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{
 "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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\nCCEukEAQQggBSCAIIYS4QAJBCCEEAP8fsaaRnsHTgwEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x50dd510>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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BAAgIgQEACAiBAQAICIEBAAjI/wHIbwwoarZYdwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x58cf070>"
       ]
      },
      {
       "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<x<6\n",
      "x1=[6,12] #for6<x<12\n",
      "x2=[12,18] #for 12<x<18\n",
      "xv=[6,12,18] #specially for shear force\n",
      "xo=[12.001,12.002] #Straight line plot\n",
      "#Shear Force Calculations\n",
      "#Summing forces in vertical direction and equating to 0\n",
      "V1=(R_l-w*x[0],R_l-w*x[1],R_l-w*x[2],R_l-w*x[3],R_l-w*x[4],R_l-w*x[5],R_l-w*x[6],R_l-w*x[7],R_l-w*x[8],R_l-w*x[9],R_l-w*x[10],R_l-w*x[11],R_l-w*x[12],R_l-w*x[13]) #N for 0<x<6\n",
      "V2=(R_l)-(w*L) #N for 6<x<18\n",
      "#Bending Moment Calculations\n",
      "M1=(R_l*x[0]-w*x[0]**2*0.5,R_l*x[1]-w*x[1]**2*0.5,R_l*x[2]-w*x[2]**2*0.5,R_l*x[3]-w*x[3]**2*0.5,R_l*x[4]-w*x[4]**2*0.5,R_l*x[5]-w*x[5]**2*0.5,R_l*x[6]-w*x[6]**2*0.5,R_l*x[7]-w*x[7]**2*0.5,R_l*x[8]-w*x[8]**2*0.5,R_l*x[9]-w*x[9]**2*0.5,R_l*x[10]-w*x[10]**2*0.5,R_l*x[11]-w*x[11]**2*0.5,R_l*x[12]-w*x[12]**2*0.5,R_l*x[13]-w*x[13]**2*0.5) #N.m for 0<x<6\n",
      "M2=(R_l*x1[0]-((w*L)*(x1[0]-3)),R_l*x1[1]-((w*L)*(x1[1]-3))) #N.m for 6<x<12\n",
      "M3=(R_l*x2[0]-((w*L)*(x2[0]-3))+M_app,R_l*x2[1]-((w*L)*(x2[1]-3))+M_app) #N.m for 12<x<18\n",
      "Mo=[-1464.8652,2509.3333]\n",
      "#Maximum bending moment\n",
      "M_max=R_l*a*0.5 #N.m\n",
      "\n",
      "#Plotting SFD & BMD\n",
      "p=[0,a,5.99,6,11.99,12,17.99,18]\n",
      "y=[0,1467,1020,1020,-1486,2514,0,0]\n",
      "z=[0,a,5.99,6,11.99,12,17.99,18]\n",
      "b=[758,0,-418,-418,-418,-418,-418,0]\n",
      "g=[0,0,0,0,0,0,0,0]\n",
      "d=transpose(p)\n",
      "e=transpose(b)\n",
      "plt.plot(d,y,d,g)\n",
      "xlabel('Span (m)')\n",
      "ylabel('B.M (N.m)')\n",
      "plt.show()\n",
      "xlabel('Span (m)')\n",
      "ylabel('S.F (N)')\n",
      "plt.plot(z,e,z,g)\n",
      "plt.show()\n",
      "\n",
      "#Result\n",
      "print'The value of reactions are: R_l=',round(R_l),\"N\",'and R_r=',round(R_r),\"N\"\n",
      "print'The point of maximum bending moment is',round(a,2),\"meters from left support\",'and maximum bending moment is',round(M_max),\"N.m\"\n",
      "print'The bending moment and shear force diagrams have been plotted'\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/CzF7jf4qKYHISLUU+2OP2fzpRB08+SRs2gTbtsH11+udxrXt3w/jxsHXX+ud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\nGEiPHj04fPiw3V6HEM6qY0f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69aNz58688MIL5ObmAqoIDR48GC8vL7y9vfHx8al275Pi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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x58e3370>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x5b14af0>"
       ]
      },
      {
       "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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cgNRUcLut4zpiyc6Ghx+G/HylCYj4iqbUglz37uByQZ0rM4S82uiaN95QsxHx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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5a0a670>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZGUlUVBR5eXmUlpZSXl5OYmIiAKNHj2b16tUArFmzhvT0dAAGDx7M5s2bLVij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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5a2a550>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The bending Moment and Shear Force diagrams have been plotted\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}