{ "metadata": { "name": "chapter8.ipynb" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 8: Forces in Beams" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.8-1, Page no 118" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Initilization of variables\n", "R_A=100 #N\n", "R_B=200 #N\n", "\n", "#Calculations\n", "#Shear force at 2m\n", "V=100 #N\n", "#Moment at 2m\n", "M=R_A*2 #N.m\n", "\n", "#Result\n", "print'The shear force at 2m is +',round(V),\"N\"\n", "print'The moment at 2m is +',round(M),\"N-m\" \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The shear force at 2m is + 100.0 N\n", "The moment at 2m is + 200.0 N-m\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.8-2, Page no 118" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "#Initilization of variables\n", "#length matrix\n", "L1=[0,3.99,4,5.99,6] #m\n", "#Bending moment matrix\n", "B=[0,400,400,0.00001,0] #N.m\n", "#Shear force plotting\n", "#Here the left side and right side lengths are considered as close as 4 to keep up with right and left distinctions\n", "L=[0,3.99,4,5.99,6]\n", "S=[100,100,-200,-200,0]\n", "g=[0,0,0,0,0]\n", "\n", "#Calculations cum Result\n", "d=transpose(L1)\n", "e=transpose(S)\n", "plt.plot(d,B)\n", "xlabel('Span (m)')\n", "ylabel('B.M (N.m)')\n", "plt.show()\n", "plt.plot(L,e,L,g)\n", "xlabel('Span (m)')\n", "ylabel('S.F (N)')\n", "plt.show()\n", "\n", "print'The graphs are the solutions'\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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2nxUWFhIYGFjrMaoHgmi4uXPhnXfUMOjQQe9qhHBfTz8N118Pf/87tGmjdzU1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\n9m7zt1vfm9aE6yovL2fkyJH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"text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "The graphs are the solutions\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.8-3, Page no 119" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "#Initilization of variables\n", "w=196 #N/m\n", "M_app=4000 #N.m\n", "L=6 #m\n", "\n", "#Calculations\n", "#Taking Moment about Point L and equating it to 0\n", "R_r=(M_app+w*L*L*0.5)/(3*L) #N\n", "#Taking Moment about Point R and equating it to 0\n", "R_l= ((((2*L)+(L/2))*(w*L))-(M_app))/(3*L) #N\n", "#finding point of zero shear\n", "a=R_l*w**-1\n", "#defining x\n", "x0=[0,18]\n", "x=[0,0.5,1,1.5,2,2.5,3,3.5,a,4,4.5,5,5.5,6] #for 0" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "The value of reactions are: R_l= 757.0 N and R_r= 418.0 N\n", "The point of maximum bending moment is 3.86 meters from left support and maximum bending moment is 1462.0 N.m\n", "The bending moment and shear force diagrams have been plotted\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.8-4, Page no 121" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "%matplotlib inline\n", "\n", "#Initlization of variables\n", "F1=2000 #lb\n", "w=100 #lb/ft\n", "\n", "#Calculations\n", "R_r=(-F1*5+w*14*13)/20 #lb\n", "R_l=(F1*25+w*14*7)/20 #lb\n", "#Shear Force matrix\n", "V=[-2000,-2000,990,990,-410,0] #lb\n", "#Bending Moment matrix\n", "B=[0,-10000,-10000,-4060,840,0]\n", "#Length matrix for shear force\n", "X_v=[0,5,5.0001,11,20.89999,20.9]\n", "#Length matrix for bendimg moment\n", "X_b=[0,4.99,5,11,19.9,20.9]\n", "g=[0,0,0,0,0,0]\n", "\n", "#Plotting of SFD & BMD.\n", "d=transpose(X_v)\n", "e=transpose(V)\n", "plt.plot(d,B,d,g)\n", "xlabel('Span (ft)')\n", "ylabel('B.M (lb.ft)')\n", "plt.show()\n", "plt.plot(X_b,e,X_b,g)\n", "xlabel('Span (ft)')\n", "ylabel('S.F (lb)')\n", "plt.show()\n", "\n", "#Result\n", "print'The bending Moment and Shear Force diagrams have been plotted'\n", "#Note\n", "#The textbook does not specify the span and hence there seems to be a disagreement between the textbook and python solution.here the values have just been plotted\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ZGUlUVBR5eXmUlpZSXl5OYmIiAKNHj2b16tUArFmzhvT0dAAGDx7M5s2bLVij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\ngg==\n", "text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "The bending Moment and Shear Force diagrams have been plotted\n" ] } ], "prompt_number": 3 } ], "metadata": {} } ] }