Keywords: self-variable stiffness, active variable damping, optimal control, reinforced concrete structures, seismic design.

A Reinforced Concrete (RC) fully braced frame changes its stiffness and adapts its properties in order to provide an optimal seismic response [2]. The frame regulates its behavior, attenuating the seismic response through autonomous disengagement of its concrete braces in tension. The advantage of concrete non-linearity in compression is also taken into account. The system has several levels of seismic regulation and a suitable one is selected for optimal response to a given earthquake.

The bracing system adopts the optimal state of the RC structure. As a result energy dissipation is increased and the seismic forces are reduced accordingly. It yields a higher seismic resistance of the structure [2,3]. If, however, the estimated seismic resistance is still not enough for a given seismic region, then an artificial variable stiffness system [4] or other energy dissipation systems, based on active or semi-active control [6] should be used.

A monolithic RC six-story two bays frame with flat-slab floors is examined. Each story has diagonal braces in both bays. The braces are reinforced in their middle part against the bending moment due to the dead load and include the constructive reinforcement only in their main part near the joints. The additional brace reinforcement carries the tensile force in the cracked stage.

The diagonal braces are designed to withstand axial tension and compression forces. Under tensile forces a brace cracks and, in the absence of reinforcement, would yield unilateral disengagement. Upon reversal of the vibration force, the cracks close and the brace is re-engaged in compression.

The structural response to real earthquakes was obtained using the ETABS [1]. The analysis shows that the optimal scheme is the "threshold" case, after which the shear deformations are stabilized and the bending ones increase. The mutual stories' displacement increases steeply after the optimal scheme. For this scheme the counteractive effect of the static loading reaches maximum. All the above-mentioned factors yield a significant reduction of the seismic forces. As a result, the next brace may remain engaged, indicating that the structure has adapted to the given earthquake, and it corresponds to an optimal scheme.

Structures with self-variable stiffness adapt themselves to an earthquake and choose an optimal scheme yielding an improved structural response. However, if an earthquake is strong enough, all the braces of the RC structure may be destroyed during their action under compression, the structure will become unbraced, and it should be repaired after an earthquake in order to make it safe for further seismic events.

Installation of an active or a semi-active damper as a part of a diagonal brace enables to avoid collapse of the brace in compression. It may save the costs required for repairing the structure after each strong earthquake. The forces applied by the dampers in each floor can be adjusted according to an optimal control theory [5], and the structural response will be further improved. Additionally, the forces in the dampers should not exceed the braces bearing capacity in compression.

By analysing the building's response during an earthquake, optimal forces at every structural level are obtained at each time increment. These forces are applied to the structure by the dampers and provide an optimal structural response to earthquakes, which is significantly improved compared to that of a structure without dampers.

1

ETABS, "The Three-Dimensional Analysis of Building Systems, User Manual", Computers & Structures Inc., Berkeley, California, U.S.A., 1990.

2

I. Iskhakov, "Study of Self Variable Stiffness System - Optimal Seismic Response with Concrete Braces", Proceedings of the International Symposium on Earthquake Engineering, Montenegro, 161-168, 2000.

3

T. Kobori, M. Takahashi, T. Nasu, N. Niwa, N. Kurata, J. Hirai, and K. Ogasawara. "Shaking Table Experiment and Practical Application of Active Variable Stiffness System", Proceedings of the 2nd Conference on Tall Buildings in Seismic Regions 55th Regional Conference; Los Angeles, California, 213-222, 1991.

4

T. Kobori and S. Kamagata. "Dynamic Intelligent Buildings - Active Seismic Response Control", Intelligent Structures 2, Monitoring and Control, Elsevier Applied Science, New York, 279-282, 1992.

5

T.T. Soong. "Active Structural Control: Theory and Practice", John Wiley & Sons, Inc., NY, 1990.

6

Y. Ribakov and J. Gluck. "Active Controlled Friction Damped MDOF Structure with Variable Stiffness", 8th Canadian Conference on Earthquake Engineering, Vancouver. Canada, 409-414, 1999.

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