Analysis of influencing factors on the seismic performance of RC beam-column exterior joints based on orthogonal experimental design

Abstract

Due to the frequent earthquakes in recent years, the importance of studying the seismic performance and optimizing the influencing factors of beam-column exterior joints has become increasingly significant. This paper designed nine RC (reinforced concrete) beam-column exterior joints, taking into account concrete strength, the anchorage style of steel bars, and reinforcement ratio as influencing factors. Quasi-static loading tests were conducted on these nine RC beam-column exterior joints utilizing an orthogonal experimental design (OED) of three factors and three levels (L₉(3³)). The failure mode, hysteretic performance, skeleton curves, ductility, cumulative energy dissipation, and ultimate bearing capacity of the joints were assessed. Additionally, the impact of variations in these factors on seismic performance was investigated. Variance analysis and range analysis were conducted on the test results to determine the primary and secondary order of factors influencing the seismic performance, thereby identifying the optimal levels of these factors. The results indicated that all three factors significantly affect on the ductility, cumulative energy dissipation, and ultimate bearing capacity. The primary and secondary orders as well as the optimal levels of the three factors, are as follows: (1) for ductility, the primary and secondary orders are: reinforcement ratio > concrete strength > anchorage style, with the optimal level being: C70 + two-sided welding +1.63%; (2) for cumulative energy dissipation, the primary and secondary orders are: concrete strength > reinforcement ratio > anchorage ratio, with the optimal level being: C70 + two-sided welding +2.08%; (3) for ultimate bearing capacity, the primary and secondary orders are: reinforcement ratio > concrete strength > anchorage style, with the optimal level being: C70 + 90-degree hooks +2.58%. From the above discussion, this paper provides a theoretical reference for optimizing the design of factors that impact the seismic performance of RC beam-column exterior joints.

Keywords

beam-column exterior joint orthogonal experimental design seismic performance ductility energy dissipation capacity

Introduction

The beam-column exterior joint, serving as the crucial link connecting beams and columns, is widely used in engineering structures due to its flexible layout and convenient production (Murad, 2020; Qiao et al., 2024). It constitutes the main component of frame structures, bearing the load from the columns and distributing the bending moment at the beam-column end. In recent years, with the frequent occurrence of earthquakes, the reliability of beam-column connections, especially the seismic performance of beam-column exterior joints, has become a research hotpot for scholars worldwide (Alagundi and Palanisamy, 2022; Gao et al., 2022; Grande et al., 2023; Kang et al., 2024; Sharma et al., 2011).

The seismic performance of beam-column exterior joints refers to their capability to dissipate seismic energy and transmit forces, including axial loads, shear forces, and bending moments when subjected to seismic loads. Previous research indicates that the seismic performance of beam-column exterior joints is primarily influenced by factors such as axial compression ratio (Wei et al., 2023), reinforcement strength (Borujerdi et al., 2021; Zhang et al., 2024), concrete strength (Hou et al., 2018, 2019), anchorage styles of reinforcement ends in the joint core (Lee and Yu, 2009; Liu et al., 2016), and longitudinal reinforcement ratio (Miao et al., 2024; Zhang et al., 2023). Deng et al. (2019) and Liang et al. (2016) conducted quasi-static tests to examine the impact of the axial compression ratio on the seismic performance of beam-column joints. They observed that an increase in axial compression ratio can improve shear bearing capacity, energy dissipation capacity, and shear deformation capacity in the joint core. Choi et al. (2022) investigated the seismic performance of exterior beam-column joints with different concrete compressive strengths and analyzed the strain behavior of reinforcement in both the beam and joint in detail. To examine the influence of anchorage styles in the joint core on joint seismic performance, Cosgun et al. (2020) conducted experimental tests to investigate the impact of three anchorage styles (90-degree hooks, 180-degree hooks, and straight bars (without hooks)) on the performance of beam-column joints. The results revealed that anchorage styles have a significant impact on the seismic performance and failure mode. In recent years, research on the seismic performance of beam-column joints has expanded beyond structural design, with increasing attention being paid to high-performance materials for joints (Borujerdi et al., 2021; Gao et al., 2024; Nie et al., 2023; Xu et al., 2024). Dangwal and Singh (2023) conducted an experimental study on eight beam-column joints repaired with high-strength fiber-reinforced concrete, analyzing their seismic performance in terms of failure modes, hysteretic performance, energy dissipation, and stiffness degradation. Wang et al. (2022) carried out experimental research and numerical analysis on eight beam-column joints with high-performance fiber-reinforced concrete under cyclic loading, and analyzing the effects of stirrup ratio, reinforcement strength, axial compression load level, and vertical reinforcing bars on load-carrying capacity. Additionally, numerous experimental studies on the seismic performance of beam-column joints with high-performance reinforcements have been conducted (Alaee and Li, 2017; Di et al., 2023; Selim et al., 2024; Son et al., 2024; Zhang et al., 2022).

