TUNED MASS DAMPERS UNDEREXCESSIVE STRUCTURAL EXCITATION

T. Haskett1, B. Breukelman1, J. Robinson1, J. Kottelenberg1

1 Motioneering Inc., Guelph, Ontario, Canada N1K 1B8

ABSTRACT

Motioneering Inc. of Guelph, Ontario, Canada specializes in the design and construction of damping systems formajor civil structures. The main design criteria of these damping systems is to mitigate structural vibration for thepurposes of serviceability and/or load resistance.

Typically, the design constraints for damping systems related to serviceability involve forces and displacements thatare generally of a magnitude which can readily be dealt with. However, when Motioneering became involved withthe Design/Build of a number of damping systems for an upcoming project in Asia, this was not the case.

Taipei 101 (formerly known as the Taipei Financial Center) currently under construction in the capital city Taipei,Taiwan will be the next world’s tallest building. It will rise to the unprecedented height of 508m - a significantachievement even if one disregards its geography where typhoons and earthquakes are common occurrences. The660 tonne Tuned Mass Damper (TMD) for the building and two TMDs for the pinnacle involve the implementationof passive technology. Although the primary function of the TMDs in this project is to reduce the effects ofwind-induced vibration, they have been designed to withstand the forces generated in up to a 2,500-year (meanrecurrence interval) seismic event. For events less than a 100-year earthquake, the building TMD will behaverelatively calmly, as does the building in which it has been installed. Approaching events with mean recurrenceintervals of 1000 to 2500 years, the design challenge was to keep the TMDs from damaging the structure, and toremain in place and intact after severe event had passed and the vibration of the structure ended.

The design approach for these two extreme loading cases, typhoon and seismic, are described and examples of theoutcome of the extensive analyses are presented herein.

INTRODUCTION

Taipei 101 is a tremendous architectural, engineering and construction achievement. Traditional Chinese elementsare integrated into a sleek modern high-rise building. The tower and associated podium will contain over 412,400m2

(4,439,000ft2) of commercial, office and hotel space. A structural scheme utilizing steel supercolumns that containreinforced concrete up to level 62, involves a total of 95,000 tonnes of high strength steel (SM570M) and 23,900m3

of high-strength concrete (70 mPa) produces a relatively stiff structure with an expected first natural vibration periodof 6.8 seconds. A pinnacle on top of the 455m high building brings the total height to 508m.

Figures 1 and 2 show the passive damping systems which are currently under construction for the Taipei 101building. They will be referred to throughout the remainder of the paper. A number of superlatives can be noted:the building TMD will be the largest passive TMD when complete and it will also be the first constructed as a keyarchitectural and visual element in the building. So, while the building TMD was implemented in order to meetserviceability criteria it also allows for a unique focal point at the top of the occupied structure.

Figure 1: Taipei 101 Building TMD Figure 2: Taipei 101 Pinnacle TMDs

WIND INDUCED RESPONSES

Rowan Williams Davies & Irwin, of Guelph, Ontario, Canada was retained by the architect, CY Lee and Partners,and structural engineer, Evergreen Consulting Engineering, to perform wind tunnel testing for the project. A varietyof tests were performed to determine the effect of the local wind environment on the pedestrians, for the design ofthe cladding system and for the structural design of the tower itself. It is interesting to note that for much of thestructural design, local loads are governed by seismic stresses. However, for the overall loading on the structure,ie, base bending moments, the wind loads govern the design. The test results were integrated into the overallscheme of Taipei 101, including a number of minor shape changes to optimize the wind loads with the proposedstructural scheme.

Building TMD

The building TMD, as shown in Figure 1, is essentially a pendulum that spans 5 floors of the structure. Havingworked out the amplitude requirements under extreme loading scenarios, as discussed in the following sections, thearchitect was able to incorporate this vibration absorber into the architectural scheme of the uppermost occupiedfloors. From the restaurant and bar, through the center of which the TMD penetrates, patrons will be able to see the660 tonne steel ball swinging slightly many days of the year, under light winds. During the strongest wind stormexpected to occur in half of a year, according to the Taipei local meteorological records, the building TMD willreduce the peak acceleration of the top occupied floor from 7.9milli-g to 5.0milli-g (where 1milli-g is 1/1000 ofEarth’s standard gravity). This performance is shown graphically in Figure 3, and contrasted against the ISOacceleration criteria, as well as the Taiwanese criteria of 5.0cm/s2 (5.1milli-g).

