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{
 "metadata": {
  "name": "chapter8.ipynb"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 8: Forces in Beams"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.8-1, Page no 118"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "R_A=100 #N\n",
      "R_B=200 #N\n",
      "\n",
      "#Calculations\n",
      "#Shear force at 2m\n",
      "V=100 #N\n",
      "#Moment at 2m\n",
      "M=R_A*2 #N.m\n",
      "\n",
      "#Result\n",
      "print'The shear force at 2m is +',round(V),\"N\"\n",
      "print'The moment at 2m is +',round(M),\"N-m\" \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The shear force at 2m is + 100.0 N\n",
        "The moment at 2m is + 200.0 N-m\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.8-2, Page no 118"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "\n",
      "#Initilization of variables\n",
      "#length matrix\n",
      "L1=[0,3.99,4,5.99,6] #m\n",
      "#Bending moment matrix\n",
      "B=[0,400,400,0.00001,0] #N.m\n",
      "#Shear force plotting\n",
      "#Here the left side and right side lengths are considered as close as 4 to keep up with right and left distinctions\n",
      "L=[0,3.99,4,5.99,6]\n",
      "S=[100,100,-200,-200,0]\n",
      "g=[0,0,0,0,0]\n",
      "\n",
      "#Calculations cum Result\n",
      "d=transpose(L1)\n",
      "e=transpose(S)\n",
      "plt.plot(d,B)\n",
      "xlabel('distance (m)')\n",
      "ylabel('B.M (N.m)')\n",
      "plt.show()\n",
      "plt.plot(L,e,L,g)\n",
      "xlabel('distance (m)')\n",
      "ylabel('S.F (N)')\n",
      "plt.show()\n",
      "\n",
      "print'The graphs are the solutions'\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3/qygoABfX996j1E7EETTLVgA//ynGgZdumhdjRCua84cuPNOeOop6NhR62rq\nuvSX5aSkpN/cx+FDRsXFxdbPN2zYYL0DKS4ujtTUVKqqqsjLy+PYsWNERUU5ujy3t2ABvP++hIEQ\nthAQAPfdB6+9pnUltmHXDiE+Pp6dO3dy8uRJunbtSlJSEiaTiezsbHQ6Hd26dePtt98GwGg0Mnr0\naIxGI56enixbtkwegLOx5GRYtQpMJgkDIWxlzhz4/e/VLqFDB62raR6Z7bSFSEmBlSvVzuCmm7Su\nRgj3Mm4cBAWp4eCsZPprAUgYCGFvublw113w/fdw3XVaV1M/zZ9DENpbuBDee0/CQAh7CgqCIUNg\n6VKtK2ke6RDc2MKFsGKFes1AwkAI+/r2W+jbF777zjm7BOkQWrC//lUNA+kMhHCM7t0hJkZ9WM1V\nSYfghl55Bd55R+0MGniUQwhhB0ePQr9+6rUEb2+tq6lLOoQWSMJACO0EB8PAgfDGG1pXcnWkQ3Aj\nr74Kb7+tDhPVmhZKCOFAR47APfeoM6K2b691Nb+SDqEFWbQI3npLwkAIrfXoAQMGuGaXIB2CG1i0\nSF3ByWSSMBDCGeTkQP/+6rUEZ+kSpENoAf72NzUMpDMQwnkYjRAdDcuWaV1J00iH4MIWL1bb0s8+\ng65