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diff --git a/Advanced_Strength_and_Applied_Elasticity/Chapter2.ipynb b/Advanced_Strength_and_Applied_Elasticity/Chapter2.ipynb new file mode 100755 index 00000000..8f910d4c --- /dev/null +++ b/Advanced_Strength_and_Applied_Elasticity/Chapter2.ipynb @@ -0,0 +1,162 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:e953f526db565d7aa504d8011697e642d2061a58d6ef5161bb85dc3f3417f791"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter2-Strain and stress -strain relations"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex1-pg38"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate radius of circle and principal stresses and distance between o and c and strain and shear strain and maxi shear stress\n",
+ "radius=((math.sqrt(195**2.+130**2.))*10**(-6.));\n",
+ "print'%s %.5f %s'%(\"radius of the circle in degree = \",radius,\"\")\n",
+ "theta1=(math.atan(130./195.))*57.3\n",
+ "print'%s %.2f %s'%(\"pricipal stresses in degree\",theta1,\"\");## print'%s %.2f %s'%laying result\n",
+ "epsilonx=510.*10**(-6.)\n",
+ "epsilony=120.*10**(-6.)\n",
+ "epsilon=(epsilonx+epsilony)/2.\n",
+ "print'%s %.5f %s'%(\"distance between O and c=\",epsilon,\"\")\n",
+ "\n",
+ "##solution a\n",
+ "angle=60.- theta1\n",
+ "print'%s %.2f %s'%(\"angle of ACA1 in degree = \",angle,\"\")## print'%s %.2f %s'%laying result\n",
+ "epsilonx1=epsilon+radius*math.cos(26.3/57.3)\n",
+ "print'%s %.5f %s'%(\"strains in x axis= \",epsilonx1,\"\")## print'%s %.2f %s'%laying result\n",
+ "epsilony1=epsilon-radius*math.cos(26.3/57.3)\n",
+ "print'%s %.5f %s'%(\"strains in y axis= \",epsilony1,\"\")## print'%s %.2f %s'%laying result\n",
+ "gammaxy=-2*(radius*math.sin(26.3/57.3))\n",
+ "print'%s %.5f %s'%(\"shear strain\",gammaxy,\"\")## print'%s %.2f %s'%laying result\n",
+ "\n",
+ "##solution b\n",
+ "epsilon1=epsilon+radius\n",
+ "print'%s %.5f %s'%(\"strains in x axis= \",epsilon1,\"\")## print'%s %.2f %s'%laying result\n",
+ "epsilon2=epsilon-radius\n",
+ "print'%s %.5f %s'%(\"strains in x axis= \",epsilon2,\"\")## print'%s %.2f %s'%laying result\n",
+ "\n",
+ "##solution c\n",
+ "gammamax=-+468*10**(-6)\n",
+ "print'%s %.5f %s'%(\"maxi shear stress= \",gammamax,\"\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "radius of the circle in degree = 0.00023 \n",
+ "pricipal stresses in degree 33.69 \n",
+ "distance between O and c= 0.00031 \n",
+ "angle of ACA1 in degree = 26.31 \n",
+ "strains in x axis= 0.00053 \n",
+ "strains in y axis= 0.00010 \n",
+ "shear strain -0.00021 \n",
+ "strains in x axis= 0.00055 \n",
+ "strains in x axis= 0.00008 \n",
+ "maxi shear stress= -0.00047 \n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg46"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate value of epsilon and gamma\n",
+ "epsilon0=190.*10**(-6)\n",
+ "epsilon60=200.*10**(-6)\n",
+ "epsilon120=-300.*10**(-6)\n",
+ "E=200.## GPa\n",
+ "v=0.3\n",
+ "epsilonx=epsilon0\n",
+ "print'%s %.4f %s'%(\"value of epsilonx is= \",epsilonx,\"\")\n",
+ "\n",
+ "## epsilon60=((epsilonx+epsilony)/2)-((epsilonx-epsilony)/4)+(gammaxy*sqrt(3))/4 eqn 1\n",
+ "## epsilon120=((epsilonx+epsilony)/2)-((epsilonx-epsilony)/4)-(gammaxy*sqrt(3))/4 eqn 2\n",
+ "\n",
+ "epsilony=(2.*(epsilon60+epsilon120)-epsilon0)/3.\n",
+ "print'%s %.4f %s'%(\"value of epsilony is= \",epsilony,\"\")\n",
+ "gammaxy=(2./math.sqrt(3.))*(epsilon60-epsilon120)## from eqn 1 and eqn 2\n",
+ "print'%s %.5f %s'%(\"value of gammaxy is= \",gammaxy,\"\")\n",
+ "epsilon1=((epsilonx+epsilony)/2.)+math.sqrt(((epsilonx-epsilony)/2.)**2.+(gammaxy/2.)**2.)## epsilony value is in negative so the sign changes in the eqn\n",
+ "print'%s %.5f %s'%(\"value of epsilon1 is= \",epsilon1,\"\")\n",
+ "epsilon2=((epsilonx+epsilony)/2.)-math.sqrt(((epsilonx-epsilony)/2.)**2+(gammaxy/2.)**2.)##epsilony value is in negative so the sign changes in the eqn\n",
+ "print'%s %.4f %s'%(\"value of epsilon2 is= \",epsilon2,\"\")\n",
+ "\n",
+ "gammamax=(2.*10**-6)*math.sqrt(((epsilonx-epsilony)/2.)**2.+(gammaxy/2.)**2)\n",
+ "print'%s %.3e %s'%(\"max shear strain is= \",gammamax,\"\")\n",
+ "thetap=math.atan((577./320.)/2.)*57.3\n",
+ "print'%s %.2f %s'%(\"orientations of principal axes is= \",thetap,\"\") ## or\n",
+ "thetap1=math.atan((577./320.)*2.)*57.\n",
+ "print'%s %.2f %s'%(\"orientations of principal axes is= \",thetap1,\"\")\n",
+ "sigma1=(200.*10**9/(1.-0.09))*(epsilon1+0.3*epsilon2)\n",
+ "print'%s %.2f %s'%(\"plane stresss is Pa= \",sigma1,\"\")\n",
+ "sigma2=(200*10**3/(1-0.09))*(epsilon2+0.3*epsilon1)\n",
+ "print'%s %.2f %s'%(\"plane stresss is MPa= \",sigma2,\"\")\n",
+ "\n",
+ "taumax=(200.*10**9./(2.*(1.+0.3)))*gammamax\n",
+ "print'%s %.2f %s'%(\"plane stresss is MPa= \",taumax,\"\")\n",
+ "#error in orientationd of principal axes because of round off error \n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of epsilonx is= 0.0002 \n",
+ "value of epsilony is= -0.0001 \n",
+ "value of gammaxy is= 0.00058 \n",
+ "value of epsilon1 is= 0.00036 \n",
+ "value of epsilon2 is= -0.0003 \n",
+ "max shear strain is= 6.601e-10 \n",
+ "orientations of principal axes is= 42.04 \n",
+ "orientations of principal axes is= 74.12 \n",
+ "plane stresss is Pa= 59348428.75 \n",
+ "plane stresss is MPa= -42.21 \n",
+ "plane stresss is MPa= 50.78 \n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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