E7Members with slender elements

This section applies to slender-element compression members, as defined in Section B4.1 for elements in axial compression.

The nominal compressive strength, $P_{n}$, shall be the lowest value based on the applicable limit states of flexural buckling, torsional buckling, and flexural-torsional buckling in interaction with local buckling.

(E7-1)

where

• $A_{e}=$ summation of the effective areas of the cross section based on reduced effective widths, $b_{e}, d_{e}$, or $h_{e}$, or the area as given by Equation E7-6 or E7-7, in. ${ }^{2}$ $\left(\mathrm{mm}^{2}\right)$
• $\begin{aligned} F_{n} & =\text { nominal stress determined in accordance with Section E3 or E4, ksi (MPa) } \\ & \text { For single angles, determine } F_{n} \text { in accordance with Section E3 only. }\end{aligned}$

User Note: The effective area, $A_{e}$, may be determined by deducting from the gross area, $A_{g}$, the reduction in area of each slender element determined as $\left(b-b_{e}\right) t$.

E7.1 Slender Element Members Excluding Round HSS

The effective width, $b_{e}$ (for tees, this is $d_{e}$; for webs, this is $h_{e}$ ), for slender elements is determined as follows:

(a) When $\lambda \leq \lambda_{r} \sqrt{\frac{F_{y}}{F_{n}}}$

(E7-2)

(b) When $\lambda>\lambda_{r} \sqrt{\frac{F_{y}}{F_{n}}}$

(E7-3)

where

• $b \quad$ = width of the element (for tees this is $d$; for webs this is $h$ ), in. (mm)
• $\begin{aligned} c_{1} & =\text { effective width imperfection adjustment factor determined from Table E7.1 } \\ c_{2} & =\frac{1-\sqrt{1-4 c_{1}}}{2 c_{1}} \end{aligned}$ (E7-4)

TABLE E7.1 Effective Width Imperfection Adjustment Factors, c1 and c2

$\lambda \quad$ = width-to-thickness ratio for the element as defined in Section B4.1

$\lambda_{r}=$ limiting width-to-thickness ratio as defined in Table B4.1a

$F_{e l}=\left(c_{2} \frac{\kappa_{r}}{\lambda}\right) F_{y}$

(E7-5)

= elastic local buckling stress determined according to Equation E7-5 or an elastic local buckling analysis, ksi (MPa)

E7.2 Round HSS

The effective area, $A_{e}$, is determined as follows:

(a) When $\frac{D}{t} \leq 0.11 \frac{E}{F_{y}}$

(E7-6)

(b) When $0.11 \frac{E}{F_{y}}<\frac{D}{t}<0.45 \frac{E}{F_{y}}$

where

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

$t \quad=$ thickness of wall, in. (mm)