Estimation of Structural Hysteretic Energy Dissipation Based on Normalized Energy Spectra Considering Ground Motion Duration

Abstract

Ground motion duration significantly affects structural hysteretic energy dissipation, especially for systems undergoing repeated inelastic deformation. To explicitly consider this effect, this study proposes a spectrum-based method for estimating structural hysteretic energy dissipation using normalized hysteretic energy spectra as a function of ground motion duration. A set of 133 spectrally equivalent ground motion records is generated using a spectral matching technique, maintaining consistent response spectra while covering a wide range of significant durations (5%–95%) from approximately 5–100 s. Nonlinear time history analyses are performed on single-degree-of-freedom (SDOF) systems with varying natural periods, hysteretic behaviors, and yield strength reduction factors. Based on the computed responses, a regression model is proposed that enables estimation of hysteretic energy demand for specific ground motion durations. The effectiveness of the proposed normalized hysteretic energy spectra considering ground motion duration is validated through comparison with classification-based models, while the overall method based on spectra is further verified using a three-story steel moment-resisting frame. Results show that hysteretic energy demand systematically increases with ground motion duration, and the proposed model effectively captures this relationship across different structural configurations. In addition, the proposed regression model demonstrates good predictive performance, with relative errors generally ranging from approximately 0.11 to 0.16 across different hysteretic models and coefficients of determination exceeding 0.89. This study provides a practical tool for incorporating duration effects into energy-based seismic design and assessment with enhanced accuracy.