{
 "metadata": {
  "name": "",
  "signature": "sha256:0f8515032ad257111ffef42eb71b2510ec7d92768034e754ca14b473e010b968"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 1. Basic Elasticity"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1, Pg. No.13"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "# variable declaration\n",
      "p = 1.5;         #pressure inside vessel (N/mm^2)\n",
      "d = 2*10**3;     #diameter of vessel (mm)\n",
      "t = 20;          #thickness of plate (mm)\n",
      "theta = 60;        #plane's inclination to axis of vessel (degree)\n",
      "load = 2500*10**3;       #axial tensile load (N)\n",
      "\n",
      "# Longitudinal stress\n",
      "sigma_x=p*d/4/t;\n",
      "print \"\\nLongitudinal stress due to internal pressure = %5.2f N/mm^2\" %(sigma_x)\n",
      "\n",
      "#circumferential stress\n",
      "sigma_y=p*d/2/t;\n",
      "print \"\\nCircumferential stress due to internal pressure =  %5.2f N/mm^2\" %(sigma_y)\n",
      "\n",
      "#axial load\n",
      "sigma_x_axial=load/(math.pi*d*t);\n",
      "print \"\\ndirect stress due to axial load = %5.2f N/mm^2\"%(sigma_x_axial)\n",
      "\n",
      "sigma_x=sigma_x+sigma_x_axial;                #total longitudinal stress\n",
      "\n",
      "#direct stress and shear stress on inclined plane AB\n",
      "#reference Fig 1.9 pg no14, equation 1.8,1.9 pg no 13\n",
      "\n",
      "sigma_n=sigma_x*math.pow(math.cos(math.radians(90-theta)),2)+sigma_y*math.pow(math.sin(math.radians(90-theta)),2)\n",
      "print \"\\ndirect stress on inclined plane AB = %5.2f N/mm^2\"%(sigma_n)\n",
      "\n",
      "tau=(sigma_x-sigma_y)/2*math.sin(math.radians(2*(90-theta)))\n",
      "print \"\\nshear stress on plane AB = %5.2f N/mm^2\"%(tau)\n",
      "\n",
      "#maximumm shear stress (theta=45 degree)\n",
      "theta=45\n",
      "tau=(sigma_x-sigma_y)/2*math.sin(math.radians(2*(90-theta)))\n",
      "print \"\\nmaximum shear stress on plane AB = %5.2f N/mm^2\"%(tau)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Longitudinal stress due to internal pressure = 37.50 N/mm^2\n",
        "\n",
        "Circumferential stress due to internal pressure =  75.00 N/mm^2\n",
        "\n",
        "direct stress due to axial load = 19.89 N/mm^2\n",
        "\n",
        "direct stress on inclined plane AB = 61.80 N/mm^2\n",
        "\n",
        "shear stress on plane AB = -7.62 N/mm^2\n",
        "\n",
        "maximum shear stress on plane AB = -8.80 N/mm^2\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.2, Pg. No.14"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#variable declaration\n",
      "load=50*10**3         #axial load (N)\n",
      "d=60                   #diameter (mm)\n",
      "t=1.5                  #offset distance from center (mm)\n",
      "T=1200*10**3                 #torque applied on a point (N.mm)\n",
      "theta=60               #angle made by plane wrt axis of cylinder(degree)\n",
      "\n",
      "#compressive stress due to axial load\n",
      "area=math.pi*math.pow(d/2,2)        #cross section area\n",
      "sigma_x_a=load/area\n",
      "print \"\\ncompressive stress due to axial load = %5.1f N/mm^2\"%sigma_x_a\n",
      "\n",
      "#compressive stress due to bending moment\n",
      "#area moment of inertia\n",
      "M=load*t\n",
      "I=math.pi*d**4/64\n",
      "\n",
      "sigma_x_b=M*d/2*(1/I)\n",
      "print \"\\ncompressive stress due to bending moment = %5.1f N/mm^2\" %sigma_x_b\n",
      "\n",
      "#total compressive stress\n",
      "sigma_x=sigma_x_a+sigma_x_b\n",
      "\n",
      "#shear stress due to torque Ref example 3.1 equation (iv) pg no 73\n",
