# Revisiting Cracking in Reinforced Concrete Beams: An Updated Analysis
## 4 Test Results
### Cracking Moment  
Several criteria can be established regarding the onset of cracking. In point 2.1, a possible criterion was presented, based on concrete strain. This criterion has generalized practical application in design and allows to know the cracking load. However, for a beam in a test, what is the cracking load? Better phrased: What is the cracking (concrete) strain? The visual criterion may be a more practical alternative. The authors can confirm that this visual criterion is not adequate. In fact, although it was possible to visualize (in some beams) crack widths of 0.01 mm, in fact, the cracking started with some previous load. This fact was (always) later confirmed in the P-d curves of the tests (P means total load and d the deflection). The most suitable criteria are based on the P-d curve. One of the possibilities is to follow the following algorithm: (i) determine the line KI tangent to State I (elastic phase of the beam behavior) in the P-d diagram; (ii) determine the line KII tangent to State II (cracking development phase); (iii) determine the intersection point \(\mathrm{P_{int}}\) between the lines KI and KII; (iv) the starting point of cracking is the point on the P-d curve closest to \(\mathrm{P_{int}}\); (v) the point, thus found on the P-d curve, determines the values of the cracking load \(\mathrm{P_{cr}}\) and the cracking deflection \(\mathrm{d_{cr}}\). For the various beams, Table 4 indicates the expected (mean) value of the tensile strength of the concrete \(\mathrm{f_{ct}}\), the expected (mean) value of the cracking moment \(\mathrm{M^{*}_{cr}}\) (Equation (1)), the cracking load \(\mathrm{P_{cr}}\), the corresponding cracking moment \(\mathrm{M_{cr}}\), \(\mathrm{M^{*}_{cr}}/\mathrm{M_{cr}}\) quotient and the cracking deflection \(\mathrm{d_{cr}}\). For axially restrained beams, the value of the axial force at the cracking point \(\mathrm{N_{cr}}\) is indicated. In order to analyze the presented results, consider the following reduced cracking moment \(\mu^{*}_{cr}\) defined by  
\[\mu^{*}_{cr}=\frac{M_{cr}}{b.h^{2}.f_{ct}} \tag{4}\]  
As the first hypothesis, Figure 10 shows the graph of reduced moments \(\mu^{*}_{cr}\) evaluated for beams considered as a function of reinforcement ratio \(\rho\). The cross markers represent Beams B19 and B20, where the axial force at the beginning of cracking was not insignificant (\(\mathrm{N_{cr}}\sim 51\) kN). The remaining beams are represented by circle markers. The indicated trend line was evaluated only for these beams. In this figure, the line corresponding to the  
Figure 9: Crack position of Beams B24–B26. cracking moment determined by Equation (1) is also represented, assuming the proposal indicated in Structural Concrete [26], i.e., that \(f_{ct}\) is determined by concrete flexural tensile strength\(f_{ctm,fl}\) (Equation (2)). Considering the value of R2 (determination coefficient), there is a significant dispersion of results for the different beams. This dispersion is more evident in tests with normally reinforced beams (\(\rho\) > 1%). Anyway, the trend line clearly shows the influence of tensioned reinforcement on cracking; the cracking moment in well-reinforced beams (\(\rho\) \(\sim\) 1.3%) reaches twice the value of insufficiently reinforced beams (\(\rho\) \(\sim\) 0.2%). Considering the value of the cracking moment estimated by Equation (1), it appears that, for weakly reinforced beams (\(\rho\) < 0.6%), the estimate is insecure, whereas the estimate is conservative for normally reinforced beams (\(\rho\) > 0.6%). This conclusion depends on the assumed value for \(f_{ct}\). In order to assess the impact of the value assumed for f\({}_{ct}\), in Figure 11, (second hypothesis), the same values indicated in Figure 10 are presented, if the proposal of the CEB manual [25] (f\({}_{ct}\) = 0.7f\({}_{ctm}\)) were adopted, which coincides with [PERSON]'s proposal [8]. It is only interesting to conclude that the cracking moment should not be evaluated following the suggestion of the CEB manual.