Truss System Tall Buildings 1995

THE STRUCTURAL DESIGN OF TALL BUILDINGS, VOl. 4, 155-168 (1995)

NEW STRUCTURAL SYSTEMS FOR TALL BUILDINGS: THE SPACE-TRUSS CONCEPT

c . c. POUANGARE~ Pouangare & Associates, 9 Nikokleous Street, Ay. Zoni, 3027, Limassol, Cyprus

AND

J. J . CONNOR~ Department of Civil Engineering, MIT, Rm 1-353, 77 Massachusetts Avenue, Cambridge, M A 02139, U.S.A.

SUMMARY The dominant structural system used for buildings over 40 stories has been the framed tube and its modifications. Recently, new concepts have emerged leading to the development of space-truss systems, which are more efficient and more economical than tubes. A few buildings have already been built on the space-truss idea. In this paper, various structural concepts for tall and super-tall buildings are proposed, and one of them is examined in detail. The issue of material selection is also addressed through a design approach based on material behavior under specific loading conditions and on the cost of the material. In addition, the generic design of a one-hundred-and-twelve story building is presented as an application of the concept.

NOTATATION The following symbols are used in this paper:

A c m

d E F 9

H I K e

M S V W

P 6

area of the truss member or column cost of the material per unit mass depth of the building Young’s modulus axial force acceleration of gravity height of the building moment of inertia stiffness of the building length of the truss member mass of the truss member or the mass of the building Strouhal number design wind speed width of the building fraction of critical damping of the building deflection of the truss member

t Director. $ Professor.

CCC 1062 - 8OO2/95/020 1 5 5 - 14 0 1995 by John Wiley & Sons, Ltd.

Received August 1994 Revised November I994

156 C. C. POUANGARE AND J . J . CONNOR

p density of the material used, or radius of gyration of a member gy yielding stress of the material

1. INTRODUCTION

The framed tube system, developed in the early 1960s by the late Fazlur Khan, made the design and construction of most tall buildings higher than 40 stories possible. Khan recognized that the ideal structural system would be a hollow tube located on the perimeter of the building. Since a building without windows is completely out of consideration for architectural, functional and aesthetic reasons, Khan proposed a frame with closely spaced columns and deep beams on all facades, that would behave as a pseudo-tube. This structural system was designated the ‘framed tube’. The need to compensate for shear lag, which is present in any framed tube building, had led to several modifications of the framed tube system, the most optimal being the bundled tube, a collection of smaller-size tubes joined together to form a large tube.

Although important, all the innovations mentioned were based on the beam-and-column mentality that governed the design of buildings for so many years. The new systems that have recently evolved are based on the very old concept that force is carried more economically by direct stress rather than by bending, as in trussed bridges. This observation actually goes back to Galileo’s work in the early 17th century (see Timoshenkol). The simple model shown in Figure 1 illustrates this point. The load is distributed between members AB and BC according to the following relations:

1

and

Noting that IIA is equal to p2 where p is the radius of gyration, for the cross section, I /AL2 is equivalent to p2/L2. This ratio is very small compared to 1 for typical structural members. It follows that BC is the dominant member. Let us take some reasonable properties for the members; A = 144 in2 (929 an2), I = 1728 in4 (71 924 cm4) and L = 15 ft (4.6 m). For these properties the axial force in member BC is 900 greater than the shear force in member AB.

In bridge engineering, this behavioral advantage was realized a long time ago and cable-supported and space-truss systems have been used since the late 18th century. In building design though, this was recently used to good advantage in the work of structural engineers, for example, W. LeMessurier’ and L. Robertson3. Both have designed and constructed tall

Figure 1 . Relative efficiency of an axial and a bending member

THE SPACE TRUSS CONCEPT 157

Figure 2. Internal and external diagonals

buildings based on the space-truss concept that have proven to be efficient and economical. The savings are considerable.

