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 "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": {}
  }
 ]
}