## 3 Materials and Methods  
The joint case proposed in this study connects two IPE240 identical profiles of S275 steel by means of two plates on both sides of the web and twelve bolts (Figure 1). The plate dimensions are conditioned by the geometry of the IPE240 profile. As shown in Figure 1a, the meeting of the flange and the web in the profile includes a circular root, so that the available web height to accommodate the plate is 190 mm. To mount the bolts inside the plate spaced at similar distances horizontally and vertically, a length of 320 mm is selected. Furthermore, these dimensions allow us to modify the position and arrangement of the bolts, whose effect is to be studied. In addition, the parameters associated with strength, dimensions, and bolt tightening are factors that are maintained for all case studies. Particularly, prestressed connecting elements included high-strength bolts. According to the standard EN ISO 4014/4022 [15], which specifies the characteristics of hexagon head bolts, an M12 C8.8 bolt was selected. Its yield strength is 640 N/mm\({}^{2}\) and its tensile strength is 800 N/mm\({}^{2}\). As contact surfaces do not need to be prepared in a special manner, the joint studied is grade A. The failure modes of this connection include tearing resistance for bolt groups, local bending, crushing, and block tearing. IDEA StatCa v.20 software was used to compute the resistance and the stress state of the joint elements. The program works with the component-based finite element method (CBFEM), which is the combination of two methods: the FEM and the component method (CM) [16]. The CM is implemented in the current Eurocodes [17; 18; 19] and applied in the majority of software for structural steel used in Europe. The component model of connections begins and stems from the decomposition of a joint to components. The constitutive equations of the material model the deformation behavior in relation to the normal and shear forces. The connection components are grouped to examine joint moment-rotational behavior and classification representation in a spring-shear model. Interactions between components incorporate boundary conditions to simulate the influence between the behavior of the connection elements for their consideration in the aggregate analysis of the connection structural performance [20]. The IDEA StatCa software calculation procedure is supported by an extensive experimental validation campaign [16]. Figure 1: Joint components: (**a**) Cross-section view with dimensions in mm; (**b**) axonometric view. The CM is based on standard procedures that evaluate the internal forces in the geometric layout of the connection and their verification, involving the prediction of resistance, stiffness, and deformation capacity. It permits predicting the 3D performance of steel joints under arbitrary loading despite the complex phenomena (nonlinearities, residual stresses, geometrical configurations, etc.) affecting the behavior of structural steel [21]. The weakness of the standard CM lies in the analysis of internal forces and stress in a joint. To overcome this limitation, the CBFEM method replaces the specific analysis of the internal forces in the joint with the general FEM. Check that methods of specific components like bolts, which are modeled as nonlinear springs, are performed according to the standard CM (Eurocode). In turn, special FEM components permit modeling the bolts behavior in a joint. All parts of one-dimensional members and all additional plates are modelled as plates. As elements are made of steel and their mechanical behavior is significantly nonlinear, the real stress-strain diagram of steel is replaced by the ideal plastic material for design purposes in building practice. The advantage of ideal plastic material is that only the yield strength and modulus of elasticity must be known to describe the material curve. As these elements are considered as an ideal elastic plastic material, their internal forces can be retrieved for evaluation.