Degradation of Energy-Based Limit Curve for Earthquake-Damaged Reinforced Concrete Moment-Resisting Frames with Steel Damper Columns

Reinforced concrete (RC) moment-resisting frames (MRFs) equipped with steel damper columns (SDCs) are damage-tolerant structural systems in which seismic energy is primarily dissipated by the damper panels in the SDCs. An energy-based limit-curve framework using cumulative input energy and maximum momentary input energy was previously developed for these systems, but it was limited to the initial, undamaged state. After prior seismic damage, residual capacity may depend on both peak deformation and cumulative loading history. This study proposes post-damage energy-based limit curves for earthquake-damaged RC MRFs with SDCs. Damaged states are defined using the Extended Critical Pseudo-Multi Impulse Analysis in terms of the peak story drift and the number of pseudo-impulsive lateral forces during the first multi-impulsive input (MI). The results show that the post-damage limit curves lie inside the corresponding initial-state limit curves, with greater degradation for larger peak deformation and more extensive cyclic loading during the first MI. Furthermore, the residual ratios of the post-damage limit curves decrease as the number of pseudo-impulsive lateral forces in the second MI increases. These findings demonstrate that, for the RC MRFs with SDCs examined in this study, post-earthquake residual seismic capacity should be evaluated using an energy-based framework that considers both the damaged state and the subsequent input.