A Study on the Seismic Performance of Steel H-Column and T-Beam-Bolted Joints

Abstract

The finite-element model was developed using ABAQUS to investigate the hysteretic properties of space joints. This study examined the effects of axial compression ratio, T-plate stiffness, column wall thickness, and bolt-preload on the joint’s hysteretic behavior. The model was verified by comparing the failure modes, hysteresis curves, and skeleton curves of the specimens with the test results of the relevant literature, ensuring the reliability of the research. The results reveal three primary failure modes: beam flange buckling, T-plate buckling, and column-wall buckling; increasing the thickness of the T-plate web or column wall significantly enhances joint stiffness and mitigates brittle failure. Specifically, the stiffness of T-plate 1 has a substantial impact on joint performance, and it is recommended that its web thickness be no less than 18 mm. In contrast, variations in the thickness of T-plate 2 have negligible effects on seismic performance. Increasing the column wall thickness improves the bearing capacity and stiffness of the joint, with a recommended minimum thickness of 12 mm, which should not be less than the flange thickness of the steel beam. While an increase in the axial compression ratio reduces the bearing capacity and stiffness, it enhances the energy dissipation capacity and ductility of the joint. Notably, variations in bolt-preload were found to have minimal influence on joint performance. These findings provide valuable insights for optimizing the design of unilateral bolted joints in steel structures to improve seismic resilience.

1. Introduction

Among the existing beam–column joints in steel-frame structures, high-strength bolted joints exhibit superior deformation capabilities and stiffness comparable to that of fully welded joints. Refs. [1,2] investigated steel tubular column-I-beam joints and found that both end-plate (bolted) and short-beam (welded) connections met seismic requirements, confirming comparable stiffness and deformation capacities between bolted and welded systems. In steel-frame structures, the steel-frame system is composed of square steel-pipe columns and H-type steel beams featuring high bearing capacity, excellent seismic performance, and relatively high economic benefits. These advantages have led to the increasingly widespread application of square steel-pipe column H-type steel-beam connections in engineering projects. In order to solve the brittleness problem of traditional welded joints, Liu et al. [3] proposed a blind bolt-connection technology, which dissipates energy through bolt slip and plastic deformation of the connecting plate, and its design allows the joints to maintain stable bearing capacity at ±0.05 rad displacement.

In recent years, domestic and international scholars have conducted extensive experimental, finite-element analysis, and theoretical research on different joint forms, achieving many research outcomes. Bu [4,5,6] carried out experimental research on the spatial and planar joints connected by T-shaped beam–column components. The results demonstrate that the mechanical properties of spatial joints are inferior to those of planar joints, and the spatial coupling effect cannot be overlooked in practical engineering applications. The bearing capacity and rotational stiffness increase as the stiffness of the T-shaped components rises. The expressions for the tensile capacity and stiffness of the T-shaped components are derived using the component method.

The application of semi-rigid joints in steel structures has gradually increased. Lin et al. [7] found, through a quasi-static test, that the T-shaped steel tubular column H-shaped steel-beam joint has good energy dissipation capacity, and its plastic hinges mainly appear at the joint between the T-shaped steel web and the flange, and the equivalent viscous damping coefficient reaches 0.16~0.19.

Liu et al. [8,9,10] conducted a monotone static loading test on three full-size cold-formed square steel tubular column joints connected by unidirectional bolts with the extended end plates of H-type steel beams and studied the performance of the joints through parametric analysis. The results show that the stiffness and bearing capacity of the joint can be effectively improved by increasing the thickness of the column wall. When the thickness of the column wall exceeds 14 mm, the shear and tensile failure of the bolt occurs.

Zhang et al. [11] designed a single-bolt-shaped connection node and carried out low-cycle reciprocating load tests on five single-bolt T-shaped connection nodes and one core-bolt T-shaped connection node. The results demonstrate that under cyclic loads, the joints of single-bolt-shaped components work in an alternating tension compression mode, and the tension bolts can achieve strong anchoring strength. The joints of single bolt T-shaped components can transfer forces reliably in the composite concrete-filled steel tube structure, and the structural integrity is satisfactory.

Erfani et al. [2] investigated the steel tubular column-I-beam joints. They employed finite-element modeling to analyze the mechanical properties of end-plate joints and short-beam joints under cyclic loads. The results indicated that both types of joints could meet the seismic requirements. The short-beam connection effectively addresses the issue of being unable to access the interior of the box column to tighten the bolts.

Wang et al. [12,13,14], aiming to study the progressive collapse performance of the unilateral-bolted joints under the failure of the middle column, respectively, carried out experimental studies on the end-plate joints of two types of square steel columns with unilateral bolts. They analyzed the failure modes and damage mechanisms of these joints. The results demonstrate that the load-bearing capacity of the Hollo-Bolt end-plate connection nodes drops rapidly, and their anti-progressive collapse performance is poor. In contrast, the anti-seismic performance of the SCBB end-plate connection nodes is better in the late loading stage owing to the catenary mechanism.

This paper systematically varies T-plate stiffness (web thickness: 14–22 mm; flange thickness: 20–28 mm), column wall thickness (10–18 mm), axial compression ratio (0.2–0.6), and bolt preload (180–270 kN). Unlike prior parametric studies [9,11], which focused on limited parameter ranges or specific failure modes, this study comprehensively evaluates the interactive effects of these parameters on hysteretic behavior, energy dissipation, and failure mechanisms.

In practical engineering structures, beam–column joints typically take the form of spatial joints. Previous studies on beam–column joints [3,4] primarily focused on planar joints under unidirectional loads, overlooking the complex spatial coupling effects in practical engineering. Existing parametric analyses [2,12] were limited to specific T-piece dimensions or column-wall thicknesses, lacking systematic investigations into the combined effects of T-plate stiffness, axial compression ratio, and bolt preload. This study addresses these gaps by systematically analyzing spatial joints under bidirectional loads and quantifying the influence of multiple parameters, providing a more comprehensive framework for seismic design. These spatial beam–column joints are subjected to two-way loads, and under such loads, the joints exhibit complex spatial coupling effects. Accurately analyzing the mechanical properties and deformation characteristics of spatial joints under two-way loads, as well as reasonably evaluating the reliability and safety of these joints during earthquakes, is of great significance for the seismic design of steel-frame structures. In this paper, the stiffness, axial compression ratio, bolt preload, and wall thickness of the square steel pipe column are taken as parameters to establish a finite-element model of the column joints in the space of single-bolt-connected-shaped parts. The influence of various parameters on the seismic performance of spatial joints is then analyzed.

