Reduction of seismic response is one of the most important problems of aseismic design of the structures. When the structures are subjected to excess seismic load, force-displacement relation has hysteresis loop characteristic. In this paper, seismic control of structure using energy absorption by elasto-plastic characteristic is examined by analytical method. As elasto-plastic characteristic, bilinear hysteresis loop is used. The equation of motion is equivalently linearized. The maximum value of the mean square value and absorbed energy are obtained for some values of the damping ratio, the natural period, the yield displacement and the stiffness ratio. It is found that the maximum value of the mean square value of the response decreases with the decrease of the yield displacement and the stiffness ratio. It is also found that the maximum value of the mean square value decreases with the increase of absorbed energy. The proposed method is applied to the secondary system and the same results are obtained.

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