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In this paper, a simplified method for estimating the seismic structural demands of a building with hysteretic dampers is proposed by extending IMP, which considers the first-mode inelastic spectral displacement and the post-elastic first-mode shape in SRSS rule of modal combination. Dampers generally yields sequentially and earlier than the frame, and such behavior is considered by a multi-spring model for the first modal response and by the equivalent stiffness and damping factors for the higher modal responses. An appropriate external force distribution for a nonlinear static pushover analysis is also proposed to appropriately estimate the post-elastic first-mode shape.

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By yielding under small inter-story deformation, hysteretic dampers installed to a response control structure absorb seismic energy and effectively control the damage to the frame. When designing such a structure, it is important to estimate the maximum deformation and the cumulative plastic deformation of the dampers against ground motions. Especially in the early stage of design, simple methods are useful for the preliminary study of determining the characteristics of the dampers. In this research, the shortcomings of the existing simple methods are discussed and a new method is proposed. Its accuracy and applicability are investigated using numerical examples.

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