Open AccessArticle

Hysteretic Behavior Study on the RBS Connection of H-Shape Columns with Middle-Flanges or Wide-Flange H-Shape Beams

School of Civil Engineering, Chang’an University, 75 Chang’an Middle Rd, Xi’an 710062, China

Author to whom correspondence should be addressed.

Buildings 2025, 15(1), 147; https://doi.org/10.3390/buildings15010147

Submission received: 1 December 2024 / Revised: 31 December 2024 / Accepted: 3 January 2025 / Published: 6 January 2025

(This article belongs to the Special Issue Advanced Studies on Steel Structures)

Browse Figures

Figure 1
RBS connection details [<a href="#B19-buildings-15-00147" class="html-bibr">19</a>]. "> Figure 2
Calculation diagram and model boundary conditions. (a) Diagram; (b) boundary conditions. "> Figure 3
Mesh of a specimen model (3000 mm × 3600 mm). "> Figure 4
Stress–strain model. "> Figure 5
SP5 specimen. (a) Schematic diagram of dimensions; (b) FE model. "> Figure 6
P–Δ curves of SP5 specimen. (a) Test; (b) ABAQUS. "> Figure 7
SPS-2 specimen. (a) Schematic diagram of dimensions; (b) FE model. "> Figure 8
P–Δ curves of SPS-2 specimen. (a) Test; (b) ABAQUS. "> Figure 9
Failure modes of SPS-2 specimen. (a) Test; (b) ABAQUS. "> Figure 10
Stress contour plot of A series joints at failure time. "> Figure 11
M-θ hysteretic curve and skeleton curve of A series specimens. "> Figure 11 Cont.
M-θ hysteretic curve and skeleton curve of A series specimens. "> Figure 12
Stress contour plot of B series joints at failure time. "> Figure 13
M-θ hysteretic curve and skeleton curve of B series specimens. "> Figure 14
Stress contour plot of C series joints at failure time. "> Figure 15
M-θ hysteretic curve and skeleton curve of C series specimens. ">

Versions Notes

Abstract

Existing research on reduced beam section (RBS) connections in steel frames rarely addresses H-shaped beams with middle and wide flanges. Therefore, this study investigates the hysteretic behavior of RBS connections in H-shaped columns connected to H-shaped beams with middle and wide flanges. Using finite element analysis, the influence of key parameters (a, b, and c, where “a” represents the unweakened beam flange extension length, “b” represents the weakened beam flange length, and “c” represents the weakened beam flange depth, respectively) on structural performance was evaluated, focusing on rotational stiffness, load-carrying capacity, plastic rotation capacity, and ductility. The results indicate that increasing a enhances initial rotational stiffness and load capacity but reduces plastic rotation and ductility, making lower a values (near 0.5b_f) optimal for ductile performance. Similarly, higher b values (up to 0.85b_f) marginally reduce stiffness and load capacity, improving plastic rotation capacity, with a greater benefit in wide-flange beams. Meanwhile, a lower c value (around 0.20b_f) offered balanced performance, with higher c values decreasing stiffness and load capacity but enhancing ductility. Overall, wider flanges improve plastic rotation and ductility but slightly decrease rotational stiffness, providing insights to guide RBS connection designs for seismic resilience.

Keywords:

RBS connection; hysteretic behavior; finite element analysis; seismic performance; rotational stiffness; ductility; H-shaped beam

1. Introduction

Before 1994, rigid beam-to-column connections were widely regarded as having strong seismic performance and were commonly employed in earthquake-prone areas. This point of view was challenged after the Northridge earthquake in 1994. Many moment-resistance frames (MRFs) did not completely collapse during the quake, but unexpected brittle fractures occurred at or near the welds between the beam lower flange and the column flange [1,2]. These failures caused a wave of research on the seismic behavior of MRF connections [3,4,5,6]. Extensive research has been conducted to develop methods for improving the seismic performance of beam-to-column connections. Different researchers have introduced many new types of connections [7,8,9].

