Damage detection in beam-like structures using deflections obtained by modal flexibility matrices

In bridge structures, damage may induce an additional deflection which may naturally contain essential information about the damage. However, inverse mapping from the damage-induced deflection to the actual damage location and severity is generally complex, particularly for statically indeterminate systems. In this paper, a new load concept, called the positive-bending-inspection-load (PBIL) is proposed to construct a simple inverse mapping from the damage-induced deflection to the actual damage location. A PBIL for an inspection region is defined as a load or a system of loads which guarantees the bending moment to be positive in the inspection region. From the theoretical investigations, it was proven that the damage-induced chord-wise deflection (DI-CD) has the maximum value with the abrupt change in its slope at the damage location under a PBIL. Hence, a novel damage localization method is proposed based on the DI-CD under a PBIL. The procedure may be summarized as: (1) identification of the modal flexibility matrices from acceleration measurements, (2) design for a PBIL for an inspection region of interest in a structure, (3) calculation of the chord-wise deflections for the PBIL using the modal flexibility matrices, and (4) damage localization by finding the location with the maximum DI-CD with the abrupt change in its slope within the inspection region. Procedures from (2)-(4) can be repeated for several inspection regions to cover the whole structure complementarily. Numerical verification studies were carried out on a simply supported beam and a three-span continuous beam model. Experimental verification study was also carried out on a two-span continuous beam structure with a steel box-girder. It was found that the proposed method can identify the damage existence and damage location for small damage cases with narrow cuts at the bottom flange.