Previous studies have primarily focused on the mechanical characteristics and seismic capacity of beam-column exterior joints, with limited research comparing the influence of various factors on their seismic performance. In the process of making joints, the parameters of beam-column joints cannot simultaneously meet the requirements of the optimal combination. Consequently, optimizing the design of parameters affecting the seismic performance of joints is of significant importance, particularly in the context of frequent earthquakes. Orthogonal experimental design (OED) is an efficient method for studying multiple factors and levels (Guo et al., 2023; Wang et al., 2023). Rooted in mathematical statistics and probability theory, it selects a subset of representative points from a comprehensive experiment based on orthogonality. The core of orthogonal experimental design lies in its orthogonality, ensuring that each level of every factor is combined at least once with each level of other factors. This approach guarantees both the comprehensiveness and representativeness of the experiments, enabling the acquisition of comprehensive and reliable information with a limited number of tests. Variance analysis and range analysis are two commonly used methods for analyzing the results of orthogonal experiments (Feng et al., 2021; Wei et al., 2023). Compared to comprehensive test, the advantages of orthogonal test are as follows: (1) significantly reducing the number of tests and the complexity of the work, (2) identifying the primary and secondary factors and change trends through statistical theory analysis, and (3) obtaining optimal levels by comprehensively considering multiple test results.

In this paper, nine RC beam-column exterior joints were subjected to cyclic loading based on a three-factor and three-level orthogonal experimental design. The failure modes, hysteresis curves, skeleton curves, ductility, and cumulative energy dissipation were investigated to evaluate the seismic performance of the joints. Additionally, variance analysis and range analysis were conducted on the test results to determine the primary and secondary factors influencing the seismic performance, thereby identifying the optimal levels of these factors. This study identifies combinations that fully utilize materials in beam-column exterior joints, improving the relevance and directionality of material selection in engineering structures.

Experimental overview

Raw materials

In this paper, concrete was made using P.O42.5 ordinary Portland cement, river sand with a fineness modulus of 2.58, continuously graded gravel ranging from 10 mm to 20 mm, ordinary Grade Ⅰ coal fly ash, grade S95 mineral powder, standard polycarboxylate water reducing admixture, and tap water. The mix proportions of concrete with different strengths are listed in Table 1.

Table 1.

The mix Proportion of concrete With Different Strength.

Type	Cement (kg)	River sand (kg)	Crushed stone (kg)	Tap water (kg)	Coal fly ash (kg)	Mineral powder (kg)	$\bar{f}$ _c (MPa)
C50	371	646	1101	178	49.5	74.2	53.06
C60	411	602	1070	182	58.7	117	61.47
C70	390	629	1071	150	90.0	120	72.37

Specimen design

According to the orthogonal experimental design with three factors and three levels, the orthogonal experimental table L₉(3³) was constructed, as illustrated in Table 2. Nine reinforced concrete beam-column exterior joints were tested under cyclic loading based on the orthogonal experimental table L₉(3³). The three variable factors in the experimental design are concrete strength grades, anchorage styles, and longitudinal reinforcement ratio, denoted as A, B, and C respectively. Each factor has three levels of variation. The concrete strength grades include C50, C60, and C70, represented by A₁, A₂, and A₃ respectively. Anchorage styles of reinforcements in the joint core consist of standard 90-degree hooks, headed anchorage, and two-sided welding, denoted as B₁, B₂, and B₃ respectively. The schematic diagram of the three anchorage styles is depicted in Figure 1. The longitudinal reinforcement ratios are 1.63%, 2.08%, and 2.58%, denoted as C₁, C₂, and C₃ respectively. The selection of concrete strength (e.g., C50, C60, and C70) as the research variable is based on the application range of reinforced concrete edge joints in practical engineering and the growing trend of using high-strength concrete in seismic design. In addition, these strength grades are commonly referenced in building engineering code (JGJ/T101-2015, 2015). The three anchorage methods—90-degree hooks, headed anchorage, and two-sided welding—represent three typical anchorage practices in current engineering, ranging from conventional to innovative technologies (Cosgun et al., 2020; Lee and Yu, 2009). This selection allows for a comprehensive comparison of the effects of different anchorage methods on joint seismic performance. Furthermore, the longitudinal reinforcement ratios (e.g., 1.63%, 2.08%, and 2.58%) are designed according to the reinforcement requirements of conventional seismic design, which can effectively encompass commonly used reinforcement ranges in joint design (JGJ/T101-2015, 2015; Jiang et al., 2023). This design can evaluate the influence of the change of reinforcement ratio on the seismic performance. Detailed parameters of all joints are presented in Table 3.

Table 2.

The orthogonal table With Three Factors and Three Levels.

Level	Factors
Level	A	B	C (%)
1	C50	90-Degree hooks	1.63
2	C60	headed anchorage	2.08
3	C70	Two-sided welding	2.58

Table 3.

The detailed Parameters of all Joints.

Specimen	A	B	C
Specimen	A	B	Beam	Column	Reinforcement ratio (%)
SA₁B₁C₁	C50	90-Degree hooks	2C16	4C18	1.63
SA₁B₂C₂	C50	Headed anchorage	2C18	4C20	2.08
SA₁B₃C₃	C50	Two-sided welding	2C20	4C22	2.58
SA₂B₁C₂	C60	90-Degree hooks	2C18	4C20	2.08
SA₂B₂C₃	C60	Headed anchorage	2C20	4C22	2.58
SA₂B₃C₁	C60	Two-sided welding	2C16	4C18	1.63
SA₃B₁C₃	C70	90-Degree hooks	2C20	4C22	2.58
SA₃B₂C₁	C70	Headed anchorage	2C16	4C18	1.63
SA₃B₃C₂	C70	Two-sided welding	2C18	4C20	2.08

Beams have a cross-section of 150 mm × 200 mm and a length of 1250 mm. The longitudinal reinforcements in the beam consist of HRB400 E reinforcements with diameters of 16 mm, 18 mm, and 20 mm. Columns have a cross-section of 200 mm × 200 mm and a length of 1600 mm. The longitudinal reinforcements in the column consist of HRB400 E reinforcements with diameters of 18 mm, 20 mm, and 22 mm. The transverse reinforcements in the beam and column are all composed of HPB300 reinforcements with a diameter of 8 mm. The geometric dimensions and reinforcement design are depicted in Figure 2.

