Abstract
Probabilistic assessments of the ductility demand and reliability analysis were carried out for hysteretic bilinear single-degree-of-freedom (SDOF) systems. The assessment considered a set of strong ground motion records, and focused on evaluating the mean and coefficient of variation of the ductility demand for a given normalized yield strength. Results indicated that the ductility demand could be modeled as a Frechet (extreme value type II) variate. Based on the obtained results, empirical equations were provided to predict the mean ductility demand for hysteretic bilinear SDOF systems considering different natural vibration periods, damping ratios, and post-yield stiffness to initial stiffness ratios. Numerical results showed that the coefficient of variation of the ductility demand can go as high as one, depending on the characteristics of the structure. Also, a simple approach was given to estimate the probabilities of incipient damage and incipient collapse using the developed probabilistic characterization of the ductility demand. This approach, which could be suitable for design code calibration analysis, is illustrated numerically in this study.
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