## J

FIGURE 22.2 Common bracing systems: (a) vertical truss system and (b) shear wall.

Frame A

Frame B

Frame A

Frame B

### FIGURE 22.3 Frames split into two subassemblies.

the sources of resistance and to compare their behavior with respect to the horizontal actions. However, this identification is not that obvious since the bracing is integral within the structure. Some assumptions need to be made in order to define the two structures for the purpose of comparison.

Figure 22.3 and Figure 22.4 represent the structures that are easy to define, within one system, two subassemblies identifying the bracing system and the system to be braced. For the structure shown in Figure 22.3, there is a clear separation of functions in which the gravity loads are resist by the hinged subassembly (Frame B) and the horizontal loads are resisted by the braced assembly (Frame A). In contrast, for the structure in Figure 22.4, since the second subassembly (Frame B) is able to resist horizontal actions as well as vertical actions, it is necessary to assume that practically all the horizontal actions are carried by the first subassembly (Frame A) in order to define this system as braced.

According to EC3 (1992a,b), a frame may be classified as braced if its sway resistance is supplied by a bracing system in which its response to lateral loads is sufficiently stiff for it to be acceptably accurate to assume all horizontal loads are resisted by the bracing system. The frame can be classified as braced if the bracing system reduces its horizontal displacement by at least 80%.

Frame A Frame B

FIGURE 22.4 Mixed frames split into two subassemblies.

For the frame shown in Figure 22.3, the hinged frame (Frame B) has no lateral stiffness and Frame A (truss frame) resists all lateral load. In this case, Frame B is considered to be braced by Frame A. For the frame shown in Figure 22.4, Frame B may be considered to be a braced frame if the following deflection criterion is satisfied:

where Aa is the lateral deflection calculated from the truss frame (Frame A) alone and AB is the lateral deflection calculated from Frame B alone.

Alternatively, the lateral stiffness of Frame A under the applied lateral load should be at least five times larger than that of Frame B:

where KA is the lateral stiffness of Frame A and KB is the lateral stiffness of Frame B.

### 22.2.5 Sway versus Nonsway Frames

A frame can be classified as nonsway if its response to in-plane horizontal forces is sufficiently stiff for it to be acceptable to neglect any additional internal forces or moments arising from horizontal displacements of the frame. In the design of a multistory building frame, it is convenient to isolate the columns from the frame and treat the stability of columns and the stability of frames as independent problems. For a column in a braced frame it is assumed that the columns are restricted at their ends from horizontal displacements and therefore are only subjected to end moments and axial loads as transferred from the frame. It is then assumed that the frame, possibly by means of a bracing system, satisfies global stability checks and that the global stability of the frame does not affect the column behavior. This gives the commonly assumed nonsway frame. The design of columns in a nonsway frame follows the conventional beam-column capacity check approach and the column effective length may be evaluated based on the column end restraint conditions. Interaction equations for various cross-section shapes have been developed through years of research in the field of beam-column design (Chen and Atsuta 1976).

Another reason for defining''sway'' and ''nonsway frames'' is the need to adopt conventional analysis in which all the internal forces are computed on the basis of the undeformed geometry of the structure. This assumption is valid if second-order effects are negligible. When there is an interaction between overall frame stability and column stability, it is not possible to isolate the column. The column and the frame have to act interactively in a ''sway'' mode. The design of sway frames has to consider the frame subassemblage or the structure as a whole. Moreover, the presence of''inelasticity'' in the columns will render some doubts on the use of the familiar concept of''elastic effective length'' (Liew et al. 1991, 1992). On the basis of the above considerations, a definition can be established for sway and nonsway frames as

A frame can be classified as nonsway if its response to in-plane horizontal forces is sufficiently stiff for it to be acceptably accurate to neglect any additional internal forces or moments arising from horizontal displacements of its nodes.

British Code: BS5950: Part 1 (1990) provides a procedure to distinguish between sway and nonsway frames as follows:

1. Apply a set of notional horizontal loads to the frame. These notional forces are to be taken as 0.5% of the factored dead plus vertical imposed loads and are applied in isolation, that is, without the simultaneous application of actual vertical or horizontal loading.

2. Perform a first-order linear elastic analysis and evaluate the individual relative sway deflection d for each story.

3. If the actual frame is uncladed, the frame may be considered to be nonsway if the interstory deflection satisfies the following limit:

0 0