To understand the behavior of a framed tube, consider a building shown in Fig. 3.31 in which the entire lateral resistance is provided by closely spaced exterior columns and deep spandrel beams. The floor system, typically considered rigid in its own plane, distributes the lateral load to various elements according to their stiffness. Its contribution to lateral resistance in terms of out-of-plane stiffness is considered negligible as in other systems. The lateral load-resisting system thus comprises four orthogonally oriented, rigidly jointed frame panels forming a tube in plan, as shown in Fig. 3.32.

The "strong" bending direction of the columns is typically aligned along the face of the building, in contrast to a typical transverse rigid frame where it is aligned perpendicular to the face. The frames parallel to the lateral load act as webs of the perforated tube, while

Figure 3.31. Schematic plan of framed tube.

the frames normal to the load act as the flanges. Gravity loads are resisted partly by the exterior frames and partly by interior columns. When subjected to bending, the primary mode of action is that of a vertical cantilever tube, in which the columns on opposite sides of the neutral axis are subjected to tensile and compressive forces. In addition, the frames parallel to the direction of the lateral load are subjected to the in-plane bending and the shearing forces associated with an independent rigid frame. The discrete columns and spandrels may be considered, in a conceptual sense, equivalent to a hollow tube cantilevering from the ground with a linear axial stress distribution, as shown in Fig. 3.33.

Although the structure has a tubelike form, its behavior is much more complex than that of a solid tube. Unlike a solid tube, it is subjected to the effects of shear lag, which

Figure 3.32. Isometric view of framed tube.
Figure 3.33. Axial stress distribution in square hollow tube with and without shear lag.

have a tendency to modify the axial distribution in the columns. The influence of shear lag, considered in the following section, is to increase the axial stresses in the corner columns and reduce those in the inner columns of both the flange and the web panels, as shown in Fig. 3.33.

Figure 3.34 shows examples of free-form tubular configurations. Although in simplistic terms, the tube is similar to a hollow cantilever, in reality its response to lateral loads is in a combined bending and shear mode. The overall bending of the tube is due to axial shortening and elongation of the columns, whereas the shear deformation is due to bending of individual columns and spandrels. The underlying principle for an efficient design is to eliminate or minimize the shear deformation.

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