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Experimental and numerical research on a new semi-rigid joint for single-layer reticulated structures
Engineering Structures 126 (2016) 725–738
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Experimental and numerical research on a new semi-rigid joint for single-layer reticulated structures Huihuan Ma ⇑, Shan Ren, Feng Fan School of Civil Engineering, Harbin Institute of Technology, 202 Haihe Road, Nangang District, Harbin 150090, PR China
a r t i c l e
i n f o
Article history: Received 20 January 2016 Revised 10 August 2016 Accepted 12 August 2016
Keywords: Semi-rigid joint Bolt-column joint Single-layer structure Test Moment-rotation curve Failure mode
a b s t r a c t Recent challenge for large-span single-layer reticulated structures is the development of a new joint that can provide these structures with adequate stiffness while satisfying various important requirements, such as easy assembly on a construction site. In this paper, a new semi-rigid joint system, which is referred to as the bolt-column (BC) joint, is developed. A series of tests was performed considering different thicknesses of the side plates, pretension forces and diameters of the bolts. A three-dimensional finite element (FE) model of the joint was developed to evaluate the bending stiffness, moment resistance, rotational capacity and failure mode of the joint. A comparison between the computations and experiments highlights the degree of accuracy of the proposed FE models. The moment-rotation curves, which can be introduced in the analysis of the structure, were obtained. The stiffnesses, strengths, rotation behaviours, and failure modes of the joints are carefully compared and discussed. Based on the results, the influence rules of the parameters on the mechanical behaviour of the new joint are obtained, which are helpful for engineers and designers. The results indicate that the application of this type of joint in construction practice is promising. The experimental results are employed to calibrate the finite element models, which are used to conduct a parametric study. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Reticulated space structures were traditionally designed assuming that the joints are ideally pinned or completely rigid. However, the majority of the joints in spatial structures have a finite stiffness and are semi-rigid; their actual behaviours do not conform to either of the two extremes. Therefore, Eurocode 3 Part 1.8 [1] recognizes the use of semi-rigid joints in addition to two conventional and idealistic joint systems: rigid systems and pinned systems. Recently, the interest in single-layer spatial structures has significantly increased [2–6]. Considerable efforts were made in previous years to assess the actual responses of reticulated space structures with semi-rigid joints. This process involves an investigation of the mechanical behaviours of traditional semi-rigid joints and the semi-rigidly jointed latticed structures and the development of a design method for latticed spatial structures with semi-rigid joints. First, many studies aim to obtain the momentrotation curves or the associated properties of some traditional existing joints to enable the incorporation of joint stiffness in the structural analysis. Joint systems that are frequently employed in ⇑ Corresponding author. E-mail address: [email protected] (H. Ma). http://dx.doi.org/10.1016/j.engstruct.2016.08.028 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved.
reticulated structures and experimentally and numerically investigated include the aluminium alloy truss connector [7], the bolt-ball joint system [8–14], the space-truss connector [15] and the socket joint system [16]. Second, both numerical and experimental studies have been conducted to investigate the effect of the stiffness of connections on the behaviours of spatial structures. Fathelbab [8] concluded that connection stiffness has a considerable effect on the load-displacement behaviour of a space structure; the safety and economic benefits of a space structure can be achieved if the effect of the joints is properly addressed during design. Observations from a previous study [17,18] confirmed that connection stiffness had a significant effect on the load-displacement behaviour and failure mode of a single-layer spatial structure. The experimental study by Ma et al. [19] concluded that the loading capacity of a single-layer cylindrical reticulated shell with semi-rigid joints falls within the loading capacities of structures with rigid joints and pin joints and that bending stiffness should be considered for analysing single-layer spatial structures. Kato et al. [20] verified that inelastic behaviour in conjunction with the influence of joint semi-rigidness is more important than imperfection sensitivity for domes designed in practice. Previous research is important in the study of the mechanical performance of latticed structures with semi-rigid joints. However,
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Nomenclature d L1 t1 t2 t3 t4 P24 P27 fy fu E M / di lij Sj.ini
bolt diameter distance between two high-strength bolts thickness of front plate thickness of side plate thickness of middle plate thickness of end plate standard preload of M24 bolt according to the code standard preload of M27 bolt according to the code yield strength of the steel material tensile strength of the steel material Young’s modulus of steel material bending moment joint rotation displacements measured at the point i on the specimens distance between the two points i and j on the specimens initial stiffness
two limitations exist in previous studies: (i) when the semi-rigid joints in the previous reference are employed in real structures, the members are usually connected to the ball node by one high strength bolt. Therefore, the stiffnesses of the joints are weak, as shown in [21]; when the structure span is 40 m and the rise to span is 1/8, the critical load of the structure with a semi-rigid bolt-ball joint is only 24% of the critical load of the rigid structure; (ii) The members that are employed in the majority of single-layer latticed structures are circular pipes. Compared with the traditional circular tube, members with H, I and cubic sections are also suitable choices for constructing single-layer lattice structures. However, the majority of semi-rigid joints are designed for circular members. With the exception of the joint in [22,23], few studies have addressed joints that are suitable for connecting H and I section members. Therefore, the main concern of engineering science in recent years is not the problem of structural design methods or analysis models but an appropriate joint design that can provide a structure with adequate stiffness, connect different section pipes, and satisfy other important requirements, such as easy erection and economic advantages. In this paper, a new semi-rigid bolt-column (BC) joint for connecting H, I and rectangular section members is developed, and a series of tests on the new joint system is performed. The basic characteristics of this type of connection, such as the bending stiffness, rotation and moment capacity, and the failure mode are investigated. The results show how the combination of different parameters can improve the stiffness of a joint and its rotational capacity. 2. Bolt-column (BC) joints The bolt-column (BC) joint system is composed of a hollow column node, high-strength bolts, washers, and an end-cone part. It can be used to connect H, I or rectangular members in real structures, as shown in Fig. 1. The end-cone part consist of five plates: one front plate, one middle plate, two side plates and one end plate. The cone parts are welded at both ends of the members in the factory. At the construction site, the two high-strength bolts are used to connect the members to the column node without any welding work. All holes in the hollow column are taped to accommodate the threaded part of the bolts. The two high-strength bolts are screwed into the hollow column node from the end-cone part. One concave washer is employed at each bolted connection; they are placed at the
Sj.pl Minf Msup KR AVG Sj.ini,anal Sj,ini,exp Msup,anal Msup,exp
cM2 fub Ft,Rd Mb Msp H As
post-limit stiffness (=0.1Sj.ini) elastic moment resistance plastic moment resistance knee-range of the M-/ curve; transition zone between the initial and post-limit stiffness average value initial stiffness; numerically obtained initial stiffness; experimentally obtained plastic moment resistance; numerically obtained plastic moment resistance; experimentally obtained partial safety factor for joint (=1.25) ultimate tensile strength for bolts tension resistance of the bolt bending capacity carried by the high-strength bolts plastic moment capacity of the side plates height of the front plate tensile stress area of the bolt
outside of the column node. The washers smoothly transmit axial compressive or tensile force. The high competitiveness of the joining technologies is related to the high bending stiffness, easy assembly, machining reduction, and high speed of construction. 3. Experimental program 3.1. Specimens A total of 14 BC joint specimens were tested to failure under monotonic loading. The configurations of the specimens are shown in Fig. 2 and Table 1. The inner diameter and outer diameter of the column node of all specimens were 200 mm and 300 mm, respectively. For each of the geometrical combinations in Table 1, two specimens were tested. Three main parameters varied among the different sets: (i) The thicknesses of the side plates: three different thicknesses-3.5 mm, 5.5 mm and 9.5 mm-were employed in the specimens S1-A, S2-B and S3-A, respectively, in the tests. (ii) The pretension value in the bolts: the pretension forces P24 = 225 kN for the M24 bolt of class 10.9 were applied in the specimens S1-A, S2-B and S3-A with the specified tightening torques. Considering the actual situation in the construction site, the pretension force in the bolts varied. Therefore, the specimens S2-A, S2-C and S2-D with 1.25P24, 0.75P24, and 0.32P24, respectively, were considered in the tests to investigate the effect of the pretension force on the mechanical behaviours of the joints. (iii) The bolt diameter d1: two different bolt diameters-24 mm and 27 mm-were employed in the test. M24 bolts were used in the specimens in the S1–S3 groups, and M27 bolts were used in the specimens in the S4 group. The larger section of the tube is provided in the test to prevent instability and local buckling in the tube prior to failure of the connections. The steel in the beam member, cone part and washers is grade steel S235. The bolts are frictional high-strength bolts (class 10.9). The material properties of the steel were obtained from tensile tests on coupons and the bolt certificate of quality, as shown in Table 2. The material properties of the plates vary with thickness; therefore, different tensile tests were performed based on different
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Fig. 1. Bolt-column joints.
Fig. 2. Detailed dimensions of specimens.
Table 1 Geometric parameters of specimens. Test ID
Number
S1-A
2
Beam section (mm)
Bolt diameter d (mm)
Bolt distance L1 (mm)
Front plate t1 (mm)
Side plates t2 (mm)
Middle plate t3 (mm)
End plate t4 (mm)
Preload P24 = 225 kN P27 = 290 kN
24
78
30
3.5
5.5
20
P24
24
78
30
5.5
5.5
20
1.25P24
24
78
30
5.5
5.5
20
P24
24
78
30
5.5
5.5
20
0.75P24
24
78
30
5.5
5.5
20
0.32P24
24
78
30
9.5
5.5
20
P24
27
87
30
7.5
5.5
20
P27
160 120 16 16 S2-A
2 160 120 16 16
S2-B
2 160 120 16 16
S2-C
2 160 120 16 16
S2-D
2 160 120 16 16
S3-A
2 160 120 16 16
S4-A
2 180 130 16 16
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Table 2 Material properties. Results of tensile coupon tests. Components
fy (N/ mm2)
fu (N/ mm2)
Young’s modulus E (N/mm2)
fy/fu
Plates in cone part
t2 = 3.5 mm t2 = 5.5 mm t2 = 7.5 mm t2 = 9.5 mm
312.65 303.93 286.57 297.58
470.81 455.58 419.95 413.87
207,053 207,848 202,476 207,882
0.67 0.67 0.68 0.66
Beam Bolts
t = 15.5 mm d = 24 mm
269.00 975.00
406.86 1171.41
205,569 213,302
0.66 0.83
thicknesses of the plates. The material properties are listed according to the thickness.
