Damaged Flexibility Matrix Method for Damage Detection of Frame Buildings

This study presents the damaged flexibility matrix method (DFM) to identify and determine the magnitude of damage in structural elements of plane frame buildings. Damage is expressed as the increment in flexibility along the damaged structural element. This method uses a new approach to assemble the flexibility matrix of the structure through an iterative process, and it adjusts the eigenvalues of the damaged flexibility matrices of each system element. The DFM was calibrated using numerical models of plane frames of buildings studied by other authors. The advantage of the DFM, with respect to other flexibility-based methods, is that DFM minimizes the adverse effect of modal truncation. The DFM demonstrated excellent accuracy with complete modal information, even when it was applied to a more realistic scenario, considering frequencies and modal shapes measured from the recorded accelerations of buildings stories. The DFM also presents a new approach to simulate the effects of noise by perturbing matrices of flexibilities. This approach can be useful for research on realistic damage detection. The combined effects of incomplete modal information and noise were studied in a ten-story four-bay building model taken from the literature. The ability of the DFM to assess structural damage was corroborated. Application of the proposed method to a ten-story four-bay building model demonstrates its efficiency to identify the flexibility increment in damaged structural elements.

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