\n", + "Ma=0.5\n", + "Imod=Icm*(1+0.5)\n", + "\n", + "Vbm50=Imod*Z\n", + "[Re_Vb1,Im_Vb1]=polar(Vbm50)\n", + "print 'Antenna current for full modulation is: %0.2f amp\\nPeak base voltage is: %0.2f/_%d volts\\nPeak base voltage is: %0.2f/_%d volts'%(Irms,Re_Vb,Theta,Re_Vb1,Theta)\n", + "# The Ans is little deviated from that of book as the decimal places considered while calculating at different stages might be different \n", + "\n", + "#Answers from the book are little deviated but the evaluated values in the scilab are correct results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.11, page no 144" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "USB freq=10005 k5Hz\n", + "USB amplitude=2.50 V\n", + "LSB freq=9995 kHz\n", + "LSB amplitude=2.50 V\n", + "Carrier amplitude=10 V\n" + ] + }, + { + "data": { + "image/png": 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bZhWEcH/PntHopKzt4oIQ77z377+cIHjhGzo0Oq5Hj+gzlOT4w/Mec4z73b27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\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7fac3ffd5150>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from math import sin\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, subplot, title, xlabel, ylabel, show\n", + "# Given\n", + "def f(x):\n", + " y=[]\n", + " for xx in x:\n", + " y.append(Ec*(1+ma*(sin(wm*xx)))*sin(wc*xx))\n", + " return y\n", + "Ec=10\n", + "ma=0.5\n", + "wm=10000*pi\n", + "wc=2*pi*1e7\n", + "x=arange(0,20*pi/10,.01)\n", + "subplot(2,1,1)\n", + "plot(x,f(x))\n", + "xlabel(\"t\")\n", + "ylabel(\"Modulated Wave\")\n", + "Fc=wc/(2*pi)\n", + "Fm=wm/(2*pi)\n", + "Fusb=(wm+wc)/(2*pi)\n", + "Flsb=(wm-wc)/(2*pi)\n", + "print 'USB freq=%d k5Hz\\nUSB amplitude=%0.2f V\\nLSB freq=%d kHz\\nLSB amplitude=%0.2f V\\nCarrier amplitude=%d V'%(Fusb*1e-3,2.5,Flsb*-1e-3,2.5,10)\n", + "F=[0,2.5,10,2.5,0]\n", + "T=[-2,-1,0,1,2]\n", + "subplot(2,1,2)\n", + "plot(T,F)\n", + "xlabel(\"Freq\")\n", + "ylabel(\"Amplitude\")\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.12 page no 145" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The depth of modulation is: 50%\n" + ] + } + ], + "source": [ + "from math import sqrt\n", + "#Given\n", + "Pc=9e3#unmodulated carrier power\n", + "Pt=10.125e3#Modulated carrier power\n", + "Ma=sqrt(2*((Pt/Pc)-1))#depth of modulation\n", + "print 'The depth of modulation is: %d%c'%(Ma*100,'%')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.13 page no 148" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The power output is: 34.45 W\n" + ] + } + ], + "source": [ + "#Given\n", + "Pt=5e3#carrier power for 95% modulation\n", + "Ma=0.95\n", + "Pc=Pt/(1+((Ma**2)/2))#carrier power\n", + "Ma=0.2#average modulation by speech signal\n", + "Psb=(Ma**2)*Pc/2#the power n the sideband\n", + "Pout=Psb/2# because one of the side band is suppressed\n", + "print 'The power output is: %0.2f W'%(Pout)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.14 page no 152" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DeltaPhi1= 10 rad\n", + "DeltaPhi2=500 rad\n", + "\n" + ] + } + ], + "source": [ + "#Given\n", + "#Phi=(wc*t+Mf*sin(wmt))....instantaneous phase of FM\n", + "fm=5000#modulating freq\n", + "deltaf=50e3#freq deviation\n", + "deltaPhi1=deltaf/fm# Advance or retard in phase\n", + "\n", + "fm=100#modulating freq in second signal\n", + "deltaPhi2=deltaf/fm\n", + "print 'DeltaPhi1= %d rad\\nDeltaPhi2=%d rad\\n'%(deltaPhi1,deltaPhi2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.14 page no 157" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Peak Phase Deviation: 0.76 rad\n", + "Peak Freq Deviation: 761 Hz\n", + "Depth of residual AM: 0.08\n", + "Residual AM freq:2 kHz\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt,atan\n", + "#Given\n", + "#e=Ec(1+0.4cos(2pie3*t))*sin(2pie7*t)\n", + "fm=1000#modulating s/g freq\n", + "deltaTheta=2*atan(0.4)#peak phase deviation\n", + "\n", + "deltaF=deltaTheta*fm#Peak freq deviation\n", + "\n", + "Ec=1\n", + "Er=sqrt((Ec**2)*(1+(0.4**2)))\n", + "m=(Er-Ec)/Ec#depth of residual AM \n", + "\n", + "AMFr=2*fm# freq ofresidual AM\n", + "print 'Peak Phase Deviation: %0.2f rad\\nPeak Freq Deviation: %d Hz\\nDepth of residual AM: %0.2f\\nResidual AM freq:%d kHz'%(deltaTheta,deltaF,(round(m*100)/100),AMFr*1e-3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.16 page no 170" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a)\n", + "Max phase deviation is:250 rad\n", + "b)\n", + "Max phase deviation is:2.50 rad\n" + ] + } + ], + "source": [ + "#Given\n", + "deltaF=25e3#freq deviation\n", + "#a\n", + "fm=100#modulation signal freq\n", + "mf=deltaF/fm# Max phase deviation\n", + "print 'a)'\n", + "print 'Max phase deviation is:%d rad'%(mf)\n", + "#b\n", + "fm=10e3#modulation signal freq\n", + "mf=deltaF/fm#Max phase deviation\n", + "\n", + "print 'b)'\n", + "print 'Max phase deviation is:%0.2f rad'%(mf)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.17, page no 171" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The maximum freq deviation is: 5 kHz\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt\n", + "#Given\n", + "gm=0.1e-3# trans-conductance variation A/V\n", + "C=0.5e-12# capactance between anode and grid\n", + "R=1e3# resistance\n", + "fo=10e6# oscillator freq\n", + "Vrms=1.414#AF RMS voltage \n", + "Vp=sqrt(2)*Vrms#Peak voltage\n", + "Ct=100e-12#tank capacitance\n", + "deltaC=gm*C*R*Vp\n", + "\n", + "deltaF=fo*(deltaC/(2*Ct))# maximum freq deviation\n", + "print 'The maximum freq deviation is: %d kHz'%(round(deltaF/1000))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.18, page no 172" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The approximate bandwidth is: 2 MHz\n" + ] + } + ], + "source": [ + "#Given\n", + "deltaF=1e6# max freq deviation\n", + "fm=10e3#modulating freq\n", + "mf=(2*deltaF)/fm# modulation coefficient\n", + "BW=mf*fm# bandwidth\n", + "print 'The approximate bandwidth is: %d MHz'%(BW/1e6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.19, page no 172" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The approximate bandwidth is: 150 kHz\n" + ] + } + ], + "source": [ + "#Given\n", + "deltaF=75e3# max freq deviation\n", + "fm=15e3#modulation freq\n", + "mf=(2*deltaF)/fm# freq modulation depth\n", + "BW=mf*fm# Bandwidth\n", + "print 'The approximate bandwidth is: %d kHz'%(BW/1e3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.21, page no 173" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overall bandwidth including guard band is 200 kHz\n" + ] + } + ], + "source": [ + "#Given\n", + "deltaF=75e3#freq deviation\n", + "fm=15e3# modulating freq\n", + "mf=deltaF/fm\n", + "BW=2*mf*fm# Bandwidth\n", + "GB=25e3#Guard Band\n", + "BWo=BW+(2*GB)# Overall bandwidth\n", + "print 'Overall bandwidth including guard band is %d kHz'%(BWo/1e3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.25, pageno 175" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Average power is: 25.17 watts\n" + ] + }, + { + "data": { + "image/png": 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TExNMTEwM5L0U0f7gXNJNJD2EHwX+jqSH8CcRsTbzmyddgY3A7oj4UMv6T6XrPinpVmBp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\nDgQzM0s5EMzMDHAgmJlZyoFgZmYA/AcgiGzn8R0TcAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f9d76e23e90>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from math import sin\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, subplot, title, xlabel, ylabel, show\n", + "#Given\n", + "#em=3sin(2*pi*1000t)+5cos(2*pi*3000t)\n", + "#ec=50sin(2*pi*500e3*t)\n", + "m1=0.06#(sine wave amplitude/ peak carrier voltage)\n", + "m2=0.1#(cosine wave amplitude/ peak carrier voltage)\n", + "Vc=50#Carrier voltage\n", + "R=50#load resistance\n", + "Pc=(Vc**2)/(2*R)#Peak carrier power\n", + "Pt=Pc*(1+((m1**2+m2**2)/2))#Total power after modulation\n", + "print 'Average power is: %0.2f watts'%(Pt)\n", + "F=[0,2.5,1.5,50,1.5,2.5,0]\n", + "T=[490,497,499,500,501,503,510]\n", + "plot(T,F)\n", + "xlabel(\"Freq\")\n", + "ylabel(\"Amplitude\")\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.26, page no 176" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Required Deviation is: 50 kHz\n", + "\n", + "Required Multipication Factor is: 5*5*5*5*2\n" + ] + } + ], + "source": [ + "#Given\n", + "mp=0.1#Modulating index\n", + "fm=400#Modulating signal freq\n", + "deltaF=mp*fm#Max freq deviation\n", + "#print deltaF)\n", + "ReqDev=50e3# Required deviation\n", + "MF=ReqDev/deltaF# multiplication factor\n", + "print 'Required Deviation is: %d kHz\\n'%(ReqDev/1e3)\n", + "print 'Required Multipication Factor is: 5*5*5*5*2'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.27, page no 176" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The Depth of modulation across the \n", + " circuit is : Ma= 49.07%\n" + ] + } + ], + "source": [ + "#Given\n", + "Q=100 #Q factor\n", + "fc=1000e3# Carrier freq\n", + "fsb1=999e3#lower Side band freq\n", + "fsb2=1001e3#Upper side Band freq\n", + "ma=0.5#Modulation depth of signal current\n", + "Ma=ma/1.019# Expression for Ma after simplification\n", + "print 'The Depth of modulation across the \\n circuit is : Ma= %0.2f%c'%(Ma*100,'%')\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.28, page no 177" + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Depth of modulation:72.90 %\n" + ] + } + ], + "source": [ + "#Given\n", + "R=1#Antenna Resistance assumed to be 1 ohm for ease of calculation\n", + "Ic=10.8# current with no modulation\n", + "Pc=Ic**2*R#power with no modulation\n", + "It=12.15#modulated current\n", + "Pt=It**2*R# modulated power\n", + "ma=(sqrt(2*(((It/Ic)**2)-1)))#modulation depth)\n", + "\n", + "print 'Depth of modulation:%0.2f %c'%(round(1000*ma)/10,'%')#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.29, page no 177" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total RF power delivered is:Pt= 112.50 kW\n" + ] + } + ], + "source": [ + "#Given\n", + "Pc=100e3#Carrier power\n", + "ma=0.5#Depth of modulation\n", + "Pt=Pc*(1+((ma**2)/2))#total RF power\n", + "print 'Total RF power delivered is:Pt= %0.2f kW'%(Pt/1e3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.30, page no 178" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Carrier power:71.17 kW\n", + "The Intelligence power: 28.83 kW\n" + ] + } + ], + "source": [ + "#Given\n", + "Pt=100e3# Total power\n", + "ma=0.9#Depth of modulation\n", + "Pc=Pt/(1+((ma**2)/2))#Carrier power\n", + "Psb=Pt-Pc# Intelligence power i.e sideband power\n", + "print 'Carrier power:%0.2f kW\\nThe Intelligence power: %0.2f kW'%(Pc/1000,Psb/1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.19, page no 178" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Modulation Index is: 64.81 \n" + ] + } + ], + "source": [ + "from math import sin,sqrt\n", + "#Given\n", + "R=1# load resistance\n", + "Eo=100#RF voltage\n", + "Po=Eo**2/R#Carrier power\n", + "E=110#Modulated RMS voltage\n", + "Pt=E**2/R#Total modulated power\n", + "ma=sqrt(2*((Pt/Po)-1))# Depth of modulation\n", + "print 'Modulation Index is: %0.2f '%(ma*100)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter5_b3JDxfA.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter5_b3JDxfA.ipynb new file mode 100644 index 00000000..e234ad9f --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter5_b3JDxfA.ipynb @@ -0,0 +1,69 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5 : Radio Transmission system" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.1, page no 230" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Freq deviation is 17.453293 Hz\n", + " Multification factor is 1718\n", + " corresponding modified max freq deviation is 30114kHz\n" + ] + } + ], + "source": [ + "from numpy import pi\n", + "#Given\n", + "#b\n", + "fm=1e2#modulation freq\n", + "Phimax=10*pi/180# Max Phase deviation\n", + "#i\n", + "Freq_dev=Phimax*fm# Freq deviation\n", + "#ii\n", + "Mul_fact=30e3/Freq_dev# Multification factor\n", + "print ' Freq deviation is %f Hz\\n Multification factor is %d\\n corresponding modified max freq deviation is 30114kHz'%(Freq_dev,Mul_fact)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter6_hxtqyXd.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter6_hxtqyXd.ipynb new file mode 100644 index 00000000..c82ada44 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter6_hxtqyXd.ipynb @@ -0,0 +1,104 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6 : Radio Receivers" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.1, page no 262" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Carrier freq for the BW to be 1% of fc is: 2000 kHz\n" + ] + } + ], + "source": [ + "#Given\n", + "#Vm(t),Vc(t),Vmod(t)\n", + "fm=10e3#modulating freq\n", + "BW=2*fm# Bandwidth\n", + "fc=100*BW#Carrier freq\n", + "print'Carrier freq for the BW to be 1%% of fc is: %d kHz'%(fc/1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example6.2, page no 262" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a)\n", + "Tuning capacitor range is: 4.579156\n", + "b)\n", + "Tuning capacitor range is: 1051\n" + ] + } + ], + "source": [ + "#Given\n", + "fmax=1600e3\n", + "fmin=500e3\n", + "IF=465e3\n", + "#i\n", + "fo1max=fmax+IF\n", + "fo1min=fmin+IF\n", + "C1max_C1min=(fo1max/fo1min)**2\n", + "#ii\n", + "fo2max=fmax-IF\n", + "fo2min=fmin-IF\n", + "C2max_C2min=(fo2max/fo2min)**2\n", + "print 'a)\\nTuning capacitor range is: %f\\nb)\\nTuning capacitor range is: %d'%(C1max_C1min,C2max_C2min)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter7_QXJtmam.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter7_QXJtmam.ipynb new file mode 100644 index 00000000..7df129c1 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter7_QXJtmam.ipynb @@ -0,0 +1,438 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 7 : Noise" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.2, page no 276" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The mean square noise voltage is: 18.363 mV\n" + ] + } + ], + "source": [ + "from numpy import sqrt,pi\n", + "from mpmath import quad\n", + "#Given\n", + "mue=25#\n", + "rp=5e3\n", + "Rl=10e3\n", + "C=1e-9\n", + "gm=mue/rp\n", + "Req=2.5/gm\n", + "\n", + "k=1.381e-23\n", + "T=293\n", + "R1=1e5\n", + "# Power density spectrum for respective res\n", + "d1=2*k*T*R1\n", + "d2=2*k*T*Req\n", + "d3=2*k*T*Rl\n", + "xo=0\n", + "x1=1e14\n", + "#w=0:inf\n", + "#H1(w)=(-gm*rp*Rl)/(rp+Rl+(1J*w*rp*Rl*C))\n", + "Vo=sqrt((20231.65e2/pi)*quad(lambda w:1/(((3e9)**2)+(w**2)),[xo,x1]))\n", + "print 'The mean square noise voltage is: %0.3f mV'%(Vo*1e3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.3, page no 279" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The mean square noise voltage is: 22.414 uV\n" + ] + } + ], + "source": [ + "from numpy import sqrt,pi\n", + "from mpmath import quad\n", + "\n", + "#Given\n", + "mue=25\n", + "rp=5e3\n", + "Rs=1e3#input resistance\n", + "#Coupling Capacitors are assumed as short circuit\n", + "Rg=1e5\n", + "gm=25/5e3\n", + "Req=2.5/gm\n", + "F=1+((((Req*(Rs+Rg)**2)+(Rg*Rs**2))/(Rs*Rg**2)))\n", + "xo=0\n", + "x1=1e10\n", + "#w=0:inf\n", + "\n", + "vo=sqrt((30145e-8/pi)*quad(lambda w:1/(((3e5)**2)+(w**2)),[xo,x1]))\n", + "print 'The mean square noise voltage is: %.3f uV'%(vo*1e6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.4, page no 283" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "overall noise Figure is: 4.33\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#Given\n", + "Ap1=10\n", + "Ap2=10\n", + "Ap3=10# # Gain of each states\n", + "F_1=6\n", + "F_2=6\n", + "F_3=6# #Noise figure of each state\n", + "F1= round(10**(F_1/10))\n", + "F2= round(10**(F_2/10))\n", + "F3= round(10**(F_3/10))# # approximating the values\n", + "\n", + "F=F1+((F2-1)/Ap1)+((F3-1)/(Ap1*Ap2))\n", + "print 'overall noise Figure is: %.2f'%(F)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.5, page no 283" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The overall noise figure is: 7.04\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#Given\n", + "Fif=15# Noise figure of IF amplifier\n", + "Ap1=10# Gain of Preamplifier\n", + "Fpa=6#Noise figure of preamplifier\n", + "F2=10**(Fif/10)\n", + "F1=10**(Fpa/10)\n", + "\n", + "F=F1+((F2-1)/Ap1)#overall noise figure\n", + "print 'The overall noise figure is: %.2f'%(F)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.6, page no 284" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overall Noise figure is: 2.055\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#Given\n", + "mue=25# tube parameters\n", + "rp=10e3# tube parameters\n", + "gm=2.5e-3# transconductance\n", + "Req=2.5/gm# equivalent resistance\n", + "Rs=1000\n", + "Rg=1e5\n", + "F1=1+(((Req*((Rs+Rg)**2))+Rg*Rs**2)/(Rs*(Rg**2)))#noise figure of the first stage\n", + "Rg2=9.1e3\n", + "Rs2=10e3\n", + "Es=1# assuming Es=1 for ease of calculation\n", + "Pi=((Es/2e3)**2)*1e3\n", + "Po=1.532e-2*Es**2\n", + "Ap1=Po/Pi\n", + "F2=1+(((Req*((Rs2+Rg2)**2))+Rg2*Rs2**2)/(Rs2*(Rg2**2)))# noise figure of the second stage\n", + "F=(F1)+((F2-1)/Ap1)\n", + "print 'Overall Noise figure is: %.3f'%(F)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.8, page no 285" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The equivalent noise temp is: 4.913 K\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#Given\n", + "g01=30# gain of 1st stage\n", + "g02=20#gain of 2nd stage\n", + "g03=40#gain of 3rd stage\n", + "F2=6# Noise factor of stage 2\n", + "F3=12# Noise factor of stage 3\n", + "Te1=4# Eq noise temp of stage 1\n", + "T=290# Room \n", + "G01=round(10**(g01/10))\n", + "G02=round(10**(g02/10))\n", + "G03=round(10**(g03/10))\n", + "F_2=round(10**(F2/10))\n", + "F_3=round(10**(F3/10))\n", + "Te2=round((F_2-1))*T\n", + "Te3=round((F_3-1))*T\n", + "Te=Te1+(Te2/G01)+(Te3/(G01*G02))# Eq overall noise temp\n", + "print 'The equivalent noise temp is: %.3f K'%(Te)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.9, page no 286" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equivalent noise temperature is 7.028 K\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#Given\n", + "g01=round(10**(25/10))#low noise amplifier gain\n", + "Te1=4#low noise amplifier noise temp\n", + "g02=round(10**(1.7))#preamplifier gain\n", + "F2=round(10**0.6)#preamplifier noise figure\n", + "F3=round(10**1.2)#preamplifier noise figure\n", + "T=290# room temp\n", + "Te2=round((F2-1)*T)\n", + "Te3=round((F3-1)*T)\n", + "Te=Te1+(Te2/g01)+(Te3/(g01*g02))#Overall noise Temperature\n", + "print 'Equivalent noise temperature is %.3f K'%(Te)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.10, page no 286" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "S/N ratio for FM is 43.29 dBs\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log10\n", + "#Given\n", + "SNRam=25# Signal to noise ratio of AM\n", + "PcFM_AM=0.9#\n", + "mf=5\n", + "SNRfm=(10*log10(3*(mf**2)*(PcFM_AM)))+SNRam\n", + "print 'S/N ratio for FM is %.2f dBs'%(SNRfm)\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.11, page no 287" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a)\n", + " New SNR for 3dB increase in input s/g is 23 dBs\n", + "b) When Modulation depth is increased to 60%\n", + " SNR becomes 25.676045 dBs\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log10\n", + "#Given\n", + "ma=0.3\n", + "SNR=20# s/n ratio\n", + "SNR1=10**(0.1*SNR)\n", + "SNR_new=SNR+3\n", + "ma2=0.6# increased new depth of modulation\n", + "Pt_Ni=SNR1*((1+(ma**2))/(ma**2))\n", + "SNR2=10*log10(Pt_Ni*((ma2**2)/(1+((ma2**2)/2))))\n", + "\n", + "print 'a)\\n New SNR for 3dB increase in input s/g is %d dBs\\nb) When Modulation depth is increased to 60%%\\n SNR becomes %f dBs'%(SNR_new,(SNR2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.12, page no 287" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a) Bit Transmission rate: 60 kbits/s\n", + " Signal to Quantization noise ratio 128 \n", + "b)\n", + " Bit Transmission rate: 5 kbits/sample\n", + " Signal to Quantization noise ratio: 64\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log\n", + "#Given\n", + "fmax=5e3#max s/g freq\n", + "S_fmin=2*fmax# Min sampling freq\n", + "B_S=6#Binary bits sent per sample\n", + "BTR=B_S*S_fmin#Bit Transmission rate\n", + "Q=2**B_S#No of Quantizable levels\n", + "MQN=0.5/Q#Max Quantization noise\n", + "S_QNR=MQN**-1# Signal to Quantization noise ratio\n", + "#b\n", + "S_QNRreq=0.5*S_QNR# Signal to Quantization noise ratio\n", + "Qreq=0.5*S_QNRreq#No of Quantizable levels\n", + "B_Sreq=log(Qreq,2)#Binary bits sent per sample\n", + "print 'a) Bit Transmission rate: %d kbits/s\\n Signal to Quantization noise ratio %d \\nb)\\n Bit Transmission rate: %d kbits/sample\\n Signal to Quantization noise ratio: %d'%(BTR/1000,S_QNR,B_Sreq,S_QNRreq)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter8_ojfkyD4.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter8_ojfkyD4.ipynb new file mode 100644 index 00000000..3631a473 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter8_ojfkyD4.ipynb @@ -0,0 +1,779 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter No 8 - Transmission Line" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.1, page no 313" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The characteristic Impedance is Zo= 154.92 ohm\n", + "\n", + "Propagation constant is Gama=0.0+7.75e-06j W\n", + "\n", + " The freq at which the line length is equal to wavelength is: 750 KHz\n", + " The velocity of propagation is: 322.75 km/sec\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt, pi\n", + "#Given\n", + "#a\n", + "L=1.2*10**-3#distributed inductance\n", + "C=0.05*10**-6#distributed capacitance\n", + "Zo=sqrt(L/C)#Characteristic Impedance\n", + "print 'The characteristic Impedance is Zo= %0.2f ohm'%(Zo)\n", + "Wo=1# Assumedfor ease of calculation \n", + "G=1J*sqrt(L*C)*Wo\n", + "print '\\nPropagation constant is Gama={0:0.1f}+{1:0.2e}j W'.format(G.real,G.imag)\n", + "#b\n", + "#i\n", + "lamda=0.4e3#wavelength=Line length\n", + "c=3e8\n", + "f=c/lamda\n", + "#ii\n", + "L=L*0.4\n", + "C=C*0.4\n", + "v=1/(sqrt(L*C))\n", + "print '\\n The freq at which the line length is equal to wavelength is: %d KHz\\n The velocity of propagation is: %0.2f km/sec'%(f*1e-3,v*1e-3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.2, page no 314" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The phase shift is: 144 degrees\n", + "Open Circuited line impedance: -688.19 ohms\n", + "Short Circuited line impedance: -363.27 ohms\n" + ] + } + ], + "source": [ + "from math import cos, sin, tan,pi\n", + "#Given\n", + "v=3e8# velocty of light\n", + "f=1.2e6# Operating Freq\n", + "lamda=v/f\n", + "#print lamda)\n", + "l=100# length of the Tx-Line\n", + "phi=2*(pi*l)/(lamda)# Phase shift in degrees\n", + "Zo=500# Characteristic impedance\n", + "#a Open circuited Line\n", + "\n", + "Zin=-1J*Zo*(cos(phi)/sin(phi))\n", + "\n", + "#b Short circuited Line\n", + "Z1in=1J*Zo*tan(phi)\n", + "print 'The phase shift is: %d degrees'%(phi*180/pi)\n", + "print 'Open Circuited line impedance: {0:0.2f}'.format(-Zin.imag),'ohms'\n", + "print 'Short Circuited line impedance: {0:.2f}'.format(Z1in.imag),'ohms'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.3, page no 315" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The Characteristic impedance:Zo= \n", + "(185.464726748-135.988363959j)\n", + "The value of Alpha=0.263 nepere/km\n", + "\n", + "The value of Beta= 0.308\n", + "the tx-Line parameters are\n", + "R= 90.72 ohms\n", + "L= 21.46 mH\n", + "G= 128.80 umhos\n", + "C= 1.76 mF\n", + "\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from cmath import exp,sqrt,log,atan\n", + "#Given\n", + "f=1600\n", + "w=1000\n", + "Zoc=2460*exp(1J*-86.5*pi/180)# Open circuited Line impedance\n", + "Zsc=21.5*exp(1J*14*pi/180)# Short circuited Line impedance\n", + "Zo=sqrt(Zoc*Zsc)# Characteristic impedance\n", + "A=(sqrt(Zsc/Zoc)).real# tan(a+ jBeta) = A + jB\n", + "B=(sqrt(Zsc/Zoc)).imag\n", + "l=1/4\n", + "alpha=(1/(4*l))*log(((1+A**2+B)**2)/(((1-A)**2)+B**2)) #Attenuation Constant\n", + "Beta=(1/(2*l))*atan((2*B)/(1-A**2-B)) #phase constant\n", + "\n", + "#the tx-Line parameters\n", + "R=(Zo*complex(alpha,Beta)).real\n", + "L=(Zo*complex(alpha,Beta)).imag\n", + "G=(complex(alpha,Beta)/Zo).real\n", + "C=(complex(alpha,Beta)/Zo).imag\n", + "print 'The Characteristic impedance:Zo= '\n", + "print Zo\n", + "print 'The value of Alpha={0:.3f} '.format(alpha.real),'nepere/km\\n'\n", + "print 'The value of Beta= {0:0.3f}'.format(Beta.real)\n", + "print 'the tx-Line parameters are\\nR= %0.2f ohms\\nL= %0.2f mH\\nG= %0.2f umhos\\nC= %0.2f mF\\n'%(R,L,G*1e6,C*1e3)\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.4, page no 316" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The atenuation constant is 0.011 nepers/mile\n", + "The Cut-off Freq is 6 KHz\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt,pi\n", + "#Given\n", + "d=0.7# distance between two insertions\n", + "Ld_m= (80e-3)*(10/7)#Loading coil inductance\n", + "#print Ld_m)\n", + "Rd_m=100/7#Loading coil resistance\n", + "#print Rd_m)\n", + "R=20+Rd_m#Line resistance \n", + "L=Ld_m# Line inductance\n", + "C=0.05e-6# Line Capacitance\n", + "alfa=0.5*R*sqrt(C/L)#Attenuation Constant\n", + "#\n", + "fc=(pi*d*sqrt(L*C))**-1#cut off freq\n", + "print 'The atenuation constant is %0.3f nepers/mile\\nThe Cut-off Freq is %d KHz'%(alfa,fc*1e-3)\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.5, page no 317" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the voltage at the mid point of the line is \n", + " 6.97+6.97j\n", + " V with Angle = -8.59degrees\n" + ] + } + ], + "source": [ + "from cmath import exp\n", + "#Given\n", + "a=0.7#attenuation constant\n", + "b=0.3#phase constant\n", + "Gamma=a+(1J*b)#propagation constant\n", + "l=0.5# half length of line( for midpoint)\n", + "Vs=10# Excitation voltage\n", + "V_mod=Vs*(exp(-a*l))#Magnitude of the Vs\n", + "\n", + "phi=b*l*180/pi#phase shift\n", + "V=V_mod*(exp(-1J*(phi*pi/180)))#voltage at the mid point\n", + "print 'the voltage at the mid point of the line is \\n {0:0.2f}+{0:.2f}j\\n V with Angle = -%0.2fdegrees'.format(V.real,V.imag)%phi\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.6, page no 317" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The characteristic impedance Zo= 22.20 /_-19.66 ohm\n", + "\n", + " The Phase velocity is: v= 2.88e+07 m/sec\n", + " Percent decrease in the voltage is 14.91%\n" + ] + } + ], + "source": [ + "from cmath import pi,sqrt,polar,phase\n", + "#Given\n", + "R=0.01\n", + "l=1e3\n", + "L=1e-6\n", + "G=1e-6\n", + "C=0.001e-6\n", + "f=1.59e3# operating freq\n", + "w=2*pi*f# angular freq\n", + "#a\n", + "Zo=sqrt((R+(1J*w*L))*0.35/(G+(1J*w*C)))#characteristic impedance\n", + "Z0=polar(Zo)\n", + "Z0r=Z0[0]\n", + "Z0i=Z0[1]\n", + "#b\n", + "\n", + "Beta=sqrt(0.5*(sqrt((((R**2)+(round(w**2)*(L**2)))*(round(G**2)+(round(w**2)*(C**2)))))-(round(R*G)-((w**2)*L*C))))#Phase constant\n", + "\n", + "v=w/Beta#phase velocity\n", + "\n", + "#c\n", + "Alpha=sqrt(0.5*(sqrt((((R**2)+((w**2)*(L**2)))*((G**2)+((w**2)*(C**2)))))+((R*G)-((w**2)*L*C))))#attenuation constant\n", + "Vs=1#Assumed for easeof calculation\n", + "A=(Vs-(Vs*exp(-Alpha*l)))*100\n", + "print 'The characteristic impedance Zo= %0.2f /_%0.2f ohm\\n'%(Z0r,Z0i*180/pi)\n", + "print ' The Phase velocity is: v= %3.2e m/sec\\n Percent decrease in the voltage is %0.2f%c'%(v.real,A.real,'%')\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.15, page no 348" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The input impedance is 526.81 /_-2.18deg\n", + "Reflection Coeff is 0.07 /_-163.77deg\n" + ] + } + ], + "source": [ + "from cmath import exp,polar,cosh,sinh\n", + "\n", + "#Given\n", + "l=100# Tx-line length\n", + "ZR=200#Terminal resistance\n", + "Zo=600#Characteristic impedance\n", + "a=0.01#attenuation constant\n", + "Beta=0.03#phase constant\n", + "d=0#reflection coeff at load is Zero\n", + "Gamma=a+1J*Beta#propagation constant\n", + "Kd=((ZR-Zo)/(ZR+Zo))*exp(-2*Gamma*d)#reflection coeff at point D d km from load\n", + "Kdd=polar(Kd)\n", + "Kdr=Kdd[0]\n", + "Kdi=Kdd[1]\n", + "d1=100# distance\n", + "Ks=((ZR-Zo)/(ZR+Zo))*exp(-2*Gamma*d1)#reflection coeff at the sending end\n", + "[Ksr,Ksi]=polar(Ks)\n", + "Zin=Zo*(((ZR*cosh(Gamma*l))+(Zo*sinh(Gamma*l)))/((Zo*cosh(Gamma*l))+(ZR*sinh(Gamma*l))))#Input impedance\n", + "Zz=polar(Zin)\n", + "Zinr=Zz[0]\n", + "Zini=Zz[1]\n", + "print 'The input impedance is %0.2f /_%0.2fdeg\\nReflection Coeff is %0.2f /_%0.2fdeg'%(Zinr,Zini*180/pi,Ksr,Ksi*180/pi)\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.15, page no 334" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The current received is= 13.64 mA at phase-22.59\n" + ] + } + ], + "source": [ + "from cmath import cosh,polar\n", + "#GivenR=0.01\n", + "x=10#line length\n", + "Zo=100# characteristic impedance\n", + "a=0.1# attenuation constant\n", + "Beta=0.05# phase constant\n", + "Is=20e-3# source current\n", + "Gamma=a+ 1J*Beta# propagation constant\n", + "\n", + "I=Is/cosh(Gamma*x)# received current\n", + "\n", + "Ii=polar(I)\n", + "I_r=Ii[0]\n", + "I_i=Ii[1]\n", + "\n", + "print 'The current received is= %0.2f mA at phase%0.2f'%(1000*I_r,I_i*180/pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.16, page no 349" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The characteristic impedance is 283.94 /_-41.38deg\n" + ] + } + ], + "source": [ + "from cmath import sqrt,polar\n", + "#Given\n", + "L=1e-3#inductance\n", + "R=40# Resistance\n", + "C=0.1e-6# capacitance\n", + "G=1e-6#conductance\n", + "w=5000# angular freq\n", + "Zo=sqrt(complex(R,(w*L))/complex(G,(w*C)))#Characteristic impedance\n", + "#Zr=sqrt(sqrt(R**2+(w*L)**2)/sqrt(G**2+(w*C)**2))\n", + "Zz=polar(Zo)\n", + "ZoR=Zz[0]\n", + "ZoI=Zz[1]\n", + "print 'The characteristic impedance is %0.2f /_%0.2fdeg'%(ZoR,ZoI*180/pi)\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.17, page no 349" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The voltage at the mid point of the line is 7.05 /_-8.59 \n" + ] + } + ], + "source": [ + "from cmath import polar,exp\n", + "#Given\n", + "l=0.5#half line distance\n", + "Vs=10#Excitation voltage\n", + "Gamma=0.7+1J*0.3#propagation constant\n", + "Vv=polar(Vs*(exp(-Gamma*l)))#vtg at mid point\n", + "Vr=Vv[0]\n", + "Vi=Vv[1]\n", + "print 'The voltage at the mid point of the line is %0.2f /_%0.2f '%(Vr,Vi*180/pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.18, page no350" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The max voltage on line is 5.92 V\n", + " The min voltage on line is 4.23 V\n" + ] + } + ], + "source": [ + "from math import sqrt\n", + "#Given\n", + "Zo=50# characteristic impedance\n", + "P=500e-3#Supplied power\n", + "S=1.4#VSWR on the line\n", + "Emax=sqrt(Zo*S*P)#Max vtg\n", + "\n", + "Emin=sqrt(Zo*P/S)# Min vtg\n", + "print 'The max voltage on line is %0.2f V\\n The min voltage on line is %0.2f V'%(Emax,Emin)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.19, page no 350" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "The voltage reflection coeff is 0.17\n", + "The VSWR is 1.40\n", + "\n", + "\n", + "The Max and min voltage and crresponding crrent is\n", + " Emax= 3.74V Imin= 26.73mA\n", + " Emin= 2.67V Imax= 37.42mA\n", + "\n", + " The Termination resistance should be 28.57 ohm\n" + ] + } + ], + "source": [ + "from math import sqrt\n", + "#Given\n", + "Zo=100# Characteristic Impedance\n", + "P=100e-3#Load power\n", + "Zr=140#Load Resistance\n", + "f=100e3# Operating freq\n", + "#a\n", + "K=(Zr-Zo)/(Zo+Zr)#Vtg Reflection coeff\n", + "\n", + "#b\n", + "S=(1+K)/(1-K)#VSWR\n", + "\n", + "#c+d\n", + "Emax=sqrt(Zr*P)#Max line vltg\n", + "Imin=Emax/Zr#Min line current\n", + "\n", + "Emin=Emax/S# Min line vltg\n", + "Imax=S*Imin#Max line current\n", + "\n", + "#e\n", + "R=14000/40\n", + "\n", + "Zr=(Zo**2)/R#\n", + "print '\\nThe voltage reflection coeff is %0.2f\\nThe VSWR is %0.2f\\n\\n\\nThe Max and min voltage and crresponding crrent is\\n Emax= %0.2fV Imin= %0.2fmA\\n Emin= %0.2fV Imax= %0.2fmA\\n\\n The Termination resistance should be %0.2f ohm'%(K,S,Emax,Imin*1e3,Emin,Imax*1e3,Zr)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.20, page no 352" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the receiving voltage will be 0.25 V\n" + ] + } + ], + "source": [ + "from math import exp,log\n", + "#Given\n", + "V=0.5#receiving vtg\n", + "Vs=2#Source vtg\n", + "al=-log(V/Vs)#attenuation\n", + "\n", + "al2=al*1.5\n", + "V=Vs*exp(-al2)#receiving voltage\n", + "print 'the receiving voltage will be %0.2f V'%(V)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.22, page no352" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The lrngth should be 25 metres\n", + "The Characteristic Impedance should be 48.79 ohms\n" + ] + } + ], + "source": [ + "from cmath import sqrt\n", + "#Given\n", + "Zin=25+1J*15# Internal Impedance\n", + "Zr=70-1J*42#load\n", + "f=3e6#operating freq\n", + "v=3e8#light velocity\n", + "L=v/(4*f)#length of the line\n", + "\n", + "Zo=sqrt(Zin*Zr)#Characteristic Impedance\n", + "\n", + "print 'The lrngth should be %d metres\\nThe Characteristic Impedance should be %0.2f ohms'%(L,Zo.real)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.23, page no353" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The cut-off freq is 3.03 KHz \n", + " the voltage being measured is 1 V\n" + ] + } + ], + "source": [ + "from math import sqrt,pi\n", + "from __future__ import division\n", + "#Given\n", + "#a\n", + "L=1e-3# inductance\n", + "C=61.25e-9#capacitance\n", + "Ld=44e-3#coil inductance\n", + "d=2#distance intervals after which coils are added\n", + "Lt=(L*2)+(Ld*2)#total inductance\n", + "Ct=C*2#total capacitance\n", + "fc=(pi*sqrt(Lt*Ct))**-1#cut off freq\n", + "\n", + "#b\n", + "I=100e-3#milliameter range\n", + "R=1#milliameter resistance\n", + "Zo=100#characteristic impedance\n", + "Zin=(Zo**2)/R#input impedance\n", + "\n", + "Er=I*R#\n", + "Es=Er*sqrt(Zin/Zo)\n", + "print 'The cut-off freq is %0.2f KHz \\n the voltage being measured is %d V'%(fc*1e-3,Es)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.24, page no 354" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the Length of the transformer(stub) is 3.75 metres\n", + " The characteristic impedance of this transformer is 224 ohms\n" + ] + } + ], + "source": [ + "#Given\n", + "f=20e6#tuned freq\n", + "ZR=100#Equivalent aerial Resistance\n", + "Zin=500#input impedance\n", + "c=3e8\n", + "lamda=c/f\n", + "l=lamda/4#lamda/4 Transformer\n", + "\n", + "Zo=sqrt(Zin*ZR)#Characteristic impedance\n", + "print 'the Length of the transformer(stub) is %0.2f metres\\n The characteristic impedance of this transformer is %d ohms'%(l,round(Zo))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.25, page no 354" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The sending end (Source end)impedance (Zl)is: \n", + "330.46+-16.35j\n" + ] + } + ], + "source": [ + "#Given\n", + "lamda=5#wavelength\n", + "Zo=200#Characteristic impedance\n", + "Zo1=100#Zo'\n", + "ZL=50+(1J*50)# load impedance\n", + "l1=0.4*lamda\n", + "l2=0.2*lamda\n", + "Beta=(2*pi/lamda)# phase difference\n", + "Z2=Zo1*(((ZL*cos(Beta*l2))+(1J*Zo1*sin(Beta*l2)))/((Zo1*cos(Beta*l2))+(1J*ZL*sin(Beta*l2))))#I/p Impedance offered by I2toI1\n", + "Z1=Zo*(((Z2*cos(Beta*l1))+(1J*Zo*sin(Beta*l1)))/((Zo*cos(Beta*l1))+(1J*Z2*sin(Beta*l1))))#I/p impedance\n", + "print 'The sending end (Source end)impedance (Zl)is: '\n", + "print '{0:0.2f}+{1:0.2f}j'.format(Z1.real,Z1.imag)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter9_1ERbfbH.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter9_1ERbfbH.ipynb new file mode 100644 index 00000000..9a611935 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter9_1ERbfbH.ipynb @@ -0,0 +1,338 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter No 9 - Aerials" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.1, page no 397" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The maximum effective aperture of the\n", + " aerial is 28.65 sq m\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import pi\n", + "\n", + "#Given\n", + "D=90# directivity\n", + "lamda=2# wavelength\n", + "Ae=(D*(lamda**2))/(4*pi)#effective aperture\n", + "print 'The maximum effective aperture of the\\n aerial is %0.2f sq m'%(Ae)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.2, page no 397" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Angular beam width is 22.92 degrees\n", + "BeamWidth is 0.40 rad\n" + ] + } + ], + "source": [ + "from math import pi,cos\n", + "#Given\n", + "n=10#no of aerial elements\n", + "d=0.5#distance in terms of wavelength\n", + "Beam_Width=2/(n*d)#\n", + "Beam_Width_degrees=Beam_Width*180/pi\n", + "print 'Angular beam width is %0.2f degrees\\nBeamWidth is %0.2f rad'%(Beam_Width_degrees,Beam_Width)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.3, pageno 397" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total power radiated is 888.89 watts\n" + ] + } + ], + "source": [ + "from numpy import arange, pi\n", + "from mpmath import quad, sin\n", + "#Given\n", + "r=1#assume distance for ease of calculation\n", + "#Pav(theta)=(1000/(3*pi*r**2))*((sin(theta))**2)\n", + "theta=arange(0, pi, 0.1)\n", + "x0=0\n", + "x1=pi\n", + "Pt=(2000/(3*r**2))*quad(lambda theta: (sin(theta))**3,[x0,x1])#Total power radiated \n", + "print 'Total power radiated is %0.2f watts'%(Pt)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.4, page no 398" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "electric field intensity is 0.25 mV/m \n", + " magnetic field intensity is 0.67 uA/m\n" + ] + } + ], + "source": [ + "from math import pi,cos\n", + "#Given\n", + "dl=2# length of wire \n", + "I=6#current in the wire\n", + "f=1e6# operating freq\n", + "r=30e3#distance at which field is to be calculated\n", + "theta=90#right angles to the wire axis\n", + "lamda=300# wavelength\n", + "w=2*pi*f#angular freq\n", + "c=3e8\n", + "t=f**-1\n", + "Phi=w*(t-(r/c))#Phase shift\n", + "Erad=25.13e-5*cos(Phi)#Radiation electric field intensity\n", + "H=Erad/(120*pi)#Radiation magnetic field intensity\n", + "print 'electric field intensity is %0.2f mV/m \\n magnetic field intensity is %0.2f uA/m'%(Erad*1e3,H*1e6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.5, page no 399" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The radiated power is 1.03 watts\n" + ] + } + ], + "source": [ + "from math import sqrt\n", + "#Given\n", + "#c\n", + "Rr=73# radition resistance\n", + "Vrms=10#RMS voltage of the signal\n", + "Zin_mod=sqrt((73**2)+(42**2))#absolute input impedance\n", + "Irms=Vrms/Zin_mod#RMS current\n", + "Pt=(Irms**2)*Rr# Radiated power\n", + "print 'The radiated power is %0.2f watts'%(round(100*Pt)/100)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.6 page no 400" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ideal directive gain is 55840\n" + ] + } + ], + "source": [ + "#Given\n", + "#b\n", + "c=3e8\n", + "f=2e9#operating freq\n", + "Ae=100#aperture area\n", + "lamda=c/f# operating wavwlength\n", + "D=((4*3.141*Ae)/(lamda**2))# Directivity\n", + "print 'Ideal directive gain is %d'%(D)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.7, pageno 400" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The angular width is 0.40 degrees\n" + ] + } + ], + "source": [ + "#Given\n", + "#b\n", + "n=10# no of aerial elements\n", + "lambda_d=2#\n", + "BeamWidth=2*lambda_d/n# Beamwidth\n", + "print 'The angular width is %0.2f degrees'%(BeamWidth)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.8, page no 400" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overall Gain is 3.52 dBs\n" + ] + } + ], + "source": [ + "from math import log10\n", + "#Given\n", + "D1=1\n", + "D2=1.5*D1 # diameters of the new reflectors D1=1assumed for ease of calculation\n", + "G_dbs=10*log10((D2/D1)**2)#Gain in dBs\n", + "print 'Overall Gain is %0.2f dBs'%(round(1000*G_dbs)/1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.9, page no 401" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Radiation resistance is 2.05 ohm\n" + ] + } + ], + "source": [ + "#Given\n", + "#b\n", + "c=3e8\n", + "f=800e3# operating freq\n", + "dl=27#effective height\n", + "lamda=c/f\n", + "\n", + "Rr=40*(3.142**2)*(dl/lamda)**2#Radiation Resistance\n", + "print 'Radiation resistance is %0.2f ohm'%(Rr)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/ctftch1_EJ1lbz2.png b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/ctftch1_EJ1lbz2.png Binary files differnew file mode 100644 index 00000000..7c959f08 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/ctftch1_EJ1lbz2.png diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/fourier_Kpk6AU4.png b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/fourier_Kpk6AU4.png Binary files differnew file mode 100644 index 00000000..c0033679 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/fourier_Kpk6AU4.png diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/modulat_XbQVmZD.png b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/modulat_XbQVmZD.png Binary files differnew file mode 100644 index 00000000..3b34f439 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/modulat_XbQVmZD.png diff --git a/Semiconductor_circuit_approximations_by_A.P._Malvino/README.txt b/Semiconductor_circuit_approximations_by_A.P._Malvino/README.txt new file mode 100644 index 00000000..55c96836 --- /dev/null +++ b/Semiconductor_circuit_approximations_by_A.P._Malvino/README.txt @@ -0,0 +1,10 @@ +Contributed By: Ashvani Kumar +Course: btech +College/Institute/Organization: Uttarakhand Technical University +Department/Designation: EN +Book Title: Semiconductor circuit approximations +Author: A.P. Malvino +Publisher: Tata McGraw - Hill Education, New Delhi +Year of publication: 2005 +Isbn: 0070994854 +Edition: 4
