{
 "metadata": {
  "name": "",
  "signature": "sha256:cb28374726804cd374e61b1808cab7ccc40447e8df5be7bbb88241dd0bce4859"
 },
 "nbformat": 3,
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter7-Numerical Methods"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3-pg204"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate tauA and tauB\n",
      "import numpy\n",
      "from numpy.linalg import inv\n",
      "a=15. ##mm\n",
      "b=10. ##mm\n",
      "h=5. ##mm\n",
      "h1=4.4 ##mm\n",
      "h2=2.45 ##mm\n",
      "h3=3. ##mm\n",
      "\n",
      "x=([[2, 0, 0, 0, 2, -4],[0, 2, 0, 1 ,-4 ,1],[0, 0, 2, -4, 1, 0],[-4, 2 ,0 ,0 ,0 ,1],[1, -4.27, 1, 0, 1.06, 0],[0, 1.25, -7.41, 1.34, 0, 0]])\n",
      "print(x)\n",
      "y=([[-2], [-2], [-2], [-2], [-2], [-2]])\n",
      "print(y)\n",
      "z=numpy.dot(inv(x),y)\n",
      "X1=z[1]\n",
      "X2=z[2]\n",
      "X3=z[3]\n",
      "X4=z[0]\n",
      "X5=z[4]\n",
      "X6=z[5]\n",
      "print(X4)\n",
      "\n",
      "print(X1)\n",
      "print(X2)\n",
      "print(X3)\n",
      "print(X5)\n",
      "print(X6)\n",
      " \n",
      "dfi=2.075 \n",
      "d3fi=-0.001\n",
      "d2fi=-1.383\n",
      "d4fi=0.002\n",
      "\n",
      "##tauB=derivative(fi,y)B\n",
      "tauB=(dfi+(d2fi/2.)-(d3fi/3.)+(d4fi/4.))\n",
      "print'%s %.2f %s'%('tauB=',tauB,' G*thetab')\n",
      "\n",
      "dfi=1.536\n",
      "d2fi=-0.613\n",
      "d3fi=-0.002\n",
      "d4fi=0.001\n",
      "d5fi=0.001\n",
      "d6fi=-0.002\n",
      "\n",
      "##tauA=derivative(fi,x)A\n",
      "tauA=(dfi+(-d2fi/2.)-(d3fi/3.)-(d4fi/4.)+(d5fi/5.)+(d6fi/6.))\n",
      "print'%s %.2f %s'%('tauA=',tauA,' G*thetaa')\n",
      "\n",
      "\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[2, 0, 0, 0, 2, -4], [0, 2, 0, 1, -4, 1], [0, 0, 2, -4, 1, 0], [-4, 2, 0, 0, 0, 1], [1, -4.27, 1, 0, 1.06, 0], [0, 1.25, -7.41, 1.34, 0, 0]]\n",
        "[[-2], [-2], [-2], [-2], [-2], [-2]]\n",
        "[ 2.07117939]\n",
        "[ 1.76075859]\n",
        "[ 0.84472513]\n",
        "[ 1.53616791]\n",
        "[ 2.45522136]\n",
        "[ 2.76320038]\n",
        "tauB= 1.38  G*thetab\n",
        "tauA= 1.84  G*thetaa\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex6-pg210"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate effective fem at joint B and the change of moment in beam segment AB  and BC\n",
      "p=15.\n",
      "P=45.\n",
      "a=3.\n",
      "b=1.5\n",
      "L1=3.\n",
      "L2=4.5\n",
      "MfAB=-(p*L1**2)/12.\n",
      "print'%s %.2f %s'%(\"in kNm is= \",MfAB,\"\")\n",
      "MfBA=(11.25)\n",
      "print'%s %.2f %s'%(\"in kNm is= \",MfBA,\"\")\n",
      "MfBC=-(P*a*b**2)/L2**2\n",
      "print'%s %.2f %s'%(\"in kNm is= \",MfBC,\"\")\n",
      "MfCB=(P*b*a**2)/L2**2\n",
      "print'%s %.2f %s'%(\"in kNm is= \",MfCB,\"\")\n",
      "B=MfBA+MfBC\n",
      "print'%s %.2f %s'%(\"effective fem at joint B in kNm is= \",B,\"\")\n",
      "AB=0.429*-B    ##                      joint rotates until a change in moment is +3.75\n",
      "print'%s %.2f %s'%(\"the change of moment in beam segment AB in kN is=\",AB,\"\")\n",
      "BC=0.571*-B\n",
      "print'%s %.2f %s'%(\"the change of moment in beam segment AB in kN is=\",BC,\"\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "in kNm is=  -11.25 \n",
        "in kNm is=  11.25 \n",
        "in kNm is=  -15.00 \n",
        "in kNm is=  30.00 \n",
        "effective fem at joint B in kNm is=  -3.75 \n",
        "the change of moment in beam segment AB in kN is= 1.61 \n",
        "the change of moment in beam segment AB in kN is= 2.14 \n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex7-pg221"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#find epsilon\n",
      "import math\n",
      "import numpy\n",
      "from numpy.linalg import inv\n",
      "p=14. ##MPa\n",
      "t=0.3 ##cm\n",
      "E=200. ##GPa\n",
      "v=0.3\n",
      "gamma1=77. ##kN/m**3\n",
      "alpha=12.*10**-6 ## per degree celcius\n",
      "A=2\n",
      "T=50. ##degree celcius\n",
      "\n",
      "D=numpy.matrix([[3.33, 0.99, 0],[0.99 ,3.3, 0],[0, 0, 1.16]])\n",
      "print(D)\n",
      "##[D*]=(t*[D])/4*A\n",
      "Dj=(10**6)*D\n",
      "\n",
      "D1=Dj/8. \n",
      "\n",
      "print(D1)\n",
      "\n",
      "##solution a: stiffness matrix\n",
      "xi=0.\n",
      "x1=0.\n",
      "xj=4.\n",
      "x2=4.\n",
      "xm=0.\n",
      "x3=0.\n",
      "yi=-1.\n",
      "y1=-1.\n",
      "yj=-1.\n",
      "y2=-1.\n",
      "ym=1.\n",
      "y3=1.\n",
      "\n",
      "ai=0.-4.\n",
      "a1=0.-4.\n",
      "print(ai,a1)\n",
      "aj=0-0.\n",
      "a2=0-0.\n",
      "print(aj,a2)\n",
      "am=4.-0.\n",
      "a3=4.-0.\n",
      "print(am,a3)\n",
      "\n",
      "bi=-1-1\n",
      "b1=-1-1\n",
      "print(bi,b1)\n",
      "bj=1.+1.\n",
      "b2=1.+1.\n",
      "print(bj,b2)\n",
      "bm=-1.+1.\n",
      "b3=-1+1.\n",
      "print(bm,b3)\n",
      "\n",
      "k11=(10**6/8.)*(3.3*4+1.16*16)\n",
      "print'%s %.2f %s'%('k11=',k11,'')\n",
      "k12=(10**6/8)*(3.3*2*-2+0)\n",
      "print'%s %.2f %s'%('k12=',k12,'')\n",
      "k13=(10**6/8)*(0+1.16*4*-4)\n",
      "print'%s %.2f %s'%('k13=',k13,'')\n",
      "k22=(10**6/8.)*(3.3*4+0)\n",
      "print'%s %.2f %s'%('k22=',k22,'')\n",
      "k23=0.\n",
      "print'%s %.2f %s'%('k23=',k23,'')\n",
      "k32=0.\n",
      "print'%s %.2f %s'%('k32=',k32,'')\n",
      "k21=(10**6/8)*(3.3*2*-2+0)\n",
      "print'%s %.2f %s'%('k21=',k21,'')\n",
      "k31=(10**6/8)*(0+1.16*4*-4)\n",
      "print'%s %.2f %s'%('k31=',k31,'')\n",
      "k33=(10**6/8.)*(0+1.16*16)\n",
      "print'%s %.2f %s'%('k33=',k33,'')\n",
      "\n",
      "kuu=numpy.matrix([[k11 ,k12, k13],[k21 ,k22 ,k23],[k31, k32, k33]])\n",
      "print(kuu)\n",
      "kuv=10**6*numpy.matrix([[2.15, -1.16, -0.99],[-0.99, 0, 0.99],[-1.16 ,1.16, 0]])\n",
      "print(kuv)\n",
      "kvv=10**6*numpy.matrix([[7.18 ,-0.58, -6.6],[-0.58, 0.58 ,0],[-6.6, 0, 6.6]])\n",
      "print(kvv)\n",
      "kvu=numpy.matrix([[2.15, -0.99, -1.16],[-1.16, 0, 1.16],[-0.99, 0.99, 0]])\n",
