Developments in the Design of Earthquake Resisting Systems for Tall buildings

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Abstract

In many tall buildings shear walls/ braced frames provide major lateral load resistance for the wind and seismic effects. Their incorporation into the architectural plan is dictated by functional requirements. The geometry of the wall/ braced frame is usually decided based on architectural and functional requirements.

For wind loading, the governing design criteria are invariably top storey deflection. When the drift limitations are satisfied it is only necessary to satisfy the strength requirements for a prescribed load factor.

In the case of seismic loading in addition to satisfying the limit states of strength and deflection, the requirement of ductility becomes important. During earthquakes, shear walls or braced frames, in addition to providing lateral load resistance should allow energy dissipation through post-elastic deformations. It becomes necessary to design these for the required lateral load resistance and also satisfy the ductility demands during cyclic loading.

Shear walls/ Braced frames when designed and detailed properly gives a greater degree of protection against non-structural damage during a moderate earthquake while assuring survival during major events. This has been demonstrated time and again during past earthquakes. Keywords – Shear walls – Shear wall/ braced frames-seismic loading- structural system performance.

Introduction

Rigid frames connect the columns and girders via moment-resistant connections. The lateral stiffness of a rigid frame depends on the bending stiffness of the columns, girders and connections to the frame. A major advantage of the rigid frame is the open rectangular spaces which allow greater planning for windows and doors. Rigid frames typically span 7 m to 10 m bays. When used as the sole lateral load resisting system, rigid frames are economical. However, they are too flexible. Increasing the member sizes would call for uneconomical solutions. Rigid frames are ideal for reinforced concrete or steel, because of the inherent rigidity of the joints. Steel frames are costly and take more effort to stiffen the moment-resistant connections. The size of the columns and girders at any level are directly proportional to the external shear at that level. Therefore, they increase in size towards the base. Floor designs are not repetitive as in the case of braced frames. Ceiling height also increases towards the base because of the larger girders at the base. Therefore the story heights may vary.

Reinforced concrete planar solid or coupled shear walls have been one of the most popular systems used for high-rise construction to resist lateral forces caused by wind and earthquakes [1]. In the case of steel structure, braced frame can provide the required stiffness instead of the shear walls. They are treated as vertical cantilevers fixed at the base. When two or more braced frames or shear walls in the same plane are interconnected by beams or slabs, as is the case with shear walls with a door or window openings, the total stiffness of the system exceeds the sum of the individual stiffness put together. This is so because the connecting beam forces the walls/frames to act as a single unit by restraining their individual cantilever actions. These systems are known as coupled wall frame systems. These used in office buildings are generally located around service and elevator cores, and stairwells. In fact, in many tall buildings, the vertical solid core made up of braced frames that enclose the building services can be used to stabilize and stiffen the building against lateral loads [2]. Many possibilities exist with single or multiple cores in a tall building with regard to their location, shape, number, and arrangement. The cores walls are essentially braced frames that can be analyzed as planar elements in each principal direction or as three-dimensional elements using computer programs.

To limit story drift under lateral loads, the depths of frame members are controlled by stiffness rather than strength. The story drift is defined as the lateral displacement of one level relative to the level below. It is of concern in serviceability. Drift limits in common usage for wind designs are of the order of 1/500 of the story height. These limits minimize damage to cladding and partitions.

The inherent flexibility of moment frames results in greater drift-induced non-structural damage under seismic loading than in other systems. It should be noted that seismic drift ?M, including inelastic response of buildings, is typically limited to 1/50 of the story height, about 10 times larger than the allowable wind drift

Rigid frames may be combined with vertical steel trusses or reinforced concrete shear walls to create a shear wall (or shear truss)-frame interaction systems. Rigid frame systems are not efficient for buildings over 30 stories in height because the shear racking component of deflection caused by the bending of columns and girders causes the building to sway excessively. On the other hand, vertical steel shear trusses or concrete shear walls alone may provide resistance for buildings up to about 10 or 35 stories depending on the height-to-width ratio of the system. When shear trusses or shear walls are combined with Moment Resisting Frames (MRF), a shear truss (or shear wall)-frame interaction system results. The approximately linear shear-type deflected profile of the MRF, when combined with the parabolic cantilever sway mode of the shear truss or shear walls, results in a common shape of the structure when the two systems are forced to deflect in the same way by the rigid floor diaphragm. The upper part of the truss is restrained by the frame, whereas at the lower part, the shear wall or truss restrains the frame (Fig.1). This effect produces increased lateral rigidity of the building. This type of system has wide applications for buildings up to about 40 to 70 stories in height. A “milestone” paper by Khan and Sbarounis [3] presented the mechanics of a shear wall-frame interaction system that led to the development of innovative structural systems that are cost-effective [4].

