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}

Formula 2

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

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

Equation F4-2

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

Formula 4

L_{b}>L_{r}

Equation F4-3

M_{n}=F_{c r} S_{x c} \leq R_{p c} M_{y c}

Equation F4-4

M_{y c}=F_{y} S_{x c}

Equation F4-5

F_{c r}=\frac{C_{b} \pi^{2} E}{\left(L_{b}\right)^{2}} \sqrt{1+0.078 \frac{J}{S_{x c} h_{o}}\left(\frac{L_{b}}{r_{t}}\right)^{2}}

Formula 8

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

\frac{I_{y c}}{I_{y}} \leq 0.23, J

Formula 9

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

\frac{S_{x t}}{S_{x c}} \geq 0.7

Equation F4-6a

F_{L}=0.7 F_{y}

Formula 11

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

\frac{S_{x t}}{S_{x c}}<0.7

Formula 12

F_{L}=F_{y} \frac{S_{x t}}{S_{x c}} \geq 0.5 F_{y}

where

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

Equation F4-7

L_{p}=1.1 r_{t} \sqrt{\frac{E}{F_{y}}}

Formula 14

L_{r}=1.95 n_{t} \frac{E}{F_{L}} \sqrt{\frac{J}{S_{x c} h_{o}}}+\sqrt{\left(\frac{J}{S_{x c} h_{o}}\right)^{2}+6.76\left(\frac{F_{L}}{E}\right)^{2}}

Formula 15

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

I_{y c} / I_{y}>0.23

Equation F4-9a

R_{p c}=\frac{M_{p}}{M_{y c}}

Formula 17

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

\frac{h_{c}}{t_{w}}>\lambda_{p w}

Formula 18

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

I_{y c} / I_{y} \leq 0.23

Formula 19

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

Formula 20

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

\lambda_{p w}=\lambda_{p}

Formula 21

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

\lambda_{r w}=\lambda_{r}

Equation F4-11

r_{t}=\frac{b_{f c}}{\sqrt{12\left(1+\frac{1}{a_{w}}\right)}}

Equation F4-12

a_{w}=\frac{h_{c} t_{w}}{b_{f c} t_{f c}}

Found in

OTHER I-SHAPED MEMBERS WITH COMPACT OR NONCOMPACT WEBS BENT ABOUT THEIR MAJOR AXIS