Innovative Structural Concept & Solution for Mega Tall Buildings Applied to One Kilometer Skyscraper

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1. Introduction

After the Great Chicago Fire in 1871 that left a big part of downtown Chicago empty, higher buildings started to emerge. A tall building is not defined by its height or number of stories. The important criterion is whether or not the design is influenced by some aspect ‘‘tallness’’. It is a building in which tallness strongly influences planning, design, construction and use. It is a building whose height creates conditions different from those that exist in common buildings of a certain region and period [1] . There are physical, code prescribed and practical reasons why tall buildings tend to be safer than low-rise buildings [2] . Undoubtedly, the factor that governs the design of a tall and slender structure most of the times is not the fully stressed state, but the drift/acceleration of the building for wind loading. It is easy to understand that the higher the building is, the more important its lateral behavior becomes. Thus, to understand the performance of high-rise buildings, the lateral resisting system of tall buildings becomes a key factor that needs to be investigated and understood.

In 1969, Fazlur Rahman Khan classified structural systems for tall buildings relating to their height with considerations for efficiency in the form of “Height for Structural Systems” diagram for both steel and concrete in Figure 1 (Ali, 2001, Ali & Armstrong, 1995; Schueller). This marked the beginning of a new era of skyscraper revolution in terms of multiple structural systems. Feasible structural systems, according to him, are rigid frames, frame shear trusses, belt trusses, framed tubes, truss-tube with interior columns, bundle tubes and truss-tube without interior columns [3] . These structural systems can reach up to about 140 stories.

The objective of this paper is to apply a new “Parallel Shear Walls Concept” to 1000.8 meter tall structural model that consists of five vertical portions (Figure 2 & Figure 3), which cover 278 stories taller than the existing tallest building in the world. Building details are shown in Table 1. To gain an adequate footprint for stability, this tower extends to nearly 102 m × 102 m at base, resulting in the 9.8:1 aspect ratio (The ratio of the height of the building to its smaller width at the base), exceeds the one held by existing tallest building in the world, Burl Khalifa which is close to 9:1 [4] .

In this “Parallel Shear Walls Concept”, as grids contain a number of shear walls, these shear walls near the perimeter undergo maximum stresses due to wind force and the stresses linearly decrease towards the core and it is minimum at the center of the building, i.e. all the shear walls in a grid taking part to resist the wind force. All the grids in each side of the building are resisting the wind forces. So the axial deformation of all the walls in a raw is nearly same. Therefore no “shear lag effect’’ will occur. On the other hand, the walls are connected by rigid beams to form vertical cantilever, when the walls deflect under the action of the lateral forces, the connecting beam’s ends are forced to rotate and displace vertically, so those beams bend in double curvature and thus resist the free bending of the walls [ [5] , p. 214]. But for the exterior or interior tube systems (tubular frames), the wind loads are resisted and concentrated on peripheral columns or to the inner core respectively. When the corner columns of the

Figure 1. Classification of tall building structural systems by Fazlur Khan (above: steel; below: concrete) [3] .

Figure 2. Levels and number of stories.

Figure 3. Floor dimensions and Tier heights.

Table 1. Building’s Data.

Figure 4. Axial stress distribution in columns of laterally loaded framed tube [3] .

periphery suffer a compressive deformation, it will tend to compress the adjacent column, since the two are connected by the spandrel beams. The compre- ssive deformations will not be identical (Figure 4) since the flexible connecting spandrel beam will bend, and the axial deformation of the adjacent column will be less, by an amount depending on the stiffness of the connecting beam. Each successive interior column will suffer a smaller deformation and hence a lower stress than the outer one [5] . This phenomenon is called the shear lag effect. Shear lag may lead to wrapping of floor slabs, local bulking on compression side & cracking on tension side.