During the last few decades, several buildings have been built utilizing belt truss and outrigger system for the lateral loads transfer throughout the world. This system is very effective when used in conjunction with the composite structures especially in tall buildings (Fig 2). Outrigger systems have been historically used by sailing ships to help resist the wind forces in their sails, making the tall and slender masts stable and strong. The core in a tall building is analogous to the mast of the ship, with outrigger acting as the spreaders and the exterior columns like the stays. As for the sailing ships, outriggers serve to reduce the overturning moment in the core that would otherwise act as a pure cantilever, and to transfer the reduced moment to the outer columns through the outriggers connecting the core to these columns (Fig2). The core may be centrally located with outriggers extending on both sides or in some cases it may be located on one side of the building with outriggers extending to the building columns on the other side [5].The outrigger systems may be formed in any combination of steel, concrete and composite construction. Because of the many functional benefits of outrigger systems and the advantages outlined above, this system has lately been very popular for super-tall buildings all over the world. A very early example of outrigger structure can be found in the Place Victoria Office Tower of 1965 in Montreal designed by Nervi and Moretti. It was also used by Fazlur Khan in the 42-story First Wisconsin Center of 1973 in Milwaukee, Wisconsin. However, major application of this structural system can be seen on contemporary skyscrapers such as the Jin Mao Building in Shanghai and the Taipei 101 Tower in Taipei.

Whether it is frame shear wall system or outrigger system or the buttressed core system used in Burj Khilifa in Dhubai [6], the behaviour of the core under lateral loads is vital for good seismic performance. Therefore let us examine the failure modes of the shear wall systems and its seismic behavior.

Potential Failure Modes

A single cantilever shear wall is shown in Fig. 3. It behaves similarly to a concrete beam. Lateral instability may arise due to plastification. However, the floor slab gives adequate lateral support. In such shear walls, which acts as a large cantilever, will be subjected to bending moment and shear force from lateral loads and axial compression induced by vertical gravity load. Accordingly, the flexural strength of the critical section can be evaluated and designed using axial load, moment interaction. The vertical reinforcement in the web portion is also used for resisting flexure. However, it is important to avoid premature failure due to shear or inadequate foundation design. It is also necessary to provide sufficient connection to all the floors to transmit horizontal forces.

The Northridge, Richter magnitude 6.7 earthquake of January 17, 1994, in California, which caused damage to over 200 steel moment-resisting frame buildings, and January 18, 1995, Richter magnitude 6.8 earthquake in Kobe, Japan, have shaken engineers’ confidence in the use of the moment frame for seismic design. In both of these earthquakes, steel moment frames did not perform as well as expected.

Flexural Strength of Tall Walls:

In shear walls with moderate heights, especially built in areas of medium seismicity like Chennai, vertical reinforcement is usually distributed over the whole section. Such arrangement does not efficiently utilize the reinforcement when developing ultimate moment. In this case, ultimate curvature and hence curvature ductility will be limited [7]. Fig. 4 shows the improvement in ductility if the reinforcement is placed near the edges. Such arrangement will be able to resist alternate flexural compression which is inevitable during seismic loading. Since the shear wall carries large gravity load also, it is necessary to provide confinement reinforcement to improve ductility to adequate levels. Closely spaced transverse ties are provided around the vertical flexural steel which may suffer softening during cyclic loading due to Bauschinger effect and open cracks. Ties spacing in such cases should be even less than that recommended by the codes [8].

The Shear Strength of Tall Shear Walls

The shear strength of shear walls, with height to depth ratio of more than 3, can be assessed the same way as that of beams. At the base of the wall, where yielding of flexural reinforcement in both faces of the section occur, the shear strength of contribution of concrete should be neglected where axial compression on gross-section is less than 12% of the concrete strength. This is because the low compression may be overcome by the vertical accelerations induced by earthquake leaving the whole wall under tension. Moreover, the cyclic shear produces sliding shear and pinching of the hysteresis loop.

Thus, the horizontal stripes in the walls should be designed to resist the whole shear force generated by the lateral load in the plastic hinge region. The plastic hinge may extend even a whole storey height. The plastic hinge length should be not less than overall depth D (see Fig. 3) of the shear wall section. It is very important to suppress the shear failure in the shear wall. This can be done only if all the over strength parameters of flexural steel- including the strength offered by secondary steel are assessed properly and web reinforcement provided such that it does not yield before flexural steel plastifies.

