*3.2. 300* × *500 mm Beam*

The section of the beam that will be analyzed below is shown in Figure 20. The corrugated steel bars studied correspond to the lower part of the beam and are those that will be placed under traction.

**Figure 20.** Position of bars studied in 300 × 500 mm beam.

#### 3.2.1. Determination of the Moment the Crack Takes Place

Loading begins in the center of the beam span, at an interval ranging from 5.20 kN to 275 kN. After applying these loads, and using Catman software, we obtain the deformation that takes place in the corrugated steel bars according to the loads applied (Table 7).


**Table 7.** Relation between loads applied and deformation of the rebars 1 and 2.

Once more, the beam has cracked before reaching the calculated cracking moment. The cracking process of the beam was observed, as with the 200 × 300 mm beam, obtaining perceptible cracking on visual inspection with a load of 58 kN. Figure 21 shows the visual control of cracking of the beam throughout the whole process.

**Figure 21.** Visual control of cracking in the 300 × 500 mm beam.

In Figure 22, we may observe the moment at which the beam cracks, as the steel deformation grows in an obvious manner. The loading at which the cracking takes place, according to the deformation measure obtained by the optic fiber is 54 kN, compared with the 58 observed in the visual inspection. Thus, it would be those 54 kN that would be taken as the loading value to calculate the cracking moment.

**Figure 22.** Deformation of the rebars 1 and 2 according to the loads applied.

3.2.2. Steel Deformation Using the Concrete Laboratory Data Compared with Steel Deformation Obtained From the Optic Fiber Sensors

The steel deformation shall first be analyzed using the data obtained in the laboratory, compared with that provided by the optic fiber. To do so, a concrete has been created with the characteristics described above, with fct = 8.9 MPa, and Mfis = 111.25 mkN.

The steel deformation is obtained using the program FAGUS. We shall show the result provided by FAGUS for a moment of 127.88 mkN, the rest of the results having been obtained in the same way (Table 8).


**Table 8.** Deformation of the rebars 1 and 2 for a moment of 127.88 mkN by FAGUS.

The same method shall be applied as for the 200 × 300 mm beam, considering the steel deformation for resistance to traction of the concrete obtained by the laboratory tests, and subsequently that obtained with the optic fiber (Table 9 and Figure 23).

**Table 9.** Theoretical deformation of the rebars 1 and 2 for Mfis = 111.25 mkN and fct = 8.90 MPa with FAGUS.


**Figure 23.** Theoretical deformation of the rebars compared with the real deformation obtained using the optic fiber sensors.

3.2.3. Deformation of the Steel at the Real Cracking Moment of the Concrete Compared with Deformation of the Steel Obtained Using Optic Fiber Sensors

For a load of 54 kN, the moment corresponds to 40.5 mkN, and applying Equation (1) we obtain a resistance to traction of the concrete of 3.24 MPa, compared with the 8.9 MPa obtained in the laboratory. In this case, the crack has opened at a point very near to the optic fiber, so the concrete can barely contribute to avoid deformation of the steel (Figure 24).

**Figure 24.** Determining deformation of the steel between cracks on 300 × 500 mm beam.

We see what happens when the resistance to traction of the concrete with which we perform the calculations using the FAGUS program corresponds to the 3.24 MPa. Table 10 shows the deformation of the corrugated steel for a moment of 127.88 mkN.


**Table 10.** Deformation of the rebars 1 and 2 for a moment of 127.88 mkN by FAGUS.

Table 11 includes the deformation of the steel without cracking, and the deformation of the steel with cracking. The deformation adopted shall be an interpolation of both values.


**Table 11.** Deformation of the rebars 1 and 2 for Mfis = 40.5 mkN and fct = 3.24 MPa with FAGUS.

Figure 25 is the graphic representation of figures in Table 11.

**Figure 25.** Deformation of the rebars with its Resistance to real traction of 2.13 MPa compared with real deformation obtained using optic fiber sensors.

We observe that by inputting the behavior real values of the concrete, the beam deformation curve corresponds to the data provided by the optic fiber sensors. In this case, as the optic fiber is very near to a crack, there is a sharp leap at the moment it takes place. As we shall see in the slope figures, these are much steeper than in the previous case, in which the optic fiber was approximately in the center between the cracks, which caused these slopes to be less steep. The slope values of these curves are recorded in Table 12.


**Table 12.** Slope values of theoretical deformation curves and of rebars 1 and 2.

In Figure 26, we observe how there is a significant first leap at a load that is in the interval [54.00;60.54], that is, that the first crack begins to form with a load of 54 kN, and it cracks until reaching 60.54 kN.

**Figure 26.** Slope theoretical deformation curves of the rebars (interpolated values) and of rebars 1 and 2.

Figure 27 shows the interval within which the crack takes place in greater detail

**Figure 27.** Detail of the first crack forming in the 300 × 500 mm beam.

The moment at which the crack in the beam takes place is evident, as the deformation of the steel grows evidently. The load at which the crack takes place is 54 kN, compared with the 58 kN observed during the visual inspection.

