path: root/Engineering_Mechanics_by_R.K_Bansal/chapter_20.ipynb

{
 "metadata": {
  "name": "chapter 20.ipynb"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 20:Beams (Shear Force And Bending Moment)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.1,Page No.730"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "\n",
      "L=2 #m #Span of beam\n",
      "L_AB=0.5 #m\n",
      "L_BC=0.7 #m\n",
      "L_CD=0.8 #m\n",
      "\n",
      "#Point Load\n",
      "F_D=800 #N\n",
      "F_C=500 #N\n",
      "F_B=300 #n\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A  be the reactions at A \n",
      "R_A=F_B+F_C+F_D #N\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#Shear Force at pt D\n",
      "V_D=F_D #N\n",
      "\n",
      "#Shear Force at pt C\n",
      "V_C1=V_D #N\n",
      "V_C2=V_D+F_C #N\n",
      "\n",
      "#Shear force at pt B\n",
      "V_B1=V_C2 #N\n",
      "V_B2=V_C2+F_B\n",
      "\n",
      "#Shear Force at pt A\n",
      "V_A=V_B2 #N\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at D\n",
      "M_D=F_D*0 #N.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=F_D*L_CD #N.m\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=F_D*(L_CD+L_BC)+F_C*L_BC #N.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=F_D*L+F_C*(L_BC+L_AB)+F_B*L_AB #N.m\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L_CD,L_CD,L_CD+L_BC,L_CD+L_BC,L_CD+L_BC+L_AB]\n",
      "Y1=[V_D,V_C1,V_C2,V_B1,V_B2,V_A]\n",
      "Z1=[0,0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_D,M_C,M_B,M_A]\n",
      "X2=[0,L_CD,L_CD+L_BC,L_CD+L_BC+L_AB]\n",
      "Z2=[0,0,0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x4dec3b0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x55eb030>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.2,Page No.733"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#lengths\n",
      "L_CB=1.5 #m \n",
      "L_AC=0.5 #m\n",
      "\n",
      "#Loads\n",
      "w=1 #KN/m #u.d.l\n",
      "\n",
      "#Calculations\n",
      "\n",
      "R_A=w*L_CB #KN\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F at B\n",
      "V_B=0\n",
      "\n",
      "#S.F at C\n",
      "V_C=w*L_CB #KN\n",
      "\n",
      "#S.F at  A\n",
      "V_A=V_C #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at B\n",
      "M_B=0\n",
      "\n",
      "#B.M at C\n",
      "M_C=w*L_CB*L_CB*2**-1\n",
      "\n",
      "#B.M at A\n",
      "M_A=w*L_CB*(L_CB*2**-1+L_AC) #KN\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L_CB,L_CB+L_AC]\n",
      "Y1=[V_B,V_C,V_A]\n",
      "Z1=[0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_C,M_A]\n",
      "X2=[0,L_CB,L_AC+L_CB]\n",
      "Z2=[0,0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wf/9+pKSkmIxJSUnBRx99BACdTojzdNa8l7W1tca/IkpLSyEIAgYNGuSMcl0e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\nkmdmAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x57035f0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DAMAFcwwAABcEAwDABcEAAHBBMAAAXBAMAAAXBAMAwMX/AZ1k8BGP4cc7AAAA\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5527150>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.3,Page No.734"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_AB=2 #m\n",
      "\n",
      "#Load\n",
      "w=2 #KN/m \n",
      "F_B=3 #KN\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#LEt R_A be the reaction at pt A\n",
      "R_A=F_B+w*L_AB\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F at B\n",
      "V_B=F_B #KN\n",
      "\n",
      "#S.F at A\n",
      "V_A=V_B+w*L_AB #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at B\n",
      "M_B=0 #KN.m\n",
      "\n",
      "#B.M at A\n",
      "M_A=F_B*L_AB+w*L_AB*L_AB*2**-1 #KN.m\n",
      "\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L_AB]\n",
      "Y1=[V_B,V_A]\n",
      "Z1=[0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_A]\n",
      "X2=[0,L_AB]\n",
      "Z2=[0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x55f06d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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336mwsFBbtmxRt27dol0WYAp6BICkMWPGqLq6WvX19ZozZw6DAGyFRAAANkeP\nAABsjoEAAGyOgQAAbI6BAABsjoEAAGyOgQAAbO5/3s4VeFi4MvMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5546a70>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.4,Page No.736"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_CB=0.5 #m\n",
      "L_AC=1.5 #m\n",
      "L=2 #m \n",
      "\n",
      "#Loads\n",
      "F_C=2 #KN\n",
      "w=1.5 #KN/m\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A be the reaction at pt A\n",
      "R_A=F_C+w*L #KN\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F at pt B\n",
      "V_B=0 #KN\n",
      "\n",
      "#S.F At pt C\n",
      "V_C1=w*L_CB #KN\n",
      "V_C2=V_C1+F_C #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A=F_C+w*L #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=0 #KN.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=w*L_CB*L_CB*2**-1\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=F_C*L_AC+w*L*L*2**-1 #KN.m\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L_CB,L_CB,L_AC+L_AC]\n",
      "Y1=[V_B,V_C1,V_C2,V_A]\n",
      "Z1=[0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_C,M_A]\n",
      "X2=[0,L_CB,L_AC+L_CB]\n",
      "Z2=[0,0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CHo9HTz/9tJKTk3Xw4EEVFxcHtPOtW7dq1apV2rRpk7KyspSVlaV169YFPUkAQMv5PcOX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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x57190d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xe4W9SOVkeQ//lo2rh+/3jh+Hvn3NNXFmzoQquiokYrlK2cOXwLZ7t7na5Suv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\niEiQUOCLiAQJBb6ISJBQ4IuIBIn/B6vzYmUHF4P4AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x55c42f0>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.5,Page No.738"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_CB=0.25 #m\n",
      "L_DC=1 #m \n",
      "L_AD=0.25 #m\n",
      "L_DB=1.25 #m\n",
      "L=1.5 #m\n",
      "\n",
      "#Loads\n",
      "F_C=3 #KN #Point Load\n",
      "w=2 #KN/m #u.d.l\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A be the reaction at A\n",
      "R_A=F_C+w*(L_DC+L_CB)\n",
      "\n",
      "#Shear Force calculations\n",
      "\n",
      "#S.F at pt B\n",
      "V_B=0\n",
      "\n",
      "#S.F at pt C\n",
      "V_C1=w*L_CB #KN\n",
      "V_C2=V_C1+F_C #KN\n",
      "\n",
      "#S.F at D\n",
      "V_D=w*(L_DC+L_CB)+F_C #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A=V_D #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=0\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=w*L_CB*L_CB*2**-1 #KN.m\n",
      "\n",
      "#B.M at pt D\n",
      "M_D=w*L_DB*L_DB*2**-1+F_C*L_DC #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=w*L_DB*(L_DB*2**-1+L_AD)+F_C*(L_DC+L_AD) #KN.m\n",
      "\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L_CB,L_CB,L_CB+L_DB,L_CB+L_DB+L_AD]\n",
      "Y1=[V_B,V_C1,V_C2,V_D,V_A]\n",
      "Z1=[0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_C,M_D,M_A]\n",
      "X2=[0,L_CB,L_DC+L_CB,L_DC+L_CB+L_AD]\n",
