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Experimental study on earthquake-resilient prefabricated cross joints with L-shaped plates
Engineering Structures 184 (2019) 74–84
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Experimental study on earthquake-resilient prefabricated cross joints with Lshaped plates
T
⁎
Zi-qin Jianga,b, Chao Douc, , Ai-lin Zhanga,b, Qi Wanga,b, Ying-xia Wua,b a
College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China Beijing Engineering Research Center of High-Rise and Large-Span Prestressed Steel Structure, Beijing 100124, China c School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Earthquake-resilient Flange cover plate Straight dog-bone weakening Damper Seismic performance Post-earthquake restoring performance
Earthquake-resilient functionality has become a leading issue in seismic engineering, and as an important component of earthquake-resilient, cross joints have become a research hotspot. A new type of earthquakeresilient prefabricated cross joint (ERPCJ) with L-shaped plates for damage control have been proposed in this study. The new type of prefabricated cross joint is constructed of a circular tubular steel column with a cantilever beam, a common beam, and a connection device consisting of a flange cover plate, L-shaped plates, and highstrength bolt groups. By controlling the thickness of the flange cover plate and the distance of the middle bolt, the rigidity of the connection can be adjusted so that the frictional sliding of the bolt and the plastic deformation of the flange cover plate can dissipate energy and ensure that the beams, columns, and other primary components do not undergo plastic failure. To study the seismic performance and earthquake-resilient performance of this new type of cross joint, three specimens were designed and fabricated. Unequal amplitude low cyclic loading tests were carried out on the three designed specimens, while 30 laps of an equivalent amplitude low cyclic loading test was carried out on a repaired specimen. The hysteresis curves, skeleton curves, and failure modes of the specimens were obtained. The effect of the distance of the middle bolt, shape of the bolt holes, and repair test on the seismic performance of the joints were investigated. The experimental results indicate that the joint can effectively utilize the plastic deformation of the flange cover plate and the sliding of the bolt for energy dissipation. Adjusting the middle bolt distance had a significant effect on the bearing capacity and energy dissipation capacity of the joint. Changing the form of the bolt hole from circular hole to slotted hole effectively improves the ductility of the joint. The repaired joint retained its good energy dissipation capability, indicating that the joint has a good post-earthquake restoring performance and can be used as a displacement-control damper.
1. Introduction For building structures, the advantages of using prefabricated steel structures, which include factory production, assembly construction, and environmental friendliness, are becoming increasingly apparent [1]. Being an important part of the design of prefabricated steel structures, a new type of joint that has a reasonable structure and good energy dissipation capacity could effectively promote the development of prefabricated steel structures [2–7]. For steel frame joints with a cantilever beam, numerous studies have conducted relevant theoretical analyses and experimental research. Astaneh-Asl [8] performed theoretical calculations for a beamcolumn joint with a cantilever beam, and proposed a design employing semi-rigid connections, which can allow the beam-column joint with a ⁎
cantilever beam to slip during a strong earthquake rather than design earthquake. The slippage at the friction surface of the bolt and the squeezing between the bolt rod and the hole wall can absorb seismic energy. Oh et al. [9] developed a method of dog-bone weakening in joints with cantilever beams. The results indicate that ductility and rotation capacity can be improved by using a dog-bone weakening form in the joint with a cantilever beam. Mullin et al. [10] studied the seismic behaviour of semi-rigid steel frames with cantilever beams. The results showed that sliding of the splicing plate and bolt can improve the deformation performance of joints and dissipate seismic energy. Li et al. [11,12] carried out theoretical analyses on the design of beamcolumn joints with cantilever beams, performed related experimental studies, and provided relevant design suggestions. The results showed that the ductility of a semi-rigid joint was better than that of traditional
Corresponding author. E-mail address: [email protected] (C. Dou).
https://doi.org/10.1016/j.engstruct.2019.01.067 Received 13 September 2018; Received in revised form 9 January 2019; Accepted 13 January 2019 0141-0296/ © 2019 Published by Elsevier Ltd.
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welded joints, as the semi-rigid joint can make full use of the slippage at the friction surface and squeezing between the bolt rod and hole wall. Zhang et al. [13,14] proposed a beam-column joint with Z-shaped cantilever beams. Experimental results showed that reducing the number of flange bolts slightly reduced the carrying capacity, but the ductility, rotation ability, and energy dissipation capacity were significantly improved. Wang et al. [15] studied the seismic behaviour of flange-stiffened joints with low cyclic loading tests and provided some design suggestions. The strengths and weaknesses of the flange-stiffened and flange-weakened joints were also compared. Chen et al. [16] compared and analysed ordinary joints and dog-bone shaped joints experimentally. Zhou et al. [17] developed a design that moved the plastic hinge to the splicing region, which allowed the steel girder splicing joint to produce a plastic hinge before a large earthquake, playing the role of a fuse. For beam-column cross joints, Li et al. [18] carried out low cyclic loading tests on three cross-shaped full-size bulkhead pierced beam-column joints, and analysed multiple aspects of the seismic performance of the joints. Kim et al. [19] compared and analysed the performance of square column-H beam cross joints and H column-H beam cross joints with a numerical simulation. Wu et al. [20] carried out experimental studies and numerical simulations on a new type of bolted beam-to-column connections for concrete filled steel tube and investigated related calculation methods for this joint. In an investigation of the holes, Ma et al. [21] conducted experiments on high strength bolt connections with slotted holes. The results suggested that the ductile deformation capacity and seismic performance of the joints could be significantly improved by sliding the bolts in the slotted holes. In a study of structural earthquake resilience, Farrokhi et al. [22] improved the earthquake resilience of joints by introducing replaceable cover plates with holes to the outside of the steel beam flange. Oh et al. [23] placed a replaceable seam steel damper at the end of the steel beam in a traditional T-type connection joint. The plastic deformation was then centralized at the damper, which can be easily replaced after an earthquake. Calado et al. [24] conducted low-cyclic-loading tests on 12 composite joints to prevent plastic damage on the main components through frictional sliding and plastic energy dissipation. Lu et al. [25] proposed three types of replaceable energy-dissipating components of beams. Test results showed that the components can be repaired quickly after the test to realize the earthquake-resilient. On the whole, by transferring the plastic hinges to the splicing region and using it to dissipate seismic energy, more advantages for the beam-column joints of steel frames with cantilever beams can be achieved. Replacing the splicing region components to achieve improved earthquake resilience is a direction for future research [26–32]. Therefore, in this study, a new type of earthquake-resilient prefabricated cross joint (ERPCJ) with L-shaped plates is proposed. Three ERPCJ specimens were designed by changing several parameters, such as the middle bolt distance and the bolt hole shape. Experimental and finite element analyses were conducted on the seismic performance of these three specimens and one repaired specimen. With a reasonable design of ERPCJ, such as the dog bone weakening of the joints and the form of the bolt hole, the sliding and plastic deformation occurs at the flange cover plate, which can improve the energy dissipation capacity of the joint and shield the main components, such as the beam and the column, from plastic damage while guaranteeing the bearing capacity. The connection device can then be quickly repaired after an earthquake, and the repaired joint retained its good energy dissipation capability, indicating that the joint has a good post-earthquake restoring performance and can be used as a displacement-control damper.
Upper flange cover plate
Circle tubular steel column
High-strength bolt group
Annular baffle Panel zone High-strength bolt group
Common beam L-shaped web connecting plate Lower flange cover plate
Cantilev er beam
Fig. 1. Construction of ERPCJ with L-shaped plates.
