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diff --git a/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter11_1.ipynb b/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter11_1.ipynb new file mode 100755 index 00000000..bf1270ca --- /dev/null +++ b/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter11_1.ipynb @@ -0,0 +1,293 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:9e6efed33049beac69942b90d39a9e8444a663ad0d711d98275d388c059ec74c" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter11:Additional Beam Topics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.11.1, Page No:394" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "V=1000 #Force acting on he section in lb\n", + "t=0.5 #Thickness in inches\n", + "#Dimensions\n", + "d=8 #Depth of the section in inches\n", + "wf=12 #Width of the flange in inches\n", + "wbf=8 #Width of the bottom flange in inches\n", + "\n", + "#Calculations\n", + "y_bar=((d*t*0)+wbf*t*4+wf*t*8)/(d*t+wbf*t+wf*t) #Location of Neutral Axis in inches\n", + "I=d*t*y_bar**2+t*d**3*12**-1+d*t*(d*t-y_bar)**2+wf*t*(8-y_bar)**2 #Moment of Inertia in in^4\n", + "\n", + "#Top Flange\n", + "q1=V*t*t*wf*(8-y_bar)*I**-1 #Shear flow in lb/in\n", + "#Bottom Flange\n", + "q2=V*t*t*d*y_bar*I**-1 #Shear Flow in lb/in\n", + "#Web\n", + "qB=2*q1 #Shear Flow in lb/in\n", + "qF=2*q2 #Shear Flow in lb/in\n", + "\n", + "#Max Shear Flow\n", + "qMAX=qB+V*t*(8-y_bar)**2*0.5*I**-1 #Maximum Shear Flow in lb/in\n", + "\n", + "#Result\n", + "print \"The Maximum Shear Flow is\",round(qMAX),\"lb/in\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Maximum Shear Flow is 133.0 lb/in\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.11.2, Page No:395" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "V=1000 #Shear Force in lb\n", + "#Rest ALL DATA is similar to previous problem\n", + "\n", + "#Calcualtions\n", + "I=t*wf**3*12**-1+t*d**3*12**-1 #Moment of Inertia\n", + "\n", + "#Part 1\n", + "q1=V*t*t*wf*3*I**-1 #Shear Flow in lb/in\n", + "q2=V*t*t*d*2*I**-1 #Shear FLow in lb/in\n", + "V1=2*3**-1*q1*wf #Shear force carried in lb\n", + "V2=2*3**-1*q2*d #Shear force carried in lb\n", + "\n", + "#Part 2\n", + "e=8*V2*V**-1 #Eccentricity in inches\n", + "\n", + "#Result\n", + "print \"The Shear Force carried by Flanges is\"\n", + "print \"Top Flange=\",round(V1,1),\"lb Bottom Flange=\",round(V2,1),\"lb\"\n", + "print \"The eccentricity is\",round(e,3),\"in\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Shear Force carried by Flanges is\n", + "Top Flange= 771.4 lb Bottom Flange= 228.6 lb\n", + "The eccentricity is 1.829 in\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.11.3, Page No:403" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import numpy as np\n", + "\n", + "#Variable Decleration\n", + "M=32 #Moment in kN.m\n", + "Iy=4.73*10**6 #Moment of inertia in y-axis in mm^4\n", + "Iz=48.9*10**6 #Moment of inertia in z-axis in mm^4\n", + "Sy=64.7*10**3 #Sectional Modulus in y-axis in mm^3\n", + "Sz=379*10**3 #Sectional Modulus in z-axis in mm^3\n", + "theta=16.2 #Angle between moment and z-axis in degrees\n", + "\n", + "#Calculations\n", + "#Part 1\n", + "alpha=np.arctan((Iz*Iy**-1)*tan(theta*pi*180**-1))*180*pi**-1 #Angle between NA and z-axis in degrees\n", + "\n", + "#Part 2\n", + "My=-M*np.sin(theta*pi*180**-1) #Bending