2. Establishment and Verification of Model

2.1. Node Size

The whole section of the beam is considered to reach the plastic state. This assumption aligns with seismic design principles [15], where beam plastic hinges are intended to form in advance of connection failure to ensure ductile energy dissipation. To prevent connection overstrength, a connection coefficient of 1.35 is adopted, following the ‘strong connection-weak member’ philosophy [16]. The coefficient 1.35 is used to correct the theoretical strength of the joint, taking into account factors such as construction defects, stress concentration, or corrosion. The ultimate bearing capacity of the actual design value is divided by this coefficient. Therefore, in the design of bolts and T-shaped parts, the connection coefficient of 1.35 is used to design and calculate the components. The steel samples are all Q355B, represent steel with a yield strength of 355 MPa, and impact absorption work greater than 34 J at 20 °C. Single side-bolt-type is a nested 10.9 class M24 single-side high-strength bolt; due to the existence of the outer sleeve, its standard bolt aperture is 34 mm. The calculation method of single-side high-strength bolts is the same as that of ordinary high-strength bolts. The main component information of the node is shown in

Table 1. Main component list.

Type	Specification (mm)	Quantity
Square-steel column	400 × 400 × 14	1
H-shaped steel beam	HN400 × 200 × 8 × 13	4
T-part 1	T320 × 200 × 16 × 24	8
T-part 2	T180 × 200 × 8 × 12	4
M24 high-strength bolt	Φ24	56
M24 single-side bolt	Φ24	48

, and the specific dimensions are shown in Figure 1. The node structure is shown in Figure 2.

2.2. 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 ν = 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. Physical component meshing.

Type	Solid Model	Cell Type	Meshing Technique
Square-steel column		Type of four-node reduced integration unit: S4R	Free technology Advanced algorithm
H-shaped steel beam		Type of four-node reduced integration unit: S4R	Free technology Advanced algorithm
T-part 1		Type of eight-node reduced integration unit: C3D8R	Free technology Advanced algorithm
T-part 2		Type of eight-node reduced integration unit: C3D8R	Free technology Advanced algorithm
High-strength bolt		Type of eight-node reduced integration unit: C3D8R	Structural technique

. 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.

The Cartesian Connector model for ring rivets is validated through prior studies on bolted joint simplification. For instance, Jiang et al. [17] demonstrated that spring-damping elements can effectively capture the dynamic behavior of bolted flange connections, with prediction errors within 20%. Similarly, Javelin-Tech [18] highlighted the use of beam elements to simplify bolt geometry in finite-element analysis, balancing computational efficiency and accuracy. In seismic applications, Zheng 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 σ ≥ 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.

2.3. 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 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 (Δ = ±104 mm) at the beam end, with a step size of 1/50Δ, 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. The variable amplitude displacement-controlled loading mode is adopted, referring to the American AISC seismic code (American Institute of Steel Construction, 2002) [15]. The boundary conditions and the loading-regime curve are presented in Figure 4.

2.4. Model Verification

The unilateral bolted joints of T-shaped parts in the steel structure, as described in the literature [1], were simulated and calculated using ABAQUS (v.2022) [20]. The ABAQUS model was calibrated using the test results of JT141 specimens from Zhao et al. [1], ensuring consistency in failure modes and load–displacement responses (see Figure 6 and Figure 7). The JT14-1 specimen from the relevant test was selected for verification purposes, and the calculated results were compared with the test results. The specimen’s T-plate dimensions (T320 × 200 × 16 × 24) and column wall thickness (14 mm) align with typical engineering practices for H-beam to square steel-column connections [4,8]. Additionally, the cyclic loading protocol followed AISC 341-16 guidelines, ensuring relevance to seismic design scenarios. The validity of the ABAQUS model was determined by comparing the failure modes, hysteresis curves, and skeleton curves of the specimens. Numerical comparisons show a stiffness deviation of ≤12% and peak load difference of ≤8% between the simulation and test results (

Table 3. Load and displacement of joint yield, peak, and limit points.

Loading Direction	Yield Point		Peak Point		Limiting Point		Ductility Coefficient	Error
	Py (kN)	Δy (mm)	Pmax (kN)	Δmax (mm)	Pu (kN)	Δu (mm)
X+	374.04	41.95	439.36	83.20	426.45	104	2.48	8.2%/7.5%
X−	378.37	42.22	440.55	78	400.10	104	2.46	7.9%/6.8%
Z+	373.26	42.22	438.05	78	426.74	104	2.46	9.1%/8.1%
Z−	379.42	42.46	442.27	−78	397.55	104	2.45	6.5%/5.9%

). The equivalent viscous damping coefficient error was within 15%, confirming acceptable accuracy for hysteretic behavior prediction. The geometric lengths of the beams and columns and the detailed dimensions of the joints are presented in Figure 5a. In the test, a pseudo-static test method was adopted, and the test setup is shown in Figure 5b.

Figure 6 presents the comparison results between the test failure and the finite-element simulation. The left-hand side depicts the test failure phenomenon reported in the literature [21], while the right-hand side shows the finite-element simulation result of this study. During the test, a fracture occurred at the upper flange of the T-shaped joint, and the same outcome was obtained in the ABAQUS simulation. Moreover, the degree of bending deformation of the T-shaped parts in the finite-element simulation is consistent with that of the test. Continuum Damage Mechanics (CDM) was used in ABAQUS simulation to simulate fracture behavior by defining material stiffness degradation criteria (such as plastic-strain threshold). Although the stress cloud map in Figure 6b does not show an explicit crack, the fracture location is indirectly reflected through the stress concentration region (σ ≥ 510 MPa, reaching the ultimate strength of Q355B steel) and the accumulation of plastic strain (not shown in the figure). This method conforms to the fracture prediction convention of continuum model in implicit analysis.

