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authorkinitrupti2017-05-12 18:40:35 +0530
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-{
- "metadata": {
- "name": "chapter13.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 13: Principle Of Virtual Work"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 13.13-1,Page No:312"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "# Initilization of variables\n",
- "\n",
- "W=1000 # N # weight to be raised\n",
- "\n",
- "# Calculations\n",
- "\n",
- "# From the Principle of virtual work,\n",
- "P=W/2 # N\n",
- "\n",
- "# Results\n",
- "\n",
- "print\"The value of force (i.e P) that can hold the system in equilibrium is \",round(P),\"N\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The value of force (i.e P) that can hold the system in equilibrium is 500.0 N\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 13.13-7,Page No:317"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "# Initilization of variables\n",
- "\n",
- "P=1000 # N # Force acting at the hinge of the 1st square\n",
- "Q=1000 # N # Force acting at the hinge of the 2nd square\n",
- "\n",
- "# Calculations\n",
- "\n",
- "# Chosing the co-ordinate system with originat A, we can write,\n",
- "theta=45 # degree\n",
- "\n",
- "# Forces that do work are P,Q & X_B. Applying the principle of virtual work & Simplyfying and solving for X_B,\n",
- "X_B=((2*P)*0.166666)*(cos(theta*(pi/180))/sin(theta*(pi/180))) # N # as 1/6=0.166666\n",
- "\n",
- "# Now give a virtual angular displacement to the whole frame about end A such that line AB turns by an angle delta_phi.\n",
- "\n",
- "# The force doing work are P,Q&Y_B.Applying the principle of virtual work & Simplyfying this eq'n and solving for Y_B,\n",
- "Y_B=((3*Q)+P)*0.166666 # N # as 1/6=0.166666\n",
- "\n",
- "# Simply by removing the support at A & replacing it by the reactions X_A & Y_A we can obtain,\n",
- "X_A=X_B # N\n",
- "Y_A=P+Q-Y_B # N\n",
- "\n",
- "# Results\n",
- "\n",
- "print\"The Horizontal component of reaction at A (X_A) is \",round(X_A,1),\"N\"\n",
- "print\"The Vertical component of reaction at A (Y_A) is \",round(Y_A,1),\"N\"\n",
- "print\"The Horizontal component of reaction at B (X_B) is \",round(X_B,1),\"N\"\n",
- "print\"The Vertical component of reaction at B (Y_B) is \",round(Y_B,1),\"N\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Horizontal component of reaction at A (X_A) is 333.3 N\n",
- "The Vertical component of reaction at A (Y_A) is 1333.3 N\n",
- "The Horizontal component of reaction at B (X_B) is 333.3 N\n",
- "The Vertical component of reaction at B (Y_B) is 666.7 N\n"
- ]
- }
- ],
- "prompt_number": 13
- }
- ],
- "metadata": {}
- }
- ]
-} \ No newline at end of file