Experimental and Numerical Analysis of a Bolted Angle Connector Beam-to-Column Joint with a Stiffener

Abstract

The seismic performance of a proposed bolted angle connector beam-to-column joint with a stiffener (hereinafter referred to as a BACS joint) was investigated utilizing quasi-static tests on six specimens with H-shaped steel members. The failure modes, hysteretic curves, skeleton curves, stiffness degradation, and energy dissipation capacity were analyzed. The test results indicated that the BACS joint exhibited a 28.1% higher moment resistance and a 12.6% greater equivalent viscous damping coefficient compared to a welded connection with the same specifications. Furthermore, when compared to a short-beam spliced connection with comparable steel consumption, the BACS joint demonstrated advantages in both the load-bearing capacity and the energy dissipation. The numerical analysis results based on ABAQUS software demonstrated that increasing the stiffener height could not only enhance the bending capacity and stiffness of the connection, but also promote the relocation of the plastic hinge towards the beam end, thereby improving the failure mode. The increase in the stiffener thickness led to a minor improvement in the bending capacity of the connection, yet the influence of the stiffener thickness on the connection stiffness was limited. Furthermore, the use of steel with a higher strength grade could substantially increase the bending capacity of the BACS joint, while the enhancement in stiffness was relatively modest. Therefore, economic considerations should be integrated into the engineering design process.

1. Introduction

In the context of promoting building standardization and industrialization, prefabricated steel structures have garnered widespread attention and applications [1,2]. Beam-to-column connections are critical components for force transfer and directly influence the structural stability and safety of buildings [3]. Traditional steel structures often employ welded connections [4,5]. However, the 1994 Northridge earthquake and 1995 Kobe earthquake revealed numerous cases of brittle fractures in welded components.

In recent years, extensive research has been conducted to determine how to improve the mechanical behavior of the connections between H-shaped steel columns and beams. These studies can be separated into two categories based on the type of innovation: innovation in connection configuration and innovation in failure mechanisms. For configurations, the main types of connections include end-plate [6,7,8,9], double T-stub [10,11,12,13,14], and short-beam [15,16]. For failure mechanisms, the current technical approaches primarily involve the following:

(1)

Damage control techniques [11,12,17,18]: This approach includes the control of the yielding sequence of the connection components to prevent brittle failure in a structure.

(2)

Incorporating replaceable energy-dissipating elements [19,20,21]: This strategy is based on the local installation of replaceable, energy-dissipating connectors within a connection. This enhances the energy dissipation capacity while endowing a structure with post-earthquake reparability.

(3)

High-strength steel technology [22,23,24]: This method employs high-strength steel to substantially enhance the overall performance of a connection.

(4)

Self-centering technology [25]: This technique allows a structure to undergo recoverable deformation, thereby dissipating seismic energy and mitigating damage to the primary structural system.

(5)

New material technology [26]: Advanced alloys, FRP (fibre-reinforced polymer) composites, or additive-manufactured components. These can be employed to enhance the performance of beam-column joints.

The aforementioned innovation techniques have proven effective for enhancing the seismic performance and post-earthquake reparability of beam-to-column connections. However, the aspect of cost-effectiveness has often been underexamined. Moreover, most of these types of connections require that bolt holes be drilled through column flanges. This practice has a limited impact on large-section columns but causes non-negligible weakening in columns with small sections. In rural China, at the time of writing, traditional dwellings are being extensively replaced by low-rise, prefabricated light-steel residential buildings. This trend has necessitated the development of cost-effective connections that guarantee mechanical performance. With the significant rise in daily labor costs, effective cost control has mandated efficient assembly methods to shorten construction periods and manage steel usage. In response to the demand for rapid assembly and economic efficiency, this paper proposes a bolted angle connector beam-to-column joint with a stiffener (BACS joint), as detailed in Figure 1. The proposed procedure for this joint and stiffener involves factory-welding an angle steel connector to a steel column, which enhances the welding precision and quality. This procedure also facilitates the implementation of techniques to mitigate welding residual stresses. On-site, a beam can simply be hoisted into position and then bolted onto the angle steel connector, which would significantly improve construction efficiency.

Currently, a substantial body of cost estimation and structural optimisation research for steel frame structures employs steel quantity as a quantitative indicator [27,28]. Although this method cannot fully and accurately simulate fabrication and installation costs, it is widely adopted due to its expediency [29]. Therefore, this study utilises the metric of “steel quantity for connection” (SQC) to quantify the connection cost of beam-column joints. This metric refers to the mass of steel within a beam-column joint excluding the primary beams and columns. It includes components such as connecting plates, stiffeners, and bolts, but excludes welding consumables like electrodes.

