{
 "metadata": {
  "name": "chapter 3.ipynb"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 3:Shear Force And Bending Moment Diagrams in Statically Determinate Beams"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.1,Page No.100"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of Variables\n",
      "\n",
      "L_AC=L_CD=1 #m #Length of AC & CD\n",
      "L_DB=1.5 #m #Lengh of DB\n",
      "L=3.5 #m #Length of Beam\n",
      "F_B=10 #KN #Force at pt B\n",
      "F_C=F_D=20 #KN #Force at pt C & D\n",
      "\n",
      "#Calculations\n",
      "\n",
      "R_A=F_C+F_D+F_B #KN #Force at support A \n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F At pt B\n",
      "V_B1=0  #KN \n",
      "V_B2=F_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 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 #KN.m\n",
      "\n",
      "#B.M AT Pt D\n",
      "M_D=F_B*L_DB #KN.m\n",
      "\n",
      "#B.M At pt C\n",
      "M_C=F_B*(L_DB+L_CD)+F_D*L_CD #KN.m\n",
      "\n",
      "#B.M At pt A\n",
      "M_A=F_B*L+F_D*(L_CD+L_AC)+F_C*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_CD+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_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,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 0x56bd6f0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pqQavCQgIEADwi1/84he/rPgKCAiw6e+yYlJMDQ0NuPfee/H999+jZ8+eGDhw\nINavX4/g4GC5SyMickmKmWJq3749PvroI4wcORKNjY2YPn06mwMRkYwUM4IgIiJlUUzMtaWsrCwE\nBQXhnnvuwZIlS4y+Zt68ebjnnnsQHh6OwsJCiStsnbn6s7Oz4e3tjcjISERGRuLNN9+UoUrjpk2b\nBrVajbCwMJOvUfK5N1e/ks89AJSWliIuLg4hISEIDQ3Fhx9+aPR1SvwdWFK7ks9/XV0dYmJiEBER\nAY1Gg5deesno65R47gHL6rf6/Nu8qiyShoYGISAgQDh16pRQX18vhIeHC0VFRQav2bZtmzBq1ChB\nEAQhLy9PiImJkaNUoyypf8+ePcLYsWNlqrB1P/74o1BQUCCEhoYafV7J514QzNev5HMvCIJQVlYm\nFBYWCoIgCNXV1UJgYKDD/PtvSe1KP//Xrl0TBEEQbt68KcTExAj/+te/DJ5X6rlvZq5+a8+/4kYQ\nllwwl5GRgeTkZABATEwMqqqqUFFRIUe5d7D0gj9BoTN7Q4YMQZcuXUw+r+RzD5ivH1DuuQcAX19f\nREREAAA8PT0RHByM8+fPG7xGqb8DS2oHlH3+O3bsCACor69HY2MjunbtavC8Us99M3P1A9adf8U1\nCGMXzJ07d87sa86ePStZja2xpH6VSoV9+/YhPDwcCQkJKCoqkrpMmyn53FvCkc59SUkJCgsLERMT\nY/C4I/wOTNWu9PPf1NSEiIgIqNVqxMXFQaPRGDyv9HNvrn5rz79iUkzNLL1g7vYuaOn7xGZJHVFR\nUSgtLUXHjh2xY8cOJCYm4sSJExJU1zaUeu4t4SjnvqamBpMmTcKyZcvg6el5x/NK/h20VrvSz7+b\nmxsOHTqEK1euYOTIkcjOzoZWqzV4jZLPvbn6rT3/ihtB9OrVC6WlpfqfS0tL4efn1+przp49i14K\nudmzJfV7eXnph4KjRo3CzZs3UVlZKWmdtlLyubeEI5z7mzdv4qGHHsLjjz+OxMTEO55X8u/AXO2O\ncP4BwNvbG6NHj8ZPP/1k8LiSz31Lpuq39vwrrkEMGDAAv/32G0pKSlBfX4/09HSMGzfO4DXjxo3D\nl19+CQDIy8uDj48P1Gq1HOXewZL6Kyoq9P8VcvDgQQiCYHSuUImUfO4tofRzLwgCpk+fDo1Gg2ef\nfdboa5T6O7CkdiWf/z/++ANVVVUAgOvXr2P37t2IjIw0eI1Szz1gWf3Wnn/FTTGZumDus88+AwDM\nnj0bCQk5anozAAADy0lEQVQJ2L59O/r164dOnTph9erVMld9iyX1b9q0CZ988gnat2+Pjh07YsOG\nDTJXfcsjjzyCnJwc/PHHH+jduzdef/113Lx5E4Dyzz1gvn4ln3sA2Lt3L9auXYv+/fvr/8/99ttv\n48yZMwCU/TuwpHYln/+ysjIkJyejqakJTU1NmDp1KoYPH+4wf3ssqd/a888L5YiIyCjFTTEREZEy\nsEEQEZFRbBBERGQUGwQRERnFBkFEREaxQRARkVFsEOSUjG1P0ZaWLl2K69evW3W8zMxMk9vXEykR\nr4Mgp+Tl5YXq6mrRPr9v37746aef0K1bN0mORyQHjiDIZRQXF2PUqFEYMGAAhg4diuPHjwMAnnzy\nSTzzzDOIjY1FQEAANm/eDEC3M+acOXMQHByMESNGYPTo0di8eTOWL1+O8+fPIy4uDsOHD9d//quv\nvoqIiAj85S9/wYULF+44/po1a/D000+3esyWSkpKEBQUhKeeegr33nsvHnvsMezatQuxsbEIDAxE\nfn6+GKeJ6BYb70tBpGienp53PHb//fcLv/32myAIupu93H///YIgCEJycrKQlJQkCIIgFBUVCf36\n9RMEQRC+/vprISEhQRAEQSgvLxe6dOkibN68WRAEQfD39xcuXbqk/2yVSiV8++23giAIwvz584U3\n33zzjuOvWbNGmDt3bqvHbOnUqVNC+/bthV9//VVoamoSoqOjhWnTpgmCIAhbt24VEhMTrT0tRFZR\n3F5MRGKoqanB/v37MXnyZP1j9fX1AHTbNTfvPBocHKy/AUxubi6SkpIAQL+/vikeHh4YPXo0ACA6\nOhq7d+9utR5Tx7xd3759ERISAgAICQnBAw88AAAIDQ1FSUlJq8cgshcbBLmEpqYm+Pj4mLyHsIeH\nh/574T/LciqVymDvf6GV5Tp3d3f9925ubmhoaDBbk7Fj3q5Dhw4Gn9v8HkuPQWQPrkGQS+jcuTP6\n9u2LTZs2AdD9QT5y5Eir74mNjcXmzZshCAIqKiqQk5Ojf87LywtXr161qobWGgyRErFBkFOqra1F\n79699V9Lly7FunXrsHLlSkRERCA0NBQZGRn617e8K1jz9w899BD8/Pyg0WgwdepUREVFwdvbGwAw\na9YsPPjgg/pF6tvfb+wuY7c/bur7299j6mcl3cmMnBNjrkStuHbtGjp16oRLly4hJiYG+/btQ48e\nPeQui0gSXIMgasWYMWNQVVWF+vp6LFq0iM2BXApHEEREZBTXIIiIyCg2CCIiMooNgoiIjGKDICIi\no9ggiIjIKDYIIiIy6v8BsxKV3Pt7cnUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x574e130>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.2,Page No.101"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of Variables\n",
      "\n",
      "w1=10 #KN/m #u.d.L\n",
      "F_D=20 #KN #Force at pt D\n",
      "F_C=30 #KN #Force at pt C\n",
      "L_DB=4 #m #Length of DB\n",
      "L_CD=L_AC=2 #m #Length of AC & CD\n",
      "L=8 #m #Length of Beam\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A And R_B be the Reactions at pt A and B \n",
      "#R_A+R_B=90 \n",
      "#Now Taking moment at A,M_A we get\n",
      "R_A=(w1*L_DB*(L_DB*2**-1)+F_D*L_DB+F_C*(L_CD+L_DB))*L**-1\n",
      "R_B=90-R_A\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=R_B-w1*L_DB #KN\n",
      "V_D2=V_D1-F_D #KN\n",
      "\n",
      "#S.F at Pt C\n",
      "V_C1=V_D2 #KN\n",
      "V_C2=V_C1-F_C  \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+w1*L_DB*L_DB*2**-1 #KN.m\n",
