Effects of Damping Uncertainties on Damping Reduction Factors

It is apparent that the dynamic response of a building depends on its energy dissipation capacity, hence damping ratio. The damping value experienced by a building during an earthquake differs significantly from the value specified in the design step. This introduces uncertainties in the design process of the building. It would be desirable to consider not only the effects of uncertainties in loading but also the uncertainties in the structural parameters. In this paper, the effects of uncertainties in the estimation of damping ratio ξ, on the use of Damping Reduction Factors (DRF) for the evaluation of high damping response spectra, are examined. Damping uncertainties are described by a lognormal probability distribution, and the Monte Carlo technique is used to generate the random values of damping. The average of the distribution is the deterministic value of damping (taken equal to 5%, 7.5%, 10%, 20%, 30% and 40%) while three different values of coefficient of variation are considered (i.e. 10%, 20% and 40%, respectively). All the DRF formulations found in the literature are not able to take into consideration damping uncertainties, leading to significant discrepancies in the high damping response spectra. Based on the results of this study, a new DRF formulation, able to account for uncertainties in damping estimation, is tentatively proposed.