## 3 Test Results
### Dynamic Test Results at Different Damage Levels
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{3}{c}{**Vertical Direction**} & \multicolumn{3}{c}{**Horizontal Direction**} \\ \multirow{2}{*}{**Beam Name**} & \multicolumn{3}{c}{**MAC Values (\%)**} & \multicolumn{3}{c}{**MAC Values (\%)**} \\ \cline{2-7}  & **First Mode** & **Second Mode** & **Third Mode** & **First Mode** & **Second Mode** & **Third Mode** \\ \hline Beam\_GFRP\_PreStr & 99.1 & 86.9 & 79.3 & 96.9 & 82.6 & 77.9 \\ Beam\_CFRP\_PreStr & 99.4 & 89.2 & 74.4 & 93.4 & 81.1 & 72.0 \\ \hline \end{tabular}
\end{table} 
Table 6: MAC values of the mode shapes of the strengthened beams. Figure 11: Mode shapes of the bare beams in the undamaged state: (**a**) first, (**b**) second, and (**c**) third mode in the vertical direction; (**d**) first, (**e**) second, and (**f**) third mode in the horizontal direction. In the table above, f1 und, f2 und, and f3 und are the undamaged state modal frequencies of the first, second, and third modes, respectively. As the level of damage increases, the modal frequencies of Beam_GFRP_PreStr decrease progressively. This indicates a reduction in stiffness caused by the damage and resulting in lower frequency values. The most significant reduction in the vertical direction is observed in the first mode, while the second mode is less affected. The second and third modes exhibit a slower rate of decline, indicating that higher modes are less sensitive to damage in the vertical direction. In the horizontal direction, the third mode shows the largest decrease in modal frequencies, whereas the second mode remains more stable across various damage levels. These findings highlight the influence of structural damage on dynamic properties, with the first mode being the most sensitive to changes in structural integrity. \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}  & & **f1/f1 und** & **f2/f2 und** & **f3/f3 und** & **f1/f1 und** & **f2/f2 und** & **f3/f3 und** \\ \hline \multirow{4}{*}{Strengthened} & Undamaged & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 \\  & D1 & 0.949 & 0.965 & 0.993 & 0.987 & 0.994 & 0.900 \\ \cline{1-1}  & D2 & 0.914 & 0.959 & 0.941 & 0.920 & 0.988 & 0.866 \\ \cline{1-1}  & D3 & 0.877 & 0.954 & 0.923 & 0.884 & 0.987 & 0.860 \\ \cline{1-1}  & D4 & 0.860 & 0.953 & 0.905 & 0.884 & 0.986 & 0.855 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Modal frequency ratios at different damage levels for Beam_GFRP_PreStr. Figure 12: Variation in modal frequency ratios at different damage levels for Beam_GFRP_PreStr in (a) the vertical direction and (b) the horizontal direction. Table 8 presents the modal frequency ratios for Beam_CFRP_PreStr at the D1 damage level, comparing the modal frequency estimates in both vertical and horizontal directions to those in the undamaged state. As previously mentioned, Beam_CFRP_PreStr failed before reaching the D2 damage level. Therefore, only the frequency ratios at the D1 damage level are given. Figure 13 illustrates the variation in these modal frequency ratios for Beam_CFRP_PreStr in both directions, highlighting the effects of structural damage on the dynamic behavior of the beam. Table 8 and Figure 13 show a significant reduction in modal frequencies as the beam was damaged at the D1 damage level, particularly in the vertical direction. The first and third modes exhibit the most pronounced decreases, indicating that these modes are more sensitive to damage. The second mode, however, shows a relatively moderate reduction, suggesting greater stability under damage. In the horizontal direction, the first and second modes exhibit smaller reductions compared to the vertical direction, indicating that horizontal dynamic behavior is less sensitive to damage at lower modes.