# A Study on the Seismic Performance of Steel H-Column and T-Beam-Bolted Joints
## 2 Establishment and Verification of Model
### Model Building  
The stress-strain curves are all founded on the ideal bi-linear isotropic hardening model. The bolts are of grade 10.9, and the preload is set at 225 kN. The mechanical properties of Q355B steel are as follows: yield strength \(f_{y}=355\) MPa, ultimate strength \(f_{u}=510\) MPa, elastic modulus \(E=206\) GPa, Poisson ratio \(\
u=0.3\). The stress-strain relationship is based on an ideal elastic-plastic bilinear model, that is, it enters the plastic flow directly after the elastic phase, without strengthening or softening behavior. In the node domain, the H-shaped steel beam and the square steel-pipe column are meshed with a global element size of 90 mm. Other components are meshed with a global element size of 30 mm. The global meshing is further adjusted with local edge-based refinement to ensure that the nodes of each element coincide as closely as possible. The solid model and the meshing details are presented in Table 2. Due to the large number of high-strength bolts and ring rivets in the entire model, in this paper, the Cartesian Connector is utilized to simplify the representation of the ring rivets.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Solid Model** & **Cell Type** &
\begin{tabular}{c} **Meshing** \\ **Technique** \\ \end{tabular} \\ \hline Square-steel column & & Type of four-node reduced integration unit: S4R & Free technology Advanced algorithm \\ \hline H-shaped steel beam & & Type of four-node reduced integration unit: S4R & Free technology Advanced algorithm \\ \hline \hline \end{tabular}
\end{table}
Table 2: Physical component meshing.  
Figure 1: Specim detail size. (**a**) Node domain, (**b**) T-part 1 size, (**c**) T-part 2 size.  
Figure 2: Node composition.  
The Cartesian Connector model for ring rivets is validated through prior studies on bolted joint simplification. For instance, [PERSON] et al. [17] demonstrated that spring-damping elements can effectively capture the dynamic behavior of bolted flange connections, with prediction errors within 20%. Similarly, [PERSON] [18] highlighted the use of beam elements to simplify bolt geometry in finite-element analysis, balancing computational efficiency and accuracy. In seismic applications, [PERSON] et al. [19] validated simplified UHPC joint models under cyclic loading, confirming that connector-based approaches preserve hysteretic behavior and energy dissipation characteristics. The tension and shear verification results of the ring rivet solid unit and the simplified model are shown in Figure 3.  
The ideal elastic-plastic model (elastic modulus \(E\) = 206 GPa, yield strength \(f_{y}\) = 355 MPa) is adopted for the material, and the region \(\sigma\geq 355\) MPa in the stress cloud map is the plastic deformation zone. Since the model does not include the strengthening stage, the stress does not increase after reaching \(f_{y}\), so the stress cloud map directly reflects the yield state of the material.  
\begin{table}
\begin{tabular}{c c c} \hline
**Type** & **Solid Model** & **Cell Type** & **Meshing Technique** \\ \hline T-part 1 & Type of eight-node reduced integration unit: C3 DSR & Free technology Advanced algorithm \\ \hline T-part 2 & Type of eight-node reduced integration unit: C3 DSR & Free technology Advanced algorithm \\ \hline High-strength bolt & Type of eight-node reduced integration unit: C3 DSR & Structural technique \\ \hline \end{tabular}
\end{table}
Table 2: _Cont._  
Figure 3: Load–displacement curve comparison diagram. (**a**) Under tension. (**b**) Under shearing force.