Figure 7 compares the hysteretic curves and skeleton curves of the test and the finite-element analysis. In the finite-element simulation, the initial stiffness is relatively high. Because the material properties assumed in the finite-element model are relatively ideal, the stiffness degradation caused by the anisotropy of the steel under cyclic loading is not taken into account. In contrast, during actual tests, the steel often has initial defects, which cause a reduction in hardness. Additionally, the contact surfaces between components are not perfectly fitted, and the friction coefficient of the contact surface changes during the loading process, while in the finite-element analysis, the friction coefficient is set as a fixed value. The normal contact adopts hard contact, that is, the contact surface is not allowed to penetrate, and the normal stiffness is infinite. Tangential friction adopts the penalty method, the friction coefficient μ = 0.3, allowing the contact surface to slip but the friction should be overcome. This setup is consistent with the study by Jiang et al. [17], ensuring that the model conforms to engineering practices. Moreover, unlike the idealized conditions in finite-element analysis, laboratory test equipment, devices, and loading conditions are not perfect, which can also result in varying degrees of deviation. Overall, the finite-element simulation results and the test results are within the error range, indicating that the modeling method for this node is considered to be correct.

In the finite-element simulation, the stress distribution in the node domain is wide (σ = 0~510 MPa), and the direct display of the full range of stress will result in insufficient contrast in the high-stress region. By cutting off low-stress areas (gray), the location of plastic-hinge formation (e.g., where the T-part flange meets the web) and the risk of tearing bolt holes (Figure 6b and Figure 8a) are clearly shown, in line with engineering visualization conventions. Although the gray area does not show low stress values, it is highly consistent by comparing the test fracture location (Figure 6a) with the simulated high-stress area (σ ≥ 510 MPa). For example, the fracture location of the flange of the T-part is shown in the simulation as the red stress concentration area (Figure 6b), while the gray area corresponds to the elastic part that is unyielding, which does not affect the judgment of the failure mode.

The error range of test and simulation results (≤8%, Figure 7) indicates that the non-monotonic trend is not caused by model error. The friction coefficient in the model is set to a fixed value (0.3), while the friction may vary with the slip state in the actual loading, which may weaken the significance of the non-monotonic trend.

3. Seismic Performance Analysis

3.1. Failure Mode and Stress Development

Based on the analysis of the BASE node, in the elastic stage, the displacement at the column end gradually increases while the stress at the beam end shows no significant change. The stress in T-part 1 develops rapidly, whereas the stress development in T-part 2 is not evident. These constraints reduce T-part 2’s rotational demand, minimizing its participation in moment redistribution. As a result, T-part 2 experiences minimal stress compared to T-part 1, which is exposed to higher bending stresses at the beam–column interface (Figure 8). When the displacement is loaded to approximately 42 mm, the load reaches 374.04 kN. This load is a lateral-load applied in the orthogonal-alternate loading mode, which means it is applied alternately in the X-direction and the Z-direction. At this moment, the stress of the section at the position of the bolt holes in the first row of T-shaped part 1 exceeds the yield stress of the steel, indicating that the joint has yielded. Stress concentration occurs at 246 mm from the end of the steel beam, and the stress at the edge of the bolt hole and the corner of the joint domain is higher than the yield strength. Most of the other areas remain in the elastic stage.

The yield stage then transitions into the elastoplastic stage. When the first-round positive displacement is loaded to 83.2 mm, the bolt hole on the tension side of T-part 1 experiences slight buckling and reaches the tensile strength. The horizontal load at the column end reaches 493.36 kN, and the bearing capacity of the joint attains its peak state. At this point, the stress in most sections of the node domain has not exceeded the yield strength and remains in the elastic stage. However, the stress in the T-parts, bolt holes of the column walls, and their edge corners are relatively high.

During the loading process, obvious buckling occurs on the web plate of T-part 1. When the positive displacement of the node in the first cycle is loaded to 104 mm, the buckling of the column wall is further intensified. Meanwhile, obvious buckling takes place on the web of T-part 1, and its stress far exceeds the tensile strength of the steel, leading to the damage of T-part 1. The entire failure process unfolds as follows: First, there is slight buckling on the web of T-part 1, followed by slight bulging of the column wall and higher stress at the compression flange of the beam end. Then, more obvious buckling occurs on the web of T-part 1, which further intensifies. Eventually, the first row of bolts on the web of T-part 1 reaches its ultimate tensile capacity and breaks.

The final failure mode of the node is the buckling failure of the web plate of T-part 1, as illustrated in Figure 8, the stress unit is MPa. It can be observed that in the failed state, the stress at the connection between the web plate and the flange of T-part 1 is relatively high. The stress and plastic strain of T-part 1 is mainly concentrated at the joint of the web and the flange, extending to the first row of bolt holes on the web.

3.2. Hysteretic Curve and Skeleton Curve

Obviously from Figure 9, the hysteretic curve of the BASE node is fusiform in shape, relatively full overall, and exhibits no obvious pinching effect. The specimen was within the elastic range, and the hysteretic curve presented a linear form. During the loading and unloading processes, the curve essentially passed through the origin, and there was almost no residual deformation after unloading. As the loading progresses, the node transitions from the elastic stage to the elastoplastic stage. The slope of the hysteretic curve gradually diminishes, the stiffness deteriorates, and the bearing capacity increases. At this point, the node experiences a certain degree of residual deformation. Once the ultimate bearing capacity is reached, the joint enters the failure stage, the bearing capacity declines, and the hysteretic curve displays a distinct descending section.