The reduced beam section (RBS) connection is designed by locally reducing the beam flange area a short distance from the column flange, effectively relocating the plastic hinge away from the beam-to-column joint. Previous laboratory experiments have demonstrated the effectiveness of RBS connections [4,10,11]. Recent studies have further optimized RBS designs using finite element analysis to enhance ductility and seismic performance [12], conducted parametric investigations on the behavior of RBS connections with jumbo beams and columns [13,14], and evaluated the cyclic performance of these connections in box-column applications [15]. Additionally, researchers have developed more accurate cyclic hysteretic models to predict the inelastic behavior of RBS connections [16], while others have explored the application of RBS designs for specific regional profiles using simulation tools [17]. Cimagala [12] pointed out that current standards offer general guidelines for RBS geometry but lack practical design tools and rules of thumb to simplify calculations and ensure optimal performance. Qi et al. [13] found that current design procedures may not provide sufficient ductility for RBS connections with jumbo sections, and while proposed improvements were identified, further experimental validation and practical design guidelines are needed. Bompa et al. [14] investigated RBS connections with member sizes exceeding the limits specified in current seismic provisions, finding that while they can perform well, very large sections increase the risk of weld fracture. This highlights the need for deeper RBS cuts to improve performance and reduce strain at the welds, suggesting a refinement of design requirements is necessary. Ghassemieh and Mirghaderi [15] evaluated the seismic performance of RBS moment connections in box columns subjected to different loading protocols, revealing key insights into connection behavior and strength degradation; however, further studies are needed to explore the long-term effects of these protocols on performance and stability. Horton et al. [16] developed a comprehensive database of modified Ibarra–Krawinkler (mIK) models to accurately capture the cyclic behavior of RBS connections under earthquake loading, revealing that conventional methods may lead to unreliable predictions. However, further research is needed to refine the mIK parameters for certain RBS geometries to enhance the accuracy of hysteresis behavior modeling. Although Indupriya and Anupriya [17] demonstrated that incorporating reduced beam sections (RBS) improves the performance of moment connections in Indian profiles under cyclic loading, their research fails to explore the impact of different RBS geometries and configurations on connection performance in various seismic scenarios.

Previous research on RBS connections, whether involving I-shaped beams with H-shaped or box columns, has predominantly focused on narrow-flange beams of normal or deep depth. No studies have yet explored middle-flange or wide-flange H-shaped beams. Gemechu and Lu [18] were the first to investigate the influence of widened beam-end flanges in mid-flange H-beams paired with box columns, revealing significant improvements in bending capacity, ductility, and seismic performance, along with optimal design parameters. However, further studies are necessary to examine wide-flange H-beams.

The unique characteristics of reduced beam-end flanges in middle-flange and wide-flange H-beams with H-columns deserve closer scrutiny, particularly regarding their effects on plastic hinge formation and stress distribution. While outward plastic hinge displacement can reduce weld stress, it introduces challenges such as increased deformation in the beam web and a higher risk of local buckling. This study addresses these gaps through comprehensive finite element simulations to evaluate the seismic performance of these connections.

The insights gained from this research will be crucial for refining connection designs, ultimately enhancing the stability and resilience of steel structures in contemporary construction practices. By understanding how these factors interact, we can develop more effective strategies to ensure the integrity and durability of structures in seismically active regions.

2. Design Standard for an RBS Connection

This study investigates an RBS connection joint that utilizes a hybrid connection of welds and bolts, illustrated in Figure 1.

The requirements for several key geometric parameters shown in Figure 1 across different design standards are provided in Table 1. In Table 1, b_f is the width of the beam flange, and d_b is the depth of the beam.

Compared to the American standard, ANSI/AISC 358-16 [19], the Chinese standard, JGJ 99-2015 [20], uses a fixed, maximal cutting depth that reflects a safety-focused design philosophy, prioritizing reliable energy dissipation and structural performance at the expense of flexibility and optimization.

BS EN 1998-3 [21], with the fixation of parameters a and b, along with a relatively deep c, suggests a design philosophy focused on balancing structural strength and ductility, ensuring predictable plastic hinge formation while maintaining sufficient load-carrying capacity and connection integrity under seismic loads.

Table 1. Comparison of geometrical characteristics of reduced beam section.

Reference Standard	Geometrical Characteristics
Reference Standard	a	b	c	e	R
ANSI/ AISC 358-16 [19]	$0.50 b_{f} \leq a \leq 0.75 b_{f}$	$0.65 d_{b} \leq b \leq 0.85 d_{b}$	$0.10 b_{f} \leq c \leq 0.25 b_{f}$	$a + b / 2$	$(4 c^{2} + b^{2}) / 8 c$
BS EN 1998-3 [21]	$0.60 b_{f}$	$0.75 d_{b}$	$0.20 b_{f} \leq c \leq 0.25 b_{f}$	$a + b / 2$	$(4 c^{2} + b^{2}) / 8 c$
JGJ99-2015 [20]	$0.50 b_{f} \leq a \leq 0.75 b_{f}$	$0.65 d_{b} \leq b \leq 0.85 d_{b}$	$0.25 b_{f}$	$a + b / 2$	$(4 c^{2} + b^{2}) / 8 c$

3. Numerical Analysis Methods

3.1. Numerical Modeling

The T-shaped joint of the external steel frame was selected, with the beam and column lengths being 3000 mm and 3600 mm, respectively, measured from the hinge center. The x-axis, y-axis, and z-axis represent the beam’s length, depth, and width. The calculation diagram is shown in Figure 2a. Both the top and bottom of the column are designed with hinges, while the beam ends remain free.

