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authorThomas Stephen Lee2015-09-04 22:04:10 +0530
committerThomas Stephen Lee2015-09-04 22:04:10 +0530
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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": {}
- }
- ]
-} \ No newline at end of file