The manufacturing process of the joint specimens is illustrated in Figure 3. Nine concrete cube specimens with a side length of 150 mm were simultaneously cast during the casting process of the joint specimens. These concrete cube specimens were cured under the identical conditions as the joint specimens for conducting 28-day compressive strength tests. The design and implementation of the compressive strength tests comply with the relevant regulations of the Chinese standard (GB/T 50081-2019, 2019). Additionally, monotonic tensile tests, complying with the Chinese standard (GB/T 228.1-2021, 2021), were conducted on the HRB400 E and HPB300 steel bars to determine their mechanical properties.

Loading pattern and loading setup

To explore the influencing factors on the seismic performance of beam-column exterior joints, the cyclic loading was conducted on the specimens. Figure 4 illustrates the cyclic loading protocol employed in the experiment. The cyclic loading protocol, utilizing displacement control loading, was developed in accordance with the Chinese standard (JGJ/T101-2015, 2015). The loading process is detailed as follows: (1) Before cracking occurs on the beam surface (i.e., the first stage), a displacement increment of 1 mm per step is applied, with one loading cycle per step, (2) After the beam cracks (i.e., the second stage), a displacement increment of 2 mm per step is applied, with one loading cycle per step, (3) After the yielding of longitudinal reinforcement in the beam (i.e., the third stage), a displacement increment of 10 mm per step is applied, with three loading cycles per step, and (4) When the specimen reaches its peak load (i.e., the fourth stage), a displacement increment of 5 mm per step is applied, with three loading cycles per step. The test stops loading until the bearing capacity decreases to 85% of the peak load. Figure 5 shows the test setup. As depicted in Figure 5(a), hinge supports are employed at both ends of the column. A vertical load was applied to the column by the actuator to achieve the target axial compression ratio of 0.4. Additionally, cyclic load was applied to the beam end using an actuator with a load capacity of 500 kN. The load and displacement of the beam end are collected by the force and displacement transducers inside the actuator.

This paper adopts a displacement control loading protocol. By implementing a phased displacement control approach, the beam-column joint is gradually subjected to different stress states throughout the process. This protocol also captures the influence of displacement loads at various stages on the failure modes. Specifically, after the beam reinforcement yields, the displacement increment is increased from 10 mm to 20 mm to drive the joint into the plastic development stage, which better simulates the potential inelastic response process under actual seismic conditions. Moreover, the phased adjustment of displacement increments allows for accurately capturing the cumulative energy dissipation of the beam-column joint at different deformation stages. Compared to a fixed displacement increment loading protocol, this protocol allows for more flexible simulation of the cumulative energy dissipation of the joints during actual earthquakes by adjusting the displacement increment amplitude. Common loading protocols in seismic engineering research include quasi-static cyclic loading and dynamic loading. Although the cyclic loading protocol adopted in this paper differs from the dynamic characteristics of actual seismic actions, it effectively captures the impact of cumulative displacements at various stages on the cumulative energy dissipation and failure modes of the joint.

Experimental results and analysis

Specimen failure modes

Figure 6 shows the failure modes of all beam-column exterior joints. It can be seen from Figure 6 that the final damage degree of each exterior joint is different. For specimen SA₁B₁C₁, when the displacement load reached ±10 mm, two intersecting diagonal cracks appeared in the core area of the joint, which gradually extended without the formation of new cracks. This was primarily due to the effective inhibition of crack propagation by the 90-degree hooks. Compared with other specimens with high reinforcement ratio, the specimen exhibited better ductility performance. For specimen SA₁B₂C₂, when the displacement load reached ±12 mm, two short diagonal cracks appeared in the core area of the joint, followed by the formation of relatively few new cracks. This indicates that the end anchorage type provided certain crack inhibition capabilities during the crack formation stage. However, under a moderate reinforcement ratio (i.e., 2.08%), the crack development and compressive performance of the concrete in the joint core area were inferior to those of specimen SA₁B₁C₁, ultimately resulting in slightly longer crack lengths than the latter. For specimen SA₁B₃C₃, when the displacement load exceeded ±15 mm, diagonal cracks in the joint core area rapidly extended along the diagonal, accompanied by the emergence of more fine cracks around them and significant concrete spalling. This indicates that specimens with reinforcement ratio of 2.58% exhibit higher bearing capacity but poorer ductility. For specimen SA₂B₁C₂, two intersecting diagonal cracks mainly appeared in the joint core, with fewer cracks and relatively minor concrete spalling. The combination of a moderate reinforcement ratio with a 90-degree hooks led to a more concentrated crack distribution, effectively improving the local crack resistance. In contrast, for specimen SA₂B₂C₃, with reinforcement ratio of 2.58% and headed anchorage, diagonal cracks in the joint core extended more rapidly, with a greater number of cracks and severe concrete spalling near the core area. Compared with the specimen SA₁B₃C₃, the anchoring effect of headed anchorage was slightly inferior, especially under high reinforcement ratio conditions, resulting in more extensive crack formation. For specimen SA₂B₃C₁, two short cracks appeared on the surface of the joint core, with minimal concrete spalling. This indicates that two-sided welding exhibited a more pronounced crack control effect under low reinforcement ratios. Compared to specimen SA₁B₁C₁ with 90-degree hooks, the crack width was slightly larger, but the concrete compressive performance improved significantly. For specimen SA₃B₁C₃, When the displacement load exceeded ±30 mm, severe spalling occurred in the concrete of joint core, and the cracks rapidly expanded, demonstrating poor crack control capability. Specimens SA₃B₂C₁ and SA₃B₃C₂ exhibited better crack control performance at the end of the loading, with the crack width remaining unchanged. This indicates that under high-strength concrete conditions, the combination of a moderate reinforcement ratio of 2.08% and a low reinforcement ratio of 1.63% effectively optimized joint performance.

