# Seismic Behaviour of CFST Space Intersecting Nodes in an Oblique Mesh
## 8 Theoretical Bearing Capacity of OMSIN  
Reference [21] provided a formula for calculating the bearing capacity of CFST short columns with steel plates to simulate the effect of elliptical connecting plates in the intersection nodes. This formula underestimates the monotonic axial compression bearing capacity of the intersection nodes. However, from the structural design perspective, this formula is conservative and can be applied to practical engineering. See Equation (10). \[N_{\rm{u}}=\left[{f_{\rm{ck}}}A_{\rm{c}}\Bigg{(}1+\frac{{f_{\rm{s}}}\big{(}A_ {\rm{s}}+A_{\rm{p}}\big{)}}{{f_{\rm{c}}}A_{\rm{c}}}\Bigg{)}+\bigg{(}1.85\frac {{t_{\rm{s}}}}{{t_{\rm{p}}}}+0.12\bigg{)}{f_{\rm{s}}}A_{\rm{p}}\right]\times \Big{(}8.49(\tan a)^{3}+1.49\Big{)} \tag{10}\]  
\[A_{\rm{c}}=A_{\rm{c1}}+A_{\rm{c2}} \tag{11}\]  
\[A_{\rm{c1}}=r(\pi-\arccos x);A_{\rm{c2}}=x\Big{(}1-x^{2}\Big{)}^{0.5} \tag{12}\]  
\[A_{\rm{s}}=L_{\rm{s}}t_{\rm{s}};A_{\rm{p}}=L_{\rm{p}}t_{\rm{p}} \tag{13}\]  
\[L_{\rm{s}}=2r(\pi-\arccos x);L_{\rm{p}}=2r\Big{(}1-x^{2}\Big{)}^{0.5} \tag{14}\]  
\[x=\
icefrac{{(r-L\tan a)}}{{r}} \tag{15}\]  
where \(t_{\rm{s}}\) is the sum of the steel tube wall thickness and the lining thickness in the node area, \(t_{\rm{p}}\) is the thickness of the elliptical connecting plate, \(A_{\rm{c}}\) is the concrete cross-sectional area, \(A_{\rm{s}}\) is the outer steel tube cross-sectional area, and \(A_{\rm{p}}\) is the elliptical connecting plate cross-sectional area. The cross-sectional selection and interpretation are shown in Figure 18. It is worth noting that Figure 18 is based on the symmetry of the OMIN, and \(1/4\) of the node area was considered. The cross-sectional area of the steel tube, core concrete, and elliptical connecting plate in the node area varies with height [21]. The section in the literature is located at a vertical distance of \(D/6\) from the centre of the component. The section in this \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Name of the** & \multicolumn{2}{c}{**Yield Point**} & \multicolumn{2}{c}{**Peak Point**} & \multicolumn{2}{c}{**Limit Point**} \\ \cline{2-7}
**Test Piece** & \(\delta_{\rm{y}}/\delta_{\rm{m}}\) & \(F_{\rm{y}}/F_{\rm{m}}\) & \(\delta_{\rm{m}}/\delta_{\rm{m}}\) & \(F_{\rm{m}}/F_{\rm{m}}\) & \(\delta_{\rm{y}}/\delta_{\rm{m}}\) & \(F_{\rm{u}}/F_{\rm{m}}\) \\ \hline Node-Concrete30 & \(\begin{matrix}0.516\\ (-0.457)\end{matrix}\) & \(\begin{matrix}0.887\\ (-0.847)\end{matrix}\) & \(\begin{matrix}1.00\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.00\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.600\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.001\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.001\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.600\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.001\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.600\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.600\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.600\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.600\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.600\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.600\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.600\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.600\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.600\\ (-1.00)\end{matrix}\) \\ Node-Concrete120 & \(\begin{matrix}0.648\\ (-0.433)\end{matrix}\) & \(\begin{matrix}0.938\\ (-0.843)\end{matrix}\) & \(\begin{matrix}1.00\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.00\\ (-1.00)\end{matrix}\) & \(\begin{matrix}1.001\\ 2.667\end{matrix}\) & \(\begin{matrix}0.891\\ 0.891\end{matrix}\) \\ \hline \hline \end{tabular} Note. \(\delta_{\rm{y}}\) and \(F_{\rm{y}}\) are the yield displacement and yield load of the node, respectively. \(0.651\)\((-0.431)\) indicates that the abscissa of the positive yield point is \(0.651\); the abscissa of the negative yield point is \(0.431\).  
\end{table} 
Table 4: \(Cont.\)article is selected based on the region where the maximum Mises stress occurred in the node region of the numerical model.