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diff --git a/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter01_12.ipynb b/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter01_12.ipynb new file mode 100755 index 00000000..8594491e --- /dev/null +++ b/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter01_12.ipynb @@ -0,0 +1,226 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:055c326b63bc3f150b8a5e433c724771cc1733887ec2b1e223ccf712fcd80848" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 01:Stress" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.1.1, Page No:9" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#NOTE:The notation has been changed to simplify the coding process\n", + "\n", + "#Variable Decleration\n", + "P_AB=4000 #Axial Force at section 1 in lb\n", + "P_BC=5000 #Axial Force at section 2 in lb\n", + "P_CD=7000 #Axial Force at section 3 in lb\n", + "A_1=1.2 #Area at section 1 in in^2\n", + "A_2=1.8 #Area at section 2 in in^2\n", + "A_3=1.6 #Area at section 3 in in^2\n", + "\n", + "#Calculation\n", + "#S indicates sigma here\n", + "S_AB=P_AB/A_1 #Stress at section 1 in psi (T)\n", + "S_BC=P_BC/A_2 #Stress at section 2 in psi (C)\n", + "S_CD=P_CD/A_3 #Stress at section 3 in psi (C)\n", + "\n", + "#Result\n", + "print \"The stress at the three sections is given as\"\n", + "print \"Stress at section 1=\",round(S_AB),\"section 2=\",round(S_BC),\"section 3=\",S_CD\n", + "\n", + "#NOTE:The answer for the following example for section 1 and section 2\n", + "#are incorrect due to rounding in the textbook\n", + "#Computed values are correct" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The stress at the three sections is given as\n", + "Stress at section 1= 3333.0 section 2= 2778.0 section 3= 4375.0\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.1.2, Page No:10" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "Ay=40 #Vertical Reaction at A in kN\n", + "Hy=60 #Vertical Reaction at H in kN\n", + "Hx=0 #Horizontal Reaction at H in kN\n", + "y=3 #Height in m\n", + "x=5 #Distance in m\n", + "p=4 #Panel distance in m\n", + "A=900 #Area of the member in mm^2\n", + "P_C=30 #Force at point C in kN\n", + "\n", + "#Calculation\n", + "#Part 1\n", + "#Applying summation of forces in the x and y direction and equating to zero\n", + "P_AB=(-Ay)*(x*y**-1) #Force in member AB in kN\n", + "P_AC=-(p*x**-1*P_AB) #Force in member AC in kN\n", + "#Using stress=force/area\n", + "S_AC=(P_AC/A)*10**3 #Stress in member AC in MPa (T)\n", + "\n", + "#Part 2\n", + "#Sum of moments about point E to zero\n", + "P_BD=(Ay*p*2-(P_C*p))*y**-1 #Force in memeber AB in kN (C)\n", + "S_BD=(P_BD/A)*10**3 #Stress in member in MPa (C)\n", + "\n", + "#Result\n", + "print \"The Stress in member AC is\",round(S_AC,1),\"MPa (T)\"\n", + "print \"The Stress in member BD is\",round(S_BD,1),\"MPa (C)\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Stress in member AC is 59.3 MPa (T)\n", + "The Stress in member BD is 74.1 MPa (C)\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.1.3, Page No:11" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import numpy as num\n", + "\n", + "#Variable Decleration\n", + "A_AB=800 #Area of member AB in m^2\n", + "A_AC=400 #Area of member AC in m^2\n", + "W_AB=110 #Safe value of stress in Pa for AB\n", + "W_AC=120 #Safe value of stress in Pa for AC\n", + "theta1=60*3.14*180**-1 #Angle in radians\n", + "theta2=40*3.14*180**-1 #Angle in radians \n", + "\n", + "#Calculations\n", + "#Applying sum of forces \n", + "#Solving by matrix method putting W as 1\n", + "A=num.array([[-cos(theta1),cos(theta2)],[sin(theta1),sin(theta2)]])\n", + "B=num.array([[1],[1]])\n", + "C=inv(A)\n", + "D=C*B\n", + "\n", + "#Using newtons third law\n", + "#Two values of W hence the change in the notation\n", + "W1=(W_AB*A_AB)*(D[1,1])**-1 #Weight W in N\n", + "W2=(W_AC*A_AC)*(D[0,1])**-1 #Weight W in N\n", + "\n", + "#Result\n", + "print \"The maximum value of W allowable is\",round(W2*1000**-1,1),\"kN\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum value of W allowable is 61.7 kN\n" + ] + } + ], + "prompt_number": 48 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.1.4, Page No:19" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "d=3*4**-1 #Rivet diameter in inches\n", + "t=7*8**-1 #Thickness of the plate in inches\n", + "tau=14000 #Shear stress limit in psi\n", + "sigma_b=18000 #Normal stress limit in psi\n", + "\n", + "#Calculations\n", + "#Design Shear Stress in Rivets\n", + "V=tau*(d**2*(pi/4))*4 #Shear force maximum allowable in lb\n", + "#Design for bearing stress in plate\n", + "Pb=sigma_b*t*d*4 #lb\n", + "\n", + "#Result\n", + "print \"The maximum load that the joint can carry is\",round(V),\"lb\"\n", + "\n", + "#NOTE:The answer in the textbook is off by 40lb" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum load that the joint can carry is 24740.0 lb\n" + ] + } + ], + "prompt_number": 55 + } + ], + "metadata": {} + } + ] +}
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