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Cyclic loading behavior of an innovative semi-rigid connection for engineered bamboo-steel hybrid frames
Accepted Manuscript Cyclic loading behavior of an innovative semi-rigid connection for engineered bamboo-steel hybrid frames Zirui Huang, Zhongfan Chen, Dongsheng Huang, Ying-Hei Chui PII:
S2352-7102(19)30175-5
DOI:
https://doi.org/10.1016/j.jobe.2019.100754
Article Number: 100754 Reference:
JOBE 100754
To appear in:
Journal of Building Engineering
Received Date: 3 February 2019 Revised Date:
26 March 2019
Accepted Date: 27 March 2019
Please cite this article as: Z. Huang, Z. Chen, D. Huang, Y.-H. Chui, Cyclic loading behavior of an innovative semi-rigid connection for engineered bamboo-steel hybrid frames, Journal of Building Engineering (2019), doi: https://doi.org/10.1016/j.jobe.2019.100754. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Cyclic loading behavior of an innovative semi-rigid connection for engineered bamboo-steel hybrid frames Zirui Huang a, d, Zhongfan Chen a,b, Dongsheng Huang* c, Ying-Hei Chui d a
Key Laboratory of RC & PC structures of Ministry of Education, Southeast University, Nanjing, China, 210096 School of Civil Engineering, Southeast University, Nanjing, China, 211189 c National Engineering Research Center of Biomaterials, Nanjing Forestry University, Nanjing, China, 210037 d Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Canada, T6G 1H9
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b
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Abstract
This paper presents an innovative semi-rigid connection for bamboo-steel hybrid moment frames that comprise
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engineered bamboo beams and steel columns. The connection incorporates a steel hinge and two steel brackets to carry shear force and moment at the end of the beam, respectively. The bracket consists of two segments-a joint segment connected to beam and an energy dissipation panel (EDP) connected to a column via a base panel. In this way, the connection not only serves as a frame joint, but also as an energy dissipation device. Cyclic loading tests were carried out on 9 connections with various EDP length-to-thickness ratios to investigate their failure mode
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and hysteresis behavior. It was found that by proper design, damage of the frame can be restricted to the EDP while other parts of the frame are virtually free of damage. Hysteresis loops for the connection exhibit less pinching than dowel or bolt type connections. The connection has adequate initial stiffness, strength and ductility
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to meet structural design requirements. A simplified formula to predict the load-carrying capacity of the connection was developed based on the experimental and numerical results. Good agreement was achieved
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between the results of calculation and experiment. Recommendations are made for the design of the proposed semi-rigid bamboo-steel hybrid connection.
Key words
Engineered bamboo products; semi-rigid connection; bamboo-steel hybrid frame; energy dissipation device
1. Introduction
1
ACCEPTED MANUSCRIPT Over the past decade, the use of engineered wood products in mid- or high-rise buildings has been growing rapidly around the world [1-5]. A number of innovative mid- and high-rise wood buildings have been constructed worldwide demonstrating the technical feasibility of using bio-based products in building construction. In China, engineered bamboo products (EBPs) have been developed as an alternative to wood products in
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construction due to the limitation of wood harvest. These products are made by gluing bamboo strands or veneers together under controlled temperature and pressure. Currently, two types of EBPs, i.e., parallel strand bamboo (PSB) and laminated veneer bamboo (LVB), are commercially available [6-8]. The mechanical properties of EBPs are similar to or even superior to those of commonly used wood products [6]. However, the relatively low
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stiffness and strength of EBPs, compared to steel and reinforced concrete, usually means larger member sizes are necessary to construct mid-rise and taller wood buildings. This is a major limitation in the use of EBPs in
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multi-storey buildings. EBP-steel hybrid moment frame, which employs steel columns connected with EBP beams to build lateral and vertical load-carrying systems, is an effective solution to extend the application of EBP to multi-storey buildings.
Obviously, the design of moment connection is a major concern of EBP-steel frames. Generally, the connection must not only have adequate initial stiffness and strength, but also enough ductility and energy
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dissipation capacity to meet the collapse prevention requirements when the frame undergoes severe seismic actions. Steel dowel connections are most common joints accepted in modern wood or EBP buildings [9,10]. Experimental investigations demonstrated that wood failure can be the dominant mode for dowel connections, and
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the load-carrying capacity of the connection usually does not exceed 20 % of the strength of the connecting beams [11, 12]. The rotational stiffness of dowel connections is also often significantly lower than the bending stiffness
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of the connecting beam [13]. Bolted connection is another type of commonly used joint, which is stronger and stiffer than dowel connections. Usually, damage of the moment frame with bolted connections is in the form of bolt yielding, timber crushing and cracking of timber members at the joint [14]. The hysteresis loops of these connections are basically characterized by pinching or degradation of stiffness and strength under reversed cyclic loading, demonstrating low energy dissipation capacity of the connections [15, 16]. Therefore, improving the load-carry capacity and hysteresis performance of connections is essential if timber / bamboo or timber / bamboo-steel hybrid structures are to be adopted as a structural form by designers. To this end, the present work investigates an innovative connection for EBP-steel frames. As presented in Fig. 1, the connection incorporates a hinge and a pair of top and seat brackets to resist the shear force and moment 2
ACCEPTED MANUSCRIPT from the connecting beam, respectively. Each bracket can be divided into two segments. One of the segments is the joint panel which is welded to a steel stub bolted to two sandwich beam panels. The other segment serves as energy dissipation panel (EDP), which is welded to a base panel through which the connection is fixed to the steel column; and the EDP is free to buckle out-of-plane. In this way, the connection behaves as a seesaw supported by
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a hinge which bears most of shear force of the connecting beam. The top and seat brackets restrict the rotation of the connection, thereby providing resistant moment and lateral stiffness for the frame, as shown in Fig.1(c). Furthermore, by an appropriate design and detailing, the first yielding of the frame can be confined to the EDPs while the other parts of the frame are protected when the frame is subjected to a lateral load. EDP
Joint panel
(a)
Stub
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Steel column
EDP Hinge
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Hinge
Base panel
Bolt
(b) Joint panel
Base panel
Bolt
Stub
EBP beam
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(c)
Fig.1 Moment connection for bamboo-steel moment frame; (a) the way of connection joint beam and column; (b) details of proposed energy-dissipating connection; (c) working principle of the connection.