This is a theoretical study so the author’s intension is to use the top of the structure as a habitable floor maximizing the total floor area to increase high value lease spaces. Usually the gross floor area can be reduced by making three voids from top to bottom on each side of the building perimeter. These voids will reduce up to 30% from Tier-1, 28% from Tier-2 & 8% from Tier-3. Besides, the central core area is so far from any natural light at the perimeter, can be a central void further to reduce the floor area. Because making voids will give negligible effect on the structural behavior. But the beams and columns will remain in the same position to transfer wind forces through the grids.

2. Primary Structural Arrangement

The tower is characterized by its symmetry. There are no transfers of vertical elements through the main body of the tower. It allows a uniform distribution of gra- vity forces through the structure. These characteristics allow for a more efficient structure.

Figure 5. Floor layout in relation to structure (Shear walls marked red color & columns marked ash color are shown on the typical floor of Tier-1).

There is no separation between the gravity system and the lateral system. The vertical structure is organized in such a way that the elements are all sized on sufficient lateral stiffness while at the same time providing strength consideration. This creates an extremely efficient structure where the materials perform double-duty (gravity and lateral support). This structure creates a uniform distribution of load reducing the differential shortening.

The building has 5 Tiers of different heights (Figure 2 & Figure 3).

The structural system consists of several parallel shear walls in each direction of the faces of building (Figures 5-10) which are essentially analogous with the buildings’ central core columns, coupling beams and conventionally reinforced concrete floor framing. This produces a completely interconnected structural system (Figure 5). The shear wall arrangements of this tower are in such a way that they provide large amount of inertia forces and stiffness to the structure. So the amount of moments carried by the beams due to wind is less. Therefore the author has selected the depth of 0.8 m and width 1.1 m of all the beams for theoretical purposes. However, maximum sizes of few beams will be 1.3 m (depth) × 1.4 m (width) near the Tier-1 during practical application as the author checked the maximum moments.

Each side of the building will resist the wind force by several parallel shear walls. The wind forces will be distributed to the structure almost uniformly to all grids due to the shear wall placements (Figure 6). Each Tier has its own core which starts from base. Several experiments show that Tiers with different heights (height of Tier-1 will be longest and gradually decrease the Tier heights towards top) give better results than the Tiers of uniform height.

In this structural system the corner portions of the Tier-1, Tier-2 & Tier-3 are kept free from shear walls for views & lightings which makes the highest value lease spaces (Figures 7-9). Figures 7-12 (Typical Floors of different Tiers) show the structural arrangement of typical floors of five different Tiers of the building & the members marked maroon are the shear walls lay-out and members marked sky blue are the columns lay-out and beams. Beams are not shown in Figures 7-10. Figure 12 is the typical floor of Tier-1. Connections of shear walls, columns and beams of a typical floor are shown in Figure 12. Same structural connections will be followed for Tier-2, Tier-3, Tier-4 & Tier-5 as shown in Figure 12

Figure 6. Wind forces are distributed in all grids (Members marked red & ash in Figure 5 & Figure 6 are shear walls and columns lay-out respectively).

Figure 7. Typical shear walls & columns arrangement of Tier-1.

Figure 8. Typical shear walls & columns arrangement of Tier-2.

Figure 9. Typical shear walls & columns arrangement of Tier-3.

Figure 10. Typical shear walls & columns arrangement of Tier-4.

Figure 11. Frame structure of Tier-5 (Typical Floor).

Figure 12. Interaction between shear walls, columns & beams.

The Tier-5 is a frame structure started from base and is composed of reinforced concrete beams, columns and slabs (Figure 11).

Various options have been studied through this parametric modeling method. The main goals were to maximize the lever arm of the shear walls, maintain the shear wall line in one single vertical plan, so as to minimize secondary forces. This shear wall arrangement can be said as an optimal balance and the most effective lateral load-resisting structure to stabilize this mega tall structure.

Cracked sections have been considered in the analysis and therefore moment of inertia has been taken half of the amount of no crack section.

Base area of Tier-1 is maximum while base areas of other Tiers gradually decreasing towards the top. The author has chosen and tuned the height increments towards bottom and gradually decreasing towards top because the moments and the shears are high at the bottom. Tower design of any height with this “Parallel Shear Wall Concept”, the structural engineers will have to tune and choose the different heights of the Tiers accordingly.

