## 3 Finite-Element Modeling (FE) and Validating
The Introduction has presented significant research previously focused on the various geometric aspects of steel-concrete composite connections. Additionally, investigations have examined the effects of stud diameter and height, as well as the transverse and longitudinal arrangement of studs, on the structural behavior. The Python-based parametrically constructed model provides a detailed analysis of the effects of geometric variations on the behavior of composite connections. In order to evaluate the research results in the area of geometric variables, it is useful to present the Eurocode specifications regarding the calculation and geometric design possibilities of connections. These specifications served as a basis for defining the parameters of the model experiments, and they are also crucial in the Discussion Section, where the results are often referenced back to the standard. According to Eurocode [10], several constraints govern the geometry and spacing of connections. The total height of a stud must be at least three times the diameter of its shank (3d) to ensure effective shear transfer and adequate embedment within the concrete slab. The stud head diameter must be at least 1.5 times the diameter of the shank (1.5d), and its depth should be no less than 0.4 times the shank diameter (0.4d). In the direction of shear force, the spacing between studs must not be less than five times the shank diameter (5d), ensuring an even distribution of shear loads without  
Figure 3:0 FE model validation. overstressing the concrete. In the transverse direction, the spacing must be a minimum of 2.5 times the shank diameter (2.5d) in solid slabs and four times the shank diameter (4d) in other cases to facilitate proper concrete flow and compaction around the studs. In the calculation of the connection, two failure cases are compared: the failure of the individual stud and the failure of the concrete material. The smaller value between the two determines the load capacity that should be used. Figure 3:1  
Figure 3:2  
with the smaller of these equations:  
Figure 3:3  
Figure 3:4  
where \(d\) is the diameter of the shank of the stud, 16 mm \(\leq d\leq\) 25 mm; \(\gamma_{v}\) is the partial factor; \(f_{u}\) is the specified ultimate tensile strength of the material of the stud maximum 500 N/mm\({}^{2}\), \(f_{ck}\) is the characteristic compressive strength (cylinder) of the concrete at the age considered, of density not less than 1750 kg/m\({}^{3}\); \(h_{sc}\) is the overall nominal height of the stud; and \(\alpha\) is a reduction factor applied for studs with small height. The standard clearly defines the load capacity for the individual stud, and the product of this force, along with the number of studs, determines the design value of the connection load capacity. Although the standard allows for the use of a stud height of at least 3d, in the event of concrete failure, a reduction factor is incorporated into the load capacity calculation. Therefore, a relationship can be inferred between concrete failure and stud length, which is more significant for lower concrete strengths and less so for higher strengths. In the case where the failure of the stud governs the design, the reduction factor due to the stud height is not considered. Indeed, the standard evaluates these two scenarios separately, accounting for the governing failure mode in each case. However, from the perspective of the actual structural behavior, both the stud and the concrete may incur damage under the increased load. In the research, the numerical model was developed using an approach that allowed for a comprehensive understanding of the Python code associated with each modeling step. The model was systematically constructed to facilitate future modifications, enabling the automatic generation of models with altered geometries while adhering to the same modeling strategy and steps. This methodology ensures that, despite variations in a single parameter, all other parameters remain fixed and the model is executed within a consistent environment.