| Section | Area, A (mm²) | Centroid in x, Cxx (mm) | Centroid in y, Cy (mm) | Second Moment of Area in x, Ixx (mm⁴) |
Second Moment of Area in y, Iyy (mm⁴) | Torsional Constant, J (mm⁴) | Section Moduli in x, Zx (mm³) | Section Moduli in y, Zy (mm³) | Comment |
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 | $$A = bd$$ | $$C_{x} = \frac{b}{2}$$ | $$C_{y} = \frac{d}{2}$$ | $$I_{xx} = \frac{bd^3}{12}$$ | $$I_{yy} = \frac{db^3}{12}$$ | $$J=\frac{d^3}{3}\bigg[b-0.63d $$ $$\qquad\left(1-\frac{d^4}{12b^4}\right)\bigg]$$ $$\text{ for } d < b $$ |
$$Z_{x,max} = Z_{x,min} $$ $$= \frac{bd^2}{6}$$ | $$Z_{y,max} = Z_{y,min} $$ $$= \frac{db^2}{6}$$ | Can be used for a square section, setting \(d=b\) |
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 | $$A = BD-bd$$ | $$C_{x} = \frac{B}{2}$$ | $$C_{y} = \frac{D}{2}$$ | $$I_{xx} = \frac{BD^3}{12} - \frac{bd^3}{12}$$ | $$I_{yy} = \frac{DB^3}{12} - \frac{db^3}{12}$$ | $$\frac{2t^2(D-t)^2(B-t)^2}{Bt+Dt-2t^2}$$ $$\text{where } t = \frac{B-b}{2}$$ $$ = \frac{D-d}{2}$$ |
$$Z_{x,max} = Z_{x,min} $$ $$= \frac{1}{6D}\left(BD^3 - bd^3\right)$$ | $$Z_{y,max} = Z_{y,min} $$ $$= \frac{1}{6B}\left(DB^3 - db^3\right)$$ | Can be used for a square section, setting \(d=b\) |
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 | $$A = \frac{\pi d^2}{4}$$ | $$C_{x} = \frac{d}{2}$$ | $$C_{y} = \frac{d}{2}$$ | $$I_{xx} = \frac{\pi d^4}{64}$$ | $$I_{yy} = \frac{\pi d^4}{64}$$ | $$J = \frac{\pi d^4}{32}$$ |
$$Z_{x,max} = Z_{x,min} $$ $$= \frac{\pi d^3}{32}$$ | $$Z_{y,max} = Z_{y,min} $$ $$= \frac{\pi d^3}{32}$$ | - |
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 | $$A = \frac{\pi D^2}{4} -\frac{\pi d^2}{4} $$ | $$C_{x} = \frac{D}{2}$$ | $$C_{y} = \frac{D}{2}$$ | $$I_{xx} = \frac{\pi D^4}{64} - \frac{\pi d^4}{64}$$ | $$I_{yy} = \frac{\pi D^4}{64} - \frac{\pi d^4}{64}$$ | $$ J = \frac{\pi}{4}(D-t)^3t $$ $$\text{where } t = \frac{D-d}{2}$$ |
$$Z_{x,max} = Z_{x,min} $$ $$= \frac{1}{32D}\left(D^3 - d^3\right)$$ | $$Z_{y,max} = Z_{y,min} $$ $$= \frac{1}{32D}\left(D^3 - d^3\right)$$ | - |
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 | $$A = \frac{bd}{2}$$ | $$C_{x} = \frac{b}{2}$$ | $$C_{y} = \frac{d}{3}$$ | $$I_{xx} = \frac{bd^3}{36}$$ | $$I_{yy} = \frac{db^3}{48}$$ | $$J = \frac{b^3 d^3}{(15b^2 + 20d^2)} $$ $$\text{for } \frac{2}{3} < \frac{b}{d} < \sqrt{3}$$ |
$$Z_{x,max} = \frac{bd^2}{12} $$ $$ Z_{x,min} = \frac{bd^2}{24}$$ | $$Z_{y,max} = Z_{y,min} $$ $$= \frac{db^2}{24}$$ | - |