\ No newline at end of file diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_02.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_02.ipynb new file mode 100644 index 00000000..c89cb397 --- /dev/null +++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_02.ipynb @@ -0,0 +1,2794 @@ +{
+ "metadata": {
+ "name": "chapter 02.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 2:Simple Stresses And Strains"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.1,Page No.14"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "P=45*10**3 #N #Load\n",
+ "E=200*10**3 #N/mm**2 #Modulus of elasticity of rod\n",
+ "L=500 #mm #Length of rod\n",
+ "d=20 #mm #Diameter of rod\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "A=pi*d**2*4**-1 #mm**2 #Area of circular rod\n",
+ "p=P*A**-1 #N/mm**2 #stress\n",
+ "e=p*E**-1 #strain \n",
+ "dell_l=(P*L)*(A*E)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"The stress in bar due to Load is\",round(p,5),\"N/mm\"\n",
+ "print\"The strain in bar due to Load is\",round(e,5),\"N/mm\"\n",
+ "print\"The Elongation in bar due to Load is\",round(dell_l,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The stress in bar due to Load is 143.23945 N/mm\n",
+ "The strain in bar due to Load is 0.00072 N/mm\n",
+ "The Elongation in bar due to Load is 0.36 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.2,Page No.15"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ " \n",
+ "A=15*0.75 #mm**2 #area of steel tape\n",
+ "P=100 #N #Force apllied\n",
+ "L=30*10**3 #mm #Length of tape\n",
+ "E=200*10**3 #N/m**2 #Modulus of Elasticity of steel tape\n",
+ "AB=150 #m #Measurement of Line AB \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "dell_l=P*L*(A*E)**-1 #mm #Elongation\n",
+ "l=L+dell_l*10**-3 #mm #Actual Length \n",
+ "AB1=AB*l*L**-1 #m Actual Length of AB\n",
+ "\n",
+ "#Result\n",
+ "print\"The Actual Length of Line AB is\",round(AB1,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Actual Length of Line AB is 150.0 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.3,Page No.15"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Let y be the yield stress\n",
+ "\n",
+ "y=250 #N/mm**2 #yield stress\n",
+ "FOS=1.75 #Factor of safety\n",
+ "P=140*10**3 #N #compressive Load\n",
+ "D=101.6 #mm #External diameter\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "p=y*(FOS)**-1 #N/mm**2 #Permissible stress\n",
+ "A=P*p**-1 #mm**2 #Area of hollow tube\n",
+ "\n",
+ "#Let d be the internal diameter of tube\n",
+ "d=-((A*4*(pi)**-1)-D**2)\n",
+ "X=d**0.5\n",
+ "t=(D-X)*2**-1 #mm #Thickness of steel tube\n",
+ "\n",
+ "#result\n",
+ "print\"The thickness of steel tube is\",round(t,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The thickness of steel tube is 3.17 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.4,Page No.16"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=25 #mm #diameter of steel\n",
+ "d2=18 #mm #Diameter at neck\n",
+ "L=200 #mm #length of stee\n",
+ "P=80*10**3 #KN #Load \n",
+ "P1=160*10**3 #N #Load at Elastic Limit\n",
+ "P2=180*10**3 #N #Max Load\n",
+ "L1=56 #mm #Total Extension\n",
+ "dell_l=0.16 #mm #Extension\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "A=pi*d**2*4**-1 #Area of steel #mm**2\n",
+ "\n",
+ "p=P1*A**-1 #Stress at Elastic Limit #N/mm**2\n",
+ "Y=P*L*(A*dell_l)**-1 #Modulus of elasticity\n",
+ "\n",
+ "#Let % elongation be x\n",
+ "x=L1*L**-1*100 \n",
+ "\n",
+ "#Percentage reduction in area\n",
+ "#Let % A be a\n",
+ "a=((pi*4**-1*d**2)-(pi*4**-1*d2**2))*(pi*4**-1*d**2)**-1*100\n",
+ "\n",
+ "#Ultimate tensile stress\n",
+ "sigma=P2*A**-1 #N/mm**2\n",
+ "\n",
+ "#result\n",
+ "print\"Stress at Elastic limit is\",round(p,2),\"N/mm**2\"\n",
+ "print\"Young's Modulus is\",round(Y,2),\"N/mm**2\"\n",
+ "print\"Percentage Elongation is\",round(a,2)\n",
+ "print\"Percentage reduction in area is\",round(P2,2)\n",
+ "print\"Ultimate tensile stress\",round(sigma,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stress at Elastic limit is 325.95 N/mm**2\n",
+ "Young's Modulus is 203718.33 N/mm**2\n",
+ "Percentage Elongation is 48.16\n",
+ "Percentage reduction in area is 180000.0\n",
+ "Ultimate tensile stress 366.69 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.5,Page No.16"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=20 #mm #Diameter of bar\n",
+ "d2=14.7 #mm #Diameter at neck \n",
+ "L=200 #mm #guage Length \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,10,20,30,40,50,60]\n",
+ "Y1=[0,32,64,95,127,160,190]\n",
+ "Z1=[0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Extension in divisions\")\n",
+ "plt.ylabel(\"Load in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "A=pi*4**-1*d**2 #mm**2 #Area of Bar\n",
+ "A2=pi*4**-1*d2**2\n",
+ "\n",
+ "P=45 #KN #Load obtained from graph\n",
+ "dell=0.143 #mm #Divisions\n",
+ "\n",
+ "#Modulus of Elasticity\n",
+ "E=P*L*(dell*A)**-1 \n",
+ "\n",
+ "BL=93*10**3 #N #Breaking Load\n",
+ "\n",
+ "#Nominal stress at Breaking point\n",
+ "sigma=BL*A**-1 #KN/mm**2 \n",
+ "\n",
+ "#True stress at breaking Point\n",
+ "sigma1=BL*A2**-1\n",
+ "\n",
+ "#Percentage Elongation \n",
+ "dell_l=(A-A2)*A**-1*100\n",
+ "\n",
+ "#Result\n",
+ "print\"The Value of ELongation is\",round(E,2),\"N/mm**2\"\n",
+ "print\"The Nominal stress at the Breaking Point\",round(sigma,2),\"KN/mm**2\"\n",
+ "print\"The True stress at the Breaking Point\",round(sigma1,2),\"KN/mm**2\"\n",
+ "print\"The Percentage Reduction in Area is\",round(dell_l,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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gwAFOnDjBRx99xNatWys876vr+8tf/kKzZs2Ii4vDVHG/iq+u7bL09HT279/P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\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x54b2a10>"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Value of ELongation is 200.33 N/mm**2\n",
+ "The Nominal stress at the Breaking Point 296.03 KN/mm**2\n",
+ "The True stress at the Breaking Point 547.97 KN/mm**2\n",
+ "The Percentage Reduction in Area is 45.98\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.6,Page No.19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=40*10**3 #N #Load \n",
+ "L1=160 #mm #Length of Bar1\n",
+ "L2=240 #mm #Length of bar2\n",
+ "L3=160 #mm #Length of bar3\n",
+ "d1=25 #mm #Diameter of Bar1\n",
+ "d2=20 #mm #diameter of bar2\n",
+ "d3=25 #mm #diameter of bar3\n",
+ "dell_l=0.285 #mm #Total Extension of bar\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "E=P*4*(dell_l*pi)**-1*(L1*(d1**2)**-1+L2*(d2**2)**-1+L3*(d3**2)**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"The Young's Modulus of the material\",round(E,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Young's Modulus of the material 198714.72 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.7,Page No.19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "E1=2*10**5 #N/mm**2 #modulus of Elasticity of material1\n",
+ "E2=1*10**5 #N/mm**2 #modulus of Elasticity of material2\n",
+ "P=25*10**3 #N #Load \n",
+ "t=20 #mm #thickness of material\n",
+ "b1=40 #mm #width of material1\n",
+ "b2=30 #mm #width of material2\n",
+ "L1=500 #mm #Length of material1\n",
+ "L2=750 #mm #Length of material2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "A1=b1*t #mm**2 #Area of materila1\n",
+ "A2=b2*t #mm**2 #Area of material2\n",
+ "\n",
+ "dell_l1=P*L1*(A1*E1)**-1 #Extension of Portion1\n",
+ "dell_l2=P*L2*(A2*E2)**-1 #Extension of portion2\n",
+ "\n",
+ "#Total Extension of Bar is\n",
+ "dell_l=dell_l1+dell_l2\n",
+ "\n",
+ "#Result\n",
+ "print\"The Total Extension of the Bar is\",round(dell_l,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Total Extension of the Bar is 0.39 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.8,Page No.20"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=1000 #mm #Length of Bar\n",
+ "l=400 #mm #Length upto which bire is drilled \n",
+ "D=30 #mm #diameter of bar\n",
+ "d1=10 #mm #diameter of bore\n",
+ "P=25*10**3 #N #Load\n",
+ "dell_l=0.185 #mm #Extension of bar\n",
+ "\n",
+ "#Calculations \n",
+ "\n",
+ "L1=L-l #Length of bar above the bore\n",
+ "L2=400 #mm #Length of bore\n",
+ "\n",
+ "A1=pi*4**-1*D**2 #Area of bar\n",
+ "A2=pi*4**-1*(D**2-d1**2) #Area of bore\n",
+ "\n",
+ "E=P*dell_l**-1*(L1*A1**-1+L2*A2**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"The Modulus of ELasticity is\",round(E,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Modulus of ELasticity is 200735.96 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.11,Page No.23"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "t=10 #mm #Thickness of steel\n",
+ "b1=60 #mm #width of plate1\n",
+ "b2=40 #mm #width of plate2\n",
+ "P=60*10**3 #Load\n",
+ "L=600 #mm #Length of plate\n",
+ "E=2*10**5 #N/mm**2\n",
+ " \n",
+ "#Calculations\n",
+ "\n",
+ "#Extension of taperong bar of rectangular section\n",
+ "dell_l=P*L*(t*E*(b1-b2))**-1*log(b1*b2**-1)\n",
+ "\n",
+ "A_av=(b1*t+b2*t)*2**-1 #Average Area #mm**2\n",
+ "dell_l2=P*L*(A_av*E)**-1 \n",
+ "\n",
+ "#PErcentage Error\n",
+ "e=(dell_l-dell_l2)*(dell_l)**-1*100\n",
+ "\n",
+ "#Result\n",
+ "print\"The Percentage Error is\",round(e,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Percentage Error is 1.35\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.12,Page No.23"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=1.5 #m #Length of steel bar\n",
+ "L1=1000 #m0 #Length of steel bar 1\n",
+ "L2=500 #m #Length of steel bar 2 \n",
+ "d1=40 #Diameter of steel bar 1\n",
+ "d2=20 #diameter of steel bar 2\n",
+ "E=2*10**5 #N/mm**2 #Modulus of Elasticity\n",
+ "P=160*10**3 #N #Load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "A1=pi*4**-1*d1**2 #Area of Portion 1\n",
+ "\n",
+ "#Extension of uniform Portion 1\n",
+ "dell_l1=P*L1*(A1*E)**-1 #mm\n",
+ "\n",
+ "#Extension of uniform Portion 2\n",
+ "dell_l2=4*P*L2*(pi*d1*d2*E)**-1 #mm\n",
+ "\n",
+ "#Total Extension of Bar\n",
+ "dell_l=dell_l1+dell_l2\n",
+ "\n",
+ "#Result\n",
+ "print\"The Elongation of the Bar is\",round(dell_l,2),\"mm\" "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Elongation of the Bar is 1.27 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.14,Page No.25"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Portion AB\n",
+ "L_AB=600 #mm #Length of AB\n",
+ "A_AB=40*40 #mm**2 #Cross-section Area of AB\n",
+ "\n",
+ "#Portion BC\n",
+ "L_BC=800 #mm #Length of BC\n",
+ "A_BC=30*30 #mm #Length of BC\n",
+ "\n",
+ "#Portion CD\n",
+ "L_CD=1000 #mm #Length of CD\n",
+ "A_CD=20*20 #mm #Area of CD\n",
+ "\n",
+ "P1=80*10**3 #N #Load1\n",
+ "P2=60*10**3 #N #Load2\n",
+ "P3=40*10**3 #N #Load3\n",
+ "\n",
+ "E=2*10**5 #Modulus of Elasticity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "P4=P1-P2+P3 #Load4\n",
+ "\n",
+ "#Now Force in AB\n",
+ "F_AB=P1\n",
+ "\n",
+ "#Force in BC\n",
+ "F_BC=P1-P2\n",
+ "\n",
+ "#Force in CD\n",
+ "F_CD=P4\n",
+ "\n",
+ "#Extension of AB\n",
+ "dell_l_AB=F_AB*L_AB*(A_AB*E)**-1\n",
+ "\n",
+ "#Extension of BC\n",
+ "dell_l_BC=F_BC*L_BC*(A_BC*E)**-1\n",
+ "\n",
+ "#Extension of CD\n",
+ "dell_l_CD=F_CD*L_CD*(A_CD*E)**-1\n",
+ "\n",
+ "#Total Extension\n",
+ "dell_l=dell_l_AB+dell_l_BC+dell_l_CD\n",
+ "\n",
+ "#Result\n",
+ "print\"The Total Extension in Bar is\",round(dell_l,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Total Extension in Bar is 0.99 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.15,Page No.26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=800 #mm #Length of bar\n",
+ "F1=30*10**3 #N #Force acting on the bar\n",
+ "F2=60*10**3 #N #force acting on the bar\n",
+ "L=800 #mm #Length of bar\n",
+ "d=25 #mm #diameter of bar \n",
+ "L_AC=275 #mm #Length of AC\n",
+ "L_CD=150 #mm #Length of CD\n",
+ "L_DB=375 #mm #Length of DB\n",
+ "E=2*10**5 #Pa #Modulus of elasticity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let P be the Reaction on tne Bar from support at A\n",
+ "\n",
+ "#Shortening of Portion AC\n",
+ "#dell_l_AC1=P*L_AC*(A*E)**-1\n",
+ "\n",
+ "#Shortening of Portion CD\n",
+ "#dell_l_CD1=(30+P)*L_CD*(A*E)**-1\n",
+ "\n",
+ "#Extension of Portion DB\n",
+ "#dell_l_DB1=(30-P)*L_DB*(A*E)**-1\n",
+ "\n",
+ "#Total Extensions=1*(A*E)**-1*(P*L_AC-(30+P)*L_CD+(30-P)*L_DB)\n",
+ "#As Supports are unyielding,Total Extensions=0\n",
+ "\n",
+ "#After substituting values in above equation and Further simplifying we get\n",
+ "P=(30*375-150*30)*800**-1\n",
+ "\n",
+ "#Reaction of support A\n",
+ "R_A=P\n",
+ "\n",
+ "#Reaction of support B\n",
+ "R_B=30-P\n",
+ "\n",
+ "#Cross-sectional Area\n",
+ "A=pi*4**-1*d**2\n",
+ "\n",
+ "#Stress in Portion AC\n",
+ "sigma1=P*10**3*A**-1 #N/mm**2\n",
+ "\n",
+ "#Stress in Portion CD\n",
+ "sigma2=(30+P)*10**3*A**-1 #N/mm**2\n",
+ "\n",
+ "#Stress in Portion DB\n",
+ "sigma3=(30-P)*10**3*A**-1 #N/mm**2\n",
+ "\n",
+ "#Shortening of Portion AC\n",
+ "dell_l_AC2=P*10**3*L_AC*(A*E)**-1 #mm \n",
+ "\n",
+ "#Shortening of Portion CD\n",
+ "dell_l_CD2=(30+P)*10**3*L_CD*(A*E)**-1 #mm \n",
+ "\n",
+ "#Extension of Portion DB\n",
+ "dell_l_DB2=(30-P)*10**3*L_DB*(A*E)**-1 #mm \n",
+ "\n",
+ "#result\n",
+ "print\"The Reactios at two Ends are:R_A\",round(R_A,2),\"KN\"\n",
+ "print\" :R_B\",round(R_B,2),\"KN\"\n",
+ "print\"Stress in Portion AC\",round(sigma1,2),\"N/mm**2\"\n",
+ "print\"Stress in Portion CD\",round(sigma2,2),\"N/mm**2\"\n",
+ "print\"Stress in Portion DB\",round(sigma3,2),\"N/mm**2\"\n",
+ "print\"Shortening of Portion AC\",round(dell_l_AC2,3),\"mm\"\n",
+ "print\"Shortening of Portion CD\",round(dell_l_CD2,3),\"mm\"\n",
+ "print\"Shortening of Portion DB\",round(dell_l_DB2,3),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Reactios at two Ends are:R_A 8.44 KN\n",
+ " :R_B 21.56 KN\n",
+ "Stress in Portion AC 17.19 N/mm**2\n",
+ "Stress in Portion CD 78.3 N/mm**2\n",
+ "Stress in Portion DB 43.93 N/mm**2\n",
+ "Shortening of Portion AC 0.024 mm\n",
+ "Shortening of Portion CD 0.059 mm\n",
+ "Shortening of Portion DB 0.082 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.19,Page No.29"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ " \n",
+ "h=4 #m #height of Pillars\n",
+ "P=20 #KN #Load at M\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let P_A,P_B,P_C,P_D be the forces introduced in the Pillars\n",
+ "#Sun of All Vertical Forces\n",
+ "#P_A+P_B+P_C+P_D=20 ....................(1)\n",
+ "\n",
+ "#Sum of moment about AB, we get\n",
+ "#P_D+P_C=12 ....................(2)\n",
+ "\n",
+ "#Sum of Moment about AD\n",
+ "#P_C+P_B=8 ....................(3)\n",
+ "\n",
+ "#Let dell_l_A,dell_l_B,dell_l-C,dell_l_D be the deformations of Pillars A,B,C,D respectively\n",
+ "#Diagonals AC and BD will remain straight Lines even after the Load is applied.\n",
+ "#Deflection of central Point is given by (dell_l_A+dell_l_C)*2**-1 & (dell_l_B+dell_l_D)*2**-1\n",
+ "\n",
+ "#dell_l_A+dell_l_C=dell_l_B+ell_l_D\n",
+ "#P_A*L*(A*E)**-1+P_C*L*(A*E)**-1=P_B*L*(A*E)**-1+P_D*L*(A*E)**-1\n",
+ "\n",
+ "#Since Pillars are identical in Length,cross-sectional area,material Property\n",
+ "#P_A+P_C=P_B+P_D ..............(4)\n",
+ "\n",
+ "#From Equations 1 and 4 we get\n",
+ "#P_B+P_D=10 ....................(5)\n",
+ " \n",
+ "#Substracting Equation 3 from Equation 2 we get\n",
+ "#P_D-P_B=4 ....................(6)\n",
+ "\n",
+ "#Adding Equation 5 and 6 we get\n",
+ "\n",
+ "P_D=14*2**-1\n",
+ "P_C=12-P_D\n",
+ "P_B=8-P_C\n",
+ "\n",
+ "#Now substituting values of P_B,P_C,P_D in equation1 we get\n",
+ "P_A=20-(P_B+P_C+P_D)\n",
+ "\n",
+ "#Result\n",
+ "print\"The Forces Developed in the Pillars are:P_A\",round(P_A,2),\"KN\"\n",
+ "print\" :P_B\",round(P_B,2),\"KN\"\n",
+ "print\" :P_C\",round(P_C,2),\"KN\"\n",
+ "print\" :P_D\",round(P_D,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Forces Developed in the Pillars are:P_A 5.0 KN\n",
+ " :P_B 3.0 KN\n",
+ " :P_C 5.0 KN\n",
+ " :P_D 7.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.20,Page No.31"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "sigma=150 #N/mm**2 #Stress\n",
+ "P=40*10**3 #N #Load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt P_A.P_B,P_C,P_D be the forces developed in wires A,B,C,D respectively\n",
+ "\n",
+ "#Let sum of all Vertical Forces=0\n",
+ "#P_A+P_B+P_C+P_D=40 ..........................(1)\n",
+ "\n",
+ "#Let x be the distance between each wires\n",
+ "#sum of all moments=0\n",
+ "#P_B*x+P_C*2*x+P_D*3*x=40*2*x\n",
+ "\n",
+ "#After further simplifying we get\n",
+ "#P_B+2*P_C+3*P_D=80 ..........................(2)\n",
+ "\n",
+ "#As the equations of statics ae not enough to find unknowns,Consider compatibilit Equations\n",
+ "\n",
+ "#Let dell_l be the increse in elongation of wire\n",
+ "\n",
+ "#dell_l_B=dell_l_A+dell_l\n",
+ "#dell_l_C=dell_l_A+2*dell_l\n",
+ "#dell_l_D=dell_l_A+3*dell_l\n",
+ "\n",
+ "#Let P1 be the force required for the Elongation of wires,then\n",
+ "#P_B=P_A+P1 ]\n",
+ "#P_C=P_A+2*P1 ]\n",
+ "#P_D=P_A+3*P1 ] ................................(3) \n",
+ "\n",
+ "#from Equation (3) and (1) we get\n",
+ "#2*P_A+3*P1=20 ................................(4)\n",
+ "\n",
+ "#from Equation (3) and (2) we get\n",
+ "#6*P_A+14*P1=80 \n",
+ "\n",
+ "#subtracting 3 times equation (4) from (3) we get\n",
+ "P1=20*5**-1\n",
+ "\n",
+ "#from Equation 4 we get\n",
+ "P_A=(80-14*P1)*6**-1\n",
+ "P_B=P_A+P1\n",
+ "P_C=P_A+2*P1 \n",
+ "P_D=P_A+3*P1\n",
+ "\n",
+ "#Let d be the diameter required,then\n",
+ "d=(P_D*10**3*4*(pi*150)**-1)**0.5\n",
+ "\n",
+ "#result\n",
+ "print\"The Required Diameter is\",round(d,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Required Diameter is 11.65 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.21,Page No.32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=20*10**3 #N #Load\n",
+ "d=6 #mm #diameter of wire\n",
+ "E=2*10**5 #N/mm**2 \n",
+ "L_BO=4000 #mm #Length of BO\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let theta be the angle between OA and OB and also between OC and OB\n",
+ "theta=30\n",
+ "\n",
+ "#Let P_OA,P_OB,P_OC be the Forces introduced in wires OA,OB,OC respectively\n",
+ "#Due to symmetry P_OA=P_OC (same angles)\n",
+ "\n",
+ "#Sum of all Vertical Forces=0\n",
+ "#P_OA*cos(theta)+P_OB+P_OC*cos(theta)=P\n",
+ "\n",
+ "#After further simplifyinf we get\n",
+ "#2*P_OA*cos(theta)+P_OB=20 ...............(1)\n",
+ "\n",
+ "#Let oo1 be the extension of BO\n",
+ "#oo1=L_A1o1*(cos(theta))**-1\n",
+ "\n",
+ "#From relation we get\n",
+ "#P_OB*L_BO=P_OA*L_AO*(cos(theta))**-1\n",
+ "\n",
+ "#But L_AO=L_BO*(cos(theta))**-1\n",
+ "\n",
+ "#After substituting value of L_AO in above equation we get\n",
+ "#P_OB=0.75*P_OA .......................(2)\n",
+ "\n",
+ "#substituting in Equation 1 we get\n",
+ "#2*P_OA*cos(theta)+0.75*P_OA=20\n",
+ "\n",
+ "P_OA=20*(2*cos(theta*pi*180**-1)+0.75)**-1\n",
+ "\n",
+ "P_OB=0.75*P_OA\n",
+ "\n",
+ "A=pi*4**-1*d**2 \n",
+ "\n",
+ "#Vertical displacement of Load\n",
+ "dell_l_BO=P_OB*10**3*L_BO*(A*E)**-1\n",
+ " \n",
+ "#Result\n",
+ "print\"Forces in each wire is:P_OA\",round(P_OA,2),\"KN\"\n",
+ "print\" :P_OB\",round(P_OB,2),\"KN\"\n",
+ "print\"Vertical displacement of Loadis\",round(dell_l_BO,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Forces in each wire is:P_OA 8.06 KN\n",
+ " :P_OB 6.04 KN\n",
+ "Vertical displacement of Loadis 4.27 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.22,Page No.34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_s=L_a=L=500 #mm #Length of bar\n",
+ "A_a=50*20 #mm #Area of aluminium strip\n",
+ "A_s=50*15 #mm #Area of steel strip\n",
+ "P=50*10**3 #N #Load\n",
+ "E_a=1*10**5 #N/mm**2 #Modulus of aluminium \n",
+ "E_s=2*10**5 #N/mm**2 #Modulus of steel\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let P_a and P_s br the Load shared by aluminium and steel strip\n",
+ "#P_a+P_s=P ..................(1)\n",
+ "\n",
+ "#For compatibility condition,dell_l_a=dell_l_s\n",
+ "#P_a*L_a*(A_a*E_a)**-1=P_s*L_s*(A_s*E_s)**-1 .....(2)\n",
+ "\n",
+ "#As L_a=L_s we get\n",
+ "#P_s=1.5*P_a .................(3)\n",
+ " \n",
+ "#From Equation 1 and 2 we get\n",
+ "P_a=P*2.5**-1\n",
+ "\n",
+ "#Substituting in equation 1 we get\n",
+ "P_s=P-P_a\n",
+ "\n",
+ "#stress in aluminium strip \n",
+ "sigma_a=P_a*A_a**-1\n",
+ "\n",
+ "#stress in steel strip\n",
+ "sigma_s=P_s*A_s**-1\n",
+ "\n",
+ "#Now from the relation we get\n",
+ "dell_l_a=dell_l_s=P_s*L_s*(A_s*E_s)**-1\n",
+ "\n",
+ "#result\n",
+ "print\"Stress in Aluminium strip is\",round(sigma_a,2),\"N/mm**2\"\n",
+ "print\"Stress in steel strip is\",round(sigma_s,2),\"N/mm**2\"\n",
+ "print\"The Extension of the bar is\",round(dell_l_s,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stress in Aluminium strip is 20.0 N/mm**2\n",
+ "Stress in steel strip is 40.0 N/mm**2\n",
+ "The Extension of the bar is 0.1 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.23,Page No.35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "D_s=20 #mm #Diameter of steel\n",
+ "D_Ci=20 #mm #Internal Diameter of Copper\n",
+ "t=5 #mm #THickness of copper bar\n",
+ "P=100*10**3 #N #Load\n",
+ "E_s=2*10**5 #N/mm**2 #modulus of elasticity of steel\n",
+ "E_c=1.2*10**5 #N/mm**2 #Modulus of Elasticity of Copper\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "A_s=pi*4**-1*D_s**2 #mm**2 #Area of steel\n",
+ "D_Ce=D_s+2*t #mm #External Diameterof Copper Tube\n",
+ "\n",
+ "A_c=pi*4**-1*(D_Ce**2-D_Ci**2) #mm**2 #Area of Copper\n",
+ "\n",
+ "#From static Equilibrium condition\n",
+ "#Let P_s and P_c be the Load shared by steel and copper in KN\n",
+ "#P_s+P_c=100 ....................................(1)\n",
+ "\n",
+ "#From compatibility Equation,dell_l_s=dell_l_c\n",
+ "#P_s*L*(A_s*E_s)**-1=P_c*L*(A_c*E_c)**-1\n",
+ "\n",
+ "#Substituting values in above Equation we get\n",
+ "#P_s=1.3333*P_C \n",
+ "\n",
+ "#Now Substituting value of P_s in Equation (1),we get\n",
+ "P_c=100*2.3333**-1 #KN\n",
+ "P_s=100-P_c #KN\n",
+ "\n",
+ "#Stress in steel\n",
+ "sigma_s=P_s*10**3*A_s**-1 #N/mm**2 \n",
+ "\n",
+ "#Stress in copper\n",
+ "sigma_c=P_c*10**3*A_c**-1 #N/mm**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Stresses Developed in Two material are:sigma_s\",round(sigma_s,2),\"N/mm**2\"\n",
+ "print\" :sigma_c\",round(sigma_c,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stresses Developed in Two material are:sigma_s 181.89 N/mm**2\n",
+ " :sigma_c 109.14 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.24,Page No.36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "A_C=230*400 #mm #Area of column\n",
+ "D_s=12 #mm #Diameter of steel Bar\n",
+ "P=600*10**3 #N #Axial compression\n",
+ "#E_s*E_c=18.67\n",
+ "n=8 #number of steel Bars\n",
+ "\n",
+ "#Calculations \n",
+ "\n",
+ "A_s=pi*4**-1*D_s**2*n #Area of steel #mm**2 \n",
+ "A_c=A_C-A_s #mm**2 #Area of concrete\n",
+ "\n",
+ "#From static Equilibrium condition\n",
+ "#P_s+P_c=600 .........(1)\n",
+ "\n",
+ "#Now from compatibility Equation dell_l_s=dell_l_c we get,\n",
+ "#P_s*L*(A_s*E_s)**-1=P_c*L*(A_c*E_c)**-1\n",
+ "\n",
+ "#Substituting values in above Equation we get\n",
+ "#P_s=0.1854*P_c\n",
+ "\n",
+ "#Now Substituting value of P_s in Equation (1),we get\n",
+ "P_c=600*1.1854**-1\n",
+ "P_s=600-P_c\n",
+ "\n",
+ "#Stress in steel\n",
+ "sigma_s=P_s*10**3*A_s**-1 #N/mm**2\n",
+ "\n",
+ "#Stress in copper\n",
+ "sigma_c=P_c*10**3*A_c**-1 #N/mm**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Stresses Developed in Two material are:sigma_s\",round(sigma_s,2),\"N/mm**2\"\n",
+ "print\" :sigma_c\",round(sigma_c,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stresses Developed in Two material are:sigma_s 103.72 N/mm**2\n",
+ " :sigma_c 5.56 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.25,Page No.36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=200*10**3 #N #Load\n",
+ "A_a=1000 #mm**2 #Area of Aluminium\n",
+ "A_s=800 #mm**2 #Area of steel\n",
+ "E_a=1*10**5 #N/mm**2 #Modulus of Elasticity of Aluminium\n",
+ "E_s=2*10**5 #N/mm**2 #Modulus of ELasticity of steel\n",
+ "sigma_a1=65 #N/mm**2 #stress in aluminium\n",
+ "sigma_s1=150 #N/mm**2 #Stress in steel\n",
+ "\n",
+ "#Calculations \n",
+ "\n",
+ "#Let P_a and P_s be the force in aluminium and steel pillar respectively\n",
+ "\n",
+ "#Now,sum of forces in Vertical direction we get\n",
+ "#2*P_a+P_s=200 .........................................(1)\n",
+ "\n",
+ "#By compatibility Equation dell_l_s=dell_l_a we get\n",
+ "#P_s=1.28*P_a ..........................................(2)\n",
+ "\n",
+ "#Now substituting value of P_s in Equation 1 we get\n",
+ "P_a=200*3.28**-1 #KN\n",
+ "P_s=200-2*P_a #KN\n",
+ "\n",
+ "#Stress developed in aluminium\n",
+ "sigma_a=P_a*10**3*A_a**-1 #N/mm**2 \n",
+ "\n",
+ "#Stress developed in steel\n",
+ "sigma_s=P_s*10**3*A_s**-1 #N/mm**2 \n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#Let sigma_a1 and sigma_s1 be the stresses in Aluminium and steel due to Additional LOad\n",
+ "\n",
+ "P_a1=sigma_a1*A_a #Load carrying capacity of aluminium\n",
+ "P_s1=1.28*P_a1\n",
+ "\n",
+ "#Total Load carrying capacity \n",
+ "P1=2*P_a1+P_s1 #N \n",
+ "\n",
+ "P_s2=sigma_s1*A_s #Load carrying capacity of steel\n",
+ "P_a2=P_s2*1.28**-1\n",
+ "\n",
+ "#Total Load carrying capacity\n",
+ "P2=2*P_a2+P_s2\n",
+ "\n",
+ "#Additional Load\n",
+ "P3=P1-P\n",
+ "\n",
+ "#Result\n",
+ "print\"Stresses Developed in Each Pillar is:sigma_a\",round(sigma_a,2),\"N/mm**2\"\n",
+ "print\" :sigma_s\",round(sigma_s,2),\"N/mm**2\"\n",
+ "print\"Additional Load taken by pillars is\",round(P3,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stresses Developed in Each Pillar is:sigma_a 60.98 N/mm**2\n",
+ " :sigma_s 97.56 N/mm**2\n",
+ "Additional Load taken by pillars is 13200.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.26,Page No.37"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=500 #mm #Length of assembly\n",
+ "D=16 #mm #Diameter of steel bolt\n",
+ "Di=20 #mm #internal Diameter of copper tube\n",
+ "Do=30 #mm #External Diameter of copper tube\n",
+ "E_s=2*10**5 #N/mm**2 #Modulus of Elasticity of steel\n",
+ "E_c=1.2*10**5 #N/mm**2 #Modulus of Elasticity of copper\n",
+ "p=2 #mm #Pitch of nut\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let P_s be the Force in bolt and P_c be the FOrce in copper tube\n",
+ "#P_s=-P_s\n",
+ "\n",
+ "dell=1*4**-1*2 #Quarter turn of nut total movement\n",
+ "\n",
+ "#dell=dell_s+dell_c\n",
+ " \n",
+ "#Area of steel\n",
+ "A_s=pi*4**-1*D**2\n",
+ "\n",
+ "#Area of copper\n",
+ "A_c=pi*4**-1*(Do**2-Di**2)\n",
+ "\n",
+ "#dell=P*L*(A_s*E_s)**-1+P*L*(A_c*E_c)**-1\n",
+ "P=dell*(1*(A_s*E_s)**-1+1*(A_c*E_c)**-1)**-1*L**-1 #LOad\n",
+ "\n",
+ "P_s=P*A_s**-1\n",
+ "P_c=P*A_c**-1\n",
+ "\n",
+ "#result\n",
+ "print\"stress introduced in bolt is\",round(P_s,2),\"N/mm**2\"\n",
+ "print\"stress introduced in tube is\",round(P_c,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "stress introduced in bolt is 107.91 N/mm**2\n",
+ "stress introduced in tube is 55.25 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.27,Page No.39"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "D=20 #mm #Diameter of Bolts\n",
+ "Di=25 #m #internal Diameter\n",
+ "t=10 #mm #Thickness of bolt\n",
+ "E_s=2*10**5 #N/mm**2 #Modulus of Elasticity\n",
+ "E_c=1.2*10**5 #N/mm**2 #Modulus of copper\n",
+ "p=3 #mm #Pitch\n",
+ "theta=30 #degree\n",
+ "L_c=500 #Lengh of copper \n",
+ "L_s=600 #Length of steel\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let P_s be the Force in each bolt and P_c be the FOrce in copper tube\n",
+ "#From Static Equilibrium condition\n",
+ "#P_c=2*P_s\n",
+ "\n",
+ "#As nut moves by 60 degree.If nut moves by 360 degree its Longitudinal movement is by 3 mm\n",
+ "dell=theta*360**-1*p\n",
+ "\n",
+ "#From Compatibility Equaton we get\n",
+ "#dell=dell_c+dell_s\n",
+ "\n",
+ "\n",
+ "A_s=pi*4**-1*Di**2 #mm**2 #Area of steel\n",
+ "A_c=pi*4**-1*(45**2-Di**2) #mm**2 #Area of copper\n",
+ "\n",
+ "#Force introduced in steel\n",
+ "P_s=0.5*(2*L_c*(A_c*E_c)**-1+L_s*(A_s*E_s)**-1)**-1 #N\n",
+ "P_s2=P_s*A_s**-1\n",
+ "\n",
+ "#Force introduced in copper \n",
+ "P_c=2*P_s*A_c**-1 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Stress introduced in bolt is\",round(P_s2,2),\"N/mm**2\"\n",
+ "print\"stress introduced in tube is\",round(P_c,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stress introduced in bolt is 74.4 N/mm**2\n",
+ "stress introduced in tube is 66.43 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.28,Page No.40"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=9 #m #Length of rigid bar\n",
+ "L_b=3000 #Length of bar\n",
+ "A_b=1000 #mm**2 #Area of bar\n",
+ "E_b=1*10**5 #N/mm**2 #Modulus of Elasticity of brasss bar\n",
+ "L_s=5000 #mm #Length of steel bar\n",
+ "A_s=445 #mm**2 #Area of steel bar\n",
+ "E_s=2*10**5 #N/mm**2 #Modulus of elasticity of steel bar\n",
+ "P=3000 #N #Load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#From static equilibrium Equation of the rod after appliying Load is\n",
+ "#P_b+P_s=P ......................(1)\n",
+ "\n",
+ "#P_b=1.8727*P_s ..................(2)\n",
+ "\n",
+ "#NOw substituting equation 2 in equation 1 we get\n",
+ "P_s=P*2.8727**-1\n",
+ "P_b=P-P_s\n",
+ "\n",
+ "d=P_s*L*P**-1 \n",
+ "\n",
+ "#Result\n",
+ "print\"Distance at which Load applied even after which bar remains horizontal is\",round(d,2),\"m\" "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Distance at which Load applied even after which bar remains horizontal is 3.13 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.29,Page No.41"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "A_b=1000 #MM**2 #Area of brass bar\n",
+ "E_b=1*10**5 #N/mm**2 #Modulus of Elasticity of brass\n",
+ "A_s=600 #N/mm**2 #Area of steel rod\n",
+ "E_s=2*10**5 #N/mm**2 #Modulus of eLasticity of steel bar\n",
+ "P=10*10**2 #N #Load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let P_b be the tensile force in brass bar and P_s be the compressive force in steel bar\n",
+ "#Now taking moment about A we get static Equilibrium condition as\n",
+ "#P_b+2*P_s=27500 ......................................(1)\n",
+ "\n",
+ "#Now from deformed shape we get\n",
+ "#dell_s=2*dell_b\n",
+ "\n",
+ "#P_s*L_s*(A_s*E_s)**-1=P_b*L_b*(A_b*E_b)**-1\n",
+ "#Further simplifying we get\n",
+ "#P_s=1.2*P_b .........................................(2)\n",
+ "\n",
+ "#Now substituting equation 1 in equation 2 we get\n",
+ "P_b=27500*3.4**-1\n",
+ "P_s=1.2*P_b \n",
+ "\n",
+ "#Tensile stress in brass bar \n",
+ "sigma_b=P_b*A_b**-1\n",
+ "\n",
+ "#compressive stress in steel bar\n",
+ "sigma_s=P_s*A_s**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Compressive Stress in Bar is\",round(sigma_s,2),\"N/mm**2\"\n",
+ "print\"tensile Stress in Bar is\",round(sigma_b,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Compressive Stress in Bar is 16.18 N/mm**2\n",
+ "tensile Stress in Bar is 8.09 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.30,Page No.44"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=12.6 #m #Length of rail\n",
+ "t1=24 #Degree celsius\n",
+ "t2=44 #degree celsius\n",
