7. Utilizing Rayleigh–Ritz Technique to Identify Damages of Multi Span Beams

In this paper, a novel technique for identifying the location and the severity of damage in multi-spans beams and “beam and column” is proposed, which has an ability to reveal the structural damage with any type of support conditions. The proposed method is an expanded version of the finite element method (FE) by the assistance of the Ritz method which is called Ritz Damage Detection Method (RDDM). The innovation of the proposed method in this paper is the omission of some limitations of the RDDM method, including unique support conditions, and applying the effects of “beam and column”. In this paper, by using the shape function, the definition of support conditions as a spring, and entering the interaction effect of “beam and column”, the equations of RDDM method are developed to provide possible damage detection of the bridges with all support conditions. Also, singular value decomposition (SVD) method is used to determine the quantity and the severity of the damage, which is sensitive to dynamic characteristics changes, originated from the damage. The efficiency and capability of the proposed method for damage detection are evaluated by a numerical sample of “a multi-span beam” and “beam to column connections. The investigation results showed that the proposed damage detection method has the ability to identify the location and the severity of the damages.