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The proposed EBP-steel frame connection can be treated as a semi-rigid connection. It may lead to smaller beam sizes because the semi-rigidity of the connection may reduce the moment at the end of the beam. As such, the moment stiffness of the connection can be adjusted for an optimal distribution of the bending moment in the beam. Considerable research has been carried out to explore the performances of semi-rigid connections in steel structures [17-20]. It has been confirmed by Pirmoz and Liu [21] that the rotational stiffness of a semi-rigid connection was about 20% lower than a rigid connection while its moment capacity was only 15% lower. Moreover, a semi-rigid connection can dissipate energy through hysteresis behavior better than rigid or pinned connections [22, 23]. For these reasons, semi-rigid connections are a good solution for seismic-resisting frames. Because of its controllable stiffness and failure mode, the concept of semi-rigid connection is an attractive 3
ACCEPTED MANUSCRIPT design philosophy for timber and bamboo structures to improve the seismic performances of the structure. One kind of semi-rigid connection for wood frames, known as Lagscrewbolt, was developed by Komatsu et al [24]. Lagscrewbolt connection can develop lateral and moment resistance through withdrawal resistance provided by the threaded rods in timber members. A recent study carried out by Mori et al [25] indicated that Lagscrewbolt
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connection has high initial stiffness and load-carrying capacity, while the hysteresis loops exhibit pronounced pinching characteristic. In an attempt to avoid timber failure, Buchanan, et al [26] inserted a box-type steel bracket between timber beam and column. Yang, et al [27] continued an investigation into the same type of connection by developing an analytical model to estimate the moment-rotation relationship for the connection. More recently,
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Karagiannis, et al [28], developed an innovated timber beam-to-tubular steel column moment connection, and monotonic loading tests were conducted to investigate the stiffness, load-carrying capacity, and failure mechanism
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of the connection. Many other types of semi-rigid connections used in structures built with different materials can be found in the literature [29-35].
This paper presents the work of a project conducted to evaluate the performance of the aforementioned connection with EDP that connects a bamboo composite beam to a steel column. Cyclic loading tests were conducted on nine connection specimens with different EDP length-to-thickness ratios to investigate the failure
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modes and hysteresis loops of the connections. A simplified model for estimating the load-carrying capacity of the connection was developed based on the experimental results.
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2. Connection detailing and material
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Details of the test connection are illustrated in Fig. 2. As aforementioned, the end segments of the two brackets free of out-of-plane restraints are energy dissipation panel (EDP). In order to restrict the damage of the connection to EDPs, the diameter and spacing of the bolts, thickness of base panel and stub were designed to ensure that the bolted connection is stronger than the EDP. When reversing loads were applied to the connection, the EDPs were subjected to alternating tension and compression forces leading to yielding or buckling of the EDP. Obviously, the dimensions of the brackets are one of the major factors impacting on the mechanical behaviour of the connection. In this study the connection specimens were designed to have the same dimensions except the width and length-to-thickness ratio of EDPs. In total nine specimens with four different EDP length-to-thickness ratios were tested. The length and the area 4
ACCEPTED MANUSCRIPT of cross-section of the EDP were kept constant at 80 mm and 600 mm2, respectively. The dimensions of EDP for each group of test specimens are presented in Table 1. Test connections were fabricated by using Q235 steel, following Chinese Standard GB50017-2017 [36]. The mechanical properties of the steel were tested in tension according to ASTM standard E8/E8M [37]. Test results of 12 steel coupons are summarized in Table 2. The
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column used in the connection test was a HPB 400 grade steel I-section, that meets the requirements of GB50017-2017 [36]. The beam was a parallel strand bamboo (PSB) composite. PSB is a kind of engineered bamboo product that has superior performances than commonly used wood products. The dimensions of PSB beam were determined to ensure enough strength to resist test load without failure in the beam. Mechanical
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properties of PSB were tested according to ASTM D143 [38], and modulus of elasticity, tensile and compressive
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strength are 13000MPa,150 MPa, 90 MPa, and 60 MPa, respectively. ghcv
EDP Stub
EBP beam
(b)
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(a)
Fig. 2 Details of connection. (a) Cross section at the end of beam; (b) detailing of steel stub. Units: mm Table 1. Dimensions of the test connections
J-8
3
J-10
3
J-12
2
Label J-6-1 J-8-1, J-8-2, J-8-3 J-10-1, J-10-2, J-10-3 J-12-1, J-12-2
Bracket length (mm) 330
EDP length (mm) 80
Width (mm) 100
Thickness (mm) 6
Cross section area (mm2) 600
EDP length-to-thickness ratio 13.33
330
80
75
8
600
10
330
80
60
10
600
8
330
80
50
12
600
6.67
Elongation ratio
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J-6
Number of specimens 1
Group
Table 2. Properties of steel of EDP and stub. Items Mean CoV
Yield strength (MPa)
Ultimate strength (MPa)
Young’s modulus (GPa)
Poisson’s ratio
315
445
209
0.30
0.32
2.37%
1.30%
5.04%
18.70%
5.0%
3. Experimental investigation
3.1 Test procedure
The test setup is schematically illustrated in Fig. 3. Since it is more efficient to anchor the steel column 5
ACCEPTED MANUSCRIPT member to the strong floor of the laboratory, the test specimen was horizontally installed, i.e., rotated 90 degrees compared to its normal service position. The beam member was made of two PSB panels with a cross section of 400 mm × 95 mm. A steel stub of 12 mm thickness was sandwiched between the two PSB panel and they were connected together using twelve 20 mm diameter bolts, referring to Fig. 3(a). According to Liu, et al [39], there is
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no significant influence on the connection response when the length of the connecting members exceeds 1 m. Therefore, the lengths of the beam and column were 2 m and 1.2 m, respectively. The connection was mounted in the middle of the steel column which was fixed to the stiff and strong concrete laboratory floor using four 40mm diameter bolts. In order to mitigate the deformation of flange of the column, web stiffeners spaced at 400 mm
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(omitted in Fig. 3 for the sake of clarity) were welded to the web of the column below the connection area. The load was applied using a double-hinged hydraulic actuator to the top of the PSB beam via specially designed
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clamping device. The distance from the loading point to the centre of hinge was maintained at 1095 mm for all tests. Two pairs of displacement sensors, labeled 5 and 6 in Fig. 3 (b), spaced at 100 mm apart were mounted to each side of the test connection to measure the transverse displacement. A sensor, labeled 7 in Fig. 3(b), was installed at the bottom to monitor the displacement of the base panel. A load cell incorporated in the actuator was employed to measure the applied force. Displacement of each sensor and applied force were simultaneously
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recorded by the TDS-530 data acquisition system using a sampling frequency of 1 Hz. The connection specimen was loaded at a displacement speed of 4 mm/min. At each displacement level, 3 reversed cycles were applied and the displacement level increment was 2 mm until failure occurred. Actuator
Clamp
Deformation sensor-1
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(a)
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(b)
Deformation sensors
Bolts
Reaction wall
5 6
Bolts to fix column to the floor
7
Steel column
Base panel
Hinge
Fig. 3 Test setup; (a) an overview; (b) details of connection
6
EDP
Joint panel
ACCEPTED MANUSCRIPT 3.2 Test results 3.2.1 Failure mode Fig. 4 and Fig. 5 graphically present the failure modes and distortions of each part of the connection. It was
