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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter5-Bending of Beams"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex1-pg128"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate meter and sigma \n",
      "Mz=11000. ##Nm\n",
      "A1=0.13*0.02 ##m\n",
      "A2=0.15*0.02 ##m\n",
      "z1=0.01 ##m\n",
      "z2=0.075 ##m\n",
      "yA=0.043 ##m\n",
      "zA=-0.106 ##m\n",
      "yB=-0.063 ##m\n",
      "zB=0.\n",
      "\n",
      "##location of the centroid\n",
      "z=(A1*z1+A2*z2)/(A1+A2)\n",
      "print'%s %.2f %s'%(\"in meter is= \",z,\"\")\n",
      "\n",
      "Iz=(0.02*(0.13)**3)/12.+ (0.13*0.02*(0.04)**2)+(0.15*(0.02)**3.)/12.+ (0.15*0.02*(0.035)**2.)\n",
      "print'%s %.5f %s'%(\"Iz in meter^4 is= \",Iz,\"\")\n",
      "Iy=(0.02*(0.13)**3)/12.+ (0.13*0.02*(0.04)**2)+(0.15*(0.02)**3)/.12+ (0.15*0.02*(0.035)**2.)\n",
      "print'%s %.5f %s'%(\"Iy in meter^4 is= \",Iy,\"\")\n",
      "Iyz=0+A1*0.04*(-0.035)+0+A2*(-0.035)*0.03\n",
      "print'%s %.2f %s'%(\"Iyz in meter^4 is= \",Iyz,\"\")\n",
      "##thetap=(atand((-2*Iyz)/(Iz-Iy)))/2\n",
      "##print'%s %.2f %s'%(thetap)\n",
      "I1=(Iz+math.sqrt(0.+(6.79*10**-6)**2.))\n",
      "print'%s %.5f %s'%(\"I1 in meter^4 is= \",I1,\"\")\n",
      "I2=(Iz-math.sqrt(0+(6.79*10**-6)**2))\n",
      "print'%s %.6f %s'%(\"I2 in meter^4 is= \",I2,\"\")\n",
      "My1=11000.*math.sin(45/57.3)\n",
      "print'%s %.2f %s'%(\"My1 in Nm is\",My1,\"\")\n",
      "Mz1=11000*math.sin(45/57.3)\n",
      "print'%s %.2f %s'%(\"Mz1 in Nm is\",Mz1,\"\")\n",
      "\n",
      "sigmaxA=((My1*(zA))/I1)-((Mz1*yA)/I2)\n",
      "print'%s %.2f %s'%(\"sigmaxA in MPa is\",sigmaxA,\"\")\n",
      "sigmaxB=0-((My1*yB)/I2)\n",
      "print'%s %.2f %s'%(\"sigmaxB in MPa is\",sigmaxB,\"\")\n",
      "\n",
      "My=0.\n",
      "y=((Mz*Iyz)*z)/(Mz*Iy) ##.......equal to z=-1.71y\n",
      "print'%s %.3f %s'%(\"y\",y,\"\")\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "in meter is=  0.04 \n",
        "Iz in meter^4 is=  0.00001 \n",
        "Iy in meter^4 is=  0.00002 \n",
        "Iyz in meter^4 is=  -0.00 \n",
        "I1 in meter^4 is=  0.00002 \n",
        "I2 in meter^4 is=  0.000005 \n",
        "My1 in Nm is 7777.72 \n",
        "Mz1 in Nm is 7777.72 \n",
        "sigmaxA in MPa is -114417761.50 \n",
        "sigmaxB in MPa is 101941050.82 \n",
        "y -0.014 \n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex4-144"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate the distance \n",
      "import scipy\n",
      "from scipy import integrate\n",
      "t=1.25 ##mm\n",
      "y=15.87 ##mm\n",
      "z=5.28 ##mm\n",
      "Iy=4765.62 ##mm**4\n",
      "Iz=21054.69 ##mm**4\n",
      "Iyz=3984.37 ##mm**4\n",
      "thetap=13.05 ##degree\n",
      "Iy1=3828.12 ##mm**4\n",
      "Iz1=21953.12##mm**4\n",
      "s=12.5\n",
      "\n",
      "##tau=(Vy/Iz1*t)*s*t(19.55+s*asind(13.05)/2)....equation 1\n",
      "##F1=integrate((tau*t)ds)\n",
      "def fun(s):\n",
      "\ty=(0)\n",
      "\treturn y\n",
      "x=scipy.integrate.quad(fun,0,1)\n",
      "x=x[0]\n",
      "##F1=0.0912*Vy1                   substituting the value of tau we get F1\n",
      "##Vy1*ez1=37.5*F1                 substituting the value of F1 we get ez1\n",
      "ez1=37.5*0.0912\n",
      "print'%s %.2f %s'%(\"the distance in mm is= \",ez1,\"\")\n",
      "\n",
      "##tau=(Vz1/Iy1*t)*s*t(12.05-s*asind(13.05)/2)....equation 2\n",
      "##F1=integrate((tau*t)ds)\n",
      "def fun(s):\n",
      "\ty=(0)\n",
      "\treturn y\n",
      "x=scipy.integrate.quad(fun,0,1)\n",
      "x=x[0]\n",
      "\n",
      "##F1=0.204*Vz1                   substituting the value of tau we get F1\n",
      "##Vz1*ey1=37.5*F1                 substituting the value of F1 we get ez1\n",
      "ey1=37.5*0.204\n",
      "print'%s %.2f %s'%(\"the distance in mm is= \",ey1,\"\")\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the distance in mm is=  3.42 \n",
        "the distance in mm is=  7.65 \n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex5-pg154"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate stress and meter\n",
      "import scipy\n",
      "from scipy import integrate\n",
      "P=70. ##kN\n",
      "c=0.05##m\n",
      "c1=c\n",
      "c2=c\n",
      "R=0.1+0.05\n",
      "A=0.005\n",
      "\n",
      "##m=(-1/(2*c))*integrate((y/R+y)dy)\n",
      "def fun(c):\n",
      "\ty=(-c)\n",
      "\treturn y\n",
      "\n",
      "x=scipy.integrate.quad(fun,0,1)\n",
      "m=-1.+(R/2.*c)*math.log((R+c)/(R-c))\n",
      "print'%s %.2f %s'%(\"m\",m,\"\")\n",
      "##m=(-1/(2*c))*integrate((y/R)-(y**2/R**2)+(y**3/R**3)-(y**4/R**4)+.....)dy)\n",
      "m=-1+(3/2.)*math.log(2.)\n",
      "print'%s %.3f %s'%(\"m\",m,\"\")\n",
      "\n",
      "M=P*R\n",
      "print'%s %.2f %s'%(\"M\",M,\"\")\n",
      "sigmatheta1=(-P*c2)/(m*A*(R-c1))\n",
      "print'%s %.2f %s'%(\"stress in Pa is= \",sigmatheta1,\"\")\n",
      "sigmatheta2=(P*c2)/(m*A*(R+c2))\n",
      "print'%s %.2f %s'%(\"stress in Pa is= \",sigmatheta2,\"\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "m -1.00 \n",
        "m 0.040 \n",
        "M 10.50 \n",
        "stress in Pa is=  -176230.22 \n",
        "stress in Pa is=  88115.11 \n"
       ]
      }
     ],
     "prompt_number": 1
    }
   ],
   "metadata": {}
  }
 ]
}