Experimental and numerical analysis of a novel tubular joint for transmission tower

Journal of Constructional Steel Research 164 (2020) 105780

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Experimental and numerical analysis of a novel tubular joint for transmission tower Li Tian a, Juncai Liu a, Cheng Chen a, b, *, Liulu Guo a, Meng Wang c, Zilong Wang d a

School of Civil Engineering, Shandong University, Jinan, Shandong, 250061, China School of Engineering, San Francisco State University, San Francisco, CA, 94132, China c School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China d Shandong Electric Power Engineering Consulting Institute Co., Ltd., Jinan, Shandong, 250013, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 March 2019 Received in revised form 18 September 2019 Accepted 23 September 2019 Available online xxx

A novel type of tubular X-joint is evaluated in this study which combines both flange connection and welded connection for practical steel tube transmission tower. Full-scale experiments are carried out to investigate the monotonic behavior of the joints under both axial tensile and compressive load. The failure modes, load-displacement curves, load-strain curves, deformation development and ultimate strength are studied and discussed. Non-linear finite element analysis of the proposed tubular X-joint not only captures the discernible behavior observed during the tests to verify the experimental results, but also help study stress distribution that cannot be directly measured during the tests. Both experimental and numerical results show that the novel type of joints have adequate bearing capacity with good safety margin and the weak parts are mainly concentrated on the vicinity of intersection regions. Finally, several different design codes are used to calculate the ultimate strength of the proposed joints under investigation. The difference between experimental results and current design methods can be attributed to the fact that the connection adopted in the joints is different from the conventional welded tubular Xjoint in codes. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Tubular X-joint Full-scale test Non-linear finite element analysis Design methods

1. Introduction Due to its high load-bearing capacity and aesthetic appearance, steel tube towers are widely used in practice. In Japan steel tube towers are used for almost all 1000 kV UHV transmission lines [1]. The failure of these steel tube towers often starts first from the joint regions due to complex stress distribution [2]. In most cases, the failure of joints will then trigger the change of load-carrying path leading to collapse of the structure. Therefore, there is an immediate need for properly designed tubular joints and accurate prediction of the performance of these joints. Much efforts have been devoted to the analysis of these joints. In the early stage of tubular joint design, major concern focused on un-stiffened tubular joints. Based on the test results of 747 specimens, Kurobane et al. [3] and Paul et al. [4] proposed simple mathematical expressions for the resistance of tubular joints with circular hollow sections under axial loading. The equations for ultimate strength were proposed and verified by test results for

* Corresponding author. School of Civil Engineering, San Francisco State University, San Francisco, CA 94132, USA. E-mail address: [email protected] (C. Chen). https://doi.org/10.1016/j.jcsr.2019.105780 0143-974X/© 2019 Elsevier Ltd. All rights reserved.

multi-planar tubular joints with TT and KK configurations. Coferet et al. [5,6] applied the continuum damage mechanics to analyze the ultimate strength for welded tubular connections under general loading. Romeyn et al. [7] conducted both numerical and experimental investigation of stress and strain concentration in multiplanar tubular joints. It was pointed out that the weld toes at multi-planar tubular joint intersections were vulnerable to failure in general. Ghanameh et al. [8] later numerically analyzed the effect of different loading and various planar tubular joint types on the stress concentration. In order to improve the bearing capacity of the weld, considerable experimental efforts [9e11] demonstrated that the fatigue life of weld toe in welded joints can be enhanced by grinding. Meanwhile, investigations on other behavior of T-joints using circular hollow section, such as failure pattern, the ultimate strength and the stress concentration factor, were explored by Thandavamoorthy et al. [12] and Chen et al. [13]. Lesani et al. [14] experimentally and numerically studied detailed behavior of unstiffened T and Y tubular joints under axial brace compressive loading. Good agreement was observed between the numerical analysis, experimental results and parametric studies. Different reinforcement details have been developed to further improve the bearing capacity of tubular joints without changing the overall design. According to the locations of reinforcement

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parts, these reinforcing methods can be categorized into either external or internal [15]. The former includes collar-plate reinforcement [16,17], doubler-plate reinforcement [18] and external stiffening rings [19,20]. More recently, Lesani [21] experimentally investigated the behavior of tubular joints with FRP reinforcement. The results showed significant strength enhancement and improved joint behavior of the reinforced joints in comparison with that of unreinforced joints. On the other hand, the internal reinforced methods include internal stiffening rings [22,23], concretefilled [24,25] and inner-plate reinforcement [26]. Compared with unreinforced tubular joints, Yang [27] showed that the inner plates effectively improved the bearing capacity of joints under compressive loading. Traditional tubular joints are often connected through welds, which has been investigated extensively by previous research. However, this type of connection is often not sufficient to satisfy the flexibility for engineering applications. For transmission towers, extra stiffening plates should be designed to satisfy the strength requirement of traditional tubular joints, which not only increase the workload for welding, but also increase the material cost. This motivates the development of an innovative tubular joint with novel type of connection. A novel type of tubular X-joint is presented and investigated in this study for applications in steel tube transmission towers. Fullscale tests are conducted to explore the failure modes, ultimate strengths and behavior of tubular X-joints under axial tensile and compressive loads. Non-linear finite element analysis is then carried out to simulate the performance of the joints. The ultimate strengths calculated by different design codes are further compared with the test results to discuss the advantages of the proposed Xjoints over the traditional ones. Through the analysis of stress distribution and failure modes of joints under monotonic loading, the study provides an effective and efficient type of tubular X-joints for future design of transmission towers.