Hysteretic performance

The hysteresis curves for each specimen are depicted in Figure 7. In the initial loading stage, the hysteresis curves of all specimens exhibited linear characteristics, indicating that the loading stiffness and unloading stiffness were essentially consistent at this stage. Compared to specimen SA₂B₃C₁ with low reinforcement ratio, SA₁B₃C₃ with high reinforcement ratio exhibited greater stiffness, highlighting that the reinforcement ratio is one of the key factors influencing the initial stiffness of the joint. Additionally, specimens with higher concrete strength (e.g., specimen SA₃B₂C₁) exhibited significantly higher stiffness compared to the C50 group, indicating that increased concrete strength substantially enhances joint stiffness. As cracks emerged and developed, the slope of the hysteresis curves for all specimens gradually decreased, demonstrating noticeable stiffness degradation. The influence of different anchorage methods on stiffness degradation was particularly significant. Compared to specimen SA₃B₁C₃, specimen SA₂B₃C₁ with two-sided welding exhibited a slower reduction in the slope of hysteresis curves. This could be attributed to the stronger anchorage force provided by two-sided welding, which effectively restricted reinforcement slippage and delayed crack propagation. In the nonlinear stage, specimen SA₂B₃C₁ with low reinforcement ratio exhibited smaller hysteresis loop, indicating limited cumulative energy dissipation, whereas specimen SA₃B₁C₃ showed larger loop areas, reflecting stronger cumulative energy dissipation. Moreover, Specimens with two-sided welding (e.g., specimen SA₃B₃C₂) displayed fuller hysteresis loops and significantly better cumulative energy dissipation compared to specimens with 90-degree hooks (e.g., specimen SA₃B₁C₃). After yielding, the peak loads during the second and third cycles under the same displacement load were significantly lower than those during the first cycle, indicating strength degradation in the joint. This degradation exhibited different trends among specimens with varying concrete strengths. Specimens with high-strength concrete (e.g., SA₃B₂C₁) showed a slower rate of strength degradation, while low-strength concrete specimens (e.g., SA₁B₂C₂) experienced more pronounced degradation. This suggests that increasing concrete strength plays a positive role in mitigating strength degradation of joints.

Skeleton curves

The skeleton curve, which is the envelope line of the peak points for each hysteresis loop in the load-displacement curves, intuitively shows the deformation characteristics of the specimen at different stages. Figure 8 presents the skeleton curves of all specimens. The cracking displacement Δ_cr, the yield displacement Δ_y, the peak displacement Δ_m, and the ultimate displacement Δ_u are summarized in Table 4. The factors affecting seismic performance studied in this test are ductility coefficient, cumulative energy dissipation and ultimate bearing capacity. μ represents the ductility coefficient, which is the ratio of the ultimate displacement Δ_u to the yield displacement Δ_y. The ductility coefficient μ is usually utilized to measure the ductility of specimen (i.e. deformation capacity). The ductility coefficient of specimen SA₂B₃C₁ is 6.97, showing high ductility. This suggests that the specimen could sustain significant deformation after yielding, demonstrating good seismic performance. In contrast, the ductility coefficient of specimen SA₁B₃C₃ is 3.42, reflecting lower ductility, which indicates relatively weaker deformation capacity and inferior seismic performance. E represents the cumulative energy dissipation, which is the total area of all hysteresis loops and serve as a crucial indicator of cumulative energy dissipation. Specimen SA₃B₃C₂ achieved a cumulative energy dissipation of 2478.78 kN·mm, demonstrating a strong cumulative energy dissipation closely associated with its high-strength concrete and two-sided welding. This strong cumulative energy dissipation can help the specimen effectively mitigate seismic loads, enhancing its seismic performance. In contrast, the cumulative energy dissipation of specimen SA₁B₁C₁ is only 776.65 kN·mm, indicating weaker cumulative energy dissipation, which could result in greater damage during an earthquake. This is primarily attributed to its relatively lower concrete strength and smaller reinforcement ratio. F_m is employed to characterize the ultimate bearing capacity of specimen. The ultimate bearing capacity of specimen SA₃B₁C₃ is 25.88 kN, indicating its ability to withstand a higher load. This is attributed to its higher concrete strength and a higher reinforcement ratio. However, the ultimate bearing capacity of specimen SA₁B₁C₁ is only 16.78 kN, reflecting weaker load-bearing capacity, primarily due to its lower concrete strength (C50) and smaller reinforcement ratio. Therefore, it is necessary to identify the primary and secondary factors affecting seismic performance and determine the best combination of factors to ensure the specimens meet seismic requirements.

Table 4.

The Characteristic Values of specimens.