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found that virtually all damages of the connection were restricted to the EDPs with no visual residual distortions observed in other parts of the connection. The failure modes can be categorized into two types, as illustrated in Fig 4. The first failure mode is characterized by EDP fracture as shown in Fig. 4(a). Specimens in groups J-6 and J-8 failed in this manner. These groups have the larger EDP length-to-thickness ratios. The second failure mode is the
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rupture of welding between EDPs and base panel, as illustrated in Fig. 4(b). Groups J-10 and J-12 failed in this mode. It should be noted that the deformations in the EDP of these specimens that failed in the weld were much
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smaller than those of first failure mode, indicating potential premature failure. These groups had the smaller EDP length-to-thickness ratios than J-6 and J-8, which indicates that the weld was the weakness in the connection and a larger length-to-thickness ratio is required to prevent the premature failure in the weld. The failure mechanism can be explained as follows. As discussed above, the connection works like a seesaw when it is subjected to reversed cyclic moments. The brackets provide resistant moment through tension in one
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side and compression in the other side. For the connection with EDP of large length-to-thickness ratio (J-6 and J-8), buckling took place in compressive side once the compressive force exceeded the buckling capacity of the EDP, whereas on the other hand, the EDP on the tensile side was still in an elastic state. The tension and
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compression of the brackets were continuously alternated as the loading direction changed. Because the buckling strength is lower than tensile strength of the steel, the stress in the brackets could never reach the tensile strength
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of the steel. This implies that load-carrying capacity of the connections that failed in the first mode was actually dominated by the compressive capacity of EDP. Because buckling always takes place on the condition of partial yielding of EDP, the compressive capacity of EDP can be recognized as the strength of partial yielding. For the connection with EDP of smaller length-to-thickness ratios, buckling could not take place and the load-carrying capacity of the connection ultimately was dependent on the tensile strength of the EDP or the weld. In the present study, the tensile strength of the weld between the EDP and base panel was lower than the tensile strength of the steel in the EDP; hence failure occurred in the weld for J-10 and J-12 specimens. In summary, by an appropriate design, the damage of a structure can be restricted to the EDPs in the connection. The residual deformations of the steel around the bolt holes are small such that they can be ignored, as 7
ACCEPTED MANUSCRIPT illustrated in Fig 5. The failure is in the form of plastic yielding of the EDPs in compression, which also acts as a source of energy dissipation. As a result, the load-carrying capacity of the connection depends on the strength of partial yielding of EDPs.
(b)
(a)
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Progressively developed crack in mid-EDP
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Failure of EDP-to-base panel welding
(b)
(a)
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Fig. 4 Typical failure modes of connections. (a) buckling and failure in the middle of EDP; (b) weld failure at the end of EDP
(c)
3.2.2 Hysteresis loops
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Fig. 5 Residual distortions: (a) steel stub; (b) the joint part of EBP beam; (c) bolts.
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The hysteresis loops and test results are summarized in Table 3. Moment-rotation response, i.e., M − θ , was obtained by directly converting load-deformation data. The rotation of the connection was estimated
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by φ = ( w7 − w6 − w5 ) / L , where, wi (i = 5, 6, 7) stands for the displacements of measurement points 5, 6, and 7, as illustrated in Fig. 3(b), and L=1095 mm is the distance from loading position to the centre of the hinge. It can be observed that only limited pinching happens in each hysteresis loop. However, the hysteresis loops of groups J-6 and J-8 are evidently different from those of groups J-10 and J-12. For connections in groups J-6 and J-8, there is post-peak strength degradation; whereas for connections in groups J-10 and J-12, almost no declining loop can be observed. It also provides evidence that the damage mechanisms of the two pairs of groups are different, and it will be further discussed in section 3.4.
3.2.3 Envelope profiles 8
ACCEPTED MANUSCRIPT The backbone curve of a hysteresis loop response was obtained by enveloping the M − θ curve of the first loading cycle at each displacement level, shown as the red curve in Table 3. It can be observed that the connections behaved linearly elastically until the load reached a proportional limit. The proportional limit depends on initial yield strength of EDP. The load-carrying capacity of a connection generally increases with a decrease in
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length-to-thickness ratio of EDP. The initial stiffness of each connection can also be obtained through the envelope profile, which is presented in Table 3.
3.2.4 Ductility ratio
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The ductility ratios of the connections were estimated following the Equivalent Energy Elastic-Plastic (EEEP) procedure of ASTM E2126 [40], as illustrated in Fig. 6. According to ASTM E2126, a line is first drawn, going
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through the origin and the point on the envelope curve where the moment equals to 40 % of the maximum moment. The yield point was determined by equating the area under the bi-linear EEEP response to the area under the test envelope curve, referring to Fig. 6. This was achieved by adjusting the horizontal line until the equivalent area criterion was met. The ductility ratio is expressed as µ = θ y / θu , where, θ y and θ u are defined as yield and ultimate displacement, respectively. For the envelope with post-peak declining branch, θ u is the rotation
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corresponding to the 0.8 maximum load, while for the envelope without declining branch, θ u is the rotation corresponding to ultimate load. The values of yielding moment and rotation, ultimate moment and rotation, elastic stiffness, and ductility for each connection are presented in Table 3. It can be concluded that the ductility ratio of
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the first failure mode (partial yielding and subsequently buckling) may reach about 3.0 while that of the second failure mode (weld fracture) only reaches about 2.0. M Peak
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M
M Yield
D
0.8M Peak
0.4M Peak
Envelope curve EEEP
B
θy
θPeak
θu
θ
Fig. 6 Ductility determination
Fig. 7 Energy dissipation determination
3.2.5 Energy dissipation
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ACCEPTED MANUSCRIPT As the energy dissipated by the connection only includes yielding or buckling energy, hence it may be estimated by [41] Ed =
∫
θ
0
1 Mdθ − kθ 2 2
(1)
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where k is the initial stiffness of the connection; M and θ are the applied moment and corresponding rotation, respectively. Thus the energy dissipated in each loading cycle equals the area of corresponding loop subtracting the triangle area which stands for the elastic work in the loading cycle. As illustrated in Fig. 7, the energy dissipation, Ed, can be calculated by
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Ed = S Loop − ( S ∆OBF + S ∆ODE )
(2)
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where SLoop stands for the area of loading circle loop, S∆OBF stands for the triangle area of ∆OBF, S∆ODE stands for the triangle area of ∆ODE. The damping ratio, ξ , can be calculated by ξ=
SLoop 1 ⋅ 2π S∆OBF + S∆ODF
(3)
The damping ratio for each test connection is presented in Table 3. It can be concluded that the damping ratios of
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the connections taken place in first failure mode can reach 30 % or more while that of the second failure mode can only reach 26%, which indicating the good energy dissipating capability of the proposed semi-rigid connection.