dta5GCFHb11+rF5i//x7atdO6GukQ3Nrixer9zhIGQjin0FD1FlRX6hKkQ3BBtcPg5pu1rkYI\n0RBn6hKkQ3BDf/+7hIEQriI0VJ3O4q23tK6kcaRDcCF//7u6EIfJJGEghKs4fFid0uL4cfDy0q4O\n6RDcyJIlahhIZyCEawkLg7vvdo0uQToEF/Daa2p38NlncMstWlcjhGiqQ4dg8GD1WoJWXYJ0CG7g\ntdfUi8gSBkK4rp494c471allnJl0CE5s6VL1wbPPPgM/P62rEUI0R3Y23Hef2iVce63jz695hzBh\nwgT0ej1hYWHW7506dYqYmBiCgoIYNGgQZWVl1p8lJycTGBhIcHAwmZmZ9izN6b3+uoSBEO4kIgL6\n9HHuLsGugfD444+zZcuWOt9LSUkhJiaG3NxcBgwYQEpKCgA5OTmsXbuWnJwctmzZwpQpUzCbzfYs\nz2m9/ro6P5GEgRDuZe5cdfGq8+e1rqR+dg2Evn370qlTpzrfS09PJyEhAYCEhAQ2btwIQFpaGvHx\n8bRq1Qo/Pz8CAgLIysqyZ3lO6Y031GmsJQyEcD+RkRAVBcuXa11J/Rx+Ubm0tBS9Xg+AXq+ntLQU\ngKKiIgwIfXqiAAAQzUlEQVS1ZmczGAwUFhY6ujxNvfGGusCNySRhIIS7mjtXXe+8slLrSi7nqeXJ\ndTodOp3uij+vT2JiovXz6OhooqOjbVyZ4y1bpoaBdAZCuLfbboPevdUu4U9/st95TCYTJpOpSfs4\nPBD0ej0lJSX4+PhQXFxM586dAfD19SU/P9+6XUFBAb4NrAFZOxDcwbJl6rjiZ59Bt25aVyOEsLe5\nc+GBB2DSJGjb1j7nuPSX5aSkpN/cx+FDRnFxcaxatQqAVatWMXz4cOv3U1NTqaqqIi8vj2PHjhEV\nFeXo8hzuzTfV9nHHDgkDIVqKXr3U6wnvvqt1JZdQ7OiRRx5RunTporRq1UoxGAzKe++9p/z000/K\ngAEDlMDAQCUmJkY5ffq0dfv58+cr/v7+Svfu3ZUtW7bUe0w7l+xQb76pKDffrCjff691JUIIR9u/\nX1EMBkWprHTM+Rrz3ikPpmnkrbcgOVkdJrr1Vq2rEUJoYdgw9WG1KVPsf67GvHdKIGjg7bdhwQJ1\nmMjfX+tqhBBa2b8fRo6E776DNm3sey7Nn1QWl3vnHZg/X8JACAG3367Oc/Tee1pXopIOwYHeeQf+\n8hd1mEjCQAgBkJUFo0bBsWP27RKkQ3AiljCQzkAIUVtUFISEwMqVWlciHYJDLF8OL7+shkFAgNbV\nCCGczb598PDDapfQurV9ziEdghN4910JAyHEld1xB/TooX2XIB2CHb37LiQlqWEQGKh1NUIIZ7Z3\nL8THQ26ufboE6RA0tGKFhIEQovHuvBO6d4eLEzloQjoEO3jvPZg3T8JACNE0n38OY8bYp0uQDkED\nljDYvl3CQAjRNL//PQQFwfvva3N+6RBsqHYYBAVpXY0QwhXt2QOPPqp2Ca1a2e640iE40MqV6pS2\nEgZCiOa46y71WSUtugTpEGzgH/+AOXPUMOjeXetqhBCubvduSEiAb7+1XZcgHYIDSBgIIWytb191\nfZTVqx17XukQmmHVKpg9W72bSMJACGFLu3bB44/D0aO26RKkQ7AjSxhIZyCEsId+/eCWW+CDDxx3\nTukQrsL778OsWWoYBAdrWooQwo3t3AkTJ6pdgqdn844lHYIdSBgIIRzlnnuga1fHdQnSITTBP/8J\nM2dKGAghHMdkgkmT4MiR5nUJTt0h+Pn50bNnTyIjI4mKigLg1KlTxMTEEBQUxKBBgygrK9OqvMus\nXq2GwbZtEgZCCMeJjoabboIPP7T/uTQLBJ1Oh8lk4uDBg2RlZQGQkpJCTEwMubm5DBgwgJSUFK3K\nq2P1apgxA7ZuVaeoFUIIR0pMVBfYqq6273k0vYZwafuSnp5OQkICAAkJCWzcuFGLsupYvRqef14N\nA6NR62qEEC1RdDT4+EBqqn3Po9k1hFtvvZUOHTpwzTXX8OSTTzJp0iQ6derE6dOnATUsrr/+euvX\n1oIdeA3hgw9g+nR1mEjCQAihpe3bYcoUyMmBa65p+v6Nee9s5o1MV2/Pnj106dKFH3/8kZiYGIIv\nGZjX6XTodLp6901MTLR+Hh0dTXR0tM3r+/BDNQykMxBCOIN774XOndUuYezY397eZDJhMpmadA6n\nuMsoKSmJ9u3bs3z5ckwmEz4+PhQXF9O/f3+OHj1aZ1tHdAgffgjPPaeGQUiIXU8lhBCNtm0bTJ0K\n33zT9C7Bae8yOnfuHGfPngWgoqKCzMxMwsLCiIuLY9XF5YJWrVrF8OHDHV6bhIEQwlkNGAA33ABr\n19rn+Jp0