Statistics of ordered peaks in the response of non-classically damped structures

This paper presents a probabilistic spectrum superposition approach for computing the expected, most probable or, for a chosen probability of no exceedance, the amplitudes of the peaks in the seismic response of MDOF structures with non-classical damping, when all the peaks are arranged in order of decreasing amplitude. Most of the available spectrum superposition approaches for non-classically damped structures are based on several idealizations and approximations to express the final response quantities directly in terms of the response-spectrum amplitudes. The present study improves upon most of the approximations by evaluating the exact response statistics from the power spectral density function (PSDF) of the response, defined in terms of the modal properties of the structure and the response-spectrum-compatible PSDF of the ground acceleration. The probabilistic estimates show good agreement with the exact time-history solution for the response of a five-storey example building with non-classical damping. In view of the improved accuracy and the fact that the proposed formulation is able to predict the amplitudes of several of the largest peaks of the response, the computational effort is not significantly higher than for the cases considered when employing commonly used approximate methods.