C-6.26.2 column bracing

This section addresses lateral bracing of columns. Recommendations for torsional bracing of columns can be found in Helwig and Yura (1999). Section E4 addresses the calculation of the strength of columns that are restrained laterally at a location other than their shear center, and thus fail by constrained-axis torsional buckling. Lateral bracing requirements for the general case of beam-column members restrained laterally at a location other than their shear center are addressed later in Commentary Section 6.4.

For point column bracing, the critical stiffness is a function of the number of intermediate braces (Winter, 1958, 1960). For one intermediate brace, $\beta_{i}=2 P_{r} / L_{b r}$, and for many braces, $\beta_{i}=4 P_{r} / L_{b r}$. The relationship between the critical stiffness and the number of braces, $n$, can be approximated (Yura, 1995) as follows:

(C-A-6-5)

The most severe case of many braces is adopted for the brace stiffness requirement in Equations A-6-4a and A-6-4b, i.e., $\beta_{b r}=2 \times 4 P_{r} / L_{b r}$. The brace stiffness in Equations A-6-4a and A-64b can be multiplied by the following ratio to account for the actual number of braces:

(C-A-6-6)

In Equations A-6-4a and A-6-4b, when the actual brace spacing is less than the value of the effective length, $L_{c}$, that enables the column to reach $P_{r}$, the calculated required stiffness may become quite conservative because the stiffness equations are inversely proportional to $L_{b r}$. In such cases, $L_{b r}$ can be taken equal to $L_{c}$. This practice constitutes a simple method of designing for partial bracing; that is, bracing that is sufficient to develop the member's required strength but is not sufficient to develop the member's strength based on $L_{c}=L_{b r}$. This substitution is also permitted for beam point lateral bracing in Equations A-6-8a and A-6-8b.

For example, a W12×53 (W310×79) with $P_{u}=400 \mathrm{~kips}(1800 \mathrm{kN})$ for LRFD or $P_{a}=267 \mathrm{~kips}(1200 \mathrm{kN})$ for ASD can have a maximum unbraced length of 18 ft (5.5 m) for ASTM A992/A992M steel. If the actual brace spacing is 8 ft (2.4 m), 18 ft (5.5 m) may be used in Equations A-6-4a and A-6-4b to determine the required stiffness. The use of $L_{b r}$ equal to the value of $L_{c}$ in Equations A-6-4a and A-6-4b provides reasonable estimates of the brace stiffness requirements; however, in some cases, this solution is significantly conservative. Improved accuracy can be obtained by treating the system as a continuous bracing system or directly determining the buckling strength of the partially braced member and the corresponding ideal bracing stiffness (Lutz and Fisher, 1985; Ziemian, 2010; Togay et al., 2015). The required bracing stiffness is taken as $2 / \phi$ (LRFD) or $2 \Omega$ (ASD) times the ideal bracing stiffness. Note that, as discussed in Commentary Section 6.1, for ASD, the ideal bracing

stiffness must be determined using 1.6 times the applicable load combinations and the resulting ideal bracing stiffness values are then multiplied by 2Ω1 6. to obtain the required brace stiffnesses.

With regard to brace strength requirements, Winter's point bracing model only accounts for force effects from lateral displacement of the brace points and would derive a brace force equal to $0.8 \%$ of $P_{r}$. To account for the additional brace forces due to member curvature and member continuity across the brace points, this theoretical force is increased to $1 \%$ of $P_{r}$ in Equation A-6-3. Member curvature and continuity across the brace points has a comparable effect on panel-bracing requirements. Therefore, the panel-bracing strength requirement of Equation A-6-1 is increased from 0.4 to $0.5 \%$ of $P_{r}$. Similar increases are applied to the panel and point lateral bracing strength requirements for beams in Equations A-6-5 and A-6-7.