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diff --git a/Statics_And_Strength_Of_Materials/ch9.ipynb b/Statics_And_Strength_Of_Materials/ch9.ipynb new file mode 100755 index 00000000..ee3b4983 --- /dev/null +++ b/Statics_And_Strength_Of_Materials/ch9.ipynb @@ -0,0 +1,509 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:9125011b4afb20e4bcb070d525e10ee7f4e22999f77038ff5e818f0e6a9e5e7f" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 9 : Concept of Strain" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.1 Page No : 193" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "length =10 \t\t\t#ft\n", + "delta =0.024 \t\t\t#in\n", + "\n", + "# Calculations\n", + "epsilon =delta/(length*12)\n", + "\n", + "# Results\n", + "print \"Axial strain =%.4f in/in\"%(epsilon)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Axial strain =0.0002 in/in\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.2 Page No : 194" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "drop = 5. \t\t\t#in\n", + "width = 8. \t\t\t#ft\n", + "\n", + "# Calculations\n", + "deltaMB =math.sqrt((width*12/2)**2 +drop**2) - (width*12/2)\n", + "epsilon =deltaMB/(width*12/2)\n", + "\n", + "# Results\n", + "print \"Strain in the wire = %.5f in/in\"%(epsilon)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Strain in the wire = 0.00541 in/in\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.3 Page no : 198" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# variables and Calculations\n", + "\n", + "E = 30000./0.001\n", + "deltaP1 = 66000. # psi\n", + "deltault = 116000 # psi\n", + "deltarup = 103000 # psi\n", + "\n", + "Pf = round(deltarup*math.pi/4*0.505**2,-2)\n", + "deltarup_ = round(Pf/(math.pi*0.425**2/4),-3)\n", + "percent_elongation = (2.375 - 2)/2*100\n", + "percent_reduction = ((math.pi*0.505**2/4) - (math.pi*0.425**2/4))/(math.pi*0.505**2/4) * 100\n", + "\n", + "# Results\n", + "print \"E = %.1e psi\"%E\n", + "print \"The load of failure Pf = %d lb\"%Pf\n", + "print \"Rupture strength : %.d psi\"%deltarup_\n", + "print \"Percent elongation = %.1f %%\"%percent_elongation\n", + "print \"Percent reduction in area = %.1f %%\"%percent_reduction\n", + "\n", + "\n", + "# note : last answer is wrong in book. please check." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "E = 3.0e+07 psi\n", + "The load of failure Pf = 20600 lb\n", + "Rupture strength : 145000 psi\n", + "Percent elongation = 18.8 %\n", + "Percent reduction in area = 29.2 %\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.4 Page No : 203" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "length =15. \t\t\t#in\n", + "tension =5000. \t\t\t#lb\n", + "UltStress =20000. \t\t\t#psi\n", + "delta =0.005 \t\t\t#in\n", + "\n", + "# Calculations\n", + "E =30*10**6 \t\t\t#psi\n", + "A1 =tension/UltStress\n", + "A2 =tension*length/(delta*E)\n", + "if A1 >= A2:\n", + " A =A1\n", + "else:\n", + " A =A2\n", + "Dia =math.sqrt(4*A/math.pi)\n", + "\n", + "# Results\n", + "print \"diameter required = %.3f in\"%( Dia)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "diameter required = 0.798 in\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.5 Page No : 204" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "L1 =5.\n", + "L2 =10.\n", + "T1 =2.5\n", + "T2 =5.\n", + "T3 =5.\n", + "T4 =5.\n", + "T5 =2.5\n", + "E =30.*10**6 \t\t\t#psi\n", + "outDia =2. \t\t\t#in\n", + "\n", + "# Calculations # Results\n", + "inDia =1./8 \t\t\t#in\n", + "RE =(T1+T2+T3+T4+T5)/2 \t\t\t#kips\n", + "RA =RE\n", + "GH =(RA*L2-T2*L1-T1*L2)/4\n", + "print \"Stress in GH =%.1f kips\"%(GH)\n", + "A =math.pi*(outDia**2-(outDia-2*inDia)**2)/4\n", + "delta =GH*10**3 *(L1*12)/(E*A)\n", + "print \" Deformation =%.3f in\"%(delta)\n", + "sigma =GH*10**3 /A\n", + "print \" Stress =%d psi\"%(round(sigma,-3))\n", + "SF =65000/sigma\n", + "print \" Factor of safety =%.3f \"%(SF)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Stress in GH =12.5 kips\n", + " Deformation =0.034 in\n", + " Stress =17000 psi\n", + " Factor of safety =3.829 \n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.6 Page No : 205" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from numpy import linalg\n", + "\t\t\t\n", + "# Variables\n", + "Es = 30.