L-shaped web connecting plates, and high-strength bolt groups. These components are made in a factory and can be quickly assembled to construct the connection device at a construction site. A gap is set between the cantilever beam and the common beam to enhance the rotation capacity of the joint and to avoid direct collision between the two beams. The setting of L-shaped web connecting plate can improved the joint rotation ability by deformation of the plate. The ERPCJ has the advantages of factory production and assembly construction. In addition, increasing the thickness of the flange of the cantilever beam and using dog-bone weakening at the flange cover plate can allow the plastic hinge of the beam end to transfer to the flange cover plate, which is easily replaced. After an earthquake, the primary components of the beam and the column will not be damaged, while the joint function can be restored by replacing the detachable connection device. 3. Test program 3.1. Specimen design and material properties Due to the proposed earthquake-resilient ERPCJs are mainly used to replace tradition cross joint, thus the yield moment of ERPCJs should be basically the same as the yield moment of the whole-span common beam when ERPCJs design. According to this design concept, three specimens (SJ1, SJ2, and SJ3) was designed in this paper, and the geometric dimensions and related constructions of them are shown in Fig. 2. and take specimen SJ1 as the standard specimen, specimens SJ2 and SJ3 assessed the effects of the middle bolt distance and bolt hole shape, respectively, on the failure mode and energy dissipation capacity. The circular tubular steel column with cantilevered beam was welded from the upper and lower circular tubular steel column to the middle column panel zone with cantilever beam, and the cantilever beam and the common beam were connected by flange cover plates and L-shaped plates. The cross-section dimensions of the upper and lower circular tubular steel columns were 377 × 16 mm. The cross-section dimensions of the middle column panel zone were 377 × 20 mm. The section of the H-shaped steel in the common beam was 300 × 200 × 6 × 12 mm. The cantilever beam was strengthened and had dimensions of 300 × 200 × 12 × 20 mm. The length of the column was 3000 mm, and the length of the cantilever beam was 700 mm (the distance from the end of the cantilever beam to the centre of the column). The length of the common beam was 1400 mm, as shown in Fig. 2. The thickness of flange cover plate was 16 mm, and it was made from Q235B steel, but all other plates were constructed of Q345B steel. Grade 10.9 M22 frictional type high-strength bolts were used.
2. Construction of ERPCJ with L-shaped plates The new ERPCJs proposed in this study consist of a circular tubular steel column with two cantilever beams, common beams, and connection devices between the two beams, as shown in Fig. 1. The connection device is composed of upper and lower connecting flange cover plates, 75
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530
Circle tubular steel column
204
28 30
Slotte d hole
The plan of the cover pla te
Flange cover plate Common beam
Stiffening rib
L-shaped plate
Cantilever beam
Slotte d hole 45 110 45
1400
12
240 20
200
512
16
20
(b) Front view of the cantilever beam
300
12
66 66
Panel zone
700
200
12
20 3000
150 84 66 66 84
30 28
300
16 377
66 66 66 66
144
30
Lbolt
700
(a) Geometric size of the specimen
(c) Top view of the cantilever beam
Fig. 2. Geometric dimensions of specimen SJ1. Table 1 Specimen parameters.
Hydraulic jack
Hinge
Specimen
Lbolt (mm)
Hole shape in the cantilever beam
SJ1 SJ2 SJ3
320 386 320
slotted hole slotted hole circular hole
According to the Chinese Code for Design of Steel Structures (GB500172013) [33], 190 kN pretension force was applied to the high-strength bolts by torque control method. The specific parameters for each specimen are summarized in Table 1, in which Lbolt is the distance of the middle bolt. Besides, to evaluate the post-earthquake restoring performance of these new types of joint, a repaired specimen (SJ1R) was created by replacing the connection device in SJ1 after testing; its basic parameters were the same as for SJ1. Material tests [34] were conducted to evaluate the material properties of steel plates, as summarized in Table 2, in which fy is the yield strength, fu is the tensile strength, and fu/fy is the radio of the intensity to yield strength.
Hinge
Fig. 3. Loading system. Table 3 Loading law.
Tests were conducted at the Engineering Structure Experimental Center of Beijing University of Technology. The loading system is shown in Fig. 3. The top and bottom of the circular tubular steel column were constrained by universal hinge constraints. The axial compression ratio was maintained at 0.3 at the top of the column. Hydraulic jacks were used to provide low cyclic loads to the ends of beams on both sides of the column. Lateral braces were placed at the ends of these beams to prevent out-of-plane deformation of the beam during the loading process. The tests were conducted in accordance with the seismic code of the American Institute of Steel Construction (AISC) [35] and used a method
Load level
Rotation of joint (rad)
Cycle index
Displacement amplitude at the common beam end (mm)
1 2 3 4 5 6 7 8 9
0.00375 0.005 0.0075 0.01 0.015 0.02 0.03 0.04 0.05
6 6 6 4 2 2 2 2 2
7.58 10.10 15.15 20.20 30.30 40.40 60.60 80.80 101.00
of variable amplitude rotation (the ratio of the common beam end displacement to the distance from the common beam end to the centre of the column) control loading by changing the common beam end displacement. The specific loading law is summarized in Table 3 and Fig. 4.
Table 2 Material properties of steel plates. Thickness (mm)
fy (MPa)
fu (MPa)
fu/fy
Flange cover plate Other plates
16 mm 6 mm 12 mm 20 mm
254 379 368 372
391 514 526 572
1.54 1.36 1.43 1.54
Lateral brace
Lateral brace
3.2. Loading system and loading law
Plates
Hydraulic jack
Hydraulic jack
3.3. Measurement program Fig. 5 shows the layout of the strain measurement points on the specimen. Strain gauges were arranged on the circular tubular steel column, the cantilever beam, the common beam, and the flange cover 76
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8
Displacement (mm)
121 81 40
4% 3% 2% 1.5%
Rotation 0.375%
0.5%
0.75%
1%
5%
-40
2 0
6
6
-81
6 4 Cycle index
2
2
-2 2
-121 -162
6 4
0
1
2
3
4
Load level
2
beams and common beams, respectively. 4. Test results and analysis
Rotation (%rad)
162
4.1. Failure modes and mechanisms The moment-rotation curve and plate deformation during loading of specimen SJ1 indicate that at the initial loading stage, SJ1 was in an elastic phase, the moment-rotation curve was linear, and no obvious plastic deformation occurred on the specimen. When the joint rotation was 0.01 rad, the hysteresis curve reached its peak, and the flange cover plate entered a plastic stage. When the joint rotation was 0.015 rad, slight buckling deformation occurred in the dog-bone weakening region on both sides of the flange cover plate. When the loading point then returned to the initial position, deformation of the dog-bone weakening region of the flange cover plate was restored. As loading progressed, deformation of the flange cover plate became more pronounced and the plastic region expanded. When the joint rotation was 0.05 rad, buckling deformation of the flange cover plate became obvious. Meanwhile, no significant deformation of the beam and column parts of the specimen was observed, as shown in Fig. 7. After loading of specimen SJ1, the deformed flange cover plates, Lshaped plates, and bolt groups were replaced with new parts and reassembled to form the repaired specimen, SJ1R. The geometric parameters of SJ1R and the material for each replacement plate were the same as for specimen SJ1. However, the loading law was different from that used for specimen SJ1. The repaired specimen, SJ1R, was subjected to a low cyclic fatigue loading of 0.03 rad for 30 cycles. The failure mode of SJ1R is shown in Fig. 8. The remaining two specimens underwent a complete loading process, and the results were roughly the same as for specimen SJ1. The primary difference was that the middle bolt distance in specimen SJ2
-4 2
5 6 7 8 9
-6 -8
Fig. 4. Loading law.
plate to measure the strain at each part of the joint during loading. Seventeen displacement meters were placed on the specimen as shown in Fig. 6. Locations W1 was chosen to measure the beam end displacement on the right side of the specimen. Location W2 was in the same plane as the column and was selected to measure the degree of lateral displacement on the column. Locations W3, and W7 were arranged on the upper flange cover plate on the left and right sides of the specimen, respectively, and were chosen to measure the relative displacements on the right side of the upper flange cover plate relative to the common beam and cantilever beam. Locations W4 and W8 were selected to measure the relative displacement on the right side of the lower flange cover plate relative to the common beam and the cantilever beam, respectively. The displacement meters at W5, and W6 were used to measure changes of the relative displacement on the cantilever
Z1
X1' X2' X3'
L1' L2' L3'
L1 L2 L3
X1 X2 X3
(a) Front view
L4'
P3'
P2'
P1'
P4'
L5'
P7'
P6'
P5'
X4'
X4
X5' X6'
X5 X6
(b) Top view Fig. 5. Strain measurement locations. 77
P1
P2
P3
L4
P7
L5
P4 P5
P6
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W2
W1'
W1
W3'
W5'
W4'
W6'
W7' W7 W4
W9'
W8' W8
W9
W5
W3
W6
W4
Fig. 6. Displacement measurement locations.