The space-truss system relies heavily on the use of diagonal members. These run not only in the facade planes (external diagonals) but also interspatially (internal diagonals), out of the planes of the facades (Figure 2). The result is a cantilever space truss with high vertical and lateral stiffness.

The extensive use of diagonals is one of the reasons that the space-truss system was not proposed earlier for building design, since architects considered the use of diagonals as aesthically, and sometimes functionally, unacceptable. Architectural trends have changed and now both external and internal diagonals are accepted. Some architects now seem to favor buildings where the structural form is clearly expressed and used as an integrated element of the whole functional and aesthetic design. Recent examples are I. M. Pei's Bank of China3 and N. Foster's Hong Kong and Shanghai Bank; both make extensive use of internal as well as external diagonals.

2. LOADING AND STRUCTURAL SYSTEMS

A structure has to resist two types of loading, vertical and lateral. Vertical loading includes the dead, live and snow loads along with the vertical component of the earthquake load. Lateral loading includes the wind load and the lateral component of the earthquake load.

It is common practice to separate the structural system that carries the vertical loading from the system that carried the lateral loading. The lateral load system of a framed tube is on the perimeter of the building; columns in the core of the building do not participate in the lateral load resisting system but do carry a major portion of the gravity load down to the foundation. A portion of the gravity load still goes to the perimeter columns. This arrangement is not efficient, since the gravity load should be used in the lateral load resisting system to balance the tensile forces in the columns due to the resulting overturning moment. When tensile forces exist at the foundation level, an expensive tie-down system is required. Furthermore, the existence of large columns in the center of the structure is equivalent to having a large quantity of material close to the neutral axis of a bending beam; this material does not contribute significantly to the bending resistance of the beam.

The need to improve the load carrying mechanism led to the transfer floor concept. The transfer floor (unlike the belt or outrigger trusses) gathers all gravity loads every 8 to 16 stories

158 C. C. POUANGARE AND J . J. CONNOR

Figure 3. Bundled tube with a transfer floor

and transfers them to the perimeter columns. Internal columns are discontinued at that level (Figure 3). This concept can be applied to any kind of tube: framed, bundled, braced etc. Transfer floors are used mainly as mechanical floors since they are usually crowded with structural members. The gravity loads prestress the exterior columns and avoid uplift under lateral loading. This design also supports the modularity concept, since the designer can repeat the same internal structure (usually called a ‘module’) every 8 to 16 stories. Only the perimeter columns change.

The spacing of transfer floors depends on many parameters. The actual need for mechanical floors, the design of the transfer floors themselves, the design of the modules above and the design of the perimeter columns must be considered. The use of transfer floors is suggested for high aspect ratio buildings where otherwise tension would occur in the perimeter columns under lateral loading. Specific values of aspect ratios where this would occur depend on the weight of the building and the lateral loading as well as the structural system.

The design of tall buildings is governed by stiffness rather than strength requirements. That is, the material requirements for reducing lateral displacements to acceptable levels are higher than the requirements for keeping the stresses below the corresponding acceptable levels (independent of using allowable stress design or ultimate strength design).

As far as lateral loading is concerned, for tall buildings wind loads are more severe than earthquake loads (Robertson et d3). A qualitative explanation can be generated by comparing the ‘smoothed’ power spectra for wind and earthquake (Figure 4). For wind, the intensity is low for small periods and increases as the period of the structure increases with a maximum well beyond the tall building range of 1-10s. On the other hand, the earthquake spectrum decreases for periods above 1.5-2.0 s and is minimal for periods exceeding 5 s. This suggests that for the first mode wind loading is the major contributor. For higher modes (especially the second) earthquake loading may have an important contribution to the motion of the building and design requirements for story shear.

