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| author | hardythe1 | 2015-04-07 15:58:05 +0530 |
|---|---|---|
| committer | hardythe1 | 2015-04-07 15:58:05 +0530 |
| commit | 92cca121f959c6616e3da431c1e2d23c4fa5e886 (patch) | |
| tree | 205e68d0ce598ac5caca7de839a2934d746cce86 /Aircraft_Structures_for_Engineering_Students/Chapter18.ipynb | |
| parent | b14c13fcc6bb6d01c468805d612acb353ec168ac (diff) | |
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diff --git a/Aircraft_Structures_for_Engineering_Students/Chapter18.ipynb b/Aircraft_Structures_for_Engineering_Students/Chapter18.ipynb new file mode 100755 index 00000000..b0550214 --- /dev/null +++ b/Aircraft_Structures_for_Engineering_Students/Chapter18.ipynb @@ -0,0 +1,155 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:a16e0822e0e7167e54e1f4ffc425aa7247562532992f7dee46fc87221365735a"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 18: Torsion of Beams"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.1 Pg.No.527"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "r=100 #radius of cylinder (mm)\n",
+ "l=2*10**3 #length of cylinder (mm)\n",
+ "torque=30*10**6 #torque at mid point (N.mm)\n",
+ "Tmax=15*10**6 \n",
+ "Tau_max=200 #max shear stress (N/mm^2)\n",
+ "G=25000 #shear modulus (N/mm^2)\n",
+ "theta =2 # rotation at mid point (degree)\n",
+ "\n",
+ "#ref equation 18.1 T=2Aq\n",
+ "tmin1=Tmax/(2*math.pi*r**2*Tau_max)\n",
+ "print \"\\nminimum thickness of beam due to stress limited to 200N/mm^2 = %3.1f mm\"%(tmin1)\n",
+ "\n",
+ "z=1*10**3 # twist at mid point (mm)\n",
+ "#equation 18.4 after integration\n",
+ "tmin2=Tmax*200*math.pi*z/(4*(math.pi*r**2)**2*G*theta*math.pi/180)\n",
+ "print \"\\nminimum thickness due to constraint on maximum angle twist = %3.1f mm\"%(tmin2)\n",
+ "t=max(tmin1,tmin2)\n",
+ "print \"\\nthickness which satisfies both conditions = %3.1f mm\"%(t)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "minimum thickness of beam due to stress limited to 200N/mm^2 = 1.2 mm\n",
+ "\n",
+ "minimum thickness due to constraint on maximum angle twist = 2.7 mm\n",
+ "\n",
+ "thickness which satisfies both conditions = 2.7 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 18.3 Pg.No 540"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#reference Fig 18.12\n",
+ "from __future__ import division\n",
+ "import math\n",
+ "from sympy import symbols\n",
+ "from sympy import integrate\n",
+ "\n",
+ "S1,S2,S3=symbols('S1,S2,S3')\n",
+ "\n",
+ "#variable declaration\n",
+ "s1=50 #length of channel (mm)\n",
+ "s2=25 #width of channel (mm)\n",
+ "t1=2.5 #thickness of web(mm)\n",
+ "t2=1.5 #thickness of flange(mm)\n",
+ "T=10*10**3 #torque applied (N.mm)\n",
+ "zeta_s=8.04 \n",
+ "G=25000 #shear modulus (N/mm^2)\n",
+ "\n",
+ "#J=Sum(st^3/3)\n",
+ "J=1/3*(s1*t1**3+2*s2*t2**3)\n",
+ "tau_max=t1*T/J\n",
+ "print \"maximum shear stress = %3.1f N/mm^2\"%(tau_max)\n",
+ "\n",
+ "#in region O2\n",
+ "s1=25\n",
+ "ARf=1/2*zeta_s*s1\n",
+ "ws=-2*ARf*T/(G*J)\n",
+ "print \"warping in O2 region is linear = %3.2f mm\"%(ws)\n",
+ "\n",
+ "#in the wall 21\n",
+ "AR=1/2*zeta_s*s2-0.5*25*s2\n",
+ "w21=-0.03*(zeta_s-s2)\n",
+ "s1=50\n",
+ "tds=2*s2*t2+s1*t1\n",
+ "\n",
+ "A12=25/2*S1\n",
+ "A23=312.5-4.02*S2\n",
+ "A34=111.5+25/2*S3\n",
+ "AR1=1/2*(integrate(A12,(S1,0,25))+integrate(5*(A23),(S2,0,50))+integrate(3*A34,(S3,0,25)))/200\n",
+ "\n",
+ "#equation 18.20\n",
+ "ws=-2*ARf*T/G/J\n",
+ "print \"warping distribution in flange 34 = %1.2f \\n\"%(ws)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "maximum shear stress = 78.9 N/mm^2\n",
+ "warping in O2 region is linear = -0.25 mm\n",
+ "warping distribution in flange 34 = -0.25 \n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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