As happened with the 200 × 300 mm beam, the theoretical deformation of the beam reinforcement is far from appearing like its real behavior. In this case, the crack has opened up at a point very near to the optic fiber, so the concrete shall not collaborate when its traction tension is reached.

In this case, we must observe what happens at the loading point of 54 kN, where the slope of the curve is much steeper, something that did not happen in the graph of beam 200 × 300 mm. This is due to the crack having opened very near to the location of the optic fiber, so that, in analysis of the section, the concrete barely collaborates in traction of the beam, and practically all the traction is borne by the steel.

It is noted that the optic fiber shows us the precise moment at which the beam cracks, that the cracks open much earlier than what the laboratory tests say, and that taking the data provided by the optic fiber, we may determine the behavior of the structural element in a much more precise way.

It is evident that when calculating a structural element, we do not know what will happen to it, when the piece will really crack. Considering an expression that draws that value closer to reality shall be a matter to be studied in future lines of investigation.

#### **4. Conclusions**

Two beams with a rectangular section in which fiber optic sensors were embedded have been tested to analyze the real deformation of the steel when they are submitted to different loading stages.

Appearance of the first cracks has been observed in both cases. These appear much earlier than the calculation predicts. The appearance of the first cracks is a fundamental matter to understand the real behavior of the structures. Fiber optic sensors were used to observe how a sudden change in deformation of the steel takes place. Moreover, with the advantage of the measurements being in real time, a fact that provides greater value to evaluation of the structural health of the elements tested. It is evident that this sudden change leads to it being deformed to greater extent as a consequence of the concrete cracking.

Thus, considering the results obtained, we may know the precise moment at which the beam cracks through embedded fiber optic sensors. On studying the deformations, it has been noted that even when test pieces extracted at the moment of concrete pouring were tested, and they were tested on the day when the tests were to be carried out, these values do not match the behavior of the concrete under traction. In both cases, the beam cracked much before the laboratory tests indicated.

Thus, placement of sensors welded on corrugated steel bars within reinforced concrete structural elements, at their maximum effort points, is a precise, reliable method to determine the moment at which the first cracks take place, as it has been possible to prove according to the results obtained.

After ascertaining the real cracking moment of the concrete, we precisely obtained its resistance to traction and, thus, the real deformation of the corrugated steel during application of the loads.

As stated in the introduction, the existing studies on concrete cracking use diverse methods to detect cracks. As is known, concrete is a material that resists compression well, but that is not the case with traction efforts. The reinforcement of the structural elements is placed, among other reasons, to bear the traction the concrete is not able to bear. The method proposed herein provides, as a novelty, detection of cracks that is observed thanks to the optic fiber sensors welded to the corrugated steel bars, at the precise moment when the steel begins to deform significantly. This causes a leap in its deformation, which is detected for the relevant load applied. Moreover, once the steel begins to deform, it is possible to know the deformation it will suffer during the whole period of application of the different loading steps to which the structural element is submitted. It has been proven that the deformation of the steel measured with optic fiber sensors corresponds to the theoretical values of the traditional materials resistance calculation, as long as the real cracking moment of the concrete is taken as the starting point.

We may conclude, considering these graphs obtained from the experiment carried out, on the one hand that laboratory tests to determine flexion-traction resistance of concrete provide very conservative results, that have nothing to do with what really happens in the structural element. And on the other, that deformation of the steel, obtained with these tests, are quite far from its real behavior. This method of evaluating the structural health of a simple element of reinforced concrete may be transferred to more complex structural elements of buildings in construction to know the behavior of the structure when the formwork removal takes place and their actual weight begins to bear down on the structures, and subsequently the application of deadweight and overburdens in use, when the building is put into operation.

A monitored building may provide us information on what overburdens it is able to bear, a highly important factor when one wishes to change the use of a building and the overburdens it is to be subject to are higher than those initially designed. In this case, and according to the data obtained, one might even be able to avoid possible structural reinforcement, as we would know what the building may really bear, with the financial savings that would involve.

**Author Contributions:** Conceptualization and methodology, J.G.D. and E.R.Á.; validation and formal analysis, N.N.C. and E.R.Á.; investigation, J.G.D.; writing—original draft preparation, J.G.D.; supervision, N.N.C. and E.R.Á. All authors have read and agree to the published version of the manuscript.

**Funding:** This research was funded by CDTI (Centro para el Desarrollo Tecnológico Industrial), assigned to the Ministry of Science, Innovation and Universities, under the R&D project "SENSOSMART" IDI-20171055.

**Acknowledgments:** The authors wish to thanks Ortiz Construcciones y Proyectos, S.A., INDAGSA and HBM for their support in the process of constructing the concrete beams and setting up the testing facility.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


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