## 3 Experimental Validation
### Experimental Set-Up  
One reinforced concrete beam externally bonded with an FRP strip was tested until failure to study the characteristics of impedance spectra in the failure process [37]. The configuration of the beam together with the trapezoidal cross-section are shown in Figure 6. The geometric characteristics of the beam as well as the diameter of the steel reinforcements are shown in the figure.  
Figure 6: Configuration of tested beam specimen (unit: millimeters): (a) elevation view; (b) cross-section.  
The material properties were as follows: (a) Concrete with compressive strength = 35 megapascal (MPa) and tensile strength = 3 MPa was used. (b) Steel with yield strength = 500 MPa and elastic modulus = 210 gigapascal (GPa) was used. (c) One FRP strip (Sika CarboDur S512, Sika, Lyndhurst, NJ, USA) of 1430 mm in length \(\times\) 50 mm in width \(\times\) 1.2 mm in thickness was used for strengthening. The tensile strength of the FRP strip was 3100 MPa, and the Young's modulus was 170 GPa. Two-part epoxy was used to attach the FRP plate to concrete.  
The beam specimen was tested under four-point bending (Figure 6). Electromechanical impedances were captured during the tests by means of nine PZT patches (Figure 7) bonded to the FRP strip. P-876.A11 and P-876-SP1 PZT types were used, except for close to the ends of the FRP strip, where P-876.A15 (61 mm \(\times\) 35 mm \(\times\) 0.8 mm) sensors were glued [41].  
The tested beam was loaded following a sequence of 16 loading-unloading steps until failure with a maximum value of the loading force for each step, as shown in Table 1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test Number** & **Load Level** & **Test Code** \\ \hline
1 & 0 kN & 1 (Baseline) \\
2 & 6 kN & 2 \\
3 & 14 kN & 3 \\
4 & 16 kN & \\
5 & 25.6 kN & \\
6 & 26.3 kN & 4 \\
7 & 31.3 kN & 5 \\
8 & 32 kN & 6 \\
9 & 38 kN & 7 \\
10 & 44 kN & 8 \\
11 & 47.9 kN & \\
12 & 53.4 kN & 9 \\
13 & 63.8 kN & \\
14 & 70 kN & \\
15 & 85.5 kN & \\
16 & 92 kN & 10 \\
17 & 94 kN & 11 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Sequence of static loading tests for the specimen.  
Figure 7: PZTs’ set-up for the specimen (dimensions in mm): (**a**) detailed scheme; (**b**) photo.  
In each loading step, once the established load maximum was reached, the beam was completely unloaded, and the impedances were measured in all the sensors. Failure occurred due to the sudden detachment of the FRP strip as a consequence of the strong concentration of stresses that originated in the vicinity of a crack at the bottom of the beam, close to the left loading point. FRP debonding propagated towards the left end of the strip (Figure 8). Prior to failure, multiple cracks formed, first in the constant moment zone and, subsequently, in other areas of the beam. All of this extended cracking contributed to the subsequent failure of the beam. The first identified vertical crack occurred during test 3.  
For each loading step and with the purpose of stabilizing the progressive cracks, a protocol of three cycles of loading and unloading were applied for each load step. To simplify this study, from the 17 tests shown in Table 1, this study only focuses on tests 1, 2, 3, 6, 7, 8, 9, 10, 12, 16, and 17. A test code (1 to 11) was assigned in the third column of Table 1 for your reference in subsequent figures.