+ "alpha=12*10**-6 #Per degree celsius\n",
+ "E=2*10**5 #N/mm**2 #Modulus of ELasticity\n",
+ "gamma=2 #mm #Gap provided for Expansion\n",
+ "sigma=20 #N/mm**2 #Stress\n",
+ "\n",
+ "#Calculations \n",
+ "\n",
+ "t=t2-t1 #Temperature Difference\n",
+ "\n",
+ "#Free Expansion of the rails\n",
+ "dell=alpha*t*L*1000 #mm \n",
+ "\n",
+ "#When no expansion joint is provided then\n",
+ "p=dell*E*(L*10**3)**-1\n",
+ "\n",
+ "#When a gap of 2 mm is provided,then free expansion prevented is\n",
+ "dell_1=dell-gamma\n",
+ "p2=dell_1*E*(L*10**3)**-1\n",
+ "\n",
+ "#When stress is developed,then gap left is\n",
+ "gamma2=-(sigma*L*10**3*E**-1-dell)\n",
+ "\n",
+ "#Result\n",
+ "print\"The minimum gap between the two rails is\",round(dell,2),\"mm\"\n",
+ "print\"Thermal Developed in the rials if:No expansionn joint is provided:p\",round(p,2),\"N/mm**2\"\n",
+ "print\" :If a gap of is provided then :p2\",round(p2,2),\"N/mm**2\"\n",
+ "print\"When stress is developed gap left between the rails is\",round(gamma2,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The minimum gap between the two rails is 3.02 mm\n",
+ "Thermal Developed in the rials if:No expansionn joint is provided:p 48.0 N/mm**2\n",
+ " :If a gap of is provided then :p2 16.25 N/mm**2\n",
+ "When stress is developed gap left between the rails is 1.76 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.31,Page No.45"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "t=20 #degree celsius\n",
+ "E_a=70*10**9 #N/mm**2 #Modulus of Elasticicty of aluminium\n",
+ "alpha_a=11*10**-6 #per degree celsius #Temperature coeff of aluminium\n",
+ "alpha_s=12*10**-6 #Per degree celsius #Temperature coeff of steel\n",
+ "L_a=1000 #mm #Length of aluminium \n",
+ "L_s=3000 #mm #Length of steel\n",
+ "E_a=7*10**4 #N/mm**2 #Modulus of Elasticity of aluminium\n",
+ "E_s=2*10**5 #N/mm*2 #Modulus of Elasticity of steel\n",
+ "A_a=600 #mm**2 #Area of aluminium\n",
+ "A_s=300 #mm**2 #Area of steel\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Free Expansion \n",
+ "dell=alpha_a*t*L_a+alpha_s*t*L_s\n",
+ " \n",
+ "#support Reaction\n",
+ "P=dell*(L_a*(A_a*E_a)**-1+L_s*(A_s*E_s)**-1)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Reaction at support is\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reaction at support is 12735.48 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.33,Page No.48"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "D=25 #mm #Diameter of Brass\n",
+ "De=50 #mm #External Diameter of steel tube\n",
+ "Di=25 #mm #Internal Diameter of steel tube\n",
+ "L=1.5 #m #Length of both bars\n",
+ "t1=30 #degree celsius #Initial Temperature\n",
+ "t2=100 #degree celsius #final Temperature\n",
+ "E_s=2*10**5 #N/mm**2 #Modulus of ELasticity of steel bar\n",
+ "E_b=1*10**5 #N/mm**2 #Modulus of Elasticity of brass bar\n",
+ "alpha_s=11.6*10**-6 #Temperature Coeff of steel\n",
+ "alpha_b=18.7*10**-6 #Temperature coeff of brass bar\n",
+ "d=20 #mm #diameter of pins\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "t=t2-t1 #Temperature Difference\n",
+ "A_s=pi*4**-1*(De**2-Di**2) #mm**2 #Area of steel\n",
+ "A_b=pi*4**-1*D**2 #mm**2 #Area of brass\n",
+ "\n",
+ "#Let P_b be the tensile force in brass bar and P_s be the compressive force in steel bar\n",
+ "#But from Equilibrium of Forces \n",
+ "#P_b=P_s=P\n",
+ "\n",
+ "#Let dell=dell_s+dell_b\n",
+ "dell=(alpha_b-alpha_s)*t*L*1000\n",
+ "\n",
+ "P=dell*(1*(A_s*E_s)**-1+1*(A_b*E_b)**-1)**-1*(L*1000)**-1\n",
+ "P_b=P_s=P\n",
+ "\n",
+ "#Stress in steel\n",
+ "sigma_s=P_s*A_s**-1\n",
+ "\n",
+ "#Stress in Brass\n",
+ "sigma_b=P_b*A_b**-1\n",
+ "\n",
+ "#Area of Pins\n",
+ "A_p=pi*4**-1*d**2\n",
+ "\n",
+ "#Since,the force is resisted by two cross section of pins\n",
+ "tou=P*(2*A_p)**-1\n",
+ " \n",
+ "#Result\n",
+ "print\"Stress in steel bar is\",round(sigma_s,2),\"N/mm**2\"\n",
+ "print\"Stress in Brass bar is\",round(sigma_b,2),\"N/mm**2\"\n",
+ "print\"Shear Stresss induced in pins is\",round(tou,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stress in steel bar is 14.2 N/mm**2\n",
+ "Stress in Brass bar is 42.6 N/mm**2\n",
+ "Shear Stresss induced in pins is 33.28 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.34,Page No.49"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "b_s=60 #mm #width of steel Bar\n",
+ "t_s=10 #mm #thickness of steel Bar\n",
+ "b_c=40 #mm #width of copper bar\n",
+ "t_c=5 #mm #thickness of copper bar\n",
+ "E_s=2*10**5 #N/mm**2 #Modulus of Elasticity of steel bar\n",
+ "E_c=1*10**5 #N/mm**2 #Modulus of Elasticity of copper bar\n",
+ "alpha_s=12*10**-6 #Per degree celsius #Temperature coeff of steel bar\n",
+ "alpha_c=17*10**-6 #Per degree celsius #Temperature coeff of copper bar\n",
+ "L_s=L_c=L=1000 #mm #Length of bar\n",
+ "t=80 #degree celsius\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "A_s=b_s*t_s #Area of steel bar\n",
+ "A_c=b_c*t_c #Area of copper bar\n",
+ "\n",
+ "#Let P_s be the tensile force in steel bar and P_c be the compressive force in copper bar\n",
+ "#The equilibrium of forces gives \n",
+ "#P_s=2*P_c\n",
+ "\n",
+ "#Let dell=dell_s+dell_b\n",
+ "dell=(alpha_c-alpha_s)*t\n",
+ "\n",
+ "P_c=dell*(2*(A_s*E_s)**-1+1*(A_c*E_c)**-1)**-1\n",
+ "P_s=2*P_c\n",
+ "\n",
+ "#Stress in copper \n",
+ "sigma_c=P_c*A_c**-1\n",
+ "\n",
+ "#Stress in steel \n",
+ "sigma_s=P_s*A_s**-1\n",
+ "\n",
+ "#Change in Length of bar\n",
+ "dell_2=alpha_s*t*L+P_s*L_s*(A_s*E_s)**-1\n",
+ "\n",
+ "#result\n",
+ "print\"Stress in copper is\",round(sigma_c,2),\"N/mm**2\"\n",
+ "print\"Stress in steel is\",round(sigma_s,2),\"N/mm**2\"\n",
+ "print\"the change in Length is\",round(dell_2,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stress in copper is 30.0 N/mm**2\n",
+ "Stress in steel is 20.0 N/mm**2\n",
+ "the change in Length is 1.06 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.35,Page No.50"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=2*10**5 #N #Weight\n",
+ "L=1 #m #Length of each rod\n",
+ "A_c=A_s=A=500 #mm**2 #Area of each rod\n",
+ "t=40 #degree celsius #temperature\n",
+ "E_s=2*10**5 #N/mm**2 #Modulus of Elasticity of steel rod\n",
+ "E_c=1*10**5 #N/mm**2 #modulus of Elastictiy of copper rod\n",
+ "alpha_s=1.2*10**-5 #Per degree Celsius #temp coeff of steel rod\n",
+ "alpha_c=1.8*10**-5 #Per degree Celsius #Temp coeff of copper rod\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let P_s be the force in each one of the copper rods and P_s be the force in steel rod\n",
+ "#2*P_c+P_s=P .....................(1)\n",
+ "\n",
+ "#Extension of copper bar=Extension of steel bar\n",
+ "#P_s*L*(A_s*E_s)**-1=P_c*L*(A_c*E_c)**-1\n",
+ "#after simplifying above equation we get\n",
+ "#P_s=2*P_c ........................(2)\n",
+ "\n",
+ "#Now substituting value of P_s in Equation 1 we get\n",
+ "P_c=P*4**-1\n",
+ "P_s=2*P_c\n",
+ "\n",
+ "#Now EXtension due to copper Load\n",
+ "dell_1=P_c*L*1000*(A_c*E_c)**-1\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#Due to rise of temperature of40 degree celsius\n",
+ "\n",
+ "#As bars are rigidly joined,let P_c1 be the compressive forccesdeveloped in copper bar and P_s1 be the tensile force in steel causing changes\n",
+ "#P_s1=2*P_c1\n",
+ "\n",
+ "#dell_s+dell_c=(alpha_c-alpha_s)*t*L .......................................(3)\n",
+ "#P_s1*L*(A_s*E_s)**-1+P_c1*L*(A_c*E_c)**-1=(alpha_c-alpha_s)*t*L ................(4)\n",
+ "#After substituting values in above equation and further simplifying we get,\n",
+ "P_c1=(alpha_c-alpha_s)*t*L*(2*(A_s*E_s)**-1+1*(A_c*E_c)**-1)**-1 #.................(5)\n",
+ "P_s1=2*P_c1\n",
+ "\n",
+ "#Extension of bar due to temperature rise\n",
+ "dell_2=alpha_s*t*L+P_s1*L*(A_s*E_s)**-1\n",
+ "\n",
+ "#Amount by which bar will descend\n",
+ "dell_3=dell_1+dell_2\n",
+ "\n",
+ "#Load carried by steel bar\n",
+ "P_S=P_s+P_s1\n",
+ "\n",
+ "#Load carried by copper bar\n",
+ "P_C=P_c-P_c1\n",
+ "\n",
+ "#Part-3\n",
+ "\n",
+ "#Let P_c1_1=P_c #For convenience\n",
+ "#Rise in temperature if Load is to be carried out by steel rod alone\n",
+ "P_c1_1=P_c\n",
+ "\n",
+ "#From equation 5 \n",
+ "t=P_c1_1*(2*(A_s*E_s)**-1+1*(A_c*E_c)**-1)*(alpha_c-alpha_s)**-1\n",
+ "\n",
+ "#result\n",
+ "print\"Extension Due top copper Load\",round(dell_1,2),\"mm\"\n",
+ "print\"Load carried by each rod:P_s\",round(P_s,2),\"N\"\n",
+ "print\" :P_c\",round(P_c,2),\"N\"\n",
+ "print\"Rise in Temperature of steel rod should be\",round(t,2),\"degree Celsius\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Extension Due top copper Load 1.0 mm\n",
+ "Load carried by each rod:P_s 100000.0 N\n",
+ " :P_c 50000.0 N\n",
+ "Rise in Temperature of steel rod should be 333.33 degree Celsius\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.36,Page No.53"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "t=40 #degree celsius #temperature\n",
+ "A_s=400 #mm**2 #Area of steel bar\n",
+ "A_c=600 #mm**2 #Area of copper bar\n",
+ "E_s=2*10**5 #N/mm**2 #Modulus of Elasticity of steel bar\n",
+ "E_c=1*10**5 #N/mm**2 #Modulus of Elasticity of copper bar\n",
+ "alpha_s=12*10**-6 #degree celsius #Temperature coeff of steel bar\n",
+ "alpha_c=18*10**-6 #degree celsius #Temperature coeff of copper bar\n",
+ "L_c=800 #mm #Length of copper bar\n",
+ "L_s=600 #mm #Length of steel bar\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let P_s be the tensile force in steel bar and P_c be the compressive force in copper bar\n",
+ "#Static Equilibrium obtained by taking moment about A\n",
+ "#P_c=2*P_s\n",
+ "\n",
+ "#From property of similar triangles we get\n",
+ "#(alpha_c*Lc-dell_c)*1**-1=(alpha_s*L_s-dell_s)*2**-1\n",
+ "#After substituting values in above equations and further simplifying we get\n",
+ "P_s=(2*alpha_c*L_c-alpha_s*L_s)*t*(L_s*(A_s*E_s)**-1+4*L_c*(A_c*E_c)**-1)**-1\n",
+ "P_c=2*P_s\n",
+ "\n",
+ "#Stress in steel rod\n",
+ "sigma_s=P_s*A_s**-1 #N/mm**2 \n",
+ "\n",
+ "#Stress in copper rod\n",
+ "sigma_c=P_c*A_c**-1 #N/mm**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Stress in steel rod is\",round(sigma_s,2),\"N/mm**2\"\n",
+ "print\"STress in copper rod is\",round(sigma_c,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stress in steel rod is 35.51 N/mm**2\n",
+ "STress in copper rod is 47.34 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.37,Page No.61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=20 #mm #Diameter of bar\n",
+ "P=37.7*10**3 #N #Load\n",
+ "L=200 #mm #Guage Length \n",
+ "dell=0.12 #mm #Extension\n",
+ "dell_d=0.0036 #mm #contraction in diameter\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Area of bar\n",
+ "A=pi*4**-1*d**2\n",
+ "\n",
+ "#Let s and dell_s be the Linear strain and Lateral strain\n",
+ "s=dell*L**-1\n",
+ "dell_s=dell_d*d**-1\n",
+ "mu=dell_s*s**-1 #Poissoin's ratio \n",
+ "\n",
+ "#dell=P*L*(A*E)**-1\n",
+ "E=P*L*(dell*A)**-1 #N/mm**2 #Modulus of Elasticity of bar\n",
+ "\n",
+ "#Modulus of Rigidity\n",
+ "G=E*(2*(1+mu))**-1 #N/mm**2\n",
+ "\n",
+ "#Bulk Modulus \n",
+ "K=E*(3*(1-2*mu))**-1 #N/mm**2\n",
+ "\n",
+ "#result\n",
+ "print\"Poisson's ratio is\",round(mu,2)\n",
+ "print\"The Elastic constant are:E\",round(E,2)\n",
+ "print\" :G\",round(G,2)\n",
+ "print\" :K\",round(K,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Poisson's ratio is 0.3\n",
+ "The Elastic constant are:E 200004.71\n",
+ " :G 76924.89\n",
+ " :K 166670.59\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.38,Page No.62"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=100 #mm #Diameter of circular rod\n",
+ "P=1*10**6 #N #Tensile Force\n",
+ "mu=0.3 #Poisson's ratio\n",
+ "E=2*10**5 #N/mm**2 #Young's Modulus \n",
+ "L=500 #mm #Length of rod\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Modulus of Rigidity\n",
+ "G=E*(2*(1+mu))**-1 #N/mm**2\n",
+ "\n",
+ "#Bulk Modulus \n",
+ "K=E*(3*(1-2*mu))**-1 #N/mm**2\n",
+ "\n",
+ "A=pi*4**-1*d**2 #mm**2 #Area of Circular rod\n",
+ "#Let sigma be the Longitudinal stress\n",
+ "sigma=P*A**-1 #N/mm**2 \n",
+ "\n",
+ "s=sigma*E**-1 #Linear strain\n",
+ "e_x=s\n",
+ "\n",
+ "#Volumetric strain\n",
+ "e_v=e_x*(1-2*mu)\n",
+ "\n",
+ "v=pi*4**-1*d**2*L\n",
+ "#Change in VOlume\n",
+ "dell_v=e_v*v\n",
+ "\n",
+ "#Result\n",
+ "print\"Bulk Modulus is\",round(E,2),\"N/mm**2\"\n",
+ "print\"Modulus of Rigidity is\",round(G,2),\"N/mm**2\"\n",
+ "print\"The change in Volume is\",round(dell_v,2),\"mm**3\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Bulk Modulus is 200000.0 N/mm**2\n",
+ "Modulus of Rigidity is 76923.08 N/mm**2\n",
+ "The change in Volume is 1000.0 mm**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.39,Page No.62"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=500 #mm #Length of rectangular cross section bar\n",
+ "A=20*40 #mm**2 #Area of rectangular cross section bar\n",
+ "P1=4*10**4 #N #Tensile Force on 20mm*40mm Faces\n",
+ "P2=2*10**5 #N #compressive force on 20mm*500mm Faces\n",
+ "P3=3*10**5 #N #Tensile Force on 40mm*500mm Faces\n",
+ "E=2*10**5 #N/mm**2 #young's Modulus \n",
+ "mu=0.3 #Poisson's Ratio\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let P_x,P_y,P_z be the forces n x,y,z directions\n",
+ "\n",
+ "P_x=P1*A**-1\n",
+ "P_y=P2*A**-1\n",
+ "P_z=P3*A**-1\n",
+ "\n",
+ "#Let e_x,e_y,e_z be the strains in x,y,z directions\n",
+ "e_x=1*E**-1*(50+mu*20-15*mu)\n",
+ "e_y=1*E**-1*(-mu*50-20-mu*15)\n",
+ "e_z=1*E**-1*(-mu*50+mu*20+15)\n",
+ "\n",
+ "#Volumetric strain\n",
+ "e_v=e_x+e_y+e_z\n",
+ "\n",
+ "#Volume\n",
+ "V=20*40*500 #mm**3\n",
+ "#Change in Volume \n",
+ "dell_v=e_v*V #mm**3\n",
+ "\n",
+ "#Result\n",
+ "print\"The change in Volume is\",round(dell_v,2),\"mm**3\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The change in Volume is 36.0 mm**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.41,Page No.65"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "E=2.1*10**5 #N/mm**2 #Young's Modulus \n",
+ "G=0.78*10**5 #N/mm**2 #Modulus of Rigidity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Now using the relation\n",
+ "#E=2*G*(1+mu)\n",
+ "mu=E*(2*G)**-1-1 #Poisson's ratio\n",
+ "\n",
+ "#Bulk Modulus \n",
+ "K=E*(3*(1-2*mu))**-1 #N/mm**2\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"The Poisson's Ratio is\",round(mu,2)\n",
+ "print\"The modulus of Rigidity\",round(K,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Poisson's Ratio is 0.35\n",
+ "The modulus of Rigidity 227500.0 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.42,Page No.65"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "G=0.4*10**5 #N/mm**2 #Modulus of rigidity\n",
+ "K=0.75*10**5 #N/mm**2 #Bulk Modulus \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Young's Modulus\n",
+ "E=9*G*K*(3*K+G)**-1\n",
+ "\n",
+ "#Now from the relation\n",
+ "#E=2*G(1+2*mu)\n",
+ "mu=E*(2*G)**-1-1 #POissoin's ratio \n",
+ "\n",
+ "#result\n",
+ "print\"Young's modulus is\",round(E,2),\"N/mm**2\"\n",
+ "print\"Poissoin's ratio is\",round(mu,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Young's modulus is 101886.79 N/mm**2\n",
+ "Poissoin's ratio is 0.27\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.43,Page No.65"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "b=60 #mm #width of bar\n",
+ "d=30 #mm #depth of bar\n",
+ "L=200 #mm #Length of bar\n",
+ "A=30*60 #mm**2 #Area of bar\n",
+ "A2=30*200 #mm**2 #Area of bar along which expansion is restrained\n",
+ "P=180*10**3 #N #Compressive force\n",
+ "E=2*10**5 #N/mm**2 #Young's Modulus\n",
+ "mu=0.3 #Poissoin's ratio\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#The bar is restrained from expanding in Y direction\n",
+ "P_z=0\n",
+ "P_x=P*A**-1 #stress developed in x direction\n",
+ "\n",
+ "#Now taking compressive strain as positive\n",
+ "#e_x=P_x*E**-1-mu*P_y*E**-1 .......................(1)\n",
+ "#e_y=-mu*P_x*E**-1+P_y*E**-1 ....................(2)\n",
+ "#e_z=-mu*P_x*E**-1-mu*P_y*E**-1 ......................(3)\n",
+ "\n",
+ "#Part-1\n",
+ "#When it is fully restrained\n",
+ "e_y=0\n",
+ "P_y=30 #N/mm**2 \n",
+ "e_x=P_x*E**-1-mu*P_y*E**-1\n",
+ "e_z=-mu*P_x*E**-1-mu*P_y*E**-1\n",
+ "\n",
+ "#Change in Length \n",
+ "dell_l=e_x*L #mm\n",
+ "\n",
+ "#Change in width\n",
+ "dell_b=b*e_y\n",
+ "\n",
+ "#change in Depth\n",
+ "dell_d=d*e_z\n",
+ "\n",
+ "#Volume of bar\n",
+ "V=b*d*L #mm**3\n",
+ "#Change in Volume\n",
+ "e_v=(e_x+e_y+e_z)*V #mm**3\n",
+ "\n",
+ "#Part-2\n",
+ "#When 50% is restrained\n",
+ "\n",
+ "#Free strain in Y direction\n",
+ "e_y1=mu*P_x*E**-1\n",
+ "\n",
+ "#As 50% is restrained,so\n",
+ "e_y2=-50*100**-1*e_y1\n",
+ "\n",
+ "#But form Equation 2 we have e_y=-mu*P_x*E**-1+P_y*E**-1 \n",
+ "#After substituting values in above equation and furthe simplifying we get\n",
+ "P_y=e_y2*E+d\n",
+ "\n",
+ "e_x2=P_x*E**-1-mu*P_y*E**-1 \n",
+ "e_z2=-mu*P_x*E**-1-mu*P_y*E**-1\n",
+ "\n",
+ "#Change in Length \n",
+ "dell_l2=e_x2*L #mm\n",
+ "\n",
+ "#Change in width\n",
+ "dell_b2=b*e_y2\n",
+ "\n",
+ "#change in Depth\n",
+ "dell_d2=d*e_z2\n",
+ "\n",
+ "#Change in Volume\n",
+ "e_v2=(e_x2+e_y2+e_z2)*V #mm**3\n",
+ "\n",
+ "#REsult\n",
+ "print\"Change in Dimension of bar is:dell_l\",round(dell_l,2),\"mm\"\n",
+ "print\" :dell_b\",round(dell_b,4),\"mm\"\n",
+ "print\" :dell_d\",round(dell_d,2),\"mm\"\n",
+ "print\"Change in Volume is\",round(e_v,2),\"mm**3\"\n",
+ "print\"Changes in material when only 50% of expansion can be reatrained:dell_l2\",round(dell_l2,2),\"mm\"\n",
+ "print\" :dell_b2\",round(dell_b2,4),\"mm\"\n",
+ "print\" :dell_d2\",round(dell_d2,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Change in Dimension of bar is:dell_l 0.09 mm\n",
+ " :dell_b 0.0 mm\n",
+ " :dell_d -0.01 mm\n",
+ "Change in Volume is 93.6 mm**3\n",
+ "Changes in material when only 50% of expansion can be reatrained:dell_l2 0.1 mm\n",
+ " :dell_b2 -0.0045 mm\n",
+ " :dell_d2 -0.01 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.44,Page No.72"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=10*10**3 #N #Load\n",
+ "E=2*10**5 #N/mm**2 #Young's Modulus\n",
+ "d2=12 #mm #Diameter of bar1\n",
+ "d1=16 #mm #diameter of bar2\n",
+ "L1=200 #mm #Length of bar1\n",
+ "L2=500 #mm #Length of bar2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let A1 and A2 be the cross Area of Bar1 & bar2 respectively\n",
+ "A1=pi*4**-1*d1**2 #mm**2\n",
+ "A2=pi*4**-1*d2**2 #mm**2\n",
+ "\n",
+ "#Let p1 and p2 be the stress in Bar1 nad bar2 respectively\n",
+ "p1=P*A1**-1 #N/mm**2\n",
+ "p2=P*A2**-1 #N/mm**2\n",
+ "\n",
+ "#Let V1 nad V2 be the Volume of of Bar1 and Bar2\n",
+ "V1=A1*(L1+L1)\n",
+ "V2=A2*L2\n",
+ "\n",
+ "#Let E be the strain Energy stored in the bar\n",
+ "E=p1**2*(2*E)**-1*V1+p2**2*V2*(2*E)**-1\n",
+ "\n",
+ "#result\n",
+ "print\"The Strain Energy stored in Bar is\",round(E,2),\"N-mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Strain Energy stored in Bar is 1602.6 N-mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 74
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.45,Page No.73"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Bar-A\n",
+ "d1=30 #mm #Diameter of bar1\n",
+ "L=600 #mm #length of bar1\n",
+ "\n",
+ "#Bar-B\n",
+ "d2=30 #mm #Diameter of bar2\n",
+ "d3=20 #mm #Diameter of bar2\n",
+ "L2=600 #mm #length of bar2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Area of bar-A\n",
+ "A1=pi*4**-1*d1**2\n",
+ "\n",
+ "#Area of bar-B\n",
+ "A2=pi*4**-1*d2**2\n",
+ "A3=pi*4**-1*d3**2\n",
+ "\n",
+ "#let SE be the Strain Energy\n",
+ "#Strain Energy stored in Bar-A\n",
+ "#SE=p**2*(2*E)**-1*V\n",
+ "#After substituting values and simolifying further we get\n",
+ "#SE=P**2*E**-1*0.4244\n",
+ "\n",
+ "#Strain Energy stored in Bar-B\n",
+ "#SE2=p1**2*V1*(2*E)**-1+p2**2*V2*(2*E)**-1\n",
+ "#After substituting values and simolifying further we get\n",
+ "#SE2=0.6897*P**2*E**-1\n",
+ "\n",
+ "#Let X be the ratio of SE in Bar-B and SE in Bar-A\n",
+ "X=0.6897*0.4244**-1\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#When Max stress is produced is same:Let p be the max stress produced\n",
+ "\n",
+ "#Stress in bar A is p throughout \n",
+ "#In bar B:stress in 20mm dia.portion=p2=p\n",
+ "\n",
+ "#Stress in 30 mm dia.portion\n",
+ "#p1=P*A2*A3**-1\n",
+ "#After substituting values and simolifying further we get\n",
+ "#p1=4*9**-1*p\n",
+ "\n",
+ "#Strain Energy in bar A\n",
+ "#SE_1=p**2*(2*E)**-1*A1*L1\n",
+ "#After substituting values and simolifying further we get\n",
+ "#SE_1=67500*p**2*pi*E**-1\n",
+ "\n",
+ "#Strain Energy in bar B\n",
+ "#SE_2=p1**2*V1*(2*E)**-1+p2**2*V2*(2*E)**-1\n",
+ "#After substituting values and simolifying further we get\n",
+ "#SE_2=21666.67*pi*p**2*E**-1\n",
+ "\n",
+ "#Let Y be the Ratio of SE in bar B and SE in bar A\n",
+ "Y=21666.67*67500**-1\n",
+ "\n",
+ "#result\n",
+ "print\"Gradually applied Load is\",round(X,2)\n",
+ "print\"Gradually applied Load is\",round(Y,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Gradually applied Load is 1.63\n",
+ "Gradually applied Load is 0.32\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.46,Page No.74"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables \n",
+ "\n",
+ "W=100 #N #Load\n",
+ "E=2*10**5 #N/mm**2 #Young's Modulus \n",
+ "h=60 #mm #Height through Load falls down\n",
+ "L=400 #mm #Length of collar\n",
+ "d=30 #mm #diameter of bar\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "A=pi*4**-1*d**2 #mm**2 #Area of bar\n",
+ "\n",
+ "#Instantaneous stress produced is\n",
+ "p=W*A**-1*(1+(1+(2*A*E*h*(W*L)**-1))**0.5)\n",
+ "\n",
+ "#Now the EXtension of the bar is neglected in calculating work doneby the Load,then\n",
+ "P=(2*E*h*W*(A*L)**-1)**0.5\n",
+ "\n",
+ "#Let percentage error be denoted by E1\n",
+ "#Percentage error in approximating is\n",
+ "E1=(p-P)*p**-1*100\n",
+ "\n",
+ "#Instantaneous Extension produced is\n",
+ "dell_l=round(P,3)*E**-1*L\n",
+ "\n",
+ "#Result\n",
+ "print\"The Instantaneous stress is\",round(p,2),\"N/mm\"\n",
+ "print\"Percentage Error is\",round(E1,2)\n",
+ "print\"The Instantaneous extension is\",round(dell_l,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Instantaneous stress is 92.27 N/mm\n",
+ "Percentage Error is 0.15\n",
+ "The Instantaneous extension is 0.18 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.47,Page No.75"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=20 #mm #Diameter of steel bar\n",
+ "L=1000 #mm #Length of bar\n",
+ "E=2*10**5 #N/mm**2 #Young's Modulus \n",
+ "p=300 #N/mm**2 #max Permissible stress\n",
+ "h=50 #mm #Height through which weight will fall\n",
+ "w=600 #N #Load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#ARea of steel bar\n",
+ "A=pi*4**-1*d**2\n",
+ "\n",
+ "#Instantaneous extension is\n",
+ "dell_l=p*L*E**-1 #mm \n",
+ "\n",
+ "#Work done by Load \n",
+ "#W=W1*(h+dell_l)\n",
+ "\n",
+ "#Volume of bar\n",
+ "V=round(A,2)*L\n",
+ "#Let E1 be the strain Energy\n",
+ "E1=p**2*(2*E)**-1*V\n",
+ "\n",
+ "#Answer in Book for Strain Energy is Incorrect \n",
+ "\n",
+ "#Now Equating Workdone by Load to strain Energy \n",
+ "W1=E1*51.5**-1\n",
+ "\n",
+ "#Now when w=600 N\n",
+ "#Let W2 be the Work done by the Load\n",
+ "#W2=w(h2*dell_l)\n",
+ "\n",
+ "h=E1*w**-1-dell_l\n",
+ "\n",
+ "#Result\n",
+ "print\"The Max Lodad which can Fall from a height of 50 mm on the collar is\",round(W1,2),\"N\"\n",
+ "print\"the Max Height from which a 600 N Load can fall on the collar is\",round(h,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Max Lodad which can Fall from a height of 50 mm on the collar is 1372.54 N\n",
+ "the Max Height from which a 600 N Load can fall on the collar is 116.31 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 40
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.48,Page No.76"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "D_s=30 #mm #Diameter of steel rod\n",
+ "d=30 #mm #Internal Diameter of copper tube\n",
+ "D=40#mm #External Diameter of copper tube\n",
+ "E_s=2*10**5 #N/mm**2 #Young's Modulus of Steel rod\n",
+ "E_c=1*10**5#N/mm**2 #Young's Modulus of copper tube\n",
+ "P=100 #N #Load\n",
+ "h=40 #mm #height from which Load falls\n",
+ "L=800 #mm #Length \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Area of steel rod\n",
+ "A_s=pi*4**-1*D_s**2\n",
+ "\n",
+ "#Area of copper tube\n",
+ "A_c=pi*4**-1*(D**2-d**2)\n",
+ "\n",
+ "#But Dell_s=dell_c=dell\n",
+ "#p_s*E_s**-1*L=p_c*L*E_c\n",
+ "#After simplifying furthe we get\n",
+ "#p_s=2*p_c\n",
+ "\n",
+ "#Now Equating internal Energy to Workdone we get\n",
+ "p_c=(2*P*h*L**-1*(4*A_s*E_s**-1+A_c*E_c**-1))**0.5\n",
+ "p_s=2*p_c\n",
+ "\n",
+ "#Result\n",
+ "print A_s\n",
+ "print\"STress produced in steel is\",round(p_s,2),\"N/mm**2\"\n",
+ "print\"STress produced in copper is\",round(p_c,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "706.858347058\n",
+ "STress produced in steel is 0.89 N/mm**2\n",
+ "STress produced in copper is 0.44 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2.49,Page No.77"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "dell=0.25 #mm #Instantaneous Extension\n",
+ "\n",
+ "#Bar-A\n",
+ "b1=25 #mm #width of bar\n",
+ "D1=500 #mm #Depth of bar\n",
+ "\n",
+ "#Bar-B\n",
+ "b2_1=25 #mm #width of upper bar\n",
+ "b2_2=15 #mm #Width of Lower Bar\n",
+ "L2=200 #mm #Length of upper bar\n",
+ "L1=300 #mm #Length of Lower bar\n",
+ "\n",
+ "E=2*10**5 #N/mm**2 #Young's Modulus of bar\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Strain\n",
+ "e=dell*D1**-1 \n",
+ "\n",
+ "#Load\n",
+ "p=e*E\n",
+ "\n",
+ "#Area of bar-A\n",
+ "A=pi*4**-1*25**2\n",
+ "\n",
+ "#Volume of bar-A\n",
+ "V=A*D1\n",
+ "\n",
+ "#Let E1 be the Energy of Blow\n",
+ "#Energy of Blow\n",
+ "E1=p**2*(E)**-1*V\n",
+ "\n",
+ "#Let p2 be the Max stress in bar B When this blow is applied.\n",
+ "#the max stress occurs in the 15mm dia. portion,Hence, the stress in 25 mm dia.portion is\n",
+ "#p2*pi*4**-1*b2_2**2*(pi*4**-1*b2_2**2=0.36*p\n",
+ "\n",
+ "#Strain Energy of bar B\n",
+ "#E2=p**2*(2*E)**-1*v1+1*(2*E)**-1*(0.36*p2)**2*v2\n",
+ "#After substituting values and Further substituting values we get\n",
+ "#E2=0.1643445*p2**2\n",
+ "\n",
+ "#Equating it to Energy of applied blow,we get\n",
+ "p2=(12271.846*0.1643445**-1)**0.5\n",
+ "\n",
+ "#Stress in top portion\n",
+ "sigma=0.36*p2\n",
+ "\n",
+ "#Extension in Bar-1\n",
+ "dell_1=p2*E**-1*L1\n",
+ "\n",
+ "#Extension in Bar-2\n",
+ "dell_2=0.36*p2*E**-1*L2\n",
+ "\n",
+ "#Extension of bar\n",
+ "dell_3=dell_1+dell_2\n",
+ "\n",
+ "#Result\n",
+ "print\"Instantaneous Max stress is\",round(sigma,2),\"N/mm**2\"\n",
+ "print\"extension in Bar is\",round(dell_3,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Instantaneous Max stress is 98.37 N/mm**2\n",
+ "extension in Bar is 0.51 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_03.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_03.ipynb new file mode 100644 index 00000000..d6656ff0 --- /dev/null +++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_03.ipynb @@ -0,0 +1,1601 @@ +{
+ "metadata": {
+ "name": "chapter 03.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 3:Shear Force And Bending Moment Diagrams in Statically Determinate Beams"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3.1,Page No.100"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_AC=L_CD=1 #m #Length of AC & CD\n",
+ "L_DB=1.5 #m #Lengh of DB\n",
+ "L=3.5 #m #Length of Beam\n",
+ "F_B=10 #KN #Force at pt B\n",
+ "F_C=F_D=20 #KN #Force at pt C & D\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "R_A=F_C+F_D+F_B #KN #Force at support A \n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F At pt B\n",
+ "V_B1=0 #KN \n",
+ "V_B2=F_B #KN\n",
+ "\n",
+ "#S.F At pt D\n",
+ "V_D1=V_B2 #KN\n",
+ "V_D2=V_D1+F_D #KN\n",
+ "\n",
+ "#S.F At pt C \n",
+ "V_C1=V_D2 #KN\n",
+ "V_C2=V_D2+F_C #KN\n",
+ "\n",
+ "#S.F At Pt A\n",
+ "V_A1=V_C2 #KN\n",
+ "V_A2=V_C2-R_A #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M At Pt B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M AT Pt D\n",
+ "M_D=F_B*L_DB #KN.m\n",
+ "\n",
+ "#B.M At pt C\n",
+ "M_C=F_B*(L_DB+L_CD)+F_D*L_CD #KN.m\n",
+ "\n",
+ "#B.M At pt A\n",
+ "M_A=F_B*L+F_D*(L_CD+L_AC)+F_C*L_AC\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_DB,L_DB,L_CD+L_DB,L_CD+L_DB,L_CD+L_DB+L_AC,L_CD+L_DB+L_AC]\n",
+ "Y1=[V_B1,V_B2,V_D1,V_D2,V_C1,V_C2,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_D,M_C,M_A]\n",
+ "X2=[0,L_DB,L_DB+L_CD,L_AC+L_CD+L_DB]\n",
+ "Z2=[0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5fcc2d0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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pqQavCQgIEADwi1/84he/rPgKCAiw6e+yYlJMDQ0NuPfee/H999+jZ8+eGDhw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\no9ggiIjIKDYIIiIy6v8BsxKV3Pt7cnUAAAAASUVORK5CYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5c11b50>"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3.2,Page No.101"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "w1=10 #KN/m #u.d.L\n",
+ "F_D=20 #KN #Force at pt D\n",
+ "F_C=30 #KN #Force at pt C\n",
+ "L_DB=4 #m #Length of DB\n",
+ "L_CD=L_AC=2 #m #Length of AC & CD\n",
+ "L=8 #m #Length of Beam\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A And R_B be the Reactions at pt A and B \n",
+ "#R_A+R_B=90 \n",
+ "#Now Taking moment at A,M_A we get\n",
+ "R_A=(w1*L_DB*(L_DB*2**-1)+F_D*L_DB+F_C*(L_CD+L_DB))*L**-1\n",
+ "R_B=90-R_A\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F At Pt B\n",
+ "V_B1=0 #KN\n",
+ "V_B2=R_B #KN\n",
+ "\n",
+ "#S.F At pt D\n",
+ "V_D1=R_B-w1*L_DB #KN\n",
+ "V_D2=V_D1-F_D #KN\n",
+ "\n",
+ "#S.F at Pt C\n",
+ "V_C1=V_D2 #KN\n",
+ "V_C2=V_C1-F_C \n",
+ "\n",
+ "#S.F at PT A\n",
+ "V_A1=V_C2 #KN\n",
+ "V_A2=V_C2+R_A #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M At Pt B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M At Pt D\n",
+ "M_D=-R_B*L_DB+w1*L_DB*L_DB*2**-1 #KN.m\n",
+ "\n",
+ "#B.M At PT C\n",
+ "M_C=-R_B*(L_DB+L_CD)+w1*L_DB*(L_DB*2**-1+L_CD)+F_D*L_CD #KN.m\n",
+ "\n",
+ "#B.M At Pt A\n",
+ "M_A=-R_B*L+w1*L_DB*(L_DB*2**-1+L_CD+L_AC)+F_D*(L_CD+L_AC)+F_C*L_AC\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_DB,L_DB,L_CD+L_DB,L_CD+L_DB,L_CD+L_DB+L_AC,L_CD+L_DB+L_AC]\n",
+ "Y1=[V_B1,V_B2,V_D1,V_D2,V_C1,V_C2,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_D,M_C,M_A]\n",
+ "X2=[0,L_DB,L_DB+L_CD,L_AC+L_CD+L_DB]\n",
+ "Z2=[0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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Pni0aGhr0vo4HrxERkcSmlo+IiMi8WApERCRhKRARkYSlQEREEpYCERFJWApE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\nICIiCUuBiIgk/w9P4ODmR+1IBgAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5cab090>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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Gt27dTE9mRiwY9ovtQ+zHlSuAv780HCkgQO00tkGRgnHr1i2kp6ejpKQEdXV1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\nx6hRo1BfX48XX3wRgYGBasd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+ "text": [
+ "<matplotlib.figure.Figure at 0x5c19930>"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3.3,Page No.102"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_DB=L_CD=1.5 #m #Length of DB & CD\n",
+ "L_AC=3 #m #Length of AC\n",
+ "F_D=80 #KN #Force at Pt D\n",
+ "w=40 #KN/m #u.v.l\n",
+ "L=6 #Length of beam\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A and R_B be the Reactions at Pt A & B respectively\n",
+ "#R_A+R_B=140 \n",
+ "#Taking moment at B we get,M_B\n",
+ "R_A=(1*2**-1*L_AC*w*(1*3**-1*L_AC+(L_CD+L_DB))+F_D*L_DB)*L**-1\n",
+ "R_B=140-R_A\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F at B\n",
+ "V_B1=0 #KN\n",
+ "V_B2=R_B #KN\n",
+ "\n",
+ "#S.F At D\n",
+ "V_D1=V_B2 #KN\n",
+ "V_D2=V_D1-F_D #KN\n",
+ "\n",
+ "#S.F at C\n",
+ "V_C=V_D2 #KN\n",
+ "\n",
+ "#S.F At A\n",
+ "V_A1=V_C-1*2**-1*w*L_AC #KN\n",
+ "V_A2=V_A1+R_A #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M At B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M At D\n",
+ "M_D=-R_B*L_DB\n",
+ "\n",
+ "#B.M At C\n",
+ "M_C=F_D*L_CD-R_B*(L_DB+L_CD)\n",
+ "\n",
+ "#B.M At A\n",
+ "M_A=F_D*(L_CD+L_AC)-R_B*L+1*2**-1*w*L_AC*(1*3**-1*L_AC)+R_A\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_DB,L_DB,L_DB+L_CD,L_DB+L_CD+L_AC,L_DB+L_CD+L_AC]\n",
+ "Y1=[V_B1,V_B2,V_D1,V_D2,V_C,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "X2=[0,L_DB,L_CD+L_DB,L_AC+L_CD+L_DB]\n",
+ "Y2=[M_B,M_D,M_C,M_A]\n",
+ "Z2=[0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5cbcdf0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5d72230>"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3.4,Page No.104"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "M_D=120 #KN.m #B.M at Pt D\n",
+ "F_C=40 #KN #Force at Pt C\n",
+ "w1=20 #KN.m\n",
+ "L_DB=1.5 #m #Length of DB\n",
+ "L_CD=1.5 #m #Length of CD\n",
+ "L_AC=3 #m #Length of AC\n",
+ "L=6 #m #Length of Beam\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A And R_B be the Reactions at pt A and B \n",
+ "#R_A+R_B=100\n",
+ "#Now Taking Moment At Pt B We get,M_B\n",
+ "R_A=-(M_D-F_C*(L_CD+L_DB)-w1*L_AC*(L_AC*2**-1+L_CD+L_DB))*L**-1\n",
+ "R_B=100-R_A\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F At Pt B\n",
+ "V_B1=0\n",
+ "V_B2=R_B\n",
+ "\n",
+ "#S.F at Pt D\n",
+ "V_D=V_B2 #KN\n",
+ "\n",
+ "#S.F At Pt C\n",
+ "V_C1=V_D #KN\n",
+ "V_C2=V_C1-F_C\n",
+ "\n",
+ "#S.F At Pt A\n",
+ "V_A1=V_C2-w1*L_AC #KN\n",
+ "V_A2=V_A1+R_A\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M At Pt B\n",
+ "M_B=0 #KN.m\n",
+ "\n",
+ "#B.M At Pt D\n",
+ "M_D1=M_B-R_B*L_DB #KN.m\n",
+ "M_D2=M_B+M_D-R_B*L_DB\n",
+ "\n",
+ "#B.M At Pt C\n",
+ "M_C=M_D-R_B*(L_CD+L_DB)\n",
+ "\n",
+ "#B.M At Pt A\n",
+ "M_A=M_D-R_B*L+F_C*L_AC+w1*L_AC*L_AC*2**-1\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_DB,L_DB+L_CD,L_DB+L_CD,L_DB+L_CD+L_AC,L_DB+L_CD+L_AC]\n",
+ "Y1=[V_B1,V_B2,V_D,V_C1,V_C2,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_B,M_D1,M_D2,M_C,M_A]\n",
+ "X2=[0,L_DB,L_DB,L_CD+L_DB,L_AC+L_CD+L_DB]\n",
+ "Z2=[0,0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5d72210>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5cc52f0>"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3.5,Page No.105"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F_C=20 #KN #Force at Pt C\n",
+ "F_D=40 #KN #Force at pt D\n",
+ "w=20 #KN.m #u.d.l \n",
+ "L_AD=L_DB=2 #m #Length of AD & DB\n",
+ "L_BC=1 #m #Length of BC\n",
+ "L=5 #m #Length of Beam\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_A and R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=100 \n",
+ "#Now Taking Moment at B,M_B we get\n",
+ "R_A=-(F_C*L_BC-F_D*L_DB-w*L_AD*(L_AD*2**-1+L_DB))*(L_AD+L_DB)**-1\n",
+ "R_B=100-R_A\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F At pt C\n",
+ "V_C1=0 #KN\n",
+ "V_C2=-F_C #KN\n",
+ "\n",
+ "#S.F At PT B\n",
+ "V_B1=V_C2 #KN\n",
+ "V_B2=V_C2+R_B #KN\n",
+ "\n",
+ "#S.F At Pt D\n",
+ "V_D1=V_B2 #KN\n",
+ "V_D2=V_D1-F_D #KN\n",
+ "\n",
+ "#S.F At Pt A\n",
+ "V_A1=V_D2-w*L_AD #KN\n",
+ "V_A2=V_A1+R_A #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M At Pt C\n",
+ "M_C=0 \n",
+ "\n",
+ "#B.M At Pt B\n",
+ "M_B=F_C*L_BC\n",
+ "\n",
+ "#B.M At Pt D\n",
+ "M_D=F_C*(L_BC+L_DB)-R_B*L_DB\n",
+ "\n",
+ "#B.M At Pt A\n",
+ "M_A=F_C*L-R_B*(L_DB+L_AD)+F_D*L_AD+w*L_AD*L_AD*2**-1\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_BC,L_BC,L_BC+L_DB,L_BC+L_DB,L_BC+L_DB+L_AD,L_BC+L_DB+L_AD]\n",
+ "Y1=[V_C1,V_C2,V_B1,V_B2,V_D1,V_D2,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_C,M_B,M_D,M_A]\n",
+ "X2=[0,L_BC,L_BC+L_DB,L_BC+L_DB+L_AD]\n",
+ "Z2=[0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5f26c10>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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Zb7/9lh07drB8+XLy8/N58cUXmTVrlrt+NSKaPpLAUlFRwZdffsnI\nkSOd91VWVgLGm/WZE1a7du3K4cOHAfj8889JSUkBcPYoONvw4cMB6NGjBx9++KHzfldOkKntmufr\n0KED3bp1A6Bbt24kJiYCEB0dTUlJSZ3XEXGVkoIElNOnT3PFFVdQWFhY48+bNm3q/PrMm/r5dYPz\n3+wvueQSAJo0aUJVVVW9Y6rpmuc7cw0w+iWceU5QUFCDrilSG00fSUC5/PLL6dChAx988AFgvAn/\n61//uuhz+vTpw4oVK3A4HBw+fJi8vLw6r9O8eXPnUcXn0xmUYmVKCuLXTpw4Qbt27Zy3//3f/+Xd\nd99l0aJFxMbGEh0dfU4z97Pn+898PWLECMLCwoiKiuK+++6jR48etGjR4oJr2Ww253OGDh3KypUr\niYuLIz8/v9bH1XbNml67tu8D+UhocT8dnS3igp9//pnLLruM//znPyQkJPDFF1/QqlUrs8MScTvV\nFERcMGTIEMrLy6msrGTatGlKCOK3NFIQEREn1RRERMRJSUFERJyUFERExElJQUREnJQURETESUlB\nRESc/j+iaB8fTwtkoQAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5d473b0>"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3.6,Page No.107"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_BC=L_EB=L_AD=1 #m #Length of spans BC,ED,AD\n",
