Abstract
본 연구는 Modal Pushover Analysis(MPA)를 기반으로 비탄성 변위비(inelastic displacement ratio, <TEX>$C_R$</TEX>)와 붕괴 강도비(collapse strength ratio, <TEX>$R_C$</TEX>)를 이용한 간략한 Incremental Dynamic Analysis (IDA) 해석법을 제안해 냈다. 이 해석법은 선형 또는 비선형 동적해석 수행 없이 다자유도 시스템의 응답을 계산하기 때문에 간단하게 IDA곡선을 얻을 수 있다. 제안한 방법의 정확성은 6층, 9층, 20층의 철골 모멘트 골조를 대상으로 44개의 지진데이터를 사용하였으며 본 연구에서 제안하는 MPA를 이용한 <TEX>$C_R-R_C$</TEX> IDA 해석결과와 비선형 동적해석 (Nonlinear Response History Analysis)을 통한 IDA 응답값, 그리고 각 주요모드의 비선형 동적해석을 통한 MPA-IDA 응답 값을 비교하여 타당성을 확인하였다. MPA를 이용한 <TEX>$C_R-R_C$</TEX> IDA 해석법은 반복된 비선형 동적해석 과정이 없기 때문에 계산시 소요시간이 가장 작았으며 비교적 정확한 결과를 나타냈다. This study develops an approximate procedure for incremental dynamic analysis (IDA) using modal pushover analysis (MPA) with empirical equations of the inelastic displacement ratio (<TEX>$C_R$</TEX>) and the collapse strength ratio (<TEX>$R_C$</TEX>). By using this procedure, it is not required to conduct linear or nonlinear response history analyses of multi- or single- degree of freedom (MDF) systems. Thus, IDA curves can be effortlessly obtained. For verification of the proposed procedure, the 6-, 9- and 20-story steel moment frames are tested under an ensemble of 44 ground motions. The results show that the MPA-based IDA with empirical equations of <TEX>$C_R$</TEX> and <TEX>$R_C$</TEX> produced accurate IDA curves of the MDF systems. The computing time is almost negligible compared to the exact IDA using repeated nonlinear response history analysis (RHA) of a structure and the original MPA-based IDA using repeated nonlinear RHA of modal SDF systems.
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