Moment in y in kN.m\n", + "Mz=-M*np.cos(theta*pi*180**-1) #Bending Moment in z in kN.m\n", + "\n", + "sigma_max=My*Sy**-1+Mz*Sz**-1 #Largest Bedning Stress in MPa\n", + "\n", + "#Result\n", + "print \"The angle between the Neutral Axis and Z-Axis is\",round(alpha,1),\"degrees\"\n", + "print \"The maximum Bending Moment is\",abs(round(sigma_max*10**6)),\"MPa\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The angle between the Neutral Axis and Z-Axis is 71.6 degrees\n", + "The maximum Bending Moment is 219.0 MPa\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.11.4, Page No:403" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "A=4.75 #Area in inches^2\n", + "Iy_dash=6.27 #Moment of inertia in in^4\n", + "Iz_dash=17.4 #Moment of inertia in in^4\n", + "ry=0.87 #Radius of Gyration in inches\n", + "tan_theta=0.44\n", + "P=1 #Force in kips\n", + "L=48 #Length in inches\n", + "y_dash_B=-4.01 #Y coordinate of point B in inches\n", + "z_dash_B=-0.487 #Z coordinate of point B in inches\n", + "\n", + "#Calcualtions\n", + "theta=np.arctan(tan_theta) #Angle in radians\n", + "Iy=A*ry**2 #Moment of inertia in y in in^4\n", + "Iz=Iy_dash+Iz_dash-Iy #Moment of inertia in y in in^4\n", + "\n", + "#Part 1\n", + "alpha=arctan(Iz*Iy**-1*tan_theta)*180*pi**-1 #Angle in radians\n", + "beta=alpha-(theta*180*pi**-1) #Angle in degrees\n", + "\n", + "#Part 2\n", + "M=P*L*4**-1 #Moment in kip.in\n", + "My=M*np.sin(theta) #Moment in y in kip.in\n", + "Mz=M*np.cos(theta) #Moment in z in kip.in\n", + "\n", + "y_B=y_dash_B*np.cos(theta)+z_dash_B*np.sin(theta) #Y coordinate in inches\n", + "z_B=z_dash_B*np.cos(theta)-y_dash_B*np.sin(theta) #Z coordinate in inches\n", + "\n", + "#Maximum Bending Stress\n", + "sigma_max=My*z_B*Iy**-1-Mz*y_B*Iz**-1 #Maximum Bedning Stress in ksi\n", + "\n", + "#Result\n", + "print \"The angle of inclination of the Neutral axis to the z-axis is\",round(beta,1),\"degrees\"\n", + "print \"The maximum Bedning Stress is\",round(sigma_max,2),\"ksi\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The angle of inclination of the Neutral axis to the z-axis is 44.1 degrees\n", + "The maximum Bedning Stress is 3.69 ksi\n" + ] + } + ], + "prompt_number": 45 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.11.5, Page No:412" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "A1=4 #Area in in^2\n", + "A2=6 #Area in in^2\n", + "r1=7.8 #Radius in inches\n", + "r2=14.8 #Radius in inches\n", + "t=0.5 #Thickness in inches\n", + "d=4 #Depth in inches\n", + "sigma_w=18 #Maximum allowable stress in kips\n", + "\n", + "#Calculations\n", + "A=A1+A2 #Area in in^2\n", + "r_bar=(A1*(r1+t)+A2*(r2+d))*(A1+A2)**-1 #Centroidal Axis in inches\n", + "#Simplfying the computation\n", + "a=(r1+2*t)/r1\n", + "b=r2/(r1+t*2)\n", + "integral=d*math.log(a)+2*t*math.log(b) #\n", + "R=A/integral #Radius of neutral Surface in inches\n", + "\n", + "#Maximum Stress\n", + "#Answers are in variable terms hence not computable\n", + "\n", + "P=sigma_w/0.7847 #Maximum Allowable load in kips\n", + "\n", + "#Result\n", + "print \"The maximum allowable load is\",round(P,1),\"kips\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum allowable load is 22.9 kips\n" + ] + } + ], + "prompt_number": 58 + } + ], + "metadata": {} + } + ] +}
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