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A steel damper column is an energy-dissipating member that is suitable for reinforced concrete (RC) buildings and multistory housing. To assess the seismic performance of buildings with steel damper columns, the peak displacement of the whole building and the energy dissipation demand of the dampers must be evaluated. This article proposes an energy-based prediction procedure for the peak and cumulative response of an RC frame building with steel damper columns. The proposed procedure considers two energy-related seismic intensity parameters, namely the maximum momentary input energy and the total input energy. The peak displacement is predicted considering the energy balance during a half cycle of the structural response, using the maximum momentary input energy. The energy dissipation demand of the dampers is then predicted considering the energy balance during a whole response cycle using the total input energy. The local responses (e.g., peak drift, maximum plastic rotation of beams, maximum shear strain, and energy dissipation demand of dampers) are predicted using pushover analysis. Numerical analysis results for 8- and 16-story RC buildings show that the proposed prediction method achieves satisfactory accuracy.

There was an error in the original publication [...]

The steel damper column is an energy-dissipating member that is suitable for reinforced concrete (RC) buildings and those used for multistory housing in particular. However, the effectiveness of steel damper columns may be affected by the behavior of surrounding members, and this effect can be severe in the case of seismic sequences. This article investigates the nonlinear response of building models with an RC moment-resisting frame (MRF) with and without steel damper columns under seismic sequences. The applicability of the concept of the momentary energy input to the prediction of the peak response of RC MRFs with damper columns under seismic sequences is also investigated. The main findings of the study are summarized as follows. (1) The peak response of RC MRFs with damper columns subjected to sequential accelerations is similar to the peak response obtained considering only the mainshock, whereas the cumulative strain energy of RC MRFs accumulates more for sequential accelerations. (2) The steel damper column is effective in reducing the peak and cumulative responses of RC MRFs in the case of sequential seismic input. (3) The relation of the hysteretic dissipated energy during a half cycle of the structural response and the peak displacement of the first modal response can be properly evaluated using the simple model proposed in this study.

In this article, the applicability of mode-adaptive bidirectional pushover analysis (MABPA) to base-isolated irregular buildings was evaluated. The point of the updated MABPA is that the peaks of the first and second modal responses are predicted considering the energy balance during a half cycle of the structural response. In the numerical examples, the main building of the former Uto City Hall, which was severely damaged in the 2016 Kumamoto earthquake, was investigated as a case study for the retrofitting of an irregular reinforced concrete building using the base-isolation technique. The comparisons between the predicted peak response by MABPA and nonlinear time-history analysis results showed that the peak relative displacement can be properly predicted by MABPA. The results also showed that the performance of the retrofitted building models was satisfactory for the ground motion considered in this study, including the recorded motions in the 2016 Kumamoto earthquake.

The test results obtained for reinforced concrete columns by several studies have revealed that the peak displacement and cumulative hysteresis energy are important parameters for evaluating the damage of columns under horizontal bidirectional and unidirectional loading. Therefore, the seismic parameters related to the nonlinear peak displacement and cumulative hysteresis energy with regard to horizontal bidirectional seismic input should be investigated. In this study, the bidirectional seismic input to an isotropic nonlinear one-mass two-degree-of-freedom system was evaluated. First, a dimensionless parameter γ, which controls the low-cycle fatigue effect, was formulated as a function of two energy input parameters (the maximum momentary input energy and total input energy) and a nonlinear system (ductility and normalized hysteresis energy absorption during a half cycle). Then, the maximum momentary input energy and total input energy were evaluated according to the ground motion characteristics (Fourier coefficient of horizontal ground motion components) and system properties. Finally, the nonlinear peak displacement and parameter γ of the nonlinear system were evaluated on the basis of the maximum momentary input energy and total input energy. The results revealed that the nonlinear peak displacement and parameter γ can be properly evaluated using two energy parameters.

The evaluation of the maximum and cumulative response is an important issue for the seismic design of new base-isolated buildings. This study predicts the maximum and cumulative response of a 14-story reinforced concrete base-isolated building using a set of pushover analyses. In the proposed pushover analysis method, the maximum and cumulative responses of the first and higher modes are evaluated from the nonlinear analysis of equivalent single-degree-of-freedom (SDOF) models. Then, the maximum local responses are predicted by enveloping the two pushover analysis results by referring to the contribution of the first and higher modal responses, while the cumulative strain energies of the lead-rubber bearings and steel dampers are predicted from the cumulative response of the first mode. The results reveal that the responses predicted by the proposed set of pushover analyses have satisfactory accuracy.

It is very unfortunate that there are some errors in the nonlinear analysis program used for this published article [...]

It is essential for the seismic design of a base-isolated building that the seismic response of the superstructure remains within the elastic range. The evaluation of the maximum seismic member force in a superstructure is thus an important issue. The present study predicts the maximum seismic member force of five- and fourteen-story reinforced concrete base-isolated frame buildings adopting pushover analysis. In the first stage of the study, the nonlinear dynamic (time-history) analysis of the base-isolated frame buildings is carried out, and the nonlinear modal responses of the first and second modes are calculated from pushover analysis results. In the second stage, a set of pushover analyses is proposed considering the combination of the first and second modal responses, and predicted maximum member forces are compared with the nonlinear time-history analysis results. Results show that the maximum member forces predicted in the proposed set of pushover analyses are satisfactorily accurate, while the results predicted considering only the first mode are inaccurate.

The seismic capacity of the main Uto City Hall building, which was severely damaged by the 2016 Kumamoto Earthquake, was evaluated by the proposed pushover-based procedure. In this procedure, the seismic capacity index of the building is defined as the maximum scaling factor of the seismic input, for which the local responses do not exceed their limit values. From the pushover analysis result, the displacement limit of the equivalent single-degree-of-freedom model was determined. Then, the seismic capacity index was evaluated using an equivalent linearization technique. The evaluated index was re-evaluated by considering the bidirectional excitation. The pushover analysis result revealed that the torsional response is significant in the nonlinear behavior of this building. The evaluated seismic capacity implied that some structural damages, including the yielding of the beam-column joint, may have occurred during the first earthquake on 14 April 2016.