## 3 Results and Discussion
### Strength and Displacement Ductility  
The ability of the structures to endure deformation without the collapse of the structure is called displacement ductility. It is one of the essential criteria related to the seismic response of structures and can be calculated using Equation (1).  
\[\mu=\frac{\Delta_{u}}{\Delta_{y}} \tag{1}\]  
where \(\Delta_{y}\) is the corresponding displacement to the yield load, and \(\Delta_{u}\) is the maximum displacement of the structure calculated using the equivalent energy method [35], as shown in Figure 10.  
The displacement, load, and drift ratio corresponding to the yield point, peak point, and ultimate point, along with the displacement ductility for all the specimens, are presented in Table 3. As shown in the table, specimens BMRC1, NEWRC1, NEWRC4, NEWRC5, and NEWRCF have excellent ductility as their ductility ratio is more significant than 5, which is greater than the code specification of MOTC, Taiwan, ROC [36], for bridges located in the seismic zone.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline
**Specimen** & **Yield Point** & \multicolumn{3}{c}{**Peak Point**} & \multicolumn{3}{c}{**Ultimate Point**} & \multicolumn{3}{c}{**Rebar Buckling**} \\ \hline  & \(P_{y}\) & \(\Theta_{y}\) & \(P_{P}\) & \(\Theta_{p}\) & \(P_{u}\) & \(\Theta_{u}\) & \(\mu=\theta_{u}/\theta_{y}\) & \(\Delta_{bb_{\text{sp}}}\) & \(\Delta_{bb_{\text{sp}}}\) & \(\Delta_{bb_{\text{sp}}}/\Delta_{bb_{\text{pred}}}\) \\ \hline  & **Kn** &  
Compared to BMRC1, NEWRC1 recorded a 4.7% decrease in displacement ductility, indicating that the material properties slightly influenced the displacement ductility. Furthermore, when other input parameters are the same, an increase in the transverse reinforcement spacing results in the rapid degradation of the displacement ductility; NEWRC2 and NEWRC3 show a reduced displacement ductility of 33.3% and 46.3%, respectively, compared to NEWRC1. On the other hand, an increase in the axial load ratio and varying transverse reinforcement strength increased the displacement ductility slightly; NEWRC4 and NEWRC5 showed an increased displacement ductility of 7.1% and 5.9%, respectively, compared to NEWRC1. The displacement ductility of the specimen NEWRCF frame is greater than 5.0, which implies that the frame has good ductility and deformation capability under quasi-static cyclic loading.  
As the primary mode of failure was identified as buckling of longitudinal rebar. Therefore, in Table 3, the deformation at rebar buckling from the experimental results \(\Delta_{bb_{\alpha\gamma}}\) was compared with the buckling failure point \(\Delta_{bb_{\alpha\gamma}}\) proposed by [PERSON] and [PERSON] [37]. The buckling limit equation is presented in Equation (2). The results suggest that the predicted values were in the acceptable range for all the columns and frame specimens.  
\[\frac{\Delta_{bb}}{L}(\%)=3.25\ \bigg{(}1+K_{e-bb}\rho_{eff}\frac{d_{b}}{D} \bigg{)}\bigg{(}1-\frac{P}{A_{g}f_{c}^{i}}\bigg{)}\bigg{(}1+\frac{L}{10\ D}\bigg{)} \tag{2}\]  
where \(\Delta_{bb}/L\) is the drift ratio at buckling failure, \(K_{e-bb}=40\) for rectangular-reinforced columns and 150 for spiral-reinforced columns but should be taken as 0 for columns with \(\frac{s}{d_{b}}>6\), \(\rho_{eff}=\rho_{s}f_{yt}/f_{c}^{\prime}\rho_{s}\) is the volumetric transverse reinforcement ratio, \(f_{yt}\) is the yield stress of the transverse reinforcement, \(L\) is the distance from the column base to the point of contra flexure, and \(D\) is the column depth.