CHl5eYwYMQKA6upqxo4dy6xZszh16hSjR4/mhx9+wM/Pj3Xr1tGxY8e6BduxQ1izBp59\nVg2D0FC7nEIIIZpl61b485/h66+b1iU05r3TKYaMmsJegZCaCs88I2EghHBuiqKumfCnP0F8fOP3\nk0BoJAkDIYQrycyEp5+Gw4cb3yU47TUEZ7J2rYSBEMK1xMRAhw6wfr1tj9uiO4S1a9WUzcyEsDCb\nHFIIIRxiyxaYNk3tEjwa8au9dAhXsG6dGgb//reEgRDC9QweDN7etu0SWmSHsG4dPPWUGgY9e9qo\nMCGEcLDNm9UHaA8d+u0uQTqEenz0kXrLloSBEMLVDRkCXl7w8ce2OV6L6hA++ki9Vevf/4bwcBsX\nJoQQGti0SZ2N+auvrtwlSIdQy/r1EgZCCPczdCi0bQsbNjT/WC2iQ1i/Xp3/Q8JACOGOMjJg9mzI\nzm64S5AOAXVsbepU9RYtCQMhhDu6/35o3Rqau4SMWwfCxx/DH/+ohkFEhNbVCCGEfeh0MG8eJCWB\n2Xz1x3HbQPjkEzUMNm+WMBBCuL9hw8DTE9LSrv4YbhkIGzaoKwtt3gyRkVpXI4QQ9mfpEl56SZ0A\n72q4XSBs2ACTJ0sYCCFanthYNRiutktwq0DYsAH+8Af1vlwJAyFES9PcLsFtAmHjRjUMNm+G227T\nuhohhNBGXJwaBp9+2vR93SIQ0tLgySclDIQQQqeDuXMhMbHpXYLLB0JaGvzf/6nDRBIGQggBDzyg\n3n6akdG0/ZwuELZs2UJwcDCBgYEsXLjwitvWDoNevRxUoBBCODkPD7VLSEpqWpfgVIFQU1PD1KlT\n2bJlCzk5OaxZs4YjR47Uu216uhoG//qXe4WByWTSugS7ktfnutz5tYH7vb7hw6GqSn2PbCynCoSs\nrCwCAgLw8/OjVatWPPLII6TVc//Up5/CpEnqC+3dW4NC7cjd/lFeSl6f63Ln1wbu9/o8PH59ermx\nXYJTBUJhYSFdu3a1fm0wGCgsLLxsuyeecM8wEEIIWxoxAior1WH1xnCqQNDpdI3aLiNDwkAIIX6L\npUt47LFG7qA4kb179yqDBw+2fr1gwQIlJSWlzjb+/v4KIB/yIR/yIR9N+PD39//N92CnWg+hurqa\n7t27s337dm666SaioqJYs2YNPXr00Lo0IYRwe55aF1Cbp6cnr7/+OoMHD6ampoaJEydKGAghhIM4\nVYcghBBCO051Ufm3NOWhNVczYcIE9Ho9YWFhWpdic/n5+fTv35+QkBBCQ0N57bXXtC7JpiorK+nT\npw8REREYjUZmzZqldUl2UVNTQ2RkJLGxsVqXYnN+fn707NmTyMhIoqKitC7HpsrKyhg1ahQ9evTA\naDSyb9++hje26VVhO6qurlb8/f2VvLw8paqqSgkPD1dycnK0Lstmdu3apRw4cEAJDQ3VuhSbKy4u\nVg4ePKgoiqKcPXtWCQoKcqu/O0VRlIqKCkVRFOXChQtKnz59lN27d2tcke0tWrRIGTNmjBIbG6t1\nKTbn5+en/PTTT1qXYRfjxo1TVqxYoSiK+u+zrKyswW1dpkNo7ENrrqpv37506tRJ6zLswsfHh4iL\ny9a1b9+eHj16UFRUpHFVtuXl5QVAVVUVNTU1XH/99RpXZFsFBQVs2rSJJ5544jcXandV7vi6zpw5\nw+7du5kwYQKgXqft0KFDg9u7TCA09qE14dxOnDjBwYMH6dOnj9al2JTZbCYiIgK9Xk///v0xGo1a\nl2RTzzzzDK+88goeHi7zltEkOp2OgQMH0rt3b5YvX651OTaTl5fH7373Ox5//HFuu+02Jk2axLlz\n5xrc3mX+dhv70JpwXuXl5YwaNYolS5bQvn17rcuxKQ8PD7KzsykoKGDXrl1uNQ1CRkYGnTt3JjIy\n0i1/iwbYs2cPBw8eZPPmzbzxxhvs3r1b65Jsorq6mgMHDjBlyhQOHDhAu3btSElJaXB7lwkEX19f\n8vPzrV/n5+djMBg0rEg0xYULF3jwwQd59NFHGT58uNbl2E2HDh24//77+eKLL7QuxWY+//xz0tPT\n6datG/Hx8ezYsYNx48ZpXZZNdenSBYDf/e53jBgxgqysLI0rsg2DwYDBYOD2228HYNSoURw4cKDB\n7V0mEHr37s2xY8c4ceIEVVVVrF27lri4OK3LEo2gKAoTJ07EaDTy9NNPa12OzZ08eZKysjIAzp8/\nz9atW4l0ozVcFyxYQH5+Pnl5eaSmpnLvvffy/vvva12WzZw7d46zZ88CUFFRQWZmptvc7efj40PX\nrl3Jzc0FYNu2bYSEhDS4vVM9mHYl7v7QWnx8PDt37uSnn36ia9euvPTSSzz++ONal2UTe/bsYfXq\n1dbb+gCSk5MZMmSIxpXZRnFxMQkJCZjNZsxmM4899hgDBgzQuiy7cbfh29LSUkaMGAGoQyxjx45l\n0KBBGldlO0uXLmXs2LFUVVXh7+/PypUrG9xWHkwTQggBuNCQkRBCCPuSQBBCCAFIIAghhLhIAkEI\nIQQggSCEEOIiCQQhhBCABIJwc4mJiSxatAiAefPmsX379ga3TUtL48iRI44q7TIZGRkkJiY2aZ8B\nAwZYH6oSorkkEIRbq/0QVVJS0hUfGNuwYQM5OTmOKKteixYtYvLkyU3a55FHHnGrydiEtiQQhNuZ\nP38+3bt3p2/fvnz77bfWUBg/fjwff/wxADNnziQkJITw8HCmT5/O3r17+fTTT5k+fTq33XYbx48f\nZ/ny5URFRREREcGoUaM4f/689ThPPfUUd911F/7+/tZjAixcuJCePXsSERFhXSjn+++/Z+jQofTu\n3Zt+/frx7bffXlZzfn4+VVVV6PV66zmmTJnCnXfeib+/PyaTiYSEBIxGY50n2OPi4khNTbXPH6Ro\neey/PIMQjvPFF18oYWFhyvnz55Wff/5ZCQgIUBYtWqQoiqKMHz9e+fjjj5WTJ08q3bt3t+5z5syZ\nOj+3qL1gypw5c5SlS5cqiqIoCQkJyujRoxVFUZScnBwlICBAURRF2bRpk/L73/9eOX/+vKIoinL6\n9GlFURTl3nvvVY4dO6YoiqLs27dPuffeey+re82aNcrUqVOtX48fP16Jj49XFEVR0tLSFG9vb+Xr\nr79WzGaz0qtXLyU7O9u6bbdu3ZTy8vKr+vMSojaXmctIiMbYvXs3I0eOpG3btrRt27beCRA7duxI\n27ZtmThxIsOGDWPYsGHWnym1ZnI5fPgwc+bM4cyZM5SXl1vnXtLpdNYZW3v06EFpaSmgThw2YcIE\n2rZtaz1PeXk5e/fu5aGHHrIet6qq6rKafvjhB+uMmxaWpSpDQ0Px8fGxTkoWEhLCiRMnCA8PB0Cv\n15Ofn09wcHAT/7SEqEsCQbgVnU5X501duWSqLkVRuOaaa8jKymL79u2sX7+e119/3XqxufY1h/Hj\nx5Oenk5YWBirVq2qs8ZB69atLzvHpecGdeGcjh07cvDgwd+s/dJ9Lefw8PCgTZs21u97eHhQXV1d\nZz93m3BOaEOuIQi30q9fPzZu3EhlZSVnz54lIyPjsm0qKiooKytj6NCh/O1vf+Orr74CwNvbm59/\n/tm6XXl5OT4+Ply4cIHVq1f/5ptuTEwMK1eutF5rOH36NNdddx3dunVj/fr1gPrmfejQocv2veWW\nWygpKbmq11xaWiprgwibkEAQbiUyMpKHH36Y8PBw7rvvPqKiour8XKfTcfbsWWJjYwkPD6dv374s\nXrwYUO/YeeWVV+jVqxfHjx/n5Zdfpk+fPtx9992XTbVeOxwsnw8ePJi4uDh69+5NZGSk9XbXDz74\ngBUrVhAREUFoaCjp6emX1X3XXXddtnBJfee49OuSkhJuuOEG2rVr16Q/JyHqI9NfC+Ek7r33Xj74\n4IPLriVcyTvvvENFRQXPPPOMHSsTLYV0CEI4ieeee4633nqrSfusXbuWSZMm2aki0dJIhyCEEAKQ\nDkEIIcRFEghCCCEACQQhhBAXSSAIIYQAJBCEEEJcJIEghBACgP8P8bSKBsl5v48AAAAASUVORK5C\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x514d530>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x5a12d10>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The graphs are the solutions\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.8-3, Page no 119"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "\n",
      "#Initilization of variables\n",
      "w=196 #N/m\n",
      "M_app=4000 #N.m\n",
      "L=6 #m\n",
      "\n",
      "#Calculations\n",
      "#Taking Moment about Point L and equating it to 0\n",
      "R_r=(M_app+w*L*L*0.5)/(3*L) #N\n",
      "#Taking Moment about Point R and equating it to 0\n",
      "R_l= ((((2*L)+(L/2))*(w*L))-(M_app))/(3*L) #N\n",
      "#finding point of zero shear\n",
