Rectangle Centroidal Moment of Inertia

I_{x} = \frac{b h ^{3}}{12} I_{y} = \frac{h b ^{3}}{12}

For a rectangle of width b (along x) and height h (along y), the centroidal I about an axis through the center parallel to the base is bh³/12. Used in beam bending and the parallel-axis theorem.

$b$ (m): Width
$h$ (m): Height
$I_{x}$ (m⁴): Second moment about centroidal x

Step-by-step solved example

Rectangle b = 200 mm, h = 300 mm. Find Ix about the horizontal centroidal axis.

Rectangle: Ix = bh³/12 about the centroidal axis parallel to b.

1. SI
b = 0.20 m, h = 0.30 m.
2. Ix
Ix = (0.20)(0.30)³/12 = 4.50×10⁻⁴ m⁴.
$I_{x} = 4.50 t im es 1 0^{- 4} t e x t m^{4}$

Answer: Ix = 4.50×10⁻⁴ m⁴

10 practice questions

0/10 correct

1.Square side a. Centroidal I about an axis parallel to a side is

2.Doubling h (b fixed) multiplies Ix by

3.I about the base of a rectangle is

4.Triangle centroidal I about its base-parallel axis is

5.b = 4, h = 2. Ix (base parallel, centroid) =

6.Units of I_area are

7.Strong-axis bending of a tall rectangle uses the larger of

8.Circle centroidal I =

9.If h → 0, Ix →

10.Ix + Iy for a rectangle equals the polar J about the centroid: