Evaluation of approximate methods for estimating maximum displacement response of MDOF systems

Abstract

This study evaluates the accuracy of seven approximate methods to estimate nonlinear maximum roof displacement and the maximum inter-story drift ratio of multi-degree-of-freedom systems. The approximate methods were classified in three groups. The first group includes methods based on equivalent single-degree-of-freedom systems; the second group contains methods based on displacement amplification factors, while the third group includes methods based on equivalent linearization. The accuracy of the approximate methods is evaluated from displacement demands computed by rigorous nonlinear time history (NLTH) analysis of a family of RC frames subjected to sets of far-field and near-field earthquake ground motions. Results obtained from this investigation showed that the average relative error between the estimated maximum roof displacement and that obtained from NLTH analysis was greater than about 31% for the first and second group of methods, while average relative error was less than 25.5% for the third group, for the range of periods of vibration considered in this study. The average relative error of all methods for estimating maximum inter-story drift ratio was in the range of 32–35% for far-field earthquake ground motion records. For near-field earthquake ground motion records, the average relative error of the first and second group was more than about 35%, while it was less than about 30% for the third group. According to the results, the third group of methods provides reasonable estimates of maximum roof displacement and interstory drift demands, which is particularly true for the near-field earthquake ground motion records.