      "Z2=[0,0,0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x55469b0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HRUUFBg8ejEGDBuGee+7xQIU2UupcsmQJoqOjYTabkZ+fj4SEBHz99dcIDg72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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x57193b0>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.6,Page No.739"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_CB=0.5 #m\n",
      "L_DC=2 #m\n",
      "L_ED=1.5 #m\n",
      "L_AE=1 #m\n",
      "L=5 #m\n",
      "\n",
      "#Forces\n",
      "F_B=2.5 #KN\n",
      "F_E=3 #KN\n",
      "w=1 #KN/m #u.d.l\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A  be the reaction at A\n",
      "R_A=F_B+F_E+w*L_DC #KN\n",
      "\n",
      "#Shear Force calculations\n",
      "\n",
      "#S.F at pt B\n",
      "V_B=F_B\n",
      "\n",
      "#S.F at pt C\n",
      "V_C=V_B #KN\n",
      "\n",
      "#S.F at pt D\n",
      "V_D=V_C+w*L_DC #KN\n",
      "\n",
      "#S.F at pt E\n",
      "V_E1=V_D #KN\n",
      "V_E2=V_D+F_E #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A=V_E2 #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=0 #KN.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=F_B*L_CB #KN.m\n",
      "\n",
      "#B.M at pt D\n",
      "M_D=w*L_DC*L_DC*2**-1+F_B*(L_CB+L_DC) #KN.m\n",
      "\n",
      "#B.M at pt E\n",
      "M_E=F_B*(L_ED+L_DC+L_CB)+w*L_DC*(L_DC*2**-1+L_ED) #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=F_B*L+w*L_DC*(L_DC*2**-1+L_ED+L_AE)+F_E*L_AE #KN.m\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L_CB,L_CB+L_DC,L_CB+L_DC+L_ED,L_CB+L_DC+L_ED,L_CB+L_DC+L_ED+L_AE]\n",
      "Y1=[V_B,V_C,V_D,V_E1,V_E2,V_A]\n",
      "Z1=[0,0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_C,M_D,M_E,M_A]\n",
      "X2=[0,L_CB,L_DC+L_CB,L_ED+L_DC+L_CB,L_ED+L_DC+L_CB+L_AE]\n",
      "Z2=[0,0,0,0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x5714df0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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EAsnoE3IcDkej+7ps2rSJqKgofvazn53zu8zMTNvv7S7WpZW+hJ39+/czZMgQ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\n2e9ZygAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x55467f0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.7,Page No.741"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "L_AB=4 #m #Length of AC\n",
      "w=2 #KN/m #u.v.l\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Shear force calculation\n",
      "\n",
      "#S.F at pt B\n",
      "V_B=0 #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A=w*L_AB*2**-1 #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=0 #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=w*L_AB**2*6**-1 #KN.m\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L_AB]\n",
      "Y1=[V_B,V_A]\n",
      "Z1=[0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_A]\n",
      "X2=[0,L_AB]\n",
      "Z2=[0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x580a3b0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bceuttzZ7Xglz6UidgPfnEgAqKiqwZ88ePPbYY23W4+x8yt7wHbkAq63XVFRU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\nEanE/wPMXV7pzFimMAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x55274d0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.8,Page No.745"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_DB=L_CD=L_AC=2 #m\n",
      "L=6 #m\n",
      "\n",
      "#Loads\n",
      "F_C=3 #KN\n",
      "F_D=6 #KN\n",
      "\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A & R_B be the reactions at pt A & B respectively\n",
      "#R_A+R_B=F_C+F_D\n",
      "\n",
      "#Taking Moment at pt A,M_A\n",
      "R_B=(F_D*(L_AC+L_CD)+F_C*L_AC)*L**-1 #KN\n",
      "R_A=(F_C+F_D)-R_B\n",
      "\n",
      "#Shear force calculations\n",
      "\n",
      "#S.F at pt B\n",
      "V_B=R_B #KN\n",
      "\n",
      "#S.F at pt D\n",
      "V_D1=R_B #KN\n",
      "V_D2=V_D1-F_D #KN\n",
      "\n",
      "#S.F at C\n",
      "V_C1=V_D2 #KN\n",
      "V_C2=V_D2-F_C #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A1=V_C2 #KN\n",
      "V_A2=V_C2+R_A #KN\n",
      "\n",
      "#Bending Moment calculations\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=0 #KNm\n",
      "\n",
      "#B.M at pt D\n",
      "M_D=-R_B*L_DB #KN.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=F_D*L_CD-R_B*(L_DB+L_CD) #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=-R_B*L+F_D*(L_CD+L_AC)+F_C*L_AC #KN.m\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L_DB,L_DB,L_DB+L_CD,L_DB+L_CD,L_DB+L_CD+L_AC,L_DB+L_CD+L_AC]\n",
      "Y1=[V_B,V_D1,V_D2,V_C1,V_C2,V_A1,V_A2]\n",
      "Z1=[0,0,0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_D,M_C,M_A]\n",
      "X2=[0,L_DB,L_CD+L_DB,L_AC+L_CD+L_DB]\n",
      "Z2=[0,0,0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x55e3470>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uSZjq6moMGjQI8fHxiI2Nxfz587UuSRH19fVISEho1cUiRhEZGYl+/fohISFB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\nsCkQEZEHmwIREXn8PyxvuFHYcXKeAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5701770>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.9,Page No.748"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#LEngths\n",
      "L_CB=3 #m\n",
      "L_AC=6 #m\n",
      "L= 9 #m\n",
      "\n",
      "#Loads\n",
      "w=10 #KN/m \n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A & R_B be the reactions at pt A & B respectively\n",
      "#R_A+R_B=w*L_AC\n",
      "\n",
      "#Taking Moment at pt A,M_A\n",
      "R_B=w*L_AC*L_AC*2**-1*L**-1 #KN.m\n",
      "R_A=w*L_AC-R_B #KN.m\n",
      "\n",
      "#Shear force calculations\n",
      "\n",
      "#S.F at pt B\n",
      "V_B1=0\n",
      "V_B2=R_B #KN\n",
      "\n",
      "#S.F at pt C\n",
      "V_C=V_B2 #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A1=V_C-w*L_AC #KN\n",
      "V_A2=V_C-w*L_AC+R_A #KN\n",
      "\n",
      "#Bending Moment calculations\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=0 #KN.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=-R_B*L_CB #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=-R_B*L+w*L_AC*L_AC*2**-1 #KN.m\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,0,L_CB,L_CB+L_AC,L_CB+L_AC]\n",
      "Y1=[V_B1,V_B2,V_C,V_A1,V_A2]\n",
      "Z1=[0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_C,M_A]\n",
      "X2=[0,L_CB,L_CB+L_AC]\n",
      "Z2=[0,0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PfyI4OBgtLS3YsGEDFi9ebIvZiMjBMQzqY9Z5CsHBwWhvb4erqyuysrJQUFBg7bmIyEkw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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x56f4bd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x55199f0>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.10,Page No.749"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_DB=3 #m\n",
      "L_CD=4 #m\n",
      "L_AC=1 #m\n",
      "L=8 #m\n",
      "\n",
      "#Loads\n",
      "w=10 #KN/m\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A & R_B be the reactions at A & B respectively\n",
      "#R_A+R_B=w*L_CD\n",
      "\n",
      "#Taking moment at pt A,M_A\n",
      "R_B=(w*L_CD*(L_CD*2**-1+L_AC))*L**-1 #KN\n",
