Figure 4.1. Structural systems for concrete buildings.

Figure 4.1. Structural systems for concrete buildings.

rows of joists commonly formed by using square domes. The domes are omitted around the columns to increase the moment and shear capacity of the slab. Any of the three systems may be used as an integral part of a lateral resisting system and all are popular for apartments and hotels in areas of low seismicity.

The slab system shown in Fig. 4.2 has two distinct actions in resisting lateral loads. First, because of its high in-plane stiffness, it distributes the lateral loads to various vertical elements in proportion to their stiffness. Second, because of its significant out-of-plane stiffness, it restrains the vertical displacements and rotations of columns as if they were interconnected by a shallow wide beam.

The concept of effective width can be used to determine the equivalent width of a flat slab-beam. Although physically no beam exists between the columns, for analytical purposes a certain width of slab may be considered as a beam framing between the columns. The effective width is, however, dependent on various parameters, such as column aspect ratios, distance between the columns, thickness of the slab, etc. Research has shown that values less than, equal to, and greater than full width are all valid depending upon the parameters mentioned above.

The American Concrete Institute (ACI) permits a full width of slab between adjacent panel center lines for both gravity and lateral load analysis with the stipulation that the effect of slab cracking be considered in evaluating stiffness of frame members. Use of a full width is explicit for gravity analysis, and implicit (because it is not specifically prohibited) for the lateral loads. However, engineers generally agree that use of a full width is unconservative for lateral analysis. It overestimates the column stiffness, compounding the error in the distribution of moments due to lateral loads.

Of particular concern in the design of a flat slab-frame is the problem of shear stress concentration at the column-slab joint. Shear reinforcement is almost always necessary to

Figure 4.2. Lateral systems using slab and columns: (a) flat plate; (b) flat slab with drop panels; (c) two-way waffle system.

improve joint behavior and avoid early stiffness deterioration under lateral cyclic loading. This is one of the primary reasons that two-way slab systems are not permitted by the ACI code in regions of high seismic risk (UBC zones 3 and 4). Their use in regions of moderate seismic risk (UBC zones 2 and 2B) is permitted, subject to certain requirements, mainly relating to reinforcement placement in the column strip.

Drop panels

Drop panels

Figure 4.3. Shear wall-flat slab system.

4.1.2. Flat Slab-Frame with Shear Walls

Frame action provided by flat slab-beam and column interaction is generally insufficient for buildings taller than about 10 stories. A system consisting of shear walls and flat slab-frames may provide an appropriate lateral bracing system. Figure 4.3 shows an example.

Coupling of walls and columns solely by slabs is a relatively weak source of energy dissipation. When sufficiently large rotations occur in the walls during an earthquake, shear transmission from slab into wall occurs mainly around the inner edges of the wall. Because of torsional cracking of the slab and shear distortions around the columns, the system hysteretic response is poor. Therefore, seismic codes discourage the use of slab-beam frames by limiting the width of slab that can be considered as an equivalent beam. For buildings in high seismic zones (UBC zones 3 and 4) the width of the equivalent beam is limited to the width of the supporting column plus 1.5 times the thickness of the slab. Only in this limited width are we allowed to place the top and bottom flexural reinforcement. This requirement precludes the use of flat slab-beams as part of a seismic system in zones of high seismicity.

It should be noted that deformation compatibility requirements impose severe punching stress demands in the flat slabs of buildings in regions of high seismic risk.

4.1.3. Coupled Shear Walls

A system of interconnected shear walls exhibits a stiffness that far exceeds the summation of the individual wall stiffnesses. This is because the interconnecting slab or beam restrains the cantilever bending of individual walls by forcing the system to work as a composite unit.

The system is economical for buildings in the 40-story range. Since planar shear walls carry loads only in their plane, walls in two orthogonal directions are generally required to resist lateral loads in two directions. Placement of walls around elevators, stairs, and utility shafts is common because they do not interfere with interior architectural layout. However, resistance to torsional loads must be considered in determining their location.

4.1.4. Rigid Frame

Cast-in-place concrete has an inherent advantage of continuity at joints. The design and detailing of joints at the intersection of beams and columns is of concern particularly in seismic design because the column height within the depth of the girder is subjected to large shear forces. Horizontal seismic ties at very close spacing may be required to avoid uncontrolled diagonal cracking and disintegration of concrete and to promote ductile behavior. The design intent in high seismic zones is to have a system that can respond to earthquake loads without loss in gravity-load carrying capacity.

A rigid frame is characterized by flexure of beams and columns and rotation at the joints. Interior rigid frames for office buildings are generally inefficient because: 1) the number of columns in any given frame is limited due to leasing considerations; and 2) the beam depths are often limited by the floor-to-floor height. However, frames located at the building exterior do not necessarily have these limitations. An efficient frame action can thus be developed by providing closely spaced columns and deep spandrels at the building exterior.

