An Energy-Based Limit Curve for Reinforced Concrete Moment-Resisting Frames with Steel Damper Columns

In the seismic design of reinforced concrete moment-resisting frame (RC MRF) structures equipped with steel damper columns (SDCs), design criteria should consider both peak responses (e.g., story drift) and cumulative responses (e.g., cumulative strain energy of damper panels in SDCs). These response measures are associated with two energy-based seismic intensity parameters: the maximum momentary input energy governing peak responses and the cumulative input energy governing cumulative responses. The relationship between these parameters depends on the characteristics of the ground motions. This study proposes an energy-based limit curve for RC MRFs with SDCs using the two seismic intensity parameters. Incremental critical pseudo-multi impulse analyses (ICPMIAs) are performed for three eight-story RC MRFs with SDCs considering various numbers of pulsive inputs. For each analysis, the input intensity is incrementally increased until predefined limit-state criteria are reached. The limit curve is constructed by connecting the equivalent velocity pairs corresponding to the two energy-based seismic intensity parameters at the limit states. The applicability of the proposed limit curve is examined through nonlinear time-history analyses (NTHAs) using recorded ground motions, including the mainshock–aftershock sequence of the 2011 off the Pacific coast of Tohoku Earthquake and the foreshock–mainshock sequence of the 2016 Kumamoto Earthquake. The results indicate that (a) considering a range of 2 to 32 pulsive inputs in ICPMIA is sufficient to cover the NTHA results examined in this study; (b) most NTHA cases satisfying the limit-state criteria are located within the proposed limit curve, whereas cases exceeding the criteria are located outside the curve; and (c) the consideration of earthquake sequences tends to result in a larger number of cases exceeding the limit-state criteria compared with single-earthquake scenarios.