Simple general solution for interfacial stresses in plated beams

The flexural strength of a reinforced concrete, metallic or timber beam can be increased by bonding a thin plate, made of steel or fiber-reinforced polymer, to its tension face. A main failure mode of such plated beams involves debonding of the plate end from the beam and such plate-end debonding depends strongly on the interfacial stresses between the beam and the plate. Consequently, many analytical solutions have been developed for the interfacial stresses of specific plated beam problems, with almost all of them being for simply supported plated straight beams of constant section subjected to simple loadings. The existing analytical solutions are therefore neither general enough nor simple enough for direct exploitation in assessing the risk of plate-end debonding failure. This paper corrects this deficiency by presenting a simple, accurate yet general solution for interfacial stresses. The solution is applicable to plated beams of all geometric (e.g., curved beams), sectional (e.g., tapered beams), loading (e.g., a linearly varying distributed load), and boundary conditions (e.g., continuous beams). The accuracy of the solution is demonstrated through comparisons with finite element results. The paper also presents simple and accurate approximations for the peak values of interfacial shear and normal stresses at the plate end. In these approximate expressions, only the sectional forces and properties of the plate end section are involved, which greatly facilitates their direct exploitation in predicting debonding failure.