path: root/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter10.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:42031753a466b3ba5ee8c11468e375015d1a3d943c879daacc89b28eec81ab67"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 10:Deflections of beams "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.1 page number 501"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Given \n",
      "dia = 400   #mm - The diameter of a pulley\n",
      "E = 200     #Gpa - Youngs modulus\n",
      "t = 0.6     #mm - The thickness of band\n",
      "c = t/2     #mm - The maximum stress is seen \n",
      "#Caliculations\n",
      "\n",
      "stress_max = E*c*(10**3)/(dia/2) #Mpa - The maximum stress on the crossection occurs at the ends\n",
      "print \"The maximum bending stress developed in the saw \",stress_max,\"Mpa\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The maximum bending stress developed in the saw  300.0 Mpa\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.3 page number 512"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Given\n",
      "import numpy\n",
      "l_ab = 1.0   #L in - The length of the beam\n",
      "F_D = 1.0    #W lb/in - The force distribution \n",
      "F = F_D*l_ab #WL - The force applied\n",
      "#Beause of symmetry the moment caliculations can be neglected\n",
      "#F_Y = 0\n",
      "R_A = F/2 #wl - The reactive force at A\n",
      "R_B = F/2 #wl - The reactive force at B\n",
      "#EI - The flxure rigidity is constant and 1/EI =1 # k\n",
      "\n",
      "#part - A\n",
      "#section 1--1\n",
      "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n",
      "M_1 = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "v = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "for i in range(10):\n",
      "    v[i] = R_A - F_D*l_1[i]  \n",
      "    M_1[i] = R_A*l_1[i] - F_D*(l_1[i]**2)/2\n",
      "# (EI)y'' = M_1[i] we will integrate M_1[i] twice where variable is l_1[i]\n",
      "#(EI)y'- \n",
      "\n",
      "M_1_intg1 = R_A*(l_1[i]**2)/4 - F_D*(l_1[i]**3)/6 - F_D*(l_ab**3)*l_1[i]/24 #integration of x**n = x**n+1/n+1\n",
      "#(EI)y- Using end conditions for caliculating constants \n",
      "\n",
      "M_1_intg2 = R_A*(l_1[i]**3)/12.0 - F_D*(l_1[i]**4)/24.0 + F_D*(l_ab**3)*l_1[i]/24.0 \n",
      "#Equations \n",
      "\n",
      "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n",
      "M_1_intg2 = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "Y = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "for i in range(10):\n",
      "    M_1_intg2[i] = (l_1[i]**3)/12.0 - (l_1[i]**4)/24.0 - l_1[i]/24.0   # discluding every term for ruling out float values\n",
      "    Y[i] = M_1_intg2[i] #W(l**4)/EI  k = 1/EI\n",
      "#The precision is very less while caliculating through this equation because the least count in X direction is 0.1\n",
      "print \"a) The maximum displacement in y direction is\",min(Y),\"W(l**4)/EI \"\n",
      "print \"a) The maximum deflection occured at\",l_1[Y.index(min(Y))],\"L\"\n",
      "\n",
      "#Part - B\n",
      "#Graphs\n",
      "import numpy as np\n",
      "values = M_1\n",
      "y = np.array(values)\n",
      "t = np.linspace(0,1,11)\n",
      "poly_coeff = np.polyfit(t, y, 2)\n",
      "import matplotlib.pyplot as plt\n",
      "plt.plot(t, y, 'o')\n",
      "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n",
      "plt.show()\n",
      "print \"b) The above graph is bending moment graph\"\n",
      "import numpy as np\n",
      "values = Y \n",
      "y = np.array(values)\n",
      "t = np.linspace(0,1,11)\n",
      "poly_coeff = np.polyfit(t, y, 2)\n",
      "import matplotlib.pyplot as plt\n",
      "plt.plot(t, y, 'o')\n",
      "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n",
      "plt.show()\n",
