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diff --git a/Mechanics_of_Materials/chapter9.ipynb b/Mechanics_of_Materials/chapter9.ipynb new file mode 100644 index 00000000..7ea9938e --- /dev/null +++ b/Mechanics_of_Materials/chapter9.ipynb @@ -0,0 +1,127 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 9: Deflections of beams" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.17, Page number 654" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"\n", + "Determine the download deflection\n", + "\"\"\"\n", + "\n", + "#Variable declaration\n", + "P = 5 #load(k)\n", + "L = 8*12 #beam length(in)\n", + "E = 30*10**6 #modulus of elasticity(psi)\n", + "I = 75.0 #moment of inertia(in^4)\n", + "q = 1.5*(1./12.)#load intensity(k/in)\n", + "\n", + "#Calculations\n", + "Sc = ((P*L**3)/(48*E*I))+((5.*q*L**4)/(384.*E*I))\n", + "\n", + "#Result\n", + "print \"The download deflection is\",Sc,\"in(Calculation mistake in textbook)\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The download deflection is 0.0001024 in(Calculation mistake in textbook)\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.23, Page number 682" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"\n", + "Determine vertical deflections\n", + "\"\"\"\n", + "\n", + "#Variable declaration\n", + "E = 30*10**6*144 #modulus of elasticity(lb/ft^2)\n", + "I = 25.92/12 #moment of inertia(ft^4)\n", + "x = 12 #ft\n", + "\n", + "#Calculations\n", + "'''The equivalent load q(x) for the beam is given by the following equation\n", + "q(x) = -700(x)^-1+800(x-6)^0 - 800(x-12)^0 - 5600(x-12)^-1 + 1500(x-16)^-1\n", + "Since the equation equals zero at all points except where x=16, we omit the last term\n", + "Taking 4th order integration, we obtain the following expression,'''\n", + "C1 = (-((350*x**3)/3)+((100*(x-6)**4)/3)-((100*(x-12)**4)/3)+((2800*(x-12)**3)/3))/12\n", + "print \"C1 =\",C1\n", + "\n", + "#For Deflection at point C\n", + "x = 6\n", + "Elv = ((350*x**3)/3)-(100*((x-6)**4)/3)+(100*((x-12)**4)/3)+(2800*((x-12)**3)/3)+(C1*x)\n", + "Sc = Elv/(E*I) #ft\n", + "\n", + "#For deflection at point D\n", + "x = 16\n", + "Elv_16 = ((350*x**3)/3)-(100*((x-6)**4)/3)+(100*((x-12)**4)/3)+(2800*((x-12)**3)/3)+(C1*x)\n", + "Sd = Elv_16/(E*I)\n", + "\n", + "#Results\n", + "print \"Deflection at point C is\",round((-Sc*12),8),\"in\"\n", + "print \"Deflection at point D is\",round((Sd*12),8),\"in\"\n", + "\n", + "print \"\\n Please note that there is a calculation mistake in textbook while calculating Elv. Hence, the difference in solution\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "C1 = -13200\n", + "Deflection at point C is 0.00027315 in\n", + "Deflection at point D is 2.06e-06 in\n", + "\n", + " Please note that there is a calculation mistake in textbook while calculating Elv. Hence, the difference in solution\n" + ] + } + ], + "prompt_number": 19 + } + ], + "metadata": {} + } + ] +}
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