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{
"metadata": {
"name": "chapter4.ipynb"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 4 : Centroid , Centre Of Mass And Centre Of Gravity"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.4-8,Page No:100"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"# Initilization of variables\n",
"\n",
"b1=20 #cm # width of top flange\n",
"t1=5 #cm # thickness of top flange\n",
"b2=5 #cm # width of web\n",
"t2=15 #cm # thickness or height of the web\n",
"b3=30 #cm # width of bottom flange\n",
"t3=5 #cm # thickness of bottom flange\n",
"\n",
"# Calculations\n",
"\n",
"A1=b1*t1 #cm^2 # area of bottom flange\n",
"A2=b2*t2 #cm^2 # area of the web\n",
"A3=b3*t3 #cm^2 # area of top flange\n",
"y1=t3+t2+(t1*0.5) #cm # y co-ordinate of the centroid of top flange\n",
"y2=t3+(t2*0.5) #cm # y co-ordinate of the centroid of the web\n",
"y3=t3*0.5 #cm # y co-ordinate of the centroid of the bottom flange\n",
"y_c=((A1*y1)+(A2*y2)+(A3*y3))/(A1+A2+A3) #cm # where y_c is the centroid of the un-symmetrycal I-section\n",
"\n",
"# Results\n",
"\n",
"print\"The centroid of the un equal I-section is \",round(y_c,2),\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The centroid of the un equal I-section is 10.96 cm\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.4-9,Page No:101"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Initilization of variables\n",
"\n",
"# The given section is Z-section which is un-symmetrycal about both the axis\n",
"\n",
"b1=20 #cm # width of bottom flange \n",
"t1=5 #cm # thickness of the bottom flange\n",
"b2=2.5 #cm # thickness of the web of the flange\n",
"t2=15 #cm # depth of the web\n",
"b3=10 #cm # width of the top flange\n",
"t3=2.5 #cm # thickness of the top flange\n",
"\n",
"# Calculations\n",
"\n",
"# Respective areas\n",
"\n",
"A1=b1*t1 # cm^2 # area of the bottom flange\n",
"A2=b2*t2 # cm^2 # area of the web\n",
"A3=b3*t3 # cm^2 # area of the top-flange\n",
"\n",
"# first we calculate the x co-ordinate of the centroid\n",
"\n",
"x1=b3-b2+(b1*0.5) #cm # for the bottom flange\n",
"x2=b3-(b2*0.5) #cm # for the web\n",
"x3=b3*0.5 #cm # for the top flange\n",
"x_c=((A1*x1)+(A2*x2)+(A3*x3))/(A1+A2+A3) #cm\n",
"\n",
"# secondly we calculate the y co-ordinate of the centroid\n",
"\n",
"y1=t1*0.5 #cm # for the bottom flange\n",
"y2=t1+(t2*0.5) #cm # for the web\n",
"y3=t1+t2+(t3*0.5) #cm # for the top flange\n",
"y_c=((A1*y1)+(A2*y2)+(A3*y3))/(A1+A2+A3) # cm\n",
"\n",
"# Results\n",
"\n",
"print\"The centroid of the cross-sectional area of a Z-section about x-axis is \",round(x_c,2),\"cm\"\n",
"print\"The centroid of the cross-sectional area of a Z-section about y-axis is \",round(y_c,2),\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The centroid of the cross-sectional area of a Z-section about x-axis is 13.56 cm\n",
"The centroid of the cross-sectional area of a Z-section about y-axis is 7.69 cm\n"
]
}
],
"prompt_number": 4
}
],
"metadata": {}
}
]
}
|