In this study, to investigate the seismic performance of the aforementioned angle steel connection, and to compare its performance with those of other typical connections in terms of its mechanical behavior and economic efficiency, six reduced-scale specimens of H-shaped steel beam-to-column connections were fabricated. Quasi-static tests were conducted on these specimens. The failure modes, hysteretic behavior, stiffness degradation, and energy dissipation capacity of each specimen were compared and analyzed. Subsequently, the specimens were modeled and validated using the finite element analysis software ABAQUS. Finally, based on the experimental validation, a parametric study was performed by varying the stiffener height, stiffener thickness, and steel grade. The influences of these parameters on the seismic performance of the connection were analyzed, and corresponding design recommendations were proposed.

2. Experiment Design

2.1. Specimens

A total of six beam-to-column connection specimens with different configurations were designed at a 1:2 scale. These configurations included a welded connection (J-1), a web-connected connection (J-2), an end-plate connection (J-3), a bolted angle connector connection (BAC joint, J-4), a BACS joint (J-5), and a stub girder connection (J-6). The detailed dimensions for all of the specimens are shown in Figure 2, and their connection methods and SQC are summarized in

Table 1. Main connection details for the specimens.

Specimen	Type of Joint	Connection Method of the Column Flange	Connection Method of the Beam		SQC (kg)
			Beam Web Plate	Flange of the Beam
J-1	Welded joint	Welding with beams	Welding with a column flange	Welding with a column flange	0
J-2	Web-connected joint	Welding with connecting plate P1	Bolted to the connecting plate P1	No connection	0.33
J-3	End-plate joint	Bolted to the end plate	Welding with the end plate	Welding with the end plate	2.03
J-4	BAC joint	Welding with the vertical section of the angle steel connector	No connection	Bolted to the horizontal section of the angle steel connector	2.55
J-5	BACS joint	Welding with the vertical section of the angle steel connector	No connection	Bolted to the horizontal section of the angle steel connector	2.94
J-6	Stub girder joint	Welding with short beams	Bolted to the stub girder web through a cover plate	Bolted to the stub girder flange through a cover plate	3.34

.

2.2. Material Properties

All of the specimens were fabricated with Q235B steel. The yield strength, ultimate tensile strength, and elongation were determined in accordance with the Chinese standard GB/T 228.1 [30], with the results presented in

Table 2. Mechanical properties of the steel.

Material	Thickness t/mm	Yield Strength ${\mathit{f}}_{\mathit{y}}$/MPa	Ultimate Strength ${\mathit{f}}_{\mathit{u}}$/MPa	Elongation δ/%	Elastic Modulus E/MPa
Beam Web, Beam Flange, and Column Web	4	373	444	21.5	214,000
Column Flange	6	346	429	19.2	202,000
End Plate, Gusset Plate, and Stiffener	6	355	424	19.7	202,000

. Grade 8.8 M12 high-strength bolts were used for the beam-to-column connections. To facilitate assembly, the diameter for each of the bolt holes in the specimens was 2 mm larger than the nominal bolt diameter. All of the bolts were tightened using a torque wrench to the specified torque value and following the procedures specified in JGJ 82-2011 [31].

2.3. Loading Schemes

The loading scheme was illustrated in Figure 3. The test setup (Figure 3a) restrained the horizontal displacement at both the top and bottom of the specimen column, while allowing free rotation at these ends. During testing, the setup was secured to the base of a universal testing machine. Cyclic loading was then applied at the beam end, utilizing the machine’s movable reaction beam [32].

A force-displacement hybrid control loading protocol was adopted. Before yielding, the specimen was loaded incrementally utilizing force control. After yielding, the loading was switched to displacement control. Each load level was cycled twice. The yield rotation (θ_y) of the specimen was taken as the reference deformation value, and the loading levels were implemented as multiples of this yield rotation (Figure 3b). In accordance with JGJ/T 101-2015 [33], the test was terminated either when the beam-end load dropped to 85% of the peak load, or when excessive deformation occurred.

