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diff --git a/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter10_3.ipynb b/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter10_3.ipynb new file mode 100755 index 00000000..913e9f20 --- /dev/null +++ b/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter10_3.ipynb @@ -0,0 +1,258 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:39be4bd5a29fce6d0d8085f52939f9fac01e348dbfffcb5b53194aa4be7d5f98" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter10:Columns" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.10.1, Page No:369" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "Le=7 #Effective length in m\n", + "P=450 #Applied axial Load in kN\n", + "FOS=3 #Factor of safety \n", + "sigma_pl=200*10**6 #Stress allowable in Pa\n", + "E=200*10**9 #Youngs Modulus in Pa\n", + "end_cond=0.7 #End Condition factor to be multiplied\n", + "\n", + "#Calculations\n", + "Pcr=P*FOS #Critical Load in kN\n", + "A=Pcr*sigma_pl**-1*10**9 #Area in mm^2\n", + "\n", + "#Part 1\n", + "I1=10**15*(Pcr*Le**2)*(pi**2*E)**-1 #Moment of Inertia Required in mm^4\n", + "#From table selecting appropriate Section W250x73\n", + "\n", + "#Part 2\n", + "I2=10**15*(Pcr*end_cond**2*Le**2)*(pi**2*E)**-1 #Moment of Inertia Required in mm^4\n", + "#From table selecting appropriate Section W200x52\n", + "\n", + "#Lightest Section that meets these criterion is W250x58 section\n", + "\n", + "\n", + "#Result\n", + "print \"From the above computation we select W250x58 section\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "From the above computation we select W250x58 section\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.10.2, Page No:375" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variabel Decleration\n", + "E=200*10**9 #Youngs Modulus in Pa\n", + "sigma_yp=380*10**6 #Stress allowable in Pa\n", + "Le=10 #Length in m\n", + "end_cond=0.5 #Support condition factor to be ,ultiplied to length\n", + "A=15.5*10**-3 #Area in m^2\n", + "\n", + "#Calculations\n", + "Cc=sqrt((2*pi**2*E)*sigma_yp**-1) #Slenderness Ratio\n", + "\n", + "#Part 1\n", + "S_R1=142.9 #Slenderness ratio \n", + "sigma_w=(12*pi**2*E)/(23*S_R1**2) #Allowable Working Stress in Pa\n", + "P=sigma_w*A #Maximum Allowable Load in kN\n", + "\n", + "#Part 2\n", + "S_R2=79.37 #Slenderness ratio \n", + "N=5*3**-1+((3*S_R2)/(8*Cc))-(S_R2**3*(8*Cc**3)**-1) #Factor Of Safety\n", + "\n", + "sigma_w2=(1-(S_R2**2*0.5*Cc**-2))*(sigma_yp*N**-1) #Allowable working Stress in Pa\n", + "P2=sigma_w2*A #Allowable Load in kN\n", + "\n", + "#Part 3\n", + "S_R3=55.56 #Slenderness Ratio\n", + "N3=5*3**-1+((3*S_R3)/(8*Cc))-(S_R3**3*(8*Cc**3)**-1) #Factor Of Safety\n", + "\n", + "sigma_w3=(1-(S_R3**2*0.5*Cc**-2))*(sigma_yp*N3**-1) #Allowable working Stress in Pa\n", + "P3=sigma_w3*A #Allowable Load in kN\n", + "\n", + "#Result\n", + "print \"The results for Part 1 are\"\n", + "print \"Maximum Allowable Load P=\",round(P*10**-3),\"kN\"\n", + "print \"Part 2\"\n", + "print \"Maximum Allowable Load P=\",round(P2*10**-3),\"kN\"\n", + "print \"Part 3\"\n", + "print \"Maximum Allowable Load P=\",round(P3*10**-3),\"kN\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The results for Part 1 are\n", + "Maximum Allowable Load P= 782.0 kN\n", + "Part 2\n", + "Maximum Allowable Load P= 2161.0 kN\n", + "Part 3\n", + "Maximum Allowable Load P= 2710.0 kN\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.10.3, Page No:383" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import numpy as np\n", + "\n", + "#Variabel Decleration\n", + "E=29*10**6 #Youngs Modulus in psi\n", + "sigma_yp=36*10**3 #Stress in psi\n", + "L=25 #Length in ft\n", + "A=17.9 #Area in in^2\n", + "Iz=640 #Moment of inertia in in^4\n", + "Sz=92.2 #Sectional Modulus in in^3\n", + "P=150*10**3 #Load in lb\n", + "e=4 #Eccentricity in inches\n", + "\n", + "#Calculations\n", + "\n", + "#Part 1\n", + "a=1.09836\n", + "sigma_max=P*A**-1+(P*e*Sz**-1)*a #Maximum Stress in psi\n", + "\n", + "#Part 2\n", + "#After simplification we get the equation to compute N\n", + "N=2.19 #Trial and Error yields\n", + "\n", + "#Part 3\n", + "v_max=e*((np.cos(sqrt((P*L**2*12**2)*(4*E*Iz)**-1)))**-1-1)\n", + "\n", + "#Result\n", + "print \"The maximum compressive stress in the Column is\",round(sigma_max,2),\"psi\"\n", + "print \"The factor of safety is\",N\n", + "print \"The maximum lateral dfelection is\",round(v_max,3),\"in\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum compressive stress in the Column is 15527.57 psi\n", + "The factor of safety is 2.19\n", + "The maximum lateral dfelection is 0.393 in\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.10.4, Page No:384" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "Le=7 #Effective Length in m\n", + "N=2 #Factor of Safety\n", + "h_max=400 #Maximum depth in mm\n", + "E=200 #Youngs Modulus in GPa\n", + "sigma_yp=250 #Maximum stress in yielding in MPa\n", + "P1=400 #Load 1 in kN\n", + "P2=900 #Load 2 in kN\n", + "x1=75 #Distance in mm\n", + "x2=125 #Distance in mm\n", + "\n", + "#Calculations\n", + "e=(P2*x2-P1*x1)*(P1+P2)**-1 #Eccentricity in mm\n", + "P=N*(P1+P2) #Applied load after factor of safety is considered in kN\n", + "\n", + "#Part 1 is not computable\n", + "I=415*10**-6 #Moment of inertia from the table in mm^4\n", + "\n", + "#Part 2\n", + "P_cr=pi**2*E*10**9*I*Le**-2 #Critical load for buckling in kN\n", + "FOS=P_cr*10**-3/(P1+P2) #Factor of safety against buckling in y-axis\n", + "\n", + "\n", + "#Result\n", + "print \"The critical load for buckling is\",round(P_cr*10**-3),\"kN\"\n", + "print \"The factor of safety is\",round(FOS,1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The critical load for buckling is 16718.0 kN\n", + "The factor of safety is 12.9\n" + ] + } + ], + "prompt_number": 27 + } + ], + "metadata": {} + } + ] +}
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