Channel section (U)

Formulas

Cross-sectional area

$$A = 2\ b\ t_f + (h - 2\ t_f)\ t_w$$

Second moment of area about the y-y axis

$$I_y = \frac{b\ h^3}{12} - \frac{(b - t_w)\ (h - 2\ t_f)^3}{12}$$

Second moment of area about the z-z axis

$$I_z = \frac{(h - 2\ t_f)\ t_w^3}{3} + \frac{2\ t_f\ b^3}{3} - \frac{1}{A}\ {\biggl[ \frac{(h - 2\ t_f)\ t_w^2}{2} + t_f\ b^2 \biggr]}^2$$

Elastic section modulus about the y-y axis

$$W_{\mathrm{el},y} = \frac{2\ I_y}{h}$$

Elastic section modulus about the z-z axis

$$W_{\mathrm{el},z} = \frac{I_z}{b - \frac{1}{A}\ \biggl[ \frac{(h - 2\ t_f)\ t_w^2}{2} + t_f\ b^2 \biggr]}$$

Plastic section modulus about the y-y axis

$$W_{\mathrm{pl},y} = \frac{b\ h^2}{4} - \frac{(b - t_w)\ (h - 2\ t_f)^2}{4}$$

Plastic section modulus about the z-z axis

if $t_w > A / (2 h)$

$$W_{\mathrm{pl},z} = \frac{4\ t_f\ b^2\ (h - t_f) + t_w^2\ (h^2 - 4\ t_f^2) - 4\ b\ t_f\ (h - 2\ t_f)\ t_w}{4\ h}$$

otherwise

$$W_{\mathrm{pl},z} = \frac{t_f\ (b - t_w)^2}{2} + \frac{b\ h\ t_w}{2} - \frac{h^2\ t_w^2}{8\ t_f}$$

Shear area along the y-y axis

$$A_{v,y} = 2\ b\ t_f$$

Shear area along the z-z axis

$$A_{v,z} = (h - 2\ t_f)\ t_w$$

Notations

• $h$section depth, in mm
• $b$section width, in mm
• $t_{w}$web thickness, in mm
• $t_{f}$flange thickness, in mm