      "R_A=w*L_CD-R_B #KN\n",
      "\n",
      "#Shear Force calculations\n",
      "\n",
      "#S.F at pt B\n",
      "V_B1=0\n",
      "V_B2=R_B #KN\n",
      "\n",
      "#S.F at pt D\n",
      "V_D=V_B2 #KN\n",
      "\n",
      "#S.F at pt C\n",
      "V_C=-w*L_CD+R_B #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A1=V_C #KN\n",
      "V_A2=V_C+R_A\n",
      "\n",
      "\n",
      "#Bending Moment calculations\n",
      "\n",
      "#B.A at pt B\n",
      "M_B=0\n",
      "\n",
      "#B.M at pt D\n",
      "M_D=-R_B*L_DB #KN.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=-R_B*(L_DB+L_CD)+w*L_CD*L_CD*2**-1 #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=-R_B*L+w*L_CD*(L_CD*2**-1+L_AC) #KN.m\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,0,L_DB,L_DB+L_CD,L_AC+L_DB+L_CD,L_AC+L_DB+L_CD]\n",
      "Y1=[V_B1,V_B2,V_D,V_C,V_A1,V_A2]\n",
      "Z1=[0,0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_D,M_C,M_A]\n",
      "X2=[0,L_DB,L_DB+L_CD,L_AC+L_CD+L_DB]\n",
      "Z2=[0,0,0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YuXMnZs+eLTuWyxJC4JFHHkFsbCyeeOIJ2XEsOnPmDBobGwEAly9fxt69e6HT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\nBTiz74A2AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x55d83d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QkJCgdFhVPPzww3B3d1c6jFq1a9cOISEhAIBmzZrBz88Pubm5Ckdl\n2r139qAWFxejtLQULVu2VDiiqi5evIikpCRMmjRJ9bW51B7f77//jj179mDChAkAABcXF7i5uSkc\nVc2++eYbeHt7o2PHjkqHUsV9990HV1dXFBUVoaSkBEVFRfDw8DD5WptKCjk5OZX+wLVaLXJychSM\nyH4YDAZkZGSgj0prTJeVlSEkJARt27bFoEGD4O/vr3RIVUydOhWLFi2Ck8rLsmo0GgwZMgS9evXC\nKnOqDSogKysLbdq0wbPPPosePXrgueeeQ1FRkdJh1ejLL79EVFSU0mGY1LJlS0yfPh2dOnVChw4d\n0KJFCwwZMsTka9X9t/cuGjUUtrFDhYWFeOKJJ/D++++jWbNmSodjkpOTE44cOYKLFy9i9+7dqisr\nsHXrVtx///3Q6XSq/y183759yMjIwLZt2/Dhhx9iz549SodURUlJCdLT0zFlyhSkp6ejadOmmD9/\nvtJhVau4uBiJiYkYO3as0qGYdP78eSxduhQGgwG5ubkoLCzEunXrTL7WppKCh4cHsrOzjT9nZ2dD\nq9UqGJHtu337Nh5//HE8/fTTGDVqlNLh1MrNzQ0jRozADz/8oHQolezfvx9btmyBl5cXIiMj8d13\n32H8+PFKh2VS+/btAQBt2rTB6NGjkZaWpnBEVWm1Wmi1WjzwwAMAgCeeeALp6ekKR1W9bdu2oWfP\nnmjTpo3SoZj0ww8/4MEHH0SrVq3g4uKCMWPGYP/+/SZfa1NJoVevXjh79iwMBgOKi4uxYcMGPPro\no0qHZbMkScLEiRPh7++PV199VelwqnX58mXk5+cDAG7evImUlBTodDqFo6osNjYW2dnZyMrKwpdf\nfom//vWv+Pzzz5UOq4qioiIUFBQAAG7cuIHk5GRV7pJr164dOnbsiDNnzgAQ8/UBAQEKR1W99evX\nIzIyUukwquXr64sDBw7g5s2bkCQJ33zzTfVTsFZa/JZNUlKS1K1bN8nb21uKjY1VOhyTxo0bJ7Vv\n315q1KiRpNVqpdWrVysdkkl79uyRNBqNFBwcLIWEhEghISHStm3blA6rimPHjkk6nU4KDg6WgoKC\npIULFyodUo1SU1NVu/vowoULUnBwsBQcHCwFBASo9t+QJEnSkSNHpF69ekndu3eXRo8erdrdR4WF\nhVKrVq2k69evKx1KjRYsWCD5+/tLgYGB0vjx46Xi4mKTr+PhNSIiMrKp6SMiImpYTApERGTEpEBE\nREZMCkREZMSkQERERkwKRERkxKRAdq2hy3Z4enri6tWrVR7ftWsXvv/+e5PvSUxMVG3ZdyLFO68R\nNaSGrpel0WhM1jrauXMnmjdvjn79+lV5Ljw8XNX9FsixcaRADuf8+fMICwtDr169MGDAAJw+fRoA\n8Pe//x2vvPIK+vfvD29vb2zatAmAqNA6ZcoU+Pn54ZFHHsGIESOMzwHA8uXL0bNnT3Tv3h2nT5+G\nwWDAypUr8d5770Gn02Hv3r2V7r927Vq8/PLLNd6zIoPBAF9fXzz77LP4y1/+gqeeegrJycno378/\nunXrhkOHDjXUHxU5ICYFcjiTJ0/G8uXL8cMPP2DRokWYMmWK8bm8vDzs27cPW7duxYwZMwAAmzdv\nxk8//YQff/wRX3zxBb7//vtKI5A2bdrg8OHDeOGFF7B48WJ4enri+eefx7Rp05CRkYGHHnqo0v3v\nHr2Yuufdzp8/j9deew2nTp3C6dOnsWHDBuzbtw+LFy9GbGysXH80RJw+IsdSWFiI77//vlKJ4+Li\nYgDiw7q8Uqyfnx9++eUXAMDevXsREREBAMZ+DhWNGTMGANCjRw9s3rzZ+Lg5FWSqu+fdvLy8jAXh\nAgICjLXwAwMDYTAYar0PkbmYFMihlJWVoUWLFsjIyDD5fKNGjYzfl3+o371ucPeHfePGjQEAzs7O\nKCkpqXNMpu55t/J7AKK3RPl7nJyc6nVPoupw+ogcyn333QcvLy98/fXXAMSH8LFjx2p8T//+/bFp\n0yZIkoRffvkFu3btqvU+zZs3N5aovhtrUJKaMSmQXSsqKkLHjh2NX0uXLsW6devw6aefIiQkBIGB\ngdiyZYvx9RXn+8u/f/zxx6HVauHv74+//e1v6NGjh8l+wRqNxvie8PBwxMfHQ6fTYd++fdW+rrp7\nmrp2dT+zIyHJiaWzicxw48YNNG3aFFeuXEGfPn2wf/9+3H///UqHRSQ7rikQmWHkyJHIz89HcXEx\noqOjmRDIbnGkQERERlxTICIiIyYFIiIyYlIgIiIjJgUiIjJiUiAiIiMmBSIiMvp/4uGCP9tYDn8A\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x57197d0>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.11,Page No.751"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_DB=2 #m \n",
      "L_CD=2 #m\n",
      "L_AC=3 #m\n",
      "L=7 #m\n",
      "\n",
      "#Loads\n",
      "w1=5 #KN/m\n",
      "w2=10 #KN/m\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A & R_B be the reactions at A & B respectively\n",
      "#R_A+R_B=w*L_AC+w*L_DB\n",
      "\n",
      "#Taking moment at pt A,M_A\n",
      "R_B=(w1*L_DB*(L_DB*2**-1+L_CD+L_AC)+w2*L_AC*L_AC*2**-1)*L**-1 #KN\n",
      "R_A=(w1*L_DB+w2*L_AC)-R_B\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F at pt B\n",
      "V_B1=0 #KN\n",
      "V_B2=R_B #KN\n",
      "\n",
      "#S.F at pt D\n",
      "V_D=R_B-w1*L_DB #KN\n",
      "\n",
      "#S.F at pt C\n",
      "V_C=V_D #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A1=V_C-w2*L_AC #KN\n",
      "V_A2=V_A1+R_A #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=0 #KN.m\n",
      "\n",
      "#B.M at pt D\n",
      "M_D=w1*L_DB*L_DB*2**-1-R_B*L_DB #KN.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=-R_B*(L_CD+L_DB)+w1*L_DB*(L_DB*2**-1+L_CD) #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=-R_B*L+w1*L_DB*(L_DB*2**-1+L_CD+L_AC)+w2*L_AC*L_AC*2**-1 #KN.m\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,0,L_DB,L_DB+L_CD,L_AC+L_CD+L_DB,L_AC+L_CD+L_DB]\n",
      "Y1=[V_B1,V_B2,V_D,V_C,V_A1,V_A2]\n",
      "Z1=[0,0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_D,M_C,M_A]\n",
      "X2=[0,L_DB,L_CD+L_DB,L_AC+L_CD+L_DB]\n",
      "Z2=[0,0,0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sOTlZ2rp1qyRJ2r8/tbW1ghN1TVNTk+Tr6yudOXOm3edltadw9OhRhISEIDAw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\nQEREehwKRESkx6FARER6/w+KE6mW6PFKAgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x55f7310>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mQJrFsVXHYwKq++H2EbkEjq06BhNQXQu3j8htcGxVfkxAdU9sCuQyOLYqLyag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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x581bcf0>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.12,Page No.752"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_DB=4 #m\n",
      "L_CD=4 #m\n",
      "L_AC=2 #m\n",
      "L=10 #m\n",
      "\n",
      "#Loads\n",
      "F_D=40 #KN\n",
      "F_C=50 #KN\n",
      "w=10 #KN/m\n",
      "\n",
      "#Calculations\n",
      "\n",
      "\n",
      "#Let R_A & R_B be the reactions at A & B respectively\n",
      "#R_A+R_B=w*L_CD+F_C+F_D\n",
      "\n",
      "#Taking moment at pt A,M_A\n",
      "R_B=(F_C*L_AC+w*L_CD*(L_CD*2**-1+L_AC)+F_D*(L_CD+L_AC))*L**-1 #KN\n",
      "R_A=(w*L_CD+F_C+F_D)-R_B #KN\n",
      "\n",
      "#Shear Force calculations\n",
      "\n",
      "#S.F at pt B\n",
      "V_B1=0 #KN\n",
      "V_B2=R_B #KN\n",
      "\n",
      "#S.F at pt D\n",
      "V_D1=V_B2 #KN\n",
      "V_D2=V_B2-F_D #KN\n",
      "\n",
      "#S.F at pt C\n",
      "V_C1=V_D2-w*L_CD #KN\n",
      "V_C2=V_C1-F_C #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A1=V_C2 #KN\n",
      "V_A2=V_C2+R_A #KN\n",
      "\n",
      "#Bending Moment calculations\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=0 #KN.m\n",
      "\n",
      "#B.M at pt D\n",
