By correlating the strain sensing layers of different installation techniques (here: MAV filtered), curvature profiles along the beam can be derived ( Figure 2  d), which align well with each other and also with the theoretical model, especially at loads up to 200 kN, where the shape of the 4-point loading setup is also well identified. Based on the test setup, the support points on each side of the beam (1850 mm from the center) can be assumed stable to evaluate the distributed displacement profiles along the beam shown in Figure2  e. The results largely confirm that the curvature profiles show good agreement with the LVDT sensors up to a load of 200 kN. At higher load steps, the displacement curves from different installation techniques match themselves but show pronounced deviations, negative from the theoretical model and positive from the LVDTs. This leads to the hypothesis that the concrete beam does not satisfy the Bernoulli assumption of a consistent cross-sectional profile. This is why the strain-based shape determination algorithm cannot capture the actual displacement behavior of the structure after significant cracking occurs.

Nonetheless, the displacements described by the theoretical model are also significantly smaller compared to the LVDT sensors, even lower in magnitude than the DFOS derivations. To investigate this marked behavior in more detail, two corresponding sensing fibers were also installed in different layers of the compression and tension reinforcement of the beam. This allows for analyzing the deformation behavior within the reinforced cross-sectional profile without the modifying effects of the concrete. Figure 3a shows the strain profiles measured along two instrumented layers of the tension reinforcement before and after severe cracking of the beam. At the 200 kN load step, the strain distributions exhibit similar behavior with a slight offset in the middle region due to the vertical loading of the structure. However, with increasing load, not only does the interlayer strain offset increase, but a pronounced bending also becomes apparent in the region between 1.0 and 1.5 m. This bending effect is caused by a large shear crack induced by the applied vertical load and the lower reinforcement arrangement on the right side of the beam (see Figure 1 ). The measurement data indicate that this crack leads to local buckling of the beam in the vertical direction. This effect is not captured by either the theoretical beam model or the DFOS derivation based on different planes of the beam. Similar conclusions regarding the influence of shear cracking have been drawn in the literature [  56 ] has drawn similar conclusions regarding the influence of shear cracking. Figure 3b shows that when determined individually for each reinforcement layer, the derived displacement profiles demonstrate that the actual deformation behavior of the beam, as represented by the LVDT measurements, can be reliably captured even at higher load steps.