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In this paper, a two-stage method for damage detection and estimation in tall shear frames is presented. This method is based on the first mode shape of a shear frame. We demonstrate that the first mode shape slope is very sensitive to the story stiffness. Thus, at the first stage, by using the grey system theory on the first mode shape slope, damage locations are identified in shear frames. Damage severity is determined at the second stage by defining the damage detection problem as an optimization problem by using grey relation coefficients. The optimization problem is solved by a socio-politically motivated global search strategy which is the imperialist competitive algorithm. The efficiency and robustness of the proposed method for the identification and estimation of damages in tall shear frames were studied by using two numerical examples. In addition, the capability of the presented method in real conditions was demonstrated by contaminating of modal data with different levels of random noises. All the obtained results from the numerical studies are shown the good performance of the presented method in the damage localization and quantification of tall buildings.

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