      "print \"b)The above graph is beam displacement graph\"\n",
      "print \"b)The maximum occures in the middle from the above graph  \"\n",
      "\n",
      "\n",
      "   \n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "a) The maximum displacement in y direction is -0.0130208333333 W(l**4)/EI \n",
        "a) The maximum deflection occured at 0.5 L\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEACAYAAACznAEdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFQQREQlRQRAREQD+H2Gz7ECR6pNEAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x8059b00>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "b) The above graph is bending moment graph\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAEACAYAAABCl1qQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\neGTFwhhjjEf/D05C44YG+g5FAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x8217320>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "b)The above graph is beam displacement graph\n",
        "b)The maximum occures in the middle from the above graph  \n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.4 page number 514"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Given\n",
      "import numpy\n",
      "l_ab = 1.0   #L in - The length of the beam\n",
      "F_D = 1.0    #W lb/in - The force distribution \n",
      "F = F_D*l_ab #WL - The force applied\n",
      "#Beause of symmetry the moment caliculations can be neglected\n",
      "#F_Y = 0\n",
      "R_A = F/2    #wl - The reactive force at A\n",
      "R_B = F/2    #wl - The reactive force at B\n",
      "#EI - The flxure rigidity is constant and 1/EI =1 # k\n",
      "#M_A and M_B are applied at the ends\n",
      "\n",
      "#part - A\n",
      "#section 1--1\n",
      "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1]    #L taking each section at 0.1L distance \n",
      "M = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "for i in range(10):\n",
      "    M[i] = l_1[i]/2.0 - (l_1[i]**2)/2.0 -1.0/12.0    #The moment euation at 1--1 section\n",
      "# M_1 = R_A*l_1[i]/2.0 - F_D*(l_1[i]**2)/2.0 -F_D*(l_ab**2)/12.0  #The moment euation at 1--1 section    \n",
      "# (EI)y'' = M_1[i] we will integrate M_1[i] twice where variable is l_1[i]\n",
      "#(EI)y'\n",
      "M_1_intg1 = R_A*(l_1[i]**2)/4 - F_D*(l_1[i]**3)/6 - F_D*(l_ab**2)*l_1[i]/12.0 #integration of x**n = x**n+1/n+1\n",
      "#(EI)y\n",
      "M_1_intg2[i] = R_A*(l_1[i]**3)/12.0 - F_D*(l_1[i]**4)/24.0 + F_D*(l_ab**2)*(l_1[i]**2)/24.0   \n",
      "\n",
      "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n",
      "M_1_intg2 = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "Y = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "for i in range(10):\n",
      "    M_1_intg2[i] = (l_1[i]**3)/12.0 - (l_1[i]**4)/24.0 - (l_1[i]**2)/24.0   # discluding every term for ruling out float values\n",
      "    Y[i] = M_1_intg2[i] #W(l**4)/EI  k = 1/EI\n",
      "    \n",
      "#Part - B\n",
      "#Graphs\n",
      "import numpy as np\n",
      "values = M\n",
      "y = np.array(values)\n",
      "t = np.linspace(0,1,11)\n",
      "poly_coeff = np.polyfit(t, y, 2)\n",
      "import matplotlib.pyplot as plt\n",
      "plt.plot(t, y, 'o')\n",
      "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n",
      "plt.show()\n",
      "print \"b) The above graph is bending moment graph\"\n",
      "import numpy as np\n",
      "values = Y \n",
      "y = np.array(values)\n",
      "t = np.linspace(0,1,11)\n",
      "poly_coeff = np.polyfit(t, y, 2)\n",
      "import matplotlib.pyplot as plt\n",
      "plt.plot(t, y, 'o')\n",
      "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n",
      "plt.show()\n",
      "\n",
      "\n",
