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diff --git a/Statics_And_Strength_Of_Materials/ch14.ipynb b/Statics_And_Strength_Of_Materials/ch14.ipynb new file mode 100755 index 00000000..0d379010 --- /dev/null +++ b/Statics_And_Strength_Of_Materials/ch14.ipynb @@ -0,0 +1,645 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:94d59c04fa299edfd91c8fbcd74f6a447f3853008eda8e5b17fed905ae2575e6" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 14 : Combined Loading" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.1 Page No : 349" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "h = 6. \t \t\t#in\n", + "x1 = 7. \t\t\t#in\n", + "x2 = 1. \t\t\t#in\n", + "x3 = 2. \t\t\t#in\n", + "P = 600. \t\t\t#lb\n", + "\t\t\t\n", + "# Calculations\n", + "By = P*(x1+x2+x3)/(x1+x2)\n", + "Bx = By*(x1+x2)/h\n", + "Fx = Bx\n", + "V = By-P\n", + "M = -P*(x2+x3)+By*x2\n", + "S1 = -Fx/(x3*h)\n", + "I = x3*h**3/12\n", + "S2 = -M*12*(h/2)/I\n", + "Scmax = S1-S2\n", + "Stmax = S1+S2\n", + "\t\t\t\n", + "# Results\n", + "print 'Maximum tensile stress at = %.1f psi'%(Scmax)\n", + "print 'Maximum compressive stress at = %.1f psi'%(Stmax)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum tensile stress at = -1133.3 psi\n", + "Maximum compressive stress at = 966.7 psi\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.2 Page No : 350" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "P = 10000. \t\t\t#lb\n", + "A = 11.77 \t\t\t#in**2\n", + "Z = 51.9 \t\t\t#in**3\n", + "x = 5. \t\t\t#ft\n", + "y = 12. \t\t\t#ft\n", + "\t\t\t\n", + "# Calculations\n", + "S1 = round(-P/A)\n", + "S2 = round(P*x*y/Z,-2)\n", + "Sc = S1-S2\n", + "St = S1+S2\n", + "\n", + "\t\t\t\n", + "# Results\n", + "print 'Axial stress at c = %.1f psi'%(Sc)\n", + "print 'Axial stress at t = %.1f psi'%(St)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Axial stress at c = -12450.0 psi\n", + "Axial stress at t = 10750.0 psi\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.3 Page No : 353" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "b = 6. \t\t \t#in\n", + "h = 12. \t\t\t#in\n", + "l = 20. \t\t\t#ft\n", + "P = 100000. \t\t#lb\n", + "\t\t\t\n", + "# Calculations\n", + "S = -P/(b*h)\n", + "S1 = l**2*6*12/(8*b*h**2)\n", + "w = -S/S1\n", + "\t\t\t\n", + "# Results\n", + "print 'Safe distributed load = %.0f lb per ft'%(w)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Safe distributed load = 333 lb per ft\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.4 Page No : 355" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "b = 4. \t\t\t#in\n", + "h = 9. \t\t\t#in\n", + "l = 6. \t\t\t#in\n", + "Mx = 600. \t\t\t#lb\n", + "My = 100. \t\t\t#lb\n", + "\t\t\t\n", + "# Calculations\n", + "Zx = b*h**3/(12*h/2)\n", + "Zy = b**3*h/(12*b/2)\n", + "S1 = Mx*l*12/Zx\n", + "S2 = My*b*12/Zy\n", + "Sb = S1+S2\n", + "Sd = -S1-S2\n", + "\t\t\t\n", + "# Results\n", + "print 'Maximum stress = %.1f psi tension)'%(Sb)\n", + "print ' Maximum stress =%.1f psi compression)'%(Sd) \n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum stress = 1000.0 psi tension)\n", + " Maximum stress =-1000.0 psi compression)\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.5 Page No : 356" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "d = 2. \t\t\t#in\n", + "Px = -600. \t\t\t#lb\n", + "Py = 1200. \t\t\t#lb\n", + "x1 = 2. \t\t\t#in\n", + "x2 = 2. \t\t\t#in\n", + "x3 = 2. \t\t\t#in\n", + "Ray = -400. \t\t\t#lb\n", + "Rax = 400. \t\t\t#lb\n", + "Rbx = 200. \t\t\t#lb\n", + "Rby = -800. \t\t\t#lb\n", + "\t\t\t\n", + "# Calculations\n", + "Mb = math.sqrt((Rax*x1)**2+(Ray*x1)**2)\n", + "Mc =math.sqrt((Rbx*x3)**2+(Rby*x3)**2)\n", + "if (Mb<Mc) :\n", + " M =Mc\n", + "else: \n", + " M = Mb \n", + "\n", + "Smax = M*12*64*(d/2)/(math.pi*d**4)\n", + "\t\t\t\n", + "# Results\n", + "print 'Maximum normal stress = %.1f psi'%(round(Smax,-2)) \n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum normal stress = 25200.0 psi\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.6 Page No : 359" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "P = 100. \t\t\t#kips\n", + "M = 400. \t\t\t#kip in\n", + "A = 14.7 \t\t\t#in**2\n", + "Z = 80.7 \t\t\t#in**3\n", + "\t\t\t\n", + "# Calculations\n", + "Smax = -(P*10**3)/A-(M*10**3)/Z\n", + "Smin = -(P*10**3)/A+(M*10**3)/Z\n", + "\t\t\t\n", + "# Results\n", + "print 'Maximum stress = %.1f psi'%(round(Smax,-2))\n", + "print 'Minimum stress =%.1f psi'%(round(Smin,-1))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum stress = -11800.0 psi\n", + "Minimum stress =-1850.0 psi\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.7 Page No : 360" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "As = 1. \t\t\t#in**2\n", + "Zs = 0.167 \t\t\t#in**3\n", + "Ah = 1. \t\t\t#in**2\n", + "Zh = 0.984 \t\t\t#in**3\n", + "es = 0.5 \t\t\t#in\n", + "eh = 0.5 \t\t\t#in\n", + "\t\t\t\n", + "# Calculations\n", + "phbyps = (1/As+es/Zs)/(1/Ah+eh/Zh)\n", + "\t\t\t\n", + "# Results\n", + "print 'ratio = %.1f'%(phbyps)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "ratio = 2.6\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.8 Page No : 365" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "Sx = 1800. \t\t\t#psi\n", + "Sy = 1000. \t\t\t#psi\n", + "angle = 30. \t\t\t#degrees\n", + "t = 0.25 \t\t\t#in\n", + "t1 = 3. \t\t\t#in\n", + "t2 = 5. \t\t\t#in\n", + "\t\t\t\n", + "# Calculations\n", + "Sx1 = Sx/(t1*t)\n", + "Sy1 = Sy/(t2*t)\n", + "S = ((Sx+Sy)/2+((Sx-Sy)/2)*math.cos(math.radians(2*angle)))+(Sx-Sy)*math.cos(math.radians(2*angle))\n", + "T = (Sx-Sy)*math.sin(math.radians(2*angle))\n", + "\t\t\t\n", + "# Results\n", + "print 'S = %.1f psi'%(S)\n", + "print 'T =%.f psi'%(T)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "S = 2000.0 psi\n", + "T =693 psi\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.9 Page No : 365" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "Sx = 1800. \t\t\t#lb\n", + "Sy = 1000. \t\t\t#lb\n", + "angle = 30. \t\t\t#degrees\n", + "\t\t\t\n", + "# Calculations\n", + "Sa =-((Sx+Sy)/2+((Sx-Sy)/2)*math.cos(math.radians(2*angle)))*math.cos(math.radians(2*angle))-(Sx-Sy)\n", + "Ta = -((Sx+Sy)/2+((Sx-Sy)/2)*math.cos(math.radians(2*angle)))*math.sin(math.radians(2*angle))\n", + "Sb =((Sx+Sy)/2+((Sx-Sy)/2)*math.cos(math.radians(2*angle)))*math.cos(math.radians(2*angle))-(Sx-Sy)\n", + "Tb = ((Sx+Sy)/2+((Sx-Sy)/2)*math.cos(math.radians(2*angle)))*math.sin(math.radians(2*angle))\n", + "\t\t\t\n", + "# Results\n", + "print 'Sa = %.1f psi'%(Sa)\n", + "print 'Sb =%.1f psi'%(Sb)\n", + "print 'Ta =%.f psi'%(round(Ta,-1))\n", + "print 'Tb =%.1f psi'%(round(Tb,-1))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Sa = -1600.0 psi\n", + "Sb =0.0 psi\n", + "Ta =-1390 psi\n", + "Tb =1390.0 psi\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.10 Page No : 369" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\t\t\n", + "# Variables\n", + "angle = 15. \t\t\t#degrees\n", + "Tyx = -1000. \t\t\t#psi\n", + "Txy = 1000. \t\t\t#psi\n", + "\t\t\t\n", + "# Calculations\n", + "Sx = Txy*math.sin(math.radians(2*angle))\n", + "Tx = Txy*math.cos(math.radians(2*angle))\n", + "Sy = Tyx*math.sin(math.radians(2*angle))\n", + "Ty = Tyx*math.cos(math.radians(2*angle))\n", + "Sx1 = Txy\n", + "Sy1 = Tyx\n", + "Txy = 0\n", + "\t\t\t\n", + "# Results\n", + "print 'Sx = %.1f psi'%(Sx)\n", + "print 'Tx = %.1f psi'%(Tx)\n", + "print 'Sy = %.1f psi'%(Sy)\n", + "print 'Ty = %.1f psi'%(Ty)\n", + "print 'Sx1 = %.1f psi'%(Sx1)\n", + "print 'Sy1 = %.1f psi'%(Sy1)\n", + "print 'Txy = %.1f psi'%(Txy)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Sx = 500.0 psi\n", + "Tx = 866.0 psi\n", + "Sy = -500.0 psi\n", + "Ty = -866.0 psi\n", + "Sx1 = 1000.0 psi\n", + "Sy1 = -1000.0 psi\n", + "Txy = 0.0 psi\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.11 Page No : 370" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "d = 4. \t\t\t#in\n", + "n = 315. \t\t\t#rpm\n", + "Ss = 8000. \t\t\t#psi\n", + "Ns = 12000. \t\t\t#psi\n", + "\t\t\t\n", + "# Calculations\n", + "T = Ss*d**4/(32*(d/2))\n", + "hp = T*math.pi*n/63000\n", + "\t\t\t\n", + "# Results\n", + "print 'T = %.1f pi lb in'%(T)\n", + "print 'horsepower rating =%.1f hp'%(round(hp,-1))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "T = 32000.0 pi lb in\n", + "horsepower rating =500.0 hp\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.12 Page No : 372" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "Sx = 9. \t\t\t#ksi\n", + "Sy = -5. \t\t\t#ksi\n", + "Txy = 4. \t\t\t#ksi\n", + "\t\t\t\n", + "# Calculations\n", + "R = math.sqrt(((Sx-Sy)/2)**2+Txy**2)\n", + "Smax = ((Sx+Sy)/2)+R\n", + "Smin = ((Sx+Sy)/2)-R\n", + "ap1 = (1./2)*math.degrees(math.atan(2*Txy/(Sx-Sy)))\n", + "ap2 = 90+ap1\n", + "Sc = (Sx+Sy)/2\n", + "Tc = R\n", + "Sd = (Sx+Sy)/2\n", + "Td = -R\n", + "a1 = (90-2*ap1)/2\n", + "a2 = 90+a1\n", + "\t\t\t\n", + "# Results\n", + "print 'Smax = %.2f ksi'%(Smax)\n", + "print 'Smin = %.2f ksi'%(Smin)\n", + "print 'R = %.2f psi'%(R)\n", + "print 'palne1 = %.2f degrees'%(ap1)\n", + "print 'plane 2 = %.2f degrees'%(ap2)\n", + "print 'Sc = %.2f ksi'%(Sc)\n", + "print 'Sd = %.2f ksi'%(Sd)\n", + "print 'Tc = %.2f ksi'%(Tc)\n", + "print 'Td = %.2f ksi'%(Td)\n", + "print 'palne1 = %.2f degrees'%(a1)\n", + "print 'plane 2 = %.2f degrees'%(a2)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Smax = 10.06 ksi\n", + "Smin = -6.06 ksi\n", + "R = 8.06 psi\n", + "palne1 = 14.87 degrees\n", + "plane 2 = 104.87 degrees\n", + "Sc = 2.00 ksi\n", + "Sd = 2.00 ksi\n", + "Tc = 8.06 ksi\n", + "Td = -8.06 ksi\n", + "palne1 = 30.13 degrees\n", + "plane 2 = 120.13 degrees\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.13 Page No : 373" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "d = 4. \t\t \t#in\n", + "T = 40000. \t\t\t #lb in\n", + "Th = 20000. \t\t\t#lb in\n", + "\t\t\t\n", + "# Calculations\n", + "t = round(T*(d/2)*32/(math.pi*d**4),-1)\n", + "S = round(Th/(math.pi*(d/2)**2),-1)\n", + "Smax = -(S/2)-math.sqrt(t**2+(S/2)**2)\n", + "Tmax = math.sqrt(t**2+(S/2)**2)\n", + "\n", + "\t\t\t\n", + "# Results\n", + "print 'Maximum normal stress = %.f psi'%(Smax)\n", + "print 'Maximum shearing stress =%.f psi'%(Tmax)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum normal stress = -4073 psi\n", + "Maximum shearing stress =3278 psi\n" + ] + } + ], + "prompt_number": 21 + } + ], + "metadata": {} + } + ] +}
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