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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:ddc392c3474d618cbae4adde9fb1f47f093e50fd2a55d0b1580decec813c6214"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 2 : Force System : Components, Resultants, Equivalence"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.3 Page No : 21"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\t\t\t\n",
+ "# Variables\n",
+ "f1 = 20. \t\t\t#lb\n",
+ "f2 = 40. \t\t\t#lb\n",
+ "alpha = 30. \t\t\t#degrees\n",
+ "\t\t\t\n",
+ "# Calculations\n",
+ "R = math.sqrt(f1**2+f2**2+2*f1*f2*math.cos(math.radians(alpha)))\n",
+ "angle = math.degrees(math.asin((f2*math.sin(math.radians(180-alpha)))/(R)))\n",
+ "\t\t\t\n",
+ "# Results\n",
+ "print 'R = %.1f lb'%(R)\n",
+ "print 'angle = %.1f degrees'%(angle)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R = 58.2 lb\n",
+ "angle = 20.1 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.4 Page No : 22"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\t\t\t\n",
+ "# Variables\n",
+ "fx = 100. \t\t\t#lb\n",
+ "f1 = 200. \t\t\t#lb\n",
+ "f2 = 100. \t\t\t#lb\n",
+ "f3 = 50. \t\t\t#lb\n",
+ "a1 = 30. \t\t\t#degrees\n",
+ "a2 = 45. \t\t\t#degrees\n",
+ "a3 = 60. \t\t\t#degrees\n",
+ "\t\t\t\n",
+ "# Calculations\n",
+ "Rx = fx+f1*math.cos(math.radians(a1))-f2*math.cos(math.radians(a2))-f3*math.cos(math.radians(a3))\n",
+ "Ry = f1*math.sin(math.radians(a1))+f2*math.sin(math.radians(a2))-f3*math.sin(math.radians(a3))\n",
+ "R = math.sqrt(Rx**2+Ry**2)\n",
+ "angle = math.degrees(math.atan(Ry/Rx))\n",
+ "\t\t\t\n",
+ "# Results\n",
+ "print 'R = %.f lb'%(R)\n",
+ "print 'angle = %.1f degrees'%(angle)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R = 218 lb\n",
+ "angle = 35.7 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.5 Page No : 25"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\t\t\t\n",
+ "# Variables\n",
+ "f1 = 100. \t\t\t#lb\n",
+ "f2 = 200. \t\t\t#lb\n",
+ "x1 = 2.\n",
+ "x2 = -3.\n",
+ "y1 = 3.\n",
+ "y2 = 5.\n",
+ "z1 = 4.\n",
+ "z2 = -2.\n",
+ "\t\t\t\n",
+ "# Calculations\n",
+ "d1 = math.sqrt(x1**2+y1**2+z1**2)\n",
+ "d2 = math.sqrt(x2**2+y2**2+z2**2)\n",
+ "f1x = f1*x1/d1\n",
+ "f1y = f1*y1/d1\n",
+ "f1z = f1*z1/d1\n",
+ "f2x = f2*x2/d2\n",
+ "f2y = f2*y2/d2\n",
+ "f2z = f2*z2/d2\n",
+ "Rx = f1x+f2x\n",
+ "Ry = f1y+f2y\n",
+ "Rz = f1z+f2z\n",
+ "R = math.sqrt(Rx**2+Ry**2+Rz**3)\n",
+ "I1 = Rx/R\n",
+ "I2 = Ry/R\n",
+ "I3 = Rz/R\n",
+ "\t\t\t\n",
+ "# Results\n",
+ "print 'R = %d lb'%(R)\n",
+ "print 'I1 = %.3f '%(I1)\n",
+ "print 'I2 = %.3f '%(I2)\n",
+ "print 'I3 = %.3f '%(I3)\n",
+ "\n",
+ "# note : rounding off error would be there for R."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R = 227 lb\n",
