A novel stochastic linearization framework for seismic demand estimation of hysteretic MDOF systems subject to linear response spectra

This paper proposes a novel computationally economical stochastic dynamics framework to estimate the peak inelastic response of yielding structures modelled as nonlinear multi degree-of-freedom (DOF) systems subject to a given linear response spectrum defined for different damping ratios. This is accomplished without undertaking nonlinear response history analyses (RHA) or, to this effect, constructing an ensemble of spectrally matched seismic accelerograms. The proposed approach relies on statistical linearization and enforces pertinent statistical conditions to decompose the inelastic d-DOF system into d linear single DOF oscillators with effective linear properties (ELPs): natural frequency and damping ratio. Each such oscillator is subject to a different stationary random process compatible with the excitation response spectrum with damping ratio equal to the oscillator effective critical damping ratio. This equality is achieved through a small number of iterations to a pre-specified tolerance, while peak inelastic response estimates for all DOFs of interest are obtained by utilization of the excitation response spectrum in conjunction with the ELPs. The applicability of the proposed framework is numerically illustrated using a 3-storey Bouc-Wen hysteretic frame structure exposed to the Eurocode 8 elastic response spectrum. Nonlinear RHA involving a large ensemble of non-stationary Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed approach in a Monte Carlo-based context. The novel feature of iterative matching between the excitation response spectrum damping ratio and the ELP damping ratio enforces the required compatibility in the damping properties of the effective linear oscillators and the imposed elastic response spectra. It is found that this latter feature reduces drastically the error of the estimates (i.e., by an order of magnitude) obtained by a non-iterative application of the framework.