      " \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEACAYAAABcXmojAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRMJUFEREJOz/A6arfahQrjHdAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x22dba90>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "b) The above graph is bending moment graph\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAEACAYAAAByG0uxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nxhhjfPb/MPjEgLOKoGcAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x81fa630>"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.5 page number 517"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Given \n",
      "#because of symmetry the problem can be solved by considering first half\n",
      "#Given\n",
      "import numpy\n",
      "l_ab = 1.0       #L in - The length of the beam\n",
      "F_D = 1.0        #W lb/in - The force distribution \n",
      "F = F_D*l_ab     #WL - The force applied\n",
      "#Beause of symmetry the moment caliculations can be neglected\n",
      "#EI - The flxure rigidity is constant and 1/EI =1 # k\n",
      "\n",
      "#part - A\n",
      "#section 1--1\n",
      "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n",
      "M_1 = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "v = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "for i in range(10):\n",
      "    v[i] = R_A - F_D*l_1[i]  \n",
      "    M_1[i] = R_A*l_1[i] - F_D*(l_1[i]**2)/2\n",
      "# (EI)y'' = M_1[i] we will integrate M_1[i] twice where variable is l_1[i]\n",
      "#(EI)y'\n",
      "M_1_intg1 = R_A*(l_1[i]**2)/2 - F_D*(l_1[i]**3)/6 - F_D*(l_ab**3)*l_1[i]/48 #integration of x**n = x**n+1/n+1\n",
      "#(EI)y\n",
      "M_1_intg2[i] = R_A*(l_1[i]**3)/6 - F_D*(l_1[i]**4)/24.0 - F_D*(l_ab**3)*l_1[i]/48.0 \n",
      "#Equations \n",
      "#R_A = #wl Unknown- The reactive force at A\n",
      "#R_B = #wl - The reactive force at B\n",
      "\n",
      "# M_1_intg2[10] = 0, the displacement at the end of rod is 0 since its rigid \n",
      "R_A =  (F_D*(l_1[10]**4)/24.0 + F_D*(l_ab**3)*l_1[10]/48.0)/((l_1[10]**3)/6.0)\n",
      "R_C = R_A #WL - symmetry\n",
      "R_B = 1-R_A+R_B # WL - F_Y = 0, the equilibrium in Y direction\n",
      "print \"The reaction at A is\",R_A ,\"WL\"\n",
      "print \"The reaction at B is\",R_B ,\"WL\"\n",
      "print \"The reaction at C is\",R_C ,\"WL\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " The reaction at A is 0.375 WL\n",
        "The reaction at B is 2.375 Wl\n",
        "The reaction at C is 0.375 Wl\n"
       ]
      }
     ],
     "prompt_number": 82
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.7 page number 521 "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l_ac = 5 #m - The length of the beam \n",
      "l_ab = 4 #m - The length of ac on beam \n",
      "l_bc = 1 #m - The length of bc on beam \n",
      "F = 20 #N - force applied on beam at 'b'\n",
      "I_ab = 4 #I The moment of inertia of part AB \n",
      "I_bc = 1 #I - The momemt of inertia of part BC\n",
      "R_A = F*(l_bc/l_ac) #N- The reaction at joint A\n",
      "R_B = F*(l_ab/l_ac) #N- The reaction at joint B\n",
      "E = 1 #E youngs modulus\n",
      "\n",
      "#0<x<4\n",
      "x = [0,1,2,3,4]\n",
      "M = [0,0,0,0,0]\n",
      "y = [0,0,0,0,0]\n",
      "for i in range(5):\n",
      "    M[i] = 4*x[i] #integration of x**n = x**n+1/n+1\n",
      "    #y_2[i] = 4*x[i]/(E*I_ab) #The \n",
      "    #y_1[i] = 4*(x[i]**2)/(E*I_ab) -4.8/(E*I_bc)  #The constant can be found by conditions y(o) = y(c) = 0\n",
      "    y[i]  =   4*(x[i]**2)/(6*E*I_ab)  -4.8*x[i]/(E*I_bc)  #elastic curve constant can be found by Y_1(0) = 0 \n",
      "\n",
      "\n",
      "#0<x_1<1\n",
      "x_1 = [4,5]\n",
      "m = [0,0]\n",
      "Y = [0,0]\n",
      "for i in range(2):\n",
      "    m[i] = 16 - 16*x_1[i]    #integration of x**n = x**n+1/n+1\n",
      "   # Y_2 = (16 - 16*x_1[i])/(E*I_ab) \n",
