## 6 Conclusions  
This study focused on four parameters (radius thickness ratio \(R\), slenderness ratio \(\lambda\), axial force ratio \(n\), and concrete filling ratio \(L_{\text{c}}/L\)) used in numerical analysis to determine horizontal load bearing capacity and buckling position in concrete-filled circular section tubes with diaphragms under monotonic loading. Based on the results, an equation for estimating the horizontal load bearing capacity of concrete-filled tubes was obtained by nonlinear regression analysis and its applicability was evaluated. The results of this study are described below.  
1. Three buckling modes were identified: buckling at the base of the steel tube, buckling just above the concrete, and buckling in both locations. The mode depends on the radius thickness ratio \(R\), the slenderness ratio \(\lambda\), axial force ratio \(n\), and concrete filling ratio \(L_{\text{c}}/L\). When buckling at the base of the steel tube or buckling in both locations occurred, the horizontal load bearing capacity did not decrease significantly with the increase in the axial force ratio \(n\), but with buckling just above the concrete, the horizontal load bearing capacity decreased rapidly.
2. Although the slenderness ratio \(\lambda\) did not affect the buckling position of the steel tube, buckling just above the concrete was more likely to occur as both the radius thickness ratio \(R\) and the axial force ratio \(n\) increased in tubes with small concrete filling ratios \(L_{\text{c}}/L\).
3. The estimation equation that did not consider different buckling positions predicted the horizontal load bearing capacity with an error of approximately \(\pm 10\%\) from the numerically analyzed values, but the error between the estimated and numerical values increases as the concrete filling ratio \(L_{\text{c}}/L\) increased from 0.4 to 0.6. On the other hand, the estimating equation that took the different buckling positions into consideration could predict the horizontal bearing capacity to within a margin of error of about \(5\%\) from the numerical value by determining the buckling position in advance.
4. The accuracy of the estimating equation was verified based on previous experimental studies. The accuracy of the estimating equation was found to be within a margin of error of approximately \(\pm 10\%\) from the experimental value when the buckling position was not taken into account, and approximately \(\pm 5\%\) when the buckling position was taken into account.  
In future work, it will be necessary to analyze models with different conditions such as diaphragms, stiffeners, and loadings in circular and rectangular cross-sections to clarify the effects of horizontal load bearing capacity and buckling position. Based on these results, a more comprehensive equation for estimating buckling position and horizontal bearing capacity will be studied.  
Figure 16: Comparison of experimental to estimated values: (a) Buckling position not considered; (b) Buckling position considered.  
Author Contributions: Conceptualization, Y.C.; methodology, Y.C.; software, S.Z.; validation, S.Z.; formal analysis, S.Z.; data curation, S.Z.; writing--original draft preparation, Y.C., S.Z. and S.S.; writing--review and editing, Y.C., S.Z. and S.S.; project administration, Y.C. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.