Currently, energy dissipation system such as hysteretic dampers and viscous dampers have been used increasingly in new and retrofit constructions. Predictors of seismic structural demands of buildings with energy dissipation systems that are less time-consuming than nonlinear dynamic analysis can be useful for structural performance assessment and for design. In this study, based on Inelastic Modal Predictor (IMP) that Funahashi et al. (2002) have proposed to estimate the seismic demands of general buildings, a predictor of seismic structural demands of a building with hysteretic dampers is proposed.
IMP consists of the square-root-of sum-of-squares rule of modal combination, and taken into account a first-mode inelastic spectral displacement and a post-elastic first-mode shape approximated by the distribution of the story drifts obtained through a nonlinear static pushover analysis (NSPA). However, IMP is not quite applicable as it is to estimate the seismic demands of a building with hysteretic dampers. The assumed tri-linear (or bi-liner) single skeleton curve for the inelastic single-degree-of freedom (SDOF) system equivalent to the multi-story frame may not be appropriate to consider the behavior of dampers, which generally yields sequentially and earlier than the frame. Kang and Mori (2014) have proposed an equivalent inelastic SDOF system with multi-springs (MS model) that can capture well the behavior of the sequential yielding of the dampers.
The IMP with the MS model proposed by Kang and Mori (K&M predictor) can accurately estimate the seismic demand on low-rise buildings. However, it cannot estimate well the demand on mid- and high-rise multi-story frames because of the several problems. This paper discusses the possible improvements of the K&M predictor, and proposes the following three enhancements.
(i) The effective elastic stiffness of the inelastic spring equivalent to the bare frame is evaluated by Eq.(12) so that the natural period of the equivalent SDOF system is equal to the 1st elastic natural period of a multi-story frame with hysteretic dampers,
(ii) A new evaluation method for the higher modal responses is proposed to take into account the change of apparent natural period, mode vector and damping coefficient of a multi-story frame with hysteretic dampers caused by earlier yielding of dampers than the multi-story frame,
(iii) In the original IMP, NSPA is performed with the external load distribution based on the Ai-distribution, which is not quite appropriate to apply to a frame without smooth stiffness distribution. In the K&M predictor, NSPA is performed with the external load distribution proportional to the 1st modal shape to consider the stiffness distribution of multi-story frame with hysteretic dampers; however, there was a tendency to underestimate the response at upper stories. It is proposed in this paper that NSPA be performed with the external load distribution based on the average value of that based on the Ai-distribution and 1st mode distribution.
The accuracy and applicability of the proposed method, along with that of the K&M predictor, is investigated using the results of nonlinear time history analysis on a series of 6-story and 12-story steel moment resisting frames with hysteretic dampers considering a variety of locations and stiffness of the dampers. According to the results, the proposed method has well improved the K&M predictor and can provide sufficiently accurate estimates of the seismic demand for all models.