+ "I1 = -0.264 \n",
+ "I2 = 0.956 \n",
+ "I3 = 0.041 \n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.6 Page No : 27"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\t\t\t\n",
+ "# Variables\n",
+ "F = 100. \t\t\t#lb\n",
+ "x1 = 6. \t\t\t#in\n",
+ "x2 = 8. \t\t\t#in\n",
+ "x3 = 2. \t\t\t#in\n",
+ "\t\t\t\n",
+ "# Calculations\n",
+ "xab = math.sqrt(x1**2+x2**2)\n",
+ "d = x3*x1/xab\n",
+ "M1 = F*d\n",
+ "Fx = F*x2/xab\n",
+ "Fy = F*x1/xab\n",
+ "M2 = Fy*xab-Fx*x1\n",
+ "M3 = Fy*x3\n",
+ "\t\t\t\n",
+ "# Results\n",
+ "print 'M1 = %.f lb.in'%(M1)\n",
+ "print 'M2 = %.f lb.in'%(M2)\n",
+ "print 'M3 = %.f lb.in'%(M3)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "M1 = 120 lb.in\n",
+ "M2 = 120 lb.in\n",
+ "M3 = 120 lb.in\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.7 Page No : 30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\t\t\t\n",
+ "# Variables\n",
+ "Fy1 = 2. \t\t\t#kips\n",
+ "Fy2 = 5. \t\t\t#kips\n",
+ "Fy3 = 10. \t\t\t#kips\n",
+ "Fy4 = 3. \t\t\t#kips\n",
+ "L = 5. \t\t\t#ft\n",
+ "\n",
+ "# Calculations\n",
+ "Ry = Fy1+Fy2+Fy3+Fy4\n",
+ "x = (Fy1*L+Fy2*2*L+Fy3*3*L+Fy4*4*L)/Ry\n",
+ "\t\t\t\n",
+ "# Results\n",
+ "print 'Ry = %.2f kips'%(Ry)\n",
+ "print 'x = %.1f ft to the right of O'%(x)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Ry = 20.00 kips\n",
+ "x = 13.5 ft to the right of O\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.8 Page No : 30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "import math \t\t\t\n",
+ "\n",
+ "# Variables\n",
+ "Fx1 = -15. \t\t\t#lb\n",
+ "Fx2 = 55. \t\t\t#lb\n",
+ "Fy1 = 70. \t\t\t#lb\n",
+ "Fy2 = -40. \t\t\t#lb\n",
+ "x1 = 4. \t\t\t#in\n",
+ "x2 = 3. \t\t\t#in\n",
+ "x3 = 5. \t\t\t#in\n",
+ "y1 = 4. \t\t\t#in\n",
+ "y2 = 2. \t\t\t#in\n",
+ "\t\t\t\n",
+ "# Calculations\n",
+ "Rx = Fx1+Fx2\n",
+ "Ry = Fy1+Fy2\n",
+ "R = math.sqrt(Rx**2+Ry**2)\n",
+ "angle = math.degrees(math.atan(Ry/Rx))\n",
+ "\t\t\t\n",
+ "# Results\n",
+ "print 'R = %.2f lb'%(R)\n",
+ "print 'angle = %.1f degrees'%(angle)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R = 50.00 lb\n",
+ "angle = 36.9 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.9 Page No : 32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "import math \n",
+ "\t\t\t\n",
+ "# Variables\n",
+ "Fy = 200. \t\t\t#lb\n",
+ "Fx = 100. \t\t\t#lb\n",
+ "y = 3. \t \t\t#in\n",
+ "x = 6. \t\t\t#in\n",
+ "\t\t\t\n",
+ "# Calculations\n",
+ "M = Fy*x-Fx*y\n",
+ "\t\t\t\n",
+ "# Results\n",
+ "print 'Moment = %.2f lb in'%(M)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Moment = 900.00 lb in\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 10:54:56 +0000