# Revisiting Cracking in Reinforced Concrete Beams: An Updated Analysis
## 4 Test Results
### Cracking Width  
Next, the graphs of the crack width values w. For the abscissa parameter, the deflection ratio d/L was chosen; d is the deflection of the beam. d/L can be referred to as reduced deflection. It is important to mention that this ratio, somehow, is (almost) directly proportional to the quotient L/h, but it is also proportional to the curvature and to the tensioned steel strain in central zone, where the first cracks arise and where the crack width was measured. Thus, the following graphs can be adapted for other beams, as long as the values of the abscissas are divided by the quotient L/h of these beams and multiplied by the new quotients. The w-value results from the average of the three (if any) highest recorded values; in Beams B24-B27, the smallest, only two values were used. The crack widths were measured with the aid of a crack width microscope (40\(\times\) magnification) at the level of the tensile reinforcement. For each beam, the first point represents the instant when it was possible to visualize the cracks. It was decided not to include, in these graphs, the starting point of cracking. The vertical lines represent the (supposed) yield point of the reinforcement. In these figures, it is important to understand the influence of the different parameters in terms of crack width in beams subjected to bending. In Figure 13, the crack width w of the beams in Groups I (B01 and B02; A\({}_{\rm s}\) = 2\(\phi\)8) and II (B03 and B04; A\({}_{\rm s}\) = 2\(\phi\)10) are presented. The w-value varies \"almost\" linearly until the reinforcement yields. In these beams, whose failure occurred due to rupture of the tensile reinforcement, after yielding, there is a crack that opens for failure. The beams with a greater amount of reinforcement show smaller crack widths. In the beams of Group I, the visualization of cracking starts for values close to d/L \(\approx\) 0.48%, with crack width  
Figure 12: Cracking quotient \(\delta_{\rm cr}\) = L/d\({}_{\rm cr}\). w \(\approx\) 0.11 mm; in Group II, d/L \(\approx\) 0.75% with w \(\approx\) 0.07 mm. The beams of Group I yield approximately at a deflection ratio of d/L \(\approx\) 2.84%, with w \(\approx\) 0.45 mm; in Group II, d/L \(\approx\) 3.70% with w \(\approx\) 0.35 mm. To conclude, regarding the type of steel (ER or NR), there are no differences to remark; only a slight reduction in w-value for beams with NR steel. Figure 14 shows the crack width values for the beams in Group III. Regarding the type of steel, Beam B10, with NR steel, has higher w-values than Beam B09, the opposite of the previous. Therefore, the type of steel is not a relevant parameter for crack widths w. It is also possible to confirm the \"almost\" linearity in the variation of w until the reinforcement yields. Recall that Beams B05 and B06, without stirrups in the central zone L\({}_{2}\), are the ones with the lowest w-value. Beams B07 and B08, with stirrups spaced 60 mm apart, are the ones with the highest w-values, except for the case of Beam B10 close to yielding. Considering that the w-values in this graph are much lower than those in the previous graph, it is possible to confirm that, to the same reduced deflection, the crack widths decreases by increasing the tensile reinforcement. For these beams, cracking visualization started at a deflection ratio of d/L \(\approx\) 0.67%, with a crack width of w = 0.032 mm (which is much smaller than the previous values). In turn, yield occurred at a deflection ratio of d/L \(\approx\) 5.2% (later), with a crack width of w \(\approx\) 0.18 mm. Figure 15 presents the crack width values for the beams in Group IV. These beams, with tensile reinforcement equivalent to those of Group III, were tested with axial restraint and were about 1 year old at the time of testing. As seen earlier, the effect of axial restraint on crack initiation is negligible (N\({}_{\rm cr}\) < 0.5 kN), but it becomes more significant as the beams approach yield (N\({}_{\rm y}\)(B11-B13) < 31 kN and N\({}_{\rm y}\)(B14) \(\approx\) 54 kN).