2.4. Data Collection

The arrangement for the load cell, displacement transducers (DTs), and dial gauges (DGs) is shown in Figure 4. A load cell was installed at the beam end to measure the vertical load (P). Simultaneously, DT1 was set up to measure the vertical displacement at the beam end. DT2 and DT3 were positioned at both ends of the column to verify the displacement readings. DG1 and DG2 were installed in the joint region to measure the slight rotations of the beam, column, and joint panel zone.

3. Results and Analysis

3.1. Failure Modes

J-1: When the load, P, increased to 29 kN, a crack with a width of approximately 0.5 mm was observed at the weld between the column and the beam’s bottom flange. Loading continued under force control until the specimen yielded, at which point the protocol switched to displacement control. As the beam-end displacement increased, the bottom flange of the beam exhibited local buckling. The load P reached its peak value of 56 kN. During the subsequent two loading cycles, P decreased rapidly, culminating in the fracture of the weld that connected the bottom flange of the beam to the column, leading to the failure of the specimen, as shown in Figure 5a.

J-2: When the load P reached 14 kN, a pronounced inflection point appeared on the load–displacement curve from the monitoring end. This was accompanied by a discernible increase in the gap between the beam flanges and the column. The loading protocol was subsequently switched to displacement control. As loading continued, a crack was initiated at the edge of the bolt hole nearest to the column in the connecting plate P1. This was followed by the fracture of the plate at the bolt hole (Figure 5b), which ultimately led to a rapid drop in the load.

J-3: When the load P increased to 24 kN, a minor crack was detected in the weld between the beam’s top flange and the end plate. With a further increase in P, the end plate exhibited residual bending deformation, and the crack at the weld deepened. The load P began to decline gradually after reaching its peak value of 42 kN. Failure culminated in a fatigue fracture at the bent location of the end plate, as illustrated in Figure 5c.

J-4: When the load P increased to 18 kN, a slight slip occurred between the angle steel connector and the beam flange. At a load of 32 kN, a crack was initiated at the edge of the first bolt hole (nearest to the column) in the angle steel connector. As P increased further, this crack propagated. After reaching the peak load of 59 kN, the plate at this bolt hole experienced a tearing fracture, as shown in Figure 5d.

J-5: When the load P increased to 28 kN, a slight slip occurred between the angle steel connector and the beam’s top flange. At a load of 56 kN, a crack was observed in the weld between the upper angle steel connector and the triangular stiffener. Concurrently, the beam’s bottom flange and the corresponding angle steel connector experienced minor buckling, which was accompanied by severe paint spalling. As the load approached approximately 70 kN, the crack at the angle steel connector-to-stiffener weld widened and propagated. During reverse loading, the stiffener itself buckled, as shown in Figure 5e.

J-6: When the load P increased to 20 kN, a relative slip occurred between the beam flange splice plates and the bolts. The loading protocol was switched to displacement control at a load of 49 kN. With the further increase in displacement, a crack developed in the upper flange of the stub beam near the column, while the splice zone plates exhibited significant bearing deformation. Ultimately, a fracture occurred in the steel plate at the weld between the stub beam and the column, as shown in Figure 5f.

3.2. Hysteresis Curve

The bending moment, M, acting on the connection was calculated as the product of the vertical load P and a lever arm with a length of 523 mm. The vertical displacement Δ_T at the beam end, recorded by DT1 (Figure 4), represented the combined deformations of the specimen components at the beam end. These deformations consisted of three components (Figure 6):

(1)

The vertical displacement, Δ₁, at beam end, resulting from the overall rotation of the beam-column joint, was calculated using Equation (1), where HD₁ and HD₂ were measured by DG1 and DG2 (Figure 4). As the vertical distance between DG1 and DG2 was 150 mm, the overall rotation angle of the beam–column joint was equal to the ratio of the difference between the measured values of DG1 and DG2 to 150 mm.

(2)

The vertical displacement, Δ₂, at the beam end, due to bending deformation under the action of a vertical load P, was given by Equation (2), where E denotes the elastic modulus of the steel beam and I_b represents its moment of inertia about the horizontal centroidal axis. L is the distance from the point of application of P to the column, namely 523 mm.