As shown in Figure 2b, the top section of the column is coupled, with the coupling point constrained in the x and z directions for linear displacement. A rigid body is defined at the bottom of the column, with the rigid body reference point constrained in the x, y, and z directions for linear displacement. A concentrated force is applied at the top of the column, corresponding to an axial load ratio of 0.3. Displacement coupling is applied to all nodes within a 150 mm range at the beam-end loading point, and a displacement load is imposed on the coupled nodes in the y direction.

ABAQUS (Version 6.1.4) finite element analysis technology is well established and reliable. The C3D8I element was selected due to its effectiveness for hysteretic behavior studies of RBS connections because it can capture complicated nonlinear stress–strain responses, handle cyclic loading easily, and properly mimic stress concentrations and plasticity in crucial locations. These characteristics make it excellent for studying the performance of H-shape columns with reinforced joint zones and varied beam flange configurations under seismic or other cyclic stress conditions. The mesh refinement criteria in hysteretic behavior investigations of RBS connections are designed to capture stress concentrations, plastic hinge formation, geometric discontinuities, and nonlinear behaviors. Mesh sizes are determined using geometric, material, loading factors, and convergence studies. The goal is to strike a compromise between accuracy and computing efficiency, with crucial regions sufficiently tuned to produce credible findings. The mesh size for the hot-rolled H-shapes is 25 mm, the steel plates are 10 mm, and the high-strength bolt is 2 mm. This same is true of plastic hinges and contact areas to enhance accuracy, whereas a coarser mesh is applied to non-critical regions to optimize computational efficiency, as illustrated in Figure 3.

Welding connections are represented using the “TIE” command in ABAQUS. The TIE command is widely used for simulating weld behavior in FEA because it simplifies the modeling process while accurately capturing the load transfer and displacement continuity between welded parts. It provides a computationally efficient and reliable approximation of weld behavior for studies focusing on global structural behavior, such as hysteretic performance in RBS connections. The pre-loading value is set according to the JGJ82-2010 [22] standard, and the “bolt load” function in ABAQUS is used to simulate it. When pre-tension is applied to high-strength bolts, multiple contact relationships are established. Key contact interfaces include plate-to-beam web, bolt-head-to-web, and bolt-shank-to-wall, and all are simulated using ABAQUS’s “surface-to-surface” contact method. The stiffer surface is assigned as the master, while the less stiff surface acts as the slave. Normal contact is “hard” contact, meaning the surfaces remain in contact under compression and separate when tension occurs. Tangential contact is modeled with Coulomb friction, using the actual friction factor of 0.44 [23] for the bolt connection surface.

3.2. Material Property

As illustrated in Figure 4, the steel and bolt materials are modeled using a three-line isotropic hardening approach, defined by a stress–strain curve with σ_y, σ_u, and σ_st representing the yield, ultimate, and failure stresses, respectively, and ε_y, ε_u, and ε_st denoting the corresponding strains. The mechanical properties of Q235 steel are averaged from the stress–strain data reported by Nie et al. [24], while those of grade 8.8 M20 bolts are derived from the findings of Kontolati et al. [25], as summarized in Table 2.

3.3. Validation

3.3.1. Validation Example 1

The SP5 specimen, designed by Song et al. [26], has geometrical dimensions, with the ABAQUS model shown in Figure 5a,b. The column and beam sections are H250 × 250 × 10 × 16 and H374 × 180 × 8 × 12, respectively, and made of Q235 steel. The loading protocol for the specimen follows ANSI/AISC 341-05 [27], which includes six cycles at inter-story drift angles of 0.375% rad, 0.5% rad, and 0.75% rad, along with four cycles at 1% rad. For drift angles of 1.5% rad, 2% rad, 3% rad, and 4% rad, two cycles are applied for each angle, with two additional cycles for every subsequent 1% rad increment. Loading is stopped when the bearing capacity drops to 85% of the maximum load. Displacement-controlled cyclic loading is applied at the beam end according to the test protocol [26]. During the test, a column top force of 500 kN is applied, with a bolt pre-tension of 190 kN and a friction coefficient of 0.35 between the connection plate, web, and bolts.

The P–Δ hysteresis curve from the SP5 specimen experiment is shown in Figure 6a, while Figure 6b presents the P–Δ curves from the finite element analysis of the SP5 specimen. Despite some differences between the experimental and finite element hysteresis curves, the shapes are similar, showing a spindle form with near symmetry and minimal pinching. The maximum load from the finite element model was 171.41 kN compared to the experimental maximum load of 169.89 kN, resulting in an error of just 0.9%. The maximum plastic rotation of the SP5 test was 0.26 rad, while the numerical analysis predicted 0.274 rad, with a 5.4% error. This indicates that the numerical analysis method used in this study is highly reliable.

