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.
Figure
Sol.: As diagram is symmetrical about the y axis that is,X = 0, x_{1} = x_{2} = 0
A_{1} = 8 × 2 = 16 cm^{2}
A_{2} = 12 × 2 = 24 cm^{2}
A_{3} = 12 × 2 = 24 cm^{2}
y_{1} = (2 + 12 + 2/2) = 15 cm
y_{2} = (2 + 12/2) = 8 cm
y_{2} = 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 = I_{X}_{X} = I_{XX1} + I_{XX2}
The moment of inertia about y-y axis = As