+ "L_ED=2 #m #Length of ED\n",
+ "w=60 #KNm #u.d.l\n",
+ "F_C=20 #KN Pt Load at C\n",
+ "L=5 #m #Span of beam \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A & R_B be the reactions at A & B respectively\n",
+ "#R_A+R_B=80 \n",
+ "#Taking Moment At A,we get M_A\n",
+ "R_B=(F_C*L+1*2**-1*L_ED*w*(2*3**-1*L_ED+L_AD))*(L_AD+L_ED+L_EB)**-1\n",
+ "R_A=80-R_B\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F At C\n",
+ "V_C1=0 #KN\n",
+ "V_C2=-F_C #KN\n",
+ "\n",
+ "#S.F At B\n",
+ "V_B1=V_C2 #KN\n",
+ "V_B2=V_C2+R_B #KN \n",
+ "\n",
+ "#S.F aT E\n",
+ "V_E=V_B2 #KN\n",
+ "\n",
+ "#S.F AT D\n",
+ "V_D=V_B2-1*2**-1*L_ED*w #KN\n",
+ "\n",
+ "#S.F At A\n",
+ "V_A1=V_D #KN \n",
+ "V_A2=V_D+R_A\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at C\n",
+ "M_C=0 #KN.m\n",
+ "\n",
+ "#B.M at B\n",
+ "M_B=F_C*L_BC #KN.m\n",
+ "\n",
+ "#B.M at E\n",
+ "M_E=F_C*(L_EB+L_BC)-R_B*L_EB #KN.m\n",
+ "\n",
+ "#B.M at D\n",
+ "M_D=F_C*(L_ED+L_EB+L_BC)-R_B*(L_ED+L_EB)+1*2**-1*L_ED*w*1*3**-1*L_ED #KN.m\n",
+ "\n",
+ "#B.M at A\n",
+ "M_A=1*2**-1*L_ED*w*(2*3**-1*L_ED+L_AD)-R_B*(L_AD+L_ED+L_EB)+F_C*L\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_BC,L_BC,L_EB+L_BC,L_ED+L_EB+L_BC,L_AD+L_ED+L_EB+L_BC,L_ED+L_EB+L_BC+L_AD]\n",
+ "Y1=[V_C1,V_C2,V_B1,V_B2,V_E,V_D,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "X2=[0,L_BC,L_BC+L_EB,L_EB+L_BC+L_ED,L_EB+L_BC+L_ED+L_AD]\n",
+ "Y2=[M_C,M_B,M_E,M_D,M_A]\n",
+ "Z2=[0,0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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Cr9fzLAHAgQMHUFpaig8++AAbNmzAvn37Ot1OUUUhJCSkwx1Vq6qqEBoaKjAR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\nAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5fc3ed0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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UlD0DZoHZoDk7OxvPPfec/SqwAoNm98HQmcjAloBZINmcwq5du5rcTwEAHnnkEeuqkgCb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\nkeDZfAAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5d72c50>"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3.7,Page No.109"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_BC=1 #m #Length of BC\n",
+ "L_DB=2 #m #Length of DB\n",
+ "L_AD=4 #m #Length 0f AD\n",
+ "M_D=30 #KN.m #Moment at D\n",
+ "w=45 #KN/m #u.d.l\n",
+ "L=7 #m #Span of beam\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_B & R_A be the Reactions at B & A respectively\n",
+ "#R_B+R_A=180+P ............(1)\n",
+ "\n",
+ "#Now Taking Moment about A,we get\n",
+ "#R_B=7*P+390 ...............(2)\n",
+ "\n",
+ "#Since R_A & R_B Are Equal\n",
+ "#2*R_B=180+P ...................(3)\n",
+ "\n",
+ "#From equation 1 and 3 we get\n",
+ "#3*(180+P)=7P+390\n",
+ "#After simplifying Further above equation we get\n",
+ "P=150*4**-1 #KN\n",
+ "R_A=R_B=(180+P)*2**-1\n",
+ "F_C=P\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F At C\n",
+ "V_C1=0 #KN\n",
+ "V_C2=-P #KN\n",
+ "\n",
+ "#S.F At B\n",
+ "V_B1=V_C2 #KN\n",
+ "V_B2=V_C2+R_B #KN \n",
+ "\n",
+ "#S.F At D\n",
+ "V_D=V_B2 #KN\n",
+ "\n",
+ "#S.F At A\n",
+ "V_A1=V_D-w*L_AD #KN\n",
+ "V_A2=V_A1+R_A #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at C\n",
+ "M_C=0 #KN.m \n",
+ "\n",
+ "#B.M at B\n",
+ "M_B=F_C*L_BC #KN.m\n",
+ "\n",
+ "#B.M at D\n",
+ "M_D1=F_C*(L_BC+L_DB)-R_B*L_DB #KN.m\n",
+ "M_D2=M_D1+M_D\n",
+ "\n",
+ "#B.M At A\n",
+ "M_A=w*L_AD*L_AD*2**-1+M_D-R_B*(L_AD+L_DB)+P*L\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_BC,L_BC,L_DB+L_BC,L_DB+L_BC+L_AD,L_DB+L_BC+L_AD]\n",
+ "Y1=[V_C1,V_C2,V_B1,V_B2,V_D,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "X2=[0,L_BC,L_DB+L_BC,L_DB+L_BC,L_AD+L_DB+L_BC]\n",
+ "Y2=[M_C,M_B,M_D1,M_D2,M_A]\n",
+ "Z2=[0,0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5cb7750>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5d72690>"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3.8,Page No.110"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=6 #m #Span Of beam\n",
+ "w=30 #KN/m #u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Due to Symmetry\n",
+ "#Let R_B and R_C be the reactions at B & C Respectively\n",
+ "R_B=R_C=w*L*2**-1 #KN\n",
+ "\n",
+ "#Let a be the overhang.The Max -ve moment occurs at the support and max +ve moment at middle of the beam\n",
+ "#Now Equating these two equations we get\n",
+ "#30*a*a*2**-1=90*(3-a)-w*L*2**-1*L*4**-1\n",
+ "#After simplifying we get an equation as\n",
+ "#a**2+6*a-9=0\n",
+ "x=1\n",
+ "y=6\n",
+ "z=-9\n",
+ "\n",
+ "p=y**2-4*x*z\n",
+ "\n",
+ "a1=(-y+p**0.5)*2**-1\n",
+ "a2=(-y-p**0.5)*2**-1\n",
+ "\n",
+ "#Now Length cannot be negative,so taking a1 into Consideration\n",
+ "\n",
+ "L_CD=L_AB=a1\n",
+ "L_BC=L-2*a1\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F At D\n",
+ "V_D=0\n",
+ "\n",
+ "#S.F At C\n",
+ "V_C1=V_D-w*L_CD #KN\n",
+ "V_C2=V_C1+R_C #KN\n",
+ "\n",
+ "#S.F At B\n",
+ "V_B1=-w*(L_BC+L_CD)+R_C\n",
+ "V_B2=V_B1+R_B\n",
+ "\n",
+ "#S.F At A\n",
+ "V_A=round(V_B2,2)-round(w*L_AB,2)\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M At D\n",
+ "M_D=0\n",
+ "\n",
+ "#B.M At C\n",
+ "M_C=w*L_CD*L_CD*2**-1 #KN.m\n",
+ "\n",
+ "#B.M At B\n",
+ "M_B=w*(L_BC+L_CD)*(L_BC+L_CD)*2**-1-R_C*L_BC*L_BC*2**-1\n",
+ "\n",
+ "#B.M At A\n",
+ "X=w*L*L*2**-1\n",
+ "Y=-R_C*(L_AB+L_BC)-R_B*L_AB\n",
+ "M_A=X+Y\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,L_CD,L_CD,L_CD+L_BC,L_CD+L_BC,L_CD+L_BC+L_AB]\n",
+ "Y1=[V_D,V_C1,V_C2,V_B1,V_B2,V_A]\n",
+ "Z1=[0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "X2=[0,L_CD,L_BC+L_CD,L_AB+L_BC+L_CD]\n",
+ "Y2=[M_D,M_C,M_B,M_A]\n",
+ "Z2=[0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5cabbb0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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lpdoNlBrD3d29Xufn5OSgoKAAAQEBAICpU6di165dTBhECnF1BY4eFXuF5+Wx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\nJMv/A+qBKcq11Z1HAAAAAElFTkSuQmCC\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5fd1a70>"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3.9,Page No.112"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F_F=6 #KN #Force at F\n",
+ "w1=w2=w=3 #KN.m #u.d.l\n",
+ "M_D=24 #KN.m \n",
+ "L_AB=L_CD=L_DE=L_EF=4 #m #Length of AB,CD,DE,EF\n",
+ "L_BC=2 #m #Length of BC\n",
+ "L=18 #m #Span of Beam\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_B and R_E be the Reactions at B & E respectively\n",
+ "#R_B+R_E=42\n",
+ "\n",
+ "#Taking Moment At Pt B,M_B\n",
+ "R_E=(F_F*(L_BC+L_CD+L_DE+L_EF)+w*(L_CD+L_DE)*((L_CD+L_DE)*2**-1+L_BC)-w*L_AB*L_AB*2**-1-M_D)*(L_BC+L_CD+L_DE)**-1\n",
+ "R_B=42-R_E #KN\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F aT F\n",
+ "V_F1=0 #KN \n",
+ "V_F2=-F_F #KN\n",
+ "\n",
+ "#S.F at E\n",
+ "V_E1=V_F2 #KN\n",
+ "V_E2=V_E1+R_E #KN\n",
+ "\n",
+ "#S.F aT C\n",
+ "V_C=V_E2-w*(L_CD+L_DE) #KN\n",
+ "\n",
+ "#S.F at B\n",
+ "V_B1=V_C #KN \n",
+ "V_B2=V_C+R_B #KN\n",
+ "\n",
+ "#S.F At A\n",
+ "V_A=V_B2-w*L_AB #KN\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M At F\n",
+ "M_F=0\n",
+ "\n",
+ "#B.M At E\n",
+ "M_E=F_F*L_EF #KN.m\n",
+ "\n",
+ "#B.M At D\n",
+ "M_D1=F_F*(L_DE+L_EF)-R_E*L_DE+w*L_DE*L_DE*2**-1 #KN.m\n",
+ "M_D2=M_D1-M_D\n",
+ "\n",
+ "#B.M At C\n",
+ "M_C=F_F*(L_CD+L_DE+L_EF)-R_E*(L_CD+L_DE)+w*(L_CD+L_DE)*(L_CD+L_DE)*2**-1-M_D\n",
+ "\n",
+ "#B.M At B\n",
+ "M_B=F_F*(L_BC+L_CD+L_DE+L_EF)-R_E*(L_BC+L_CD+L_DE)-M_D+w*(L_CD+L_DE)*((L_CD+L_DE)*2**-1+L_BC)\n",
+ "\n",
+ "#B.M At A\n",
+ "M_A=w*L_AB*L_AB*2**-1-R_B*L_AB+w*(L_CD+L_DE)*((L_CD+L_DE)*2**-1+L_BC+L_AB)-R_E*(L_AB+L_BC+L_CD+L_DE)+F_F*L-M_D\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_EF,L_EF,L_EF+L_DE+L_CD,L_EF+L_DE+L_CD+L_BC,L_EF+L_DE+L_CD+L_BC,L_EF+L_DE+L_CD+L_BC+L_AB]\n",
+ "Y1=[V_F1,V_F2,V_E1,V_E2,V_C,V_B1,V_B2,V_A]\n",
+ "Z1=[0,0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "X2=[0,L_EF,L_DE+L_EF,L_DE+L_EF,L_CD+L_DE+L_EF,L_CD+L_DE+L_EF+L_BC,L_CD+L_DE+L_EF+L_BC+L_AB]\n",
+ "Y2=[M_F,M_E,M_D1,M_D2,M_C,M_B,M_A]\n",
+ "Z2=[0,0,0,0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5d72d10>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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VxMfHIzs7G/369cOvv/6KcePG4bHHHnNknEROixVL5KzMziBqa2uRmJiIMWPG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\nfyRzHAAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5cbc210>"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3.10,Page No.114"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_DC=L_BA=2 #m #Length of BA & DC\n",
+ "L_CB=1 #m #Length of CB\n",
+ "F_A=10 #KN #Force at pt A\n",
+ "F_B=20 #KN #Force at pt B\n",
+ "w=4 #KN.m #u.d.l\n",
+ "L=5 #m #Length of beam\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_D be the reactions at Pt D\n",
+ "R_D=F_B+F_A+w*L_DC #KN\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F at Pt A\n",
+ "V_A1=0 #KN\n",
+ "V_A2=F_A #KN\n",
+ "\n",
+ "#S.F At Pt B\n",
+ "V_B1=V_A2\n",
+ "V_B2=F_B+F_A\n",
+ "\n",
+ "#S.F at Pt C\n",
+ "V_C=F_B+F_A #KN \n",
+ "\n",
+ "#S.F At Pt D\n",
+ "V_D1=V_B2+w*L_DC\n",
+ "V_D2=F_B+F_A+w*L_DC-R_D\n",
+ "\n",
+ "#B.M At Pt A\n",
+ "M_A=0\n",
+ "\n",
+ "#B.M At Pt B\n",
+ "M_B=F_A*L_BA\n",
+ "\n",
+ "#B.M at Pt C\n",
+ "M_C=F_B*L_CB+F_A*(L_BA+L_CB) #KN\n",
+ "\n",
+ "#B.M At Pt D\n",
+ "M_D1=F_A*L+F_B*(L_CB+L_DC)+w*L_DC*L_DC*2**-1\n",
+ "M_D2=(F_A*L+F_B*(L_CB+L_DC)+w*L_DC*L_DC*2**-1)-M_D1\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_BA,L_BA,L_BA+L_CB,L_BA+L_CB+L_DC,L_BA+L_CB+L_DC]\n",
+ "Y1=[V_A1,V_A2,V_B1,V_B2,V_C,V_D1,V_D2]\n",
+ "Z1=[0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_A,M_B,M_C,M_D1,M_D2]\n",
+ "X2=[0,L_BA,L_CB+L_BA,L_CB+L_BA+L_DC,L_CB+L_BA+L_DC]\n",
+ "Z2=[0,0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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e3542bZr69++vhIQEzZ49WyNGjNAFF1wgSbrxxht15ZVXen+5e/LxJ0/9axiG\n8vLy9Oc//1kxMTFatWqV8vLyvMNNvo71tX3yMb6+tvMUxDh7XM4JWzp8+LAiIiL0ww8/aPTo0dq8\nebP69OljdSwgKBjjhy1NnjxZNTU1amho0L333kvpw1Y44wcAm2GMHwBshuIHAJuh+AHAZih+ALAZ\nih8AbIbiBwCb+T+gqVKkQGpm/QAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5d63a10>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5fe5130>"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3.11,Page No.115"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "w=20 #KN/m #u.v.l\n",
+ "F_C=40 #KN #Force at Pt C\n",
+ "M_D=40 #KN.m #Moment at pt D\n",
+ "L_AB=3 #m #Length of AB\n",
+ "L_BC=1 #m #Length of BC\n",
+ "L_CD=L_DE=2 #m #Length of CD & DE\n",
+ "L=8 #8 #Length of beam\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A & R_E be the Reactions at A & E respectively\n",
+ "#R_A+R_E=70\n",
+ "\n",
+ "#Taking Moments At Pt A we get,M_A\n",
+ "R_E=(F_C*(L_AB+L_BC)+1*2**-1*L_AB*w*2+40)*L**-1\n",
+ "R_A=70-R_E\n",
+ "\n",
+ "#shear Force Calculations\n",
+ "\n",
+ "#S.F At Pt E\n",
+ "V_E1=0\n",
+ "V_E2=R_E #KN\n",
+ "\n",
+ "#S.F aT pt D\n",
+ "V_D=V_E2\n",
+ "\n",
+ "#S.F At PT C\n",
+ "V_C1=V_D\n",
+ "V_C2=V_D-F_C #KN\n",
+ "\n",
+ "#S.F At Pt A\n",
+ "V_A1=V_C2-(1*2**-1*w*L_AB)\n",
+ "V_A2=V_A1+R_A\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M At Pt E\n",
+ "M_E=0\n",
+ "\n",
+ "#B.M At Pt D\n",
+ "M_D1=M_E-R_E*L_DE\n",
+ "M_D2=M_D1+M_D\n",
+ "\n",
+ "#B.M At Pt C\n",
+ "M_C=-R_E*(L_DE+L_CD)+M_D\n",
+ "\n",
+ "#B.M At Pt B\n",
+ "M_B=-R_E*(L_DE+L_CD+L_BC)+M_D+F_C*L_BC\n",
+ "\n",
+ "#B.M At Pt A\n",
+ "M_A=-R_E*L+M_D+(1*2**-1*L_AB*w*2)+F_C*(L_BC+L_AB)\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_DE,L_CD+L_DE,L_CD+L_DE,L_CD+L_DE+L_AB,L_CD+L_DE+L_AB]\n",
+ "Y1=[V_E1,V_E2,V_D,V_C1,V_C2,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "Y2=[M_E,M_D1,M_D2,M_C,M_B,M_A]\n",
+ "X2=[0,L_DE,L_DE,L_CD+L_DE,L_DE+L_CD+L_BC,L_AB+L_BC+L_CD+L_DE]\n",
+ "Z2=[0,0,0,0,0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5fd1b90>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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PZcuW8dRTT5GZmcnOnTtp1KgRI0aMsPs+cvTnxbp1U4fwLFyoO4nzTCaYMkWt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\nd/r0aduBO+VVUFCA2Wxm+/b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6ePR5C6Jyk56CqHT27dtHt27daNu2LXfddRdpaWkAPPbY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\nGhPHAAAAAElFTkSuQmCC\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5f260d0>"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3.12,Page No.116"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F_G=10 #KN #Force at Pt G\n",
+ "F_B=F_E=15 #KN #Force at Pt B & E\n",
+ "w=20 #KN/m #U.d.L\n",
+ "L_FG=L_EF=L_DE=L_CD=L_BC=L_AB=1 #m #Lengths of FG,EF,DE,CD,BC,AB respectively\n",
+ "L=6 #m #Length of beam\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt R_F & R_A be the Reactions at E & A respectively\n",
+ "#R_F+R_A=60\n",
+ "\n",
+ "#Taking Moment At Pt A,M_A\n",
+ "R_F=(F_G*L+F_E*(L_AB+L_BC+L_CD+L_DE)+w*L_CD*(L_AB+L_BC+L_CD*2**-1)+F_B*L_AB)*(L_AB+L_BC+L_CD+L_DE+L_EF)**-1\n",
+ "R_A=60-R_F\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F At G\n",
+ "V_G1=0 #KN \n",
+ "V_G2=F_G #KN\n",
+ "\n",
+ "#S.F At F\n",
+ "V_F1=V_G2 #KN\n",
+ "V_F2=V_F1-R_F\n",
+ "\n",
+ "#S.F At E\n",
+ "V_E1=V_F2 #KN\n",
+ "V_E2=V_F2+F_E\n",
+ "\n",
+ "#S.F At D\n",
+ "V_D=V_E2\n",
+ "\n",
+ "#S.F At C\n",
+ "V_C=V_E2+w*L_CD\n",
+ "\n",
+ "#S.F At B\n",
+ "V_B1=V_C\n",
+ "V_B2=V_B1+F_B\n",
+ "\n",
+ "#S.F At A\n",
+ "V_A1=V_B2\n",
+ "V_A2=V_B2-R_A\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M At Pt G\n",
+ "M_G=0\n",
+ "\n",
+ "#B.M At F\n",
+ "M_F=F_G*L_FG \n",
+ "\n",
+ "#B.M At E\n",
+ "M_E=F_G*(L_FG+L_EF)-R_F*L_EF\n",
+ "\n",
+ "#B.M At D\n",
+ "M_D=F_G*(L_FG+L_EF+L_DE)-R_F*(L_EF+L_DE)+F_E*L_DE\n",
+ "\n",
+ "#B.M At C\n",
+ "M_C=F_G*(L_FG+L_EF+L_DE+L_CD)-R_F*(L_EF+L_DE+L_CD)+F_E*(L_DE+L_CD)+w*L_CD*L_CD*2**-1\n",
+ "\n",
+ "#B.M At B\n",
+ "M_B=F_G*(L_FG+L_EF+L_DE+L_CD+L_BC)-R_F*(L_EF+L_DE+L_CD+L_BC)+F_E*(L_DE+L_CD+L_BC)+w*L_CD*(L_CD*2**-1+L_BC)\n",
+ "\n",
+ "#B.M At A\n",
+ "M_A=F_G*L-R_F*(L_EF+L_DE+L_CD+L_BC+L_AB)+F_E*(L_DE+L_CD+L_BC+L_AB)+F_B*L_AB+w*L_CD*(L_CD*2**-1+L_BC+L_AB)\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,0,L_FG,L_FG,L_FG+L_EF,L_FG+L_EF,L_FG+L_EF+L_DE,L_FG+L_EF+L_DE+L_CD,L_FG+L_EF+L_DE+L_CD+L_BC,L_FG+L_EF+L_DE+L_CD+L_BC,L_FG+L_EF+L_DE+L_CD+L_BC+L_AB,L_FG+L_EF+L_DE+L_CD+L_BC+L_AB]\n",
+ "Y1=[V_G1,V_G2,V_F1,V_F2,V_E1,V_E2,V_D,V_C,V_B1,V_B2,V_A1,V_A2]\n",
+ "Z1=[0,0,0,0,0,0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "X2=[0,L_FG,L_EF+L_FG,L_EF+L_FG+L_DE,L_EF+L_FG+L_DE+L_CD,L_EF+L_FG+L_DE+L_CD+L_BC,L_EF+L_FG+L_DE+L_CD+L_BC+L_AB]\n",
+ "Y2=[M_G,M_F,M_E,M_D,M_C,M_B,M_A]\n",
+ "Z2=[0,0,0,0,0,0,0]\n",
+ "plt.plot(X2,Y2)\n",
+ "plt.xlabel(\"Lenght in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5febb90>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5c11c90>"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3.13,Page No.117"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "L_AB=L_BC=L_CD=L_DE=L_EF=1 #m #LEngth of AB,BC,CD,DE,EF respectively\n",
+ "M_A=50 #KN/m #Moment at A\n",
+ "w=5 #KN/m #u.v.l\n",
+ "F_D=10 #KN\n",
+ "w2=5 #KN/m #u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_B & R_E be the Reactions at B and E respectively\n",
+ "#R_B+R_E=20\n",
+ "\n",
+ "#Taking Moment At Pt B,M_B\n",
+ "R_E=(w2*L_EF*(L_EF*2**-1+L_DE+L_CD+L_BC)+w*L_BC*2**-1*2*3**-1+50+F_D*(L_BC+L_CD))*3**-1\n",
+ "R_B=17.5-R_E #KN\n",
+ "\n",
+ "#Shear Force Calculations\n",
+ "\n",
+ "#S.F At F\n",
+ "V_F=0\n",
+ "\n",
+ "#S.F aT E\n",
+ "V_E1=-w2*L_EF #KN\n",
+ "V_E2=V_E1+R_E\n",
+ "\n",
+ "#S.F at D\n",
+ "V_D1=R_E-w2*L_EF #KN\n",
+ "V_D2=V_D1-F_D #KN\n",
+ "\n",
+ "#S.F At C\n",
+ "V_C=V_D2\n",
+ "\n",
+ "#S.F aT B\n",
+ "V_B1=-L_BC*w*2**-1-F_D+R_E-w2*L_EF\n",
+ "V_B2=V_B1+R_B\n",
+ "\n",
+ "#Bending Moment Calculations\n",
+ "\n",
+ "#B.M at F\n",
+ "M_F=0 #KN.m\n",
+ "\n",
+ "#B.M At E\n",
+ "M_E=w2*L_EF*L_EF*2**-1 #KN.m\n",
+ "\n",
+ "#B.M at D\n",
+ "M_D=-R_E*L_DE+w2*L_EF*(L_EF*2**-1+L_DE) #KN.m\n",
+ "\n",
+ "#B.M At C\n",
+ "M_C=F_D*L_CD*R_E*(L_CD+L_DE)+w2*L_EF*(L_EF*2**-1+L_DE+L_CD) #KN.m\n",
+ "\n",
+ "#B.M At B\n",
+ "M_B=F_D*(L_CD+L_BC)-R_E*(L_BC+L_CD+L_DE)+w2*L_EF*(L_EF*2**-1+L_BC+L_CD+L_DE)+1*2**-1*L_BC*w*2*3**-1\n",
+ "\n",
+ "#B.M At A\n",
+ "M_A1=w*L_EF*(L_EF*2**-1+L_AB+L_BC+L_CD+L_DE)-R_E*(L_AB+L_BC+L_CD+L_DE)+F_D*(L_AB+L_BC+L_CD)+1*2**-1*L_BC*w*(2*3**-1*L_BC+L_AB)-R_B*L_AB\n",
+ "M_A2=M_A1+M_A\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,L_EF,L_EF,L_DE+L_EF,L_DE+L_EF,L_CD+L_DE+L_EF,L_CD+L_DE+L_EF+L_BC,L_CD+L_DE+L_EF+L_BC]\n",
+ "Y1=[V_F,V_E1,V_E2,V_D1,V_D2,V_C,V_B1,V_B2]\n",
+ "Z1=[0,0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Plotting the Bendimg Moment Diagram\n",
+ "\n",
+ "X2=[0,L_EF,L_DE+L_EF,L_CD+L_DE+L_EF,L_CD+L_DE+L_EF+L_BC,L_CD+L_DE+L_EF+L_BC+L_AB,L_CD+L_DE+L_EF+L_BC+L_AB]\n",
+ "Y2=[M_F,M_E,M_D,M_C,M_B,M_A1,M_A2]\n",
+ "Z2=[0,0,0,0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in m\")\n",
+ "plt.ylabel(\"Bending Moment in kN.m\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5462a10>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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LlixREhMTLY8fMWKEsm/fvjuex4ZfSQi7euUVRXnxRa1TuIdr1xRFr1eUb77R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\nQmCC\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5f0c690>"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_04.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_04.ipynb new file mode 100644 index 00000000..584f8c5e --- /dev/null +++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_04.ipynb @@ -0,0 +1,1661 @@ +{
+ "metadata": {
+ "name": "chapter 04.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 4:Stresses in Beams"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.1,Page no.130"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=5000 #mm #Length of Beam\n",
+ "a=2000 #mm #Length of start of beam to Pt Load\n",
+ "b=3000 #mm #Length of Pt load to end of beam\n",
+ "A=150*250 #m**2 #Area of beam \n",
+ "b=150 #mm #Width of beam\n",
+ "d=250 #mm #Depth of beam\n",
+ "sigma=10#N/mm**2 #stress\n",
+ "l=2000 #m #Load applied from one end\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Moment of Inertia\n",
+ "I=1*12**-1*b*d**3 #m**4\n",
+ "\n",
+ "#Distance from N.A to end\n",
+ "y_max=d*2**-1 #m\n",
+ "\n",
+ "#Section Modulus\n",
+ "Z=1*6**-1*b*d**2 #mm**3\n",
+ "\n",
+ "#Moment Carrying Capacity\n",
+ "M=sigma*Z #N-mm\n",
+ "\n",
+ "#Let w be the Intensity of the Load in N/m,then Max moment\n",
+ "#M_max=w*L**2*8**-1 #N-mm\n",
+ "#After substituting values and further simplifying we get\n",
+ "#M_max=w*25*100*8**-1\n",
+ "\n",
+ "#EQuating it to moment carrying capacity,we get max intensity load\n",
+ "w=M*(25*1000)**-1*8*10**-3\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#Let P be the concentrated load,then max moment occurs under the load and its value\n",
+ "#M1=P*a*b*L**-1 #N-mm\n",
+ "\n",
+ "#Equting it to moment carrying capacity we get\n",
+ "P=M*1200**-1*10**-3 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Intensity of u.d.l it can carry\",round(w,3),\"KN-m\"\n",
+ "print\"MAx concentrated Load P apllied at 2 m from one end is\",round(P,3),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Intensity of u.d.l it can carry 5.0 N-mm\n",
+ "MAx concentrated Load P apllied at 2 m from one end is 13.021 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.2,Page no.131"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "D=70 #mm #External Diameter\n",
+ "t=8 #mm #Thickness of pipe\n",
+ "L=2500 #mm #span \n",
+ "sigma=150 #N/mm**2 #stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Internal Diameter \n",
+ "d=D-2*t #mm\n",
+ "\n",
+ "#M.I Of Pipe\n",
+ "I=pi*64**-1*(D**4-d**4) #mm**4\n",
+ "\n",
+ "y_max=D*2**-1 #mm\n",
+ "Z=I*(y_max)**-1 #mm**3\n",
+ "\n",
+ "#Moment Carrying capacity\n",
+ "M=sigma*Z #N*mm\n",
+ "\n",
+ "#Max moment int the beam occurs at the mid-span and is equal to\n",
+ "#m=P*L*4**-1\n",
+ "\n",
+ "#Equating Max moment to moment carrying capacity we get,\n",
+ "#M=P*2.5*L*4**-1\n",
+ "#After substituting and simplifying we get\n",
+ "P=4*M*(L)**-1*10**-3 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Max concentrated load that can be applied at the centre of span is\",round(P,3),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max concentrated load that can be applied at the centre of span is 5.22 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.3,Page no.132"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Flanges Dimension\n",
+ "b1=180 #mm #Width\n",
+ "d1=10 #mm #Thickness\n",
+ "\n",
+ "D=500 #mm #Overall depth\n",
+ "t=8 #mm #Thickness of web\n",
+ "\n",
+ "#Plate Dimensions\n",
+ "b2=240 #mm #Width\n",
+ "t2=12 #mm #Thickness\n",
+ "\n",
+ "sigma=150 #N/mm**2 #Stress\n",
+ "L=3000 #mm #span\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Distance of centroid from bottom fibre\n",
+ "y_bar=(b2*t2*(D+t2*2**-1)+b1*d1*(D-t1*2**-1)+(D-2*t1)*t*D*2**-1+(b1*t1*t1*2**-1))*(b2*t2+b1*d1+b1*d1+(D-2*d1)*t)**-1\n",
+ "\n",
+ "#M.I of section\n",
+ "I=(1*12**-1*b2*t2**3+b2*t2*(D+t2*2**-1-y_bar)**2+1*12**-1*b1*d1**3+b1*d1*(D-t1*2**-1-y_bar)**2+1*12**-1*b1*t1**3+b1*t1*(t1*2**-1-y_bar)**2+1*12**-1*t*(D-2*t1)**3+t*(D-2*t1)*(D*2**-1-y_bar)**2)\n",
+ "\n",
+ "#Section Modulus\n",
+ "Z=I*(y_bar)**-1 #mm**3\n",
+ "\n",
+ "#Moment or Resistance\n",
+ "M=sigma*Z\n",
+ "\n",
+ "#Let Load on Cantilever be w/m Length \n",
+ "#Max M.I produced\n",
+ "#M_max=w*L**2**-1 \n",
+ "\n",
+ "#Now Equating Moment of resistance to Max moment,we get Max load\n",
+ "#4.5*w=M\n",
+ "#After rearranging and further simplifying we get\n",
+ "w=M*4.5**-1*10**3*10**-9\n",
+ "\n",
+ "#Result\n",
+ "print\"Moment of Resistance is\",round(M,2),\"KN-mm\"\n",
+ "print\"Load the section can carry is\",round(w,3),\"KN/m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Moment of Resistance is 198770121.83 KN-mm\n",
+ "Load the section can carry is 44.171 KN/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.4,Page no.134"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Flange (Top)\n",
+ "b1=80 #mm #Width \n",
+ "t1=40 #mm #Thickness\n",
+ "\n",
+ "#Flange (Bottom)\n",
+ "b2=160 #mm #width\n",
+ "t2=40 #mm #Thickness\n",
+ "\n",
+ "#web\n",
+ "d=120 #mm #Depth\n",
+ "t3=20 #mm #Thickness\n",
+ "\n",
+ "D=200 #mm #Overall Depth\n",
+ "sigma1=30 #N/mm**2 #Tensile stress\n",
+ "sigma2=90 #N/mm**2 #Compressive stress\n",
+ "L=6000 #mm #Span\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Distance of centroid from bottom fibre\n",
+ "y_bar=(b1*t1*(D-t1*2**-1)+d*t3*(d*2**-1+t2)+b2*t2*t2*2**-1)*(b1*t1+d*t3+b2*t2)**-1 #mm\n",
+ "\n",
+ "#Moment of Inertia\n",
+ "I=1*12**-1*b1*t1**3+b1*t1*(D-t1*2**-1-round(y_bar,2))**2+1*12**-1*t3*d**3+t3*d*(d*2**-1+t2-round(y_bar,2))**2+1*12**-1*b2*t2**3+b2*t2*(t2*2**-1-round(y_bar,2))**2\n",
+ "\n",
+ "#Extreme fibre distance of top and bottom fibres are y_t and y_c respectively\n",
+ "\n",
+ "y_t=y_bar #mm\n",
+ "y_c=D-y_bar #mm\n",
+ "\n",
+ "#Moment carrying capacity considering Tensile strength \n",
+ "M1=sigma1*I*y_t**-1*10**-6 #KN-m\n",
+ "\n",
+ "#Moment carrying capacity considering compressive strength \n",
+ "M2=sigma2*I*y_c**-1*10**-6 #KN-m\n",
+ "\n",
+ "#Max Bending moment in simply supported beam 6 m due to u.d.l\n",
+ "#M_max=w*L*10**-3*8**-1\n",
+ "#After simplifying further we get\n",
+ "#M_max=4.5*w\n",
+ "\n",
+ "#Now Equating it to Moment carrying capacity, we get load carrying capacity\n",
+ "w=M1*4.5**-1 #KN/m\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Uniformly Distributed Load is\",round(w,3),\"KN/m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Uniformly Distributed Load is 5.096 KN/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.5,Page no.136"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Flanges\n",
+ "b=200 #mm #Width\n",
+ "t=25 #mm #Thickness \n",
+ "\n",
+ "D1=500 #mm #Overall Depth\n",
+ "t2=20 #mm #Thickness of web\n",
+ "\n",
+ "d=450 #mm #Depth of web\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Consider,Element of Thickness \"y\" at Distance \"dy\" from N.A \n",
+ "#Let Bending stress \"sigma_max\"\n",
+ "\n",
+ "#Stress on the element \n",
+ "#sigma=y*(D*2**-1)*sigma_max ..............(1)\n",
+ "\n",
+ "#Area of Element\n",
+ "#A=b*dy .................................(2)\n",
+ "\n",
+ "#Force on Element \n",
+ "#F=y*250**-1*sigma_max*b*dy\n",
+ "\n",
+ "#Let M be the Moment of resistance\n",
+ "#M=y*250**-1*sigma_max*b*dy*y\n",
+ "\n",
+ "#Moment of Resistance of top flange be M1\n",
+ "def integrand(y, b, D):\n",
+ " return b*y**2*D**-1\n",
+ "b=200 \n",
+ "D=250\n",
+ "\n",
+ "X = quad(integrand, 225, 250, args=(b,D))\n",
+ "\n",
+ "Y=2*X[0]\n",
+ "\n",
+ "#M1=Y*sigma\n",
+ "\n",
+ "#Now Moment of Inertia I section is\n",
+ "X=b*D1**3\n",
+ "Y=(b-t2)*d**3\n",
+ "I=(X-Y)*12**-1*10**-8\n",
+ "\n",
+ "#Moment acting on the entire section\n",
+ "#since sigmais the value at y=250\n",
+ "y_max=250\n",
+ "Z=I*10**8*y_max**-1\n",
+ "#M=sigma*Z \n",
+ "#After Simplifying Further we get\n",
+ "#M2=Z*sigma\n",
+ "\n",
+ "#Percentage Moment resisted by Flanges\n",
+ "P1=2258333.3*(2865833.3)**-1*100\n",
+ "\n",
+ "#Percentage Moment resisted by web\n",
+ "P2=100-P1\n",
+ "\n",
+ "#Result\n",
+ "print\"Percentage Moment resisted by Flanges\",round(P1,2),\"%\"\n",
+ "print\"Percentage Moment resisted by web\",round(P2,2),\"%\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Percentage Moment resisted by Flanges 78.8 %\n",
+ "Percentage Moment resisted by web 21.2 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 38
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.6,Page no.137"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Flanges\n",
+ "b1=200 #mm #Width\n",
+ "t1=10 #mm #Thickness\n",
+ "\n",
+ "#Web\n",
+ "d=380 #mm #Depth \n",
+ "t2=8 #mm #Thickness\n",
+ "\n",
+ "D=400 #mm #Overall Depth\n",
+ "sigma=150 #N/mm**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Area\n",
+ "A=b1*t1+d*t2+b1*t1 #mm**2\n",
+ "\n",
+ "#Moment of Inertia\n",
+ "I=1*12**-1*(b1*D**3-(b1-t2)*d**3)\n",
+ "\n",
+ "#Bending Moment\n",
+ "M=sigma*I*(D*2**-1)**-1\n",
+ "\n",
+ "#Square Section\n",
+ "\n",
+ "#Let 'a' be the side\n",
+ "a=A**0.5\n",
+ "\n",
+ "#Moment of Resistance of this section\n",
+ "M1=1*6**-1*a*a**2*sigma\n",
+ "\n",
+ "X=M*M1**-1\n",
+ "\n",
+ "#Rectangular section\n",
+ "#Let 'a' be the side and depth be 2*a\n",
+ "\n",
+ "a=(A*2**-1)**0.5\n",
+ "\n",
+ "#Moment of Rectangular secction\n",
+ "M2=1*6**-1*a*(2*a)**2*sigma\n",
+ "\n",
+ "X2=M*M2**-1\n",
+ "\n",
+ "#Circular section\n",
+ "#A=pi*d1**2*4**-1\n",
+ "\n",
+ "d1=(A*4*pi**-1)**0.5\n",
+ "\n",
+ "#Moment of circular section\n",
+ "M3=pi*32**-1*d1**3*sigma\n",
+ "\n",
+ "X3=M*M3**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Moment of resistance of beam section\",round(M,2),\"mm\"\n",
+ "print\"Moment of resistance of square section\",round(X,2),\"mm\"\n",
+ "print\"Moment of resistance of rectangular section\",round(X2,2),\"mm\"\n",
+ "print\"Moment of resistance of circular section\",round(X3,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Moment of resistance of beam section 141536000.0 mm\n",
+ "Moment of resistance of square section 9.58 mm\n",
+ "Moment of resistance of rectangular section 6.78 mm\n",
+ "Moment of resistance of circular section 11.33 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.7,Page no.139"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F=12 #KN #Force at End of beam\n",
+ "L=2 #m #span\n",
+ "\n",
+ "#Square section \n",
+ "b=d=200 #mm #Width and depth of beam\n",
+ "\n",
+ "#Rectangular section\n",
+ "b1=150 #mm #Width\n",
+ "d1=300 #mm #Depth\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Max bending Moment\n",
+ "M=F*L*10**6 #N-mm\n",
+ "\n",
+ "#M=sigma*b*d**2\n",
+ "sigma=M*6*(b*d**2)**-1 #N/mm**2\n",
+ "\n",
+ "#Let W be the central concentrated Load in simply supported beam of span L1=3 m\n",
+ "#MAx Moment\n",
+ "#M1=W*L1*4**-1\n",
+ "#After Further simplifying we get\n",
+ "#M1=0.75*10**6 #N-mm\n",
+ "\n",
+ "#The section has a moment of resistance\n",
+ "M1=sigma*1*6**-1*b1*d1**2\n",
+ "\n",
+ "#Equating it to moment of resistance we get max load W\n",
+ "#0.75*10**6*W=M1\n",
+ "#After Further simplifying we get\n",
+ "W=M1*(0.75*10**6)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Minimum Concentrated Load required to brek the beam\",round(W,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Minimum Concentrated Load required to brek the beam 54.0 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.8,Page no.140"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=3 #m #span\n",
+ "sigma_t=35 #N/mm**2 #Permissible stress in tension\n",
+ "sigma_c=90 #N/mm**2 #Permissible stress in compression\n",
+ "\n",
+ "#Flanges\n",
+ "t=30 #mm #Thickness\n",
+ "d=250 #mm #Depth\n",
+ "\n",
+ "#Web\n",
+ "t2=25 #mm #Thickness\n",
+ "b=600 #mm #Width\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let y_bar be the Distance of N.A from Extreme Fibres\n",
+ "y_bar=(t*d*d*2**-1*2+(b-2*t)*t2*t2*2**-1)*(t*d*2+(b-2*t)*t2)**-1\n",
+ "\n",
+ "#Moment of Inertia\n",
+ "I=(1*12**-1*t*d**3+t*d*(d*2**-1-y_bar)**2)*2+1*12**-1*(b-2*t)*t2**3+(b-2*t)*t2*(t2*2**-1-y_bar)**2\n",
+ "\n",
+ "#Part-1\n",
+ "\n",
+ "#If web is in Tension\n",
+ "y_t=y_bar #mm\n",
+ "y_c=d-y_bar #mm\n",
+ "\n",
+ "#Moment carrying caryying capacity From consideration of tensile stress\n",
+ "M=sigma_t*I*(y_bar)**-1 #N-mm\n",
+ "\n",
+ "#Moment carrying caryying capacity From consideration of compressive stress\n",
+ "M1=sigma_c*I*(y_c)**-1 #N-mm\n",
+ "\n",
+ "#If w KN/m is u.d.l in beam,Max bending moment\n",
+ "#M=wl**2*8**-1\n",
+ "#After further simplifyng we get\n",
+ "#M=1.125*w*10**6 N-mm\n",
+ "w=M*(1.125*10**6)**-1 #KN\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#If web is in compression\n",
+ "y_t2=178.299 #mm\n",
+ "y_c2=71.71 #mm \n",
+ "\n",
+ "#Moment carrying caryying capacity From consideration of tensile stress\n",
+ "M2=sigma_t*I*(y_t2)**-1 #N-mm\n",
+ "\n",
+ "#Moment carrying caryying capacity From consideration of compressive stress\n",
+ "M3=sigma_c*I*(y_c2)**-1 #N-mm\n",
+ "\n",
+ "#Moment of resistance is M2\n",
+ "\n",
+ "#Equating it to bending moment we get\n",
+ "#M2=1.125*10**6*w2\n",
+ "#After further simplifyng we get\n",
+ "w2=M2*(1.125*10**6)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Uniformly Distributed Load carrying capacity if:web is in Tension\",round(w,2),\"KN\"\n",
+ "print\" :web is in compression\",round(w2,3),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Uniformly Distributed Load carrying capacity if:web is in Tension 73.21 KN\n",
+ " :web is in compression 29.446 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.9,Page no.141"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "b1=200 #mm #Width at base\n",
+ "b2=100 #mm #Width at top\n",
+ "\n",
+ "L=8 #m Length\n",
+ "P=500 #N #Load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Consider a section at y metres from top\n",
+ "\n",
+ "#At this section diameter d is\n",
+ "#d=b2+y*L**-1*(b1-b2)\n",
+ "#After Further simplifying we get\n",
+ "#d=b2+12.5*y #mm\n",
+ "\n",
+ "#Moment of Inertia\n",
+ "#I=pi*64**-1*d**4\n",
+ "\n",
+ "#Section Modulus \n",
+ "#Z=pi*32**-1*(b1+12.5*y)**3\n",
+ "\n",
+ "#Moment \n",
+ "#M=5*10**5*y #N-mm\n",
+ "\n",
+ "#Let sigma be the fibre stress at this section then\n",
+ "#M=sigma*Z\n",
+ "#After sub values in above equation and further simplifying we get\n",
+ "#sigma=5*10**5*32*pi**-1*y*((b2+12.5*y)**3)**-1\n",
+ "\n",
+ "#For sigma to be Max,d(sigma)*(dy)**-1=0\n",
+ "#16*10**6*pi**-1*((b2+12.5*y)**-3+y*(-3)*(b2+12.5*y)**-4*12.5)\n",
+ "#After Further simplifying we get\n",
+ "#b2+12.5*y=37.5*y\n",
+ "#After Further simplifying we get\n",
+ "y=b2*25**-1 #m\n",
+ "\n",
+ "#Stress at this section\n",
+ "sigma=5*10**5*32*pi**-1*y*((b2+12.5*y)**3)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Stress at Extreme Fibre is max\",round(y,2),\"m\"\n",
+ "print\"Max stress is\",round(sigma,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stress at Extreme Fibre is max 4.0 m\n",
+ "Max stress is 6.04 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.10,Page no.143"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "H=10 #mm #Height\n",
+ "A1=160*160 #mm**2 #area of square section at bottom\n",
+ "L1=160 #mm #Length of square section at bottom\n",
+ "b1=160 #mm #width of square section at bottom\n",
+ "A2=80*80 #mm**2 #area of square section at top\n",
+ "L2=80 #mm #Length of square section at top\n",
+ "b2=80 #mm #Width of square section at top\n",
+ "P=100 #N #Pull\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Consider a section at distance y from top.\n",
+ "#Let the side of square bar be 'a'\n",
+ "#a=L2+y*(H)**-1*(b1-b2)\n",
+ "#After further simplifying we get\n",
+ "#a=L2+8*y\n",
+ "\n",
+ "#Moment of Inertia\n",
+ "#I=2*1*12**-1*a*(2)**0.5*(a*((2)**0.5)**-1)**3\n",
+ "#After further simplifying we get\n",
+ "#I=a**4*12**-1\n",
+ "\n",
+ "#Section Modulus \n",
+ "#Z=a**4*(12*a*(2)**0.5)**-1\n",
+ "#After further simplifying we get\n",
+ "#Z=2**0.5*a**3*(12)**-1 #mm**3\n",
+ "\n",
+ "#Bending moment at this section=100*y N-mm\n",
+ "#M=100*10**3*y #N-mm\n",
+ "\n",
+ "#But\n",
+ "#M=sigma*Z\n",
+ "#After sub values in above equation we get\n",
+ "#sigma=M*Z**-1\n",
+ "#After further simplifying we get\n",
+ "#sigma=1200*10**3*(2**0.5)**-1*y*((80+80*y)**3)**-1 .......(1)\n",
+ "\n",
+ "#For Max stress df*(dy)**-1=0\n",
+ "#After taking Derivative of above equation we get\n",
+ "#df*(dy)**-1=1200*10**3*(2**0.5)**-1*((80+8*y)**-3+y(-3)*(80+8*y)**-4*8)\n",
+ "#After further simplifying we get\n",
+ "y=80*16**-1 #m\n",
+ "\n",
+ "#Max stress at this level is\n",
+ "sigma=1200*10**3*(2**0.5)**-1*y*((80+8*y)**3)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Bending stress is Developed at\",round(y,3),\"m\"\n",
+ "print\"Value of Max Bending stress is\",round(sigma,3),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Bending stress is Developed at 5.0 m\n",
+ "Value of Max Bending stress is 2.455 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.12,Page no.147"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "b=200 #mm #Width of timber \n",
+ "d=400 #mm #Depth of timber\n",
+ "t=6 #mm #Thickness\n",
+ "b2=200 #mm #width of steel plate\n",
+ "t2=20 #mm #Thickness of steel plate\n",
+ "M=40*10**6 #KN-mm #Moment\n",
+ "#Let E_s*E_t**-1=X\n",
+ "X=20 #Ratio of Modulus of steel to timber\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#let y_bar be the Distance of centroidfrom bottom most fibre\n",
+ "y_bar=(b*d*(b+t)+t2*b2*t*t*2**-1)*(b*d+t2*b2*t)**-1 #mm\n",
+ "\n",
+ "#Moment of Inertia\n",
+ "I=1*12**-1*b*d**3+b*d*(b+t-round(y_bar,3))**2+1*12**-1*t2*b2*t**3+b2*t2*t*(round(y_bar,3)-t*2**-1)**2\n",
+ "\n",
+ "#distance of the top fibre from N-A\n",
+ "y_1=d+t-y_bar #mm\n",
+ "\n",
+ "#Distance of the junction of timber and steel From N-A\n",
+ "y_2=y_bar-t #mm\n",
+ "\n",
+ "#Stress in Timber at the top\n",
+ "Y=M*I**-1*y_1 #N/mm**2\n",
+ "\n",
+ "#Stress in the Timber at the junction point\n",
+ "Z=M*I**-1*y_2\n",
+ "\n",
+ "#Coressponding stress in steel at the junction point\n",
+ "Z2=X*Z #N/mm**2 \n",
+ "\n",
+ "#The stress in Extreme steel fibre \n",
+ "Z3=X*M*I**-1*y_bar\n",
+ "\n",
+ "#Result\n",
+ "print\"Stress in Extreme steel Fibre\",round(Z3,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stress in Extreme steel Fibre 69.67 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.13,Page no.149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Timber size\n",
+ "b=150 #mm #Width\n",
+ "d=300 #mm #Depth\n",
+ "\n",
+ "t=6 #mm #Thickness of steel plate\n",
+ "l=6 #m #Span\n",
+ "\n",
+ "#E_s*E_t**-1=20 \n",
+ "#m=E_s*E_t**-1\n",
+ "m=20 \n",
+ "sigma_timber=8 #N/mm**2 #Stress in timber\n",
+ "sigma_steel=150 #N/mm**2 #Stress in steel plate\n",
+ "\n",
+ "#Let m*t=Y\n",
+ "Y=m*t #mm\n",
+ "L=(2*t+b)*m #mm #Width of flitched beam\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Due to synnetry cenroid,the neutral axis is half the depth\n",
+ "I=(1*12**-1*L*t**3+L*t*(b+t*2**-1)**2)*2+1*12**-1*(Y+b+Y)*d**3 #mm**4\n",
+ "\n",
+ "y_max1=150 #mm #For timber\n",
+ "y_max2=156 #mm #For steel\n",
+ "\n",
+ "#stress in steel\n",
+ "f_t1=1*m**-1*sigma_steel #N/mm**2\n",
+ "\n",
+ "#Moment of resistance\n",
+ "M=f_t1*(I*y_max2**-1)\n",
+ "\n",
+ "#load\n",
+ "w=8*M*(l**2)**-1*10**-6 #KN/m\n",
+ "\n",
+ "#Result\n",
