Axial Tensile Experiment of the Lap-Type Asymmetric K-Shaped Square Tubular Joints with Built-In Stiffeners

Abstract

To study the mechanical properties of asymmetric K-shaped square tubular joints with built-in stiffening rib lap joints, axial tensile tests were carried out on one K-shaped joint without built-in stiffening ribs and four K-shaped joints with built-in stiffening ribs using an electro-hydraulic servo structural testing system. The effects of the addition of stiffening ribs and the welding method of the stiffening ribs on the mechanical properties were studied comparatively. The failure mode of the K-shaped joint was obtained, and the strain distribution and peak displacement reaction force in the nodal region were analyzed. A finite element analysis of the K-shaped joint was carried out, and the finite element results were compared with the experimental results. The results showed that the addition of transverse reinforcement ribs and more complete welds shared the squeezing effect of the brace on the chord. Arranging more reinforcing ribs in the fittings makes the chord more uniformly stressed and absorbs more energy while increasing the flexural load capacity of the fittings’ side plates. The presence of a weld gives a short-lived temperature increase in the area around the crack, and the buckling of the structure causes the surface temperature in the buckling area to continue to increase for some time. The temperature change successfully localized where the structure was deforming and creating cracks. The addition of the reinforcing ribs resulted in a change in the deformation pattern of the model, and the difference occurred because the flexural capacity of the brace with the added reinforcing ribs was greater than that of the side plate buckling.

1. Introduction

The tubular joint is a key bearing part in the truss structure of a bridge [1,2,3,4,5,6]. Affected by the material defects of the structure, weld defects, structural design defects, etc., tubular nodes are prone to weld cracking, chord extrusion deformation, brace axial buckling, and other damage [7,8,9,10]. To improve the bearing capacity of tubular joints, researchers at home and abroad have conducted extensive studies on strengthening methods for tubular joints. Increasing the wall thickness of the chord in the nodal region [11,12,13] and grouting inside the pipe [14] are common methods. In addition, placing reinforcing ribs on the exterior of the nodal structure is one of the common reinforcement methods. Qu et al. [10] conducted static load tests on a group of K-nodes with external reinforced rings, combined with finite element simulations to parameterize the chord compression ratio and gusset plate length, etc. They summarized a formula for predicting the ultimate load-carrying capacity of a ring with external reinforcement. This method of reinforcement is carried out on site directly on the structure’s exterior and enables the construction to be completed quickly [15]. However, external reinforcement structures can give an abrupt appearance at the nodes, and the reinforcement materials and their weldments are exposed for a long time and are susceptible to damage due to durability and corrosion. Therefore, in structure engineering, the location of reinforcement is often chosen to be inside the structure. By reinforcing the interior of the nodes, the reinforcement can be better integrated with the original structure [16]. Azair [17], to study the reinforcing effect of the internal ring, parameterized the structure of joints with internally reinforced rings using finite element analysis results and summarized the law of the geometry of the internally reinforced ring on the ultimate structural bearing capacity. Reasonable internal reinforcement design can make the node under the action of load stress distribution more uniform and improve the utilization of materials. The quality of the welding between the reinforced structure and the original structure is high.

Most of the previous studies have been based on a reinforcement method that parametrically analyzes the geometry of the reinforcement material while ignoring the effect of the quality of the weld between the reinforcement material and the original structure on the structural load-carrying capacity. However, in the actual processing process, the presence of defects such as porosity, slag entrapment, and lack of weld penetration in the weld seam often leads to a reduction in the load-bearing capacity of the structure [18,19,20,21,22,23,24,25,26]. K-shaped hollow square tubular joints are one of the most common node forms, and lap nodes have a higher load-bearing capacity compared to separated nodes [27,28,29]. Therefore, the hazards of welding defects on the structure are explored to investigate the effect of additional axial stiffening ribs inside the K-shaped joint on its stiffness. In this paper, a set of built-in stiffening rib lap-type asymmetric K-shaped square tubular joints are tested in axial tension, and the damage modes and stress distributions of K-shaped joints under axial tension are analyzed through the test phenomena and finite element simulation results.

2. Materials and Methods

2.1. Test Specimen

The nodes used for the experiments refer to the truss structure of the Luoxizhou Bridge located in Ganzhou City, Jiangxi Province, China. The specific dimensions of the test specimens were determined based on the Z16 joints therein (shown in Figure 1), where the dimensions of the chords and the braces were scaled down by a factor of 10 from the original project. The geometric model of the built-in stiffening rib lap-type asymmetric K-shaped square tubular joint is shown in Figure 2.

