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

• Published in: Structural safety Vol. 72; pp. 84 - 98
• Main Authors: Mitseas, Ioannis P., Kougioumtzoglou, Ioannis A., Giaralis, Agathoklis, Beer, Michael
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.05.2018; Elsevier BV
• Subjects: Bouc-Wen model; Building codes; Compatibility; Computer simulation; Damping; Damping ratio; Degrees of freedom; Earthquake accelerograms; Elastic properties; Excitation spectra; Hysteresis; Hysteretic MDOF structure; Iterative methods; Linearization; Mathematical models; Monte Carlo simulation; Nonlinear analysis; Nonlinear response; Nonlinear stochastic dynamics; Nonlinear systems; Oscillators; Seismic design; Seismic response spectrum analysis; Statistical linearization; Statistics; Stochastic models; Stochastic processes; Hysteretic MDOF structure; Bouc-Wen model; Seismic response spectrum analysis; Stochastic processes; Statistical linearization; Nonlinear stochastic dynamics
• ISSN: 0167-4730; 1879-3355
• DOI: 10.1016/j.strusafe.2017.12.008

•Efficient inelastic stochastic design spectrum analysis of hysteretic MDOF systems.•A novel computationally economical stochastic dynamics framework.•Enhanced accuracy due to the novel feature of updating the imposed elastic spectrum.•The framework is tailored to facilitate code-compliant seismic demand estimation.•The iterative process solves at the current iteration a system identification problem. 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.