tubes with the elastic Young's modulus of 206 GPa. Fig. 2 shows the actual transmission tower and the detailed size of the suspension tower is presented in Fig. 3. A novel type of tubular joint is investigated in this study for the intersection regions of the suspension type tower. This novel tubular joint consists of two intersecting steel tubes, where one of which is disconnected at the intersection and the other is penetrated the entire joint. The bolts and the chords are assembled on the outside of a steel tube to not only reinforce component of the steel tube but also ensure its integrity. The disconnected tubes are welded to the chord, and the collar plates are welded to both ends of the chord. It can be observed that the material consumption decreases significantly, and the application of bolts and chords enables the field assembly of the tubular joint without need for extra welding workload. Fig. 3 shows the proposed tubular joint in

2. Experimental study 2.1. Specimen design The 500 kV long span transmission tower-line system across Yellow River is considered as the prototype structure for the experimental study in this study. There are a total of 5 transmission towers, of which two are tension type towers and the rest three are suspension type towers. The schematic diagram of long span transmission tower-line system is shown in Fig. 1. The tension type tower is 69 m high and the weight of the tower is approximately 216.94 t, while the suspension type tower is 135.8 m high and the weight of the tower is approximately 459.37 t. Moreover, both the tension and the suspension towers are constructed using steel

Suspension type

Fig. 2. A photograph of long span transmission tower.

Suspension type

Transmission line

Suspension type

Transmission line

Tension type

Tension type

Yellow River 358 m

1331 m

1227 m

Fig. 1. Schematic diagram of long span transmission tower-line system.

866 m

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2.2. Experimental setup

Fig. 3. Elevation of transmission tower (m).

the suspension type tower at the locations of TG 180, TG 325, TG 325, TG 299 and TG 273. The schematics of the tubular joints is shown in Fig. 4. The tubular joints at TG 180 and TG 270, as shown in Fig. 3, are selected for investigation in this study and are referred to hereafter as Joint A and Joint B, respectively. Fig. 5 presents geometric details of two specimens. Braces of Joint A are welded perpendicularly to the chords, while the angle between braces and chords is 74
for Joint B. Both tubular joints use Q345 steel which is commonly used in Chinese construction industry. The size of the weld is 10 mm. Flange plates of both Joint A and B are connected by with a total of 12 and 18 of 22 mm diameter Grade 8.8 bolts, respectively. A total of 12 specimens are fabricated, including 6 identical specimens of Joint A numbered as A1 to A6 and 6 identical specimens of Joint B numbered as B1 to B6. Table 1 presents details of the twelve specimens. Different types of axial load are considered in the experimental investigations of Joint A and B to explore the failure mechanism and to determine the ultimate static strength, where A1-A3 and B1eB3 are subjected to axial tensile load, while A4-A6 and B4eB6 are subjected to axial compressive load. Repeated tests are planned and conducted to minimize potential influence of geometric imperfection and the measurement error on experimental results. To ensure the reliability and accuracy of test results, the tensile tests were first conducted to determine the properties of the steel material. Different thickness are considered for different types of members. The steel specimens are labeled as T1-T5 for 6, 10, 12, 16 and 20 mm, respectively, as shown in Fig. 6 for 20 mm specimen. The material properties are measured and summarized in Table 2.

