Formulas: Point Bracing

Equation A-6-9

M_{b r}=\frac{3.6 L}{n E I_{y e f f}}\left(\frac{M_{r}}{C_{b}}\right)^{2}\left(\frac{L_{b r}}{500 h_{o}}\right) \geq 0.02 M_{r}

Equation A-6-10

\beta_{b r}=\frac{\beta_{T}}{\left(1-\frac{\beta_{T}}{\beta_{s e c}}\right)}

Equation A-6-11a

\beta_{T}=\frac{1}{\phi} \frac{3.6 L}{n E I_{y e f f}}\left(\frac{M_{r}}{C_{b}}\right)^{-}( \text { LRFD })

Equation A-6-11b

\beta_{T}=\Omega \frac{3.6 L}{n E I_{\text {yeff }}}\left(\frac{M_{r}}{C_{b}}\right)^{-1} \quad \text { (ASD) }

Equation A-6-12

\beta_{s e c}=\frac{3.3 E}{h_{o}}\left(\frac{1.5 h_{o} t_{w}^{3}}{12}+\frac{t_{s l} b_{s}^{3}}{12}\right)

Formula 6

User Note: The relationship between $\phi$ and $\Omega$ used in Equations A-6-11a and A-6-11b is $\Omega=1.5^{2} / \phi=3.00$ , because the moment term is squared.

\Omega=1.5^{2} / \phi=3.00

Formula 7

$\beta_{s e c}$ can be taken as equal to infinity, and $\beta_{b r}=\beta_{T}$ , when a cross-frame is attached near both flanges or a vertical diaphragm element is used that is approximately the same depth as the beam being braced.

\beta_{b r}=\beta_{T}

Formula 8

User Note: If $\beta_{s e c}<\beta_{T}$ , Equation A-6-10 is negative, which indicates that torsional beam bracing will not be effective due to inadequate web distortional stiffness.

\beta_{s e c}<\beta_{T}

Formula 9

User Note: For doubly symmetric members, $c=t$ and $I_{y e f f}=$ out-of-plane moment of inertia, $I_{y}$ , in.

c=t

Found in

BEAM BRACING