First, the joint specimens were loaded to a small degree and unloaded to assure proper operation of the loading apparatus and the displacement gauges and enable proper coordination of the different parts of the specimen. Then, the test was performed under force control in the elastic range of the joints. Second, when the joints were loaded to their nonlinear region, the test control was changed to displacement control until failure of the joint. In this phase, the moment-rotation curve of the joint moves from the stiff part to the soft part. During the test, the minimum sustained time of each load increment to ensure a sufficient and stable transformation was ten minutes. 4. Test results and discussion
3.2. Setup and measurement The test setup is shown in Fig. 3. The instrument arrangement and typology were considered to evaluate the main characteristics of the new semi-rigid joints (stiffness, strength, rotation behaviour, and failure mode). The bottom plate of the specimen was employed to fix the specimen on the rigid frame; it is welded to the support beam to prevent slippage. The bending moment at the joint can be applied via the horizontal hydraulic jack. The horizontal hydraulic jack was connected by hinges to the specimen to ensure that it did not provide rotational restraints at the point of their attachment. During the loading process, the measured variables were as follows: The horizontal load was introduced by a hydraulic jack with a loading capacity of 300 kN. The applied horizontal loads were measured by the load cell between the hydraulic jacks and the specimen at each step during loading. The displacements at the points D1–D3, which were measured by linear variable displacement transducers (LVDTs) at each load step, and the displacement value of the front plate at point D4 was measured by a dial indicator. The distances between the LVDTs on the specimen were recorded prior to starting the test. The strains at the side plates (g1/10 -g7/70 ), column node (g8), front plate (g9) and rectangular beams (g10) at each load step were measured by the strain gauges, as shown in Fig. 3. 3.3. Load procedures The positions of the displacement measurement devices need to be recorded to calculate the rotation of the joint. The loading process was controlled as follows:
The test results include the bending stiffnesses, strengths, rotation behaviours, and failure modes of the joints, as well as the influence of various parameters on the mechanical behaviours of the joints. The mechanical behaviours of the semi-rigid connections can be represented by M-/ curves that describe the relationship between the applied bending moment M and the corresponding rotation / of the joint. In this experimental study, the M-/ curves were indirectly established as the values of M and / are calculated based on the readings of the load cells and the displacement transducers. The bending moment M, which acts on the connection, is equivalent to the product of the applied load F and the distance between the load application point and the end plate—460 mm—as shown in Fig. 2. In these tests, the connection rotation / can be calculated based on the level displacements at points D1–D3, which are obtained by the LVDTs in Fig. 3 as
Pn /¼
k¼1 /ij
ð1Þ
n
/ij ¼ arctan
di dj lij
ð2Þ
where di and dj are the displacements measured at points i and j (points D1–D3 in Fig. 3), and lij is the distance between the two points i and j. To obtain accurate data, all values of the distances lij were recorded after the specimens and the measurement devices were installed. The curves reflect the initial bending stiffness, moment resistance and rotation capacity. To provide a convenient method for analysing the experimental results, the following characteristics are assessed for the different specimens by the method in [16], as shown in Fig. 4.
Fig. 3. Test setup for the BC joints.
Moment (kN⋅m)
H. Ma et al. / Engineering Structures 126 (2016) 725–738
M sup
S j.in
S j.p-l
B Knee-range KR
M inf A Connection rotation (rad)
φinf
φsup Fig. 4. Main features of the M-/ curve.
4.1. Effect of side plates’ thicknesses on the mechanical behaviours of the BC joint The influence of the thicknesses of the side plates on the total behaviours of the BC joints was investigated. The three different
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thicknesses of the side plates, including 3.5 mm, 5.5 mm and 9.5 mm, were employed in the test. All specimens were tested to failure, indicating the excessive deformation of the specimens, which is a distinct nonlinearity, and that plasticity had significantly developed and the deformation of the specimen continued to increase without additional loading; thus, the specimen is not suitable for additional loading, as shown in Fig. 5. The M-/ curves for the six BC joints subjected to bending are plotted in Fig. 6. In the figure, the plastic moment resistance Msup for each curve is marked, and the deformation of the joint at this step is also indicated. The following observations were noted: (i) the response of the connection exhibits linear behaviour in the early loading sequence and subsequent nonlinearity, which embodies typical elasto-plastic behaviour; (ii) the side plates of the S1-A and S2-B joints exhibited large deformation at the step when the bending is equivalent to the plastic moment resistance Msup; subsequently, the bending decreases with an increase in rotation; (iii) when the bending is equivalent to the plastic moment resistance Msup, the deformation of the side plates of S3-A joints was small and the bending continued to increase after the plastic moment resistance Msup. The main features of the M-/ curves and the failure model of the six joints are summarized in Table 3. The major difference among the joints is the thicknesses of the side plates. The results indicate that the initial stiffness Sj,ini, the elastic flexural resistance
Fig. 5. Picture of the test.
Fig. 6. Moment-rotation response of the joints with different thicknesses of the side plates.
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Minf, the plastic moment resistance Msup, and the knee-range KR distinctly increase with an increase in the thicknesses of the side plates. The elastic flexural resistance Minf of S3-A is almost four times the Minf of S1-A, and the plastic moment resistance Msup of S3-A is more than twice the Msup of S1-A. The bending-stress curves of the joints in Fig. 7 show that the side plates of the S1-A specimens did not yield when the bending reached Minf and Msup. The locations monitored by the strain gauges 1 and 3–7 at the side plates of S2-B specimens yield when the bending reached approximately Msup. The entire side plates of the S3-A specimens yield before the bending reached Minf. Therefore, the failure mode of S1-A, as listed in Table 3, was caused by the sudden buckling of the thin side plates. For S3-A specimens, the side plates yield when the bending increases to a certain value, and the concave deformation gradually increases. The situation for the S2-A specimens falls between the situation for the specimens S1-A and S3-A.
Based on the displacement value of the front plate at point D4, which was measured by a dial indicator (as shown in Fig. 3), the deformation of the high-strength bolt at the tensional side was obtained, and the stress of the tensional bolt was calculated. The curves and the deformation figures are shown in Fig. 8: (i) the deformations of the tension bolts in the S1-A and S2-B specimens is small under the bending moment, and the deformation is linear. The deformations of the tension bolts in the specimens S1-A and S2-B specimens attained the values 0.17 mm and 0.48 mm, respectively, when the bending attained the plastic moment resistance Msup. The largest gap between the front plate and the column node of the S2-B specimens was small, and almost no gap formed between the front plate and the column node of the S1-A specimens during the loading process, as shown in Fig. 8; (ii) With an increase in the side plate’s thickness, the deformation of the tension bolts increase. When the thickness of the side plates is 9.5 mm, the tension bolt undergoes elastic-plastic deformation,
Table 3 Main characteristics of bending moment-rotation curves of the joints with different thicknesses of the side plates. Specimens
Sj.in (kN m/rad)
Minf (kN m)
Sj.pl (kN m/rad)
Msup (kN m)
KR (kN m)
S1-A-1 S1-A-2 AVG
1454.02 1344.97 1399.50
5.55 5.55 5.55
145.40 134.50 139.95
10.26 10.06 10.16
4.71 4.51 4.61
2329.11 2260.31 2294.71
11.34 11.38 11.36
232.91 226.03 229.47
17.82 17.52 17.67
6.48 6.41 6.45
3220.73 3202.66 3211.70
19.49 19.74 19.62
322.07 320.27 321.17
28.71 28.42 28.57
9.22 8.68 8.95
Failure mode
S2-B-1 S2-B-2 AVG Failure mode
S3-A-1 S3-A-2 AVG Failure mode
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500 400
t=3.5mm; fy=312.65MPa
200
100 Msup=10.26kN⋅m
Minf=5.55kN⋅m 2
4
6
8
10
12
14
Moment M (kN⋅m)
-100 -200
-500
100 0
3
6
9
Msup=17.82kN⋅m Minf=11.34kN⋅m 12 15 18 21
-100
Moment M (kN⋅m)
-200
2 3 4 5
-300 -400
t=5.5mm; fy=303.93MPa
300
200
0
1 6 7
Compression side
400
Stress (MPa)
Stress (MPa)
300
500
1 6 7
Compression side
t=3.5mm; fy=-312.65MPa
Tension side
-300
t=5.5mm; fy=-303.93MPa
-400 -500
Tension side
(a) S1-A-1
2 3 4 5
(b) S2-B-1
500
Compression side
400 t=9.5mm; fy=297.58MPa
300
1 6 7
Stress (MPa)
200 100
Minf=19.74kN⋅m Msup=28.42kN⋅m
0
5
10
15
20
-100
25
30
Moment M (kN⋅m)
-200 -300
t=9.5mm; fy=-297.58MPa
-400 -500
Tension side
2 3 4 5
(c) S3-A-1 Fig. 7. Moment-stress curves of the joints with different thicknesses of the side plates.
Deformation (mm)
2.0
S1-A S2-B S3-A
1.5 1.0 0.5
1
1.95mm
0.80mm
2
0.48mm 0.36mm 0.17mm
0.0
3
Msup=28.42kN⋅m
Msup=17.82kN⋅m
Msup=10.26kN⋅m
-0.5 0
10
20
30
40
Moment M (kN·m) Fig. 8. Stress value and deformation figure of the tensional bolt in the joints with different thicknesses of the side plates.
and the final maximum deformation value is 1.95 mm. The final gap between the front plate and the column node of the S3-A specimens was distinct. The results reveal that the bolts may have failed before the side plate yields with the increase in the thicknesses of the side plates. The failure modes of the high-strength bolts is primarily brittle, and the connections incur fatal damage after failure. Thus, failure of the high-strength bolts should be avoided in the connection
design. Increasing the thickness of the side plates can improve the mechanical behaviours of the BC joints, including the bending stiffness, the elastic flexural resistance Minf, the plastic moment resistance Msup. If the side plates are too thin, the bending stiffnesses and ultimate moment strengths of the joints will be low; if the side plate are too thick, fractures may occur in the bolts before the side plate yields. Fracture of the bolts will cause the brittle failure of all joints, and the joints cannot enter the plastic
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yielding phase prior to failure. To achieve better bending stiffness, moment capacity and ductility, the thickness should be properly determined. According to Eurocode 3 [1], the tension resistance Ft,Rd of the high-strength bolt can be calculated by the following equation:
F t;Rd ¼
0:9f ub As
ð1Þ
cM2
To ensure that unwanted brittle failure modes do not control, the bending capacity carried by the bolts should be larger than the bending capacity carried by the side plates.
