Question

Determine the moment of inertia of the symmertic I-section shown in Fig. about its centroidal axis x-x and y-y. 

Also, determine moment of inertia of the section about a centroidal axis perpendicular to x-x axis and y-y axis.

Answer 1

The section is divided into three rectangles A₁, A₂ and A₃. 

Area A₁ = 200 × 9 = 1800 mm² 

Area A₂ = (250 – 9 × 2) × 6.7 = 1554.4 mm² 

Area A₃ = 200 × 9 = 1800 mm² 

Total Area A = 5154.4 mm² 

The section is symmetrical about both x-x and y-y axis. Therefore, its centroid will coincide with the centroid of rectangle A₂. 

With respect to the centroidal axis x-x and y-y, the centroid of rectangle A₁ is g₁ (0.0, 120.5), that of A₂ is g₂ (0.0, 0.0) and that of A₃ is g₃ (0.0, 120.5).

I_xx = Moment of inertia of A₁ + Moment of inertia of A₂ + Moment of inertia of A₃ about x-x axis

Moment of inertia of the section about a centroidal axis perpendicular to x-x and y-y axis is nothing but polar moment of inertia, and is given by: 

I_xx = I_xx + I_yy 

= 59269202 + 12005815 

I_yy = 7,12,75,017 mm⁴