The width of the main branch $a$ is equal to 146 mm, the height of the main $b_1$ and the height of the branch $b_2$ are equal to 80 mm and 60 mm, respectively, the length of the main $L$ is equal to 800 mm, and the thicknesses of the fittings $t_1$ and the reinforcing ribs $t_2$ are equal to 1.4 mm and 1.2 mm, respectively. The angle ${\theta }_1$ of Chord with Brace #1 is 59°, and the angle ${\theta }_2$ with Brace #2 is 57°.

A total of five lap-type asymmetric K-shaped joints were subjected to axial compression tests. One is an unreinforced joint with a specimen labeled K-0, and the remaining four have built-in stiffening ribs. Specimens with built-in reinforcing ribs can be divided into two groups depending on the number of rib arrangements. RK-1 and RK-1F are one group, and both indicate that the tubing cross-section form is 1 × 1; RK-2 and RK-2F are another group, and both indicate that the tubing cross-section form is 2 × 1. To restore the defects of welding in the actual project and to compare and study the effect of welds on the load-carrying capacity, the reinforcing ribs of the two specimens within each group are set up with different welding methods: they are divided into full welding and partial welding. A partial weld indicates that the weld between the reinforcing rib and the tubing is interrupted, with a distance of 10 cm between welds and a single weld rod length of 4 cm (as shown in Figure 3). Due to the small thickness of the plates in the structure, all welding is CO₂ shielded. The same material is used for all parts. In the label, specimens with an F at the end indicate a full weld, and those without an F indicate a partial weld.

2.2. Raw Materials

The materials used in the tests were all Q235 steel, produced in Ma’anshan, China. To obtain the material parameters of the k-joint, standard tensile specimens were manufactured according to the materials used in the experiments, and standard tensile tests were carried out on the standard tensile specimens. According to the metal tensile test specification GB/T228.1-2021 [30], the standard tensile specimen is shown in Figure 4A. To obtain the displacement changes occurring in the calibration section, a digital image correlation method was used: the surface of the specimen was sprayed with white paint, and random scattering was drawn on the calibration section. A video of the tensile process of the specimen was imported into the commercial software GOM Correlate 2018 for displacement tracking. The stress–strain curves of the materials used in the tests are shown in Figure 4B.

Tensile tests were performed on the strength of the welds. The same standard tensile specimen was taken and cut into two halves uniformly in the height direction. The two were then rewelded together using the same welding process used for the test. As shown in Figure 5, the weld of this specimen is a butt weld, and the thickness of the weld is the same as that of the standard tensile specimen. By testing, none of the specimens fractured at the weld.

2.3. Tensile Test

The test loading device is a JAW-1000K/2 electro-hydraulic servo structure test system produced by Hangzhou Popwil Instrument Co., Ltd., produced in Hangzhou, China. The device has a stroke of 0–300 mm and an ultimate loading force of 1000 KN. The test setup is shown in Figure 6. The two braces of the specimen were nested in the sleeves of the articulating supports, and the position of the braces was fixed with six bolts with limit blocks. The articulating support is fixed to the ground anchor. By applying a horizontal tensile force to the main pipe, the chord is stressed, the force is transferred to the braces, and the two braces are subjected to axial tension and pressure, respectively. The brace in tension is lapped on the brace in compression.

According to Eurocode 3: Design of steel structures-Part 1–8: Design of joints [31], the loading process of this test was divided into two stages: force loading and displacement loading. The initial phase of the test was displacement loading. Force loading was performed when the test loading force was less than 80% of the finite element simulation result. The loading process was graded, with each level being 20% of the simulation results, and the holding time between each level was 2 min. For the safety of the test, when the loading force was greater than 80% of the finite element estimate, it was changed to displacement loading, with each grade being approximately 10% of the simulation result. Before formal loading, the specimen was preloaded in advance with a magnitude of 20% of the finite element estimate to make full contact between the indenter and the specimen. Also, we checked that the hinge support could be rotated to avoid self-locking. The loading speed and single-stage load value should be adjusted according to the real-time monitoring of the damage pattern of the specimen during the loading process and the load value returned by the sensor, and if there is a decrease in the growth rate of the load value, then the loading speed and the single-stage span of the load should be reduced. If the specimen shows obvious deformation, the test should be stopped immediately.