M b ¼ F t;Rd L1 < M sp ¼ W p1f y
ð2Þ
where Mb is the bending capacity carried by the high-strength bolts; Msp is the plastic moment capacity of the side plates; L1 is the dis2
tance of the two bolts; W p1 ¼ 2 t24H is the relevant plastic modulus of the section of the side plates; and t2 and H are the thickness of the side plate and the height of the side plate, respectively. Based on Eqs. (1) and (2), the maximum thickness of the side plate can be determined by the following relationship:
t2 <
1:8f ub As f y cM2 H2
ð3Þ
L1
4.2. Effect of the pretension force in the bolts on the mechanical behaviour of the BC joint All component parts of the bolt-column joints are fabricated in the factory; at the construction site, two high-strength bolts are used to connect the members to the column node without any welding work. In this paper, the specimens S2-A, S2-B, S2-C and S2-D with different pretension values 1.25P24, P24, 0.75P24, and 0.32P24, respectively, were tested to investigate the effect of the pretension force in the bolts on the mechanical behaviours of the BC joints. The M-/ curves for the four joints with different pretension forces are plotted in Fig. 9. In the figure, the plastic moment resistance Msup for each curve is marked, and the deformation of the joint at this step is shown. The main features of the M-/ curves and the failure model of the eight joints are summarized in Table 4. The results indicate that (i) all M-/ curves of the connection with different pretension forces in the bolts exhibit typical
elasto-plastic behaviour; the deformation of the joints are similar at the step of the plastic moment resistance Msup, as shown in Fig. 9; (ii) when the pretension varied among 0.75P24–1.25P24, the initial bending stiffness, the elastic flexural resistance Minf, and the plastic moment resistance Msup of the joints exhibited minimal variation, whereas the knee-range of the M-/ curve KR exhibited a distinct decrease with an increase in the pretension force in the bolts. For the S2-A specimen, in which the pretension force is 1.25P24, the curve significantly decreased after the plastic moment resistance Msup, as shown in Fig. 9; (iii) when the pretension decreased to 0.32P24, the initial bending stiffness decreased approximately 16.4% compared with the joints with pretension P24. The elastic flexural resistance Minf and the plastic moment resistance Msup of the joints exhibited a minimal decrease, whereas the knee-range of the M-/ curve KR increased compared with the joints with a pretension force range of 0.75P24–1.25P24. Although the effect of the pretension value of 0.32P24 is larger than other pretension forces, the value is too low for the class 10.9 bolt and not typical for a realistic structure. The value of 0.32P24 is employed in this study to investigate the effect of the pretension in the bolts on the mechanical behaviours of the joints. The deformation of the high-strength bolt at the tension side was obtained; the curves are given in Fig. 10. The figure indicates that the deformation curves of the tension bolts in the specimens with different pretension forces are linear; the higher is the pretension force in the bolt, the smaller is the gap between the front plate and the column node. Therefore, the initial stiffnesses of the joints increases with an increase of the pretension force in the bolts. From the moment-stress curves of the joints shown in Fig. 11, the stresses on the side plates of the joints, in which the pretension force is 1.25P24, are lower than the stresses on the side plates of the joints with smaller pretension forces. The stresses on the side plates of the S2-A specimens did not yield when the bending reached Msup, and the locations monitored by strain gauges 3–7 of the side plates of the specimens S2-B, S2-C and S2-D yield when the bending reached approximately Msup. 4.3. Effect of bolt diameter on the mechanical behaviour of the BC joint The high-strength bolts are important component parts of the joint system. To study the effect of the diameters of the bolts on the mechanical behaviours of the BC joints, two different diameters of the bolts-24 mm (M24) and 27 mm (M27)-were considered in
Bending moment M (kN·m)
25
20
15
S2-A S2-B S2-C S2-D
10
5
0 0.00
0.02
0.04
0.06
0.08
Rotation φ (rad) Fig. 9. Moment-stress curves of the joints with different pretension forces.
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H. Ma et al. / Engineering Structures 126 (2016) 725–738 Table 4 Main characteristics of moment-rotation curves of the joints with different pretension forces. Specimens
Sj.ini (kN m/rad)
Minf (kN m)
Sj.pl (kN m/rad)
Msup (kN m)
KR (kN m)
S2-A-1 S2-A-2 AVG Failure mode
2282.56 2367.08 2324.82
11.92 13.01 12.47
228.26 236.71 232.49
16.74 16.94 16.84
4.82 3.93 4.38
S2-B-1 S2-B-2 AVG Failure mode
2329.11 2260.31 2294.71
11.34 11.38 11.36
232.91 226.03 229.47
17.82 17.52 17.67
6.48 6.41 6.45
S2-C-1 S2-C-2 AVG Failure mode
2179.63 2203.38 2191.51
12.02 11.14 11.58
217.96 220.34 219.15
17.42 17.51 17.47
5.40 6.10 5.75
S2-D-1 S2-D-2 AVG Failure mode
1878.94 1960.91 1919.93
10.36 9.37 9.87
187.89 196.09 191.99
17.38 17.41 17.40
7.02 8.04 7.53
the test. The M-/ curves for the six joints are plotted in Fig. 12. The main features of the M-/ curves and the failure models of the joints S4-A with M27 bolts are summarized in Table 5; the failure models of the joints S3-A with M24 bolts are listed in Table 3. Compared with the thickness (9.5 mm) of each side plate in S3-A with M24 bolts, the thickness (7.5 mm) of each side plate in S4-A with M27 bolts is smaller. The results indicate that the initial bending stiffness of S4-A with M27 bolts is 12.4% higher than the initial bending stiffness of S3-A with M24 bolts. The elastic flexural resistance Minf, plastic moment resistance Msup and knee-range KR of the joints also improved when the diameters of the high-strength bolts
increase. Therefore, the effect of the diameters of the bolts on the mechanical behaviour of the BC joint is significant. 4.4. Discussion of the effect of initial imperfections The results reveal that the M-/ curves of the two specimens of one joint are not consistent despite their proximity to each other. Some failure modes of the two specimens of one joint are not identical, and the deformation of the two side plates in S2-B-1 is asymmetric, as shown in Fig. 13. The reasons for these differences may be attributed to the existence of residual stresses and deformation
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0.8
Deformation (mm)
Msup=17.43 kN·m
0.58mm 0.55mm 0.49mm
0.6
0.4
3 4 2
Msup=17. 38 kN·m
Msup=17.68 kN·m
0.36mm
1
Msup=16.74 kN·m
S2-A S2-B S2-C S2-D
0.2
0.0 0
5
10
15
20
25
Bending moment M (kN·m) Fig. 10. Deformation of the tension bolts in the joints with different pretension forces.
Compression side
400 t=5.5mm;fy=303.93MPa
Stress (MPa)
300
500
1 6 7
Msup=16.74kN⋅m
0
M (kN⋅m)
-100 -200
1 6 7
200 100
Minf=12.02kN⋅m Msup=17.42kN⋅m
0
M (kN⋅m)
-100 -200
-300
-300
2 3 4 5
t=5.5mm;fy=-303.93MPa
-400 -500
t=5.5mm;fy=303.93MPa
300
200 100
Compression side
400
Stress (Mpa)
500
Tension side
t=5.5mm;fy=-303.93MPa
-400 -500
Tension side
(a) S2-A-1 500
(b) S2-C-1
Compression side
400
1 6 7
t=5.5mm;fy=303.93MPa
300
Stress (Mpa)
2 3 4 5
200 100 Minf=10.36kN⋅m
0
Msup=17.38kN⋅m
M (kN⋅m)
-100 -200 -300 -400 -500
t=5.5mm;fy=-303.93MPa Tension side
2 3 4 5
(c) S2-D-1 Fig. 11. Bending moment-stress curves of the joints with different pretension forces.
caused by the welding work in the cone part, and a machining error and installation error may occur during fabrication and installation of the joint, such as defects with different sizes, overfit, bolt tightness and friction.
5. Finite element model The mechanical behaviour of the bolt-column connections substantially changes with different geometric parameters and
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50
Moment M (kN·m)
40
S4-A-2 S4-A-3
1(29.97/30.31 kN⋅m)
30
S3-A-1 S3-A-2
2 (28.42/28.71 kN⋅m)
20 10 0 0.00
0.02
0.04
0.06
0.08
0.10
0.12
Rotation φ (rad) Fig. 12. Moment-stress curves of the joints with different bolt diameters.