Specimen	Δ_cr (mm)	Δ_y (mm)	Δ_m (mm)	Δ_u (mm)	μ	E (kN·mm)	F_m (kN)
SA₁B₁C₁	2.02	8.15	20.00	45.87	5.63	776.65	16.78
SA₁B₂C₂	3.00	8.59	33.94	39.00	4.54	856.07	18.24
SA₁B₃C₃	2.99	9.02	17.00	30.87	3.42	644.21	20.88
SA₂B₁C₂	3.01	8.89	30.99	51.65	5.81	1244.61	22.68
SA₂B₂C₃	2.99	9.23	21.01	42.09	4.56	989.11	23.48
SA₂B₃C₁	2.00	8.61	24.88	60.00	6.97	1821.33	17.32
SA₃B₁C₃	3.00	10.57	32.99	46.94	4.44	1095.10	25.88
SA₃B₂C₁	3.00	8.09	25.01	55.13	6.81	1841.84	17.59
SA₃B₃C₂	2.99	8.30	26.90	52.03	6.27	2478.78	22.79

Factors analysis based on orthogonal experimental design

Analysis of variance (ANOVA)

Without considering the interactive effects of various factors, the steps for conducting variance analysis of experimental results based on orthogonal table are as follows: (1) calculating the Sum of Square Total (S_T) of the experimental results, as is shown in equations (1) and (2) calculating the Sum of Square deviations for each factor (S_j) and for error (S_e), as shown in equations (2), and (3) calculating the value of F and applying F-test for analysis. It is worth noting that the Sum of Square deviation for error (S_e) is the difference between S_T and S_j of each factor, which can be expressed as equation (3).

S_{T} = \sum_{i = 1}^{n} {(y_{i} - \bar{y})}^{2} = \sum_{i = 1}^{n} y_{i}^{2} - \frac{1}{n} {(\sum_{i = 1}^{n} y_{i})}^{2}

(1)

Where n represents the total number of tests, y_i represents the result of the i-th test, and

\bar{y}

represents the average value of test results.

S_{j} = \frac{r}{n} \sum_{i = 1}^{r} K_{ij}^{2} - \frac{1}{n} {(\sum_{i = 1}^{n} y_{i})}^{2}

(2)

Where r represents the number of levels for each factor, S_j represents the Sum of Square deviations of the j-th column. When the j-th column is factor A, it is denoted as S_j = S_A.

S_{T} = S_{A} + S_{B} + \cdot \cdot \cdot + S_{e}

(3)

Table 5 presents the results of variance analysis for ductility coefficient, cumulative energy dissipation, and bearing capacity. According to the variance analysis of the ductility coefficient in Table 5, it can be seen that S_A, S_B, and S_C are 1.972, 0.493, and 11.933, respectively. For the variance analysis of the cumulative energy dissipation, the values for S_A, S_B, and S_C are 1.652 × 10⁶, 0.583 × 10⁶, and 0.708 × 10⁶, respectively. Regarding the variance analysis of the bearing capacity, the values for S_A, S_B, and S_C are 19.168, 6.456, and 59.025, respectively. Through the F-test method, the significance of influence of various factors on the seismic performance indexes can be analyzed. The larger the value of F, the more significant the influence of the factor on seismic performance. Figure 9 shows the results of the F-test method for seismic performance indexes. Results indicate that the primary and secondary order of factors affecting ductility coefficient is longitudinal reinforcement ratio > concrete strength > anchorage style. The primary and secondary order of factors affecting cumulative energy dissipation is concrete strength > longitudinal reinforcement ratio > anchorage style. The primary and secondary order of factors affecting bearing capacity is longitudinal reinforcement ratio > concrete strength > anchorage style. Therefore, it is considered that the influence of longitudinal reinforcement ratio on ductility coefficient and bearing capacity is more significant than that of concrete strength and anchorage style. However, for the cumulative energy dissipation, the influence of concrete strength is more significant than that of longitudinal reinforcement ratio and anchorage style.

Table 5.

The table of variance Analysis.

Factors Parameters	μ			E			F _m
Factors Parameters	A	B	C	A	B	C	A	B	C
K _1j	14.08	15.81	19.90	2.277 × 10³	3.116 × 10³	4.440 × 10³	55.90	65.34	51.69
K _2j	15.81	14.94	16.06	4.055 × 10³	3.687 × 10³	4.579 × 10³	63.48	59.31	63.71
K _3j	17.52	16.66	11.45	5.416 × 10³	4.944 × 10³	2.728 × 10³	66.26	60.99	70.24
S _T	14.451			2.997 × 10⁶			85.348
S _j	1.972	0.493	11.933	1.652 × 10⁶	0.583 × 10⁶	0.708 × 10⁶	19.168	6.456	59.025
S _e	0.053			0.054 × 10⁶			0.699
F	37.208	9.302	225.151	30.593	10.796	13.111	27.422	9.236	84.442
Significance	C>A>B			A>C>B			C>A>B

Range analysis

In the process of calculating the range, the total sum of the indicator values K_ij for each factor at the same level is calculated first. Then the average test result $\bar{K}$ _ij of each factor at each level is calculated, which is calculated by 1/SK_ij, where S represents the number of occurrences of level i in column j. In this paper, S is 3. Finally, the range R_j is determined using the equation (4).

