Formulas: Lateral-Torsional Buckling

Formula 1

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

L_{b} \leq L_{p}

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

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

M_{n}=M_{p}-\left(M_{p}-M_{y}\right)\left(\frac{L_{b}-L_{p}}{L_{r}-L_{p}}\right)

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

L_{b}>L_{r}

M_{n}=M_{c r}

\begin{aligned} L_{p} & =1.76 r_{y} \sqrt{\frac{E}{F_{y}}} \\ L_{r} & =1.95\left(\frac{E}{F_{y}}\right) \frac{\sqrt{I_{y} J}}{S_{x}} \sqrt{2.36\left(\frac{F_{y}}{E}\right) \frac{d S_{x}}{J}+1} \\ M_{c r} & =\frac{1.95 E}{L_{b}} \sqrt{I_{y} J}\left(B+\sqrt{1+B^{2}}\right) \\ B & =2.3\left(\frac{d}{L_{b}}\right) \sqrt{\frac{I_{y}}{J}} \\ d & =\text { depth of tee or width of web leg in tension, in. (mm) } \end{aligned}

B=-2.3\left(\frac{a}{L_{b}}\right) \sqrt{\frac{r_{y}}{J}}

where

$d=$ depth of tee or width of web leg in compression, in. (mm)