Maximum acceleration at the top of the building and motion perception are also of critical concern for the designer. Although codes do not provide for guidelines or specific limits, there are generally accepted criteria relating frequency and acceleration to thresholds of perceptible and tolerable motion. For the range of tall buildings discussed in this paper, a cross-wind acceleration can be greater than along-wind acceleration. Approximate methods for calculating both along-wind and across-wind accelerations of tall buildings do exist (see S ~ l a r i , ~ Simiu and Scanlan’), but the industry traditionally relies on wind tunnel tests to prove that a building satisfies the acceleration related criteria.


Wind and Earthquake Spectra

0.1 1 10

T (sec) 100

~ Wind Spectrum - Earthquake Spectrum 1

Figure 4. Wind and earthquake spectra

Vickery et d6 showed that the along-wind acceleration of a building is inversely proportional to the square root of the mass, the stiffness and the fraction of critical damping of the building

a,, = C/(MKP)’/’ (3) where C is a constant, M is the mass, K is the stiffness and P is the fraction of critical damping of the structure.

The across-wind acceleration of the building is inversely proportional to only the fraction of critical damping of the building

aac x C/fi’” (4) The criterion most commonly used is to limit the maximum acceleration due to wind with

return period 10 years to 0.029 (where g is the acceleration due to gravity).

3. MATERIALS

Analytical studies of members under simple modes of loading can give expressions relating the strength or the stiffness of the member and the material (see Ashby and Jones’). For example, if we have a truss member of an arbitrary section A, the deflection 6 under the axial load F is

Fd a = - E A

where t is the length of the member and E the Young’s modulus of the material. The total mass M of the material used is

M = p d A (6) where p is the density of the material. Combining equations (3) and (4), we can express the mass M as


So, for a given length G and a desired stiffness F/6, the optimum material is that with maximum

The stress 0 of the member is property ratio E / p .

l? 1

( J -

A

Combining equations (4) and (6), the mass is given by P M = F C - CY

(9)

So for a given length 8 and a desired strength F the optimum material will be that with maximum property ratio cy/p.

In a real design problem, the cost of the material can never be left out of the selection process. The total cost of the simple truss member discussed here is C, x M where C, is the cost of the material per unit mass. So, for a stiffness-based design the quantity E / p C , is the one that should be maximized. Correspondingly, for a strength-based design the quantity uy/pCm should be maximized.

Table I summarizes the quantity that should be maximized to have optimum behavior under the simple modes of loading that are important for building design. Table I1 gives a list of engineering materials and their characteristic property ratios. CFRP stands for carbon fiber reinforced polymer and GFRP stands for glass fiber reinforced polymer. A1 7075-T76, A1 2024-T3 and A1 6061-T6 are aluminum alloys of different composition and different treatment. Table I11 lists the same materials when the cost of the material in place is also considered.

For concrete, the numbers shown in Tables I1 and I11 refer only to compression members (without buckling) since concrete behaves differently in tension and compression. There are also other issues a designer has to take into consideration to design a structure and select the optimum material. Aluminum alloys are vulnerable to high temperature and susceptible to stress corrosion. Both GFRP and CFRP are unidirectional materials (for the strengths mentioned). Using concrete for diagonal members is far more expensive than the prices taken into consideration for the development of these tables, so the property ratios, including cost, will change. The weldability of the 100 ksi steel available in the U.S.A. is still a major problem.

Examination of Table I11 can lead to some interesting conclusions as to the efficiency of construction materials. For example, even the cheapest concrete is four times better than steel for stiffness based design. An additional major advantage of concrete is that its modulus of elasticity increases approximately in proportion to the square root of its strength, while the modulus of elasticity of steel remains approximately the same no matter what the strength is.

Table I. Material properties that control optimality

Quantity to maximize

Member and loading Design for strength Design for stiffness

Compression members (governed by buckling) -

p : density; E = Young's modulus; uy = yield stress; C, = material cost.