+ "print\"Load beam can carry is\",round(w,2),\"KN/m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Load beam can carry is 19.1 KN/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.14,Page no.151"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=6000 #mm #Span of beam\n",
+ "W=20*10**3 #N #Load\n",
+ "sigma=8 #N/mm**2 #Stress\n",
+ "b=200 #mm #Width of section\n",
+ "d=300 #mm #Depth of section\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#let x be the distance from left side of beam\n",
+ "\n",
+ "#Bending moment\n",
+ "#M=W*2**-1*x #Nmm .......(1)\n",
+ "\n",
+ "#But M=sigma*Z ..........(2)\n",
+ "\n",
+ "#Equating equation 1 and 2 we get\n",
+ "#W*2**-1*x=sigma*Z ............(3)\n",
+ "\n",
+ "#Section Modulus \n",
+ "#Z=1*6*b*d**2 ...............(4)\n",
+ "\n",
+ "#Equating equation 3 and 4 we get\n",
+ "#b*d**2=3*W*x*sigma**-1 .............(5)\n",
+ "\n",
+ "#Beam of uniform strength of constant depth\n",
+ "#b=3*W*x*(sigma*d**2) \n",
+ "\n",
+ "#When x=0\n",
+ "b=0\n",
+ "\n",
+ "#When x=L*2**-1\n",
+ "b2=3*W*L*(2*sigma*d**2)**-1 #mm\n",
+ "\n",
+ "#Beam with constant width of 200 mm\n",
+ "\n",
+ "#We have\n",
+ "#d=(3*W*x*(sigma*d)**-1)**0.5\n",
+ "#thus depth varies as (x)**0.5\n",
+ "\n",
+ "#when x=0\n",
+ "d1=0\n",
+ "\n",
+ "#when x=L*2**-1\n",
+ "d2=(3*W*L*(2*sigma*200)**-1)**0.5 #mm\n",
+ "\n",
+ "#Result\n",
+ "print\"Cross section of rectangular beam is:\",round(b2,2),\"mm\"\n",
+ "print\" :\",round(d2,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Cross section of rectangular beam is: 250.0 mm\n",
+ " : 335.41 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.15,Page no.154"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=800 #mm #Span\n",
+ "n=5 #number of leaves\n",
+ "b=60 #mm #Width\n",
+ "t=10 #mm #thickness\n",
+ "sigma=250 #N/mm**2 #Stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#section Modulus\n",
+ "Z=n*6**-1*b*t**2 #mm**3\n",
+ "\n",
+ "#from the relation\n",
+ "#sigma*Z=M ...................(1)\n",
+ "#M=P*L*4**-1\n",
+ "#sub values of M in equation 1 we get\n",
+ "P=sigma*Z*4*L**-1*10**-3 #KN #Load\n",
+ "\n",
+ "#Length of Leaves\n",
+ "L1=0.2*L #mm\n",
+ "L2=0.4*L #mm\n",
+ "L3=0.6*L #mm\n",
+ "L4=0.8*L #mm\n",
+ "L5=L #mm\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Load it can take is\",round(P,2),\"KN\"\n",
+ "print\"Length of leaves:L1\",round(L1,2),\"mm\"\n",
+ "print\" :L2\",round(L2,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Load it can take is 6.25 KN\n",
+ "Length of leaves:L1 160.0 mm\n",
+ " :L2 320.0 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.16,Page no.161"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F=20*10**3 #N #Shear Force\n",
+ "\n",
+ "#Tee section\n",
+ "\n",
+ "#Flange\n",
+ "b=100 #mm #Width\n",
+ "t=12 #mm #Thickness\n",
+ "\n",
+ "#Web\n",
+ "d=88 #mm #Depth\n",
+ "t2=12 #mm #Thicknes\n",
+ "\n",
+ "D=100 #mm #Overall Depth\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Distance of C.G from Top Fibre\n",
+ "y=(b*t*t*2**-1+t2*d*(d*2**-1+t))*(b*t+d*t2)**-1 #mm \n",
+ "\n",
+ "#Moment Of Inertia\n",
+ "I=1*12**-1*b*t**3+b*t*(y-t*2**-1)**2+1*12**-1*t2*d**3+t2*d*(t+d*2**-1-y)**2 #mm**4\n",
+ "\n",
+ "#shear stress at bottom Flange\n",
+ "\n",
+ "#Area above this level\n",
+ "A=b*t #mm**2\n",
+ "\n",
+ "#C.G of this area from N-A\n",
+ "y2=y-t*2**-1\n",
+ "\n",
+ "#Stress at bottom of flange\n",
+ "sigma=F*A*y2*(b*I)**-1 #N/mm**2 \n",
+ "\n",
+ "#sigma2 at same level but in web where width is 12 mm\n",
+ "sigma2=F*A*y2*(t2*I)**-1 #N/mm**2 \n",
+ "\n",
+ "#To find shear stress at N-A\n",
+ "X=t*b*(y-t*2**-1)+t2*(y-t2)*(y-t2)*2**-1 #mm**3\n",
+ "\n",
+ "sigma3=F*X*(t2*I)**-1 #N/mm**2\n",
+ "\n",
+ "#Shear stress at top and bottom fibre is zero\n",
+ "#sigma4 and sigma5 are top and bottom fibre shear stress\n",
+ "sigma4=sigma5=0\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,t,t,y,D]\n",
+ "Y1=[sigma4,sigma,sigma2,sigma3,sigma5]\n",
+ "Z1=[0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in m\")\n",
+ "plt.ylabel(\"Shear Force in kN\")\n",
+ "plt.show()\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force and Bending Moment Diagrams are the results\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5452a90>"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.17,Page no.163"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F=40*10**3 #N #shear Force\n",
+ "\n",
+ "#I-section\n",
+ "\n",
+ "#Flanges\n",
+ "b=80 #mm #Width of flange\n",
+ "t=20 #mm #Thickness\n",
+ "\n",
+ "#Web\n",
+ "d=200 #mm #Depth\n",
+ "t2=20 #mm #Thickness\n",
+ "\n",
+ "#Flange-2\n",
+ "b2=160 #mm #Width\n",
+ "t3=20 #mm #Thickness\n",
+ "\n",
+ "D=240 #mm #Overall Depth\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Distance of N-A from Top Fibre \n",
+ "y=(b*t*t*2**-1+d*t2*(t+d*2**-1)+b2*t3*(t+d+t3*2**-1))*(b*t+d*t2+b2*t3)**-1 #mm\n",
+ "\n",
+ "#Moment of Inertia\n",
+ "I=1*12**-1*b*t**3+b*t*(y-(t*2**-1))**2+1*12**-1*t2*d**3+t2*d*(y-(t+d*2**-1))**2+1*12**-1*b2*t3**3+t3*b2*((d+t+t3*2**-1)-y)**2 #mm**4\n",
+ "\n",
+ "#Shear stress bottom of flange\n",
+ "sigma=F*b*t*(y-t*2**-1)*(b*I)**-1 #N/mm**2\n",
+ "\n",
+ "#At same Level but in web\n",
+ "sigma2=F*b*t*(y-t*2**-1)*(t2*I)**-1 #N/mm**2\n",
+ "\n",
+ "#for shear stress at N.A\n",
+ "X=b*t*(y-t*2**-1)+t2*(y-t)*(y-t)*2**-1 #mm**3\n",
+ "sigma3=F*X*(t2*I)**-1 #N/mm**2\n",
+ "\n",
+ "#Shear stress at bottom of web\n",
+ "\n",
+ "X=b2*t3*((D-y)-t3*2**-1) #mm**3\n",
+ "\n",
+ "#Stress at bottom of web\n",
+ "sigma4=F*X*(t2*I)**-1 #N/mm**2\n",
+ "\n",
+ "#Stress at Lower flange\n",
+ "sigma5=F*X*(b2*I)**-1 #N/mm**2\n",
+ "\n",
+ "#Result\n",
+ "print \"The Shear Force Diagram is the result\"\n",
+ "\n",
+ "#Plotting the Shear Force Diagram\n",
+ "\n",
+ "X1=[0,20,20,140,220,220,240]\n",
+ "Y1=[0,sigma,sigma2,sigma3,sigma4,sigma5,0]\n",
+ "Z1=[0,0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length in mm\")\n",
+ "plt.ylabel(\"Shear Force in N\")\n",
+ "plt.show()\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Shear Force Diagram is the result\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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OnYL/+i/TF3DLLWZPgXbt7K5KRHyRwsAGJ0+afoBXXjHNQOvXQ1iY3VWJiC8r1gj183MN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\n/w/qZz1xEBCKMwAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5c91e90>"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.18,Page no.164"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F=30*10**3 #N #Shear Force\n",
+ "\n",
+ "#Channel Section\n",
+ "d=400 #mm #Depth of web \n",
+ "t=10 #mm #THickness of web\n",
+ "t2=15 #mm #Thickness of flange\n",
+ "b=100 #mm #Width of flange\n",
+ "\n",
+ "#Rectangular Welded section\n",
+ "b2=80 #mm #Width\n",
+ "d2=60 #mm #Depth\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Distance of Centroid From Top Fibre\n",
+ "y=(d*t*t*2**-1+2*t2*(b-t)*((b-t)*2**-1+10)+d2*b2*(d2*2**-1+t))*(d*t+2*t2*(b-t)+d2*b2)**-1 #mm\n",
+ "\n",
+ "#Moment Of Inertia of the section about N-A\n",
+ "I=1*12**-1*d*t**3+d*t*(y-t*2**-1)**2+2*(1*12**-1*t2*(b-t)**3+t2*(b-t)*(((b-t)*2**-1+t)-y)**2)+1*12**-1*d2**3*b2+d2*b2*(d2*2**-1+t-y)**2\n",
+ "\n",
+ "#Shear stress at level of weld\n",
+ "sigma=F*d*t*(y-t*2**-1)*((b2+t2+t2)*I)**-1 #N/mm**2\n",
+ "\n",
+ "#Max Shear Stress occurs at Neutral Axis\n",
+ "X=d*t*(y-t*2**-1)+2*t2*(y-t)*(y-t)*2**-1+b2*(y-t)*(y-t)*2**-1\n",
+ "\n",
+ "sigma_max=F*X*((b+t)*I)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Shear stress in the weld is\",round(sigma,2),\"N/mm**2\"\n",
+ "print\"Max shear stress is\",round(sigma_max,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Shear stress in the weld is 3.62 N/mm**2\n",
+ "Max shear stress is 4.48 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.19,Page no.165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Wooden Section\n",
+ "b=300 #mm #Width\n",
+ "d=300 #mm #Depth\n",
+ "\n",
+ "D=100 #mm #Diameter of Bore\n",
+ "F=10*10**3 #N #Shear Force\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Moment Of Inertia Of Section\n",
+ "I=1*12**-1*b*d**3-pi*64**-1*D**4\n",
+ "\n",
+ "#Shear stress at crown of circle\n",
+ "sigma=F*b*D*(d*2**-1-D*2**-1)*(b*I)**-1\n",
+ "\n",
+ "#Let a*y_bar=X\n",
+ "X=b*d*2**-1*d*4**-1-pi*8**-1*D**2*4*D*2**-1*(3*pi)**-1 #mm**3\n",
+ "\n",
+ "#Shear Stress at Neutral Axis\n",
+ "sigma2=F*X*((b-D)*I)**-1 #N/mm**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Shearing Stress at Crown of Bore\",round(sigma,3),\"N/mm**2\"\n",
+ "print\"Shear Stress at Neutral Axis\",round(sigma2,3),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Shearing Stress at Crown of Bore 0.149 N/mm**2\n",
+ "Shear Stress at Neutral Axis 0.246 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.20,Page no.166"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#flanges\n",
+ "b=200 #mm #width\n",
+ "t1=25 #mm #Thickness\n",
+ "\n",
+ "#web\n",
+ "d=450 #mm #Depth \n",
+ "t2=20 #mm #thickness\n",
+ "\n",
+ "D=500 #mm #Total Depth of section\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Moment Of Inertia of the section about N-A\n",
+ "I=1*12**-1*b*D**3-1*12**-1*(b-t2)*d**3 #mm**4\n",
+ "\n",
+ "#Consider an element in the web at distance y from y from N-A\n",
+ "#Depth of web section=225-y\n",
+ "\n",
+ "#C.G From N-A\n",
+ "#y2=y+(((D*2**-1-t)-y)*2**-1)\n",
+ "\n",
+ "#ay_bar for section at y\n",
+ "#Let ay_bar be X\n",
+ "#X=X1 be of Flange + X2 be of web above y\n",
+ "#X=b*t1*(D*2**-1-t1*2**-1)+t2*(d-t1)*(d-t1+y)*2**-1\n",
+ "#After Sub values and Further simplifying we get\n",
+ "#X=1187500+10*(225**2-y**2)\n",
+ "\n",
+ "#Shear stress at y\n",
+ "#sigma_y=F*(X)*(t2*I)**-1\n",
+ "\n",
+ "#Shear Force resisted by the Element\n",
+ "#F1=F*X*t2*dy*(t2*I)**-1\n",
+ "\n",
+ "#Shear stress resisted by web \n",
+ "#sigma=2*F*I**-1*(X)*dy\n",
+ "\n",
+ "#After Integrating above equation and further simplifying we get\n",
+ "#sigma=0.9578*F\n",
+ "\n",
+ "sigma=0.9578*100\n",
+ "\n",
+ "#Result\n",
+ "print\"Shear Resisted by web\",round(sigma,2),\"%\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Shear Resisted by web 95.78 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.21,Page no.167"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Wooden Beam\n",
+ "\n",
+ "b=150 #mm #width\n",
+ "d=250 #mm #Depth\n",
+ "\n",
+ "L=5000 #mm #span\n",
+ "m=11.2 #N/mm**2 #Max Bending stress\n",
+ "sigma=0.7 #N/mm**2 #Max shear stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let 'a' be the distance from left support\n",
+ "#Max shear force\n",
+ "#F=R_A=W*(L-a)*L**-1 \n",
+ "\n",
+ "#Max Moment\n",
+ "#M=W*(L-a)*a*L**-1\n",
+ "\n",
+ "#But M=sigma*Z\n",
+ "#W*(L-a)*a*L**-1=m*1*6**-1*b*d**2 .....................(1)\n",
+ "\n",
+ "#In Rectangular Section MAx stress is 1.5 times Avg shear stress\n",
+ "F=sigma*b*d*1.5**-1\n",
+ "\n",
+ "#W*(L-a)*L**-1=F .....................(2)\n",
+ "\n",
+ "#Dividing Equation 1 nad 2 we get\n",
+ "a=m*6**-1*b*d**2*1.5*(sigma*b*d)**-1\n",
+ "\n",
+ "#Sub above value in equation 2 we get\n",
+ "W=(L-a)**-1*L*F*10**-3 #KN \n",
+ "\n",
+ "#Result\n",
+ "print\"Load is\",round(W,2),\"KN\"\n",
+ "print\"Distance from Left support is\",round(a,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Load is 21.87 KN\n",
+ "Distance from Left support is 1000.0 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.22,Page no.168"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=1000 #mm #span\n",
+ "\n",
+ "#Rectangular Section\n",
+ "\n",
+ "b=200 #mm #width\n",
+ "d=400 #mm #depth\n",
+ "\n",
+ "sigma=1.5 #N/mm**2 #Shear stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let AB be the cantilever beam subjected to load W KN at free end\n",
+ "\n",
+ "#MAx shear Force\n",
+ "#F=W*10**3 #KN\n",
+ "\n",
+ "#Since Max shear stress in Rectangular section\n",
+ "#sigma_max=1.5*F*A**-1 \n",
+ "#After sub values and further simplifyng we get\n",
+ "W=1.5*b*d*(1.5*1000)**-1 #KN\n",
+ "\n",
+ "#Moment at fixwed end\n",
+ "M=W*1 #KN-m\n",
+ "y_max=d*2**-1 #mm\n",
+ "\n",
+ "#M.I\n",
+ "I=1*12**-1*b*d**3 #mm**3\n",
+ "\n",
+ "#MAx Stress\n",
+ "sigma_max=M*10**6*I**-1*y_max\n",
+ "\n",
+ "#Result\n",
+ "print\"Concentrated Load is\",round(sigma_max,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Concentrated Load is 15.0 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4.24,Page no.170"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=4000 #mm #span\n",
+ "\n",
+ "#Rectangular Cross-section\n",
+ "b=100 #mm #Width\n",
+ "d=200 #mm #Thickness\n",
+ "\n",
+ "F_per=10 #N/mm**2 #Max Bending stress\n",
+ "q_max=0.6 #N/mm**2 #Shear stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#If the Load W is in KN/m\n",
+ "\n",
+ "#Max shear Force\n",
+ "#F=w*l*2**-1 #KN\n",
+ "#After substituting values and further simplifying we get\n",
+ "#M=2*w #KN-m\n",
+ "\n",
+ "#Max Load from Consideration of moment\n",
+ "#M=1*6**-1*b*d**2*F_per\n",
+ "#After substituting values and further simplifying we get\n",
+ "w=(1*6**-1*b*d**2*F_per)*(2*10**6)**-1 #KN/m\n",
+ "\n",
+ "#Max Load from Consideration of shear stress\n",
+ "#q_max=1.5*F*(b*d)**-1 #N\n",
+ "#After substituting values and further simplifying we get\n",
+ "F=q_max*(1.5)*b*d #N\n",
+ "\n",
+ "#If w is Max Load in KN/m,then\n",
+ "#2*w*1000=8000\n",
+ "#After Rearranging and Further simplifying we get\n",
+ "w2=8000*(2*1000)**-1 #KN/m\n",
+ "\n",
+ "#Result\n",
+ "print\"Uniformly Distributed Load Beam can carry is\",round(w,2),\"KN/m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Uniformly Distributed Load Beam can carry is 3.33 KN/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_05.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_05.ipynb new file mode 100644 index 00000000..63be0774 --- /dev/null +++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_05.ipynb @@ -0,0 +1,1019 @@ +{
+ "metadata": {
+ "name": "chapter 05.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 5:Deflections Of Beams By Double Integration Methods"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5.2,Page No.192"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=3000 #mm #span of beam\n",
+ "a=2000 #mm\n",
+ "W1=20*10**3 #N #Pt Load Acting on beam\n",
+ "W2=30*10**3 #N #Pt Load Acting on beam\n",
+ "E=2*10**5 #N/mm**2 #Young's Modulus\n",
+ "I=2*10**8 #mm**4 #M.I\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Deflection at free End Due to W2\n",
+ "dell1=W2*L**3*(3*E*I)**-1 #mm\n",
+ "\n",
+ "#Deflection at free end Due to W1\n",
+ "dell2=W1*a**3*(3*E*I)**-1+(L-a)*W1*a**2*(2*E*I)**-1 #mm\n",
+ "\n",
+ "#Total Deflection at free end\n",
+ "dell=dell1+dell2 #mm\n",
+ "\n",
+ "#Result\n",
+ "print\"Deflection at Free End is\",round(dell,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Deflection at Free End is 9.08 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5.4,Page No.193"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "E=2*10**5 #N/mm**2 #Young's Modulus\n",
+ "I=180*10**6 #mm**4 #M.I\n",
+ "W1=20 #N/m #u.d.l\n",
+ "W2=20*10**3 #N #Pt load\n",
+ "L=3000 #m #Span of beam\n",
+ "a=2000 #m #Span of u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Displacement of free End due to 20 KN Pt load at free end\n",
+ "dell1=W2*L**3*(3*E*I)**-1 #mm\n",
+ "\n",
+ "#Displacement of free end due to u.d.l\n",
+ "dell2=W1*a**4*(8*E*I)**-1+(L-a)*W1*a**3*(6*E*I)**-1\n",
+ "\n",
+ "#Deflection at free end\n",
+ "dell=dell1+dell2 #mm\n",
+ "\n",
+ "#Result\n",
+ "print\"The Displacement of Free End of cantilever beam is\",round(dell,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Displacement of Free End of cantilever beam is 6.85 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5.10,Page No.201"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "E=200*10**6 #KN/m**2 #Young's Modulus\n",
+ "I=15*10**-6 #m**4 #M.I\n",
+ "a=4000 #m \n",
+ "L_AB=6 #m #Span of beam\n",
+ "L_CB=2 #m #Length of CB\n",
+ "F_C=18 #KN #force at C\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let V_A & V_B be the Reactions at A & B Respectively\n",
+ "#V_A+V_B=18\n",
+ "#Now taking moment at B,we get M_B\n",
+ "V_A=(F_C*L_CB)*L_AB**-1\n",
+ "V_B=18-V_A\n",
+ "\n",
+ "#Now Taking Moment at distance x\n",
+ "#M_x=6*x-18*(x-4)\n",
+ "#EI*d**2*y*(d*x**2)**-1=6*x-18*(x-4)\n",
+ "\n",
+ "#Now Integrating above equation,we get\n",
+ "#EI*dy*(dx)**-1=C1+3*x**2-9(x-4)**4\n",
+ "\n",
+ "#Again Integrating above equation we get\n",
+ "#EI*y=C2+C1*x+x**3-3*(x-4)**3\n",
+ "\n",
+ "#The Boundary conditions\n",
+ "x=0\n",
+ "y=0 #.....(a)\n",
+ "\n",
+ "x=6\n",
+ "y=0 #....(b)\n",
+ "\n",
+ "#From Boundary Condition(B.C) a we get\n",
+ "C2=0\n",
+ "\n",
+ "#From Boundary Condition(B.C) b we get\n",
+ "#6*C1+216-3*8\n",
+ "#After Further simplifying we get\n",
+ "C1=-(216-24)*6**-1\n",
+ "\n",
+ "#EI*y=-32*x+x**3-3*(x-4)**3\n",
+ "#EI*dy*(dx)**-1=-32+3*x**2-9(x-4)**4\n",
+ "\n",
+ "#For Max Deflection\n",
+ "#Assume it inthe Porion AC i.e x=4=a\n",
+ "#0=-32+3*x**2\n",
+ "x=(32*3**-1)**0.5\n",
+ "\n",
+ "#Value of Max deflection is\n",
+ "ymax=(-32*x+x**3)*(E*I)**-1 #mm\n",
+ "\n",
+ "#slope at mid-span\n",
+ "\n",
+ "#EI*(dy*(dx)**-1)_centre=-32+3*x**2\n",
+ "#at centre ,\n",
+ "x1=3 #m\n",
+ "\n",
+ "#Let (dy*(dx)**-1)_centre=X\n",
+ "X=-(-32+3*x1**2)*(E*I)**-1 #Radian\n",
+ "\n",
+ "#Deflection at Load Point\n",
+ "x2=4 #m\n",
+ "#EI*y_c=-32*x2+x2**3\n",
+ "\n",
+ "y_c=-(-32*x2+x2**3)*(E*I)**-1\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Value of Max Deflection\",round(ymax,4),\"mm\"\n",
+ "print\"SLope at mid-span\",round(X,4),\"radian\"\n",
+ "print\"Deflection at the Load Point is\",round(y_c,4),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Value of Max Deflection -0.0232 mm\n",
+ "SLope at mid-span 0.0017 radian\n",
+ "Deflection at the Load Point is 0.0213 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5.11,Page No.203"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_CB=2 #m #Length of CB\n",
+ "L_AC=4 #m #Length of AB\n",
+ "M_C=15 #KN.m #Moment At Pt C\n",
+ "F_C=30 #KN\n",
+ "L=6 #m Span of Beam\n",
+ "\n",
+ "#Let X=E*I\n",
+ "X=10000 #KN-m**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let V_A and V_B be the reactions at A & B respectively\n",
+ "#V_A+V_B=30\n",
+ "\n",
+ "#Taking Moment a A,we get\n",
+ "V_B=(F_C*L_AC+M_C)*L**-1\n",
+ "V_A=30-V_B\n",
+ "\n",
+ "#Now Taking Moment at distacnce x from A\n",
+ "#M_x=7.5*x-30*(x-4)+15\n",
+ "\n",
+ "#By using Macaulay's Method\n",
+ "#EI*(d**2*x/dx**2)=M_x=7.5*x-30*(x-4)+15\n",
+ "\n",
+ "#Now Integrating above Equation we get\n",
+ "#EI*(dy/dx)=C1+7.5*x**2*2**-1-15*(x-4)**2+15*(x-4) ............(1)\n",
+ "\n",
+ "#Again Integrating above Equation we get\n",
+ "#EIy=C2+C1*x+7.5*6**-1*x**3-5*(x-4)**3+15*(x-4)**2*2**-1..........(2)\n",
+ "\n",
+ "#Boundary Cinditions\n",
+ "x=0\n",
+ "y=0\n",
+ "\n",
+ "#Substituting above equations we get \n",
+ "C2=0\n",
+ "\n",
+ "x=6 #m\n",
+ "y=0\n",
+ "\n",
+ "C1=-(7.5*6**3*6**-1-5*2**3+15*2**2*2**-1)*6**-1\n",
+ "\n",
+ "#EIy_c=C2+C1*x+7.5*6**-1*x**3-5*(x-4)**3+15*(x-4)**2*2**-1\n",
+ "#Sub values in Above equation we get\n",
+ "y_c=(93.3333*(X)**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"The Deflection at C\",round(y_c,4),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Deflection at C 0.0093 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5.12,Page No.204"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_AC=L_CD=L_DB=2 #m #Length of AC,CD,DB\n",
+ "F_C=40 #KN #Force at C\n",
+ "w=20 #KN/m #u.d.l\n",
+ "L=6 #m #span of beam\n",
+ "\n",
+ "#Let E*I=X\n",
+ "X=15000 #KN-m**2\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let V_A & V_B be the reactions at A & B respectively\n",
+ "#V_A+V_B=80\n",
+ "\n",
+ "#Taking Moment B,M_B\n",
+ "V_A=(F_C*(L_CD+L_DB)+w*L_DB*L_DB*2**-1)*L**-1 #KN\n",
+ "V_B=80-V_A #KN\n",
+ "\n",
+ "#Taking Moment at distance x from A\n",
+ "#M_x=33.333*x-40*(x-2)-20*(x-4)**2*2**-1\n",
+ "#EI*(d**2/dx**2)=33.333*x-40*(x-2)-10*(x-4)**2\n",
+ "\n",
+ "#Integrating above equation we get\n",
+ "#EI*(dy/dx)=C1+33.333*x**2*2**-1-20*(x-2)**2-10*3**-1*(x-4)**3\n",
+ "\n",
+ "#Again Integrating above equation we get\n",
+ "#EI*y=C2+C1*x+33.333*x**3*6**-1-20*3**-1*(x-2)**3-10*12**-1*(x-4)**4\n",
+ "\n",
+ "#At\n",
+ "x=0\n",
+ "y=0\n",
+ "C2=0\n",
+ "\n",
+ "#At\n",
+ "x=6\n",
+ "y=0\n",
+ "C1=-760*6**-1\n",
+ "\n",
+ "#Assuming Deflection to be max in portion CD and sustituting value of C1 in equation of slope we get\n",
+ "#EI*y=C2+C1*x+33.333*x**3*6**-1-20*3**-1*(x-2)**3-10*12**-1*(x-4)**4\n",
+ "#0=-126.667+33.333*x**2**-1-20*(x-2)**2\n",
+ "\n",
+ "#After rearranging and simplifying further we get\n",
+ "\n",
+ "#x**2-24*x+62=0\n",
+ "#From above equations\n",
+ "a=1\n",
+ "b=-24\n",
+ "c=62\n",
+ "\n",
+ "y=(b**2-4*a*c)**0.5\n",
+ "\n",
+ "x1=(-b+y)*(2*a)**-1\n",
+ "x2=(-b-y)*(2*a)**-1\n",
+ "\n",
+ "#Taking x2 into account\n",
+ "x=2.945 #m\n",
+ "C1=-126.667\n",
+ "C2=0\n",
+ "\n",
+ "y_max=(C2+C1*x+33.333*x**3*6**-1-20*3**-1*(x-2)**3)*X**-1 #mm\n",
+ "\n",
+ "#Max slope occurs at the ends\n",
+ "#At A,\n",
+ "#EI*(dy/dx)_A=-126.667\n",
+ "#At B\n",
+ "#EI*(dy/dx)_B=126.667+33.333*6**2*2**-1-20*4**2-10*2**3\n",
+ "#After simplifying Further we get\n",
+ "#EI*(dy/dx)_B=73.3273\n",
+ "\n",
+ "#Now Max slope is EI(dy/dx)_A=-126.667\n",
+ "#15000*(dy/dx)_=-126.667\n",
+ "\n",
+ "#Let Y=dy/dx\n",
+ "Y=-126.667*X**-1 #Radians\n",
+ "\n",
+ "#Result\n",
+ "print\"Maximum Deflection for Beam is\",round(y_max,4),\"mm\"\n",
+ "print\"Maximum Slope for beam is\",round(Y,4),\"radians\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Maximum Deflection for Beam is -0.0158 mm\n",
+ "Maximum Slope for beam is -0.0084 radians\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5.13,Page No.206"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "E=2*10**8 #KN/m**2\n",
+ "I=450*10**-6 #m**4\n",
+ "L_AC=1 #m #Length of AC\n",
+ "L_CD=3 #m #Length of CD\n",
+ "L_DB=2 #m #Length of DB\n",
+ "w=10 #KN/m #u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let V_A & V_B be the reactions at A & B respectively\n",
+ "#V_A+V_B=30\n",
+ "\n",
+ "#Taking Moment at distance x from A\n",
+ "#M_x=17.5*x-10*(x-1)**2*2**-1+10*(x-4)**2*2**-1\n",
+ "#EI*(d**2/dx**2)=17.5*x-10*(x-1)**2*2**-1+10*(x-4)**2*2**-1\n",
+ "\n",
+ "#Now Integrating Above equation we get\n",
+ "#EI(dy/dx)=C1+17.5*x**2*2**-1-5*3**-1*(x-1)**2+5*3**-1*(x-4)**3\n",
+ "\n",
+ "#Again Integrating Above equation we get\n",
+ "#EI*y=C2+C1*x+17.5*x**3*6**-1-5*12**-1*(x-1)**4+5*12**-1*(x-4)**4\n",
+ "\n",
+ "#At \n",
+ "x=0\n",
+ "y=0\n",
+ "C2=0\n",
+ "\n",
+ "#At \n",
+ "x=6 \n",
+ "y=0\n",
+ "C1=(-17.5*x**3*6**-1+5*12**-1*(x-1)**4-5*12**-1*(x-4)**4)*x**-1\n",
+ "\n",
+ "# 1)Slope at A .i.e at x=0\n",
+ "#EI*(dy/dx)_A=C1=-62.708 #KN-m**2\n",
+ "#let (dy/dx)=X\n",
+ "X=C1*(E*I)**-1 #radiams\n",
+ "\n",
+ "#Deflection at mid-span\n",
+ "x=3 #m\n",
+ "#EI*y_centre=C1*x+17.5*x**3*6**-1-5*12**-1*(x-1)**2\n",
+ "y_centre=-(C1*x+17.5*x**3*6**-1-5*12**-1*(x-1)**4)*(E*I)**-1\n",
+ "\n",
+ "#Maximum Deflection\n",
+ "\n",
+ "#At point of Max deflection (dy/dx)=0\n",
+ "#Assuming it in portion CD\n",
+ "\n",
+ "#0=C1*x+17.5*x**2*2**-1-5*3**-1*(x-1)**3\n",
+ "\n",
+ "#Now Let\n",
+ "#F(x)=C1+17.5*x**2*2**-1-5*3**-1*(x-1)**3\n",
+ "\n",
+ "#Let F(x)=Y\n",
+ "#At \n",
+ "x=2.5\n",
+ "Y1=-(C1+17.5*x**2*2**-1-5*3**-1*(x-1)**3)\n",
+ "\n",
+ "#AT\n",
+ "x=3\n",
+ "Y2=-(C1+17.5*x**2*2**-1-5*3**-1*(x-1)**3)\n",
+ "\n",
+ "#At\n",
+ "x=2.9 #m\n",
+ "Y3=-(C1+17.5*x**2*2**-1-5*3**-1*(x-1)**3)\n",
+ "\n",
+ "#A curve may be plotted for (F(x) and the value for which F(x)=0 may be found\n",
+ "#For F(x)=0 for x=2.92 m\n",
+ "#Therefore y_max occur at x=2.92\n",
+ "\n",
+ "x=2.92 #m\n",
+ "y_max=(C1*x+17.5*x**3*6**-1-5*12**-1*(x-1)**4)*(E*I)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Slope at A\",round(X,6),\"mm\"\n",
+ "print\"Deflection at mid-span\",round(y_centre,6),\"mm\"\n",
+ "print\"Maxmimum Deflection is\",round(y_max,5),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Slope at A -0.000697 mm\n",
+ "Deflection at mid-span 0.001289 mm\n",
+ "Maxmimum Deflection is -0.00129 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5.14,Page No.208"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_AC=LDE=L_EB=1 #m #Length of AC\n",
+ "L_CD=2 #m #Length of CD\n",
+ "E=200 #KN/mm**2\n",
+ "I=60*10**6 #mm**4 #M.I\n",
+ "F_C=20 #KN #Force at C\n",
+ "F_E=30 #KN #Force at E\n",
+ "w=10 #KN/m #u.d.l\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "X=E*I*10**-6 #KN-m**2\n",
+ "\n",
+ "#Let V_A & V_B be the reactions at A & B respectively\n",
+ "#V_A+V_B=70\n",
+ "\n",
+ "#Taking Moment at distance x from A\n",
+ "#M_x=34*x-20*(x-1)-10*(x-1)**2*2**-1+10*(x-3)**2*2**-1-30*(x-4)\n",
+ "#EI*(d**2y/dx**2)=34*x-20*(x-1)-10*(x-1)**2*2**-1+10*(x-3)**2*2**-1-30*(x-4)\n",
+ "\n",
+ "#Now Integrating Above equation,we get\n",
+ "#EI*(dy/dx)=C1+17*x**2-10*(x-1)**2-5*3**-1*(x-1)**3+5*3**-1*(x-3)**3-15*(x-4)**2\n",
+ "\n",
+ "#Again Integrating Above equation,we get\n",
+ "#EI*y=C2+C1*x+17*3**-1*x**3-10*3**-1*(x-1)**3-5*12**-1*(x-1)**4+5*12**-1*(x-3)**4-5*(x-4)**3\n",
+ "\n",
+ "#At\n",
+ "x=0\n",
+ "y=0\n",
+ "C2=0\n",
+ "\n",
+ "#At \n",
+ "x=5 #m\n",
+ "y=0\n",
+ "C1=(-17*3**-1*x**3+10*3**-1*(x-1)**3+5*12**-1*(x-1)**4-5*12**-1*(x-3)**4+5*(x-4)**3)*5**-1\n",
+ "\n",
+ "#EI*y=C2+C1*x+17*3**-1*x**3-10*3**-1*(x-1)**3-5*12**-1*(x-1)**4+5*12**-1*(x-3)**4-5*(x-4)**3\n",
+ "C2=0\n",
+ "C1=-78\n",
+ "x=1\n",
+ "y_c=(-78*x+17*3**-1*x)*(X)**-1\n",
+ "\n",
+ "#EI*y_D=C2+C1*x+17*3**-1*x**3-10*3**-1*(x-1)**3-5*12**-1*(x-1)**4\n",
+ "x=3\n",
+ "C1-78\n",
+ "C2=0\n",
+ "y_D=(C2+C1*x+17*3**-1*x**3-10*3**-1*(x-1)**3-5*12**-1*(x-1)**4)*(X**-1)\n",
+ "\n",
+ "#EI*y_E=C2+C1*x+17*3**-1*x**3-10*3**-1*(x-1)**3-5*12**-1*(x-1)**4+5*12**-1*(x-3)**4\n",
+ "x=4\n",
+ "C1-78\n",
+ "C2=0\n",
+ "y_E=(C2+C1*x+17*3**-1*x**3-10*3**-1*(x-1)**3-5*12**-1*(x-1)**4+5*12**-1*(x-3)**4)*X**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Deflections at C\",round(y_c,5),\"mm\"\n",
+ "print\"Deflections at D\",round(y_D,5),\"mm\"\n",
+ "print\"Deflections at E\",round(y_E,4),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Deflections at C -0.00603 mm\n",
+ "Deflections at D -0.00953 mm\n",
+ "Deflections at E -0.0061 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 45
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5.15,Page No.209"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "E=200 #KN/mm**2 #Modulus of Elasticity\n",
+ "I=300*10**6 #mm\n",
+ "L_AB=L_BC=L_CD=L_DE=1 #m #Length of AB,BC,CD,DE respectively\n",
+ "F_A=20 #KN #Force at A\n",
+ "F_C=10 #KN #Force at C\n",
+ "w=30 #KN/m #u.d.l\n",
+ "\n",
+ "#Let E*I=X\n",
+ "X=E*I*10**-6 #KN-2**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let V_E be the reactions at E\n",
+ "V_E=F_A+F_C+w*(L_BC+L_CD) #KN \n",
+ "\n",
+ "#Taking Moment at distance x\n",
+ "#EI*(d**2x/dy**2)=M=-20*x-30*(x-1)**2*2**-1-10*(x-2)+30*(x-3)**2*2**-1\n",
+ "\n",
+ "#Integrating above equation we get\n",
+ "#EI*(dy/dx)=C1-10*x**2-5*(x-1)**3-5*(x-2)**2+5*(x-3)**3\n",
+ "\n",
+ "#Again Integrating above equation\n",
+ "#EI*y=C2+C1*x-10*x**3*3**-1-5*(x-1)**4*4**-1-5*(x-3)**4*4**-1-5*3*(x-2)**3\n",
+ "\n",
+ "#At\n",
+ "#dy/dx=0\n",
+ "x=4 #m\n",
+ "C1=10*x**2+5*(x-1)**3+5*(x-2)**2-5*(x-3)**3\n",
+ "\n",
+ "#AT\n",
+ "x=4\n",
+ "y=0\n",
+ "C2=-C1*4+10*x**3*3**-1+5*(x-1)**4*4**-1-5*(x-3)**4*4**-1+5*3**-1*(x-2)**3\n",
+ "\n",
+ "#Max Deflection and Max slopes occurs at Free end in case of cantilever\n",
+ "y_max=y_A=C2*X**-1\n",
+ "\n",
+ "#EI*(dy/dx)_max=C1\n",
+ "#Let (dy/dx)=Y\n",
+ "Y=C1*X**-1 #radian\n",
+ "\n",
+ "#Now deflection at x=1 #m\n",
+ "C2=-913.333\n",
+ "C1=310\n",
+ "x=1\n",
+ "y_B=(C2+C1*x-10*x**3*3**-1)*X**-1\n",
+ "\n",
+ "#Now Deflection at x=2 #m\n",
+ "C2=-913.333\n",
+ "C1=310\n",
+ "x=2 #m\n",
+ "y_C=(C2+C1*x-10*x**3*3**-1-5*(x-1)**4*4**-1)*X**-1\n",
+ "\n",
+ "#Now Deflection at x=3 #m\n",
+ "C2=-913.333\n",
+ "C1=310\n",
+ "x=3 #m\n",
+ "y_D=(C2+C1*x-10*x**3*3**-1-5*(x-1)**4*4**-1-5*3**-1*(x-2)**3)*X**-1\n",
+ "\n",
+ "y_E=0\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Deflection for Beam\",round(y_A,4),\"mm\"\n",
+ "print\"Max Slope for beam\",round(Y,5),\"radians\"\n",
+ "\n",
+ "#Plotting the ELastic Curve\n",
+ "\n",
+ "Y2=[y_E,y_D,y_C,y_B,y_A]\n",
+ "X2=[L_AB+L_BC+L_CD+L_DE,L_AB+L_BC+L_CD,L_AB+L_BC,L_AB,0]\n",
+ "Z2=[0,0,0,0,0]\n",
+ "plt.plot(X2,Y2,X2,Z2)\n",
+ "plt.xlabel(\"Length in mm\")\n",
+ "plt.ylabel(\"Deflection in mm\")\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Deflection for Beam -0.0152 mm\n",
+ "Max Slope for beam 0.00517 radians\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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8yjGZmZkkJSWRmZlJSkoKM2bMoLKy8pxilcZbsQJGj4Y//QkWL1aSEWnvaq3R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\nL+mlAAAAAElFTkSuQmCC\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5554430>"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5.16,Page No.211"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_BD=L_CB=L_AC=2 #m #Length of BD,CB,AC\n",
+ "F_C=40 #KN #Force at C\n",
+ "F_D=10 #KN Force at D\n",
+ "L=6 #m spna of beam\n",
+ "\n",
+ "#EI is constant in this problem\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let V_A & V_B be the reactions at A & B Respectively\n",
+ "#V_A+V_B=50\n",
+ "\n",
+ "#Taking Moment at Pt A\n",
+ "V_B=(F_D*L+F_C*L_AC)*(L_AC+L_CB)**-1\n",
+ "V_A=50-V_B\n",
+ "\n",
+ "#Now Taking Moment at distance x from A,M_x\n",
+ "#M_x=15*x-40*(x-2)+35*(x-4)\n",
+ "#EI*(d**2*y/dx**2)=15*x-40*(x-2)+35*(x-4)\n",
+ "\n",
+ "#Now Integrating above equation we get\n",
+ "#EI*(dy/dx)=C1+7.5*x**2-20*(x-2)**2+17.5(x-4)**2\n",
+ "\n",
+ "#Again Integrating above equation we get\n",
+ "#EI*y=C2+C1*x+2.5*x**2-20*3**-1*(x-2)**3+17.5*(x-4)**3*3**-1\n",
+ "\n",
+ "#At\n",
+ "x=0\n",
+ "y=0\n",
+ "#we get\n",
+ "C2=0\n",
+ "\n",
+ "#At\n",
+ "x=4 \n",
+ "y=0\n",
+ "#we get\n",
+ "C1=(2.5*4**3-20*3**-1*2**3)*4**-1\n",
+ "\n",
+ "#Now Deflection at C\n",
+ "x=2\n",
+ "C1=-26.667\n",
+ "C2=0\n",
+ "y_C=C2+C1*x+2.5*x**3\n",
+ "\n",
+ "#Now Deflection at D\n",
+ "C1=-21.667\n",
+ "C2=0\n",
+ "y_D=-26.667*6+2.5*6**3-20*3**-1*4**3+17.5*2**3*3**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Deflections Under Loads are:y_D\",round(y_D,4)\n",
+ "print\" :y_C\",round(y_C,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Deflections Under Loads are:y_D -0.002\n",
+ " :y_C -33.33\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5.17,Page No.212"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_BC=L_EB=2 #m #Length of BC & EB\n",
+ "E=200*10**6 #KN/m**2 #Modulus of eLasticity\n",
+ "I=45*10**-6 #mm**4 #M.I\n",
+ "L_DE=3 #m #Length of DE\n",
+ "L_AD=1 #m #Length of AD\n",
+ "w=20 #KN/m #u.d.l\n",
+ "L=8 #m #span of beam\n",
+ "F_C=30 #KN #Force at C\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let V_A & V_B be the reactions at A & B respectively\n",
+ "#V_A+V_B=90\n",
+ "\n",
+ "#Taking Moment at A,M_A\n",
+ "V_B=(w*L_DE*(L_DE*2**-1+L_AD)+F_C*L)*(L_AD+L_DE+L_EB)**-1\n",
+ "V_A=90-V_B\n",
+ "\n",
+ "#Taking Moment at distance x\n",
+ "#M_x=25*x-20*(x-1)**2*2**-1+20*(x-4)**2*2**-1+65*(x-6)\n",
+ "\n",
+ "#Integrating above equation we get\n",
+ "#EI*(d**2*y/dx**2)=25*x-10*(x-1)**2+10*(x-4)**2+65*(x-6)\n",
+ "\n",
+ "#again Integrating above equation we get\n",
+ "#EI*(dy/dx)=C1+25*x**2*2**-1-10*3**-1*(x-1)**3+10*3**-1*(x-4)**2+65*2**-1*(x-6)**2\n",
+ "\n",
+ "#again Integrating above equation we get\n",
+ "#EI*y=C2+C1*x+25*6**-1*x**3-10*12**-1*(x-1)**4+10*12**-1*(x-4)**4+65*6**-1*(x-6)**3\n",
+ "\n",
+ "x=0\n",
+ "y=0\n",
+ "#Sub these values in above equation,we get\n",
+ "C2=0\n",
+ "\n",
+ "x=6 #m\n",
+ "y=0\n",
+ "C1=-(25*6**-1*6**3-10*12**-1*5**4+10*12**-1*2**4)*6**-1\n",
+ "\n",
+ "#deflection at C is given by\n",
+ "x=8\n",
+ "y_c=(C2+C1*x+25*6**-1*x**3-10*12**-1*(x-1)**4+10*12**-1*(x-4)**4+65*6**-1*(x-6)**3)*(E*I)**-1\n",
+ "\n",
+ "#Assuming y is max in the portion DE,then\n",
+ "#(dy/dx)=0 for that point\n",
+ "\n",
+ "#0=-65.417+25*2**-1*x**2-10*3**-1*x(-1)**3\n",
+ "\n",
+ "#Let F(x)=-65.417+25*2**-1*x**2-10*3**-1*x(-1)**3\n",
+ "#Let z=F(x)\n",
+ "\n",
+ "#AT \n",
+ "x=3\n",
+ "z=-65.417+25*2**-1*x**2-10*3**-1*(x-1)**3\n",
+ "\n",
+ "x=2.5\n",
+ "z1=-65.417+25*2**-1*x**2-10*3**-1*(x-1)**3\n",
+ "\n",
+ "x=2.4\n",
+ "z2=-65.417+25*2**-1*x**2-10*3**-1*(x-1)**3\n",
+ "\n",
+ "#The assumption is max in portion DE\n",
+ "x=2.46\n",
+ "y_max=(-65.417*x+25*6**-1*x**3-10*12**-1*1.46**4)*(E*I)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Deflection at free end C\",round(y_c,4),\"mm\"\n",
+ "print\"Max Deflection between A and B\",round(y_max,4),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Deflection at free end C -0.0101 mm\n",
+ "Max Deflection between A and B -0.0114 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5.18,Page No.213"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L_DB=L_AC=L_ED=2 #m #Length of DB & AC\n",
+ "L_CD=4 #m #Length of CD\n",
+ "L_CE=2 #m #Length of CE\n",
+ "F_A=40 #KN #Force at C\n",
+ "F_B=20 #KN #Force at A\n",
+ "E=200*10**6 #KN/mm**2 #Modulus of Elasticity\n",
+ "I=50*10**-6 #m**4 #M.I\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#LEt V_C & V_D be the reactions at C & D respectively\n",
+ "#V_C+V_D=60\n",
+ "\n",
+ "#Taking Moment At D,M_D\n",
+ "V_C=-(-F_A*(L_AC+L_CE+L_ED)+F_B*L_DB)*L_CD**-1\n",
+ "V_D=60-V_C\n",
+ "\n",
+ "#Now Taking Moment at Distance x from A,\n",
+ "#M_x=-40*x+50*(x-2)+10*(x-6)\n",
+ "\n",
+ "#EI*(d**2*y/dx**2)=-40*x+50*(x-2)+10*(x-6)\n",
+ "\n",
+ "#Now Integrating above Equation we get\n",
+ "#EI*(dy/dx)=C1+20*x**2-25*(x-2)+5*(x-6)**2\n",
+ "\n",
+ "#Again Integrating above Equation we get\n",
+ "#EI*y=C2+C1*x-20*3**-1*x**3+25*3**-1*(x-2)**3+5*3**-1*(x-6)**3\n",
+ "\n",
+ "#At\n",
+ "x=0\n",
+ "y=0\n",
+ "#C2+2*C1=-53.33 ...............(1)\n",
+ "\n",
+ "#At \n",
+ "x=6\n",
+ "y=0\n",
+ "#C2+6*C1=906.667 ...............(2)\n",
+ "\n",
+ "#Subtracting Equation 1 from 2 we get\n",
+ "C1=853.333*4**-1\n",
+ "C2=53.333-2*C1\n",
+ "x=0\n",
+ "y_A=(C2+C1*x-20*3**-1*x**3+25*3**-1*(x-2)**3+5*3**-1*(x-6)**3)*(E*I)**-1\n",
+ "\n",
+ "#Answer For y_A is incorrect in textbook\n",
+ "\n",
+ "#At Mid-span\n",
+ "C1=853.333*4**-1\n",
+ "C2=53.333-2*C1\n",
+ "x=4\n",
+ "y_E=(C2+C1*x-20*3**-1*x**3+25*3**-1*(x-2)**3+5*3**-1*(x-6)**3)*(E*I)**-1\n",
+ "\n",
+ "#Answer For y_E is incorrect in textbook\n",
+ "\n",
+ "#At B\n",
+ "C1=853.333*4**-1\n",
+ "C2=53.333-2*C1\n",
+ "x=8\n",
+ "y_B=(C2+C1*x-20*3**-1*x**3+25*3**-1*(x-2)**3+5*3**-1*(x-6)**3)*(E*I)**-1\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Deflection relative to the level of the supports:at End A\",round(y_A,4),\"mm\"\n",
+ "print\" :at End B\",round(y_B,4),\"mm\"\n",
+ "print\" :at Centre of CD\",round(y_E,4),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Deflection relative to the level of the supports:at End A -0.08 mm\n",
+ " :at End B -0.0267 mm\n",
+ " :at Centre of CD 0.0107 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_06.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_06.ipynb new file mode 100644 index 00000000..61dcdcc2 --- /dev/null +++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_06.ipynb @@ -0,0 +1,1518 @@ +{
+ "metadata": {
+ "name": "chapter 06.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter No.6:Torsion"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.1,Page No.225"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=10000 #mm #Length of solid shaft\n",
+ "d=100 #mm #Diameter of shaft\n",
+ "n=150 #rpm\n",
+ "P=112.5*10**6 #N-mm/sec #Power Transmitted\n",
+ "G=82*10**3 #N/mm**2 #modulus of Rigidity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "J=pi*d**4*(32)**-1 #mm**3 #Polar Modulus\n",
+ "T=P*60*(2*pi*n)**-1 #N-mm #Torsional moment\n",
+ "\n",
+ "r=50 #mm #Radius\n",
+ "\n",
+ "q_s=T*r*J**-1 #N/mm**2 #Max shear stress intensity\n",
+ "Theta=T*L*(G*J)**-1 #angle of twist\n",
+ "\n",
+ "#Result\n",
+ "print\"Max shear stress intensity\",round(q_s,2),\"N/mm**2\"\n",
+ "print\"Angle of Twist\",round(Theta,3),\"radian\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max shear stress intensity 36.48 N/mm**2\n",
+ "Angle of Twist 0.089 radian\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.2,Page No.226"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=440*10**6 #N-m/sec #Power transmitted\n",
+ "n=280 #rpm\n",
+ "theta=pi*180**-1 #radian #angle of twist\n",
+ "L=1000 #mm #Length of solid shaft\n",