      "\n",
      "#B.M At PT C\n",
      "M_C=-R_B*(L_DB+L_CD)+w1*L_DB*(L_DB*2**-1+L_CD)+F_D*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)+F_D*(L_CD+L_AC)+F_C*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_CD+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_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,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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Pni0aGhr0vo4HrxERkcSmlo+IiMi8WApERCRhKRARkYSlQEREEpYCERFJWApE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\nICIiCUuBiIgk/w9P4ODmR+1IBgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x568a0b0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Gt27dTE9mRiwY9ovtQ+zHlSuAv780HCkgQO00tkGRgnHr1i2kp6ejpKQEdXV1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\nsrBgEBGRLP8PAOBgfwTG6goAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x57c6450>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.3,Page No.102"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of Variables\n",
      "\n",
      "L_DB=L_CD=1.5 #m #Length of DB & CD\n",
      "L_AC=3 #m #Length of AC\n",
      "F_D=80 #KN #Force at Pt D\n",
      "w=40 #KN/m #u.v.l\n",
      "L=6 #Length of beam\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A and R_B be the Reactions at Pt A & B respectively\n",
      "#R_A+R_B=140 \n",
      "#Taking moment at B we get,M_B\n",
      "R_A=(1*2**-1*L_AC*w*(1*3**-1*L_AC+(L_CD+L_DB))+F_D*L_DB)*L**-1\n",
      "R_B=140-R_A\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F at B\n",
      "V_B1=0 #KN\n",
      "V_B2=R_B #KN\n",
      "\n",
      "#S.F At D\n",
      "V_D1=V_B2 #KN\n",
      "V_D2=V_D1-F_D #KN\n",
      "\n",
      "#S.F at C\n",
      "V_C=V_D2 #KN\n",
      "\n",
      "#S.F At A\n",
      "V_A1=V_C-1*2**-1*w*L_AC #KN\n",
      "V_A2=V_A1+R_A #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M At B\n",
      "M_B=0 #KN.m\n",
      "\n",
      "#B.M At D\n",
      "M_D=-R_B*L_DB\n",
      "\n",
      "#B.M At C\n",
      "M_C=F_D*L_CD-R_B*(L_DB+L_CD)\n",
      "\n",
      "#B.M At A\n",
      "M_A=F_D*(L_CD+L_AC)-R_B*L+1*2**-1*w*L_AC*(1*3**-1*L_AC)+R_A\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_AC,L_DB+L_CD+L_AC]\n",
      "Y1=[V_B1,V_B2,V_D1,V_D2,V_C,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",
      "X2=[0,L_DB,L_CD+L_DB,L_AC+L_CD+L_DB]\n",
      "Y2=[M_B,M_D,M_C,M_A]\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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UiIhIxlAgIiIZQ4GIiGQMBSIikjEUyKlYe9qMDRs24OrVqxbf3wcffOB0U8GT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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x58cfed0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CBUEIDRWEv/9d7kpIbVz53SnLDGPjxo0YOHAg9u3bh/T0dKSlpQEAjEYjsrKy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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x57e26f0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.4,Page No.104"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of Variables\n",
      "\n",
      "M_D=120 #KN.m #B.M at Pt D\n",
      "F_C=40 #KN #Force at Pt C\n",
      "w1=20 #KN.m\n",
      "L_DB=1.5 #m #Length of DB\n",
      "L_CD=1.5 #m #Length of CD\n",
      "L_AC=3 #m #Length of AC\n",
      "L=6 #m #Length of Beam\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A And R_B be the Reactions at pt A and B \n",
      "#R_A+R_B=100\n",
      "#Now Taking Moment At Pt B We get,M_B\n",
      "R_A=-(M_D-F_C*(L_CD+L_DB)-w1*L_AC*(L_AC*2**-1+L_CD+L_DB))*L**-1\n",
      "R_B=100-R_A\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F At Pt B\n",
      "V_B1=0\n",
      "V_B2=R_B\n",
      "\n",
      "#S.F at Pt D\n",
      "V_D=V_B2 #KN\n",
      "\n",
      "#S.F At Pt C\n",
      "V_C1=V_D #KN\n",
      "V_C2=V_C1-F_C\n",
      "\n",
      "#S.F At Pt A\n",
      "V_A1=V_C2-w1*L_AC #KN\n",
      "V_A2=V_A1+R_A\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=M_B-R_B*L_DB #KN.m\n",
      "M_D2=M_B+M_D-R_B*L_DB\n",
      "\n",
      "#B.M At Pt C\n",
      "M_C=M_D-R_B*(L_CD+L_DB)\n",
      "\n",
      "#B.M At Pt A\n",
      "M_A=M_D-R_B*L+F_C*L_AC+w1*L_AC*L_AC*2**-1\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_DB+L_CD,L_DB+L_CD+L_AC,L_DB+L_CD+L_AC]\n",
      "Y1=[V_B1,V_B2,V_D,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_D1,M_D2,M_C,M_A]\n",
      "X2=[0,L_DB,L_DB,L_CD+L_DB,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 0x567e5b0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sNP3OaDQiICAAQUFByMrKssvrp6QAFy4An39ul6cnBdBoxDWr1auBoiK505Ac1HDIzh7M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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x57c6b50>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.5,Page No.105"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of Variables\n",
      "\n",
      "F_C=20 #KN #Force at Pt C\n",
      "F_D=40 #KN #Force at pt D\n",
      "w=20 #KN.m #u.d.l \n",
