The role of the stochastic equivalent linearization method in the analysis of the non‐linear seismic response of building structures

The stochastic equivalent linearization method has been significantly improved during the last two decades, leading to rather efficient and accurate estimates of the first‐ and second‐order statistical moments of the random response process, even when the non‐stationarity of the excitation and the hysteretic degrading non‐linearities of the structural system are taken into account. The purpose of this paper, apart from presenting a short survey of the most relevant methods developed in this area, indicating their main restrictions, is to call attention to the remarkable possibilities of the equivalent linearization technique as the most powerful approximate method to deal with the seismic response analysis of MDOF non‐linear building structures, deserving to be considered by the engineering codes in the near future as an appropriate formulation for that purpose. To illustrate the real interest of this method, several applications concerning a simple shear‐building structural model are presented, considering columns with non‐linear restoring forces, either bilinear elastic or hysteretic, and the results obtained by some computer programs developed on the basis of the equivalent linearization technique are compared with the estimates achieved by digital simulation in order to check the level of accuracy. Moreover, these results are also used to evaluate limit violation (failure) probabilities, based on the vulnerability function concept.