Systems for Steel Buildings
1.3 CONCENTRIC BRACED FRAMES
Generally speaking, rigid frame systems are not efficient for buildings taller than about 20 stories because the shear racking component of deflection due to bending of columns and girders causes the drift to be too large. A braced frame improves upon the efficiency of a rigid frame by virtu-ally eliminating the bending of columns and girders. This is because by adding web members such as diagonals or chevron braces, the horizontal shear is resisted by the web. The webs carry the lateral shear predominantly by axial forces in the braces thus minimizing bending of beams and columns.
1.3.1 Behavior
In simple terms, braced frames may be considered as 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 web members resisting the horizontal shear in axial com-pression or tension. Because the lateral load is reversible, braces are subjected to both compres-sion and tencompres-sion; consequently, they are most often designed for the more stringent requirements of compression.
When a brace frame is subjected to lateral loads, the resulting axial deformation of the columns tend to cause a flexural deformation of the frame with concavity downwind and maximum slope at the top as shown in Figure 1.15a. On the other hand, the axial deformation of the diagonals tend to cause a “shear” mode deformation with concavity upwind, a maximum slope at the base, and a zero slope at the top (see Figure 1.15b). The resulting deflected shape shown in Figure 1.15c is thus a combination of flexural and shear modes with the flexural deflection most often dominating the deflection scene.
The role of web members in resisting the horizontal shear can be demonstrated by following the load path down the braced bent. Consider the braced frames, shown in Figure 1.16, subjected to an
18 Structural Analysis and Design of Tall Buildings: Steel and Composite Construction
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 Figure 1.16b, the forces in the braces connecting to each beam-end are in equilibrium horizontally with the beam carrying insignificant axial load.
In Figure 1.16c, half of each beam is in compression while the other half is in tension. In Figure 1.16d, the braces are alternately in compression and tension while the beams remain basically unstressed. And finally in Figure 1.16e, the end parts of the beam are in compression and tension with the entire beam subjected to bending in double curvature as shown by the dotted lines. Observe that with a reversal in the direction of horizontal load, all actions and deformations in each member will also be reversed.
The principal function of web members is to resist horizontal shear forces. However, depending upon their configuration, the web members may pick up substantial compressive forces as the col-umns shorten vertically under gravity loads. Consider, for example, the bracing configuration shown in Figure 1.17. As the columns shown in Figure 1.17a and b shorten, the diagonals are subjected to compression forces because the beams at each end of the braces are effective in resisting the
(c) (b)
+ =
(a)
FIGURE 1.15 Braced frame deformation: (a) flexural deformation; (b) shear deformation; (c) combined configuration.
(b)
0 0
0 0
0 0
(c) (d) (e)
(a)
FIGURE 1.16 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.
Lateral Load Resisting Systems for Steel Buildings 19
horizontal component of the compressive forces in the diagonal. At a first glance, this may appear to be the case for the frame shown in Figure 1.17c. However, the diagonals shown therein, will not attract significant gravity forces because there is no triangulation at the ends of beams where the diagonals are not connected as, for example, at nodes A and D. The only horizontal restraint at the beam-end is by the bending resistance of columns, which usually is of minor significance in the overall behavior. Similarly, in Figure 1.17d, the vertical restraint from the bending stiffness of the beam is too large; therefore, as in the previous case, the diagonals experience only negligible gravity forces.
1.3.2 tyPes oF ConCentriC BraCes
Braced frames may be grouped into two categories as either concentric braced frames (CBF) or eccentric braced frames (EBFs). In CBFs, the axes of all members, that is, columns, beams, and braces intersect at a common point such that the member forces are axial without significant moments. On the other hand, EBFs, utilize axis offsets to deliberately introduce flexure and shear in preselected beam segments to increase ductility.
Braced frames can take on many configurations some of which are shown in Figure 1.18. The diagonal member often consists of double angles, channels, tees, tubes or wide flange shapes, their
(a) (b)
(d) 0
0
0
0 0
0 0 0
(c)
A B
0 0 0 0 0 0 0 0 C
D
FIGURE 1.17 Gravity load path in braced frames: (a) single diagonal single direction bracing; (b) X-bracing;
(c) single diagonal alternate direction bracing; (d) chevron bracing.
20 Structural Analysis and Design of Tall Buildings: Steel and Composite Construction
(a) (b)
(d) (c)
(e)
(j) (k) (l) (m) (n)
(f) (g) (h) (i)
FIGURE 1.18 Bracing configurations.
Lateral Load Resisting Systems for Steel Buildings 21
From architectural considerations, the least objectionable locations for braces are around ser-vice cores and elevators, where frame diagonals may be enclosed within permanent walls. The braces can be joined together to form a closed or partially closed three-dimensional cell for effec-tively resisting torsional loads. Any reasonable configuration with single or multiple braced bays, as shown in Figure 1.18, may be designed for resisting lateral loads. However, availability of proper depth for bracing is often an overriding consideration. As a preliminary guide, a height-to-width ratio of 8–10 is considered proper for a reasonably efficient bracing system.
Braced-frame systems tend to be more economical than moment-resisting frames when mate-rial, fabrication, and erection costs are considered. These efficiencies are often offset by reduced flexibility in floor plan layout, space planning, and electrical and mechanical routing, encoun-tered as a result of the space requirements for the brace members. Braced frames are, therefore, typically located in walls that stack vertically between floor levels. In a typical office building, these walls generally occur in the “core” area around stair and elevator shafts, central restrooms, and mechanical and electrical rooms. This generally allows for greater architectural flexibility in articulating vertical modulations of the building envelope. Depending on the plan location and the size of the core area of the building, the torsional resistance offered by the braced frames may become a controlling design parameter. Differential drift between stories at the building perimeter must be considered with this type of layout, as rotational displacements of the floor diaphragms may impose deformation demands on the cladding system and other nonstructural elements of the building.