Keywords

1 Introduction

Rectangular (square) tube sections exhibit excellent tensile, compressive, bending, and torsional properties, and they are often used in the truss structures [1]. Among these, the double-layer Vierendeel truss, characterized by the absence of diagonal members with all joints being X-type nodes, is known for its simplicity and aesthetic appearance. In steel tube trusses, complex joints are frequently reinforced locally to meet the design requirements for strong connections, ensuring the structural load-bearing capacity [2]. Steel tube joint reinforcement is typically achieved through external or internal strengthening, with good reinforcement effects achieved by welding ring plates on the joint surface.

Existing research has shown that ring plates are effective in strengthening joints, but this method does not allow for the observation of joint failure modes. Therefore, building upon the concept of ring corner plates, a new method for joint reinforcement, namely, the upward movement of reinforcement plates, is proposed as slot-type ring plate upward movement. To investigate its impact on joint hysteresis performance, this study focuses on X-type joints in double-layer Vierendeel trusses. After understanding their static performance, the axial hysteresis performance of the joints is studied [3].

2 Arrangement of Axial Reciprocating Loading Test

2.1 Specimen Design

Under the action of planar bending moments, different values of \(\beta\) will result in different failure modes at the joint [4]. Therefore, specimens with \(\beta =\) 0.7 and \(\beta =\) 1.0 are designed as reference specimens, denoted as URX-70B and URX-100B, respectively. Specimens of joints reinforced with ring corner plates with \(\beta =\) 0.7 (slot-type ring plates with no upward movement) and slot-type ring plates with \(\beta =\) 0.7 are also designed, denoted as CPX-70-A and CPX-70-B, respectively. In these specimens, the ring corner plates are square tubes one size larger than the main pipe, with holes cut in the upper and lower flanges based on the branch pipe size. These plates are then cut along the symmetrical planes of the steel pipe's longitudinal axis and welded onto the unreinforced joint. The slot-type ring plates are also square tubes one size larger than the main pipe, with holes cut in the upper and lower flanges based on the branch pipe size. The steel pipe is cut into four symmetrical parts along two symmetric planes and then welded onto the unreinforced joint after being raised to a certain height [5]. The geometric parameters of the reinforced joints CPX-70-A and CPX-70-B are defined as shown in Fig. 1 (with the unreinforced joint as a reference), and the dimensions of each joint are listed in Table 1. The lengths of the main pipe, branch pipe, and reinforcement plate are denoted as \(l_{0}\), \(l_{1}\), \(l_{p}\), respectively, with corresponding cross-sectional dimensions as \(b_{0} \times h_{0} \times t_{0}\), \(b_{{1}} \times h_{1} \times t_{1}\), and \(b_{p} \times h_{p} \times t_{p}\). The upward movement height of the slot-type plate is denoted as \(h\). All test joints are welded, with weld bead dimensions greater than or equal to 5 mm. Cold-formed hollow steel sections are used for the steel components, and the material test results are presented in Table 2.

Fig. 1
Two diagrams a and b display the side and cross-sectional views of reinforced joints with the components such as the main pipe, branch pipe, ring plate, and slot-type ring plate indicated.

Parameter definitions of joints

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Table 1 Geometries of test joints(mm)
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Table 2 Mechanical properties
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2.2 Loading Procedure

The test specimens are arranged vertically. The far end of the branch pipe is connected to the support using pin connections, while the support is connected to the self-balancing reaction frame, main pipe loading plate, and actuator using high-strength bolts. Vertical loading is applied using an MTS-100 kN servo actuator. To obtain a co-directional bending moment M at the intersection point of the branch pipe and the main pipe, a force F is applied at the end of the main pipe, resulting in an equivalent force of 1/2F at the far end of the branch pipe, perpendicular to it. Before the formal loading, a 25% cyclic preloading is applied to ensure that all instruments and equipment are functioning properly and to eliminate installation gaps. The formal loading is initially controlled by load control, with three cycles at 50 and 75%. After that, displacement control based on yielding displacement is used, with three cycles at 1, 2, and 3% strain increments, followed by two cycles for each subsequent increment until failure of the specimen, at which point loading is stopped [6].