Table 11. Material properties (cost factor not included)

Material E/P E’I2/p .YIP 4 ’ 3 1 P CFRP 126 92 700 69 GFRP 24 3-5 620 58 100 ksi steel 36.5 1.8 88 10 50 ksi steel 26.5 1-8 44 6.3 36 ksi steel 26.5 1.8 32 5.1

55 5.1 20 ksi concrete 18.4 - 14 ksi concrete 16.0 39 -

14 A1 7075-T76 26.0 3.0 167 21.6 Al 2024-T3 26.2 3.1 124 17-8 Al 6061-T6 24.6 3-0 100 15.3

-

- - 5 ksi concrete 108

Table 111. Material properties (cost factor included)

Material E/(~c , ) x 104 ~l/*/(pc,,,) x 104 uy/(pc,) x 103 u ; ’ ~ / ( ~ c , ) x lo4

CFRP GFRP 100 ksi steel 50 ksi steel 36 ksi steel 20 ksi concrete 14 ksi concrete 5 ksi concrete

A1 7075-T76 Al 2024T3 A1 6061-T6

6 3 68

120 120 160 840 840 660 74 74 74

4.6

8.2 8.2

10

11

- 8.6 8.6 8.6

3.5 180 40 20 14

250 200 85 48 35 28

3.45 165 45 28 32

- 62 51 44

Again, for stiffness based design, low strength steel is better than high strength steel. Aluminum alloys or even more exotic materials like CFRP and GFRP are definitely out of the question. Polymer composites have very high material property ratios but their high price rules them out of consideration for use in the construction of buildings. In structures like airplanes, where savings in weight can generate profit and not just material savings, the use of these materials is more feasible.

Concrete is also superior for strength based design. Low strength concrete, though better than steel, is definitely inferior to high and super-high strength concrete. It is obvious from Table I11 that if a reasonable price can be kept for concrete then super-high strength concrete not only makes sense but is the most promising material for structural/building applications. The GFRP is also very efficient in strength based design, and its use in problems where deflection does not govern is recommended.

Although the actual weight of the building is generally of minor importance (this is not the case when we have foundation on difficult soil) the weight of the material used can provide a good estimate for the cost of the structure and the economy offered by the material used. The mass of the building also has a significant role in the dynamic response of the building under turbulent wind loading. The bigger the mass the smaller the top story along-wind


acceleration (see equation (3)). Also, for the same stiffness a higher mass makes the period longer and the acceleration less perceptible.

The final material selection for a specific design involves durability and availability issues as well as strength and stiffness. For example, if the environment is highly corrosive then fiber reinforced polymers may be the only choice. For tall buildings, concrete and streel are the most efficient and economical materials.

4. PROPOSED SYSTEM

Previous work on framed tube structures (see Connor and Pouangare8) led to a deep understanding of the behavior of this system and revealed its limitations. It was clear then that a new system should be developed for an efficient 100-story structure. The new system would be a necessity for higher buildings of the order of 150 or even 200 stories.

The purpose of this paper is not to present every structural system and its modifications that apply to 100-story building construction. We present here the evolution of the new system from previous ones.

The most efficient way to transfer loads is by axial forces and not by bending. Hence the framed tube concept, which relies on the bending of beams and columns. was abandoned. A step back was taken and the motivation that led to the development of the framed tube system was investigated. We concluded that the tube concept could also be abandoned.

The creation of the braced tube system, which was applied successfully to the John Hancock building in Chicago, was a revolutionary modification. Although presented as a braced tube-type system, it is actually of space truss type. The fact that for this specific structure the lateral load resisting system lies only on the perimeter qualifies the system to be termed of braced tube type, but this is not the primary behavior of the structural system. The fact that the system was named in the literature ‘braced tube’ had some negative effects on the development of structural systems for tall buildings. First, the efficiency of the space truss system was not addressed at all, so no development or research effort was made in that direction. Presenting the system as an efficient tube locked the engineers into the ‘ideal tube’ behavior mind set. Hence, after its use in 1968 for the John Hancock building in Chicago, the space truss system was left unexplored only some direct copies of it were proposed and built for several lower buildings in the U.S.A. Only in the early 1980s did designers, especially the structural engineer W. LeMessurier, start developing the space truss system and proposing i t for various structures (see Rastorfer’). Later, engineer L. Robertson proposed and built the China Bank tower in Hong Kong, for which he used the space truss concept very effectively (see Robertson ct d3).

