Determination of damage location in RC beams using mode shape derivatives

Abstract This paper describes the determination of the location of damage due to single cracks and due to honeycombs in RC beams using mode shape derivatives from modal testing. The cracks were induced by application of point loads at predetermined locations on the RC beams. The load was increased in stages to obtain different crack heights to simulate the extent and severity of damage. Experimental modal analysis was performed on the beams with cracks prior to and after each load cycle, on a control beam, and beams with honeycombs. The mode shapes and the eigenvectors were used to determine the location of damage. The indicator | λ 4 | was obtained by rearranging the equation for free transverse vibration of a uniform beam, and applying the fourth order centered finite-divided difference formula to the regressed mode shape data. The equation is an eigenvalue problem, and the value of | λ 4 | will be a constant. Differences in the values indicate stiffness change, and the affected region indicates the general area of damage. Analysis of results using | λ 4 | was able to indicate the general region of damage, the exact location being around the center of the region. Curve fitting with Chebyshev series rationals onto the mode shape also highlighted points of high residuals around the region of damage. The proposed algorithm on the mode shape can form the basis of a technique for structural health monitoring of damaged reinforced concrete structures.

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