(3)

Vertical displacement Δ₃ at the beam end induced by the relative rotation between the beam and column under load P (Equation (3)):

$${∆}_1={\displaystyle \frac{\left|{HD}_1-{HD}_2\right|·523}{150}}$$

(1)

$${∆}_2={\displaystyle \frac{{PL}^3}{3E{I}_b}}$$

(2)

$$∆={∆}_3={∆}_T-{∆}_1-{∆}_2$$

(3)

The relative rotation between the beam and column under the applied vertical load P was determined using Equation (4):

$$\theta ={\displaystyle \frac{{∆}_3}{523}}$$

(4)

In all analytical and finite element calculations throughout this study, the millimetre-newton (mm-N) unit system was consistently applied to ensure dimensional homogeneity. Accordingly, material properties (e.g., elastic modulus) and sectional dimensions used in formulas were expressed in N/mm² (MPa) and mm, respectively. For the clarity and convenience of engineering interpretation, the results presented in figures and tables (e.g., forces, moments) were converted to and reported in the conventional kilonewton (kN) and kilonewton-metre (kN·m) units.

The moment-rotation (M-θ) hysteretic curves for all specimens are presented in Figure 7. As shown in the figure, the hysteretic loop for J-1 was full and spindle-shaped, indicating that the welded connection exhibited excellent energy dissipation capacity. The negative load reached its peak value when the rotation θ increased to 3%. During the two subsequent loading cycles, the load-carrying capacity of the specimen deteriorated abruptly, exhibiting a distinct brittle failure. Specimen J-2 exhibited a relatively low load-carrying capacity with severely pinched hysteretic loops, indicating poor energy dissipation capacity. In comparison with J-2, Specimen J-3 demonstrated significantly higher load-carrying capacity and superior energy dissipation. When compared with J-1, although J-3 showed a reduction in load-carrying capacity, a notable improvement in ductility was observed.

As shown in Figure 7d, the hysteretic loops of J-4 exhibited a certain degree of pinching, and its load-carrying capacity was comparable to that of J-1. However, its failure mode remained suboptimal. Compared with J-4, Specimen J-5, which had a 15.3% increase in the SQC, displayed a largely similar hysteretic loop shape. Yet, the triangular stiffener enhanced the stiffness of the connection, restrained the rotation induced by the slip of the angle steel connector along the beam, and consequently achieved a higher load-carrying capacity. Specifically, J-5 exhibited a 23.8% higher peak bending moment, a 7.4% increase in the flexural stiffness prior to yielding, and a 23.3% improvement in post-yield flexural stiffness compared to J-4. Furthermore, its failure mode approximated a ductile failure. The hysteretic loops of J-5 exhibited no pronounced descending branch, indicating a strong load-carrying capacity even at large rotation angles, which characterized it as a relatively ideal connection type. As can be seen from Figure 7f, the load-carrying capacity of J-6 was 18.2% higher than that of J-1, but 14.6% lower than that of J-5. The hysteretic loops of J-6 exhibited minor pinching, demonstrating favorable energy dissipation performance.

3.3. Skeleton Curves and Feature Points

The skeleton curves for all the specimens are presented in Figure 8, allowing for a comparison of the influences of various connection configurations on the joint performance. Key hysteretic performance indicators are summarized in

Table 3. Feature points of skeleton curves.

Test Specimen	Loading Direction	Peak Moment ${\mathit{M}}_{\mathit{p}}/(\mathbf{k}\mathbf{N}·\mathbf{m})$	Peak Rotation ${\mathit{\theta }}_{\mathit{p}}/\mathit{\%}$	Yield Moment ${\mathit{M}}_{\mathit{y}}/(\mathbf{k}\mathbf{N}·\mathbf{m})$	Yield Rotation ${\mathit{\theta }}_{\mathit{y}}/\mathit{\%}$	Ultimate Moment ${\mathit{M}}_{\mathit{u}}/(\mathbf{k}\mathbf{N}·\mathbf{m})$	Ultimate Rotation ${\mathit{\theta }}_{\mathit{u}}/\mathit{\%}$	μ
J-1	Positive	29.31	2.77	25.57	1.24	24.91	6.31	5.09
	Negative	30.32	2.76	25.28	1.42	27.54	3.84	2.70
J-2	Positive	10.09	4.34	7.11	1.23	8.58	5.88	4.78
	Negative	8.83	3.59	7.48	1.54	7.51	4.29	2.79
J-3	Positive	21.84	4.68	17.02	2.81	21.35	6.65	2.37
	Negative	17.88	4.16	13.76	1.48	15.49	6.54	4.42
J-4	Positive	31.18	5.68	26.84	2.37	30.85	6.08	2.57
	Negative	28.47	7.54	23.57	2.13	24.20	7.91	3.71
J-5	Positive	38.58	4.22	33.38	1.72	38.06	5.70	3.31
	Negative	37.78	7.25	32.28	2.40	37.78	7.25	3.02
J-6	Positive	34.65	5.74	28.46	1.63	29.91	6.40	3.93
	Negative	31.61	5.39	24.44	1.54	29.47	6.98	4.53

