{ "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": {} } ] }