Table 5 Main characteristics of moment-rotation curves of the joints with different bolt diameters. Specimens
Sj.in (kN m/rad)
Minf (kN m)
Sj.pl (kN m/rad)
Msup (kN m)
KR (kN m)
S2-B S3-A S4-A-1 S4-A-2 AVG Failure mode
2294.71 3211.70 3643.26 3574.16 3608.71
11.36 19.62 20.40 19.20 19.80
229.47 321.17 364.33 357.42 360.88
17.67 28.57 29.97 30.31 30.14
6.45 8.95 9.57 11.11 10.34
Fig. 13. Different failure modes of the joints with identical parameters.
different loading conditions. Assessing their behaviours solely based on experimental investigations is a cost-prohibitive and time-consuming task. Therefore, the use of appropriately validated FE models represents an attractive approach for the future development of a characteristic database for a new joint. These numerical simulations can also offer valuable insight into the component interactions that occur within semi-rigid joints, which is difficult to measure during a test. In this paper, three-dimensional FE models are established using the commercial FEA software ABAQUS [24]; the results are validated against the experimental data. 5.1. Proposed modelling approach The three-dimensional finite element model has the same configuration and dimensions of the tested specimens. The entire
experimental joint, including the column node, the cone part, the bolts and the rectangular member, is modelled with eight-node solid elements C3D8R, which are available in the ABAQUS library [24]. The numerical models incorporated a number of detailed features, such as contact phenomena, bolt slippage definition and bolt pretension application, as described in the next section. – Contact surfaces Surface-to-surface contact interactions are defined between two parts in the FE models with a self-contact element and a surface-to-surface contact element, such as the front plate and the column node, the bolt surfaces and the screw hole, and the washers, the front plate and the nut of the bolts. The contact
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Fig. 14. FE model and contact surface setting of the BC joints.
properties that correspond to these surfaces are defined in the normal direction, which enables surfaces to be separated after contact has occurred. The coefficient of friction for the contact surfaces in the BC joints is assumed to be 0.4 (as defined in the steel joint systems [25]). – Bolt slippage and pretension Special attention was paid to faithful modelling of the geometric details of the 2 mm space between the bolt shanks and the screw holes, according to the code [1]. When assembling the test specimens, the pretension force is generated in the joint by tightening the bolt with wrenches. In the FE models, the pretension force in the joint is defined according to the real value measured during the test. – Mesh method A number of mesh sensitivity studies were performed to arrive at an optimum representation, which involves a comparatively finer mesh for the cone part, bolts and washers, as well as the areas within the column node and members in contact with these components, whereas a relatively coarser mesh was employed elsewhere. The dimensions of the elements within the final adopted mesh ranged between 6 mm within the refined region to 100 mm within the coarser region. The boundary conditions and loading procedure that were adopted in the numerical analyses replicated the boundary conditions and loading procedure employed in the experimental studies: the column node is fixed and the forces act on the end of the member. Fig. 14 shows the model mesh, the contact setting, the boundary condition and the force locations for the joints.
5.2. Material properties Based on the coupon test results listed in Table 2, the stressstrain relationship for the different parts of the joints is modelled for the nonlinear analysis as an elasto-plastic material with a strain hardening and yielding plateau beyond the elastic phase. It is assigned a three-linear stress-strain law—symmetrical in tension and compression—as shown in Fig. 15. 6. Comparison of the results from the FE models and experiments A total of 14 tests, which were conducted based on different pretension forces, thicknesses of the side plates and diameters of the bolts, are employed to validate the FE model. The real initial geometric imperfections of the side plates are considered for all joints during the numerical simulation. The moment-rotation curves that are obtained via FE models and tests are shown in Fig. 16. The definition and calculation method of the rotation deformation / is identical for all tests. Similar curves are numerically and experimentally obtained. The numerical curve describes the experimental results with acceptable approximation. The numerical curves of the specimens in groups S1 and S2 is slightly higher than the numerical curves that were experimentally obtained after the plastic flexural resistance. This variation can be attributed to the sudden buckling that occurred on the compression side of the thin side plates of the experimental specimens. Table 6 shows the comparison between the numerical results and the experimental results in terms of initial stiffness (Sj,in) and plastic moment resistance (Msup). In particular, the FE model reveals that the plastic moment resistance of the joints is consistent with the experimental results, and the difference is less than
䠄㻜㻚㻜㻟㻣㻥䠈 㻠㻡㻡㻚㻡㻤㻌㻹 㻼㼍䠅
Stress (MPa)
Stress (MPa)
䠄㻜㻚㻜㻟㻡㻞䠈 㻝㻝㻣㻝㻚㻠㻝㻌㻹 㻼㼍䠅 䠄㻜㻚㻜㻜㻠㻡㻣䠈 㻥㻣㻡㻌㻹 㻼㼍䠅
Strain
(a) stress-strain curve for bolts
䠄㻜㻚㻜㻜㻝㻠㻢䠈 㻟㻜㻟㻚㻥㻟㻌㻹 㻼㼍䠅
Strain
(b) stress-strain curve for S2-B side plates
Fig. 15. Stress-strain behaviours of the joint’s components.
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Fig. 16. Moment-rotation and failure mode comparison of the joints.
Table 6 Comparison of the main characteristics of bending moment-rotation curves. Specimens
Sj.ini,anal (kN m/rad)
Sj.ini,exp (kN m/rad)
Sj;ini;exp Sj;ini;anal Sj;ini;exp
Msup,anal (kN m)
Msup,exp (kN m)
Msup;exp Msup;anal M sup;exp
S1-A S2-A S2-B S2-C S2-D S3-A S4-A
1551.65 2314.72 2292.84 2243.32 2043.78 3262.39 3841.75
1454.02 2282.56 2260.31 2179.63 1878.94 3202.66 3643.26
6.71% 1.41% 1.44% 2.92% 8.44% 1.86% 5.45%
10.30 16.57 17.58 17.39 17.12 28.06 30.79
10.46 16.74 17.52 17.43 17.28 28.77 30.86
1.53% 1.02% 0.34% 0.23% 0.93% 2.47% 0.27%
Sj.in,anal and Msup,anal is the initial bending stiffness and plastic flexural resistance obtained by numerical models, Sj.in,exp and Msup,exp is the initial bending stiffness and plastic flexural resistance obtained by tests.
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3%. The majority of the differences of the initial stiffness is less than 3%, with the exception of the specimens S1-A(6.71%), S2-D (8.44%) and S4-A(5.45%). Therefore, the FE models are effective and convenient for evaluating the moment-rotation curves. The reliability of the FE models is proven by the agreement between the numerical deformed configuration at failure and the numerical deformed configuration observed after the tests, as shown in Fig. 16.
Acknowledgements This research is supported by grants from the Natural Science Foundation of China (Grant No. 51308153), the China Postdoctoral Science Foundation funded project (Grant No. 2013M531020 and Grant No. 2014T70346), and The National Science Fund for Distinguished Young Scholars (Grant No. 51525802). References
7. Conclusions A series of experiments was conducted on BC joints under monotonic loading to investigate the mechanical behaviour of the new joint system, which can be employed in single-layer structures. The experimental programme enabled a direct assessment of the influence of a number of main considerations, such as the thicknesses of the side plates, pretension forces and diameters of the bolts. In addition, a three-dimensional FE model was developed to simulate the behaviour of the BC joints. Consistency with the experimental results confirms that the detailed FE models are able to simulate the mechanical behaviour of BC joints with reasonable accuracy. The M-/ curves and failure modes of the joints are obtained based on different parameters. The results are compared and discussed. The conclusions of this study are as follows: (1) The new BC joint system exhibits an adequate bending stiffness and bending capacity. The response of the connection embodies a typical elasto-plastic behaviour under a bending moment. (2) The initial stiffness Sj,ini, the elastic flexural resistance Minf, the plastic moment resistance Msup, and the knee-range KR of the joint can be significantly improved with an increase in the thickness of the side plates. However, high-strength bolt fracture may occur when the thickness of the side plates in the joints is excessive. Therefore, the maximum thickness of the side plate was developed based on the bolt diameters in the joints to achieve a higher stiffness and moment capacity and to avoid brittle failure. (3) For the joints under a bending moment, the effect of the pretension force on the mechanical behaviours of the joints is small. With an increase in the tension in the bolts, the initial bending stiffness of the joints slightly increases at the cost of slightly decreasing the plastic moment resistance Msup and decreasing the knee-range KR. According to the experimental results, the tension value P24 = 225 kN for the joints with M24 bolts is better than other values. (4) Increasing the diameter of the bolts can significantly improve the initial bending stiffness of the joints; and the elastic flexural resistance Minf, plastic moment resistance Msup and knee-range KR of the joints also slightly improve when the diameter of the high-strength bolts increases. (5) Some initial imperfections, such as residual stresses and deformation and machining and installation errors, may cause a slight difference in the M-/ curves and failure mode of the two specimens of one joint.