R_{j} = \max {K_{ij}} - \min {K_{ij}}

(4)

The results of range analysis are summarized in Table 6. The steps for obtaining the optimal combination of factors based on range analysis are as follows: (1) analyze the trends in seismic performance indicators as factor levels vary, and (2) identify the factor levels most conducive to improving the seismic performance of the joint according to the range of factor levels in this paper. The relationship diagram is plotted with factor levels as the horizontal axis and K_ij as the vertical axis, as illustrated in Figure 10. As can be seen from Figure 10(a), the higher concrete strength, the greater ductility coefficient. Compared with the concrete strength of C50, the ductility coefficient increases by 24.52% when the concrete strength is C70. By comparing the influence of three anchorage styles on ductility, it is found that the beam-column exterior joint with Two-sided welding exhibits better ductility. Additionally, the ductility coefficient decreases with the increase of the longitudinal reinforcement ratio. Compared with the longitudinal reinforcement ratio of 1.63%, the ductility coefficient decreases by 73.56% when the longitudinal reinforcement ratio is 2.58%. This indicates that the increase of the longitudinal reinforcement ratio has an adverse effect on the ductility of the beam-column exterior joint. In summary, for the ductility coefficient, the optimal level is C70 + Two-sided welding +1.63%. For the cumulative energy dissipation, the cumulative energy dissipation increases with the increase of the concrete strength. Compared with the concrete strength of C50, the cumulative energy dissipation increases by 137.15% when the concrete strength is C70. Meanwhile, it can be found from Figure 10(b) that the cumulative energy dissipation of beam-column exterior joint with welded anchorage is stronger compared to joints with 90-degree hooks and headed anchorage. As the longitudinal reinforcement ratio increases, the cumulative energy dissipation of the joint first rises and then declines. The optimal cumulative energy dissipation is achieved when the longitudinal reinforcement ratio is 2.08%. Thus, for the cumulative energy dissipation, the optimal level is C70 + Two-sided welding +2.08%. For ultimate bearing capacity of beam-column exterior joints, it can be seen from Figure 10(c) that the higher concrete strength, the higher ultimate bearing capacity. Compared with the concrete strength of C50, the ultimate bearing capacity increases by 18.82% when the concrete strength is C70. It is found that the beam-column exterior joint with 90-degree hook exhibits higher ultimate bearing capacity compared with the beam-column exterior joint with headed anchorage and welded anchorage. Additionally, the greater longitudinal reinforcement ratio, the higher ultimate bearing capacity. Thus, for the ultimate bearing capacity, the optimal level is C70 + 90-degree hooks +2.58%.

Table 6.

The table of Range Analysis.

Factors Parameters	μ			E			F _m
Factors Parameters	A	B	C	A	B	C	A	B	C
K _1j	14.08	15.81	19.90	2.277 × 10³	3.116 × 10³	4.440 × 10³	55.90	65.34	51.69
K _2j	15.81	14.94	16.06	4.055 × 10³	3.687 × 10³	4.579 × 10³	63.48	59.31	63.71
K _3j	17.52	16.66	11.45	5.416 × 10³	4.944 × 10³	2.728 × 10³	66.26	60.99	70.24
$\bar{K}$ _1j	4.69	5.27	6.63	0.759 × 10³	1.039 × 10³	1.480 × 10³	18.63	21.78	17.23
$\bar{K}$ _2j	5.27	4.98	5.35	1.352 × 10³	1.229 × 10³	1.526 × 10³	21.16	19.77	21.24
$\bar{K}$ _3j	5.84	5.55	3.82	1.805 × 10³	1.648 × 10³	0.909 × 10³	22.09	20.33	23.41
R _j	3.44	1.72	8.45	3.139 × 10³	1.828 × 10³	1.851 × 10³	10.36	6.03	18.55
Significance		C>A>B			A>C>B			C>A>B
Optimal level		A ₃ B ₃ C ₁			A ₃ B ₃ C ₂			A ₃ B ₁ C ₃

As can be seen from the above discussion, with increase of the concrete strength, the ductility, cumulative energy dissipation, and ultimate bearing capacity of beam-column exterior joints improve accordingly. This is mainly due to the following reasons: (1) Shear-compression ratio of the joints decreases with increase of the concrete strength, and the ductility of the joints can be improved by reducing the shear-compression ratio. Deng et al. (2019) also drew the similar conclusion. (2) A higher concrete strength can more effectively mitigate the decrease in compressive strength and stiffness during the process of cyclic loading, thereby enhancing the bond performance between steel and concrete (Paulay et al., 1978).

For anchorage styles, the ductility and cumulative energy dissipation of beam-column exterior joints with Two-sided welding are better. Figure 11(a) shows the force mechanism of two-sided welding. As shown in the Figure 11(a), two-sided welding increases the contact area between the reinforcement and the concrete, effectively enhancing their synergistic interaction and delaying the degradation of joint performance. Additionally, the anchoring effect of two-sided welding primarily includes bond strength and end-bearing pressure, which together generate a strong anchorage force that, to some extent, suppresses the slippage of longitudinal reinforcement. Compared to other anchorage methods, two-sided welding provides uniform anchorage on both sides of the reinforcement, effectively avoiding stress concentration and ensuring more uniform force distribution within the joint. However, as shown in Figure 11(b), the effectiveness of headed anchorage mainly relies on the bearing effect at the head, which results in a limited anchorage stress range. Additionally, the smaller contact area between the reinforcement and the concrete reduces its ability to restrain longitudinal reinforcement slippage. Besides, it can be found from Figure 11(c) that the bearing capacity of beam-column exterior joints with 90-degree hooks is better, which is primarily because this anchorage method provides additional mechanical interlocking, creating better confinement with the concrete in the core region, which prevents reinforcement slippage and enhances the overall load-bearing capacity of the joint. Additionally, the hook ensures a more uniform pressure distribution in the concrete, reducing the risk of brittle failure in the core region and helping the joint maintain a high load-bearing capacity. Furthermore, the localized pressure at the bend increases the confinement effect on the concrete, suppressing crack propagation and contributing to the integrity of the core area. For longitudinal reinforcement ratio, the ductility and cumulative energy dissipation of beam-column exterior joints decrease with the increase of longitudinal reinforcement ratio. This is mainly because in this paper, the longitudinal reinforcement ratio is increased by increasing the diameter of the longitudinal reinforcement. However, the larger the diameter of the longitudinal reinforcement is, the more likely it is to slip.

