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+{

+ "metadata": {

+  "name": "",

+  "signature": "sha256:a847652c7729f38097f73bfa8bb0c1fa136b92fa8a1c23926acab13f8bc56911"

+ },

+ "nbformat": 3,

+ "nbformat_minor": 0,

+ "worksheets": [

+  {

+   "cells": [

+    {

+     "cell_type": "heading",

+     "level": 1,

+     "metadata": {},

+     "source": [

+      "Chapter 2:Elastic Constants"

+     ]

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Problem 2.1,page no.60"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "from __future__ import division\n",

+      "import math\n",

+      "\n",

+      "#Given\n",

+      "#Variable declaration\n",

+      "L=4*(10**3)       #Length of the bar in mm\n",

+      "b=30              #Breadth of the bar in mm\n",

+      "t=20              #Thickness of the bar in mm\n",

+      "P=30*(10**3)      #Axial pull in N\n",

+      "E=2e5             #Young's modulus in N/sq.mm\n",

+      "mu=0.3            #Poisson's ratio\n",

+      "\n",

+      "#Calculation\n",

+      "A=b*t                        #Area of cross-section in sq.mm\n",

+      "long_strain=P/(A*E)          #Longitudinal strain \n",

+      "delL=long_strain*L           #Change in length in mm\n",

+      "lat_strain=mu*long_strain    #Lateral strain\n",

+      "delb=b*lat_strain            #Change in breadth in mm\n",

+      "delt=t*lat_strain            #Change in thickness in mm\n",

+      "\n",

+      "#Result\n",

+      "print \"change in length =\",delL,\"mm\"\n",

+      "print \"change in breadth =\",delb,\"mm\"\n",

+      "print \"change in thickness =\",delt,\"mm\"\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "change in length = 1.0 mm\n",

+        "change in breadth = 0.00225 mm\n",

+        "change in thickness = 0.0015 mm\n"

+       ]

+      }

+     ],

+     "prompt_number": 2

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Problem 2.2,page no.61"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Given\n",

+      "#Variable declaration\n",

+      "L=30                #Length in cm\n",

+      "b=4                 #Breadth in cm\n",

+      "d=4                 #Depth in cm\n",

+      "P=400*(10**3)       #Axial compressive load in N\n",

+      "delL=0.075          #Decrease in length in cm\n",

+      "delb=0.003          #Increase in breadth in cm\n",

+      "\n",

+      "#Calculation\n",

+      "A=(b*d)*1e2                      #Area of cross-section in sq.mm\n",

+      "long_strain=delL/L               #Longitudinal strain\n",

+      "lat_strain=delb/b                #Lateral strain\n",

+      "mu=lat_strain/long_strain        #Poisson's ratio\n",

+      "E=int((P)/(A*long_strain))       #Young's modulus\n",

+      "\n",

+      "#Result\n",

+      "print \"Poisson's ratio =\",mu\n",

+      "print \"Young's modulus = %.e N/mm^2\"%E\n",

+      "\n",

+      "\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Poisson's ratio = 0.3\n",

+        "Young's modulus = 1e+05 N/mm^2\n"

+       ]

+      }

+     ],

+     "prompt_number": 2

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Problem 2.3,page no.63"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Given\n",

+      "#Variable declaration\n",

+      "L=4000        #Length of the bar in mm\n",

+      "b=30          #Breadth of the bar in mm\n",

+      "t=20          #Thickness of the bar in mm\n",

+      "mu=0.3        #Poisson's ratio\n",

+      "delL=1.0      #delL from problem 2.1\n",

+      "\n",

+      "#Calculation\n",

+      "ev=(delL/L)*(1-2*mu)         #Volumetric strain \n",

+      "V=L*b*t                      #Original volume in mm^3\n",

+      "delV=ev*V                    #Change in volume in mm^3\n",

+      "F=int(V+delV)                #Final volume in mm^3\n",

+      "\n",

+      "#Result\n",

+      "print \"Volumetric strain =\",ev\n",

+      "print \"Final volume =\",F,\"mm^3\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Volumetric strain = 0.0001\n",

+        "Final volume = 2400240 mm^3\n"

+       ]

+      }

+     ],

+     "prompt_number": 3

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Problem 2.4,page no.63"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "from __future__ import division\n",