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3.4 Conclusions from experimental investigation The results of experimental investigation can be summarized as follows:
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(1) By a proper design, the damage of the frame with EDP connections can be restricted to the EDP while the other parts of the connection, the beam and column of the frame, can be free of damage. The hysteresis loops of the connections exhibit limited pinching and provide a high damping ratio, indicating that the connection has good energy dissipation capability. The ductility ratio and damping ratio of the connections can reach more than 3.0 and 30%, respectively. (2) The failure mode of connection depends on the length-to-thickness ratio of the EDP. For the connections with large EDP length-to-thickness ratio, the failure was ductile and occurred in the middle of EDP after some reversed cyclic loading action. For the connections with small EDP length-to-thickness ratio, the failure occurred prematurely at the weld joint between EDP and base plate, and virtually no post-peak strength degradation was 10
ACCEPTED MANUSCRIPT observed in their envelop profiles. Since the length-to-thickness ratio plays a key role in dictating the mode of failure, it should be possible to detail the connection to avoid weld failure and achieve the more desirable ductile failure mode. This issue will be addressed in Section 4.
Table 3. Experimental results Hysteretic loops 80
Hysteretic loop Envelope curve
60 40
M /kN·m
Yield moment: 68.66 / -69.35 kNm
20
Ultimate moment: 62.05 / -63.17 kNm
0
-20
Yield Rotation: 0.000460/ -0.000496 rad
-40
Ultimate rotation: 0.001390 /-0.001431 rad
-60 -0.02
100 60
M /kN·m
0.00
θ /rad
0.01
0.02
Hysteretic loop Envelope curve
80
J-8
-0.01
40
Yield Rotation: 0.000521/ -0.000592 rad
-40
Ultimate rotation: 0.001800/ -0.001855 rad
-0.02
-0.01
0.00
θ /rad
0.01
0.02
100
Hysteretic loop Envelope curve
80 40
Yield Rotation:0.000595 / -0.000535 rad
-40
0.269
2.1/1.9
0.264
Ultimate rotation:0.001226/ -0.001215 rad
-60
Elastic stiffness: 135781 / 152317 kNm /rad
-80 -0.010
-0.005
0.000
θ /rad
100
0.005
0.010
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Hysteretic loop Envelope curve
80 60 40 20 0 -20
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M /kN·m
2.3/2.2
Ultimate moment: 88.63 / -90.90 kNm
0
-20
-40
-0.005
0.000
θ /rad
0.005
Ultimate moment: 88.18 / -85.79 kN.m Yield Rotation:0.000489/ -0.000565 rad Elastic stiffness: 154212 / 137168 kNm /rad
-80
-0.010
Yield moment: 75.41/-77.50 kNm
Ultimate rotation:0.001049/ -0.001059 rad
-60
-100
0.331
Yield moment: 80.79/-81.49 kNm
20
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M /kN·m
60
J-12
3.5/3.1
Elastic stiffness: 149846 / 137719 kNm /rad
-80
-100
0.311
Ultimate moment: 69.61/ -72.02 kNm
0 -20 -60
J-10
3.0 / 2.9
Yield moment: 78.07/-81.53 kNm
20
-100
Damping ratio
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Elastic stiffness: 149130 / 139819 kNm/rad
-80
Ductility ratio
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J-6
Mechanical Parameters*
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Tested sample
0.010
*Values are given for positive and negative side of the response.
4. Simplified modeling 4.1 Assumptions The objective of this section is to develop a manual calculation procedure to predict the load-carrying capacity 11
ACCEPTED MANUSCRIPT of the proposed semi-rigid connection. As presented above, the desirable failure mode is the one with failure in the middle of EDP and which exhibits good ductile and energy dissipating capability. For this reason, a manual calculation procedure for predicting load-carrying capacity is developed based on this failure mode. On the basis of experimental results, the following assumptions are adopted to develop manual calculation procedure for
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design: (1) the deformations of steel column, EBP beam, and the jointed panel of the brackets can be omitted; (2) the friction of the hinge is ignored; and (3) the first yield of EDP is induced by buckling of the panel while the load-carrying capacity depends on the partial yielding of the EDP.
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4.2 Initial yield load and stiffness
The initial yielding is the point when the stress of EDP reaches the yield strength of steel, f y . Thus the tensile
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or compressive force in EDP must be FEDP = f y bt when initial yielding takes place; hence the initial yield moment can be calculated by M y = f ybt ( h + t )
(4)
The initial moment stiffness of the connection can be calculated by K y = f ybt ( h + t ) / θ y , where, θ y represents
be calculated by Ebt ( h + t )
2
2l
(5)
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Ky =
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the rotation of connection, which can be calculated by θ y = 2 f yl / E ( h + t ) . Thus the initial rotational stiffness can
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where, b and t are width and thickness of EDP respectively, l represents length of EDP; h stands for the clear distance between the two EDPs.
4.3 Load-carrying capacity
According to assumption (3), the maximum force of EDP at the ultimate limit state can be expressed as FEDP = η f u bt , where f u is the ultimate strength of the EDP steel. Therefore, the failure moment of the connection can be expressed as M u = η f ubt ( h + t )
(6)
12
ACCEPTED MANUSCRIPT where, η is partial yield coefficient, that represents the degree of which depends on the EDP length-to-thickness ratio. In this study, finite element analyses were performed to estimate the partial yield coefficient. As illustrated in Fig. 8, the bracket of the connection is divided into two segments, the EDP and joint panel, respectively. Obviously, the EDP can be freely deformed out of its own plane leading to large nonlinear
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deformation. On the other hand, the out-of-plane movement of the joint panel is restricted by the beam and the stub, which means it performs as a rigid panel to apply tensile or compressive force to the EDP. For this reason, in the finite element (FE) modeling, the out-of-plane movement of the joint panel was restricted and the compressive load was applied to EDP through the joint panel. The end of EDP is assumed to be rigid to simulate welding
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boundary. Therefore, the simplified model as shown in Fig. 8(c) was used in the finite element analyses.
