Ground motions with increasingly large amplitudes have been recommended in a seismic design of super high-rise buildings for long-period ground motion in recent years. Increasing the number of dampers is an effective way to reduce story drift. An Excessively large amount of steel dampers in passively controlled buildings, however, potentially amplify floor acceleration in the small range of ductility factor. In order to overcome the trade-off relationship, this paper proposes the combination of a tuned mass damper and steel-type story damper to reduce both story drift and floor accretion in a wide range of seismic intensity.
A moment resisting frame with nonlinear steel dampers is modeled as an SDOF system. A linear tuned mass damper (TMD) mounted on the rooftop are considered. A Bouc-Wen model is employed to represent hysteresis of the steel dampers. A Fokker-Planck equation is derived with respect to the 2-DOF model consisting of the building and the TMD. Stochastic time history analysis is conducted based on the statistical linearization in terms of two parameters. One is a stiffness ratio which is post-yield stiffness to the initial stiffness of the SDOF. The other is a ductility factor of the steel dampers.
Firstly, optimal stiffness and damping ratio of the TMD is numerically estimated by solving nonlinear programming problem. The objective function is either inter-story drift or floor acceleration. It is confirmed that the optimal tuning ratio minimizing the story drift is approximately calculated in the followings concept without time history analysis. In the optimal tuning ratio, an initial natural frequency of the building is replaced by equivalent frequency computed by the scant stiffness corresponding to the peak story drift. An evaluation method of the optimal tuning ratio minimizing floor acceleration is also developed in a similar manner, provided that the corresponding story drift is slightly modified. This modification reflects the empirical fact that the optimal tuning ratio is almost unchanged from its initial value up to certain nonlinearity.
Secondary, the seismic effectiveness of the TMD is summarized in terms of the stiffness ratio and the ductility factor. A practical evaluation method of the seismic effectiveness of the TMD is proposed based on the linear stochastic vibration theory. The predicted response show excellent agreement with the response obtained by the Fokker-Planck equation.
Finally, peak deformation of the TMD is discussed. Peak displacement of the TMD to the floor displacement gradually decreases in association with the development of yielding in the steel damper. This is well explained by de-tuning phenomenon accompanied with elongation of an equivalent natural period of the SDOF system. As a result, large amplitude of the TMD is avoidable during strong ground motions. This is one of the advantages of the proposed passively controlled system.
