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Experimental study of ultra-large capacity end-plate joints
Journal of Constructional Steel Research 128 (2017) 354–361
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Journal of Constructional Steel Research
Experimental study of ultra-large capacity end-plate joints Gang Shi ⁎, Xuesen Chen, Dongyang Wang Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Department of Civil Engineering, Tsinghua University, Beijing 100084, PR China
a r t i c l e
i n f o
Article history: Received 24 January 2016 Received in revised form 5 September 2016 Accepted 6 September 2016 Available online xxxx Keywords: Steel structure Beam-to-column joint Ultra-large capacity End-plate connection Experimental study
a b s t r a c t When bolted joints are required in steel structures involving large spans or heavy loads, ultra-large capacity endplate joints with 12 bolts or 16 bolts in tension should be applied if ordinary end-plate joints or large capacity end-plate joints cannot meet the resistance requirement. Four full-scale specimens of ultra-large capacity endplate joints were tested subjected to monotonic load. The moment-rotation curves of all the specimens were obtained, and the moment resistance, rotational stiffness, and distribution of the bolt strain increments in tension were analyzed when the bolt diameter, the end-plate thickness, or the layout of the bolts changed. The tested ultra-large capacity end-plate joints shared the failure mode of end-plate yielding followed by bolt fracture or necking, and the thickness of the end plate had an obvious influence on the joint resistance. A significantly inhomogeneous distribution of bolt strain increments was observed. Bolts in corners, which made little contribution to the moment resistance in the tests, could be removed or considered as shear-resistant bolts. In the design of this kind of joint, the resistance of the panel zone can be decided according to the Chinese code, the American code, or the Eurocode, and the equivalent number of the bolts in tension is recommended to be 7.0 based on a proposed distribution model of the tension load resisted by bolts in tension, derived from the tests. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The extended end-plate joint, with an end plate welded at the end of the beam and connected to the flange of the column by bolts, is among the widely adopted beam-to-column joints in steel frames. This joint form has an advantage in construction without field welding. Also, large rotational stiffness and satisfactory ductility can be developed in this joint provided it is properly designed [1,2,3,4,5,6,7]. Conventional configurations of extended end-plate joints are shown in Fig. 1, with eight bolts in total, four of which are arranged in tension. End-plate stiffeners are often applied to improve joint performance when the joint is designed as a rigid one. Many investigations on the performance of conventional extended end-plate joints have been conducted [8,9,10,11,12, 13], and several design methods have been proposed in different design codes or guides [14,15,16,17,18,19]. The design method in the Chinese code [14] and that in the American code [18] regard conventional extended end-plate joints as rigid, so only the moment resistance needs to be checked. In both methods the four bolts in tension are considered to share the tension force equally and the T-stub analogy method is employed to check the resistance of end plates. Also, yield line models based on plate theories are specified in several design codes or guides [15,16,17,18] with equations to check the end-plate thickness provided. In Eurocode 3, all joints must be estimated to determine whether they are rigid, semi-rigid, or just pinned, ⁎ Corresponding author. E-mail address: [email protected] (G. Shi).
http://dx.doi.org/10.1016/j.jcsr.2016.09.001 0143-974X/© 2016 Elsevier Ltd. All rights reserved.
based on the ratio of rotational stiffness to beam line stiffness [19], so both the moment resistance and the rotational stiffness must be checked. The component method is adopted to predict the joints' moment resistance and initial rotational stiffness, and the basic component in extended end-plate joints is the T-stub [10]. It also should be noted that the specified ultimate states of the high-strength bolts in the Chinese code are different with that in the other two codes above. In the Chinese code the employment of slip-critical high-strength bolts is recommended in end-plate connections and it is specified that the ultimate state of such bolts in tension is the state when the connected plates separate from each other around the bolts [14], whereas in the American code and the Eurocode, the bolt reaches its ultimate state when it fails. As the moment resistance demand for beam-to-column joints is increased in steel frames involving large spans or heavy loads, conventional extended end-plate joints might not meet the resistance requirement, being limited by the axial tension capacity of the bolts. Two improved configurations, both referred to as large capacity endplate joints with eight bolts arranged in tension, have been proposed and investigated [20,21,22]. The first configuration, illustrated in Fig. 2(a), features a wide end plate and two 4-bolt rows in tension, and the component method in Eurocode with T-stubs can be adopted in the design of such joints in theory if the stiffeners are ignored. The second configuration, illustrated in Fig. 2(b), features a long end plate and four bolt-rows in tension. A method based on the research of Murray and Kukreti [20] was proposed in the American code for the design of stiffened long-end-plate joints [16,18], and the component method can also be applied to design this kind of joint theoretically. Based on
G. Shi et al. / Journal of Constructional Steel Research 128 (2017) 354–361
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Notation tep-nom nominal thickness of end plate width of beam bb depth of beam hb thickness of beam flange tbf thickness of beam web tbw thickness of end plate tep width of column bc depth of column hc thickness of column flange tcf thickness of column web tcw E Young's modulus yield strength fy yield strain εy strain at the end of yielding plateau εst ultimate tensile strength fu connection rotation φc panel zone shear rotation φpz M moment at beam end ultimate moment resistance Mu yield moment resistance My φ joint rotation joint rotation corresponding to ultimate moment φu resistance plastic join rotation corresponding to ultimate moment φup resistance joint rotation corresponding to yield moment resistance φy rotational stiffness Kφ γ engineering principal shear strain in plane tension load resisted by the bolt most likely to fail Nt equivalent number of tension bolts Neq tension resistance of a single bolt Nb
the existing investigations, large capacity end-plate joints can show heightened rotational stiffness [22] but the axial forces in different bolts in tension develop quite inconsistently, with the stress increments of the outer bolts significantly lower than that of the inner bolts close to the web or extended stiffeners [23]. The moment resistance of large capacity end-plate joints may still be insufficient in situations with special requirements. Therefore, a new end-plate joint called the ultra-large capacity end-plate joint is proposed in this paper. As illustrated in Fig. 3, this new joint form has an arrangement of 32 bolts or 24 bolts in total, with half of the bolts located in the tension side. As in large capacity end-plate joints, bolts in tension in
Column flange End plate End-plate stiffener
Column web
Beam web
Beam flange
Bolt Continuous plate (a)
(b)
Fig. 1. Conventional configurations of extended end-plate joints: (a) with end-plate stiffeners; (b) without end-plate stiffeners.
(a)
(b)
Fig. 2. Configurations of large capacity end-plate joints: (a) with wide end plate; (b) with long end plate.
ultra-large capacity end-plate joints are considered to develop a complex distribution of axial force. It should be noted that end plates with stiffeners, which are recommended to improve joint performance, can experience a complex stress state, so that ultra-large capacity endplate joints cannot be properly divided into conventional T-stubs, indicating that the existing design methods given above for end-plate joints cannot be applied in the design of this joint form directly. Also, the yield line models in existing codes are all corresponding to connection configurations with one bolt column in each side and cannot be applied in design of the two-column bolt group in ultra-large capacity end-plate joints. To determine a proper design method for the tested joint form, it is necessary to analyze the performance of this kind of joint. In this paper, four full-scale specimens of ultra-large capacity endplate joints with different end-plate thickness, bolt diameter, or bolt layout were subjected to monotonic loads to investigate the performance of this new joint form. Failure modes as well as moment-rotation curves are discussed and the distribution of the tension strain increments in the bolts is analyzed. 2. Experimental program 2.1. Specimens Four ultra-large capacity end-plate joint specimens, fabricated with welded H-section beams and columns, were designed with different joint parameters. The beams and the columns shared the same welded section H800 × 500 × 60 × 30. The total length of 5 m for the columns was determined based on a typical steel frame design, and the cantilever beam, connected to the flange with end plate and bolts in the middle of the column, was 3 m in length. The parameters of the joints are shown in Table 1 and the measured dimensions of all the specimens are given in Table 2. The name of each specimen is constituted by the sequence number (1–4), the nominal thickness of the end plate (EP32 for the 32 mm thick end plate and EP25 for the 25 mm thick end plate), the nominal bolt diameter (M30 bolt or M27 bolt) and a letter for the bolt layout (A or B). The specimen 1-EP32-M30-A was designed as a standard specimen whereas specimens 2–4 changed end plate thickness, bolt diameter, and bolt layout respectively compared to the standard specimen. The bolt layout types are illustrated in Fig. 3, where layout type A has 32 bolts in total and layout type B removes 8 of the bolts. There are 8 bolt rows and 4 bolt columns, and for convenience in the
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B13 B14
B21 B22
B23 B24
B31 B32
B33 B34 B43 B44
B13 B12 B23 B24 B21 B22
B31 B32 B42
B33 B34 B43
340
B41 B42
100 100 100 100 70
B11 B12
60100 90 90 100 60
70 100 100 100 100
70 100 100 100 100
340
100 100 100 100 70
60 100 90 90 100 60
(a)
(b)
(c)
Fig. 3. Configurations of ultra-large capacity end-plate joints: (a) sketch; (b) bolt layout A; (c) bolt layout B (units: mm).