(a) Deformation of the joint
(b) Deformation of the flange cover plate
Fig. 7. Deformation of specimen SJ1.
(a) Deformation of the joint
(b) Deformation of the flange cover plate
Fig. 8. Deformation of specimen SJ1R. 78
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(a) Deformation of the joint
(b) Deformation of the flange cover plate
Fig. 9. Deformation of specimen SJ2.
(a) Deformation of the joint
(b) Deformation of the flange cover plate
Fig. 10. Deformation of specimen SJ3.
rotation of specimen SJ1 was the same with SJ1R), the hysteretic curves of the two specimens were basically same and plump, and their energy dissipation capacity was also very similar. The energy dissipation of the repaired specimen, SJ1R, was stable under low cyclic fatigue loading, indicating that this joint has a good post-earthquake restoring performance and can be used as a displacement-control damper. Specimen SJ2 had a similar hysteresis curve to SJ1 in the early loading stages. Owing to the larger middle bolt distance of the flange cover plate in specimen SJ2, the deformation of the flange cover plate was large in the later stages, which caused the common beam flange to squeeze the cantilever beam flange. After this change of the force transfer mechanism of the specimen, there was a rapid increase in bearing capacity and a sharp corner appeared in the hysteresis curve. Specimen SJ3 also experienced an elastic phase, plate strengthening stage, and energy dissipation stage caused by the instability of the flange cover plate, and thus the hysteresis curve for specimen SJ3 was much the same as that for specimen SJ1. The bearing capacity and energy dissipation capacity were also approximately the same. The cumulative energy dissipation curves for the specimens at each loading level are shown in Fig. 12, and the trends of these curves for the three specimens are generally consistent. The energy dissipation curve for specimen SJ2 was smaller than the other two specimens, which is the result of the larger middle bolt distance on specimen SJ2, namely the longer length of unconstrained flange cover plate, which was more likely to result in instability deformation for flange cover plate under axial pressure. Thus, the bearing capacity was also slightly lower, while the hysteresis loop tended to be flatter, and the total energy dissipation of the specimen was smaller. The energy dissipation curve for specimen SJ3 was slightly higher than that of SJ1 because the holes in the flange of SJ3 were circular, and thus the development of plasticity in the squeeze of bolts and hole walls could also dissipate some energy. For the repaired specimen, SJ1R, the energy dissipation curve of the specimen was obtained by summing the area of the hysteresis loop every five laps, and is shown in Fig. 13. As the results show, with increasing
was larger than the other specimens. When the joint rotation was 0.01 rad, the flange cover plate of specimen SJ2 exhibited a slight bending deformation, and when the joint rotation of specimen SJ2 was 0.04 rad, the common beam and the cantilever beam were squeezed. The failure modes of specimens SJ2 and SJ3 are shown in Figs. 9 and 10, respectively. 4.2. Hysteresis curves and energy dissipation The joint rotation and the cantilever beam root bending moment of each specimen were used to create hysteresis curves, as shown in Fig. 11. These results show that the hysteresis curves were plump, indicating that the joints had good bearing capacity, energy dissipation capacity, and rotation capacity. Take the base specimen, SJ1, as an example, the specimen underwent an elastic stage, a plastic strengthening stage of the flange cover plate, and an energy dissipation stage caused by the buckling of the flange cover plate. During the initial stage of loading, the specimen only exhibited bending deformation and the moment-rotation curve changed linearly. As loading progressed, the flange cover plate entered a plastic strengthening stage, and the bearing capacity reached its peak. Then, the specimen entered a buckling stage at the flange cover plate, the bearing capacity of the specimen exhibited a gradual downward trend, and the buckling deformation of the flange cover plate became more obvious. After the specimen was unloaded, no significant plastic deformation was observed in any of the parts, except for the buckling deformation of the flange cover plate. The load value of the second cycle in each load level of hysteresis curve was always lower than the load value of the first cycle. This was mainly a result of the plastic damage to the flange cover plate and a decrease in the friction coefficient at the interface. In the early stage of loading, due to the different loading law, the hysteretic curves of SJ1 and SJ1R were different. However, when the specimen SJ1 reached the 7th load level (at which point the loading 79
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320
Cantilever beam root bending moment (kN·m)
Cantilever beam root bending moment (kN·m)
Z.-q. Jiang et al.
Experiment FEA Model
240 160 80 0 -80 -160 -240 -320 -5
-4
-3
-2
-1
0
1
2
3
4
5
Rotation (%)
320
Experiment FEA Model
240 160 80 0 -80 -160 -240 -320 -5
-4
-3
Cantilever beam root bending moment (kN·m)
Cantilever beam root bending moment (kN·m)
160 80 0 -80 -160 -240 -320 -5
-4
-3
-2
-1
0
1
2
0
1
2
3
4
5
3
4
5
(b) Specimen SJ1R
Experiment FEA Model
240
-1
Rotation(%)
(a) Specimen SJ1
320
-2
3
4
5
Rotation (%)
320
Experiment FEA Model
240 160 80 0 -80 -160 -240 -320 -5
-4
-3
-2
-1
0
1
2
Rotation (%)
(c) Specimen SJ2
(d) Specimen SJ3
Fig. 11. Hysteresis curves of specimens.
100 SJ1 SJ2 SJ3
150
90 80
Energy dissipation (kJ)
Cumulative energy dissipation (kJ)
200
100
50
70 60 50 40 30 20 10
0
0
1
2
3
4
0
5
Rotation (%)
1-5
6-10
11-15 16-20 Cycles
21-25
26-30
Fig. 12. Cumulative energy dissipation curves.
Fig. 13. Energy dissipation curve for SJ1R.
number of load cycles, the energy dissipation capacity of SJ1R showed a gradual downward trend, which eventually tended to become stable. At this time, the friction coefficient at the plate interface also tended to be stable.
common beam, and the column of the specimen at each loading level are shown in Fig. 14. Results of the material test indicate that the plastic strain at the specimen flange was approximately 1800 με. These results show that from the start of loading to the end, the flanges of the cantilever beams and common beams, and joint panel zone in each specimen were all in an elastic phase. The stress development for each specimen was similar, and the stress at the flange of the cantilever beam was larger than that at the flange of the common beam. When the joint
4.3. Strain analysis The measured strain of the flange at the cantilever beam and the 80
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1600
1600
1400
1400
1200
1200
1000
1000
Strain ( )
Strain ( )
Z.-q. Jiang et al.
800 600 400 200 0
0.01 0.015 0.02 0.03 0.04 0.05 X4
800
0.01 0.015 0.02 0.03 0.04 0.05
600 400 200 0
X5
X6
L4
L5
X4
Z2
X5
X6
L4
Strain gauge
Strain gauge
(a) Specimen SJ1
(b) Specimen SJ2
L5
Z2
1600 1400
Strain ( )
1200 1000 800 600 400 200 0
0.01 0.015 0.02 0.03 0.04 0.05 X4
X5
X6
L4
L5
Z2
Strain gauge
(c) Specimen SJ3 Fig. 14. Strain curves of specimen at each loading level.
