Discrete Rotation in RC Beams

The ability of a RC beam to rotate is extremely important at both the serviceability and ultimate limit states as it affects deflection, moment redistribution, and the absorption of energy. The rotation in a RC beam can be considered to have two components: the continuous rotation that occurs in the homogenous portions of the beam and that can be determined by straightforward integration of the curvature and the discrete rotation due to the rigid body displacement between crack faces. In this paper, generic closed-form solutions are derived for the discrete rotation across crack faces, which are limited by debonding or fracture of the reinforcement in tension, or softening of the concrete in compression. It is shown how closed-form solutions can be derived for the moment/discrete rotation for the simplest case of a RC beam with a single layer of reinforcement, which could be used as the starting position for much more complex scenarios. The technique developed is generic as it can cope with any type reinforcement and concrete. DOI: 10.1061/(ASCE)EM.1943-7889.0000436. (C) 2012 American Society of Civil Engineers.