F7Square and rectangular HSS and box sections

This section applies to square and rectangular HSS, and box sections bent about either axis, having compact, noncompact, or slender webs or flanges, as defined in Section B4.1 for flexure.

The nominal flexural strength, $M_{n}$, shall be the lowest value obtained according to the limit states of yielding (plastic moment), flange local buckling, web local buckling, and lateral-torsional buckling under pure flexure.

F7.1 Yielding

M₁ = Mp=FZ (F7-1)

where

$Z=$ plastic section modulus about the axis of bending, in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$

F7.2 Flange Local Buckling

(a) For compact sections, the limit state of flange local buckling does not apply.

• (b) For sections with noncompact flanges

2-Jpf M, M,-(M,-FS) SMp (F7-2) Joof-hopp

where

$\begin{aligned} S & =\text { elastic section modulus about the axis of bending, in. }^{3}\left(\mathrm{~mm}^{3}\right) \\ \lambda & =\frac{b}{t_{f}}\end{aligned}$

$b \quad$ = width of compression flange as defined in Section B4.1b, in. (mm)

$t_{f} \quad$ = thickness of the flange, in. (mm)

$\lambda_{p f}=\lambda_{p}$, the limiting width-to-thickness ratio for a compact flange as defined in Table B4.1b

$\lambda_{r f}=\lambda_{r}$, the limiting width-to-thickness ratio for a noncompact flange as defined in Table B4.1b

(c) For sections with slender flanges

(F7-3)

where

$S_{e}=$ effective section modulus determined with the effective width, $b_{e}$, of the compression flange taken as follows:

(1) For HSS

(2) For box sections

F7.3 Web Local Buckling

• (a) For compact sections, the limit state of web local buckling does not apply.
• (b) For sections with noncompact webs

where

h λ tw

$h \quad=$ depth of web, as defined in Section B4.1b, in. (mm)

$t_{w}$ = thickness of the web, in. (mm)

$\lambda_{p w}=\lambda_{p}$, the limiting width-to-thickness ratio for a compact web as defined in Table B4.1b

$\lambda_{n w}=\lambda_{r}$, the limiting width-to-thickness ratio for a noncompact web as defined in Table B4.1b

(c) For sections with slender webs and compact or noncompact flanges

(F7-7)

where

$R_{p g}$ is defined by Equation F5-6 with $a_{w}=2 h t_{w} /\left(\left.b t_{f}\right)\right)$

User Note: Box sections with slender webs and slender flanges are not ad- dressed in this Specification.

User Note: There are no HSS with slender webs.

F7.4 Lateral-Torsional Buckling

(a) When $L_{b} \leq L_{p}$, the limit state of lateral-torsional buckling does not apply.

• (b) When $L_{p}<L_{b} \leq L_{r}$

(F7-8)

(c) When $L_{b}>L_{r}$

(F7-9)

where

$A_{g}=$ gross area of member, in. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$

$L_{p}$, the limiting laterally unbraced length for the limit state of yielding, in. (mm), is

(F7-10)

$L_{r}$, the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling, in. (mm), is

User Note: Lateral-torsional buckling will not occur in square sections or sec- tions bending about their minor axis. In HSS sizes, deflection will usually control before there is a significant reduction in flexural strength due to lateral-torsional buckling. The same is true for box sections, and lateral-torsional buckling will usually only be a consideration for sections with high depth-to-width ratios.