following analysis, the bolts in row i and column j are identified by Bij as shown in Fig. 3. 2.2. Materials The steel of all the specimens was Q345 and the nominal yield strength was 345 MPa. Tensile tests were conducted with three identical coupons for each plate thickness except for the 60 mm plates, which exceeded the upper limit of plate thickness allowed by the coupon test machine. The test results are summarized in Table 3 and the stressstrain curves of the plates are shown in Fig. 4. The maximum elastic moment developed by the beams was calculated as 7778 kN·m based on the nominal yield strength of the beam, and that level of resistance was sufficient for the members to remain elastic during the experiments. Thus it could be ensured that specimen failure would occur in the joint region rather than in the members. All the bolts used in the specimens were Grade 10.9 high-strength bolts with pre-tension force applied to meet the requirements of the Chinese code [10]. For the M30 bolts the pre-tension force was specified as 355 kN and for the M27 bolts it was 290 kN. The Young's modulus of the bolts was 206 GPa and the ultimate strength was 1175 MPa according to the quality certification of the bolts. 2.3. Test setup The test setup is shown in Fig. 5. The column was placed horizontally and restrained by two anchor bolt supports at each end, and a horizontal constraint was fixed at the south end, simulating the hinge supports at the column ends. A 3000kN actuator was fixed on the reaction wall with a connecting beam. The horizontal push load provided by this actuator was applied at the height of 3.025 m from the upper face of the column's upper flange. Out-of-plane restraints were fixed on the reaction frame with a beam in each side, as illustrated in Fig. 5 (b), at the
Table 1 Summary of the parameters of the connections in the specimens. Specimen
tep-nom (mm)
Bolt size
Bolt layout
1-EP32-M30-A 2-EP25-M30-A 3-EP32-M27-A 4-EP32-M30-B
32 25 32 32
M30 M30 M27 M30
A A A B
height of 2.895 m from the upper face of the column's upper flange. A 5 mm-wide space was left between the beam edge and the out-ofplane restraint in each side, but during the loading progress the maximum lateral displacement of each beam was no more than 1.05 mm, indicating that the out-of-plane restraints made no influence to the test results. Before the monotonic push load was applied, pre-tension forces were applied by fastening the bolts using the torque wrench method. 2.4. Instrumentation The axial strain of every high-strength bolt adopted in the specimens was measured with strain gauges pre-embedded into the bolt in accordance with the method proposed in reference [24] to analyze the distribution of axial force increments in bolts. Extensometers were arranged to obtain the joint rotation as shown in Fig. 6(a). According to the Eurocode, a joint is constituted by the connections and the panel zone in the column web [19], so the joint rotation of end-plate joints can be divided into two components [25]. The first is the connection rotation φc that can be calculated by the relative displacement between the end plate and the column flange in the centerline of the beam flanges, based on Eq. (1). The other component is the panel zone shear rotation φpz that can be calculated by the increments of the diagonal length of the panel zone, based on Eq. (2). The symbols in the equations are illustrated in Fig. 6(a).
φc ¼
φpz
δ1 −δ2 hb −t bf
δ4 −δ3 ¼ 2
ð1Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 bpz þ hpz bpz hpz
ð2Þ
The shear strain of the panel zone was measured by strain rosettes as illustrated in Fig. 6(b). The in-plane principal shear strain γ was calculated by Eq. (3), where ε0, ε45, and ε90 represent the strains in the directions with angles to the horizontal plane equaling 0°, 45°, and 90°, respectively [26].
γ¼
pffiffiffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðε 0 −ε 45 Þ2 þ ðε45 −ε 90 Þ2
ð3Þ
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Table 2 Summary of the measured dimensions of the specimens. Specimen
bb (mm)
hb (mm)
tbf (mm)
tbw (mm)
tep (mm)
bc (mm)
hc (mm)
tcf (mm)
tcw (mm)
1-EP32-M30-A 2-EP25-M30-A 3-EP32-M27-A 4-EP32-M30-B
500.1 500.3 500.1 499.8
800.3 799.6 799.4 799.4
59.76 59.85 60.02 59.93
30.11 30.12 29.85 29.86
32.11 25.08 31.86 31.92
499.5 499.2 499.8 500.0
799.9 800.1 800.0 799.6
59.77 60.08 59.89 60.03
29.93 30.08 30.11 29.86
3.1. Failure mode All the specimens shared a similar failure mode: end plate yielding followed by bolt fracture or necking. Fig. 7(a)–(c) shows the overall setting of specimen 2-EP25-M30-A and the local deformation of the end plate of this specimen in the failure state, indicating that significant rotation developed in this joint and the tension side of the end plate obviously yielded in this failure mode. The other specimens showed deformations at the end of loading similar to those illustrated in Fig. 7(a)–(c). When the joint failed, paint cracking of the end plate was observed along the edge of the beam flange and end-plate stiffener on the tension side. The open displacements between the end plate and the column flange in the centerline of the beam tension flange, illustrated in Fig. 7(b) and marked as δ1, reached maximums of 10.7 mm, 18.5 mm, 10.3 mm, and 11.5 mm for Specimens 1 to 4 respectively. This open displacement was greatest in specimen 2-EP25-M30-A that had the least end-plate thickness. As the open displacement, caused mainly by the bending deformation of the end plate, is a basic component of the joint's plastic rotation, a thinner end plate is expected to contribute to a greater capacity for plastic deformation. Significant open displacements also developed between the end plate and the column flange in the centerline of the end-plate stiffener at the edge of the end plate in tension, identified in Fig. 7(c) and marked as δs. This displacements reached maximums of 12.5 mm, 21.0 mm, 13.6 mm, and 14.1 mm for Specimens 1 to 4 respectively. Although the displacements δ1 and δs were considerable, the corners of the end plates still remained in contact with the column flange for all specimens, indicating that biaxial bending deformations were developed in the end plates in tension. Such deformations were more complex than simple planar bending or existing yield line models for the design of end plates. To design end plates in ultra-large capacity end-plate joints, new analysis methods with biaxial bending taken into consideration should be adopted. The failed bolts in specimen 2-EP25-M30-A are illustrated in Fig. 7(d), showing two typical failure modes of the bolt, fracture and necking. Bolt failures were observed in each specimen and the distribution of the failed bolts in all specimens is illustrated in Fig. 8. According to this figure, 6 bolts failed in specimen 2-EP25-M30-A, 5 bolts being fractured and one necked, and 12 bolts were necked in specimen 3-EP32M27-A. These findings indicate that when a thinner end plate was applied, the inner bolts B22, B23, B32 and B33 might withstand most of the load increments after the yielding of the end plate, so that the other bolts in tension could not develop full strength, which was uneconomical in the structural design. When smaller bolts or a thicker end plate were used, an economical design could be obtained such that most of