2.3 Measurement Plan

As shown in Fig. 2, YWC-50 displacement sensors are positioned at the axis of the lower flange of the branch pipe (50 mm from the center) to observe the corresponding angular deformations of the branch pipes. Displacement sensors are symmetrically placed on the upper side of the loading plate along the plane containing the axis of the main pipe sidewall to detect any out-of-plane deformations of the components. Strain gauges and rosettes are placed at corresponding positions on the main pipe flange and sidewall. Data collection is carried out using a DH 3816N static data acquisition system.

Fig. 2
A diagram presents the front view vertical loading frame with branch pipes supporting the supervisor loading board with weights added to the loading board and branch pipes. The dimensions of the frame are indicated.

Site layout plan (e.g. CPX-70-B)

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3 Results and Discussion

3.1 Joint Failure Test Observations

During the loading of URX-70B, there were no significant deformations or cracking observed. In the first three levels of displacement loading, the specimen exhibited minor cracks at the weld corner of the main pipe flange (Fig. 3a), and these cracks gradually closed as compressive forces were applied to the branch pipe flange side (Fig. 3b). However, during the fourth level of displacement loading in the first cycle, cracks appeared at the weld corner of the main pipe flange (Fig. 3c). With the continued application of load, the load-carrying capacity began to decrease, and the cracks extended outward, causing deformation in the main pipe flange (Fig. 3d). Loading was stopped when the load-carrying capacity dropped below 85%. URX-100B did not exhibit significant deformation or cracking during the preloading and 50% loading phases. During the first 75% loading cycle, minor cracks appeared at the weld corner of the main pipe sidewall (Fig. 4a). In the first three levels of displacement loading, cracks on the main pipe sidewall gradually extended towards the corner (Fig. 4b), and these cracks closed gradually as compressive forces were applied to the branch pipe flange side. However, during the fourth level of displacement loading in the first cycle, significant cracking occurred at the weld corner of the main pipe sidewall (Fig. 4c). With the continued application of displacement load, the load-carrying capacity gradually decreased, and the cracks at the root of the weld on the main pipe sidewall penetrated through, resulting in deformation of the main pipe sidewall and flange (Fig. 4d). The maximum crack width reached 7 mm, and loading was stopped when the load-carrying capacity dropped below 85%.

Fig. 3
Four photographs a to d display minor cracks on the main pipe, closure of cracks in the main flange plate, cracking of the main flange plate, cracking, and damage to the main flange plate, respectively.

Performance of URX-70B

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Fig. 4
Four photographs a to d display minor cracks on the side wall of the main pipe, cracks on the side wall of the supervisor spread to corners, cracking at the corners of the weld seam, cracking, and penetration failure at the root of the weld seam, respectively.

Performance of URX-100B

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During the loading and the first three levels of displacement cycling of CPX-70-A, there were no significant deformations or cracking observed. When loading reached the first cycle of the sixth level of displacement loading, minor cracks appeared at the weld corner of the joint (Fig. 5a). As the load was applied, cracks developed in the branch pipe at the weld corner (Fig. 5b). When loading reached the seventh level of displacement loading, cracks in the branch pipe at the weld corner became pronounced (Fig. 5c). By the eighth level of displacement loading, the cracks in the branch pipe had completely penetrated (Fig. 5d), and the joint lost its load-carrying capacity. Loading was stopped at this point. For CPX-70-B, there were no significant deformations or cracking during the initial loading. However, when loading reached the first cycle of the second level of displacement loading, minor cracks appeared at the root of the main pipe-branch pipe weld (Fig. 6a). As the load was applied, cracks in the branch pipe flange became more noticeable, and minor cracks also appeared at the weld corner of the slot-type ring plate-branch pipe (Fig. 6b). When loading reached the fifth level of displacement loading, cracks at the weld corner of the slot-type ring plate-branch pipe became more pronounced and extended outward (Fig. 6b). By the seventh level of displacement loading, the cracks at the weld corner of the slot-type ring plate-branch pipe had completely penetrated (Fig. 6c), and the slot-type ring plate's flange and sidewall exhibited deformation (Fig. 6d). At this point, the joint lost its load-carrying capacity, and loading was stopped. The upward movement of the reinforcement plate facilitated the observation of deformations and crack development in the main and branch pipes of the joint, but the deformations in the flange and sidewall of the slot-type ring plate were more pronounced.

