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

This paper presents closed form expressions linking the ultimate bearing capacity to the ultimate curvature of rectangular RC sections subjected to axial load and bending moment acting in one of the two symmetry planes of the section. With respect to possible simplified formulations the following effects are also considered: confinement of the concrete, hardening of the longitudinal reinforcement, and 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 using the proposed approach also allow one to determine the compression level that makes the ultimate bending moment maximum as well as to evaluate the curvature corresponding to the first yielding of the principal reinforcement in tension. Comparing this value of curvature with the ultimate one, an approximate estimation of the available ductility of curvature of the section can be made. The analytical procedure is validated by comparing the results with those obtained using a typical numerical approach. Some experimental results are also considered. © 2013 Springer Science+Business Media Dordrecht.