If the lateral deflection patterns of braced and unbraced frames were similar, the lateral loads would be distributed between the two systems according to their relative stiffness. However, in general, the unbraced and braced frames deform with their own characteristic shapes, resulting in a heavy interaction between the two, particularly at the upper levels of the buildings.

Insofar as the lateral-load-resistance is concerned, rigid and braced frames can be considered as two distinct units. The basis of classification is the mode of deformation of the two when subjected to lateral loading.

The deflection characteristics of a braced frame are similar to those of a cantilever beam. Near the bottom, the braced frame is relatively stiff, and therefore, the floor-to-floor deflections will be less than half the values near the top. Near the top, the floor-to-floor deflections increase rather rapidly, resulting mainly from the cumulative effect of braced frame rotation due to axial deformations of the columns. Since this effect occurs at every floor, the resulting deflection at the top is cumulative. This type of deflection due to axial strains in columns—often referred to as chord drift—is difficult to control unless the column areas are increased far above those required for gravity needs.

Rigid frames deform predominantly in a shear mode. The relative story deflections depend primarily on the magnitude of shear applied at each story level. Although the deflections are larger near the bottom and smaller near the top as compared to the braced frames, the floor-to-floor deflections can be considered more nearly uniform throughout the

Figure 3.16. Interaction between braced and unbraced frames: (a) characteristic deformation shapes; (b) variation of shear forces resulting from interaction.

height. When the two systems—the braced and rigid frames—are connected by rigid floor diaphragms, a nonuniform shear force develops between the two. The resulting interaction typically results in a more economical system.

Figure 3.16 shows the deformation patterns of a braced and unbraced frame subjected to lateral loads. Also shown are the horizontal shear forces between the two, the length of arrows schematically representing the level of interaction between them. Observe that the braced frame acts as a vertical cantilever beam, with the slope of the deflection greatest at the top, indicating that in this region the braced frame contributes the least to the lateral stiffness.

The rigid frame, on the other hand, deforms in a shear mode, with the slope greater at the base of the structure where the shear is maximum. Since the lateral deflection characteristics of the two frames are entirely different, the rigid frame tends to pull back the brace frame in the upper portion of the building while pushing it forward in the lower portion. As a result, the rigid frame participates more effectively in the upper portion of the building where lateral shears are relatively weaker, while the braced frame carries most of the shear in the lower portion of the building. Because of the distinct difference in the deflection characteristics, the two systems tend to help each other a great deal. The rigid frame tends to reduce the lateral deflection of the brace frame at the top, while the braced frame supports the rigid frame near the base. A typical variation of horizontal shear carried by each frame is shown in Fig. 3.16b, in which the length of arrows conceptually indicates the magnitude of interacting shear forces.

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