{
"metadata": {
"name": "",
"signature": "sha256:1d0b1f24c9d10ade871ede95388991dbd93c7a64d0a0c3e5beb35a6a045b6a61"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 3:Principal Stresses and Strains"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 3.8,page no.98"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given\n",
"#Variable declaration\n",
"sigma1=100 #Major principal stress in N/sq.mm\n",
"sigma2=-60 #Minor principal stress in N/sq.mm\n",
"theta=90-50 #Angle of inclination in degrees\n",
"\n",
"#Calculation\n",
"sigman=round(((sigma1+sigma2)/2)+(((sigma1-sigma2)/2)*math.cos(math.radians(2*theta))),2)\n",
"sigmat=round((sigma1-sigma2)/2*(math.sin(math.radians(2*theta))),3)\n",
"sigmaR=round(math.sqrt(sigman**2+sigmat**2),3)\n",
"sigmat_max=int((sigma1-sigma2)/2)\n",
"\n",
"#Result\n",
"print \"Normal stress =\",sigman,\"N/mm^2\"\n",
"print \"Shear stress =\",sigmat,\"N/mm^2\"\n",
"print \"Resultant stress =\",sigmaR,\"N/mm^2\"\n",
"print \"Maximum shear stress =\",sigmat_max,\"N/mm^2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Normal stress = 33.89 N/mm^2\n",
"Shear stress = 78.785 N/mm^2\n",
"Resultant stress = 85.765 N/mm^2\n",
"Maximum shear stress = 80 N/mm^2\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 3.9,page no.99"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given\n",
"#Variable declaration\n",
"sigma1=100 #Major principal stress in N/sq.mm\n",
"sigma2=-40 #Minor principal stress in N/sq.mm\n",
"theta=90-60 #Angle of inclination in degrees\n",
"\n",
"#Calculation\n",
"sigman=((sigma1+sigma2)/2)+(((sigma1-sigma2)/2)*math.cos(math.radians(2*theta)))\n",
"sigmat=round((sigma1-sigma2)/2*(math.sin(math.radians(2*theta))),2)\n",
"sigmaR=round(math.sqrt(sigman**2+sigmat**2),1)\n",
"sigmat_max=int((sigma1-sigma2)/2)\n",
"phi=int(math.degrees(math.atan(sigmat/sigman)))\n",
"\n",
"#Result\n",
"print \"Resultant stress in magnitude =\",sigmaR,\"N/mm^2\"\n",
"print \"Direction of resultant stress =\",phi,\"degrees\"\n",
"print \"Maximum shear stress =\",sigmat_max,\"N/mm^2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resultant stress in magnitude = 88.9 N/mm^2\n",
"Direction of resultant stress = 43 degrees\n",
"Maximum shear stress = 70 N/mm^2\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 3.13,page no.111"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given\n",
"#Variable declaration\n",
"sigma1=120 #Major tensile stress in N/sq.mm\n",
"sigma2=-90 #Minor compressive stress in N/sq.mm\n",
"sigma_gp=150 #Greatest principal stress in N/sq.mm\n",
"\n",
"#Calculation\n",
" #case(a):Magnitude of the shearing stresses on the two planes\n",
"tau=round(math.sqrt(((sigma_gp-((sigma1+sigma2)/2))**2)-(((sigma1-sigma2)/2)**2)),3)\n",
" #case(b):Maximum shear stress at the point\n",
"sigmat_max=int((math.sqrt((sigma1-sigma2)**2+(4*tau**2)))/2)\n",
"\n",
"#Result\n",
"print \"Shear stress on the two planes =\",tau,\"N/mm^2\"\n",
"print \"Maximum shear stress at the point =\",sigmat_max,\"N/mm^2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Shear stress on the two planes = 84.853 N/mm^2\n",
"Maximum shear stress at the point = 135 N/mm^2\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 3.16,page no.115"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given\n",
"#Variable declaration\n",
"sigma1=600 #Major tensile stress in N/sq.mm\n",
"sigma2=300 #Minor tensile stress in N/sq.mm\n",
"tau=450 #Shear stress in N/sq.mm\n",
"theta1=45 #Angle of inclination in degrees\n",
"theta2=135 #Angle of inclination in degrees\n",
"\n",
"#Calculation\n",
"sigman1=int(((sigma1+sigma2)/2)+(((sigma1-sigma2)/2)*math.cos(math.radians(2*theta1)))+(tau*math.sin(math.radians(2*theta1)))) \n",
"sigman2=int(((sigma1+sigma2)/2)+(((sigma1-sigma2)/2)*math.cos(math.radians(2*theta2)))+(tau*math.sin(math.radians(2*theta2)))) \n",
"sigmat1=int(round((sigma1-sigma2)/2*(math.sin(math.radians(2*theta1)))-(tau*math.cos(math.radians(2*theta1))),0))\n",
"sigmat2=int(round((sigma1-sigma2)/2*(math.sin(math.radians(2*theta2)))-(tau*math.cos(math.radians(2*theta2))),0)) \n",
"\n",
"#Result\n",
"print \"Normal stress(when theta is 45 degrees)=\",sigman1,\"N/mm^2\"\n",
"print \"Normal stress(when theta is 135 degrees)=\",sigman2,\"N/mm^2\" \n",
"print \"Tangential stress(when theta is 45 degrees)=\",sigmat1,\"N/mm^2\"\n",
"print \"Tangential stress(when theta is 135 degrees)=\",sigmat2,\"N/mm^2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Normal stress(when theta is 45 degrees)= 900 N/mm^2\n",
"Normal stress(when theta is 135 degrees)= 0 N/mm^2\n",
"Tangential stress(when theta is 45 degrees)= 150 N/mm^2\n",
"Tangential stress(when theta is 135 degrees)= -150 N/mm^2\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}