[1] CEN. Eurocode 3: design of steel structures. Part 1. 8: design of joints (EN 1993-1-8); 2005. [2] Kato S, Kim JM, Cheong MC. A new proportioning method for member sections of single layer reticulated domes subjected to uniform and non-uniform loads. Eng Struct 2003;25:1265–78. [3] Han QH, Liu XL. Ultimate bearing capacity of the welded hollow spherical joints in spatial reticulated structures. Eng Struct 2004;26:73–82. [4] Bruno L, Sassone M, Venuti F. Effects of the Equivalent Geometric Nodal Imperfections on the stability of single layer grid shells. Eng Struct 2016;112:184–99. [5] Yan JC, Qin F, Cao ZG, Fan F, Mo YL. Mechanism of coupled instability of singlelayer reticulated domes. Eng Struct 2016;114:158–70. [6] Liu HJ, Zhang W, Yuan H. Structural stability analysis of single-layer reticulated shells with stochastic imperfections. Eng Struct 2016;124:473–9. [7] Hiyama Y, Takashima H, Iijima T, Kato S. Buckling behaviour of aluminium ball jointed single layered reticular domes. Int J Space Struct 2000;15(2):81–94. [8] Fathelbab FA. The effect of joints on the stability of shallow single layer lattice domes Ph.D. Thesis. Cambridge: University of Cambridge; 1987. [9] López A, Puente I, Serna MA. Numerical model and experimental tests on single-layer latticed domes with semi-rigid joints. Comput Struct 2007;85:360–74. [10] Ma HH, Fan F, Shen SZ. Numerical parametric investigation of single-layer latticed domes with semi-rigid joints. J IASS 2008;49(2):99–110. [11] Lee SL, See T, Swaddiwudhipong S. Development and testing of a universal space frame connector. Int J Space Struct 1990;5(2):130–8. [12] Swaddiwudhipong S, Koh CG, Lee SL. Development and experimental investigation of a space frame connector. Int J Space Struct 1994;9(2):99–106. [13] Shibata R, Kato S, Yamada S. Experimental study on the ultimate strength of single-layer reticular domes. In: Proceedings of the fourth international conference of space structures. UK: University of Surry; 1993. p. 387–95. [14] Ueki T, Matsushita F, Shibata, Kato S. Design procedure for large single-layer latticed domes. In: Proceedings of the fourth international conference of space structures. UK: University of Surry; 1993. p. 237–46. [15] Fulop A, Ivanyi M. Experimentally analyzed stability and ductility behaviour of a space-truss roof system. Thin Wall Struct 2004;42:309–20. [16] Fan F, Ma HH, Chen GB, Shen SZ. Experimental study of semi-rigid joint systems subjected to bending with and without axial force. J Constr Steel Res 2012;68(1):126–37. [17] See T. Large displacement elastic buckling space structures Ph.D. Thesis. Cambridge: University of Cambridge; 1983. [18] López A, Puente I, Serna MA. Direct evaluation of the buckling loads of semirigidly jointed single-layer latticed domes under symmetric loading. Thin Wall Struct 2007;29:101–9. [19] Ma HH, Fan F, Wen P, Zhang H, Shen SZ. Experimental and numerical studies on a single-layer cylindrical reticulated shell with semi-rigid joints. Thin Wall Struct 2015;86(1):1–9. [20] Kato S, Mutoh I, Shomura M. Collapse of semi-rigidly jointed reticulated domes with initial geometric imperfections. J Constr Steel Res 1998;48:145–68. [21] Ma HH, Fan F, Zhong J, Shen SZ. Stability analysis of single-layer elliptical paraboloid latticed shells with semi-rigid joints. Thin Wall Struct 2013;72 (1):128–38. [22] Lopez A, Puente I, Aizpurua H. Experimental and analytical studies on the rotational stiffness of joints for single-layer structures. Eng Struct 2011;33 (12):731–7. [23] Ma HH, Ren S, Fan F. Parametric study and analytical characterization of the bolt–column (BC) joint for single-layer reticulated structures. Eng Struct 2016;123:108–23. [24] ABAQUS/CAE. Hibbit, Karlsson & Sorensen Inc; 2005. [25] Maggi YI, Gonçalves RM, Leon RT, Ribeiro LFL. Parametric analysis of steel bolted end plate connections using finite element modeling. J Constr Steel Res 2005;61:689–708.
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Experimental and numerical research on a new semi-rigid joint for single-layer reticulated structures Huihuan Ma ⇑, Shan Ren, Feng Fan School of Civil Engineering, Harbin Institute of Technology, 202 Haihe Road, Nangang District, Harbin 150090, PR China
a r t i c l e
i n f o
Article history: Received 20 January 2016 Revised 10 August 2016 Accepted 12 August 2016
Keywords: Semi-rigid joint Bolt-column joint Single-layer structure Test Moment-rotation curve Failure mode
a b s t r a c t Recent challenge for large-span single-layer reticulated structures is the development of a new joint that can provide these structures with adequate stiffness while satisfying various important requirements, such as easy assembly on a construction site. In this paper, a new semi-rigid joint system, which is referred to as the bolt-column (BC) joint, is developed. A series of tests was performed considering different thicknesses of the side plates, pretension forces and diameters of the bolts. A three-dimensional finite element (FE) model of the joint was developed to evaluate the bending stiffness, moment resistance, rotational capacity and failure mode of the joint. A comparison between the computations and experiments highlights the degree of accuracy of the proposed FE models. The moment-rotation curves, which can be introduced in the analysis of the structure, were obtained. The stiffnesses, strengths, rotation behaviours, and failure modes of the joints are carefully compared and discussed. Based on the results, the influence rules of the parameters on the mechanical behaviour of the new joint are obtained, which are helpful for engineers and designers. The results indicate that the application of this type of joint in construction practice is promising. The experimental results are employed to calibrate the finite element models, which are used to conduct a parametric study. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Reticulated space structures were traditionally designed assuming that the joints are ideally pinned or completely rigid. However, the majority of the joints in spatial structures have a finite stiffness and are semi-rigid; their actual behaviours do not conform to either of the two extremes. Therefore, Eurocode 3 Part 1.8 [1] recognizes the use of semi-rigid joints in addition to two conventional and idealistic joint systems: rigid systems and pinned systems. Recently, the interest in single-layer spatial structures has significantly increased [2–6]. Considerable efforts were made in previous years to assess the actual responses of reticulated space structures with semi-rigid joints. This process involves an investigation of the mechanical behaviours of traditional semi-rigid joints and the semi-rigidly jointed latticed structures and the development of a design method for latticed spatial structures with semi-rigid joints. First, many studies aim to obtain the momentrotation curves or the associated properties of some traditional existing joints to enable the incorporation of joint stiffness in the structural analysis. Joint systems that are frequently employed in ⇑ Corresponding author. E-mail address: [email protected] (H. Ma). http://dx.doi.org/10.1016/j.engstruct.2016.08.028 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved.
reticulated structures and experimentally and numerically investigated include the aluminium alloy truss connector [7], the bolt-ball joint system [8–14], the space-truss connector [15] and the socket joint system [16]. Second, both numerical and experimental studies have been conducted to investigate the effect of the stiffness of connections on the behaviours of spatial structures. Fathelbab [8] concluded that connection stiffness has a considerable effect on the load-displacement behaviour of a space structure; the safety and economic benefits of a space structure can be achieved if the effect of the joints is properly addressed during design. Observations from a previous study [17,18] confirmed that connection stiffness had a significant effect on the load-displacement behaviour and failure mode of a single-layer spatial structure. The experimental study by Ma et al. [19] concluded that the loading capacity of a single-layer cylindrical reticulated shell with semi-rigid joints falls within the loading capacities of structures with rigid joints and pin joints and that bending stiffness should be considered for analysing single-layer spatial structures. Kato et al. [20] verified that inelastic behaviour in conjunction with the influence of joint semi-rigidness is more important than imperfection sensitivity for domes designed in practice. Previous research is important in the study of the mechanical performance of latticed structures with semi-rigid joints. However,
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Nomenclature d L1 t1 t2 t3 t4 P24 P27 fy fu E M / di lij Sj.ini
bolt diameter distance between two high-strength bolts thickness of front plate thickness of side plate thickness of middle plate thickness of end plate standard preload of M24 bolt according to the code standard preload of M27 bolt according to the code yield strength of the steel material tensile strength of the steel material Young’s modulus of steel material bending moment joint rotation displacements measured at the point i on the specimens distance between the two points i and j on the specimens initial stiffness
two limitations exist in previous studies: (i) when the semi-rigid joints in the previous reference are employed in real structures, the members are usually connected to the ball node by one high strength bolt. Therefore, the stiffnesses of the joints are weak, as shown in [21]; when the structure span is 40 m and the rise to span is 1/8, the critical load of the structure with a semi-rigid bolt-ball joint is only 24% of the critical load of the rigid structure; (ii) The members that are employed in the majority of single-layer latticed structures are circular pipes. Compared with the traditional circular tube, members with H, I and cubic sections are also suitable choices for constructing single-layer lattice structures. However, the majority of semi-rigid joints are designed for circular members. With the exception of the joint in [22,23], few studies have addressed joints that are suitable for connecting H and I section members. Therefore, the main concern of engineering science in recent years is not the problem of structural design methods or analysis models but an appropriate joint design that can provide a structure with adequate stiffness, connect different section pipes, and satisfy other important requirements, such as easy erection and economic advantages. In this paper, a new semi-rigid bolt-column (BC) joint for connecting H, I and rectangular section members is developed, and a series of tests on the new joint system is performed. The basic characteristics of this type of connection, such as the bending stiffness, rotation and moment capacity, and the failure mode are investigated. The results show how the combination of different parameters can improve the stiffness of a joint and its rotational capacity. 2. Bolt-column (BC) joints The bolt-column (BC) joint system is composed of a hollow column node, high-strength bolts, washers, and an end-cone part. It can be used to connect H, I or rectangular members in real structures, as shown in Fig. 1. The end-cone part consist of five plates: one front plate, one middle plate, two side plates and one end plate. The cone parts are welded at both ends of the members in the factory. At the construction site, the two high-strength bolts are used to connect the members to the column node without any welding work. All holes in the hollow column are taped to accommodate the threaded part of the bolts. The two high-strength bolts are screwed into the hollow column node from the end-cone part. One concave washer is employed at each bolted connection; they are placed at the
Sj.pl Minf Msup KR AVG Sj.ini,anal Sj,ini,exp Msup,anal Msup,exp
cM2 fub Ft,Rd Mb Msp H As
post-limit stiffness (=0.1Sj.ini) elastic moment resistance plastic moment resistance knee-range of the M-/ curve; transition zone between the initial and post-limit stiffness average value initial stiffness; numerically obtained initial stiffness; experimentally obtained plastic moment resistance; numerically obtained plastic moment resistance; experimentally obtained partial safety factor for joint (=1.25) ultimate tensile strength for bolts tension resistance of the bolt bending capacity carried by the high-strength bolts plastic moment capacity of the side plates height of the front plate tensile stress area of the bolt
outside of the column node. The washers smoothly transmit axial compressive or tensile force. The high competitiveness of the joining technologies is related to the high bending stiffness, easy assembly, machining reduction, and high speed of construction. 3. Experimental program 3.1. Specimens A total of 14 BC joint specimens were tested to failure under monotonic loading. The configurations of the specimens are shown in Fig. 2 and Table 1. The inner diameter and outer diameter of the column node of all specimens were 200 mm and 300 mm, respectively. For each of the geometrical combinations in Table 1, two specimens were tested. Three main parameters varied among the different sets: (i) The thicknesses of the side plates: three different thicknesses-3.5 mm, 5.5 mm and 9.5 mm-were employed in the specimens S1-A, S2-B and S3-A, respectively, in the tests. (ii) The pretension value in the bolts: the pretension forces P24 = 225 kN for the M24 bolt of class 10.9 were applied in the specimens S1-A, S2-B and S3-A with the specified tightening torques. Considering the actual situation in the construction site, the pretension force in the bolts varied. Therefore, the specimens S2-A, S2-C and S2-D with 1.25P24, 0.75P24, and 0.32P24, respectively, were considered in the tests to investigate the effect of the pretension force on the mechanical behaviours of the joints. (iii) The bolt diameter d1: two different bolt diameters-24 mm and 27 mm-were employed in the test. M24 bolts were used in the specimens in the S1–S3 groups, and M27 bolts were used in the specimens in the S4 group. The larger section of the tube is provided in the test to prevent instability and local buckling in the tube prior to failure of the connections. The steel in the beam member, cone part and washers is grade steel S235. The bolts are frictional high-strength bolts (class 10.9). The material properties of the steel were obtained from tensile tests on coupons and the bolt certificate of quality, as shown in Table 2. The material properties of the plates vary with thickness; therefore, different tensile tests were performed based on different
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Fig. 1. Bolt-column joints.
