The ultimate bearing capacity correlation equations for symmetrically reinforced concrete eccentric compression members

The current methods for assessing the ultimate bearing capacity of reinforced concrete (RC) eccentric compression members have several limitations, including complex modeling, and difficulties in simplifying composite internal force expressions. Additionally, explicit correlation equations accounting for the P-δ effect have yet to be developed. This paper introduces universal ultimate bearing capacity correlation equations (U-CEs) applicable to both first-order and second-order analyses for symmetrically RC uniaxial eccentric compression members with various cross-sections, such as rectangular, circular, annular, box-, and I-sections. Initially, characteristic points used to describe the ultimate bearing capacity of RC members were identified based on the GB 50010–2010, leading to the formulation of first-order U-CE. Secondly, the stability coefficient φ and the magnifying coefficient of bending moment η were incorporated into the first-order U-CE, which enabled the development of two second-order U-CEs that consider the P-δ effect, utilizing the section load balancing method (SLBM) and the multi-point reduction method (MPRE). Subsequently, the computational accuracy of the first-order U-CE and the two second-order U-CEs was further validated using 325 experimental data points and 182 numerical finite element (FE) data points. Finally, the bending-compression curves generated by various formulas for RC members under different conditions were compared. The research demonstrates that the first-order and second-order U-CEs, developed by characteristic points, can directly determine the bending-compression curves of RC eccentric compression members throughout the eccentric loading process, showcasing strong computational accuracy and applicability.