Tubular joints are usually subjected to complex loadings and can be the critical parts within a latticed structure. For the proposed tubular joints, the chords are assembled on the outside of the steel tube by several bolts and the disconnected braces are welded to the exterior surface of chords, so the chords act as constraint for the connection. Thus, one end of the brace is subjected to loads in the axial direction and both ends of the chords are considered free as the first step to experimentally evaluate the performance of proposed tubular joints [28,29]. Fig. 7 shows schematics of the experimental setup for tubular joints subjected to different axial loads. An MTS hydraulic testing system is used to impose the axial tensile load. Both ends of the tubular joints are welded with horizontal steel plate, one end of which is connected with MTS, and the other end is directly connected to the foundation. Compressionshear testing machine is used to apply axial compressive load to the brace member. The end of the tubular joints directly connected with compression-shear testing machine so the connection between the machine and the tubular joints can be considered as fixed. During the experiments, the static load increases monotonically and the force increment is adjusted with the increase of load. Fig. 8 shows a representative loading protocol of which the load first increases with the increment of 50 kN, and then with the increment reduced to 30 kN when the load reaches 250 kN. When the load is in the range of 490 kNe730 kN, the increment of 20 kN is used. Finally, the load continues to increase in the increment of 10 kN until either the tubular joints exhibit noticeable failure or the load amplitude exceeds the capacity of the machine. The deformation and strain of key members as well as the ultimate load-carrying capacities of the specimens are measured and recorded for the purpose of analysis. Quite a number of strain gauges were arranged on the flange plates and the exterior surface of the braces during the experiment. To avoid repetition, only typical results of strain gauge measurement in key locations are selected to be presented in this paper. Figs. 9 and 10 show the locations of selected strain gauges for the specimens A and B, respectively. Strain gauge 1 is attached to the upper braces, which is located 30 cm away from the upper edge of chords, and the other two are located at the middle of the flange plate. The outer diameter of chord is measured before and after loading to monitor its deformation during the loading. It is worth noting that throughout the experiment, strain data is collected after each stage of required load is reached and stabilized. This is to ensure that the values of each strain gauge are desired results for the specified load. 3. Experimental results 3.1. Identification of limit states Before presenting the experimental results, it is necessary to determinate the limit states of the tubular joints. In general, there are three typical failure modes of tubular joints [30], which are defined as A, B and C as shown in Fig. 11. The axial force of brace is used as ordinate and the deformation of chord is used as abscissa. It can be observed from Fig. 11 that the elastic developments of three methods are consistent at the initial stage of loading. When the tubular joints develop plastic deformation with the increase of load, the three failure modes exhibit significant difference. For mode A, the axial force of brace increases continuously and reaches the extreme point with the increase of deformation. Analogously, mode B also can record the extreme point, but the axial force of brace tends to decrease first and then increase with the increase of deformation. Accordingly, the axial force of brace at the extreme point of both mode A and B is considered to be the ultimate bearing capacity of the tubular joint. In contrast, when the tubular joint

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Fig. 4. Schematics of the proposed of tubular joint.

develops the plastic deformation, the axial force imposed to the brace increases as the deformation increases. That is to say, mode C cannot capture the extreme point even if there is a large plastic deformation. It should be noted that the excessive plastic deformation of the local area may be unacceptable in practice even if the ultimate bearing capacity of the tubular joints is not reached. Therefore, when the plastic deformation of chord exceeds the ultimate deformation, the tubular joint is still considered to reach the ultimate bearing capacity and to fail. According to the previous suggestion [30,31], the ultimate deformation can be determined to be 3% of outer diameter of the chord. On the whole, if the deformation at the extreme point is smaller than the ultimate deformation, the axial force at the extreme point is considered to be the ultimate bearing capacity of the tubular joint. If the deformation at the extreme point is larger than the ultimate deformation or the extreme point cannot be recorded, the axial force of brace at the ultimate deformation is considered to be the ultimate bearing capacity of the tubular joint. Therefore, the ultimate deformation of the tubular joint can be taken as a supplement to determine the ultimate bearing capacity. Based on above criteria, the ultimate loads obtained from tests and failure modes of the Joints A and B are presented in Table 3,

where PDe and PExp represent the design and experimental values, respectively. The design values are the strengths that satisfy the expected minimum requirements in the design process of the steel tube tower. The experimental results show that the ultimate bearing capacity is relatively high for the proposed tubular joints, which indicates that these tubular joints can satisfy the design requirement and have sufficient strength reserve and enough safety margin. In addition, collar plate exerts hooping effect on the chord, thus effectively limiting the deformation of the chord and increasing the ultimate bearing capacity of the tubular joints. It should be noted that failure modes of the three identical specimens are found to be different in tests and show significant dispersion although they are subject to the same loading. Similar observation was also reported in previous research [32]. 3.2. Failure mode Fig. 12 compares deformation of specimens A1-A3 subjected to axial tensile load. Almost no deformation was observed on specimen A1 at the beginning of the test. Plastic deformation and local denting were observed on the brace when the axial load reaches

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Fig. 5. Geometric details of two specimens.

Table 1 Properties of tubular joint (mm). Joint

A B

Brace

Chord

q

Bolt

d1

t1

d0

t0

L

d2

n

S

e

180 273

6 6

207 296

12 10

330 480

22 22

12 18

50 50

40 40

Collar plate t2

90
74


8 8

Notes-d1 and t1 are diameter and thickness of brace, respectively; d0, t0 and L are diameter, thickness and length of chord, respectively; d2, n, S and e are diameter, number, spacing and edge distance of bolts, respectively; q is the angle of brace and chord; t2 is thickness of collar plate.

Fig. 6. Steel specimens.