. In the table, M_p, M_y, and M_u denote the peak moment, yield moment, and ultimate moment, respectively, while θ_p, θ_y, and θ_u represent the corresponding rotations at the peak, yield, and ultimate moments. The yield moment on the M-θ skeleton curve was determined using the equal energy method [34] (Figure 9), and the point corresponding to 85% of the peak load on the descending branch of the skeleton curve was taken as the ultimate point. The ductility factor μ is defined as the ratio of θ_u to θ_y. The following observations were drawn from Figure 8 and Table 3:

(1)

The skeleton curves of J-1, J-2, and J-3 exhibited an “S” shape, which could be categorized into the elastic, elastoplastic, and failure stages. J-1 demonstrated the highest initial stiffness, and its peak moment occurred the earliest. However, the peak moment was followed by rapid failure. Although the welded connection offered favorable load-carrying capacity and stiffness, its characteristic brittle failure indicated that it was not an ideal connection type. J-2 exhibited a relatively low load-carrying capacity and stiffness, rendering it unsuitable for moment-resisting frames. In comparison, J-3 demonstrated a more balanced performance in terms of the load-carrying capacity, stiffness, and failure mode.

(2)

As shown in Figure 8b, the skeleton curves of J-4, J-5, and J-6 were generally similar. Their peak moments occurred later, and they maintained substantial load-carrying capacity even at large rotation angles. The SQC for J-5 was 1.15 times that of J-4, while the peak moment and the ultimate moment for J-5 increased by 27.9% and 37.7%, respectively. This demonstrated that the incorporation of stiffeners could significantly enhance both the strength and the deformation capacity of this connection type. Although the SQC of J-5 was only 88% of that exhibited by J-6, its peak and ultimate moments were 17.1% and 27.7% higher, respectively. Therefore, when considering both economic and mechanical performance, J-5 represents a more favorable option.

(3)

The mean ductility factors (μ) of all specimens under both positive and negative loading directions exceeded 3. Among them, J-5 and J-6 exhibited the smallest difference between the positive and negative directions, demonstrating good and stable plastic deformation capacity.

3.4. Stiffness Degradation

To characterize the stiffness degradation of structural components under low-cycle reversed loading, the secant stiffness K_j at each displacement level was adopted [33]. The calculation for the secant stiffness K_j is given in Equation (5), as illustrated in Figure 10:

$$K_j={\displaystyle \frac{\left|+P_j\right|+\left|-P_j\right|}{\left|+{∆}_j\right|+\left|-{∆}_j\right|}}$$

(5)

where K_j is the secant stiffness at the j-th displacement level, and P_j and Δ_j are the peak load and its corresponding displacement, respectively, during the cyclic loading at the j-th displacement level. The plus and minus signs preceding P_j and Δ_j denote the positive and negative directions, respectively.

The stiffness degradation for all of the specimens primarily underwent two distinct stages: (1) rapid stiffness deterioration, and (2) gradual stiffness degradation. When the rotation θ was less than 2%, the secant stiffness of each specimen decreased rapidly with the increasing load. After θ exceeded 2%, the rate of stiffness degradation slowed, indicating an enhanced deformation capacity. The initial stiffness of J-1 was 1.53 times and 1.06 times those of J-2 and J-3, respectively, demonstrating that the welded connection effectively improved the initial stiffness of the specimen. Similarly, the initial stiffness of J-5 was 1.35 times and 1.11 times those of J-4 and J-6, respectively, indicating that the presence of the triangular stiffener enhanced the connection performance and increased the initial stiffness of the joint. Compared with J-4, the yield stiffness of J-5 increased by 43.6%. Furthermore, in the later loading stages, J-5 demonstrated comparatively higher stiffness, indicating that the stiffener mitigated the stiffness deterioration of the specimen for large deformations. For J-6, because of the bearing deformation between the bolts and bolt hole walls, as well as the slip between the splice plates and bolts, the stiffness degradation rate also slowed in the later loading phase. However, the secant stiffness of J-6 at identical rotation angles was slightly lower than that of J-5.

