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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": {}
}
]
}
|