      "L_AD=L_DB=2 #m #Length of AD & DB\n",
      "L_BC=1 #m #Length of BC\n",
      "L=5 #m #Length of Beam\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#LEt R_A and R_B be the reactions at A & B respectively\n",
      "#R_A+R_B=100 \n",
      "#Now Taking Moment at B,M_B we get\n",
      "R_A=-(F_C*L_BC-F_D*L_DB-w*L_AD*(L_AD*2**-1+L_DB))*(L_AD+L_DB)**-1\n",
      "R_B=100-R_A\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=V_C2 #KN\n",
      "V_B2=V_C2+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-w*L_AD #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 \n",
      "\n",
      "#B.M At Pt B\n",
      "M_B=F_C*L_BC\n",
      "\n",
      "#B.M At Pt D\n",
      "M_D=F_C*(L_BC+L_DB)-R_B*L_DB\n",
      "\n",
      "#B.M At Pt A\n",
      "M_A=F_C*L-R_B*(L_DB+L_AD)+F_D*L_AD+w*L_AD*L_AD*2**-1\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_BC,L_BC,L_BC+L_DB,L_BC+L_DB,L_BC+L_DB+L_AD,L_BC+L_DB+L_AD]\n",
      "Y1=[V_C1,V_C2,V_B1,V_B2,V_D1,V_D2,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_C,M_B,M_D,M_A]\n",
      "X2=[0,L_BC,L_BC+L_DB,L_BC+L_DB+L_AD]\n",
      "Z2=[0,0,0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\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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DoVBVVUVFRQWHDx82t8/9uRxhYWGEhobWeT4zM5OkpCR8fX0JDAwkODiY3NzcyzqWiFxY\ncDB89BEEBDjvVPp+5FhaqQaXuTh69CiDBw8GwDAMcxucM4q//vrrJi+mpKSEYcOGmY8DAgIoLi5u\n8uOISG3t28OyZRATA7fcAvPmwUMPgU+jxhKkJWkwFAoLCy/rD8fFxVFWVlbn+SeeeIKJEyc2+u/Y\nbLbLqkNEGi8hwXm2kJQEmzfD6tXQvbvVVUlzcrkg3qXKycm56H169+5NUVGR+fjgwYP07t273vem\npqaa29HR0URHR1/08USkrp/8BLZuhd/8BgYNgtdfd85tEO/jcDhwOBwAHDjQuH0sXRAvJiaGJUuW\nmENT+fn5TJs2jdzcXIqLixk9ejR79+6tc7agBfGctCCeuFt2tnNuw+zZ8KtfQZs2Vlckl6rJFsRz\nh/Xr19OnTx+2b9/OzTffzPjx4wGw2+0kJiZit9sZP348y5cv1/CRiIXGjXMukeFwOG9dLS21uiJx\ntwueKZw5c4bw8HB2797dnDW5pDMFJ50pSHOpqoJFi+DFF2HVKhg71uqK5GI1yZlC27ZtCQsLY//+\n/U1anIh4lzZtnCutrl0Ls2bB/Plw+rTVVYk7uLzQXFFRQXh4OEOHDqVDhw6A83/qWVlZbi9ORDzL\nyJHw+eeQnOzcXrPGeWFaWg6XobBw4cLmqENEvET37rBxIzz9tHMp7j/+0Tm3QVoGteP0YrqmIFbb\nvt05pyE+Xv2gPV2T3X308ccfc+2119KxY0d8fX3x8fGhc+fOTVaoiHivYcOcw0lFRTB8OOzda3VF\ncrlchsJ9993Hn//8Z0JCQjh16hQrVqxgzpw5zVGbiHgB9YNuWRo1TyEkJISqqiratGnDjBkzyM7O\ndnddIuJF1A+65XAZCh06dOB///sfAwcO5JFHHmHp0qUazxeReqkftPdzGQp/+tOfqK6u5vnnn8fP\nz4+DBw+SkZHRHLWJiBdSP2jv1qi7j06cOEFRURH9+vVrjppc0t1HTrr7SDzdl1/C1KkQEeGcDd2p\nk9UVtV5NdvdRVlYWkZGRjP1+XnteXh7x8fFNU6WItGg1/aD9/Jz9oPPyrK5IXHEZCqmpqXzyySd0\n7doVgMjISLc02BGRlsnPzznBbcECGDNG/aA9nctQ8PX1pUuXLrV3UjsmEblI6gftHVx+u4eHh/PG\nG29w5swZCgoKuP/++xk+fHhz1CYiLYz6QXs+l6Hw3HPP8eWXX9K+fXuSkpLo3LkzzzzzTHPUJiIt\nUE0/6N//3rlm0uLFUF1tdVVSQ2sfeTHdfSTebv9+57BSly7qB+1uTXb30e7du7n77ruJi4sjJiaG\nmJgYRo0adVnFzZs3j/79+zNw4EAmTZrEf//7X/O1tLQ0QkJCCAsLY9OmTZd1HBHxbDX9oAcOdPaD\n3rrV6orE5ZnCNddcw+zZsxk0aBBtvm/QarPZzL7KlyInJ4fY2Fh8fHxISUkBID093ezR/Omnn5o9\nmvfs2VPnwrbOFJx0piAtifpBu1djzxRc9lPw9fVl9uzZTVYYQFxcnLkdFRVlzpDOzMwkKSkJX19f\nAgMDCQ4OJjc3l2HDhjXp8UXE89T0g77zTmdP6DfegF69rK6q9WkwFCoqKjAMg4kTJ/LCCy8wadIk\n2p+zWHq3bt2apIBXX32VpKQkAEpKSmoFQEBAAMXFxfXuV1LSJIf3ahUVVlcg0rR+9CPIyXH2gx40\nSP2grdBgKAwaNAibzWY+XrJkiblts9lcTmCLi4ujrKyszvNPPPEEEydOBGDRokW0a9eOadOmNfh3\nzq3hXP36pZrb7dpF07599AXraansdqsrEGlaNf2gR450njXccQcsXAi+vlZX5n0cDgcOhwOAAwca\nt49ldx+tWrWKl19+mb/+9a9cccUVgPO6AmBeZxg3bhwLFiwgKiqq1r66piDSOhw65OwHfeSI+kFf\nrsu+++jTTz+ltLTUfLx69Wri4+P5xS9+QcVljltkZ2ezePFiMjMzzUAAiI+PZ+3atVRWVrJv3z4K\nCgoYOnToZR1LRLxXTT/oW291LsW9YYPVFbV8DYbCPffcY15D+Nvf/kZKSgrJycl07tyZe+6557IO\nev/993P8+HHi4uKIjIw0O7nZ7XYSExOx2+2MHz+e5cuXNzh8JCKtg48PzJsHmZnw4IPwwAPwv/9Z\nXVXL1eDw0cCBA/nHP/4BwL333kv37t1JTU2t85oVNHwk0jp9+y3MmgWFhbBunXPZDGmcyx4+qqqq\n4vTp0wB88MEHxMTEmK+dOXOmicoUEWm8rl3hL39RP2h3avDuo6SkJEaOHMlVV12Fn58fI0aMAKCg\noKDOqqkiIs2lph/08OHOBj5//atzLSU/P6sraxkuePfRxx9/TFlZGWPGjKFDhw4A7Nmzh+PHjzNo\n0KBmK/J8Gj4SEYBjx5wzoHfuhDff1C3aF9LY4SMtiCciXs0wnJPcHnkEnnzSuVSG7k+pq8kWxBMR\n8WQ2mzMItm6FpUth+nTnGYRcGoWCiLQIdrv6QTcFhYKItBjqB335FAoi0uKc2w968mTn/AZpHIWC\niLRINf2g+/RxrriqftCNo1AQkRZL/aAvnkJBRFq8hATnRej162HCBOfqq1I/hYKItArn9oOOjFQ/\n6IYoFESk1fD1hbQ0eOUVuP12511KVVVWV+VZFAoi0urU9IPeuhXi4tTe91wKBRFplWr6QUdHOye7\nvf++1RV5BoWCiLRaNf2g16519mlISYHvOwa0WpaEwm9+8xsGDhxIREQEsbGxFBUVma+lpaUREhJC\nWFgYmzZtsqI8EWllRo6Ezz+HXbuc2/v3W12RdSxZJfXYsWN06tQJgOeee45//OMfvPLKK+Tn5zNt\n2jQ+/fRTiouLGT16NHv27MHHp3Z2aZVUEXGH6mp4+mlYsgReesl5K2tL4dGrpNYEAsDx48e56qqr\nAMjMzCQpKQlfX18CAwMJDg4mNzfXihJFpBVSP2gLryn86le/4sc//jGrVq1i/vz5AJSUlBAQEGC+\nJyAggOLiYqtKFJFWatgw53DSwYPODm9791pdUfNpsB3n5YqLi6OsrKzO80888QQTJ05k0aJFLFq0\niPT0dObOncvKlSvr/Tu2BrplpKammtvR0dFER0c3RdkiIsDZftDLlzv7QT/7rHOhPW/icDhwOBwA\nHDjQuH0s77x24MABbrrpJr744gvS09MBSElJAWDcuHEsWLCAqKioWvvomoKINKe8PGc/6JEjvbcf\ntEdfUygoKDC3MzMziYyMBCA+Pp61a9dSWVnJvn37KCgoYOjQoVaUKCJiiox0TnY7eRKGDoX8fKsr\nch+3DR9dyPz589m9ezdt2rShb9++vPjiiwDY7XYSExOx2+20bduW5cuXNzh8JCLSnDp1gtdec/aD\nHjmy5faDtnz46FJo+EhErJSfD4mJEBEBL77oDAxP59HDRyIi3qwl94NWKIiIXIKaftC//S2MHdty\n+kErFERELsPttzvbfraUftAKBRGRy3RuP+jISO/uB61QEBFpAjX9oJ95xrv7QSsURESakLf3g1Yo\niIg0MW/uB61