Appendix E — Centroids and Area Moment of Inertia for Common Shapes
| Shape | \(\bar{x}\) | \(\bar{y}\) | Area |
|---|---|---|---|
 |
\(\frac{b}{3}\) | \(\frac{h}{3}\) | \(\frac{1}{2}bh\) |
 |
\(\frac{4r}{3\pi}\) | \(\frac{4r}{3\pi}\) | \(\frac{1}{4}\pi r^2\) |
 |
r | \(\frac{4r}{3\pi}\) | \(\frac{1}{2}\pi r^2\) |
 |
\(\frac{3}{4}b\) | \(\frac{3}{10}h\) | \(\frac{1}{3}ah\) |
| Shape | Ix | Iy |
|---|---|---|
 |
\(I_x=\frac{bh^3}{3}\) \(\bar{I_{x'}}=\frac{bh^3}{12}\) |
\(I_y=\frac{hb^3}{3}\) \(\bar{I_{y'}}=\frac{hb^3}{12}\) |
 |
\(I_x=\frac{bh^3}{12}\) \(\bar{I_{x'}}=\frac{bh^3}{36}\) |
\(I_y=\frac{hb^3}{12}\) \(\bar{I_{y'}}=\frac{hb^3}{36}\) |
 |
\(\bar{I_{x'}}=\frac{\pi r^4}{4}\) | \(\bar{I_{y'}}=\frac{\pi r^4}{4}\) |
 |
\(I_x=\frac{\pi r^4}{8}\) | \(I_y=\frac{\pi r^4}{8}\) |
References
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Appendix E figures: Kindred Grey. 2024. CC BY-NC-SA.