3.3.2. Validation Example 2

Gao’s SPS-2 specimen [28] was examined using the dimensions shown in Figure 7. The beam and column were fabricated from Q235 steel, with hot-rolled steel sections of HN300 × 150 × 6.5 × 9 for the beam and HW250 × 250 × 9 × 14 for the column. The material properties of Q235 steel include a yield strength of 299.2 MPa and a tensile strength of 420.6 MPa. Based on ANSI/AISC 341-05 [27], the loading protocol involved displacement-controlled cyclic loading applied at the beam end, with testing halting once the load reduced to 85% of the maximum. Key parameters for the experiment included a column top force of 850 kN (compression ratio = 0.4), a bolt pre-loading of 155 kN, and a friction coefficient of 0.35.

Figure 8a,b present a comparison of the experimental and finite element P–Δ hysteresis curves, while Figure 9a,b illustrate the consistent failure modes observed in both cases. The hysteresis curves exhibited a spindle-like symmetry with minimal pinching. The finite element model predicted a maximum load of 164.23 kN, which closely aligned with the experimental value of 153.73 kN (an error of 6.8%). The test reached a maximum plastic rotation of 0.392 rad, while the numerical analysis estimated 0.375 rad, resulting in an error of −4.43%, confirming the reliability of the analysis method.

4. Design of Analysis Specimens with Middle-Flange or Wide-Flange H-Shape Beams

4.1. Specimens with Middle-Flange H-Shape Beams

The column’s cross-sectional dimensions are HW502 × 470 × 20 × 25, with a height of 3600 mm, while the beam has dimensions of HM340 × 250 × 9 × 14 and a span of 3000 mm. The analysis focused on three key design parameters for the widened flange connection, a, b, and c, as illustrated in Figure 1. The study considered three series: MRA, MRB, and MRC. For each series, three joint configurations were modeled for finite element analysis, as detailed in Table 3. The steel used was Q235, with material properties provided in Table 2. The design parameters adhere to the standards of ANSI/AISC 358-16 [19] and JGJ99-2015 [20].

In Table 3, the naming convention for the specimens is as follows: in MRA, MRB, and MRC, “M” represents H-shaped steel specimens with middle flanges; “R” indicates that the connection is of the RBS type; and “A”, “B”, and “C” correspond to the varying parameters a, b, and c, respectively. The numbers “−1”, “−2”, and “−3” denote the three parallel specimens within a group.

4.2. Specimens with Wide-Flange H-Shape Beams

Specimens with wide-flange H-shape beams were defined as the W series of specimens, with HW502 × 470 × 20 × 25 for columns (height 3600 mm) and HM350 × 350 × 12 × 19 for beams (span 3000 mm). The steel was Q235, with material properties provided in Table 2. Three series were analyzed: WRA, WRB, and WRC. Three joint configurations were modeled for each series for finite element analysis (see Table 3).

In Table 3, the naming convention for the wide-flange H-shaped steel series specimens, WRA, WRB, and WRC, is the same as for the middle-flange H-shaped specimens described in Section 4.1. The only difference is that the letter “W” replaces “M” to indicate wide-flange H-shaped steel specimens.

5. Analysis Results and Discussion

5.1. A Series Joints

We defined all specimens with the varying parameter “a” as Series A specimens, including three middle-flange and three wide-flange beam specimens. Their failure modes, hysteresis curves, and skeleton curves are shown in Figure 10 and Figure 11, respectively. The load-carrying capacities of the specimens, determined from the skeleton curves, are listed in Table 4. R_ki represents the initial rotational stiffness. M_y, M_max, and M_u denote the yield, peak, and ultimate moments, respectively, with corresponding rotational displacements θ_y, θ_max, and θ_u. According to FEMA 350 [29], θ_p is defined as the rotation capacity. The ductility factor, μ, is calculated as μ = θ_u/θ_y.

Observing Figure 10 reveals that plastic hinges formed at the reduced sections in all specimens. However, the plastic hinge regions varied depending on the value of “a”. When “a” was at the lower limit (0.5b_f), severe buckling deformation occurred in the beam-end flange plate, whereas deformation was smaller when “a” was at the upper limit (0.75b_f).

