Mechanical Performance of Tube-Gusset X-Joints Enhanced by Ring Plates

Li, Xiaolu; Yang, Zhe; Zhao, Yan; Wang, Xinwu; Xue, Xiaomin; Wang, Xueming

doi:https://doi.org/10.1155/2024/6929522

Advances in Civil Engineering

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Abstract Introduction Discussion Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2024 | Article ID 6929522 | https://doi.org/10.1155/2024/6929522

Mechanical Performance of Tube-Gusset X-Joints Enhanced by Ring Plates

Xiaolu Li,¹Zhe Yang,¹Yan Zhao,¹Xinwu Wang,¹Xiaomin Xue,²and Xueming Wang³

Academic Editor: Tafsir Tafsirojjaman

Received06 Dec 2023

Revised24 Feb 2024

Accepted20 Mar 2024

Published04 Apr 2024

Abstract

This study aims to investigate the effect of the ring plate on the mechanical performance of X-type tube-gusset joints. The failure modes, ultimate strengths, and failure mechanisms of X-joints with ring plates were investigated through experiments and finite element analyses. The results indicated that the ring plate and the chord within the effective range of the ring plate constituted the primary bearing structure of the X-joint. Increases in the ring plate thickness and width increased the ultimate strength of the X-joint. By considering the forces of the braces as a superposition of the bending moment and the force acting on the gusset of the X-joint, a simplified calculation method for the ultimate strength of X-joints was established. The derivation process was validated and refined through experiments and finite element analyses. Finally, a safe and reliable formula was derived for evaluating the ultimate strength of X-joints.

1. Introduction

Tubular steel towers have become increasingly prevalent in ultra-high voltage transmission lines owing to their exceptional mechanical properties and architectural appeal. The joints in a tubular steel tower are created by the convergence of members within the tower, making the study of the mechanical properties and failure modes of these joints crucial for the design of these towers [1]. Two types of joints are commonly used in tubular towers: tubular and tube-gusset [2]. In the tubular joint, each diagonal member is directly welded to a chord; this underlines the precise processing and high-quality welding. Therefore, the application of tubular joints is limited because tubular steel towers are primarily deployed in harsh and remote environments. Accordingly, this has led to the development of tube-gusset joints that are argued to be more suitable for constructing transmission towers. The tube-gusset joint comprises gussets, bolts, chords, and brace members. The gusset is welded to the chord wall, and bolts connect the brace members to the gusset. In addition, ring plates are commonly used in tube-gusset joints to enhance their mechanical properties [3, 4]. However, no prominent design guide is available for the ring plate; thus, the dimensions of the annular plate are primarily determined based on experience [5]. Therefore, this study evaluated the ultimate strength of tube-gusset joints with ring plates.

The exploration of tube-gusset joints was initiated by Japanese scholars in 1974 [6], and various standards have since been established for designing tube-gusset joints, including those proposed by IIW [7], CIDECT [8], KBC [9], and AISC [10]. To date, several techniques have been used to strengthen the chord wall [11, 12]. Nassiraei [13, 14] discussed the effect of collar plates on the static capacity and local joint flexibility of circular hollow section X-joints through experimental and numerical investigations. They noted that the collar plates made the deformation of the reinforced joints in the near joint intersection more uniform than that of the unreinforced joints. Therefore, the collar plate could significantly increase the static strength of the joints. In addition, the collar plate size could affect the ultimate strength of joints [15]. A theoretical formula was also proposed based on the yield body theory. In addition, research has shown that fiber-reinforced polymers can improve the static capacity of tubular X-joints [16]. Similarly, ring plates are effective in reinforcing tube-gusset joints. Furthermore, the introduction of ring plates notably influences the performance of the tube-gusset joints. The Japanese Steel Tubular Association proposed a formula for designing tube-gusset joints stiffened by annular plates [17]; however, these formulae are deemed overly complex for practical engineering applications. Moreover, the empirical evidence suggests that the results obtained from these formulae tend to be overly conservative [17, 18].

