# Seismic Response and Recentering Behavior of Reinforced Concrete Frames: A Parametric Study
## 3 Model Validation  
The numerical study conducted here starts by simulating the seismic behavior of a real archetype prototype frame model tested in the laboratory. In particular, the one-bay, one-story RC frame tested by [PERSON] et al. [21] has been considered, whose geometry and reinforcement configuration is shown in Figure 2. The RC frame is characterized by a clear span equal to 4.1 m and a net height of 3.075 m, assuming for the columns a fixed restraint at half of the foundation beam height, which is appropriate for capturing the initial stiffness of the RC frame in the first loading cycles (while avoiding explicitly modeling the bar slip and yield penetration phenomena). This prototype RC frame was tested in the laboratory [21], assuming an increasing cyclic horizontal loading protocol applied to the upper part of the frame, while no additional gravity load (apart from the self-weight) was applied. Figure 1: Example of pivot hysteresis model. The experimental load-displacement curve obtained experimentally has been simulated in a numerical model implemented in SAP2000 [16] by adopting the assumptions summarized in the previous section. According to the experimental source paper [21], concrete with a specified compressive strength of 21 MPa, an average compressive strength of 29.8 Mpa, and a modulus of elasticity of 24.8 GPa has been assumed, while reinforcing steel bars have been assumed to have average values of yield stress (455.9-497.6 MPa), tensile stress (580.5-656.6 MPa), and elongation (11.5-13.4%) dependent on the nominal size of the bar. The concrete cover, 3 cm thick in each section, has been assumed with no compressive strength. The pivot hysteresis model has been assumed for both the concrete and reinforcing steel, using the equations of [PERSON] et al. [12] for the \(\alpha\) and \(\beta\) parameter calculations (cf. Equations (3)-(6)). Since no axial load has been applied and, consequently, \(ALR=0\), \(\alpha\rightarrow\infty\) (a large value has been inputted), and \(\beta=0.115\) for both the beam and column members, the value of \(\eta\) has been assumed to be equal to 0. The fiber-hinge model P-M2-M3 has been adopted for both the beam and column members. Hinges have been applied at either end of the frame members. Cyclic pushover analysis has been performed through a sequence of pushover analyses, with each pushover analysis pushing the structure in the direction opposite to that of the preceding analysis and adopting the stiffness resulting from the end of the previous analysis, except for the first analysis where the initial stiffness has been used. Pushover analyses have been performed through a displacement-control load application at the beam-column joint, with a monitored displacement dependent on a specific cycle. A five-cycle loading protocol has been applied, with a monitored displacement of 22 mm for the first cycle, 29 mm for the second cycle, 42 mm (positive) and 41 mm (negative) for the third cycle, 52 mm for the fourth cycle, and 65 mm (positive) and 52 mm (negative) for the fifth and last cycle. The comparison between the load-displacement curve obtained from the cyclic pushover analysis performed on the numerical model and the experimental load-displacement curve is shown in Figure 3, while the main characteristic parameters of the curves, including maximum load (positive and negative), residual load (positive and negative) and global energy dissipated, are listed in Table 1.  
Figure 2: Geometric and reinforcement details of the RC frame simulated in this study. As reported in Section 2, no specific relationships were given for the \(\eta\) parameter. In the pivot hysteresis model implemented in SAP2000 [16], \(\eta\) can assume values between 0 (minimum stiffness degradation) and 1 (maximum stiffness degradation).