Construction Joints across Shear Walls

Earthquake damages in shear walls of high-rise buildings have often occurred at the construction joints [9].Shear force-slip relationship for a typical construction joint specimen subjected to cyclic shear shows that, after yielding slip in excess of 2.5 cm in each direction have been witnessed. This is unsuitable for earthquake resistant structures. In fact, every effort should be taken to suppress this failure. From tests results it is seen that up to a slip of 0.25 mm the contribution of dowel action is negligible [10]. Dowel strength becomes significant when movement is about 2.5 mm or more. Therefore the vertical reinforcement across the construction joint should be designed to supply the required clamping force. The basic strength of construction joint for shear can be assessed as

(1)

Where

Vuf = average ultimate shear stress to be transferred across the construction joint

Avf = vertical steel utilized for supplying the clamping force

Ag = gross area of shear wall section

N = axial force on the section taken positive when producing compression

fy = yield strength of reinforcement

lv = reinforcing steel content.

It is normal practice to provide a nominal minimum amount of vertical reinforcement equal to lv = 0.0015 to 0.0025. However, in the lower part of the shear wall, where large shear force may be carried, this steel content may have to be considerably increased in accordance with equation (1) suppressing sliding shear. It is important that the required vertical reinforcement be provided at close spacing because the clamping force supplied by each bar is effective to close to its axis only. Reinforcement provided for flexure and situated near the extreme vertical edges of shear wall, should not be included in the evaluation of clamping force required across the core of the shear wall section.

Squat Shear Walls

The behavior of walls with height to depth ratio less than 2 is more like deep beams. However, they have to be evaluated as shear walls rather than beams because the load transfer mechanism in these shears walls is very much different.

Behavior of Low-Rise Shear Wall

Unlike Tall walls, the moment and shear are more intimately interrelated in squat walls. Since the bending moments are not large, the steel may be evenly distributed across the length with marginal increase near the edges. In such walls, the steel requirements for flexure may be satisfied by providing minimum steel. Moreover, in such walls, the elastic performance can be made to absorb a major portion of seismic energy. In addition, it may be difficult to design suitable foundation to avoid overturning before the flexural strength is reached. Hence, the lack of ductility of such walls is not as serious as the problems listed above with regard to shear. It is not proper to propose a deep beam test as shown in Fig. 5a for a shear wall. In order to evaluate the contribution of stirrups, it is appropriate to do a test as indicated in Fig. 5b [11].

The crack pattern, shown somewhat idealized in Fig. 6 indicates the formation of diagonal struts and the engagement of wall reinforcement in the shear resistance of squat walls. From a consideration of free body marked 1, it can be seen that horizontal reinforcement is required to resist shear stress applied at top edge. The diagonal compression force requires vertical stirrups also. In the free body marked 2, vertical forces need to be developed for maintaining moment equilibrium.

Experienced Evidence of Squat Shear Wall behavior

Based on three types of squat wall tests (H/L = 1) (Fig. 7), the following conclusions have been drawn:

a) if a ductile failure mechanism is to occur in a low rise shear wall shear failure should be suppressed

b) and because flexural failure is associated with large cracks, concrete’s shear resistance should be ignored while designing the squat shear wall and consequently the whole shear should be resisted by stirrups.

Fig. 8 shows the better behavior of adequately designed wall against shear.

Moment-Axial Load Interaction for Shear Wall Section

Flanged walls normally behave better. When significant gravity compression is present the whole area of the flange may be in compression when steel (tension) yields. Under such circumstances, it is necessary to provide secondary confinement reinforcement in the compression flanges. Flanged walls give rise to large flexural capacity. In such cases appropriate horizontal and vertical shear reinforcement must be provided so that the shear stirrups do not yield.

The moment capacity of unsymmetrical wall sections, in the presence of an axial load, needs to be assessed for each possible direction of the loading. It is worthwhile to construct a load-moment interactive curve. This enables the selection of appropriate steel at various sections of the wall. Note that there are four quadrants of the P-M curve. Fig. 9 shows such a chart for a channel-shaped wall with a section aspect ratio of 3 in which vertical reinforcement is uniformly distributed. The radiating lines C indicate the position of neutral axis from the compression edges as a fraction of depth D of the section. This shows the extent of compression area at the time of attainment of strength. In this region confining reinforcement is required.