In total, three groups of EDPs with cross sectional sizes of 6mm × 100mm, 8mm × 75mm and 10mm × 60mm
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respectively were numerically investigated. The lengths of the EDPs were varied to achieve length-to-thickness ratio between 6 and 16 for each group. Material properties input into the FE model were obtained by testing the same batch steel used to fabricate experimental connections as presented in Table 1. Monotonic loading regime was chosen in the numerical simulation.
The numerical analysis was implemented by using ABAQUS software. Nominal stress and strain were
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transferred to true stress and strain by the formulas
σ tru = σ nom (1 + ε nom ) and ε tru = ln (1 + ε nom ) specified by
ABAQUS code, where, the subscripts, tru and nom, stand for the actual and nominal quantity, respectively. The
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correspondence of the true stress and strain with the nominal stress and strain is presented in Table 4.
Table 4. The correspondence of true and nominal stress and strain in FE model Nominal stress (MPa)
Nominal strain
Actual stress (MPa)
True strain
Plastic strain
0.0015
314.5
0.0015
0
315
0.003
315.9
0.003
0.0015
445
0.15
511.75
0.139
0.137
445
0.40
580.0
0.340
0.337
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314
Solid element C3D8R was selected to model the EDP. The “element depth” technique provided by ABAQUS was employed to simulate the crack growth of EDP. Fig. 8(d) presents the distribution of compressive stress in EDP. It can be observed that the stress in the mid-EDP reaches maximum value due to global buckling, which approximately equals to the actual yield stress.
13
ACCEPTED MANUSCRIPT (b)
(d)
(c)
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(a)
Fig. 8 Simplified model to estimate the load-carrying capacity of EDP. (a) top view; (b) side view; (c) model for FE analysis; (d) compressive stress in EDP calculated using FE analysis.
Considering the fact that the cross section of EDP cannot fully yield when connection failed, a coefficient
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η =σ u / f u is used to quantify the partial yielding effect, where σ u is the ultimate compressive stress obtained from
FE analysis, which was estimated by σ u = Fu, FE / AEDP , where, Fu, FE and AEDP are the ultimate load calculated by
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FE model and the cross-section area of EDP, respectively; f u is the ultimate strength of the steel which is obtained through test and is presented in Table 1. Fig. 9 presents how the partial yielding coefficient varies with the length-to-thickness ratio, λ = l / t , of EDP. An empirical relationship between η and λ can be obtained by data fitting which is expressed as follows
6.6 ≤ λ ≤ 7.2
0.978
η =
−
(7)
7.2<λ ≤ 16.0
1.897
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0.749 + 1.150e
λ
Furthermore, the load-carrying capacity of the connection can be calculated by Eq. (6). Table 5 compares the
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ultimate moments computed by Eq. (6) with that obtained by testing for groups J-6 and J-8. Good agreements can be observed between the two results.
Coefficient of partial yield
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1.00 0.95
η = 0.978 λ − η = 0.749 + 1.150e 1.897
0.90 0.85 0.80 0.75 6
7
8
9
10
11
12
13
14
15
16
Length-to-thickness ratio
Fig. 9 Variation of partial yield coefficient with EDP length-to-thickness
14
ACCEPTED MANUSCRIPT Table 5. Comparing the load-carrying capacity between calculation and experiments Peak moment Specimen J-6-1
J-8-3
Elastic stiffness
Experiments*
Error*
Calculation
Experiments*
Error*
Calculation
Experiments*
Error*
(kNm)
(kNm)
(%)
(kNm)
(kNm)
(%)
(kNm/rad)
(kNm/rad)
(%)
81.30
76.81 / -78.96
5.85 / 2.96
76.73
68.66 / -69.35
11.41 / 9.55
129810
149130 / 139819
13.06 / 7.16
87.11 / -87.41
8.60 / 5.91
77.94 /-78.33
4.50 / 1.52
87.01/ -90.02
5.49 / 8.65
78.07/ -81.53
2.0 / 5.42
79.21 /-81.79
3.81 / 5.40
72.83/ -76.04
5.46 / 1.23
J-8-1 J-8-2
Moment of initial yielding
Calculation
82.23
77.11
131090
133680 / 128830
1.94 / 1.75
149846 / 137719
12.52 / 4.81
123231 / 124656
6.38 / 5.16
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*Values are given for positive and negative side of the response.
5. Summary and discussions
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The semi-rigid connection proposed in this study uses a hinge and a pair of brackets to carry shear force and moment, respectively. The structure of the connection provides a possible way to control the damage mechanism
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and failure mode of connections, i.e. to restrict damage to the two EDPs by controlling its length-to-thickness ratio to force a specific failure mode. Based on the results of experiments and numerical analysis, it can be concluded that the suitable length-to-thickness ratio is in the range of 8 - 16. This is because within this range, the failure mode of the EDP is ductile, thereby providing not only adequate load-carrying capacity but energy dissipating capability to resist seismic loads.
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The load-carrying capacity of the connection was found to be dependent on the compressive strength of EDP. Theoretically, the compressive strength of EDP must be determined by the fatigue strength of steel. Although there are models available to predict the fatigue strength of steel, to determine the stress level for each loading cycle in
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damage process would require a substantial amount of work, which is beyond the scope of the current project. Instead, the present work provides an approximate formula to predict the moment capacity of the connection
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based on use of a partial yielding coefficient. The partial yielding coefficient was obtained from finite element analyses and is expressed as a function of the length-to-thickness ratio of the EDP. Comparison of predicted moment capacity with the measured capacity reveals a good agreement between the two. On the basis of this study, suggestions for the connection design are as follows: (1) the strength of EBP beam-to-stub connection and the column-to-base panel connection should be designed to fail first; (2) the length-to-thickness ratio of EDP should be in the range of 8 to 16; (3) the damage and failure of the weld should be avoided; and (4) the yield moment and initial stiffness can be calculated by Eqs. (4) and (5), and the ultimate moment capacity can be calculated by Eq. (6). A further study for the engineered bamboo-steel frame with the proposed connection is need and results will 15
ACCEPTED MANUSCRIPT be reported in another paper in near future.
Acknowledgements
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The study was supported by National Intensive Research Project, 2017YFC0703500, which was provided by the Ministry of Science and Technology, China. Their support is gratefully acknowledged.
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19
ACCEPTED MANUSCRIPT Highlights
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We innovated a semi-rigid connection for mid- and high-rise bamboo-steel hybrid structures. The connection can be used as not only a moment-frame joint, but also an energy dissipation device. The performances, damage and failure mode of the connection can be well controlled as expected. Formulas for predicting the stiffness and strength of the connection are provided. Suggestions for the design of connection were proposed.
