An Analytical Method for Elastic Seismic Response of Structures Considering the Effect of Ground Motion Duration

The response to earthquake ground motion is composed of three basic elements, namely, amplitude, frequency, and duration. The seismic response of a structure is controlled by the particular combination of these three elements. The seismic response spectra reflect the earthquake ground motion’s frequency-domain features and provide the maximum response amplitude of a single-degree-of-freedom system to a given earthquake ground motion but do not consider the duration factor. However, the analysis of post-earthquake damage shows that the seismic response duration has a strong impact on the damage to structures. Therefore, it is necessary to develop a simple and practical analytical method to account for the seismic response duration. The present study was conducted based on the response spectra theory. We introduce an analytical method of elastic seismic response, which considers its duration by adding the time-domain dimension of earthquakes. The time-domain spectral matrix is used to solve the time-dependent seismic response through the vibration mode decomposition method. The time-domain vibration mode decomposition reaction spectrum not only takes into account the maximum seismic reaction of each vibration mode but also considers the seismic reaction of different vibration modes occurring at the same time, at each moment. The dynamic time duration of the structure’s seismic reaction is quantified by the time-domain seismic reaction spectrum to obtain a more accurate analysis method for the seismic reaction of the structure.