200
rotation was 0.015 rad, the strains at the flanges of the cantilever beam and common beam decreased because of the appearance of the plastic hinges on the flange cover plate. This analysis shows that strengthening the cantilever beam and weakening the flange cover plate can effectively control the plastic hinge on the replaceable flange cover plate, allowing the main components of the specimen to remain in an elastic state, which is helpful for repairing the joint after an earthquake.
150
Load (kN)
100
SJ1 SJ2 SJ3
50 0 -50
4.4. Skeleton curves
-100 Fig. 15 shows the skeleton curves for each specimen. These skeleton curves in the elastic phase were basically linear, and the stiffness was much the same. When the beam load reached approximately 150 kN, the flange cover plate yielded, and the skeleton curve began to decline slowly. Owing to the large middle bolt distance on the flange cover plate in specimen SJ2, the flange cover plate of SJ2 was more prone to buckling. As a result, the ultimate bearing capacity of SJ2 was slightly less than that of SJ1, and its bearing capacity decreased more rapidly after instability. In the late stages, the common beam and the cantilever beam of SJ2 were squeezed, which increased the bearing capacity of SJ2. As specimen SJ3 had a circular bolt hole, the decrease in the
-150 -200
-100
-50
0
50
100
Displacement (mm) Fig. 15. Skeleton curves.
bearing capacity of SJ3 was the most gradual. In addition, the skeleton curves for the two loading directions of the specimens were not 81
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Table 4 Primary performance indicators of specimens. Specimen
Py (kN)
SJ1 SJ2 SJ3
Δy (mm)
Pmax (kN)
SJ1 SJ2 SJ3
μ
PLD
NLD
PLD
NLD
PLD
NLD
PLD
NLD
PLD
NLD
140.57 130.97 130.98
144.75 146.42 137.74
16.74 16.91 16.4
17.04 16.29 16.88
156.01 147.74 150.29
147.97 151.56 139.67
54.74 51.63 79.45
55.41 55.74 81.32
3.27 3.06 4.84
3.25 3.42 4.82
loading stages, although the bearing capacity of the specimen increased significantly because of the collision of the common beam and the cantilever beam, the hysteresis curve was pinched, and the total energy dissipation remained low. Therefore, the equivalent viscous damping coefficient was significantly lower at a rotation of 0.05 rad.
Table 5 Energy dissipation indicators of the specimens. Specimen
Δ0.8Pmax (mm)
Equivalent damping ratio of the specimens for each joint rotation 1.0%
1.5%
2.0%
3.0%
4.0%
5.0%
0.099 0.077 0.091
0.215 0.230 0.245
0.321 0.305 0.317
0.382 0.347 0.346
0.369 0.326 0.362
0.348 0.237 0.358
5. Finite element analysis 5.1. Finite element model Finite element software ABAQUS [37] was used to carry out finite element analyses on the seismic performance of the above four specimens. The beam, column, and bolts were modelled with solid element C3D8R, as shown in Fig. 16. Contact relationships were set between the flange cover plate and the beam flange as well as bolts, and L-shaped plate and the beam web as well as bolts. The friction coefficient was considered on interfaces, and its value was 0.45 [31,33]. In addition, a preload of 190 kN was applied to the bolts. The plate material, boundary conditions, and loading law were consistent with the previous tests. The element number of each finite element model was about 332 thousand, and the full Newton-Raphson method was adopted for the solution.
completely symmetrical owing to the accumulated damage and the initial installation defects of the plates under the action of a reciprocating load. 4.5. Primary performance indicators The test data for each specimen was processed to obtain the yield load, Py the yield displacement, Δy , the ultimate load, Pmax , corresponding displacement Δ0.8Pmax when the bearing capacity of the specimen reduces to 0.8Pmax , and the displacement ductility coefficient, μ = Δ0.8Pmax /Δy . The energy dissipation capacity of the specimen can be described by the equivalent viscous damping coefficient, h e [36]. The primary performance indicators and the equivalent viscous damping coefficient for each specimen are listed in Tables 4 and 5. The use of PLD and NLD in Table 4 denotes data that was obtained during the positive loading procedure and the negative loading procedure, respectively. Table 4 indicates that the ductility coefficients for the three specimens in both the positive and negative directions were all greater than 3.0, and this ductility is sufficient to meet the limit requirements of seismic performance. Table 5 indicates that the equivalent viscous damping coefficient for each specimen was approximately greater than 0.3 for rotations of 0.03 rad or greater, thus each specimen has good energy dissipation capacity. Owing to the larger distance between the bolts on specimen SJ2, the stiffness of the flange cover plate was small, and the initial bearing capacity of the specimen was low. In the late
5.2. Finite element verification Fig. 11 shows a comparison between the numerical simulation results and the experimental results for the hysteresis curves of each specimen beam end. These results indicate that the trends of the two hysteresis curves of the specimens were largely the same, and the curves were in good agreement. Each specimen exhibited good bearing capacity, energy dissipation capacity, and rotation capacity. In specimen SJ2, the early instability of the flange cover plate resulted in the flange of the cantilever beam and the common beam being squeezed at a rotation of 0.04 rad, which caused the bearing capacity to exhibit an upward trend and sharp corners to appear in the hysteresis curve. This was not reflected in the numerical analysis results, as the numerical
Fig. 16. Finite element model. 82
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(a) Experimental result for specimen SJ1
(b) FE result for specimen SJ1
(c) Experimental result for specimen SJ1R
(d) FE result for specimen SJ1R
(e) Experimental result for specimen SJ2
(f) FE result for specimen SJ2
(g) Experimental result for specimen SJ3
(h) FE result for specimen SJ3
Fig. 17. Comparison of experimental results and numerical simulations of the deformation of the specimens.
had good bearing capacity, energy dissipation capacity, and rotation capacity. The plastic damage to the joints was largely concentrated on the replaceable plate. By replacing the flange cover plates and high-strength bolts, the joint can be quickly repaired after an earthquake. (2) The energy dissipation of a repaired specimen during low cyclic fatigue loading was stable, which indicates that this ERPCJ has good earthquake resilience and can be used as a displacement-dependent damper. (3) Altering the middle bolt distance on the flange cover plate can change the connection rigidity. As connection stiffness decreases, the bearing capacity and energy dissipation capacity will also decrease. At this point, a collision between the two beams may occur, resulting in local damage to the primary components. (4) A comparison of results from the numerical simulation and the experiment indicates that both the hysteresis curves and the deformation modes were in good agreement, which verified the correctness and reliability of the finite element model.
analysis failed to accurately consider the impact of initial installation error and plate material properties change after buckling. A comparison of the deformation modes in the experiments and the numerical simulations for each specimen are shown in Fig. 17. These results show that the deformation mode of each specimen obtained from the numerical analysis largely agreed with the experimental results. No rotation occurred at the cantilever beams of each specimen; the rotation occurred primarily on the common beam. The flange cover plates on both sides exhibited a large degree of bending deformation, and the L-shaped web connecting plate had also rotated slightly. The results of the numerical analysis indicates that during the entire loading process, only the dog-bone weakening region of the flange cover plate and the L-shaped web connecting plate entered into plasticity, while the main components, such as the column, the cantilever beam, and the common beam, largely remained in an elastic stage. This suggests that replacing the plastic flange cover plates can ensure the overall seismic performance of the specimen, allowing for realization of its earthquake resilience function. In general, the results of the finite element analysis agreed well with the experimental results. In the future, this finite element analysis method could be used to conduct a more in-depth analysis of the joints.
Acknowledgements The authors appreciated the funding supported by the National Natural Science Foundation of China (Grant No. 51608014), the Beijing Natural Science Foundation (Grant No. 8174060) and the China Postdoctoral Science Foundation (Grant No. 2017T100020).