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 | $$A = \frac{bd}{2}$$ | $$C_{x} = \frac{b}{3}$$ | $$C_{y} = \frac{d}{3}$$ | $$I_{xx} = \frac{bd^3}{36}$$ | $$I_{yy} = \frac{db^3}{36}$$ | - |
$$Z_{x,max} = \frac{bd^2}{12} $$ $$ Z_{x,min} = \frac{bd^2}{24}$$ | $$Z_{y,max} = \frac{db^2}{12} $$ $$ Z_{y,min} = \frac{db^2}{24}$$ | - |
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 | $$A=2(bt_{f})+ $$ $$ (d-2t_{f})t_{w} $$ | $$C_{x} = \frac{b}{2}$$ | $$C_{y} = \frac{d}{2}$$ | $$I_{xx} = \frac{1}{12}(bd^3-$$ $$[b-t_{w}][d-2t_{f}]^3)$$ | $$I_{yy} = \frac{1}{12}(b^3d-$$ $$[b-t_{w}]^3[d-2t_{f}])$$ | $$\frac{2t_{f}^3b + t_{w}^3d}{3} $$ |
$$Z_{x,max} = Z_{x,min} $$ $$= \frac{1}{6d}(bd^3-$$ $$[b-t_{w}][d-2t_{f}]^3)$$ | $$Z_{y,max} = Z_{y,min} $$ $$= \frac{1}{6b}(b^3d-$$ $$[b-t_{w}]^3[d-2t_{f}])$$ | - |
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 | $$A=2(bt_{f})+ $$ $$ (d-2t_{f})t_{w} $$ | $$C_{x} = \frac{1}{A}\bigg(bt_{f}^2+ $$ $$\qquad\frac{{t_f}^2}{2}\bigg[d-2t_{f}\bigg]\bigg)$$ | $$C_{y} = \frac{d}{2}$$ | $$I_{xx} = \frac{1}{12}(bd^3-$$ $$[b-t_{w}][d-2t_{f}]^3)$$ | $$\frac{1}{3}(t_{f}b^3+2dt_{w}^3 $$ $$-2t_{w}^3t_{f})-AC_{y}^2$$ | $$\frac{2t_{f}^3b + t_{w}^3d}{3} $$ |
$$Z_{x,max} = Z_{x,min} $$ $$= \frac{1}{6d}(bd^3-$$ $$[b-t_{w}][d-2t_{f}]^3)$$ | $$Z_{y,max} = \frac{I_{yy}}{C_{x}}$$ $$Z_{y,min} = \frac{I_{yy}}{b-C_{x}}$$ | - |
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 | $$A=(bt_{f})+ $$ $$ (d-t_{f})t_{w} $$ | $$C_{x} = \frac{b}{2}$$ | $$C_{y} = \frac{t(bt+d^2-t^2)}{2A}$$ $$\text{when } t_{f}=t_{w}=t$$ | $$\frac{t}{3}(bt^2+d^3 $$ $$-t^3)-AC_{y}^2$$ $$\text{when } t_{f}=t_{w}=t$$ | $$\frac{1}{12}(b^3t+t^3(d-t))$$ $$\text{when } t_{f}=t_{w}=t$$ | $$\frac{t_{f}^3b + t_{w}^3d}{3} $$ |
$$Z_{x,max} = \frac{I_{xx}}{C_{y}}$$ $$Z_{x,min} = \frac{I_{xx}}{d-C_{y}}$$ | $$Z_{y,max} = \frac{I_{yy}}{C_{x}}$$ $$Z_{y,min} = \frac{I_{yy}}{b-C_{x}}$$ | Assumes constant thickness, i.e. $$t_{f} = t_{w}$$ |
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 | $$A=t[b+(d-t)] $$ | $$C_{x} = \frac{t(dt+b^2-t^2)}{2A}$$ | $$C_{y} = \frac{t(bt+d^2-t^2)}{2A}$$ | $$\frac{t}{3}(bt^2+d^3 $$ $$ -t^3)-AC_{y}^2$$ | $$\frac{t}{3}(dt^2+b^3-t^3)-AC_{x}^2$$ | $$\frac{t_{f}^3b + t_{w}^3d}{3} $$ |
$$Z_{x,max} = \frac{I_{xx}}{C_{y}}$$ $$Z_{x,min} = \frac{I_{xx}}{d-C_{y}}$$ | $$Z_{y,max} = \frac{I_{yy}}{C_{x}}$$ $$Z_{y,min} = \frac{I_{yy}}{b-C_{x}}$$ | Assumes constant thickness. Also has u-u and v-v principal axes. |
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