3.5. Energy Dissipation

The relationships between the cumulative energy dissipation E and θ for all specimens at each loading level are shown in Figure 11. It can be observed from the figure that when θ < 2%, the energy dissipation capacities of the specimens showed no significant differences. When θ > 6%, the cumulative energy dissipation E of J-1, J-5, and J-6 reached relatively high levels, whereas J-2 and J-4 exhibited comparatively lower energy dissipation capacities. In the early loading stages, the energy dissipation capacity of J-5 was similar to that of J-4. However, with increasing rotation, the energy dissipation capacity of J-5 became significantly superior. This indicated that the incorporation of the triangular stiffener not only enhanced the bending capacity of the connection, but also improved its ductility and energy dissipation capability.

The hysteretic loop corresponding to the loading cycle at the peak moment was plotted, and the equivalent viscous damping coefficient h_e for that cycle was calculated according to Figure 12a [33] and Equation (6). The values of h_e for each specimen at the peak moment are shown in Figure 12b.

$$h_e={\displaystyle \frac{1}{2\pi }}·{\displaystyle \frac{S_{ABCD}}{S_{ (OBE+ODF) }}}$$

(6)

Here, S_ABCD is the area enclosed by the complete hysteresis loop ABCD, representing the energy dissipated in one cycle. The denominator, S_(OBE+ODF), is the sum of the areas of triangles OBE and ODF. This term defines the reference elastic strain energy, which corresponds to the elastic energy stored in an equivalent linear system at the peak displacement points of the cycle.

It can be observed from the figure that the h_e values of J-1, J-3, J-5, and J-6 all exceeded 0.25, indicating relatively high energy dissipation, while those of J-2 and J-4 were comparatively lower. This demonstrated that in the BACS joint, the addition of stiffeners could significantly enhance the energy dissipation capacity of the specimen, underscoring the necessity of incorporating stiffeners. Furthermore, because of its greater steel quantity, J-6 exhibited both a higher h_e value and achieved the highest cumulative energy dissipation.

4. FE Simulation

This section describes how the finite element software ABAQUS (version 2020) was used to conduct a further analysis of the BACS joint, with the goal of investigating the influence of key parameters on the connection’s performance.

4.1. FE Model

4.1.1. Mesh Properties and Size

The finite element models, designated as FJ-4 and FJ-5, were established with identical dimensions, boundary conditions, and loading protocols to those of specimens J-4 and J-5, as illustrated in Figure 13. C3D8R elements were adopted for the steel beams, columns, angle steel connector, and stiffeners. During meshing, a convergence study was conducted by progressively refining the mesh of each component. The simulation results were recorded until they stabilized with further mesh refinement [35].

4.1.2. Stress–Strain Relationships

The Q235B steel in the model utilized the stress–strain relationship provided by Han [36], as shown in Figure 14. The term fp denotes the proportional limit of the steel. This was the stress value at which the stress–strain curve deviated from linearity and could be obtained from the tested material curve. The values for fy, fu, and E are listed in Table 2, and the Poisson’s ratio was taken as 0.3. In Figure 14, ε_e = 0.8f_y/E, ε_e1 = 1.5ε_e, ε_e2 = 10ε_e1, and ε_e3 = 100ε_e1. The high-strength steel in the bolts was modeled using a bilinear constitutive relationship, which was characterized by an elastic stage followed by a strain-hardening stage. The elastic modulus of the hardening stage was taken as 0.01E [34].

4.1.3. Interaction

The interaction between the angle steel connector and the beam flanges was simulated using a surface-to-surface contact approach. The tangential behavior was defined as penalty friction, while the normal behavior was defined as hard contact. A friction coefficient of 0.3 was specified between the steel plates [14].

4.2. FE Model Verification

The Mises stress contour plots of FJ-4 and FJ-5 at the maximum rotation during the final loading cycle are presented in Figure 15. As shown in Figure 15a, the high-stress regions in model FJ-4 were primarily distributed in the horizontal segment of the angle steel connector near the column. This was consistent with the experimental observation of the crack initiation and eventual fracture at this location. Figure 15b indicates that the high-stress regions in model FJ-5 were located at the weld between the triangular stiffener and the horizontal segment of the angle steel connector, with the stress magnitudes increasing with the distance from the column. A stress concentration phenomenon was observed at the end of the weld, which was highly consistent with the experimental findings.

A comparison of the M-θ hysteretic curves between the finite element models FJ-4, FJ-5, and their corresponding specimens is presented in Figure 16.

