## 4 Structural Models and Nonlinear Static Analysis
### Pushover Analysis  
To grasp the overall force-displacement behavior of structures, a Pushover analysis was first carried out for each frame. The analysis adopted the inverted triangular distribution of lateral loads, and considered the P-\(\Delta\) effect of structures. During the pushover process, the top displacement of the structure was monitored. When the overall displacement angle of the structure (the ratio of the top displacement to the total height) reached 1/25, the loading was stopped. In order to compare the pushover results of different structures, four feature points were introduced. (1) Yield point, which means the whole structure yields. This paper adopted the suggestions of [PERSON] et al. [PERSON] et al. (2018), and used the farthest point method to define the yield point of the structure. (2) Limit point, which is the corresponding point on the pushover curve when the displacement angle on any floor of the structure reaches 1/50 (the deformation limit in the Chinese standard ([PERSON] et al., 2018)). (3) Collapse point, which is the corresponding point when the bearing capacity drops to 80% of the limit point, and is used to evaluate the ductility storage capacity of the structure. (4) Column yield point, which is the corresponding point on the pushover curve when the plastic hinge appears on the column for the first time. The pushover curves and characteristic points of various structures are shown in Figure 11.  
According to the stiffness before yielding, the emulated frames will show a relatively low second stiffness after the design seismic force, which is especially obvious when the connection strength is insufficient. This is due to the premature cracking of the beam end interface in emulated connections. Therefore, it is necessary to make the structure overstrength when designing such precast frames; otherwise, structural damage will occur under the design earthquake, which will increase the repair cost after earthquakes. The overstrength factor \(R_{s}\) (see Formula (1), where \(V_{p}\) is the peak bearing capacity and \(V_{d}\) is the design seismic force) of the PCE-S frame was calculated as 2.16, so it is recommended that the overstrength factor of emulated frames should be at least 2:  
\[R_{s}=\frac{V_{p}}{V_{d}} \tag{1}\]  
Through observing the yield points of various structures, it can be found that the emulated frames yielded before the RC frame, and the reduction of the joint strength of the PCE-S frame caused the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Structure Form** & **Cast-In-Situ Connection** & \multicolumn{3}{c}{**Emulated Connections**} & \multicolumn{3}{c}{**Non-Emulated Connections**} \\
**Abbreviation** & **RC** & **PCE** & **PCE-S** & **PCE-D** & **PCH** & **PCH-F** & **PCH-T** \\ \hline Bearing capacity & \(\surd\) & \(\Circle\) & \(\times\) & \(\Circle\) & \(\surd\) & \(\surd\) & \(\surd\) \\ Ductility capacity & \(\surd\) & \(\Circle\) & \(\times\) & \(\surd\) & \(\times\) & \(\Circle\) \\ Energy dissipation capacity & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\Circle\) & \(\times\) \\ Self-centering capacity & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\Circle\) & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular} Note: \(\surd\) means good performance, \(\Circle\) means general performance and \(\times\) means poor performance.  
\end{table} 
Table 2: The connection forms researched. Figure 11: Pushover curves of frames: (**a**) Comparison of emulated frames and the RC frame; (**b**) comparison of non-emulated frames and the RC frame. structure to yield earlier. The moment when the plastic hinge appears on column is always later than the moment when the structure yields. Thus, when designing according to the principle of strong columns and weak beams, the yield of the frame structure is controlled by the beam, and the earlier yield of the beam in the emulated frames will delay the yield of the structural column. For limit points, the displacement values of each frame are relatively close.