Damage Pattern of Reinforced Concrete Beams Based on the Flexibility Matrix

In this study, the damage patterns of reinforced concrete beams based on the modal flexibility matrices are investigated and discussed. The study is carried out on the experimental modal data of four reinforced concrete beam specimens were gradually damaged until failure state. Two of the specimens were strengthened with externally bonded CFRP sheets when load reached approximately half of the predicted failure load. The damage patterns of the specimens are obtained by the changes of modal flexibility matrices before and after damage. To improve the damage patterns, a new method is proposed based on the flexibility matrices and the Ritz vectors. The consistency of the proposed damage pattern with experimental observations is discussed. The proposed method based on the Ritz vectors agrees well with the state of damage developments in the reinforced concrete beams. The loss of the stiffness along the length of beam specimens and the effectiveness of CFRP strengthening can be estimated by the proposed method.