+ "q_s=40 #N/mm**2 #Max torsional shear stress\n",
+ "G=84*10**3 #N/mm**2 #Modulus of rigidity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#P=2*pi*n*T*(60)**-1 #Equation of Power transmitted\n",
+ "T=P*60*(2*pi*n)**-1 #N-mm #torsional moment\n",
+ "\n",
+ "#From Consideration of shear stress\n",
+ "d1=(T*16*(pi*40)**-1)**0.333333 \n",
+ "\n",
+ "#From Consideration of angle of twist\n",
+ "d2=(T*L*32*180*(pi*84*10**3*pi)**-1)**0.25\n",
+ "\n",
+ "#result\n",
+ "print\"Diameter of solid shaft is\",round(d1,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Diameter of solid shaft is 124.09 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.3,Page No.227"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "G=80*10**3 #N/mm**2 #Modulus of rigidity\n",
+ "q_s=80 #N/mm**2 #Max sheare stress\n",
+ "P=736*10**6 #N-mm/sec #Power transmitted\n",
+ "n=200\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "T=P*60*(2*pi*n)**-1 #N-mm #Torsional moment\n",
+ "\n",
+ "#Now From consideration of angle of twist\n",
+ "theta=pi*180**-1\n",
+ "#L=15*d\n",
+ "\n",
+ "d=(T*32*180*15*(pi**2*G)**-1)**0.33333\n",
+ "\n",
+ "#Now corresponding stress at the surface is\n",
+ "q_s2=T*32*d*(pi*2*d**4)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Max diameter required is\",round(d,2),\"mm\"\n",
+ "print\"Corresponding shear stress is\",round(q_s2,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max diameter required is 156.66 mm\n",
+ "Corresponding shear stress is 46.55 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.4,Page No.228"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=25 #mm #Diameter of steel bar\n",
+ "p=50*10**3 #N #Pull\n",
+ "dell_1=0.095 #mm #Extension of bar\n",
+ "l=200 #mm #Guage Length\n",
+ "T=200*10**3 #N-mm #Torsional moment\n",
+ "theta=0.9*pi*180**-1 #angle of twist\n",
+ "L=250 #mm Length of steel bar\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "A=pi*4**-1*d**2 #Area of steel bar #mm**2\n",
+ "E=p*l*(dell_1*A)**-1 #N/mm**2 #Modulus of elasticity \n",
+ "\n",
+ "J=pi*32**-1*d**4 #mm**4 #Polar modulus\n",
+ "\n",
+ "G=T*L*(theta*J)**-1 #Modulus of rigidity #N/mm**2\n",
+ "\n",
+ "#Now from the relation of Elastic constants\n",
+ "mu=E*(2*G)**-1-1\n",
+ "\n",
+ "#result\n",
+ "print\"The Poissoin's ratio is\",round(mu,3)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Poissoin's ratio is 0.292\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.5,Page No.229"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=6000 #mm #Length of circular shaft\n",
+ "d1=100 #mm #Outer Diameter\n",
+ "d2=75 #mm #Inner Diameter\n",
+ "R=100*2**-1 #Radius of shaft\n",
+ "T=10*10**6 #N-mm #Torsional moment\n",
+ "G=80*10**3 #N/mm**2 #Modulus of Rigidity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "J=pi*32**-1*(d1**4-d2**4) #mm**4 #Polar Modulus \n",
+ "\n",
+ "#Max Shear stress produced\n",
+ "q_s=T*R*J**-1 #N/mm**2\n",
+ "\n",
+ "#Angle of twist\n",
+ "theta=T*L*(G*J)**-1 #Radian\n",
+ "\n",
+ "#Result\n",
+ "print\"MAx shear stress produced is\",round(q_s,2),\"N/mm**2\"\n",
+ "print\"Angle of Twist is\",round(theta,2),\"Radian\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "MAx shear stress produced is 74.5 N/mm**2\n",
+ "Angle of Twist is 0.11 Radian\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.6,Page No.229"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d1=200 #mm #External Diameter of shaft\n",
+ "t=25 #mm #Thickness of shaft\n",
+ "n=200 #rpm\n",
+ "theta=0.5*pi*180**-1 #Radian #angle of twist\n",
+ "L=2000 #mm #Length of shaft\n",
+ "G=84*10**3 #N/mm**2\n",
+ "d2=d1-2*t #mm #Internal Diameter of shaft\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "J=pi*32**-1*(d1**4-d2**4) #mm**4 #Polar Modulus \n",
+ "\n",
+ "#Torsional moment\n",
+ "T=G*J*theta*L**-1 #N/mm**2 \n",
+ "\n",
+ "#Power Transmitted\n",
+ "P=2*pi*n*T*60**-1*10**-6 #N-mm\n",
+ "\n",
+ "#Max shear stress transmitted\n",
+ "q_s=G*theta*(d1*2**-1)*L**-1 #N/mm**2 \n",
+ "\n",
+ "#Result\n",
+ "print\"Power Transmitted is\",round(P,2),\"N-mm\"\n",
+ "print\"Max Shear stress produced is\",round(q_s,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power Transmitted is 824.28 N-mm\n",
+ "Max Shear stress produced is 36.65 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.7,Page No.230"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=3750*10**6 #N-mm/sec\n",
+ "n=240 #Rpm\n",
+ "q_s=160 #N/mm**2 #Max shear stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#d2=0.8*d2 #mm #Internal Diameter of shaft\n",
+ "\n",
+ "#J=pi*32**-1*(d1**4-d2**4) #mm**4 #Polar modulus\n",
+ "#After substituting value in above Equation we get\n",
+ "#J=0.05796*d1**4\n",
+ "\n",
+ "T=P*60*(2*pi*n)**-1 #N-mm #Torsional moment\n",
+ "\n",
+ "#Now from Torsion Formula\n",
+ "#T*J**-1=q_s*R**-1 ......................................(1)\n",
+ "\n",
+ "#But R=d1*2**-1 \n",
+ "\n",
+ "#Now substituting value of R and J in Equation (1) we get\n",
+ "d1=(T*(0.05796*q_s*2)**-1)**0.33333\n",
+ "\n",
+ "d2=d1*0.8\n",
+ "\n",
+ "#Result\n",
+ "print\"The size of the Shaft is:d1\",round(d1,3),\"mm\"\n",
+ "print\" :d2\",round(d2,3),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The size of the Shaft is:d1 200.362 mm\n",
+ " :d2 160.289 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.8,Page No.231"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=245*10**6 #N-mm/sec #Power transmitted\n",
+ "n=240 #rpm\n",
+ "q_s=40 #N/mm**2 #Shear stress\n",
+ "theta=pi*180**-1 #radian #Angle of twist\n",
+ "L=1000 #mm #Length of shaft\n",
+ "G=80*10**3 #N/mm**2\n",
+ "\n",
+ "#Tmax=1.5*T\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "T=P*60*(2*pi*n)**-1 #N-mm #Torsional Moment\n",
+ "Tmax=1.5*T\n",
+ "\n",
+ "#Now For Solid shaft\n",
+ "#J=pi*32*d**4\n",
+ "\n",
+ "#Now from the consideration of shear stress we get\n",
+ "#T*J**-1=q_s*(d*2**-1)**-1\n",
+ "#After substituting value in above Equation we get\n",
+ "#T=pi*16**-1*d**3*q_s\n",
+ "\n",
+ "#Designing For max Torque\n",
+ "d=(Tmax*16*(pi*40)**-1)**0.33333 #mm #Diameter of shaft\n",
+ "\n",
+ "#For max Angle of Twist\n",
+ "#Tmax*J**-1=G*theta*L**-1 \n",
+ "#After substituting value in above Equation we get\n",
+ "d2=(Tmax*32*180*L*(pi**2*G)**-1)**0.25\n",
+ "\n",
+ "#For Hollow Shaft\n",
+ "\n",
+ "#d1_2=Outer Diameter\n",
+ "#d2_2=Inner Diameter\n",
+ "\n",
+ "#d2_2=0.5*d1_2\n",
+ "\n",
+ "# Polar modulus\n",
+ "#J=pi*32**-1*(d1_2**4-d2_2**4)\n",
+ "#After substituting values we get\n",
+ "#J=0.092038*d1_2**4\n",
+ "\n",
+ "#Now from the consideration of stress\n",
+ "#Tmax*J**-1=q_s*(d1_2*2**-1)**-1\n",
+ "#After substituting values and further simplifying we get\n",
+ "d1_2=(Tmax*(0.092038*2*q_s)**-1)**0.33333\n",
+ "\n",
+ "#Now from the consideration of angle of twist\n",
+ "#Tmax*J**-1=G*theta*L**-1\n",
+ "#After substituting values and further simplifying we get\n",
+ "d1_3=(Tmax*180*L*(0.092038*G*pi)**-1)**0.25\n",
+ "\n",
+ "d2_2=0.5*d1_2\n",
+ "\n",
+ "#result\n",
+ "print\"Diameter of shaft is:For solid shaft:d\",round(d,2),\"mm\"\n",
+ "print\" :For Hollow shaft:d1_2\",round(d1_2,3),\"mm\"\n",
+ "print\" : :d2_2\",round(d2_2,3),\"mm\" "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Diameter of shaft is:For solid shaft:d 123.01 mm\n",
+ " :For Hollow shaft:d1_2 125.69 mm\n",
+ " : :d2_2 62.845 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.11,Page No.235"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=250*10**6 #N-mm/sec #Power transmitted\n",
+ "n=100 #rpm\n",
+ "q_s=75 #N/mm**2 #Shear stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#From Equation of Power we have\n",
+ "T=P*60*(2*pi*n)**-1 #N-mm #Torsional moment\n",
+ "\n",
+ "#Now from torsional moment equation we have\n",
+ "#T=j*q_s*(d/2**-1)**-1\n",
+ "#After substituting values in above equation and further simplifying we get\n",
+ "#T=pi*16**-1**d**3*q_s\n",
+ "d=(T*16*(pi*q_s)**-1)**0.3333 #mm #Diameter of solid shaft\n",
+ "\n",
+ "#PArt-2\n",
+ "\n",
+ "#Let d1 and d2 be the outer and inner diameter of hollow shaft\n",
+ "#d2=0.6*d1\n",
+ "\n",
+ "#Again from torsional moment equation we have\n",
+ "#T=pi*32**-1*(d1**4-d2**4)*q_s*(d1/2)**-1\n",
+ "d1=(T*16*(pi*(1-0.6**4)*q_s)**-1)**0.33333\n",
+ "d2=0.6*d1\n",
+ "\n",
+ "#Cross sectional area of solid shaft\n",
+ "A1=pi*4**-1*d**2 #mm**2\n",
+ "\n",
+ "#cross sectional area of hollow shaft\n",
+ "A2=pi*4**-1*(d1**2-d2**2)\n",
+ "\n",
+ "#Now percentage saving in weight\n",
+ "#Let W be the percentage saving in weight\n",
+ "W=(A1-A2)*100*A1**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Percentage saving in Weight is\",round(W,3),\"%\"\n",
+ "print\"Size of shaft is:solid shaft:d\",round(d,3),\"mm\"\n",
+ "print\" :Hollow shaft:d1\",round(d1,3),\"mm\"\n",
+ "print\" : :d2\",round(d2,3),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Percentage saving in Weight is 29.735 %\n",
+ "Size of shaft is:solid shaft:d 117.418 mm\n",
+ " :Hollow shaft:d1 123.031 mm\n",
+ " : :d2 73.818 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.12,Page No.237"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "d=100 #mm #Diameter of solid shaft\n",
+ "d1=100 #mm #Outer Diameter of hollow shaft\n",
+ "d2=50 #mm #Inner Diameter of hollow shaft\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Torsional moment of solid shaft\n",
+ "#T_s=J*q_s*(d*2**-1)**-1 \n",
+ "#After substituting values in above equation and further simplifying we get\n",
+ "#T_s=pi*16*d**3*q_s ...............(1)\n",
+ "\n",
+ "#torsional moment for hollow shaft is\n",
+ "#T_h=J*q_s*(d1**4-d2**4)**-1*(d1*2**-1)\n",
+ "#After substituting values in above equation and further simplifying we get\n",
+ "#T_h=pi*32**-1*2*d1**-1*(d1**4-d2**4)*q_s ...........(2)\n",
+ "\n",
+ "#Dividing Equation 2 by 1 we get\n",
+ "#Let the ratio of T_h*T_s**-1 Be X\n",
+ "X=1-0.5**4\n",
+ "\n",
+ "#Loss in strength \n",
+ "#Let s be the loss in strength\n",
+ "#s=T_s*T_h*100*T_s**-1\n",
+ "#After substituting values in above equation and further simplifying we get\n",
+ "s=(1-0.9375)*100\n",
+ "\n",
+ "#Weight Ratio \n",
+ "#Let w be the Weight ratio\n",
+ "#w=W_h*W_s**-1\n",
+ "\n",
+ "A_h=pi*32**-1*(d1**2-d2**2) #mm**2 #Area of Hollow shaft\n",
+ "A_s=pi*32**-1*d**2 #mm**2 #Area of solid shaft\n",
+ "\n",
+ "w=A_h*A_s**-1 \n",
+ "\n",
+ "#Result\n",
+ "print\"Loss in strength is\",round(s,2)\n",
+ "print\"Weight ratio is\",round(w,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Loss in strength is 6.25\n",
+ "Weight ratio is 0.75\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.13,Page No.239"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "T=8 #KN-m #Torque \n",
+ "d=100 #mm #Diameter of portion AB\n",
+ "d1=100 #mm #External Diameter of Portion BC\n",
+ "d2=75 #mm #Internal Diameter of Portion BC\n",
+ "G=80 #KN/mm**2 #Modulus of Rigidity\n",
+ "L1=1500 #mm #Radial Distance of Portion AB\n",
+ "L2=2500 #mm #Radial Distance ofPortion BC\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "R=d*2**-1 #mm #Radius of shaft\n",
+ "\n",
+ "#For Portion AB,Polar Modulus\n",
+ "J1=pi*32**-1*d**4 #mm**4 \n",
+ "\n",
+ "#For Portion BC,Polar modulus \n",
+ "J2=pi*32**-1*(d1**4-d2**4) #mm**4\n",
+ "\n",
+ "#Now Max stress occurs in portion BC since max radial Distance is sme in both cases\n",
+ "q_max=T*J2**-1*R*10**6 #N/mm**2 \n",
+ "\n",
+ "#Let theta1 be the rotation in Portion AB and theta2 be the rotation in portion BC\n",
+ "theta1=T*L1*(G*J1)**-1 #Radians\n",
+ "theta2=T*L2*(G*J2)**-1 #Radians\n",
+ "\n",
+ "#Total Rotational at end C\n",
+ "theta=(theta1+theta2)*10**3 #Radians\n",
+ "\n",
+ "#Result\n",
+ "print\"Max stress induced is\",round(q_max,2),\"N/mm**2\"\n",
+ "print\"Angle of Twist is\",round(theta,3),\"radians\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max stress induced is 59.6 N/mm**2\n",
+ "Angle of Twist is 0.053 radians\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.14,Page No.240"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "q_b=80 #N/mm**2 #Shear stress in Brass\n",
+ "q_s=100 #N/mm**2 #Shear stress in Steel\n",
+ "G_b=40*10**3 #N/mm**2 \n",
+ "G_s=80*10**3 \n",
+ "L_b=1000 #mm #Length of brass shaft\n",
+ "L_s=1200 #mm #Length of steel shaft\n",
+ "d1=80 #mm #Diameter of brass shaft\n",
+ "d2=60 #mm #Diameter of steel shaft\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Polar modulus of brass rod\n",
+ "J_b=pi*32**-1*d1**4 #mm**4 \n",
+ "\n",
+ "#Polar modulus of steel rod\n",
+ "J_s=pi*32**-1*d2**4 #mm**4\n",
+ "\n",
+ "#Considering bras Rod:AB\n",
+ "T1=J_b*q_b*(d1*2**-1)**-1 #N-mm \n",
+ "\n",
+ "#Considering Steel Rod:BC\n",
+ "T2=J_s*q_s*(d2*2**-1)**-1 #N-mm\n",
+ "\n",
+ "#Max Torque that can be applied\n",
+ "T2\n",
+ "\n",
+ "#Let theta_b and theta_s be the rotations in Brass and steel respectively\n",
+ "theta_b=T2*L_b*(G_b*J_b)**-1 #Radians\n",
+ "theta_s=T2*L_s*(G_s*J_s)**-1 #Radians\n",
+ "\n",
+ "theta=theta_b+theta_s #Radians #Rotation of free end\n",
+ "\n",
+ "#Result\n",
+ "print\"Total of free end is\",round(theta,3),\"Radians\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total of free end is 0.076 Radians\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.15,Page No.241"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "G=80*10**3 #N/mm**2 #Modulus of Rigidity\n",
+ "d1=100 #mm #Outer diameter of hollow shft\n",
+ "d2=80 #mm #Inner diameter of hollow shaft\n",
+ "d=80 #mm #diameter of Solid shaft\n",
+ "d3=60 #mm #diameter of Solid shaft having L=0.5m\n",
+ "L1=300 #mm #Length of Hollow shaft\n",
+ "L2=400 #mm #Length of solid shaft\n",
+ "L3=500 #mm #LEngth of solid shaft of diameter 60mm\n",
+ "T1=2*10**6 #N-mm #Torsion in Shaft AB\n",
+ "T2=1*10**6 #N-mm #Torsion in shaft BC\n",
+ "T3=1*10**6 #N-mm #Torsion in shaft CD\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Now Polar modulus of section AB\n",
+ "J1=pi*32**-1*(d1**4-d2**4) #mm**4 \n",
+ "\n",
+ "#Polar modulus of section BC\n",
+ "J2=pi*32**-1*d**4 #mm**4\n",
+ "\n",
+ "#Polar modulus of section CD\n",
+ "J3=pi*32**-1*d3**4 #mm**4\n",
+ "\n",
+ "#Now angle of twist of AB\n",
+ "theta1=T1*L1*(G*J1)**-1 #radians\n",
+ "\n",
+ "#Angle of twist of BC\n",
+ "theta2=T2*L2*(G*J2)**-1 #radians\n",
+ "\n",
+ "#Angle of twist of CD\n",
+ "theta3=T3*L3*(G*J3)**-1 #radians\n",
+ "\n",
+ "#Angle of twist\n",
+ "theta=theta1-theta2+theta3 #Radians\n",
+ "\n",
+ "#Shear stress in AB From Torsion Equation\n",
+ "q_s1=T1*(d1*2**-1)*J1**-1 #N/mm**2 \n",
+ "\n",
+ "#Shear stress in BC\n",
+ "q_s2=T2*(d*2**-1)*J2**-1 #N/mm**2 \n",
+ "\n",
+ "#Shear stress in CD\n",
+ "q_s3=T3*(d3*2**-1)*J3**-1 #N-mm**2\n",
+ "\n",
+ "#As max shear stress occurs in portion CD,so consider CD\n",
+ "\n",
+ "#Result\n",
+ "print\"Angle of twist at free end is\",round(theta,5),\"Radian\"\n",
+ "print\"Max Shear stress\",round(q_s3,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angle of twist at free end is 0.00496 Radian\n",
+ "Max Shear stress 23.58 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.16,Page No.242"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=1000 #mm #Length of bar\n",
+ "L1=600 #mm #Length of Bar AB\n",
+ "L2=400 #mm #Length of Bar BC\n",
+ "d1=60 #mm #Outer Diameter of bar BC\n",
+ "d2=30 #mm #Inner Diameter of bar BC\n",
+ "d=60 #mm #Diameter of bar AB\n",
+ "T=2*10**6 #N-mm #Total Torque\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Polar Modulus of Portion AB\n",
+ "J1=pi*32**-1*d**4 #mm*4\n",
+ "\n",
+ "#Polar Modulus of Portion BC\n",
+ "J2=pi*32**-1*(d1**4-d2**4) #mm**4\n",
+ "\n",
+ "#Let T1 be the torque resisted by bar AB and T2 be torque resisted by Bar BC\n",
+ "#Let theta1 and theta2 be the rotation of shaft in portion AB & BC\n",
+ "\n",
+ "#theta1=T1*L1*(G*J1)**-1 #radians\n",
+ "#After substituting values and further simplifying we get \n",
+ "#theta1=32*600*T1*(pi*60**4*G)**-1\n",
+ "\n",
+ "#theta2=T2*L*(J2*G)**-1 #Radians\n",
+ "#After substituting values and further simplifying we get \n",
+ "#theta2=32*400*T2*(pi*60**4*(1-0.5**4)*G)**-1 \n",
+ "\n",
+ "#Now For consistency of Deformation,theta1=theta2\n",
+ "#After substituting values and further simplifying we get \n",
+ "#T1=0.7111*T2 ..................................................(1)\n",
+ "\n",
+ "#But T1+T2=T=2*10**6 ...........................................(2)\n",
+ "#Substituting value of T1 in above equation\n",
+ "\n",
+ "T2=T*(0.7111+1)**-1\n",
+ "T1=0.71111*T2\n",
+ "\n",
+ "#Max stress in Portion AB\n",
+ "q_s1=T1*(d*2**-1)*(J1)**-1 #N/mm**2\n",
+ "\n",
+ "#Max stress in Portion BC\n",
+ "q_s2=T2*(d1*2**-1)*J2**-1 #N/mm**2 \n",
+ "\n",
+ "#Result\n",
+ "print\"Stresses Developed in Portion:AB\",round(q_s1,2),\"N/mm**2\"\n",
+ "print\" :BC\",round(q_s2,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stresses Developed in Portion:AB 19.6 N/mm**2\n",
+ " :BC 29.4 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.17,Page No.243"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d1=80 #mm #External Diameter of Brass tube\n",
+ "d2=50 #mm #Internal Diameter of Brass tube\n",
+ "d=50 #mm #Diameter of steel Tube\n",
+ "G_b=40*10**3 #N/mm**2 #Modulus of Rigidity of brass tube\n",
+ "G_s=80*10**3 #N/mm**2 #Modulus of rigidity of steel tube\n",
+ "T=6*10**6 #N-mm #Torque\n",
+ "L=2000 #mm #Length of Tube\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Polar Modulus of brass tube\n",
+ "J1=pi*32**-1*(d1**4-d2**4) #mm**4 \n",
+ "\n",
+ "#Polar modulus of steel Tube\n",
+ "J2=pi*32**-1*d**4 #mm**4\n",
+ "\n",
+ "#Let T_s & T_b be the torque resisted by steel and brass respectively\n",
+ "#Then, T_b+T_s=T ............................................(1)\n",
+ "\n",
+ "#Since the angle of twist will be the same\n",
+ "#Theta1=Theta2\n",
+ "#After substituting values and further simplifying we get \n",
+ "#Ts=0.360*Tb ...........................................(2)\n",
+ "\n",
+ "#After substituting value of Ts in eqn 1 and further simplifying we get \n",
+ "T_b=T*(0.36+1)**-1 #N-mm\n",
+ "T_s=0.360*T_b\n",
+ "\n",
+ "#Let q_s and q_b be the max stress in steel and brass respectively\n",
+ "q_b=T_b*(d1*2**-1)*J1**-1 #N/mm**2\n",
+ "q_s=T_s*(d2*2**-1)*J2**-1 #N/mm**2\n",
+ "\n",
+ "#Since angle of twist in brass=angle of twist in steel\n",
+ "theta_s=T_s*L*(J2*G_s)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Stresses Developed in Materials are:Brass\",round(q_b,2),\"N/mm**2\"\n",
+ "print\" :Steel\",round(q_s,2),\"N/mm**2\"\n",
+ "print\"Angle of Twist in 2m Length\",round(theta_s,3),\"Radians\" "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stresses Developed in Materials are:Brass 51.79 N/mm**2\n",
+ " :Steel 64.71 N/mm**2\n",
+ "Angle of Twist in 2m Length 0.065 Radians\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.18,Page No.245"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d1=60 #mm #External Diameter of aluminium Tube\n",
+ "d2=40 #mm #Internal Diameter of aluminium Tube\n",
+ "d=40 #mm #Diameter of steel tube\n",
+ "q_a=60 #N/mm**2 #Permissible stress in aluminium\n",
+ "q_s=100 #N/mm**2 #Permissible stress in steel tube\n",
+ "G_a=27*10**3 #N/mm**2 \n",
+ "G_s=80*10**3 #N/mm**2 \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Polar modulus of aluminium Tube\n",
+ "J_a=pi*32**-1*(d1**4-d2**4) #mm**4\n",
+ "\n",
+ "#Polar Modulus of steel Tube\n",
+ "J_s=pi*32**-1*d**4 #mm**4\n",
+ "\n",
+ "#Now the angle of twist of steel tube = angle of twist of aluminium tube\n",
+ "#T_s*L_s*(J_s*theta_s)**-1=T_a*L_a*(J_a*theta_a)**-1\n",
+ "#After substituting values in above Equation and Further simplifyin we get\n",
+ "#T_s=0.7293*T_a .....................(1)\n",
+ "\n",
+ "#If steel Governs the resisting capacity\n",
+ "T_s1=q_s*J_s*(d*2**-1)**-1 #N-mm\n",
+ "T_a1=T_s1*0.7293**-1 #N-mm\n",
+ "T1=(T_s1+T_a1)*10**-6 #KN-m #Total Torque in steel Tube\n",
+ "\n",
+ "#If aluminium Governs the resisting capacity \n",
+ "T_a2=q_a*J_a*(d1*2**-1) #N-mm\n",
+ "T_s2=T_a2*0.7293 #N-mm\n",
+ "T2=(T_s2+T_a2)*10**-6 #KN-m #Total Torque in aluminium tube\n",
+ "\n",
+ "#Result\n",
+ "print\"Steel Governs the torque carrying capacity\",round(T1,2),\"KN-m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Steel Governs the torque carrying capacity 2.98 KN-m\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.19,Page No.247"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P=225*10**6 #N-mm/sec #Power Trasmitted\n",
+ "q_b=80 #N/mm**2 #Shear stress\n",
+ "n=200 #Rpm\n",
+ "q_k=100 #N/mm**2 #PErmissible stress in Keys\n",
+ "D=300 #mm #Diameter of bolt circle\n",
+ "L=150 #mm #Length of shear key\n",
+ "d=16 #mm #Diameterr of bolt\n",
+ "\n",
+ "#Calculations\n",
+ "T=60*P*(2*pi*n)**-1 #N-mm #Torque\n",
+ "\n",
+ "#Now From Torsion Formula\n",
+ "#T*J**-1=q_s*R**-1\n",
+ "#After substituting values we get\n",
+ "#T=pi*16*d**3*n\n",
+ "#After further simplifying we get\n",
+ "d1=(T*16*(pi*q_s)**-1)**0.33333\n",
+ "\n",
+ "#Let b be the width of shear Key\n",
+ "#T=q_k*L*b*R\n",
+ "#After simplifying further we get\n",
+ "b=T*(q_k*L*(d1*2**-1))**-1 #mm\n",
+ "\n",
+ "#Let n2 be the no. of bolts required at bolt circle of radius\n",
+ "R_b=D*2**-1 #mm \n",
+ "\n",
+ "n2=T*4*(q_b*pi*d**2*R_b)**-1\n",
+ "\n",
+ "#result\n",
+ "print\"Minimum no. of Bolts Required are\",round(n2,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Minimum no. of Bolts Required are 4.45\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.20,Page No.250"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "T=2*10**6 #N-mm #Torque transmitted\n",
+ "G=80*10**3 #N/mm**2 #Modulus of rigidity\n",
+ "d1=40 #mm \n",
+ "d2=80 #mm\n",
+ "r1=20 #mm\n",
+ "r2=40 #mm\n",
+ "L=2000 #mm #Length of shaft\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Angle of twist \n",
+ "theta=2*T*L*(r1**2+r1*r2+r2**2)*(3*pi*G*r2**3*r1**3)**-1 #radians\n",
+ "\n",
+ "#If the shaft is treated as shaft of average Diameter\n",
+ "d_avg=(d1+d2)*2**-1 #mm\n",
+ "\n",
+ "theta1=T*L*(G*pi*32**-1*d_avg**4)**-1 #Radians\n",
+ "\n",
+ "#Percentage Error\n",
+ "#Let Percentage Error be E\n",
+ "X=theta-theta1\n",
+ "E=(X*theta**-1)*100 \n",
+ "\n",
+ "#Result\n",
+ "print\"Percentage Error is\",round(E,2),\"%\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Percentage Error is 32.28 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 42
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.21,Page No.252"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "G=80*10**3 #N/mm**2 \n",
+ "P=1*10**9 #N-mm/sec #Power\n",
+ "n=300 \n",
+ "d1=150 #mm #Outer Diameter\n",
+ "d2=120 #mm #Inner Diameter\n",
+ "L=2000 #mm #Length of circular shaft\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "T=P*60*(2*pi*n)**-1 #N-mm\n",
+ "\n",
+ "#Polar Modulus \n",
+ "J=pi*32**-1*(d1**4-d2**4) #mm**4\n",
+ "\n",
+ "q_s=T*J**-1*(d1*2**-1) #N/mm**2 \n",
+ "\n",
+ "\n",
+ "#Strain ENergy\n",
+ "U=q_s**2*(4*G)**-1*pi*4**-1*(d1**2-d2**2)*L\n",
+ "\n",
+ "#Result\n",
+ "print\"Max shear stress is\",round(q_s,2),\"N/mm**2\"\n",
+ "print\"Strain Energy stored in the shaft is\",round(U,2),\"N-mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max shear stress is 81.36 N/mm**2\n",
+ "Strain Energy stored in the shaft is 263181.37 N-mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 51
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.22,Page No.254"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=12 #mm #Diameter of helical spring\n",
+ "D=150 #mm #Mean Diameter\n",
+ "R=D*2**-1 #mm #Radius of helical spring\n",
+ "n=10 #no.of turns\n",
+ "G=80*10**3 #N/mm**2 \n",
+ "W=450 #N #Load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Max shear stress \n",
+ "q_s=16*W*R*(pi*d**3)**-1 #N/mm**2\n",
+ "\n",
+ "#Strain Energy stored\n",
+ "U=32*W**2*R**3*n*(G*d**4)**-1 #N-mm\n",
+ "\n",
+ "#Deflection Produced\n",
+ "dell=64*W*R**3*n*(G*d**4)**-1 #mm\n",
+ "\n",
+ "#Stiffness Spring\n",
+ "k=W*dell**-1 #N/mm\n",
+ "\n",
+ "#Result\n",
+ "print\"Max shear stress is\",round(q_s,2),\"N/mm**2\"\n",
+ "print\"Strain Energy stored is\",round(U,2),\"N-mm\"\n",
+ "print\"Deflection Produced is\",round(dell,2),\"mm\"\n",
+ "print\"Stiffness spring is\",round(k,2),\"N/mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max shear stress is 99.47 N/mm**2\n",
+ "Strain Energy stored is 16479.49 N-mm\n",
+ "Deflection Produced is 73.24 mm\n",
+ "Stiffness spring is 6.14 N/mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 53
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.23,Page No.255"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "K=5 #N/mm #Stiffness\n",
+ "L=100 #mm #Solid Length\n",
+ "q_s=60 #N/mm**2 #Max shear stress\n",
+ "W=200 #N #Max Load\n",
+ "G=80*10**3 #N/mm**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#K=W*dell**-1\n",
+ "#After substituting values and further simplifying we get\n",
+ "#d=0.004*R**3*n ........(1) #mm #Diameter of wire\n",
+ "#n=L*d**-1 ........(2)\n",
+ "\n",
+ "#From Shearing stress\n",
+ "#q_s=16*W*R*(pi*d**3)**-1 \n",
+ "#After substituting values and further simplifying we get\n",
+ "#d**4=0.004*R**3*n .................(4)\n",
+ "\n",
+ "#From Equation 1,2,3\n",
+ "#d**4=0.004*(0.0785*d**3)**3*100*d**-1\n",
+ "#after further simplifying we get\n",
+ "d=5168.101**0.25\n",
+ "n=100*d**-1\n",
+ "R=(d**4*(0.004*n)**-1)**0.3333\n",
+ "\n",
+ "#Result\n",
+ "print\"Diameter of Wire is\",round(d,2),\"mm\"\n",
+ "print\"No.of turns is\",round(n,2)\n",
+ "print\"Mean Radius of spring is\",round(R,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Diameter of Wire is 8.48 mm\n",
+ "No.fo turns is 11.79\n",
+ "Mean Radius of spring is 47.83 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 54
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.24,Page No.255"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "m=5*10**5 #Wagon Weighing\n",
+ "v=18*1000*36000**-1 \n",
+ "d=300 #mm #Diameter of Beffer springs\n",
+ "n=18 #no.of turns\n",
+ "G=80*10**3 #N/mm**2\n",
+ "dell=225\n",
+ "R=100 #mm #Mean Radius\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Energy of Wagon\n",
+ "E=m*v**2*(9.81*2)**-1 #N-mm\n",
+ "\n",
+ "#Load applied\n",
+ "W=dell*G*d**4*(64*R**3*n)**-1 #N \n",
+ "\n",
+ "#Energy each spring can absorb is\n",
+ "E2=W*dell*2**-1 #N-mm\n",
+ "\n",
+ "#No.of springs required to absorb energy of Wagon\n",
+ "n2=E*E2**-1 *10**7\n",
+ "\n",
+ "#Result\n",
+ "print\"No.of springs Required for Buffer is\",round(n2,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "No.of springs Required for Buffer is 4.47\n"
+ ]
+ }
+ ],
+ "prompt_number": 66
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.25,Page No.259"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "b=180 #mm #width of flange\n",
+ "d=10 #mm #Depth of flange\n",
+ "t=10 #mm #Thickness of flange\n",
+ "D=400 #mm #Overall Depth \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "I_xx=1*12**-1*(b*D**3-(b-t)*(D-2*d)**3)\n",
+ "I_yy=1*12**-1*((D-2*d)*t**3+2*t*b**3)\n",
+ "\n",
+ "#If warping is neglected\n",
+ "J=I_xx+I_yy #mm**4\n",
+ "\n",
+ "#Since b/d>1.6,we get\n",
+ "J2=1*3**-1*d**3*b*(1-0.63*d*b**-1)*2+1*3**-1*t**3*(D-2*d)*(1-0.63*t*b**-1)\n",
+ "\n",
+ "#Over Estimation of torsional Rigidity would have been \n",
+ "T=J*J2**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Error in assessing torsional Rigidity if the warping is neglected is\",round(T,2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Error in assessing torsional Rigidity if the warping is neglected is 808.28\n"
+ ]
+ }
+ ],
+ "prompt_number": 68
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6.26,Page No.261"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d1=100 #mm #Outer Diameter\n",
+ "d2=95 #mm #Inner Diameter\n",
+ "T=2*10**6 #N-mm #Torque\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "J=pi*32**-1*(d1**4-d2**4) #mm**4 #Polar Modulus\n",
+ "\n",
+ "#Shear stress\n",
+ "q_max=T*J**-1*d1*2**-1 #N/mm**2 \n",
+ "\n",
+ "#Now theta*L**-1=T*(G*J)**-1\n",
+ "#After substituting values and further simplifying we get\n",
+ "#Let theta*L**-1=X\n",
+ "X=T*J**-1\n",
+ "\n",
+ "#Now Treating it as very thin walled tube\n",
+ "d=(d1+d2)*2**-1 #mm\n",
+ "\n",
+ "r=d*2**-1 \n",
+ "t=(d1-d2)*2**-1\n",
+ "q_max2=T*(2*pi*r**2*t)**-1 #N/mm**2\n",
+ "\n",
+ "X2=T*(2*pi*r**3*t)**-1 \n",
+ "\n",
+ "#Result\n",
+ "print\"When it is treated as hollow shaft:Max shear stress\",round(q_max,2),\"N/mm**2\"\n",
+ "print\" :Angle of Twist per unit Length\",round(X,3)\n",
+ "print\"When it is very thin Walled Tube :Max shear stress\",round(q_max2,2),\"N/mm**2\"\n",
+ "print\" :Angle of twist per Unit Length\",round(X2,3)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "When it is treated as hollow shaft:Max shear stress 54.91 N/mm**2\n",
+ " :Angle of Twist per unit Length 1.098\n",
+ "When it is very thin Walled Tube :Max shear stress 53.57 N/mm**2\n",
+ " :Angle of twist per Unit Length 1.099\n"
+ ]
+ }
+ ],
+ "prompt_number": 72
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_07.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_07.ipynb new file mode 100644 index 00000000..3d27c2e5 --- /dev/null +++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_07.ipynb @@ -0,0 +1,1328 @@ +{
+ "metadata": {
+ "name": "chapter 07.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter No.7:Compound Stresses And Strains"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.1,Page No.269"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "sigma1=30 #N/mm**2 #Stress in tension\n",
+ "d=20 #mm #Diameter \n",
+ "sigma2=90 #N/mm**2 #Max compressive stress\n",
+ "sigma3=25 #N/mm**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#In TEnsion\n",
+ "\n",
+ "#Corresponding stress in shear\n",
+ "P=sigma1*2**-1 #N/mm**2\n",
+ "\n",
+ "#Tensile force\n",
+ "F=pi*4**-1*d**2*sigma1\n",
+ "\n",
+ "#In Compression\n",
+ "\n",
+ "#Correspong shear stress\n",
+ "P2=sigma2*2**-1 #N/mm**2\n",
+ "\n",
+ "#Correspong compressive(axial) stress\n",
+ "p=2*sigma3 #N/mm**2 \n",
+ "\n",
+ "#Corresponding Compressive force\n",
+ "P3=p*pi*4**-1*d**2 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Failure Loads are:\",round(F,2),\"N\"\n",
+ "print\" :\",round(P3,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Failure Loads are: 9424.78 N\n",
+ " : 15707.96 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.2,Page No.270"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=25 #mm #Diameter of circular bar\n",
+ "F=20*10**3 #N #Axial Force\n",
+ "theta=30 #Degree #angle \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Axial stresses\n",
+ "p=F*(pi*4**-1*d**2)**-1 #N/mm**2\n",
+ "\n",
+ "#Normal Stress\n",
+ "p_n=p*(cos(30*pi*180**-1))**2\n",
+ "\n",
+ "#Tangential Stress\n",
+ "p_t=p*2**-1*sin(2*theta*pi*180**-1)\n",
+ "\n",
+ "#Max shear stress occurs on plane where theta2=45 \n",
+ "theta2=45\n",
+ "sigma_max=p*2**-1*sin(2*theta2*pi*180**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Stresses developed on a plane making 30 degree is:\",round(p_n,2),\"N/mm**2\"\n",
+ "print\" :\",round(p_t,2),\"N/mm**2\"\n",
+ "print\"stress on max shear stress is\",round(sigma_max,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stresses developed on a plane making 30 degree is: 30.56 N/mm**2\n",
+ " : 17.64 N/mm**2\n",
+ "stress on max shear stress is 20.37 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 38
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.3,Page No.272"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "theta=30 #degree\n",
+ "\n",
+ "#Stresses acting on material\n",
+ "p1=120 #N/mm**2\n",
+ "p2=80 #N/mm**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Normal Stress\n",
+ "P_n=(p1+p2)*2**-1+(p1-p2)*2**-1*cos(2*theta*pi*180**-1) #N/mm**2\n",
+ "\n",
+ "#Tangential stress\n",
+ "P_t=(p1-p2)*2**-1*sin(2*theta*pi*180**-1)\n",
+ "\n",
+ "#Resultant stress\n",
+ "P=(P_n**2+P_t**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Inclination to the plane\n",
+ "phi=arctan(P_n*P_t**-1)*(180*pi**-1)\n",
+ "\n",
+ "#Angle made by resultant with 120 #N/mm**2 stress\n",
+ "phi2=phi+theta #Degree\n",
+ "\n",
+ "#Result\n",
+ "print\"Normal Stress is\",round(P_n,2),\"N/mm**2\"\n",
+ "print\"Tangential Stress is\",round(P_t,2),\"N/mm**2\"\n",
+ "print\"Angle made by resultant\",round(phi2,2),\"Degree\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Normal Stress is 110.0 N/mm**2\n",
+ "Tangential Stress is 17.32 N/mm**2\n",
+ "Angle made by resultant 111.05 Degree\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.4,Page No.272"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Direct Stresses\n",
+ "P1=60 #N/mm**2 \n",
+ "P2=100 #N/mm**2\n",
+ "\n",
+ "Theta=25 #Degree #Angle\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Normal Stress\n",
+ "P_n=(P1-P2)*2**-1+(P1+P2)*2**-1*cos(2*Theta*pi*180**-1) #N/mm**2\n",
+ "\n",
+ "#Tangential Stress\n",
+ "P_t=(P1+P2)*2**-1*sin(Theta*2*pi*180**-1) #N/mm**2\n",
+ "\n",
+ "#Resultant stress\n",
+ "P=(P_n**2+P_t**2)**0.5 #N/mm**2\n",
+ "\n",
+ "theta2=arctan(P_n*P_t**-1)*(180*pi**-1)\n",
+ "\n",
+ "#Result\n",
+ "print\"Stresses on the plane AC is:\",round(P_n,2),\"N/mm**2\"\n",
+ "print\" \",round(P_t,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stresses on the plane AC is: 31.42 N/mm**2\n",
+ " 61.28 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.6,Page No.278"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Stresses acting on material\n",
+ "p_x=180 #N/mm**2 \n",
+ "p_y=120 #N/mm**2\n",
+ "\n",
+ "q=80 #N/mm**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "theta=arctan(2*q*(p_x-p_y)**-1)*(180*pi**-1) #degrees\n",
+ "theta2=theta*2**-1 #Degrees\n",
+ "theta3=theta+180 #Degrees\n",
+ "theta4=theta3*2**-1 #Degrees\n",
+ "\n",
+ "#Stresses\n",
+ "p_1=(p_x+p_y)*2**-1+(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "p_2=(p_x+p_y)*2**-1-(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Max shear stress\n",
+ "q_max=(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of Principal stress is:\",round(p_1,2),\"N/mm**2\"\n",
+ "print\" \",round(p_2,2),\"N/mm**2\"\n",
+ "print\"Magnitude of max shear stress is\",round(q_max,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of Principal stress is: 235.44 N/mm**2\n",
+ " 64.56 N/mm**2\n",
+ "Magnitude of max shear stress is 85.44 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 40
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.7,Page No.279"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#stresses\n",
+ "p_x=60 #N/mm**2\n",
+ "p_y=-40 #N/mm**2\n",
+ "\n",
+ "q=10 #N/mm**2 #shear stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Principal Stresses\n",
+ "p1=(p_x+p_y)*2**-1+(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "p2=(p_x+p_y)*2**-1-(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Max shear stress\n",
+ "q_max=(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Inclination of principal stress to plane\n",
+ "theta=arctan(2*q*(p_x-p_y)**-1)*(180*pi**-1)#Degrees\n",
+ "theta2=(theta)*2**-1 #degrees\n",
+ "\n",
+ "theta3=(theta+180)*2**-1 #degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Principal Stresses are:\",round(p1,2),\"N/mm**2\"\n",
+ "print\" :\",round(p2,2),\"N/mm**2\"\n",
+ "print\"Max shear stresses\",round(q_max,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Principal Stresses are: 60.99 N/mm**2\n",
+ " : -40.99 N/mm**2\n",
+ "Max shear stresses 50.99 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.8,Page No.280"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#stresses\n",
+ "p_x=-120 #N/mm**2\n",
+ "p_y=-80 #N/mm**2\n",
+ "\n",
+ "q=-60 #N/mm**2 #shear stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Principal Stresses\n",
+ "p1=(p_x+p_y)*2**-1+(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "p2=(p_x+p_y)*2**-1-(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Max shear stress\n",
+ "q_max=(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Inclination of principal stress to plane\n",
+ "theta=arctan(2*q*(p_x-p_y)**-1)*(180*pi**-1)#Degrees\n",
+ "theta2=(theta)*2**-1 #degrees\n",
+ "\n",
+ "theta3=(theta+180)*2**-1 #degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Principal Stresses are:\",round(p1,2),\"N/mm**2\"\n",
+ "print\" :\",round(p2,2),\"N/mm**2\"\n",
+ "print\"Max shear stresses\",round(q_max,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Principal Stresses are: -36.75 N/mm**2\n",
+ " : -163.25 N/mm**2\n",
+ "Max shear stresses 63.25 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.9,Page No.282"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#stresses\n",
