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"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"
]
},
{
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"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
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}
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