      "    #Y_1 = (16*x_1[i]-8*(x_1[i]**2) +8 - 4.8)/(E*I_ab)#The constant can be found by conditions y(o) = y(c) = 0\n",
      "    Y[i] =  (8*(x_1[i]**2)-8*(x_1[i]**3)/3 +(8-4.8)*x_1[i] - 4*4.8 )/(E*I_ab) #elastic curve constant can be found by Y_1(0) = 0\n",
      "\n",
      "#Graphs\n",
      "import numpy as np\n",
      "values = y\n",
      "y = np.array(values)\n",
      "t = np.linspace(0,1,5)\n",
      "poly_coeff = np.polyfit(t, y, 2)\n",
      "import matplotlib.pyplot as plt\n",
      "plt.plot(t, y, 'o')\n",
      "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n",
      "plt.show()\n",
      "print \"b) The shape from x belongs to 0<x<4\"\n",
      "import numpy as np\n",
      "values = Y \n",
      "y = np.array(values)\n",
      "t = np.linspace(0,1,2)\n",
      "poly_coeff = np.polyfit(t, y, 2)\n",
      "import matplotlib.pyplot as plt\n",
      "plt.plot(t, y, 'o')\n",
      "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n",
      "plt.show()\n",
      "print \"b) The shape from x belongs to 4<x<5\"\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/j9lJ+moq4xgJQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa792dd8>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "b) The shape from x belongs to 0<x<4\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "C:\\Users\\Kowshik\\AppData\\Local\\Enthought\\Canopy\\User\\lib\\site-packages\\numpy\\lib\\polynomial.py:588: RankWarning: Polyfit may be poorly conditioned\n",
        "  warnings.warn(msg, RankWarning)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQl6d+sBHAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa6b60f0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "b) The shape from x belongs to 4<x<5\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.10 page number 529"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "k = 24.0*(10**12)    #N.mm2 Flexure rigidity\n",
      "E = 200.0            #Gpa - Youngs modulus of the string\n",
      "l = 5000.0           #mm - The length of the string\n",
      "C_A = 300.0          #mm2 - crossection area \n",
      "P = 50.0             #KN - The force applies at the end \n",
      "a = 2000.0           #mm - The distance C-F\n",
      "x = 1#X - let it be a variable X\n",
      "y_d = x*(a**3)/(3*k)                                 #Xmm The displacement at D, lets keep the variable in units part\n",
      "y_p  = -P*(10**3)*(16*(a**3)-12*(a**3)+(a**3))/(k*6) #mm The displacement due to p \n",
      "e_rod = l/(C_A*E*(10**3))                            #Xmm -deflection, The varible is in units \n",
      "e_rod\n",
      "X = y_p/(2*e_rod+y_d)  # By equating deflections \n",
      "y_d_1 = X*(a**3)/(3*k) # the deflection of point D\n",
      "print \"The deflection of point D\",round(y_d_1,2),\"mm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the deflection of point D -5.56 mm\n"
       ]
      }
     ],
     "prompt_number": 78
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.11 page number 530  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l = 15          #in - The length of the crossection \n",
      "b = 33.9        #in - the width of the crossection\n",
      "L = 100         #in The length of the cantilever \n",
      "E = 29*(10**6)  #psi The youngs modulus of the material used \n",
      "I_Z = 315       #in4 - the moment of inertia wrt Z axis \n",
      "I_y = 8.13      #in4 - the moment of inertia wrt Y axis\n",
      "o = 5           # degrees - the angle of acting force \n",
      "P = 2000        #k the acting force \n",
      "P_h = P*math.sin(math.radians(o)) #k - The horizantal component of P\n",
      "P_v = P*math.cos(math.radians(o)) #k - The vertical  component of P\n",
      "e_h =  P_h*(L**3)/(3*E*I_y)       # the horizantal component of deflection \n",
      "e_v =  P_v*(L**3)/(3*E*I_Z )      # the vertical component of deflection\n",