      "M_D=-R_B*L_DB #KN.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=-R_B*(L_DB+L_CD)+F_D*L_CD+w*L_CD*L_CD*2**-1 #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=-R_B*L+F_D*(L_CD+L_AC)+F_C*L_AC+w*L_CD*(L_CD*2**-1+L_AC)\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,0,L_DB,L_DB,L_DB+L_CD,L_DB+L_CD,L_DB+L_CD+L_AC,L_DB+L_CD+L_AC]\n",
      "Y1=[V_B1,V_B2,V_D1,V_D2,V_C1,V_C2,V_A1,V_A2]\n",
      "Z1=[0,0,0,0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_D,M_C,M_A]\n",
      "X2=[0,L_DB,L_DB+L_CD,L_AC+L_CD+L_DB]\n",
      "Z2=[0,0,0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xzTffYOrUqbj55pvh7OyM2bNn4+uvv5YdSyp3d3fzGS5qamowbNiwTl9vVwUx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\nESliQRARkSIWBBERKfp/qsHjWC7FrDIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x55f0c30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uidE8Z2CQ3rj72eknYS0O/fnPf0ZUVBT69++P8ePH49KlS/af5eTkwGQyITIy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\nchvDg4iI3Pb/RhPU7IsV5i8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x581db70>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.13,Page No.758"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "L_AB=5 #m #Length of AB\n",
      "F_1=800 #N u.d.l\n",
      "F_2=1600 #N u.v.l\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Load on beam due to u.d.l of 800 N/m\n",
      "w1=F_1*L_AB #N\n",
      "\n",
      "#Load on beam due to triangular Loading\n",
      "w2=F_1*L_AB*2**-1 #N\n",
      "\n",
      "#Calculation of reactions R_A & R_B\n",
      "#Taking moment about A,we get\n",
      "#R_B=w1*L_AB*2**-1+w2**(2*5**-1of5)\n",
      "#After further simplifying we get\n",
      "R_B=2000+1333.33 #N\n",
      "R_A=(w1+w2)-R_B #N\n",
      "\n",
      "#Consider any section X-X at a distance x from A.\n",
      "#Rate of Loading at the section X-X\n",
      "#w_x=800+160*x\n",
      "\n",
      "#Total Load on length AX\n",
      "#W=800*x+80*x**2\n",
      "\n",
      "#Now the S.F at the section X-X is given by,\n",
      "#F_x=R_A-Load on length AX\n",
      "#After sub values and further simplifying we get\n",
      "#F_x=2666.67-800*x-80*x**2    ............................(1)\n",
      "\n",
      "#Equation 1 shows that shear force between A & B \n",
      "#At A\n",
      "x=0\n",
      "F_x1=F_x=2666.67-800*x-80*x**2 #N\n",
      "\n",
      "#At B\n",
      "x=5\n",
      "F_x2=F_x=2666.67-800*x-80*x**2 #N\n",
      "\n",
      "#Finding the position of zero shear.Equating S.F equal to zero in eqn(1)\n",
      "#0=2666.67-800*x-80*x**2\n",
      "#Further simplifying we get\n",
      "#x**2+10*x-33.33=0\n",
      "a=1\n",
      "b=10\n",
      "c=-33.33\n",
      "\n",
      "X=b**2-4*a*c\n",
      "\n",
      "x1=(-b+X**0.5)*(2*a)**-1 #m\n",
      "x2=(-b-X**0.5)*(2*a)**-1 #m\n",
      "\n",
      "#B.M Diagram\n",
      "#B.M at the section X-X is given by\n",
      "#M_x=R_A*x-800*x**2*2**-1-x**3*80*3**-1\n",
      "#Further simplifyng we get\n",
      "#M_x=2666.67*x-400*x**2-80*3**-1*x**3    ............2\n",
      "\n",
      "#Equation 2 shows that B.M between A & B varies \n",
      "#At A\n",
      "x=0\n",
      "M_x1=2666.67*x-400*x**2-80*3**-1*x**3 #KN/m\n",
      "\n",
      "#At B\n",
      "x=5\n",
      "M_x2=2666.67*x-400*x**2-80*3**-1*x**3 #KN/m\n",
      "\n",
      "#value of M_X2 is very small .i.e equal to zero\n",
      "#MAx B.M occurs where S.F is zero.\n",
      "#But shear force is zero at distance of 2.637m from A.\n",
      "#hence max B.M is Obtained by sub \n",
      "x=2.637 #m\n",
      "M_x=2666.67*x-400*x**2-80*3**-1*x**3\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L_AB]\n",
      "Y1=[F_x1,F_x2]\n",
      "Z1=[0,0,]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_x1,M_x2]\n",
      "X2=[0,L_AB]\n",
      "Z2=[0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\n",
      "plt.xlabel(\"Length in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x55e3f10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QNSzZq0q4U26uNlvq+HFYvBhuvVXviISoH848O2tNHIcPH+aTTz4hJSWF7t27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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x581d150>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.14,Page No.760"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "L_AB=4 #m\n",
      "L_BC=2 #m\n",
      "L=6 #m\n",
      "w=2 #KN/m #u.d.l\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A and R_B be the reactions at A & B respectively\n",
      "#R_A+R_B=w*L\n",
      " \n",
      "#Taking Moment at A,M_A\n",
      "R_B=(w*L*L*2**-1)*L_AB**-1 #KN\n",
      "R_A=w*L-R_B #KN\n",
      "\n",
      "#Shear Force calculations \n",
      "\n",
      "#S.f at pt C\n",
      "V_C=0\n",
      "\n",
      "#S.F at pt B\n",
      "V_B1=-w*L_BC #KN\n",
      "V_B2=V_B1+R_B #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A1=V_B2-w*L_AB #KN\n",
      "V_A2=V_A1+R_A #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=0 #KN.m\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=w*L_BC #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=w*L*L*2**-1-R_B*L_AB #KN.m\n",
      "\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L_BC,L_BC,L_BC+L_AB,L_BC+L_AB]\n",
      "Y1=[V_C,V_B1,V_B2,V_A1,V_A2]\n",
      "Z1=[0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_C,M_B,M_A]\n",
      "X2=[0,L_BC,L_BC+L_AB]\n",
      "Z2=[0,0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HNv/evXujqqrK8XlVVRWCgoIkVkTNceHCBWRkZOCuu+5CWlqa7HI007lzZ4we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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x56f6910>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1yMnJAQBkZWVh9+7d2LJlCwIDA6HT6bBz506Pjsm5ACLyZb521pCqVgxzdTAR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\njE2AiEjD2ASIiDTs/wHh5qCI0kKmvgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x581a470>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.15,Page No.762"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_AB=4 #m\n",
      "L_BC=2 #m\n",
      "L=6 #m\n",
      "\n",
      "#Loads\n",
      "w=2 #KN/m\n",
      "F_C=2 #KN\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A and R_B be the reactions at A & B respectively\n",
      "#R_A+R_B=w*L+F_C\n",
      " \n",
      "#Taking Moment at A,M_A\n",
      "R_B=(F_C*L+w*L*L*2**-1)*L_AB**-1 #KN\n",
      "R_A=(w*L+F_C)-R_B #KN\n",
      "\n",
      "#Shear Force calculations\n",
      "\n",
      "#S.F at pt C\n",
      "V_C1=0 #KN\n",
      "V_C2=F_C #KN\n",
      "\n",
      "#S.F at pt B\n",
      "V_B1=-w*L_BC-F_C #KN\n",
      "V_B2=V_B1+R_B #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A1=V_B2-w*L_AB #KN\n",
      "V_A2=V_A1+R_A #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=0 #KN.m\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=w*L_BC*L_BC*2**-1+F_C*L_BC #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=F_C*L+w*L*L*2**-1-R_B*L_AB #KN.m\n",
      "\n",
      "#Result\n",
      "print\"The Shear Force and Bending Moment are the Results\"\n",
      "\n",
      "#Plotting Shear Force Diagram\n",
      "\n",
      "X1=[0,0,L_BC,L_BC,L_BC+L_AB,L_AB+L_BC]\n",
      "Y1=[V_C1,V_C2,V_B1,V_B2,V_A1,V_A2]\n",
      "Z1=[0,0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length in m\")\n",
      "plt.ylabel(\"Shear Force in KN\")\n",
