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With loads measured in tens of thousands kips, there is little room in the design of high-rise buildings for excessively complex thoughts. Indeed, the better high-rise buildings carry the universal traits of simplicity of thought and clarity of expression.
It does not follow that there is no room for grand thoughts. Indeed, it is with such grand thoughts that the new family of high-rise buildings has evolved. Perhaps more important, the new concepts of but a few years ago have become commonplace in today’ s technology.
Omitting some concepts that are related strictly to the materials of construction, the most commonly used structural systems used in high-rise buildings can be categorized as follows:
1. Moment-resisting frames.
2. Braced frames, including eccentrically braced frames.
3. Shear walls, including steel plate shear walls.
4. Tube-in-tube structures.
5. Tube-in-tube structures.
6. Core-interactive structures.
7. Cellular or bundled-tube systems.
Particularly with the recent trend toward more complex forms, but in response also to the need for increased stiffness to resist the forces from wind and earthquake, most high-rise buildings have structural systems built up of combinations of frames, braced bents, shear walls, and related systems. Further, for the taller buildings, the majorities are composed of interactive elements in three-dimensional arrays.
The method of combining these elements is the very essence of the design process for high-rise buildings. These combinations need evolve in response to environmental, functional, and cost considerations so as to provide efficient structures that provoke the architectural development to new heights. This is not to say that imaginative structural design can create great architecture. To the contrary, many examples of fine architecture have been created with only moderate support from the structural engineer, while only fine structure, not great architecture, can be developed without the genius and the leadership of a talented architect. In any event, the best of both is needed to formulate a truly extraordinary design of a high-rise building.
While comprehensive discussions of these seven systems are generally available in the literature, further discussion is warranted here .The essence of the design process is distributed throughout the discussion.
Moment-Resisting Frames
Perhaps the most commonly used system in low-to medium-rise buildings, the moment-resisting frame, is characterized by linear horizontal and vertical members connected essentially rigidly at their joints. Such frames are used as a stand-alone system or in combination with other systems so as to provide the needed resistance to horizontal loads. In the taller of high-rise buildings, the system is likely to be found inappropriate for a stand-alone system, this because of the difficulty in mobilizing sufficient stiffness under lateral forces.
Analysis can be accomplished by STRESS, STRUDL, or a host of other appropriate computer programs; analysis by the so-called portal method of the cantilever method has no place in today’s technology.
Because of the intrinsic flexibility of the column/girder intersection, and because preliminary designs should aim to highlight weaknesses of systems, it is not unusual to use center-to-center dimensions for the frame in the preliminary analysis. Of course, in the latter phases of design, a realistic appraisal in-joint deformation is essential.
Braced Frames
The braced frame, intrinsically stiffer than the moment –resisting frame, finds also greater application to higher-rise buildings. The system is characterized by linear horizontal, vertical, and diagonal members, connected simply or rigidly at their joints. It is used commonly in conjunction with other systems for taller buildings and as a stand-alone system in low-to medium-rise buildings.
While the use of structural steel in braced frames is common, concrete frames are more likely to be of the larger-scale variety.
Of special interest in areas of high seismicity is the use of the eccentric braced frame.
Again, analysis can be by STRESS, STRUDL, or any one of a series of two –or three dimensional analysis computer programs. And again, center-to-center dimensions are used commonly in the preliminary analysis.
The shear wall is yet another step forward along a progression of ever-stiffer structural systems. The system is characterized by relatively thin, generally (but not always) concrete elements that provide both structural strength and separation between building functions.
In high-rise buildings, shear wall systems tend to have a relatively high aspect ratio, that is, their height tends to be large compared to their width. Lacking tension in the foundation system, any structural element is limited in its ability to resist overturning moment by the width of the system and by the gravity load supported by the element. Limited to a narrow overturning, One obvious use of the system, which does have the needed width, is in the exterior walls of building, where the requirement for windows is kept small.
Structural steel shear walls, generally stiffened against buckling by a concrete overlay, have found application where shear loads are high. The system, intrinsically more economical than steel bracing, is particularly effective in carrying shear loads down through the taller floors in the areas immediately above grade. The sys tem has the further advantage of having high ductility a feature of particular importance in areas of high seismicity.
The analysis of shear wall systems is made complex because of the inevitable presence of large openings through these walls. Preliminary analysis can be by truss-analogy, by the finite element method, or by making use of a proprietary computer program designed to consider the interaction, or coupling, of shear walls.
The concept of the framed or braced or braced tube erupted into the technology with the IBM Building in Pittsburgh, but was followed immediately with the twin 110-story towers of the World Trade Center, New York and a number of other buildings .The system is characterized by three –dimensional frames, braced frames, or shear walls, forming a closed surface more or less cylindrical in nature, but of nearly any plan configuration. Because those columns that resist lateral forces are placed as far as possible from the cancroids of the system, the overall moment of inertia is increased and stiffness is very high.
The analysis of tubular structures is done using three-dimensional concepts, or by two- dimensional analogy, where possible, whichever method is used, it must be capable of accounting for the effects of shear lag.
