Displacement-based seismic design for buildings installed hysteretic dampers with hardening post-yielding stiffness

Passive energy dissipation devices have been proved to be effective and low-cost means of structural control, and a variety of dampers have been developed over the past decades. Hysteretic dampers with hardening post-yielding stiffness have multiphased energy dissipation characteristics because of their hardening behavior, which can compensate for stiffness loss and postpone the collapse of damaged structures. In this article, a hysteretic model is proposed for hysteretic dampers with hardening post-yielding stiffnesses, and a formula is derived for equivalent yield strength expressed by the additional damping of the structure. A procedure is developed for displacement-based seismic design that transforms the relatively complex damping into an acceptable yield strength. A numerical example is only presented for demonstrating the design process and simply validating the proposed method. The results show that the proposed procedure is easy to implement and could produce adequate hysteretic dampers with hardening post-yielding stiffness hardening behavior. The maximum displacement responses of the existing structure retrofitted using the proposed procedure satisfy the expected performance objective well. Thus, this procedure could be an alternative to seismic retrofitting for structures with energy dissipation systems.