Recently, the application of ring plates in joint designs has attracted increasing attention. Li and Deng [19, 20] delved into the ultimate bearing capacities of planar K- and multiplanar DK-joints through experimental and numerical investigations, revealing a “push–pull” deformation mechanism in both the K and DK joints. Li et al. [21, 22] explored the impact of ring plates on the ultimate strengths of KT- and X-joints. Qu and Sun [23–28] conducted a comprehensive examination of the mechanical performance of KT joints and highlighted the inapplicability of the formulae designed for low-strength steel in the context of high-strength steel joints. Comparisons between the mechanical properties of the KK-type and K-type joints were also presented [29]. Sitong et al. [30] investigated an analytical model for the load distribution in multiple-ring-stiffened tube-gusset joints, whereas Chen et al. [31] studied the application of ring plates in tubular joints. In general, 1/4 ring plates are primarily used in K-type or KK-type joints, and full-ring plates are generally used in X-type joints. Gaps still exist in the understanding of the impact of ring plates on the load-bearing performance of tube-gusset joints.

This study focussed on examining the mechanical behavior of X-type tube-gusset joints with ring plates, as shown in Figure 1. By analyzing the forces acting on the X-joints and considering the joint under the action of the braces as a superposition of the bending moment (M) and force (P), the ring plate and the chord within the effective range of the ring plate were regarded as the primary bearing structures of the X-joint. A simplified calculation method for the ultimate strength of an X-joint was proposed. To optimize this method, specimens with a 90° angle between the brace and the chord were selected, corresponding precisely to the condition of the force (P) on both sides of the chord. Concurrently, finite element analysis was performed on the X-joint, and the results were compared with the experimental results. Subsequently, a parameter analysis was performed using the validated finite element model. The failure mode and ultimate strength of the X-joints under force and bending moment were investigated, and the main factors influencing the ultimate strength of the X-joints were discussed. Finally, a suitable formula for the ultimate strength of X-joints was proposed and demonstrated to be safe and reliable. This contribution is invaluable for designing X-joints with ring plates.

2. Force Analysis of the Tube-Gusset Joint

2.1. Calculations for JSSC

Because of the influence of the ring plate, the primary resistance of the joint lies in the ring plate and its accessories. According to Japanese Society of Steel Construction (JSSC) [17], the forces exerted by the braces are converted into a force that acts directly on the ring plate. As shown in Figure 2, the force on the brace (F) is transformed into the bending moment (M) and tensile (or compression) force (P) acting on the root center of the gusset plate.

(a)

(b)

Subsequently, these forces are further converted to the positions of the ring plates as follows:

Table 1 presents the computational formula proposed by JSSC for tube-gusset joints with ring plates.

2.2. Analytical Model

As indicated in Table 1, the calculation process is complex for designers, and the formula results exhibit a conservative bias. In this study, we aimed to derive a more straightforward and reliable calculation formula.

According to Equations (1)–(3), the force on the brace (F) is transformed into the bending moment (M), tensile (or compression) force (P), and shear force (Q). The consideration of punching shear is omitted because of the large axial compression ratios of the chords in transmission towers [14]. Consequently, as illustrated in Figure 2(a), the joint under the influence of the braces is viewed as a superposition of the bending moment (M) and force (P).

Next, the resistance mechanism of the X-joint is simplified to a circular ring with a T-shaped cross-section, where Be represents the effective range of the ring plate, as shown in Figure 2(b). The load on the X-joint can be reasonably equated to that on the ring plate adhering to the following equilibrium conditions.where M_p denotes the cross-sectional plastic moment, and r_p denotes the radius of the ring. The failure load of the structure can be determined according to the principles of virtual work as follows:

In accordance with Chinese standard DL/T5085-1990 (1999), the effective range of the ring plate is defined as follows:

Assuming , the value of f is <1 for R within the range 0.25 ≤ R/D ≤ 0.75. Thus, the neutral axis of the cross-section can be expressed as follows:

The radius of the ring, r_p, can be expressed as follows:

The cross-section plastic moment of the ring can be expressed as follows:

Substituting into Equation (10), the failure load of the X-joint can be obtained as follows:

3. Test Program and Finite Element Analysis

3.1. Specimens and Loading

Considering the test conditions, specimens with a 90° angle between the brace and the chord were selected. This configuration corresponds precisely to the force condition (P) on both sides of the chord, as illustrated in Figure 2. Figure 3 shows a schematic of the specimen. Seven specimens were examined; their main geometric dimensions are listed in Table 2. Notably, because of limitations in the sample size, the experiment primarily focused on investigating the effect of the ring plate on the ultimate strength of the joints. Table 2 presents the adoption of three types of steel tubes (Φ194 × 6, Φ273 × 6, and Φ356 × 8) for the chord members. Additionally, to mitigate the end condition effect in the tests [32], the chord length (L) was set to 2,000 mm. To prevent overall buckling, the selected brace members were fashioned from Φ159 × 6 steel tubes with a length of 500 mm. The width (H) and thickness (t_g) of the gusset plate were 300 and 16 mm, respectively.