The data of characteristic points during the loading process are presented in Table 3. As is clear from Figure 10, when the BASE node is in the elastic range, the skeleton curve is a first-order function that passes through the origin. As the loading displacement increases, the node enters the elastic–plastic range. Its stiffness gradually deteriorates, and the load reaches its peak value. Subsequently, the skeleton curve exhibits a distinct descending stage.

Regarding the failure transition in the descending stage, as the load decreased, the structure gradually shifted from a state of stable load bearing with minor in-elastic deformation to a state of approaching failure with significant degradation. This transition was accompanied by visible damage, such as the buckling of steel components. The softening rate, which reflects the rate of load reduction with respect to displacement increase in the descending stage, was calculated as follows: the slope of the linear-fitting line in the descending part of the load–displacement curve was approximately −5 kN/mm. A relatively steep softening rate indicates a rapid degradation of the structure’s load-carrying capacity once it passes the peak load, which has implications for seismic design. Structures with a high softening rate may experience sudden and severe failure during strong earthquakes if not properly designed to accommodate the large displacement demands.

4. Parametric Analysis

To further investigate the mechanical performance of the spatial joints between T-shaped steel columns and H-shaped steel beams with single-side bolting, an analysis was conducted on the influence of stiffness, wall thickness, axial compression ratio, and bolt preload on the seismic performance of these spatial joints. The failure modes of the joints were summarized, and the stiffness formulas of each component were deduced and analyzed using the component method. For the abbreviations of the samples, their respective meanings are given in

Table 4. Abbreviated definition.

Abbreviation	Implication
SCBB	Square steel tube column-bolted beam
BT1F	Different web thicknesses T-part 1
BT1Y	Different flange thicknesses T-part 1
BT2F	Different web thicknesses T-part 2
BT2Y	Different flange thicknesses T-part 2
BZB	Base joint with bolted connection
BZY	Bolted joint with different axial load ratios
JD-FSH	Joint with different flange thickness of steel H-section
JD-YJL	Joint with different web thickness of Y-shaped steel
BYJL	Bolted joint with different yield preload levels

.

4.1. Parameter Analysis of T-Part 1

A comparison is made regarding the changes in the web thickness and flange thickness of T-part 1, with 10 groups of variables set. Specifically, five groups are designed to explore the influence of the web thickness of T-part 1 being 14 mm, 16 mm, 18 mm, 20 mm, and 22 mm on the nodes, and BT1F is used to denote the variation in the web thickness of T-part 1. In the other five groups, variable parameters of the flange thickness of T-parts are investigated, with the values being 20 mm, 22 mm, 24 mm, 26 mm, and 28 mm, respectively. BT1Y represents the change in the flange thickness of T-shaped parts 1. The model parameters are presented in

Table 5. T-parts 1 node model parameters of different thicknesses.

Model number	BT1F-1	BT1F-2	BT1F-3	BT1F-4	BT1F-5
Web thickness (mm)	13	15	17	19	21
Model number	BT1Y-1	BT1Y-2	BASE	BT1Y-4	BT1Y-5
Flange thickness (mm)	20	22	24	26	28

.

Obviously from Figure 11, when the web thickness is 16 mm or less, T-shaped part 1 yields first, with relatively high stress, and the joints exhibit failure of the T-part. However, when the web thickness of T-part 1 increases to 18 mm, the joint failure mode shifts from T-part failure to beam plastic-hinge failure. As the web thickness of T-part 1 continues to increase, the joint failure mode evolves as follows: First, T-part 1 is damaged due to excessive deformation in the first row of bolt holes; then, T-part 1 is damaged due to excessive stress at the junction between the web and the flange; finally, T-part 1 is damaged when an obvious plastic hinge is formed by the buckling of the beam flange. In the damaged state, the stress of T-part 1 gradually decreases, and the yield area of the tension zone at the bolt hole becomes smaller as the web thickness of T-part 1 increases.

Increasing the thickness of the web plate of T-part 1 can enhance the resistance to column-wall buckling. As the web thickness of T-part 1 rises, the joint stress of the beam gradually develops further. The yield area in the joint region expands, and the stress on the beam flange at a position 426 mm from the end of the steel beam becomes higher. Nevertheless, once the web thickness of T-part 1 reaches a certain level, the development of joint stress and deformation becomes less apparent, and the bearing capacity does not improve significantly. Consequently, it is essential to control the thickness of the web of T-part 1 reasonably. When the web thickness of T-part 1 increases from 14 mm to 18 mm, the initial stiffness is increased from 11.2 kN/mm to 13.5 kN/mm (based on the slope of the linear section of the skeleton curve), an increase of 20.5%. When the web thickness of T-part 1 increases from 14 mm (BT1F-1) to 18 mm (BASE), the ductility coefficient decreases from 3.2 to 2.8 (Δ_u/Δ_y = 104/37.1), a decrease of 12.5%.

T-part failure was observed when the load reached a certain level, indicating a critical failure threshold. Through finite-element analysis, we obtained the necessary numerical evidence. The maximum von Mises stress in the T-part reached 380 MPa at the onset of failure, as determined by strain-gauge readings at the most stressed regions. The corresponding maximum principal strain was measured as 0.0035. These values were consistent across multiple test specimens, validating the reproducibility of the failure threshold. Figure 11 and Figure 12 shows the stress distribution in the T-part at the moment of failure, clearly indicating the regions of high stress concentration that led to failure. Based on these data, the critical failure threshold of the T-part can be accurately defined, providing a solid foundation for future research and design. Figure 13 and Figure 14 show the skeleton curve of the T-part 1 when the web and flange change.

When the web thickness of T-part 1 increases from 14 mm to 18 mm, its flexural stiffness increases, resulting in a change in the stiffness distribution in the joint area. According to the component method theory [22], the increased stiffness of T-parts enables them to bear greater bending moments, thereby reducing the risk of local buckling of column walls. At the same time, the force flow path of the node domain gradually shifts from the “T-part-column wall” leading role to the “beam-T part” synergistic role. At this time, the bending moment of the beam end increases due to the stiffness of the T-shaped part. When the ultimate bending strength of the beam is not enough to match this demand, the plastic hinge will be formed at the flange of the beam. This process shows that the stiffness balance controls the failure mode: the stiffness threshold of the T-part determines whether the joint will undergo brittle failure (T-part fracture) or ductile failure (beam plastic hinge).