6. Conclusion Low cyclic loading tests and numerical analyses of earthquake resilient prefabricated steel cross joints were carried out. The following conclusions were drawn from analysis of the hysteretic behaviour, deformation mode, and failure mechanism of each specimen:
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Experimental study on earthquake-resilient prefabricated cross joints with Lshaped plates
T
⁎
Zi-qin Jianga,b, Chao Douc, , Ai-lin Zhanga,b, Qi Wanga,b, Ying-xia Wua,b a
College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China Beijing Engineering Research Center of High-Rise and Large-Span Prestressed Steel Structure, Beijing 100124, China c School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Earthquake-resilient Flange cover plate Straight dog-bone weakening Damper Seismic performance Post-earthquake restoring performance
Earthquake-resilient functionality has become a leading issue in seismic engineering, and as an important component of earthquake-resilient, cross joints have become a research hotspot. A new type of earthquakeresilient prefabricated cross joint (ERPCJ) with L-shaped plates for damage control have been proposed in this study. The new type of prefabricated cross joint is constructed of a circular tubular steel column with a cantilever beam, a common beam, and a connection device consisting of a flange cover plate, L-shaped plates, and highstrength bolt groups. By controlling the thickness of the flange cover plate and the distance of the middle bolt, the rigidity of the connection can be adjusted so that the frictional sliding of the bolt and the plastic deformation of the flange cover plate can dissipate energy and ensure that the beams, columns, and other primary components do not undergo plastic failure. To study the seismic performance and earthquake-resilient performance of this new type of cross joint, three specimens were designed and fabricated. Unequal amplitude low cyclic loading tests were carried out on the three designed specimens, while 30 laps of an equivalent amplitude low cyclic loading test was carried out on a repaired specimen. The hysteresis curves, skeleton curves, and failure modes of the specimens were obtained. The effect of the distance of the middle bolt, shape of the bolt holes, and repair test on the seismic performance of the joints were investigated. The experimental results indicate that the joint can effectively utilize the plastic deformation of the flange cover plate and the sliding of the bolt for energy dissipation. Adjusting the middle bolt distance had a significant effect on the bearing capacity and energy dissipation capacity of the joint. Changing the form of the bolt hole from circular hole to slotted hole effectively improves the ductility of the joint. The repaired joint retained its good energy dissipation capability, indicating that the joint has a good post-earthquake restoring performance and can be used as a displacement-control damper.
1. Introduction For building structures, the advantages of using prefabricated steel structures, which include factory production, assembly construction, and environmental friendliness, are becoming increasingly apparent [1]. Being an important part of the design of prefabricated steel structures, a new type of joint that has a reasonable structure and good energy dissipation capacity could effectively promote the development of prefabricated steel structures [2–7]. For steel frame joints with a cantilever beam, numerous studies have conducted relevant theoretical analyses and experimental research. Astaneh-Asl [8] performed theoretical calculations for a beamcolumn joint with a cantilever beam, and proposed a design employing semi-rigid connections, which can allow the beam-column joint with a ⁎
cantilever beam to slip during a strong earthquake rather than design earthquake. The slippage at the friction surface of the bolt and the squeezing between the bolt rod and the hole wall can absorb seismic energy. Oh et al. [9] developed a method of dog-bone weakening in joints with cantilever beams. The results indicate that ductility and rotation capacity can be improved by using a dog-bone weakening form in the joint with a cantilever beam. Mullin et al. [10] studied the seismic behaviour of semi-rigid steel frames with cantilever beams. The results showed that sliding of the splicing plate and bolt can improve the deformation performance of joints and dissipate seismic energy. Li et al. [11,12] carried out theoretical analyses on the design of beamcolumn joints with cantilever beams, performed related experimental studies, and provided relevant design suggestions. The results showed that the ductility of a semi-rigid joint was better than that of traditional
Corresponding author. E-mail address: [email protected] (C. Dou).
https://doi.org/10.1016/j.engstruct.2019.01.067 Received 13 September 2018; Received in revised form 9 January 2019; Accepted 13 January 2019 0141-0296/ © 2019 Published by Elsevier Ltd.
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welded joints, as the semi-rigid joint can make full use of the slippage at the friction surface and squeezing between the bolt rod and hole wall. Zhang et al. [13,14] proposed a beam-column joint with Z-shaped cantilever beams. Experimental results showed that reducing the number of flange bolts slightly reduced the carrying capacity, but the ductility, rotation ability, and energy dissipation capacity were significantly improved. Wang et al. [15] studied the seismic behaviour of flange-stiffened joints with low cyclic loading tests and provided some design suggestions. The strengths and weaknesses of the flange-stiffened and flange-weakened joints were also compared. Chen et al. [16] compared and analysed ordinary joints and dog-bone shaped joints experimentally. Zhou et al. [17] developed a design that moved the plastic hinge to the splicing region, which allowed the steel girder splicing joint to produce a plastic hinge before a large earthquake, playing the role of a fuse. For beam-column cross joints, Li et al. [18] carried out low cyclic loading tests on three cross-shaped full-size bulkhead pierced beam-column joints, and analysed multiple aspects of the seismic performance of the joints. Kim et al. [19] compared and analysed the performance of square column-H beam cross joints and H column-H beam cross joints with a numerical simulation. Wu et al. [20] carried out experimental studies and numerical simulations on a new type of bolted beam-to-column connections for concrete filled steel tube and investigated related calculation methods for this joint. In an investigation of the holes, Ma et al. [21] conducted experiments on high strength bolt connections with slotted holes. The results suggested that the ductile deformation capacity and seismic performance of the joints could be significantly improved by sliding the bolts in the slotted holes. In a study of structural earthquake resilience, Farrokhi et al. [22] improved the earthquake resilience of joints by introducing replaceable cover plates with holes to the outside of the steel beam flange. Oh et al. [23] placed a replaceable seam steel damper at the end of the steel beam in a traditional T-type connection joint. The plastic deformation was then centralized at the damper, which can be easily replaced after an earthquake. Calado et al. [24] conducted low-cyclic-loading tests on 12 composite joints to prevent plastic damage on the main components through frictional sliding and plastic energy dissipation. Lu et al. [25] proposed three types of replaceable energy-dissipating components of beams. Test results showed that the components can be repaired quickly after the test to realize the earthquake-resilient. On the whole, by transferring the plastic hinges to the splicing region and using it to dissipate seismic energy, more advantages for the beam-column joints of steel frames with cantilever beams can be achieved. Replacing the splicing region components to achieve improved earthquake resilience is a direction for future research [26–32]. Therefore, in this study, a new type of earthquake-resilient prefabricated cross joint (ERPCJ) with L-shaped plates is proposed. Three ERPCJ specimens were designed by changing several parameters, such as the middle bolt distance and the bolt hole shape. Experimental and finite element analyses were conducted on the seismic performance of these three specimens and one repaired specimen. With a reasonable design of ERPCJ, such as the dog bone weakening of the joints and the form of the bolt hole, the sliding and plastic deformation occurs at the flange cover plate, which can improve the energy dissipation capacity of the joint and shield the main components, such as the beam and the column, from plastic damage while guaranteeing the bearing capacity. The connection device can then be quickly repaired after an earthquake, and the repaired joint retained its good energy dissipation capability, indicating that the joint has a good post-earthquake restoring performance and can be used as a displacement-control damper.
Upper flange cover plate
Circle tubular steel column
High-strength bolt group
Annular baffle Panel zone High-strength bolt group
Common beam L-shaped web connecting plate Lower flange cover plate
Cantilev er beam
Fig. 1. Construction of ERPCJ with L-shaped plates.
