# Revisiting Cracking in Reinforced Concrete Beams: An Updated Analysis
###### Abstract
Since then, it became reasonably well-known how to calculate the width once the crack spacing is determined. The crack width calculation used in this study was similar to the expression used in European Concrete Design Standard EC2 [1]. The adaptation for beams subject to bending consisted of determining an area around the tensile reinforcement where the stress field would be assumed to be uniform. The results then determined were, however, updated, namely, the deformation for the onset of cracking and the minimum spacing between cracks. The study did not consider the presence of stirrups in the RC beams. In 1988, [PERSON] [8] presented a work primarily applicable to large structures; however, the general concepts presented are applicable to any concrete structure. [PERSON] explicitly wrote that \"Cracking occurs when tensile stresses exceed the tensile strength of concrete. Therefore, to control concrete cracking, the tensile strength of concrete is of primary importance\". However (differently), he also wrote that \"concrete cracks when the tensile strain exceeds 0.010 to 0.012%. This limiting tensile strain is essentially independent of concrete strength\". Another aspect that deserves to be mentioned in the context of the present work is that [PERSON] proposed that \"The 5 percentile of the tensile strength should be used in design to locate areas in the structure that are likely to crack\". [PERSON] recommended using small bar diameters and a small spacing of reinforcement for the best control of cracking. He also drew attention to the minimum tensile reinforcement for preventing sudden failure when cracking occurs. Around the 1990s, experimental works that incorporated computational methodologies began to emerge, with [PERSON]'s PhD thesis [9] being one example. Having focused his study on T-deep beams, [PERSON] completely ignored the presence of stirrups in the location of the cracks. All the theory so far developed from RC elements subject to pure tension continued to be followed and applied to beams subject to bending. By this time (1990s), the methodologies for estimating crack spacing and width had become well-established. First, the crack spacing was estimated and then the width. Some models had previously considered the crack width to be dependent on the diameter of tensioned reinforcement but were quickly abandoned [7,10]. The crack width was considered proportional to steel stress and crack spacing. This model persists in the current regulations. There is also a transformation of the models to evaluate crack widths and the spacing. Initially, the strategy for establishing these models involved selecting several parameters with an impact on cracking and determining their coefficients using statistical regressions. After that, the strategy shifted towards using semi-theoretical and semi-empirical formulas based on the analysis of the cracking mechanism, such as the fracture energy criterion and strength criterion. These formulas are derived from mechanical models, but some of the coefficients are determined through experiments. The current models used in main regulations have used this approach [1,2]. Considering the crack spacing, by this time (the 1990s), many parameters were considered: the concrete cover c [8,9,11,12,13], and/or the bar spacing [8,9,11,12,13,11,13], and/or the steel stress \(\sigma\)s [11], and/or the concrete properties (compressive strength f\({}_{\text{c}}\), tensile strength f\({}_{\text{ct}}\), elastic modulus E\({}_{\text{c}}\)) [7,14,15], and/or the bond stress \(\sigma_{\text{b}}\) [7,14,15], and/or the bond properties (if high bond bars or plain surface) [8], and/or the bar diameter \(\phi\) [7,9,11,12,14], and/or the effective reinforcement ratio \(\rho_{\text{eff}}\) (determined in an effective area of concrete in tension surrounding the reinforcement) [7,9,14,15, 9], and/or coefficient which takes account of the distribution of strain (if bending or pure tension) [8]. In general, all models were derived from knowledge of RC elements subject to pure tension.