the bolts in tension developed their strength adequately as in specimen 3-EP32-M27-A after end-plate yielding, but the plastic deformation capacity could be decreased because of the limited bending deformation of the end plate. Therefore, it can be deduced that the thickness of the end plate and the diameter of the bolts should be compatible so that the resistances corresponding to end-plate yielding and bolt failure are comparable. 3.2. Moment-rotation curves The moment-rotation curves (M-φ curves) of the specimens are shown in Fig. 9. M represents the moment at the column face obtained by multiplying the loads applied by the actuator and a distance of 3.25 m, as illustrated in Fig. 5, and φ represents the joint rotation constituted by φc and φpz. The main performance indexes are summarized in Table 4, where the yield moment My is determined as 2/3 of the ultimate moment Mu according to reference [10]. This definition of My is coincident with the elastic limitation for end-plate joints specified in the Eurocode 3 [19] so that the joint rotational stiffness Kφ can be determined based on this moment. Compared to the resistance of specimen 1-EP32-M30-A, the moment resistance of specimens 2-EP25-M30-A and 3-EP32-M27-A showed a decrease of 17.6% and 9.1% respectively, whereas the moment resistance of specimen 4-EP32-M30-B only decreased by 3.7%. Therefore, it can be concluded that the corner bolts removed in layout B exerted almost no influence on the moment resistance of the ultra-large capacity end-plate joint. Furthermore, the rotational stiffness of specimen 4-EP32-M30-B showed a small increase compared to that of specimen 1-EP32-M30-A. Fig. 10 illustrates the moment-principal shear strain (M-γ) curves of the specimens. The design moment resistance of the panel zone was calculated to be 4318 kN·m, 4309 kN·m, and 4132 kN·m based on the Chinese code [14], the American code [27], and the Eurocode [19], respectively. The design moment resistances obtained by the Chinese code and the Eurocode are shown in Fig. 10; the result obtained by the American code was almost the same as that of the Chinese code. It is concluded that the design methods specified in these three codes could provide satisfactory predictions of the design moment resistance of the panel zone, although the resistance based on the Eurocode was a little lower than that of the Chinese and the American codes. Therefore, the existing design methods for the panel zone can be applied directly in
Stress /MPa
3. Results and analysis
600 500 400
25mm plate 30mm plate 32mm plate
300 200
Table 3 Summary of results of coupon tests.
100
Nominal plate thickness
E (MPa)
fy (MPa)
εy
εst
fu (MPa)
25 30 32
201,251 213,891 204,726
349.4 404.4 414.6
0.00174 0.00189 0.00203
0.01895 0.01585 0.02709
516.9 566.3 558.1
Strain
0 0
0.05
0.1
0.15
0.2
Fig. 4. Stress–strain curves of coupons.
0.25
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3.3. Distribution of the bolt tension strain increment
3000kN actuator
2895
anchor bolt support
3025
beam for out-of-plane restraints
beam
reaction wall
connecting beam
reaction frame
150t
N
anchor bolt horizontal support restraint
column 2500
2500 (a)
beam for out-of-plane restraints out-of-plane restraints
specimen
(b) Fig. 5. Test setup: (a) front view; (b) vertical view (units: mm).
predicting the resistance of ultra-large capacity end-plate joints. It is also noted that, in the late stage of the loading process, the panel zone of the joints except for specimen 2-EP25-M30-A had yielded and developed a considerable plastic shear deformation, providing part of the joint plastic rotation. Therefore, in ultra-large capacity end-plate joints a balanced design of resistance is recommended to provide a larger rotational capacity, taking full advantage of the ductility of both the end plate and the panel zone.
In ultra-large capacity end-plate joints, the axial forces transferred by different bolts can be quite diverse because of the bending deformation of the end plate. Thus it is necessary to decide the proportional relationship of the tension loads taken by the bolts in tension in order to predict the moment resistance of the joints. Based on reference [28] the tension load transferred by a bolt is approximately proportional to the tension force increment of the bolt when all the bolts are pretensioned, whereas in the elastic state, the tension force increment of a bolt is proportional to its tension strain increment, which can be measured by the gauges pre-embedded in the bolt. Therefore, the proportional relationship of the tension loads taken by the bolts could be represented by the ratio between the tension strain increments of the bolts. With the moment when all the pre-tension forces of the bolts were applied defined as the initial state, the normalized tension strain increments of the bolts, which were normalized by the strain increment of bolt B 22 at the state M = My , are listed in Table 5. It was proved by the absolute bolts strains measured in the test that all the bolts in the tested joints still kept elastic in the state corresponding to My with the bolt strains less than the yield strain. The bolt layout of each specimen is symmetrical about the centerline of the beam web, so only the bolts on one side were analyzed and the data in Table 5 are the mean values of the strain increments of two bolts in symmetrical positions. From Table 5 it can be observed that the tension strains of the corner bolts on the tension side (B11 and B41) in bolt layout A showed no increase but a little decrease, therefore no contribution was made by the corner bolts to the moment resistance and these bolts could be removed as bolt layout B or just regarded as shear-resistant bolts. Large tension strain increments developed in B22 and B32, indicating that these inner bolts were most likely to fail. Therefore, bolt B22 was regarded as the standard bolt and a distribution model of the tension load resisted by the bolts, as illustrated in Fig. 11, is proposed based on the data in Table 5. The sum of the normalized strain increments of the bolts in tension (except for the corner bolts) is defined as the equivalent number of tension bolts Neq because the resistance of the end-plate connections should be designed with the limitation of the bolt most likely to fail. According to Table 5, the Neq of the specimens changed from 7.06 to 7.45 with a mean value of 7.23, and the Neq based on the proposed model in Fig. 11 was 7.0, a finding that is a little conservative compared to the experimental results. Therefore, this model can provide a safe prediction of the moment resistance controlled by the bolts. Considering the recommended value of Neq, the moment resistance MR can be predicted by Eq. (4), where Nb is the tension resistance of a single bolt and taken as 540.5 kN and 657.9 kN for M27 bolt and M30 bolt respectively according to the quality certification. MR ¼ Neq Nb ðhb −t bf Þ
M
340
A 3
4
15
340 15
b pz = 650
M
2
1
B
h pz = 650 (a)
ð4Þ
(b)
Fig. 6. Instrumentation in joint region: (a) extensometers; (b) strain rosettes (units: mm).
Based on Eq. (4), the moment resistance controlled by the bolts of the tested joints were 2572.6 kN·m for Specimen 3-EP32-M27-A and 3131.5 kN·m for the other specimens that were with M30 bolts, respectively. The predicted moment resistance seemed to significantly underestimate the capacity of the tested joints compared to the measured ultimate moment resistance in Table 4, but it is a safe limitation that is acceptable for engineering design, because the fracture of the high-strength bolts is a typical brittle failure mode with the risk of progressive fractures in the bolt group and should be avoided in practice. Thus, the most dangerous bolt is recommended to be controlled in elasticity in design, which causes the underestimation of the moment resistance with the strength of the other bolts not fully developed.
G. Shi et al. / Journal of Constructional Steel Research 128 (2017) 354–361
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Fig. 7. Specimen 2-EP32-M25-A in failure state: (a) overall setting; (b) front view of end-plate local deformation; (c) lateral view of end-plate local deformation; (d) failed bolts.