L-shaped web connecting plates, and high-strength bolt groups. These components are made in a factory and can be quickly assembled to construct the connection device at a construction site. A gap is set between the cantilever beam and the common beam to enhance the rotation capacity of the joint and to avoid direct collision between the two beams. The setting of L-shaped web connecting plate can improved the joint rotation ability by deformation of the plate. The ERPCJ has the advantages of factory production and assembly construction. In addition, increasing the thickness of the flange of the cantilever beam and using dog-bone weakening at the flange cover plate can allow the plastic hinge of the beam end to transfer to the flange cover plate, which is easily replaced. After an earthquake, the primary components of the beam and the column will not be damaged, while the joint function can be restored by replacing the detachable connection device. 3. Test program 3.1. Specimen design and material properties Due to the proposed earthquake-resilient ERPCJs are mainly used to replace tradition cross joint, thus the yield moment of ERPCJs should be basically the same as the yield moment of the whole-span common beam when ERPCJs design. According to this design concept, three specimens (SJ1, SJ2, and SJ3) was designed in this paper, and the geometric dimensions and related constructions of them are shown in Fig. 2. and take specimen SJ1 as the standard specimen, specimens SJ2 and SJ3 assessed the effects of the middle bolt distance and bolt hole shape, respectively, on the failure mode and energy dissipation capacity. The circular tubular steel column with cantilevered beam was welded from the upper and lower circular tubular steel column to the middle column panel zone with cantilever beam, and the cantilever beam and the common beam were connected by flange cover plates and L-shaped plates. The cross-section dimensions of the upper and lower circular tubular steel columns were 377 × 16 mm. The cross-section dimensions of the middle column panel zone were 377 × 20 mm. The section of the H-shaped steel in the common beam was 300 × 200 × 6 × 12 mm. The cantilever beam was strengthened and had dimensions of 300 × 200 × 12 × 20 mm. The length of the column was 3000 mm, and the length of the cantilever beam was 700 mm (the distance from the end of the cantilever beam to the centre of the column). The length of the common beam was 1400 mm, as shown in Fig. 2. The thickness of flange cover plate was 16 mm, and it was made from Q235B steel, but all other plates were constructed of Q345B steel. Grade 10.9 M22 frictional type high-strength bolts were used.
2. Construction of ERPCJ with L-shaped plates The new ERPCJs proposed in this study consist of a circular tubular steel column with two cantilever beams, common beams, and connection devices between the two beams, as shown in Fig. 1. The connection device is composed of upper and lower connecting flange cover plates, 75
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530
Circle tubular steel column
204
28 30
Slotte d hole
The plan of the cover pla te
Flange cover plate Common beam
Stiffening rib
L-shaped plate
Cantilever beam
Slotte d hole 45 110 45
1400
12
240 20
200
512
16
20
(b) Front view of the cantilever beam
300
12
66 66
Panel zone
700
200
12
20 3000
150 84 66 66 84
30 28
300
16 377
66 66 66 66
144
30
Lbolt
700
(a) Geometric size of the specimen
(c) Top view of the cantilever beam
Fig. 2. Geometric dimensions of specimen SJ1. Table 1 Specimen parameters.
Hydraulic jack
Hinge
Specimen
Lbolt (mm)
Hole shape in the cantilever beam
SJ1 SJ2 SJ3
320 386 320
slotted hole slotted hole circular hole
According to the Chinese Code for Design of Steel Structures (GB500172013) [33], 190 kN pretension force was applied to the high-strength bolts by torque control method. The specific parameters for each specimen are summarized in Table 1, in which Lbolt is the distance of the middle bolt. Besides, to evaluate the post-earthquake restoring performance of these new types of joint, a repaired specimen (SJ1R) was created by replacing the connection device in SJ1 after testing; its basic parameters were the same as for SJ1. Material tests [34] were conducted to evaluate the material properties of steel plates, as summarized in Table 2, in which fy is the yield strength, fu is the tensile strength, and fu/fy is the radio of the intensity to yield strength.
Hinge
Fig. 3. Loading system. Table 3 Loading law.
Tests were conducted at the Engineering Structure Experimental Center of Beijing University of Technology. The loading system is shown in Fig. 3. The top and bottom of the circular tubular steel column were constrained by universal hinge constraints. The axial compression ratio was maintained at 0.3 at the top of the column. Hydraulic jacks were used to provide low cyclic loads to the ends of beams on both sides of the column. Lateral braces were placed at the ends of these beams to prevent out-of-plane deformation of the beam during the loading process. The tests were conducted in accordance with the seismic code of the American Institute of Steel Construction (AISC) [35] and used a method
Load level
Rotation of joint (rad)
Cycle index
Displacement amplitude at the common beam end (mm)
1 2 3 4 5 6 7 8 9
0.00375 0.005 0.0075 0.01 0.015 0.02 0.03 0.04 0.05
6 6 6 4 2 2 2 2 2
7.58 10.10 15.15 20.20 30.30 40.40 60.60 80.80 101.00
of variable amplitude rotation (the ratio of the common beam end displacement to the distance from the common beam end to the centre of the column) control loading by changing the common beam end displacement. The specific loading law is summarized in Table 3 and Fig. 4.
Table 2 Material properties of steel plates. Thickness (mm)
fy (MPa)
fu (MPa)
fu/fy
Flange cover plate Other plates
16 mm 6 mm 12 mm 20 mm
254 379 368 372
391 514 526 572
1.54 1.36 1.43 1.54
Lateral brace
Lateral brace
3.2. Loading system and loading law
Plates
Hydraulic jack
Hydraulic jack
3.3. Measurement program Fig. 5 shows the layout of the strain measurement points on the specimen. Strain gauges were arranged on the circular tubular steel column, the cantilever beam, the common beam, and the flange cover 76
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8
Displacement (mm)
121 81 40
4% 3% 2% 1.5%
Rotation 0.375%
0.5%
0.75%
1%
5%
-40
2 0
6
6
-81
6 4 Cycle index
2
2
-2 2
-121 -162
6 4
0
1
2
3
4
Load level
2
beams and common beams, respectively. 4. Test results and analysis
Rotation (%rad)
162
4.1. Failure modes and mechanisms The moment-rotation curve and plate deformation during loading of specimen SJ1 indicate that at the initial loading stage, SJ1 was in an elastic phase, the moment-rotation curve was linear, and no obvious plastic deformation occurred on the specimen. When the joint rotation was 0.01 rad, the hysteresis curve reached its peak, and the flange cover plate entered a plastic stage. When the joint rotation was 0.015 rad, slight buckling deformation occurred in the dog-bone weakening region on both sides of the flange cover plate. When the loading point then returned to the initial position, deformation of the dog-bone weakening region of the flange cover plate was restored. As loading progressed, deformation of the flange cover plate became more pronounced and the plastic region expanded. When the joint rotation was 0.05 rad, buckling deformation of the flange cover plate became obvious. Meanwhile, no significant deformation of the beam and column parts of the specimen was observed, as shown in Fig. 7. After loading of specimen SJ1, the deformed flange cover plates, Lshaped plates, and bolt groups were replaced with new parts and reassembled to form the repaired specimen, SJ1R. The geometric parameters of SJ1R and the material for each replacement plate were the same as for specimen SJ1. However, the loading law was different from that used for specimen SJ1. The repaired specimen, SJ1R, was subjected to a low cyclic fatigue loading of 0.03 rad for 30 cycles. The failure mode of SJ1R is shown in Fig. 8. The remaining two specimens underwent a complete loading process, and the results were roughly the same as for specimen SJ1. The primary difference was that the middle bolt distance in specimen SJ2
-4 2
5 6 7 8 9
-6 -8
Fig. 4. Loading law.
plate to measure the strain at each part of the joint during loading. Seventeen displacement meters were placed on the specimen as shown in Fig. 6. Locations W1 was chosen to measure the beam end displacement on the right side of the specimen. Location W2 was in the same plane as the column and was selected to measure the degree of lateral displacement on the column. Locations W3, and W7 were arranged on the upper flange cover plate on the left and right sides of the specimen, respectively, and were chosen to measure the relative displacements on the right side of the upper flange cover plate relative to the common beam and cantilever beam. Locations W4 and W8 were selected to measure the relative displacement on the right side of the lower flange cover plate relative to the common beam and the cantilever beam, respectively. The displacement meters at W5, and W6 were used to measure changes of the relative displacement on the cantilever
Z1
X1' X2' X3'
L1' L2' L3'
L1 L2 L3
X1 X2 X3
(a) Front view
L4'
P3'
P2'
P1'
P4'
L5'
P7'
P6'
P5'
X4'
X4
X5' X6'
X5 X6
(b) Top view Fig. 5. Strain measurement locations. 77
P1
P2
P3
L4
P7
L5
P4 P5
P6
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W2
W1'
W1
W3'
W5'
W4'
W6'
W7' W7 W4
W9'
W8' W8
W9
W5
W3
W6
W4
Fig. 6. Displacement measurement locations.