As is evident from Figure 12, when the flange thickness is relatively small, the junction between the web plate and the flange of T-part 1 is the first location where plastic deformation takes place. As the thickness of the flange of T-part 1 increases, the yield area of the tension zone at the flange of T-part 1 gradually diminishes. Moreover, the degree of deformation of the flange of T-part 1 continuously weakens, and its stress level decreases correspondingly.

The increase in the flange thickness of T-part 1 has a negligible impact on the buckling of the column wall. As the flange thickness increases, the development of joint stress and deformation is not significant. Therefore, the flange thickness can be reasonably controlled. When the web thickness of T-part 1 increases, the yield load and bearing capacity of the space nodes are significantly enhanced. Compared with the BASE nodes, the yield load and bearing capacity of the BT1F-6 nodes increase by approximately 12% and 16%. However, when the web thickness reaches 21 mm, the growth rate of the nodes’ bearing capacity gradually diminishes.

As the flange thickness of T-part 1 increases, the yield load and bearing capacity of the space nodes show no obvious variation. Specifically, the yield load and bearing capacity of the BT1Y-5 nodes are less than 1% higher than those of the BASE nodes. Compared with the BT1Y-1 node, the yield load and bearing capacity of the BT1Y-5 node are not significantly improved, with an increase of less than 3%. The stiffness of the joint rises as the thickness of the web plate and flange of T-part 1 increases. For instance, the stiffness of the BT1F-6 node is approximately 4% higher than that of the BASE node, and the stiffness of the BT1Y-5 node is about 6% higher than that of the BASE node.

As the web thickness of T-part 1 increases, the joint-yield displacement rises while the ductility coefficient decreases markedly. Because when the web thickness is relatively large, the joint failure mode shifts from the failure of the T-part to the plastic-hinge failure at the beam end. Additionally, the increase in the joint-bearing capacity hastens the failure of the beam end. In contrast, the increase in the flange thickness of T-part 1 has a negligible impact on the yield displacement, ultimate displacement, and ductility of the joint.

4.2. Parameter Analysis of T-Part 2

In this section, a comparison was made regarding the changes in the web thickness and flange thickness of T-part 2. A total of 10 groups of variables were set up. Specifically, five groups were designed to explore the influence of the web thickness of T-part 2 being 6 mm, 8 mm, 10 mm, 12 mm, and 14 mm on the nodes, with BT2F denoting the variation in the web thickness of T-part 2. In the other five groups, variable parameters were assigned to the flange thickness of T-shaped parts, with values of 8 mm, 10 mm, 12 mm, 14 mm, and 16 mm, respectively. BT2Y represents the change in the flange thickness of T-parts 2. The model parameters are presented in

Table 6. T-parts 2 node model parameters of different thicknesses.

Model number	BT2F-1	BASE	BT2F-3	BT2F-4	BT2F-5
Web thickness (mm)	6	8	10	12	14
Model number	BT2Y-1	BT2Y-2	BASE	BT2Y-4	BT2Y-5
Flange thickness (mm)	8	10	12	14	16

.

The stress of the joint and T-part 2 under different web thicknesses of T-part 2 is presented in Figure 15. From Figure 15, it is obvious that when the web thickness is small, the interface area between the web of T-part 2 and the flange, as well as the bolt holes on the web, are the first areas to experience plastic deformation. As the web thickness of T-part 2 increases, the yield area in the tensile zone of the web of T-part 2 gradually diminishes. Moreover, the degree of deformation of the web of T-part 2 also weakens, and the corresponding stress level decreases. The increase in web thickness of T-part 2 has little effect on joint failure mode. The influence of web thickness on the development of joint stress and deformation is not obvious.

The stress of the nodes and T-part 2 under different flange thicknesses of T-part 2 is depicted in Figure 16. When the flange thickness is small, the deformation in the flange-hole area of T-shaped part 2 is significant, and the stress from the flange bolt holes to the junction with the web is high. As the flange thickness of T-part 2 increases, the degree of deformation weakens. The clearance between the flange of T-part 2 and the web of the H-shaped steel beam becomes smaller, the yield area of the flange gradually decreases, and the stress level also drops. Increasing the flange thickness of T-part 2 has no obvious impact on joint stress and deformation. Moreover, the change in flange thickness has little effect on the joint failure mode.

Figure 17 and Figure 18 present the comparison diagrams of the skeleton curves of nodes under different web and flange thicknesses of T-parts 2. The results indicate that as the web thickness of T-part 2 increases, the yield load and bearing capacity of the space nodes increase, yet the improvement degree is not significant. Specifically, the yield load and bearing capacity of the BT2F-5 nodes increase by less than 1% compared to those of the BASE nodes. The change in web thickness of T-part 2 has little effect on the slope of the skeleton curve (Figure 17), indicating that its contribution to the initial stiffness is limited.

As the flange thickness of T-part 2 increases, the yield load and bearing capacity of the space nodes show no obvious changes, and the yield load and bearing capacity of the BT2Y-5 nodes are less than 1% higher than those of the BASE nodes. The web thickness of T-part 2 has no obvious impact on the joint stiffness. The stiffness of the joint increases with the growth of the flange thickness of T-part 2. Specifically, the stiffness of the BT2Y-5 node is approximately 6% higher than that of the BT2Y-1 node. The increase in the web thickness of T-part 2 has little effect on the yield displacement, ultimate displacement, and ductility of the joints. As the flange thickness of T-part 2 increases, the joint yield displacement increases, and the ductility coefficient decreases slightly.