      "plt.show()\n",
      "\n",
      "#plotting the Bending Moment Diagram\n",
      "\n",
      "X2=[0,L_BC,L_BC+L_AB]\n",
      "Y2=[M_C,M_B,M_A]\n",
      "Z2=[0,0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\n",
      "plt.xlabel(\"Length in m\")\n",
      "plt.ylabel(\"Bending Moment in KN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment are the Results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x570da70>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HG2+8gfz8fDRr1gyLFi1y+VpFmnuHDh1QUlLi+L2kpATh4eFKlEI+evjwIUaP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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5527cd0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.16,Page No.763"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_BD=L_CA=2 #m\n",
      "L_AB=8 #m\n",
      "L=12 #m\n",
      "\n",
      "#Loads\n",
      "F_D=F_C=1000 #N\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A & R_b be the reactions at A & B respectively\n",
      "#As the Load on the beam is symmetrical,R_A and R_B will be equal\n",
      "#Their magnitude will be half of the total Load\n",
      "\n",
      "R_A=R_B=(F_C+F_D)*2**-1 #N\n",
      "\n",
      "#Shear force calculations\n",
      "\n",
      "#S.F at pt D\n",
      "V_D1=0 #N\n",
      "V_D2=-F_D #N\n",
      "\n",
      "#s.F at pt B\n",
      "V_B1=V_D2 #N\n",
      "V_B2=V_B1+R_B #N\n",
      "\n",
      "#S.F at pt A\n",
      "V_A1=V_B2 #N\n",
      "V_A2=V_A1+R_A #N\n",
      "\n",
      "#S.F at pt C\n",
      "V_C1=V_A2 #N\n",
      "V_C2=V_C1-F_C\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at pt D\n",
      "M_D=0 #KN.m\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=F_D*L_BD #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=F_D*(L_BD+L_AB)-R_B*L_AB #KN.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=F_D*L-R_B*(L_AB+L_CA)-R_A*L_CA #KN.m\n",
      "\n",
      "\n",
      "#Result\n",
      "print\"The Shear Force And Bending Moment diagrams are the Results\"\n",
      "\n",
      "#plotting Shear Force Diagram\n",
      "\n",
      "X1=[0,0,L_BD,L_BD,L_BD+L_AB,L_BD+L_AB,L_CA+L_BD+L_AB,L_CA+L_BD+L_AB]\n",
      "Y1=[V_D1,V_D2,V_B1,V_B2,V_A1,V_A2,V_C1,V_C2]\n",
      "Z1=[0,0,0,0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length in m\")\n",
      "plt.ylabel(\"Shear force in N\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting Bending Moment diagram\n",
      "\n",
      "X2=[0,L_BD,L_BD+L_AB,L_CA+L_AB+L_BD]\n",
      "Y2=[M_D,M_B,M_A,M_C]\n",
      "Z2=[0,0,0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\n",
      "plt.xlabel(\"Length in m\")\n",
      "plt.ylabel(\"Bending Moment in N.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force And Bending Moment diagrams are the Results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x55f8150>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IyOjwnICAAAEAH3zwwQcfPXgEBAT06PvYJAiCAJVrbW3Fbbfdhn/961+49dZb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\nEBGR0/4fEsvDXVDtsKwAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x55da4f0>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.17,Page No.765"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_BE=2 #m\n",
      "L_DB=L_CA=3 #m\n",
      "L_AD=5 #m\n",
      "L_AB=8 #m\n",
      "L=13 #m\n",
      "\n",
      "#Loads\n",
      "F_E=1000 #N\n",
      "F_C=800  #N\n",
      "F_D=2000 #N\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A and R_B be the reactions at pt A and B respectively\n",
      "#Taking Moment at pt A\n",
      "R_B=(-F_C*L_CA+F_D*L_AD+F_E*(L_AD+L_DB+L_BE))*L_AB**-1 #KN\n",
      "R_A=(F_C+F_D+F_E)-R_B   #KN\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F at pt E\n",
      "V_E1=0 #KN\n",
      "V_E2=-F_E #KN\n",
      "\n",
      "#S.F at pt B\n",
      "V_B1=V_E2 #KN\n",
      "V_B2=V_B1+R_B #KN\n",
      "\n",
      "#S.F at pt D\n",
      "V_D1=V_B2 #KN\n",
      "V_D2=V_D1-F_D #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A1=V_D2 #KN\n",
      "V_A2=V_A1+R_A #KN\n",
      "\n",
      "#S.F at pt C\n",
      "V_C1=V_A2 #KN\n",
      "V_C2=V_C1-F_C #KN\n",
      " \n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at pt E\n",
      "M_E=0 #KN.m \n",
      "\n",
      "#B.M at pt B\n",
      "M_B=F_E*L_BE #KN,m\n",
      "\n",
      "#B.M at pt D\n",
      "M_D=F_E*(L_BE+L_DB)-R_B*L_DB #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=F_D*L_AD+F_E*(L_AD+L_DB+L_BE)-R_B*(L_DB+L_AD) #KN.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=F_E*L+F_D*(L_AD+L_CA)-R_A*L_CA-R_B*(L_CA+L_AD+L_DB) #KN.m\n",
      "\n",
      "#Result\n",
      "print\"The Shear Force and Bending Moment diagrams are the results\"\n",
      "\n",
      "#Plotting Shear force Diagrams\n",
      "\n",
      "X1=[0,0,L_BE,L_BE,L_BE+L_DB,L_BE+L_DB,L_AD+L_BE+L_DB,L_AD+L_BE+L_DB,L_AD+L_BE+L_DB+L_CA,L_AD+L_BE+L_DB+L_CA]\n",
      "Y1=[V_E1,V_E2,V_B1,V_B2,V_D1,V_D2,V_A1,V_A2,V_C1,V_C2]\n",
      "Z1=[0,0,0,0,0,0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length in m\")\n",
      "plt.ylabel(\"Shear Force in KN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_E,M_B,M_D,M_A,M_C]\n",
      "X2=[0,L_BE,L_BE+L_DB,L_BE+L_DB+L_AD,L_BE+L_DB+L_AD+L_CA]\n",
      "Z2=[0,0,0,0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\n",
      "plt.xlabel(\"Length in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x55e3c10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NREVFIS0tDcOHD8epU6eg0Wjg7++PS5cuaUv1A7r/YhjjM73mzze/TaxKSoBW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\nyeWQkBBER0dDrVZDrVYjISEBABAdHQ0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       "text": [
        "<matplotlib.figure.Figure at 0x5519f10>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.18,Page No.766"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables \n",
      "L=10 #m #span\n",
      "w=1 #KN/m #u.d.l\n",
      "l=6 #m #Span betwen A & B\n",
      "l_AC=2.23 #m #Length AC\n",
      "l_BD=1.77 #m #LEngth BD\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A  & R_B be the reactions at A & B respectively\n",
      "#Taking moment at A\n",
      "#x**2*x*2**-1+R_B*l=(10-x)**2*2**-1\n",
      "#After simplifying we get,\n",
      "#R_A=5*3**-1*(5-x)\n",
      "#R_B=5*3**-1*(1+x)\n",
      "\n",
      "#Let y be the distance at which B.M is maximum at section ABfrom  C\n",
      "#S.F at section AB \n",
      "#R_A=y\n",
      "#Substituting value of R_A from above equation\n",
      "#y=5*3**-1*(1+x)...................................1\n",
      "\n",
      "#B.M at A\n",
      "#M_A=x**2*2**-1 \n",
      "\n",
      "#B.M at distance y from C\n",
      "#M_C=y**2*2**-1+R_A*(y-x)....................2\n",
      "#After further simplifying we get\n",
      "#M_C=5*18**-1*(-x**2+4*x+5).............................3\n",
      "\n",
      "#EQuating equations 1 & 2,we get quadratic equation as\n",
      "#14x**2-20x-25=0\n",
      "a=14\n",
      "b=-20\n",
      "c=-25\n",
      "\n",
      "X=b**2-4*a*c\n",
      "x=(-b+X**0.5)*(2*a)**-1\n",
      "\n",
      "#Substituing value of x in equation 1 we get\n",
