Reliability of bilinear SDOF systems subjected to earthquake loading

Probabilistic assessment of the ductility demand and reliability analysis were carried out for bilinear hysteretic SDOF systems. The assessment considered two sets of strong ground motion records, and was focused on the evaluation of the mean and the coefficient of variation of the ductility demand for a given value of the normalized yield strength. The results indicate 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 of the ductility demand for bilinear SDOF systems of different natural vibration periods, damping ratios, and ratios of the post yield stiffness to the initial stiffness. The numerical results show that the coefficient of variation (cov) of the ductility demand can go as high as to about 1.0 depending on the characteristics of the structure. Also, a simple approach was given to estimate the probability of incipient damage and the probability of incipient collapse using the developed probabilistic characterization of the ductility demand. The approach, which could be suitable for carrying out design code calibration analysis, is illustrated numerically.