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32.5.6 Torsional Bracing

In order for a brace to effectively increase the load-carrying capacity of a member, it must restrain the movement of the lowest buckling mode. Depending on the cross-section, the lowest buckling mode of a compression member may be flexural (lateral), torsional, or a combined flexural-torsional. Bracing against flexural modes must prevent the lateral translation of the member cross-section. Bracing against torsional modes must restrain the twist of the cross-section. Bracing details such as a rod framing into a wide-flange column web (Figure 32.8) resist lateral buckling about the weak axis but do not prevent twist and are ineffective torsional braces.

For doubly symmetric sections such as wide-flange columns, weak-axis flexural buckling controls for an unbraced member. Providing sufficient weak-axis lateral bracing, in some instances, will result in the section being controlled by the torsional buckling mode. If bracing is provided that prevents both translation and twist of a doubly symmetric cross-section, weak-axis buckling will always control.

The torsional buckling load, PT, for a column restrained about an axis modified by t is given by the following (see Figure 32.9) [5]:

Axis of restraint along weak axis of column:

Axis of restraint along strong axis of column:

where x,r, Jbr are the coordinates of axis of restraint with respect to column centroid, d is the column depth, and Pey is the Euler load based on a column length between points of zero twist.

To compensate for the assumption in the derivation of Equations 32.16 and 32.17 that the brace is infinitely stiff, the maximum factored column load should be limited to 0.90PT [3].

If column loads greater than PT are required, torsional bracing must be provided. Two typical bracing schemes are shown in Figure 32.10. For continuous girts with moment connections, twisting restraint is provided. However, partial depth stiffeners should be used to control web distortion. The design requirements for torsional bracing are based on the nodal requirements presented in Section 32.5.3 and are obtained by introducing equal and opposite brace forces on each flange. The magnitude of these forces is based on the assumption that each flange carries one-half of the total column load. The resulting brace moment, MT = 0.5Pbrd. Using the angle of twist 6 = Did as shown in Figure 32.9b, the stiffness requirement bT = MTi6 = 0.5Pbrd2iD reduces to bT = 0.5bbrd2 (32.18)

where bbr is the nodal brace stiffness requirement from Section 32.5.3.

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