Another early form of the space truss system is the famous Citicorp Center, New York (see Figure 5). This building is famous for its tuned mass damper at the top to eliminate excessive vibrations under extreme wind loading. Chronologically, Citicorp was the first building to use crossbracing in a way that gathers several floors together into a single module (see Rastorfer2). The diagonals shown lie in the facade planes.

The efficiency of the space truss system was demonstrated by the structural system proposed for the Bank of Southwest, Houston (see Figure 6). The diagonals shown are not on the facade but in internal planes parallel to each facade plane. Although the building was not built, the solution that was given would have saved more than US $20 million from the structural system cost alone. Another building, also designed by W. LeMessurier, is the theoretical study for a half-mile tall building (21 0 stories) using a space truss system with internal and external diagonals running parallel to each other. The module used is shown in Figure 2.

It is true that internal space diagonals limit the efficiency of its use (especially in ofice


Figure S. Structural system for the Citicorp Center (Engineer W. LeMessurier)

Figure 6. Structural system for the Bank of Southwest (Engineer W. LeMessurier)

buildings) but creative solutions to this problem do exist (like the one N. Foster gave to the Hong Kong and Shanghai Bank building). Internal diagonals are usually made of steel, so fireproofing protection and treatment has to be applied similar to that used in conventional steel buildings.

The principles for the development of space truss systems are as follows.

The desired structural system should carry both vertical and lateral load with members working mainly in tension or compression. The gravity load should be redirected to the perimeter columns (vertical members) so as to balance any tension in the columns due to the lateral load. All members used for the resistance of the gravity load should contribute to the resistance of the lateral load also. No material should be wasted in being used only for one of the two resisting systems. The equivalent moment of inertia of the horizontal section of the building should be maximized, if possible, in both directions (for the same amount of material).

Using the above principles, various modules based on the space truss idea can be generally designed. Studies at MIT led to the development of three different modules. At this stage of the research, one of the three modules developed was chosen for further investigation, and a 11Zstory building was designed (see Figure 7) to prove the efficiency of the system.

All modules have four jumbo corner columns where all the gravity load is directed (see Figure 8). The diagonals will support secondary columns that carry the gravity load which they will redirect (in a smooth way) to the corner columns. Based on the material selection approach presented in the previous section, it is recommended that the corner columns be made of super-high strength concrete ( f b 2 12 OOO psi). The four corner columns proposed maximize the moment of inertia of the building so as better to resist the overturning moment from lateral


Figure 7. The 112-story building Figure 8. Plan of a module

loading. All the material used contributes fully to the moment of inertia in either direction, which (for a square building of side d ) is given by

I , , = A d 2 (10)

where A is the area of one column (only major axes are considered). For the first module, which is the one chosen for further investigation, there are both external

and internal X-diagonals as shown in Figure 9. Gravity loading will be gathered by secondary columns that will sit on both internal and external diagonals. The load flows from there to the jumbo corner columns and through them to the foundation. Every module (see Figure 10) is repeated as many times as necessary to create the desired structural system. The dimensions of the jumbo columns increase from module to module towards the base of the building. The dimensions of the diagonals may or may not change in each module. The gravity load coming to the diagonals is the same for each module but the forces generated by the lateral loading

Figure 9. The first X-diagonal module (MIT concept) Figure 10. A 16-story module


Figure 11. How X-diagonals work

are greater near the base of the building. This would require larger diagonals near the base if we have a strength based design. A stiffness based design, which is the best way to design a tall or super-tall building, may require the same diagonals over the entire height of the building (see Pouangare and Connorg).

