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, 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 = I_XX  = I_XX1  + I_XX2

The moment of inertia about  y-y axis =
As