QEBFxg5p+0CtWeFc/aIWCiIgbjR3rXf2gFQoiIm7mTf2gFQoiIs3AW/pBKxRERJqR\np/eDViiIiDSz7t1h40aYNMm5FPeGDVZXdJZCQUTEAj4+8Mtfnu0H/YtfeEY/aIWCiIiFavpBFxd7\nRj9ohYKIiMVq+kHPnOnsB71mjXW1WBoKTz/9ND4+PlRUVJjPpaWlERISQlhYGJs2bbKwOhGR5mOz\nwb33wqZN8PjjcPfdcOJE89dhWSgUFRWRk5PDT37yE/O5/Px81q1bR35+PtnZ2cyZM4dqb1xRSkTk\nEp3fD/rLL5v3+JaFwkMPPcRTTz1V67nMzEySkpLw9fUlMDCQ4OBgcnNzLapQRMQaNf2gH37YOeHt\n1Vebr4GPJaGQmZlJQEAA11xzTa3nS0pKCAgIMB8HBARQXFzc3OWJiFjOZoMZM5zLYyxdCnfeCceO\nuf+4bd31h+Pi4igrK6vz/KJFi0hLS6t1veBCjaRtNlu9z6empprb0dHRREdHX3KtIiKeqqYf9Ny5\nziUy1q1zDjE1hsPhwOFwAHDgQOP2sRkX+kZ2gy+++ILY2Fj8/PwAOHjwIL179+aTTz5h5cqVAKSk\npAAwbtw4FixYQFRUVO2ibbYLBomISEu0dq1zPsNjjzkvSjfwf+Z6bdsGI0a4/u5s9lA4X1BQEDt2\n7KBbt27k5+czbdo0cnNzKS4uZvTo0ezdu7fO2YJCQURaq717YepUZ8+GFSuct7M2RmNDwfJ5Cud+\n4dvtdhITE7Hb7YwfP57ly5c3OHwkItIaubsftOVnCpdCZwoiIs41k37+c+dyGQ8/7Fw6oyFec6Yg\nIiKXxh39oBUKIiJe7Px+0N/fbHTJFAoiIl7u3H7QSUmX1w9aoSAi0kI0RT9ohYKISAtyuf2gdfeR\niEgLtXWrc3mMO+5wnkWMGuUFk9cuhUJBRKRxDh2C5GRnT+jiYt2SKiLSqtX0g547t3Hv15mCiEgr\n0ZjvTp0piIiISaEgIiImhYKIiJgUCiIiYlIoiIiISaEgIiImS0IhNTWVgIAAIiMjiYyM5L333jNf\nS0tLIyQkhLCwsFp9nEVExP0sCQWbzcZDDz1EXl4eeXl5jB8/HoD8/HzWrVtHfn4+2dnZzJkzh+rq\naitK9BqOy10ntwXRZ3GWPouz9FlcHMuGj+qbQJGZmUlSUhK+vr4EBgYSHBxMbm6uBdV5D/2DP0uf\nxVn6LM7SZ3FxLAuF5557joEDB3LXXXdx5MgRAEpKSggICDDfExAQQHFxsVUlioi0Om4Lhbi4OK6+\n+uo6P1lZWcyePZt9+/axc+dOevXqxcMPP9zg37HZbO4qUUREzmdYbN++fcaAAQMMwzCMtLQ0Iy0t\nzXxt7Nixxvbt2+vs07dvXwPQj370ox/9XMRP3759XX4nt8UCpaWl9OrVC4D169dz9dVXAxAfH8+0\nadN46KGHKC4upqCggKFDh9bZf+/evc1ar4hIa2FJKDz66KPs3LkTm81GUFAQL730EgB2u53ExETs\ndjtt27Zl+fLlGj4SEWlGXrl0toiIuIfXzWjOzs4mLCyMkJAQnnzySavLsczMmTPx9/c3h95as6Ki\nImJiYggPD2fAgAE8++yzVpdkmVOnThEVFUVERAR2u5358+dbXZLlqqqqiIyMZOLEiVaXYqnAwECu\nueYaIiMj6x2Wr+FVZwpVVVX069ePDz74gN69e3PttdeyZs0a+vfvb3Vpze7DDz+kY8eO/PSnP+Wf\n//yn1eVYqqysjLKyMiIiIjh+/DiDBw9mw4YNrfLfBcCJEyfw8/PjzJkz3HDDDSxZsoQbbrjB6rIs\ns3TpUnbs2MGxY8fIysqyuhzLBAUFsWPHDrp163bB93nVmUJubi7BwcEEBgbi6+vL7bffTmZmptVl\nWWLEiBF07drV6jI8Qs+ePYmIiACgY8eO9O/fn5KSEourso6fnx8AlZWVVFVVufwSaMkOHjzIu+++\ny6xZs9StERr1GXhVKBQXF9OnTx/zsSa3yfkKCwvJy8sjKirK6lIsU11dTUREBP7+/sTExGC3260u\nyTIPPvggixcvxsfHq77q3MJmszF69GiGDBnCyy+/3OD7vOqT0p1IciHHjx9nypQpLFu2jI4dO1pd\njmV8fHzYuXMnBw8e5G9/+1urXeZh48aN9OjRg8jISJ0lAH//+9/Jy8vjvffe44UXXuDDDz+s931e\nFQq9e/emqKjIfFxUVFRrWQxpvU6fPs3kyZO58847SUhIsLocj/CDH/yAm2++mc8++8zqUizx0Ucf\nkZWVRVBQEElJSWzevJmf/vSnVpdlmZq5Yd27d+fWW29tcF05rwqFIUOGUFBQQGFhIZWVlaxbt474\n+HiryxKLGYbBXXfdhd1uZ+7cuVaXY6lvvvnGXEvs5MmT5OTkEBkZaXFV1njiiScoKipi3759rF27\nllGjRvGnP/3J6rIsceLECY4dOwbAd999x6ZNmxq8c9GrQqFt27Y8//zzjB07FrvdztSpU1vtHSZJ\nSUkMHz6cPXv20KdPH1auXGl1SZb5+9//zuuvv86WLVvMHh3Z2dlWl2WJ0tJSRo0aRUREBFFRUUyc\nOJHY2Fjr9G82AAADwElEQVSry/IIrXn4uby8nBEjRpj/LiZMmMCYMWPqfa9X3ZIqIiLu5VVnCiIi\n4l4KBRERMSkURETEpFAQERGTQkFEREwKBRERMSkUpEVx9/IWzzzzDCdPnmzy47399tuteil48Rya\npyAtSqdOncyZm+4QFBTEZ599xg9/+MNmOZ5Ic9OZgrR4//73vxk/fjxDhgzhxhtvZPfu3QD87Gc/\n44EHHuD666+nb9++ZGRkAM5VRufMmUP//v0ZM2YMN998MxkZGTz33HOUlJQQExNTa5bwr3/9ayIi\nIrjuuuv4z3/+U+f4c+fOZeHChQC8//77jBw5ss57Vq1axf3333/Bus5VWFhIWFgYM2bMoF+/ftxx\nxx1s2rSJ66+/ntDQUD799NPL/+CkdTJEWpCOHTvWeW7UqFFGQUGBYRiGsX37dmPUqFGGYRhGcnKy\nkZiYaBiGYeTn5xvBwcGGYRjGW2+9Zdx0002GYRhGWVmZ0bVrVyMjI8MwDMMIDAw0Dh8+bP5tm81m\nbNy40TAMw3jkkUeM3/3ud3WOf+LECSM8PNzYvHmz0a9fP+Prr7+u855Vq1YZ99133wXrOte+ffuM\ntm3bGl988YVRXV1tDB482Jg5c6ZhGIaRmZlpJCQkuPysROrT1upQEnGn48eP8/HHH3PbbbeZz1VW\nVgLOtXBqVlTt378/5eXlAGzbto3ExEQAsydBQ9q1a8fNN98MwODBg8nJyanzniuvvJKXX36ZESNG\nsGzZMoKCgi5Yc0N1nS8oKIjw8HAAwsPDGT16NAADBgygsLDwgscQaYhCQVq06upqunTpQl5eXr2v\nt2vXztw2vr+8ZrPZaq2/b1zgspuvr6+57ePjw5kzZ+p9365du+jevXujm0LVV9f52rdvX+vYNftc\nqA4RV3RNQVq0zp07ExQUxF/+8hfA+QW7a9euC+5z/fXXk5GRgWEYlJeXs3XrVvO1Tp06cfTo0Yuq\nYf/+/SxdutRscFLfOvYXCh6R5qRQkBblxIkT9OnTx/x55plneOONN1ixYgUREREMGDCgVvP2c5dT\nrtmePHkyAQEB2O12pk+fzqBBg/jBD34AwD333MO4cePMC83n73/+8syGYTBr1iyefvppevbsyYoV\nK5g1a5Y5hNXQvg1tn79PQ49b8zLRcnl0S6pIPb777js6dOjA4cOHiYqK4qOPPqJHjx5WlyXidrqm\nIFKPCRMmcOTIESorK3nssccUCNJq6ExBRERMuqYgIiImhYKIiJgUCiIiYlIoiIiISaEgIiImhYKI\niJj+H1U+eMmY8O6MAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x56a4870>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hwfgdp6SYHY1vc8uS1I0bNxIfH0/nzp2JiYkhJiam0Qli165dzq8zMzOJi4sD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\nRESc/j+iaB8fTwtkoQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5671e50>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.6,Page No.107"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of Variables\n",
      "\n",
      "L_BC=L_EB=L_AD=1 #m #Length of spans BC,ED,AD\n",
      "L_ED=2 #m #Length of ED\n",
      "w=60 #KNm #u.d.l\n",
      "F_C=20 #KN Pt Load at C\n",
      "L=5 #m #Span of beam \n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A & R_B be the reactions at A & B respectively\n",
      "#R_A+R_B=80 \n",
      "#Taking Moment At A,we get M_A\n",
      "R_B=(F_C*L+1*2**-1*L_ED*w*(2*3**-1*L_ED+L_AD))*(L_AD+L_ED+L_EB)**-1\n",
      "R_A=80-R_B\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F At C\n",