(a) Deformation of the joint
(b) Deformation of the flange cover plate
Fig. 7. Deformation of specimen SJ1.
(a) Deformation of the joint
(b) Deformation of the flange cover plate
Fig. 8. Deformation of specimen SJ1R. 78
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(a) Deformation of the joint
(b) Deformation of the flange cover plate
Fig. 9. Deformation of specimen SJ2.
(a) Deformation of the joint
(b) Deformation of the flange cover plate
Fig. 10. Deformation of specimen SJ3.
rotation of specimen SJ1 was the same with SJ1R), the hysteretic curves of the two specimens were basically same and plump, and their energy dissipation capacity was also very similar. The energy dissipation of the repaired specimen, SJ1R, was stable under low cyclic fatigue loading, indicating that this joint has a good post-earthquake restoring performance and can be used as a displacement-control damper. Specimen SJ2 had a similar hysteresis curve to SJ1 in the early loading stages. Owing to the larger middle bolt distance of the flange cover plate in specimen SJ2, the deformation of the flange cover plate was large in the later stages, which caused the common beam flange to squeeze the cantilever beam flange. After this change of the force transfer mechanism of the specimen, there was a rapid increase in bearing capacity and a sharp corner appeared in the hysteresis curve. Specimen SJ3 also experienced an elastic phase, plate strengthening stage, and energy dissipation stage caused by the instability of the flange cover plate, and thus the hysteresis curve for specimen SJ3 was much the same as that for specimen SJ1. The bearing capacity and energy dissipation capacity were also approximately the same. The cumulative energy dissipation curves for the specimens at each loading level are shown in Fig. 12, and the trends of these curves for the three specimens are generally consistent. The energy dissipation curve for specimen SJ2 was smaller than the other two specimens, which is the result of the larger middle bolt distance on specimen SJ2, namely the longer length of unconstrained flange cover plate, which was more likely to result in instability deformation for flange cover plate under axial pressure. Thus, the bearing capacity was also slightly lower, while the hysteresis loop tended to be flatter, and the total energy dissipation of the specimen was smaller. The energy dissipation curve for specimen SJ3 was slightly higher than that of SJ1 because the holes in the flange of SJ3 were circular, and thus the development of plasticity in the squeeze of bolts and hole walls could also dissipate some energy. For the repaired specimen, SJ1R, the energy dissipation curve of the specimen was obtained by summing the area of the hysteresis loop every five laps, and is shown in Fig. 13. As the results show, with increasing
was larger than the other specimens. When the joint rotation was 0.01 rad, the flange cover plate of specimen SJ2 exhibited a slight bending deformation, and when the joint rotation of specimen SJ2 was 0.04 rad, the common beam and the cantilever beam were squeezed. The failure modes of specimens SJ2 and SJ3 are shown in Figs. 9 and 10, respectively. 4.2. Hysteresis curves and energy dissipation The joint rotation and the cantilever beam root bending moment of each specimen were used to create hysteresis curves, as shown in Fig. 11. These results show that the hysteresis curves were plump, indicating that the joints had good bearing capacity, energy dissipation capacity, and rotation capacity. Take the base specimen, SJ1, as an example, the specimen underwent an elastic stage, a plastic strengthening stage of the flange cover plate, and an energy dissipation stage caused by the buckling of the flange cover plate. During the initial stage of loading, the specimen only exhibited bending deformation and the moment-rotation curve changed linearly. As loading progressed, the flange cover plate entered a plastic strengthening stage, and the bearing capacity reached its peak. Then, the specimen entered a buckling stage at the flange cover plate, the bearing capacity of the specimen exhibited a gradual downward trend, and the buckling deformation of the flange cover plate became more obvious. After the specimen was unloaded, no significant plastic deformation was observed in any of the parts, except for the buckling deformation of the flange cover plate. The load value of the second cycle in each load level of hysteresis curve was always lower than the load value of the first cycle. This was mainly a result of the plastic damage to the flange cover plate and a decrease in the friction coefficient at the interface. In the early stage of loading, due to the different loading law, the hysteretic curves of SJ1 and SJ1R were different. However, when the specimen SJ1 reached the 7th load level (at which point the loading 79
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320
Cantilever beam root bending moment (kN·m)
Cantilever beam root bending moment (kN·m)
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Experiment FEA Model
240 160 80 0 -80 -160 -240 -320 -5
-4
-3
-2
-1
0
1
2
3
4
5
Rotation (%)
320
Experiment FEA Model
240 160 80 0 -80 -160 -240 -320 -5
-4
-3
Cantilever beam root bending moment (kN·m)
Cantilever beam root bending moment (kN·m)
160 80 0 -80 -160 -240 -320 -5
-4
-3
-2
-1
0
1
2
0
1
2
3
4
5
3
4
5
(b) Specimen SJ1R
Experiment FEA Model
240
-1
Rotation(%)
(a) Specimen SJ1
320
-2
3
4
5
Rotation (%)
320
Experiment FEA Model
240 160 80 0 -80 -160 -240 -320 -5
-4
-3
-2
-1
0
1
2
Rotation (%)
(c) Specimen SJ2
(d) Specimen SJ3
Fig. 11. Hysteresis curves of specimens.
100 SJ1 SJ2 SJ3
150
90 80
Energy dissipation (kJ)
Cumulative energy dissipation (kJ)
200
100
50
70 60 50 40 30 20 10
0
0
1
2
3
4
0
5
Rotation (%)
1-5
6-10
11-15 16-20 Cycles
21-25
26-30
Fig. 12. Cumulative energy dissipation curves.
Fig. 13. Energy dissipation curve for SJ1R.
number of load cycles, the energy dissipation capacity of SJ1R showed a gradual downward trend, which eventually tended to become stable. At this time, the friction coefficient at the plate interface also tended to be stable.
common beam, and the column of the specimen at each loading level are shown in Fig. 14. Results of the material test indicate that the plastic strain at the specimen flange was approximately 1800 με. These results show that from the start of loading to the end, the flanges of the cantilever beams and common beams, and joint panel zone in each specimen were all in an elastic phase. The stress development for each specimen was similar, and the stress at the flange of the cantilever beam was larger than that at the flange of the common beam. When the joint
4.3. Strain analysis The measured strain of the flange at the cantilever beam and the 80
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1600
1400
1400
1200
1200
1000
1000
Strain ( )
Strain ( )
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800 600 400 200 0
0.01 0.015 0.02 0.03 0.04 0.05 X4
800
0.01 0.015 0.02 0.03 0.04 0.05
600 400 200 0
X5
X6
L4
L5
X4
Z2
X5
X6
L4
Strain gauge
Strain gauge
(a) Specimen SJ1
(b) Specimen SJ2
L5
Z2
1600 1400
Strain ( )
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0.01 0.015 0.02 0.03 0.04 0.05 X4
X5
X6
L4
L5
Z2
Strain gauge
(c) Specimen SJ3 Fig. 14. Strain curves of specimen at each loading level.
