Gluck et al. [4] presented an optimal control theory for viscous dampers' properties selection. The main difficulty of this solution is that it requires different levels of damping at each story, which can be expensive and inconvenient. Ribakov et al. [5,6] proposed a method for design of structures with viscous dampers using mechanical levers and amplifying devices. Constantinou et al. [3] presented other configurations of energy dissipating devices, based on a toggle-brace mechanism, and on a scissors-jack system [2].

The amplifying techniques result in device displacements and velocities that are larger than the structural drifts and drift velocities. Thus, the energy that needs to be dissipated by the damping system can be obtained with significantly reduced damping forces, requiring dampers with lower damping coefficients. In other words, less damping units are required and the cost of the damping system reduces. Furthermore, common damper connections to Chevron or diagonal braces use the spaces in the bays where they are installed, and using less damping units increases the number of open bays.

A simplified technique proposed for optimal design of viscous damped structures with amplifiers [6] assumes that small displacements and velocities, are transferred to the damper, and neglects their squared (second-order) values. This simplified algorithm is suitable for relatively small amplifying ratios, small drifts and small drift velocities. For these conditions it results in a structural response that is close to the optimal one. However, a structure designed according to this method with large amplifying ratios or under large drifts and drift velocities would not necessarily have this response. An alternative algorithm, which is more suitable for cases of relatively large amplifying ratios and large drifts induced by strong earthquakes, is proposed in this study. This method takes into account more accurate values of the damper displacements and velocities and hence it is also suitable and more effective for cases of relatively large amplifying ratios and large drifts.

A numerical example of an eight-story reinforced concrete frame was carried out in order to investigate the proposed method. The results show that the proposed algorithm yields under relatively strong earthquakes a structural response superior to that of the simplified algorithm, and closer to that of the optimally designed one.

The top floor peak displacements obtained with the proposed method are significantly reduced compared to the uncontrolled structure, whereas for the simplified method these reductions are relatively moderate. This result is more pronounced under earthquakes of higher peak ground accelerations. Furthermore, in certain cases the simplified method yields story displacements that are larger than those of the uncontrolled structure.

Structures with limited number of damping devices have the additional advantage of fewer obstructions per story. Hence dampers should be connected to high efficiency amplifiers with large amplifying ratios, in which case the dampers should be designed according to the proposed method.

1

M.C. Constantinou, M.D. Symans, P. Tsopelas, D.P. Taylor "Fluid Viscous Damping in Applications of Seismic Energy Dissipation and Seismic Isolation". ATC-17-1, Applied Technology Council, San Francisco, 1993.

2

M.C. Constantinou, A.N. Sigaher "Energy Dissipation System Configurations for Improved Performance", Advanced Techniques in Structural Engineering: Proceedings of the 2000 Structures Congress & Exposition, ASCE, May 2000, Philadelphia, U.S.A, 2000. doi:10.1061/40492(2000)117

3

M.C. Constantinou, P. Tsopetas, W. Hammet, A.N. Sigaher "Toggle-Brace-Damper Seismic Energy Dissipation Systems", ASCE Journal of Structural Engineering, 127 (2), pp. 105-112, 2001. doi:10.1061/(ASCE)0733-9445(2001)127:2(105)

4

N. Gluck, A .M. Reinhorn, J. Gluck, R. Levy "Design of supplemental dampers for control of structures", ASCE Journal of Structural Engineering, 122(12), 1394-1399, 1996. doi:10.1061/(ASCE)0733-9445(1996)122:12(1394)

5

Y. Ribakov, J. Gluck, N. Gluck "Practical Design of MDOF Structures with Supplemental Viscous Dampers Using Mechanical Levers". ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability, Notre Dame, U.S.A., July 24-26, Paper No 2000-005, 2000.

6

Y. Ribakov, A.N. Dancygier, J. Gluck "Amplifying Devices for Application of Standard Viscous Dampers in Optimal Seismic Design of MDOF Structures", European Earthquake Engineering, XV (3), 2001.

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