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1. 2. 3. 4. 5.
S2352-7102(19)30175-5
DOI:
https://doi.org/10.1016/j.jobe.2019.100754
Article Number: 100754 Reference:
JOBE 100754
To appear in:
Journal of Building Engineering
Received Date: 3 February 2019 Revised Date:
26 March 2019
Accepted Date: 27 March 2019
Please cite this article as: Z. Huang, Z. Chen, D. Huang, Y.-H. Chui, Cyclic loading behavior of an innovative semi-rigid connection for engineered bamboo-steel hybrid frames, Journal of Building Engineering (2019), doi: https://doi.org/10.1016/j.jobe.2019.100754. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Cyclic loading behavior of an innovative semi-rigid connection for engineered bamboo-steel hybrid frames Zirui Huang a, d, Zhongfan Chen a,b, Dongsheng Huang* c, Ying-Hei Chui d a
Key Laboratory of RC & PC structures of Ministry of Education, Southeast University, Nanjing, China, 210096 School of Civil Engineering, Southeast University, Nanjing, China, 211189 c National Engineering Research Center of Biomaterials, Nanjing Forestry University, Nanjing, China, 210037 d Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Canada, T6G 1H9
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b
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Abstract
This paper presents an innovative semi-rigid connection for bamboo-steel hybrid moment frames that comprise
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engineered bamboo beams and steel columns. The connection incorporates a steel hinge and two steel brackets to carry shear force and moment at the end of the beam, respectively. The bracket consists of two segments-a joint segment connected to beam and an energy dissipation panel (EDP) connected to a column via a base panel. In this way, the connection not only serves as a frame joint, but also as an energy dissipation device. Cyclic loading tests were carried out on 9 connections with various EDP length-to-thickness ratios to investigate their failure mode
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and hysteresis behavior. It was found that by proper design, damage of the frame can be restricted to the EDP while other parts of the frame are virtually free of damage. Hysteresis loops for the connection exhibit less pinching than dowel or bolt type connections. The connection has adequate initial stiffness, strength and ductility
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to meet structural design requirements. A simplified formula to predict the load-carrying capacity of the connection was developed based on the experimental and numerical results. Good agreement was achieved
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between the results of calculation and experiment. Recommendations are made for the design of the proposed semi-rigid bamboo-steel hybrid connection.
Key words
Engineered bamboo products; semi-rigid connection; bamboo-steel hybrid frame; energy dissipation device
1. Introduction
1
ACCEPTED MANUSCRIPT Over the past decade, the use of engineered wood products in mid- or high-rise buildings has been growing rapidly around the world [1-5]. A number of innovative mid- and high-rise wood buildings have been constructed worldwide demonstrating the technical feasibility of using bio-based products in building construction. In China, engineered bamboo products (EBPs) have been developed as an alternative to wood products in
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construction due to the limitation of wood harvest. These products are made by gluing bamboo strands or veneers together under controlled temperature and pressure. Currently, two types of EBPs, i.e., parallel strand bamboo (PSB) and laminated veneer bamboo (LVB), are commercially available [6-8]. The mechanical properties of EBPs are similar to or even superior to those of commonly used wood products [6]. However, the relatively low
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stiffness and strength of EBPs, compared to steel and reinforced concrete, usually means larger member sizes are necessary to construct mid-rise and taller wood buildings. This is a major limitation in the use of EBPs in
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multi-storey buildings. EBP-steel hybrid moment frame, which employs steel columns connected with EBP beams to build lateral and vertical load-carrying systems, is an effective solution to extend the application of EBP to multi-storey buildings.
Obviously, the design of moment connection is a major concern of EBP-steel frames. Generally, the connection must not only have adequate initial stiffness and strength, but also enough ductility and energy
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dissipation capacity to meet the collapse prevention requirements when the frame undergoes severe seismic actions. Steel dowel connections are most common joints accepted in modern wood or EBP buildings [9,10]. Experimental investigations demonstrated that wood failure can be the dominant mode for dowel connections, and
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the load-carrying capacity of the connection usually does not exceed 20 % of the strength of the connecting beams [11, 12]. The rotational stiffness of dowel connections is also often significantly lower than the bending stiffness
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of the connecting beam [13]. Bolted connection is another type of commonly used joint, which is stronger and stiffer than dowel connections. Usually, damage of the moment frame with bolted connections is in the form of bolt yielding, timber crushing and cracking of timber members at the joint [14]. The hysteresis loops of these connections are basically characterized by pinching or degradation of stiffness and strength under reversed cyclic loading, demonstrating low energy dissipation capacity of the connections [15, 16]. Therefore, improving the load-carry capacity and hysteresis performance of connections is essential if timber / bamboo or timber / bamboo-steel hybrid structures are to be adopted as a structural form by designers. To this end, the present work investigates an innovative connection for EBP-steel frames. As presented in Fig. 1, the connection incorporates a hinge and a pair of top and seat brackets to resist the shear force and moment 2
ACCEPTED MANUSCRIPT from the connecting beam, respectively. Each bracket can be divided into two segments. One of the segments is the joint panel which is welded to a steel stub bolted to two sandwich beam panels. The other segment serves as energy dissipation panel (EDP), which is welded to a base panel through which the connection is fixed to the steel column; and the EDP is free to buckle out-of-plane. In this way, the connection behaves as a seesaw supported by
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a hinge which bears most of shear force of the connecting beam. The top and seat brackets restrict the rotation of the connection, thereby providing resistant moment and lateral stiffness for the frame, as shown in Fig.1(c). Furthermore, by an appropriate design and detailing, the first yielding of the frame can be confined to the EDPs while the other parts of the frame are protected when the frame is subjected to a lateral load. EDP
Joint panel
(a)
Stub
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Steel column
EDP Hinge
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Hinge
Base panel
Bolt
(b) Joint panel
Base panel
Bolt
Stub
EBP beam
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(c)
Fig.1 Moment connection for bamboo-steel moment frame; (a) the way of connection joint beam and column; (b) details of proposed energy-dissipating connection; (c) working principle of the connection.