      "# tau=Tr/J\n",
      "J=math.pi*d**4/32    #torsion constant\n",
      "tau_xy=T*d/2/J\n",
      "print \"\\nshear stress due to torque = %5.1f N/mm^2\" %tau_xy\n",
      "\n",
      "#direct and shear on inclined plane, ref eq 1.8,1.9\n",
      "sigma_y=0\n",
      "sigma_n=-sigma_x*math.pow(math.cos(math.radians(90-theta)),2)-tau_xy*math.sin(math.radians(2*(90-theta)))\n",
      "print \"\\ndirect stress on inclined plane = %3.1f N/mm^2\"%sigma_n\n",
      "\n",
      "tau=-sigma_x/2*math.sin(math.radians(2*(90-theta)))+tau_xy*math.cos(math.radians(2*(90-theta)))\n",
      "print \"\\nshear stress on inclined plane = %3.1f N/mm^2\"%tau\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "compressive stress due to axial load =  17.7 N/mm^2\n",
        "\n",
        "compressive stress due to bending moment =   3.5 N/mm^2\n",
        "\n",
        "shear stress due to torque =  28.3 N/mm^2\n",
        "\n",
        "direct stress on inclined plane = -40.4 N/mm^2\n",
        "\n",
        "shear stress on inclined plane = 5.0 N/mm^2\n"
       ]
      }
     ],
     "prompt_number": 95
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.3, Pg. No.20"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import numpy\n",
      "import math\n",
      "#import matplotlib\n",
      "%pylab inline\n",
      "#from pylab import *          #change comment to above line to see undocked graph, all values will be visible as mouse-pointer moves\n",
      "#variable declaration\n",
      "sigma_x=160          #stress in x direction (N/mm^2)\n",
      "sigma_y=-120          #stress in y direction (N/mm^2)\n",
      "sigma=200             #stress on inclined plane (N/mm^2)\n",
      "\n",
      "tau_xy=((sigma-sigma_x)*(sigma-sigma_y))**0.5\n",
      "print \"\\nallowable shear stress, tau_xy = %4.1f N/mm^2 \"%tau_xy\n",
      "\n",
      "coeff=[1,-(sigma_x+sigma_y),sigma_x*sigma_y-tau_xy**2]\n",
      "sigma=numpy.roots(coeff)\n",
      "print \"\\nprincipal stresses, sigma_I = %3.0f N/mm^2  sigma_II = %3.0f N/mm^2\"%(sigma[0],sigma[1])\n",
      "\n",
      "tau_max=(abs(sigma[0])+abs(sigma[1]))/2\n",
      "print \"\\nmaximum shear stress, tau_max = %3.0f N/mm^2\"%tau_max\n",
      "\n",
      "#plotting Mohr circle\n",
      "x_cent=(sigma_x+sigma_y)/2\n",
      "y_cent=0\n",
      "\n",
      "X1=(sigma_x,tau_xy)\n",
      "X2=(sigma_y,-tau_xy)\n",
      "\n",
      "radius=(math.hypot(X2[0]-X1[0], X2[1] - X1[1]))/2\n",
      "\n",
      "cir=linspace(0,2*pi,100)\n",
      "plot(radius*cos(cir)+x_cent,radius*sin(cir)+y_cent,'r')\n",
      "plot(sigma_x,tau_xy,'ro',sigma_y,-tau_xy,'ro',x_cent,y_cent,'b+',sigma[0],0,'bo',sigma[1],0,'bo',20,tau_max,'go')\n",
      "text(sigma_x+10,tau_xy,'Q1')\n",
      "text(sigma_y+10,-tau_xy,'Q2')\n",
      "text(20,tau_max+10,r'$\\tau_{max}$')\n",
      "text(-150,0,r'$\\sigma_2$')\n",
      "text(200,10,r'$\\sigma_1$')\n",
      "text(-20,+10,'O')\n",
      "text(30,-20,'C')\n",
      "#plot([sigma_y,tau_xy],[sigma_x,-tau_xy],'r-')\n",
      "xlabel(r'$\\sigma$')\n",
      "ylabel(r'$\\tau$')\n",
      "title('Mohr Cirle')\n",
      "axis('equal')\n",
      "grid(True)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n",
        "\n",
        "allowable shear stress, tau_xy = 113.1 N/mm^2 \n",
        "\n",
        "principal stresses, sigma_I = 200 N/mm^2  sigma_II = -160 N/mm^2\n",
        "\n",
        "maximum shear stress, tau_max = 180 N/mm^2\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEZCAYAAAC99aPhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nxZVZr61+AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa137240>"