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Figure 4: VDD power handling requirements during 100-year wind event

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Figure 3: Effectiveness of building TMD under moderate winds

However, being a completely passive device means that the building TMD is also in motion during substantiallystronger wind events, e.g. 100 years. The design of the TMD must be economically justifiable with regards topossible damage to component parts and the surrounding structure. At such wind levels, the most sensitive devicesin this assembly are the Viscous Damping Devices (VDD). These VDDs must be able to dissipate, as heat, enoughof the energy that they are removing from the structure to avoid overheating and subsequent failure. An exampletime history of the power absorbed by a single VDD is shown in Figure 4.

This is achieved without the use of supplemental liquid cooling by a heat-resistant VDD design (e.g. hightemperature seals, a working fluid which is thermally stable, etc.). Extensive testing by the chosen supplier hasdemonstrated such a level of capability, far beyond the norm in the hydraulic damper industry.

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Figure 5: Fatigue cycle accumulation by Vortex Induced Oscillation(VIO)

Pinnacle TMDs

Due to the strong wind climate in Taipei, the slenderness of the Pinnacle, and the structural discontinuities at thetop of the structure as it steps down from the full building width to the pinnacle diameter, there exist a number ofvibrational modes which cause Vortex Induced Oscillation (VIO) at common wind speeds.

The principal difficulty with VIO in this instance is not that of design wind load, but rather the rapid accumulationof fatigue cycles. VIO has been identified to occur at several frequencies, as follows: 0.656Hz, 0.860Hz, and1.082Hz. All of the associated mode shapes involve a simple bending translation of the Pinnacle, with no inflectionpoints. It is the behaviour of the levels below the spire base, through to the wide roof and below, that differ in eachmode. Also, because of the symmetry of the structure, perpendicular mode shapes are paired at near-identicalfrequencies; the pairs of modes 7 & 8, 10 & 11, and 12 & 13, will be hereafter referred to by only the first mode ineach pairing.

A TMD is very effective in reducing structural response due to narrow banded excitation, as is the case with VIO.On the other hand, the more problematic frequencies (0.86Hz and 1.08Hz, corresponding to modes 10 and 12,respectively) are too far apart to be effectively controlled by a single TMD. Therefore, 2 separate TMDs have beendesigned, as shown in Figure 2. Each TMD is built to target a different structural frequency, and controls theamplitude in both principal perpendicular directions. Figure 5 gives a graphical representation of bins of numberof cycles, and the associated base bending moment, induced by VIO in 100 years of wind. This figure also showsthe effect of adding the TMDs to the Pinnacle. Note that the number of cycles have not been reduced by the TMDs,but the magnitude of the bending moments have been.

Given the pinnacle size, height and wind climate, the quantity of wind energy that is accepted by the structure is verylarge. In order to achieve the bending moment reductions shown, for the duration of a VIO event that may last forseveral hours, all of this power must be dissipated by the VDDs as heat. This challenge was met, in the very tightconfines shown in Figure 2, by using external fluid circulation in the hydraulic cylinders (VDDs), and a forcedair/oil heat exchanger.

SEISMIC STRUCTURAL RESPONSES

If Taipei 101 had been destined to grace the skylines of Miami, or Hong Kong, then the TMD design efforts wouldhave been complete after investigating the wind-induced performance. Instead, the most difficult TMD designaspect was that of handling the seismicity of the region. Due to the differing nature of the building and Pinnacledevices, from their size, to their proximity to occupants, completely different seismic design approaches have beentaken.

The structural engineer provided assistance by sharing an appropriate number of site-specific seismic groundacceleration time histories. These records are utilized to determine the elastic building responses in events up to100 year return periods. For design events of longer return period (e.g. 1000 years, and/or 2500 years), due to thenon-linear (elasto-plastic deformation) structural response, time domain position responses of the floors nearby theTMD were used to evaluate the nuances of building/TMD interaction. The time domain simulations for theseextreme design periods were performed by the structural engineering using DRAIN2D. A rather small conservatismis realized by assuming that the TMD does not reduce the response levels during these design events.

Building TMD

In strong seismic events, e.g. those with return periods up to 100 years, the designed response characteristics of thebuilding TMD are quite tame. The steel ring and lower set of 8 dampers, shown in Figure 1 on the floor at elevation374m, is a secondary system (named a “snubber ring”) designed to engage the TMD only at relative amplitudeswhich exceed 1m. While the primary structural response remains linear in seismic events of this strength, therecruitment of this secondary set of VDDs becomes highly nonlinear.

To address this computational challenge, a complete kinematic model was assembled to determine the behavioursof TMD/snubber ring collisions, and the sub-linear force-velocity damping profiles of the connected secondaryVDDs. These lower 8 VDDs are drawn from the rail-freight industry, where low speed collisions between heavyrail cars are an everyday occurrence. The sub-linear force-velocity profile means that upon contact with the snubberring, at higher stroke velocities, the desired damping force is exerted immediately. As the velocities of the bodiesbegin to approach each other (a relative velocity approaching zero due to the exerted viscous forces), this preferredlevel of viscous damping force is maintained with very little change.

Substantially more difficulty was encountered when contending with the seismic events of 2500 years’ strength.An interesting observation can be made about the nature of the response of a TMD, tuned only to the first mode ofsuch a slender structure; as many building modes are excited simultaneously, the TMD is seen to respond very little.In essence, the TMD remains almost still in an inertial reference frame, while the building oscillates wildly allaround it. In this manner, and due to the phenomenal quantity of energy present in the building during such a strongearthquake, the front-most issue is one of amplitude control (to prevent collision damage), instead of energydissipation.

It was with this in mind that the strength of the snubber system was designed. One difficulty in handling the largeviscous forces induced by the snubber ring is the moment it creates on the TMD mass. When the snubber pinengages the snubber ring, well below the TMD, high cable loads are induced on one side of the TMD to resist theoverturning of the mass. Conceptually, this occurs as the cables resist the “diving” of the TMD over the snubberring. In Figure 6, typical peak loads can be seen to be well in excess of twice the self-weight gravity load of theTMD. The outcome of these types of simulations were incorporated into the design of the supporting wire ropecables and other supporting structural components.

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Figure 6: Tension of corner cable group in 2500-year seismic event

Pinnacle TMDs

In the design earthquake the tip of the Taipei 101 Pinnacle is expected to whip back-and forth with peakaccelerations near 14 g (where g is Earth’s standard gravity). Under these circumstances, there is no reasonable rolethat a TMD might be designed to accomplish in terms of vibration reduction. The mass ratio of the Pinnacle TMDs,useful for VIO suppression, and nearly a practical maximum given the dimensions of the Pinnacle structure, iscompletely inadequate to the task of moderating the structural response in strong-to-extreme seismic events. Referto Figure 7 for a typical illustration of the amplitudes traversed by the Pinnacle tip in a 100-year, completely elasticresponse, earthquake.

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Figure 7: Pinnacle tip motions in 100-year seismic event

The usual means of handling such excitation do not work in this environment. Enough clearance cannot be givento the TMDs’ translations to prevent extreme collisions with the interior of the Pinnacle. Any effort to avoid/restrictlarge relative TMD motion by increasing the VDD force/velocity coefficient will have a deleterious effect on theperformance of the TMDs against VIO. It was at last decided to passively “lock out” the Pinnacle TMDs withrobust secondary mechanisms. In this manner, the TMDs will travel as inert mass locked to the Pinnacle structuralsystem, and avoid any damage that would occur from strong internal collisions - in effect, they will “ride out” theearthquake.

This operation happens automatically whenever the TMDs exceed a nominal clearance with sufficient kinetic energyremaining to compress an integrated system of rubber bumpers. “Unlocking”, or freeing this mechanically locked-out state can be accomplished by a single person upon cessation of the seismic event, with the use of furtherintegrated hardware. The ground motion sufficient to cause the Pinnacle TMDs to lock out is a Peak GroundAcceleration (PGA) of approximately 30cm/s2. By this estimate, the manual unlocking of the Pinnacle TMDs maybe required approximately once per year. Most reasonable, a sensor device can be installed to detect this conditionand signal the need for an unlocking operation.

CONCLUSIONS

Designing a passive damping system for both wind and seismic excitation forces the engineer to investigate theproblem from two different viewpoints. Generally, the magnitude of forces in wind events tends to be moderatefor which designing the system components is readily achievable. However, during extended design wind events,such as typhoons, the amount of energy to dissipated is large and accommodating this within the design can bedifficult. Seismic design considerations are generally the opposite, where the total energy to be dissipated isgenerally much than that for wind, whereas dealing with extremes in force and displacement provide significantchallenges for the damping system designer.

Taipei 101, where passive TMDs are being implemented to reduce the effects of wind-induced motion on theoccupants as well as limiting fatigue damage, is an excellent example of how these two different designconsiderations are dealt with. By collaborating with both the architect and structural engineer these seeminglyconflicting design requirements are effectively integrated - a physical portrayal of the Yin and Yang.