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diff --git a/Statics_And_Strength_Of_Materials/ch10.ipynb b/Statics_And_Strength_Of_Materials/ch10.ipynb new file mode 100755 index 00000000..b18a635e --- /dev/null +++ b/Statics_And_Strength_Of_Materials/ch10.ipynb @@ -0,0 +1,500 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:fa8306a7ccf6683f3bb43ba03db574b371457c13bfcbb27905e40f6b1eacde3b" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 10 : Torsion" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.1 Page No : 229" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \t\t\t\n", + "\n", + "# Variables\n", + "L = 50. \t\t\t#ft\n", + "Do = 2 \t\t\t#in\n", + "Di = 1.5 \t\t\t#in\n", + "Mt = 10000. \t\t\t#lb in\n", + "G = 12.*10**6\n", + "\t\t\t\n", + "# Calculations\n", + "Tmax = 16*Mt*Do/(math.pi*(Do**4-Di**4))\n", + "angle = (Mt*L*12*32)*57.3/(G*math.pi*(Do**4-Di**4))\n", + "\t\t\t\n", + "# Results\n", + "print 'Maximum shearing strees = %.f psi'%(round(Tmax,-1))\n", + "print 'twist angle = %.1f degrees'%(angle)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum shearing strees = 9310 psi\n", + "twist angle = 26.7 degrees\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.2 Page No : 229" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "d = 4. \t\t\t#ft\n", + "T = 5000. \t\t\t#psi\n", + "angle = 0.1 \t\t\t#degrees\n", + "\t\t\t\n", + "# Calculations\n", + "T1 = (math.pi*d**3)*T/16\n", + "T2 =angle*math.pi*G*math.pi*d**4/(180*12*32)\n", + "\t\t\t\n", + "# Results\n", + "if (T1<T2): \n", + " print 'Safe torque = %.2f lb in'%(T1)\n", + "else:\n", + " print 'Safe torque = %.2f lb'%(T2)\n", + "\n", + "# note : anwer is wrong in book. plz check." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Safe torque = 43864.91 lb\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.3 Page No : 229" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy import linalg\n", + "\t\t\t\n", + "# Variables\n", + "Ds = 1. \t\t\t#in\n", + "Db = 1.5 \t\t\t#in\n", + "Ls = 4. \t\t\t#in\n", + "Lb = 6. \t\t\t#in\n", + "Gs = 12.*10**6 \t\t\t#psi\n", + "Gb = 6.4*10**6 \t\t\t#psi\n", + "T = 10000. \t\t\t#lb in\n", + "\t\t\t\n", + "# Calculations\n", + "A = [[1,1],[(Ls*12/(Gs*Ds**4)),(-Lb*12/(Gb*Db**4))]]\n", + "b = [T,0]\n", + "c = linalg.solve(A,b)\n", + "Tab = c[0]\n", + "Tbc = c[1]\n", + "\t\t\t\n", + "# Results\n", + "print 'Torque in section AB = %.f lb in'%(Tab)\n", + "print 'Torque in section AB = %.f lb in'%(Tbc)\n", + "\n", + "# note : Answers are slightly different because of inbuilt solve function of python." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Torque in section AB = 3571 lb in\n", + "Torque in section AB = 6429 lb in\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.4 Page No : 230" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "T = 10000. \t\t\t#lb in\n", + "G = 12.*10**6\n", + "Dab = 1.5 \t\t\t#in\n", + "Lab = 4. \t\t\t#in\n", + "Dcd = 1. \t\t\t#in\n", + "Lcd = 3. \t\t\t#in\n", + "\t\t\t\n", + "# Calculations\n", + "F = T/2\n", + "Tab = F*Lab\n", + "angle = ((T*32*12*Lcd/(G*math.pi*Dcd**4))+2*(Tab*32*12*Lab/(G*math.pi*Dab**4)))*(180/math.pi)\n", + "\t\t\t\n", + "# Results\n", + "print 'angle of twist = %.0f degrees'%(angle)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "angle of twist = 36 degrees\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.5 Page No : 231" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "Tallowable = 5000. \t\t\t#psi\n", + "power = 250. \t \t\t#hp\n", + "n = 1800. \t\t\t#rpm\n", + "\t\t\t\n", + "# Calculations\n", + "T = 63000*power/n\n", + "d = (16*T/(math.pi*Tallowable))**(1/3.)\n", + "\t\t\t\n", + "# Results\n", + "print 'Torque = %.2f lb in'%(T)\n", + "print 'diameter =%.2f in'%(d)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Torque = 8750.00 lb in\n", + "diameter =2.07 in\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.6 Page No : 232" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "ds = 2. \t\t\t#in\n", + "n = 315. \t\t\t#rpm\n", + "Gs = 12.