Furthermore, the ring plates were prepared from Q235 steel, and Q345 steel was used for the remaining parts of the specimens. Tensile tests were conducted to assess the mechanical performances of the steel materials, and the results are listed in Table 3.

The test setup is shown in Figure 4. The specimen was horizontally positioned in the loading frame. Both ends of the chord were welded to the endplate, with bolts securing the chord ends to the loading frame. Hydraulic machines were used to load the brace members with an axial force.

(a)

(b)

To eliminate potential gaps between the specimens and the hydraulic machine, a preloaded force of approximately 1–2 kN was applied to each brace member before the test. During the test, the two brace members were progressively loaded in a 1 : 1 ratio until the joint collapsed.

Four linear variable differential transformers (LVDTs) were used in the tests (Figure 4). LVDT1 and LVDT2 were positioned at the two sides of the chord near the left ring plate, whereas LVDT3 and LVDT4 were situated near the right ring plate. Strain gauges were strategically placed on both the chord and ring plate. Given the symmetrical structure of the X-joint, the strain gauges were arranged on only one side of the joint, as shown in Figure 4(b). Strain gauges on the chord were spaced 30° apart at the section near the ring plate, whereas those on the ring plate were positioned at 0° and ±90°.

3.2. FE Analytical Method

General nonlinear finite element software ANSYS was employed for the numerical analysis of the X-joints. The eight-node shell element (shell281) was used. The specimen material was simulated using an isotropic hardening model based on the Von Mises yield criterion. The stress–strain curves derived from the tensile tests were incorporated into the finite element (FE) models. By employing a time-stepping nonlinear analysis with a large allowance for deformation and a Newton–Raphson method equation solver, the FE models of the X-joints are illustrated in Figure 5(a). As shown in Figure 5(a), no bolt model was established; instead, coupling around the bolt holes was achieved using MPC184. Similarly, each end of the chord and brace members was coupled with MPC184 to facilitate the load application. Compared with fatigue analysis, the influence of welds on the accuracy of static analysis is relatively small [2, 33, 34]. Qu et al. [26] and Sitong et al. [30] used the shell281 element to model the tube-gusset joints in their research but did not establish a weld model. The accuracy of the FE model was evaluated by comparing its results with the test results, including the failure mode, strain–load relationship, and load–displacement curve. The FE model matched well with the experimental results. Sitong et al. [30] proved that the proposed analytical model could accurately predict the distributed load of every ring stiffener at the tube-gusset joint with errors never exceeding 5%. In the present study, the failure mode of the X-joint was caused by chord depression and ring-plate deformation. The strain and deformation results were obtained around the chord surface weld. Therefore, the weld was not modeled in this study.

(a)

(b)

In line with the observations by Vegte and Makino [32], the strength of the joint was assumed to be significantly influenced by the boundary conditions. However, this effect was only notable for brace tension cases with low brace angles [35]. Consequently, this study adopted a fixed boundary condition for the chord. The two ends of the braces were restrained except for the axial displacement. Figure 5(b) shows the equivalent model of the X-joints, where the brace forces were substituted by a force on the gusset plate.

A preliminary finite element analysis was performed to examine the influence of the mesh size on the ultimate strength of the X-joint. As shown in Figure 6, the gained ultimate strength increased, and the computing time decreased when the finite element mesh size increased. The ultimate strength did not significantly differ within a mesh size of <12 mm. However, a further reduction in the mesh size would significantly increase the computing time. Thus, a nominal element size of 12 mm was selected for the FE model to ensure accuracy and efficiency.

4. Discussion

4.1. Verification of the FE Analysis

Given that the gusset plate, braces, and welds remained undamaged throughout the tests, this study did not explore punching shear failure. The numerically determined load-deformation curves, along with the dotted lines representing the tests, are plotted in Figure 7. The predominant failure modes occurred in the chord wall and ring plates, as shown in Figure 8. A significant correlation was observed between the experimental and numerical analysis results for the failure modes. Table 4 outlines the ultimate strength derived from the FE analysis, demonstrating a mean error of 3.8% with a corresponding standard deviation of 0.035. Table 4 lists the calculation results for the three specimens without ring plates. Notably, the setting of the ring plates could significantly improve the ultimate strength of the tube-gusset joint. The strain results at the critical points, as illustrated in Figure 9, confirmed that the FE model accurately reflected the strain state of the X-joints.