As shown in the hysteresis and skeleton curves in Figure 11, as the “a” parameter increases, the bearing capacity of the specimen slightly improves. Further analysis of Table 4 shows that as the value of “a” increases, the joints’ rotational stiffness and load-carrying capacities increase. The initial rotational stiffness increased very slightly and negligibly: for the MRA specimens, the middle and upper values showed increases of 0.23% and 0.37%, respectively, compared to the lower limit (0.5b_f); for the WRA specimens, these increases were 0.24% and 0.40%, respectively. The increase in maximum load-carrying capacity (peak moment) was smaller for both groups, with the MRA specimens showing increases of 2.6% and 4.0%, and the WRA specimens showing increases of 2% and 2.9%. Although the joints’ plastic rotation capacities and ductility factors initially decreased (with lower mid values) and then increased as “a” increased, both θ_p and μ at the upper limit of “a” were smaller than those at the lower limit. Comparing the MRA and WRA specimens, the WRA specimens showed greater reductions at the mid-value of “a” (with decreases of 5.5% in θ_p and 7.2% in μ) than the MRA specimens (with decreases of 1.8% in θ_p and 6.4% in μ). Similarly, at the upper limit, the WRA specimens had larger reductions (1.4% in θ_p and 5.2% in μ) than the MRA specimens (0.4% in θ_p and 1.8% in μ). This indicates that widening the beam flange led to degradation in the plastic rotation capacity and ductility of the RBS connections.

Based on the observations and data analysis, in conclusion, an “a” value near the lower limit (0.5b_f) is recommended for achieving better ductility and plastic rotation capacity, especially in wide-flange beams (WRA specimens). While a higher “a” improves stiffness and load-carrying capacity, it reduces ductility and rotation capacity, which is crucial for RBS connections. Designs prioritizing ductility should thus use a lower “a” value, whereas stiffness-focused designs can consider a moderate increase, with caution against excessive flange widening. Generally, increasing the value of “a” reduces the plastic rotation capacity and ductility of RBS connections due to changes in plastic hinge location, moment gradient, and strain localization. These effects have significant practical design implications, particularly for seismic performance, where sufficient ductility and energy dissipation are critical.

5.2. B Series Joints

We defined all specimens with the varying parameter “b” as Series B specimens, which included three middle-flange beam specimens and three wide-flange beam specimens. Their failure modes, hysteresis curves, and skeleton curves are shown in Figure 9 and Figure 10, respectively. The load-carrying capacities of the specimens, determined from the skeleton curves, are listed in Table 5.

Observing Figure 12 reveals that plastic hinges formed at the reduced sections in all specimens. However, the plastic hinge regions varied depending on the value of “b”. When “b” was at the lower limit (0.65d_b), severe buckling deformation occurred in the beam-end flange plate, with less buckling in the web. At the upper limit (0.85 d_b), flange and web buckling deformations were more pronounced, resulting in a larger plastic hinge region.

As shown in the hysteresis and skeleton curves in Figure 13, as the “b” parameter increases, the bearing capacity of the specimen slightly improves. Further analysis of Table 5 shows that as “b” increases, the joints’ rotational stiffness and load-carrying capacities slightly decrease, but the reduction is minimal—less than 1% for both the MRB and WRB specimens, making this difference negligible. These results confirm the effectiveness of these configurations in obtaining ductile behavior while maintaining strength and stiffness, providing them with acceptable options for practical structural designs, especially in seismic applications. The joints’ plastic rotation capacity and ductility factor increase with an increase in “b”. Comparing the MRB and WRB specimens, the increase at the mid-value of “b” for the MRB specimens (2.2% in θ_p and 1.4% in μ) was smaller than that for the WRB specimens (8.5% in θ_p and 2.2% in μ). Similarly, at the upper limit, the increase in the MRB specimens (5.9% in θ_p and 2.4% in μ) was smaller than in the WRB specimens (14.6% in θ_p and 3.0% in μ). This indicates that widening the beam flange improves the plastic rotation capacity and ductility of the RBS connections. However, further increases in WRB specimens require additional design refinements to ensure consistent and reliable behavior.

In conclusion, a higher “b” value close to the upper limit (0.85d_b) is recommended, as it enhances the plastic rotation capacity and ductility of the RBS connections with minimal impact on rotational stiffness and load-carrying capacity. Widening the beam flange further benefits plastic hinge formation, particularly in WRB specimens, by reducing buckling effects and improving overall ductility.

5.3. C Series Joints

Six specimens with varying parameters “c” were defined as Series C specimens. The failure modes, hysteresis curves, and skeleton curves for these specimens are presented in Figure 14 and Figure 15, respectively. The load-carrying capacities, as determined from the skeleton curves, are detailed in Table 6.

