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{
"metadata": {
"name": "",
"signature": "sha256:28eceabccc986d95bd8fd4a32c3e228a185da4101f3a8dcc4e232e8945315e7d"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 12: Review of Centroids and Moments of Inertia "
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12.2, page no. 833"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math \n",
"\n",
"#initialisation\n",
"A1 = 6*0.5 # Partial Area in in2\n",
"A2 = 20.8 # from table E1 and E3\n",
"A3 = 8.82 # from table E1 and E3\n",
"y1 = (18.47/2.0) + (0.5/2.0) # Distance between centroid C1 and C2\n",
"y2 = 0 # Distance between centroid C2 and C2\n",
"y3 = (18.47/2.0) + 0.649 # Distance between centroid C3 and C2\n",
"\n",
"#calculation\n",
"A = A1 + A2 + A3 # Area of entire cross section\n",
"Qx = (y1*A1) + (y2*A2) - (y3*A3) # First moment of entire cross section\n",
"y_bar = Qx/A # Distance between x-axis and centroid of the cross section\n",
"print \"The distance between x-axis and centroid of the cross section is \", round(-y_bar,2), \"inch\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The distance between x-axis and centroid of the cross section is 1.8 inch\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12.5, page no. 840"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math \n",
"\n",
"#initialisation\n",
"A1 = 6*0.5 # Partial Area in in2\n",
"A2 = 20.8 # from table E1 and E3\n",
"A3 = 8.82 # from table E1 and E3\n",
"y1 = (18.47/2.0) + (0.5/2.0) # Distance between centroid C1 and C2\n",
"y2 = 0 # Distance between centroid C2 and C2\n",
"y3 = (18.47/2.0) + 0.649 # Distance between centroid C3 and C2\n",
"\n",
"#calculation\n",
"A = A1 + A2 + A3 # Area of entire cross section\n",
"Qx = (y1*A1) + (y2*A2) - (y3*A3) # First moment of entire cross section\n",
"y_bar = Qx/A # Distance between x-axis and centroid of the cross section\n",
"c_bar = -(y_bar)\n",
"\n",
"I1 = (6*0.5**3)/12.0 # Moment of inertia of A1 \n",
"I2 = 1170 # Moment of inertia of A2 from table E1\n",
"I3 = 3.94 # Moment of inertia of A3 from table E3\n",
"Ic1 = I1 + (A1*(y1+c_bar)**2) # Moment of inertia about C-C axis of area C1\n",
"Ic2 = I2 + (A2*(y2+c_bar)**2) # Moment of inertia about C-C axis of area C2\n",
"Ic3 = I3 + (A3*(y3-c_bar)**2) # Moment of inertia about C-C axis of area C3\n",
"Ic = Ic1 + Ic2 + Ic3 # Moment of inertia about C-C axis of whole area\n",
"print \"The moment of inertia of entire cross section area about its centroidal axis C-C\", round(Ic), \"in^4\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The moment of inertia of entire cross section area about its centroidal axis C-C 2200.0 in^4\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12.7, page no. 851"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math \n",
"import numpy\n",
"\n",
"#initialisation\n",
"Ix = 29.29e06 # Moment of inertia of crosssection about x-axis\n",
"Iy = 5.667e06 # Moment of inertia of crosssection about y-axis\n",
"Ixy = -9.336e06 # Moment of inertia of crosssection \n",
"\n",
"#calculation\n",
"tp1 = (numpy.degrees(numpy.arctan((-(2*Ixy)/(Ix-Iy)))))/2.0 # Angle definig a Principle axix\n",
"tp2 = 90 + tp1 \n",
"print \"The Principle axis is inclined at an angle\", round(tp1,2), \"degree\"\n",
"print \"Second angle of inclination of Principle axis is\", round(tp2,2), \"degree\"\n",
"Ix1 = (Ix+Iy)/2.0 + ((Ix-Iy)/2.0)*math.cos(math.radians(tp1)) - Ixy*math.sin(math.radians(tp1))\n",
"Ix2 = (Ix+Iy)/2.0 + ((Ix-Iy)/2.0)*math.cos(math.radians(tp2)) - Ixy*math.sin(math.radians(tp2))\n",
"print \"Principle Moment of inertia corresponding to tp1\", round(Ix1), \"mm^4\"\n",
"print \"Principle Moment of inertia corresponding to tp2\", round(Ix2), \"mm^4\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Principle axis is inclined at an angle 19.16 degree\n",
"Second angle of inclination of Principle axis is 109.16 degree\n",
"Principle Moment of inertia corresponding to tp1 31700001.0 mm^4\n",
"Principle Moment of inertia corresponding to tp2 22420295.0 mm^4\n"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}
|
