Two models, Model Fiber and Model Rotational Spring (RS), simulating the seismic performance of repaired column-to-cap beam/footing connections using a carbon fiber-reinforced polymer (CFRP) donut are presented in this paper. In Model Fiber, distributed plasticity was assumed over a plastic hinge length of the nonlinear beam-column element. In Model RS, concentrated plasticity was considered using a nonlinear moment rotational spring located at the repaired cross section. Previous concrete damage and low-cycle fatigue of longitudinal steel bars as well as bond-slip between the damaged steel bars and surrounding concrete were included in the proposed numerical models. Numerical simulations show that the results are in good agreement with the experiments in terms of structural response, cumulative hysteretic energy, and moment-rotation capacity. Model Fiber can also predict the local response and low-cycle fatigue of the longitudinal steel bars. Using appropriate pinching parameters, Model RS can model accurate pinching behavior for both the repaired cast-in-place (CIP) and precast concrete specimens.

Through proper arranging of a hybrid combination of longitudinal fiber reinforced polymer (FRP) bars and steel bars in the tensile region of the beam, the advantages of both FRP and steel materials can be sufficiently exploited to enhance the flexural capacity and ductility of a concrete beam. In this paper, a methodology for the flexural strength design of hybrid FRP-steel reinforced concrete (RC) beams is proposed. Firstly, based on the mechanical features of reinforcement and concrete and according to the latest codified provisions of longitudinal reinforcement conditions to ensure ductility level, the design-oriented allowable ranges of reinforcement ratio corresponding to three common flexural failure modes are specified. Subsequently, the calculation approach of nominal flexural strength of hybrid FRP-steel RC beams is established following the fundamental principles of equilibrium and compatibility. In addition to the common moderately-reinforced beams, the proposed general calculation approach is also applicable to lightly-reinforced beams and heavily-reinforced beams, which are widely used but rarely studied. Furthermore, the calculation process is properly simplified and the calculation accuracy is validated by the experimental results of hybrid FRP-steel RC beams in the literature. Finally, with the ductility analysis, a novel strength reduction factor represented by net tensile steel strain and reinforcement ratio is proposed for hybrid FRP-steel RC beams.

End concrete cover separation is one of the most common failure modes for RC beams strengthened with external FRP reinforcement. The premature failure mode significantly restricts the application of FRP materials and could incur serious safety problems. In this paper, an innovative stress field-based analytical approach is proposed to assess the failure strength of end concrete cover separation and the conventional plane-section analysis is extended to evaluate the corresponding carrying capacity of FRP-strengthened RC beams. First, the dowel action of reinforcement and the induced concrete splitting, reflecting the interaction between concrete, steel and FRP, are considered in establishing the geometrical relationships of stress field for cracked concrete block. Then, the cracking angle and innovative failure criterion, considering the arrangement of steel and FRP reinforcement and cracking status of concrete and its softening effect, are derived to predict the occurrence of concrete cover separation and related mixed modes of debonding failure. Subsequently, an extended sectional analytical approach, in which the components of effective tensile strain of FRP resulted from flexural and shear actions are both considered, is presented to evaluate the carrying capacity of strengthened beams. Finally, the proposed calculational model is effectively validated by experimental results available in the literature.