Serviceability design of reinforced concrete members – Closed form solution

The present work describes an analytical and graphical procedure to evaluate stresses in reinforced concrete sections to be used in the verification of the serviceability limit states. The stress limitation imposed in EC2 [1], as well as, the calculation of crack widths and deflections make mandatory the evaluation of concrete and steel stresses at critical cross sections subjected to the service combinations of actions. The serviceability limit states verification is actually very important in the case of higher strength classes of concrete and steel, where it may be determinative in the design. The stress distribution in reinforced and pre-stressed concrete cross-sections is not continuous, due to the fact that the tensile stress of concrete in cracking tension zones is disregarded, and only the compression concrete is considered. The problem formulation is possible by the use of Heaviside functions, similarly to what is made for ultimate limit design of cross-sections in Barros et al. [2]. The integration process through Heaviside functions and MAPLE software is original, it permits a closed form solution to solve the problem, and to obtain abacus relevant for design. This paper presents the theoretical developments and examples of the design abacus for singly and doubly reinforced rectangular and T sections.