# Strengthening of RC Beams with CFC Panels for Improving Impact Resistance
## 6 Parametric Study  
The impact resistance performance of RC beams and RC beams reinforced with CFC panels were verified through falling-weight impact experiments and SPH analysis simulations. Tests were conducted until the residual displacement reached the design limit. In this study, the impact behavior of each specimen was examined up to the ultimate limit through a parametric analysis. Specifically, fracture simulations were performed for all the specimens subjected to three repeated impacts at a constant impact velocity of 3.0 m/s, and the relationship between the number of impacts and the cumulative residual displacement was investigated. Additionally, the fracture behavior of each specimen was considered when the impact velocity was increased to 4.0 m/s and 5.0 m/s. Table 2 lists the specific analytical conditions used.  
Three repeated impact simulations were performed for three types of CFC-reinforced test specimens, but the ordinary RC beam was excluded from the study because a large residual displacement occurred with one impact.  
As shown in Figure 24, it is recognized that when the number of repeated impacts increases, the residual displacement correspondingly increases as the damaged area increases. When subjected to three repeated impacts, RC_F3S_CFC exhibits the best performance among the strengthened specimens. During the first two impacts, the effectiveness of the three strengthening methods were ranked as follows: RC_F3S_CFC < RC_FB_CFC < RC_P3S_CFC; however, after the third impact, RC_P3S_CFC outperformed RC_FB_CFC. Thus, the relative superiority of RC_P3S_CFC and RC_FB_CFC depend on the adhesive strength of the CFC panels or the reinforcement area of the RC_P3S_CFC specimen. However, in general, it is expected that safety against ultimate failure is higher for RC_P3S_CFC, which reinforces the bottom and side surfaces.  
As shown in Figure 25, when subjected to an impact velocity of 5.0 m/s, all the specimens except RC_F3S_CFC experienced significant fractures with residual displacements of 30 mm or more after a single impact; however, RC_F3S_CFC displayed a residual displacement of 10.35 mm, demonstrating remarkable impact resistance.  
In addition, under relatively severe impact conditions, such as impact velocities of 4.0 m/s or 5.0 m/s, RC_P3S_CFC exhibited superior impact resistance compared to RC_FB_CFC after a single impact. This indicates that RC_P3S_CFC offers greater safety than RC_FB_CFC.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Specimen ID**} & \multicolumn{3}{c}{**Parameter of Parametric Study**} \\ \cline{2-3}  & **Impact Velocity** & **Simulation Type** \\ \hline RC\({}^{*}\) & & \\ \hline RC\_FB\_CFC & & \\ \hline RC\_P3S\_CFC & & \\ \hline RC\_F3S\_CFC & & \\ \hline RC\_4 m/s & & \\ \hline RC\_FB\_CFC\_4 m/s & & Single impact \\ \hline RC\_P3S\_CFC\_4 m/s & & \\ \hline RC\_5 m/s & & \\ \hline RC\_FB\_CFC\_5 m/s & & \\ \hline RC\_P3S\_CFC\_5 m/s & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parametric study. \({}^{*}\) is same as in Figure 24.  
Figure 24: Results of parametric study on three repeated impacts prediction: (**a**) displacement at midspan; (**b**) impact force at midspan; (**c**) relationship between cumulative residual displacement and number of impacts. Note: *—Cannot demonstrate residual displacement.  
Figure 25: _Cont_.