# A Study on the Seismic Performance of Steel H-Column and T-Beam-Bolted Joints
## 2 Establishment and Verification of Model
### Boundary Condition  
In the finite-element model of spatial nodes, the columns are aligned along the Y-axis. The beams in the east, south, west, and north directions are orthogonal along the X and Z directions. The translations in the X, Y, and Z directions at the bottom of the column are fixed, and the torsion around the Y-direction is also fixed. Meanwhile, the rotational around the X and Z directions are released to simulate a hinged condition at the column end. The vertical displacements and torsions of the east, south, west, and north beams are constrained. This constraint on the y-direction translation of the beams is to simulate the interaction between the beam and other components (such as columns, floor slabs, etc.) in the actual structure. These components limit the displacement of the beam in the y-direction, making its deformation within a reasonable range. By setting this constraint, it can more realistically reflect the mechanical properties and deformation characteristics of the node under complex loading conditions, providing effective support for accurately analyzing the mechanical properties of spatial nodes under two-way loads and evaluating the reliability and safety of nodes during earthquakes, which is of great significance for the seismic design of steel-frame structures. The boundary conditions are illustrated in Figure 4a. The loading process is carried out in three steps. In the first step, the bolt preload is applied. This is further divided into two sub-analytical steps. In the first sub-step, a preload of 225 kN is applied to the bolt. Then, in the second sub-step, the bolt is fixed at its current length while maintaining the 225 kN preload. The second step involves the application of axial pressure, which is completed within one analysis step. The third step is the application  
Figure 4: Boundary condition and loading regime. (**a**) Boundary condition setting. (**b**) Loading in X direction. (**c**) Loading in Z direction. of the column top displacement. In the actual steel-frame structure, the beam-column joints, as space joints, will be subjected to bidirectional loads. When the beam is under load, although it will have a certain deformation in the y-direction, this deformation is not free but is constrained by the surrounding structure. Constraining the translation of the beam in the y-direction can simulate the interaction between the beam and other components (such as columns, floors, etc. ), which will limit the displacement of the beam in the y-direction and keep its deformation within a reasonable range. This constraint setting can more truly reflect the mechanical properties and deformation characteristics of the joints under complex stress conditions and, then, provide effective support for accurate analysis of the mechanical characteristics of the space joints under two-way loads and an evaluation of the reliability and safety of the joints in earthquakes, which is of great significance for the seismic design of steel-frame structures. The simulation adopts displacement control loading, applying cyclic horizontal displacement (\(\Delta=\pm 104\) mm) at the beam end, with a step size of \(1/50\Delta\), a total of 200 steps. This setup is consistent with the test loading regime (Figure 5), ensuring that the simulation results can be directly compared with the test. A pseudo-static test is used to load the nodes according to low-frequency constant-amplitude cyclic load, so as to reflect the mechanical performance of the nodes under reciprocating load and then understand some of the properties and failure modes of the nodes under real earthquake action. The loading at the column end is more in line with the actual force-transmission mechanism of frame nodes under horizontal earthquake actions. Therefore, the horizontal load at the column end is applied in an orthogonal-alternate loading mode. Specifically, in each loading-grade cycle, the horizontal load at the column end is applied alternately in the X-direction and the Z-direction.