F10Single angles

This section applies to single angles with and without continuous lateral restraint along their length.

Single angles with continuous lateral-torsional restraint along the length are permitted to be designed on the basis of geometric axis (x, y) bending. Single angles without continuous lateral-torsional restraint along the length shall be designed using the provisions for principal axis bending except where the provision for bending about a geometric axis is permitted.

If the moment resultant has components about both principal axes, with or without axial load, or the moment is about one principal axis and there is axial load, the combined stress ratio shall be determined using the provisions of Section H2.

User Note: For geometric axis design, use section properties computed about the x- and y-axis of the angle, parallel and perpendicular to the legs. For principal axis design, use section properties computed about the major and minor principal axes of the angle.

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

User Note: For bending about the minor principal axis, only the limit states of yielding and leg local buckling apply.

F10.1 Yielding

Mn = 1.5My (F10-1)

F10.2 Lateral-Torsional Buckling

For single angles without continuous lateral-torsional restraint along the length

(a) When $\frac{M_{y}}{M_{c r}} \leq 1.0$

(b) When $\frac{M_{y}}{M_{c r}}>1.0$

(F10-3)

where

$M_{c r}$, the elastic lateral-torsional buckling moment, is determined as follows:

• (1) For bending about the major principal axis of single angles

(F10-4)

where

• $C_{b}$ is computed using Equation F1-1 with a maximum value of 1.5
• $A_{g}=$ gross area of angle, in. ${ }^{2}\left(\mathrm{~mm}^{2}\right)$

$L_{b}=$ laterally unbraced length of member, in. (mm)

• $r_{z}=$ radius of gyration about the minor principal axis, in. (mm)
• $t \quad$ = thickness of angle leg, in. (mm)

$\beta_{w}=$ section property for single angles about major principal axis, in. (mm). $\beta_{w}$ is positive with short legs in compression and negative with long legs in compression for unequal-leg angles, and zero for equal-leg angles. If the long leg is in compression anywhere along the unbraced length of the member, the negative value of $\beta_{w}$ shall be used.

User Note: The equation for $\beta_{w}$ and values for common angle sizes are listed in the Commentary.

• (2) For bending about one of the geometric axes of an equal-leg angle with no axial compression
• (i) With no lateral-torsional restraint
• (a) With maximum compression at the toe

$M_{c r}=\frac{0.58 E b^{4} t C_{b}}{L_{b}^{2}}\left[\sqrt{1+0.88\left(\frac{L_{b} t}{b^{2}}\right)^{2}}-1\right]$

(F10-5a)

• (b) With maximum tension at the toe

0.58Eb C Lbt Mer 1+0.88 +1 (F10-5b) L₁² b²

where

My shall be taken as 0.80 times the yield moment calculated using the geometric section modulus.

$b=$ width of leg, in. (mm)

• (ii) With lateral-torsional restraint at the point of maximum moment only:

$M_{c r}$ shall be taken as 1.25 times $M_{c r}$ computed using Equation F10-5a or F10-5b.

$M_{y}$ shall be taken as the yield moment calculated using the geometric section modulus.

User Note: $M_{n}$ may be taken as $M_{y}$ for single angles with their vertical leg toe in compression, and having a span-to-depth ratio less than or equal to

$\frac{1.64 E}{F_{y}} \sqrt{\left(\frac{t}{b}\right)^{2}-1.4 \frac{F_{y}}{E}}$

F10.3 Leg Local Buckling

The limit state of leg local buckling applies when the toe of the leg is in compression.

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

(F10-6)

(c) For sections with slender legs

(F10-7)

where

(F10-8)

• $S_{c}=$ elastic section modulus to the toe in compression relative to the axis of bending, in. ${ }^{3}\left(\mathrm{~mm}^{3}\right)$. For bending about one of the geometric axes of an equal-leg angle with no lateral-torsional restraint, $S_{c}$ shall be 0.80 of the geometric axis section modulus.
• $b \quad$ = full width of leg in compression, in. (mm)