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-{

- "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": {}

-  }

- ]

-}
\ No newline at end of file