      "print(kvu)\n",
      "\n",
      "\n",
      "\n",
      "##solution b:\n",
      "Fx=0\n",
      "Fy=0.077 ##N/cm**2\n",
      "Qbe=[0,0,0,-0.0308,-0.0308,-0.0308]##N\n",
      "print(Qbe)\n",
      "\n",
      "\n",
      "Qp3=numpy.matrix([[0,-420,-420,0,-840,-840]])\n",
      "print('Qp3')\n",
      "\n",
      "epsilon=alpha*T\n",
      "print'%s %.2f %s'%('epsilon=',epsilon,'')\n",
      "##Qte=[B']*[D]*epsilon*At\n",
      "Qte=(1/8.)*numpy.matrix([[-2, 0, -4],[2, 0, 0],[0, 0, 4],[0, -4, -2],[0 ,0, 2],[0, 4 ,0]])*((200*10**5)/0.91)*numpy.matrix([[1, 0.3, 0,],[0.3 ,1 ,0],[0, 0 ,0.35]])*numpy.matrix([[0.0006],[0.0006],[0]])*(1.2)\n",
      "print(Qte)\n",
      "\n",
      "Qe=numpy.matrix([[-5142.85,4742.85,-400,-10285.71,-840.03,9445.67]])\n",
      "print (Qe)\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 3.33  0.99  0.  ]\n",
        " [ 0.99  3.3   0.  ]\n",
        " [ 0.    0.    1.16]]\n",
        "[[ 416250.  123750.       0.]\n",
        " [ 123750.  412500.       0.]\n",
        " [      0.       0.  145000.]]\n",
        "(-4.0, -4.0)\n",
        "(0.0, 0.0)\n",
        "(4.0, 4.0)\n",
        "(-2, -2)\n",
        "(2.0, 2.0)\n",
        "(0.0, 0.0)\n",
        "k11= 3970000.00 \n",
        "k12= -1650000.00 \n",
        "k13= -2320000.00 \n",
        "k22= 1650000.00 \n",
        "k23= 0.00 \n",
        "k32= 0.00 \n",
        "k21= -1650000.00 \n",
        "k31= -2320000.00 \n",
        "k33= 2320000.00 \n",
        "[[ 3970000. -1650000. -2320000.]\n",
        " [-1650000.  1650000.        0.]\n",
        " [-2320000.        0.  2320000.]]\n",
        "[[ 2150000. -1160000.  -990000.]\n",
        " [ -990000.        0.   990000.]\n",
        " [-1160000.  1160000.        0.]]\n",
        "[[ 7180000.  -580000. -6600000.]\n",
        " [ -580000.   580000.        0.]\n",
        " [-6600000.        0.  6600000.]]\n",
        "[[ 2.15 -0.99 -1.16]\n",
        " [-1.16  0.    1.16]\n",
        " [-0.99  0.99  0.  ]]\n",
        "[0, 0, 0, -0.0308, -0.0308, -0.0308]\n",
        "Qp3\n",
        "epsilon= 0.00 \n",
        "[[ -5142.85714286]\n",
        " [  5142.85714286]\n",
        " [     0.        ]\n",
        " [-10285.71428571]\n",
        " [     0.        ]\n",
        " [ 10285.71428571]]\n",
        "[[ -5142.85   4742.85   -400.   -10285.71   -840.03   9445.67]]\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex8-pg223"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate epsilon and sigma \n",
      "import numpy\n",
      "from numpy.linalg import inv\n",
      "t=0.3 ##cm\n",
      "E=200 ##GPa\n",
      "v=0.3\n",
      "i=2.\n",
      "j=4.\n",
      "m=3.\n",
      "L=5000. ##N\n",
      "\n",
      "a1=0-4\n",
      "a2=0-4\n",
      "print(a1,a2)\n",
      "aj=4-0\n",
      "a4=4-0\n",
      "print(aj,a4)\n",
      "am=4-4\n",
      "a3=4-4\n",
      "print(am,a3)\n",
      "\n",
      "bi=1-1\n",
      "b2=1-1\n",
      "print(bi,b2)\n",
      "bj=1+1\n",
      "b4=1+1\n",
      "print(bj,b4)\n",
