Braced Frames

Rigid frame systems are not efficient for buildings taller than about 20 stories because the shear racking component of deflection due to the bending of columns and beams causes the story drift to be too great. Addition of diagonal or V-braces within the frame transforms the system into a vertical truss, virtually eliminating the bending of columns and beams. High stiffness is achieved because the horizontal shear is now primarily absorbed by the web members and not by the columns. The webs resist lateral forces by developing internal axial actions and relatively small flexural actions. The braces can be configured by using any number of steel shapes such as I-shaped sections, rectangular or circular tubes, single or double angles stitched together, T-shape sections, or channels. Brace connections to the framing systems commonly consist of gusset plates with bolted or welded connections to the braces.

In simple terms, braced frames may be considered cantilevered vertical trusses resisting lateral loads primarily through the axial stiffness of columns and braces. The columns act as the chords in resisting the overturning moment, with tension in the windward column and compression in the leeward column. The diagonals work as the web members resisting the horizontal shear in axial compression or tension, depending on the direction of inclination. The beams act axially, when the system is a fully triangulated truss. They undergo bending only when the braces are eccentrically connected to them. Because the

Figure 3.5. Braced frame deformation: (a) flexural deformation; (b) shear deformation; (c) combined configuration.

Figure 3.5. Braced frame deformation: (a) flexural deformation; (b) shear deformation; (c) combined configuration.

lateral loads are reversible, braces are subjected to both compression and tension; they are most often designed for the more stringent case of compression.

The effect of axial deformation of the columns results in a "flexural" configuration of the deflection with concavity downwind and a maximum slope at the top (Fig. 3.5a). The axial deformations of the web members, on the other hand, cause a "shear" configuration of deflection with concavity upwind, a maximum slope at the base, and a zero slope at the top (Fig. 3.5b). The resulting deflected shape of the frame (Fig. 3.5c) is a combination of the effects of the flexural and shear curves, with a resultant configuration depending on their relative magnitudes, as determined mainly by the type of bracing. Nevertheless, it is the flexural deflection that most often dominates the deflection characteristics.

The role of web members in resisting shear can be demonstrated by following the path of the horizontal shear down the braced bent. Consider the braced frames shown in Fig. 3.6a-e, subjected to an external shear force at the top level. In Fig. 3.6a, the diagonal in each story is in compression, causing the beams to be in axial tension; therefore, the shortening of the diagonal and extension of the beams gives rise to the shear deformation of the bent. In Fig. 3.6b, the forces in the braces connecting to each beam-end are in equilibrium horizontally with the beam carrying insignificant axial load. In Fig. 3.6c, half of each beam is in compression while the other half is in tension. In Fig. 3.6d, the braces are alternately in compression and tension while the beams remain basically unstressed. Finally, in Fig. 3.6e, the end parts of the beam are in compression and tension with the entire beam subjected to double curvature bending. Observe that with a reversal in the direction of horizontal load, all actions and deformations in each member will also be reversed.

In a braced frame, the principal function of web members is to resist the horizontal shear forces. However, depending on the configuration of the bracing, the web members may pick up substantial compressive forces as the columns shorten vertically under gravity loads. Consider, for example, the typical bracing configurations shown in Fig. 3.7a through d. As the columns in Fig. 3.7a and b shorten, the diagonals are subjected to

Figure 3.6. Load path for horizontal shear through web numbers: (a) single diagonal bracing; (b) X-bracing; (c) chevron bracing; (d) single-diagonal, alternate direction bracing; (e) knee bracing.

Figure 3.7. Gravity load path: (a) single diagonal single direction bracing; (b) X-bracing; (c) single diagonal alternate direction bracing; (d) chevron bracing.

compression forces because the beams at each end of the braces are effective in resisting the horizontal component of the compressive forces in the diagonal. At first glance, this may appear to be the case for the frame shown in Fig. 3.7c. However, the diagonal shown in Fig. 3.7c will not attract significant gravity forces because there is no triangulation at the ends of beams where the diagonals are not connected (nodes A and D, in Fig. 3.7c). The only horizontal restraint at the end is by the bending resistance of columns, which usually is of minor significance in the overall behavior. Similarly, in Fig. 3.7d, the vertical restraint from the bending stiffness of the beam is not large; therefore, as in the previous case, the braces experience only negligible gravity forces.

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