3.4. Joint rotation The two components of joint rotation, φc and φpz, were identified based on Eq. (1) and Eq. (2), and the composition of the joint rotation at the state M = My and M = Mu is shown in Fig. 12. According to this figure, the connection rotations accounted for 34.6%–50.3% of the joint rotation when M = My, and when M = Mu this percentage increased to 51.6%–63.9%. It can be inferred that, before yielding of the joint, the bolted end-plate connection could provide a rotational stiffness as
great as the shear rotational stiffness of the panel zone, and after yielding, the connection rotation developed more rapidly than the panel zone shear rotation, especially when a thinner end plate was employed. These characteristics of rotational performance make it possible for ultra-large capacity end-plate joints to demonstrate high rotational stiffness and a ductile yielding mechanism with great deformability. The joint rotational capacities φu and the plastic rotational capacities φup obtained in the tests are listed in Table 4, where φu is defined as the joint rotation corresponding to the ultimate moment resistance Mu, and φup is determined by Eq. (5).
6000
(a)
(b)
Mu Kφ
ð5Þ
M/kN·m
φup ¼ φu −
5000 4000
1-EP32-M30-A 2-EP25-M30-A 3-EP30-M27-A 4-EP32-M30-B
3000 2000
(c) Necked bolt
(d) Fractured bolt
1000 /rad 0 0
Fig. 8. Failed bolts in tension of each specimen: (a) 1-EP32-M30-A; (b) 2-EP25-M30-A; (c) 3-EP32-M27-A; (d) 4-EP32-M30-B.
0.005
0.01
0.015
0.02
Fig. 9. Moment-rotation curves of the specimens.
0.025
360
G. Shi et al. / Journal of Constructional Steel Research 128 (2017) 354–361
Table 4 Performance indexes of specimens. Specimen identifier
Mu (kN·m)
φu (rad)
φup (rad)
My (kN·m)
φy (rad)
Kφ (kN·m)
1-EP32-M30-A 2-EP25-M30-A 3-EP32-M27-A 4-EP32-M30-B
6091.0 5021.9 5534.6 5923.3
0.0207 0.0193 0.0211 0.0228
0.0148 0.0131 0.0143 0.0175
4060.7 3347.9 3689.7 3948.9
0.00390 0.00412 0.00451 0.00355
1.041 × 106 0.813 × 106 0.818 × 106 1.112 × 106
7000
5000
M/kN·m
M/kN·m
7000
6000
6000 5000
Chinese code Eurocode
4000
Chinese code Eurocode
4000
3000
3000
2000
1-A 1-B
A
1000
2000
B
0
2-A 2-B
A
1000
B
0 0
0.002
0.004
0.006
0.008
0.01
0
0.002
0.004
(a)
5000
M/kN·m
7000 M/kN·m
7000 6000
0.006
0.008
0.01
(b)
6000 5000
Chinese code
4000
Chinese code Eurocode
4000
Eurocode
3000
3000
2000
3-A 3-B
A
1000
2000
B
1000
B
0
4-A 4-B
A
0 0
0.002
0.004
0.006
0.008
0.01
0
0.002
0.004
(c)
0.006
0.008
0.01
(d)
Fig. 10. Moment-principal shear strain curves of the specimens: (a) 1-EP32-M30-A; (b) 2-EP25-M30-A; (c) 3-EP32-M27-A; (d) 4-EP32-M30-B.
From Table 4 it can be observed that the joint rotational capacities were between 0.0193 rad and 0.0228 rad and the plastic rotational capacities were between 0.0131 rad and 0.0175 rad for the specimens. The joint rotational capacity of 2-EP25-M30-A was the lowest of the specimens, mainly due to the insufficient development of the panel zone shear rotation under a lower ultimate moment resistance than the other specimens, as illustrated in Fig. 10. Therefore, a balanced design for the resistance is important to increase the rotational capacity of this joint. According to the American code and the Eurocode, the seismic performance of a joint is evaluated by plastic story drift rather than by joint rotation [29,30]. However, the four specimens in this research were designed to develop failure modes in the joint region, so that a large beam section and a short span were applied, features that made the specimens atypical for estimating story drift because a full-strength joint design with joint moment resistance greater than the plastic moment of the beam is recommended in practice. Also, cyclic experiments are expected to check the ductility and the energy dissipation capacity of this joint. Further study is needed with practically designed specimens subjected to cyclic loads, to investigate the seismic performance of ultra-large capacity end-plate joints.
Table 5 Normalized tension strain increments of bolts in tension under the yielding moment. Specimen
1-EP32-M30-A 2-EP25-M30-A 3-EP32-M27-A 4-EP32-M30-B Average
Normalized tension strain increment
4. Conclusions Four full-scale ultra-large capacity end-plate joints were subjected to monotonic loads. The failure modes as well as the moment-rotation relationships of this joint form were studied. A distribution model of the tension load resisted by the bolts in tension was proposed, based on analysis of the bolt strain increments. The following conclusions can be drawn from this investigation. (1) The specimens shared a similar failure mode, with end-plate yielding followed by fracture or necking of several bolts in tension. Significant biaxial bending of the end plates was observed in all specimens, and this yielding mechanism could not be covered by T-stub analysis. It is necessary, therefore, to develop new methods or models for design of the end plates in ultra-large capacity end-plate joints.
0
0.45Nt
0.45Nt
0
0.55Nt
Nt
Nt
0.55Nt
0.55Nt
0.8Nt
0.8Nt
0.55Nt
0
0.15Nt
0.15Nt
0
Neq
B11
B12
B21
B22
B31
B32
B41
B42
−0.10 −0.04 −0.08 – −0.07
0.57 0.20 0.20 0.77 0.43
0.46 0.58 0.69 0.51 0.56
1.00 1.00 1.00 1.00 1.00
0.53 0.64 0.66 0.47 0.57
1.02 1.13 0.87 0.90 0.98
−0.05 −0.01 −0.01 – −0.03
−0.07 0.06 0.16 0.09 0.06
7.06 7.21 7.14 7.45 7.23
Fig. 11. A distribution model of the tension load resisted by the bolts in tension.
G. Shi et al. / Journal of Constructional Steel Research 128 (2017) 354–361
0.025
M=My
4
1
51.6% 48.4%
3
63.9% 42.9%
2
36.1%
60.4% 49.0% 51.0%
1
39.6%
34.6% 65.4%
0.000
41.5% 58.5%
0.010
57.1%
Panel zone shear rotation
0.015
0.005
References
M=Mu
Connection rotation
50.3% 49.7%
Rotation /rad
0.020
361
2
3
4
Specimen Fig. 12. Composition of joint rotation of the specimens.
(2) The flexural yielding of the end plate is a ductile yielding mechanism, and a significant part of the plastic rotation is provided by this yielding mechanism before the bolts fail. Thinner end plates and larger bolts could increase the deformability of the joint but may result in uneconomical design, with only some bolts bearing most of the load increments after end-plate yielding. Therefore, end plate thickness should be properly designed to be compatible with the bolt size so that the resistances corresponding to end-plate yielding and bolt failure are comparable. (3) For ultra-large capacity end-plate joints, connection rotational stiffness can be as large as the shearing stiffness of the panel zone with appropriate design, indicating that high rotational stiffness can be developed by this joint. After yielding of the joint, the connection rotation, caused mainly by the bending of the end plate, increased rapidly while the panel zone also developed plastic rotation. Therefore, balanced design of the end-plate connection and the panel zone is recommended to obtain a good ductility. (4) Under the yielding moment the inner bolts close to the center of the beam tension flange were most likely to fail while the corner bolts could be ignored in the moment resistance design. Based on the results, a distribution model of the tension load resisted by the bolts in tension is proposed for ultra-large capacity end-plate joints. This model can also be adopted in the analysis of end plates. (5) In the design of ultra-large capacity end-plate joints, the resistance of the panel zone can be calculated based on the Chinese code, the American code, or the Eurocode. The moment resistance controlled by the bolts can be designed with the equivalent tension bolt number of 7.0. (6) Further studies are needed with practically designed specimens subjected to cyclic loads to investigate the seismic performance of ultralarge capacity end-plate joints.
Acknowledgements The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (No. 51478244) and the Excellent Young Scientist Programme of the National Natural Science Foundation of China (No. 51522806).