      "e = pow((e_h**2 + e_v**2),0.5)\n",
      "print \"the horizantal component of deflection\",round(e_h,3) ,\"in\"\n",
      "print \"the vertical component of deflection\",round(e_v,3) ,\"in\"\n",
      "print \"the resultant deflection\",round(e,3) ,\"in\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the horizantal component of deflection 0.246 in\n",
        "the vertical component of deflection 0.073 in\n",
        "the resultant deflection 0.257 in\n"
       ]
      }
     ],
     "prompt_number": 88
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.13 page number 533"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Given \n",
      "l = 50.0           #mm - The length of the crossection \n",
      "b = 50.0           #mm - the width of the crossection\n",
      "m = 15.3           # mass of the falling body\n",
      "h = 75.0           #mm - The height of the falling body \n",
      "p = m*9.81         #N the force acted due to the body\n",
      "L = 1000.0         #mm The length of the cantilever\n",
      "E = 200  #Gpa The youngs modulus of the material used \n",
      "I = (l**4)/12 #mm - the moment of inertia \n",
      "k = 300 #N/mm -the stiffness of the spring \n",
      "#Rigid supports \n",
      "e = m*9.81*(L**3)*(10**-3)/(48*E*I) #mm - the deflection of beam \n",
      "imp_fact_a = 1 +pow((1 +2*h/e),0.5) #no units , impact factor \n",
      "#spring supports\n",
      "e_spr = h/k #mm the elongation due to spring \n",
      "e_total = e_spr + e \n",
      "imp_fact_b =  1 +pow((1 +2*h/e_total),0.5) #no units , impact factor\n",
      "print \"a) The maximum deflection when the beam is on rigid supports\",round(e,3),\"mm with impact factor\",round(imp_fact_a ,2),\n",
      "print \"b) The maximum deflection when the beam is on spring supports\",round(e_total,2),\"mm with impact factor\",round(imp_fact_b,2) ,\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "a) The maximum deflection when the beam is on rigid supports 0.03 mm with impact factor 71.7 b) The maximum deflection when the beam is on spring supports 0.28 mm with impact factor 24.17\n"
       ]
      }
     ],
     "prompt_number": 111
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.15 page number 536 "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Given\n",
      "E = 30*(10**3) #ksi - The youngs modulus of the material \n",
      "stress_y = 40 #Ksi - yield stress\n",
      "stress_max = 24.2 #Ksi - the maximum stress\n",
      "l = 2          #in - The length of the crossection \n",
      "b = 3       #in - the width of the crossection\n",
      "h = 3 #in - the depth of the crossection\n",
      "#lets check ultimate capacity for a 2 in deep section \n",
      "M_ul = stress_y*b*(l**2)/4 #K-in the ultimate capacity \n",
      "curvature = 2*stress_y/(E*(h/2) ) #in*-1 the curvature of the beam \n",
      "curvature_max = stress_max/(E*(h/2)) #in*-1 The maximum curvature \n",
      "print \"the ultimate capacity\",M_ul,\"K-in\"\n",
      "print \"the ultimate curvature\",curvature_max,\"in*-1\"\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the ultimate capacity 120 K-in\n",
        "the ultimate curvature 0.000806666666667 in*-1\n"
       ]
      }
     ],
     "prompt_number": 114
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.16 page number 543"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Given \n",
      "l_ad = 1600 #mm - The total length of the beam \n",
      "l_ab = 600  #mm - The length of AB\n",
      "l_bc = 600  #mm - The length of BC\n",
      "e_1 = 0.24  #mm - deflection \n",
      "e_2 = 0.48  #mm - deflection\n",
      "E = 35      #Gpa\n",
      "#Caliculation \n",
      "\n",
      "A_afe = -(l_ab+l_bc)*e_1*(10**-3)/(2*E)\n",
      "A_afe = -(l_ab)*e_2*(10**-3)/(4*E)\n",
