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{
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 4 Centroid Centre of mass and Centre of Gravity"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Example 4.8 Centroid of a composite plane figure"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
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},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The centroid of the un equal I-section is 10.961538 cm \n",
"\n"
]
}
],
"source": [
"# Initilization of variables\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",
"# Calculations\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+(t1/2) #cm # y co-ordinate of the centroid of top flange\n",
"y2=t3+(t2/2) #cm # y co-ordinate of the centroid of the web\n",
"y3=t3/2 #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-symmetrical I-section\n",
"# Results\n",
"print('The centroid of the un equal I-section is %f cm \\n'%y_c)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Example 4.9 Centroid of a composite plane figure"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The centroid of the cross-sectional area of a Z-section about x-axis is 13.557692 cm \n",
"\n",
"The centroid of the cross-sectional area of a Z-section about y-axis is 7.692308 cm \n",
"\n"
]
}
],
"source": [
"# Initilization of variables\n",
"# The given section is Z-section which is un-symmetrycal about both the axis\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",
"# Calculations\n",
"# Respective areas\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",
"# first we calculate the x co-ordinate of the centroid\n",
"x1=b3-b2+(b1/2) #cm # for the bottom flange\n",
"x2=b3-(b2/2) #cm # for the web\n",
"x3=b3/2 #cm # for the top flange\n",
"x_c=((A1*x1)+(A2*x2)+(A3*x3))/(A1+A2+A3) #cm\n",
"# secondly we calculate the y co-ordinate of the centroid\n",
"y1=t1/2 #cm # for the bottom flange\n",
"y2=t1+(t2/2) #cm # for the web\n",
"y3=t1+t2+(t3/2) #cm # for the top flange\n",
"y_c=((A1*y1)+(A2*y2)+(A3*y3))/(A1+A2+A3) # cm\n",
"# Results\n",
"print('The centroid of the cross-sectional area of a Z-section about x-axis is %f cm \\n'%x_c)\n",
"print('The centroid of the cross-sectional area of a Z-section about y-axis is %f cm \\n'%y_c)"
]
}
],
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