+      "#Given\n",

+      "#Variable declaration\n",

+      "L=300              #Length in mm\n",

+      "b=50               #Width in mm\n",

+      "t=40               #Thickness in mm\n",

+      "P=300*10**3        #Pull in N\n",

+      "E=2*10**5          #Young's modulus in N/sq.mm\n",

+      "mu=0.25            #Poisson's ratio\n",

+      "\n",

+      "#Calculation\n",

+      "V=L*b*t                           #Original volume in mm^3\n",

+      "Area=b*t                          #Area in sq.mm   \n",

+      "stress=P/Area                     #Stress in N/sq.mm \n",

+      "ev=(stress/E)*(1-2*mu)            #Volumetric strain \n",

+      "delV=int(ev*V)                    #Change in volume in mm^3                     \n",

+      "\n",

+      "#Result\n",

+      "print \"Change in volume =\",delV,\"mm^3\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        " Change in volume = 225 mm^3\n"

+       ]

+      }

+     ],

+     "prompt_number": 5

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Problem 2.7,page no.69"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "import math\n",

+      "\n",

+      "#Given\n",

+      "#Variable declaration\n",

+      "L=5*10**3                #Length in mm\n",

+      "d=30                     #Diameter in mm\n",

+      "P=50*10**3               #Tensile load in N\n",

+      "E=2e5                    #Young's modulus in N/sq.mm\n",

+      "mu=0.25                  #Poisson's ratio\n",

+      "\n",

+      "#Calculation\n",

+      "V=int(round((math.pi*d**2*L)/4,-2))        #Volume in mm^3 \n",

+      "e=P*4/(math.pi*(d**2)*E)                   #Strain of length\n",

+      "delL=round(e*L,3)                          #Change in length in mm\n",

+      "lat_strain=round(mu*round(e,7),7)          #Lateral strain \n",

+      "deld=lat_strain*d                          #Change in diameter in mm\n",

+      "delV=round(V*(0.0003536-(2*lat_strain)),2) #Change in volume in mm^3\n",

+      "\n",

+      "#Result\n",

+      "print \"Change in length =\",delL,\"mm\"\n",

+      "print \"Change in diameter =\",deld,\"mm\"\n",

+      "print \"Change in volume =\",delV,\"mm^3\"\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Change in length = 1.768 mm\n",

+        "Change in diameter = 0.002652 mm\n",

+        "Change in volume = 624.86 mm^3\n"

+       ]

+      }

+     ],

+     "prompt_number": 7

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Problem 2.10,page no.79"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Given\n",

+      "#Variable declaration\n",

+      "E=1.2e5                  #Young's modulus in N/sq.mm\n",

+      "C=4.8e4                  #Modulus of rigidity in N/sq.mm\n",

+      "\n",

+      "#Calculation\n",

+      "mu=(E/(2*C))-1           #Poisson's ratio \n",

+      "K=int(E/(3*(1-2*mu)))    #Bulk modulus in N/sq.mm\n",

+      "\n",

+      "#Result\n",

+      "print \"Poisson's ratio =\",mu\n",

+      "print \"Bulk modulus = %.0e N/mm^2\"%K\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Poisson's ratio = 0.25\n",

+        "Bulk modulus = 8e+04 N/mm^2\n"

+       ]

+      }

+     ],

+     "prompt_number": 8

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Problem 2.11,page no.79"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Given\n",

+      "#Variable declaration\n",

+      "A=8*8         #Area of section in sq.mm\n",

+      "P=7000        #Axial pull in N\n",

+      "Ldo=8         #Original Lateral dimension in mm\n",

+      "Ldc=7.9985    #Changed Lateral dimension in mm\n",

+      "C=0.8e5       #modulus of rigidity in N/sq.mm\n",

+      "\n",

+      "#Calculation\n",

+      "lat_strain=(Ldo-Ldc)/Ldo                                        #Lateral strain\n",

+      "sigma=P/A                                                       #Axial stress in N/sq.mm\n",

+      "mu=round(1/((sigma/lat_strain)/(2*C)-1),3)                      #Poisson's ratio\n",

+      "E=round((sigma/lat_strain)/((sigma/lat_strain)/(2*C)-1),-1)     #Modulus of elasticity in N/sq.mm\n",

+      "\n",

+      "#Result\n",

+      "print \"Poisson's ratio =\",mu\n",

+      "print \"Modulus of elasticity = %.4e N/mm^2\"%E\n",

+      "\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Poisson's ratio = 0.378\n",

+        "Modulus of elasticity = 2.2047e+05 N/mm^2\n"

+       ]

+      }

+     ],

+     "prompt_number": 9

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [],

+     "language": "python",

+     "metadata": {},

+     "outputs": []

+    }

+   ],

+   "metadata": {}

+  }

+ ]

+}
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