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The proposed EBP-steel frame connection can be treated as a semi-rigid connection. It may lead to smaller beam sizes because the semi-rigidity of the connection may reduce the moment at the end of the beam. As such, the moment stiffness of the connection can be adjusted for an optimal distribution of the bending moment in the beam. Considerable research has been carried out to explore the performances of semi-rigid connections in steel structures [17-20]. It has been confirmed by Pirmoz and Liu [21] that the rotational stiffness of a semi-rigid connection was about 20% lower than a rigid connection while its moment capacity was only 15% lower. Moreover, a semi-rigid connection can dissipate energy through hysteresis behavior better than rigid or pinned connections [22, 23]. For these reasons, semi-rigid connections are a good solution for seismic-resisting frames. Because of its controllable stiffness and failure mode, the concept of semi-rigid connection is an attractive 3
ACCEPTED MANUSCRIPT design philosophy for timber and bamboo structures to improve the seismic performances of the structure. One kind of semi-rigid connection for wood frames, known as Lagscrewbolt, was developed by Komatsu et al [24]. Lagscrewbolt connection can develop lateral and moment resistance through withdrawal resistance provided by the threaded rods in timber members. A recent study carried out by Mori et al [25] indicated that Lagscrewbolt
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connection has high initial stiffness and load-carrying capacity, while the hysteresis loops exhibit pronounced pinching characteristic. In an attempt to avoid timber failure, Buchanan, et al [26] inserted a box-type steel bracket between timber beam and column. Yang, et al [27] continued an investigation into the same type of connection by developing an analytical model to estimate the moment-rotation relationship for the connection. More recently,
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Karagiannis, et al [28], developed an innovated timber beam-to-tubular steel column moment connection, and monotonic loading tests were conducted to investigate the stiffness, load-carrying capacity, and failure mechanism
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of the connection. Many other types of semi-rigid connections used in structures built with different materials can be found in the literature [29-35].
This paper presents the work of a project conducted to evaluate the performance of the aforementioned connection with EDP that connects a bamboo composite beam to a steel column. Cyclic loading tests were conducted on nine connection specimens with different EDP length-to-thickness ratios to investigate the failure
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modes and hysteresis loops of the connections. A simplified model for estimating the load-carrying capacity of the connection was developed based on the experimental results.
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2. Connection detailing and material
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Details of the test connection are illustrated in Fig. 2. As aforementioned, the end segments of the two brackets free of out-of-plane restraints are energy dissipation panel (EDP). In order to restrict the damage of the connection to EDPs, the diameter and spacing of the bolts, thickness of base panel and stub were designed to ensure that the bolted connection is stronger than the EDP. When reversing loads were applied to the connection, the EDPs were subjected to alternating tension and compression forces leading to yielding or buckling of the EDP. Obviously, the dimensions of the brackets are one of the major factors impacting on the mechanical behaviour of the connection. In this study the connection specimens were designed to have the same dimensions except the width and length-to-thickness ratio of EDPs. In total nine specimens with four different EDP length-to-thickness ratios were tested. The length and the area 4
ACCEPTED MANUSCRIPT of cross-section of the EDP were kept constant at 80 mm and 600 mm2, respectively. The dimensions of EDP for each group of test specimens are presented in Table 1. Test connections were fabricated by using Q235 steel, following Chinese Standard GB50017-2017 [36]. The mechanical properties of the steel were tested in tension according to ASTM standard E8/E8M [37]. Test results of 12 steel coupons are summarized in Table 2. The
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column used in the connection test was a HPB 400 grade steel I-section, that meets the requirements of GB50017-2017 [36]. The beam was a parallel strand bamboo (PSB) composite. PSB is a kind of engineered bamboo product that has superior performances than commonly used wood products. The dimensions of PSB beam were determined to ensure enough strength to resist test load without failure in the beam. Mechanical
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properties of PSB were tested according to ASTM D143 [38], and modulus of elasticity, tensile and compressive
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strength are 13000MPa,150 MPa, 90 MPa, and 60 MPa, respectively. ghcv
EDP Stub
EBP beam
(b)
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(a)
Fig. 2 Details of connection. (a) Cross section at the end of beam; (b) detailing of steel stub. Units: mm Table 1. Dimensions of the test connections
J-8
3
J-10
3
J-12
2
Label J-6-1 J-8-1, J-8-2, J-8-3 J-10-1, J-10-2, J-10-3 J-12-1, J-12-2
Bracket length (mm) 330
EDP length (mm) 80
Width (mm) 100
Thickness (mm) 6
Cross section area (mm2) 600
EDP length-to-thickness ratio 13.33
330
80
75
8
600
10
330
80
60
10
600
8
330
80
50
12
600
6.67
Elongation ratio
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J-6
Number of specimens 1
Group
Table 2. Properties of steel of EDP and stub. Items Mean CoV
Yield strength (MPa)
Ultimate strength (MPa)
Young’s modulus (GPa)
Poisson’s ratio
315
445
209
0.30
0.32
2.37%
1.30%
5.04%
18.70%
5.0%
3. Experimental investigation
3.1 Test procedure
The test setup is schematically illustrated in Fig. 3. Since it is more efficient to anchor the steel column 5
ACCEPTED MANUSCRIPT member to the strong floor of the laboratory, the test specimen was horizontally installed, i.e., rotated 90 degrees compared to its normal service position. The beam member was made of two PSB panels with a cross section of 400 mm × 95 mm. A steel stub of 12 mm thickness was sandwiched between the two PSB panel and they were connected together using twelve 20 mm diameter bolts, referring to Fig. 3(a). According to Liu, et al [39], there is
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no significant influence on the connection response when the length of the connecting members exceeds 1 m. Therefore, the lengths of the beam and column were 2 m and 1.2 m, respectively. The connection was mounted in the middle of the steel column which was fixed to the stiff and strong concrete laboratory floor using four 40mm diameter bolts. In order to mitigate the deformation of flange of the column, web stiffeners spaced at 400 mm
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(omitted in Fig. 3 for the sake of clarity) were welded to the web of the column below the connection area. The load was applied using a double-hinged hydraulic actuator to the top of the PSB beam via specially designed
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clamping device. The distance from the loading point to the centre of hinge was maintained at 1095 mm for all tests. Two pairs of displacement sensors, labeled 5 and 6 in Fig. 3 (b), spaced at 100 mm apart were mounted to each side of the test connection to measure the transverse displacement. A sensor, labeled 7 in Fig. 3(b), was installed at the bottom to monitor the displacement of the base panel. A load cell incorporated in the actuator was employed to measure the applied force. Displacement of each sensor and applied force were simultaneously
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recorded by the TDS-530 data acquisition system using a sampling frequency of 1 Hz. The connection specimen was loaded at a displacement speed of 4 mm/min. At each displacement level, 3 reversed cycles were applied and the displacement level increment was 2 mm until failure occurred. Actuator
Clamp
Deformation sensor-1
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(a)
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(b)
Deformation sensors
Bolts
Reaction wall
5 6
Bolts to fix column to the floor
7