Table 2 Results of tensile tests. Specimens

t (mm)

f0 (N/mm2)

fu (N/mm2)

E (105 N/mm2)

T1 T2 T3 T4 T5

6 10 12 16 20

375 380 395 390 366

535 546 576 580 551

2.04 2.06 2.09 2.10 2.03

Notes-f0 and fu are the yield strength and the ultimate strength of steel, respectively.

800 kN, and continues to develop with the increase of axial load. Cracks are observed in the welding zone between the upper brace and the chord when the load reaches 930 kN implying the beginning of the failure. With the increase of the load specimen A2 develops plastic deformation and local denting on upper brace as well as warping on the inner edge of flange plate. When the load increases to around 1000 kN, the test was terminated as the vertical chord deformation exceeds the capacity of the MTS machine. The failure mode of specimen A3 is similar to that of specimen A1. However brittle fracture was observed at 960 kN in the welding zone between the upper brace and the chord. The comparison of deformation is shown in Fig. 13 for specimens B1eB3. As the axial tensile force increases to the loading capacity of the testing facility, no significant plastic deformation or crack is observed in either the members or their welding zones. The tests were therefore terminated at 1100 kN. It can be concluded from the axial tensile test of the specimens A1-A3 and B1eB3 that plastic deformation initially occurs at brace, which later leads to local dent until the tubular joints reach their final failure. Moreover, due to inevitable defects, the welding zone is vulnerable to stress concentration and prone to brittle fracture resulting in sudden loss of bearing capacity. The deformation of chord exceeding the maximum value is therefore used as supplement to determine the failure of those specimens. The specimens A4-A6 are subjected to axial compression load, and the comparison of their deformation is shown in Fig. 14. At the initial stage of test, no obvious deformation is observed on specimen A4. When the load increases to 1000 kN, two flange plates show noticeable vertical deformation. At the same time, brace develops plastic deformation and local denting, while at the same

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Fig. 7. Experimental setup.

Fig. 8. Loading protocol for both tension and compression.

Fig. 10. Strain gauges arrangements of specimen B.

Fig. 11. Failure modes of tubular joints. Fig. 9. Strain gauges arrangements of specimen A.

time the chord deforms and shows the ovalization. When approximately 1225 kN is reached, the relative distance between the upper and lower chords is remarkably reduced with observed local

dent due to the direct load of upper brace. The failure mode of specimen A5 and A6 is similar to that of specimen A4. In addition to the aforementioned phenomenon, slight crack is observed in the

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Table 3 Experimental results of joints A and B. Joint

Load type

I.D.

PExp (kN)

PDe (kN)

KS

Test termination reason

A

Axial tension

A1 A2 A3 A4 A5 A6 B1 B2 B3 B4 B5 B6

930 1000 960 1255 1050 980 >1100 >1100 >1100 1240 1180 1340

900 900 900 900 900 900 1000 1000 1000 800 800 800

1.03 1.11 1.07 1.39 1.17 1.09 >1.10 >1.10 >1.10 1.55 1.47 1.67

Weld cracking weld cracking Weld cracking Excessive chord deformation Excessive chord deformation Excessive chord deformation Loading device limit Loading device limit Loading device limit Excessive chord deformation Excessive chord deformation Excessive brace deformation

Axial compression

B

Axial tension

Axial compression

Fig. 12. The comparison of deformation of specimens A.

Fig. 13. The comparison of deformation of specimens B.

weld of specimen A5 yet without causing the specimen failure. It can therefore be concluded that local plastic dents of brace and excessive chord deformation are the two main factors for the failure of specimens An under axial compression load. The specimens B4eB6 are subjected to axial compressive load, and the comparison of deformation of those specimens is shown in Fig. 15. The deformation development of specimen B4 is similar to that of specimens A4 under axial compressive load. As the load increases, upper brace develops local plastic dent, chord deforms from circular to oval, and the outer edge of flange plate shows warping. When the load reaches 1240 kN, these deformation phenomena further aggravate. Finally, the deformation of chord exceeds the limit value, indicating the failure of the specimen. Similar

failure also occurs for the specimens B5 and B6. It can therefore be concluded that excessive deformation of chord is the main contribution to the failure of Joint B. 3.3. Loading-displacement curve analysis The axial tensile load-displacement curves of the specimens A and B are presented in Fig. 16. It can be observed that the axial tensile loads of specimens A increase first linearly with respect to displacement, which implies no plastic deformation. When the load increases to about 800 kN, the increment of the axial load reduces with the same increment in the displacement as neither the local plastic deformation of brace nor weld cracks are beneficial

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Fig. 14. The comparison of deformation of specimens A.

Fig. 15. The comparison of deformation of specimens B.

