Theorems for Flexural Design of RC Members

Abstract

Three theorems of the flexural theory for RC members are derived to identify two critical points on a moment–curvature curve: (1) the onset of flexural strength and (2) the onset of the so-called true ultimate curvature. The true ultimate curvature is reached at the exact moment when a RC member loses its integrity. The first two theorems concern the first point and the third relates to the second. Exact analytical solutions of the extreme concrete strain for these two critical points are derived for general RC members, including underreinforced and overreinforced beams and RC columns. The solutions can be used to calculate the exact strength and the corresponding deformation and to evaluate concrete damage at the onset of the two critical points. The analytical results can also be used in practice for the design of RC members, which is particularly useful when precise evaluations of flexural strength and damage conditions at the onset of maximum moment or ultimate displacement are required.