      "y=5*3**-1*(1+x)\n",
      "\n",
      "#Sub values of x & y we get values of R_A & R_B as follows\n",
      "R_B=5*3**-1*(5-x)\n",
      "R_A=5*3**-1*(1+x)\n",
      "\n",
      "#Shear Force calculations\n",
      "\n",
      "#S.F at pt C\n",
      "V_C=0\n",
      "\n",
      "#S.F at A\n",
      "V_A1=-w*l_AC #KN\n",
      "V_A2=V_A1+R_A #KN\n",
      "\n",
      "#S.F at pt B\n",
      "V_B1=V_A2-1*l #KN\n",
      "V_B2=V_B1+R_B #KN\n",
      "\n",
      "#S.F at D\n",
      "V_D=V_B2-l_BD\n",
      "\n",
      "#BEnding Moment calculations\n",
      "\n",
      "#B.M at C\n",
      "M_C=0\n",
      "\n",
      "#B.M at A\n",
      "M_A=-w*l_AC**2*2**-1 #KNm\n",
      "\n",
      "#B.M at E i.e at y=5.38 m\n",
      "M_E=-w*y**2*2**-1+R_A*(y-l_AC)\n",
      "\n",
      "#B.M at B\n",
      "M_B=-w*(l_AC+l)**2*2**-1+R_A*l\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,l_AC,l_AC,l_AC+l,l_AC+l,l_AC+l+l_BD]\n",
      "Y1=[V_C,V_A1,V_A2,V_B1,V_B2,V_D]\n",
      "Z1=[0,0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_C,M_A,M_E,M_B]\n",
      "X2=[0,l_AC,l_AC+y,l_AC+l]\n",
      "Z2=[0,0,0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\n",
      "plt.xlabel(\"Length in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VM8jLoi/MQSY9YQ6yfGwEGlU+B/n772VXQ1QzzEGWi41Aw+w5yI8/Lm4TaRlz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\ng2MjICIyuP8H+JpvorKE/gUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x581de50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xpe8feXp6VjVXhdlT8QeAggJgyBCgdm3ZEM7J5PsqKk1iotx9i316yJ7NnStn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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5829270>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.19,Page No.770"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_EB=L_DE=L_CD=L_AC=1 #m\n",
      "L=4 #m\n",
      "\n",
      "#Loads\n",
      "#point Load\n",
      "\n",
      "#At pt D\n",
      "F_D1=200*sin(45*pi*180**-1)\n",
      "F_D2=200*cos(45*pi*180**-1)\n",
      "\n",
      "#At pt C\n",
      "F_C1=100*sin(60*pi*180**-1)\n",
      "F_C2=100*cos(60*pi*180**-1)\n",
      "\n",
      "#At pt E\n",
      "F_E1=300*sin(30*pi*180**-1)\n",
      "F_E2=300*cos(30*pi*180**-1)\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A and R_B be the reactions at pt A and B respectively\n",
      "#R_A+R_B=F_D1+F_C1+F_E1 #KN\n",
      "\n",
      "#Taking Moment at pt A\n",
      "R_B=(F_E1*(L_AC+L_CD+L_DE)+F_D1*(L_AC+L_CD)+F_C1*L_AC)*L**-1 #KN\n",
      "R_A=(F_D1+F_C1+F_E1)-R_B #KN\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F at pt B\n",
      "V_B1=0 #N\n",
      "V_B2=R_B #N\n",
      "\n",
      "#S.F at pt E\n",
      "V_E1=V_B2 #N\n",
      "V_E2=V_E1-F_E1 #N\n",
      "\n",
      "#S.F at pt D\n",
      "V_D1=V_E2 #N\n",
      "V_D2=V_D1-F_D1 #N\n",
      "\n",
      "#S.F at pt C\n",
      "V_C1=V_D2 #N\n",
      "V_C2=V_C1-F_C1 #N\n",
      "\n",
      "#S.F at pt A\n",
      "V_A1=V_C2 #N\n",
      "V_A2=V_A1+R_A\n",
      "\n",
      "#Bending Moment Diagrams\n",
      "\n",
      "#B.M At pt B\n",
      "M_B=0 #KN.m\n",
      "\n",
      "#B.M at pt E\n",
      "M_E=-R_B*L_EB #KN.m\n",
      "\n",
      "#B.M at pt D\n",
      "M_D=-R_B*(L_DE+L_EB)+F_E1*L_DE #KN.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=-R_B*(L_CD+L_DE+L_EB)+F_E1*(L_CD+L_DE)+F_D1*L_CD #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=-R_B*L+F_E1*(L_CD+L_DE+L_AC)+F_D1*(L_AC+L_CD)+F_C1*L_AC #KN.m\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,0,L_EB,L_EB,L_EB+L_DE,L_EB+L_DE,L_EB+L_DE+L_CD,L_EB+L_DE+L_CD,L_EB+L_DE+L_CD,L_EB+L_DE+L_CD]\n",
      "Y1=[V_B1,V_B2,V_E1,V_E2,V_D1,V_D2,V_C1,V_C2,V_A1,V_A2]\n",
      "Z1=[0,0,0,0,0,0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_E,M_D,M_C,M_A]\n",
      "X2=[0,L_EB,L_DE+L_EB,L_DE+L_EB+L_CD,L_DE+L_EB+L_CD+L_AC]\n",
      "Z2=[0,0,0,0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\n",
      "plt.xlabel(\"Length in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zxy4oz0QqKyuJi4sjJiaGsLAwvvOd71BWVtZlmb1797Jy5Urg/AWNra2tNDc3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\n2v8Bj/w2ELkj9AoAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5829330>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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iQgghrCZJRAghhNUkiQghhLCaJBEhhBBWkyQihBDCapJEhBBCWE2S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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x55e3a70>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.20,Page No.772"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_AC=L_CD=L_DE=L_EB=2 #m\n",
      "L=8 #m\n",
      "\n",
      "#Loads\n",
      "#point Load\n",
      "\n",
      "#At pt E\n",
      "F_E1=6*sin(pi*180**-1*45) #KN\n",
      "F_E2=6*cos(pi*180**-1*45) #KN\n",
      "\n",
      "#At pt D\n",
      "F_D1=8*sin(pi*180**-1*60) #KN\n",
      "F_D2=8*cos(pi*180**-1*60) #KN\n",
      "\n",
      "#At pt C\n",
      "F_C1=4*sin(pi*180**-1*30) #KN\n",
      "F_C2=4*cos(pi*180**-1*30) #KN\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A and R_B be the reactions at pt A and B respectively\n",
      "#R_A+R_B=F_D1+F_C1+F_E1 #KN\n",
      "\n",
      "#Taking Moment at pt A\n",
      "R_B=(F_E1*(L_AC+L_CD+L_DE)+F_D1*(L_AC+L_CD)+F_C1*L_AC)*L**-1 #KN\n",
      "R_A=(F_D1+F_C1+F_E1)-R_B #KN\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F at pt B\n",
      "V_B1=0 #N\n",
      "V_B2=R_B #N\n",
      "\n",
      "#S.F at pt E\n",
      "V_E1=V_B2 #N\n",
      "V_E2=V_E1-F_E1 #N\n",
      "\n",
      "#S.F at pt D\n",
      "V_D1=V_E2 #N\n",
      "V_D2=V_D1-F_D1 #N\n",
      "\n",
      "#S.F at pt C\n",
      "V_C1=V_D2 #N\n",
      "V_C2=V_C1-F_C1 #N\n",
      "\n",
      "#S.F at pt A\n",
      "V_A1=V_C2 #N\n",
      "V_A2=V_A1+R_A\n",
      "\n",
      "#Bending Moment Diagrams\n",
      "\n",
      "#B.M At pt B\n",
      "M_B=0 #KN.m\n",
      "\n",
      "#B.M at pt E\n",
      "M_E=-R_B*L_EB #KN.m\n",
      "\n",
      "#B.M at pt D\n",
      "M_D=-R_B*(L_DE+L_EB)+F_E1*L_DE #KN.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=-R_B*(L_CD+L_DE+L_EB)+F_E1*(L_CD+L_DE)+F_D1*L_CD #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=-R_B*L+F_E1*(L_CD+L_DE+L_AC)+F_D1*(L_AC+L_CD)+F_C1*L_AC #KN.m\n",
      "\n",
      "\n",
      "#Result\n",
      "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,0,L_EB,L_EB,L_EB+L_DE,L_EB+L_DE,L_EB+L_DE+L_CD,L_EB+L_DE+L_CD,L_EB+L_DE+L_CD,L_EB+L_DE+L_CD]\n",
      "Y1=[V_B1,V_B2,V_E1,V_E2,V_D1,V_D2,V_C1,V_C2,V_A1,V_A2]\n",
      "Z1=[0,0,0,0,0,0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_E,M_D,M_C,M_A]\n",
      "X2=[0,L_EB,L_DE+L_EB,L_DE+L_EB+L_CD,L_DE+L_EB+L_CD+L_AC]\n",
      "Z2=[0,0,0,0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\n",
      "plt.xlabel(\"Length in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x55fdb30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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O5TNopNCtWzfk5+cjOzsbWVlZPKSOqk2nE4ubx4+LY7q9vMTNXZwNNJ5Tp4CO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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x55f8b50>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.21,Page No.774"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_CB=4 #m\n",
