# Strain Response Characteristics of RC Beams Strengthened with CFRP Sheet Using BOTDR
## 4 Experimental and Numerical Results
### Strain Behavior of CFRP Sheet  
The ultimate strain results in the middle of the CFRP sheets from the experiments and numerical simulations are summarized in Table 4. In the experiment, the strain was monitored using two types of instruments: a conventional electrical strain gauge and a BOTDR sensor. When using the strain gauge, the ultimate strain for the M-30 specimen, which had an unbound area in the middle of the beam structure, was 30% lower than the one for the A-100 specimen, which was strengthened perfectly. It is shown that placing the strengthening CFRP sheets in the middle of the beam structure results in a more advantageous performance of the CFRP sheets on the structural behavior. In the simulation,  
Figure 7: Comparison of load-deflection curves between experiment and analysis. (**a**) C-0, (**b**) A-100, (**c**) M-50, (**d**) M-30, (**e**) E-50, (**f**) E-30, (**g**) LE-50, and (**h**) LH-50. the ultimate strains were slightly over-predicted by 15% in contrast to those from the strain gauges. The ultimate strains that were monitored using the BOTDR sensors were 17% lower than those from the strain gauges. Figure 8 presents the comparison of the load-strain curves in the experiment and analysis in the CFRP sheet. In most cases, the predicted load-strain behaviors corresponded well with the observed loads and strains when using the strain gauges and BOTDR sensors. The slopes of the load-strain curves in the numerical simulation were relatively lower than those in the experiments. It is thought that the difference of the slopes in the numerical simulation and experiments was a result of the measuring conditions in the experiments. The strain from the strain gauge affected the surface condition where the strain gauge was placed and could be roughly measured due to the adhesive epoxy. In the case of the BOTDR sensor, the strain was considered to be more stable than the one that was from the strain gauge because the sensor was perfectly bonded with the CFRP sheet and the strain result's average value was in the range of 500 mm. Therefore, it was found that the numerical results were relatively close to the experimental results using the BOTDR sensor. The load-strain response seen in Figure 8e from the BOTDR sensor shows the difference with other curves. Considering the fact that it happened only in the E-30 specimen and the load-deflection response for the E-30 specimen were reasonable, it is thought to be caused by the slip of the BOTDR fiber sensor which needed to be fully constrained in the epoxy during the experiment. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Specimen** & \multicolumn{3}{c}{**CFRP Strain (\(\mu\)c)**} & \multicolumn{2}{c}{**Gauge/FEM**} & \multicolumn{1}{c}{**Gauge/BOTDR**} \\ \hline  & Gauge & FEM & BOTDR & & \\ A-100 & 6035.70 & 6114.95 & 4261.06 & 0.99 & 1.42 \\ M-50 & 2867.61 & 4113.02 & 3190.17 & 0.70 & 0.90 \\ M-30 & 1896.72 & 2810.13 & 459.20 & 0.67 & 4.13 \\ E-50 & 2407.52 & 2952.68 & 2106.83 & 0.82 & 1.14 \\ E-30 & 3405.64 & 2998.07 & 2482.14 & 1.14 & 1.37 \\ LE-50 & 4594.38 & 5347.05 & 3056.74 & 0.86 & 1.50 \\ LH-50 & 2877.01 & 3908.65 & 3967.69 & 0.74 & 0.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the strains in the carbon-fiber-reinforced polymer (CFRP) sheet. Figure 8: _Cont._  
In addition, the strain distribution for the CFRP sheets was investigated using the strain results through the BOTDR sensors and numerical simulations. The strain distributions that used experimental strain results were visualized using Origin, a numerical analysis program. In the visualization, the strain distributions were classified in 8 levels following the order of the magnitude and a thin plate spline algorithm was utilized to improve the visibility. Figure 9 shows the strain distribution of the CFRP sheet in the A-100 specimen from the experiment and simulation. As seen in Figure 9, the predicted strain distribution matched well with the experimental result in terms of the magnitude of the strain and the shape of the strain distribution.