diff options
Diffstat (limited to 'Statics_And_Strength_Of_Materials/ch12.ipynb')
| -rwxr-xr-x | Statics_And_Strength_Of_Materials/ch12.ipynb | 493 |
1 files changed, 493 insertions, 0 deletions
diff --git a/Statics_And_Strength_Of_Materials/ch12.ipynb b/Statics_And_Strength_Of_Materials/ch12.ipynb new file mode 100755 index 00000000..2d6e383c --- /dev/null +++ b/Statics_And_Strength_Of_Materials/ch12.ipynb @@ -0,0 +1,493 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:80d6cc3748bed03e9fd030c70419175672c3c9a4d62b5544fe9d0f908939d53e" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 12 : Stresses in Beams" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.1 Page No : 281" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "L = 20. \t\t\t#ft\n", + "b1 = 12. \t\t\t#in\n", + "h1 = 4. \t\t\t#in\n", + "b2 = 4. \t\t\t#in\n", + "h2 = 12. \t\t\t#in\n", + "Fs = 1200. \t\t\t#psi\n", + "La = 5. \t\t\t#ft\n", + "Lb = 15. \t\t\t#ft\n", + "\t\t\t\n", + "# Calculations\n", + "Ina = b1*h1**3/12\n", + "P1 = (Fs*Ina*4)/((h1/2)*12*La*3)\n", + "Ina1 = b2*h2**3/12\n", + "P2 = (Fs*Ina1*4)/((h2/2)*12*La*3)\n", + "\t\t\t\n", + "# Results\n", + "print 'P max in first case = %.0f lb'%(P1)\n", + "print 'P max in second case = %.2f lb'%(P2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "P max in first case = 853 lb\n", + "P max in second case = 2560.00 lb\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.2 Page No : 282" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "b = 0.5 \t\t\t#in\n", + "h = 1./32 \t\t\t#in\n", + "d = 4. \t\t\t#ft\n", + "E = 30.*10**6\n", + "\t\t\t\n", + "# Calculations\n", + "stress = E*(h/2)/((d/2)*12)\n", + "Ina = b*h**3/12\n", + "M = stress*Ina/(h/2)\n", + "\t\t\t\n", + "# Results\n", + "print 'maximum stress = %.2f psi'%(round(stress,-2))\n", + "print 'internal moment = %.2f lb in'%(M) \n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "maximum stress = 19500.00 psi\n", + "internal moment = 1.59 lb in\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.3 Page No : 283" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "W = 1000. \t\t\t#lb/ft\n", + "L = 10. \t\t\t#in\n", + "b1 = 4. \t\t\t#in\n", + "h1 = 1. \t\t\t#in\n", + "b2 = 1. \t\t\t#in\n", + "h2 = 6. \t\t\t#in\n", + "\t\t\t\n", + "# Calculations\n", + "Mmax = 12500 \t\t\t#lb ft\n", + "y = ((b1*h1*h1/2)+(b2*h2*((h2/2)+h1)))/(b1*h1+b2*h2)\n", + "Ina = round((b1*h1**3/12)+b1*h1*(y-h1/2)**2+(b2*h2**3/12)+b2*h2*(h1+h2-y-(h2/2))**2,1)\n", + "sigmat = Mmax*12*y/Ina\n", + "sigmac = Mmax*12*(h1+h2-y)/Ina\n", + "\n", + "\t\t\t\n", + "# Results\n", + "print 'maximum tensile stress = %.2f psi'%(round(sigmat,-1))\n", + "print 'maximum compressive bending stress = %.2f psi'%(round(sigmac,-2)) \n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "maximum tensile stress = 8180.00 psi\n", + "maximum compressive bending stress = 13800.00 psi\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.4 Page No : 287" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "st = 1200. \t\t\t#psi\n", + "sc = 100. \t\t\t#psi\n", + "h = 12. \t\t\t#in\n", + "b = 4. \t\t\t#in\n", + "\t\t\t\n", + "# Calculations\n", + "I = b*h**3/12\n", + "P1 = st*I/(b*12*(h/2))\n", + "P2 = 2*sc*b*12/3\n", + "if (P1<P2):\n", + " print 'Safe value of p = %.f lB'%(P1)\n", + "else: \n", + " print 'Safe value of p = %.f lB'%(P2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Safe value of p = 2400 lB\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.5 Page No : 287" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "W = 600. \t\t\t#lb/ft\n", + "L1 = 8. \t\t\t#in\n", + "L2 = 4. \t\t\t#in\n", + "b = 6. \t\t\t#in\n", + "h = 8. \t\t\t#in\n", + "t = 1. \t\t\t#in\n", + "\t\t\t\n", + "# Calculations\n", + "R1 = W*(L1+L2)*((L1+L2)/2)/L1\n", + "R2 = W*(L1+L2)*(L1-(L1+L2)/2)/L1\n", + "Vmax = 3000 \t\t\t#lb\n", + "I = (b*h**3/12)-(L2*b**3/12)\n", + "Ay = b*L2*(L2/2)-L2*b/2*b/4\n", + "b = t+t\n", + "Tmax = Vmax*Ay/(I*b)\n", + "\t\t\t\n", + "# Results\n", + "print 'maximum shear stress = %.0f psi'%(Tmax) \n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "maximum shear stress = 245 psi\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.6 