# Flexural Behavior of an RC Beam Externally Strengthened with a Steel- and CFRP-Based Method
## 3 Results and Discussion
### Critical Parameters  
Table 3 lists the critical parameters, which are determined according to the specimen critical states during the experiment. \(M_{\text{cr}}\), \(M_{\text{y}}\), and \(M_{\text{u}}\) represent the crack moment, yield moment, and ultimate moment, respectively. Notably, the ultimate moment and the initial stiffness were adopted to determine the \(M_{\text{y}}\) of the specimen;\(f_{\text{cr}}\),\(f_{\text{y}}\), and\(f_{\text{u}}\) are defined as the midspan deflection corresponding to \(M_{\text{cr}}\), \(M_{\text{y}}\), and \(M_{\text{u}}\), and are named as the crack deflection, yield deflection, and ultimate deflection, respectively. The ductility coefficient \(\mu\) represents the ratio of \(f_{\text{u}}\) to \(f_{\text{y}}\). The nominal improvement from the retrofitted specimen to the standard specimen is plotted in Figure 7.  
Figure 6: Load–deflection relationship. The enhancements of the single methods (L2-A and L3-C) were only 2.0% and 5.1% for \(M_{\rm cr}\), respectively, as there was limited contact between the angle steel and the standard beam. A single CFRP plate could not effectively control the appearance of the crack until the deformation of the beam was achieved to a certain extent. However, with the collaborative methods, the improvement varied from 26.7% to 84.9%. As there were steel plates bonded to the bottom surface of the beam, either directly or indirectly, they significantly contributed to the control of the crack occurrence. Notably, the crack moment of L5-C-St-A was 45.9% larger than that of L4-St-A. The CFRP was tightly bonded to the concrete due to the pressure from the steel plate, which led to an early retrofitting of the CFRP plate to the beam. As the \(M_{\rm cr}\) of L6-C-Ss-A was close to that of L4-St-A, it was demonstrated that the separated steel plate had little positive influence on the suppression of the crack. The tendency of the yield moment was rather similar to that of the ultimate moment. The improvement ratios varied from 1.72 to 4.58 for \(M_{\rm y}\) and from 2.21 to 4.41 for \(M_{\rm u}\). As the enhancements of the collaborative methods were significantly larger than those of the single methods, especially Specimens L4-St-A and L5-C-St-A, the working mechanism of the proposed retrofitting method was demonstrated to be feasible. However, it should be noted that there was an obvious decrease in the \(M_{\rm u}\) of L6-C-Ss-A with respect to L4-St-A (6.75%) and L5-C-St-A (12.4%). The decrease rate for \(M_{\rm y}\) was even more significant. This phenomenon indicated that the separated steel plate could not effectively transfer the complete load from the CFRP plate to the angle steel with the partial load borne by the middle part of the retrofitting unit. Therefore, although the corresponding increase for L6-C-Ss-A was larger than those of both L2-A and L3-C, the collaborative retrofitting method is not recommended with respect to the construction cost and efficiency. Concerning the deformation, when the initial crack appeared, only Specimens L3-C, L5-C-St-A, and L6-C-Ss-A achieved a larger midspan deflection than the standard specimen L1 (see Figure 8). Notably, the \(f_{\rm cr}\) of L3-C was only 1.2% larger than that of L1, while that of \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen No.**} & \multicolumn{3}{c}{**M (kN-m)**} & \multicolumn{3}{c}{**\(f\) (mm)**} & \multirow{2}{*}{\(\mu\)} \\  & \(M_{\rm cr}\) & \(M_{\rm y}\) & \(M_{\rm u}\) & \(f_{\rm cr}\) & \(f_{\rm y}\) & \(f_{\rm u}\) \\ \hline L1 & 34.33 & 68.86 & 77.15 & 2.51 & 19.93 & 36.43 & 1.83 \\ L2-A & 35.00 & 193.10 & 217.10 & 2.26 & 26.10 & 43.24 & 1.66 \\ L3-C & 36.09 & 118.11 & 170.61 & 2.54 & 20.20 & 42.99 & 2.13 \\ L4-St-A & 43.51 & 294.25 & 320.00 & 1.69 & 25.40 & 54.55 & 2.15 \\ L5-C-St-A & 63.47 & 315.07 & 340.57 & 3.36 & 30.96 & 43.20 & 1.40 \\ L6-C-Ss-A & 47.67 & 230.39 & 298.42 & 3.25 & 21.84 & 36.40 & 1.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mechanical properties.