# Strain Response Characteristics of RC Beams Strengthened with CFRP Sheet Using BOTDR
## 4 Experimental and Numerical Results
### Failure Load and Load-Deflection Response  
The test results are summarized in Table 3. The initial crack loads for the A-100, M-50, E-50, E-30 and LE-50 specimens were higher than the initial crack load for the C-0 specimen. The M-30 and LH-30 specimens were shown to be vulnerable to cracking, because the initial crack loads for the M-30 and LH-50 specimens decreased by 2.01% and 15.35%, respectively. Additionally, while the initial crack load for the LH-50 specimen, which was strengthened in the front, increased 120% when compared to the initial crack load for C-0, the initial crack load for the LH-50 specimen, which was strengthened in the back, decreased 15%. This is because the strengthening done using CFRP sheet asymmetrically caused a reduction of load capacity with load eccentricity. However, the ultimate load for all of the specimens varied over 10% in comparison to the one for the C-0 specimen. It is thought that the un-bond area did not affect the ultimate load of the structure, while the initial crack dominated the un-bonded area of the structure. Nevertheless, it is considered in order to carefully monitor the failures in the RC beam structures because the failure resulted in a reduction of structural performance over a long-term period. Figure 7 shows the comparison of the load-deflection curves between the experiments and numerical simulations. While the behavior of the beam structure during the stage where the load was distributed to the steel bars and the CFRP sheet slightly differed, the load-deflection behaviors between the experiment and simulation in terms of the initial slope of the curve, global trend and steel bar yielding point matched well. In the simulation, the ultimate loads were over-predicted by 2% to 4%. This is reasonably acceptable when it is considered that the beam structure exhibits the  
Figure 6: Delamination failure mode (E-30). (**a**) Experiment, (**b**) Analysis. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Specimen** & \(P_{\sigma,EX}\) & \(R_{\sigma}\) & \(P_{u,EX}\) & \(P_{u,FE}\) & \(P_{u,FE}\) & \(R_{u}\) & \(\Delta_{u,EX}\) & \(\Delta_{u,FE}\) & \(\Delta_{u,FE}\) & **Failure Mode** \\  & **(kN)** & **(\%)** & **(kN)** & **(kN)** & \(P_{u,EX}\) & **(\%)** & **(mm)** & **(mm)** & **(\%)** & **Failure Mode** \\ \hline C-0 & 14.46 & 0.0 & 101.62 & 100.52 & 1.01 & 0.0 & 50.02 & 43.51 & 0.87 & Flexural \\ A-100 & 35.43 & 145.02 & 145.74 & 150.62 & 0.97 & 43.42 & 45.78 & 35.75 & 0.78 & Interface De-bonding \\ M-50 & 19.74 & 36.51 & 128.98 & 134.42 & 0.96 & 26.92 & 44.43 & 44.95 & 1.01 & Interface De-bonding \\ M-30 & 14.17 & \(-\)20.1 & 129.9 & 133.35 & 0.97 & 27.83 & 41.87 & 32.99 & 0.79 & Interface De-bonding \\ E-50 & 27.66 & 91.29 & 122.54 & 125.41 & 0.98 & 20.59 & 50.70 & 51.87 & 1.02 & Cover Delamination \\ E-30 & 20.00 & 38.31 & 102.92 & 106.67 & 0.96 & 1.28 & 50.06 & 47.72 & 0.95 & Cover Delamination \\ LE-50 & 16.69 & 15.42 & 123.54 & 127.82 & 0.97 & 21.57 & 43.19 & 33.35 & 0.77 & Interface Debonding \\ LH-50 & Front: 32.12 & Front: 122.13 & & & & & & & & \\ Back: 12.24 & Back: \(-\)15.35 & 114.08 & 128.40 & 0.89 & 12.26 & 34.21 & 36.21 & 1.06 & Interface Debonding \\ \hline \hline \end{tabular}  
* \(P_{\sigma,EX}\): initial crack load; \(P_{u,EX}\): ultimate load of experiment; \(P_{u,FE}\): ultimate load of FEM; \(R_{\sigma}\): ration of crack load increase compared to the control specimen (C-0); \(R_{u}\): ration of ultimate load increase compared to the control specimen (C-0); \(\Delta_{u,EX}\): midspan deflection of experiment at ultimate load, \(\Delta_{u,EX}\): midspan deflection of FEM at ultimate load.  
\end{table} 
Table 3: Comparison of loads and failure mode *. anisotropic non-linear behavior. In the LH-50 specimen, the predicted ultimate load was approximately 10% higher than the one from the experiment and the failure behaviors from the experiment and the simulation differed.