Fig. 16. Axial tensile load-displacement curve.

to the bearing capacity of the tubular joints. As for specimens B, even if the axial tensile load applied on upper brace reaches the capacity of the MTS machine, i.e. 1100 kN, the loadedisplacement curve remains linear. The tests are terminated due to the load capacity of the experimental setup. The axial load-displacement curves are shown in Fig. 17 for specimens A and B under compression. At the beginning of the loading, the initial stiffness gradually increases before reaching a

stable value. This phenomenon can be attributed to the gaps between the upper and lower flange plates and between the specimen and the loading device. As the load continues to increase, the gap decreases and the faces start to contact with each other, resulting in increased stiffness. When the axial compressive load of the specimens A increases to 900 kN and that of B specimens increases to 1100 kN, the loadedisplacement curve starts to show inflexion points, indicating that the tubular joints start developing

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Fig. 17. Axial compressive load-displacement curve.

plastic deformation. Even if the local deformation reaches the failure criterion as mentioned previously, it is difficult to determine the failure load of the joints from Figs. 16 and 17. The specimens still have strength reserve and do not fail suddenly. 3.4. Load strain curve analysis of key parts The flange plates of specimens A and B are connected by bolts. Under the external load, the bolts transfer the force to the flange plate. Due to the small contact area between the flange plates and the bolts, the flange plates develop large deformation, which finally leads to the loss of bearing capacity of the tubular joints. It is therefore important to prevent the flange plate from any local damage induced by improper design during the loading process. Strain gauges are placed at the middle of the flange plate and the load-strain curves for the flange plates are shown in Figs. 18e21 of the specimens A and B, respectively. It should be noted that not all results are presented due to the fact that some of strain gauges fell off or were damaged during the test. It can be observed from Fig. 18 that the strain increases proportionally with the axial tensile load before the plastic deformation. When the load increases to 750 kN, plastic deformation occurs and the strain begins to increase rapidly. The strain gauges 2 and 3 of flange plate of specimens A are in compressive state. As shown in Fig. 19, when specimens B are loaded up to 850 kN, the curve still remains linear, indicating that the flange plate has not yielded. When the load is increased to 1000 kN, the slope of the curve changes implying the plastic deformation. The strain gauges 2, 3, 4 and 5 of flange plate of specimens B are in compressive state.

Fig. 20 shows the loadestrain curve of flange plate of specimens An under compression. When the load increases to 900 kN, the flange plates of specimens A start to yield. The plastic deformation develops quickly and significantly. Thereafter, the stiffness of the flange plate decreases obviously. The strain gauges 2 and 3 of flange plates of specimens A are in tensile state. Fig. 21 shows the compressive loadestrain curve of flange plate of specimens B. At the beginning, the load increases linearly with the increase of strain of flange plate. When approximately 900 kN is reached, the curve shows fluctuation, indicating the occurrence of plasticity. When the load reaches 1000 kN, the curve starts to inflect and the strain increases significantly. The strain gauges 2, 3,4 and 5 of flange plate of specimens B are in tensile state. 4. Finite element analysis 4.1. Finite element model The finite element modeling software ABAQUS [33] is employed to emulate the failure mode and to predict the ultimate strength of the proposed tubular joints. To obtain accurate results from the finite element analysis, the geometric dimensions of all the tubular joint components are the same as those of the specimens described in the experiment. Typical finite element models are shown in Figs. 22 and 23 for specimens A and B, respectively. It should be noted that the material properties in the FEM use the tensile test results in Table 2. Although the weld has significant influence on the fatigue life, it is not modeled in the finite element models, between the collar plate and the chords, and between the braces

Fig. 18. Tensile load-strain curve for flange plate of specimens A.

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Fig. 19. Tensile load-strain curve for flange plate of specimens B.

Fig. 20. Compressive load-strain curve for flange plate of specimens A.

Fig. 21. Compressive load-strain curve for flange plate of specimens B.

and the chords, due to the little effect on the static strength of a tubular joint [16,34]. Therefore, the welds can be simulated by the “tie” command in ABAQUS, which attaches the nodes on the intersecting surface of the braces to the nodes on the chord with the same coordinates. Other surface-to-surface contact interactions are modeled as hard contact property in the direction normal to the interface plane and “penalty” option in the tangent direction. The penalty frictional formulation with a friction coefficient is equal to 0.15 for steel-to-steel interface [35]. To account for the sensitivity of the numerical analyses to the element type and mesh generation, the solid element C3D8R, an eight-node linear brick element with reduced integration and hourglass control [36], is used. In order to

guarantee high quality meshes, all the components are followed a medial axis algorithm and meshed in hex shape by means of sweep technique [37]. Accordingly, a fine mesh with size of 4 mm  4 mm  4 mm is used to balance between computational efforts and efficient convergence. The pre-tightening force of the bolt is imposed to the cross section of the bolt by means of “bolt load” option in ABAQUS [38,39]. Three analysis steps are defined in the process of pre-tightening force analysis. First, a small pretightening force of 10 N is applied in order to make convergence easier. Secondly, pre-tightening fore is adjusted to 125 kN and applied. In the third step, the fix at current length method is selected to maintain the adjusted pre-tightening force. After these

L. Tian et al. / Journal of Constructional Steel Research 164 (2020) 105780

Fig. 22. FEM of specimen A.

