It is necessary to consider providing damping performance only for the effective deformation when modeling passive control devices in a multi-degree-of-freedom model. In this study, we proposed a method to replace the dashpot with a spring of appropriate stiffness. As a result, the responses of the multi-degree-of-freedom model and the three-dimensional frame model exactly matched. Furthermore, we investigated the effective stiffness that maximizes the cost-effectiveness of a passive controlled building. It was shown that the structure can be economically designed by not exceeding a certain stiffness.