+ "p_x=-40 #N/mm**2\n",
+ "p_y=80 #N/mm**2\n",
+ "\n",
+ "q=48 #N/mm**2 #shear stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Max shear stress\n",
+ "q_max=((((p_x-p_y)*2**-1)**2)+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Inclination of principal stress to plane\n",
+ "theta=arctan(2*q*(p_x-p_y)**-1)*(180*pi**-1)#Degrees\n",
+ "theta2=(theta)*2**-1 #degrees\n",
+ "\n",
+ "theta3=(theta+180)*2**-1 #degrees\n",
+ "\n",
+ "#Normal Corresponding stress\n",
+ "p_n=(p_x+p_y)*2**-1+(p_x-p_y)*2**-1*cos(2*(theta2+45)*pi*180**-1)+q*sin(2*(theta2+45)*pi*180**-1) #Degrees\n",
+ "\n",
+ "#Resultant stress\n",
+ "p=((p_n**2+q_max**2)**0.5) #N/mm**2\n",
+ "\n",
+ "phi=arctan(p_n*q_max**-1)*(180*pi**-1) #Degrees\n",
+ "\n",
+ "#Inclination to the plane\n",
+ "alpha=round((theta2+45),2)+round(phi ,2)#Degree\n",
+ "\n",
+ "#Answer in book is incorrect of alpha ie41.25\n",
+ "\n",
+ "#Result\n",
+ "print\"Planes of max shear stress:\",round(p_n,2),\"N/mm**2\"\n",
+ "print\" \",round(q_max,2),\"N/mm*2\"\n",
+ "print\"Resultant Stress is\",round(p,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Planes of max shear stress: 20.0 N/mm**2\n",
+ " 76.84 N/mm*2\n",
+ "Resultant Stress is 79.4 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 40
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.10,Page No.283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Stresses\n",
+ "p_x=50*cos(35*pi*180**-1)\n",
+ "q=50*sin(35*pi*180**-1)\n",
+ "p_y=0\n",
+ "\n",
+ "theta=40 #Degrees #Plane AB inclined to vertical\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Normal Stress on AB\n",
+ "p_n=(p_x+p_y)*2**-1+(p_x-p_y)*2**-1*cos(2*theta*pi*180**-1)+q*sin(2*theta*pi*180**-1)\n",
+ "\n",
+ "#Tangential Stress on AB\n",
+ "p_t=(p_x-p_y)*2**-1*sin(2*theta*pi*180**-1)-q*cos(2*theta*pi*180**-1) #N/mm**2\n",
+ "\n",
+ "#Resultant stress\n",
+ "p=(p_n**2+p_t**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Angle of resultant\n",
+ "phi=arctan(p_n*p_t**-1)*(180*pi**-1) #degrees\n",
+ "phi2=phi+theta #Degrees\n",
+ "\n",
+ "#Result\n",
+ "print\"Magnitude of resultant stress is\",round(p,2),\"N/mm**2\"\n",
+ "print\"Direction of Resultant stress is\",round(phi2,2),\"Degrees\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnitude of resultant stress is 54.44 N/mm**2\n",
+ "Direction of Resultant stress is 113.8 Degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.12,Page No.285"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Direct stresses\n",
+ "p_x=120 #N/mm**2 #Tensile stress\n",
+ "p_y=-100 #N/mm**2 #Compressive stress\n",
+ "p1=160 #N/mm**2 #Major principal stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let q be the shearing stress\n",
+ "\n",
+ "#p1=(p_x+p_y)*2**-1+((((p_x+p_y)*2**-1)**2)+q**2)**0.5\n",
+ "#After further simplifying we get\n",
+ "q=(p1-((p_x+p_y)*2**-1))**2-((p_x-p_y)*2**-1)**2 #N/mm**2\n",
+ "q2=(q)**0.5 #N/mm**2\n",
+ "\n",
+ "#Minimum Principal stress\n",
+ "p2=(p_x+p_y)*2**-1-(((p_x-p_y)*2**-1)**2+q2**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Max shearing stress\n",
+ "q_max=(((p_x-p_y)*2**-1)**2+q2**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Shearing stress of material\",round(q,2),\"N/mm**2\"\n",
+ "print\"Min Principal stress\",round(p2,2),\"N/mm**2\"\n",
+ "print\"Max shearing stress\",round(q_max,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Shearing stress of material 10400.0 N/mm**2\n",
+ "Min Principal stress -140.0 N/mm**2\n",
+ "Max shearing stress 150.0 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.14,Page No.291"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "F=40*10**3 #N #Shear Force\n",
+ "M=20*10**6 #Bending Moment\n",
+ "\n",
+ "#Rectangular section\n",
+ "b=100 #mm #Width\n",
+ "d=200 #mm #Depth\n",
+ "\n",
+ "x=20 #mm #Distance from Top surface upto point\n",
+ "y=80 #mm #Distance from point to Bottom\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "I=1*12**-1*b*d**3 #mm**4 #M.I\n",
+ "\n",
+ "#At 20 mm Below top Fibre\n",
+ "f_x=M*I**-1*y #N/mm**2 #Stress\n",
+ "\n",
+ "#Assuming sagging moment ,f_x is compressive p_x=f_x=-24 #N/mm**2\n",
+ "p_x=f_x=-24 #N/mm**2\n",
+ "\n",
+ "#Shearing stress\n",
+ "q=F*(b*I)**-1*(b*x*(b-x*2**-1)) #N/mm**2\n",
+ "\n",
+ "#Direct stresses\n",
+ "\n",
+ "p_y=0 #N/mm**2\n",
+ "\n",
+ "p1=(p_x+p_y)*2**-1+(((p_x+p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "p2=(p_x+p_y)*2**-1-(((p_x+p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Directions of principal stresses at a point below 20mm is:\",round(p1,2),\"N/mm**2\"\n",
+ "print\" \",round(p2,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Directions of principal stresses at a point below 20mm is: 0.05 N/mm**2\n",
+ " -24.05 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.15,Page No.292"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=4000 #mm #Span\n",
+ "W1=W2=W3=2*10**3 #N #Load\n",
+ "\n",
+ "#SEction of beam\n",
+ "b=100 #mm #Width\n",
+ "d=240 #mm #Dept\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A and R_B be the reactions\n",
+ "R_A=R_B=(W1+W2+W3)*2**-1 #KN\n",
+ "\n",
+ "#Now at the section 1.5m from left support A\n",
+ "#Shear Force\n",
+ "F=R_A-W1 #KN\n",
+ "\n",
+ "#B.M\n",
+ "M=R_A*1.5-W1*0.5 #KN-m\n",
+ "\n",
+ "#M.I\n",
+ "I=1*12**-1*b*d**3 #mm**4\n",
+ "\n",
+ "#Bending stress\n",
+ "#f=M*I**-1*y\n",
+ "#After Sub values and further simplifying we get\n",
+ "#f=3.04*10**-2*y\n",
+ "\n",
+ "#As it varies Linearly\n",
+ "\n",
+ "#at distance 0 From NA \n",
+ "f1=0\n",
+ "#at distance 60 mm from NA\n",
+ "f2=1.823 #N/mm**2\n",
+ "#at distance 120 mm from NA\n",
+ "f3=3.646 #N/mm**2\n",
+ "\n",
+ "#Shearing stress\n",
+ "q=F*b*d*2**-1*d*4**-1*(b*I)**-1\n",
+ "\n",
+ "#At 60 mm above NA\n",
+ "q2=F*b*d*4**-1*(d*2**-1-d*8**-1)*(b*I)**-1\n",
+ "\n",
+ "#At 120 mm above NA\n",
+ "q3=0 \n",
+ "\n",
+ "#At NA element is under pure shear\n",
+ "p1=q #N/mm**2\n",
+ "p2=-q #N/mm**2 \n",
+ "\n",
+ "#Inclination of principal plane to vertical\n",
+ "#theta=2*q*0**-1\n",
+ "#Further simplifying we get\n",
+ "#theta=infinity\n",
+ "\n",
+ "#therefore\n",
+ "theta=90*2**-1 #degrees\n",
+ "theta2=270*2**-1 #degrees\n",
+ "\n",
+ "#At 60 mm From NA\n",
+ "p_x=-1.823 #N/mm**2 \n",
+ "p_y=0\n",
+ "q=0.0469 #N/mm**2\n",
+ "\n",
+ "#principal planes\n",
+ "P1=(p_x+p_y)*2**-1+(((p_x+p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "P2=(p_x+p_y)*2**-1-(((p_x+p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Principal planes inclination to hte plane of p_x is given by\n",
+ "theta3=(arctan(2*q*(p_x-p_y)**-1)*(180*pi**-1))\n",
+ "theta4=theta3*2**-1#degrees\n",
+ "\n",
+ "theta5=theta3+180 #Degrees\n",
+ "\n",
+ "#At 120 mm From N-A\n",
+ "p_x2=3.646 #N/mm**2\n",
+ "p_y2=0 #N/mm**2\n",
+ "q2=0 #N/mm**2\n",
+ "\n",
+ "P3=p_x2 #N/mm**2\n",
+ "P4=0 #N/mm**2\n",
+ "\n",
+ "#Answer for P2 at 60 mm from NA is incorrect\n",
+ "\n",
+ "#Result\n",
+ "print\"Principal Planes at 60 mm from NA:\",round(p_x,2),\"N/mm**2\"\n",
+ "print\" \",round(p_y,2),\"N/mm**2\"\n",
+ "print\"Principal Stresses at 60 mm From NA\",round(P1,4),\"N/mm**2\"\n",
+ "print\" \",round(P2,4),\"N/mm**2\"\n",
+ "print\"Principal Planes at 60 mm from NA:\",round(p_x2,4),\"N/mm**2\"\n",
+ "print\" \",round(p_y2,4),\"N/mm**2\"\n",
+ "print\"Principal Stresses at 60 mm From NA\",round(P3,4),\"N/mm**2\"\n",
+ "print\" \",round(P4,4),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Principal Planes at 60 mm from NA: -1.82 N/mm**2\n",
+ " 0.0 N/mm**2\n",
+ "Principal Stresses at 60 mm From NA 0.0012 N/mm**2\n",
+ " -1.8242 N/mm**2\n",
+ "Principal Planes at 60 mm from NA: 3.646 N/mm**2\n",
+ " 0.0 N/mm**2\n",
+ "Principal Stresses at 60 mm From NA 3.646 N/mm**2\n",
+ " 0.0 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.16,Page No.295"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=8000 #mm #Span of beam\n",
+ "w=40*10**6 #N/mm #udl\n",
+ "\n",
+ "#I-section\n",
+ "\n",
+ "#Flanges\n",
+ "b=100 #mm #Width\n",
+ "t=10 #mm #Thickness\n",
+ "\n",
+ "D=400 #mm #Overall Depth\n",
+ "t2=10 #mm #thickness of web\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let R_A and R_B be the Reactions at A & B respectively\n",
+ "R_A=w*2**-1*L*10**-9 #KN\n",
+ "\n",
+ "#Shear force at 2m for left support\n",
+ "F=R_A-2*w*10**-6 #KN\n",
+ "\n",
+ "#Bending Moment\n",
+ "M=R_A*2-2*w*10**-6 #KN-m\n",
+ "\n",
+ "#M.I\n",
+ "I=1*12**-1*b*D**3-1*12**-1*(b-t)*(D-2*t2)**3 #mm**4\n",
+ "\n",
+ "#Bending stress at 100 mm above N_A\n",
+ "f=M*10**6*I**-1*b\n",
+ "\n",
+ "#Shear stress \n",
+ "q=F*10**3*(t*I)**-1*(b*t*(D-t)*2**-1 +t2*(b-t2)*145) #N/mm**2\n",
+ "\n",
+ "p_x=-197.06 #N/mm**2 \n",
+ "p_y=0 #N/mm**2\n",
+ "q=21.38 #N/mm**2\n",
+ "\n",
+ "#Principal Stresses\n",
+ "\n",
+ "P1=(p_x+p_y)*2**-1+(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "P2=(p_x+p_y)*2**-1-(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Max shear stress\n",
+ "q_max=(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Principal Stresses are:\",round(P1,2),\"N/mm**2\"\n",
+ "print\" \",round(P2,2),\"N/mm**2\"\n",
+ "print\"Max shear stress\",round(q_max,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Principal Stresses are: 2.29 N/mm**2\n",
+ " -199.35 N/mm**2\n",
+ "Max shear stress 100.82 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 48
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.18,Page No.298"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=100 #mm #Diameter of shaft\n",
+ "M=3*10**6 #N-mm #B.M\n",
+ "T=6*10**6 #N-mm #Twisting Moment\n",
+ "mu=0.3\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Max principal Stress\n",
+ "\n",
+ "P1=16*(pi*d**3)**-1*(M+(M**2+T**2)**0.5) #N/mm**2 \n",
+ "P2=16*(pi*d**3)**-1*(M-(M**2+T**2)**0.5) #N/mm**2 \n",
+ "\n",
+ "#Direct stress\n",
+ "P=round(P1,2)-mu*round(P2,2) #N/mm**2 \n",
+ "\n",
+ "#Result\n",
+ "print\"Principal stresses are:\",round(P1,2),\"N/mm**2\"\n",
+ "print\" :\",round(P2,2),\"N/mm**2\"\n",
+ "print\"Stress Producing the same strain is\",round(P,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Principal stresses are: 49.44 N/mm**2\n",
+ " : -18.89 N/mm**2\n",
+ "Stress Producing the same strain is 55.11 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 51
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.19,Page No.299"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=75 #mm #diameter \n",
+ "P=30*10**6 #W #Power transmitted\n",
+ "W=6 #N-mm/sec #Load\n",
+ "L=1000 #mm \n",
+ "N=300 #r.p.m\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#B.M\n",
+ "M=W*L*4**-1 #N-mm\n",
+ "T=P*60*(2*pi*N)**-1 #Torque transmitted\n",
+ "\n",
+ "#M.I\n",
+ "I=pi*64**-1*d**4 #mm**4\n",
+ "\n",
+ "#Bending stress\n",
+ "f_A=M*I**-1*(d*2**-1) #N/mm**2\n",
+ "\n",
+ "#At A\n",
+ "p_x=f_A\n",
+ "p_y=0\n",
+ "\n",
+ "#Polar Modulus\n",
+ "J=pi*32**-1*d**4 #mm**4\n",
+ "\n",
+ "#Shearing stress\n",
+ "q=T*J**-1*(d*2**-1) #N/mm**2\n",
+ "\n",
+ "#Principal Stresses\n",
+ "P1=(p_x+p_y)*2**-1+(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "P2=(p_x+p_y)*2**-1-(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Max shear stress\n",
+ "q_max=(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Bending stress\n",
+ "p_x2=0\n",
+ "p_y2=0\n",
+ "\n",
+ "#Shearing stress\n",
+ "q2=T*J**-1*d*2**-1 #N/mm**2\n",
+ "\n",
+ "#Principal stresses\n",
+ "P3=(p_x2+p_y2)*2**-1+(((p_x2-p_y2)*2**-1)**2+q2**2)**0.5 #N/mm**2\n",
+ "P4=(p_x2+p_y2)*2**-1-(((p_x2-p_y2)*2**-1)**2+q2**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Max shear stress\n",
+ "q_max2=(((p_x2-p_y2)*2**-1)**2+q2**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Answer for Principal Stresses P1,P2 and Max stress i.e q_max is incorrect in Book\n",
+ "\n",
+ "#Result\n",
+ "print\"Principal Stresses at vertical Diameter:P1\",round(P1,2),\"N/mm**2\"\n",
+ "print\" :P2\",round(P2,2),\"N/mm**2\"\n",
+ "print\"Max stress at vertical Diameter : \",round(q_max,2),\"N/mm**2\"\n",
+ "print\"Principal Stresses at Horizontal Diameter:P3\",round(P3,2),\"N/mm**2\"\n",
+ "print\" :P4\",round(P4,2),\"N/mm**2\"\n",
+ "print\"Max stress at Horizontal Diameter : \",round(q_max2,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Principal Stresses at vertical Diameter:P1 11.55 N/mm**2\n",
+ " :P2 -11.51 N/mm**2\n",
+ "Max stress at vertical Diameter : 11.53 N/mm**2\n",
+ "Principal Stresses at Horizontal Diameter:P3 11.53 N/mm**2\n",
+ " :P4 -11.53 N/mm**2\n",
+ "Max stress at Horizontal Diameter : 11.53 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.20,Page No.302"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d1=100 #mm #External Diameter\n",
+ "d2=50 #mm #Internal Diameter\n",
+ "N=500 #mm #r.p.m\n",
+ "P=60*10**6 #N-mm/sec #Power\n",
+ "p=100 #N/mm**2 #principal stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#M.I\n",
+ "I=pi*(d1**4-d2**4)*64**-1 #mm**4\n",
+ "\n",
+ "#Bending Stress\n",
+ "#f=M*I*d1*2**-1 #N/mm**2\n",
+ "\n",
+ "#Principal Planes\n",
+ "#p_x=32*M*(pi*(d1**4-d2**4))*d1\n",
+ "#p_y=0\n",
+ "\n",
+ "#Shear stress\n",
+ "#q=T*J**-1*(d1*2**-1)\n",
+ "#After sub values and further simplifying we get\n",
+ "#q=16*T*d1*(pi*(d1**4-d2**4))*d1\n",
+ "\n",
+ "#Principal stresses\n",
+ "#P1=(p_x+p_y)*2**-1+(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "#After sub values and further simplifying we get\n",
+ "#P1=16*(pi*(d1**4-d2**4))*d1*(M+(M**2+t**2)**0.5) ...............(1)\n",
+ "\n",
+ "#P=2*pi*N*T*60**-1\n",
+ "#After sub values and further simplifying we get\n",
+ "T=P*60*(2*pi*N)**-1*10**-6 #N-mm\n",
+ "\n",
+ "#Again Sub values and further simplifying Equation 1 we get\n",
+ "M=(337.533)*(36.84)**-1 #KN-m\n",
+ "\n",
+ "#Min Principal stress\n",
+ "#P2=(p_x+p_y)*2**-1-(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "#Sub values and further simplifying we get\n",
+ "P2=16*(pi*(d1**4-d2**4))*d1*(M-(M**2+T**2)**0.5)*10**-11\n",
+ "\n",
+ "#Result\n",
+ "print\"Bending Moment safely applied to shaft is\",round(M,2),\"KN-m\"\n",
+ "print\"Min Principal Stress is\",round(P2,3),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Bending Moment safely applied to shaft is 9.16 KN-m\n",
+ "Min Principal Stress is -0.336 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.21,Page No.303"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=150 #mm #Diameter\n",
+ "T=20*10**6 #N #Torque\n",
+ "M=12*10**6 #N-mm #B.M\n",
+ "F=200*10**3 #N #Axial Thrust\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#M.I\n",
+ "I=(pi*64**-1*d**4)\n",
+ "\n",
+ "#Bending stress \n",
+ "f_A=M*I**-1*(d*2**-1) #N/mm**2\n",
+ "f_B=-f_A #N/mm**2\n",
+ "\n",
+ "#Axial thrust due to thrust\n",
+ "sigma=F*(pi*4**-1*d**2)**-1\n",
+ "\n",
+ "#At A\n",
+ "p_x=f_A-sigma #N/mm**2\n",
+ "\n",
+ "#At B\n",
+ "p_x2=f_B-sigma #N/mm**2\n",
+ "\n",
+ "p_y=0 #At A and B\n",
+ "\n",
+ "#Polar Modulus\n",
+ "J=pi*32**-1*d**4 #mm**4\n",
+ "\n",
+ "#Shearing stress at A and B\n",
+ "q=T*J**-1*(d*2**-1) #N/mm**2\n",
+ "\n",
+ "\n",
+ "#Principal Stresses\n",
+ "#At A\n",
+ "P1=(p_x+p_y)*2**-1+(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "P2=(p_x+p_y)*2**-1-(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Max shear stress\n",
+ "q_max1=(((p_x-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#At B\n",
+ "P1_2=(p_x2+p_y)*2**-1+(((p_x2-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "P2_2=(p_x2+p_y)*2**-1-(((p_x2-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "#Max shear stress\n",
+ "q_max2=(((p_x2-p_y)*2**-1)**2+q**2)**0.5 #N/mm**2\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"MAx Principal Stresses:P1\",round(P1,2),\"N/mm**2\"\n",
+ "print\" :P2\",round(P2,2),\"N/mm**2\"\n",
+ "print\"Min Principal Stresses:P1_2\",round(P1_2,2),\"N/mm**2\"\n",
+ "print\" :P2_2\",round(P2_2,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "MAx Principal Stresses:P1 45.1 N/mm**2\n",
+ " :P2 -20.2 N/mm**2\n",
+ "Min Principal Stresses:P1_2 14.65 N/mm**2\n",
+ " :P2_2 -62.18 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.22,Page No.311"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#strains\n",
+ "e_A=500 #microns\n",
+ "e_B=250 #microns\n",
+ "e_C=-150 #microns\n",
+ "E=2*10**5 #N/mm**2 #Modulus of Elasticity\n",
+ "mu=0.3 #Poissoin's ratio\n",
+ "theta=45 #Degrees\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "e_x=e_A=500\n",
+ "e_45=e_B=250\n",
+ "e_y=e_C=-150 \n",
+ "\n",
+ "#e_45=(e_x+e_y)*2**-1+(e_x-e_y)*2**-1*cos(2*theta)+rho_x_y*2**-1*sin(2*theta)\n",
+ "#After sub values and further simplifying we get\n",
+ "rho_x_y=(e_45-(e_x+e_y)*2**-1-(e_x-e_y)*2**-1*cos(2*theta*pi*180**-1))*(sin(2*theta*pi*180**-1))**-1*2\n",
+ "\n",
+ "#Principal strains are given by\n",
+ "e1=(e_x+e_y)*2**-1+(((e_x-e_y)*2**-1)**2+(rho_x_y*2**-1)**2)**0.5 #microns\n",
+ "e2=(e_x+e_y)*2**-1-(((e_x-e_y)*2**-1)**2+(rho_x_y*2**-1)**2)**0.5 #microns\n",
+ "\n",
+ "#Principal Stresses\n",
+ "sigma1=E*(e1+mu*e2)*(1-mu**2)**-1*10**-6 #N/mm**2\n",
+ "sigma2=E*(e2+mu*e1)*(1-mu**2)**-1*10**-6 #N/mm**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Principal Strains are:e1\",round(e1,2),\"N/mm**2\"\n",
+ "print\" :e2\",round(e2,2),\"N/mm**2\"\n",
+ "print\"Principal Stresses are:sigma1\",round(sigma1,2),\"N/mm**2\"\n",
+ "print\" :sigma2\",round(sigma2,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Principal Strains are:e1 508.54 N/mm**2\n",
+ " :e2 -158.54 N/mm**2\n",
+ "Principal Stresses are:sigma1 101.31 N/mm**2\n",
+ " :sigma2 -1.31 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.7.23,Page No.313"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Strains\n",
+ "e_A=600 #microns\n",
+ "e_B=-450 #microns\n",
+ "e_C=100 #micron\n",
+ "E=2*10**5 #N/mm**2 #Modulus of Elasticity\n",
+ "mu=0.3 #Poissoin's ratio\n",
+ "theta=240\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "e_x=e_A=600\n",
+ "\n",
+ "#e_A=(e_x+e_y)*2**-1+(e_x-e_y)*2**-1*cos(theta)+rho_x_y*2**-1*sin(theta)\n",
+ "#After sub values and further simplifying we get\n",
+ "#-450=(e_x+e_y)*2**-1-(e_x-e_y)*2**-1*(0.5)-0.866*2**-1*rho_x_y .....................(1)\n",
+ "\n",
+ "#e_C=(e_x+e_y)*2**-1+(e_x-e_y)*2**-1*cos(2*theta)+rho_x_y*2**-1*sin(2*theta)\n",
+ "#After sub values and further simplifying we get\n",
+ "#100=(e_x+e_y)*2**-1-0.5*(e_x-e_y)*2**-1*(0.5)-0.866*2**-1*rho_x_y .....................(2)\n",
+ "\n",
+ "#Adding Equation 1 and 2 we get equations as\n",
+ "#-350=e_x+e_y-(e_x-e_y)*2**-1 ...............(3)\n",
+ "#Further simplifying we get\n",
+ "\n",
+ "e_y=(-700-e_x)*3**-1 #micron \n",
+ "\n",
+ "rho_x_y=(e_C-(e_x+e_y)*2**-1-(e_x-e_y)*2**-1*cos(2*theta*pi*180**-1))*(sin(2*theta*pi*180**-1))**-1*2 #micron\n",
+ "\n",
+ "#Principal strains\n",
+ "e1=(e_x+e_y)*2**-1-(((e_x-e_y)*2**-1)**2+(rho_x_y*2**-1)**2)**0.5 #microns\n",
+ "e2=(e_x+e_y)*2**-1+(((e_x-e_y)*2**-1)**2+(rho_x_y*2**-1)**2)**0.5 #microns\n",
+ "\n",
+ "#Principal Stresses\n",
+ "sigma1=E*(e1+mu*e2)*(1-mu**2)**-1*10**-6 #N/mm**2\n",
+ "sigma2=E*(e2+mu*e1)*(1-mu**2)**-1*10**-6 #N/mm**2\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"Principal Stresses are:sigma1\",round(sigma1,2),\"N/mm**2\"\n",
+ "print\" :sigma2\",round(sigma2,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Principal Stresses are:sigma1 -69.49 N/mm**2\n",
+ " :sigma2 117.11 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_08.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_08.ipynb new file mode 100644 index 00000000..420944a4 --- /dev/null +++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_08.ipynb @@ -0,0 +1,1531 @@ +{
+ "metadata": {
+ "name": "chapter 08.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter No.8:Thin And Thick Cyclinders And Spheres"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.1,Page No.322"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=3000 #mm #Length\n",
+ "d1=1000 #mm #Internal diameter\n",
+ "t=15 #mm #Thickness\n",
+ "P=1.5 #N/mm**2 #Fluid Pressure\n",
+ "E=2*10**5 #n/mm**2 #Modulus of elasticity\n",
+ "mu=0.3 #Poissoin's ratio\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Hoop stress\n",
+ "f1=P*d1*(2*t)**-1 #N/mm**2\n",
+ "\n",
+ "#Longitudinal Stress\n",
+ "f2=P*d1*(4*t)**-1 #N/mm**2\n",
+ "\n",
+ "#Max shear stress\n",
+ "q_max=(f1-f2)*2**-1 #N/mm**2\n",
+ "\n",
+ "#Diametrical Strain\n",
+ "#Let e1=dell_d*d**-1 .....................(1)\n",
+ "e1=(f1-mu*f2)*E**-1 \n",
+ "\n",
+ "#Sub values in equation 1 and further simplifying we get\n",
+ "dell_d=e1*d1 #mm\n",
+ "\n",
+ "#Longitudinal strain\n",
+ "#e2=dell_L*L**-1 ......................(2)\n",
+ "e2=(f2-mu*f1)*E**-1 \n",
+ "\n",
+ "#Sub values in equation 2 and further simplifying we get\n",
+ "dell_L=e2*L #mm\n",
+ "\n",
+ "#Change in Volume \n",
+ "#Let Z=dell_V*V**-1 ................(3)\n",
+ "Z=2*e1+e2\n",
+ "\n",
+ "#Sub values in equation 3 and further simplifying we get\n",
+ "dell_V=Z*pi*4**-1*d1**2*L\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Intensity of shear stress\",round(q_max,2),\"N/mm**2\"\n",
+ "print\"Change in the Dimensions of the shell is:dell_d\",round(dell_d,2),\"mm\"\n",
+ "print\" :dell_L\",round(dell_L,2),\"mm\"\n",
+ "print\" :dell_V\",round(dell_V,2),\"mm**3\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Intensity of shear stress 12.5 N/mm**2\n",
+ "Change in the Dimensions of the shell is:dell_d 0.21 mm\n",
+ " :dell_L 0.15 mm\n",
+ " :dell_V 1119192.38 mm**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.2,Page No.323"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=2000 #mm #Length\n",
+ "d=200 #mm # diameter\n",
+ "t=10 #mm #Thickness\n",
+ "dell_V=25000 #mm**3 #Additional volume\n",
+ "E=2*10**5 #n/mm**2 #Modulus of elasticity\n",
+ "mu=0.3 #Poissoin's ratio\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let p be the pressure developed\n",
+ "\n",
+ "#Circumferential Stress\n",
+ "\n",
+ "#f1=p*d*(2*t)**-1 #N/mm**2\n",
+ "#After sub values and further simplifying\n",
+ "#f1=10*p\n",
+ "\n",
+ "#f1=p*d*(4*t)**-1 #N/mm**2\n",
+ "#After sub values and further simplifying\n",
+ "#f1=5*p\n",
+ "\n",
+ "#Diameterical strain = Circumferential stress\n",
+ "#Let X=dell_d*d**-1 ................................(1)\n",
+ "#X=e1=(f1-mu*f2)*E**-1 \n",
+ "#After sub values and further simplifying\n",
+ "#e1=8.5*p*E**-1\n",
+ "\n",
+ "#Longitudinal strain\n",
+ "#Let Y=dell_L*L**-1 ......................................(2)\n",
+ "#Y=e2=(f2-mu*f1)*E**-1 \n",
+ "#After sub values and further simplifying\n",
+ "#e2=2*p*E**-1\n",
+ "\n",
+ "#Volumetric strain\n",
+ "#Let X=dell_V*V**-1 \n",
+ "#X=2*e1+e2\n",
+ "#After sub values and further simplifying\n",
+ "#X=19*p*E**-1\n",
+ "#After further simplifying we get\n",
+ "p=dell_V*(pi*4**-1*d**2*L)**-1*E*19**-1 #N/mm**2\n",
+ "\n",
+ "#Hoop Stress\n",
+ "f1=p*d*(2*t)**-1\n",
+ "\n",
+ "X=e1=8.5*p*E**-1\n",
+ "#Sub value of X in equation 1 we get\n",
+ "dell_d=8.5*p*E**-1*d\n",
+ "\n",
+ "Y=e2=2*p*E**-1\n",
+ "#Sub value of Y in equation 2 we get\n",
+ "dell_L=2*p*E**-1*L\n",
+ "\n",
+ "#Result\n",
+ "print\"Pressure Developed is\",round(p,2),\"N/mm**2\"\n",
+ "print\"Hoop stress Developed is\",round(f1,2),\"N/mm**2\"\n",
+ "print\"Change in diameter is\",round(dell_d,2),\"mm\"\n",
+ "print\"Change in Length is\",round(dell_L,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Pressure Developed is 4.19 N/mm**2\n",
+ "Hoop stress Developed is 41.88 N/mm**2\n",
+ "Change in diameter is 0.04 mm\n",
+ "Change in Length is 0.08 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.3,Page No.324"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=750 #mm #Diameter of water supply pipes\n",
+ "h=50*10**3 #mm #Water head\n",
+ "sigma=20 #N/mm**2 #Permissible stress\n",
+ "rho=9810*10**-9 #N/mm**3\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Pressure of water\n",
+ "P=rho*h #N/mm**2\n",
+ "\n",
+ "#Stress\n",
+ "#sigma=p*d*(2*t)**-1\n",
+ "#After further simplifying\n",
+ "t=P*d*(2*sigma)**-1 #mm \n",
+ "\n",
+ "#Result\n",
+ "print\"Thickness of seamless pipe is\",round(t,3),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Thickness of seamless pipe is 9.197 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.4,Page No.326"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=2500 #mm #Diameter of riveted boiler\n",
+ "P=1 #N/mm**2 #Pressure\n",
+ "rho1=0.7 #Percent efficiency\n",
+ "rho2=0.4 #Circumferential joints\n",
+ "sigma=150 #N/mm**2 #Permissible stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Equating Bursting force to longitudinal joint strength ,we get\n",
+ "#p*d*L=rho1*2*t*L*sigma\n",
+ "#After rearranging and further simplifying we get\n",
+ "t=P*d*(2*sigma*rho1)**-1 #mm\n",
+ "\n",
+ "#Considering Longitudinal force\n",
+ "#pi*d**2*4**-1*P=rho2*pi*d*t*sigma\n",
+ "#After rearranging and further simplifying we get\n",
+ "t2=P*d*(4*sigma*rho2)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Thickness of plate required is\",round(t,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Thickness of plate required is 11.9 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 45
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.5,Page No.326"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Boiler Dimensions\n",
+ "t=16 #mm #Thickness\n",
+ "p=2 #N/mm**2 #internal pressure\n",
+ "f=150 #N/mm**2 #Permissible stress\n",
+ "rho1=0.75 #Longitudinal joints\n",
+ "rho2=0.45 #circumferential joints\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Equating Bursting force to longitudinal joint strength ,we get\n",
+ "d1=rho1*2*t*f*p**-1 #mm\n",
+ "\n",
+ "#Considering circumferential strength \n",
+ "d2=4*rho2*t*f*p**-1 #mm\n",
+ "\n",
+ "#Result\n",
+ "print\"Largest diameter of Boiler is\",round(d1,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Largest diameter of Boiler is 1800.0 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 52
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.6,Page No.329"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=250 #mm #Diameter iron pipe\n",
+ "t=10 #mm #Thickness\n",
+ "d2=6 #mm #Diameter of steel\n",
+ "p=80 #N/mm**2 #stress\n",
+ "P=3 #N/mm**2 #Pressure\n",
+ "E_c=1*10**5 #N/mm**2\n",
+ "mu=0.3 #poissoin's ratio\n",
+ "E_s=2*10**5 #N/mm**2\n",
+ "n=1 #No.of wires\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "L=6 #mm #Length of cyclinder\n",
+ "\n",
+ "#Force Exerted by steel wire at diameterical section\n",
+ "F=p*2*pi*d2**2*1*4**-1 #N\n",
+ "\n",
+ "#Initial stress in cyclinder\n",
+ "f_c=F*(2*t*d2)**-1 #N/mm**2\n",
+ "\n",
+ "#LEt due to fluid pressure alone stresses developed in steel wire be F_w and in cyclinder f1 and f2\n",
+ "f2=P*d*(4*t)**-1 #N/mm**2\n",
+ "\n",
+ "#Considering the equilibrium of half the cyclinder, 6mm long we get\n",
+ "#F_w*2*pi*4**-1*d2**2*n+f1*2*t*d2=P*d*d2\n",
+ "#After further simplifying we get\n",
+ "#F_w+2.122*f1=79.58 . ......................................(1)\n",
+ "\n",
+ "#Equating strain in wire to circumferential strain in cyclinder \n",
+ "#F_w=(f1-mu*f2)*E_s*E_c**-1 #N/mm**2\n",
+ "#After further simplifying we get\n",
+ "#F_w=2*f1-11.25 ....................................(2)\n",
+ "\n",
+ "#Sub in equation in1 we get\n",
+ "f1=(79.58+11.25)*(4.122)**-1 #N/mm**2\n",
+ "F_w=2*f1-11.25 #N/mm**2\n",
+ "\n",
+ "#Final stresses\n",
+ "#1) In steel Wire\n",
+ "sigma=F_w+p #N/mm**2\n",
+ "\n",
+ "#2) In Cyclinder\n",
+ "sigma2=f1-f_c\n",
+ "\n",
+ "#Result\n",
+ "print\"Final Stresses developed in:cyclinder is\",round(sigma,2),\"N/mm**2\"\n",
+ "print\" :Steel is\",round(sigma2,2),\"N/mm**2\" "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Final Stresses developed in:cyclinder is 112.82 N/mm**2\n",
+ " :Steel is -15.66 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.7,Page No.332"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=750 #mm #Diameter of shell\n",
+ "t=8 #mm #THickness\n",
+ "p=2.5 #N/mm**2\n",
+ "E=2*10**5 #N/mm**2\n",
+ "mu=0.25 #Poissoin's ratio\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Hoop stress\n",
+ "f1=f2=p*d*(4*t)**-1 #N/mm**2\n",
+ "\n",
+ "#Change in Diameter\n",
+ "dell_d=d*p*d*(1-mu)*(4*t*E)**-1 #mm\n",
+ "\n",
+ "#Change in Volume\n",
+ "dell_V=3*p*d*(1-mu)*(4*t*E)**-1*pi*6**-1*d**3\n",
+ "\n",
+ "#Answer for Change in diameter is incorrect in book\n",
+ "\n",
+ "#Result\n",
+ "print\"Stress introduced is\",round(f1,2),\"N/mm**2\"\n",
+ "print\"Change in Diameter is\",round(dell_d,2),\"N/mm**2\"\n",
+ "print\"Change in Volume is\",round(dell_V,2),\"mm**3\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stress introduced is 58.59 N/mm**2\n",
+ "Change in Diameter is 0.16 N/mm**2\n",
+ "Change in Volume is 145608.33 mm**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 56
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.8,Page No.333"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d=600 #mm #Diameter of sherical shell\n",
+ "t=10 #mm #Thickness\n",
+ "f=80 #N/mm**2 #Permissible stress\n",
+ "rho=0.75 #Efficiency joint\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Max Pressure\n",
+ "p=f*4*t*rho*d**-1 #N/mm**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Pressure is\",round(p,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Pressure is 4.0 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 60
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.9,Page No.333"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=1000 #mm #Length of shell\n",
+ "d=200 #mm #Diameter\n",
+ "t=6 #mm #Thickness\n",
+ "p=1.5 #N/mm**2 #Internal Pressure\n",
+ "E=2*10**5 #N/mm**2\n",
+ "mu=0.25 #Poissoin's Ratio\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Change in Volume of sphere\n",
+ "dell_V_s=3*p*d*(1-mu)*(4*t*E)**-1*pi*6**-1*d**3\n",
+ "\n",
+ "#Hoop stress\n",
+ "f1=p*d*(2*t)**-1 #N/mm**2\n",
+ "\n",
+ "#Longitudinal stress\n",
+ "f2=p*d*(4*t)**-1 #N/mm**2\n",
+ "\n",
+ "#Principal strain\n",
+ "e1=(f1-mu*f2)*E**-1\n",
+ "e2=(f2-mu*f1)*E**-1\n",
+ "\n",
+ "V_c=1000 #mm**3\n",
+ "\n",
+ "#Change in Volume of cyclinder\n",
+ "dell_V_c=(2*e1+e2)*pi*4**-1*d**2*L\n",
+ "\n",
+ "#Total Change in Diameter\n",
+ "dell_V=dell_V_s+dell_V_c #mm**3\n",
+ "\n",
+ "#Result\n",
+ "print\"Change in Volume is\",round(dell_V,2),\"mm**3\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Change in Volume is 8443.03 mm**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 66
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.10,Page No.337"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d1=400 #mm #Internal Diameter\n",
+ "t=100 #mm #Thickness\n",
+ "p=80 #N/mm**2 #Fluid pressure\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Internal Radius\n",
+ "r1=d1*2**-1 #mm\n",
+ "\n",
+ "#Outer Radius\n",
+ "r_o=r1+t #mm\n",
+ "\n",
+ "p1=80 #N/mm**2\n",
+ "p2=0\n",
+ "\n",
+ "#Now From Lame's Euation\n",
+ "#p_x=b*(x**2)**-1-a\n",
+ "#at x=200 #mm \n",
+ "p_x=80 #N/mm**2\n",
+ "#80=b*(200**2)**-1-a ..........................(1)\n",
+ "\n",
+ "#at x=300 #mm\n",
+ "#p_x2=0\n",
+ "#0=b*(300**2)**-1-a ...........................(2)\n",
+ "\n",
+ "#Sub equation 2 from 1\n",
+ "#80=b*(200**2)**-1-b*(300**2)**-1\n",
+ "#After Further simplifying we get\n",
+ "b=(50000)**-1*(200**2*300**2*80)\n",
+ "\n",
+ "#From equation 2 we get\n",
+ "a=b*(300**2)**-1\n",
+ "\n",
+ "#Variation of radial pressure p_x;\n",
+ "#p_x=b*(x**2)**-1-a\n",
+ "#After sub values and further simplifying we get\n",
+ "\n",
+ "#Radial pressure Variation\n",
+ "#At \n",
+ "x=200 #mm\n",
+ "p_x=b*(x**2)**-1-a #N/mm**2\n",
+ "\n",
+ "#At\n",
+ "x2=250 #mm\n",
+ "p_x2=b*(x2**2)**-1-a #N/mm**2\n",
+ "\n",
+ "#At \n",
+ "x3=300 #mm\n",
+ "p_x3=b*(x3**2)**-1-a #N/mm**2\n",
+ "\n",
+ "\n",
+ "#Hoop stress Distribution\n",
+ "#Variation of F_x\n",
+ "\n",
+ "#At \n",
+ "x=200 #mm\n",
+ "F_x=b*(x**2)**-1+a #N/mm**2\n",
+ "\n",
+ "#At\n",
+ "x2=250 #mm\n",
+ "F_x2=b*(x2**2)**-1+a #N/mm**2\n",
+ "\n",
+ "#At\n",
+ "x3=300 #mm\n",
+ "F_x3=b*(x3**2)**-1+a #N/mm**2\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Hoop stress is\",round(F_x,2),\"N/mm**2\"\n",
+ "print\"Min Hoop stress is\",round(F_x3,2),\"N/mm**2\"\n",
+ "print\"Plot of Hoop stress\"\n",
+ "\n",
+ "#Plotting Variation of hoop stress\n",
+ "\n",
+ "X1=[x,x2,x3]\n",
+ "Y1=[p_x,p_x2,p_x3]\n",
+ "Y2=[-F_x,-F_x2,-F_x3]\n",
+ "Z1=[0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Y2,X1,Z1)\n",
+ "plt.xlabel(\"Length x in mm\")\n",
+ "plt.ylabel(\"Radial Stress Distribution & Hoop Stress Distribution in N/mm**2\")\n",
+ "plt.show()\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Hoop stress is 208.0 N/mm**2\n",
+ "Min Hoop stress is 128.0 N/mm**2\n",
+ "Plot of Hoop stress\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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skdWFW7ZsQffu3XH8+HGMGzcOY8aMAaA9wnfKlCkIDg7GmDFjEBcXJ7WK4uLi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\nbm5uYtOmTUII3b27hBBCoVCIHTt2CCG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+ "text": [
+ "<matplotlib.figure.Figure at 0x5544430>"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.11,Page No.338"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d_o=300 #mm #Outside diameter \n",
+ "d2=200 #mm #Internal Diameter\n",
+ "p=14 #N/mm**2 #internal Fluid pressure\n",
+ "t=50 #mm #Thickness\n",
+ "r_o=150 #mm #Outside Diameter\n",
+ "r2=100 #mm #Internal Diameter\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#From Lame's Equation\n",
+ "#p_x=b*(x**2)**-1-a #N/mm**2 ...................(1)\n",
+ "#F_x=b*(x**2)**-1+a #N/mm**2 ...................(2)\n",
+ "\n",
+ "#At \n",
+ "x=r2=100 #mm\n",
+ "p_x=14 #N/mm**2\n",
+ "\n",
+ "#Sub value of p_x in equation 1 we get\n",
+ "#14=(100)**-1*b-a ............................(3)\n",
+ "\n",
+ "#At\n",
+ "x2=r_o=150 #mm\n",
+ "p_x2=0 #N/mm**2\n",
+ "\n",
+ "#Sub value in equation 1 we get\n",
+ "#0=b*(150**2)**-1-a ......................(4)\n",
+ "\n",
+ "#From Equations 3 and 4 we get\n",
+ "#14=b*(100**2)**-1-b*(100**2)**-1\n",
+ "#After sub values and further simplifying we get\n",
+ "b=14*100**2*150**2*(150**2-100**2)**-1\n",
+ "\n",
+ "#From equation 4 we get\n",
+ "a=b*(150**2)**-1\n",
+ "\n",
+ "#Hoop Stress\n",
+ "#F_x=b*(x**2)**-1+a #N/mm**2\n",
+ "\n",
+ "#At \n",
+ "x=100 #mm\n",
+ "F_x=b*(x**2)**-1+a #N/mm**2\n",
+ "\n",
+ "#At\n",
+ "x2=125 #mm\n",
+ "F_x2=b*(x2**2)**-1+a #N/mm**2\n",
+ "\n",
+ "#At\n",
+ "x3=150 #mm\n",
+ "F_x3=b*(x3**2)**-1+a #N/mm**2\n",
+ "\n",
+ "#If thin Cyclindrical shell theory is used,hoop stress is uniform and is given by\n",
+ "F=p*d2*(2*t)**-1 #N/mm**2\n",
+ "\n",
+ "#Percentage error in estimating max hoop tension\n",
+ "E=(F_x-F)*F_x**-1*100 #%\n",
+ "\n",
+ "#Result\n",
+ "print\"Max Hoop Stress Developed in the cross-section is\",round(F,2),\"N/mm**2\"\n",
+ "print\"Plot of Variation of hoop stress\"\n",
+ "\n",
+ "#Plotting Variation of hoop stress\n",
+ "\n",
+ "X1=[x,x2,x3]\n",
+ "Y1=[F_x,F_x2,F_x3]\n",
+ "Z1=[0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in mm\")\n",
+ "plt.ylabel(\"Radial Stress Distribution & Hoop Stress Distribution in N/mm**2\")\n",
+ "plt.show()\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max Hoop Stress Developed in the cross-section is 28.0 N/mm**2\n",
+ "Plot of Variation of hoop stress\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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29vaQJAknTpx4bAP379/HiBEjMGzYMMycOdNwT41GA1dXV2RkZGDgwIEcMiIi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\nSUVORK5CYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5d6d6b0>"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.12,Page No.339"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d_o=300 #mm #Outside diameter \n",
+ "d2=200 #mm #Internal Diameter\n",
+ "p=12 #N/mm**2 #internal Fluid pressure\n",
+ "F_max=16 #N/mm**2 #Tensile stress\n",
+ "r_o=150 #mm #Outside Diameter\n",
+ "r2=100 #mm #Internal Diameter\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let p_o be the External Pressure applied.\n",
+ "#From LLame's theorem\n",
+ "#p_x=b*(x**2)**-1-a ..............(1)\n",
+ "#F_x=b*(x**2)**-1+a ...........................(2)\n",
+ "\n",
+ "#Now At\n",
+ "x=100 #mm\n",
+ "p_x=12 #N/mm**2\n",
+ "#sub in equation 1 we get\n",
+ "#12=b*(100**2)**-1-a . ..................(3)\n",
+ "\n",
+ "#The Max Hoop stress occurs at least value of x where\n",
+ "x=r1=100 #mm\n",
+ "#16=b*(100**2)**-1+a .......................(4)\n",
+ "\n",
+ "#From Equations 1 and 2 we get\n",
+ "#28=b*(100**2)**-1+b*(100**2)**-1\n",
+ "#After furhter Simplifying we get\n",