      "L_AC=2 #m\n",
      "L=6 #m\n",
      "\n",
      "#Loads\n",
      "m=24 #KN.m #couple\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A and R_B be the reactions at pt A and B respectively\n",
      "#R_A+R_B=0\n",
      "#Taking Moment at pt A\n",
      "R_B=m*L**-1 #KN\n",
      "R_A=-R_B #KN\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.f at pt B\n",
      "V_B1=0 #KN\n",
      "V_B2=R_B #KN\n",
      "\n",
      "#S.F at pt C\n",
      "V_C=V_B2 #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A1=V_C #KN\n",
      "V_A2=V_A1+R_A #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=0 #KN.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C1=-R_B*L_CB #KN.m\n",
      "M_C2=M_C1+m #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=-R_B*L+m #KN.m\n",
      "\n",
      "#Result\n",
      "print\"The Shear Force and Bending Moment are the results\"\n",
      "\n",
      "#Plotting Shear Force Diagram\n",
      "\n",
      "X1=[0,0,L_CB,L_CB+L_AC,L_CB+L_AC]\n",
      "Y1=[V_B1,V_B2,V_C,V_A1,V_A2]\n",
      "Z1=[0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length in m\")\n",
      "plt.ylabel(\"Shear Force in KN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting Bending Moment Diagram\n",
      "\n",
      "X1=[0,L_CB,L_CB,L_CB+L_AC]\n",
      "Y1=[M_B,M_C1,M_C2,M_A]\n",
      "Z1=[0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length in m\")\n",
      "plt.ylabel(\"Bending Moment in KN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KlCmS5HlWQEu6deumsWPHSpKSk5O1d+/eq9bT0j4bi4qK8kz6NWjQII0cOVKS\nFB8fL7fbfdV9AN4gBNCp1dXVqU+fPsrLy2t2ebdu3Tzvjf/eHrPZbA3m0Deuctusa9eunvcBAQGq\nqalptabm9tlY9+7dG2z3yjpt3QfQVtwTQKfWq1cvRUVFafv27ZIun3S//PLLq65z7733aseOHTIM\nQ6Wlpdq3b59nWc+ePXX+/HmvarhaiAD+RgigU7l48aIiIiI8r9dff11btmzRxo0blZiYqPj4eGVl\nZXna158i+cr7SZMmKTw8XHFxcZoxY4aSkpI8z2idO3euHnjgAc+N4cbrNzflcuPvW3rfeJ2WPne2\naZ3hX/xEFGhGRUWFgoKCdPbsWaWkpOjw4cPq37+/v8sCfI57AkAzxo0bp7KyMlVVVenZZ58lANBp\ncSUAABbGPQEAsDBCAAAsjBAAAAsjBADAwggBALAwQgAALOz/AbEdCOnDkhV6AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x55f0730>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IUVH2/j8m35+62fP7s+f3ZirF5xS2b9+OUaNGAQDKy8vh6ekp/czT0xNlZWVK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\nEUmYFIiISMKkQEREEiYFIiKS/D8xbsU2dVdsUgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x570f5d0>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20.22,Page No.775"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Declaration Of Variables\n",
      "\n",
      "#Lengths\n",
      "L_DB=L_CD=2.5 #m\n",
      "L_AC=5 #m\n",
      "L=L=10 #m\n",
      "\n",
      "#Loads\n",
      "m=15000 #Nm #couple\n",
      "w=1000 #N/m #u.d.l\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A and R_B be the reactions at pt A and B respectively\n",
      "#R_A+R_B=w*L_AC\n",
      "#Taking Moment at pt A\n",
      "R_B=(w*L_AC*L_AC*2**-1-m)*L**-1 #KN\n",
      "R_A=w*L_AC-R_B #KN\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F  at pt B\n",
      "V_B1=0 #KN\n",
      "V_B2=R_B #KN\n",
      "\n",
      "#S.F at pt D\n",
      "V_D=V_B2 #KN\n",
      "\n",
      "#S.F at pt C\n",
      "V_C=V_D #KN\n",
      "\n",
      "#S.F at pt A\n",
      "V_A1=V_C-w*L_AC #KN\n",
      "V_A2=V_A1+R_A #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at pt B\n",
      "M_B=0 #KN.m\n",
      "\n",
      "#B.M at pt D\n",
      "M_D1=-R_B*L_DB #KN.m\n",
      "M_D2=M_D1-m #KN.m\n",
      "\n",
      "#B.M at pt C\n",
      "M_C=-R_B*(L_CD+L_DB)-m #KN.m\n",
      "\n",
      "#B.M at pt A\n",
      "M_A=-R_B*L-m+w*L_AC*L_AC*2**-1 #KN.m\n",
      "\n",
      "#Result\n",
      "print\"The Shear Force and Bending Moment Diagrams are the results\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,0,L_DB,L_CD+L_DB,L_CD+L_DB+L_AC,L_CD+L_DB+L_AC]\n",
      "Y1=[V_B1,V_B2,V_D,V_C,V_A1,V_A2]\n",
      "Z1=[0,0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "Y2=[M_B,M_D1,M_D2,M_C,M_A]\n",
      "X2=[0,L_DB,L_DB,L_DB+L_CD,L_AC+L_CD+L_DB]\n",
      "Z2=[0,0,0,0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\n",
      "plt.xlabel(\"Length in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Shear Force and Bending Moment Diagrams are the results\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x5ba4110>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5c60jCsiI0UIIR3rxRdiwQcKmsakxcKp2ExZCCEdZsgTeeQdSU6FDB72rEXVJ\nxlUVQtQby5dDTAx89hnYcUAToRMJHCFEvbBiBURHa2HTqZPe1Qh7kMARQuhu1Sp49VXtNFqVoRFF\nI2MzcJYvX16tN4LBYKBt27b4+/vTq1cvuxcohGjc3nwTXnpJC5u77tK7GmFPNqcnSE9P51//+hf5\n+flYLBbeeOMNtm7dyp///GeWLl3qiBqFEI3U6tXwwgvafTZduuhdjbA3m0c4ubm5ZGRk0Lp1awAW\nLFhAWFgYn332Gf7+/jKpmRCiVtauhblz4dNPwcND72qEI9gMnOPHj9OiylR6zs7OHDt2jFtvvZVb\nZCIKIUQtvPcePP20FjaennpXIxzFZuA89NBD9O/fn5EjR6KUYsuWLTz44IOcPXsWb29vR9QohGhE\n4uPhySe1sdG8vPSuRjjSdQ3euWfPHr766isMBgP33nsvffv2dURtDiND29QNGdpG2LJxozanTXIy\n9OihdzXiZtTp0DZV9enTxzqJmcFg4OjRo9x55521KlII0TQlJMC0adrkaRI2TZPNwHnttdeYP38+\nHTp0oHnz5tb2b7/91q6FCSEaj48+0qaG/vhj6N1b72qEXmwGzquvvsr3339f41TTQghxLUlJMHky\nbNkCjexsvLhBNu/DufPOO63TE9SV9evX4+PjQ/PmzcnIyKi2bPHixZjNZry8vEhOTra2p6en4+fn\nh9lsZubMmdb2srIyoqKiMJvNBAYGcuTIEeuy2NhYPD098fT0ZO3atXX6GYQQtm3fDhMmwObN0L+/\n3tUIvdk8wunSpQsDBgxg2LBh1u7RNzsfjp+fH5s2beKxxx6r1p6ZmUl8fDyZmZlYLBYGDx5MVlYW\nBoOBqVOnEhMTQ0BAAGFhYSQlJREaGkpMTAyurq5kZWURHx/PnDlziIuLo6ioiAULFpCeng6Av78/\n4eHhtGvXrtZ1CyGu386d8OCDWkeBe+7RuxpRH1zXEc7gwYMpLy/nzJkzlJSUUFJSclM79fLywvMq\nne8TEhIYO3Yszs7OdO7cGQ8PD9LS0igoKKCkpISAgAAAJkyYwObNmwFITExk4sSJAERERLBjxw4A\ntm3bRkhICO3ataNdu3YEBweTlJR0U3ULIa7P559DZCR88AH84Q96VyPqC5tHOI6cFyc/P5/AwEDr\na5PJhMViwdnZGVOVEf2MRiMWiwUAi8WCu7s7AE5OTrRt25YTJ06Qn59fbZ1L2xJC2NeuXTB6NLz/\nPgQF6V2ZEQgkAAAXzUlEQVSNqE9qDJyZM2eyYsUKhg8ffsUyg8FAYmLiNTccHBxMYWHhFe2LFi26\n6jb1VjVYg4KCCJL/pwhxw9LSYORIWLcOBg/WuxpRl1JTU0lNTb2pbdQYOOPHjwfgySefrNWGU1JS\nbngdo9FIbm6u9XVeXh4mkwmj0UheXt4V7ZfWOXr0qPU+oeLiYlxdXTEajdW+nNzcXAYOHFjjvmWG\nUyFuzt69MHw4rFkDQ4boXY2oa5f/IT5//vwb34jSUVBQkNq7d6/19YEDB1TPnj1VWVmZ+vHHH1XX\nrl1VZWWlUkqpgIAAtXv3blVZWamGDh2qtm7dqpRSatWqVeovf/mLUkqp999/X0VFRSmllDpx4oTq\n0qWLOnnypCoqKrI+vxqdv4ZGIy1NqX799K5C6CEjQ6kOHZRKSNC7EuEotfndrPEIx8/Pr8aQMhgM\n7N+//8bT7RebNm1ixowZ/PzzzwwbNozevXuzdetWvL29iYyMxNvbGycnJ6KjozEYDABER0czadIk\nSktLCQsLIzQ0FIApU6Ywfvx4zGYzrq6uxMXFAdC+fXuee+45+vXrB8Dzzz8vPdSEsIP//heGDoXX\nX4fwcL2rEfVZjWOp5eTkANoPPWin2JRSvPvuuwCNai4cGUutbshYak3Pd99BcLA2PXRkpN7VCEeq\nze+mzcE7e/XqxTfffFOtrXfv3uzbt+/GK6ynJHDqhgRO03LwIAwaBC+/rN1vI5qW2vxu2rwPRynF\nl19+aX391VdfyY+zEE3c999rRzZLlkjYiOtn8z6c1atX8/DDD1NcXAxAu3btePvtt+1emBCifjp0\nSOvyvGCBNmyNENfLZuD4+/uzf/9+a+C0bdvW7kUJIeqn7GztNNpzz2kDcgpxI2wGzvnz59m4cSM5\nOTlUVFQA2rm7uXPn2r04IUT9ceQIDBwIc+ZoUw0IcaNsBs6IESNo164d/v7+3HLLLY6oSQhRz+Tm\namEza5Y2iZoQtWEzcCwWC9u2bXNELUKIeshi0cLmr3+FGTP0rkY0ZDZ7qd1zzz03dZOnEKLhKijQ\nwuaRR+AmZiQRAriOI5wvvviCt99+my5dutCyZUvg5kcaEELUf8eOaR0Exo/XrtsIcbNsBs7WrVsd\nUYcQoh45flzr+hwZCf/4h97ViMbC5im1zp07k5uby86dO+ncuTOtWrWSGz+FaMROnNDCJjwcnn9e\n72pEY2IzcObNm8dLL73E4sWLASgvL2fcuHF2L0wI4XgnT2ojCAwZAi++CL+MnStEnbAZOJs2bSIh\nIYFWrVoB2vwzNzvFtBCi/jl1CkJCtFk6ly