Stochastic linearization of inelastic seismic torsional response: formulation and case studies

Abstract

The stochastic equivalent linearization method (SELM) is adopted for the analysis of hysteretic torsionally coupled oscillators under bi-axial random earthquake loading. A new formulation of the method is presented which is based on polynomial expansions of various nonlinear terms and the implementation of the properties of Gaussian variables. The resulting expressions incorporate the interaction of the hysteretic components of the two translational modes as well as the torsional coupling and form the basis for the evaluation of the expected ductility ratio and the mean rate of hysteretic energy dissipation. The accuracy of the introduced approximations is confirmed through selected tests against numerical integrations and Monte Carlo simulations. Furthermore, the ability of the methodology to model the behaviour of one-storey torsionally coupled structures is assessed through comparisons with results reported in the literature which are based on a somewhat more realistic approach to structural modelling.