# Study of Effective Length Factor of Frame-Core Wall Structure with Cross-Layer Columns
## 6 Conclusions  
1. The lateral stiffness ratio of the structure decreases, and the maximum inter-story displacement angle and natural vibration period increase, as the height and number of cross-layer columns increase.
2. The overall buckling load of the structure decreases with the increase in the number of cross-layer columns and the number of stories. The buckling coefficient increases with the increase in the number of cross-layer columns and the decrease in the number of stories. The remaining beams and columns of the structure with cross-layer columns can be regarded as sub-structures, and their lateral stiffness can be calculated according to the ordinary frame structure, thus simplifying the calculation model.
3. GB 50017-2017 only considers the force of the frame in the weak axis direction and does not include the influence of the core wall on the distribution of bearing capacity, which is somewhat different from the actual force mechanism. Therefore, this study proposes a new modification method for determining the effective length factor of the cross-layer columns, which considers the interaction between the substructure and the cross-layer columns, as well as the core wall on the frame. The modified effective length factor of the cross-layer columns is more consistent with the actual force situation.
4. In this study, a typical frame-core wall structure of 140 m was selected for analysis with a constant superstructure height, and it is assumed in the simplified model that the frame is connected to the core wall by rigid links hinged at both ends. Therefore, the applicability of the modified formula proposed in this study for different axial compression ratios and the effect of frame-to-core wall interaction need to be further investigated.  
Conceptualization, Z.M. and Z.F.; methodology, Y.X.; software, Y.X.; validation, Z.F. and Y.X.; formal analysis, Y.X.; investigation, Y.X. and Y.Y.; resources, Z.F.; data curation, Y.X.; writing--original draft preparation, Y.X.; writing--review and editing, Y.Y. and Y.X.; visualization, Y.X. and Y.Y.; supervision, Z.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China grant number 51578064 and the Natural Science Foundation of Beijing Municipality grant number 8172031.  
All the data supporting the results were provided within the article.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Column Number**} & \multicolumn{2}{c}{**Finite Element Method**} & \multicolumn{2}{c}{**GB50017 Method**} \\  & **Vertical Force kN** & \(\mu\) & **Before Modification \(\mu\)** & **After Modification \(\mu\)** \\ \hline C1 & \(1.2714\times 10^{7}\) & 1.5430 & 1.7612 & 1.8320 \\ C9 & \(1.8367\times 10^{7}\) & 1.2838 & / & 1.5242 \\ C10 & \(1.8919\times 10^{7}\) & 1.2649 & / & 1.5018 \\ C11 & \(1.8919\times 10^{7}\) & 1.2649 & / & 1.5018 \\ C12 & \(1.8367\times 10^{7}\) & 1.2838 & / & 1.5242 \\ C5 & \(1.2714\times 10^{7}\) & 1.5430 & 1.7612 & 1.8320 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Effective length factor in Model 3.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Column Number**} & \multicolumn{2}{c}{**Finite Element Method**} & \multicolumn{2}{c}{**GB50017 Method**} \\  & **Vertical Force kN** & \(\mu\) & **Before Modification \(\mu\)** & **After Modification \(\mu\)** \\ \hline C1 & \(1.2625\times 10^{7}\) & 1.2853 & 1.6775 & 1.4239 \\ C9 & \(1.7981\times 10^{7}\) & 1.0770 & / & 1.1931 \\ C10 & \(1.8500\times 10^{7}\) & 1.0618 & / & 1.1763 \\ C11 & \