Formulas: Lateral-Torsional Buckling

Formula 1

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

L_{b} \leq L_{p}

(b) When $L_{p}<L_{b} \leq L_{r}$

L_{p}<L_{b} \leq L_{r}

M_{n}=C_{b}\left|M_{p}-\left(M_{p}-0.7 F_{y} S_{x}\right)\left(\frac{L_{b}-L_{p}}{L_{r}-L_{p}}\right)\right| \leq M_{p}

L_{b}>L_{r}

M_{n}=2 E C_{b} \frac{\sqrt{J A_{g}}}{L_{b} / r_{y}} \leq M_{p}

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

L_{p}=0.13 E r_{y} \frac{\sqrt{J A_{g}}}{M_{p}}

L_{r}=2 E r_{y} \frac{\sqrt{J A_{g}}}{0.7 F_{y} S_{x}}