Observing Figure 11 reveals that plastic hinges formed at the reduced sections in all specimens. However, the regions of the plastic hinges varied depending on the value of “c”. When “c” was set at 0.20b_f, severe buckling deformation occurred in the beam-end flange plate, while the web experienced minimal buckling. At the upper limit (0.25b_f), the deformation of the beam-end flange plate decreased (with the deformation of the wide flange WRC specimens being smaller than that of the MRC specimens), while the buckling deformation of the web increased, resulting in a larger plastic hinge region.

As shown in the hysteresis and skeleton curves in Figure 15, as the “c” parameter increases, the bearing capacity of the specimen greatly decreases. Further analysis of Table 6 shows that as the value of “c” increases, the joints’ rotational stiffness and load-carrying capacities decrease, with a reduction from −1.4% to −3.9% in initial rotational stiffness and a reduction in load-carrying capacity ranging from −5.3% to −13.0%. The joints’ plastic rotation capacity and ductility factor increase as “c” increases. Comparing the MRC and WRC specimens, the increases at the mid-value of “c” for the MRC specimens (3.6% in θ_p and 17.0% in μ) were greater than those for the WRC specimens (2.4% in θ_p and 12.0% in μ). Similarly, at the upper limit, the increases for the MRC specimens (6.2% in θ_p and 48.0% in μ) were larger than those for the WRC specimens (4.2% in θ_p and 26.6% in μ). This indicates that widening the beam flange results in a smaller increase in the plastic rotation capacity and ductility of the RBS connections.

Based on this analysis, a “c” value between the lower limit (0.20b_f) and the mid-limit (0.225b_f) is recommended to balance rotational stiffness, load-carrying capacity, and ductility in RBS connections. While increasing “c” enhances plastic rotation capacity and ductility, it leads to great decreases in initial rotational stiffness (less than −2%) and load-carrying capacity (−5.3% to −6.0%). Furthermore, widening the beam flange lessens the positive impact of a higher “c” value on plastic rotation capacity and ductility. Therefore, a lower “c” value offers a more optimal performance balance.

5.4. Discussion

RBS (reduced beam section) connections are designed to improve seismic performance by concentrating plastic deformations in the beam. The parameters a, b, and c affect the connection’s stiffness, load-bearing capacity, plastic rotation capacity, and ductility in the following ways:

Parameter a (Unweakened Beam Flange Extension Length):

A longer “a” increases stiffness and load-bearing capacity but reduces plastic rotation and ductility. This is because the unweakened section delays the formation of a plastic hinge, limiting flexibility and energy absorption. The results of this study on RBS connections for mid- and wide-flange H-shaped steel beams, along with previous findings on RBS connections for narrow-flange H-shaped steel beams [9], provide strong support for this conclusion. An “a” value near the lower limit (0.50b_f) is recommended, aligning with the ranges suggested in ANSI/AISC 358-16 [19] and JGJ99-2015 [20]. However, the value specified in BS EN 1998 [21] (0.60b_f) may be overly large, prioritizing load-bearing capacity at the expense of connection ductility.

2.: Parameter b (Weakened Beam Flange Length):

A larger “b” reduces stiffness but improves plastic rotation and ductility by allowing for more deformation. This enhances energy dissipation, but excessive weakening can decrease load-bearing capacity. Unlike RBS connections for narrow-flange H-shaped steel beams [9], the “b” values for mid- and wide-flange H-shaped steel beam RBS connections in this study are better suited to the upper limit (0.85d_b) of the range recommended by ANSI/AISC 358-16 [19] and JGJ99-2015 [20]. In contrast, the value specified in BS EN 1998 [21] (0.75d_b) is more appropriate for narrow-flange beams falling near the median of the ranges in the other two standards.

3.: Parameter c (Weakened Beam Flange Depth):

A smaller “c” improves load-bearing capacity but reduces plastic rotation and ductility. Larger “c” values allow for more deformation, improving ductility and energy absorption. This aligns with findings from studies on narrow-flange H-shaped steel beam RBS connections [9]. The flange width is significantly larger for mid- and wide-flange H-shaped steel beams than for narrow-flange beams. When the flange reduction ratio adopts the mid-to-lower-limit values (0.20b_f~0.225b_f) specified in BS EN 1998 [21], it effectively balances load-bearing capacity and ductility in RBS connections. In contrast, the values in JGJ99-2015 [20] result in excessive section weakening, overly compromising load-bearing capacity, while the lower limit design in ANSI/AISC 358-16 [19] overly sacrifices ductility.

Optimizing a, b, and c is essential for balancing stiffness, load-bearing capacity, and ductility in RBS connections, which improves seismic performance.

