Formulas: Cross Section

Formula 1

(1) When $P_{u} / \phi_{c} P_{y} \leq 0.125$

P_{u} / \phi_{c} P_{y} \leq 0.125

\lambda_{p d}=3.76 \sqrt{\frac{E}{F_{y}}}\left(1-\frac{2.75 P_{u}}{\phi_{c} P_{y}}\right)

(2) When $P_{u} / \phi_{c} P_{y}>0.125$

P_{u} / \phi_{c} P_{y}>0.125

\tau_{p d}=1.12 \sqrt{\frac{E}{F_{y}}}\left(2.33-\frac{P_{u}}{\phi_{c} P_{y}}\right) \geq 1.49 \sqrt{\frac{E}{F_{y}}}

where

$\begin{aligned} P_{u} & =\text { required axial strength in compression, using LRFD load combinations, } \\ & \text { kips (N) }\end{aligned}$
$\begin{aligned} P_{y} & =\text { axial yield strength, kips (N) } \\ & =F_{y} A_{g}\end{aligned}$
$h \quad$ = as defined in Section B4.1, in. (mm)
$t_{w}=$ thickness of web, in. (mm)
= resistance factor for compression

= 0.90

\lambda_{p d}=0.045 E / F_{y}

where

D = outside diameter of round HSS, in. (mm)