# Revisiting Cracking in Reinforced Concrete Beams: An Updated Analysis
## 2 Initial Considerations
### Crack Control  
It should be ensured that cracks will not impair the serviceability and durability of the structure or cause its appearance to be unacceptable. For EC2 [1], these specific requirements may be met by an appropriate limitation of crack widths \(\text{w}_{\text{max}}\). If crack control is required, it should be \(\text{w}_{\text{k}}\leq\text{w}_{\text{max}}\), where \(\text{w}_{\text{k}}\) is the calculated crack width (characteristic value). ACI [2] prescribes rules for distribution of flexural reinforcement to control flexural cracking in beams. Several bars at moderate spacing are much more effective in controlling cracking than one or two larger bars of equivalent area. According to ACI [2], extensive laboratory work involving deformed bars has confirmed that crack width at service loads is proportional to steel stress. The significant variables reflecting steel detailing were found to be the thickness of concrete cover, the spacing of reinforcement, and the minimum reinforcement. Crack width is inherently subject to wide scatter even in careful laboratory work and is influenced by shrinkage and other time-dependent effects. Improved crack control is obtained when the steel reinforcement is well distributed over the zone of maximum concrete tension and crack width can be limited by an increase in the amount of reinforcement used (by reducing the stress at the service load level). When high strength reinforcing steels are used at high service load stresses, visible cracks should be expected. However, at the same time, ACI admits that crack widths in structures are highly variable. In addition, ACI establishes requirements regarding transverse reinforcement, both in terms of quantity and in terms of maximum spacing. Regarding the spacing between transverse reinforcements, ACI prescribes: Spacing of shear reinforcement placed perpendicular to axis of member shall not exceed d/2 (d means effective depth of a cross-section; d\(-\)0.9 h) in no prestressed members and indicates that shear reinforcement restrains the growth of inclined cracking. With regard to the indirect control of crack width by limiting steel spacing, it is important to say that EC2 [1] is a little more restrictive than ACI [2]: for example, for a case  
Figure 1: Stress–strain behavior of concrete in tension. where the service stress in the steel is \(\sigma\gamma\sim\) 250 MPa, the limit spacing in EC2 is less than 250 mm; for ACI, this limit oscillates between {-300--350 mm}, depending on the cover. When calculating crack width \(w_{k}\) in concrete structures, EC2 standards suggest that it may be determined using the following equation:  
\[w_{k}=S_{\rm r,max}.(\epsilon_{\rm sm}-\epsilon_{\rm cm}) \tag{3}\]  
where \(S_{\rm r,max}\) is the maximum crack spacing, \(\epsilon_{\rm sm}\) is the mean strain in the reinforcement under the relevant combination of loads, and \(\epsilon_{\rm cm}\) is the mean strain in the concrete between cracks. Because the concrete strain \(\epsilon_{\rm cm}\) is significantly less than the steel strain \(\epsilon_{\rm sm}\), EC2 calculates \(w_{k}\) based on the steel strain. The issue that needs to be highlighted here concerns the calculation of \(S_{\rm r,max}\). For EC2, \(S_{\rm r,max}\) depends on the cover of longitudinal reinforcement c, on the bar diameter \(\epsilon\) and on the effective reinforcement ratio for longitudinal reinforcement \(\rho_{\rm p,eff}\) (defined in the effective area of concrete in tension surrounding the reinforcement). It is not important here to indicate the corresponding expressions. It is interesting to point out that, for current cases of beams, it is possible to evaluate values greater than 250 mm for \(S_{\rm r,max}\). Regarding the maximum crack spacing, [PERSON] [28] proposes a (simpler) expression dependent on the cover, diameter, and average spacing of the bars.