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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 2: Strain"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.1 page no. 70"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"e_z= 4 #Constant\n",
"ab = 0.200 #m, dimension\n",
"from scipy import integrate\n",
"#Calculations\n",
"#Part a)\n",
"import math\n",
"def f(z):\n",
" return(1+(40*10**-3)*(math.sqrt(z)))\n",
"z=integrate.quad(f,0,ab) #Strain formula for short line segment = delta(sdash) =(1+e_z)delta(s) \n",
"deltaB= z[0]-ab\n",
"deltaB_mm= deltaB*1000\n",
"\n",
"#Part b)\n",
"\n",
"e_avg = deltaB/ab# Normal strain formula e = (delta(sdash) -delta(s))/delta(s)\n",
"\n",
"#Display\n",
"print\"The displacement at the end of the rod is = \",round(deltaB_mm,2),\"mm\"\n",
"print\"The average normal strain in the rod is =\",round(e_avg,4),\"mm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The displacement at the end of the rod is = 2.39 mm\n",
"The average normal strain in the rod is = 0.0119 mm\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.2 page no. 71"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"theta = 0.05 #degree, angle\n",
"L1=300.0 #mm, length\n",
"L2 = 400.0 #mm\n",
"\n",
"#Calculations\n",
"import math\n",
"alpha=math.atan(L2/L1)*180/3.14\n",
"phi=90-alpha+theta\n",
"Lad=math.sqrt(L1**2+L2**2)\n",
"Lbd=math.sqrt(Lad**2+L2**2-2*L2*Lad*math.cos(36.92*3.14/180.0))\n",
"epsilonBD=(Lbd-L1)/(L1)\n",
"dLbd=(theta*3.14/180.0)*L2\n",
"\n",
"#Display\n",
"print\"The average normal strain =\",round(epsilonBD,3),\"mm/mm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The average normal strain = 0.001 mm/mm\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.3 page no. 72"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"#The given dimension are\n",
"ab= 250.0 #mm\n",
"bbdash_x = 3.0 #mm\n",
"bbdash_y = 2.0 #mm\n",
"ac = 300.0 #mm\n",
"\n",
"#calculations\n",
"#Part(a)\n",
"import math\n",
"abdash = math.sqrt((ab - bbdash_y)**2 + (bbdash_x)**2) #Pythagoras theorem\n",
"avg_normal_strain = (abdash-ab)/ab\n",
"\n",
"#Part(b)\n",
"gamma_xy = math.atan(bbdash_x/(ab - bbdash_y)) #shear strain formula\n",
"\n",
"#Display\n",
"print\"The average normal strain along AB is =\",round(avg_normal_strain,4),\"mm/mm\"\n",
"print\"The average shear strain =\",round(gamma_xy,4),\"rad\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The average normal strain along AB is = -0.0079 mm/mm\n",
"The average shear strain = 0.0121 rad\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.4 page no. 73"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"ab = 150 #mm\n",
"bc = 150 #mm\n",
"disp_cd= 2 #mm\n",
"ab_half = ab/2.0\n",
"addash_half = (bc+disp_cd)/2.0 \n",
"\n",
"#Calculations\n",
"#Part(a)\n",
"import math\n",
"ac = sqrt((ab)**2 + (bc)**2) #Pythagoras theorem in mm\n",
"ac_m = ac/1000.0 #in m\n",
"acdash = sqrt((ab)**2 + (bc+disp_cd)**2) #Pythagoras theorem in mm\n",
"acdash_m = acdash/1000.0 #in m\n",
"avg_strain_ac = (acdash_m - ac_m)/ac_m #Normal strain formula\n",
"\n",
"#Part(b)\n",
"theta_dash = 2* math.atan((addash_half)/(bc/2.0)) \n",
"gamma_xy = (math.pi / 2.0)- theta_dash \n",
"\n",
"#Display\n",
"print\"The average normal strain along the diagonal AC is =\",round(avg_strain_ac,5),\"mm/mm\"\n",
"print\"The shear strain at E relative to the x,y axes =\",round(gamma_xy,4),\"rad\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The average normal strain along the diagonal AC is = 0.00669 mm/mm\n",
"The shear strain at E relative to the x,y axes = -0.0132 rad\n"
]
}
],
"prompt_number": 22
}
],
"metadata": {}
}
]
}
|
