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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": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-22 05:09:39 +0000