      "bm=-1-1\n",
      "b3=-1-1\n",
      "print(bm,b3)\n",
      "\n",
      "k22=(10**6/8.)*(3.3*0+1.16*16)\n",
      "print'%s %.2f %s'%('k22=\\n',k22,'')\n",
      "k44=(10**6/8.)*(3.3*4*+1.16*16)\n",
      "print'%s %.2f %s'%('k44=\\n',k44,'')\n",
      "k24=(10**6/8.)*(3.3*0+1.16*4*-4)\n",
      "print'%s %.2f %s'%('k24=\\n',k24,'')\n",
      "k42=(10**6/8)*(3.3*0+1.16*4*-4)\n",
      "print'%s %.2f %s'%('k42=\\n',k42,'')\n",
      "k23=0\n",
      "print'%s %.2f %s'%('k23=\\n',k23,'')\n",
      "k32=0\n",
      "print'%s %.2f %s'%('k32=\\n',k32,'')\n",
      "k43=(10**6/8)*(3.3*2*-2+1.16*0)\n",
      "print'%s %.2f %s'%('k43=\\n',k43,'')\n",
      "k34=(10**6/8)*(3.3*2*-2+1.16*0)\n",
      "print'%s %.2f %s'%('k34=\\n',k34,'')\n",
      "k33=(10**6/8)*(3.3*4+1.16*0)\n",
      "print'%s %.2f %s'%('k33=\\n',k33,'')\n",
      "\n",
      "\n",
      "kuu=numpy.matrix([[k22, k23, k24],[k32, k33, k34,],[k42, k43, k44]])\n",
      "print(kuu)\n",
      "kuv=10**6*numpy.matrix([[0 ,1.16 ,-1.16],[0.99 ,0 ,-0.99],[-0.99, -1.16, 2.15]])\n",
      "print(kuv)\n",
      "kvv=10**6*numpy.matrix([[6.6, 0 ,-6.6],[0, 0.58, -0.58],[-6.6 ,-0.58, 7.18]])\n",
      "print(kvv)\n",
      "kvu=10**6*numpy.matrix([[0 ,0.99, -0.99],[1.16, 0, -1.16],[-1.16 ,-0.99, 2.15]])\n",
      "print(kvu)\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "k1=numpy.matrix([[3.97, -1.65, -2.32, 0],[-1.65, 1.65 ,0 ,0],[-2.32, 0, 2.32, 0],[0, 0 ,0 ,0]])\n",
      "print(k1)\n",
      "k2=numpy.matrix([[2.15, -1.16, -0.99, 0],[-0.99, 0, 0.99, 0],[-1.16, 1.16, 0, 0],[0, 0 ,0 ,0]])\n",
      "print(k2)\n",
      "k3=numpy.matrix([[2.15, -0.99 ,-1.16, 0],[-1.16, 0 ,1.16, 0],[-0.99 ,0.99, 0 ,0],[0 ,0, 0, 0]])\n",
      "print(k3)\n",
      "k4=numpy.matrix([[7.18 ,-0.58, -6.6, 0],[-0.58, 0.58, 0 ,0],[-6.6, 0, 6.6, 0],[0, 0 ,0, 0]])\n",
      "print(k4)\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "k5=numpy.matrix([[0, 0 ,0 ,0],[0 ,2.32, 0, -2.32],[0, 0, 1.65, -1.65],[0 ,-2.32, -1.65, 3.97]])\n",
      "print(k5)\n",
      "k6=numpy.matrix([[0, 0, 0 ,0],[0, 0 ,1.16, -1.16],[0, 0.99, 0 ,-0.99],[0, -0.99, -1.16, 2.15]])\n",
      "print(k6)\n",
      "k7=numpy.matrix([[0, 0 ,0 ,0],[0, 0, 0.99, -0.99],[0 ,1.16, 0, -1.16],[0, -1.16, -0.99, 2.15]])\n",
      "print(k7)\n",
      "k8=numpy.matrix([[0 ,0, 0 ,0],[0 ,6.6 ,0 ,-6.6],[0, 0 ,0.58 ,-0.58],[0 ,-6.6 ,-0.58, 7.18]])\n",
      "print(k8)\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "Qy4=((3.*(-5000.))/4.*1.)*((1./2.)*(1.+1.)+0.33*(-0.25*(1.-1.+1.)-0.75))\n",
      "print'%s %.2f %s'%('Qy4=',Qy4,'')                                 ## textbook ans is wrong\n",
      "Qy2=((3*(-5000))/4*1)*((1/2)*(1+1)-0.33*(1+0.75*(1-1+1)-0.75))\n",
      "print'%s %.2f %s'%('Qy2=',Qy2,'')                                 ## textbook ans is wrong\n",
      "\n",
      "Q=numpy.matrix([[0, 0, 0, 0 ,0 ,Qy4 ,0, Qy2]])\n",
      "print(Q)\n",
      "u1=0\n",
      "u3=0\n",
      "v1=0\n",
      "v3=0\n",
      "\n",
