Hollow I-Section Second Moment of Area
Hollow I-Section Second Moment of Area
Subtracting the inner void from the outer rectangle gives the inertia of an I or box section — the basis of its bending efficiency.
The second moment of area is I = (B·H³ − b·h³)/12. where B, H are the outer and b, h the inner breadth and depth.
Inputs
B := 200 mm=200 mm
H := 400 mm=400 mm
b := 180 mm=180 mm
h := 360 mm=360 mm
Subtract the inner rectangle’s inertia from the outer.
I := (B·H^3 - b·h^3)/12=3.67e-04 m^4
Results
Removing material near the neutral axis barely reduces I while saving weight — the reason beams are I-shaped rather than solid.
Assumptions & limitations
- Symmetric hollow rectangular section.
- Bending about the strong axis.
- Thin-wall local effects ignored.