3. Results Analysis

Drift Limits in common usage for building design are in the order of 1/600 to 1/400 of the building height (ASCE). Generally, for tall buildings allowable drift is considered as H/500, which becomes 2001.6 mm for this “One Kilometer Structure”.

The dynamic analysis (Time History Analysis) for wind has been carried out by STAAD/PRO. Table 2 shows the results for dynamic & static analysis at the top.

SRSS value for six Modes (Square Root of the Sum of Squares) of dynamic wind analysis is 1995 mm.

Dynamic analysis of this 1 Km tower shows that the habitable/usable floor is at height 723 m (Record breaking habitable height at 201 story) where accelera-

Table 2. Drift at the top of the Structure.

Table 3. Configurations of some TDMs currently in use.

tion is 30 milli-g which is acceptable according to NBCC 1990 [10] .

Whereas the habitable floor level for the existing tallest building of the world at the height of 584.5 m (154th Story).

Damping is an important issue as the human comfort due to excessive acceleration beyond 25 milli-g, in the range of 35 to 50 milli-g, may have to be designed for. Tuned mass dampers and viscoelastic dampers are often used [11] .

Acceleration due to dynamic analysis at top is 47.7 milli-g. It is seen that Tuned Mass Dampers (TMDs) transmit inertial force to the building’s frame to reduce its motion around up to 50%. Therefore 47.7 milli-g acceleration of this 1 Km tower can be reduced by introducing Tuned Mass Damper accordingly to make this height habitable floor level.

In Table 3, there are some examples of tall buildings which reduced their accelerations by introducing TDMs.

Vanity/Spire height: In theory, we’re in the midst of a “golden age’’ of skyscraper construction. But why, of the ten tallest building on Earth, nearly 30 percent of each structure totally unusable spire? In truth, this information is readily available to anyone with eyeballs. All supertalls (e.g., any building over 1000 feet tall) have substantial spires and unoccupied upper floors, which serve to house hardware, observation decks, and often, mass damper that counter the sway

Table 4. Vanity Height of the Towers [12] .

of the building in the wind. But even taking into account the necessary infrastructure, the majority of spires are totally unnecessary.

In fact, without the vanity height, 60 percent of the world’s supertalls wouldn’t actually be supertalls at all. The Burj Khalifa would lose more than 700 feet. If an angry giant broke off the Burj’s spire and planted it on the ground, it’d still be the 11th tallest building in Europe. The worst offender of all is the Burj Al Arab, of which 39 percent is vanity spire [13] .

In Table 4, there are some examples of vanity height of tall buildings.

If the author adds the vanity height (194 m) of Burj Khalifa then author’s 1000.8 meters tower would be 1194.8 m.

4. Author’s 831 Meters High Tower by Applying Same Structural Arrangements (Comparison with the World’s Existing Tallest Building)

Author’s 1 Km tower has been reduced to 831.6 m tall (nearly same height of the World’s existing Tallest Building). The 831.6 m tower height is achieved by removing 169.2 m from the top of the 1000.8 m tower.

Results of the analysis show that drift and acceleration at 831.6 m (top) are 1041 mm and 26.9 milli-g (acceptable) respectively. So the habitable/usable floor is at height 831.6 m (231 stories). Whereas the world tallest building (Burj Khalifa) will have a drift of 2000 mm [14] at top (828 m) and habitable floor at height 584.5 m (154 stories).

5. Covered Vertical Area at Base and Structural Materials

Area covered by shear walls at ground floor = 1440.24 m^{2} Area covered by columns at ground floor = 72 m^{2}

Gross area at ground floor = 102 m × 102 m = 10,404 m^{2} Area covered by vertical elements (shear walls and columns) at ground floor in percentage

.

Note: Percentage of gross floor area with respect to vertical elements (shear walls and columns) is one of the main efficiencies of structural arrangements.

