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authorkinitrupti2017-05-12 18:40:35 +0530
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-{
- "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": {}
- }
- ]
-} \ No newline at end of file