6. Conclusions

This study examined the hysteretic behavior of reduced beam section (RBS) connections in H-shaped columns with middle-flange and wide-flange H-shaped beams. Key parameters (a, b, and c) were varied to investigate their impact on structural performance, including rotational stiffness, load-carrying capacity, plastic rotation capacity, and ductility. The following conclusions can be drawn:

Increasing “a” slightly enhanced the initial rotational stiffness and load-carrying capacity but significantly decreased plastic rotation capacity and ductility. Therefore, lower “a” values near the minimum (0.5b_f) are recommended for enhanced ductility, especially for wide-flange beams (WRA specimens).
Higher values of “b” led to slightly reduced rotational stiffness and load capacity but with minimal impact (less than 1%). Conversely, plastic rotation capacity and ductility improved with an increasing “b” value. Thus, a “b” value close to the upper limit (0.85b_f) is recommended to achieve optimal plastic behavior, particularly in WRA specimens.
As “c” increased, rotational stiffness and load-carrying capacity decreased while plastic rotation capacity and ductility improved. However, increasing “c” was less significant in wide-flange beams. A lower “c” value (0.20b_f) is preferable for balanced structural performance.
Widening the beam flange generally enhanced plastic rotation capacity and ductility but decreased rotational stiffness. This study’s insights can inform design decisions to optimize RBS connections for seismic resilience, achieving a balance between stiffness, load capacity, and ductility in mid- and wide-flange H-shaped beam connections.

Author Contributions

Conceptualization, L.L.; investigation. S.M.A.A.A.-S.; validation, S.M.A.A.A.-S., O.Z.Y.A.-A. and S.A.; resources, L.L.; writing—original draft preparation, S.M.A.A.A.-S. and L.L.; writing—review and editing, L.L.; project administration, L.L.; funding acquisition, L.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Nature Science Foundation of China (NSFC), grant number 51278061.

Data Availability Statement

The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Figure 1. RBS connection details [19].

Figure 2. Calculation diagram and model boundary conditions. (a) Diagram; (b) boundary conditions.

Figure 3. Mesh of a specimen model (3000 mm × 3600 mm).

Figure 4. Stress–strain model.

Figure 5. SP5 specimen. (a) Schematic diagram of dimensions; (b) FE model.

Figure 6. P–Δ curves of SP5 specimen. (a) Test; (b) ABAQUS.

Figure 7. SPS-2 specimen. (a) Schematic diagram of dimensions; (b) FE model.

Figure 8. P–Δ curves of SPS-2 specimen. (a) Test; (b) ABAQUS.

Figure 9. Failure modes of SPS-2 specimen. (a) Test; (b) ABAQUS.

Figure 10. Stress contour plot of A series joints at failure time.

Figure 11. M-θ hysteretic curve and skeleton curve of A series specimens.

Figure 12. Stress contour plot of B series joints at failure time.

Figure 13. M-θ hysteretic curve and skeleton curve of B series specimens.

Figure 14. Stress contour plot of C series joints at failure time.

Figure 15. M-θ hysteretic curve and skeleton curve of C series specimens.

Table 2. Material properties of Q235 Steel and grade 8.8 bolt.

Material Samples	E/MPa	σ_y/MPa	ε_y	σ_u/MPa	ε_u	σ_st/MPa	ε_st
Q235 steel	197,000	320	0.001748	451.667	0.14361	360.643	0.19653
8.8 grade M20 bolt	161,000	645.0	0.004	793.5	0.025	636.9	0.121

Table 3. Properties of specimens.

Specimen No.	a (mm)		b (mm)		c (mm)
MRA-1	0.5b_f	125	0.75d_b	255	0.20b_f	50
MRA-2	0.65b_f	162.5	0.75d_b	255	0.20b_f	50
MRA-3	0.75b_f	187.5	0.75d_b	255	0.20b_f	50
MRB-1	0.65b_f	162.5	0.65d_b	221	0.20b_f	50
MRB-2	0.65b_f	162.5	0.75d_b	255	0.20b_f	50
MRB-3	0.65b_f	162.5	0.85d_b	289	0.20b_f	50
MRC-1	0.65b_f	162.5	0.75d_b	255	0.20b_f	50
MRC-2	0.65b_f	162.5	0.75d_b	255	0.225b_f	56.25
MRC-3	0.65b_f	162.5	0.75d_b	255	0.25b_f	62.5
WRA-1	0.5b_f	175	0.75d_b	262.5	0.20b_f	70
WRA-2	0.65b_f	227.5	0.75d_b	262.5	0.20b_f	70
WRA-3	0.75b_f	262.5	0.75d_b	262.5	0.20b_f	70
WRB-1	0.65b_f	227.5	0.65d_b	227.5	0.20b_f	70
WRB-2	0.65b_f	227.5	0.75d_b	262.5	0.20b_f	70
WRB-3	0.65b_f	227.5	0.85d_b	297.5	0.20b_f	70
WRC-1	0.65b_f	227.5	0.75d_b	262.5	0.20b_f	70
WRC-2	0.65b_f	227.5	0.75d_b	262.5	0.225b_f	78.75
WRC-3	0.65b_f	227.5	0.75d_b	262.5	0.25b_f	87.5

Table 4. Mechanical performance indexes of A series joints.

