# Revisiting Cracking in Reinforced Concrete Beams: An Updated Analysis
## 4 Test Results
### Cracking Width
However, its impact is not such as to condition the conclusions in terms of deformations. The visualization of cracking started at a deflection ratio of d/L \(\approx\) 1.1%, with a crack width of w = 0.052 mm. These crack width values are higher than those determined for the beams in Group III. In turn, the yield occurred for equivalent amounts: d/L \(\approx\) 5.2%, with w \(\approx\) 0.18 mm. These results suggest that the difference in age between the beams tested at one month and those tested at one year old did not significantly affect the evaluation of crack width. Figure 13: Cracking width. Beams in Groups I and II. Most notable is the influence of the spacing of the stirrups. If the previous experiments with Group III beams suggest that crack width w tended to increase as the stirrup spacing s decreased, the opposite appears to be true for the beams in this group. Beams B11 (without stirrups in L\({}_{2}\) zone) and B14 (with a stirrup spacing of 180 mm) have higher crack width values, while Beams B12 and B13 (with a stirrup spacing of 60 mm) have significantly lower values. This highlights the difference between B12 (A's = 2\(\phi\)10) and B13 (A's = 2\(\phi\)6); Beam B13, which had a reduced amount of compression reinforcement, showed the lowest crack width values. That is, a greater amount of compressed reinforcement tends to increase the crack widths for the same sag. It is possible that the high crack width values observed in Beam B14 (A's = 3\(\phi\)16; N\({}_{y}\)(B14) \(\approx\) 54 kN) were primarily due to the amount of compressed reinforcement. Figure 16 shows the w-values for the beams in Group V, containing about half of the tensile reinforcement compared to the beams in the previous two groups. Two beams were tested with axial restraint: N\({}_{y}\)(B15) = 33.7 kN and N\({}_{y}\)(B17) = 29.7 kN. The first shows the highest values w; the second, the smallest. Therefore, the axial restraint is not a relevant parameter for crack width in terms of deflection ratio. Figure 14: Cracking width. Beams in Group III. Figure 15: Cracking width. Beams in Group IV. Notably, in Group V, Beam B18 (s = 180 mm) shows smaller w relative to Beam B16 (s = 60 mm), which raises the question of whether a smaller spacing of the stirrups contributes to higher w-values in the short term, but in the long term, the opposite is observed. In any case, the visualization of cracking started at d/L \(\approx\) 0.84%, with w = 0.042 mm. These values are higher than those determined for the Group III beams. In turn, the yield occurred for equivalent amounts, with d/L \(\approx\) 4.8% and w \(\approx\) 0.2 mm. These values confirm that the lower tensile reinforcement there is, the greater the w-value and the sooner the yield occurs. The w-values of the beams in Group VI (A\({}_{\rm s}\) = 3\(\upphi\)16) are shown in Figure 17. These beams were tested at about 2 years old. Here, the axial constraint was initially activated: N\({}_{\rm cr}\)\(\approx\) 51 kN and N\({}_{\rm y}\)\(\approx\) 120 kN. It is also important to point out that it was used a self-compacting concrete with shrinkage reducing admixtures. The lower w-values of Beam B19 (A's = 2\(\upphi\)10) relative to Beam B20 (A's = 2\(\upphi\)16) confirm that less compressive reinforcement results in lower w-values and later yielding. For these beams, cracking visualization started at d/L \(\approx\) 0.67%, with w = 0.020 mm. In turn, the yield occurred for equivalent amounts; d/L \(\approx\) 4.9%, with w \(\approx\) 0.20 mm. Regarding the previous results (Groups III and IV), the comparison must consider the axial restriction. In any case, yield occurs for a similar sag, with a deviation of less than 6.5%; the w-value is relatively higher, with about 11% deviation. In order to be able to compare with Beam B19, the curve related to Beam B12 was added to Figure 17. These beams are equivalent, differing only in that Beam B12 was tested at about 1 year old and with passive axial restraint: N\({}_{\rm cr}\) = 0.1 kN and N\({}_{\rm y}\) = 30.8 kN.