Moment of Inertia (Second Moment of Area)

The moment of inertia (more precisely the second moment of area, I, in mm⁴) is a purely geometric property describing how a cross-section's area is distributed about its neutral axis. The further material lies from the axis, the larger I and the stiffer the section in bending — which is why I-sections and hollow tubes are efficient.

For a rectangle b×D about its centroidal axis, I = bD³/12; for a circle of diameter d, I = πd⁴/64. Composite and built-up sections use the parallel-axis theorem I = Ig + A·y² to shift each part's inertia to the common neutral axis. I directly governs flexural stiffness EI, deflection (δ ∝ 1/EI), and the section modulus Z = I/y used in bending-stress checks. For RCC, the cracked transformed section's I is used for deflection per IS 456 Annex C.