Formulas: Lateral-Torsional Buckling

Formula 1

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

\frac{M_{y}}{M_{c r}} \leq 1.0

Formula 2

M_{n}=\left(1.92-1.17 \sqrt{\frac{M_{y}}{M_{c r}}}\right) M_{y} \leq 1.5 M_{y}

Formula 3

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

\frac{M_{y}}{M_{c r}}>1.0

Equation F10-3

M_{n}=\left(0.92-\frac{0.17 M_{c r}}{M_{y}}\right) M_{c r}

Equation F10-4

M_{c r}=\frac{9 E A_{g} r_{z} t C_{b}}{8 L_{b}} \sqrt{1+\left(4.4 \frac{\beta_{w} r_{z}}{L_{b} t}\right)^{2}+4.4 \frac{\beta_{w} r_{z}}{L_{b} t}}

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.

Formula 6

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]

Found in

SINGLE ANGLES