One should notice the advantage of having the X-diagonals meet the jumbo corner columns in pairs. As shown in Figure 11, an X-diagonal is composed of an ‘arch’ section (upper part) and a ‘suspension’ section (lower part). Diagonals meet the columns always in pairs. One of the diagonals belongs to an arch section and the other to a suspension section. The result is that there is no net horizontal force applied to the column provided that the gravity load flowing through each of the diagonals is the same. The resultant force will always be vertical. Even in the case where the two diagonals carry loads, the horizontal resultant will only be the difference of the horizontal components of the two forces, which will themselves be small.

Overstressing of the diagonals due to lateral loading as well as overstressing due to column shortening can be compensated by inducing an initial tensile prestress (lack of fit) in the diagonal members.

For a building with a plan like that of Figure 8, the internal diagonals disturb the interior design of the usable space for only half the stories. So in each module half the stones have undisturbed users’ space and the rest have diagonals merging from the floor to the ceiling at four locations. Users that would consider the existence of the diagonals unacceptable have half the floors in each module to choose from.

A system composed of modules of this kind has very high strength and stiffness, making the system very efficient and very well suited for tall and super-tall buildings. Provided that the lateral deflection criteria are satisfied, the serviceability criteria related to the accelerations of the structure are expected to be satisfied as well. The higher stiffness is expected to increase the earthquake loads but, as shown in the generic design later on, this will not affect the design.

The plan of the structure can be designed so that every secondary column transfers its load to a diagonal. The external diagonals take only a small portion of the gravity load so that their strength is reserved to resist lateral loading. Some or all the advantages mentioned above can also be found in the other two modules that were developed and are presented below.

The second module utilizes K-diagonals (external and internal) as shown in Figure 12. The third module utilizes again K-diagonals but the internal diagonals are rotated 45” about the vertical axis and sit on the external diagonals (see Figure 13). The load flows from secondary columns to internal diagonals, from there to the external diagonals and to the jumbo corner columns. The third system stresses the external diagonals more than the second one.

All these modules can be connected in different ways to create the structural system. Modules

166 C. C. POUANGARE AND J. J. CONNOR

Figure 12. The K-diagonal module Figure 13. Modified K-diagonal module

of the same kind but to different scales or even modules of different kinds in the same structural system can be used according to the needs of the design considered.

5. A GENERIC DESIGN

The generic design of a 112-story building is presented to show the efficiency of the space truss system. It was not done for a specific building and was designed without taking into consideration any architectural, functional or interior design criteria.

The system is composed of seven 16-story modules of the first type with X-diagonals (see Figures 8 and 9). Because of the lack of a systematic design methodology, our experience combined with a trial-and-error procedure was used for the design. Actually it was the distinct lack of a robust method that made us develop our new design method (see Pouangare and Connor').

The building has a height of 1469 ft (448 m) and a square plan 236 ft x 236 ft (72 m x 72 m). The floor units are 59ft x 59ft (18m x 18m) as shown in Figure 14 illustrating the

- I

4 9 f t ' -

I I I I


Table IV. MIT design compared to other structures

Aspect Period Steel Concrete cost Building # Stories ratio 6) (lb sf-’) (Ibsf-’) (US $ sf-’)

- World Trade Center 110 6.9 11.0 37 26.9 Sears Tower 109 6.4 7.6 33 240 MIT design 112 6-5 5.1 18 43 17.5

-

floor framing system. The design was carried out for Zone 4 earthquake loading and a wind speed of 89 m.p.h. (50-year return period). The ANSI A58.1-1982 code was used throughout the design.

The corner columns vary from 27 ft x 27 ft (8.23 m x 8.23 m) square at the base to 5 ft x 5 ft (132 m x 152 m) square using 14 ksi (96 MPa) concrete. The external diagonals vary from 1 6 x 6 0 (40 cm x 152 cm) at the bottom to 16” x 3 0 (40 cm x 76 cm) at the top all made of 2” ( 5 cm) thick, 50 ksi (345 MPa) steel, plates. The internal diagonals are 4 0 x 40” (102 cm x 102 cm) made of 2“ (5 cm) thick, 50 ksi (345 MPa) plates for all 7 modules.