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Contents lists available at ScienceDirect
Journal of Constructional Steel Research
Experimental study of ultra-large capacity end-plate joints Gang Shi ⁎, Xuesen Chen, Dongyang Wang Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Department of Civil Engineering, Tsinghua University, Beijing 100084, PR China
a r t i c l e
i n f o
Article history: Received 24 January 2016 Received in revised form 5 September 2016 Accepted 6 September 2016 Available online xxxx Keywords: Steel structure Beam-to-column joint Ultra-large capacity End-plate connection Experimental study
a b s t r a c t When bolted joints are required in steel structures involving large spans or heavy loads, ultra-large capacity endplate joints with 12 bolts or 16 bolts in tension should be applied if ordinary end-plate joints or large capacity end-plate joints cannot meet the resistance requirement. Four full-scale specimens of ultra-large capacity endplate joints were tested subjected to monotonic load. The moment-rotation curves of all the specimens were obtained, and the moment resistance, rotational stiffness, and distribution of the bolt strain increments in tension were analyzed when the bolt diameter, the end-plate thickness, or the layout of the bolts changed. The tested ultra-large capacity end-plate joints shared the failure mode of end-plate yielding followed by bolt fracture or necking, and the thickness of the end plate had an obvious influence on the joint resistance. A significantly inhomogeneous distribution of bolt strain increments was observed. Bolts in corners, which made little contribution to the moment resistance in the tests, could be removed or considered as shear-resistant bolts. In the design of this kind of joint, the resistance of the panel zone can be decided according to the Chinese code, the American code, or the Eurocode, and the equivalent number of the bolts in tension is recommended to be 7.0 based on a proposed distribution model of the tension load resisted by bolts in tension, derived from the tests. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The extended end-plate joint, with an end plate welded at the end of the beam and connected to the flange of the column by bolts, is among the widely adopted beam-to-column joints in steel frames. This joint form has an advantage in construction without field welding. Also, large rotational stiffness and satisfactory ductility can be developed in this joint provided it is properly designed [1,2,3,4,5,6,7]. Conventional configurations of extended end-plate joints are shown in Fig. 1, with eight bolts in total, four of which are arranged in tension. End-plate stiffeners are often applied to improve joint performance when the joint is designed as a rigid one. Many investigations on the performance of conventional extended end-plate joints have been conducted [8,9,10,11,12, 13], and several design methods have been proposed in different design codes or guides [14,15,16,17,18,19]. The design method in the Chinese code [14] and that in the American code [18] regard conventional extended end-plate joints as rigid, so only the moment resistance needs to be checked. In both methods the four bolts in tension are considered to share the tension force equally and the T-stub analogy method is employed to check the resistance of end plates. Also, yield line models based on plate theories are specified in several design codes or guides [15,16,17,18] with equations to check the end-plate thickness provided. In Eurocode 3, all joints must be estimated to determine whether they are rigid, semi-rigid, or just pinned, ⁎ Corresponding author. E-mail address: [email protected] (G. Shi).
http://dx.doi.org/10.1016/j.jcsr.2016.09.001 0143-974X/© 2016 Elsevier Ltd. All rights reserved.
based on the ratio of rotational stiffness to beam line stiffness [19], so both the moment resistance and the rotational stiffness must be checked. The component method is adopted to predict the joints' moment resistance and initial rotational stiffness, and the basic component in extended end-plate joints is the T-stub [10]. It also should be noted that the specified ultimate states of the high-strength bolts in the Chinese code are different with that in the other two codes above. In the Chinese code the employment of slip-critical high-strength bolts is recommended in end-plate connections and it is specified that the ultimate state of such bolts in tension is the state when the connected plates separate from each other around the bolts [14], whereas in the American code and the Eurocode, the bolt reaches its ultimate state when it fails. As the moment resistance demand for beam-to-column joints is increased in steel frames involving large spans or heavy loads, conventional extended end-plate joints might not meet the resistance requirement, being limited by the axial tension capacity of the bolts. Two improved configurations, both referred to as large capacity endplate joints with eight bolts arranged in tension, have been proposed and investigated [20,21,22]. The first configuration, illustrated in Fig. 2(a), features a wide end plate and two 4-bolt rows in tension, and the component method in Eurocode with T-stubs can be adopted in the design of such joints in theory if the stiffeners are ignored. The second configuration, illustrated in Fig. 2(b), features a long end plate and four bolt-rows in tension. A method based on the research of Murray and Kukreti [20] was proposed in the American code for the design of stiffened long-end-plate joints [16,18], and the component method can also be applied to design this kind of joint theoretically. Based on
G. Shi et al. / Journal of Constructional Steel Research 128 (2017) 354–361
355
Notation tep-nom nominal thickness of end plate width of beam bb depth of beam hb thickness of beam flange tbf thickness of beam web tbw thickness of end plate tep width of column bc depth of column hc thickness of column flange tcf thickness of column web tcw E Young's modulus yield strength fy yield strain εy strain at the end of yielding plateau εst ultimate tensile strength fu connection rotation φc panel zone shear rotation φpz M moment at beam end ultimate moment resistance Mu yield moment resistance My φ joint rotation joint rotation corresponding to ultimate moment φu resistance plastic join rotation corresponding to ultimate moment φup resistance joint rotation corresponding to yield moment resistance φy rotational stiffness Kφ γ engineering principal shear strain in plane tension load resisted by the bolt most likely to fail Nt equivalent number of tension bolts Neq tension resistance of a single bolt Nb
the existing investigations, large capacity end-plate joints can show heightened rotational stiffness [22] but the axial forces in different bolts in tension develop quite inconsistently, with the stress increments of the outer bolts significantly lower than that of the inner bolts close to the web or extended stiffeners [23]. The moment resistance of large capacity end-plate joints may still be insufficient in situations with special requirements. Therefore, a new end-plate joint called the ultra-large capacity end-plate joint is proposed in this paper. As illustrated in Fig. 3, this new joint form has an arrangement of 32 bolts or 24 bolts in total, with half of the bolts located in the tension side. As in large capacity end-plate joints, bolts in tension in
Column flange End plate End-plate stiffener
Column web
Beam web
Beam flange
Bolt Continuous plate (a)
(b)
Fig. 1. Conventional configurations of extended end-plate joints: (a) with end-plate stiffeners; (b) without end-plate stiffeners.
(a)
(b)
Fig. 2. Configurations of large capacity end-plate joints: (a) with wide end plate; (b) with long end plate.
ultra-large capacity end-plate joints are considered to develop a complex distribution of axial force. It should be noted that end plates with stiffeners, which are recommended to improve joint performance, can experience a complex stress state, so that ultra-large capacity endplate joints cannot be properly divided into conventional T-stubs, indicating that the existing design methods given above for end-plate joints cannot be applied in the design of this joint form directly. Also, the yield line models in existing codes are all corresponding to connection configurations with one bolt column in each side and cannot be applied in design of the two-column bolt group in ultra-large capacity end-plate joints. To determine a proper design method for the tested joint form, it is necessary to analyze the performance of this kind of joint. In this paper, four full-scale specimens of ultra-large capacity endplate joints with different end-plate thickness, bolt diameter, or bolt layout were subjected to monotonic loads to investigate the performance of this new joint form. Failure modes as well as moment-rotation curves are discussed and the distribution of the tension strain increments in the bolts is analyzed. 2. Experimental program 2.1. Specimens Four ultra-large capacity end-plate joint specimens, fabricated with welded H-section beams and columns, were designed with different joint parameters. The beams and the columns shared the same welded section H800 × 500 × 60 × 30. The total length of 5 m for the columns was determined based on a typical steel frame design, and the cantilever beam, connected to the flange with end plate and bolts in the middle of the column, was 3 m in length. The parameters of the joints are shown in Table 1 and the measured dimensions of all the specimens are given in Table 2. The name of each specimen is constituted by the sequence number (1–4), the nominal thickness of the end plate (EP32 for the 32 mm thick end plate and EP25 for the 25 mm thick end plate), the nominal bolt diameter (M30 bolt or M27 bolt) and a letter for the bolt layout (A or B). The specimen 1-EP32-M30-A was designed as a standard specimen whereas specimens 2–4 changed end plate thickness, bolt diameter, and bolt layout respectively compared to the standard specimen. The bolt layout types are illustrated in Fig. 3, where layout type A has 32 bolts in total and layout type B removes 8 of the bolts. There are 8 bolt rows and 4 bolt columns, and for convenience in the
356
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B13 B14
B21 B22
B23 B24
B31 B32
B33 B34 B43 B44
B13 B12 B23 B24 B21 B22
B31 B32 B42
B33 B34 B43
340
B41 B42
100 100 100 100 70
B11 B12
60100 90 90 100 60
70 100 100 100 100
70 100 100 100 100
340
100 100 100 100 70
60 100 90 90 100 60
(a)
(b)
(c)
Fig. 3. Configurations of ultra-large capacity end-plate joints: (a) sketch; (b) bolt layout A; (c) bolt layout B (units: mm).