(a)

(b)

(c)

(a)

(b)

(a)

(b)

Considering Figures 7–9 and Table 4, in conclusion, the FE model successfully predicted the structural performance and strength of the X-joints. Figure 10 further confirms the matching between the equivalent model and the FE models with braces, validating their use in subsequent studies.

4.2. Failure Mode of X-Joints

As shown in Figure 7, during the initial loading period, the chord deformation increased linearly with load. As the load continued to increase, a turning point appeared in the load–displacement curve. At last, the chord displacement rapidly increased, and eventually, the joint failed. A similar trend was observed in the variation of the strain values at the measurement points. As shown in Figure 9(b), the strain increased linearly when the load was less than 200 kN. As the load continued to increase, the increased rate of strain gradually accelerated. A turning point appeared on the curve. After the load reached 450 kN, the load did not increase significantly; however, the strain rapidly increased. This indicated that the joint had already failed.

Figure 11 illustrates the stress nephograms of Φ273 × 6 − 6 × 72 under forces of 216 and 250 kN. Combining Figure 9(a), the failure process of the X-joints could be analyzed as follows: in the initial loading phase, the strain values at the chord wall were within 0.001. This indicated that the chord wall deformation was in the elastic range. As the load increased, the chord deformation continued to increase. When F = 360 kN, the strain values at positions 0°, 90°, 180°, and −90° on the chord were close to 0.001. When the loading continued, at F = 460 kN, the strain values at these four positions were significantly higher than those at the other positions. This indicated that four plastic hinges appeared at positions 0°, 90°, 180°, and −90° on the chord.

(a)

(b)

Figure 12 illustrates stress nephograms of Φ273 × 6 − 6 × 72 under a bending moment. Deformation of the chord and warping of ring plates were observed. During the elastic stage, the stress on the chord was relatively high only at the position near the ring plate, whereas the stress at other positions was minimal. In the final state, one side of the chord was concave, whereas the other side was elongated, resulting in an elliptical deformation of the ring plates near the chord (Figure 12(b)).

(a)

(b)

The failure mode suggested that the ring plate and the chord within the effective range of the ring plate constituted the main bearing structure of the X-joint, thereby validating the theoretical derivation in Section 2.

4.3. Comparison between Force and Bending Moment on Gusset Plates

Under the bending moment, one side of the chord was concave, whereas the other side was elongated. Considering the absolute value of the chord deformation as the horizontal coordinate would produce the load–deformation curve, as shown in Figure 13. The deformation trends at the two locations were essentially identical. During the initial loading period, the deformation increased linearly with the load, indicating an elastic stage. When the deformation exceeded 2 mm, the chord deformed rapidly until the joint failed. However, the deformation at the chord compression point was slightly greater than that at the tension point. For design safety considerations, the ultimate strength of the joint was determined based on the location with more substantial deformation, that is, the compression point.

Figure 14 shows a comparison between the ultimate strengths of the X-joints under force and bending moment, revealing extremely close values with a mean ratio of 0.9767 and a standard deviation of 0.0365. This confirmed the reasonableness of the calculation method in Equations (1)–(3).

5. Parameter Analysis

In this section, the verified simulation model is used to discuss the mechanical properties of the X-joint under an axial force. To enhance the calculation efficiency, the X-joint model was simplified by eliminating brace member deformations and applying forces directly to the gusset plates.

The results indicated that an increase in the thickness and width of the ring plate improved the ultimate strength of the X-joints. Two dimensionless parameters, namely, the ring plate thickness-to-chord ratio (t_r/T) and the width of the ring plate to the chord diameter ratio (R/D), were considered. Following the Code for Design of Steel–Concrete Composite Structure in China (1999), parametric study parameters were set at 0.25 ≤ R/D ≤ 0.75 and 219 mm ≤ D ≤ 426 mm.

Figures 15 and 16 show the effects of t_r/T and R/D, respectively, on the ultimate strengths of the X-joints under an axial force. As shown in Figure 15, as R/D increased, the ultimate strength of the joint increased in a near-linear manner. Similarly, a near-linear relationship was observed between the ultimate strength of the X-joints and the value of t_r/T, as shown in Figure 16. Therefore, the joint strength was inferred to be increased by the ring plates.

