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Q. An I section has dimensions Top flange = 8 cm × 2 cm; Bottom flange = 12 cm × 2 cm; Web = 12 cm × 2 cm; Over all the depth of section = 16 cm. Determine M.I. of I section about 2 centroidal axes.
Sol.: As diagram is symmetrical about the y axis that is,X = 0, x1 = x2 = 0
A1 = 8 × 2 = 16 cm2
A2 = 12 × 2 = 24 cm2
A3 = 12 × 2 = 24 cm2
y1 = (2 + 12 + 2/2) = 15 cm
y2 = (2 + 12/2) = 8 cm
y2 = 2/2 = 1 cm
Y = (A1y1 + A2y2 + A3y3)/(A1 + A2 + A3)
= (16 × 15 + 24 × 8 + 24 × 1)/(16 + 24 + 24) = 7.125cm
C.G. = (0, 7.125)
Moment of inertia (M.I.) about x-x axis = IXX = IXX1 + IXX2
The moment of inertia about y-y axis = As
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