# Seismic Response and Recentering Behavior of Reinforced Concrete Frames: A Parametric Study
## 4 Parametric Study
### Results in Terms of Force-Drift Curves  
The force-drift results obtained for \(ALR=0.05-p_{l}=4\%-p_{s}=1.20\%\) are reported in Figure 6a; in this case, the frame tends to exhibit a stable cyclic response with prominent pinching effects. Since the applied axial load is very low compared with the column compressive capacity, the frame exhibits high displacement capacity as well as good recentering capacity since the observed unloading residual force value is low, while the hardening behavior is moderate due to a high amount of longitudinal reinforcement. It follows that the frame is characterized by a low recentering index \(F_{0}/F_{y}\) and intermediate values of hardening and ductility indexes \(F_{max}/F_{y}\) and \(\mu\), respectively, as reported in Figure 6b.  
The force-drift results obtained for \(ALR=0.20-p_{l}=4\%-p_{s}=1.60\%\) are illustrated in Figure 7a; also in this case, the frame tends to exhibit a stable cyclic response and significant pinching effects. The applied axial load is low compared with the column compressive capacity; therefore, the frame shows a high displacement capacity and good recentering behavior, although it is slightly lower than the case when \(ALR=0.05\), while the hardening behavior is high due to the high reinforcement percentage and the higher \(ALR\) value. It follows that the frame is characterized by a low recentering index \(F_{0}/F_{y}\), a high hardening index \(F_{max}/F_{y}\), and an intermediate ductility index \(\mu\), as illustrated in Figure 7b.  
Figure 6: Force–drift curve (**a**) and bilinear idealization (**b**) for \(ALR=0.05-p_{l}=4\%-p_{s}=1.20\%\).  
The force-drift results obtained for \(ALR\) = 0.40, \(p_{l}\) = 3% and \(p_{s}\) = 1.20% are illustrated in Figure 8a; in this case, the cyclic response is still stable, and the pinching effects are instead attenuated. Therefore, the frame presents a lower recentering capacity (than in the previous cases) since the observed unloading residual force value is higher. Since the applied axial load is moderate and close to the value corresponding to the maximum flexural strength, the frame shows a high displacement capacity and a moderate hardening behavior. It follows that the frame is characterized by a high \(F_{0}/F_{y}\) value, an intermediate \(F_{max}/F_{y}\) value, and a high \(\mu\) value, as illustrated in Figure 8b.  
The force-drift results obtained for \(ALR\) = 0.60, \(p_{l}\) = 2%, and \(p_{s}\) = 0.80% are illustrated in Figure 9a; in this case, the cyclic response becomes unstable, and the pinching effects are very attenuated. The recentering capacity is moderate since the observed unloading residual force is small, but since the applied axial load has reached a significant intensity, the frame shows a low displacement capacity, exhibiting a brittle failure occurring at a relatively low drift value. It follows that the frame is characterized by intermediate values of \(F_{0}/F_{y}\), \(F_{max}/F_{y}\), and \(\mu\), as depicted in Figure 9b.  
Finally, the force-drift results obtained for \(ALR\) = 0.80, \(p_{l}\) = 2% and \(p_{s}\) = 1.20% are shown in Figure 10a. Although the graphs in this case are poorly visible because of the adoption of a consistent axis scale with the previous plots, it can be noted that the cyclic response is very unstable, and the pinching effects are almost null. Since the applied axial load has reached a very high intensity, the frame shows a negligible displacement capacity, reaching a brittle failure for a very low drift value. The hardening behavior and recentering capacity are evidently affected by the low drift value reached, as confirmed by the values of \(F_{0}/F_{y}\), \(F_{max}/F_{y}\), and \(\mu\), as shown in Figure 10b.  
Figure 8: Force–drift curve (**a**) and bilinear idealization (**b**) for \(ALR\) = 0.40 – \(p_{l}\) = 3% – \(p_{s}\) = 1.20%.