Page No : 290" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "w = 4000. \t\t\t#lb/ft\n", + "l = 20. \t\t\t#ft\n", + "y = 0.96\n", + "A = 4.18 \t\t\t#in**2\n", + "Icq = 5.6 \t\t\t#in**4\n", + "d = 28. \t\t\t#in\n", + "b = 0.5 \t\t\t#in\n", + "T = 8000. \t\t\t#psi\n", + "d1 = 0.75 \t\t\t#in\n", + "\t\t\t\n", + "# Calculations\n", + "V = w*l/2\n", + "Ay = 2*A*((d/2)-y)\n", + "I = b*d**3/12+4*(Icq+A*((d/2)-y)**2)\n", + "p = (2*T*(math.pi/4)*d1**2*I)/(V*Ay)\n", + "\t\t\t\n", + "# Results\n", + "print 'Rivet spacing = %.2f in'%(p) \n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rivet spacing = 6.13 in\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.7 Page No : 293" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "# Variables\n", + "Es = 30.*10**6\n", + "Ew = 1.5*10**6\n", + "w = 500. \t\t\t#lb per ft\n", + "span = 12. \t\t\t#ft\n", + "t = 0.25 \t\t\t#in\n", + "h = 12. \t\t\t#in\n", + "n = 3.\n", + "b = 5. \t\t\t#in\n", + "\t\t\t\n", + "# Calculations\n", + "bw = Es*t/Ew\n", + "Ina = n*b*h**3/12\n", + "M = (w*span*(h/2)*12)/4\n", + "S = M*(h/2)/I\n", + "Ss = Es*S/Ew\n", + "bs = Ew*bw/Es\n", + "Ina1 = n*t*h**3/12\n", + "Ss1 = M*(h/2)/Ina1\n", + "Sw = Ew*Ss1/Es\n", + "\t\t\t\n", + "# Results\n", + "print 'Maximum bending stress in steel = %.3f psi'%(Ss1)\n", + "print 'Maximum bending stress in wood = %.2f psi'%(Sw)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum bending stress in steel = 6000.000 psi\n", + "Maximum bending stress in wood = 300.00 psi\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.8 Page No : 294" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "Ss = 15000. \t\t\t#psi\n", + "Sa = 6000. \t\t\t#psi\n", + "Es = 30.*10**6\n", + "Ea = 10.*10**6\n", + "Sl = 16. \t\t\t#ft\n", + "ba = 3. \t\t\t#in\n", + "ha = 8. \t\t\t#in\n", + "hs = 1. \t\t\t#in\n", + "b = 1. \t\t\t#in\n", + "\t\t\t\n", + "# Calculations and Resuls\n", + "bs = (Ea/Es)*ba\n", + "Y = ((ba-b)*b*(hs/2)+(ha+b)*b*((ha/2)+(hs/2)))/(ba*b+ha*b)\n", + "I = (ba*hs**3/12)+ba*hs*(Y-(hs/2))**2+((b*ha**3/12)+b*ha*(ha-Y-(ha/2))**2)\n", + "w1 = Ss*I/(Y*(1./2)*ha*(ha)*12)\n", + "Ss = Es*Sa/Ea\n", + "w2 = Ss*I/((ha-Y)*(1./2)*ha*(ha)*12)\n", + "if (w1<w2):\n", + " print 'Greatest uniformly distributed load = %d lb per ft'%(w1)\n", + "else:\n", + " print 'Greatest uniformly distributed load = %d lb per ft'%(w2)\n", + "\n", + "# note : rounding off error" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Greatest uniformly distributed load = 781 lb per ft\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.9 Page No : 297" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "M = 500000. \t\t\t#lb in\n", + "r = 15.\n", + "n = 3.\n", + "b = 20. \t\t\t#in\n", + "l = 12. \t\t\t#in\n", + "As = 1. \t\t\t#in**2\n", + "\t\t\t\n", + "# Calculations\n", + "At = r*As*n\n", + "x = (-2*At+math.sqrt((2*At)**2+8*At*b*l))/(2*l)\n", + "Ina = ((l*x**3)/3)+At*(b-x)**2\n", + "Scmax = M*x/Ina\n", + "Ssmax = r*M*(b-x)/Ina\n", + "\t\t\t\n", + "# Results\n", + "print 'Maximum bending stress in concrete = %.0f psi'%(Scmax)\n", + "print 'Maximum bending stress in steel = %.2f psi'%(Ssmax)\n", + "\n", + "# note : answer is accurate. please check with calculator." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum bending stress in concrete = 542 psi\n", + "Maximum bending stress in steel = 9815.22 psi\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.10 Page No : 298" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "# Variables\n", + "Sc = 800. \t\t\t#psi\n", + "Ss = 18000. \t\t\t#psi\n", + "ratio = 15.\n", + "d = 5/8. \t\t\t#in\n", + "l = 20. \t\t\t#in\n", + "b = 10. \t\t\t#in\n", + "\t\t\t\n", + "# Calculations\n", + "x = Sc*ratio*l/(Ss+Sc*ratio)\n", + "As = b*x*(x/2)/((l-x)*ratio)\n", + "Ina = (b*x**3/3)+ratio*As*(l-x)**2\n", + "M = Sc*I/x\n", + "N = As/(math.pi*(d/2)**2)\n", + "\t\t\t\n", + "# Results\n", + "print 'Number of steel bars required = %.2f'%(N)\n", + "print (\"it rounds to 6 bars\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of steel bars required = 5.79\n", + "it rounds to 6 bars\n" + ] + } + ], + "prompt_number": 11 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file |