       ]
      }
     ],
     "prompt_number": 141
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.4, Pg. No.33"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#variable declaration\n",
      "sigma_x=83       # stress in x direction (N/mm^2)\n",
      "sigma_y=65       # stress in y direction (N/mm^2)\n",
      "E=200000         # Young's Modulus (N/mm^2)\n",
      "v=0.3           # poisson's ratio\n",
      "\n",
      "# strains in x,y and z directions\n",
      "epsln_x=1.0/E*(sigma_x-v*sigma_y)\n",
      "epsln_y=1.0/E*(sigma_y-v*sigma_x)\n",
      "epsln_z=-v/E*(sigma_x+sigma_y)\n",
      "print \"\\nstrain in x direction, epsln_x = %5.3e\"%epsln_x\n",
      "print \"\\nstrain in y direction, epsln_y = %5.3e\"%epsln_y\n",
      "print \"\\nstrain in z direction, epsln_z = %5.3e\"%epsln_z\n",
      "\n",
      "tau_max=(sigma_x-sigma_y)/2\n",
      "print \"\\nmaximum shear stress, tau_max = %2.2f N/mm^2\"%tau_max\n",
      "\n",
      "gama_max=2*(1+v)*tau_max/E\n",
      "print \"\\nmaximum shear strain, y_max = %2.2e \" %gama_max"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "strain in x direction, epsln_x = 3.175e-04\n",
        "\n",
        "strain in y direction, epsln_y = 2.005e-04\n",
        "\n",
        "strain in z direction, epsln_z = -2.220e-04\n",
        "\n",
        "maximum shear stress, tau_max = 9.00 N/mm^2\n",
        "\n",
        "maximum shear strain, y_max = 1.17e-04 \n"
       ]
      }
     ],
     "prompt_number": 111
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.5, Pg. No.33"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#import matplotlib.pyplot as plt\n",
      "%pylab inline\n",
      "#variable declaration\n",
      "sigma_x=60            #stress in x direction (N/mm^2)\n",
      "sigma_y=-40           #stress in y direction (N/mm^2)\n",
      "tau_xy=50             #shear stress (N/mm^2)\n",
      "E=2*10**5             #Young's Modulus (N/mm^2)\n",
      "v=0.3                #poisson's ratio\n",
      "\n",
      "#strains in x and y direction\n",
      "epsln_x=1.0/E*(sigma_x-v*sigma_y)\n",
      "epsln_y=1.0/E*(sigma_y-v*sigma_x)\n",
      "print \"\\nstrains in x and y directions, epsi_x =%4.1e  epsi_y =%4.1e \"%(epsln_x,epsln_y)     \n",
      "\n",
      "G=E/2/(1+v)\n",
      "print \"\\nshear modulus, G = %6.1f\"%G\n",
      "\n",
      "gama_xy=tau_xy/G\n",
      "print \"\\nshear strain, gama_xy = %4.1e\"%gama_xy\n",
      "\n",
      "#principal strains\n",
      "epsln_I=(epsln_x+epsln_y)/2+1.0/2*((epsln_x-epsln_y)**2+gama_xy**2)**0.5\n",
      "epsln_II=(epsln_x+epsln_y)/2-1.0/2*((epsln_x-epsln_y)**2+gama_xy**2)**0.5\n",
      "print \"\\nprincipal strains, epsln_I = %4.2e  epsln_II = %4.2e\"%(epsln_I,epsln_II)\n",
      "\n",
      "#inclination\n",
      "theta=1.0/2*math.atan(gama_xy/(epsln_x-epsln_y))\n",
      "print \"\\ninclination to the plane on which sigma_x acts, theta = %4.1f or %4.1f\"%(theta*180/math.pi,theta*180/math.pi+90)\n",
      "\n",
      "#plotting Mohr circle\n",
      "x_cent=(epsln_x+epsln_y)/2\n",
      "y_cent=0\n",
      "\n",
      "X1=(epsln_x,gama_xy/2)\n",
      "X2=(epsln_y,-gama_xy/2)\n",
      "\n",
      "radius=(math.hypot(X2[0]-X1[0], X2[1] - X1[1]))/2\n",
      "print radius\n",
      "cir=linspace(0,2*pi,100)\n",
      "plot(radius*cos(cir)+x_cent,radius*sin(cir),'r')\n",
      "plot(epsln_x,gama_xy/2,'ro',epsln_y,-gama_xy/2,'ro',x_cent,y_cent,'b+',epsln_II,0,'go',epsln_I,0,'go')\n",
      "text(epsln_x,gama_xy/2,'Q1')\n",
      "text(epsln_y,-gama_xy/2,'Q2')\n",
      "text(-0.00050,0,r'$\\epsilon_2$')\n",
