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| author | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
|---|---|---|
| committer | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
| commit | 4a1f703f1c1808d390ebf80e80659fe161f69fab (patch) | |
| tree | 31b43ae8895599f2d13cf19395d84164463615d9 /Engineering_Mechanics_by_Tayal_A.K./chapter13_6.ipynb | |
| parent | 9d260e6fae7328d816a514130b691fbd0e9ef81d (diff) | |
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diff --git a/Engineering_Mechanics_by_Tayal_A.K./chapter13_6.ipynb b/Engineering_Mechanics_by_Tayal_A.K./chapter13_6.ipynb new file mode 100755 index 00000000..690eeb8a --- /dev/null +++ b/Engineering_Mechanics_by_Tayal_A.K./chapter13_6.ipynb @@ -0,0 +1,121 @@ +{
+ "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": {}
+ }
+ ]
+}
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