Experimental tests of axial compression of built-in stiffening rib lap-type asymmetric K-shaped square tubular joints include loading values, axial force values of the braces, and global temperature changes. Camera #1 and camera #2 were arranged on the left and right sides of the specimen to observe the experimental phenomena. Four unidirectional strain gauges, #1, #2, #3, and #4, were arranged on the brace to obtain the trend of the change in the axial force of the brace during the loading process. To obtain the deformation pattern of the chord, four unidirectional strain gauges #5, #6, #7, and #8 were arranged on the chord. The exact arrangement of the strain gauges is shown in Figure 7. The strain gauges were centrally glued to the left side of the specimen. Strain gauge model BX120-10AA used a resistance value of 120 Ω and a sensitivity factor of 2.08%. To obtain the global deformation pattern and also to compare the values of the reference strain gauges, a random scattering image was plotted on the right surface of the specimen using the numerical correlation method. The right side of the specimen was arranged with a high-speed camera in a fixed position with a recording frequency of 10 HZ. Images were imported into GOM Correlate 2018 to obtain global real-time displacement clouds and stress–strain clouds. To investigate the changes in the structure at the temperature level during the deformation process, an infrared camera was arranged on the right side of the specimen. The specific site layout is shown in Figure 8.

3. Results and Discussion

3.1. Failure Mode

Figure 9 plots the deformation of the specimen on the left and right faces under the condition of horizontal tension, respectively. Each column from Figure 9 represents the deformation process of one specimen, arranged chronologically from left to right. Each image represents a change in the deformation characteristics of the structure. For specimen K-0, weld cracking occurred on the left side at the connection between the chord and the lapped brace after a crisp ring in the direction of the applied tensile force, while the right side did not show any significant change. When the crack on the left side began to expand laterally, the specimen emitted a continuous sound, and local buckling occurred in the portion of the lap brace to the chord connection on the right side. With further increase in displacement, the overall structure of the chord tilted to the right side, the lap weld on the left side started to fall off, and the plastic deformation zone on the right side expanded into the chord, causing the chord to locally buckle as well. For specimen RK-1, continuous rattling occurred, and cracks appeared simultaneously on both sides of the connection between the main and the lapped brace, with the cracks gradually progressing toward the end of the main. For specimens RK-1F, RK-2, and RK-2F, local buckling occurred simultaneously on the left and right sides of the laps of the braces, followed by localized buckling of the portion of the chord near the lapped branch. As the displacement increases, the chord partially flexes to an increasing extent, and the end of the chord gradually buckles.

According to the above experimental phenomena, K-0 and RK-1 showed obvious cracks in the experiments, and K-1 even showed the phenomenon of main pipe rotation, while RK-1F, RK-2F, and RK-2 did not show any cracks, which indicates that transverse reinforcing ribs and more complete welds shared the extrusion of the brace on the main pipe. In RK-1, the greater range of buckling occurring in RK-2 indicates that arranging more reinforcing ribs in the fittings makes the chord more uniformly stressed and absorbs more energy while increasing the buckling load capacity of the fittings’ side plates. In contrast, the structure continued to emit a sustained phasic sound when the surface of the specimen was not showing significant changes, indicating that the sound originated from the internal reinforcing ribs. This can be inferred from the fact that the reinforcing ribs buckled before the side panels during the deformation of the structure.

Figure 10 plots the displacement reaction force curves for the experimental specimens. The trends of the displacement reaction forces of the five specimens are essentially the same: in the preloading period, the specimens are in the elastic stage, and their displacement reaction force curves increase linearly until the reaction force of the structure reaches the peak value for the first time. At this point, the brace restricts the axial displacement of the chord, the side plates of the chord deform plastically, and the lap branch receives compression from the chord and buckles. The stiffness of specimen RK-2 in the elastic phase was higher than that of RK-1 and RK-0, and the stiffness of specimens RK-1 and RK-2 was also higher than that of the other three specimens, suggesting that the addition of the reinforcing ribs and the more complete welds enhanced the stiffness of the structure. The lack of stiffness resulted in stress concentrations and cracks at the junction of the chords and braces in specimens K-0 and RK-1. With the addition of reinforcing ribs, the peak load capacity of the specimens obtained a significant increase. For specimens with the same tubing cross-section size, the peak reaction force of K-0 is 60.43 KN, while that of RK-1 is 74.96 KN, which is a 24.04% increase in load-carrying capacity. The peak reaction force of RK-2 was 91.11 KN, which increased the load-bearing capacity by 50.77% compared to K-0. A complete weld likewise led to an increase in the load capacity of the specimen. The peak reaction force of RK-1F was 98.88 KN, which increased the load capacity by 31.91% compared with RK-1. The peak reaction force of RK-2F was 105.43 KN, which increased the load-bearing capacity by 15.72% compared to RK-2.