4.3. Parameter Analysis of Column Wall Thickness

The stress cloud diagram of the column wall at different thicknesses is depicted in Figure 19. As can be observed from the stress cloud diagram, with the increase in the column wall thickness, the yield area around the bolt holes of the square steel pipe column wall gradually diminishes, and the degree of column wall buckling also decreases. When the wall thickness is 10 mm and 12 mm, the column wall in the node domain experiences deformation and damage, with relatively high wall stress. In the design process, it is necessary to control the wall thickness of the square steel pipe to ensure that wall damage does not occur with an appropriate amount of steel usage. The stress cloud diagram of the column wall at different thicknesses is depicted in Figure 19. As can be observed from the stress cloud diagram; with the increase in the column wall thickness, the yield area around the bolt holes of the square steel pipe column wall gradually diminishes, and the degree of column wall buckling also decreases.

When the column wall thickness is 10 mm (BZB-1), the main failure modes are column wall buckling and bolt-hole tearing. Due to the thin column wall, the stress concentration around the bolt hole is significant, resulting in local buckling of the column wall at the initial stage of loading (Figure 19a). With the increase in displacement, the buckling region expands, and finally the edge of the bolt hole tears due to excessive deformation, showing brittle failure characteristics (Δ_u/Δ_y = 2.1, low ductility coefficient). When the thickness of the column wall increases to 18 mm (BZB-5), the failure mode changes to the formation of the plastic hinge at the beam end. Due to the significant increase in column wall stiffness (38.12% increase in initial stiffness compared to BZB-1), stress concentration is transferred to the flange of the H-shaped steel beam, and the plastic hinge is eventually formed at the beam end (Figure 19b). In this model, the nodes exhibit ductile failure characteristics (Δ_u/Δ_y = 3.5, ductility coefficient is significantly improved).

The results demonstrate that as the column wall thickness increases, the yield load and bearing capacity of the joints gradually rise. In comparison with the BZB-1 node, the yield load of the BZB-5 node has increased by 37.85%, and the bearing capacity has increased by 33.4%. Compared with the BASE node, the yield load of the BZB-5 node has increased by 7.58%, and the bearing capacity has increased by 6.71%. Conversely, with the decrease in column wall thickness, the yield load and bearing capacity of the joint are reduced.

Compared with the BASE node, the yield load of the BZB-1 node has decreased by 21.96%, and the bearing capacity has decreased by 20.01%. As the column wall thickness increases, the joint yield displacement gradually decreases, while the ductility coefficient increases. The node stiffness also increases with the increase in column wall thickness. Compared with the BZB-1 node, the stiffness of the BZB-5 node has increased by 38.12%. Additionally, compared with the BASE node, the stiffness of the BZB-5 node has increased by approximately 13%. When the column wall thickness increases from 10 mm to 18 mm, the initial stiffness increases from 8.7 kN/mm to 12.0 kN/mm, an increase of 37.9%. When the column wall thickness increases from 10 mm (BZB-1) to 18 mm (BZB-5), the ductility coefficient increases from 2.1 to 3.5 (Δ_u/Δ_y = 104/29.7) by 66.7%.

Skeleton curves of nodes with different column wall thicknesses are shown in Figure 20, and the energy-dissipation curve of the nodes is shown in Figure 21. As the wall thickness of the square steel-pipe column increases, the joint energy consumption gradually rises while the equivalent viscous damping coefficient first decreases and then increases. The equivalent damping coefficient is 1/2π of the ratio of the area of the hysteresis curve to the deformation value. Under the same displacement, with the increase in column wall thickness, the energy consumption of the node increases. However, when the column wall thickness reaches a certain level, the growth rate of the weekly energy consumption gradually slows down in the later stage of the node’s behavior, and the increase in the equivalent viscous damping coefficient also gradually becomes smaller. Continuing to increase the column wall thickness has little impact on the improvement of energy-dissipation efficiency. Therefore, the column wall thickness should be reasonably controlled. When the column wall thickness is 12 mm (BASE), the equivalent viscous damping coefficient reaches 0.23 when the displacement is ±104 mm. When the thickness is 18 mm (BZB-5), the value increases to 0.28 (Figure 21b).

When the column wall thickness increases from 10 mm (BZB-1) to 18 mm (BZB-5), the ductility coefficient increases significantly from 2.1 (Δ_u/Δ_y = 104/49.5) to 3.5 (Δ_u/Δ_y = 104/29.7) by 66.7% (Table 3, Figure 20). This increase indicates that as the thickness of the column wall increases, the joints shift from brittle failure (dominated by column wall buckling) to ductile failure (dominated by plastic-hinge formation at the beam end). The increase in ductility coefficient directly enhances the energy absorption capacity of the node. When the column wall thickness is 18 mm (BZB-5), the equivalent viscous damping coefficient reaches 0.28 at a displacement of ±104 mm (Figure 21b), which is 47% higher than that of BZB-1 (0.19), indicating that the plastic hinge mechanism achieves more efficient energy dissipation through greater deformation capacity.

4.4. Parameter Analysis of Axial Compression Ratio

The stress cloud diagram of the node and column wall under different axial compression ratios is presented in Figure 22. The variation in the axial compression ratio has a negligible impact on the stress distribution of the joints. With an increase in the axial compression ratio, the yield area at the bolt hole and the tension area in the joint region increase slightly. Additionally, the stress at the top of the square steel-tube column rises as the axial compression ratio increases. Due to the partition within the column, the wall bulging of the square steel-tube column is not obvious.

The hysteresis curves of nodes under different axial compression ratios are depicted in Figure 23. With the increase in the axial compression ratio, the contraction of the hysteresis curve increases slightly. This indicates that the change in the axial compression ratio has a minor impact on the sliding of high-strength bolts. The envelope area of the curve enlarges as the axial compression ratio rises, suggesting that the seismic performance of the node gradually improves.

Figure 24 presents the skeleton curves of nodes under different axial compression ratios. The analysis results indicate that as the axial compression ratio increases, the yield load and bearing capacity of the space nodes gradually decline. Compared with the BASE node, the yield load of the BZY-5 node decreases by approximately 8%, and the bearing capacity decreases by about 9%. In contrast, compared with the BASE node, the yield load of the BZY-1 node increases by about 2.5%, and the bearing capacity increases by about 3%.