      "Z=numpy.matrix([[3.97, -2.32, 0, -1.16],[-2.32, 3.97, -0.99, 2.15],[0, -0.99, 7.18, -6.6],[-1.16, 2.15, -6.6, 7.18]])\n",
      "print(Z)\n",
      "z=numpy.linalg.inv(Z)\n",
      "print(z)\n",
      "X=z*numpy.matrix([[0],[0],[-2512.5],[-2512.5]]) \n",
      "print(X)\n",
      "X1= X*10**-6\n",
      "print(\"u2 u4 v2 v4 is= \",X1,\"\")\n",
      "\n",
      "Y=numpy.matrix([[-2, 2, 0, 0, 0, 0],[0, 0, 0, -4, 0, 4],[-4 ,0, 4, -2, 2, 0]])\n",
      "print(Y)\n",
      "W=Y*numpy.matrix([[0],[-0.0012],[0],[0],[-0.0068],[0]])\n",
      "print(W)\n",
      "W1=W*(1./8.)\n",
      "print(\"W1\")\n",
      "\n",
      "y=numpy.matrix([[1, 0.3, 0],[0.3, 1, 0],[0, 0, 0.35]])*W1\n",
      "print(y)\n",
      "u=(200.*10**9/0.91)\n",
      "print(u)\n",
      "U=u*y\n",
      "print(U,\"sigmax sigmay tauxy in Pa is= \")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(-4, -4)\n",
        "(4, 4)\n",
        "(0, 0)\n",
        "(0, 0)\n",
        "(2, 2)\n",
        "(-2, -2)\n",
        "k22=\n",
        " 2320000.00 \n",
        "k44=\n",
        " 30624000.00 \n",
        "k24=\n",
        " -2320000.00 \n",
        "k42=\n",
        " -2320000.00 \n",
        "k23=\n",
        " 0.00 \n",
        "k32=\n",
        " 0.00 \n",
        "k43=\n",
        " -1650000.00 \n",
        "k34=\n",
        " -1650000.00 \n",
        "k33=\n",
        " 1650000.00 \n",
        "[[  2320000.         0.  -2320000.]\n",
        " [        0.   1650000.  -1650000.]\n",
        " [ -2320000.  -1650000.  30624000.]]\n",
        "[[       0.  1160000. -1160000.]\n",
        " [  990000.        0.  -990000.]\n",
        " [ -990000. -1160000.  2150000.]]\n",
        "[[ 6600000.        0. -6600000.]\n",
        " [       0.   580000.  -580000.]\n",
        " [-6600000.  -580000.  7180000.]]\n",
        "[[       0.   990000.  -990000.]\n",
        " [ 1160000.        0. -1160000.]\n",
        " [-1160000.  -990000.  2150000.]]\n",
        "[[ 3.97 -1.65 -2.32  0.  ]\n",
        " [-1.65  1.65  0.    0.  ]\n",
        " [-2.32  0.    2.32  0.  ]\n",
        " [ 0.    0.    0.    0.  ]]\n",
        "[[ 2.15 -1.16 -0.99  0.  ]\n",
        " [-0.99  0.    0.99  0.  ]\n",
        " [-1.16  1.16  0.    0.  ]\n",
        " [ 0.    0.    0.    0.  ]]\n",
        "[[ 2.15 -0.99 -1.16  0.  ]\n",
        " [-1.16  0.    1.16  0.  ]\n",
        " [-0.99  0.99  0.    0.  ]\n",
        " [ 0.    0.    0.    0.  ]]\n",
        "[[ 7.18 -0.58 -6.6   0.  ]\n",
        " [-0.58  0.58  0.    0.  ]\n",
        " [-6.6   0.    6.6   0.  ]\n",
        " [ 0.    0.    0.    0.  ]]\n",
        "[[ 0.    0.    0.    0.  ]\n",
        " [ 0.    2.32  0.   -2.32]\n",
        " [ 0.    0.    1.65 -1.65]\n",
        " [ 0.   -2.32 -1.65  3.97]]\n",
        "[[ 0.    0.    0.    0.  ]\n",
        " [ 0.    0.    1.16 -1.16]\n",
        " [ 0.    0.99  0.   -0.99]\n",
        " [ 0.   -0.99 -1.16  2.15]]\n",
        "[[ 0.    0.    0.    0.  ]\n",
        " [ 0.    0.    0.99 -0.99]\n",
        " [ 0.    1.16  0.   -1.16]\n",
        " [ 0.   -1.16 -0.99  2.15]]\n",