Shear Walls with Openings

Windows, doors and service ducts require openings to be provided in shear walls. Irrational shear walls warrant finite element studies for evaluating internal forces. An example of the irrational shear wall is shown in Fig. 10(a). The staggered arrangement of openings may seriously limit the shear transfer between the openings. Fig 10(b) shows a shear wall supported on sloping legs. Such irregularity may lead to deflection opposite to the direction of motion. Such structures invite disaster.

Coupled Shear Walls

Many shear walls contain one or more rows of openings. Examples are shear cores, lift wells, stair wells etc. The walls are connected by beams which are short and deep. A coupled shear wall structure and its deformations due to lateral loading is shown in Fig.11

Assessment of Behavior and Effectiveness of Coupling

While analyzing coupled shear walls, it is necessary to consider apart from flexural deformation of various components, the axial deformation of the walls and shear deformation of the beams. In a standard computer program with a few available modifications, these can be incorporated. In a mathematical model proposed by Beck Rosman [12], the discrete beams are replaced by an equivalent lamina. This idealization enables the shear force in the beams to be expressed as a continuous function of the height. The solution is now well documented and is extensively used.

The overturning moment Mo, is resisted by (see Fig. 12)

(a) a moment induced in wall 1,

(b) a moment induced in wall 2 and

(c) equal and opposite axial forces T generated in both walls (one in compression and the other in tension).

The corresponding equilibrium equation is

Mo = M1+M2+lT (2)

The axial force induced in the walls result from the accumulation of shear from beams. If the shear transfer is efficient lT component will be large. This is desirable since large internal lever arm “l” will ensure that moment capacity is maintained. Efficient coupling provides for greater stiffness and minimizes deflection.

Fig.13 illustrates the influence of efficiency of coupling. An inefficient coupling throws more moment on walls. One may say that the coupling is efficient if more than 50% of Mo is resisted by ‘lT’. The pattern of cracking significantly reduces the stiffness of beams. Hence allowance has to be made for cracking while evaluating the design forces.

Elasto Plastic Behaviour of Coupled Shear Walls

The sequence of hinge formation during the non-linear response of the structure to lateral load will depend on relative stiffness and strength of components of the shear wall system. A preferred sequence should be for the beams to plastify before the walls. The designer must postulate a preferred sequence of failure of the components. The hinges which form earlier must be ductile enough so that collapse does not occur. After all or most of the beams reach their capacity walls may be permitted to attain ultimate load.

The elastic analysis of Rosman, explained earlier, may be extended to deal with partial or full plastification of the beams. At this stage, large ductility demands will be imposed on the coupling system.Fig.14 shows the results of an elastoplastic analysis for the structure illustrated in Fig.13. The ultimate load is attained in stages. At each stage ductility demands on the components have been computed and presented. By the beams plasifying before the walls, large energy can be dissipated by the coupling system so that there is a higher degree of protection to the walls and foundation [13].

Strength and Ductility of Coupling Beams

The deep coupling beams tend to have the large flexural strength and hence they fail by shear. Observations after earthquakes in Alaska and other locations have repeatedly shown that coupling beams

– fail in diagonal tension (see Fig 15a)

– such failures have been reproduced in tests indicating the brittle mode of failure (see Fig. 15b)

– Even if excess shear steel is included sliding shear failure takes place as shown in (Fig. 15c)

To overcome the limitation of conventionally reinforced beams, the principal reinforcements can be provided along the diagonals (9). Fig. 16 shows the model of such a beam; such beams have shown excellent stable hysteresis loops under reversed cyclic loads. A typical arrangement of such reinforcement for an example coupling beam is shown in Fig.17. Conventionally and diagonally reinforced coupling beams were subjected to the same kind of cyclic reversed loading and this enabled a comparison to be made with respect to ductility. Fig. 18 presents the results in terms of cumulative ductility and shows superior performance of diagonally reinforced coupling beams.

The Strength of Coupled Walls

At the critical section above foundation level, the reinforcement is determined with the help of load moment-interaction curves such as that given in Fig.9. The confining reinforcement in the plastic hinge zone which may extend even beyond the first storey level has to be provided. Particular attention must be paid to the shear strength in the pressure of axial tension in the wall as well as presence of the construction joint. These areas are indicated as 2 and 3 in Fig.11. There is evidence [14] that at the development of plastic hinge in the coupled walls substantial redistribution of the shear resistance occurs. A considerable portion of shear force resisted by tension wall before the onset of extensive yielding in flexural reinforcement may be transferred to the compression wall. The compression wall can transmit this large shear force due to enormous seismic compression being borne by it.

