## 2 Materials and Methods  
In this Section, the finite element analysis of CFTs is examined. Figure 1 depicts the composite members sections examined here, which are the most applied in engineering practice, i.e., rectangular and circular sections. For the rectangular section, B, H, t\({}_{\text{f}}\), and t\({}_{\text{w}}\) are the section width, height, flange thickness, and web thickness, respectively, as shown in Figure 1. Furthermore, for the circular section, D and t denote the diameter and thickness of the steel tube, respectively. To develop an extended and reliable database for the behavior of CFT members with rectangular and circular sections, a 3D nonlinear finite element model was created, utilizing the ATENA [14] finite element analysis. To ensure precision in the simulation, factors such as the nonlinear behavior of confined concrete, the local buckling of steel tubes, and the interface action between concrete and steel tubes were considered. Furthermore, selecting the appropriate element type and mesh size that offer precise results within a reasonable computational time frame is crucial in the simulation procedure. This model takes into consideration both geometrical and material nonlinearities. Various element types were tested to determine the most suitable ones for simulating the behavior of CFT rectangular and circular columns. It was found that shell elements are ideal for modeling the steel tube, while solid elements are best suited for representing the concrete core [15; 16]. These element types were subsequently utilized in the finite element analyses. The steel tube is represented using 8-node shell elements, while the concrete core is modeled using 20-node solid elements. To account for symmetry, only half of the column is modeled, as depicted in Figure 2. In all cases, this Figure is showing only half of each section, cut along the symmetry plane mentioned in the text. The meshes demonstrate the \"refined discretization\" described, especially at the base region. A refined discretization is applied to the base region of the column, with the height equal to the width of the cross-section for rectangular sections or to the diameter for circular sections. The nodes on the symmetry plane are appropriately constrained, while the remaining nodes are free to displace in any direction. To optimize computational efficiency, only one half of the column is modeled, resulting in a vertical plane of symmetry that bisects the column. The nodes situated along this symmetry plane are assigned specific movement limitations to accurately simulate the behavior of the entire column. These constraints generally encompass a) the prohibition of movement perpendicular to the symmetry plane, which ensures that the model functions as if the other half of the column were included; b) allowance for free movement parallel to the symmetry plane, which permits the model to deform naturally along the symmetry plane; and c) restriction on rotation around axes parallel to the symmetry plane, which prevents unrealistic twisting that would not occur in a complete column. To solve the nonlinear equations of motion, the Newmark step-by-step time integration method in conjunction with Newton-Raphson iterations is employed in ATENA [14]. A suitable constraint model has been used for the interface where the relative movement between the concrete core and the steel jacket is minimal. Similar discretization and modeling of CFTs with rectangular and circular sections have been applied by [PERSON] et al. [15] and [PERSON] et al. [16]. Figure 1: Concrete-filled steel tube rectangular and circular sections.