## 3 Test Results
### Dynamic Test Results at Different Damage Levels
These results suggest that while damage affects both directions, the vertical dynamic response is more significantly impacted, particularly in the first mode for the beam strengthened with CFRP. Table 9 presents the modal frequency ratios for Beam_GFRP_PostStr at various damage levels. Initially, Beam_GFRP_PostStr is a bare beam, and the modal frequencies are estimated for both the undamaged state and the D1 damage level. Subsequently, the beam is strengthened with GFRP, and the modal frequencies are extracted again at the D1 damage level. The beam is then subjected to further damage, and the modal frequencies are estimated at the D2, D3, and D4 damage levels. Figure 14 illustrates the variation in modal frequency ratios in both directions, tracking the effects of both damage progression and strengthening. Table 9 and Figure 14 present the dynamic response of Beam_GFRP_PostStr throughout its testing process. Initially, the bare beam exhibits a consistent decrease in modal frequencies as damage increases from the undamaged state to the D\({}_{1}\) damage level. After GFRP strengthening, the modal frequencies in the vertical direction show a decrease, which can be attributed to the effects of the beam's transport during the strengthening process and the week-long waiting period for the strengthening material to cure under its own weight (i.e., in the vertical direction), potentially leading to additional damage. In the vertical direction, the third mode exhibits a more gradual decline, while the second mode remains relatively stable until higher damage levels. In the horizontal direction, after strengthening with GFRP at the D\({}_{1}\) damage level, the modal frequencies show a significant recovery, with all modes increasing beyond their undamaged state. This suggests that GFRP strengthening is effective in restoring and even enhancing the beam's stiffness, par  
Figure 14: Variation in modal frequency ratios at different damage levels for Beam_GFRP_PostStr in (**a**) the vertical direction and (**b**) the horizontal direction. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Damage Level**} & \multicolumn{4}{c}{**Vertical Direction**} & \multicolumn{4}{c}{**Horizontal Direction**} \\ \cline{3-8}  & & **f\({}_{1}\)/f\({}_{1}\)und** & **f\({}_{2}\)/f\({}_{2}\)und** & **f\({}_{3}\)/f\({}_{3}\)und** & **f\({}_{1}\)/f\({}_{1}\)und** & **f\({}_{2}\)/f\({}_{2}\)und** & **f\({}_{3}\)/f\({}_{3}\)und** \\ \hline \multirow{2}{*}{Bare} & Undamaged & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 \\  & D\({}_{1}\) & 0.988 & 0.991 & 0.955 & 0.872 & 0.993 & 0.917 \\ \hline \multirow{4}{*}{Strengthened} & D\({}_{1}\) & 0.899 & 0.959 & 0.921 & 1.196 & 1.035 & 1.033 \\  & D\({}_{2}\) & 0.848 & 0.925 & 0.861 & 1.097 & 0.947 & 0.924 \\ \cline{1-1}  & D\({}_{3}\) & 0.836 & 0.916 & 0.781 & 1.093 & 0.947 & 0.919 \\ \cline{1-1}  & D\({}_{4}\) & 0.829 & 0.916 & 0.775 & 1.092 & 0.947 & 0.916 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Modal frequency ratios at different damage levels for Beam_GFRP_PostStr. ticularly in the horizontal direction. However, as the beam is subjected to further damage at the D\({}_{2}\), D\({}_{3}\), and D\({}_{4}\) damage levels, the modal frequencies progressively decrease again, indicating that the strengthening cannot fully mitigate the impact of higher damage levels. In overall, the results suggest that the GFRP strengthening improves the dynamic response of Beam_GFRP_PostStr at lower damage levels, but its effectiveness diminishes as more severe damage is introduced. Table 10 shows the modal frequency ratios for Beam_CFRP_PostStr at different damage levels, both in the vertical and horizontal directions. Initially, Beam_CFRP_PostStr is tested as a bare beam, with modal frequencies estimated in the undamaged state and at the D\({}_{1}\) damage level. Subsequently, the beam is strengthened using CFRP, and the modal frequencies are estimated again at the D\({}_{1}\) damage level.