Evidence of Ductility of Coupled Walls

Two one quarter full size seven storey R.C coupled walls were tested under simulated earthquake loading. To qualify as a ductile structure, the design practice calls for the ability of a structure to deflect under lateral load at roof level, four times as much deflection which could occur at the onset of yield. This should be achieved at least four times in either direction with a strength loss less than 20%.

The load-displacement (roof level deflection) history of the structure may be seen in Fig.19a. The sample maintained 80% of its theoretical ultimate capacity when the deflection at roof level was equal to one-half of storey height. The hysteresis curve in Fig. 19a, however, shows shear pinching indicating progressive damage and diminishing stiffness. Wall B was identical with wall A. It was provided with diagonally reinforced coupling beams. Fig.19b shows the characteristics of a steel member subjected to reversed cyclic loading and convincingly demonstrates superior performance.

Design Principles for Ductile Coupled Shear Walls

Desirable behavior can be expected only if the structure is made capable of following a preferred sequence of yielding. From the point of view of damage control and possible repair, it is desirable that, the wall components do not reach ultimate load before most beams fail. It is preferable to provide diagonally reinforced coupling beams from the point of view of ductility. When diagonal reinforcement is used, adequate ties are provided to enable the compression strut to sustain yield load without buckling. This will ensure very ductile performance. The walls are proportioned in accordance with principles of RC sections under limit states of strains. Use axial load-moment interaction relationship, taking into account lack of symmetry. Particular care of detailing plastic hinge zones is required. The principles outlines above are equally applicable when more than two walls are coupled by rows of beams and other systems using shear walls and deep beams.

Conclusion

The principles of design of seismic resistant systems for tall buildings were discussed. The behavior of coupling beams was analyzed. The problems of construction joints were highlighted. Finally, the principles for the design of coupled shear walls explained.

References

1. Mir.M.Ali and Kyoung Sun Moon “ Structural Developments in Tall Buildings: Current Trends and Future Prospects, Architectural Science Review, Volume 50.3, 2007,pp 205-223.

2. Fintel M., “Ductile Shear Walls in Earthquake Resistant Multistory Buildings”, Journal ACI, Vol.71, No.6 June 1974 pp 296-305.

3. Khan, F.R., & Sbarounis, J. “Interaction of shear walls and frames in concrete structures under lateral loads”, Structural Journal of the American Society of Civil Engineers, 90(ST3), 1964, 285-335.

4. Ali, M.M. “ Art of the Skyscraper: The Genius of Fazlur Khan”, New York: Rizzoli. 2001

5. Taranath, B. “Steel, Concrete, & Composite Design of Tall Buildings”. New York: McGraw-Hill. 1998.

6. William F. Baker “Burj Khalifa: A new Paragidm” Indian Concrete Journal Vol.85, No. 7, July 2011

7. Cardenas, AE and Magara DD, “Strength of High-rise Shear Walls – Rectangular Cross-section” – Response of Multi-storey Concrete Structures to Lateral Forces, Publication SP-36, ACI, Detroit 1973 pp 119-150.

8. IS 13920: 1993 Indian Standard Code of Practice for Ductile Detailing of RC Structures Subjected to Seismic Forces, BIS, New Delhi.

9. Jennings P.C., “Engineering Features of San Fernando Earthquake, February 9, 1971”, California Institute of Technology, Report EERL-71-102 Pasadena, California, June 1971, 512 pp.

10. Panlay. T., Park R and Phillips MH, “Horizontal Construction Joints in Cast-in-place RC”, Shear in RC, SP-42 ACI, 1974.

11. Leonhardt, F and Walther R, “Wandartige Trager” Deutscher Aussschuss fur Stabil beton, Bulletin No. 178, Wilhelm Erust and Sohn, Berlin 1966 159pp.

12. Rosman, B., “Approximate Analysis of Shear Walls Subjected to Lateral Loads”, Journal ACI, Vol. 61, June 1964 pp717-733.

13. Panlay.T. “Design Aspects of Shear Walls for Seismic Areas”, Research Report, University of Canterbury, Christchurch, New Zealand October 1974.

14. Santhakumar, A.R, “The Ductility of Coupled Shear Walls”, Ph.D. Thesis, University of Canterburg, Christchurch New Zealand 1974.

A.R.Santhakumar

Former Dean (Civil Engineering),

Anna University, Chennai, India

Original Source

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