Closed-Form High-Order Analysis of RC Beams Strengthened with FRP Strips

A closed-form high-order analytical solution for the analysis of concrete beams strengthened with externally bonded fiber-reinforced plastic (FRP) strips is presented. The model is based on equilibrium and deformations compatibility requirements in and between all parts of the strengthened beam, i.e., the concrete beam, the FRP strip, and the adhesive layer. The governing equations representing the behavior of the strengthened beam, along with the appropriate boundary and the continuity conditions, are derived and solved with closed-form analytical solutions. Comparison of the closed-form high-order model with other simplified approaches, based on one- and two-parameter elastic foundation concepts, is included. It is shown that the current high-order model can be reduced, by omitting the appropriate terms, to the simplified theories. A numerical example of a typical RC beam strengthened with an externally bonded FRP strip is discussed with emphasis on the shear and peeling stress distributions at the edge of the FRP strip. Stress analysis results concerning the edge stresses determined by the high-order model are compared with those determined by the elastic foundation models and finite elements. Finally, a parametric study that characterizes the main parameters governing the magnitude and intensity of the edge stresses is performed. The paper is concluded with a summary and recommendations for the design of the strengthened beam.