(a)

(b)

(a)

(b)

Figure 17 shows the effect of D/T on the ultimate strength of X-joints with R = 80 mm and t_r = 8 mm. An increase in the value of D/T resulted in a decrease in the ultimate strength of the X-joints. However, the ultimate strength changed only slightly when D/T > 60. Because changes in D/T significantly affected the weight of the X-joints, the impact caused by D/T was not as significant as those caused by R/D and t_r/T.

6. Recommended Formulae for the Ultimate Strength of the X-Joint

6.1. Revised Formula for the Ultimate Strength of the X-Joint

In Section 2.2, the resistance mechanism of the X-joint is simplified to a circular ring with a T-shaped cross-section. When the X-joint fails, four plastic hinges appear at positions 0°, 90°, 180°, and −90° on the circular ring. This assumption raises two questions. First, the impact of the deformation on the remaining parts of the chord wall is not considered. Second, the variations in the curvature of each arc segment are not considered. Based on the comparison in Table 5 and Figure 18, notably, when the value of R was small, the T-shaped section reached yield; however, the remaining parts of the chord wall still had a certain bearing capacity. Therefore, the calculation result was rather small. When the value of R was high, the strength of the circular ring with a T-shaped section was greater. The total deformation of the chord wall reached 3% D because of the change in the curvature of the circular ring; however, the plastic hinge of the circular ring had not yet been fully formed. This led to higher calculation results. Therefore, a nonlinear regression analysis was employed to enhance the computational precision. These data, derived from tests and finite element calculations conducted for parameter analysis, were incorporated. Science and , make:

An optimal fit was achieved with a fitted correlation coefficient of 0.8480. The ultimate strengths of the X-joints were calculated as follows:

6.2. Comparison with Existing Formulas

Table 5 lists the ultimate strength results obtained from the tests and existing formulae. In Table 5, “P_y−1” represents the calculation results of the derived formula, that is, Equation 15, and “P_y−2” represents the calculation results of the proposed formula, that is, Equation 17. As listed in Table 5, the results of the JSSC were considerably conservative, and the errors of the JSSC were approximately −33%. In comparison, the mean error of the proposed equation was 0.3%. Figure 18 illustrates the ultimate strength results obtained from the FE analysis and existing formulae. All the FE results were compared with the predictions from the proposed formula in Figure 19. The mean ratio of the formula calculation results to the FE results was 0.9937, and the standard deviation was 0.1168. The calculation results of the proposed formula (Equation 17) are closely aligned with the outcomes of the FE analyses, effectively reflecting the changes in the ultimate strength of the X-joints. Furthermore, the calculation process of the formula was recommended to be simplified compared to the design formula in Table 1. In summary, the proposed formula was stable and reliable, providing valuable insights into the design of ring-stiffened tube-gusset X-joints.

7. Conclusions

This study examined the mechanical behavior of X-type tube-gusset joints with ring plates. Based on the analysis results of the forces acting on the X-joints, we considered the forces acting on the X-joint as a superposition of the bending moment (M) and force (P). Through both experiments and FE analysis, the failure mode of the X-joints manifested as the deformation of the chord and warping of the ring plates, irrespective of the X-joint was subjected to a bending moment or force. Throughout the entire loading phase, the stress on the chord was notably high, only near the ring plate, whereas the stress at the other positions remained minimal. Therefore, we regarded the ring plate and the chord within the effective range of the ring plate as the primary bearing structure of the X-joint. The equivalent force at the ring plate position was used to determine the ultimate strength of the X-joints. In addition, a parameter analysis was performed using the verified simulation model, demonstrating a near-linear increase in the ultimate strength of the X-joint by increasing ratios R/D or t_r/T. By contrast, the changes caused by D/T were not significant. Finally, we devised a formula using a combination of theoretical derivations and regression analysis. These research findings provide a theoretical and experimental basis for the design of X-joints with ring plates.

Symbols

D:	Chord external diameter
T:	Chord thickness
R:	Ring plate width
t_r:	Ring plate thickness
B:	Gusset plate length
t_g:	Gusset plate thickness
H:	Gusset plate width
F:	Axial load of the braces
P_v:	Force on the ring plate
P_y:	Ultimate strength of the joint
Be:	The effective range of the ring plate
σ_y, σ_yr:	Yield strength of the chord, the ring plate
σ_Br:	Tensile strength of the ring plate.

Data Availability

The (DATA TYPE) data used to support the findings of this study are included within the article.

Conflicts of Interest

All the authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

Xiaolu Li reported that the financial support was provided by the Henan Provincial Department of Science and Technology (222102320114 and 222102320376).

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Copyright © 2024 Xiaolu Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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