        "[[ 0.    0.    0.    0.  ]\n",
        " [ 0.    6.6   0.   -6.6 ]\n",
        " [ 0.    0.    0.58 -0.58]\n",
        " [ 0.   -6.6  -0.58  7.18]]\n",
        "Qy4= -2512.50 \n",
        "Qy2= 1237.50 \n",
        "[[    0.      0.      0.      0.      0.  -2512.5     0.   1237.5]]\n",
        "[[ 3.97 -2.32  0.   -1.16]\n",
        " [-2.32  3.97 -0.99  2.15]\n",
        " [ 0.   -0.99  7.18 -6.6 ]\n",
        " [-1.16  2.15 -6.6   7.18]]\n",
        "[[ 0.42911692  0.17986034  0.25168713  0.24682604]\n",
        " [ 0.17986034  0.4831756  -0.25583582 -0.3507947 ]\n",
        " [ 0.25168713 -0.25583582  1.36613468  1.37304916]\n",
        " [ 0.24682604 -0.3507947   1.37304916  1.54633026]]\n",
        "[[-1252.51435698]\n",
        " [ 1524.15919903]\n",
        " [-6882.19940602]\n",
        " [-7334.94080944]]\n",
        "('u2 u4 v2 v4 is= ', matrix([[-0.00125251],\n",
        "        [ 0.00152416],\n",
        "        [-0.0068822 ],\n",
        "        [-0.00733494]]), '')\n",
        "[[-2  2  0  0  0  0]\n",
        " [ 0  0  0 -4  0  4]\n",
        " [-4  0  4 -2  2  0]]"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "[[-0.0024]\n",
        " [ 0.    ]\n",
        " [-0.0136]]\n",
        "W1\n",
        "[[ -3.00000000e-04]\n",
        " [ -9.00000000e-05]\n",
        " [ -5.95000000e-04]]"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "2.1978021978e+11\n",
        "(matrix([[ -6.59340659e+07],\n",
        "        [ -1.97802198e+07],\n",
        "        [ -1.30769231e+08]]), 'sigmax sigmay tauxy in Pa is= ')\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex9-pg226"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate sigma \n",
      "L=76.2 ##mm\n",
      "h=50.8 ##mm\n",
      "t=25.4 ##mm\n",
      "p=6895. ##kPa\n",
      "E=207. ##GPa\n",
      "v=0.15\n",
      "\n",
      "##solution a: exact solution\n",
      "##p=Mh/I\n",
      "##sigmax=-(y/h)*p\n",
      "sigmay=0.\n",
      "tauxy=0.\n",
      "##derivative(u,x)=-(yp/Eh)\n",
      "##derivative(v,y)=(v*y*p)/(Eh)\n",
      "##derivative(u,y)+derivative(v,x)=0\n",
      "##u=-(p/E*h)*x*y                        ## for u(0,0)=v(0,0)=0 and u(L,0)=0\n",
      "##v=-(p/2*E*h)*(x**2+v*y**2)\n",
      "##sigmax=-(1/0.0508)*(y*p)\n",
      "sigmaxmax=6895. ##kPa\n",
      "##u(0.0762,-0.0254)=25.4*10**-6 ##m\n",
      "##v(0.0762,0)=1.905*10**-6 ##m\n",
      "\n",
      "##solution b:\n",
      "Qx10=((0.0254*0.0254)/6.)*((2.*sigmaxmax)+3447.5)\n",
      "print'%s %.2f %s'%(\"in mN is= \",Qx10,\"\")\n",
      "Qx11=((0.0254*0.0254)/6.)*(2*3447.5+sigmaxmax)+((0.0254*0.0254)/6)*(2*3447.5+0.)\n",
      "print'%s %.2f %s'%(\"in mN is= \",Qx11,\"\")\n",
      "Qx12=((0.0254*0.0254)/6.)*(0+3447.5)\n",
      "print'%s %.2f %s'%(\"in mN is= \",Qx12,\"\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "in mN is=  1.85 \n",
        "in mN is=  2.22 \n",
        "in mN is=  0.37 \n"
       ]
      }
     ],
     "prompt_number": 3
    }
   ],
   "metadata": {}
  }
 ]
}