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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter 3: Elements of the Theory of Plasticity"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Example 3.1, True Stress and True Strain, Page No. 76"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "Engineering Stress at maximum load = 99852.1 psi\n",
+      "True Fracture Stress = 112785 psi\n",
+      "True Strain at fracture = 0.344939\n",
+      "Engineering strain at fracture = 0.411903\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import pi\n",
+    "from math import log\n",
+    "from math import exp\n",
+    "\n",
+    "#variable declaration\n",
+    "D_i=0.505;\n",
+    "L=2;\n",
+    "P_max=20000;\n",
+    "P_f=16000;\n",
+    "D_f=0.425;\n",
+    "\n",
+    "#calculation\n",
+    "E_St= P_max*4/(pi*D_i**2);\n",
+    "T_fr_St= P_f*4/(pi*D_f**2);\n",
+    "e_f=log(D_i**2/D_f**2);\n",
+    "e=exp(e_f)-1;\n",
+    "\n",
+    "#result\n",
+    "print('\\nEngineering Stress at maximum load = %g psi\\nTrue Fracture Stress = %g psi\\nTrue Strain at fracture = %g\\nEngineering strain at fracture = %g')%(E_St,T_fr_St,e_f,e);\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Example 3.2, Yielding Criteria for Ductile Metals, Page No. 78"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "\n",
+    "\n",
+    "from math import sqrt\n",
+    "\n",
+    "#variable declaration\n",
+    "sigma00=500;\n",
+    "sigma_z=-50;\n",
+    "sigma_y=100;\n",
+    "sigma_x=200;\n",
+    "T_xy=30;\n",
+    "T_yz=0;\n",
+    "T_xz=0;\n",
+    "\n",
+    "#calculation\n",
+    "sigma0=sqrt((sigma_x-sigma_y)**2+(sigma_y-sigma_z)**2+(sigma_z-sigma_x)**2+6*(T_xy**2+T_yz**2+T_xz**2))/sqrt(2);\n",
+    "s=sigma00/sigma0;\n",
+    "\n",
+    "#result\n",
+    "print('\\nSince the calculated value of sigma0 = %g MPa, which is less than the yield strength of the aluminium alloy\\nThus safety factor is = %g')%(sigma0,s);\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Example 3.3, Tresca Criterion, Page No. 81"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "\n",
+    "\n",
+    "#variable declaration\n",
+    "sigma00=500;\n",
+    "sigma_z=-50;\n",
+    "sigma_y=100;\n",
+    "sigma_x=200;\n",
+    "T_xy=30;\n",
+    "T_yz=0;\n",
+    "T_xz=0;\n",
+    "\n",
+    "#calculation\n",
+    "sigma0=sigma_x-sigma_z;\n",
+    "s=sigma00/sigma0;\n",
+    "\n",
+    "#result\n",
+    "print('\\nSince the calculated value of sigma0 = %g MPa, which is less than the yield strength of the aluminium alloy\\nThus safety factor is = %g')%(sigma0,s);\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "Example 3.4, Levy-Mises Equation, Page No. 91"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "Plastic Strain = 0.199532\n"
+     ]
+    }
+   ],
+   "source": [
+    "from math import sqrt\n",
+    "\n",
+    "#variable declaration\n",
+    "r_t=20;\n",
+    "p=1000;\n",
+    "\n",
+    "#calculation\n",
+    "sigma1=p*r_t;\n",
+    "sigma1=sigma1/1000;                     #conversion to ksi\n",
+    "sigma=sqrt(3)*sigma1/2;\n",
+    "e=(sigma/25)**(1/0.25);\n",
+    "e1=sqrt(3)*e/2;\n",
+    "\n",
+    "#result\n",
+    "print('\\nPlastic Strain = %g')%(e1);\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}