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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Chapter 13 Principle of Virtual Work"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Example 13.1 Application of Principle of Virtual Work"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The value of force (i.e P) that can hold the system in equilibrium is 500 N\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Initilization of variables\n",
+    "W=1000 # N # weight to be raised\n",
+    "# Calculations\n",
+    "# From the Principle of virtual work,\n",
+    "P=W/2 # N\n",
+    "# Results\n",
+    "print('The value of force (i.e P) that can hold the system in equilibrium is %d N'%P)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Example 13.7 Application of Principle of Virtual Work"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The Horizontal component of reaction at A (X_A) is 333.333333 N\n",
+      "The Vertical component of reaction at A (Y_A) is 1333.333333 N\n",
+      "The Horizontal component of reaction at B (X_B) is 333.333333 N\n",
+      "The Vertical component of reaction at B (Y_B) is 666.666667 N\n"
+     ]
+    }
+   ],
+   "source": [
+    "import math\n",
+    "# Initilization of variables\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",
+    "# Calculations\n",
+    "# Chosing the co-ordinate system with originat A, we can write,\n",
+    "theta=45 # degree\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)/6)*(math.cos(theta*math.pi/180)/math.sin(theta*math.pi/180)) # 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",
+    "# 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)/6 # 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",
+    "# Results\n",
+    "print('The Horizontal component of reaction at A (X_A) is %f N'%X_A)\n",
+    "print('The Vertical component of reaction at A (Y_A) is %f N'%Y_A)\n",
+    "print('The Horizontal component of reaction at B (X_B) is %f N'%X_B)\n",
+    "print('The Vertical component of reaction at B (Y_B) is %f N'%Y_B)"
+   ]
+  }
+ ],
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+}