Analytical study of beams strengthened by adhesively bonded reinforcement with variable properties using state space method

This paper uses the state space method to present an analytical solution for beams that are strengthened by externally bonded reinforcement with variable cross-sectional properties. The external reinforcement can be any elastic material, such as fiber-reinforced polymer (FRP) or steel (before yielding), and the variation of the cross-sectional properties of the externally bonded material can be stepped or continuous. Specific interest is directed to the interfacial shear stress and tensile stress of the externally bonded reinforcement, which are important to debonding analyses and the evaluation of strengthening effectiveness but were previously investigated only for externally bonded materials with uniform properties along the span. Solutions for beams under both concentrated and distributed loads are obtained, considering multiple spring supports. Numerical results are presented to evaluate the method and to investigate the interfacial stresses of beams externally bonded by FRP with different types of cross-sections. These results confirm the experimental observations that a tapered section can significantly reduce interfacial shear stress.