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In recent years some multi-mode pushover procedures taking into account higher mode effects, have been proposed. The responses of considered modes are combined by the quadratic combination rules, while using the elastic modal combination rules in the inelastic phases is not valid. Here, an optimum weighted mode combination method for nonlinear static analysis is presented. Genetic algorithm is used for optimization of the modal weight. The proposed procedure is applied for a sample building. The results show that the resulted response from the proposed method has minimal error in comparison with the response of the nonlinear time history analysis.

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In this paper, optimal design of hybrid low damping base isolation and magnetorheological (MR) damper has been studied. Optimal hybrid base isolation system has been designed to minimize the maximum base drift of low damping base isolation system where for solving the optimization problem, genetic algorithm (GA) has been used. In design procedure the maximum acceleration of the structure has been limited, too. To determine the volatge of semi-active MR damper the H2/LQG and clipped-optimal control algorithm has been applied. For numerical simulations, a three-story frame equipped with the hybrid base isolation and MR damper subjected to the scaled El Centro excitation and optimal hybrid system has been designed. Results of numerical simulations have proven the effectiveness of the optimal hybrid control system in controlling the maximum base drift of isolated structure. Also comparing the performance of hybrid, low and high damping base isolation systems has shown that adding MR damper to low damping base isolation system has improved its performance so that the hybrid system has worked better th an high damping base isolation in reducing the maximum base drift. Testing optimal hybrid control system under different excitations has shown its efficiency.