      "text(.00050,0,r'$\\epsilon_1$')\n",
      "text(-.000060,0.00002,'O')\n",
      "text(0,0,'C')\n",
      "xlabel(r'$\\epsilon$')\n",
      "ylabel(r'$\\gamma$')\n",
      "title('Mohr Cirle')\n",
      "axis('equal')\n",
      "grid(True)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n",
        "\n",
        "strains in x and y directions, epsi_x =3.6e-04  epsi_y =-2.9e-04 \n",
        "\n",
        "shear modulus, G = 76923.1\n",
        "\n",
        "shear strain, gama_xy = 6.5e-04\n",
        "\n",
        "principal strains, epsln_I = 4.95e-04  epsln_II = -4.25e-04\n",
        "\n",
        "inclination to the plane on which sigma_x acts, theta = 22.5 or 112.5\n",
        "0.000459619407771\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZoAAAEZCAYAAACuIuMVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xcc10a20>"
       ]
      }
     ],
     "prompt_number": 185
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.7, Pg. No.40"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#variable declaration\n",
      "epsln_a=1000*10**(-6)     #readings of strain gauges \n",
      "epsln_b=-200*10**(-6)     #straing gauges 'a'  and 'c' are\n",
      "epsln_c=-300*10**(-6)     #in line and perpendicular to axis of bar\n",
      "d=50                      #diameter of bar (mm)\n",
      "E=70000                   #Young's modulus (N/mm^2)\n",
      "v=0.3                     #poisson's ratio\n",
      "\n",
      "#principal strains\n",
      "epsln_I=1.0/2*(epsln_a+epsln_c)+(1.0/2**0.5)*((epsln_a-epsln_b)**2+(epsln_c-epsln_b)**2)**0.5\n",
      "epsln_II=1.0/2*(epsln_a+epsln_c)-(1.0/2**0.5)*((epsln_a-epsln_b)**2+(epsln_c-epsln_b)**2)**0.5\n",
      "print \"\\nfirst principal strain, epsln_I = %4.3e\"%epsln_I\n",
      "print \"\\nsecond principal strain, epsln_II = %4.3e\"%epsln_II\n",
      "\n",
      "#principal stresses\n",
      "sigma_I=E/(1-v**2)*(epsln_I+v*epsln_II)\n",
      "sigma_II=E/(1-v**2)*(v*epsln_I+epsln_II)\n",
      "print \"\\nfirst principal stress, sigma_I= %4.1f N/mm^2\"%sigma_I #mistake in book\n",
      "print \"\\nsecond principal stress, sigma_II= %4.1f N/mm^2\"%sigma_II\n",
      "\n",
      "sigma_x=sigma_I+sigma_II\n",
      "print \"\\nstress in x direction,sigma_x = %4.1f N/mm^2\"%sigma_x\n",
      "\n",
      "#axial tensile load calculation\n",
      "A=math.pi*d**2/4\n",
      "P=sigma_x*A\n",
      "print \"\\naxial load, P = %4.1f kN\"%(P/1000)\n",
      "\n",
      "tau_xy=1.0/2*((sigma_x/2-sigma_II)**2*4-sigma_x**2)**0.5\n",
      "print \"\\nshear stress, tau_xy = %4.1f N/mm^2\"%tau_xy\n",
      "\n",
      "#torque calculation\n",
      "J=math.pi*d**4/32\n",
      "T=tau_xy*J/d*2\n",
      "print \"\\ntorque applied on circular bar, T = %4.1f kNm\"%(T/10**6)\n",
      "\n",
      "sigma_x=E*epsln_a\n",
      "print \"\\naxial stress from classical stress strain relationship, sigma_x =%4.0f N/mm^2\"%sigma_x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "first principal strain, epsln_I = 1.201e-03\n",
        "\n",
        "second principal strain, epsln_II = -5.015e-04\n",
        "\n",
        "first principal stress, sigma_I= 80.8 N/mm^2\n",
        "\n",
        "second principal stress, sigma_II= -10.8 N/mm^2\n",
        "\n",
        "stress in x direction,sigma_x = 70.0 N/mm^2\n",
        "\n",
        "axial load, P = 137.4 kN\n",
        "\n",
        "shear stress, tau_xy = 29.6 N/mm^2\n",
        "\n",
        "torque applied on circular bar, T =  0.7 kNm\n",
        "\n",
        "axial stress from classical stress strain relationship, sigma_x =  70 N/mm^2\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}