Ratio between peak inelastic and elastic responses with uncertain structural properties

A systematical assessment of the impact of the uncertainty in the natural vibration period and damping ratio on the peak displacement of linear elastic and elastoplastic single-degree-of-freedom systems is carried out using more than 200 strong ground-motion records. The assessment is based on the ratio of the peak inelastic displacement with uncertain structural properties to the peak linear elastic displacement and, the ratio of the peak linear elastic displacement to the yield displacement. Statistical analysis for the ratios obtained is presented. The analysis results indicate that the impact of the uncertainty in the damping ratio on these ratios is less significant than that of the uncertainty in the natural vibration period. The results also show that the consideration of uncertainty in the natural vibration period slightly alters the average peak displacement of the linear or elastoplastic systems. However, the coefficients of variation of these ratios change significantly, especially, if the mean of the natural vibration period is less than about 0.1 s. Simple to use empirical equations, based on the results obtained, are suggested in evaluating the mean and the coefficient of variation of the ratios considering the uncertainty in structural properties.