Fig. 23. FEM of specimen B.

three steps the axial force is applied to the top surface of the brace in the subsequent analysis steps. 4.2. Comparison and analysis The deformation of specimens A from finite element analysis is presented in Figs. 24 and 25 and compared with the test results. Obviously, the FEM enables accurate prediction of the failure modes for these specimens. It can also be observed from Table 3 that the failure of specimens An under tensile load can be attributed to the crack on the weld zone and excessive local dent on the upper brace, which is consistent with the expansion of the yield stress distribution at the intersecting region. In addition, the FEM shows that the inner side of flange plate develops significant warping. For the specimens subjected to axial compressive loading, the chord of the specimen A deforms with a tendency of vertical contraction and lateral expansion. At the same time, obvious plastic stress distribution appears at the edge of collar plate, indicating that collar plate plays an important role in limiting the occurrence of the deformation of chord. The comparison between test results and FEM results is presented in Table 4 for specimens A and. When the axial tensile load increases to 900 kN in the FEM, the transverse deformation (Dt ) and vertical deformation (Dv ) of chord are 6.49 and 7.44 mm, respectively. Both deformation exceeds the required limit value of chord (Du ), which agrees well with the experiment results. The relative distance of flange plates (df ) in the FEM is observed to be slightly smaller than the test results, which can be attributed to the fact that the tensile load applied in the FEM is slightly less than the average value of tests. When specimens A are subjected to axial compression force,

11

specimen A4 and A6 failed due to excessive chord deformation and expansion of local plastic area on upper brace. Although similar deformation is also observed in specimen A5, it however still retains good capacity. In the FEM, when the load is imposed to 1000 kN, both Dt and Dv of specimen A5 satisfy the acceptable deformation requirements. When load increases to 1100 kN, the tubular joint failed due to excessive deformation of chord. Overall, the FEM results of specimen A5agree well with the test results. The comparison of failure mode from experiments and FEM analysis is shown in Figs. 26 and 27 for specimens B. When the FEM of specimen B is subjected to tensile load, vertical expansion and lateral contraction of chord can be observed, which is similar to the deformation mode observed from experiments. Moreover, it can also be observed from Fig. 26(b) that the local plastic stress distribution does not occur over the whole joint indicating extra bearing capacity. This is consistent with the test results presented earlier. As shown in Fig. 27(d), the yielding of the upper brace extends to local region of chord under the axial compressive load, resulting in the dent. At the same time, plastic stress distribution can be observed at the edge of collar plate, which is consistent with the slight out-of-plane deformation observed from tests. Table 5 presents the comparison of test results with FEM analysis for specimens B. When the axial tensile load applied to the FEM reaches 1000 kN, Dt is 6.13 mm and Dv is 4.04 mm. After the load continue to 1100 kN, namely, the limit of MTS machine, neither Dt nor Dv exceeds Du , indicating that the joint still has the capacity. Good agreement is again observed between the FEM analysis and the experiments. Moreover, when the axial compressive force increases from 1200 kN to 1275 kN, the vertical contraction of chord aggravates for the FEM with Dt increasing from 8.03 mm to 9.43 mm which exceeds the required limit of 8.88 mm. At the same time, the outside of flange plate develops warping in the FEM and the maximum relative displacement reaches 9.80 mm, which again agrees with the experimental results. Fig. 28 compares the loadestrain curves from FEM and tests for specimens An under axial tensile and compressive load. Similarity can be observed between the strain histories from FEM to those from tests. In the early stage of the loading process, the strain increases linearly with the increase of the load. When the axial tensile load increases to approximately 900 kN for the specimens A1-A3 and 980 kN for the specimens A4-A6, the curves start to show inflection points. This phenomenon may be attributed to the fact that slight local concave or convex deformation on the upper brace results in stress redistribution on the brace. This could potentially improve the bearing capacity of the joints to a certain extent. To maintain certain safety margin, the joints are still considered to fail if the deformation of brace or chord exceeds the required limit. The loadestrain curves of specimen B under axial tensile and compressive load obtained by FEM and tests are compared and presented in Fig. 29. It again can be observed that the predicted results by the FEM analysis are consistent with corresponding test results. During the entire loading process, the strain of strain gauge 1 increases linearly as the load increases indicating no significant plastic deformation. The strain gauge 1 is not located at a position where the upper brace has the largest deformation. It should also be noted that plastic deformation does not necessary occur at the same location. When the axial compressive load is about 300 kN, the strain gauges 1 of the specimens B4 and B5 fell off, but the recorded data before that agree well with the FEM results. To further assess the performance of proposed tubular joints, a safety margin coefficient is defined as

KS ¼

PExp PDe

(1)

As can be observed from Table 3, the bearing capacity of

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Fig. 24. Comparison of test and finite element results of specimens An under tensile load.

