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-{

- "metadata": {

-  "name": "chapter5.ipynb"

- },

- "nbformat": 3,

- "nbformat_minor": 0,

- "worksheets": [

-  {

-   "cells": [

-    {

-     "cell_type": "heading",

-     "level": 1,

-     "metadata": {},

-     "source": [

-      "Chapter 5: General Case Of Forces In Plane"

-     ]

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 5.5-2,Page No:111"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "#Inilization of variables\n",

-      "\n",

-      "W=2000 #N\n",

-      "Lab=2 #m #length of the member from the vertical to the 1st load of 2000 N\n",

-      "Lac=5 #m #length of the member from the vertical to the 2nd load of 2000 N\n",

-      "Lpq=3.5 #m\n",

-      "\n",

-      "#Calculations\n",

-      "\n",

-      "Rq=((W*Lab)+(W*Lac))/Lpq #N #take moment abt. pt P\n",

-      "Xp=Rq #N #sum Fx=0\n",

-      "Yp=2*W #N #sum Fy=0\n",

-      "Rp=(Xp**2+Yp**2)**0.5 #N\n",

-      "\n",

-      "#Resuts\n",

-      "\n",

-      "print\"The reaction at P is \",round(Rp,1),\"N\"\n",

-      "print\"The reaction at Q is \",round(Rq),\"N\"\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The reaction at P is  5656.9 N\n",

-        "The reaction at Q is  4000.0 N\n"

-       ]

-      }

-     ],

-     "prompt_number": 1

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 5.5-3,Page No:112"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "import numpy as np\n",

-      "#Initilization of vaiables\n",

-      "\n",

-      "W=25 #N # self weight of the ladder\n",

-      "M=75 #N # weight of the man standing o the ladder\n",

-      "theta=63.43 #degree # angle which the ladder makes with the horizontal\n",

-      "alpha=30 #degree # angle made by the string with the horizontal\n",

-      "Loa=2 #m # spacing between the wall and the ladder\n",

-      "Lob=4 #m #length from the horizontal to the top of the ladder touching the wall(vertical)\n",

-      "\n",

-      "#Calculations\n",

-      "\n",

-      "#Using matrix to solve the simultaneous eqn's 3 & 4\n",

-      "\n",

-      "A=np.array([[2 ,-4],[1, -0.577]])\n",

-      "B=np.array([100,100])\n",

-      "C=np.linalg.solve(A,B)\n",

-      "\n",

-      "#Results\n",

-      "\n",

-      "print\"The reaction at A i.e Ra is \",round(C[0],2),\"N\"\n",

-      "print\"The reaction at B i.e Rb is \",round(C[1],2),\"N\"\n",

-      "\n",

-      "#Calculations\n",

-      "\n",

-      "T=C[1]/cos(alpha*(pi/180)) #N # from (eqn 1)\n",

-      "\n",

-      "#Results\n",

-      "\n",

-      "print\"The required tension in the string is \",round(T,2),\"N\"\n",

-      "\n",

-      "#answer may vary due to decimal variance"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The reaction at A i.e Ra is  120.27 N\n",

-        "The reaction at B i.e Rb is  35.14 N\n",

-        "The required tension in the string is  40.57 N\n"

-       ]

-      }

-     ],

-     "prompt_number": 2

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 5.5-4,Page No:113"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "#Initilization of variables\n",

-      "\n",

-      "W=100 #N\n",

-      "theta=60 #degree #angle made by the ladder with the horizontal\n",

-      "alpha=30 #degree #angle made by the ladder with the vertical wall\n",

-      "Lob=4 #m # length from the horizontal to the top of the ladder touching the wall(vertical)\n",

-      "Lcd=2 #m # length from the horizontal to the centre of the ladder where the man stands\n",