200
rotation was 0.015 rad, the strains at the flanges of the cantilever beam and common beam decreased because of the appearance of the plastic hinges on the flange cover plate. This analysis shows that strengthening the cantilever beam and weakening the flange cover plate can effectively control the plastic hinge on the replaceable flange cover plate, allowing the main components of the specimen to remain in an elastic state, which is helpful for repairing the joint after an earthquake.
150
Load (kN)
100
SJ1 SJ2 SJ3
50 0 -50
4.4. Skeleton curves
-100 Fig. 15 shows the skeleton curves for each specimen. These skeleton curves in the elastic phase were basically linear, and the stiffness was much the same. When the beam load reached approximately 150 kN, the flange cover plate yielded, and the skeleton curve began to decline slowly. Owing to the large middle bolt distance on the flange cover plate in specimen SJ2, the flange cover plate of SJ2 was more prone to buckling. As a result, the ultimate bearing capacity of SJ2 was slightly less than that of SJ1, and its bearing capacity decreased more rapidly after instability. In the late stages, the common beam and the cantilever beam of SJ2 were squeezed, which increased the bearing capacity of SJ2. As specimen SJ3 had a circular bolt hole, the decrease in the
-150 -200
-100
-50
0
50
100
Displacement (mm) Fig. 15. Skeleton curves.
bearing capacity of SJ3 was the most gradual. In addition, the skeleton curves for the two loading directions of the specimens were not 81
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Table 4 Primary performance indicators of specimens. Specimen
Py (kN)
SJ1 SJ2 SJ3
Δy (mm)
Pmax (kN)
SJ1 SJ2 SJ3
μ
PLD
NLD
PLD
NLD
PLD
NLD
PLD
NLD
PLD
NLD
140.57 130.97 130.98
144.75 146.42 137.74
16.74 16.91 16.4
17.04 16.29 16.88
156.01 147.74 150.29
147.97 151.56 139.67
54.74 51.63 79.45
55.41 55.74 81.32
3.27 3.06 4.84
3.25 3.42 4.82
loading stages, although the bearing capacity of the specimen increased significantly because of the collision of the common beam and the cantilever beam, the hysteresis curve was pinched, and the total energy dissipation remained low. Therefore, the equivalent viscous damping coefficient was significantly lower at a rotation of 0.05 rad.
Table 5 Energy dissipation indicators of the specimens. Specimen
Δ0.8Pmax (mm)
Equivalent damping ratio of the specimens for each joint rotation 1.0%
1.5%
2.0%
3.0%
4.0%
5.0%
0.099 0.077 0.091
0.215 0.230 0.245
0.321 0.305 0.317
0.382 0.347 0.346
0.369 0.326 0.362
0.348 0.237 0.358
5. Finite element analysis 5.1. Finite element model Finite element software ABAQUS [37] was used to carry out finite element analyses on the seismic performance of the above four specimens. The beam, column, and bolts were modelled with solid element C3D8R, as shown in Fig. 16. Contact relationships were set between the flange cover plate and the beam flange as well as bolts, and L-shaped plate and the beam web as well as bolts. The friction coefficient was considered on interfaces, and its value was 0.45 [31,33]. In addition, a preload of 190 kN was applied to the bolts. The plate material, boundary conditions, and loading law were consistent with the previous tests. The element number of each finite element model was about 332 thousand, and the full Newton-Raphson method was adopted for the solution.
completely symmetrical owing to the accumulated damage and the initial installation defects of the plates under the action of a reciprocating load. 4.5. Primary performance indicators The test data for each specimen was processed to obtain the yield load, Py the yield displacement, Δy , the ultimate load, Pmax , corresponding displacement Δ0.8Pmax when the bearing capacity of the specimen reduces to 0.8Pmax , and the displacement ductility coefficient, μ = Δ0.8Pmax /Δy . The energy dissipation capacity of the specimen can be described by the equivalent viscous damping coefficient, h e [36]. The primary performance indicators and the equivalent viscous damping coefficient for each specimen are listed in Tables 4 and 5. The use of PLD and NLD in Table 4 denotes data that was obtained during the positive loading procedure and the negative loading procedure, respectively. Table 4 indicates that the ductility coefficients for the three specimens in both the positive and negative directions were all greater than 3.0, and this ductility is sufficient to meet the limit requirements of seismic performance. Table 5 indicates that the equivalent viscous damping coefficient for each specimen was approximately greater than 0.3 for rotations of 0.03 rad or greater, thus each specimen has good energy dissipation capacity. Owing to the larger distance between the bolts on specimen SJ2, the stiffness of the flange cover plate was small, and the initial bearing capacity of the specimen was low. In the late
5.2. Finite element verification Fig. 11 shows a comparison between the numerical simulation results and the experimental results for the hysteresis curves of each specimen beam end. These results indicate that the trends of the two hysteresis curves of the specimens were largely the same, and the curves were in good agreement. Each specimen exhibited good bearing capacity, energy dissipation capacity, and rotation capacity. In specimen SJ2, the early instability of the flange cover plate resulted in the flange of the cantilever beam and the common beam being squeezed at a rotation of 0.04 rad, which caused the bearing capacity to exhibit an upward trend and sharp corners to appear in the hysteresis curve. This was not reflected in the numerical analysis results, as the numerical
Fig. 16. Finite element model. 82
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(a) Experimental result for specimen SJ1
(b) FE result for specimen SJ1
(c) Experimental result for specimen SJ1R
(d) FE result for specimen SJ1R
(e) Experimental result for specimen SJ2
(f) FE result for specimen SJ2
(g) Experimental result for specimen SJ3
(h) FE result for specimen SJ3
Fig. 17. Comparison of experimental results and numerical simulations of the deformation of the specimens.
had good bearing capacity, energy dissipation capacity, and rotation capacity. The plastic damage to the joints was largely concentrated on the replaceable plate. By replacing the flange cover plates and high-strength bolts, the joint can be quickly repaired after an earthquake. (2) The energy dissipation of a repaired specimen during low cyclic fatigue loading was stable, which indicates that this ERPCJ has good earthquake resilience and can be used as a displacement-dependent damper. (3) Altering the middle bolt distance on the flange cover plate can change the connection rigidity. As connection stiffness decreases, the bearing capacity and energy dissipation capacity will also decrease. At this point, a collision between the two beams may occur, resulting in local damage to the primary components. (4) A comparison of results from the numerical simulation and the experiment indicates that both the hysteresis curves and the deformation modes were in good agreement, which verified the correctness and reliability of the finite element model.
analysis failed to accurately consider the impact of initial installation error and plate material properties change after buckling. A comparison of the deformation modes in the experiments and the numerical simulations for each specimen are shown in Fig. 17. These results show that the deformation mode of each specimen obtained from the numerical analysis largely agreed with the experimental results. No rotation occurred at the cantilever beams of each specimen; the rotation occurred primarily on the common beam. The flange cover plates on both sides exhibited a large degree of bending deformation, and the L-shaped web connecting plate had also rotated slightly. The results of the numerical analysis indicates that during the entire loading process, only the dog-bone weakening region of the flange cover plate and the L-shaped web connecting plate entered into plasticity, while the main components, such as the column, the cantilever beam, and the common beam, largely remained in an elastic stage. This suggests that replacing the plastic flange cover plates can ensure the overall seismic performance of the specimen, allowing for realization of its earthquake resilience function. In general, the results of the finite element analysis agreed well with the experimental results. In the future, this finite element analysis method could be used to conduct a more in-depth analysis of the joints.
Acknowledgements The authors appreciated the funding supported by the National Natural Science Foundation of China (Grant No. 51608014), the Beijing Natural Science Foundation (Grant No. 8174060) and the China Postdoctoral Science Foundation (Grant No. 2017T100020).
6. Conclusion Low cyclic loading tests and numerical analyses of earthquake resilient prefabricated steel cross joints were carried out. The following conclusions were drawn from analysis of the hysteretic behaviour, deformation mode, and failure mechanism of each specimen:
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