6.3beam bracing

Beams shall be restrained against rotation about their longitudinal axis at points of support. When a braced point is assumed in the design between points of support, lateral bracing, torsional bracing, or a combination of the two shall be provided to limit the relative displacement of the top and bottom flanges (i.e., to resist twist). In members subjected to double curvature bending, the inflection point shall not be considered a braced point unless bracing is provided at that location.

The requirements of this section shall apply to bracing of doubly and singly symmetric I-shaped members subjected to flexure within a plane of symmetry and zero net axial force.

6.3.1 Lateral Bracing

Lateral bracing shall be attached at or near the beam compression flange, except as follows:

• (a) At the free end of a cantilevered beam, lateral bracing shall be attached at or near the top (tension) flange.
• (b) For braced beams subjected to double curvature bending, bracing shall be attached at or near both flanges at the braced point nearest the inflection point.

It is permitted to use either panel or point bracing to provide lateral bracing for beams.

6.3.1a Panel Bracing

The panel bracing system shall have the strength and stiffness specified in this section. The connection of the bracing system to the member shall have the strength specified in Section 6.3.1b for a point brace at that location.

User Note: The stiffness contribution of the connection to the panel bracing system should be assessed as provided in the User Note to Section 6.2.1.

The required shear strength of the bracing system is

(A-6-5)

and, the required shear stiffness of the bracing system is

(A-6-6a)

(A-6-6b)

$\phi=0.75$ (LRFD) $\quad \Omega=2.00$ (ASD)

where

$C_{d}=1.0$, except in the following case

• = 2.0 for the brace closest to the inflection point in a beam subjected to double curvature bending

$L_{b r}=$ unbraced length within the panel under consideration, in. (mm)

• $M_{r}=$ required flexural strength of the beam within the panel under consideration using LRFD or ASD load combinations, kip-in. (N-mm)
• $h_{o}=$ distance between flange centroids, in. (mm)

6.3.1b Point Bracing

In the direction perpendicular to the longitudinal axis of the beam, the required strength of end and intermediate point braces is

(A-6-7)

and the required stiffness of the brace is

(A-6-8a)

(A-6-8b)

$\phi=0.75$ (LRFD) $\quad \Omega=2.00$ (ASD)

where

$L_{b r}=$ unbraced length adjacent to the point brace, in. (mm)

$M_{r}=$ largest of the required flexural strengths of the beam within the unbraced lengths adjacent to the point brace using LRFD or ASD load combinations, kip-in. (N-mm)

When the unbraced lengths adjacent to a point brace have different $M_{r} / L_{b r}$ values, the larger value shall be used to determine the required brace stiffness.

For intermediate point bracing of an individual beam, $L_{b r}$ in Equations A-6-8a or A-6-8b need not be taken as less than the maximum effective length, $L_{b}$, permitted for the beam based upon the required flexural strength, $M_{r}$.

6.3.2 Torsional Bracing

It is permitted to attach torsional bracing at any cross-section location, and it need not be attached near the compression flange.

User Note: Torsional bracing can be provided as point bracing, such as cross-frames, moment-connected beams, or vertical diaphragm elements, or as continuous bracing, such as slabs or decks.

6.3.2a Point Bracing

About the longitudinal axis of the beam, the required flexural strength of the brace is

(A-6-9)

and the required flexural stiffness of the brace is

(A-6-10)

where

(A-6-11a)

(A-6-11b)

(A-6-12)

and

$\phi=0.75$ (LRFD); $\Omega=3.00$ (ASD)

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.

$\beta_{s e c}$ 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.

• $E \quad=$ modulus of elasticity of steel
• = 29,000 ksi (200 000 MPa)

$I_{\text {yeff }}=$ effective out-of-plane moment of inertia, in. ${ }^{4}\left(\mathrm{~mm}^{4}\right)$

• $=I_{y c}+\left(t / c\right) I_{y t}$
• $I_{y c} \quad=$ moment of inertia of the compression flange about the $y$-axis, in. ${ }^{4}\left(\mathrm{~mm}^{4}\right)$
• $I_{y t} \quad=$ moment of inertia of the tension flange about the $y$-axis, in. ${ }^{4}\left(\mathrm{~mm}^{4}\right)$

$L^{y}=$ length of span, in. (mm)

$L_{b r}=$ unbraced length adjacent to the point brace, in. (mm)

• $\begin{aligned} M_{r} & =\text { largest of the required flexural strengths of the beam within the unbraced } \\ & \text { lengths adjacent to the point brace, using LRFD or ASD load combinations, } \\ & \text { kip-in. (N-mm) }\end{aligned}$

$M_{r}$

• $\frac{M_{r}}{C_{b}}=$ maximum value of the required flexural strength of the beam divided by the moment gradient factor, within the unbraced lengths adjacent to the point brace, using LRFD or ASD load combinations, kip-in. (N-mm)
• $b_{s} \quad$ = stiffener width for one-sided stiffeners, in. (mm)
• = twice the individual stiffener width for pairs of stiffeners, in. (mm)
• $c \quad$ = distance from the neutral axis to the extreme compressive fibers, in. (mm)
• $n \quad=$ number of braced points within the span
• $t \quad=$ distance from the neutral axis to the extreme tensile fibers, in. (mm)
• $t_{s t}$ = thickness of web stiffener, in. (mm)
• $t_{w}$ = thickness of beam web, in. (mm)
• $\beta_{T} \quad$ = overall brace system required stiffness, kip-in./rad (N-mm/rad)
• $\begin{aligned} \beta_{s e c} & =\text { web distortion stiffness, including the effect of web transverse stiffeners, } \\ & \text { if any, kip-in./rad (N-mm/rad) }\end{aligned}$

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.

User Note: For doubly symmetric members, $c=t$ and $I_{y e f f}=$ out-of-plane moment of inertia, $I_{y}$, in. ${ }^{4}\left(\mathrm{~mm}^{4}\right)$.

When required, a web stiffener shall extend the full depth of the braced member and shall be attached to the flange if the torsional brace is also attached to the flange. Alternatively, it is permissible to stop the stiffener short by a distance equal to $4 t_{w}$ from any beam flange that is not directly attached to the torsional brace.

When the expression, $\left(M_{r} / C_{b}\right)^{2} L_{b r}$, within the unbraced lengths adjacent to a point brace, has different values, the larger value shall be used to determine the required brace strength and stiffness.

In Equation A-6-9, $L_{b r}$ need not be taken as less than the maximum unbraced length permitted for the beam based upon the required flexural strength, $M_{r}$.

6.3.2b Continuous Bracing

For continuous torsional bracing:

• (a) The brace strength requirement per unit length along the beam shall be taken as Equation A-6-9 divided by the maximum unbraced length permitted for the beam based upon the required flexural strength, $M_{r}$. The required flexural strength, $M_{r}$, shall be taken as the maximum value throughout the beam span.
• (b) The brace stiffness requirement per unit length shall be given by Equations A-6-10 and A-6-11 with $L / n=1.0$.
• (c) The web distortional stiffness shall be taken as

(A-6-13)