## 7 Discussion  
This study examined the behavior of concrete-filled steel tubes, with rectangular and circular sections, under pure axial/compressive loads, pure bending moments, and combined axial load-bending moment loads. From the statistical analysis of finite element results of Section 2, the following empirical expressions have been proposed:  
* Equation (9): the maximum compressive bearing capacity for composite rectangular sections;
* Equation (18): the maximum compressive bearing capacity for composite circular sections;
* Equation (27): the maximum flexural bearing capacity for composite rectangular sections;
* Equation (36): the maximum flexural bearing capacity for composite circular sections;
* Equation (39): the normalized axial force-bending moment interaction curve for composite rectangular sections;
* Equation (41): the normalized axial force-bending moment interaction curve for composite circular sections.  
It is important to note that the previously mentioned equations were among the simplest equations that accurately represented the numerical data exhibiting concave curves in every direction. These equations were obtained through the utilization of Table Curve 3D software (Version 5.01, Systat, Richmond, CA, USA) after extensive testing of approximately 8000 mathematical equations. The selection of these equations was based on the criterion for achieving the minimum absolute residual error using the Pearson VII limit, specifically minimizing the sum of \(\ln[\surd(1-\text{residual}^{2})]\).  
Equations (9), (18), (27) and (36) take into account the ratio of external section dimensions to the tube thickness, e.g., \(B/\!t_{p}\), \(H/\!t_{w}\) (rectangular section) and D/t (circular section). The proposed empirical equations can be used for the following range: \(30\leq(B/\!t_{p}\) or \(H/\!t_{w}\) or \(D/\!t)\leq 120\). Furthermore, these equations also consider the material strength ratio, \(f_{p}/\!f_{C}\), which can range: \(3.5\leq f_{p}/\!f_{C}\leq 18\).  
Moreover, Equations (39) and (41) describe the axial force-bending moment curves for rectangular and circular sections, respectively, and they are expressed in normalized form, i.e., \(\mathrm{P}/\mathrm{Pmax}-\mathrm{M}/\mathrm{Mmax}\). They take into account the relative strength ratio (see Equation (37)), which can range: \(0.20\leq k\leq 2.0\).  
The suggested equations eradicate the necessity of the existing section classification to estimate the compressive strength of the steel tube section caused by local buckling. It is worth noting that these empirical equations were derived from an advanced finite element model, capable of effectively simulating local buckling phenomena (refer to [15,16] for further details).  
As detailed in Section 1, the Finite Element Method (FEM) was utilized to simulate the system being studied. The findings from this analysis are depicted graphically throughout the manuscript, offering a visual summary of the principal results. In particular, the figures illustrate the outcomes of the FEM analysis. These visual representations provide an extensive overview of the system's behavior under varying conditions, as anticipated by the FEM model. While the section on formula derivation emphasizes the theoretical framework, it is crucial to recognize that the FEM results serve to directly inform and validate these mathematical formulations. The interaction between the theoretical model and the FEM analysis represents a significant strength of this research.