Fig. 2. Detailed dimensions of specimens.
Table 1 Geometric parameters of specimens. Test ID
Number
S1-A
2
Beam section (mm)
Bolt diameter d (mm)
Bolt distance L1 (mm)
Front plate t1 (mm)
Side plates t2 (mm)
Middle plate t3 (mm)
End plate t4 (mm)
Preload P24 = 225 kN P27 = 290 kN
24
78
30
3.5
5.5
20
P24
24
78
30
5.5
5.5
20
1.25P24
24
78
30
5.5
5.5
20
P24
24
78
30
5.5
5.5
20
0.75P24
24
78
30
5.5
5.5
20
0.32P24
24
78
30
9.5
5.5
20
P24
27
87
30
7.5
5.5
20
P27
160 120 16 16 S2-A
2 160 120 16 16
S2-B
2 160 120 16 16
S2-C
2 160 120 16 16
S2-D
2 160 120 16 16
S3-A
2 160 120 16 16
S4-A
2 180 130 16 16
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Table 2 Material properties. Results of tensile coupon tests. Components
fy (N/ mm2)
fu (N/ mm2)
Young’s modulus E (N/mm2)
fy/fu
Plates in cone part
t2 = 3.5 mm t2 = 5.5 mm t2 = 7.5 mm t2 = 9.5 mm
312.65 303.93 286.57 297.58
470.81 455.58 419.95 413.87
207,053 207,848 202,476 207,882
0.67 0.67 0.68 0.66
Beam Bolts
t = 15.5 mm d = 24 mm
269.00 975.00
406.86 1171.41
205,569 213,302
0.66 0.83
thicknesses of the plates. The material properties are listed according to the thickness.
First, the joint specimens were loaded to a small degree and unloaded to assure proper operation of the loading apparatus and the displacement gauges and enable proper coordination of the different parts of the specimen. Then, the test was performed under force control in the elastic range of the joints. Second, when the joints were loaded to their nonlinear region, the test control was changed to displacement control until failure of the joint. In this phase, the moment-rotation curve of the joint moves from the stiff part to the soft part. During the test, the minimum sustained time of each load increment to ensure a sufficient and stable transformation was ten minutes. 4. Test results and discussion
3.2. Setup and measurement The test setup is shown in Fig. 3. The instrument arrangement and typology were considered to evaluate the main characteristics of the new semi-rigid joints (stiffness, strength, rotation behaviour, and failure mode). The bottom plate of the specimen was employed to fix the specimen on the rigid frame; it is welded to the support beam to prevent slippage. The bending moment at the joint can be applied via the horizontal hydraulic jack. The horizontal hydraulic jack was connected by hinges to the specimen to ensure that it did not provide rotational restraints at the point of their attachment. During the loading process, the measured variables were as follows: The horizontal load was introduced by a hydraulic jack with a loading capacity of 300 kN. The applied horizontal loads were measured by the load cell between the hydraulic jacks and the specimen at each step during loading. The displacements at the points D1–D3, which were measured by linear variable displacement transducers (LVDTs) at each load step, and the displacement value of the front plate at point D4 was measured by a dial indicator. The distances between the LVDTs on the specimen were recorded prior to starting the test. The strains at the side plates (g1/10 -g7/70 ), column node (g8), front plate (g9) and rectangular beams (g10) at each load step were measured by the strain gauges, as shown in Fig. 3. 3.3. Load procedures The positions of the displacement measurement devices need to be recorded to calculate the rotation of the joint. The loading process was controlled as follows:
The test results include the bending stiffnesses, strengths, rotation behaviours, and failure modes of the joints, as well as the influence of various parameters on the mechanical behaviours of the joints. The mechanical behaviours of the semi-rigid connections can be represented by M-/ curves that describe the relationship between the applied bending moment M and the corresponding rotation / of the joint. In this experimental study, the M-/ curves were indirectly established as the values of M and / are calculated based on the readings of the load cells and the displacement transducers. The bending moment M, which acts on the connection, is equivalent to the product of the applied load F and the distance between the load application point and the end plate—460 mm—as shown in Fig. 2. In these tests, the connection rotation / can be calculated based on the level displacements at points D1–D3, which are obtained by the LVDTs in Fig. 3 as
Pn /¼
k¼1 /ij
ð1Þ
n
/ij ¼ arctan
di dj lij
ð2Þ
where di and dj are the displacements measured at points i and j (points D1–D3 in Fig. 3), and lij is the distance between the two points i and j. To obtain accurate data, all values of the distances lij were recorded after the specimens and the measurement devices were installed. The curves reflect the initial bending stiffness, moment resistance and rotation capacity. To provide a convenient method for analysing the experimental results, the following characteristics are assessed for the different specimens by the method in [16], as shown in Fig. 4.
Fig. 3. Test setup for the BC joints.
Moment (kN⋅m)
H. Ma et al. / Engineering Structures 126 (2016) 725–738
M sup
S j.in
S j.p-l
B Knee-range KR
M inf A Connection rotation (rad)
φinf
φsup Fig. 4. Main features of the M-/ curve.
4.1. Effect of side plates’ thicknesses on the mechanical behaviours of the BC joint The influence of the thicknesses of the side plates on the total behaviours of the BC joints was investigated. The three different
729
thicknesses of the side plates, including 3.5 mm, 5.5 mm and 9.5 mm, were employed in the test. All specimens were tested to failure, indicating the excessive deformation of the specimens, which is a distinct nonlinearity, and that plasticity had significantly developed and the deformation of the specimen continued to increase without additional loading; thus, the specimen is not suitable for additional loading, as shown in Fig. 5. The M-/ curves for the six BC joints subjected to bending are plotted in Fig. 6. In the figure, the plastic moment resistance Msup for each curve is marked, and the deformation of the joint at this step is also indicated. The following observations were noted: (i) the response of the connection exhibits linear behaviour in the early loading sequence and subsequent nonlinearity, which embodies typical elasto-plastic behaviour; (ii) the side plates of the S1-A and S2-B joints exhibited large deformation at the step when the bending is equivalent to the plastic moment resistance Msup; subsequently, the bending decreases with an increase in rotation; (iii) when the bending is equivalent to the plastic moment resistance Msup, the deformation of the side plates of S3-A joints was small and the bending continued to increase after the plastic moment resistance Msup. The main features of the M-/ curves and the failure model of the six joints are summarized in Table 3. The major difference among the joints is the thicknesses of the side plates. The results indicate that the initial stiffness Sj,ini, the elastic flexural resistance
Fig. 5. Picture of the test.
Fig. 6. Moment-rotation response of the joints with different thicknesses of the side plates.
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Minf, the plastic moment resistance Msup, and the knee-range KR distinctly increase with an increase in the thicknesses of the side plates. The elastic flexural resistance Minf of S3-A is almost four times the Minf of S1-A, and the plastic moment resistance Msup of S3-A is more than twice the Msup of S1-A. The bending-stress curves of the joints in Fig. 7 show that the side plates of the S1-A specimens did not yield when the bending reached Minf and Msup. The locations monitored by the strain gauges 1 and 3–7 at the side plates of S2-B specimens yield when the bending reached approximately Msup. The entire side plates of the S3-A specimens yield before the bending reached Minf. Therefore, the failure mode of S1-A, as listed in Table 3, was caused by the sudden buckling of the thin side plates. For S3-A specimens, the side plates yield when the bending increases to a certain value, and the concave deformation gradually increases. The situation for the S2-A specimens falls between the situation for the specimens S1-A and S3-A.
Based on the displacement value of the front plate at point D4, which was measured by a dial indicator (as shown in Fig. 3), the deformation of the high-strength bolt at the tensional side was obtained, and the stress of the tensional bolt was calculated. The curves and the deformation figures are shown in Fig. 8: (i) the deformations of the tension bolts in the S1-A and S2-B specimens is small under the bending moment, and the deformation is linear. The deformations of the tension bolts in the specimens S1-A and S2-B specimens attained the values 0.17 mm and 0.48 mm, respectively, when the bending attained the plastic moment resistance Msup. The largest gap between the front plate and the column node of the S2-B specimens was small, and almost no gap formed between the front plate and the column node of the S1-A specimens during the loading process, as shown in Fig. 8; (ii) With an increase in the side plate’s thickness, the deformation of the tension bolts increase. When the thickness of the side plates is 9.5 mm, the tension bolt undergoes elastic-plastic deformation,
Table 3 Main characteristics of bending moment-rotation curves of the joints with different thicknesses of the side plates. Specimens
Sj.in (kN m/rad)
Minf (kN m)
Sj.pl (kN m/rad)
Msup (kN m)
KR (kN m)
S1-A-1 S1-A-2 AVG
1454.02 1344.97 1399.50
5.55 5.55 5.55
145.40 134.50 139.95
10.26 10.06 10.16
4.71 4.51 4.61
2329.11 2260.31 2294.71
11.34 11.38 11.36
232.91 226.03 229.47
17.82 17.52 17.67
6.48 6.41 6.45
3220.73 3202.66 3211.70
19.49 19.74 19.62
322.07 320.27 321.17
28.71 28.42 28.57
9.22 8.68 8.95
Failure mode
S2-B-1 S2-B-2 AVG Failure mode
S3-A-1 S3-A-2 AVG Failure mode
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500 400
t=3.5mm; fy=312.65MPa
200
100 Msup=10.26kN⋅m
Minf=5.55kN⋅m 2
4
6
8
10
12
14
Moment M (kN⋅m)
-100 -200
-500
100 0
3
6
9
Msup=17.82kN⋅m Minf=11.34kN⋅m 12 15 18 21
-100
Moment M (kN⋅m)
-200
2 3 4 5
-300 -400
t=5.5mm; fy=303.93MPa
300
200
0
1 6 7
Compression side
400
Stress (MPa)
Stress (MPa)
300
500
1 6 7
Compression side
t=3.5mm; fy=-312.65MPa
Tension side
-300
t=5.5mm; fy=-303.93MPa
-400 -500
Tension side
(a) S1-A-1
2 3 4 5
(b) S2-B-1
500
Compression side
400 t=9.5mm; fy=297.58MPa
300
1 6 7
Stress (MPa)
200 100
Minf=19.74kN⋅m Msup=28.42kN⋅m
0
5
10
15
20
-100
25
30
Moment M (kN⋅m)
-200 -300
t=9.5mm; fy=-297.58MPa
-400 -500
Tension side
2 3 4 5
(c) S3-A-1 Fig. 7. Moment-stress curves of the joints with different thicknesses of the side plates.
