F4Other I-shaped members with compact or noncompact webs bent about their major axis

This section applies to doubly symmetric I-shaped members bent about their major axis with noncompact webs and singly symmetric I-shaped members with webs attached to the mid-width of the flanges, bent about their major axis, with compact or noncompact webs, as defined in Section B4.1 for flexure.

User Note: I-shaped members for which this section is applicable may be de- signed conservatively using Section F5.

The nominal flexural strength, $M_{n}$, shall be the lowest value obtained according to the limit states of compression flange yielding, lateral-torsional buckling, compression flange local buckling, and tension flange yielding.

F4.1 Compression Flange Yielding

(F4-1)

where

$\begin{aligned} M_{y c} & =\text { yield moment in the compression flange, kip-in. (N-mm) } \\ & =F_{y} S_{x c}\end{aligned}$

$R_{p c}=$ web plastification factor, determined in accordance with Section F4.2(c)(6)

$S_{x c}=$ elastic section modulus referred to compression flange, in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$

F4.2 Lateral-Torsional Buckling

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

• (b) When $L_{p}<L_{b} \leq L_{r}$

(F4-2)

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

(F4-3)

where

(1) $M_{y c}$, the yield moment in the compression flange, kip-in. (N-mm), is

(F4-4)

(2) $F_{c r}$, the critical stress, ksi (MPa), is

(F4-5)

For $\frac{I_{y c}}{I_{y}} \leq 0.23, J$ shall be taken as zero,

where

$\begin{aligned} I_{y c} & =\text { moment of inertia of the compression flange about the } y\text {-axis, in. }^{4} \\ & \left(\mathrm{mm}^{4}\right)\end{aligned}$

• (3) $F_{L}$, nominal compression flange stress above which the inelastic buckling limit states apply, ksi (MPa), is determined as follows:

(i) When $\frac{S_{x t}}{S_{x c}} \geq 0.7$

(F4-6a)

(ii) When $\frac{S_{x t}}{S_{x c}}<0.7$

where

$S_{x t}=$ elastic section modulus referred to tension flange, in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$

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

(F4-7)

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

• (6) $R_{p c}$, the web plastification factor, is determined as follows:

(i) When $I_{y c} / I_{y}>0.23$

(a) When $\frac{h_{c}}{t_{w}}$

(F4-9a)

(b) When $\frac{h_{c}}{t_{w}}>\lambda_{p w}$

Mp Mp 2-p My Re Rpc M ус Myc w-pw Myc (F4-9b)

(ii) When $I_{y c} / I_{y} \leq 0.23$

(F4-10)

where

$M_{p}=F_{y} Z_{x} \leq 1.6 F_{y} S_{x}$

$h_{c}=$ twice the distance from the centroid to the following: the inside face of the compression flange less the fillet or corner radius, for rolled shapes; the nearest line of fasteners at the compression flange or the inside face of the compression flange when welds are used, for built-up sections, in. (mm)

λ

$h_{c}$

$t_{\mathrm{r}}$

tw

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

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

• (7) $r_{t}$, the effective radius of gyration for lateral-torsional buckling, in. (mm), is determined as follows:
• (i) For I-shapes with a rectangular compression flange

(F4-11)

where

(F4-12)

$b_{f c}=$ width of compression flange, in. (mm)

$t_{f c}=$ thickness of compression flange, in. (mm)

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

• (ii) For I-shapes with a channel cap or a cover plate attached to the compression flange
• $r_{t}=$ radius of gyration of the flange components in flexural compression plus one-third of the web area in compression due to application of major-axis bending moment alone, in. (mm)

F4.3 Compression Flange Local Buckling

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

• (b) For sections with noncompact flanges

(F4-13)

(c) For sections with slender flanges

(F4-14)

where

$\begin{aligned} F_{L} & \text { is defined in Equations F4-6a and F4-6b } \\ R_{p c} & \text { is the web plastification factor, determined by Equation F4-9a, F4-9b, or F4-10 } \\ k_{c} & =\frac{4}{\sqrt{h / t_{w}}} \text { and shall not be taken as less than } 0.35 \text { nor greater than } 0.76 \text { for cal- } \\ & \text { culation purposes } \\ \lambda & =\frac{b_{f c}}{2 t_{f c}}\end{aligned}$

$\lambda_{p f}=\lambda_{p}$, 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

F4.4 Tension Flange Yielding

(a) When $S_{x t} \geq S_{x c}$, the limit state of tension flange yielding does not apply.

• (b) When $S_{x t}<S_{x c}$

(F4-15)

where

$\begin{aligned} M_{y t} & =\text { yield moment in the tension flange, kip-in. (N-mm) } \\ & =F_{y} S_{x t}\end{aligned}$

$R_{p t}$, the web plastification factor corresponding to the tension flange yielding limit state, is determined as follows:

(1) When $I_{y c} / I_{y}>0.23$

(i) When hc pw tw

(F4-16a)

(ii) When $\frac{h_{c}}{t_{w}}>\lambda_{p w}$

(2) When $I_{y c} / I_{y} \leq 0.23$

(F4-17)

where

$M_{p}=F_{y} Z_{x} \leq 1.6 F_{y} S_{x}$

$\lambda=\frac{h}{t_{w}}$

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

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