## 1 Introduction  
Reinforced concrete (RC) structures such as highways and railway bridges are subject to harsh working environments, where steel bars are prone to corrosion and will be subject to high-cycle fatigue loading. To avoid accidents, it is necessary to inspect and strengthen these structures. Carbon fiber reinforced polymer (CFRP) is often used to strengthen RC structures such as bridges due to its advantages such as light weight, high strength, fatigue resistance and corrosion resistance [1]. Currently, many studies have been conducted on the flexural behavior and strengthening effect of CFRP-strengthened corroded RC beams under static load. [PERSON] [2] and [PERSON] [3] repaired corroded RC beams using different strengthening schemes and found that the strength of the corroded beams was restored to an uncorroded state after CFRP strengthening and the ultimate deflection of the strengthened beams was less than the ultimate deflection of the unstrengthened beams. [PERSON] et al. [4] determined four equilibrium damage and five damage modes based on the stress states of concrete, corroded steel bars and CFRP plates during bending damage of beams and proposed a simplified calculation method for the bending load capacity of corroded RC beams reinforced with CFRP plates under each failure mode, which proved the validity of the proposed calculation method through the verification of experimental data. [PERSON] et al. [5] studied FRP-strengthenedcorroded RC beams through nonlinear finite element analysis, and the results showed that the interface properties between FRP and concrete were crucial for accurately predicting the bearing capacity and failure modes of the strengthened beams. [PERSON] et al. [6] numerically modeled CFRP-strengthened corroded RC beams using the finite element method to predict the flexural load capacity of the strengthened beams, and the results showed that the predicted residual load capacity was in good agreement with the experimental results. In contrast, there are limited studies related to CFRP-strengthened corroded RC beams under fatigue loading. [PERSON] et al. [7] conducted fatigue tests on CFRP-strengthened corroded RC beams and found that the fatigue strength of the steel bars was reduced due to corrosion and all the tested beams were damaged by fatigue damage of the tensile steel bars. [PERSON] et al. [8] found through experimental studies that the flexural fatigue performance of moderately corroded beams strengthened with CFRP could be improved to the level of uncorroded beams, and the flexural fatigue performance of heavily corroded strengthened beams were somewhat improved but could not reach the level of uncorroded beams. [PERSON] et al. [9] proposed a fatigue evaluation model for prestressed CFRP-strengthened corroded RC beams, which was used to evaluate the damage mode, fatigue life, fatigue strength and post-fatigue ultimate load capacity of prestressed CFRP-strengthened corroded RC beams, and showed that the reinforcement design factors for corroded RC beams under cyclic fatigue loading are in the order of stiffness, fatigue life, fatigue strength and ultimate load capacity. [PERSON] et al. [10] studied the flexural behavior of prestressed CFRP-strengthened corroded RC beams through experiments, and the experimental results showed that the coupling effect of corrosion and cyclic loading significantly reduced the flexural stiffness of the strengthened beams but had little effect on the ultimate load of the strengthened beams, indicating the effectiveness of the prestressed reinforcement system. It can be seen that most scholars' research on CFRP-strengthened corroded RC beams under fatigue loading mainly focuses on the experimental study of their flexural performance, while in actual engineering, the deformation of the structure also needs to be verified via calculation in order to meet the normal function of the structure.