Discrete rotation deflection of reinforced concrete beams at serviceability

Quantifying the deflection of reinforced concrete flexural members is complex, owing to the formation of discrete cracks which widen through slip between the reinforcement and the adjacent concrete causing increases in deflection. A common method of analysis and design is to use a full-interaction strain-based moment–curvature approach to derive flexural rigidities, which then need to be calibrated by comparison with test results. As this approach is based on full interaction, that is, there is no slip between the reinforcement and the concrete, it cannot cope directly with the discrete rotation at a flexural crack. Consequently, this approach cannot cope directly with the deflection associated with flexural crack widening that requires slip between the reinforcement and the concrete, that is, partial interaction. In this paper, a partial-interaction structural mechanics model is developed for quantifying the deflection owing to the discrete rotation at each individual crack. The results are shown to compare well with the semi-empirical effective flexural rigidity approaches and also with experimental data. Importantly, this is a mechanics-based approach that does not require components of the mechanism, as opposed to the material properties, to be determined experimentally. Hence, this partial-interaction approach should be useful in refining existing deflection design models and in quantifying the deflection of reinforced concrete members with new types of reinforcement.