Formulas: Round and Rectangular HSS Subjected to Torsion

Formula 1

Formula (H3-2b: $F_{cr} = \frac{0.60E}{(D/t^{3/2}}$

F_{cr} = \frac{0.60E}{(D/t^{3/2}}

(1) When $h / t \leq 2.45 \sqrt{E / F_{y}}$

h / t \leq 2.45 \sqrt{E / F_{y}}

F_{c r}=0.6 F_{y}

(2) When $2.45 \sqrt{E / F_{\mathrm{y}}} < h / t \leq 3.07 \sqrt{E / F_{\mathrm{y}}}$

2.45 \sqrt{E / F_{\mathrm{y}}} < h / t \leq 3.07 \sqrt{E / F_{\mathrm{y}}}

F_{c r}=\frac{0.6 F_{y}\left(2.45 \sqrt{E / F_{y}}\right)}{\left(\frac{h}{t}\right)}

(3) When $3.07 \sqrt{E / F_{y}}<h / t \leq 260$

3.07 \sqrt{E / F_{y}}<h / t \leq 260

F_{c r}=\frac{0.458 \pi^{2} E}{\left(\frac{h}{t}\right)^{2}}

where

$h=$ flat width of longer side, as defined in Section B4.1b(d), in. (mm)

For round HSS: $C=\frac{\pi(D-t)^{2} t}{2}$

C=\frac{\pi(D-t)^{2} t}{2}

For rectangular HSS: $C=2(B-t)(H-t) t-4.5(4-\pi) t^{3}$

C=2(B-t)(H-t) t-4.5(4-\pi) t^{3}