      "V_C1=0 #KN\n",
      "V_C2=-F_C #KN\n",
      "\n",
      "#S.F At B\n",
      "V_B1=V_C2 #KN\n",
      "V_B2=V_C2+R_B #KN \n",
      "\n",
      "#S.F aT E\n",
      "V_E=V_B2 #KN\n",
      "\n",
      "#S.F AT D\n",
      "V_D=V_B2-1*2**-1*L_ED*w #KN\n",
      "\n",
      "#S.F At A\n",
      "V_A1=V_D #KN \n",
      "V_A2=V_D+R_A\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at C\n",
      "M_C=0 #KN.m\n",
      "\n",
      "#B.M at B\n",
      "M_B=F_C*L_BC #KN.m\n",
      "\n",
      "#B.M at E\n",
      "M_E=F_C*(L_EB+L_BC)-R_B*L_EB #KN.m\n",
      "\n",
      "#B.M at D\n",
      "M_D=F_C*(L_ED+L_EB+L_BC)-R_B*(L_ED+L_EB)+1*2**-1*L_ED*w*1*3**-1*L_ED #KN.m\n",
      "\n",
      "#B.M  at A\n",
      "M_A=1*2**-1*L_ED*w*(2*3**-1*L_ED+L_AD)-R_B*(L_AD+L_ED+L_EB)+F_C*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=[0,0,L_BC,L_BC,L_EB+L_BC,L_ED+L_EB+L_BC,L_AD+L_ED+L_EB+L_BC,L_ED+L_EB+L_BC+L_AD]\n",
      "Y1=[V_C1,V_C2,V_B1,V_B2,V_E,V_D,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",
      "X2=[0,L_BC,L_BC+L_EB,L_EB+L_BC+L_ED,L_EB+L_BC+L_ED+L_AD]\n",
      "Y2=[M_C,M_B,M_E,M_D,M_A]\n",
      "Z2=[0,0,0,0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\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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Cr9fzLAHAgQMHUFpaig8++AAbNmzAvn37Ot1OUUUhJCSkwx1Vq6qqEBoaKjAR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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x57e37b0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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UlD0DZoHZoDk7OxvPPfec/SqwAoNm98HQmcjAloBZINmcwq5du5rcTwEAHnnkEeuqkgCb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\nkeDZfAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x58eb990>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.7,Page No.109"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of Variables\n",
      "\n",
      "L_BC=1 #m #Length of BC\n",
      "L_DB=2 #m #Length of DB\n",
      "L_AD=4 #m #Length 0f AD\n",
      "M_D=30 #KN.m #Moment at D\n",
      "w=45 #KN/m #u.d.l\n",
      "L=7 #m #Span of beam\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_B & R_A be the Reactions at B & A respectively\n",
      "#R_B+R_A=180+P  ............(1)\n",
      "\n",
      "#Now Taking Moment about A,we get\n",
      "#R_B=7*P+390   ...............(2)\n",
      "\n",
      "#Since R_A & R_B Are Equal\n",
      "#2*R_B=180+P  ...................(3)\n",
      "\n",
      "#From equation 1 and 3 we get\n",
      "#3*(180+P)=7P+390\n",
      "#After simplifying Further above equation we get\n",
      "P=150*4**-1 #KN\n",
      "R_A=R_B=(180+P)*2**-1\n",
      "F_C=P\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F At C\n",
      "V_C1=0 #KN\n",
      "V_C2=-P #KN\n",
      "\n",
      "#S.F At B\n",
      "V_B1=V_C2 #KN\n",
      "V_B2=V_C2+R_B #KN \n",
      "\n",
      "#S.F At D\n",
      "V_D=V_B2 #KN\n",
      "\n",
      "#S.F At A\n",
      "V_A1=V_D-w*L_AD #KN\n",
      "V_A2=V_A1+R_A #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at C\n",
      "M_C=0 #KN.m \n",
      "\n",
      "#B.M at B\n",
      "M_B=F_C*L_BC #KN.m\n",
      "\n",
      "#B.M at D\n",
      "M_D1=F_C*(L_BC+L_DB)-R_B*L_DB #KN.m\n",
      "M_D2=M_D1+M_D\n",
      "\n",
      "#B.M At A\n",
      "M_A=w*L_AD*L_AD*2**-1+M_D-R_B*(L_AD+L_DB)+P*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=[0,0,L_BC,L_BC,L_DB+L_BC,L_DB+L_BC+L_AD,L_DB+L_BC+L_AD]\n",
      "Y1=[V_C1,V_C2,V_B1,V_B2,V_D,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",
      "X2=[0,L_BC,L_DB+L_BC,L_DB+L_BC,L_AD+L_DB+L_BC]\n",
      "Y2=[M_C,M_B,M_D1,M_D2,M_A]\n",
      "Z2=[0,0,0,0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\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 0x58e7ef0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8GOrV0zuNfcjLU608Pv8chg9X01BXJwmEKJVZFr2FsKQmTeCJJ9QJcFE5ly/D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\nznqnEML6ScEQDs/FBUaNUms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       "text": [
        "<matplotlib.figure.Figure at 0x57c6bd0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.8,Page No.110"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of Variables\n",
      "\n",
      "L=6 #m #Span Of beam\n",
      "w=30 #KN/m #u.d.l\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Due to Symmetry\n",
      "#Let R_B and R_C be the reactions at B & C Respectively\n",
      "R_B=R_C=w*L*2**-1 #KN\n",
      "\n",
      "#Let a be the overhang.The Max -ve moment occurs at the support and max +ve moment at middle of the beam\n",
      "#Now Equating these two equations we get\n",
      "#30*a*a*2**-1=90*(3-a)-w*L*2**-1*L*4**-1\n",
      "#After simplifying we get an equation as\n",
      "#a**2+6*a-9=0\n",
      "x=1\n",
      "y=6\n",
      "z=-9\n",
      "\n",
      "p=y**2-4*x*z\n",
      "\n",
      "a1=(-y+p**0.5)*2**-1\n",
      "a2=(-y-p**0.5)*2**-1\n",
