structuralDESIGN
Discussing Engineered Damping We engineer building mass and stiffness but not damping, making it highly uncertain. By Ron Aquino, PEng, Shayne Love, PEng, and Jamieson Robinson, PEng
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e 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.
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 measureImpact of High Uncertainty in Non-Engineered ments generally reporting damping below 3%. Note as well that these early measurements were likely done on buildings that were generally Damping on Structural Design shorter than the tall, slender buildings we see more of in the present Research papers (e.g. Tamura et al, 2000; Bashor & Kareem, 2009) 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 Mass damping systems can be slightly more effective even if the inherent damping ratio is lower than assumed in the design. The supplemental damping level can tall buildings. also be engineered to provide maximum damping at amplitudes where it is needed the most. Images shown are results from specific projects. Research since the
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