The presence of shear lag, detected first in aircraft structures, is a serious limitation in the stiffness of framed tubes. The concept has limited recent applications of framed tubes to the shear of 60 stories. Designers have developed various techniques for reducing the effects of shear lag, most noticeably the use of belt trusses. This system finds application in buildings perhaps 40stories and higher. However, except for possible aesthetic considerations, belt trusses interfere with nearly every building function associated with the outside wall; the trusses are placed often at mechanical floors, mush to the disapproval of the designers of the mechanical systems. Nevertheless, as a cost-effective structural system, the belt truss works well and will likely find continued approval from designers. Numerous studies have sought to optimize the location of these trusses, with the optimum location very dependent on the number of trusses provided. Experience would indicate, however, that the location of these trusses is provided by the optimization of mechanical systems and by aesthetic considerations, as the economics of the structural system is not highly sensitive to belt truss location.
Tube-in-Tube Structures
The tubular framing system mobilizes every column in the exterior wall in resisting over-turning and shearing forces. The term‘tube-in-tube’is largely self-explanatory in that a second ring of columns, the ring surrounding the central service core of the building, is used as an inner framed or braced tube. The purpose of the second tube is to increase resistance to over turning and to increase lateral stiffness. The tubes need not be of the same character; that is, one tube could be framed, while the other could be braced.
In considering this system, is important to understand clearly the difference between the shear and the flexural components of deflection, the terms being taken from beam analogy. In a framed tube, the shear component of deflection is associated with the bending deformation of columns and girders (i.e, the webs of the framed tube) while the flexural component is associated with the axial shortening and lengthening of columns (i.e, the flanges of the framed tube). In a braced tube, the shear component of deflection is associated with the axial deformation of diagonals while the flexural component of deflection is associated with the axial shortening and lengthening of columns.
Following beam analogy, if plane surfaces remain plane (i.e, the floor slabs),then axial stresses in the columns of the outer tube, being farther form the neutral axis, will be substantially larger than the axial stresses in the inner tube. However, in the tube-in-tube design, when optimized, the axial stresses in the inner ring of columns may be as high, or even higher, than the axial stresses in the outer ring. This seeming anomaly is associated with differences in the shearing component of stiffness between the two systems. This is easiest to under-stand where the inner tube is conceived as a braced (i.e, shear-stiff) tube while the outer tube is conceived as a framed (i.e, shear-flexible) tube.
Core interactive structures are a special case of a tube-in-tube wherein the two tubes are coupled together with some form of three-dimensional space frame. Indeed, the system is used often wherein the shear stiffness of the outer tube is zero. The United States Steel Building, Pittsburgh, illustrates the system very well. Here, the inner tube is a braced frame, the outer tube has no shear stiffness, and the two systems are coupled if they were considered as systems passing in a straight line from the “hat” structure. Note that the exterior columns would be improperly modeled if they were considered as systems passing in a straight line from the “hat” to the foundations; these columns are perhaps 15% stiffer as they follow the elastic curve of the braced core. Note also that the axial forces associated with the lateral forces in the inner columns change from tension to compression over the height of the tube, with the inflection point at about 5/8 of the height of the tube. The outer columns, of course, carry the same axial force under lateral load for the full height of the columns because the columns because the shear stiffness of the system is close to zero.
The space structures of outrigger girders or trusses, that connect the inner tube to the outer tube, are located often at several levels in the building. The AT&T headquarters is an example of an astonishing array of interactive elements:
1. The structural system is 94 ft (28.6m) wide, 196ft(59.7m) long, and 601ft (183.3m) high.
2. Two inner tubes are provided, each 31ft(9.4m) by 40 ft (12.2m), centered 90 ft (27.4m) apart in the long direction of the building.
3. The inner tubes are braced in the short direction, but with zero shear stiffness in the long direction.
4. A single outer tube is supplied, which encircles the building perimeter.
5. The outer tube is a moment-resisting frame, but with zero shear stiffness for the center50ft (15.2m) of each of the long sides.
6. A space-truss hat structure is provided at the top of the building.
7. A similar space truss is located near the bottom of the building
8. The entire assembly is laterally supported at the base on twin steel-plate tubes, because the shear stiffness of the outer tube goes to zero at the base of the building.
A classic example of a cellular structure is the Sears Tower, Chicago, a bundled tube structure of nine separate tubes. While the Sears Tower contains nine nearly identical tubes, the basic structural system has special application for buildings of irregular shape, as the several tubes need not be similar in plan shape, It is not uncommon that some of the individual tubes one of the strengths and one of the weaknesses of the system.
This special weakness of this system, particularly in framed tubes, has to do with the concept of differential column shortening. The shortening of a column under load is given by the expression
△=ΣfL/E
For buildings of 12 ft (3.66m) floor-to-floor distances and an average compressive stress of 15 ksi (138MPa), the shortening of a column under load is 15 (12)(12)/29,000 or 0.074in (1.9mm) per story. At 50 stories, the column will have shortened to 3.7 in. (94mm) less than its unstressed length. Where one cell of a bundled tube system is, say, 50stories high and an adjacent cell is, say, 100stories high, those columns near the boundary between .the two systems need to have this differential deflection reconciled.
Major structural work has been found to be needed at such locations. In at least one building, the Rialto Project, Melbourne, the structural engineer found it necessary to vertically pre-stress the lower height columns so as to reconcile the differential deflections of columns in close proximity with the post-tensioning of the shorter column simulating the weight to be added on to adjacent, higher columns
