# Seismic Response and Recentering Behavior of Reinforced Concrete Frames: A Parametric Study
## 6 Conclusions  
In this paper, the seismic response and recentering behavior of RC frames has been analyzed numerically in order to construct novel design abacuses in the form of practical 3D surface/contour plots. These plots were useful to anticipate the inelastic response of a building structure based on the actual mechanical parameters of the RC sections at each story level. Cyclic pushover analysis has been performed on a wide spectrum of RC frames having different axial load levels and reinforcing details within a parametric study including 80 scenarios, covering a reasonable set of configurations that can be encountered in the existing RC-framed structures. A fiber-hinge formulation combined with the versatile pivot hysteresis model has been adopted, validated against experimental findings, and used in the cyclic pushover analyses of the parametric study. The main results of this work can be summarized as follows:  
1. The cyclic behavior of the RC frames has been described by a backbone branch enveloping the peaks for each cycle of the cyclic pushover analysis and then idealized through a bilinear curve with hardening. The unloading residual force has also been incorporated in the parametric study to investigate the recentering behavior of the RC frames related to the possible pinching effects of the existing RC structures with poor construction details. 2. The inelastic behavior of the RC frames can be described synthetically by means of three behavioral indexes, namely a recentering index, a hardening index, and a ductility index, whose trends have been described in this work through 3D surface and contour plots. These indexes were able to describe the backbone as well as the hysteretic behavior of the RC frame as a whole, depending on the axial load ratio \(ALR\)  
Figure 24: Inter-story drift time histories obtained for floors 3 and 8.  
longitudinal reinforcement percentage \(p_{s}\), and volumetric transverse reinforcement percentage \(p_{s}\) of each story level. 3. The recentering index was much more sensitive to the \(ALR\) than to the longitudinal and transverse reinforcement. The variations were more marked for low amounts of steel reinforcement and tended to diminish for higher amounts of steel reinforcement. The poorest recentering behavior was generally observed in a range of \(ALR=0.35-0.40\), which characterized most of the RC column configurations encountered in existing buildings. 4. The hardening index was highly correlated with the longitudinal reinforcement since, as reasonably expected, higher values of \(p_{l}\) led to an increase in the overall flexural capacity of the RC frame. A reciprocal influence between the hardening behavior and the loading condition in terms of axial load has been detected in the analyses, as the peak values of the hardening index were identified in a range of \(ALR\) values that somehow depended on the transverse reinforcement. 5. The deformation capacity of the RC frame, expressed by the ductility index, was higher for lower \(ALR\) scenarios. Moreover, the increase in the transverse reinforcement led to higher confinement effects in the RC columns, and this trend was consistently reflected in the numerical results obtained in the parametric study. 6. The estimates of the behavioral indexes reported in the contour plots of the parametric study were compared with the actual values obtained from the NTHAs on an eight-story building representative of the substandard RC frames built in the 1960s-1970s in Italy. The excellent agreement between the two sets of results has emphasized the usefulness of the constructed 3D surface and contour plots in predicting the seismic response and recentering behavior of a generic RC building, depending on the actual mechanical parameters of the RC sections at each story level, thus highlighting the importance of this parametric study for practical design purposes. Conceptualization, D.D.D., E.G. and A.G.; methodology, D.D.D., E.G. and A.G.; software, A.G; validation, E.G. and A.G.; formal analysis, D.D.D., E.G.