6VsBF1z2bgtGzZkmbNfn3b2bNn7VqQEMLxTp+G0FC4\n+25YvlzCRtiHzcAZM2YMjz32GKdOneLNN99k0KBBPPLII46oTQjhAGfOQFgY9O6tTTMgYSPsxeb0\nBADJyckkJycDMGTIEIKDg+1emCPJ9AR1Q6YnaHjOntXCxtMT3ngDmtn8E1QIjV2mJwAICQnh5Zdf\nZs6cOQwePLhWxVW1fv16fHx8aN68Oenp6db2lJQU+vbtS48ePejbty87d+60LktPT8fPzw+z2czM\nmTOt7WVlZURFRWE2mwkMDOTIkSPWZbGxsXh6euLp6cnatWtvum4hGpNz52D4cOjaVcJGOEhNc0/v\n2rVL3X///eqBBx5QGRkZysfHR3Xs2FHdcccd6pNPPrnhuayrOnjwoPr+++9VUFCQSk9Pt7bv27dP\nFRQUKKWU+u6775TRaLQu69evn0pLS1NKKTV06FC1detWpZRSq1atUlOnTlVKKRUXF6eioqKUUkqd\nOHFCde3aVZ08eVKdPHnS+vxqrvE1iBuQlqZUv356VyGuR2mpUsHBSo0bp1RFhd7ViIaoNr+bNf5N\nM336dJ599lnGjh3LgAED+Pe//01hYSGff/45zzzzzE2FnJeXF56enle09+rVCzc3NwC8vb0pLS3l\nwoULFBQUUFJSQkBAAAATJkxg8+bNACQmJjJx4kQAIiIi2LFjBwDbtm0jJCSEdu3a0a5dO4KDg0lK\nSrqpuoVoDMrK4IEHwNUV3n4bmjfXuyLRVNQYOBcvXiQkJIQxY8bw29/+lsDAQEALC4MDripu3LgR\nf39/nJ2dsVgsmEwm6zKj0YjFYgG0wUXd3d0BcHJyom3btpw4cYL8/Pxq65hMJus6QjRV5eUQEQGt\nW8O6deBkc6wRIepOjf+5VQ2V2kxLEBwcTGFh4RXtixYtYvjw4ddc98CBAzz99NOkpKTc8H5ra968\nedbnQUFBBAUFOWzfQjjChQsQFQXOzvDeexI24sakpqaSmpp6U9uo8T+5/fv306ZNGwBKS0utzy+9\ntqW2YZGXl8eoUaNYt24dXbp0AbQjmry8vGrvuXT0YjQaOXr0KJ06daKiooLi4mJcXV0xGo3Vvpzc\n3FwGDhxY436rBo4Qjc2FCzB2LFy8CBs2aKEjxI24/A/x+fPn3/A2rnlKraSkhJKSEioqKqzPL72u\nK6pKt7pTp04xbNgwli5dyt13321t/+1vf4uLiwtpaWkopVi3bh0jRowAIDw8nNjYWAA2bNjAoEGD\nAK1nXXJyMqdOneLkyZOkpKQwZMiQOqtbiIaiokIb8fncOVi/Hlq00Lsi0WTVedeF6/Dhhx8qk8mk\nbrnlFtWxY0cVGhqqlFLqhRdeUK1atVK9evWyPo4fP66UUmrv3r3K19dXdevWTT3++OPWbZ0/f16N\nGTNGeXh4qP79+6vs7GzrstWrVysPDw/l4eGh1qxZU2M9On0NjY70Uqt/KiqUeughrUdaaane1YjG\npDa/m9d142djJzd+1g258bN+qayEyZO16aG3bIFbb9W7ItGY1OZ3Uy4bCtEIVVbCo49CdjZ88omE\njagfJHCEaGSUgmnT4H//g6Qk+GWgdyF0J4EjRCOiFDz+OPz3v7Btm3a/jRD1hQSOEI2EUjB7tnYN\nLSUFXFz0rkiI6iRwhGgElIKnnoLPP4ft26FtW70rEuJKEjhCNHBKwd//rh3VfPop3Hab3hUJcXUS\nOEI0cPPmad2ed+6E9u31rkaImkngCNGAvfCCNlTNzp1w++16VyPEtUngCNFALVkC774LqanQoYPe\n1QhhmwSOEA3Q8uUQEwOffQa/TCElRL0ngSNEA7NiBURHa2HTqZPe1Qhx/SRwhGhAVq2CV1/VTqNV\nmV9QiAZBAkeIBuLNN+Gll7SwuesuvasR4sZJ4AjRAKxerfVI27kTfpmXUIgGRwJHiHouNhbmztVu\n6vTw0LsaIWpPAkeIeuy99+CZZ7Sw8fTUuxohbk6NU0zb0/r16/Hx8aF58+ZkZGRcsfzo0aO0bt2a\n5cuXW9vS09Px8/PDbDYzc+ZMa3tZWRlRUVGYzWYCAwM5cuSIdVlsbCyenp54enqydu1a+34oIWqp\nogIKCmDfPm06gTVrtHtspk2DJ5/Uhqzx8tK7SiFuni5HOH5+fmzatInHHnvsqstnz57NsGHDqrVN\nnTqVmJgYAgICCAsLIykpidDQUGJiYnB1dSUrK4v4+HjmzJlDXFwcRUVFLFiwgPT0dAD8/f0JDw+n\nXbt2dv98QlRWQlERFBZqj2PHrv68sBBOntSGpHFz0x4dO2r/enhoXZ/lyEY0FroEjtc1/lzbvHkz\nXbt2pVWVWaMKCgooKSkhICAAgAkTJrB582ZCQ0NJTExk/vz5AERERDB9+nQAtm3bRkhIiDVggoOD\nSUpK4k9/+pO9PpZo5JSC06erh0VNQXL8uDYXzaUQqRokvr6/Pndz04akcZKT26IJqFf/mZ85c4aX\nXnqJ7du3s2zZMmu7xWLBVOWmA6PRiMVisS5zd3cHwMnJibZt23LixAny8/OrrWMymazrCFHV2bPX\nPgKp+rpFi+phcen5PfdUf92hA7RsqfcnE6J+sVvgBAcHU1hYeEX7okWLGD58+FXXmTdvHrNmzeLW\nW29FKWWv0mrc9yVBQUEEBQU5dP+ibpWVaUFxPUFSUVE9LC4979Wr+uuOHWW6ZtF0paamkpqaelPb\nsFvgpKSk3PA6X3/9NRs3buSpp57i1KlTNGvWjN/85jeMGjWKvLw86/vy8vKsRy9Go5GjR4/SqVMn\nKioqKC4uxtXVFaPRWO3Lyc3NZeDAgTXuu2rgiPqpokI7VXWtU1mXnp85ox1lXB4knp5w333Vg8TF\nBQwGvT+dEPXb5X+IX7qUcSN0P6VW9Ujm888/tz6fP38+bdq0Ydq0aQC4uLiQlpZGQEAA69atY8aM\nGQCEh4cTGxtLYGAgGzZsYNCgQQCEhITw7LPPcurUKZRSpKSksHTpUgd+MnE9ql5cv9aprGPHtPdd\n7eK6uzv07Vv9esltt0EzXfpgCiFqokvgbNq0iRkzZvDzzz8zbNgwevfuzdatW6+5TnR0NJMmTaK0\ntJSwsDBCQ0MBmDJlCuPHj8dsNuPq6kpcXBwA7du357nnnqNfv34APP/889JDzUEuv7h+rdNacnFd\niKbDoBx9saQeMhgMDr9m1Bh98412pOHkVPPF9ctfy8V1IRqm2vxuSuAggVNXlAKLRTudJRfXhWjc\nJHBqSQJHCCFuTG1+N+WyqhBCCIeQwBFCCOEQEjhCCCEcQgJHCCGEQ0jgCCGEcAgJHCGEEA4hgSOE\nEMIhJHCEEEI4hASOEEIIh5DAEUII4RASOEIIIRxCAkcIIYRDSOAIIYRwCF0CZ/369fj4+NC8eXMy\nMjKqLdu/fz933303vr6+9OjRg/LycgDS09Px8/PDbDYzc+ZM6/vLysqIiorCbDYTGBjIkSNHrMti\nY2Px9PTE09OTtWvXOubDCSGEuDqlg4MHD6rvv/9eBQUFqfT0dGv7hQsXVI8ePdT+/fuVUkoVFRWp\nixcvKqWU6tevn0pLS1NKKTV06FC1detWpZRSq1atUlOnTlVKKRUXF6eioqKUUkqdOHFCde3aVZ08\neVKdPHnS+vxqdPoa6qWdO3fqXUK9Id+FRr6HX8l38ava/G7qcoTj5eWFp6fnFe3Jycn06NEDPz8/\nAG677TaaNWtGQUEBJSUlBAQEADBhwgQ2b94MQGJiIhMnTgQgIiKCHTt2ALBt2zZCQkJo164d7dq1\nIzg4mKSkJEd8vAYtNTVV7xLqDfkuNPI9/Eq+i5tTr67hZGVlYTAYCA0Nxd/fn2XLlgFgsVgwmUzW\n9xmNRiwWi3WZu7s7AE5OTrRt25YTJ06Qn59fbR2TyWRdRwghhOM52WvDwcHBFBYWXtG+aNEihg8f\nftV1Lly4wJdffsnevXv5zW9+w6BBg/D396dt27b2KlMIIYSD2C1wUlJSbngdd3d37rvvPtq3bw9A\nWFgYGRkZjBs3jry8POv78vLyrEcvRqORo0eP0qlTJyoqKiguLsbV1RWj0Vjt8Dc3N5eBAwdedb/d\nunXDYDDccL2N1fz58/Uuod6Q70Ij38Ov5LvQdOvW7YbX0f2UmqoyJ/aQIUP49ttvKS0tpaKigs8+\n+wwfHx/c3NxwcXEhLS0NpRTr1q1jxIgRAISHhxMbGwvAhg0bGDRoEAAhISEkJydz6tQpTp48SUpK\nCkOGDLlqDYcOHUIpJQ95yEMe8rjOx6FDh2r1g+9wH374oTKZTOqWW25RHTt2VKGhodZl77zzjvLx\n8VG+vr5qzpw51va9e/cqX19f1a1bN/X4449b28+fP6/GjBmjPDw8VP/+/VV2drZ12erVq5WHh4fy\n8PBQa9ascchnE0IIcXUGpZSyHUtCCCHEzdH9lJqekpKS8PLywmw2s3TpUr3L0U1ubi4DBgzAx8cH\nX19fVq5cqXdJurt48SK9e/eusYNLU3Hq1ClGjx5N9+7d8fb2Zvfu3XqXpJvFixfj4+ODn58fDz74\nIGVlZXqX5DCTJ0+mY8eO1ltWAIqKiggODsbT05OQkBBOnTplcztNNnAuXrzI9OnTSUpKIjMzk/ff\nf5+DBw/qXZYunJ2deeWVVzhw4AC7d+9m1apVTfa7uGTFihV4e3s3+c4kM2fOJCwsjIMHD7J//366\nd++ud0m6yMnJ4a233iIjI4Nvv/2WixcvEhcXp3dZDvPwww9fcR/jkiVLCA4O5ocffmDQoEEsWbLE\n5naabOB8/fXXeHh40LlzZ5ydnfnTn/5EQkKC3mXpws3NjV69egHQunVrunfvTn5+vs5V6ScvL49P\nPvmERx55hKZ8xrm4uJgvvviCyZMnA7/e59YUubi44OzszLlz56ioqODcuXMYjUa9y3KYP/zhD9x2\n223V2qredD9x4kTrzfjX0mQDp+oNoyA3hl6Sk5PDvn376N+/v96l6GbWrFksW7aMZs2a7P89AMjO\nzuaOO+7g4Ycfpk+fPvz5z3/m3Llzepeli/bt2/Pkk09y55130qlTJ9q1a8fgwYP1LktXx44do2PH\njgB07NiRY8eO2Vynyf4/qqmfKrmaM2fOMHr0aFasWEHr1q31LkcXH330ER06dKB3795N+ugGoKKi\ngoyMDKZNm0ZGRgatWrW6rtMmjdHhw4d59dVXycnJIT8/nzNnzvDuu+/qXVa9YTAYrus3tckGjtFo\nJDc31/o6Nze32lA4Tc2FCxeIiIhg3LhxjBw5Uu9ydLNr1y4SExPp0qULY8eO5dNPP2XChAl6l6UL\nk8mEyWSiX79+AIwePfqK0d2bir1793LPPffg6uqKk5MTo0aNYteuXXqXpauOHTtaR5MpKCigQ4cO\nNtdpsoHTt29fsrKyyMnJoby8nPj4eMLDw/UuSxdKKaZMmYK3tzdPPPGE3uXoatGiReTm5pKdnU1c\nXBwDBw5sslNbuLm54e7uzg8//ADA9u3b8fHx0bkqfXh5ebF7925KS0tRSrF9+3a8vb31LktXVW+6\nj42Nva4/VO02tE195+TkxD//+U+GDBnCxYsXmTJlSpPtgfPVV1/xzjvv0KNHD3r37g1oXUBDQ0N1\nrkx/Tf3U62uvvcZDDz1EeXk53bp14+2339a7JF307NmTCRMm0LdvX5o1a0afPn149NFH9S7LYcaO\nHctnn33Gzz//jLu7OwsWLODpp58mMjKSmJgYOnfuzAcffGBzO3LjpxBCCIdosqfUhBBCOJYEjhBC\nCIeQwBFCCOEQEjhCCCEcQgJHCCGEQ0jgCCGEcAgJHCFugL2H/Hn11VcpLS29of1t2bKlSU+vIRoO\nuQ9HiBvQpk0bSkpK7Lb9Ll26sHfvXlxdXR2yPyEcSY5whLhJhw8fZujQofTt25f77ruP77//HoBJ\nkyYxc+ZM7r33Xrp168bGjRsBqKysZNq0aXTv3p2QkBCGDRvGxo0bee2118jPz2fAgAEMGjTIuv1/\n/OMf9OrVi7vvvpuffvrpiv2vWbOGxx9//Jr7rConJwcvLy8efvhhfve73/HQQw+RnJzMvffei6en\nJ3v27LHH1ySEBI4QN+vRRx/ltddeY+/evSxbtoxp06ZZlxUWFvLVV1/x0Ucf8fTTTwPw4YcfcuTI\nEQ4ePMi6dev4z3/+g8Fg4PHHH6dTp06kpqayY8cOAM6ePcvdd9/NN998w3333cdbb711xf4vH37n\navu83OHDh/nb3/7G//73P77//nvi4+P56quvePnll1m0aFFdfTVCVNNkx1IToi6cOXOG//znP4wZ\nM8baVl5eDmhBcGlAw+7du1vnC/nyyy+JjIwEtBF3BwwYUOP2W7RowbBhwwDw9/cnJSXlmvXUtM/L\ndenSxToQp4+Pj3VuF19fX3Jycq65DyFqSwJHiJtQWVlJu3bt2Ldv31WXt2jRwvr80uVSg8FQba6d\na11GdXZ2tj5v1qwZFRUVNmu62j4v17Jly2rbvbTO9e5DiNqQU2pC3AQXFxe6dOnChg0bAO0Hfv/+\n/ddc595772Xjxo0opTh27BifffaZdVmbNm04ffr0DdUg/X5EQyGBI8QNOHfuHO7u7tbHq6++yrvv\nvktMTAy9evXC19eXxMRE6/urXl+59DwiIgKTyYS3tzfjx4+nT58+tG3bFtCuB4WGhlo7DVy+/tWm\nS7i8vabnl69T0+umPiWDsB/pFi2EDs6ePUurVq04ceIE/fv3Z9euXdc1Y6IQDZlcwxFCB3/84x85\ndeoU5eXlzJ07V8JGNAlyhCOEEMIh5BqOEEIIh5DAEUII4RASOEIIIRxCAkcIIYRDSOAIIYRwCAkc\nIYQQDvH/Aft+XWP0flPgAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5832130>"
       ]
      }
     ],
     "prompt_number": 26
    }
   ],
   "metadata": {}
  }
 ]
}