It can be observed from the figure that these hysteretic curves were similarly shaped. However, the finite element models exhibited fuller hysteretic loops and slightly higher yield and peak moments compared to the physical specimens. This discrepancy arose because the specimens were inevitably subject to initial imperfections and welding residual stresses during fabrication, which adversely affected the connection performance to some extent. In contrast, the finite element models were relatively idealized in this regard. Ultimately, the peak load of J-4 showed a 4.8% discrepancy with FJ-4, while that of J-5 differed by only 3.3% from FJ-5. These minor deviations confirmed that the settings in the finite element model, including the element selection and material parameters, were reasonable, and that the simulation results could effectively predict the mechanical behavior of the beam-to-column connections.

4.3. Parametric Analysis

In specimen J-5, the triangular stiffener had a height of 70 mm, a thickness of 6 mm, and was made of Q235B steel. This section describes how finite element analyses were conducted on models with different parameters listed in

Table 4. FE model parameters.

Model ID	Stiffener Height (mm)	Stiffener Thickness (mm)	Steel Grade
FJ5-S40	40	6	Q235B
FJ-5	70	6	Q235B
FJ5-S100	100	6	Q235B
FJ5-S130	130	6	Q235B
FJ5-T4	70	4	Q235B
FJ5-T8	70	8	Q235B
FJ5-345	70	6	Q345B
FJ5-420	70	6	Q420B

, based on the FJ-5 model, to investigate the influence of these parameters on the connection performance. All of the other parameters in these models remained identical to those of J-5.

Each model was subjected to cyclic loading and simulated following the same loading protocol and boundary conditions as used in the tests. Since J-5 failed at θ = −7.12%, each model was loaded to an identical rotation angle to this to ensure comparability of the results. The Mises stress contour plots of each model at the peak moment during the final loading cycle are shown in Figure 17.

4.3.1. Effect of the Stiffener Height

The M-θ skeleton curves and stiffness degradation curves for models FJ5-S40, FJ-5, FJ5-S100, and FJ5-S130 are shown in Figure 18. By combining Figure 15 and Figure 17, it can be observed that as the stiffener height increased, the Mises stress in the column web within the joint zone gradually decreased. The stress in the beam end near the column remained relatively unchanged, while the stress in the region farther from the column gradually increased. For FJ5-S130, the beam even yielded outside the joint zone. The high-stress region in the angle steel connector also shifted gradually from the areas near the column to those farther away. The 12 bolts in FJ5-S40 were unevenly loaded, whereas in the subsequent three models, the bolt forces became progressively more uniform, indicating a more rational load transfer. The analysis above demonstrated that increasing the stiffener height could progressively shift the yielding region of the connection from the column toward the beam end.

As shown in Figure 18a, with the increase in the stiffener height in the angle steel connector, the initial slope of the skeleton curves progressively increased, indicating a gradual enhancement of the connection’s initial stiffness. Compared to FJ-5, the peak moments of FJ5-S40, FJ5-S100, and FJ5-S130 changed by −8.4%, 24.9%, and 54.9%, respectively. Figure 18b reveals that, relative to specimen FJ-5, the initial stiffness of specimens FJ5-S100 and FJ5-S130 increased by 12.1% and 16.4%, respectively, whereas that of FJ5-S40 remained virtually unchanged. This indicates that variations in the stiffener height have a significant influence on the initial stiffness when the height exceeds 70 mm, but a negligible influence when it is less than 70 mm.

Steel beams are typically integrated with floor slabs ranging from 90 to 140 mm in thickness. Therefore, the height of a stiffener should not exceed this range, as it can significantly enhance the mechanical performance of the connection while remaining fully concealed within the slab depth.

4.3.2. Effect of the Stiffener Thickness

The M-θ skeleton curves and stiffness degradation curves for models FJ5-T4, FJ-5, and FJ5-T8 are presented in Figure 19. Combined with Figure 17, it can be observed that the stiffener in FJ5-T4 was in a high-stress state overall (Figure 17j), with some areas having even yielded or buckled, while the stress at the steel beam end was relatively low. This made the connection itself more prone to failure rather than the beam end. In contrast, for FJ-5 and FJ5-T8, the high-stress zones in the stiffeners shifted slightly towards the beam end (Figure 17d,l), and the yielded region at the beam end also expanded. Furthermore, in specimen FJ5-T4, the bolts closer to the column exhibited lower stress, whilst those further away exhibited higher stress. This uneven stress distribution indicates that the angle connector could not transfer the load uniformly with a thinner stiffener. This situation was somewhat alleviated in specimen FJ-5 and showed a more pronounced improvement in FJ5-T8. This enhanced integrity is favorable for achieving the design objective of relocating the plastic hinge away from the connection.