The yield displacement of the joint decreases as the axial compression ratio increases. When the axial compression ratio increases from 0.2 to 0.6, the ductility coefficient of the joint rises, increasing from 2.41 to 2.69. The change in the axial compression ratio has a negligible impact on joint stiffness. The initial stiffness slightly decreases with the increase in the axial compression ratio, with a maximum reduction of approximately 3%. In summary, as the axial compression ratio increases, the yield load and bearing capacity of the joint decrease significantly, the ductility coefficient increases slightly, and the initial stiffness decreases slightly.

The energy-dissipation curve of the nodes is presented in Figure 25. As the horizontal displacement continuously increases, the energy consumption of the nodes gradually rises. The increase in the axial compression ratio has a negligible impact on the energy-dissipation capacity of the nodes, and there is little difference in the energy dissipation among various nodes. However, as the axial compression ratio increases, the equivalent viscous damping coefficient gradually increases. When the displacement is the same, the dissipated energy of each node shows little variation, but the bearing capacity decreases significantly with the increase in the axial compression ratio, causing the equivalent viscous damping coefficient to increase accordingly. Although the bearing capacity of the node decreases as the axial compression ratio increases, the difference in the weekly energy consumption is slightly smaller, and the energy-dissipation efficiency increases. In conclusion, the increase in the axial compression ratio enhances the energy consumption capacity of the node. With the increase in axial compression ratio, the initial slope of skeleton curve decreases slightly (the maximum decrease is about 3%), but the overall stiffness degradation is not significant. When the axial compression ratio increases from 0.2 (BZY-1) to 0.6 (BZY-5), the ductility coefficient increases from 2.41 (Δ_u/Δ_y = 104/43.1) to 2.69 (Δ_u/Δ_y = 104/38.7) by 11.6%. When the axial compression ratio is 0.2 (BZY-1), the equivalent damping coefficient is 0.22. When the axial pressure ratio is increased to 0.6 (BZY-5), this value increases to 0.27 (Figure 25b).

The increase in the axial pressure ratio increases the positive pressure of the contact surface of the node (Figure 22), thus increasing the friction energy consumption between the bolt and the connecting plate. Although the bearing capacity decreases as the axial compression ratio increases (by about 9%), the frictional energy consumption increases as a proportion of the total energy, increasing the equivalent viscous damping coefficient from 0.22 (axial compression ratio 0.2) to 0.27 (axial compression ratio 0.6) (Figure 25b). The increase in axial pressure ratio leads to the intensification of microcrack propagation inside the joints (Figure 22a), and the nonlinear behavior of the materials is enhanced. Although the bearing capacity decreases, the equivalent damping coefficient increases due to the energy released during damage accumulation.

4.5. Parameter Analysis of High-Strength Bolt Preload

Figure 26 depicts the stress program of the joint when it attains the ultimate bearing capacity under the hysteretic loading mode with different high-strength bolt preloading forces. As the preloading force increases from 180 kN to 270 kN, the yield surface of the joint shows no significant change. The stress on the wall of the square steel-pipe column increases to some extent, yet it has almost no impact on the overall stress of the joint. The joint exhibited identical failure modes to the BASE joint, characterized by trough plate buckling and beam weld fracture.

Figure 27 presents the hysteresis curves of nodes under different high-strength bolt preloading forces. The hysteresis curves of each node are fusiform. Under a small pre-tightening force, the pinching effect of the node is pronounced, suggesting that the degree of bolt slip increases when the pre-tightening force is small. The change in the preloading of high-strength bolts has no impact on the ultimate bearing capacity of the joints.

Skeleton curves of joints with different bolt preloading forces are shown in Figure 28, and Figure 29 shows the energy-dissipation curve of the nodes. As the displacement increases gradually, the equivalent viscous damping coefficient of each node shows an upward trend. With the increase in the bolt preloading, the equivalent viscous damping coefficient of the node first increases and then decreases, yet this pattern is not very distinct. The energy consumption of the joint reaches its maximum when the bolt preloading is 270 kN. In conclusion, the pre-tightening force of the high-strength bolt has a negligible impact on the energy consumption of the node.

When the preload is increased from 180 kN (0.8 P) to 270 kN (1.2 P), the maximum stress at the edge of the bolt hole of the column wall is increased from 285 MPa to 312 MPa (increase by 9.5%). The maximum stress on the web plate of T-part 1 only increased from 345 MPa to 358 MPa (3.8% increase) (Figure 26). These increases are much smaller than the yield strength of the material (355 MPa for Q355B steel), indicating that changes in preloading force have a limited effect on the overall stress distribution. When the preload increases from 180 kN (BYJL-1) to 270 kN (BYJL-5), the yield load of the node increases from 372.1 kN to 379.5 kN (an increase of 1.9%), and the peak load increases from 436.8 kN to 442.3 kN (an increase of 1.3%) (Table 3, Figure 28). These increases are much smaller than the material strength dispersion (Q355B steel yield strength is 355 MPa), confirming the conclusion that the preload has ‘no material effect’ on the joint performance.

The non-monotonic trend of the equivalent viscous damping coefficient is mainly due to the coupling effect of the interface slip and friction effect: at the initial stage (axial pressure ratio ≤ 0.4), the increase in positive pressure on the contact surface strengthens the friction energy dissipation, and the equivalent damping increases. When the axial compression ratio is greater than 0.4, the combined action of bolt preload and axial compression leads to closer contact surface, reduced slip, and a slower or even lower friction energy consumption increase (Figure 25b). When the preloading force is low (such as 180 kN), the bolt slip is significant, and the friction energy consumption is dominant. When the preload is too high (e.g., 270 kN), the joint stiffness increases to inhibit the slip, and the energy dissipation becomes dependent on the plastic deformation of the material, resulting in the equivalent damping first rising and then decreasing (Figure 29b).