This one kilometer high tower requires Young’s Modulus of 42,038 MPa and compressive strength of 80 MPa for columns, shear walls and Young’s Modulus of 29,725 MPa and compressive strength of 40 MPa for beams and slabs.

6. Impact on Sway for Different Tier Heights

During the research work, the structure is analyzed in two different shapes (Type-1 & Type-2). The total height, thickness & sizes of the structural members are kept the same. Only the Tier heights have been changed.

a) Type-1 (Equal Tier height): This building consisted of five Tiers. Height of first 4 Tiers from bottom is 226.8 m each & height of top Tier is 93.6 m. The result of the analysis show that sway at top is 220.18 mm.

b) Type-2 (Different Tier heights) There are 4 different Tier heights keeping the top Tier height same as Type-1. Tier-1 (280.8 m), Tier-2 (244.8 m), Tier-3 (208.8 m) & Tier-4 (172.8 m). The result of the analysis shows that the sway at top is 1930 mm. So it is observed that the height of Tiers greatly influence the drift (sway) of the structure.

7. Three Different Models of Height 734.4 Meters Analyzed by Developing Author’s Structural Concept

A 734.4 meters high tower is modeled in three different shapes. Model-1 holds 3 Tiers with Aspect Ratio 7.2:1 (Figure 13), Model-2 holds three Tiers with Aspect Ratio 9.415:1 (Figure 14), & Model-3 holds four Tiers with Aspect Ratio 9.415:1 (Figure 15). The shapes & analysis results of these models are shown in Table 5.

8. Philosophy behind This One Kilometer Tower’s Structural Arrangements

Consider a beam cantilevered from the earth. When lateral forces are applied to the beam, the beam will bend. The maximum compression and tension stresses will be on the two opposite sides along the force direction. Tension and compression will decrease linearly towards middle & will be zero at the mid. Now consider a mega tall building of height 1000.8 meters and base 102 m × 102 m with the shear walls being placed perpendicular to the face of building (can be called “Shear Walls toward periphery”) around the periphery and continuing towards center of the building for a certain distance (Figures 7-9) along the direction of force. Let the summation of moment of inertia be “Im” with respect to the line passing through the center & the maximum stress will be at compression face say “e1”.

On the other hand if the same number of shear walls is placed around the center to make an inner core to resist the lateral force, the summation of moment of inertia will be less than “Im” & the maximum stress at compression face will be greater than “e1”. As the deflection is inversely proportional to the inertia forces, the deflection will be more for inner core system.

So when the structure is becoming taller, it is wiser to consider the outer core arrangement concept (Shear walls toward periphery) for resisting lateral forces.

This concept with some additional structure arrangements is applied to the

Figure 13. Model-1.

Figure 14. Model-2.

Figure 15. Model-3.

Table 5. Three different models.

“One Kilometer Tower” research work. Figure 16 shows four different mode shapes due to wind forces.

To understand this phenomenon, consider the building as a cantilever beam.

Figure 16. Four different mode shapes due to dynamic responses (Horizontal displacements are shown to large scale).

The horizontal cross sectional area at any height of the shear walls are considered the beam’s sectional area which absorbs the bending and axial stresses and at the same time resists the deflection of the structure.

Figure 12 shows that when wind hits the structure at any face, the shear walls (Maroon color) which are parallel to the wind direction, connected by moment resisting members (beams), will mostly resist the lateral load by the composite action of the individual wall piers and the frame action resulting from the moment connection between them. Also the frame action between shear walls (perpendicular to wind direction) and the connecting beams will also resist part of the lateral loads (Figure 12).

9. Basic Concept for Tower of Different Heights

The proper arrangement of the shear walls is the main task of this concept. The shear walls arrangement as shown in the figures is sufficient to withstand One Kilometer High Tower with aspect ratio around 9.8:1. For the tower of lower heights, the structural engineer can minimizes length & thickness of the shear walls in every grid, and can maximizes the spacing of the shear walls in a grid as well as the grid spacing (Figures 7-10). But the shear walls in a grid should be connected with the beams to get composite action of the shear walls. The grids and the shear walls in a grid can be moved, if required for the architectural issue. But it should be kept in mind that the centroid of all the shear wall’s cross sections should be as near as possible to the mid of building’s face to minimize the twisting effects of the building due to lateral loads.