*10**6\n", + "Lab = 5. \t\t\t#in\n", + "Lbc = 15. \t\t\t#in\n", + "Pa = 10. \t\t\t#hp\n", + "Pc = 40. \t\t\t#hp\n", + "Pb = 50. \t\t\t#hp\n", + "\t\t\t\n", + "# Calculations\n", + "Tab = 63000*Pa/n\n", + "Tbc = 63000*Pc/n\n", + "angle = ((32*Tbc*Lbc*12/(math.pi*ds**4*G))-(32*Tab*Lab*12/(math.pi*ds**4*G)))*(180/math.pi)\n", + "\t\t\t\n", + "# Results\n", + "print 'angle of twist of gear C releative to a = %.2f degrees'%(angle)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "angle of twist of gear C releative to a = 4.01 degrees\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.7 Page No : 234" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "k1 = 6.*10**6 \t\t\t#lb in/rad\n", + "k2 = 3.*10**6 \t\t\t#lb in/rad\n", + "k3 = 2.*10**6 \t\t\t#lb in/rad\n", + "T = 10000. \t\t\t#lb in\n", + "\t\t\t\n", + "# Calculations\n", + "ke = 1/((1/k1)+(1/k2)+(1/k3))\n", + "angle = T*180/(ke*math.pi)\n", + "\t\t\t\n", + "# Results\n", + "print 'equivalent spring constant = %.2e lb in/rad'%(ke)\n", + "print 'angle of twist d/a = %.2f degrees'%(angle)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "equivalent spring constant = 1.00e+06 lb in/rad\n", + "angle of twist d/a = 0.57 degrees\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.8 Page No : 234" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "k1 = 2.*10**6 \t\t\t#lb in/rad\n", + "k2 = 3.*10**6 \t\t\t#lb in/rad\n", + "T = 20000. \t\t\t#lb in\n", + "\t\t\t\n", + "# Calculations\n", + "ke = k1+k2\n", + "angle = T*180/(ke*math.pi)\n", + "\t\t\t\n", + "# Results\n", + "print 'equivalent spring consmath.tant = %.2e lb in/rad'%(ke)\n", + "print 'angle of twist at B = %.3f degrees'%(angle)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "equivalent spring consmath.tant = 5.00e+06 lb in/rad\n", + "angle of twist at B = 0.229 degrees\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.9 Page no : 238" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# variables\n", + "n = 10 # coils\n", + "P = 1200. # axial load lb\n", + "R = 2. \n", + "K = 1.33 # factor\n", + "d = 1.\n", + "\n", + "# Calculations\n", + "Tmax = round(K*(16*P*R)/(math.pi*d**3),-2)\n", + "delta = 64*P*R**3*n/(12*10**6*d**4)\n", + "\n", + "# Results\n", + "print \"Stress = %d psi\"%Tmax\n", + "print \"The deflection = %.3f in\"%delta\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Stress = 16300 psi\n", + "The deflection = 0.512 in\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.10 Page No : 239" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "di = 0.2 \t\t\t#in\n", + "dm = 2. \t\t\t#in\n", + "n = 10.\n", + "F = 10. \t\t\t#lb\n", + "G = 12.*10**6\n", + "\t\t\t\n", + "# Calculations\n", + "k = G*di**4/(64*dm**3*n)\n", + "ke = 1/((1/(k+k))+(1/k)+(1/k))\n", + "delta = F/ke\n", + "\t\t\t\n", + "# Results\n", + "print 'elongation = %.2f in'%(delta)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "elongation = 6.67 in\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.11 Page No : 241" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "d = 0.5 \t\t\t#in\n", + "n = 315. \t\t\t#rpm\n", + "t1 = 5000. \t\t\t#psi\n", + "r1 = 8. \t\t\t#in\n", + "r2 = 4. \t\t\t#in \n", + "n1 = 6.\n", + "n2 = 4.\n", + "\t\t\t\n", + "# Calculations\n", + "t2 = r2*t1/r1\n", + "T = r1*n1*(math.pi/4)*d**2*t1+r2*n2*(math.pi/4)*d**2*t2\n", + "hp = T*n/63000\n", + "\t\t\t\n", + "# Results\n", + "print 'Premissible horsepower = %.f hp'%(hp)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Premissible horsepower = 275 hp\n" + ] + } + ], + "prompt_number": 10 + } + ], + "metadata": {} + } + ] +}
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