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| author | hardythe1 | 2014-07-28 14:01:58 +0530 |
|---|---|---|
| committer | hardythe1 | 2014-07-28 14:01:58 +0530 |
| commit | 7876eeaf85f7c020ec1f3530963928cd2bc26a66 (patch) | |
| tree | 67f4da564402aeb9869eaaf6f1e83ec7f1f75aa9 /Mechanics_of_Materials/Chapter2.ipynb | |
| parent | 1c1ea29e3e213559fef5f928df109b7d17c21f24 (diff) | |
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adding book
Diffstat (limited to 'Mechanics_of_Materials/Chapter2.ipynb')
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1 files changed, 207 insertions, 0 deletions
diff --git a/Mechanics_of_Materials/Chapter2.ipynb b/Mechanics_of_Materials/Chapter2.ipynb new file mode 100755 index 00000000..c29910ba --- /dev/null +++ b/Mechanics_of_Materials/Chapter2.ipynb @@ -0,0 +1,207 @@ +{
+ "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": {}
+ }
+ ]
+}
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