{
 "metadata": {
  "name": "",
  "signature": "sha256:e953f526db565d7aa504d8011697e642d2061a58d6ef5161bb85dc3f3417f791"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter2-Strain and stress -strain relations"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex1-pg38"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate radius of circle and principal stresses and distance between o and c and strain and shear strain and maxi shear stress\n",
      "radius=((math.sqrt(195**2.+130**2.))*10**(-6.));\n",
      "print'%s %.5f %s'%(\"radius of the circle in degree = \",radius,\"\")\n",
      "theta1=(math.atan(130./195.))*57.3\n",
      "print'%s %.2f %s'%(\"pricipal stresses in degree\",theta1,\"\");## print'%s %.2f %s'%laying result\n",
      "epsilonx=510.*10**(-6.)\n",
      "epsilony=120.*10**(-6.)\n",
      "epsilon=(epsilonx+epsilony)/2.\n",
      "print'%s %.5f %s'%(\"distance between O and c=\",epsilon,\"\")\n",
      "\n",
      "##solution a\n",
      "angle=60.- theta1\n",
      "print'%s %.2f %s'%(\"angle of ACA1 in degree = \",angle,\"\")## print'%s %.2f %s'%laying result\n",
      "epsilonx1=epsilon+radius*math.cos(26.3/57.3)\n",
      "print'%s %.5f %s'%(\"strains in x axis= \",epsilonx1,\"\")## print'%s %.2f %s'%laying result\n",
      "epsilony1=epsilon-radius*math.cos(26.3/57.3)\n",
      "print'%s %.5f %s'%(\"strains in y axis= \",epsilony1,\"\")## print'%s %.2f %s'%laying result\n",
      "gammaxy=-2*(radius*math.sin(26.3/57.3))\n",
      "print'%s %.5f %s'%(\"shear strain\",gammaxy,\"\")## print'%s %.2f %s'%laying result\n",
      "\n",
      "##solution b\n",
      "epsilon1=epsilon+radius\n",
      "print'%s %.5f %s'%(\"strains in x axis= \",epsilon1,\"\")## print'%s %.2f %s'%laying result\n",
      "epsilon2=epsilon-radius\n",
      "print'%s %.5f %s'%(\"strains in x axis= \",epsilon2,\"\")## print'%s %.2f %s'%laying result\n",
      "\n",
      "##solution c\n",
      "gammamax=-+468*10**(-6)\n",
      "print'%s %.5f %s'%(\"maxi shear stress= \",gammamax,\"\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "radius of the circle in degree =  0.00023 \n",
        "pricipal stresses in degree 33.69 \n",
        "distance between O and c= 0.00031 \n",
        "angle of ACA1 in degree =  26.31 \n",
        "strains in x axis=  0.00053 \n",
        "strains in y axis=  0.00010 \n",
        "shear strain -0.00021 \n",
        "strains in x axis=  0.00055 \n",
        "strains in x axis=  0.00008 \n",
        "maxi shear stress=  -0.00047 \n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex2-pg46"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate value of epsilon and gamma\n",
      "epsilon0=190.*10**(-6)\n",
      "epsilon60=200.*10**(-6)\n",
      "epsilon120=-300.*10**(-6)\n",
      "E=200.## GPa\n",
      "v=0.3\n",
      "epsilonx=epsilon0\n",
      "print'%s %.4f %s'%(\"value of epsilonx is= \",epsilonx,\"\")\n",
      "\n",
      "## epsilon60=((epsilonx+epsilony)/2)-((epsilonx-epsilony)/4)+(gammaxy*sqrt(3))/4 eqn 1\n",
      "## epsilon120=((epsilonx+epsilony)/2)-((epsilonx-epsilony)/4)-(gammaxy*sqrt(3))/4 eqn 2\n",
      "\n",
      "epsilony=(2.*(epsilon60+epsilon120)-epsilon0)/3.\n",
      "print'%s %.4f %s'%(\"value of epsilony is= \",epsilony,\"\")\n",
      "gammaxy=(2./math.sqrt(3.))*(epsilon60-epsilon120)## from eqn 1 and eqn 2\n",
      "print'%s %.5f %s'%(\"value of gammaxy is= \",gammaxy,\"\")\n",
      "epsilon1=((epsilonx+epsilony)/2.)+math.sqrt(((epsilonx-epsilony)/2.)**2.+(gammaxy/2.)**2.)## epsilony value is in negative so the sign changes in the eqn\n",
      "print'%s %.5f %s'%(\"value of epsilon1 is= \",epsilon1,\"\")\n",
      "epsilon2=((epsilonx+epsilony)/2.)-math.sqrt(((epsilonx-epsilony)/2.)**2+(gammaxy/2.)**2.)##epsilony value is in negative so the sign changes in the eqn\n",
      "print'%s %.4f %s'%(\"value of epsilon2 is= \",epsilon2,\"\")\n",
      "\n",
      "gammamax=(2.*10**-6)*math.sqrt(((epsilonx-epsilony)/2.)**2.+(gammaxy/2.)**2)\n",
      "print'%s %.3e %s'%(\"max shear strain is= \",gammamax,\"\")\n",
      "thetap=math.atan((577./320.)/2.)*57.3\n",
      "print'%s %.2f %s'%(\"orientations of principal axes is= \",thetap,\"\") ## or\n",
      "thetap1=math.atan((577./320.)*2.)*57.\n",
      "print'%s %.2f %s'%(\"orientations of principal axes is= \",thetap1,\"\")\n",
      "sigma1=(200.*10**9/(1.-0.09))*(epsilon1+0.3*epsilon2)\n",
      "print'%s %.2f %s'%(\"plane stresss is Pa= \",sigma1,\"\")\n",
      "sigma2=(200*10**3/(1-0.09))*(epsilon2+0.3*epsilon1)\n",
      "print'%s %.2f %s'%(\"plane stresss is MPa= \",sigma2,\"\")\n",
      "\n",
      "taumax=(200.*10**9./(2.*(1.+0.3)))*gammamax\n",
      "print'%s %.2f %s'%(\"plane stresss is MPa= \",taumax,\"\")\n",
      "#error in orientationd of principal axes because of round off error \n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "value of epsilonx is=  0.0002 \n",
        "value of epsilony is=  -0.0001 \n",
        "value of gammaxy is=  0.00058 \n",
        "value of epsilon1 is=  0.00036 \n",
        "value of epsilon2 is=  -0.0003 \n",
        "max shear strain is=  6.601e-10 \n",
        "orientations of principal axes is=  42.04 \n",
        "orientations of principal axes is=  74.12 \n",
        "plane stresss is Pa=  59348428.75 \n",
        "plane stresss is MPa=  -42.21 \n",
        "plane stresss is MPa=  50.78 \n"
       ]
      }
     ],
     "prompt_number": 3
    }
   ],
   "metadata": {}
  }
 ]
}