      "\n",
      "#Now Length cannot be negative,so taking a1 into Consideration\n",
      "\n",
      "L_CD=L_AB=a1\n",
      "L_BC=L-2*a1\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F At D\n",
      "V_D=0\n",
      "\n",
      "#S.F At C\n",
      "V_C1=V_D-w*L_CD #KN\n",
      "V_C2=V_C1+R_C #KN\n",
      "\n",
      "#S.F At B\n",
      "V_B1=-w*(L_BC+L_CD)+R_C\n",
      "V_B2=V_B1+R_B\n",
      "\n",
      "#S.F At A\n",
      "V_A=round(V_B2,2)-round(w*L_AB,2)\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M At D\n",
      "M_D=0\n",
      "\n",
      "#B.M At C\n",
      "M_C=w*L_CD*L_CD*2**-1 #KN.m\n",
      "\n",
      "#B.M At B\n",
      "M_B=w*(L_BC+L_CD)*(L_BC+L_CD)*2**-1-R_C*L_BC*L_BC*2**-1\n",
      "\n",
      "#B.M At A\n",
      "X=w*L*L*2**-1\n",
      "Y=-R_C*(L_AB+L_BC)-R_B*L_AB\n",
      "M_A=X+Y\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",
      "X2=[0,L_CD,L_BC+L_CD,L_AB+L_BC+L_CD]\n",
      "Y2=[M_D,M_C,M_B,M_A]\n",
      "Z2=[0,0,0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\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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lXLhwAQBw6dIlHDhwwKleBejt7Q0/Pz+UlpYCAA4ePIiwsLAub6vKm9f6yt3d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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5604db0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LUVxcrNtAqS48PDxqdH5WVhby8vIQEBAAAJg4cSJ27NjBhEGkEDc3ID5e7BWe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\nMQcOHJASExMlb29vtUPRi6y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       "text": [
        "<matplotlib.figure.Figure at 0x5677790>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.9,Page No.112"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of Variables\n",
      "\n",
      "F_F=6 #KN #Force at  F\n",
      "w1=w2=w=3 #KN.m #u.d.l\n",
      "M_D=24 #KN.m \n",
      "L_AB=L_CD=L_DE=L_EF=4 #m #Length of AB,CD,DE,EF\n",
      "L_BC=2 #m #Length of BC\n",
      "L=18 #m #Span of Beam\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#LEt R_B and R_E be the Reactions at B & E respectively\n",
      "#R_B+R_E=42\n",
      "\n",
      "#Taking Moment At Pt B,M_B\n",
      "R_E=(F_F*(L_BC+L_CD+L_DE+L_EF)+w*(L_CD+L_DE)*((L_CD+L_DE)*2**-1+L_BC)-w*L_AB*L_AB*2**-1-M_D)*(L_BC+L_CD+L_DE)**-1\n",
      "R_B=42-R_E #KN\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F aT F\n",
      "V_F1=0 #KN \n",
      "V_F2=-F_F #KN\n",
      "\n",
      "#S.F at E\n",
      "V_E1=V_F2 #KN\n",
      "V_E2=V_E1+R_E #KN\n",
      "\n",
      "#S.F aT C\n",
      "V_C=V_E2-w*(L_CD+L_DE) #KN\n",
      "\n",
      "#S.F at B\n",
      "V_B1=V_C #KN \n",
      "V_B2=V_C+R_B #KN\n",
      "\n",
      "#S.F At A\n",
      "V_A=V_B2-w*L_AB #KN\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M At F\n",
      "M_F=0\n",
      "\n",
      "#B.M At E\n",
      "M_E=F_F*L_EF #KN.m\n",
      "\n",
      "#B.M At D\n",
      "M_D1=F_F*(L_DE+L_EF)-R_E*L_DE+w*L_DE*L_DE*2**-1 #KN.m\n",
      "M_D2=M_D1-M_D\n",
      "\n",
      "#B.M At C\n",
      "M_C=F_F*(L_CD+L_DE+L_EF)-R_E*(L_CD+L_DE)+w*(L_CD+L_DE)*(L_CD+L_DE)*2**-1-M_D\n",
      "\n",
      "#B.M At B\n",
      "M_B=F_F*(L_BC+L_CD+L_DE+L_EF)-R_E*(L_BC+L_CD+L_DE)-M_D+w*(L_CD+L_DE)*((L_CD+L_DE)*2**-1+L_BC)\n",
      "\n",
      "#B.M At A\n",
      "M_A=w*L_AB*L_AB*2**-1-R_B*L_AB+w*(L_CD+L_DE)*((L_CD+L_DE)*2**-1+L_BC+L_AB)-R_E*(L_AB+L_BC+L_CD+L_DE)+F_F*L-M_D\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_EF,L_EF,L_EF+L_DE+L_CD,L_EF+L_DE+L_CD+L_BC,L_EF+L_DE+L_CD+L_BC,L_EF+L_DE+L_CD+L_BC+L_AB]\n",
      "Y1=[V_F1,V_F2,V_E1,V_E2,V_C,V_B1,V_B2,V_A]\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",
      "X2=[0,L_EF,L_DE+L_EF,L_DE+L_EF,L_CD+L_DE+L_EF,L_CD+L_DE+L_EF+L_BC,L_CD+L_DE+L_EF+L_BC+L_AB]\n",
      "Y2=[M_F,M_E,M_D1,M_D2,M_C,M_B,M_A]\n",
      "Z2=[0,0,0,0,0,0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\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 0x58e8ef0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VxMfHIzs7G/369cOvv/6KcePG4bHHHnNknEROixVL5KzMziBqa2uRmJiIMWPG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\nfyRzHAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5682230>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.10,Page No.114"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of Variables\n",
      "\n",
      "L_DC=L_BA=2 #m #Length of BA & DC\n",
      "L_CB=1 #m #Length of CB\n",
      "F_A=10 #KN #Force at pt A\n",
      "F_B=20 #KN #Force at pt B\n",
      "w=4 #KN.m #u.d.l\n",
      "L=5 #m #Length of beam\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_D be the reactions at Pt D\n",
      "R_D=F_B+F_A+w*L_DC #KN\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F at Pt A\n",
      "V_A1=0 #KN\n",
      "V_A2=F_A #KN\n",
      "\n",
      "#S.F At Pt B\n",
      "V_B1=V_A2\n",
      "V_B2=F_B+F_A\n",
      "\n",
      "#S.F at Pt C\n",
      "V_C=F_B+F_A #KN \n",