The M-θ skeleton curves and the stiffness degradation curves for models FJ5-T4, FJ-5, and FJ5-T8 are shown in Figure 19. As can be seen from Figure 19a, the initial stiffness of the models showed no significant change with the increasing stiffener thickness. Compared to FJ-5, the peak moments of FJ5-T4 and FJ5-T8 changed by −17.3% and 10.7%, respectively. Figure 19b indicates that the differences in the stiffness degradation curves among the three models were minimal. This also demonstrates that while the bending stiffness of the connection changed only slightly with the increasing stiffener thickness, the bending capacity gradually improved, and the failure mode became more favorable. Therefore, the thickness of a stiffener should be appropriately increased in designs to mitigate damage to the connection.

4.3.3. Effect of Steel Strength

The M-θ skeleton curves and the stiffness degradation curves for models FJ-5, FJ5-345, and FJ5-420 are shown in Figure 20. Combined with Figure 17, it can be observed that as the steel strength increased, the stress at the beam ends of the three models progressively decreased, with a reduction in the yielded zones, while the stress in the connection plates showed relatively minor changes.

The skeleton curves of the models with different steel strengths showed little difference when θ < 2%. As θ continued to increase, the models using higher-strength steel exhibited higher peak moments. Compared with specimen FJ-5, the peak moment of specimens FJ5-345 and FJ5-420 increased by 31.5% and 52.1%, respectively. The performance improvement of FJ5-420 over FJ5-345 was significantly smaller than that of FJ5-345 over FJ-5. The stiffness degradation trends of the three specimens were consistent. The flexural stiffness gradually increased with the improvement in the steel strength, but the increase in the stiffness from FJ-5 to FJ5-345 was more pronounced, whereas the improvement from FJ5-345 to FJ5-420 was more moderate.

A comparison of the skeleton curves of FJ5-S130 and FJ5-420 reveals that both specimens achieved a comparable peak moment. However, the secant stiffness of FJ5-S130 during the loading phase was considerably greater, whilst its cost was substantially lower. This indicates that merely increasing the steel grade to enhance joint performance offers limited effectiveness and is economically inefficient. In contrast, a more advantageous approach is to rationally increase the height or thickness of the stiffeners.

5. Conclusions and Recommendations

In this study, the hysteretic behavior of BACS joints was comparatively investigated through experimental and numerical simulation methods. The conclusions were as follows:

(1)

The welded connection exhibited favorable bending capacity and energy dissipation capacity, yet it was prone to brittle failure. The web-connected connection demonstrated relatively weak bending capacity and stiffness, rendering it unsuitable for moment-resisting frames. The end-plate connection with comparable specifications demonstrated moderate performance in both load-bearing capacity and energy dissipation, but it could experience a ductile failure mode. Therefore, practical engineering applications should ensure that a connection is designed following the principle of preventing failure in the end-plate itself.

(2)

The BAC joint exhibited a bending capacity comparable to that of a welded connection with the same specifications, but with a lower he. After the addition of stiffeners to the angle steel connector, the SQC increased by 15%, while the bending capacity and h_e of the connection improved by 22.1% and 49%, respectively. The BACS joint demonstrated slightly a higher bending capacity and h_e compared to the stub girder connection, while its SQC was only 88% of that of the stub girder connection, thus exhibiting a clear technical advantage.

(3)

Finite element analysis indicated that an increase in the stiffener height not only enhanced the bending capacity, stiffness, and energy dissipation of the connection but also improved its failure mode. In comparison, increasing the stiffener thickness also improves the failure mode and enhances the load-carrying capacity of the joint; however, its influence on the capacity is less pronounced than that of the stiffener height. Similarly, increasing the steel strength can improve both the load-carrying capacity and stiffness of the joint, but with diminishing effectiveness at higher strength levels.

(4)

The BACS joint investigated in this study is suitable for residential steel-frame buildings of up to three storeys in seismically active regions where seismic design is required. It is important to note that the scope of this work was limited to connections where the H-shaped steel column is joined to the beam about its strong axis. Furthermore, due to constraints in the testing setup, the experimental programme was conducted solely on specimens at a 1:2 scale. Future work will therefore focus on enhancing the understanding of connections about the weak axis of H-shaped columns and on conducting tests using full-scale specimens.