Modeling of Fatigue Behavior of RC Beams Strengthened in Shear with Embedded Through-Section FRP Bars

This study presents an analytical investigation of the fatigue shear behavior of reinforced concrete (RC) beams strengthened with embedded through-section (ETS) fiber-reinforced polymer (FRP) bars. The flexural–shear deformation theory previously proposed by the authors is refined to analyze the beam behavior at a given loading cycle. Several fatigue approaches, including a stress‒life (S-N)-based approach, a fracture mechanics–based approach, and mixed models, are developed. The S-N method accounts for fatigue degradation of concrete and steel. Meanwhile, the fracture mechanics approach evaluates stress at shear crack tips and is then developed to incorporate the contributions of transverse steel and ETS-FRP bars by assessing the stress intensity factor. Mixed models couple concrete fatigue damage with dual steel crack growth rules. This study also examines the role of ETS-FRP bars in inhibiting stirrup crack propagation under fatigue. The results showed that the proposed fatigue frameworks accurately predicted the deflection responses of beams under cyclic loading. Computed displacements matched experiments in the initial and stable stages, particularly beams without failure, while beams that failed exhibited log( N f_pred )/log( N f_exp ) ≈ 1.0. Mixed-model formulations captured the rapid deflection increase near failure. Predicted shear reinforcement strains and postfatigue load–deflection behavior of unstrengthened and strengthened beams agreed well with the measurements. The mean predicted-to-experimental remaining shear capacities ranged from 0.80 to 0.85, with coefficients of variation below 30%, demonstrating the models’ reliability and consistency.