Joint Number	R_ki /kN·m·rad⁻¹	M_y /kN·m	θ_y /rad	M_max /kN·m	θ_max /rad	M_u /kN·m	θ_u /rad	θ_p /rad	μ
MRA-1	7537.78	168	0.048	201.48	0.0904	171.30	0.1058	0.0999	2.20
MRA-2	7554.80	172	0.052	206.71	0.0910	175.70	0.1069	0.0981	2.06
MRA-3	7566.02	178	0.050	209.53	0.0938	178.10	0.1082	0.0995	2.16
WRA-1	12,815.30	315	0.054	369.61	0.0936	314.17	0.1353	0.1264	2.51
WRA-2	12,845.50	310	0.055	376.89	0.0937	320.36	0.1283	0.1195	2.33
WRA-3	12,866.20	319	0.056	380.29	0.0939	323.25	0.1335	0.1246	2.38

Table 5. Mechanical performance indexes of B series joints.

Joint Number	R_ki /kN·m·rad⁻¹	M_y /kN·m	θ_y /rad	M_max /kN·m	θ_max /rad	M_u /kN·m	θ_u /rad	θ_p /rad	μ
MRB-1	7594.83	173	0.048	207.30	0.0940	176.21	0.1010	0.0960	2.10
MRB-2	7554.80	172	0.052	206.70	0.0910	175.70	0.1110	0.0981	2.13
MRB-3	7520.65	170	0.052	205.11	0.0937	174.06	0.1120	0.1017	2.15
WRB-1	12,890.95	318	0.053	375.92	0.0938	319.50	0.1223	0.1035	2.31
WRB-2	12,845.49	317	0.055	374.70	0.0937	317.40	0.1296	0.1123	2.36
WRB-3	12,792.21	317	0.056	374.11	0.0931	316.70	0.1334	0.1186	2.38

Table 6. Mechanical performance indexes of C series joints.

Joint Number	R_ki /kN·m·rad⁻¹	M_y /kN·m	θ_y /rad	M_max /kN·m	θ_max /rad	M_u /kN·m	θ_u /rad	θ_p /rad	μ
MRC-1	7554.80	172	0.052	206.71	0.0939	175.70	0.1070	0.0981	2.06
MRC-2	7439.26	174	0.046	195.75	0.0933	166.4	0.1110	0.1016	2.41
MRC-3	7310.81	145	0.037	183.92	0.0931	156.33	0.113	0.1042	3.05
WRC-1	12,845.49	310	0.055	376.89	0.0937	320.36	0.1283	0.1195	2.33
WRC-2	12,610.51	305	0.051	354.39	0.0920	301.23	0.1330	0.1224	2.61
WRC-3	12,341.15	275	0.047	327.82	0.0913	278.65	0.1388	0.1245	2.95

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MDPI and ACS Style

Al-Saeedi, S.M.A.A.; Lu, L.; Al-Ansi, O.Z.Y.; Ali, S. Hysteretic Behavior Study on the RBS Connection of H-Shape Columns with Middle-Flanges or Wide-Flange H-Shape Beams. Buildings 2025, 15, 147. https://doi.org/10.3390/buildings15010147

AMA Style

Al-Saeedi SMAA, Lu L, Al-Ansi OZY, Ali S. Hysteretic Behavior Study on the RBS Connection of H-Shape Columns with Middle-Flanges or Wide-Flange H-Shape Beams. Buildings. 2025; 15(1):147. https://doi.org/10.3390/buildings15010147

Chicago/Turabian Style

Al-Saeedi, Saleem Mohammed Ali Ahmed, Linfeng Lu, Osama Zaid Yahya Al-Ansi, and Saddam Ali. 2025. "Hysteretic Behavior Study on the RBS Connection of H-Shape Columns with Middle-Flanges or Wide-Flange H-Shape Beams" Buildings 15, no. 1: 147. https://doi.org/10.3390/buildings15010147

APA Style

Al-Saeedi, S. M. A. A., Lu, L., Al-Ansi, O. Z. Y., & Ali, S. (2025). Hysteretic Behavior Study on the RBS Connection of H-Shape Columns with Middle-Flanges or Wide-Flange H-Shape Beams. Buildings, 15(1), 147. https://doi.org/10.3390/buildings15010147

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