From Figure 12(a) and (b), it can be observed that the ductility coefficient generally decreases with an increase in longitudinal reinforcement ratio. In Figure 12(a), the impact of reinforcement ratio variation on the ductility coefficient is relatively minor under the 90-degree hooks, indicating that this anchorage method provides some degree of adjustment for rebar yielding and joint deformation. However, under the two-sided welding, the ductility coefficient shows the most significant decrease, particularly as the reinforcement ratio increases from 2.08% to 2.58%, exhibiting a sharp downward trend. This suggests that the welding connection characteristics of two-sided welding may limit rebar slippage and the plastic deformation capacity of the joint. Compared to 90-degree hooks and headed anchorage, the two-sided welding is more sensitive to changes in reinforcement ratio, resulting in a notable decline in ductility performance. Figure 12(b) illustrates the trend of the ductility coefficient with varying reinforcement ratios under different concrete strengths. It can be observed that the ductility coefficient decreases significantly as the reinforcement ratio increases, regardless of the concrete strength. Compare with the concrete strength of C50, the concrete strength of C60 and C70 significantly enhance the overall level of the ductility coefficient. However, the increase in reinforcement ratio still has a detrimental effect on the ductility coefficient across all concrete strength levels. This phenomenon suggests that the interaction effect between reinforcement ratio and concrete strength is relatively minor. Figure 12(c) shows the variation in the ductility coefficient under the combined influence of different anchorage methods and concrete strengths. For the 90-degree hooks, a significant decrease in the ductility coefficient is observed as the concrete strength increases from C60 to C70, suggesting that high-strength concrete in this anchorage method may restrict the plastic deformation capacity of the joint. In the case of headed anchorage, the ductility coefficient remains relatively stable as the concrete strength increases from C50 to C60 but shows a notable increase when the concrete strength reaches C70. This phenomenon might be attributed to the limited contribution of concrete properties to the ductility coefficient in the lower strength range (C50 to C60), where ductility performance is primarily governed by the anchorage method itself. However, as the concrete strength improves to C70, the enhanced material properties of the concrete may compensate for the constraints imposed by the anchorage, thereby improving the ductility performance. From Figure 12(d), it can be observed that when the reinforcement ratio increases to 2.08%, the cumulative energy dissipation of the two-sided welded rises sharply, reaching its peak, which is significantly higher than that of the 90-degree hooks and headed anchorage. However, as the reinforcement ratio further increases to 2.58%, the cumulative energy dissipation of the two-sided welded drops drastically to its lowest value, whereas the cumulative energy dissipation of the headed anchorage shows a slight recovery, and the cumulative energy dissipation of the 90-degree hooks remains relatively stable. Figure 12(e) illustrates the trend of cumulative energy dissipation with varying reinforcement ratios under different concrete strengths. It can be observed that the cumulative energy dissipation decreases significantly as the reinforcement ratio increases. This also indicates that as the concrete strength increases, its pronounced brittle characteristics adversely affect the cumulative energy dissipation of the joint. In Figure 12(f), for concrete strength of C50, the cumulative energy dissipation of the three anchorage methods is relatively similar, with the cumulative energy dissipation of the two-sided welding being slightly lower than the other two anchorage methods. As the concrete strength increases to C60, the cumulative energy dissipation of the two-sided welding increases significantly, surpassing that of the headed anchorage and 90-degree hooks by a wide margin. When the concrete strength is further enhanced to C70, the cumulative energy dissipation of the two-sided welding continues to rise, reaching its highest value. Meanwhile, the cumulative energy dissipation of the headed anchorage also shows a slight upward trend, though the increase is less pronounced. This indicates that the two-sided welding demonstrates stronger adaptability to improvements in concrete strength, especially when combined with high-strength concrete, effectively maximizing cumulative energy dissipation of joint. As observed in Figure 12(g), the bearing capacity of the 90-degree hooks increases significantly and steadily with the reinforcement ratio. This is attributed to the effective mechanical interlock provided by the hook, which enhances the bond performance at the reinforcement-concrete interface, especially under higher reinforcement ratios. For headed anchorage, the bearing capacity shows little variation at low reinforcement ratios, likely because the anchorage head cannot effectively distribute the load when fewer reinforcing bars are present. However, as the reinforcement ratio increases, the effective support area at the anchorage end expands considerably, resulting in a significant growth in bearing capacity at higher reinforcement ratios. As shown in Figure 12(h), when the concrete strength increases from C50 to C70, the ultimate bearing capacity significantly improves with the increase in reinforcement ratio. This indicates that high-strength concrete possesses greater compressive strength and confinement capability, which can better restrict the deformation of reinforcements and, to some extent, delay the yielding of reinforcements. As shown in Figure 12(i), the bearing capacity of 90-degree hooks consistently increases with the rise in concrete strength. Headed anchorage reaches its peak bearing capacity at a concrete strength of C60 but shows a decline at C70, likely due to the brittleness of high-strength concrete reducing the efficiency of the anchorage head. The bearing capacity of two-sided welding is the lowest at C60 but significantly improves at C70, surpassing the other two anchorage methods. This trend suggests that the performance of two-sided welding is highly influenced by concrete strength, making it potentially more suitable as an anchorage method under high-strength concrete conditions.

