## 3 Materials and Methods
### Numerical Modeling
#### 3.3.1 Material Properties  
The Bilinear Isotropic Hardening (BISO) [27; 41] model was adopted in conjunction with the von Mises yield criterion [42], as implemented in ANSYS(r) software, to represent the mechanical behavior of the structural components. The BISO model is widely used in numerical simulations of metallic structures due to its simplicity and computational efficiency [41; 43; 44]. Although the present analysis is restricted to the elastic regime,  
Figure 9: Test setup and monitoring points.  
defining a plastic model is essential to prevent unrealistic material behavior extrapolations and enable the software to recognize the onset of nonlinearity correctly.  
The geometry was subdivided into regular volumes to generate a structured mesh, ensuring continuity between the contact surfaces. The materials implemented followed item 3.1 mentioned, and the steel implemented corresponded to S275. The material properties are presented in Table 1.  
Standards such as Eurocode 3 [45] and Specification for Structural Steel Buildings (AISC) [46] recognize that the stiffness of structural elements does not remain constant throughout the applied load [47]. To capture the transition from the elastic to the plastic regime, it is necessary to reduce the initial elasticity modulus (\(E\)) using the tangent modulus (ET), which represents the decreased stiffness of the material after yielding [48].  
According to AISC [46] for structural elements loaded in the inelastic regime, the tangent modulus (\(E_{T}\)) is lower than the initial elasticity modulus (\(E\)) and decreases as plasticity develops [46]. The standard introduces the concept of the inelastic stiffness reduction factor (\(\alpha_{a}\)), defined as the ratio between \(E_{T}\) and \(E\), allowing adjustments in structural modeling to account for second-order effects [49].  
Studies indicate that, for simulations using the BISO model, the tangent modulus typically varies between \(E_{T}=0.005\cdot E\) and \(E_{T}=0.02\cdot E\), depending on the steel's specific properties and the adopted hardening criterion [49]. This approach is widely applied in stability and progressive collapse analysis of steel structures [49].  
In this study, S275 steel was used, with an adopted elasticity modulus of 210 GPa. To represent the elastoplastic behavior, a 0.007 factor was applied, resulting in a tangent modulus of \(E_{T}=0.007\cdot E\), equivalent to \(1.45\times 10^{9}\) N/m\({}^{2}\) (1.45 GPa) [41; 47]. It ensures numerical stability and consistency with the physical properties of structural steel, as demonstrated in recent studies on structural resistance and progressive collapse analysis [48].  
SOLID186 is a higher-order 3D 20-node element with quadratic displacement behavior, well-suited for modeling irregular geometries and complex nonlinear analyses. It supports large deformation effects, plasticity, creep, and stress stiffening, making it particularly effective for simulating structural components undergoing significant loading and contact interactions. The element formulation reduces integration without additional displacement shapes, enhancing numerical stability and computational efficiency. Given these capabilities, SOLID186 was employed in this study to ensure an accurate representation of the structural response, particularly in regions with stress concentrations and contact interactions [27].