Deformation (mm)
2.0
S1-A S2-B S3-A
1.5 1.0 0.5
1
1.95mm
0.80mm
2
0.48mm 0.36mm 0.17mm
0.0
3
Msup=28.42kN⋅m
Msup=17.82kN⋅m
Msup=10.26kN⋅m
-0.5 0
10
20
30
40
Moment M (kN·m) Fig. 8. Stress value and deformation figure of the tensional bolt in the joints with different thicknesses of the side plates.
and the final maximum deformation value is 1.95 mm. The final gap between the front plate and the column node of the S3-A specimens was distinct. The results reveal that the bolts may have failed before the side plate yields with the increase in the thicknesses of the side plates. The failure modes of the high-strength bolts is primarily brittle, and the connections incur fatal damage after failure. Thus, failure of the high-strength bolts should be avoided in the connection
design. Increasing the thickness of the side plates can improve the mechanical behaviours of the BC joints, including the bending stiffness, the elastic flexural resistance Minf, the plastic moment resistance Msup. If the side plates are too thin, the bending stiffnesses and ultimate moment strengths of the joints will be low; if the side plate are too thick, fractures may occur in the bolts before the side plate yields. Fracture of the bolts will cause the brittle failure of all joints, and the joints cannot enter the plastic
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yielding phase prior to failure. To achieve better bending stiffness, moment capacity and ductility, the thickness should be properly determined. According to Eurocode 3 [1], the tension resistance Ft,Rd of the high-strength bolt can be calculated by the following equation:
F t;Rd ¼
0:9f ub As
ð1Þ
cM2
To ensure that unwanted brittle failure modes do not control, the bending capacity carried by the bolts should be larger than the bending capacity carried by the side plates.
M b ¼ F t;Rd L1 < M sp ¼ W p1f y
ð2Þ
where Mb is the bending capacity carried by the high-strength bolts; Msp is the plastic moment capacity of the side plates; L1 is the dis2
tance of the two bolts; W p1 ¼ 2 t24H is the relevant plastic modulus of the section of the side plates; and t2 and H are the thickness of the side plate and the height of the side plate, respectively. Based on Eqs. (1) and (2), the maximum thickness of the side plate can be determined by the following relationship:
t2 <
1:8f ub As f y cM2 H2
ð3Þ
L1
4.2. Effect of the pretension force in the bolts on the mechanical behaviour of the BC joint All component parts of the bolt-column joints are fabricated in the factory; at the construction site, two high-strength bolts are used to connect the members to the column node without any welding work. In this paper, the specimens S2-A, S2-B, S2-C and S2-D with different pretension values 1.25P24, P24, 0.75P24, and 0.32P24, respectively, were tested to investigate the effect of the pretension force in the bolts on the mechanical behaviours of the BC joints. The M-/ curves for the four joints with different pretension forces are plotted in Fig. 9. In the figure, the plastic moment resistance Msup for each curve is marked, and the deformation of the joint at this step is shown. The main features of the M-/ curves and the failure model of the eight joints are summarized in Table 4. The results indicate that (i) all M-/ curves of the connection with different pretension forces in the bolts exhibit typical
elasto-plastic behaviour; the deformation of the joints are similar at the step of the plastic moment resistance Msup, as shown in Fig. 9; (ii) when the pretension varied among 0.75P24–1.25P24, the initial bending stiffness, the elastic flexural resistance Minf, and the plastic moment resistance Msup of the joints exhibited minimal variation, whereas the knee-range of the M-/ curve KR exhibited a distinct decrease with an increase in the pretension force in the bolts. For the S2-A specimen, in which the pretension force is 1.25P24, the curve significantly decreased after the plastic moment resistance Msup, as shown in Fig. 9; (iii) when the pretension decreased to 0.32P24, the initial bending stiffness decreased approximately 16.4% compared with the joints with pretension P24. The elastic flexural resistance Minf and the plastic moment resistance Msup of the joints exhibited a minimal decrease, whereas the knee-range of the M-/ curve KR increased compared with the joints with a pretension force range of 0.75P24–1.25P24. Although the effect of the pretension value of 0.32P24 is larger than other pretension forces, the value is too low for the class 10.9 bolt and not typical for a realistic structure. The value of 0.32P24 is employed in this study to investigate the effect of the pretension in the bolts on the mechanical behaviours of the joints. The deformation of the high-strength bolt at the tension side was obtained; the curves are given in Fig. 10. The figure indicates that the deformation curves of the tension bolts in the specimens with different pretension forces are linear; the higher is the pretension force in the bolt, the smaller is the gap between the front plate and the column node. Therefore, the initial stiffnesses of the joints increases with an increase of the pretension force in the bolts. From the moment-stress curves of the joints shown in Fig. 11, the stresses on the side plates of the joints, in which the pretension force is 1.25P24, are lower than the stresses on the side plates of the joints with smaller pretension forces. The stresses on the side plates of the S2-A specimens did not yield when the bending reached Msup, and the locations monitored by strain gauges 3–7 of the side plates of the specimens S2-B, S2-C and S2-D yield when the bending reached approximately Msup. 4.3. Effect of bolt diameter on the mechanical behaviour of the BC joint The high-strength bolts are important component parts of the joint system. To study the effect of the diameters of the bolts on the mechanical behaviours of the BC joints, two different diameters of the bolts-24 mm (M24) and 27 mm (M27)-were considered in
Bending moment M (kN·m)
25
20
15
S2-A S2-B S2-C S2-D
10
5
0 0.00
0.02
0.04
0.06
0.08
Rotation φ (rad) Fig. 9. Moment-stress curves of the joints with different pretension forces.
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H. Ma et al. / Engineering Structures 126 (2016) 725–738 Table 4 Main characteristics of moment-rotation curves of the joints with different pretension forces. Specimens
Sj.ini (kN m/rad)
Minf (kN m)
Sj.pl (kN m/rad)
Msup (kN m)
KR (kN m)
S2-A-1 S2-A-2 AVG Failure mode
2282.56 2367.08 2324.82
11.92 13.01 12.47
228.26 236.71 232.49
16.74 16.94 16.84
4.82 3.93 4.38
S2-B-1 S2-B-2 AVG Failure mode
2329.11 2260.31 2294.71
11.34 11.38 11.36
232.91 226.03 229.47
17.82 17.52 17.67
6.48 6.41 6.45
S2-C-1 S2-C-2 AVG Failure mode
2179.63 2203.38 2191.51
12.02 11.14 11.58
217.96 220.34 219.15
17.42 17.51 17.47
5.40 6.10 5.75
S2-D-1 S2-D-2 AVG Failure mode
1878.94 1960.91 1919.93
10.36 9.37 9.87
187.89 196.09 191.99
17.38 17.41 17.40
7.02 8.04 7.53
the test. The M-/ curves for the six joints are plotted in Fig. 12. The main features of the M-/ curves and the failure models of the joints S4-A with M27 bolts are summarized in Table 5; the failure models of the joints S3-A with M24 bolts are listed in Table 3. Compared with the thickness (9.5 mm) of each side plate in S3-A with M24 bolts, the thickness (7.5 mm) of each side plate in S4-A with M27 bolts is smaller. The results indicate that the initial bending stiffness of S4-A with M27 bolts is 12.4% higher than the initial bending stiffness of S3-A with M24 bolts. The elastic flexural resistance Minf, plastic moment resistance Msup and knee-range KR of the joints also improved when the diameters of the high-strength bolts
increase. Therefore, the effect of the diameters of the bolts on the mechanical behaviour of the BC joint is significant. 4.4. Discussion of the effect of initial imperfections The results reveal that the M-/ curves of the two specimens of one joint are not consistent despite their proximity to each other. Some failure modes of the two specimens of one joint are not identical, and the deformation of the two side plates in S2-B-1 is asymmetric, as shown in Fig. 13. The reasons for these differences may be attributed to the existence of residual stresses and deformation
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0.8
Deformation (mm)
Msup=17.43 kN·m
0.58mm 0.55mm 0.49mm
0.6
0.4
3 4 2
Msup=17. 38 kN·m
Msup=17.68 kN·m
0.36mm
1
Msup=16.74 kN·m
S2-A S2-B S2-C S2-D
0.2
0.0 0
5
10
15
20
25
Bending moment M (kN·m) Fig. 10. Deformation of the tension bolts in the joints with different pretension forces.
