It is being revealed that occurrence of the Nankai-Trough earthquake might cause significant damage to low-damped super high rise steel buildings in some metropolitan areas in Japan. Addition of supplemental damping devices is effective means to mitigate the damage caused by the great earthquake. However, the seismic effectiveness of dampers connected to a structural frame tends to lose due to overall bending deformation in a slender steel building. On the other hand, a tuned mass damper (TMD) connected to the frame work well even if the overall bending deformation is quite large. The combination of the two kinds of dampers therefore is expected to be effective in slender buildings with a large aspect ratio. However, an optimal design parameter of the TMD mounted on highly damped buildings and its seismic effectiveness are not clarified. The objective of this paper is to develop a design procedure of the two different damping devices. Both the dampers are limited to a linear viscous damper in this study.
Firstly, a lumped mass stick model with shear springs and rotational springs is employed to take account of the overall bending deformation. Two degree of freedom (2-DOF) system is derived from this model with the help of dynamic reduction technique. The 2-DOF system becomes non-proportional damping system. Subsequently, a linear viscous TMD are connected to the 2-DOF system and a 3-DOF system is obtained for the TMD-building interaction system. Optimal design parameters of the TMD are obtained by solving a Lyapunov equation of the 3-DOF system. The optimal stiffness of the TMD is summarized in terms of equivalent damping factor due to only dampers installed into the stories. The computed optimal stiffness is almost consistent with the result of SDOF system with the same equivalent damping factor. This fact admits to use regression formulae of the optimal stiffness proposed by several researchers. It is also confirmed that the optimal parameters obtained by the criterion of minimizing top displacement and story drift is almost the same.
Secondary, equivalent damping factor of the TMD-building interaction system are investigated through stochastic dynamic analysis. As a result, the equivalent damping decreases according to increase of the amount of the dampers within stories. The convenient regression formula is proposed in terms of the equivalent damping factor of the building. The equivalent damping factor is directly evaluated with a slenderness ratio of the building and a damping factor by using the formula.
Finally, a design procedure of the TMD is formulated. Required amount of the TMD mass is proposed based on the concept that the loss of damping factor is equal to the additional equivalent damping factor added by the TMD.