Fig. 25. Comparison of test and finite element results of specimens An under compressive load.

specimens An under axial tensile and compressive load is higher than the design values, indicating certain safety margin. The specimens B subjected to axial tensile load of 1100 kN were not damaged, and the safety margin coefficient is therefore higher than 1.1. The safety margin coefficients of the specimens B under compressive load are as high as 1.57. Overall, the proposed tubular joints in this study have significant safety margin for the external load. Moreover, based on the previous comparison of axial loadstrain curves, failure modes and ultimate strengths, it can be

concluded that the FEM analysis can accurately and reliably predict the performance of the tubular joints. The comparisons between test results and calculated values of bearing capacity are listed in Table 6. As shown in Table 6, the error between FEM result and the test value is small, and the maximum difference was only 7%. 4.3. Comparison of design codes Current design codes on tubular X-joint, such as “Technical

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Table 4 Comparison of specimen A between test results and results of FEM. Specimens

Du (mm)

P (kN)

Dt (mm)

Dv (mm)

df (mm)

Specimens

P (kN)

Dt (mm)

Dv (mm)

df (mm)

A1 A2 A3 PExp PFEM

6.2 6.2 6.2 6.2 6.2

930 1000 960 963 900 1000

5 7 5 5.67 6.49 13.55

10 9 7 8.67 7.44 15.99

5 4 4 4.33 3.23 6.79

A4 A5 A6 PExp PFEM

1255 1050 980 1095 1000 1100

9 3 11 7.67 2.20 8.73

11 4 13 9.33 2.90 8.93

7 2 8 5.67 1.81 7.47

Notes: PFEM is the result of FEM and P is the final result recorded; PExp is the average of the final test results.

Fig. 26. Comparison of test and finite element results of specimens B under tensile load.

Fig. 27. Comparison of test and finite element results of specimens B under compressive load.

regulation of design for steel tubular tower structures of overhead transmission line DL/T 5254-2010 (DL)” [40], “Specification for structural steel building ANSI/AISC 360-05 (AISCE)” [41] and

“Eurocode 3:Design of steel structures” (EC3) [42], are utilized to calculate the ultimate strength of the test specimens. The bearing capacity of tubular X-joints under compressive and

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L. Tian et al. / Journal of Constructional Steel Research 164 (2020) 105780

Table 5 Comparison of specimen B between test results and results of FEM. Specimens

Du (mm)

P (kN)

Dt (mm)

Dv (mm)

df (mm)

Specimens

P (kN)

Dt (mm)

Dv (mm)

df (mm)

B1 B2 B3 PExp PFEM

8.88 8.88 8.88 8.88 8.88 8.88

1100 1100 1100 1100 1000 1100

3 5 4 4 6.13 8.14

7 4 6 5.67 4.04 5.85

3 3 4 3.3 5.29 7.83

B4 B5 B6 PExp PFEM

1240 1180 1340 1253 1200 1275

9 10 6 8.33 8.03 9.43

10 7 6 7.67 6.81 6.20

7 8 8 7.67 8.31 9.80

Fig. 28. The comparison of load-strain of specimen A between test and FEM.

Fig. 29. The comparison of load-strain of specimen B between test and FEM.

Table 6 Comparison between test results and calculated values of bearing capacity. Specimen

Axial load type

DL (kN) NDL

FDL

NAISCE

FAISCE

NEC3

FEC3

A

tension compression tension compression

1445.3 1048.5 1308.4 851.7

1033.8 1033.8 1322.8 1322.8

1096.6 1096.6 890.8 890.8

1430.0 1430.0 2189.3 2189.3

1000.4 1000.4 812.7 812.7

1163.3 1163.3 1816.0 1816.0

B

AISCE (kN)

EC3 (kN)

PExp (kN)

PFEM (kN)

Error (%)

963 1095 >1100 1253

900 1100 1100 1275

6.54 0.46 0 1.76

tensile load can be expressed as for DL, respectively:

N cDL ¼

5:45t 20 f0

j ð1  0:81bÞsin q h

(2)


0:2 d NtDL ¼ 0:78 0 NcDL t0

(3)

The AISC formula for bearing capacity of tubular X-joints can be expressed as:

L. Tian et al. / Journal of Constructional Steel Research 164 (2020) 105780

f0 t 2 ½5:7=ð1  0:81bÞ jn NASIC ¼ 0 sin q

(4)

The EC3 formula for bearing capacity of tubular X-joints can be expressed as:

