Analytical prediction of ultimate moment and curvature of RC rectangular sections in compression

This paper presents closed form expressions of the ultimate moment and curvature of rectangular RC sections subjected to axial load and bending moment acting in one of the two symmetry plane of the section. With respect to possible simplified formulations the following effects are also considered: confinement of the concrete, hardening of the longitudinal reinforcement, presence of reinforcing bars distributed orthogonally to the neutral axis. The formulation is proposed in dimensional terms after a preliminary definition of the geometrical and mechanical parameters governing the structural response of the class of sections considered. The analytical expressions derived by the proposed approach allow one to determine also the compression level that makes the ultimate bending moment maximum as well as to evaluate the ductility of curvature of the section, by analytical expressions of the curvature corresponding to the first yielding of the principal reinforcement in tension. Theoretical predictions are compared with experimental results taken by the literature.