Long- and short-term serviceability behavior of reinforced concrete beams: Mechanics models for deflections and crack widths

Analysis and design of reinforced concrete (RC) flexural members at the serviceability limit state is complicated by the localized bond slip or partial interaction (PI) between tensile reinforcement and the surrounding concrete. Localized slip is responsible for crack formation, crack widening, and tension stiffening and is further complicated by the time-dependent nature of concrete, which results in reduced tension stiffening and widening of cracks. Analysis techniques commonly applied in design are typically formulated on the assumption of full interaction between the reinforcement and the surrounding concrete. Hence, they do not simulate the behaviors observed in practice, but rather they correlate analytical predictions with experimental observations through the use of empiricisms, such as effective flexural rigidities and statistically derived expressions for crack widths. In this paper, it is shown how PI theory can be directly incorporated into elastic analysis procedures to develop simple expressions for flexural rigidities and crack widths under both instantaneous and sustained loading. The proposed approach should simplify not only the design process but also the development of design guidelines and material models, as it provides a simple rational method for investigating the time-dependent flexural behavior of RC members.