Fig. 5
Four photographs a to d display minor cracks in the corner branch pipe, cracking of the weld corner branch pipe, cracking of the weld seam, branch pipe cracking, and penetration, respectively.

Performance of CPX-70-A

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Fig. 6
Four photographs a to d display minor cracks at the root of the weld seam, cracking of the weld corner branch pipe, weld cracking and penetration, and concave-convex deformation of the groove type ring mouth plate, respectively.

Performance of CPX-70-B

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3.2 The Hysteresis Loops and Skeleton Curves

Figure 7 provides the hysteresis loops and skeleton curves for each specimen. It can be observed that the hysteresis loops of all specimens are relatively full. URX-70B, CPX-70-A, and CPX-70-B exhibit no significant pinching behavior in their hysteresis loops, while URX-100B exhibits some pinching, which may be attributed to slight slippage in the loading direction during the joint loading process. Previous research has indicated that when the plastic rotation angle of a joint exceeds 0.03 radians, the joint is considered to possess strong plastic deformation capacity. The tested joints all exhibit plastic rotation angles of 0.04 radians or more, suggesting that they have good ductility [7]. The peak points of each level's first-cycle M-θ curves were used to create skeleton curves. It can be seen that the positive and negative moments of the joint are essentially symmetrical, indicating good tensile-compression symmetry.

Fig. 7
Five graphs. Graphs a to e plot M versus Cieta. In graphs a to d, the lines are plotted for C P X-70-A, U R X-70-B, and U R X-100-B. Graphs a to d display hysteresis loops, while the lines plotted in graph e depict an increasing trend.

The hysteresis loops and skeleton curves

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Fig. 8
A scatter plot plots the relationship between the equivalent viscous damping coefficient and load loading level. The values are plotted for U R X-70-B, U R X-100-B, C P X-70-A, and C P X-70-B. The best-fitted lines for all values depict an increasing trend.

\(\zeta eq\) of each test specimen

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3.3 Energy Dissipation

The equivalent viscous damping coefficient (\(\zeta eq\)) was used to assess the energy dissipation capacity of the joints (Fig. 8) [8]. The unreinforced joints showed an initial increase followed by a decrease in energy dissipation, while the reinforced joints did not exhibit a decreasing trend. CPX-70-A had a better \(\zeta eq\) compared to CPX-70-B. In comparison to URX-70B and URX-100B, specimens CPX-70-A and CPX-70-B exhibited significantly increased energy dissipation while reducing the equivalent viscous damping coefficient, but with a less pronounced reduction. Among the two reinforcement methods, the upward movement reinforcement of the slot-type ring plate had a greater efficiency in reducing the energy dissipation capacity of the joint.

4 Conclusion

  1. (1)

    The reinforcement of the ring flange corner plate and the relocation of the slotted ring flange can mitigate the deformation of the main pipe. The upward movement of the slotted ring flange enables effective observation of the deformation of the main pipe's flange plate and side walls, as well as the cracking in the main pipe-supporting pipe weld zone. This is highly advantageous for the timely monitoring of the deformation of the main branch pipe.

  2. (2)

    Due to the upward movement, the deformation of the slotted ring flange's flange plate is more pronounced compared to the deformation of the ring flange corner plate's flange plate.

  3. (3)

    The hysteresis curves for unreinforced and reinforced nodes in the plane are both relatively full. Among them, the hysteresis loop area for reinforced nodes is greater than that of unreinforced nodes.

  4. (4)

    The equivalent viscous damping coefficient of reinforced nodes is smaller than that of unreinforced nodes, and node reinforcement mitigates the trend of reduced equivalent viscous damping coefficient under cyclic loads for unreinforced nodes. The reinforcement method using ring flange corner plates results in a smaller reduction in the equivalent viscous damping coefficient of nodes compared to the method involving the upward movement of slotted ring flanges.

  5. (5)

    From the comparison of data, it can be seen that the mechanical properties of the two reinforcement methods are not significantly different and both meet the requirements of the specifications. However, the structural parameters for the upward movement reinforcement of the groove type annular plate were selected based on experience, and the impact of different structural parameters on its performance was not explored.