Closed-form stochastic response of linear building structures to spectrum-consistent seismic excitations

Design codes typically define the seismic action in terms of pseudo-acceleration response spectra, encouraging the use of the modal superposition method for the evaluation of the structural response. For linear structural systems, provided that the ground shaking has been appropriately modelled, the full characterization of the response processes of interest can be achieved with the application of random vibration theory. An analytical model for the power spectral density (PSD) functions consistent with seismic response spectra has been recently proposed. In this paper, taking advantage of this novel PSD model, closed-form approximate expressions of the spectral moments are derived and numerically validated for the seismic response of single- and multi-degree of freedom systems. For demonstration purposes, the proposed formulation is applied to the case of base isolated multi-story buildings, aimed at overcoming the difficulties associated with the non-classical nature of their damping. The paper shows how the proposed approach can be used for a computationally efficient evaluation of the probabilistic distribution of the structural response maxima.