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