      "a=R_l*w**-1\n",
      "#defining x\n",
      "x0=[0,18]\n",
      "x=[0,0.5,1,1.5,2,2.5,3,3.5,a,4,4.5,5,5.5,6] #for 0<x<6\n",
      "x1=[6,12] #for6<x<12\n",
      "x2=[12,18] #for 12<x<18\n",
      "xv=[6,12,18] #specially for shear force\n",
      "xo=[12.001,12.002] #Straight line plot\n",
      "#Shear Force Calculations\n",
      "#Summing forces in vertical direction and equating to 0\n",
      "V1=(R_l-w*x[0],R_l-w*x[1],R_l-w*x[2],R_l-w*x[3],R_l-w*x[4],R_l-w*x[5],R_l-w*x[6],R_l-w*x[7],R_l-w*x[8],R_l-w*x[9],R_l-w*x[10],R_l-w*x[11],R_l-w*x[12],R_l-w*x[13]) #N for 0<x<6\n",
      "V2=(R_l)-(w*L) #N for 6<x<18\n",
      "#Bending Moment Calculations\n",
      "M1=(R_l*x[0]-w*x[0]**2*0.5,R_l*x[1]-w*x[1]**2*0.5,R_l*x[2]-w*x[2]**2*0.5,R_l*x[3]-w*x[3]**2*0.5,R_l*x[4]-w*x[4]**2*0.5,R_l*x[5]-w*x[5]**2*0.5,R_l*x[6]-w*x[6]**2*0.5,R_l*x[7]-w*x[7]**2*0.5,R_l*x[8]-w*x[8]**2*0.5,R_l*x[9]-w*x[9]**2*0.5,R_l*x[10]-w*x[10]**2*0.5,R_l*x[11]-w*x[11]**2*0.5,R_l*x[12]-w*x[12]**2*0.5,R_l*x[13]-w*x[13]**2*0.5) #N.m for 0<x<6\n",
      "M2=(R_l*x1[0]-((w*L)*(x1[0]-3)),R_l*x1[1]-((w*L)*(x1[1]-3))) #N.m for 6<x<12\n",
      "M3=(R_l*x2[0]-((w*L)*(x2[0]-3))+M_app,R_l*x2[1]-((w*L)*(x2[1]-3))+M_app) #N.m for 12<x<18\n",
      "Mo=[-1464.8652,2509.3333]\n",
      "#Maximum bending moment\n",
      "M_max=R_l*a*0.5 #N.m\n",
      "\n",
      "#Plotting SFD & BMD\n",
      "p=[0,a,5.99,6,11.99,12,17.99,18]\n",
      "y=[0,1467,1020,1020,-1486,2514,0,0]\n",
      "z=[0,a,5.99,6,11.99,12,17.99,18]\n",
      "b=[758,0,-418,-418,-418,-418,-418,0]\n",
      "g=[0,0,0,0,0,0,0,0]\n",
      "d=transpose(p)\n",
      "e=transpose(b)\n",
      "plt.plot(d,y)\n",
      "xlabel('distance (m)')\n",
      "ylabel('B.M (N.m)')\n",
      "plt.show()\n",
      "xlabel('distance (m)')\n",
      "ylabel('S.F (N)')\n",
      "plt.plot(z,e,z,g)\n",
      "plt.show()\n",
      "\n",
      "#Result\n",
      "print'The value of reactions are: R_l=',round(R_l),\"N\",'and R_r=',round(R_r),\"N\"\n",
      "print'The point of maximum bending moment is',round(a,2),\"meters from left support\",'and maximum bending moment is',round(M_max),\"N.m\"\n",
