## 3 Test Results and Discussions
### Flexural Ductility  
To examine the flexural ductility of beams in the F-series specimens subjected to a reversal cyclic load, this study calculated the member displacement ductility ratio (\(\mu_{A}=\Delta_{n}/\Delta_{y}\)) [14] and the work \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{3}{c}{**Diagonal Shear Crack Strength**} & \multicolumn{3}{c}{**Ultimate Shear Strength**} \\ \cline{2-9}  & \(\begin{array}{c}\mathbf{V_{cr}^{*}}\\ \mathbf{(kN)}\end{array}\) & \(\begin{array}{c}\mathbf{V_{cr}^{*}}\\ \mathbf{(kN)}\end{array}\) & \(\begin{array}{c}\mathbf{V_{cr}^{*}}\\ \mathbf{(kN)}\end{array}\) & \(\begin{array}{c}\mathbf{V_{cr}^{*}}\\ \mathbf{(kN)}\end{array}\) & \(\begin{array}{c}\mathbf{V_{cr}^{*}}\\ \mathbf{(kN)}\end{array}\) & \(\begin{array}{c}\mathbf{V_{cr}^{*}}\\ \mathbf{(kN)}\end{array}\) & \(\begin{array}{c}\mathbf{V_{cr}^{*}}\\ \mathbf{(kN)}\end{array}\) & \(\begin{array}{c}\mathbf{V_{cr}^{*}}\\ \mathbf{(kN)}\end{array}\) & \(\begin{array}{c}\mathbf{V_{cr}^{*}}\\ \mathbf{(kN)}\end{array}\) & \(\begin{array}{c}\mathbf{V_{cr}^{*}}\\ \mathbf{(kN)}\end{array}\) & \(\begin{array}{c}\mathbf{V_{cr}^{*}}\\ \mathbf{(kN)}\end{array}\) & \(\begin{array}{c}\mathbf{V_{cr}^{*}}\\ \mathbf{(kN)}\end{array}\) & \(\begin{array}{c}\mathbf{V_{cr}^{*}}\\ \mathbf{(kN)}\end{array}\) \\ \hline S–H–C & 260 & 263 & 261.5 & 0.18 & 511.4 & 431.6 & 471.5 & 0.31 \\ S–H–G & 187 & 192 & 189.5 & 0.14 & 260.4 & 292.8 & 276.6 & 0.19 \\ \hline \hline \end{tabular} Notes. \(\overline{V_{cr}^{*}}\) is shear cracking strength; \(\overline{v_{cr}}\) is shear cracking stress; \(\overline{V_{cr}}\) is the measured shear capacity; and \(\overline{v_{n}}\) is the ultimate shear stress.  
\end{table} 
Table 4: Summary of test results in the beam of S-series specimens. Figure 8: Applied load–displacement relationship of beam element. damage indicator (\(W_{i}\)) [17], where \(\Delta_{n}\) is the displacement upon the peak load of the beam. Figure 9 shows the variation of \(W_{i}\) values determined from the envelope curve at each loading cycle. In general, the specimens reinforced with longitudinal GFRP bars possessed lower \(W_{i}\) values at each cycle when compared with the companion specimens with steel bars, resulting in that the differences gradually increased with the increase in the loading cycle. Thus, \(W_{i}\) values calculated up to the peak load (\(W_{p}\)) and ultimate failure (\(W_{f}\)) were lower by 93% and 97%, respectively, for the specimen F-N-G when compared with the companion specimen F-N-C, as listed in Table 3. The corresponding \(W_{i}\) values calculated from the comparison of \(W_{p}\) and \(W_{f}\) for both specimens F-H-G and F-H-C were 29% and 84%, respectively. Overall, the low elastic modulus and limited elongation capacity of GFRP bars are unfavorable for the flexural ductility of beams. Furthermore, the lack of an anchorage length of GFRP bars in the exterior beam-column connection can significantly reduce the flexural ductility of the beam element. It is also interesting that both specimens F-N-G and F-H-G exhibited a similar increasing rate of \(W_{i}\) up to the beam failure whereas the specimen F-N-C had higher \(W_{i}\) values than the specimen F-H-C, indicating a 7.91 times higher value of \(W_{p}\) in the specimen F-N-C. This trend was also observed for \(\mu_{\Delta}\) values. The value of \(\mu_{\Delta}\) determined in specimen F-N-C was 1.89 times higher than that of specimen F-H-C. The flexural ductility of beams significantly depends on the longitudinal reinforcement index (\(\omega_{s}\)). [PERSON] et al. [18] showed that the \(\mu_{\Delta}\) values decrease was proportional to the exponential function with the increase in \(\omega_{s}\).