The structure was subjected to equivalent static wind and earthquake loading in addition to gravity loading. The deflection was in the range of H/1200, which is well below the acceptable limits of H / 5 0 0 .

The dynamic response of the structure subjected to the wind loading was estimated using a simplified procedure (see Solari4) and the top story acceleration due to the 10-year wind is limited to only 0.00259. Nonlinear dynamic analysis of the structure subjected to the El Centro earthquake was also performed (maximum acceleration 0.34s). The structure displayed superior performance since no element yielded under this severe dynamic loading and the maximum displacement stayed well below the acceptable limits. Because of this, there is no need for special detailing and standard ductile connections can be used.

These investigations showed that the initial design is too stiff. Further refinement reduced the size of the corner columns without any problems. The design of the same building using the design procedure developed at MIT is presented by the present authors in Reference 9.

The efficiency of the system is made clear by Table IV, which shows a comparison of the structure under discussion, the World Trade Center, NY, and Sears Tower, Chicago. It should be also noted that both the World Trade Center and Sears Tower were designed for less severe wind and earthquake loadings. The cost calculations are based on material prices in place for only the structural parts considered in this paper. The structure used in this comparison is the original design, which proved to be very stiff. Further refinement of the design leads to even more savings.

6. SUMMARY AND CONCLUSIONS

A new concept for the structural system design of tall buildings based on space truss behavior has been presented. The concept is limited only by the imagination of the designer. The generic design of a 113-story building, when compared to existing structures, shows excellent results both structurally and economically. The system is not only more efficient than other alternatives but is also cheaper.

A rational approach to material selection has also been presented and applied to the building designed. The classical materials used for building construction (concrete and steel) once again


proved to be the wisest choices for the designer. In addition, the superiority of concrete compared to steel was proved (in axial loading only). The research has also shown the benefits of developing concrete of even higher strength, provided that the price does not grow out of proportion.

From all the work presented, we can conclude that a new generation of structural systems is emerging that could very well raise the limit of tall building design, should this prove to be economically and socially desirable. The technology is now developed and the existing materials are adequate to support it. New materials and techniques will certainly improve the state of the art but are not considered absolutely necessary.

REFERENCES

1. J. P. Timoshenko, History of Strength of Materials, McGraw-Hill, 1953. 2. D. Rastorfer, ‘William J. LeMessurier super tall structures: architecture and engineering’, Architectural

3. L. Robertson, R. Zottola and P. Asp, ‘Structural system for the New Bank of China building’, Proc.

4. G. Solari, ‘Along-wind response estimation: closed form solution’, J. Struct. Division, ASCE, 108,

5. E. Simiu and R. H. Scanlan, Wind Effects on Structures, Wiley, 1986. 6. €3. J. Vickery, N. Isyumov and A. G. Davenport, ‘The role of damping, mass and stiffness in the

7. M. F. Ashby and D. R. Jones, Engineering Materials, Pergamon, 1980. 8. J. J. Connor and C. C. Pouangare, ‘A simple model for the design and analysis of framed tube

9. C. C. Pouangare and J. J. Connor, ‘A new method for the design of tall buildings’, Struct. Design Tall

10. A. G. Davenport, ‘Tall buildings-an anatomy of wind risk’, Construction, South Africa, December

Record, McGraw-Hill, February 1985.

4th Int. Con$ on Tall Buildings, Japan, 1988.

January 1982.

reduction of wind effects on structures’, J. Wind Engng & Indust. Aerodynam., 11, 1983.

structures’, J . Struct. Diuision, ASCE, 117(12), 3623-3644 (1991).

Buildings, 4, 169-184 (1995).

1975,

Truss System Tall Buildings 1995

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