3.2. Strain Distribution

Figure 11 plots a schematic of the structural strain field of K-0 acquired by the high-speed camera-based DIC system [32]. It can be seen that the region of maximum stress in the joint is concentrated in the lap region of the brace. Figure 12 plots the strain loading curve at each stress measurement point. In conjunction with the experimental phenomena of the structure, the force characteristics of the structure are derived from the trend of the strain load curve: During the elastic phase, when the structure is under tension, one of the braces is continuously under tension, and the other is continuously under pressure. The first half of the chord is dominated by the pull. As the chord is squeezed by the brace, the middle section of the chord is bent, in which the upper half of the region is tensile and the lower half is compressive. At this time, the neutralization axis of the chord is downward, so the compressive strain in the lower part of the chord is less than the tensile strain in the upper part.

3.3. Temperature Distribution

An infrared camera captured the temperature changes when there was a visible crack in the structure. Taking specimen K-0 as an example, from the infrared camera image (shown in Figure 13A), it can be noticed that when a crack appeared between the brace and the chord, a brief flickering occurred at the location where the crack appeared, which indicates that the appearance of the crack caused the temperature in the area around the crack to be briefly elevated. An infrared camera can also capture temperature changes as the structure undergoes local buckling. In the case of specimen RK-2F, for example, as shown in Figure 13B, when local buckling first occurs at the brace lap of the structure, sustained highlighting occurs in the area where buckling occurs [33], indicating that buckling of the structure causes the surface temperature in the buckled area to continue to increase for a while. The temperature variations successfully localized the locations where deformation and cracks occurred in the structure, which also proved the feasibility of infrared camera-based structural monitoring.

3.4. Finite Element Analysis

3.4.1. Finite Element Model

To compare and analyze the axial compression experiments of built-in stiffening rib lap-type asymmetric K-shaped square tubular joints, a finite element analysis model is created according to the finite element method. Based on the finite element software ABAQUS 6.14, the K-shaped joint structure is modeled using quadrilateral shell units (S4R). The end plates are modeled using 2D rigid body modeling (R3D4). The modeling position of the shell is defined as the midplane. The mesh delineation diagram is shown in Figure 14A, and the global mesh size is set to 5 mm. Based on the data of the standard tensile specimen in Figure 4, the ideal elastic-plastic intrinsic model with linear reinforcement is developed. According to the AISC Steel Construction Manual [34], the density $\rho$ of Q235 steel is set to 7850 kg/${\mathrm{m}}^3$, Poisson’s ratio $\mu$ is 0.29, and the modulus of elasticity $E$ is $2.1\times {10}^{11} \mathrm{P}\mathrm{a}$.

Select the quasi-static analysis step. Tie constraints are added to the portion of the end plate that is attached to the structure. Add a generic contact globally to the structure and set the friction coefficient for tangential contact to 0.2. Set normal contact to hard contact [35]. The boundary conditions of the model are shown in Figure 14B. Create reference point RP1 on the end plate connected to the main chord and reference points RP2 and RP3 on the end plates connected to each of the two braces, coupling them to the end faces. To simulate the actual boundary conditions of the structure, the six degrees of freedom of RP1 are constrained, and the chord axial displacement constraints are opened. Add displacement constraints in three directions for RP2 and RP3. Add axial displacement to RP1. Displacement is loaded with a smooth amplitude curve [36]. This curve has a slope of 0 at the start and midpoint to minimize the effect of stress waves during acceleration on the simulation results.

3.4.2. Finite Element Verification

Figure 15 compares the experimental results and finite element simulation results of the specimen deformation. It can be seen that the deformation in the experiment is similar to the simulation results. The chord is squeezed and deformed by the lapped brace. The horizontal loading device remains flat during the force applied to the specimen, while the chord deflects downward and downward during the rotation of the brace, bending the pressure branch. This is confirmed in the stress analysis of the finite elements below.