      "print'The bending moment and shear force diagrams have been plotted'\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rpZRteZXbb79dWa1WpZRSW7ZsUbfffnuV3O+//7564IEH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\nURFCCGE3UlSEEELYzf8DHQ8WrN8pOOEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5d1cd10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vfWbxEN/3zDPuvc7vugvatzedRqRxOP3B+scfYfFiqKiY69X5tVY8qhIVFUVx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\nhT7EAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x60b29d0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of reactions are: R_l= 757.0 N and R_r= 418.0 N\n",
        "The point of maximum bending moment is 3.86 meters from left support and maximum bending moment is 1462.0 N.m\n",
        "The bending moment and shear force diagrams have been plotted\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.8-4, Page no 121"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initlization of  variables\n",
      "F1=2000 #lb\n",
      "w=100 #lb/ft\n",
      "\n",
      "#Calculations\n",
      "R_r=(-F1*5+w*14*13)/20 #lb\n",
      "R_l=(F1*25+w*14*7)/20 #lb\n",
      "#Shear Force matrix\n",
      "V=[-2000,-2000,990,990,-410,0] #lb\n",
      "#Bending Moment matrix\n",
      "B=[0,-10000,-10000,-4060,840,0]\n",
      "#Length matrix for shear force\n",
      "X_v=[0,5,5.0001,11,20.89999,20.9]\n",
      "#Length matrix for bendimg moment\n",
      "X_b=[0,4.99,5,11,19.9,20.9]\n",
      "g=[0,0,0,0,0,0]\n",
      "\n",
      "#Plotting of SFD & BMD.\n",
      "d=transpose(X_v)\n",
      "e=transpose(V)\n",
      "plt.plot(d,B)\n",
      "xlabel('distance (ft)')\n",
      "ylabel('B.M (lb.ft)')\n",
      "plt.show()\n",
      "plt.plot(X_b,e,X_b,g)\n",
      "xlabel('distance (ft)')\n",
      "ylabel('S.F (lb)')\n",
      "plt.show()\n",
      "\n",
      "#Result\n",
      "print'The bending Moment and Shear Force diagrams have been plotted'\n",
      "#Note\n",
      "#The textbook does not specify the span and hence there seems to be a disagreement between the textbook and python solution.here the values have just been plotted\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x5c00290>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Z2YwaNYrQ0FDCw8OJiIhg27ZtlJaWUlFRQUJCAgBjx45l9erVAKxZs4a0tDQA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\nRMRjFCoiIuIxChUREfEYhYqIiHjM/wMjUibUs6KdhgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5a4e330>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The bending Moment and Shear Force diagrams have been plotted\n"
       ]
      }
     ],
     "prompt_number": 6
    }
   ],
   "metadata": {}
  }
 ]
}