Statistical analysis of the response of nonlinear systems subjected to earthquakes

The dynamic response of single degree of freedom nonlinear systems subjected to earthquake excitations is considered with the purpose of reviewing previous recommendations for deriving inelastic design spectra, and to evaluate the effect of damping combined with nonlinear behavior and the influence of the type of material nonlinearity on inelastic response. Three nonlinear models are used: the elastoplastic and bilinear idealizations, and a stiffness degrading model. Considering the various conditions and ground motions used, results for about 12,000 different cases are obtained and summarized in the form of inelastic response spectra. A statistical procedure is developed to analyze the data; from this analysis, factors for deriving the characteristic trapezoidal design spectrum are obtained. Such factors reflect, in an explicit manner, the effect of the damping factor and the type of material nonlinearity on inelastic response.