{
 "metadata": {
  "name": "chapter25.ipynb"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 25 :Shear Force And Bending Moment"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 25.25-5,Page No:628"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "\n",
      "# Initilization of variables\n",
      "L_AB=3 # m # length of the beam\n",
      "L_AC=1 # m\n",
      "L_BC=2 # m\n",
      "M_C=12 # kNm # clockwise moment at C\n",
      "\n",
      "# Calculations\n",
      "\n",
      "# REACTIONS\n",
      "R_B=M_C/L_AB # kN # moment at A\n",
      "R_A=-M_C/L_AB # kN # moment at B\n",
      "\n",
      "# S.F\n",
      "F_A=R_A # kN \n",
      "F_B=R_A # kN\n",
      "\n",
      "# B.M\n",
      "M_A=0 # kNm\n",
      "M_C1=R_A*L_AC # kNm # M_C1 is the BM just before C\n",
      "M_C2=(R_A*L_AC)+M_C # kNm # M_C2 is the BM just after C\n",
      "M_B=0 # kNm\n",
      "\n",
      "# Plotting SFD & BMD\n",
      "x=[0, 0.99, 1, 3]\n",
      "y=[-4, -4, -4, -4]\n",
      "a=[0, 0.99, 1, 3]\n",
      "b=[0, -4, 8, 0]\n",
      "g=[0,0,0,0]\n",
      "d=transpose(x)\n",
      "e=transpose(b)\n",
      "plt.plot(d,y)\n",
      "plt.show()\n",
      "plt.plot(a,e,a,g)\n",
      "plt.show()\n",
      "\n",
      "# Results\n",
      "print \"The graphs are the solutions\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x5b828b0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x5c897b0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The graphs are the solutions\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 25.25-7,Page No:631"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "import numpy as np\n",
      "\n",
      "# Initilization of variables\n",
      "\n",
      "L_AD=8 # m # length of the beam\n",
      "L_AB=2 # m \n",
      "L_BC=4 # m\n",
      "L_CD=2 # m\n",
      "UDL=1 # kN/m\n",
      "P=2 # kN # point load at A\n",
      "\n",
      "# Calculations\n",
      "\n",
      "# REACTIONS\n",
      "\n",
      "# solving eqn's 1&2 using matrix to get R_B & R_C as,\n",
      "\n",
      "A=np.array([[1, 1],[ 1, 3]])\n",
      "B=np.array([8,15])\n",
      "C=np.linalg.solve(A,B)\n",
      "\n",
      "# SHEAR FORCE\n",
      "\n",
      "# the term F with suffixes 1 & 2 indicates SF just to left and right \n",
      "F_A=-P # kN\n",
      "F_B1=-P # kN\n",
      "F_B2=-P+C[0] # kN\n",
      "F_C1=-P+C[0]-(UDL*L_BC) # kN\n",
      "F_C2=-P+C[0]-(UDL*L_BC)+C[1] # kN\n",
      "F_D=0\n",
      "\n",
      "# BENDING MOMENT\n",
      "\n",
      "# the term F with suffixes 1 & 2 indicates BM just to left and right\n",
      "M_A=0 # kNm\n",
      "M_B=(-P*L_CD) # kNm\n",
      "M_C=(-P*(L_AB+L_BC))+(C[0]*L_BC)-(UDL*L_BC*(L_BC/2)) # kNm\n",
      "M_D=0 # kNm\n",
      "\n",
      "# LOCATION OF MAXIMUM BM\n",
      "\n",
      "# Max BM occurs at E at a distance of 2.5 m from B i.e x=L_AE=4.5 m from free end A. Thus max BM is given by taking moment at B\n",
      "L_AE=4.5 # m # given\n",
      "M_E=(-2*L_AE)+(4.5*(L_AE-2))-((1/2)*(L_AE-2)**2) # kNm\n",
      "\n",
      "#Plotting\n",
      "x_p=linspace(2,6,40)\n",
      "M_p=-2*+4.5*(x_p-2)-((x_p-2)**2)*0.5\n",
      "\n",
      "# PLOTTING SFD & BMD\n",
      "x=[0,1.99,2,4.5,5.99,6,8]\n",
      "y=[-2,-2,2.5,0,-1.5,2,0]\n",
      "z=[0,0,0,0,0,0,0]\n",
      "a=[0,2,4.5,6,8]\n",
      "b=[0,-4,-0.875,-2,0]\n",
      "g=[0,0,0,0,0]\n",
      "d=transpose(x)\n",
      "plt.plot(d,y,x,z)\n",
      "plt.show()\n",
      "e=transpose(b)\n",
      "plt.plot(a,e,a,g)\n",
      "plt.show()\n",
      "\n",
      "\n",
      "# Results\n",
      "\n",
      "print\"The graphs are the solutions\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Q0FAMaaGpmJmZ2fC5yWSCyWRqI3xqjBWTa1EUYMUKYORI4I9/BJYvlx1R25jo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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5b10e30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+5Ofno6KiQu1QwrLZbJgxYwby8/NRWFiodjhBXbt2DQsWLEBWVhays7PR1tam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\n/T/kZq6+7dkZ0AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5baadb0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The graphs are the solutions\n"
       ]
      }
     ],
     "prompt_number": 16
    }
   ],
   "metadata": {}
  }
 ]
}