73/3848–12FE Reference Handbook 10.6 · Statics · p. 99 rectangle row: centroidal Ixc = bh³/12; base-axis Ix = bh³/3
1. Moment & Equilibrium2. Centroid of a Composite Area3. Coulomb Friction4. Force Resultant5. Rectangle Centroidal Moment of Inertia6. Parallel-Axis Theorem7. Distributed Load Resultant8. Method of Joints9. Two-Force Member10. Ideal Pulley11. Moment of a Force12. Simply Supported Beam Reactions13. Load–Shear–Moment Relations14. Method of Sections (Truss)15. Sagging Cable (Small Sag)16. Overhanging-Beam Reactions17. Radius of Gyration18. Triangle Area Moment of Inertia19. Triangular Distributed Load Resultant20. Three-Force Member21. Couple Moment22. Frames: Multi-Force Members23. Zero-Force Truss Members

Handbook formula

Rectangle Centroidal Moment of Inertia

On the p. 99 rectangle row, b is the base and h the height. The centroidal column gives Ixc = bh³/12 about the axis through the center parallel to the base. The same row’s Ix = bh³/3 is about the base, not the centroid. Do not swap those columns. A full circle’s centroidal inertia on p. 100 is πa⁴/4.

(m)
Width
(m)
Height
(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.

Ixb = 200 mmh = 300 mmCentroidal Ix = b h³ / 12Ix = 4.50×10⁻⁴ m⁴Replay
Rectangle: Ix = bh³/12 about the centroidal axis parallel to b.

  1. 1. SI

    b = 0.20 m, h = 0.30 m.

  2. 2. Ix

    Ix = (0.20)(0.30)³/12 = 4.50×10⁻⁴ m⁴.

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: