By Ron Aquino, PEng, Shayne Love, PEng, and Jamieson Robinson, PEng
Click here to view the article and images in June 2024 digital edition of STRUCTURE magazine.
We have been engineering mass and stiffness in tall buildings, but not damping.
When a tall building is subjected to a dynamic load, such as wind, seismic, or traffic, the structure is typically simplified to be represented as an equivalent spring-mass-dashpot system. In structural design, the mass and stiffness are normally “engineered” since these values can be directly calculated using material properties. When a structural engineer starts to size structural components such as beams, columns, walls, and slabs, the engineer is effectively selecting a mass and stiffness value for the individual component based on its geometry and material properties. Then by taking all components and defining their joint connectivity (fixed, pinned, or spring), the structural engineer is defining the global stiffness and mass characteristics of the structure, from which the system frequencies are determined.
While such mass and stiffness properties of structural materials are well defined, little is known about the damping or energy dissipation properties of materials. Damping is therefore a “non-engineered,” highly uncertain property that is assumed, rather than calculated, at the time of design. For simplicity in the design process, a global value for each mode of vibration is assigned based on experience with similar structures. For further simplicity, one damping value is generally used for all modes for a particular loading scenario. For example, a 5% damping ratio is typically used for each mode when performing seismic analysis. When calculating wind loads corresponding to the ultimate limit state, perhaps 2.5% damping is assumed for each mode. For service limit states, the ASCE 7-22 Commentary states that values between 1% and 2% are typically used in the U.S. while also referring to the ISO 4354 which suggests 1% and 1.5% for steel and concrete buildings, respectively. In practice, we have seen some engineers use anywhere between 0.8% to 2% for service conditions (including accelerations and wind-induced drift loads), and between 1.5% and 3% for Ultimate Limit State (ULS) wind load cases.
Impact of High Uncertainty in Non-Engineered Damping on Structural Design
Research papers (e.g. Tamura et al, 2000; Bashor & Kareem, 2009) have considered that the coefficient of variation (COV) of damping could be somewhere between 30% and 70%, whereas the COV of natural building periods or frequencies is no higher than 10%. The COV is the ratio of one standard deviation to the mean of a data set. A COV of 30% can be taken to represent a range of values from 30% below to 30% above the mean.
The structural design implication of a high COV for damping is significant. If 1.5% damping is typically assumed for the serviceability design of a concrete building, a COV of 30% means that it is reasonable to expect that the actual damping ratio could range between 1% and 2%. In terms of building accelerations, this implies a variation of ±20% from the expected acceleration if 1.5% damping was assumed in design. Such a variation is significant and would materially affect the motion comfort of the building and may also dictate if mitigation needs to be considered to reduce accelerations. Similarly, this variability of damping could also alter the wind-induced building drifts by up to ±20% from the expected value. If the damping variation were more than 30%, the variability or uncertainty in response quantities would increase as well. For wind loading, a proposal by Bashor & Kareem (2009) was made to effectively increase wind loads by approximately 20% on account of a 30% COV in damping, together with a 5% COV in natural frequency.
Observations From Measured Damping in Tall Buildings
For the most part, the damping values used in design are based on full-scale measurements on completed structures. However, most measurements are conducted at very low excitation amplitudes compared to what the buildings are expected to experience during design wind events with return periods from 10 years or longer. Research in the 1980s (e.g. Davenport & Hill-Carroll, 1986) showed a somewhat linearly increasing trend of damping ratio with amplitude, with most of the measurements generally reporting damping below 3%. Note as well that these early measurements were likely done on buildings that were generally shorter than the tall, slender buildings we see more of in the present day. According to the Tall Buildings Database by the Council on Tall Buildings and Urban Habitat (CTBUH), there were only 13 “super tall” buildings as of 1990 (i.e. those that were taller than 300 meters). As of 2010, that number of super tall buildings was 49, and as of 2020, there were more than 100 super tall buildings.
Research since the 1990s (e.g. Nakamura et al, 1993; Tamura et al, 2000; Cruz & Miranda, 2021; Xu et al, 2023) which is inclusive of tall (above 200m) to super tall buildings, has shown that the damping ratio can often be lower than what is typically assumed in design. Moreover, some research (e.g. Tamura, 2012) suggests that above a certain threshold of motion, the damping begins to decrease with increasing amplitude, suggesting it may be unconservative to use higher damping ratios for design loads. Motioneering, Inc. has measured inherent damping of completed buildings that is less than half of what was assumed during design for common wind events. Few research works (e.g. Aquino, 2013; Spence & Kareem, 2014) have investigated potential mechanisms behind this unusual trend of the amplitude-dependence of damping. However, if damping could increase and decrease with amplitude, such findings only beg the question, “what then is the appropriate damping value for design?”
Is It Possible to Engineer Damping?
Structural engineers can account for damping uncertainty by using more conservative assumptions, but this can have substantial financial implications for the project. Generally, a stiffer tower is required, which adds material costs and also decreases the useable space on each floor—undesirable consequences for any project. As engineers, the next question then that we might ask is, “Is it possible to engineer damping?” The short answer is “yes”. In fact, this has been done before. In nautical, aerospace, and even automotive applications, some form of engineered damping devices are commonplace. In civil engineering structures, damping devices have been introduced to reduce the impact of high seismic demands. However, certain damping systems have also been demonstrated to control lower amplitudes under wind excitation to meet occupant comfort and serviceability criteria. However, for the most part engineered damping is not yet front-and-center at the design stage. Typically, the need for an engineered damping solution is not something discovered until after the preliminary building design has been carried out. Or worse, motion issues might be observed only after the building is built.
Two general approaches are used for an engineered damping solution.The first is a distributed damping system. Distributed damping has been widely used for decades in seismic applications where the amplitudes of concern (e.g. interstory drifts, building accelerations) are very high. Under low-level excitations associated with occupant comfort, such as under 1-month to 1-year wind loads, distributed damping systems may be constrained by internal friction mechanisms and system compliance that render them ineffective as a damping solution. The second approach is the use of mass damper systems, or dynamic vibrations absorbers, which employ a secondary dynamic system with its own mass, damping, and stiffness. These devices are typically used for wind response control, in which the motions are much smaller than seismic applications. However, mass damping systems have been used to reduce both wind and seismic load effects. In general, distributed damping systems can be more easily integrated into architectural systems but have limitations when it comes to wind applications. Mass damping systems require space near the top of the building but can provide more reliable performance during service level excitation events. Having a mass damping system at one area of the building allows simplified coordination as it can be viewed as another building service alongside the HVAC, plumbing, fire, building maintenance units (BMU), and other similar services located on the roof or mechanical penthouse floors of tall buildings. In the succeeding discussion, the focus will be on mass damping systems for controlling the wind response of tall buildings.
Types of Mass Damping Systems
Two types of mass damping systems are most used in tall buildings: tuned mass damper (TMD) systems and tuned liquid damper (TLD) systems. The main difference between the two is that TMDs employ a solid mass, while TLDs typically employ water as mass. Two common configurations of TMDs are discussed in the next section. TLDs require a tank to hold the water; however, it is the shape and size of the tank that determines its mass, damping, and stiffness parameters. TLDs can be further broken down into two sub-types: tuned sloshing dampers (TSDs) and tuned liquid column dampers (TLCDs). TLCDs generally act in only one direction, whereas TSDs can be designed to act in two directions. TLCDs generally provide lower supplemental damping than a TSD for the same amount of water. From experience, the authors have found that TLCDs are less effective than TSDs, and therefore do not recommend them unless specific space constraints require the use of TLCDs.
Successful Implementation of Engineered Mass Damping Systems in Tall Buildings Using Performance-Based Design Principles
The simplest type of TMD system is the simple pendulum type. A classic example of this is the Taipei 101 TMD. A simple pendulum TMD involves the use of cables with a specific length to prescribe the frequency of the damping system. The solid mass in this case is of steel ballast material. Viscous damping devices (VDDs) are attached between the solid mass and structure to provide a certain level of internal damping. The TMD frequency, via cable length, and internal damping, via the VDDs, are initially selected to provide the optimum amount of damping based on textbook first principles assuming linear properties and simple excitation. However, for actual TMD systems, a performance-based approach considering nonlinear properties, particularly for the VDDs, and random excitations, based on more realistic input characteristics to simulate wind and earthquake loading, are used. Inherent friction in the system should also be included in the simulations. The result is a sufficiently robust design that will provide a steady level of supplemental damping across a wide range of as-built conditions for the tall building. Full scale measurements are performed once the TMD is installed and tuned to demonstrate that the TMD performs as designed.
One downside of a simple pendulum system is that it could necessitate a very tall room due to the cable length requirement. For example, a tall building with a 6-second period requires approximately 30 feet of cable length—equivalent to about three stories. To account for variability in building frequency, this cable length may need to be increased to approximately 36 feet—equivalent to almost four stories tall. A solution has been developed and successfully implemented to resolve this issue: the use of an opposed-pendulum type of system. One example of this is the 111 West 57th TMD in New York City; some details of this TMD have been presented in a New York Times article. An opposed-pendulum TMD consists of a simple pendulum system attached to an inverted pendulum (a secondary mass suspended from the floor via steel columns). The TMD frequency is determined by proper configuration of the ratio between the two masses and the cable length and column height. For the 111 West 57th TMD, the required height of the TMD room would have increased four-fold had a simple pendulum TMD been implemented.
While opposed pendulum systems require the least amount of space, they do require slightly more engineering and higher costs. If space is not as much of a concern, especially if the required supplemental damping and therefore damper mass is not too high, TLD systems may be considered. However, only 60% to 80% of the water in TLD tanks actually participates as dynamic mass within the mass damper system. On one project, a 1000-ton TMD was required, but the client opted for a less expensive TSD alternative that, in the end, held nearly 2,000 tons of water!
On one project in Australia though, where the damper mass requirement was only in the order of approximately 200 tons, a TSD was the perfect solution for the client. An earlier consultant recommended a three-tank TLCD system, but by using performance-based design principles, constant coordination with the client, and full-scale building frequency measurements during construction, the project ended up employing just a one-tank TSD system that allowed the client to introduce a new penthouse apartment unit that more than made up for the cost of the TSD implementation. One key factor in the success of such a TSD design is that the water TSD tank was incorporated into the fire suppression water storage system. In short, the tank served dual purposes: as a TSD and as fire suppression water storage. During commissioning of the TSD system, full scale measurements were done and analysis of the data reveal that the TSD is performing as expected.
However, not all projects can accommodate a rectangular, box-shaped TSD tank. Again, as part of a performance-based design approach, coordination with clients reveals that only an irregular shaped tank can be accommodated in some projects. The numerical modelling used in the performance-based analysis and design of TSDs is verified using data collected from scale-model testing in the laboratory. For irregular tanks, the same approach is used. One project in China has used a triangular, wedge-shaped tank. Certain types of spire-like structures on buildings or on-ground have used annular-shaped (i.e. “donut-shaped”) tanks. On one super tall building in New York City, the building could only accommodate a tank that wrapped around the concrete core— effectively requiring a “square bagel”-shaped tank (i.e. a rectangle with a smaller rectangle cutout in the middle). By employing a performance-based design approach, it is possible to employ a wide variety of tank shapes that can still achieve the performance objectives.
Summary and Conclusion
Various damping technologies are available that provide a reliable level of damping, meet performance requirements, and fit within the project’s space constraints. Successful examples of TMD and TSD systems for wind response control have been implemented in tall building projects across the globe, where performance-based design principles were used, and in-situ performance verification has been demonstrated. ■
REFERENCES
ASCE (2022). Minimum design loads and associated criteria for buildings and other structures (ASCE 7-22). American Society of Civil Engineers.
Aquino, R.E.R. (2013). Damping in buildings for wind-resistant design based on a stick-slip model. Doctoral dissertation, Tokyo Polytechnic University.
Aquino, R.E.R., Love, J.S., Haskett, T., Clarke, G., and Kelly, D. (2022). Demonstration of tuned mass damper effectiveness via long-term structural monitoring. Proc. 9th International Operational Modal Analysis Conference (IOMAC). Vancouver, BC, Canada.
Aquino, R.E.R., and Tamura, Y. (2013). Framework for new structural damping predictor models based on stick-slip mechanism for use in the wind resistant design of buildings. Proc. 6th European and African Conference on Wind Engineering (EACWE). Cambridge, UK.
Aquino, R.E.R., and Tamura, Y. (2017). Structural damping estimation using a simple equation based on the equivalent viscous damping concept. Proc. 10th International Conference on Structural Dynamics (EURODYN 2017). Rome, Italy.
Bashor, R., & Kareem, A. (2009). Load factors for dynamically sensitive structures. Proc. 11th Americas Conference on Wind Engineering (ACWE). San Juan, Puerto Rico.
Council on Tall Buildings and Urban Habitat. (2024). The 100 Tallest Completed Buildings in the world in 2024 – The Skyscraper Center. https://www.skyscrapercenter.com/buildings
Cruz, C., and Miranda, E. (2021). Damping ratios of the first mode for the seismic analysis of buildings. J. Struct. Eng. 147(1): 04020300.
Davenport, A.G., and Hill-Carroll, P. (1986). Damping in tall buildings: its variability and treatment in design. Proc. ASCE Spring Convention: Building Motion in Wind, 42-57.
Grondahl, M. (2015). Reducing skyscraper sway. New York Times. https://www.nytimes.com/interactive/2015/08/06/realestate/Reducing-Skyscraper-Sway.html
ISO (1997). Wind actions on structures (ISO 4354). International Organization for Standardization.
Love, J.S., and Haskett, T.C. (2022). The practical effects of friction for tuned mass dampers installed in tall buildings. Engineering Structures 265: 114495.
Love, J.S., Morava, B., Robinson, J.K., Haskett, T.C. (2021). Tuned Sloshing Dampers in Tall Buildings: A Practical Performance-Based Design Approach. Practice Periodical of Structural Design and Construction 26(3): 04021016.
Nakamura, Y., Okada, K., Yokota, H., Kitada, Y., Tsuji, E., Ukita, T., and Yamaura, N. (1993). Dynamic Vibration Tests of ORC200 Symbol Tower: Part 2 Variation in Dynamic Characteristics. Summaries of Technical Papers of Annual Meeting of Architectural Institute of Japan: Structures 1, 877-878.
Pieterse, M.J., Aquino, R.E.R., and Morava, B. (2020). Successful implementation of a tuned sloshing damper in Melbourne: from concept to commissioning. Proc. Australasian Structural Engineering Conference (ASEC 2020).
Satake, N., Suda, K., Arakawa, T., Sasaki, A., and Tamura, Y. (2003). Damping evaluation using full-scale data of buildings in Japan. J. Struct. Eng. 129(4):470.
Spence, S.M.J., and Kareem, A. (2014). Tall buildings and damping: a concept-based data-driven model. J. Struct. Eng. 140(5): 04014005.
Tamura, Y. (2012). Amplitude dependency of damping in buildings and critical tip drift ratio. Int. J. High-Rise Buildings. 1(1), 1-13.
Tamura, Y., Suda, K., and Sasaki, A. (2000). Damping in buildings for wind resistant design. Proc. International Symposium on Wind and Structures for the 21st century. Cheju, Korea.
Xu, K., Li, Q.S., Zhou, K., Han, X.L., and Wan, J.W. (2023). Modal identification of 38 supertall buildings and establishment of predictive models. J. Struct. Eng., 149(4): 04023017.