      "y_1_b = A_afe + A_afe #rad the slope at the tip  B\n",
      "x_1 = 1200            #com from B\n",
      "x_2 = 800             #com from B\n",
      "y_b = A_afe*x_1 + A_afe*x_2 #mm The maximum deflection at tip B\n",
      "print\"The maximum deflection at tip B\",round(y_b,2),\"mm\"\n",
      "print \"The slope at the tip  B\",round(y_1_b,2) ,\"radians\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The maximum deflection at tip B -4.11 mm\n",
        "The slope at the tip  B -0.0 radians\n"
       ]
      }
     ],
     "prompt_number": 126
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.19 page number 547 "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Given\n",
      "import numpy\n",
      "l_ab = 1.0   #L in - The length of the beam\n",
      "F_D = 1.0    #W lb/in - The force distribution \n",
      "F = F_D*l_ab #WL - The force applied\n",
      "#Beause of symmetry the moment caliculations can be neglected\n",
      "#F_Y = 0\n",
      "R_A = F/2 #wl - The reactive force at A\n",
      "R_B = F/2 #wl - The reactive force at B\n",
      "#EI - The flxure rigidity is constant and 1/EI =1 # k\n",
      "\n",
      "#part - A\n",
      "#section 1--1\n",
      "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n",
      "M_1 = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "v = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "for i in range(10):\n",
      "    v[i] = R_A - F_D*l_1[i]  \n",
      "    M_1[i] = R_A*l_1[i] - F_D*(l_1[i]**2)/2\n",
      "# (EI)y'' = M_1[i] we will integrate M_1[i] twice where variable is l_1[i]\n",
      "#(EI)y'- \n",
      "\n",
      "M_1_intg1 = R_A*(l_1[i]**2)/4 - F_D*(l_1[i]**3)/6 - F_D*(l_ab**3)*l_1[i]/24 #deflection integration of x**n = x**n+1/n+1\n",
      "#(EI)y- Using end conditions for caliculating constants \n",
      "\n",
      "M_1_intg2 = R_A*(l_1[i]**3)/12.0 - F_D*(l_1[i]**4)/24.0 + F_D*(l_ab**3)*l_1[i]/24.0 \n",
      "#Equations \n",
      "\n",
      "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n",
      "M_1_intg2 = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "Y = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "for i in range(10):\n",
      "    M_1_intg2[i] = (l_1[i]**3)/12.0 - (l_1[i]**4)/24.0 - l_1[i]/24.0   # discluding every term for ruling out float values\n",
      "    Y[i] = M_1_intg2[i] #W(l**4)/EI  k = 1/EI\n",
      "#The precision is very less while caliculating through this equation because the least count in X direction is 0.1\n",
      "print \" The maximum displacement in y direction is\",min(Y),\"W(l**4)/EI \"\n",
      "print \" The maximum deflection occured at\",l_1[Y.index(min(Y))],\"L\"\n",
      "\n",
      "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n",
      "M_1_intg1 = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "Y = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "for i in range(10):\n",
      "    M_1_intg1[i] = R_A*(l_1[i]**2)/4 - F_D*(l_1[i]**3)/6 - F_D*(l_ab**3)*l_1[i]/24\n",
      "print \" The maximum deflection is\",min(M_1_intg1 ),\"W(l**3)/EI \""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " The maximum displacement in y direction is -0.0130208333333 W(l**4)/EI \n",
        " The maximum deflection occured at 0.5 L\n",
        " The maximum deflection is -0.05775 W(l**3)/EI \n"
       ]
      }
     ],
     "prompt_number": 132
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.23 page number 554 "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy\n",
      "l_ab = 1.0   #L in - The length of the beam\n",
      "F_D = 1.0    #W lb/in - The force distribution \n",
      "F = F_D*l_ab #WL - The force applied\n",
      "#Beause of symmetry the moment caliculations can be neglected\n",
      "#F_Y = 0\n",
      "R_A = F/2    #wl - The reactive force at A\n",
      "R_B = F/2    #wl - The reactive force at B\n",
