A closed-form solution of the interfacial stresses and strains in steel beams strengthened with externally bonded plates using ductile adhesives

Ductile adhesives are known to be beneficial in enhancing the capacity and ductility of bonded joints. However, there is a lack of closed-form analytical solutions for plated metallic beams that account for adhesive plasticity. This paper presents a first order, elastic-plastic bond analysis for beams strengthened with externally bonded fiber reinforced polymer (FRP) plates using ductile adhesives, based on a shear-lag formulation. This model is able to analyze arbitrary mechanical and thermal loading conditions and closed-form solutions under shearing and peeling are given. Following a review of the existing stress-based analytical solutions, a comparison between the existing and proposed analyses is also presented. The shear solution was validated by comparing with the experimental results of carbon fiber reinforced polymer (CFRP) strengthened steel beams under moderately elevated temperatures. A comprehensive parametric study has been conducted to illustrate the effects of different design parameters on the bond behavior. It is found that the adhesive shear toughness is the most critical parameter in determining the debonding failure load while the adhesive Young's modulus does not significantly affect the bond stresses in the elastic-plastic regime. Further, the magnitude of the peak peeling stresses is self-limiting after shear yielding, and the use of a thinner plate with higher Young's modulus is beneficial in further reducing the peeling stress.