Calculation of Steel Stresses in Cracked Reinforced Rectangular Concrete Elements Loaded in Bending

An accurate calculation of steel stresses is essential for assessing reinforced concrete structures’ serviceability limit state, e.g., assessing crack widths. The steel stresses in elements loaded in bending are not known but are estimated by steel stress calculations. To get a more accurate crack width prediction, the calculated steel stress should approximately represent the actual steel stress at the location of the crack after the crack has been formed. Existing methods for calculating steel stresses are frequently based on numerous assumptions; e.g., the tensile stresses or tension softening effects in the cross-section are neglected, and a linear stress-strain distribution is assumed for the concrete in compression. This paper presents a method to calculate steel stresses based on existing constitutive theoretical relations that consider concrete's non-linear behaviour in compression and tension. They are compared with strain measurements of the reinforcement bars using distributed optical fiber sensors obtained from experiments described in the literature. Results showed that existing methods frequently overestimated the steel stress, especially when the first cracks were formed. Therefore, a method was developed for an improved calculation of steel stresses in elements loaded in bending with a rectangular cross-section. The paper demonstrated that the developed method could estimate steel stresses more accurately from the first to the final crack. The presented method applies to rectangular cross-sections with a single reinforcement layer but can be straightforwardly extended to other shapes in a similar procedure and can be used to assess the accuracy of crack width formulations based on experimental results.