Comparison and suggestions

Previous study (Qiao et al., 2024) have shown that increasing the concrete strength generally leads to a reduction in the ductility of beam-column joints. However, in this paper, by increasing the concrete strength (from C50 to C70) and adopting two-sided welding, the ductility coefficient showed an increase of 24.52%. This improvement can be attributed to the two-sided welding, which provides better stress distribution and crack control within the joint core. Unlike single-sided welding, the two-sided welding used in this paper effectively suppresses longitudinal bar slippage in the core region, thereby achieving superior ductility. This significant difference indicates that the combination of two-sided welding and high-strength concrete holds potential for engineering applications. Wang et al. (2013) and Lee et al. (2009) observed that under the same stirrup ratio in joints, the seismic performance of 90-degree hooks and headed anchorage was roughly equivalent, with similar cumulative energy dissipation. The results of this paper demonstrate that the combination of high-strength concrete and two-sided welding can significantly enhance the cumulative energy dissipation of joints. This is primarily because two-sided welding creates a stronger anchorage force within the joint, effectively limiting rebar slippage under cyclic loading and controlling crack propagation, thereby improving cumulative energy dissipation. Furthermore, when the concrete strength reaches C70, the improvement in cumulative energy dissipation for 90-degree hooks is relatively limited. This is likely due to the higher brittleness of high-strength concrete, which reduces the ability of the 90-degree hooks to restrain cracks under loading, thereby impacting energy dissipation performance. In terms of ultimate bearing capacity, the 90-degree hooks outperform other anchorage methods, particularly when the concrete strength is C70, where the ultimate bearing capacity improves by 18.82%. Compared to the findings of Cosgun et al. (2020), this paper reveals that a higher longitudinal reinforcement ratio (2.58%) can further enhance the ultimate bearing capacity of the joint. In addition, this result complements the shortcomings of the existing literature on the ultimate bearing capacity of joints under different anchoring methods.

Concrete strength of C70 exhibits the best performance in terms of ductility, cumulative energy dissipation, and ultimate bearing capacity. It is recommended for use in structural designs with high seismic requirements. If budget or material supply is limited, C60 also provides good seismic performance. The two-sided welding enhances ductility and cumulative energy dissipation, making it particularly suitable for earthquake-prone regions, while the 90-degree hooks is advantageous for improving the ultimate bearing capacity of joints, suitable for structures subjected to heavy loads. A reinforcement ratio of 2.08% achieves a balance between ductility and cumulative energy dissipation, making it ideal for regular seismic designs that require both deformation capacity and cumulative energy dissipation. A reinforcement ratio of 2.58% is better suited for increasing the ultimate bearing capacity, making it ideal for structures with high load demands.

Conclusion

In this paper, quasi-static loading tests were carried out on the nine RC beam-column exterior joints using an orthogonal experimental design of three factors and three levels. The variance analysis and range analysis were performed on test results. The main conclusions are as follows:

(1) Concrete strength, anchorage style, and longitudinal reinforcement ratio have a significant impact on seismic performance of beam-column exterior joints. Through the variance analysis on test results, the primary and secondary order of factors effecting on ductility of joints could be: reinforcement ratio > concrete strength > anchorage style. The primary and secondary order of factors effecting on cumulative energy dissipation of joints could be: Concrete strength > Longitudinal reinforcement ratio > Anchorage style. The primary and secondary order of factors effecting on ultimate bearing capacity of joints could be: Longitudinal reinforcement ratio > Concrete strength > Anchorage style.

(2) When the concrete strength is between C50 and C70, the ductility, cumulative energy dissipation and ultimate bearing capacity all increase as the concrete strength increase. Two-sided welding is most effective in enhancing the ductility and cumulative energy dissipation of joints. In contrast, 90-degree hooks are the most beneficial for improving the ultimate bearing capacity of the joints. While a higher longitudinal reinforcement ratio can increase the ultimate bearing capacity of the joint, it tends to reduce both ductility and cumulative energy dissipation.

(3) Based on the range analysis of the test analysis, the optimal factor levels for maximizing the ductility of the joints are: C70 concrete strength, two-sided welding, and a 1.63% longitudinal reinforcement ratio. For maximizing cumulative energy dissipation, the optimal levels are: C70 concrete strength, two-sided welding anchorage, and a 2.08% longitudinal reinforcement ratio. To achieve the highest ultimate bearing capacity, the optimal levels are: C70 concrete strength, 90-degree hooks, and a 2.58% longitudinal reinforcement ratio. This finding provides valuable theoretical references for engineering design.

Footnotes

Acknowledgments

The authors gratefully acknowledge the financial support from the Key Project of Joint Fund of National Natural Science Foundation of China [Grant number U22A20244] and the National Natural Science Foundation of China [Grant number 52278467].

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by the Key Project of Joint Funds of the National Natural Science Foundation of China [Grant number U22A20244] and the National Natural Science Foundation of China [Grant number 52278467].

ORCID iDs

Rui Hu

Jia-Qi Yang

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