Analysis and sizing of RC beams reinforced by external bonding of imperfect functionally graded plate

An analytical method based on the compatibility of deformations and equilibrium of forces is investigated to predict the reinforcement plate area in concrete beams strengthened with Functionally Graded (FG) plates bonded to the tension face of the beams. The models are given for beams having rectangular and T-crosssections. The effect of porosity that can happen inside FGM materials during their manufacture is also shown. New rules of the mixture that take into account different distribution rates of porosity in FG plates have been developed in this study. A parametric study is conducted to investigate the effect of several parameters such as the ultimate moment, plate stiffness, the distribution rate of the porosity, and compressive strength of the concrete. The results obtained show a significant gain in the reinforcement plate area of the RC beam strengthened with an FG plate relative to another reinforced with FRP plate, which makes it possible to reduce the interfacial stresses and prevents detachment of the reinforcing plate.