      "\n",
      "#S.F At Pt D\n",
      "V_D1=V_B2+w*L_DC\n",
      "V_D2=F_B+F_A+w*L_DC-R_D\n",
      "\n",
      "#B.M At Pt A\n",
      "M_A=0\n",
      "\n",
      "#B.M At Pt B\n",
      "M_B=F_A*L_BA\n",
      "\n",
      "#B.M at Pt C\n",
      "M_C=F_B*L_CB+F_A*(L_BA+L_CB) #KN\n",
      "\n",
      "#B.M At Pt D\n",
      "M_D1=F_A*L+F_B*(L_CB+L_DC)+w*L_DC*L_DC*2**-1\n",
      "M_D2=(F_A*L+F_B*(L_CB+L_DC)+w*L_DC*L_DC*2**-1)-M_D1\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_BA,L_BA,L_BA+L_CB,L_BA+L_CB+L_DC,L_BA+L_CB+L_DC]\n",
      "Y1=[V_A1,V_A2,V_B1,V_B2,V_C,V_D1,V_D2]\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_A,M_B,M_C,M_D1,M_D2]\n",
      "X2=[0,L_BA,L_CB+L_BA,L_CB+L_BA+L_DC,L_CB+L_BA+L_DC]\n",
      "Z2=[0,0,0,0,0]\n",
      "plt.plot(X2,Y2,X2,Z2)\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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e3542bZr69++vhIQEzZ49WyNGjNAFF1wgSbrxxht15ZVXen+5e/LxJ0/9axiG\n8vLy9Oc//1kxMTFatWqV8vLyvMNNvo71tX3yMb6+tvMUxDh7XM4JWzp8+LAiIiL0ww8/aPTo0dq8\nebP69OljdSwgKBjjhy1NnjxZNTU1amho0L333kvpw1Y44wcAm2GMHwBshuIHAJuh+AHAZih+ALAZ\nih8AbIbiBwCb+T+gqVKkQGpm/QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x58e5e50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4EoAKvyJSQ8nAz6nwKyKNoWTgZ1T4FZGmUDLwcSr8iogRlAx8kAq/ImI0JQMf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\nCwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x58d7890>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.11,Page No.115"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of Variables\n",
      "\n",
      "w=20 #KN/m #u.v.l\n",
      "F_C=40 #KN #Force at Pt C\n",
      "M_D=40 #KN.m #Moment at pt D\n",
      "L_AB=3 #m #Length of AB\n",
      "L_BC=1 #m #Length of BC\n",
      "L_CD=L_DE=2 #m #Length of CD & DE\n",
      "L=8 #8 #Length of beam\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_A & R_E be the Reactions at A & E respectively\n",
      "#R_A+R_E=70\n",
      "\n",
      "#Taking Moments At Pt A we get,M_A\n",
      "R_E=(F_C*(L_AB+L_BC)+1*2**-1*L_AB*w*2+40)*L**-1\n",
      "R_A=70-R_E\n",
      "\n",
      "#shear Force Calculations\n",
      "\n",
      "#S.F At Pt E\n",
      "V_E1=0\n",
      "V_E2=R_E #KN\n",
      "\n",
      "#S.F aT pt D\n",
      "V_D=V_E2\n",
      "\n",
      "#S.F At PT C\n",
      "V_C1=V_D\n",
      "V_C2=V_D-F_C #KN\n",
      "\n",
      "#S.F At Pt A\n",
      "V_A1=V_C2-(1*2**-1*w*L_AB)\n",
      "V_A2=V_A1+R_A\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M At Pt E\n",
      "M_E=0\n",
      "\n",
      "#B.M At Pt D\n",
      "M_D1=M_E-R_E*L_DE\n",
      "M_D2=M_D1+M_D\n",
      "\n",
      "#B.M At Pt C\n",
      "M_C=-R_E*(L_DE+L_CD)+M_D\n",
      "\n",
      "#B.M At Pt B\n",
      "M_B=-R_E*(L_DE+L_CD+L_BC)+M_D+F_C*L_BC\n",
      "\n",
      "#B.M At Pt A\n",
      "M_A=-R_E*L+M_D+(1*2**-1*L_AB*w*2)+F_C*(L_BC+L_AB)\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_DE,L_CD+L_DE,L_CD+L_DE,L_CD+L_DE+L_AB,L_CD+L_DE+L_AB]\n",
      "Y1=[V_E1,V_E2,V_D,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_E,M_D1,M_D2,M_C,M_B,M_A]\n",
      "X2=[0,L_DE,L_DE,L_CD+L_DE,L_DE+L_CD+L_BC,L_AB+L_BC+L_CD+L_DE]\n",
      "Z2=[0,0,0,0,0,0]\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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KRQ4dOoS8vDz4+/sjISEBe/bswX333Sc6Vo/cdNNNAIDhw4fjrrvucqh1zVQq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\niEjGUiAiItn/A+2hg5gYC1MHAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x58eb5d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PZcuW8dRTT5GZmcnOnTtp1KgRI0aMsPs+cvTnxbp1U4fwLFyoO4nzTCaYMkWt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\nGhPHAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5699b50>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.12,Page No.116"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of Variables\n",
      "\n",
      "F_G=10 #KN #Force at Pt G\n",
      "F_B=F_E=15 #KN #Force at Pt B & E\n",
      "w=20 #KN/m #U.d.L\n",
      "L_FG=L_EF=L_DE=L_CD=L_BC=L_AB=1 #m #Lengths of FG,EF,DE,CD,BC,AB respectively\n",
      "L=6 #m #Length of beam\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#LEt R_F & R_A be the Reactions at E & A respectively\n",
      "#R_F+R_A=60\n",
      "\n",
      "#Taking Moment At Pt A,M_A\n",
      "R_F=(F_G*L+F_E*(L_AB+L_BC+L_CD+L_DE)+w*L_CD*(L_AB+L_BC+L_CD*2**-1)+F_B*L_AB)*(L_AB+L_BC+L_CD+L_DE+L_EF)**-1\n",
      "R_A=60-R_F\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F At G\n",
      "V_G1=0 #KN \n",
      "V_G2=F_G #KN\n",
      "\n",
      "#S.F At F\n",
      "V_F1=V_G2 #KN\n",
      "V_F2=V_F1-R_F\n",
      "\n",
      "#S.F At E\n",
      "V_E1=V_F2 #KN\n",
      "V_E2=V_F2+F_E\n",
      "\n",
      "#S.F At D\n",
      "V_D=V_E2\n",
      "\n",
      "#S.F At C\n",
      "V_C=V_E2+w*L_CD\n",
      "\n",
      "#S.F At B\n",
      "V_B1=V_C\n",
      "V_B2=V_B1+F_B\n",
      "\n",
      "#S.F At A\n",
