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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": {}
}
]
}
|
