Toughness of cracked concrete beams post-strengthened with FRP

In this research, a theoretical method to predict the toughness or fracture resistance of a cracked concrete beam with rectangular cross section post-strengthened with FRP sheets and subjected to an external loading system of three-point bending is developed. The unidirectional FRP sheets are laid out near the bottom surface of the tensile zone (Fig. 1) of the cracked beam. The loading capacity of such an FRP reinforced concrete structure has been investigated in a separate paper, in which some of the formulations and results can be referenced in the current analysis. The research is based on the consideration of the constitutive relations and deformation properties of individual constituents, i.e., plain concrete and FRP sheets. From the global equilibrium of the cracked cross-section, the change of the fracture resistance of the beam against crack depth is determined. A fictitious crack approach which has been used previously in conjunction with finite element method in the fracture analysis of concrete is adopted here to estimate the equivalent bridge effect of the fracture process zone (FPZ) of the concrete. During the modelling analysis it is assumed that there is no interface slip between FRP and the concrete. Numerical result demonstrates that the FPZ, the stiffness of FRP as well as some geometric parameters (initial crack length for example), all play an important role in the analysis of fracture resistance of the beam. Large FPZ is more effective to increase the resistance behaviour of the beam.