## 3 Results and Analysis
### Nature of concrete
#### 3.3.4 Restoring Force Model of Frame  
The restoring force model of a structure or member needs to be established for the non-linear seismic response analysis. The restoring force characteristic curve shows the relationship between the resistance and the deformation in an attempt to restore the original state when the structure is deformed by the external force. At the same time, it also reflects the strength, stiffness, stiffness degradation, deformation capacity, and energy dissipation capacity of the structure and components in the process of repeated loads.  
The restoring force model is based on the low cycle repeated load test. According to the obtained restoring force skeleton curve and the law of each cycle curve, the skeleton curve determines each characteristic point of the model. It is the connecting line of each characteristic point in the 1/4 hysteresis cycle. The hysteresis loop indicates the walking path and stiffness degradation of the model in the process of positive and negative loading and unloading, then it is simplified according to certain conditions (such as the equivalence of intensity and energy dissipation capacity) [14].  
In this paper, based on the analysis of the hysteretic curve of the RC frame with a low yield point under low cyclic loading, research on the restoring force characteristics of the RC frame was carried out. The restoring force models of reinforced concrete frames with different yield points were established. According to the hysteretic curve of a reinforced concrete frame with different yield points and the skeleton curve connecting each vertex of the hysteretic curve, this paper adopted the degenerate three-line restoring force model (Figure 14), and its stiffness in each stage was:  
\begin{table}
\begin{tabular}{c c c c} \hline
**Specimen Number** & **Loading Direction** & **Elastic Displacement Angle \(\theta_{e}\)** & **Elasticplastic Displacement Angle \(\theta_{p}\)** \\ \hline KJ-1 & Forward & 1/129.4 & 1/43.1 \\  & Reverse & 1/137.1 & 1/45.7 \\ \hline KJ-2 & Forward & 1/122.5 & 1/40.8 \\  & Reverse & 1/125.0 & 1/41.7 \\ \hline KJ-3 & Forward & 1/112.8 & 1/37.6 \\  & Reverse & 1/120.1 & 1/40.0 \\ \hline \end{tabular}
\end{table}
Table 10: Yield displacement angle of displacement for the frames.  
Stiffness of OA section: the elastic loading rule, the frames had no stiffness degradation and residual deformation before the restoring force reached \(P_{y}\), and the specimens were loaded according to the walking route of O-A. The stiffness formula is expressed as:  
\[K_{1}=P_{y}/\Delta_{y} \tag{4}\]  
Stiffness of AB section: the elastic-plastic loading rule. When the restoring force was between the yield load and the peak load, the incremental stiffness of the specimens after yield was taken during loading. The stiffness formula is expressed as:  
\[K_{2}=\frac{P_{\text{max}}-P_{y}}{\Delta_{\text{max}}-\Delta_{y}} \tag{5}\]  
Stiffness of BC section: When the restoring force exceeded the peak load \(P_{u}\), it began to enter the descending section. The stiffness formula is expressed as:  
\[K_{3}=\frac{P_{u}-P_{\text{max}}}{\Delta_{u}-\Delta_{\text{max}}} \tag{6}\]  
Unloading stiffness before yield and maximum load according to the loading rules of the elastic stage. The stiffness formula is expressed as:  
\[K_{4}=K_{1} \tag{7}\]  
Unloading stiffness after maximum load. Stiffness formula is expressed as:  
\[K_{5}=\alpha K_{4},\alpha=\left(\frac{\Delta_{y}}{\Delta_{i}}\right)^{0.35} \tag{8}\]  
\(\Delta_{i}\)--Displacement value of the unloading point of the \(i\) time cycle after the highest load. The definition of reverse stiffness is the same as that of forwarding stiffness.