Figure 16 compares the experimental and finite element displacement reaction force curves. The difference between the peak reaction force of specimen K-0 and the simulation results is large because cracks appeared in specimen K-0 during the experiment, and the stress release of the specimen occurred in advance before reaching the load-carrying capacity. The finite element pressure is ideal uniform tension, while in the actual experimental process, the specimen in the initial stage of tension in the tensile phenomenon occurs within the tensile non-uniformity, which causes the finite element results of the peak of the moment to be significantly earlier than the actual experimental occurrence of the peak of the moment. The simulated values of the load-carrying capacity of the remaining two groups are intermediate between the experimental values of the structure at the response size under partially welded and fully welded conditions, and their deformation trends coincide with each other. Overall, the simulation results are in good agreement with the experimental results. This indicates that the finite element model built in this paper is reliable.

3.4.3. Finite Element Results

Figure 17 plots the first principal stress cloud for each finite element model at different moments of deformation. According to Figure 17, at the moment $t_1$, the individual models experienced a stress concentration at the junction of the pressure brace and the chord. The location where the stress concentration occurs is likewise the location where the K-0 experimental model produces cracks. At the moment $t_2$, the model without reinforcement ribs buckled at the top of the pressure brace, while the model with reinforcement ribs buckled in the region of its neighboring chord. At the moment $t_3$, the side panels of the chord without ribs buckled, while the model with ribs buckled at the lap, which is consistent with the deformation pattern of the experimental specimen. At the moment $t_4$, the horizontal loading device stays flat while the brace stays rotated, resulting in a height difference between the chord and the loading device, and the pressure stub is thus bent. It is also clear that an inclined shear plane exists at the middle end of the chord, and the angle of inclination of the shear plane of the model with additional reinforcing ribs is less than that of the model without ribs. Based on the deformation pattern of the finite elements described above, the addition of the reinforcing ribs resulted in a change in the deformation pattern of the model: the unribbed model flexes first in the brace and later in the chord under tension in the main tube, whereas the ribbed model first experiences flexion at the location of the chord, and flexion occurs after the brace. The difference occurs because the flexural bearing capacity of the additional reinforced ribbed brace is greater than the bearing capacity of the side plate in flexure.

4. Conclusions and Future Direction

Based on the structural dimensions of the truss structure of the bridge, static load tests were carried out on K-shaped joints with internally reinforced ribs. Combining the experimental and finite element results, the effect of reinforcing ribs and their welding patterns on the deformation patterns of K-shaped joints was investigated, and the following conclusions were finally obtained:

(1)

The addition of transverse reinforcement ribs and more complete welds share the squeezing effect of the brace on the chord. Arranging more reinforcing ribs in the fittings makes the chord more uniformly stressed and absorbs more energy while increasing the flexural load capacity of the fittings’ side plates.

(2)

The appearance of a crack gives a short-lived temperature increase in the area around the crack, and the buckling of the structure causes the surface temperature in the buckling area to continue to increase for a period of time. The change in temperature successfully localized where the structure was deforming and creating cracks.

(3)

The addition of reinforcing ribs resulted in a change in the deformation pattern of the model: The unribbed model flexes first in the brace and later in the chord under tension in the main tube, whereas the ribbed model first experiences flexion at the location of the chord, and flexion occurs after the brace. The difference occurs because the flexural bearing capacity of the additional reinforced ribbed brace is greater than the bearing capacity of the side plate in flexure.

The authors believe that idealized boundary conditions are adopted in the finite element analysis. During the actual experimental process, factors such as the loading equipment, the slippage of the supports, and the displacement of the nodes will all have an impact on the stiffness characteristics in the structural curve. Therefore, in this part, the authors only analyze and interpret the experimental phenomena and the characteristics of the joint buckling, instead of conducting an analysis from the aspects of the characteristics of stiffness and deformation.

Through the attempts in this paper, the authors believe that an infrared camera can effectively capture the heat-dissipation phenomenon during the yielding process of steel. However, due to the limitations of the experimental conditions, these infrared characteristics are quite sensitive to external environmental factors. For example, the thermal radiation from humans, animals, and oil sources can interfere with the results. In subsequent research, the authors will adjust the data-collection environment and set up certain shielding measures to eliminate interfering factors and achieve accurate collection and calibration of buckling characteristics. This is another limitation of this paper and also one of the authors’ future research directions.