## Jt

FIGURE 32.15 Cross-section distortion.

Attach when brace is attached to flange

FIGURE 32.16 Web stiffener details for torsional beam bracing.

Attach when brace is attached to flange

FIGURE 32.16 Web stiffener details for torsional beam bracing.

ts = thickness of web stiffener(s)

bs = stiffener width for one-sided stiffeners, which is twice the individual stiffener width for pairs of stiffeners bT represents the torsional stiffness of the brace member itself. For flexible connections, Equation 32.2 should be used. bsec is the torsional stiffness associated with the beam web and any transverse web stiffeners that maybe present (web distortional stiffness). The required torsional brace stiffness, bTb, will be negative if bsec < bT, which indicates the brace will not be effective due to insufficient web distortional stiffness. The coefficient 2.4 in Equation 32.29 comes from using twice the ideal stiffness with a 20% increase to account for top-flange loading. The required strength, Mbr, assumes an initial twist of 1° (0.0175 rad).

When web stiffeners are required, the AISC LRFD specification requires they extend the full depth of the brace as shown in Figure 32.16. When the brace is attached to the beam flange the stiffeners must also be attached to the flange. When the brace is not attached to the beam flange, the stiffener may be terminated at a distance equal to 4tw from the flange.

The continuous torsional beam bracing requirements use the same formulations as the nodal bracing requirements. For continuous bracing, the term L/n in Equations 32.27 and 32.29 is taken equal to 1.0 and the unbraced length, Lb, in Equation 32.27 is taken equal to Lq, the maximum unbraced beam length necessary to carry the required factored loads.

For singly symmetric cross-sections, an effective moment of inertia, Ieff, is used in place of Iy as given by leff — lyc + ~ lyt

where Iyc is the compression flange out-of-plane moment of inertia, Iyt is the tension flange out-of-plane moment of inertia, yc is the distance from centroid to extreme compression fiber, and yt is the distance from centroid to extreme tension fiber.

The torsional stiffness of typical beam-type braces is shown in Figure 32.17. Adjacent girders connected on the top flanges with decking, for example, will buckle in the same direction and develop the reverse-curvature stiffness of the brace. The stiffnesses of typical truss-type diaphragm systems are shown in Figure 32.18 and are based on elastic truss analyses. For X-systems designed for tension only, the horizontal members in the truss are not required. For K-brace systems, only one horizontal member is necessary.

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