C-6.46.4 beam-column bracing

The provisions for beam-column bracing reflect the research by Lokhande and White (2015) and White et al. (2011). This research proposes the following guidelines for beam-column bracing.

Beam-Columns Braced by a Combination of Lateral and Torsional Bracing. For beam-columns braced by a combination of lateral and torsional bracing, the following applies:

• (a) The required lateral bracing stiffness can be determined using Equations A-6-2a and A-6-2b for panel lateral bracing, or Equations A-6-4a and A-6-4b for point lateral bracing, based on the required member axial force, $P_{r}$. In Equations A-6-4a and A-6-4b, $L_{b r}$ can be taken as the actual unbraced length; the provision in Section 6.2.2 that $L_{b r}$ need not be taken as less than the maximum permitted effective length based on $P_{r}$ should not be applied.
• (b) The required torsional bracing stiffness can be determined using Equation A-6-10, with an equivalent moment equal to $M_{r}+P_{r} h_{o} / 2$, where $P_{r}$ is the axial force in the member being braced.
• (c) The required lateral brace strength can be determined using Equation A-6-1 for panel lateral bracing, or Equation A-6-3 for point lateral bracing, based on 1.3 of the required axial force, 1.3$P_{r}$.
• (d) The required torsional brace strength can be determined using Equation A-6-9 with an equivalent moment equal to $M_{r}+P_{r} h_{o} / 2$, where $P_{r}$ is the axial force in the member being braced.

Beam-Columns Braced by a Single Lateral Bracing System. For beam-columns braced by a single lateral bracing system attached at or near a flange subjected to flexural compression throughout the member length, the following applies:

• (a) For panel bracing, when the opposite flange is subjected to a net tension force due to the axial and moment loading throughout the member length, the required bracing stiffness can be taken as the sum of the values determined using Equations A-6-2a and A-6-2b with an equivalent axial force equal to $P_{r} / 2$ and Equations A-6-6a and A-6-6b with the required moment, $M_{r}$. The required bracing strength can be taken as the sum of the values determined using Equation A-6-1 with an equivalent axial force equal to $P_{r} / 2$ and Equation A-6-5 with the required moment.
• (b) For panel bracing, when the opposite flange is subjected to a net compression force due to the axial and moment loading at any position within the member length, the required bracing stiffness can be taken as the sum of the values determined using Equations A-6-2a and A-6-2b with an equivalent axial force equal to $2.5 P_{r}$ and Equations A-6-6a and A-6-6b with the required moment, $M_{r}$. The required bracing strength can be taken as the sum of the values determined using

Equation A-6-1 with an equivalent axial force equal to $2.5 P_{r}$ and Equation A-6-5 with the required moment, $M_{r}$.

• (c) For point bracing, when the opposite flange is subjected to a net tension force due to the axial and moment loading throughout the member length, the required bracing stiffness can be taken as the sum of the values determined using Equations A-6-4a and A-6-4b with an equivalent axial force equal to $P_{r} / 2$ and Equations A-6-8a and A-6-8b with the required moment, $M_{r}$. In Equations A-6-4a and A-6-4b and Equations A-6-8a and A-6-8b, $L_{b r}$ can be taken as the actual unbraced length; the provisions in Sections 6.2.2 and 6.3.1b, that $L_{b r}$ need not be taken as less than the maximum permitted effective length based on $P_{r}$ and $M_{r}$, should not be applied. The required bracing strength can be taken as the sum of the values determined using Equation A-6-3 with an equivalent axial force equal to $P_{r} / 2$ and Equation A-6-7 with the required moment, $M_{r}$.
• (d) For point bracing, when the opposite flange is subjected to a net compression force due to the axial and moment loading at any position within the member length, the required bracing stiffness can be taken as the sum of the values determined using Equations A-6-4a and A-6-4b with an equivalent axial force equal to $2.5 P_{r}$ and Equations A-6-8a and A-6-8b with the required moment, $M_{r}$. In Equations A-6-4a and A-6-4b and Equations A-6-8a and A-6-8b, $L_{b r}$ can be taken as the actual unbraced length; the provisions in Sections 6.2.2 and 6.3.1b, that $L_{b r}$ need not be taken as less than the maximum permitted effective length based on $P_{r}$ and $M_{r}$, should not be applied. The required bracing strength can be taken as the sum of the values determined using Equation A-6-3 with an equivalent axial force equal to $2.5 P_{r}$ and Equation A-6-7 with the required moment, $M_{r}$.

In the application of these guidelines, where the member is subjected to axial compression larger than $P_{c} / 10$, the slenderness ratio, $L_{b r} / r_{y f}$, of the flange that does not have the additional lateral bracing should not be greater than 200,

where

• $L_{b r}=$ unbraced length between the points where the flange having the larger unbraced length is restrained laterally, in. (mm)
• $\begin{aligned} P_{c} & =\text { available axial compressive strength of the member determined according to } \\ & \text { Chapter E, kip (N) }\end{aligned}$
• $r_{y f}=$ radius of gyration of the flange having the larger unbraced length, taken about its principal axis parallel to the plane of the web, in. (mm)

This avoids potential excessive amplification of the bracing demands in cases where one flange is braced at closer intervals while the other flange has a large brace spacing.

Summary—Additional Guidelines for Beam-Column Bracing. The guidelines for beam-column bracing recommended in the preceding discussion utilize a simplified combination of the requirements for columns and for beams from Sections 6.2 and 6.3, respectively.

For beam-columns braced by a combination of lateral and torsional bracing, the lateral bracing is designed based on the column bracing provisions of Section 6.2 given the required axial compression of $1.0 P_{r}$ for the lateral bracing stiffness requirement and $1.3 P_{r}$ for the lateral bracing strength requirement. Correspondingly, the

torsional bracing is designed based on the beam torsional bracing provisions of Section 6.3 using an equivalent moment equal to $M_{r} / C_{b}+P_{r} h_{o} / 2$. The second term in this expression accounts for the increased demands on the torsional bracing caused by the presence of the axial compression force.

For beam-columns braced by a single lateral bracing system attached at or near a flange subjected to flexural compression throughout the member length, and when the opposite flange is subjected to a net tension due to the axial and moment loading at any position within the member length, the lateral bracing may be designed based on the sum of the requirements from the column bracing rules of Section 6.2 with an axial force of $P_{r} / 2$ and the beam torsional bracing rules of Section 6.3 with the moment, $M_{r}$.

The bracing requirements for other more general bracing configurations may be determined using a buckling analysis or a second-order load deflection analysis as discussed in Section 6.1.