Formulas: Unbraced Length

Equation A-1-5

L_{p d}=\left(0.12-0.076 \frac{M_{1}^{\prime}}{M_{2}}\right) \frac{E}{F_{y}} r_{y}

where

$r_{y}=$ radius of gyration about minor axis, in. (mm)

(2) When $M_{\text {mid }} \leq\left(M_{1}+M_{2}\right) / 2$

M_{\text {mid }} \leq\left(M_{1}+M_{2}\right) / 2

M_{1}^{\prime}=M_{1}

(3) When $M_{\text {mid }}>\left(M_{1}+M_{2}\right) / 2$

M_{\text {mid }}>\left(M_{1}+M_{2}\right) / 2

M_{1}^{\prime}=\left(2 M_{\text {mid }}-M_{2}\right)<M_{2}

where

$M_{\text {mid }}=$ moment at middle of unbraced length, kip-in. (N-mm)

$\begin{aligned} M_{1} & =\text { smaller moment at end of unbraced length, kip-in. (N-mm) }\end{aligned}$

$M_{2} \quad=$ larger moment at end of unbraced length, kip-in. (N-mm) (shall be taken as positive in all cases)
$\begin{aligned} M_{1}^{\prime} & =\text { effective moment at end of unbraced length opposite from } M_{2} \\ & \text { kip-in. (N-mm) }\end{aligned}$