Ductile Design of Reinforced Concrete Beams Retrofitted with Fiber Reinforced Polymer Plates

For reinforced concrete beams retrofitted with fiber-reinforced polymer (FRP) plates, an analytical method is derived for determining the allowable plate area to achieve a targeted value of ductility. Nonlinear models for concrete and reinforcement are applied, and the effects of concrete confinement and spalling and of FRP plate rupture are considered. The derivation of equilibrium and compatibility equations for a rectangular cross section is presented, and the solution to the nonlinear equation for determining the allowable plate area is demonstrated with examples. Analytical results are compared with numerical and experimental data reported in the literature. Subsequently a simplified version of the method is derived, based on regression analysis, to relate the curvature ductility to the FRP plate ratio. It is noted that additional conditions need to be checked to ensure ductile performance, such as local failure of the concrete layer between tension reinforcement and FRP plate or debonding of the plate itself.