*10**6 \t\t\t#psi\n", + "As = 1. \t\t\t#in**2\n", + "Ea = 10.*10**6 \t\t\t#psi\n", + "Aa = 2. \t\t\t#in**2\n", + "Ls = 10. \t\t\t#ft\n", + "La = 5. \t\t\t#ft\n", + "\t\t\t\n", + "# Calculations\n", + "A =[[(Ls/(Es*As)) ,(-La/(Ea*Aa))],[1 ,1]]\n", + "b = [0,1]\n", + "c = linalg.solve(A,b)\n", + "Fa = c[0]\n", + "Fb = c[1]\n", + "d = Fb*Ls\n", + "\t\t\t\n", + "# Results\n", + "print 'distance = %.2f ft'%(d)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "distance = 5.71 ft\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.7 Page No : 206" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "P =40000. \t\t\t#lb\n", + "L =15. \t\t\t#in\n", + "delta =0.0032 \t\t\t#in\n", + "dia =4. \t\t\t#in\n", + "axial =0.0032 \t\t\t#in\n", + "lateral =0.00022 \t\t\t#in\n", + "\n", + "# Calculations # Results\n", + "E =P*L/(delta*math.pi*(dia/2)**2)\n", + "print \"Modulus of elasticity =%.2f psi\"%(E)\n", + "Mu =lateral*L/(axial*dia)\n", + "print \"Poisson ratio = %.2f\"%(Mu)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Modulus of elasticity =14920775.91 psi\n", + "Poisson ratio = 0.26\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.8 Page No : 207" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Variables\n", + "alpha =11.2*10**(-6) \t\t\t#in/in/F\n", + "E =15*10**6 \t\t\t#psi\n", + "L =60. \t\t\t#in\n", + "deltaT1 =0.01 \t\t\t#in\n", + "T2 =50 \t\t\t#F\n", + "\n", + "# Calculations # Results\n", + "deltaT =deltaT1/(alpha*L)\n", + "print \"The temperature increase necessary to cause free end to touch B =%.1f F\"%(deltaT)\n", + "sigma =(alpha*L*T2-deltaT1)*E/L\n", + "print \"Stress in the rod =%d psi\"%(sigma+1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The temperature increase necessary to cause free end to touch B =14.9 F\n", + "Stress in the rod =5900 psi\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "\n", + "Example 9.9 Page No : 208" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "weight =25000. \t\t\t#Kg\n", + "A =2 \t\t\t #sq.in\n", + "alphaS =6.5*10**(-6) \t\t\t#in/in/F\n", + "alphaB =11.2*10**(-6) \t\t\t#in/in/F\n", + "Es =30*10**6 \t\t\t#psi\n", + "Eb =15*10**6 \t\t\t#psi\n", + "\n", + "# Calculations # Results\n", + "deltaT =weight/(Es*A*(alphaB-alphaS))\n", + "print \"Net temperature drop =%.1f F\"%(deltaT)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Net temperature drop =88.7 F\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.10 Page No : 209" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "S =5. \t\t\t#in\n", + "Al =6. \t\t\t#in\n", + "alphaS =6.5*10**(-6) \t\t\t#in/in/F\n", + "alphaAl =13.1*10**(-6) \t\t\t#in/in/F\n", + "Es =30.*10**6 \t\t\t#psi\n", + "EAl =10.*10**6 \t\t\t#psi\n", + "As =1. \t\t\t#in**2\n", + "AAl =2. \t\t\t#in**2\n", + "T =50. \t\t\t#F\n", + "dia =1 \t\t\t#in\n", + "\n", + "# Calculations # Results\n", + "P =(alphaS*S*12*T + alphaAl*Al*12*T)/(S*12/(Es*As) + Al*12/(EAl*AAl))\n", + "print \"Shearing force = %d lb\"%(round(P,-1))\n", + "T =P/(math.pi*(dia/2.)**2)\n", + "print \" The shear stress in the pin =%d psi\"%(round(T,-2))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Shearing force = 11900 lb\n", + " The shear stress in the pin =15200 psi\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.11 Page No : 211" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "edge = 2. \t\t\t#in\n", + "height =3. \t\t\t#in\n", + "F = 20000. \t\t\t#lb\n", + "deltaS = 0.00234 \t\t\t#in\n", + "deltaA = 0.00088 \t\t\t#in\n", + "\n", + "# Calculations # Results\n", + "E = F*height/(deltaA*edge*edge)\n", + "print \"Modulus of elasticity = %.1e psi\"%(E)\n", + "G =F*height/(deltaS*edge*edge)\n", + "print \" Modulus of Rigidity = %.1e psi\"%(G)\n", + "Mu =E/(2*G) -1\n", + "print \" Poisson ratio = %.1f \"%(Mu)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Modulus of elasticity = 1.7e+07 psi\n", + " Modulus of Rigidity = 6.4e+06 psi\n", + " Poisson ratio = 0.3 \n" + ] + } + ], + "prompt_number": 14 + } + ], + "metadata": {} + } + ] +}
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