4.1.5. Tube System with Widely Spaced Columns

The term tube, in usual building terminology, suggests a system of closely spaced columns say, 8 to 15 ft on center (2.43 to 4.57 m) tied together with a relatively deep spandrel. However, for buildings with compact plans it is possible to achieve tube action with relatively widely spaced columns interconnected with deep spandrels. As an example, the plan of a 28-story building constructed in New Orleans, LA, is shown in Fig. 4.4. Lateral resistance is provided by a perimeter frame consisting of columns 5 ft (1.5 m) wide, spaced at 25-ft (7.62-m) centers, and tied together with a spandrel 5 ft (1.53 m) deep.

4.1.6. Rigid Frame with Haunch Girders

Office buildings usually have a lease depth of about 40 ft (12.19 m) without interior columns. A girder about 2 ft-6 in. (0.76 m) in depth is required to carry gravity loads for

Figure 4.4. Tube building with widely spaced perimeter columns.
Figure 4.5. A 28-story haunch girder building: typical floor framing plan.

a 40-ft (12.19-m) span unless the girder is post-tensioned. The beam depth has an impact on the floor-floor height and is often limited because of the additional cost for the increased height of interior partitions, a curtain wall, and the added heating and cooling loads due to the increased volume of the building. A variable-depth haunch girder, as shown in Fig. 4.5, is often the solution for resisting both gravity and lateral loads. No increase in floor-to-floor height is required because the depth of girder at the midsection is flush with the floor system, thus providing ample beamless space for passage of mechanical ducts.

4.1.7. Core-Supported Structures

Shear walls around building cores can be considered as a spatial system capable of transmitting lateral loads in both directions. The advantage of shear walls around the elevator and staircases is that, being spatial structures, they are able to resist gravity loads, shear forces, bending moments, and torsion in two directions, especially when adequate stiffness and strength are provided between the openings. The shape of the core is governed by the elevator and stair requirements, and can vary from a single rectangular core to multiple cores. Structural floor framing surrounding the core may consist of any type of common system such as cast-in-place concrete, precast concrete, or structural steel (Fig. 4.6).

4.1.8. Shear Wall-Frame Interaction

Without question, this system is one of the most—if not the most—popular systems for resisting lateral loads in medium- to high-rise buildings. The system has a broad range of application and has been used for buildings as low as 10 stories to as high as 50 stories or even taller. With the advent of haunch girders, the applicability of the system can be extended to buildings in the 70- to 80-story range.

Center Rigidity Shear Walls
Figure 4.6. Examples of shear core buildings: (a) cast-in-place shear walls with precast surround; (b) shear walls with post-tensioned flat plate; (c) shear walls with one-way joist system.

The classical mode of interaction between a prismatic shear wall and a moment frame is shown in Fig. 4.7; the frame deflects in a so-called shear mode whereas the shear wall predominantly responds by bending as a cantilever. Compatibility of horizontal deflection generates interaction between the two. The linear sway of the moment frame, combined with the parabolic sway of the shear wall, results in enhanced stiffness because the wall is restrained by the frame at the upper levels while at the lower levels the shear wall is restrained by the frame. However, a frame consisting of closely spaced columns

Figure 4.6. (Continued )

and deep beams tends to behave more like a shear wall responding predominantly in a bending mode. And similarly, a shear wall weakened by large openings acts more like a frame by deflecting in a shear mode. The combined structural action, therefore, depends on the relative rigidity of the two, and their modes of deformation.

4.1.9. Frame Tube System

In this system, the perimeter of the building consists of closely spaced columns connected by deep spandrels. The system works as a hollow vertical cantilever and is efficient because of the maximum distance separating the windward and leeward columns. However, lateral drift due to the axial displacement of the columns—commonly referred to as chord drift—and web drift, caused by shear and bending deformations of the spandrels and columns, may be quite large depending upon the tube geometry. For example, if the plan aspect ratio is large, say, much in excess of 1:2.5, it is likely that supplemental lateral bracing may be necessary to satisfy drift limitations. The economy of the tube system

Figure 4.7. Shear wall-frame interaction.

therefore depends on factors such as spacing and size of columns, depth of perimeter spandrels, and the plan aspect ratio of the building. This system should, however, be given consideration for buildings taller than about 40 stories.

4.1.10. Exterior Diagonal Tube

By applying structural principles similar to those of a trussed steel tube, it is possible to visualize a concrete system consisting of closely spaced exterior columns with blocked-out windows at each floor to create a diagonal pattern on the building facade. The diagonals carry lateral shear forces in axial compression and tension, thus eliminating bending in the columns and girders. Currently, two buildings have been built using this approach. The first is a 50-story office building in New York, and the second is a mixed-use building in Chicago. The structural system for the building in New York consists of a combination of a framed and a trussed tube interacting with a system of interior core walls. The building is 570 ft (173.73 m) tall with a height-to-width ratio of 8:1. Schematic elevation and floor plan of the building are shown in Fig. 4.8.

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