Probabilistic Constant-Strength Ductility Demand Spectra

A procedure is presented to develop probabilistic constant-strength ductility demand spectra based on statistical analyses of the results of comprehensive dynamic time history simulations of bilinear single-degree-freedom systems. The procedure offers an approach to estimate both the mean and standard deviation of the ductility demand, given the normalized strength and fundamental system period. The probabilistic distribution of the ductility demands conditional on normalized strength and natural period is validated through goodness-of-fit test. The effects of post-yield stiffness ratio on ductility demand are also investigated. The proposed spectra can allow the treatment of the frequency content and peak intensity measure of the ground motion separately, and describe the state variation of a structure from elastic to inelastic as a function of the peak ground acceleration, which enables its application in stochastic seismic displacement analysis and probabilistic seismic demand analysis. An illustrative example of a seven-story planar frame structure is presented to demonstrate the applicability and utility of the proposed methodology.