Closed-form model for curved brittle substrates reinforced with FRP strips

Externally bonded Fiber Reinforced Polymer (FRP) strips have been proved to be effective for strengthening masonry structures. The role played by the bond between composite and substrate is crucial for transferring tensile stresses from masonry to the reinforcing system, thus has become the object of extensive investigation. When the reinforced components are curved, such as arches and vaults, which appear quite commonly in masonry buildings, the influence of the substrate curvature on the bonding cannot be ignored. The debonding mechanism can be studied with a concise model in which the substrate is rigid and the FRP plate is elastic, and the interface where the two are bonded is assumed to lump all the nonlinearities. In this paper, a fully analytical approach for FRP strengthened curved masonry prisms is proposed based on this model, providing closed-form solutions for different geometrical configurations. The interface cohesive law is assumed to be piecewise linear with elastic, softening and residual strength stages. The influence of the normal stress appearing at the interface due to the substrate curvature is considered in the cohesive law for both extrados and intrados strengthening cases. An extensive validation carried out considering both existing experimental results and alternative numerical approaches indicates that the procedure proposed is able to accurately predict the bond strength as well as to reproduce the global bond behavior, requiring few parameters and little calculation effort.