1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
|
{
"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.sce"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"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",
"clc\n",
"printf('The value of force (i.e P) that can hold the system in equilibrium is %f N \n',P)"
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 13.7: Application_of_Principle_of_Virtual_Work.sce"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// 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)*(cosd(theta)/sind(theta)) // 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",
"clc\n",
"printf('The Horizontal component of reaction at A (X_A) is %f N \n',X_A)\n",
"printf('The Vertical component of reaction at A (Y_A) is %f N \n',Y_A)\n",
"printf('The Horizontal component of reaction at B (X_B) is %f N \n',X_B)\n",
"printf('The Vertical component of reaction at B (Y_B) is %f N \n',Y_B)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Scilab",
"language": "scilab",
"name": "scilab"
},
"language_info": {
"file_extension": ".sce",
"help_links": [
{
"text": "MetaKernel Magics",
"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
}
],
"mimetype": "text/x-octave",
"name": "scilab",
"version": "0.7.1"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
|
