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Semi-active control of buildings and structures with magnetorheological (MR) dampers for earthquake hazard mitigation represents a relatively new research area. In this paper, the Bingham model of MR damper is introduced, and the formula relating the yielding shear stress and the control current of MR dampers is put forward that matches the experimental data. Then an on-line real-time control method for semi-active control of structures with MR dampers is proposed. This method considers the time-delay problem of semi-active control, which can solve distortion of the responses of structures. Finally, through a numerical example of a three-storey reinforced concrete structure, a comparison is made between controlled structure and uncontrolled structure. The calculated results show that MR dampers can reduce the seismic responses of structures effectively. Moreover, the on-line real-time control method is compared with the traditional elastoplastic time-history analysis method, and the efficacy of the on-line real-time control method is demonstrated. In addition, the Levenberg-Marquardt algorithm is used to train the on-line control neural network, and studies show that the algorithm has a very fast convergence rate.

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