-      "\n",

-      "#Calculations\n",

-      "\n",

-      "Lab=Lob*(1/cos(alpha*(pi/180))) #m #length of the ladder\n",

-      "Lad=Lcd*tan(alpha*(pi/180)) #m\n",

-      "Rb=(W*Lad)/Lab #N #take moment at A\n",

-      "Xa=Rb*sin(theta*(pi/180)) #N # From eq'n 1\n",

-      "Ya=W+Rb*cos(theta*(pi/180)) #N #From eq'n 2\n",

-      "\n",

-      "#Results\n",

-      "\n",

-      "print\"The reaction at B i.e Rb is \",round(Rb),\"N\"\n",

-      "print\"The horizontal reaction at A i.e Xa is \",round(Xa,2),\"N\"\n",

-      "print\"The vertical reaction at A i.e Ya is \",round(Ya,1),\"N\"\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The reaction at B i.e Rb is  25.0 N\n",

-        "The horizontal reaction at A i.e Xa is  21.65 N\n",

-        "The vertical reaction at A i.e Ya is  112.5 N\n"

-       ]

-      }

-     ],

-     "prompt_number": 6

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 5.5-5,Page No:114"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "#Initilization of variables\n",

-      "\n",

-      "W=100 #N #self weight of the man\n",

-      "alpha=30 #degree # angle made by the ladder with the wall\n",

-      "Lob=4 #m # length from the horizontal to the top of the ladder touching the wall(vertical)\n",

-      "Lcd=2 #m\n",

-      "\n",

-      "#Calculations\n",

-      "\n",

-      "# using the equiblirium equations\n",

-      "\n",

-      "Ya=W #N # From eq'n 2\n",

-      "Lad=Lcd*tan(alpha*(pi/180)) #m #Lad is the distance fom pt A to the point where the line from the cg intersects the horizontal\n",

-      "Rb=(W*Lad)/Lob #N # Taking sum of moment abt A\n",

-      "Xa=Rb #N # From eq'n 1\n",

-      "\n",

-      "#Results\n",

-      "\n",

-      "print\"The horizontal reaction at A i.e Xa is \",round(Xa,2),\"N\"\n",

-      "print\"The vertical reaction at A i.e Ya is \",round(Ya),\"N\"\n",

-      "print\"The reaction at B i.e Rb is \",round(Rb,2),\"N\"\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The horizontal reaction at A i.e Xa is  28.87 N\n",

-        "The vertical reaction at A i.e Ya is  100.0 N\n",

-        "The reaction at B i.e Rb is  28.87 N\n"

-       ]

-      }

-     ],

-     "prompt_number": 8

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 5.5-6,Page No:115"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "#Initilization of variables\n",

-      "\n",

-      "d=0.09 #m #diametre of the right circular cylinder\n",

-      "h=0.12 #m #height of the cyinder\n",

-      "W=10 #N # self weight of the bar\n",

-      "l=0.24 #m #length of the bar\n",

-      "\n",

-      "#Calculations\n",

-      "\n",

-      "theta=arctan(h/d)*(180/pi) # angle which the bar makes with the horizontal\n",

-      "Lad=(d**2+h**2)**0.5 #m # Lad is the length of the bar from point A to point B\n",

-      "Rd=(W*h*cos(theta*(pi/180)))/Lad #N # Taking moment at A\n",

-      "Xa=Rd*sin(theta*(pi/180)) #N # sum Fx=0.... From eq'n 1\n",

-      "Ya=W-(Rd*cos(theta*(pi/180))) #N # sum Fy=0..... From eq'n 2\n",

-      "Ra=(Xa**2+Ya**2)**0.5 #resultant of Xa & Ya\n",

-      "\n",

-      "#Results\n",

-      "\n",

-      "print\"The horizontal reaction at A i.e Xa is \",round(Xa,2),\"N\"\n",

-      "print\"The vertical reaction at A i.e Ya is \",round(Ya,2),\"N\"\n",

-      "print\"Therefore the reaction at A i.e Ra is \",round(Ra,2),\"N\"\n",

-      "print\"The reaction at D i.e Rd is \",round(Rd,2),\"N\"\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The horizontal reaction at A i.e Xa is  3.84 N\n",

-        "The vertical reaction at A i.e Ya is  7.12 N\n",

-        "Therefore the reaction at A i.e Ra is  8.09 N\n",

-        "The reaction at D i.e Rd is  4.8 N\n"

-       ]

-      }

-     ],

-     "prompt_number": 10

-    }

-   ],

-   "metadata": {}

-  }

- ]

-}
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