Insights into damping ratios in buildings

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Abstract
This paper analyzes how soil–structure interaction affects the overall damping ratio of multistory buildings and compares theoretical results with empirical data inferred from seismic responses of buildings in California. A method is presented for obtaining effective periods and damping ratios of a replacement fixed‐base multiple‐degree‐of‐freedom structure capable of reproducing the response of a structure with a rigid, circular foundation, sitting on an elastic half‐space. Sensitivity analyses are then conducted to assess the parameters influencing the soil–structure interaction. It is shown that for a given shear wave velocity of the soil, the aspect ratio is the parameter that primarily affects the effective damping ratio. For the fundamental mode, the effective damping ratio decreases approximately hyperbolically with increasing building height, causing an increment of effective damping in squatty structures, while for slender structures the effective damping ratio is reduced. These analytical results are compared with damping ratios inferred from seismic responses of buildings in California. It is shown that the variation of effective damping ratio with building height, computed analytically, closely follows the median trend of the empirical data, indicating that the reduction in damping ratios with increasing building height that has been reported in various studies is primarily due to soil–structure interaction. Finally, it is shown that effective damping ratios of higher modes increase with increasing effective modal frequency, matching the trend in empirical data. The results of this investigation are of paramount importance, as they suggest that soil–structure interaction primarily controls the overall damping ratio of buildings subjected to earthquakes.

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