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+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:bc596ba82da68e58c73271eb1045592b064349244b750ab69aa9f03ab4de2fbd"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "Chapter 27: Open Section Beams\n"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 27.2 Pg.No. 735"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#reference Fig 27.20\n",
+      "\n",
+      "from __future__ import division\n",
+      "import math\n",
+      "from sympy import integrate\n",
+      "from sympy import solve, symbols\n",
+      "\n",
+      "# variable declaration\n",
+      "P=100                  #vertical load (kN)\n",
+      "A_R=1.25*10**3         #from previous question\n",
+      "E=200000               #young's modulus (N/mm^2)\n",
+      "Gama_R=2.08*10**10     #torsion bending constant (mm^6)\n",
+      "mu=0.54*10**-3        #from previous question\n",
+      "A=400*5                #area of beam\n",
+      "\n",
+      "#moment couple\n",
+      "M_Tau=-P*2*A_R\n",
+      "print \"\\nValue of moment couple at the top of column = %2.2e kN.mm^2\"%(M_Tau)  #calculation mistake in book\n",
+      "\n",
+      "d2tdz2 = M_Tau*10**3/E/Gama_R\n",
+      "# @z=3000 mm \n",
+      "D=0.04*10**-3\n",
+      "z=symbols('z')\n",
+      "F= -0.08*math.cosh(0)\n",
+      "\n",
+      "def theta(z):\n",
+      "    return 0.08*(math.cosh(0.54*10**(-3)*z))\n",
+      "\n",
+      "print \"\\ntwist at the top of the column = %2.2f rad\\n\"%(theta(3000))\n",
+      "\n",
+      "M_Tau=-E*Gama_R*0.02*10**-6\n",
+      "print \"value of moment couple at bottom of column=%2.2e N.mm^2\\n\"%(M_Tau)\n",
+      "\n",
+      "P=-100*10**3    # stress(N)\n",
+      "def sigma_z(A_R2):\n",
+      "    return P/A+M_Tau*A_R2/Gama_R\n",
+      "print \"sigma_z1=sigma_z4=%2.1f N/mm^2\\n\"%(sigma_z(-7.5*10**3))\n",
+      "print \"sigma_z2=sigma_z3=%2.1f N/mm^2\\n\"%(sigma_z(2.5*10**3))\n",
+      "\n",
+      "#please put the value of 2AR from Fig 27.21 in the equation of sigma_z\n",
+      "#these values in book need correction"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "Value of moment couple at the top of column = -2.50e+05 kN.mm^2\n",
+        "\n",
+        "twist at the top of the column = 0.21 rad\n",
+        "\n",
+        "value of moment couple at bottom of column=-8.32e+07 N.mm^2\n",
+        "\n",
+        "sigma_z1=sigma_z4=-20.0 N/mm^2\n",
+        "\n",
+        "sigma_z2=sigma_z3=-60.0 N/mm^2\n",
+        "\n"
+       ]
+      }
+     ],
+     "prompt_number": 26
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 48
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
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