NEC3 ¼

½5:2=ð1  0:81bÞt 20 f0 jn sin q

(5)

where, b ¼ d1 =d0 ; f0 is the design value of the bearing strength of chord; q is the angle of chord and brace; jh is calculation parameter and jn ¼ 1. Equations (2)e(5) calculate the overall bearing capacity of tubular X-joint and do not account for the effect of weld. From the above analysis of failure mode, it can be observed that the crack in the weld presents essential influence on the bearing capacity of tubular joints. Therefore, the working performance of the weld should be taken into account. According to DL, the weld length of the intersection region can be calculated as follows: (a) If d1 =d0 < 0:65


 0:534 LW ¼ ð3:25d1  0:025d0 Þ þ 0:466 sinq

(6)

(b) if d1 =d0 > 0:65


 0:534 LW ¼ ð3:81d1  0:389d0 Þ þ 0:466 sinq

(7)

where d1 is diameter of brace; d0 is diameter of chord. Based on “Code for design of steel structure GB 50017-2017” [43], the bearing capacity of weld (FDL ) can be determined as:

Transverse fillet weld

Longitudinal fillet weld

sf ¼

FDL  bf f w f he LW

(8)

FDL  fw f he LW

(9)

tf ¼

where, he is effective thickness of fillet weld; sf and tf are the normal stress and shear stress calculated according to the effective area of the weld, respectively; f w f is design value of weld strength; and bf is the amplifying coefficient of the design strength of transverse fillet weld. The calculation method of weld (FAISCE ) in AISCE is:

  FAISCE ¼ 0:604FEXX 1 þ 0:50 sin1:5 q Aw

(10)

where, 4 ¼ 0:75; FEXX is electrode classification number, i.e., minimum specified strength; q is the angle of loading measured from the weld longitudinal axis; and Aw is the effective area of weld throat. The EC3 specifies the weld strength (FEC3 ) as:

FEC3 ¼ fvw:d Aw

fvw:d ¼

fu

(11)

.pffiffiffi 3

bw gM2

(12)

where, fvw:d is the design shear strength of the weld; fu is the nominal ultimate tensile strength of the weaker part joined; bw is the appropriate correlation factor; gM2 is the resistance of welds. The ultimate strengths of the tubular X-joints calculated by different design codes are presented in Table 6. It is worth noting that the proposed tubular joint is composed of brace welded to

15

chord and assembled by flange plate and bolt, which is different from traditional tubular X-joint specified in the codes. Under the axial tensile load, the bearing capacity from DL is significantly higher than the experimental value. The bearing capacity from AISCE and EC3 are close to the test resultsf for specimens A, but differs for specimens B. Under the axial compressive load, the design codes provide good estimates of the strength for the specimens A, but underestimate that of the specimens B. It can be observed that the proposed tubular joints has significantly improved the ultimate compressive strength when compared with the traditional tubular joints. Meanwhile, Eqs. (2)e(5) show that the bearing capacity of the X-joints can be improved by increasing to or b during the design process. The strengths of the intersecting weld calculated by different standards are also listed in Table 6. Comparing the results of AISCE and EC3, the strengths of fillet welds calculated by DL lead to a larger safety margin.

5. Conclusions This study proposes a new type of tubular X-joint for application in steel transmission tower. Full-scale tests are carried out for the Xjoints under axial tensile and compressive loads. The loaddisplacement curves and load-strain curves are investigated, and the failure modes and ultimate strengths of the joints are analyzed. FEM analysis is then conducted using ABAQUS to simulate the performance of the joints under investigation. The ultimate strengths calculated by different design codes are presented and compared with those of the tests. Based on the experimental and FEM analysis presented in this study, the following conclusions can be made: (1) Under monotonic axial load, failure modes of proposed tubular X-joint mainly include weld failure, upper brace dent and excessive chord deformation. It should be noted that the weld failure is mainly attributed to the complex stress distribution at the vicinity of the welds, which is difficult to be simulated and analyzed by the FEM. (2) Through the load-strain curves and load-displacement curves obtained from tests, both types of proposed X-joints show clear elastic and plastic stage. The safety margin coefficients are consistently larger than 1 under different axial loads, indicating that the proposed tubular joints achieve the expected ultimate strength. (3) The non-linear finite element modeling is verified by test results of the tubular X-joint. The FEM analysis is shown to accurately and reliably predicts behavior of the X-joints under axial loads in terms of load-strain curves, failure modes and ultimate strength. . Moreover, the FEM also provides additional data to investigate the development of stress and deformation in the proposed tubular joints. (4) Several existing codes on tubular X-joints, such as DL, AISCE and EC3, are used to calculate the ultimate strength and compare with the test results. The axial tension capacity of specimens A by AISCE and EC3 are close to the results of tests. For the specimens under axial compression, all three design codes provide good estimation of the strength for specimens A, but underestimate the strength of specimens B. This phenomenon may be attributed to the different connection of the tubular X-joint in the study.

Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jcsr.2019.105780.

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