10. Advantages of This New Structural Concept

1) The main concept of this system is to place the shear walls parallel to each other. When wind force is applied to the structure, each grid (consisting of several shear walls) will function individually to resist the wind force of their average span length (Figure 6 & Figure 17). Due to this phenomenon, when this structural system is subjected to lateral loads such as wind load, the axial

Figure 17. Typical shear walls spacing (Red lines & circles indicate shear walls & columns respectively).

stresses in the shear walls is nearly linear. Therefore Shear Lag effect is minimized.

2) Shear walls can be moved on both sides from mid (if required for architectural demands) by keeping the area of centroid of the vertical sections at the same position. This will make negligible effect on sway.

3) The shear walls are placed almost uniformly over the base, so the gravity loads are distributed almost uniformly to all the vertical elements (shear walls). Therefore, reduce the differential settlement.

4) Plenty of natural sunlight will pass through the building perimeter due to parallel shear wall arrangements.

5) Simple structural system.

6) No additional lateral load resisting system is required, like outriggers, belts or cross bracings, except tuned mass dampers (TMD).

7) Parallel shear walls from both the direction forming a perpendicular arrangement. The effect of the perpendicular walls will be to stiffen the structure in torsion, to reduce the twist, and, in doing so, to influence the contributions to the parallel wall shear and moment that result from the structure’s twisting [ [5] , p. 189].

11. Conclusions

Engineering field professionals are trying to build buildings taller than the existing tallest ones. Generally these high-rise buildings require additional lateral systems to control the drift. But the use of the “Parallel Shear Walls” concept in Skyscraper design is a relatively new idea which does not take any help of additional lateral systems except TMD (If the building’s height is above 850 meters). This structural arrangement can be applied to any tall building of any height to get a perfect and optimized structure.

The research work carried out on three models of heights 1000.8 meters, 830 meters & 734 meters with this structural arrangement. It is observed that the structures of heights 830 meters & 734 meters have less value for drift and acceleration than the allowable limits as per international codes/standards. No bracings, outriggers or damper is required for such mega tall structures. Only damping system is required for 1000.8 meter high structure. That is, this “Innovative Structural Arrangement” is a simple method to go for tall and mega tall structures.

The details and further analysis of the structural models are kept (ETABS & STAAD/PRO softwares) for reference can be discussed as needed.

Note: A book is published on 2012-12-26 (ISBN-13: 978-3-639-66041-8, author: Feroz Alam) in details on this concept from “Scholars’ Press” (Omni Publisher). The title of the book is “Innovative Concept on Structural Engineering of Mega Tall Buildings”. Part-2 of this book describes the concept of concrete reduction (minimum 8%) from shear walls without affecting the structural integrity of tall buildings. This concept is suitably applicable for the buildings above 30 stories. The book is available in Amazon.com, MoreBooks and many other European websites.

Acknowledgements

The research work would not have achieved without the support, advice and endless effort from my senior colleague Professor Mr. M Ali, Ph.D., S.E., Fellow ASCE, Fellow CTBUH, Professor Emeritus of Structure, Adjunct Professor, Uni- versity of Illinois at Urbana-Champaign. I am immensely grateful for the invaluable guidance, support and encouragement from him. Over the years of my study, I have benefited greatly from his wisdom and experience. I sincerely appreciate all the help received from him during the research work. Comments by the reviewers significantly contributed to the quality of this paper. I appreciate to my family members, wife Sharmin Alam, son Faizan Tazwar Alam and my sister Khurshida Ahmed (Polly) for their encouragements on my research project. Finally I thank to Engr. Anwar Hossain Akon, Dr. Habibur Rahman (Author― The Emergence of Qatar) and my brother Dr. Parvez Alam-USA for providing encouragements, suggestions/comments on this research.

References

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