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A two-stage method is proposed to properly identify the location and the extent of damage in shear frames. In the first stage, a story displacement index (SDI) is presented to precisely locate the damage in the shear frame which is calculated using the modal analysis information of the damaged structure. In the second stage, by defining a new objective function, the extent of the actual damage is determined via an imperialist competitive algorithm. The performance of the proposed method is demonstrated by implementing the technique to three examples containing five-, ten-, and twenty-five-story shear frames with  noises and without them in modal data. Moreover, the performance of the proposed method has been verified through using a benchmark problem. Numerical results show the high efficiency of the proposed method for accurately identifying the location and the extent of structural damage in shear frames

A Two-Stage Method for Structural Damage Prognosis in Shear Frames Based on Story Displacement Index and Modal Residual Force