following analysis, the bolts in row i and column j are identified by Bij as shown in Fig. 3. 2.2. Materials The steel of all the specimens was Q345 and the nominal yield strength was 345 MPa. Tensile tests were conducted with three identical coupons for each plate thickness except for the 60 mm plates, which exceeded the upper limit of plate thickness allowed by the coupon test machine. The test results are summarized in Table 3 and the stressstrain curves of the plates are shown in Fig. 4. The maximum elastic moment developed by the beams was calculated as 7778 kN·m based on the nominal yield strength of the beam, and that level of resistance was sufficient for the members to remain elastic during the experiments. Thus it could be ensured that specimen failure would occur in the joint region rather than in the members. All the bolts used in the specimens were Grade 10.9 high-strength bolts with pre-tension force applied to meet the requirements of the Chinese code [10]. For the M30 bolts the pre-tension force was specified as 355 kN and for the M27 bolts it was 290 kN. The Young's modulus of the bolts was 206 GPa and the ultimate strength was 1175 MPa according to the quality certification of the bolts. 2.3. Test setup The test setup is shown in Fig. 5. The column was placed horizontally and restrained by two anchor bolt supports at each end, and a horizontal constraint was fixed at the south end, simulating the hinge supports at the column ends. A 3000kN actuator was fixed on the reaction wall with a connecting beam. The horizontal push load provided by this actuator was applied at the height of 3.025 m from the upper face of the column's upper flange. Out-of-plane restraints were fixed on the reaction frame with a beam in each side, as illustrated in Fig. 5 (b), at the
Table 1 Summary of the parameters of the connections in the specimens. Specimen
tep-nom (mm)
Bolt size
Bolt layout
1-EP32-M30-A 2-EP25-M30-A 3-EP32-M27-A 4-EP32-M30-B
32 25 32 32
M30 M30 M27 M30
A A A B
height of 2.895 m from the upper face of the column's upper flange. A 5 mm-wide space was left between the beam edge and the out-ofplane restraint in each side, but during the loading progress the maximum lateral displacement of each beam was no more than 1.05 mm, indicating that the out-of-plane restraints made no influence to the test results. Before the monotonic push load was applied, pre-tension forces were applied by fastening the bolts using the torque wrench method. 2.4. Instrumentation The axial strain of every high-strength bolt adopted in the specimens was measured with strain gauges pre-embedded into the bolt in accordance with the method proposed in reference [24] to analyze the distribution of axial force increments in bolts. Extensometers were arranged to obtain the joint rotation as shown in Fig. 6(a). According to the Eurocode, a joint is constituted by the connections and the panel zone in the column web [19], so the joint rotation of end-plate joints can be divided into two components [25]. The first is the connection rotation φc that can be calculated by the relative displacement between the end plate and the column flange in the centerline of the beam flanges, based on Eq. (1). The other component is the panel zone shear rotation φpz that can be calculated by the increments of the diagonal length of the panel zone, based on Eq. (2). The symbols in the equations are illustrated in Fig. 6(a).
φc ¼
φpz
δ1 −δ2 hb −t bf
δ4 −δ3 ¼ 2
ð1Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 bpz þ hpz bpz hpz
ð2Þ
The shear strain of the panel zone was measured by strain rosettes as illustrated in Fig. 6(b). The in-plane principal shear strain γ was calculated by Eq. (3), where ε0, ε45, and ε90 represent the strains in the directions with angles to the horizontal plane equaling 0°, 45°, and 90°, respectively [26].
γ¼
pffiffiffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðε 0 −ε 45 Þ2 þ ðε45 −ε 90 Þ2
ð3Þ
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357
Table 2 Summary of the measured dimensions of the specimens. Specimen
bb (mm)
hb (mm)
tbf (mm)
tbw (mm)
tep (mm)
bc (mm)
hc (mm)
tcf (mm)
tcw (mm)
1-EP32-M30-A 2-EP25-M30-A 3-EP32-M27-A 4-EP32-M30-B
500.1 500.3 500.1 499.8
800.3 799.6 799.4 799.4
59.76 59.85 60.02 59.93
30.11 30.12 29.85 29.86
32.11 25.08 31.86 31.92
499.5 499.2 499.8 500.0
799.9 800.1 800.0 799.6
59.77 60.08 59.89 60.03
29.93 30.08 30.11 29.86
3.1. Failure mode All the specimens shared a similar failure mode: end plate yielding followed by bolt fracture or necking. Fig. 7(a)–(c) shows the overall setting of specimen 2-EP25-M30-A and the local deformation of the end plate of this specimen in the failure state, indicating that significant rotation developed in this joint and the tension side of the end plate obviously yielded in this failure mode. The other specimens showed deformations at the end of loading similar to those illustrated in Fig. 7(a)–(c). When the joint failed, paint cracking of the end plate was observed along the edge of the beam flange and end-plate stiffener on the tension side. The open displacements between the end plate and the column flange in the centerline of the beam tension flange, illustrated in Fig. 7(b) and marked as δ1, reached maximums of 10.7 mm, 18.5 mm, 10.3 mm, and 11.5 mm for Specimens 1 to 4 respectively. This open displacement was greatest in specimen 2-EP25-M30-A that had the least end-plate thickness. As the open displacement, caused mainly by the bending deformation of the end plate, is a basic component of the joint's plastic rotation, a thinner end plate is expected to contribute to a greater capacity for plastic deformation. Significant open displacements also developed between the end plate and the column flange in the centerline of the end-plate stiffener at the edge of the end plate in tension, identified in Fig. 7(c) and marked as δs. This displacements reached maximums of 12.5 mm, 21.0 mm, 13.6 mm, and 14.1 mm for Specimens 1 to 4 respectively. Although the displacements δ1 and δs were considerable, the corners of the end plates still remained in contact with the column flange for all specimens, indicating that biaxial bending deformations were developed in the end plates in tension. Such deformations were more complex than simple planar bending or existing yield line models for the design of end plates. To design end plates in ultra-large capacity end-plate joints, new analysis methods with biaxial bending taken into consideration should be adopted. The failed bolts in specimen 2-EP25-M30-A are illustrated in Fig. 7(d), showing two typical failure modes of the bolt, fracture and necking. Bolt failures were observed in each specimen and the distribution of the failed bolts in all specimens is illustrated in Fig. 8. According to this figure, 6 bolts failed in specimen 2-EP25-M30-A, 5 bolts being fractured and one necked, and 12 bolts were necked in specimen 3-EP32M27-A. These findings indicate that when a thinner end plate was applied, the inner bolts B22, B23, B32 and B33 might withstand most of the load increments after the yielding of the end plate, so that the other bolts in tension could not develop full strength, which was uneconomical in the structural design. When smaller bolts or a thicker end plate were used, an economical design could be obtained such that most of