Compression side
400 t=5.5mm;fy=303.93MPa
Stress (MPa)
300
500
1 6 7
Msup=16.74kN⋅m
0
M (kN⋅m)
-100 -200
1 6 7
200 100
Minf=12.02kN⋅m Msup=17.42kN⋅m
0
M (kN⋅m)
-100 -200
-300
-300
2 3 4 5
t=5.5mm;fy=-303.93MPa
-400 -500
t=5.5mm;fy=303.93MPa
300
200 100
Compression side
400
Stress (Mpa)
500
Tension side
t=5.5mm;fy=-303.93MPa
-400 -500
Tension side
(a) S2-A-1 500
(b) S2-C-1
Compression side
400
1 6 7
t=5.5mm;fy=303.93MPa
300
Stress (Mpa)
2 3 4 5
200 100 Minf=10.36kN⋅m
0
Msup=17.38kN⋅m
M (kN⋅m)
-100 -200 -300 -400 -500
t=5.5mm;fy=-303.93MPa Tension side
2 3 4 5
(c) S2-D-1 Fig. 11. Bending moment-stress curves of the joints with different pretension forces.
caused by the welding work in the cone part, and a machining error and installation error may occur during fabrication and installation of the joint, such as defects with different sizes, overfit, bolt tightness and friction.
5. Finite element model The mechanical behaviour of the bolt-column connections substantially changes with different geometric parameters and
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50
Moment M (kN·m)
40
S4-A-2 S4-A-3
1(29.97/30.31 kN⋅m)
30
S3-A-1 S3-A-2
2 (28.42/28.71 kN⋅m)
20 10 0 0.00
0.02
0.04
0.06
0.08
0.10
0.12
Rotation φ (rad) Fig. 12. Moment-stress curves of the joints with different bolt diameters.
Table 5 Main characteristics of moment-rotation curves of the joints with different bolt diameters. Specimens
Sj.in (kN m/rad)
Minf (kN m)
Sj.pl (kN m/rad)
Msup (kN m)
KR (kN m)
S2-B S3-A S4-A-1 S4-A-2 AVG Failure mode
2294.71 3211.70 3643.26 3574.16 3608.71
11.36 19.62 20.40 19.20 19.80
229.47 321.17 364.33 357.42 360.88
17.67 28.57 29.97 30.31 30.14
6.45 8.95 9.57 11.11 10.34
Fig. 13. Different failure modes of the joints with identical parameters.
different loading conditions. Assessing their behaviours solely based on experimental investigations is a cost-prohibitive and time-consuming task. Therefore, the use of appropriately validated FE models represents an attractive approach for the future development of a characteristic database for a new joint. These numerical simulations can also offer valuable insight into the component interactions that occur within semi-rigid joints, which is difficult to measure during a test. In this paper, three-dimensional FE models are established using the commercial FEA software ABAQUS [24]; the results are validated against the experimental data. 5.1. Proposed modelling approach The three-dimensional finite element model has the same configuration and dimensions of the tested specimens. The entire
experimental joint, including the column node, the cone part, the bolts and the rectangular member, is modelled with eight-node solid elements C3D8R, which are available in the ABAQUS library [24]. The numerical models incorporated a number of detailed features, such as contact phenomena, bolt slippage definition and bolt pretension application, as described in the next section. – Contact surfaces Surface-to-surface contact interactions are defined between two parts in the FE models with a self-contact element and a surface-to-surface contact element, such as the front plate and the column node, the bolt surfaces and the screw hole, and the washers, the front plate and the nut of the bolts. The contact
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Fig. 14. FE model and contact surface setting of the BC joints.
properties that correspond to these surfaces are defined in the normal direction, which enables surfaces to be separated after contact has occurred. The coefficient of friction for the contact surfaces in the BC joints is assumed to be 0.4 (as defined in the steel joint systems [25]). – Bolt slippage and pretension Special attention was paid to faithful modelling of the geometric details of the 2 mm space between the bolt shanks and the screw holes, according to the code [1]. When assembling the test specimens, the pretension force is generated in the joint by tightening the bolt with wrenches. In the FE models, the pretension force in the joint is defined according to the real value measured during the test. – Mesh method A number of mesh sensitivity studies were performed to arrive at an optimum representation, which involves a comparatively finer mesh for the cone part, bolts and washers, as well as the areas within the column node and members in contact with these components, whereas a relatively coarser mesh was employed elsewhere. The dimensions of the elements within the final adopted mesh ranged between 6 mm within the refined region to 100 mm within the coarser region. The boundary conditions and loading procedure that were adopted in the numerical analyses replicated the boundary conditions and loading procedure employed in the experimental studies: the column node is fixed and the forces act on the end of the member. Fig. 14 shows the model mesh, the contact setting, the boundary condition and the force locations for the joints.
5.2. Material properties Based on the coupon test results listed in Table 2, the stressstrain relationship for the different parts of the joints is modelled for the nonlinear analysis as an elasto-plastic material with a strain hardening and yielding plateau beyond the elastic phase. It is assigned a three-linear stress-strain law—symmetrical in tension and compression—as shown in Fig. 15. 6. Comparison of the results from the FE models and experiments A total of 14 tests, which were conducted based on different pretension forces, thicknesses of the side plates and diameters of the bolts, are employed to validate the FE model. The real initial geometric imperfections of the side plates are considered for all joints during the numerical simulation. The moment-rotation curves that are obtained via FE models and tests are shown in Fig. 16. The definition and calculation method of the rotation deformation / is identical for all tests. Similar curves are numerically and experimentally obtained. The numerical curve describes the experimental results with acceptable approximation. The numerical curves of the specimens in groups S1 and S2 is slightly higher than the numerical curves that were experimentally obtained after the plastic flexural resistance. This variation can be attributed to the sudden buckling that occurred on the compression side of the thin side plates of the experimental specimens. Table 6 shows the comparison between the numerical results and the experimental results in terms of initial stiffness (Sj,in) and plastic moment resistance (Msup). In particular, the FE model reveals that the plastic moment resistance of the joints is consistent with the experimental results, and the difference is less than
䠄㻜㻚㻜㻟㻣㻥䠈 㻠㻡㻡㻚㻡㻤㻌㻹 㻼㼍䠅
Stress (MPa)
Stress (MPa)
䠄㻜㻚㻜㻟㻡㻞䠈 㻝㻝㻣㻝㻚㻠㻝㻌㻹 㻼㼍䠅 䠄㻜㻚㻜㻜㻠㻡㻣䠈 㻥㻣㻡㻌㻹 㻼㼍䠅
Strain
(a) stress-strain curve for bolts
䠄㻜㻚㻜㻜㻝㻠㻢䠈 㻟㻜㻟㻚㻥㻟㻌㻹 㻼㼍䠅
Strain
(b) stress-strain curve for S2-B side plates
Fig. 15. Stress-strain behaviours of the joint’s components.
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Fig. 16. Moment-rotation and failure mode comparison of the joints.
Table 6 Comparison of the main characteristics of bending moment-rotation curves. Specimens
Sj.ini,anal (kN m/rad)
Sj.ini,exp (kN m/rad)
Sj;ini;exp Sj;ini;anal Sj;ini;exp
Msup,anal (kN m)
Msup,exp (kN m)
Msup;exp Msup;anal M sup;exp
S1-A S2-A S2-B S2-C S2-D S3-A S4-A
1551.65 2314.72 2292.84 2243.32 2043.78 3262.39 3841.75
1454.02 2282.56 2260.31 2179.63 1878.94 3202.66 3643.26
6.71% 1.41% 1.44% 2.92% 8.44% 1.86% 5.45%
10.30 16.57 17.58 17.39 17.12 28.06 30.79
10.46 16.74 17.52 17.43 17.28 28.77 30.86
1.53% 1.02% 0.34% 0.23% 0.93% 2.47% 0.27%
Sj.in,anal and Msup,anal is the initial bending stiffness and plastic flexural resistance obtained by numerical models, Sj.in,exp and Msup,exp is the initial bending stiffness and plastic flexural resistance obtained by tests.
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3%. The majority of the differences of the initial stiffness is less than 3%, with the exception of the specimens S1-A(6.71%), S2-D (8.44%) and S4-A(5.45%). Therefore, the FE models are effective and convenient for evaluating the moment-rotation curves. The reliability of the FE models is proven by the agreement between the numerical deformed configuration at failure and the numerical deformed configuration observed after the tests, as shown in Fig. 16.
Acknowledgements This research is supported by grants from the Natural Science Foundation of China (Grant No. 51308153), the China Postdoctoral Science Foundation funded project (Grant No. 2013M531020 and Grant No. 2014T70346), and The National Science Fund for Distinguished Young Scholars (Grant No. 51525802). References
7. Conclusions A series of experiments was conducted on BC joints under monotonic loading to investigate the mechanical behaviour of the new joint system, which can be employed in single-layer structures. The experimental programme enabled a direct assessment of the influence of a number of main considerations, such as the thicknesses of the side plates, pretension forces and diameters of the bolts. In addition, a three-dimensional FE model was developed to simulate the behaviour of the BC joints. Consistency with the experimental results confirms that the detailed FE models are able to simulate the mechanical behaviour of BC joints with reasonable accuracy. The M-/ curves and failure modes of the joints are obtained based on different parameters. The results are compared and discussed. The conclusions of this study are as follows: (1) The new BC joint system exhibits an adequate bending stiffness and bending capacity. The response of the connection embodies a typical elasto-plastic behaviour under a bending moment. (2) The initial stiffness Sj,ini, the elastic flexural resistance Minf, the plastic moment resistance Msup, and the knee-range KR of the joint can be significantly improved with an increase in the thickness of the side plates. However, high-strength bolt fracture may occur when the thickness of the side plates in the joints is excessive. Therefore, the maximum thickness of the side plate was developed based on the bolt diameters in the joints to achieve a higher stiffness and moment capacity and to avoid brittle failure. (3) For the joints under a bending moment, the effect of the pretension force on the mechanical behaviours of the joints is small. With an increase in the tension in the bolts, the initial bending stiffness of the joints slightly increases at the cost of slightly decreasing the plastic moment resistance Msup and decreasing the knee-range KR. According to the experimental results, the tension value P24 = 225 kN for the joints with M24 bolts is better than other values. (4) Increasing the diameter of the bolts can significantly improve the initial bending stiffness of the joints; and the elastic flexural resistance Minf, plastic moment resistance Msup and knee-range KR of the joints also slightly improve when the diameter of the high-strength bolts increases. (5) Some initial imperfections, such as residual stresses and deformation and machining and installation errors, may cause a slight difference in the M-/ curves and failure mode of the two specimens of one joint.
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