*3.1. 200* × *300 mm Beam*

The section studied is shown in Figure 13. The corrugated steel bars correspond to those located in the lower part of the beam, which will be subject to traction.

**Figure 13.** Position of the rebars studied in the 200 × 300 mm beam.

3.1.1. Determining the Moment When the Crack Takes Place

The loads began to be applied in the center of the beam span, within an interval ranging from 0.56 kN to 42.24 kN. Using Catman software, we obtained the deformation that takes place in corrugated steel bars according to the loads applied in Table 1.


**Table 1.** Relation between loads applied and deformation of the rebars 3 and 4.

As shown in Figure 14, the steel deformation is about five or six μm/m for increases in load between one and two kN, while it is 20 μm/m when the load is from 8.07 to 9.05 kN.

**Figure 14.** Deformation of rebars according to the loads applied.

These results imply the need to reconsider the moment of the concrete cracking and the steel deformation, as the moment of real cracking is less than that obtained by calculation as well as by visual inspection. It is evident that micro-cracks that are invisible to the human eye are formed, but that the optic fiber is able to detect. One may thus determine that a load of 8.5 kN is what makes the concrete crack.

3.1.2. Steel Deformation with Laboratory Data on the Concrete Compared with Steel Deformation Obtained by Optic Fiber Sensors

A comparison shall be made between the theoretical deformation obtained by calculation and the real deformation process indicated by the sensors. To that end, a concrete with the characteristics obtained in the laboratory has been created, with a resistance to traction of 5.4 MPa, which provides a cracking moment of 16.2 mkN. Although all the moments acting have been checked in FAGUS, Table 2 shows the deformation of the steel for the moment of 31.68 mkN.


**Table 2.** Deformation of the rebars 3 and 4 for a moment of 31.68 mkN by FAGUS.

The rest of the deformation values are shown in Table 3 and Figure 15.

**Table 3.** Theoretical deformation of the rebars 3 and 4 for Mfis = 16.2 mkN and fct = 5.4 MPa with FAGUS.


**Figure 15.** Theoretical deformation of the rebars compared with real deformation obtained with the optic fiber sensors.

It is evident that the deformation of the steel is in fact greater than what is stated in the theoretical calculations. This is caused by cracking of the beam that, as aforementioned, happened before it was expected.

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

We shall now see how the steel in the beam is deformed at theoretical level with the real data for traction resistance of the concrete and the real cracking moment. We have already noted that the beam cracks under a load of 8.5 kN, which corresponds to a cracking moment of 6.38 mkN. With that moment, and applying Equation (1) given above.

We obtain the real resistance to traction of the concrete, that shall be 2.13 MPa. With that data, we input the value in the characteristics of our concrete in the FAGUS program. The program provides a value of the steel deformation in the crack, and another in the uncracked concrete. The section studied is between two cracks, so that figure must be averaged. Table 4 provides the values with and without cracking, for a moment of 28.31 mkN. The rest of the values have been obtained the same way.


**Table 4.** Deformation of rebars 3 and 4 for a moment of 28.31 mkN by FAGUS.

In Figure 16 one observes, on the one hand, the position of the optic fiber, the distance between cracks, which is 300 mm, and the position related to the crack on the left side of the optic fiber, which is 180 mm. That means that the concrete between fissures contributes to traction of the beam, and to the steel becoming deformed, but not if it is in the crack.

**Figure 16.** Determining deformation of the steel between cracks on 200 × 300 mm beam.

Table 5 includes the steel deformation without cracking and the steel deformation with cracking. The deformation adopted shall be an interpolation between both figures.


**Table 5.** Deformation of the rebars 3 and 4 for Mfis = 8.5 mkN and fct = 2.13 MPa with FAGUS.

Considering these results, Figure 17 shows that the theoretical deformation of the steel is in keeping with that obtained by the optic fiber sensors. The contribution by the concrete between cracks plays an important role in determining the steel deformation.

**Figure 17.** Theoretical deformation of the rebars with its real resistance to traction of 2.13 MPa compared with the real deformation obtained with the optic fiber sensors.

We observe that the theoretical deformation value interpolated grows over a soft curve. This is due to the sensor being approximately in the center between cracks, which makes the concrete between cracks contribute to less deformation of the steel than if the sensor were to be very near to a crack or in the actual crack. That is precisely what happens in the following beam studied, where we observe that the interpolation curve suffers a major leap at the moment of the cracks taking place.

In order to be able to determine the precise moment when the crack takes place and how this grows by application of the successive loads, we shall transform Figure 17 into a graphic, Figure 18 that shows, in an equivalent manner to Figure 17, the deformation slope curves according to the loads. The greater the slope, the greater the deformation.

**Figure 18.** Slope curves of the theoretical deformation of the corrugated steel (interpolated values) and of rebars 3 and 4.

In Figure 18 we observe how the first significant leap in loading takes place, which is in the interval [8.07;9.05], that is, that the first crack begins to form at a load of 8.07 kN, and it cracks until reaching 9.05 kN. The slope values of these curves are shown in Table 6.


**Table 6.** Slope values of the theoretical deformation curves and of rebars 3 and 4.

It is evident that concrete is a material regarding which we cannot do more than approach its behavior by experience, although with embedded sensors we are able to know the moment at which the material cracks, and with that result, know its behavior much better. Figure 19 shows the interval in which the crack arises in greater detail.

**Figure 19.** Detail of the first crack forming in the 200 × 300 mm beam.

One may see that, while the beam has not cracked, the steel is gradually deformed, on the contrary to what traditional structure calculation theory says as, in this, the traction is absorbed by the concrete, a fact that is proven not to be the case in these graphs. Once the cracks start, when we go from 8.07 to 9.05 kN applied load, the deformation of the steel is much more significant, as the concrete contributes to a lesser extent to absorb the traction. The greater or lesser contribution by the concrete depends on the position of the sensor between the cracks.