the bolts in tension developed their strength adequately as in specimen 3-EP32-M27-A after end-plate yielding, but the plastic deformation capacity could be decreased because of the limited bending deformation of the end plate. Therefore, it can be deduced that the thickness of the end plate and the diameter of the bolts should be compatible so that the resistances corresponding to end-plate yielding and bolt failure are comparable. 3.2. Moment-rotation curves The moment-rotation curves (M-φ curves) of the specimens are shown in Fig. 9. M represents the moment at the column face obtained by multiplying the loads applied by the actuator and a distance of 3.25 m, as illustrated in Fig. 5, and φ represents the joint rotation constituted by φc and φpz. The main performance indexes are summarized in Table 4, where the yield moment My is determined as 2/3 of the ultimate moment Mu according to reference [10]. This definition of My is coincident with the elastic limitation for end-plate joints specified in the Eurocode 3 [19] so that the joint rotational stiffness Kφ can be determined based on this moment. Compared to the resistance of specimen 1-EP32-M30-A, the moment resistance of specimens 2-EP25-M30-A and 3-EP32-M27-A showed a decrease of 17.6% and 9.1% respectively, whereas the moment resistance of specimen 4-EP32-M30-B only decreased by 3.7%. Therefore, it can be concluded that the corner bolts removed in layout B exerted almost no influence on the moment resistance of the ultra-large capacity end-plate joint. Furthermore, the rotational stiffness of specimen 4-EP32-M30-B showed a small increase compared to that of specimen 1-EP32-M30-A. Fig. 10 illustrates the moment-principal shear strain (M-γ) curves of the specimens. The design moment resistance of the panel zone was calculated to be 4318 kN·m, 4309 kN·m, and 4132 kN·m based on the Chinese code [14], the American code [27], and the Eurocode [19], respectively. The design moment resistances obtained by the Chinese code and the Eurocode are shown in Fig. 10; the result obtained by the American code was almost the same as that of the Chinese code. It is concluded that the design methods specified in these three codes could provide satisfactory predictions of the design moment resistance of the panel zone, although the resistance based on the Eurocode was a little lower than that of the Chinese and the American codes. Therefore, the existing design methods for the panel zone can be applied directly in
Stress /MPa
3. Results and analysis
600 500 400
25mm plate 30mm plate 32mm plate
300 200
Table 3 Summary of results of coupon tests.
100
Nominal plate thickness
E (MPa)
fy (MPa)
εy
εst
fu (MPa)
25 30 32
201,251 213,891 204,726
349.4 404.4 414.6
0.00174 0.00189 0.00203
0.01895 0.01585 0.02709
516.9 566.3 558.1
Strain
0 0
0.05
0.1
0.15
0.2
Fig. 4. Stress–strain curves of coupons.
0.25
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G. Shi et al. / Journal of Constructional Steel Research 128 (2017) 354–361
3.3. Distribution of the bolt tension strain increment
3000kN actuator
2895
anchor bolt support
3025
beam for out-of-plane restraints
beam
reaction wall
connecting beam
reaction frame
150t
N
anchor bolt horizontal support restraint
column 2500
2500 (a)
beam for out-of-plane restraints out-of-plane restraints
specimen
(b) Fig. 5. Test setup: (a) front view; (b) vertical view (units: mm).
predicting the resistance of ultra-large capacity end-plate joints. It is also noted that, in the late stage of the loading process, the panel zone of the joints except for specimen 2-EP25-M30-A had yielded and developed a considerable plastic shear deformation, providing part of the joint plastic rotation. Therefore, in ultra-large capacity end-plate joints a balanced design of resistance is recommended to provide a larger rotational capacity, taking full advantage of the ductility of both the end plate and the panel zone.
In ultra-large capacity end-plate joints, the axial forces transferred by different bolts can be quite diverse because of the bending deformation of the end plate. Thus it is necessary to decide the proportional relationship of the tension loads taken by the bolts in tension in order to predict the moment resistance of the joints. Based on reference [28] the tension load transferred by a bolt is approximately proportional to the tension force increment of the bolt when all the bolts are pretensioned, whereas in the elastic state, the tension force increment of a bolt is proportional to its tension strain increment, which can be measured by the gauges pre-embedded in the bolt. Therefore, the proportional relationship of the tension loads taken by the bolts could be represented by the ratio between the tension strain increments of the bolts. With the moment when all the pre-tension forces of the bolts were applied defined as the initial state, the normalized tension strain increments of the bolts, which were normalized by the strain increment of bolt B 22 at the state M = My , are listed in Table 5. It was proved by the absolute bolts strains measured in the test that all the bolts in the tested joints still kept elastic in the state corresponding to My with the bolt strains less than the yield strain. The bolt layout of each specimen is symmetrical about the centerline of the beam web, so only the bolts on one side were analyzed and the data in Table 5 are the mean values of the strain increments of two bolts in symmetrical positions. From Table 5 it can be observed that the tension strains of the corner bolts on the tension side (B11 and B41) in bolt layout A showed no increase but a little decrease, therefore no contribution was made by the corner bolts to the moment resistance and these bolts could be removed as bolt layout B or just regarded as shear-resistant bolts. Large tension strain increments developed in B22 and B32, indicating that these inner bolts were most likely to fail. Therefore, bolt B22 was regarded as the standard bolt and a distribution model of the tension load resisted by the bolts, as illustrated in Fig. 11, is proposed based on the data in Table 5. The sum of the normalized strain increments of the bolts in tension (except for the corner bolts) is defined as the equivalent number of tension bolts Neq because the resistance of the end-plate connections should be designed with the limitation of the bolt most likely to fail. According to Table 5, the Neq of the specimens changed from 7.06 to 7.45 with a mean value of 7.23, and the Neq based on the proposed model in Fig. 11 was 7.0, a finding that is a little conservative compared to the experimental results. Therefore, this model can provide a safe prediction of the moment resistance controlled by the bolts. Considering the recommended value of Neq, the moment resistance MR can be predicted by Eq. (4), where Nb is the tension resistance of a single bolt and taken as 540.5 kN and 657.9 kN for M27 bolt and M30 bolt respectively according to the quality certification. MR ¼ Neq Nb ðhb −t bf Þ
M
340
A 3
4
15
340 15
b pz = 650
M
2
1
B
h pz = 650 (a)
ð4Þ
(b)
Fig. 6. Instrumentation in joint region: (a) extensometers; (b) strain rosettes (units: mm).
Based on Eq. (4), the moment resistance controlled by the bolts of the tested joints were 2572.6 kN·m for Specimen 3-EP32-M27-A and 3131.5 kN·m for the other specimens that were with M30 bolts, respectively. The predicted moment resistance seemed to significantly underestimate the capacity of the tested joints compared to the measured ultimate moment resistance in Table 4, but it is a safe limitation that is acceptable for engineering design, because the fracture of the high-strength bolts is a typical brittle failure mode with the risk of progressive fractures in the bolt group and should be avoided in practice. Thus, the most dangerous bolt is recommended to be controlled in elasticity in design, which causes the underestimation of the moment resistance with the strength of the other bolts not fully developed.
G. Shi et al. / Journal of Constructional Steel Research 128 (2017) 354–361
359
Fig. 7. Specimen 2-EP32-M25-A in failure state: (a) overall setting; (b) front view of end-plate local deformation; (c) lateral view of end-plate local deformation; (d) failed bolts.
