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diff --git a/Strength_of__Materials_by_Dr.R.K.Bansal/chapter3.ipynb b/Strength_of__Materials_by_Dr.R.K.Bansal/chapter3.ipynb new file mode 100644 index 00000000..43fe6e11 --- /dev/null +++ b/Strength_of__Materials_by_Dr.R.K.Bansal/chapter3.ipynb @@ -0,0 +1,220 @@ +{
+ "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": {}
+ }
+ ]
+}
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