      "V_A1=V_B2\n",
      "V_A2=V_B2-R_A\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M At Pt G\n",
      "M_G=0\n",
      "\n",
      "#B.M At F\n",
      "M_F=F_G*L_FG \n",
      "\n",
      "#B.M At E\n",
      "M_E=F_G*(L_FG+L_EF)-R_F*L_EF\n",
      "\n",
      "#B.M At D\n",
      "M_D=F_G*(L_FG+L_EF+L_DE)-R_F*(L_EF+L_DE)+F_E*L_DE\n",
      "\n",
      "#B.M At C\n",
      "M_C=F_G*(L_FG+L_EF+L_DE+L_CD)-R_F*(L_EF+L_DE+L_CD)+F_E*(L_DE+L_CD)+w*L_CD*L_CD*2**-1\n",
      "\n",
      "#B.M At B\n",
      "M_B=F_G*(L_FG+L_EF+L_DE+L_CD+L_BC)-R_F*(L_EF+L_DE+L_CD+L_BC)+F_E*(L_DE+L_CD+L_BC)+w*L_CD*(L_CD*2**-1+L_BC)\n",
      "\n",
      "#B.M At A\n",
      "M_A=F_G*L-R_F*(L_EF+L_DE+L_CD+L_BC+L_AB)+F_E*(L_DE+L_CD+L_BC+L_AB)+F_B*L_AB+w*L_CD*(L_CD*2**-1+L_BC+L_AB)\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_FG,L_FG,L_FG+L_EF,L_FG+L_EF,L_FG+L_EF+L_DE,L_FG+L_EF+L_DE+L_CD,L_FG+L_EF+L_DE+L_CD+L_BC,L_FG+L_EF+L_DE+L_CD+L_BC,L_FG+L_EF+L_DE+L_CD+L_BC+L_AB,L_FG+L_EF+L_DE+L_CD+L_BC+L_AB]\n",
      "Y1=[V_G1,V_G2,V_F1,V_F2,V_E1,V_E2,V_D,V_C,V_B1,V_B2,V_A1,V_A2]\n",
      "Z1=[0,0,0,0,0,0,0,0,0,0,0,0]\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",
      "X2=[0,L_FG,L_EF+L_FG,L_EF+L_FG+L_DE,L_EF+L_FG+L_DE+L_CD,L_EF+L_FG+L_DE+L_CD+L_BC,L_EF+L_FG+L_DE+L_CD+L_BC+L_AB]\n",
      "Y2=[M_G,M_F,M_E,M_D,M_C,M_B,M_A]\n",
      "Z2=[0,0,0,0,0,0,0]\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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jv+M1m812xjUDjHbGbn5+fuZtHx8fNTY2trncl19+qcGDB3f4olBt5Tpbr169\nzlj3qde0lwNwhpkCvFrfvn01dOhQ/fWvf5XU8gH75Zdftvuayy67TDk5OTIMQ7W1tdqyZYv5XEBA\ngA4dOnROGfbv368//elP5gVc2jpPf3vFA3gSpQCvcuzYMYWGhpo/Tz31lF577TWtXLlScXFxGjZs\nmPLy8szlTz8F9KnbM2bMUEhIiGJiYjRnzhyNHDnSvJ7t/PnzdeWVV5qD5rNff/YppQ3D0Lx58/TE\nE08oKChIK1eu1Lx588xdWI5e6+j22a9xdN/bTm0Nz+ErqUAbjh49Kn9/fx08eFAJCQn65JNPNGTI\nEKtjAW7HTAFow89+9jPV19eroaFBDz74IIWAboMtBQCAiZkCAMBEKQAATJQCAMBEKQAATJQCAMBE\nKQAATP8HttSK1NQ812EAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x567d350>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Xmnfs2FFmtKCkEJzUi0GscPq0cWr5xRehc2ero3GPW0khMTHxghf+9ttvqx1Y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\nkcIBAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x58ce950>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.13,Page No.117"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of Variables\n",
      "L_AB=L_BC=L_CD=L_DE=L_EF=1 #m #LEngth of AB,BC,CD,DE,EF respectively\n",
      "M_A=50 #KN/m #Moment at A\n",
      "w=5 #KN/m #u.v.l\n",
      "F_D=10 #KN\n",
      "w2=5 #KN/m #u.d.l\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let R_B & R_E be the Reactions at B and E respectively\n",
      "#R_B+R_E=20\n",
      "\n",
      "#Taking Moment At Pt B,M_B\n",
      "R_E=(w2*L_EF*(L_EF*2**-1+L_DE+L_CD+L_BC)+w*L_BC*2**-1*2*3**-1+50+F_D*(L_BC+L_CD))*3**-1\n",
      "R_B=17.5-R_E #KN\n",
      "\n",
      "#Shear Force Calculations\n",
      "\n",
      "#S.F At F\n",
      "V_F=0\n",
      "\n",
      "#S.F aT E\n",
      "V_E1=-w2*L_EF #KN\n",
      "V_E2=V_E1+R_E\n",
      "\n",
      "#S.F at D\n",
      "V_D1=R_E-w2*L_EF #KN\n",
      "V_D2=V_D1-F_D #KN\n",
      "\n",
      "#S.F At C\n",
      "V_C=V_D2\n",
      "\n",
      "#S.F aT B\n",
      "V_B1=-L_BC*w*2**-1-F_D+R_E-w2*L_EF\n",
      "V_B2=V_B1+R_B\n",
      "\n",
      "#Bending Moment Calculations\n",
      "\n",
      "#B.M at F\n",
      "M_F=0 #KN.m\n",
      "\n",
      "#B.M At E\n",
      "M_E=w2*L_EF*L_EF*2**-1 #KN.m\n",
      "\n",
      "#B.M at D\n",
      "M_D=-R_E*L_DE+w2*L_EF*(L_EF*2**-1+L_DE) #KN.m\n",
      "\n",
      "#B.M At C\n",
      "M_C=F_D*L_CD*R_E*(L_CD+L_DE)+w2*L_EF*(L_EF*2**-1+L_DE+L_CD) #KN.m\n",
      "\n",
      "#B.M At B\n",
      "M_B=F_D*(L_CD+L_BC)-R_E*(L_BC+L_CD+L_DE)+w2*L_EF*(L_EF*2**-1+L_BC+L_CD+L_DE)+1*2**-1*L_BC*w*2*3**-1\n",
      "\n",
      "#B.M At A\n",
      "M_A1=w*L_EF*(L_EF*2**-1+L_AB+L_BC+L_CD+L_DE)-R_E*(L_AB+L_BC+L_CD+L_DE)+F_D*(L_AB+L_BC+L_CD)+1*2**-1*L_BC*w*(2*3**-1*L_BC+L_AB)-R_B*L_AB\n",
      "M_A2=M_A1+M_A\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_EF,L_EF,L_DE+L_EF,L_DE+L_EF,L_CD+L_DE+L_EF,L_CD+L_DE+L_EF+L_BC,L_CD+L_DE+L_EF+L_BC]\n",
      "Y1=[V_F,V_E1,V_E2,V_D1,V_D2,V_C,V_B1,V_B2]\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",
      "X2=[0,L_EF,L_DE+L_EF,L_CD+L_DE+L_EF,L_CD+L_DE+L_EF+L_BC,L_CD+L_DE+L_EF+L_BC+L_AB,L_CD+L_DE+L_EF+L_BC+L_AB]\n",
      "Y2=[M_F,M_E,M_D,M_C,M_B,M_A1,M_A2]\n",
      "Z2=[0,0,0,0,0,0,0]\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 0x56940b0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LlixREhMTLY8fMWKEsm/fvjuex4ZfSQi7euUVRXnxRa1TuIdr1xRFr1eUb77R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\ntnx2yhiGEEIIm0jBEEIIYRM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       "text": [
        "<matplotlib.figure.Figure at 0x58f3170>"
       ]
      }
     ],
     "prompt_number": 13
    }
   ],
   "metadata": {}
  }
 ]
}