3.4. Joint rotation The two components of joint rotation, φc and φpz, were identified based on Eq. (1) and Eq. (2), and the composition of the joint rotation at the state M = My and M = Mu is shown in Fig. 12. According to this figure, the connection rotations accounted for 34.6%–50.3% of the joint rotation when M = My, and when M = Mu this percentage increased to 51.6%–63.9%. It can be inferred that, before yielding of the joint, the bolted end-plate connection could provide a rotational stiffness as
great as the shear rotational stiffness of the panel zone, and after yielding, the connection rotation developed more rapidly than the panel zone shear rotation, especially when a thinner end plate was employed. These characteristics of rotational performance make it possible for ultra-large capacity end-plate joints to demonstrate high rotational stiffness and a ductile yielding mechanism with great deformability. The joint rotational capacities φu and the plastic rotational capacities φup obtained in the tests are listed in Table 4, where φu is defined as the joint rotation corresponding to the ultimate moment resistance Mu, and φup is determined by Eq. (5).
6000
(a)
(b)
Mu Kφ
ð5Þ
M/kN·m
φup ¼ φu −
5000 4000
1-EP32-M30-A 2-EP25-M30-A 3-EP30-M27-A 4-EP32-M30-B
3000 2000
(c) Necked bolt
(d) Fractured bolt
1000 /rad 0 0
Fig. 8. Failed bolts in tension of each specimen: (a) 1-EP32-M30-A; (b) 2-EP25-M30-A; (c) 3-EP32-M27-A; (d) 4-EP32-M30-B.
0.005
0.01
0.015
0.02
Fig. 9. Moment-rotation curves of the specimens.
0.025
360
G. Shi et al. / Journal of Constructional Steel Research 128 (2017) 354–361
Table 4 Performance indexes of specimens. Specimen identifier
Mu (kN·m)
φu (rad)
φup (rad)
My (kN·m)
φy (rad)
Kφ (kN·m)
1-EP32-M30-A 2-EP25-M30-A 3-EP32-M27-A 4-EP32-M30-B
6091.0 5021.9 5534.6 5923.3
0.0207 0.0193 0.0211 0.0228
0.0148 0.0131 0.0143 0.0175
4060.7 3347.9 3689.7 3948.9
0.00390 0.00412 0.00451 0.00355
1.041 × 106 0.813 × 106 0.818 × 106 1.112 × 106
7000
5000
M/kN·m
M/kN·m
7000
6000
6000 5000
Chinese code Eurocode
4000
Chinese code Eurocode
4000
3000
3000
2000
1-A 1-B
A
1000
2000
B
0
2-A 2-B
A
1000
B
0 0
0.002
0.004
0.006
0.008
0.01
0
0.002
0.004
(a)
5000
M/kN·m
7000 M/kN·m
7000 6000
0.006
0.008
0.01
(b)
6000 5000
Chinese code
4000
Chinese code Eurocode
4000
Eurocode
3000
3000
2000
3-A 3-B
A
1000
2000
B
1000
B
0
4-A 4-B
A
0 0
0.002
0.004
0.006
0.008
0.01
0
0.002
0.004
(c)
0.006
0.008
0.01
(d)
Fig. 10. Moment-principal shear strain curves of the specimens: (a) 1-EP32-M30-A; (b) 2-EP25-M30-A; (c) 3-EP32-M27-A; (d) 4-EP32-M30-B.
From Table 4 it can be observed that the joint rotational capacities were between 0.0193 rad and 0.0228 rad and the plastic rotational capacities were between 0.0131 rad and 0.0175 rad for the specimens. The joint rotational capacity of 2-EP25-M30-A was the lowest of the specimens, mainly due to the insufficient development of the panel zone shear rotation under a lower ultimate moment resistance than the other specimens, as illustrated in Fig. 10. Therefore, a balanced design for the resistance is important to increase the rotational capacity of this joint. According to the American code and the Eurocode, the seismic performance of a joint is evaluated by plastic story drift rather than by joint rotation [29,30]. However, the four specimens in this research were designed to develop failure modes in the joint region, so that a large beam section and a short span were applied, features that made the specimens atypical for estimating story drift because a full-strength joint design with joint moment resistance greater than the plastic moment of the beam is recommended in practice. Also, cyclic experiments are expected to check the ductility and the energy dissipation capacity of this joint. Further study is needed with practically designed specimens subjected to cyclic loads, to investigate the seismic performance of ultra-large capacity end-plate joints.
Table 5 Normalized tension strain increments of bolts in tension under the yielding moment. Specimen
1-EP32-M30-A 2-EP25-M30-A 3-EP32-M27-A 4-EP32-M30-B Average
Normalized tension strain increment
4. Conclusions Four full-scale ultra-large capacity end-plate joints were subjected to monotonic loads. The failure modes as well as the moment-rotation relationships of this joint form were studied. A distribution model of the tension load resisted by the bolts in tension was proposed, based on analysis of the bolt strain increments. The following conclusions can be drawn from this investigation. (1) The specimens shared a similar failure mode, with end-plate yielding followed by fracture or necking of several bolts in tension. Significant biaxial bending of the end plates was observed in all specimens, and this yielding mechanism could not be covered by T-stub analysis. It is necessary, therefore, to develop new methods or models for design of the end plates in ultra-large capacity end-plate joints.
0
0.45Nt
0.45Nt
0
0.55Nt
Nt
Nt
0.55Nt
0.55Nt
0.8Nt
0.8Nt
0.55Nt
0
0.15Nt
0.15Nt
0
Neq
B11
B12
B21
B22
B31
B32
B41
B42
−0.10 −0.04 −0.08 – −0.07
0.57 0.20 0.20 0.77 0.43
0.46 0.58 0.69 0.51 0.56
1.00 1.00 1.00 1.00 1.00
0.53 0.64 0.66 0.47 0.57
1.02 1.13 0.87 0.90 0.98
−0.05 −0.01 −0.01 – −0.03
−0.07 0.06 0.16 0.09 0.06
7.06 7.21 7.14 7.45 7.23
Fig. 11. A distribution model of the tension load resisted by the bolts in tension.
G. Shi et al. / Journal of Constructional Steel Research 128 (2017) 354–361
0.025
M=My
4
1
51.6% 48.4%
3
63.9% 42.9%
2
36.1%
60.4% 49.0% 51.0%
1
39.6%
34.6% 65.4%
0.000
41.5% 58.5%
0.010
57.1%
Panel zone shear rotation
0.015
0.005
References
M=Mu
Connection rotation
50.3% 49.7%
Rotation /rad
0.020
361
2
3
4
Specimen Fig. 12. Composition of joint rotation of the specimens.
(2) The flexural yielding of the end plate is a ductile yielding mechanism, and a significant part of the plastic rotation is provided by this yielding mechanism before the bolts fail. Thinner end plates and larger bolts could increase the deformability of the joint but may result in uneconomical design, with only some bolts bearing most of the load increments after end-plate yielding. Therefore, end plate thickness should be properly designed to be compatible with the bolt size so that the resistances corresponding to end-plate yielding and bolt failure are comparable. (3) For ultra-large capacity end-plate joints, connection rotational stiffness can be as large as the shearing stiffness of the panel zone with appropriate design, indicating that high rotational stiffness can be developed by this joint. After yielding of the joint, the connection rotation, caused mainly by the bending of the end plate, increased rapidly while the panel zone also developed plastic rotation. Therefore, balanced design of the end-plate connection and the panel zone is recommended to obtain a good ductility. (4) Under the yielding moment the inner bolts close to the center of the beam tension flange were most likely to fail while the corner bolts could be ignored in the moment resistance design. Based on the results, a distribution model of the tension load resisted by the bolts in tension is proposed for ultra-large capacity end-plate joints. This model can also be adopted in the analysis of end plates. (5) In the design of ultra-large capacity end-plate joints, the resistance of the panel zone can be calculated based on the Chinese code, the American code, or the Eurocode. The moment resistance controlled by the bolts can be designed with the equivalent tension bolt number of 7.0. (6) Further studies are needed with practically designed specimens subjected to cyclic loads to investigate the seismic performance of ultralarge capacity end-plate joints.
Acknowledgements The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (No. 51478244) and the Excellent Young Scientist Programme of the National Natural Science Foundation of China (No. 51522806).
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