A Stochastic Dynamics Approach for Seismic Response Spectrum-Based Analysis of Hysteretic MDOF Structures

An efficient nonlinear stochastic dynamics methodology has been developed for estimating the peak inelastic response of hysteretic multi-degree-offreedom (MDOF) structural systems subject to seismic excitations specified via a given uniform hazard spectrum (UHS), without the need of undertaking computationally demanding non-linear response time-history analysis (NRHA). The proposed methodology initiates by solving a series of inverse stochastic dynamics problems for the determination of input power spectra compatible in a stochastic sense with a given elastic response UHS of specified damping ratio. Relying on statistical linearization and utilizing an efficient decoupling approach the nonlinear N-degree-of-freedom system is decoupled and cast into (N) effective linear singledegree-of-freedom (SDOF) oscillators with effective linear properties (ELPs): natural frequency and damping ratio. Subsequently, each DOF is subject to a stochastic process compatible with the UHS adjusted to the oscillator effective damping ratio. Next, an efficient iterative scheme is devised achieving convergence of the damping coefficients of all the N effective linear SDOF oscillators and the UHS corresponding to each DOF. Finally, peak inelastic responses for all N DOFs are estimated through the updated UHS for the N different sets of SDOF oscillators ELPs. The proposed approach is numerically illustrated using a yielding 3-storey building exposed to the Eurocode 8 (EC8) UHS following the Bouc-Wen hysteretic model. NRHA involving an ensemble of EC8 compatible accelerograms is conducted to assess the accuracy of the proposed approach in a Monte Carlo-based context