+ "b=28*100**2*2**-1\n",
+ "\n",
+ "#sub in equation 1 we get\n",
+ "a=-(12-(b*(100**2)**-1))\n",
+ "\n",
+ "#Thus At\n",
+ "x2=150 #mm\n",
+ "p_o=b*(x2**2)**-1-a\n",
+ "\n",
+ "#Result\n",
+ "print\"Minimum External applied is\",round(p_o,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Minimum External applied is 4.22 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.13,Page No.340"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d1=160 #mm #Internal Diameter \n",
+ "r1=80 #mm #External Diameter\n",
+ "p1=40 #N/mm**2 #Internal Diameter\n",
+ "P_max=120 #N/mm**2 #Allowable stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#From Lame's Equation we have\n",
+ "#p_x=b*(x**2)**-1-a ..........................(1)\n",
+ "#F_x=b*(x**2)**-1+a ...........................(2)\n",
+ "\n",
+ "#At \n",
+ "x=r1=80 #N/mm**2 \n",
+ "#Sub in equation 1 we get\n",
+ "#120=b*(80**2)**-1+a ........................(3)\n",
+ "\n",
+ "#The hoop tension at inner edge is max stress\n",
+ "#Hence\n",
+ "#120=b*(80**2)**-1+a .............................(4)\n",
+ "\n",
+ "#From Equation 3 and 4 we get\n",
+ "b=160*80**2*2**-1 \n",
+ "\n",
+ "#Sub in equation 3 we get\n",
+ "a=-(40-(b*(80**2)**-1))\n",
+ "\n",
+ "#Let External radius be r_o.Since at External Surface is Zero,we get\n",
+ "#0=b*(r_o)**-1-a\n",
+ "#After Further simplifying we get\n",
+ "r_o=(b*a**-1)**0.5\n",
+ "\n",
+ "#Thickness of Cyclinder \n",
+ "t=r_o-r1 #mm\n",
+ "\n",
+ "#Result\n",
+ "print\"Thickness Required is\",round(t,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Thickness Required is 33.14 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.14,Page No.341"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d_o=300 #mm #Outside diameter \n",
+ "d1=180 #mm #Internal Diameter\n",
+ "p=12 #N/mm**2 #internal Fluid pressure\n",
+ "p_o=6 #N/mm**2 #External Pressure\n",
+ "r_o=150 #mm #Outside Diameter\n",
+ "r=90 #mm #Internal Diameter\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#From Lame's Equation we have\n",
+ "#p_x=b*(x**2)**-1-a ..........................(1)\n",
+ "#F_x=b*(x**2)**-1+a ...........................(2)\n",
+ "\n",
+ "#At \n",
+ "x=r1=90 #N/mm**2 \n",
+ "p=42 #N/mm**2\n",
+ "#Sub in equation 1 we get\n",
+ "#42=b*(90**2)**-1-a ..............................(3)\n",
+ "\n",
+ "#At \n",
+ "x=r_o=150 #mm\n",
+ "p2=6 #N/mm**2\n",
+ "#sub in equation 1 we get\n",
+ "#6=b*(150**2)**-1-a ..............................(4)\n",
+ "\n",
+ "#From equations 3 and 4 weget\n",
+ "#36=b*(90**2)**-1-b2(150**2)**-1\n",
+ "#After further simplifying we get\n",
+ "b=36*90**2*150**2*(150**2-90**2)**-1\n",
+ "\n",
+ "#Sub value of b in equation 4 we get\n",
+ "a=b*(150**2)**-1-p_o\n",
+ "\n",
+ "#At \n",
+ "x=r1=90 #mm\n",
+ "F_x=b*(x**2)**-1+a #N/mm**2\n",
+ "\n",
+ "#At \n",
+ "x2=r_o=150 #mm \n",
+ "F_x2=b*(x2**2)**-1+a #N/mm**2\n",
+ "\n",
+ "#Now if External pressure is doubled i.e p_o2=12 #N/mm**2 We have\n",
+ "p_o2=12 #N/mm**2\n",
+ "#sub in equation 4 we get\n",
+ "#12=b2*(150**2)**-1-a2 ..........................(5)\n",
+ "\n",
+ "#Max Hoop stress is to be 70.5 #N/mm**2,which occurs at x=r1=90 #mm\n",
+ "#Sub in equation 4 we get\n",
+ "#70.5=b*(90**2)**-1+a2 ................................(6)\n",
+ "\n",
+ "#Adding equation 5 and 6\n",
+ "#82.5=b2*(150**2)**-1+b*(90**2)**-1\n",
+ "#After furhter simplifying we get\n",
+ "b2=82.5*150**2*90**2*(150**2+90**2)**-1\n",
+ "\n",
+ "#Sub in equation 5 we get\n",
+ "a2=b2*(150**2)**-1-12 \n",
+ "\n",
+ "#If p_i is the internal pressure required then from Lame's theorem\n",
+ "p_i=b2*(r1**2)**-1-a2\n",
+ "\n",
+ "#Result\n",
+ "print\"Stresses int the material are:F_x\",round(F_x,2),\"N/mm**2\"\n",
+ "print\" :F_x2\",round(F_x2,2),\"N/mm**2\"\n",
+ "print\"Internal Pressure that can be maintained is\",round(p_i,2),\"N/mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stresses int the material are:F_x 70.5 N/mm**2\n",
+ " :F_x2 34.5 N/mm**2\n",
+ "Internal Pressure that can be maintained is 50.82 N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.15,Page No.344"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "r1=200 #mm #Inner Radius\n",
+ "r2=250 #mm #Radius at common surface\n",
+ "r3=300 #mm #Outer radius\n",
+ "p=6 #N/mm**2 #Inital pressure\n",
+ "p2=80 #N/mm**2 #Pressure\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Inner Cyclinder:\n",
+ "\n",
+ "#From Lame's Equation we have\n",
+ "#p_x=b*(x**2)**-1-a ..........................(1)\n",
+ "#F_x=b*(x**2)**-1+a ...........................(2)\n",
+ "\n",
+ "#At \n",
+ "x=r1=200 #mm\n",
+ "p_x=0\n",
+ "#0=b1*(250**2)**-1-a1 .................(3)\n",
+ "\n",
+ "#At x=r2=250 #mm\n",
+ "p_x2=6 #N/mm**2\n",
+ "#6=b1*(250**2)-a1 ...................(4)\n",
+ "\n",
+ "#From Equation 3 and 4 we get\n",
+ "b1=6*200**2*250**2*(200**2-250**2)**-1\n",
+ "\n",
+ "#From equation 3 we get\n",
+ "a1=b1*(200**2)**-1\n",
+ "\n",
+ "F_200=b1*(200**2)**-1+a1\n",
+ "F_250=b1*(250**2)**-1+a1\n",
+ "\n",
+ "#For outer cyclinder \n",
+ "#From Lame's Equation we have\n",
+ "#p_x2=b2*(x**2)**-1-a2 ..........................(5)\n",
+ "#F_x2=b2*(x**2)**-1+a2 ...........................(6)\n",
+ "\n",
+ "\n",
+ "#At \n",
+ "x2=r2=250 #mm\n",
+ "p_x2=6 #N/mm**2\n",
+ "#6=b2*(250**2)**-1-a2 ...........................(7) \n",
+ "\n",
+ "#At\n",
+ "x3=300 #mm\n",
+ "#p_x2=0\n",
+ "#0=b2**2*(300**2)**-1-a2 .................................(8)\n",
+ "\n",
+ "#from equation 7 and 8 we get\n",
+ "b2=6*250**2*300**2*(300**2-250**2)**-1\n",
+ "\n",
+ "#sub in equation 8 we get\n",
+ "a2=b2*(300**2)**-1\n",
+ "\n",
+ "F_250_2=b2*(250**2)**-1+a2\n",
+ "F_300_2=b2*(300**2)**-1+a2\n",
+ "\n",
+ "#When Fluid is admitted\n",
+ "#Let Lame's equation be\n",
+ "#p_x3=b3*(x**2)**-1-a3 ..........................(5)\n",
+ "#F_x3=b3*(x**2)**-1+a3 ...........................(6)\n",
+ "\n",
+ "\n",
+ "#At x=200\n",
+ "p_x3=80 #N/mm**2\n",
+ "#80=b3*(200**2)**-1-a3 ................................(7)\n",
+ "\n",
+ "#At x=300 #mm\n",
+ "#p_x=0\n",
+ "#0=b3*(300**2)**-1-a3 ..............................(8)\n",
+ "\n",
+ "#from Equation 7 and 8 we get\n",
+ "b3=80*200**2*300**2*(300**2-200**2)**-1\n",
+ "\n",
+ "#From Equation 8 we get\n",
+ "a3=b3*(300**2)**-1\n",
+ "\n",
+ "#Hoop stresses \n",
+ "F_200_3=b3*(200**2)**-1+a3 #N/mm**2\n",
+ "F_250_3=b3*(250**2)**-1+a3 #N/mm**2\n",
+ "F_300_3=b3*(300**2)**-1+a3 #N/mm**2\n",
+ "\n",
+ "#Pressure at common surface\n",
+ "p_250=b3*(250**2)**-1-a3 #N/mm**2\n",
+ "\n",
+ "#final stress\n",
+ "f_200=F_200+F_200_3 #N/mm**2\n",
+ "f_250=F_250+F_250_3 #N/mm**2\n",
+ "f_300=F_250_2+F_250_3 #N/mm**2\n",
+ "f_300_2=F_300_2+F_300_3 #N/mm**2\n",
+ "\n",
+ "#Result\n",
+ "print\"final Hoop stress are:f_200\",round(f_200,2),\"N/mm**2\"\n",
+ "print\" :f_250\",round(f_250,2),\"N/mm**2\"\n",
+ "print\" :f_300\",round(f_300,2),\"N/mm**2\"\n",
+ "print\" :f_300_2\",round(f_300_2,2),\"N/mm**2\"\n",
+ "print\"Variation of Hoop stress and Radial stress\"\n",
+ "\n",
+ "#Final stresses\n",
+ "#Variation of hoop stress \n",
+ " \n",
+ "X1=[x,x2,x3,x3]\n",
+ "Y1=[f_200,f_250,f_300,f_300_2]\n",
+ "Z1=[0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in mm\")\n",
+ "plt.ylabel(\"Hoop Stress Distribution in N/mm**2\")\n",
+ "plt.show()\n",
+ "\n",
+ "#Due to Fluid\n",
+ "#Variation of hoop stress \n",
+ " \n",
+ "X1=[x,x2,x3]\n",
+ "Y1=[F_200_3,F_250_3,F_300_3]\n",
+ "Z1=[0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in mm\")\n",
+ "plt.ylabel(\"Hoop Stress Distribution in N/mm**2\")\n",
+ "plt.show()\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "final Hoop stress are:f_200 174.67 N/mm**2\n",
+ " :f_250 128.83 N/mm**2\n",
+ " :f_300 189.43 N/mm**2\n",
+ " :f_300_2 155.27 N/mm**2\n",
+ "Variation of Hoop stress and Radial stress\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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MHz4cr7zyCmbPno1///vf1fIBnZeXp/l+8+bNmhVR0dHR+P7771FYWIjMzExcvHgRnTp1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\nVw+AnLO4d++eQY0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+ "text": [
+ "<matplotlib.figure.Figure at 0x55443f0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5d51e10>"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.16,Page No.348"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "do=200 #mm #Inner Diameter\n",
+ "r_o=100 #mm #Inner radius\n",
+ "d1=300 #mm #outer diameter\n",
+ "r1=150 #mm #Outer radius\n",
+ "d2=250 #mm #Junction Diameter\n",
+ "r2=125 #mm #Junction radius\n",
+ "E=2*10**5 #N/mm**2 #Modulus of Elasticity\n",
+ "p=30 #N/mm**2 #radial pressure\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#from Lame's Equation we get\n",
+ "#p_x=b*(x**2)**-1-a ..........................(1)\n",
+ "#F_x=b*(x**2)**-1+a ...........................(2)\n",
+ "\n",
+ "#Then from Boundary condition \n",
+ "#p_x=0 at x=100 #mm\n",
+ "#0=b1*(100**2)**-1-a1 .....................(3)\n",
+ "\n",
+ "#p_x2=30 #N/mm**2 at x2=125 #mm\n",
+ "#30=b1*(125**2)**-1-a1 ................................(4)\n",
+ "\n",
+ "#From equation 3 and 4 we get\n",
+ "b1=30*125**2*100**2*(100**2-125**2)**-1\n",
+ "\n",
+ "#From Equation 3 we get\n",
+ "a1=b1*(100**2)**-1\n",
+ "\n",
+ "#therefore Hoop stress in inner cyclinder at junction\n",
+ "F_2_1=b1*(125**2)**-1+a1 #N/mm**2\n",
+ "\n",
+ "#Outer Cyclinder\n",
+ "#p_x=b*(x**2)**-1-a ..........................(5)\n",
+ "#F_x=b*(x**2)**-1+a ...........................(6)\n",
+ "\n",
+ "#Now at x=125 #mm\n",
+ "#p_x3=30 #N/mm**2\n",
+ "#30=b2*(125**2)**-1-a2 ..................................(7)\n",
+ "\n",
+ "#At x=150 #mm\n",
+ "#p_x4=0\n",
+ "#0=b2*(150**2)**-1-a2 ...................................(8)\n",
+ "\n",
+ "#From equations 7 and 8\n",
+ "b2=30*150**2*125**2*(150**2-125**2)**-1\n",
+ "\n",
+ "#From eqauation 8 we get\n",
+ "a2=b2*(150**2)**-1\n",
+ "\n",
+ "#Hoop stress at junction \n",
+ "F_2_0=b2*(125**2)**-1+a2 #N/mm**2\n",
+ "\n",
+ "rho_r=(F_2_0-F_2_1)*E**-1*r2\n",
+ "\n",
+ "#Result\n",
+ "print\"Shrinkage Allowance is\",round(rho_r,3),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Shrinkage Allowance is 0.189 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 40
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.17,Page No.350"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d_o=500 #mm #Outer Diameter\n",
+ "r_o=250 #mm #Outer Radius\n",
+ "d1=300 #mm #Inner Diameter\n",
+ "r1=150 #mm #Inner Radius\n",
+ "d2=400 #mm #Junction Diameter\n",
+ "E=2*10**5 #N/mm**2 #Modulus ofElasticity\n",
+ "alpha=12*10**-6 #Per degree celsius\n",
+ "dell_d=0.2 #mm\n",
+ "dell_r=0.1 #mm\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let p be the radial pressure developed at junction\n",
+ "#Let Lame's Equation for internal cyclinder be\n",
+ "#p_x=b*(x**2)**-1-a ................................(1)\n",
+ "#F_x=b*(x**2)**-1+a ...............................(2)\n",
+ "\n",
+ "#At \n",
+ "x=150 #mm \n",
+ "p_x=0\n",
+ "#Sub in equation 1 we get\n",
+ "#0=b*(150**2)**-1-a .........................(3)\n",
+ "\n",
+ "#At \n",
+ "x2=200 #mm\n",
+ "#p_x2=p\n",
+ "#p=b*(200**2)**-1-a ......................(4)\n",
+ " \n",
+ "#From Equation 3 and 4\n",
+ "#p=b*(200**2)**-1-b(150**2)**-1\n",
+ "#after further simplifying we get\n",
+ "#b=-51428.571*p\n",
+ "\n",
+ "#sub in equation 3 we get\n",
+ "#a1=-2.2857*p\n",
+ "\n",
+ "#therefore hoop stress at junction is\n",
+ "#F_2_1=-21428.571*p*(200**2)**-1-2.2857*p\n",
+ "#after Further simplifying we geet\n",
+ "#F_2_1=3.5714*p\n",
+ "\n",
+ "#Let Lame's Equation for cyclinder be \n",
+ "#p_x=b*(x**2)**-1-a .........................5\n",
+ "#F_x=b*(x**2)**-1+a .............................6\n",
+ "\n",
+ "#At \n",
+ "x=200 #mm\n",
+ "#p_x=p2\n",
+ "#p2=b2*(20**2)**-1-a2 ...................7\n",
+ "\n",
+ "#At\n",
+ "x2=200 #mm\n",
+ "p_x2=0\n",
+ "#0=b2*(250**2)**-1-a2 ....................8\n",
+ "\n",
+ "#from equation 7 and 8 we get\n",
+ "#p2=b2*(200**2)**-1-b2*(250**2)**-1\n",
+ "#After further simplifying we get\n",
+ "#p2=b2*(250**2-200**2)*(200**2*250**2)**-1\n",
+ "#b2=111111.11*p\n",
+ "\n",
+ "#from equation 7\n",
+ "#a2=b2*(250**2)**-1\n",
+ "#further simplifying we get\n",
+ "#a2=1.778*p\n",
+ "\n",
+ "#At the junctionhoop stress in outer cyclinder \n",
+ "#F_2_0=b2*(200**2)**-1+a2\n",
+ "#After further simplifying we get\n",
+ "#F_2_0=4.5556*p\n",
+ "\n",
+ "#Considering circumferential strain,the compatibility condition\n",
+ "#rho_r*r2**-1=1*E**-1*(F_2_1+F_2_0)\n",
+ "#where F_2_1 is compressive and F_2_0 is tensile\n",
+ "#furter simplifying we get\n",
+ "p=0.1*200**-1*2*10**5*(3.5714+4.5556)**-1\n",
+ "\n",
+ "#Let T be the rise in temperature required\n",
+ "#dell_d=d*alpha*T\n",
+ "#After sub values and further simplifying we get\n",
+ "d=250 #mm\n",
+ "T=dell_d*(d*alpha)**-1 #Per degree celsius\n",
+ "\n",
+ "#Result\n",
+ "print\"Radial Pressure Developed at junction\",round(p,2),\"N/mm**2\"\n",
+ "print\"Min Temperatureto outer cyclinder\",round(T,2),\"Per degree Celsius\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Radial Pressure Developed at junction 12.3 N/mm**2\n",
+ "Min Temperatureto outer cyclinder 66.67 Per degree Celsius\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Example 8.8.18,Page No.355"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "d_o=400 #mm #Outer Diameter\n",
+ "r_o=200 #mm #Outer radius\n",
+ "t=50 #mm #Thickness\n",
+ "r1=150 #mm #Internal Radius\n",
+ "p=50 #N/mm**2 #Internal Pressure\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#The Radial Pressure and hoop stress at any radial distance x are given by\n",
+ "#p_x=b*(x**2)**-1-a ..........................(1)\n",
+ "#F_x=b*(x**2)**-1+a ...........................(2)\n",
+ "\n",
+ "#Now at\n",
+ "x=150 #N/mm**2\n",
+ "p_x1=50 #N/mm**2\n",
+ "#Sub in equation 1 we get\n",
+ "#50=2*b*(150**3)**-1-a ...........................(3)\n",
+ "\n",
+ "#At x=200 #mm\n",
+ "p_x2=0\n",
+ "#0=2*b*(200**2)**-1-a ....................(4)\n",
+ "\n",
+ "#From equation 3 and 4 we get\n",
+ "#50=2*b*(150**3)**-1-2*b*(200**3)**-1\n",
+ "#After further simplifying we get\n",
+ "b=50*150**3*200**3*(200**3-150**3)**-1*2**-1\n",
+ "\n",
+ "#Sub in equation 3 we get\n",
+ "a=b*(200**3)**-1\n",
+ "\n",
+ "#Now At\n",
+ "x=150 #mm\n",
+ "F_x=b*(x**3)**-1+a\n",
+ "\n",
+ "#Now At\n",
+ "x2=160 #mm\n",
+ "F_x2=b*(x2**3)**-1+a\n",
+ "\n",
+ "#Now At\n",
+ "x3=170 #mm\n",
+ "F_x3=b*(x3**3)**-1+a\n",
+ "\n",
+ "#Now At\n",
+ "x4=180 #mm\n",
+ "F_x4=b*(x4**3)**-1+a\n",
+ "\n",
+ "#Now At\n",
+ "x5=190 #mm\n",
+ "F_x5=b*(x5**3)**-1+a\n",
+ "\n",
+ "#Now At\n",
+ "x6=200 #mm\n",
+ "F_x6=b*(x6**3)**-1+a\n",
+ "\n",
+ "#Result\n",
+ "print\"Plot of Variation of hoop stress\"\n",
+ "\n",
+ "#Plotting Variation of hoop stress\n",
+ "\n",
+ "X1=[x,x2,x3,x4,x5,x6]\n",
+ "Y1=[F_x,F_x2,F_x3,F_x4,F_x5,F_x6]\n",
+ "Z1=[0,0,0,0,0,0]\n",
+ "plt.plot(X1,Y1,X1,Z1)\n",
+ "plt.xlabel(\"Length x in mm\")\n",
+ "plt.ylabel(\"Hoop Stress Distribution in N/mm**2\")\n",
+ "plt.show()\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Plot of Variation of hoop stress\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5d55f30>"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_09.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_09.ipynb new file mode 100644 index 00000000..eae6bfbc --- /dev/null +++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_09.ipynb @@ -0,0 +1,779 @@ +{
+ "metadata": {
+ "name": "chapter 09.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 9:Columns And Struts"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9.1,Page No.377"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "L=5000 #mm #Length of strut\n",
+ "dell=10 #mm #Deflection\n",
+ "W=10 #N #Load\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Central Deflection of a simply supported beam with central concentrated load is\n",
+ "#dell=W*L**3*(48*E*I)**-1 \n",
+ "\n",
+ "#Let E*I=X\n",
+ "X=W*L**3*(48*dell)**-1 #mm\n",
+ "\n",
+ "#Euler's Load\n",
+ "#Let Euler's Load be P\n",
+ "P=pi**2*X*(L**2)**-1\n",
+ "\n",
+ "#Result\n",
+ "print\"Critical Load of Bar is\",round(P,2),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Critical Load of Bar is 1028.08 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9.2,Page No.377"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=2000 #mm #Length of square column\n",
+ "E=12*10**3 #N/mm**2 #Modulus of Elasticity\n",
+ "sigma=12 #N/mm*2 #stress\n",
+ "W1=95*10**3 #N #Load1\n",
+ "W2=200*10**3 #N #Load2\n",
+ "FOS=3\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#From Euler's Formula\n",
+ "#P=pi**2*E*I*(L**2)**-1 .........(1)\n",
+ "\n",
+ "#Working Load\n",
+ "#W=P*(FOS)**-1\n",
+ "\n",
+ "#Part-1\n",
+ "\n",
+ "#At W1=95*10**3 #N\n",
+ "#W1=P*(3*L**2)**-1\n",
+ "\n",
+ "#Let 'a' be the side of the square\n",
+ "#I=1*12**-1*a**4\n",
+ "\n",
+ "#sub value of I in Equation 1 and further rearranging we get\n",
+ "a=(W1*3*12*L**2*(pi**2*E)**-1)**0.25 #mm\n",
+ "\n",
+ "#From Consideration of direct crushing\n",
+ "#sigma*a**2=W1\n",
+ "#After Reaaranging the above equation we get\n",
+ "a2=(W1*(sigma)**-1)**0.5 #mm\n",
+ "\n",
+ "#required size is 103.67*103.67 i.e a*a\n",
+ "\n",
+ "#Part-2\n",
+ "\n",
+ "#At W2=200*10**3 #N\n",
+ "#W2=P*(3*L**2)**-1\n",
+ "#After substituting values and further Rearranging the above equation we get\n",
+ "a3=(W2*3*12*L**2*(pi**2*E)**-1)**0.25 #mm\n",
+ "\n",
+ "#From consideration of direct compression,size required is\n",
+ "a4=(W2*sigma**-1)**0.5\n",
+ "\n",
+ "#required size is 129.10*129.10 i.e a4*a4\n",
+ "\n",
+ "#Result\n",
+ "print\"For W1 Load Required size is\",round(a*a,2),\"mm**2\"\n",
+ "print\"For W2 Load Required size is\",round(a4*a4,2),\"mm**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "For W1 Load Required size is 10747.38 mm**2\n",
+ "For W1 Load Required size is 16666.67 mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9.3,Page No.378"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Flange \n",
+ "b=100 #mm #Width\n",
+ "\n",
+ "D=80 #mm #Overall Depth\n",
+ "t=10 #mm #Thickness of web and flanges\n",
+ "L=3000 #mm #Length of strut\n",
+ "E=200*10**3 #N/mm**2 #Modulus of Elasticity\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let centroid be at depth y_bar from top fibre\n",
+ "y_bar=(b*t*t*2**-1+(D-t)*t*((D-t)*2**-1+t))*(b*t+(D-t)*t)**-1 #mm \n",
+ "\n",
+ "#M.I at x-x axis\n",
+ "I_x=1*12**-1*b*t**3+b*t*(y_bar-t*2**-1)**2+1*12**-1*t*((D-t))**3+t*((D-t))*((((D-t)*2**-1)+t)-y_bar)**2\n",
+ "\n",
+ "#M.I at y-y axis\n",
+ "I_y=1*12**-1*t*b**3+1*12**-1*(D-t)*t**3 #mm**3\n",
+ "\n",
+ "#Least M.I\n",
+ "I=I_y\n",
+ "\n",
+ "#Since both ends are hinged\n",
+ "#Feective Length=Actual Length\n",
+ "L=l=3000 #mm\n",
+ "\n",
+ "#Buckling Load \n",
+ "P=pi**2*E*I*(l**2)**-1*10**-3 #KN\n",
+ "\n",
+ "#Result\n",
+ "print\"The Buckling Load for strut of tee section\",round(P,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Buckling Load for strut of tee section 184.05 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9.4,Page No.379"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "D=400 #mm #Overall Depth\n",
+ "\n",
+ "#Flanges\n",
+ "b=300 #mm #Width\n",
+ "t=50 #mm #Thickness\n",
+ "\n",
+ "t2=30 #mm #Web Thickness\n",
+ "\n",
+ "dell=10 #mm #Deflection\n",
+ "w=40 #N/mm #Load\n",
+ "FOS=1.75 #Factor of safety\n",
+ "E=2*10**5 #N/mm**2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#M.I at x-x axis\n",
+ "I_x=1*12**-1*(b*D**3-(b-t2)*b**3) #mm**4\n",
+ "\n",
+ "#Central Deflection\n",
+ "#dell=5*w*L**4*(384*E*I)**-1\n",
+ "#After sub values in above equation and further simplifying we get\n",
+ "L=(dell*384*E*I_x*(5*w)**-1)**0.25\n",
+ "\n",
+ "#M.I aty-y axis\n",
+ "I=I_y=1*12**-1*t*b**3+1*12**-1*b*t2**3+1*12**-1*t*b**3 #mm**4\n",
+ "\n",
+ "#Both the Ends of column are hinged\n",
+ "\n",
+ "#Crippling Load\n",
+ "P=pi**2*E*I*(L**2)**-1 #N\n",
+ "\n",
+ "#Safe Load\n",
+ "S=P*(FOS)**-1*10**-3 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Safe Load if I-section is used as column with both Ends hhinged\",round(S,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Safe Load if I-section is used as column with both Ends hhinged 4123.29 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9.5,Page No.381"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "D=200 #mm #External Diameter\n",
+ "t=20 #mm #hickness\n",
+ "d=200-2*t #mm #Internal Diameter\n",
+ "E=1*10**5 #N/mm**2\n",
+ "a=1*(1600)**-1 #Rankine's Constant\n",
+ "L=4.5 #m #Length\n",
+ "sigma=550 #N/mm**2 #Stress\n",
+ "FOS=2.5\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Moment of Inertia\n",
+ "I=pi*D**4*64**-1-pi*d**4*64**-1\n",
+ "\n",
+ "#Both Ends are fixed\n",
+ "\n",
+ "#Effective Length\n",
+ "l=1*2**-1*L*10**3 #mm\n",
+ "\n",
+ "#Euler's Critical Load\n",
+ "P_E=pi**2*E*I*(l**2)**-1\n",
+ "\n",
+ "A=pi*4**-1*(D**2-d**2) #mm*2\n",
+ "\n",
+ "k=(I*A**-1)**0.5\n",
+ "\n",
+ "#Rankine's Critical Load\n",
+ "P_R=sigma*A*(1+a*(l*k**-1)**2)**-1\n",
+ "\n",
+ "X=P_E*P_R**-1 \n",
+ "\n",
+ "#Safe Load using Rankine's Formula\n",
+ "S=P_R*(FOS)**-1*10**-3 #KN\n",
+ "\n",
+ "#Result\n",
+ "print\"Safe Load by Rankine's Formula is\",round(S,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Safe Load by Rankine's Formula is 1404.36 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 39
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9.6,Page No.382"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "L=3000 #mm #Length of column\n",
+ "W=800*10**3 #N #Load\n",
+ "a=1*1600**-1 #Rankine's constant\n",
+ "FOS=4 #Factor of safety\n",
+ "sigma=550 #N/mm**2 #stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Effective Length\n",
+ "l=L*2**-1 #mm \n",
+ "\n",
+ "#Let d1=outer diameter & d2=inner diameter\n",
+ "#d1=5*8**-1*d2\n",
+ "\n",
+ "#M.I\n",
+ "#I=pi*64**-1*(d1**4-d2**4) #mm**4\n",
+ "\n",
+ "#Area of section\n",
+ "#A=pi4**-1*(d1**2-d2**2) #mm**2\n",
+ "\n",
+ "#k=(I*A**-1) \n",
+ "#substituting values in above equation \n",
+ "#k=1*16**-1*(d1**2-d2**2)\n",
+ "#after simplifying further we get\n",
+ "#k=0.2948119.d1\n",
+ "\n",
+ "#X=l*k**-1\n",
+ "#substituting values in above equation and after simplifying further we get\n",
+ "#X=5087.9898*d1**-1\n",
+ "\n",
+ "#Crtitcal Load\n",
+ "P=W*FOS #N\n",
+ "\n",
+ "#From Rankine's Load\n",
+ "#P2=sigma*A*(1+a*(X)**2)**-1\n",
+ "#substituting values in above equation and after simplifying further we get\n",
+ "#d1**4-12156618*d1**4-1.96691*10**8=0\n",
+ "#Solving Quadratic Equation we get\n",
+ "#d1**2-12156618*d1-196691000=0\n",
+ "a=1\n",
+ "b=-12156.618\n",
+ "c=-196691000\n",
+ "\n",
+ "Y=b**2-4*a*c\n",
+ "\n",
+ "d1_1=((-b+Y**0.5)*(2*a)**-1)**0.5 #mm\n",
+ "d1_2=((-b-Y**0.5)*(2*a)**-1) #mm\n",
+ "\n",
+ "d2=5*8**-1*d1_1\n",
+ "\n",
+ "#Result\n",
+ "print\"Section of cast iron hollow cylindrical column is:d1_1\",round(d1_1,2),\"mm\"\n",
+ "print\" :d2 \",round(d2,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Section of cast iron hollow cylindrical column is:d1_1 146.16 mm\n",
+ " :d2 91.35 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9.7,Page No.383"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "#Let X=(P*A**-1) #Average Stress at Failure \n",
+ "Lamda_1=70 #Slenderness Ratio\n",
+ "Lamda_2=170 #Slenderness Ratio\n",
+ "X1=200 #N/mm**2 \n",
+ "X2=69 #N/mm**2 \n",
+ "\n",
+ "#Rectangular section\n",
+ "b=60 #mm #width\n",
+ "t=20 #mm #Thickness\n",
+ "\n",
+ "L=1250 #mm #Length of strut\n",
+ "FOS=4 #Factor of safety\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Slenderness ratio\n",
+ "#Lamda=L*k**-1\n",
+ "\n",
+ "#The Rankine's Formula for strut\n",
+ "#P=sigma*A*(1+a*(L*k**-1)**-1\n",
+ "\n",
+ "#From test result 1,\n",
+ "#After sub values in above equation we get and further simplifying we get\n",
+ "#sigma_1=200+980000*a ...................(1)\n",
+ "\n",
+ "#From test result 2,\n",
+ "#After sub values in above equation we get and further simplifying we get\n",
+ "#sigma_2=69+1994100*a ...................(2)\n",
+ "\n",
+ "#Substituting it in equation (1) we get\n",
+ "a=131*1014100**-1 \n",
+ "\n",
+ "#Substituting a in equation 1\n",
+ "sigma_1=200+980000*a #N/mm**2\n",
+ "\n",
+ "#Effective Length \n",
+ "l=1*2**-1*L #mm\n",
+ "\n",
+ "#Least of M.I\n",
+ "I=1*12**-1*b*t**3 #mm**4\n",
+ "\n",
+ "#Area \n",
+ "A=b*t #mm**2 \n",
+ "\n",
+ "k=(I*A**-1)**0.5\n",
+ "\n",
+ "#Slenderness ratio\n",
+ "Lamda=l*k**-1\n",
+ "\n",
+ "#From Rankine's Ratio\n",
+ "P=sigma_1*A*(1+a*(Lamda)**2)**-1\n",
+ "\n",
+ "#Safe Load\n",
+ "S=P*(FOS)**-1*10**-3 #N\n",
+ "\n",
+ "#Result\n",
+ "print\"Constant in the Formula is:a \",round(a,6)\n",
+ "print\" :sigma_1\",round(sigma_1,2)\n",
+ "print\"Safe Load is\",round(S,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Constant in the Formula is:a 0.000129\n",
+ " :sigma_1 326.6\n",
+ "Safe Load is 38.98 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 38
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9.8,Page No.385"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "D=200 #mm #Depth\n",
+ "b=140 #mm #width\n",
+ "\n",
+ "#Plate\n",
+ "b2=160 #mm #Width\n",
+ "t2=10 #mm #Thickness\n",
+ "\n",
+ "L=l=4000 #mm #Length\n",
+ "FOS=4 #Factor of safety\n",
+ "sigma=315 #N/mm**2 #stress\n",
+ "a2=1*7500**-1 \n",
+ "I_xx=26.245*10**6 #mm**4 #M.I at x-x\n",
+ "I_yy=3.288*10**6 #mm**4 #M.I at y-y\n",
+ "a=3671 #mm**2 #Area\n",
+ "k_x=84.6#mm\n",
+ "k_y=29.9 #mm\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Total Area\n",
+ "A=a+2*t2*b2 #mm**2\n",
+ "\n",
+ "#M.I\n",
+ "I=I_yy+2*12**-1*t2*b2**3 #mm**4\n",
+ "\n",
+ "k=(I*A**-1)**0.5 #mm\n",
+ "\n",
+ "#Let X=L*k**-1\n",
+ "X=L*k**-1\n",
+ "\n",
+ "#Appliying Rankine's Formula\n",
+ "P=sigma*A*(1+a2*(X)**2)**-1 #N\n",
+ "\n",
+ "#Safe Load\n",
+ "S=P*(FOS)**-1*10**-3 #KN\n",
+ "\n",
+ "#Result\n",
+ "print\"Safe axial Load is\",round(S,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Safe axial Load is 220.93 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 48
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9.9,Page No.389"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "E=200*10**3 #N/mm**2 #Modulus of elasticity\n",
+ "sigma=330 #N/mm**2 #Stress\n",
+ "a=1*7500**-1 #Rankine's constant\n",
+ "A=5205 #mm**2 #area of column\n",
+ "I_xx=59.431*10**6 #mm**4 #M.I at x-x axis\n",
+ "I_yy=8.575*10**6 #mm**24#M.I at y-y axis\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Total M.I\n",
+ "I=I_xx+I_yy #mm**4\n",
+ "\n",
+ "#Area of compound Section \n",
+ "A2=2*A #mm**2\n",
+ "\n",
+ "k=(I*A2**-1)**0.5 #mm\n",
+ "\n",
+ "#Equating Euler's Load to Rankine's Load we get\n",
+ "#pi**2*E*I*(L**2)**-1=sigma*A*(1+a*(L*k)**2)**-1\n",
+ "#After Substitt=uting values and further simplifying we get\n",
+ "L=(39076198*(1-0.7975432)**-1)**0.5*10**-3 #m\n",
+ "\n",
+ "#Result\n",
+ "print\"Length of column for which Rankine's formula and Euler's Formula give the same result is\",round(L,2),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Length of column for which Rankine's formula and Euler's Formula give the same result is 13.89 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 47
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9.10,Page No.387"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "sigma=326 #N/mm**2 #stress\n",
+ "E=2*10**5 #N/mm**2 #Modulus of Elasticity\n",
+ "FOS=2 #Factor of safety\n",
+ "a=1*7500**-1 #Rankine's constant\n",
+ "D=350 #mm #Overall Depth \n",
+ "\n",
+ "#Cover plates\n",
+ "b1=500 #mm #width\n",
+ "t1=10 #mm #Thickness\n",
+ "\n",
+ "d=220 #mm #Distance between two channels\n",
+ "\n",
+ "L=6000 #mm #Length of column\n",
+ "\n",
+ "A=5366 #mm**2 #Area of Column section \n",
+ "I_xx=100.08*10**6 #mm**4 #M.I of x-x axis\n",
+ "I_yy=4.306*10**6 #mm**4 #M.I of y-y axis\n",
+ "C_yy=23.6 #mm #Centroid at y-y axis\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Symmetric axes are the centroidal axes is\n",
+ "\n",
+ "#M.I of Channel at x-x axis\n",
+ "I_xx_1=2*I_xx+2*(1*12**-1*b1*t1**3+b1*t1*(D*2**-1+t1*2**-1)**2)\n",
+ "\n",
+ "#M.I of Channel at y-y axis\n",
+ "I_yy_1=2*(I_yy+A*(d*2**-1+C_yy)**2)+2*12**-1*t1*b1**3\n",
+ "\n",
+ "#As I_yy<I_xx\n",
+ "#So\n",
+ "I=I_yy_1 #mm**4 \n",
+ "\n",
+ "A2=2*A+2*t1*b1 #Area of channel\n",
+ "\n",
+ "k=(I*A2**-1)**0.5 #mm\n",
+ "\n",
+ "#Critical Load\n",
+ "P=sigma*A2*(1+a*(L*k**-1)**2)**-1 \n",
+ "\n",
+ "#Safe Load\n",
+ "S=P*2**-1*10**-3 #KN\n",
+ "\n",
+ "#Result\n",
+ "print\"Safe Load carrying Capacity is\",round(S,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Safe Load carrying Capacity is 2717.35 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 67
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9.11,Page No.390"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "I=4.085*10**8 #mm**4 #M.I\n",
+ "A=20732.0 #mm**2 #area of column\n",
+ "f_y=250 #N/mm**2 \n",
+ "L=6000 #mm #Length of column\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "k=(I*A**-1)**0.5 #mm\n",
+ "lamda=L*k**-1 #Slenderness ratro\n",
+ "\n",
+ "#From Indian standard table\n",
+ "lamda_1=40 \n",
+ "sigma_a_c_1=139 #N/mm**2\n",
+ "lamda_2=50 \n",
+ "sigma_a_c_2=132 #N/mm**2 \n",
+ "\n",
+ "#Linearly interpolating between these values for lambda=42.744\n",
+ "\n",
+ "sigma_a_c_3=sigma_a_c_1-2.744*10**-1*(sigma_a_c_1-sigma_a_c_2)\n",
+ "\n",
+ "#Safe Load carrying capacity of column\n",
+ "P=sigma_a_c_3*A*10**-3\n",
+ "\n",
+ "#Result\n",
+ "print\"Safe Load carrying capacity is\",round(P,2),\"KN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Safe Load carrying capacity is 2841.93 KN\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_10.ipynb b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_10.ipynb new file mode 100644 index 00000000..8b69b917 --- /dev/null +++ b/Strength_Of_Materials_by_S_S_Bhavikatti/chapter_10.ipynb @@ -0,0 +1,280 @@ +{
+ "metadata": {
+ "name": "chapter 10.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 10:Theory of Failures"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.10.10.1,Page No.401"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "P_e=300 #N/mm**2 #Elastic Limit in tension\n",
+ "FOS=3 #Factor of safety\n",
+ "mu=0.3 #Poissoin's ratio\n",
+ "P=12*10**3 #N Pull \n",
+ "Q=6*10**3 #N #Shear force\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let d be the diameter of the shaft\n",
+ "\n",
+ "#Direct stress\n",
+ "#P_x=P*(pi*4**-1*d**3)**-1\n",
+ "#After substituting values and further simplifying we get\n",
+ "#P_x=48*10**3\n",
+ "\n",
+ "#Now shear stress at the centre of bolt\n",
+ "#q=4*3**-1*q_av\n",
+ "#After substituting values and further simplifying we get\n",
+ "#q=32*10**3*(pi*d**2)**-1\n",
+ "\n",
+ "#Principal stresses are\n",
+ "#P1=P_x*2**-1+((P_x*2**-1)**2+q**2)**0.5\n",
+ "#After substituting values and further simplifying we get\n",
+ "#p1=20371.833*(d**2)**-1\n",
+ "\n",
+ "#P2=P_x*2**-1-((P_x*2**-1)**2+q**2)**0.5\n",
+ "#After substituting values and further simplifying we get\n",
+ "#P2=-5092.984*(d**2)**-1\n",
+ "\n",
+ "#q_max=((P_x*2**-1)**2+q**2)**0.5\n",
+ "\n",
+ "#From Max Principal stress theory\n",
+ "#Permissible stress in Tension\n",
+ "P1=100 #N/mm**2 \n",
+ "d=(20371.833*P1**-1)**0.5\n",
+ "\n",
+ "#Max strain theory\n",
+ "#e_max=P1*E**-1-mu*P2*E**-1\n",
+ "#After substituting values and further simplifying we get\n",
+ "#e_max=21899.728*(d**2*E)**-1\n",
+ "\n",
+ "#According to this theory,the design condition is\n",
+ "#e_max=P_e*(E*FOS)**-1\n",
+ "#After substituting values and further simplifying we get\n",
+ "d2=(21899.728*3*300**-1)**0.5 #mm\n",
+ "\n",
+ "#Max shear stress theory\n",
+ "#e_max=shear stress at elastic*(FOS)**-1\n",
+ "#After substituting values and further simplifying we get\n",
+ "d3=(12732.421*6*300**-1)**0.5 #mm\n",
+ "\n",
+ "#Result\n",
+ "print\"Diameter of Bolt by:Max Principal stress theory\",round(d,2),\"mm\"\n",
+ "print\" :Max strain theory\",round(d2,2),\"mm\"\n",
+ "print\" :Max shear stress theory\",round(d3,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Diameter of Bolt by:Max Principal stress theory 14.27 mm\n",
+ " :Max strain theory 14.8 mm\n",
+ " :Max shear stress theory 15.96 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.10.10.2.Page No.402"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "M=40*10**6 #N-mm #Bending moment\n",
+ "T=10*10**6 #N-mm #TOrque\n",
+ "mu=0.25 #Poissoin's ratio\n",
+ "P_e=200 #N/mm**2 #Stress at Elastic Limit\n",
+ "FOS=2\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#Let d be the diameter of the shaft\n",
+ "\n",
+ "#Principal stresses are given by\n",
+ "\n",
+ "#P1=16*(pi*d**3)**-1*(M+(M**2+T**2)**0.5)\n",
+ "#After substituting values and further simplifying we get\n",
+ "#P1=4.13706*10**8*(d**3)**-1 ............................(1)\n",
+ "\n",
+ "#P2=16*(pi*d**3)**-1*(M-(M**2+T**2)**0.5)\n",
+ "#After substituting values and further simplifying we get\n",
+ "#P2=-6269718*(pi*d**3)**-1 ..............................(2)\n",
+ "\n",
+ "#q_max=(P1-P2)*2**-1\n",
+ "#After substituting values and further simplifying we get\n",
+ "#q_max=2.09988*10**8*(d**3)**-1\n",
+ "\n",
+ "#Max Principal stress theory\n",
+ "#P1=P_e*(FOS)**-1\n",
+ "#After substituting values and further simplifying we get\n",
+ "d=(4.13706*10**8*2*200**-1)**0.33333 #mm \n",
+ "\n",
+ "#Max shear stress theory\n",
+ "#q_max=shear stress at elastic limit*(FOS)**-1\n",
+ "#After substituting values and further simplifying we get\n",
+ "d2=(2.09988*10**8*4*200**-1)**0.33333\n",
+ "\n",
+ "#Max strain energy theory\n",
+ "#P_3=0\n",
+ "#P1**2+P2**2-2*mu*P1*P2=P_e**2*(FOS)**-1\n",
+ "#After substituting values and further simplifying we get\n",
+ "d3=(8.62444*10**12)**0.166666\n",
+ "\n",
+ "#Result\n",
+ "print\"Diameter of shaft according to:MAx Principal stress theory\",round(d,2),\"mm\"\n",
+ "print\" :Max shear stress theory\",round(d2,2),\"mm\"\n",
+ "print\" :Max strain energy theory\",round(d3,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Diameter of shaft according to:MAx Principal stress theory 160.52 mm\n",
+ " :Max shear stress theory 161.33 mm\n",
+ " :Max strain energy theory 143.2 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example No.10.10.3,Page No.403"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "#Initilization of Variables\n",
+ "\n",
+ "f_x=40 #N/mm**2 #Internal Fliud Pressure\n",
+ "d1=200 #mm #Internal Diameter\n",
+ "r1=d1*2**-1 #mm #Radius\n",
+ "q=300 #N/mm**2 #Tensile stress\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "#From Lame's Equation we have,\n",
+ "\n",
+ "#Hoop Stress\n",
+ "#f_x=b*(x**2)**-1+a ..........................(1)\n",
+ "\n",
+ "#Radial Pressure\n",
+ "#p_x=b*(x**2)**-1-a .........................(2)\n",
+ "\n",
+ "#the boundary conditions are\n",
+ "x=d1*2**-1 #mm \n",
+ "#After sub values in equation 1 and further simplifying we get\n",
+ "#40=b*100**-1-a ..........................(3)\n",
+ "\n",
+ "#Max Principal stress theory\n",
+ "#q*(FOS)**-1=b*100**2+a ..................(4)\n",
+ "#After sub values in above equation and further simplifying we get\n",
+ "\n",
+ "#From Equation 3 and 4 we get\n",
+ "a=80*2**-1\n",
+ "#Sub value of a in equation 3 we get\n",
+ "b=(f_x+a)*100**2\n",
+ "\n",
+ "#At outer edge where x=r_0 pressure is zero\n",
+ "r_0=(b*a**-1)**0.5 #mm\n",
+ "\n",
+ "#thickness\n",
+ "t=r_0-r1 #mm\n",
+ "\n",
+ "#Max shear stress theory\n",
+ "P1=b*(100**2)**-1+a #Max hoop stress\n",
+ "P2=-40 #pressure at int radius (since P2 is compressive)\n",
+ "\n",
+ "#Max shear stress\n",
+ "q_max=(P1-P2)*2**-1\n",
+ "\n",
+ "#According max shear theory the design condition is\n",
+ "#q_max=P_e*2**-1*(FOS)**-1\n",
+ "#After sub values in equation we get and further simplifying we get\n",
+ "#80=b*(100**2)**-1+a\n",
+ "#After sub values in equation 1 and 3 and further simplifying we get\n",
+ "b2=120*100**2*2**-1\n",
+ "\n",
+ "#from equation(3)\n",
+ "a2=120*2**-1-a\n",
+ "\n",
+ "#At outer radius r_0,radial pressure=0\n",
+ "r_02=(b2*a2**-1)**0.5\n",
+ "\n",
+ "#thickness\n",
+ "t2=r_02-r1\n",
+ "\n",
+ "#Result\n",
+ "print\"Thickness of metal by:Max Principal stress theory\",round(t,2),\"mm\"\n",
+ "print\" :Max shear stress thoery\",round(t2,2),\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Thickness of metal by:Max Principal stress theory 41.42 mm\n",
+ " :Max shear stress thoery 73.21 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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