      "#EI - The flxure rigidity is constant and 1/EI =1 # k\n",
      "#M_A and M_B are applied at the ends\n",
      "\n",
      "#part - A\n",
      "#section 1--1\n",
      "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1]    #L taking each section at 0.1L distance \n",
      "M = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "for i in range(10):\n",
      "    M[i] = l_1[i]/2.0 - (l_1[i]**2)/2.0 -1.0/12.0    #The moment euation at 1--1 section\n",
      "# M_1 = R_A*l_1[i]/2.0 - F_D*(l_1[i]**2)/2.0 -F_D*(l_ab**2)/12.0  #The moment euation at 1--1 section    \n",
      "# (EI)y'' = M_1[i] we will integrate M_1[i] twice where variable is l_1[i]\n",
      "#(EI)y'\n",
      "M_1_intg1 = R_A*(l_1[i]**2)/4 - F_D*(l_1[i]**3)/6 - F_D*(l_ab**2)*l_1[i]/12.0 #integration of x**n = x**n+1/n+1\n",
      "#(EI)y\n",
      "M_1_intg2[i] = R_A*(l_1[i]**3)/12.0 - F_D*(l_1[i]**4)/24.0 + F_D*(l_ab**2)*(l_1[i]**2)/24.0   \n",
      "\n",
      "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n",
      "M_1_intg2 = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "Y = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "for i in range(10):\n",
      "    M_1_intg2[i] = (l_1[i]**3)/12.0 - (l_1[i]**4)/24.0 - (l_1[i]**2)/24.0   # discluding every term for ruling out float values\n",
      "    Y[i] = M_1_intg2[i] #W(l**4)/EI  k = 1/EI\n",
      "    \n",
      "print \"The moment at the end is \",M[0],\"wl**2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The moment at the end is  -0.0833333333333 wl**2\n"
       ]
      }
     ],
     "prompt_number": 133
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.25 pagenumber 556"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# This problem is divided into two parts\n",
      "#Part _1\n",
      "#Given\n",
      "l = 1.0 #l - The length of the beam\n",
      "p = 1.0 #W - The total load applied\n",
      "#since it is triangular distribution \n",
      "l_com = 0.66*L #l - The distance of force of action from one end\n",
      "#F_Y = 0\n",
      "#R_A + R_B = p\n",
      "#M_a = 0 Implies that R_B = 2*R_A\n",
      "R_A = p/3.0\n",
      "R_B = 2.0*p/3\n",
      "\n",
      "#Taking Many sections \n",
      "\n",
      "#Section 1----1\n",
      "l = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n",
      "M = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "v = [0,0,0,0,0,0,0,0,0,0,0]\n",
      "for i in range(10):\n",
      "    v[i] = p*(l[i]**2) - p/3.0\n",
      "    M[i] = p*(l[i]**3)/(3.0)- p*l[i]/3.0\n",
      "\n",
      "v[10] = R_B #again concluded Because the value is tearing of  \n",
      "\n",
      "\n",
      "#Graph\n",
      "import numpy as np\n",
      "values = M\n",
      "y = np.array(values)\n",
      "t = np.linspace(0,1,11)\n",
      "poly_coeff = np.polyfit(t, y, 2)\n",
      "import matplotlib.pyplot as plt\n",
      "plt.plot(t, y, 'o')\n",
      "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n",
      "plt.show()\n",
      "import numpy as np\n",
      "values = v\n",
      "y = np.array(values)\n",
      "t = np.linspace(0,1,11)\n",
      "poly_coeff = np.polyfit(t, y, 2)\n",
      "import matplotlib.pyplot as plt\n",
      "plt.plot(t, y, 'o')\n",
      "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n",
      "plt.show()\n",
      "\n",
      "\n",
      "#part B\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEACAYAAABcXmojAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nY/L8f6G/NIrkiT5JAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa6d47f0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEACAYAAAC08h1NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nbKRBM81FAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x80d0f98>"
       ]
      }
     ],
     "prompt_number": 134
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}