5. Conclusions

In this paper, a comparative analysis is conducted on the differences in failure modes, hysteretic curves, skeleton curves, initial stiffness, ductility, bearing capacity, and energy consumption of space joints under different T-shaped stiffness, column wall thicknesses, axial compression ratios, and bolt preloading. Previous studies on beam–column joints mainly focused on planar joints, and the research on spatial joints under two-way loads was relatively insufficient. This study fills this gap by establishing a finite-element model of column joints in the space of single-bolt-connected T-shaped parts and comprehensively analyzes the influence of various parameters on the seismic performance of spatial joints, providing a more comprehensive theoretical basis for the seismic design of steel-frame structures. Through parameter optimization (such as T-part 1 web ≥ 18 mm, column wall ≥ 12 mm), this study solves the problem that the seismic performance of space nodes is worse than that of plane nodes, pointed out by Bu et al. [4]. Compared with the cold-formed steel pipe joint proposed by Liu et al. (2021) [3], the ductility coefficient of this joint is increased by 20%~30% under the same coaxial pressure ratio (Figure 20, Table 3). The stiffness calculation formulas of each component are derived and analyzed based on the component method, and the following conclusions are drawn:

(1)

For T-parts in unilateral bolted space joints, there are three failure modes: plastic-hinge failure of the beam flange; joint brittle failure caused by column wall-buckling failure; and joint brittle failure caused by T-part fracture. When the thickness of the column wall is extremely small, the bolt holes and their edges will yield due to stress concentration, and the column wall will buckle. Moreover, the buckling phenomenon becomes more pronounced as the displacement increases, eventually leading to the buckling failure of the column wall. When the web thickness of T-part 1 is thin, the first row of bolt holes on the web of T-part 1 is pulled off. To fully exploit the performance of the single-bolted space joints of T-parts, the stiffness of the joint domain can be enhanced by increasing the thickness of the web or column wall of the T-parts.

(2)

The stiffness of T-part 1 exerts a significant influence on the joint. By increasing the thickness of the web plate of T-part 1, the bearing capacity and stiffness of the space joint can be enhanced. To prevent the brittle failure of joints resulting from the web fracture of T-part 1, achieve the ideal failure mode of forming a plastic hinge on the beam flange, and optimize the steel usage, it is recommended that the web thickness of T-part 1 should not be less than 18 mm. Specifically, compared with the BASE nodes, when the web thickness increases from 16 mm to 18 mm, the yield load and bearing capacity of the space node increase by approximately 12% and 16%, respectively, (see Figure 13).

(3)

The thickness variations in the web and flange of T-part 2 have a negligible impact on the seismic resistance of the joint. Whether the stiffness of T-part 2 decreases or increases, the yield load, bearing capacity, initial stiffness, and ductility of the joints do not exhibit significant changes. When the web thickness of T-part 2 increased from 6 mm to 14 mm, the yield load increased by only 0.8% (from 372.5 kN to 375.5 kN), and the peak load increased by 1.1% (from 435.2 kN to 439.9 kN) (Table 5, Figure 17). The stiffness varies by less than 6%, and the ductility coefficient (Δ_u/Δ_y = 2.7~2.8) is almost unchanged (Table 3).

(4)

When the thickness of the column wall is overly thin, the column wall is prone to buckling failure. As the wall thickness increases, the bearing capacity and stiffness of the joint increase. Additionally, the increase in wall thickness alleviates the deformation of the column wall to a certain degree. This paper recommends that the wall thickness of the joint column should be no less than the flange thickness of the steel beam and should not be less than 12 mm. When the column wall thickness increases from 10 mm to 12 mm, the yield load and bearing capacity increase by 37.85% and 33.4%, respectively, compared with the 10 mm thick column wall node (see Figure 20). When the column wall thickness increases (e.g., from 10 mm to 18 mm), the column wall stiffness increases significantly (initial stiffness increases by 38.12%), effectively limiting local buckling around the bolt hole (Figure 19b). The thicker column wall delays brittle failure (e.g., tearing) by preventing stress concentration, which in turn guides the plastic deformation to the H-shaped steel-beam flange, resulting in a plastic hinge at the beam end (Δu/Δy increased from 2.1 to 3.5).

(5)

As the axial compression ratio increases, the bearing capacity and stiffness of the joint decrease, yet the degree of stiffness reduction is not conspicuous. Conversely, the energy-dissipation capacity and ductility increase with the rise in the axial compression ratio.

(6)

The increase or decrease in the pre-tightening force of the high-strength bolt has no impact on the overall performance of the node. The yield load, bearing capacity, initial stiffness, and ductility of the joints with high-strength bolts do not change significantly as the preloading force varies. When the bolt preload increases from 180 kN to 270 kN, the yield load fluctuates ±1.9% (372.1 kN~379.5 kN), and the peak load fluctuates ±1.3% (436.8 kN~442.3 kN) (Table 3, Figure 28). These fluctuations are much lower than the material strength dispersion (Q355B steel yield strength standard deviation of about 5%).

(7)

Based on the research results, the recommended design threshold is given: The web thickness of the T-shaped part 1 is ≥18 mm (to ensure the formation of the plastic hinge, Δu/Δy ≥ 3.0); column wall thickness ≥ 12 mm (to prevent column wall buckling, initial stiffness ≥ 10 kN/mm); and axial compression ratio ≤ 0.4 (equilibrium bearing capacity and energy consumption, equivalent damping ≥ 0.25).

In the future, it is planned to expand the test validation, carry out low-cycle repeated tests on full-size joints, verify the prediction ability of the finite-element model for complex stress states (such as three-way stress), and supplement the parameter analysis of different steel strengths (such as Q420B). A long-term performance study was carried out to explore the durability and fatigue properties of the nodes under a corrosive environment. Combined with an electrochemical accelerated corrosion test, a life prediction model was established. A new type of connection was developed, combining the T-part connection with the semi-rigid node, further improving energy consumption efficiency and construction convenience by optimizing the bolt layout and contact surface treatment. Engineering application verification was conducted, application of this node in actual steel frame projects was piloted, its real response in earthquakes through health monitoring systems was evaluated, and data support for code revision was provided.