## 1 Introduction
[19] built an analytical framework regarding the strength of a uniaxial short column considering the concrete cover spalling, reduction of concrete strength and supporting role of stirrup to longitudinal reinforcement caused by a corrosion stirrup. According to the process of concrete cracking induced by the longitudinal rebar corrosion, [PERSON] et al. [20] divided the bearing capacity degeneration into three stages: pre-cracking, cracking and splitting, and the assessment model of the bearing capacity for the small eccentric compressive members was established, considering the biaxial stress condition in the stage of pre-cracking, the shear-tensile stress condition in the stage of cracking and the failure of the cover in the stage of splitting. Such models focus on the mechanism of materials deterioration on the structure under a single mechanical state. The essence is to modify the residual strength of a dangerous section under the specific eccentricity, which keeps good consistency with the calculation formulas for uncorroded members. In fact, the eccentric compression component is a member carrying both the bending moment and axial force. The effect of the axial force and bending moment is mutually restrictive. When the axial force is given, there is a unique bending moment corresponding to it [21]. A continuous moment-axial force (M-N) curve is the complete expression of the bearing capacity of members whose geometrical dimensions and physical properties are determined. The second type is the model based on the M-N curve. [PERSON] et al. [22; 23] presented a bridge pier column strength evaluation method utilizing a numerical procedure based on the layer method. The method uses damaged material properties, and accounts for amount of corrosion and exposed bar length for each reinforcement, concrete loss, bond failure, and type of stresses in the corroding reinforcement. [PERSON] et al. [24] established a numerical model to obtain a time-varying moment-axial domain of sound and corroded bridge piers by discretizing the cross-sections into a series of fiber cells. [PERSON] et al. [25] built a semi-quantitative assessment framework for the interaction diagrams development using a simplified nonlinear finite element method. [PERSON] et al. [26] developed a simplified model to calculate the interaction diagrams of RC columns subjected to corrosion processes, which was constituted by three branches and four points. Compared to the single point calculation mode of the first type models, an M-N curve formed by multi-points connection can more comprehensively and intuitively reflect the corrosion effect on the degradation of bearing capacity of components under different loading conditions. However, how to construct the M-N curve of corroded members has not yet reached a unified consensus. More work is required to further understand and improve the bearing capacity evaluation method of RC components. This paper mainly focuses on the bearing capacity evaluation method for corroded RC columns based on M-N curves. With consideration of the mathematical thoughts in [27; 28], a new federated bearing capacity evaluation method is established by integrating Hermite interpolation and Fourier fitting, which unifies the three stress states of axial compression, eccentric compression and pure bending. Unlike the existing calculation approaches, there are only three feature points that need to be computed to obtain continuous smooth M-N curves in this paper, which has obvious advantages in computational complexity. The performance of the proposed method is demonstrated by experimental data from forty-five RC columns. Compared with the prediction accuracy of the existing model, the proposed method can achieve satisfactory prediction results.