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Diffstat (limited to 'Statics_And_Strength_Of_Materials/ch13.ipynb')
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diff --git a/Statics_And_Strength_Of_Materials/ch13.ipynb b/Statics_And_Strength_Of_Materials/ch13.ipynb new file mode 100755 index 00000000..6f6d6663 --- /dev/null +++ b/Statics_And_Strength_Of_Materials/ch13.ipynb @@ -0,0 +1,359 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:6b0b86bd9b0d0e04cc91f26a51f01e1dfca0b27db56af40f6330128871970df2" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 13 : Deflection of Beams" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.1 Page No : 313" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "E = 1.5*10**6\n", + "F1 = -100. \t\t\t#lb\n", + "F2 = -100. \t\t\t#lb\n", + "x1 = 6 \t\t\t#in\n", + "x2 = 6 \t\t\t#in\n", + "Ina = 64 \t\t\t#in**4\n", + "h1 = -600 \t\t\t#lb ft\n", + "h2 = -1200 \t\t\t#lb ft\n", + "xa1 = 10 \t\t\t# in\n", + "xa2 = 8 \t\t\t#in\n", + "\t\t\t\n", + "# Calculations\n", + "deltamax = ((1./2)*x1*xa1*h1+(1./2)*(x1+x2)*h2*xa2)*(1728)/(E*Ina)\n", + "\t\t\t\n", + "# Results\n", + "print 'maximum deflection = %.2f in'%(deltamax)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "maximum deflection = -1.36 in\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.2 Page No : 314" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "E = 1.5*10**6\n", + "I = 50. \t \t\t#in**4\n", + "delta = -1. \t\t\t#in\n", + "l = 8. \t\t\t#ft\n", + "\t\t\t\n", + "# Calculations\n", + "w = -delta*8*E*I/(l**4*1728)\n", + "\t\t\t\n", + "# Results\n", + "print 'distributed weight = %.1f lb per ft'%(w)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "distributed weight = 84.8 lb per ft\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.3 Page No : 315" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "W = 50. \t\t\t#lb/ft\n", + "x = 5. \t\t\t#ft\n", + "x1 = 2. \t\t\t#ft\n", + "\t\t\t\n", + "# Calculations\n", + "V = W*x\n", + "M = W*((x/2)+x1)*x\n", + "M1 = W*x*(x+x1)\n", + "M2 = -M\n", + "M3 = -W*x*x/2\n", + "EIdeltamax = ((1./2)*(x+x1)*M1*((x+x1)/3))+(x+x1)*M2*((x+x1)/2)+(1./3)*x*M3*(x/4)\n", + "\t\t\t\n", + "# Results\n", + "print 'maximum value of EIdeltax = %.1f lb ft**3'%(round(EIdeltamax,-2))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "maximum value of EIdeltax = -14600.0 lb ft**3\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.5 Page No : 329" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "w = 180. \t\t\t#lb/ft\n", + "l = 8. \t\t\t#ft\n", + "P = 1200. \t\t\t#lb\n", + "b = 6. \t\t\t#ft\n", + "E = 3*10.**6\n", + "I = 64. \t\t\t#in**4\n", + "\t\t\t\n", + "# Calculations\n", + "delta = ((w*l**4)/(8))+((P*b**2)*(3*l-b)/(6))\n", + "\t\t\t\n", + "# Results\n", + "print 'deflection of the free end = %.1fbyEI ft'%(round(delta,-3))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "deflection of the free end = 222000.0byEI ft\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.6 Page No : 329" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "P = 6. \t\t\t#kips\n", + "w = 3. \t \t\t#kips/ft\n", + "L1 = 8. \t\t\t#ft\n", + "L2 = 8. \t\t\t#ft\n", + "\t\t\t\n", + "# Calculations\n", + "delta = (P*(L1+L2)**3/192)+(w*(L1+L2)**4/768)\n", + "\t\t\t\n", + "# Results\n", + "print 'midspan value of deflection = %.1f kip ft**3'%(delta)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "midspan value of deflection = 384.0 kip ft**3\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.7 Page No : 331" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "x1 = 3. \t\t\t#ft\n", + "x2 = 3. \t\t\t#ft\n", + "x3 = 3. \t\t\t#ft\n", + "x4 = 3. \t\t\t#ft\n", + "W1 = 4. \t\t\t#kips\n", + "W2 = 8. \t\t\t#kips\n", + "l = x1+x2+x3+x4\n", + "\t\t\t\n", + "# Calculations\n", + "b = x2+x3+x4\n", + "b1 = x4\n", + "a = x1\n", + "x = l/2\n", + "P = (((W1*b*(l/b*(x-a)**3+(l**2-b**2)*x-x**3))/(6*l))+((W2*b1*x*(l**2-x**2-b1**2))/(6*l)))*(48/l**3)\n", + "R1 = 3+2-(P/2)\n", + "R2 = P\n", + "R3 = 1+6-(P/2)\n", + "\t\t\t\n", + "# Results\n", + "print 'R1 = %.3f kips'%(R1)\n", + "print 'R2 =%.2f kips'%(R2)\n", + "print 'R3 =%.3f kips'%(R3)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "R1 = 0.875 kips\n", + "R2 =8.25 kips\n", + "R3 =2.875 kips\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.8 Page No : 333" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy import linalg\n", + "\t\t\t\n", + "# Variables\n", + "P = 680. \t\t\t#lb\n", + "K = 1000. \t\t\t#lb/in\n", + "L = 6. \t\t\t#ft\n", + "E = 30.*10**6\n", + "Ina = 1.728 \t\t\t#in**4\n", + "\t\t\t\n", + "# Calculations\n", + "A = [[((L*12)**3/(3*E*Ina)),-(1/K)],[1,1]]\n", + "b = [0,P]\n", + "c = linalg.solve(A,b)\n", + "Pb = c[0]\n", + "Ps = c[1]\n", + "\t\t\t\n", + "# Results\n", + "print 'Force in the spring = %.2f psi'%(Ps)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Force in the spring = 480.00 psi\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.9 Page No : 334" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "I = 1.5 \t\t\t#in**4\n", + "Da = 0.5 \t\t\t#in\n", + "E = 30.*10**6\n", + "l = 60. \t\t\t#in\n", + "\t\t\t\n", + "# Calculations\n", + "F = 6*Da*E*I/(l**3)\n", + "\t\t\t\n", + "# Results\n", + "print 'F = %.2f lb'%(F)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "F = 625.00 lb\n" + ] + } + ], + "prompt_number": 8 + } + ], + "metadata": {} + } + ] +}
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