Steel column
Base panel
Hinge
Fig. 3 Test setup; (a) an overview; (b) details of connection
6
EDP
Joint panel
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found that virtually all damages of the connection were restricted to the EDPs with no visual residual distortions observed in other parts of the connection. The failure modes can be categorized into two types, as illustrated in Fig 4. The first failure mode is characterized by EDP fracture as shown in Fig. 4(a). Specimens in groups J-6 and J-8 failed in this manner. These groups have the larger EDP length-to-thickness ratios. The second failure mode is the
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rupture of welding between EDPs and base panel, as illustrated in Fig. 4(b). Groups J-10 and J-12 failed in this mode. It should be noted that the deformations in the EDP of these specimens that failed in the weld were much
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smaller than those of first failure mode, indicating potential premature failure. These groups had the smaller EDP length-to-thickness ratios than J-6 and J-8, which indicates that the weld was the weakness in the connection and a larger length-to-thickness ratio is required to prevent the premature failure in the weld. The failure mechanism can be explained as follows. As discussed above, the connection works like a seesaw when it is subjected to reversed cyclic moments. The brackets provide resistant moment through tension in one
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side and compression in the other side. For the connection with EDP of large length-to-thickness ratio (J-6 and J-8), buckling took place in compressive side once the compressive force exceeded the buckling capacity of the EDP, whereas on the other hand, the EDP on the tensile side was still in an elastic state. The tension and
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compression of the brackets were continuously alternated as the loading direction changed. Because the buckling strength is lower than tensile strength of the steel, the stress in the brackets could never reach the tensile strength
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of the steel. This implies that load-carrying capacity of the connections that failed in the first mode was actually dominated by the compressive capacity of EDP. Because buckling always takes place on the condition of partial yielding of EDP, the compressive capacity of EDP can be recognized as the strength of partial yielding. For the connection with EDP of smaller length-to-thickness ratios, buckling could not take place and the load-carrying capacity of the connection ultimately was dependent on the tensile strength of the EDP or the weld. In the present study, the tensile strength of the weld between the EDP and base panel was lower than the tensile strength of the steel in the EDP; hence failure occurred in the weld for J-10 and J-12 specimens. In summary, by an appropriate design, the damage of a structure can be restricted to the EDPs in the connection. The residual deformations of the steel around the bolt holes are small such that they can be ignored, as 7
ACCEPTED MANUSCRIPT illustrated in Fig 5. The failure is in the form of plastic yielding of the EDPs in compression, which also acts as a source of energy dissipation. As a result, the load-carrying capacity of the connection depends on the strength of partial yielding of EDPs.
(b)
(a)
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Progressively developed crack in mid-EDP
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Failure of EDP-to-base panel welding
(b)
(a)
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Fig. 4 Typical failure modes of connections. (a) buckling and failure in the middle of EDP; (b) weld failure at the end of EDP
(c)
3.2.2 Hysteresis loops
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Fig. 5 Residual distortions: (a) steel stub; (b) the joint part of EBP beam; (c) bolts.
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The hysteresis loops and test results are summarized in Table 3. Moment-rotation response, i.e., M − θ , was obtained by directly converting load-deformation data. The rotation of the connection was estimated
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by φ = ( w7 − w6 − w5 ) / L , where, wi (i = 5, 6, 7) stands for the displacements of measurement points 5, 6, and 7, as illustrated in Fig. 3(b), and L=1095 mm is the distance from loading position to the centre of the hinge. It can be observed that only limited pinching happens in each hysteresis loop. However, the hysteresis loops of groups J-6 and J-8 are evidently different from those of groups J-10 and J-12. For connections in groups J-6 and J-8, there is post-peak strength degradation; whereas for connections in groups J-10 and J-12, almost no declining loop can be observed. It also provides evidence that the damage mechanisms of the two pairs of groups are different, and it will be further discussed in section 3.4.
3.2.3 Envelope profiles 8
ACCEPTED MANUSCRIPT The backbone curve of a hysteresis loop response was obtained by enveloping the M − θ curve of the first loading cycle at each displacement level, shown as the red curve in Table 3. It can be observed that the connections behaved linearly elastically until the load reached a proportional limit. The proportional limit depends on initial yield strength of EDP. The load-carrying capacity of a connection generally increases with a decrease in
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length-to-thickness ratio of EDP. The initial stiffness of each connection can also be obtained through the envelope profile, which is presented in Table 3.
3.2.4 Ductility ratio
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The ductility ratios of the connections were estimated following the Equivalent Energy Elastic-Plastic (EEEP) procedure of ASTM E2126 [40], as illustrated in Fig. 6. According to ASTM E2126, a line is first drawn, going
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through the origin and the point on the envelope curve where the moment equals to 40 % of the maximum moment. The yield point was determined by equating the area under the bi-linear EEEP response to the area under the test envelope curve, referring to Fig. 6. This was achieved by adjusting the horizontal line until the equivalent area criterion was met. The ductility ratio is expressed as µ = θ y / θu , where, θ y and θ u are defined as yield and ultimate displacement, respectively. For the envelope with post-peak declining branch, θ u is the rotation
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corresponding to the 0.8 maximum load, while for the envelope without declining branch, θ u is the rotation corresponding to ultimate load. The values of yielding moment and rotation, ultimate moment and rotation, elastic stiffness, and ductility for each connection are presented in Table 3. It can be concluded that the ductility ratio of
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the first failure mode (partial yielding and subsequently buckling) may reach about 3.0 while that of the second failure mode (weld fracture) only reaches about 2.0. M Peak
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M
M Yield
D
0.8M Peak
0.4M Peak
Envelope curve EEEP
B
θy
θPeak
θu
θ
Fig. 6 Ductility determination
Fig. 7 Energy dissipation determination
3.2.5 Energy dissipation
9
ACCEPTED MANUSCRIPT As the energy dissipated by the connection only includes yielding or buckling energy, hence it may be estimated by [41] Ed =
∫
θ
0
1 Mdθ − kθ 2 2
(1)
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where k is the initial stiffness of the connection; M and θ are the applied moment and corresponding rotation, respectively. Thus the energy dissipated in each loading cycle equals the area of corresponding loop subtracting the triangle area which stands for the elastic work in the loading cycle. As illustrated in Fig. 7, the energy dissipation, Ed, can be calculated by
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Ed = S Loop − ( S ∆OBF + S ∆ODE )
(2)
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where SLoop stands for the area of loading circle loop, S∆OBF stands for the triangle area of ∆OBF, S∆ODE stands for the triangle area of ∆ODE. The damping ratio, ξ , can be calculated by ξ=
SLoop 1 ⋅ 2π S∆OBF + S∆ODF
(3)
The damping ratio for each test connection is presented in Table 3. It can be concluded that the damping ratios of
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the connections taken place in first failure mode can reach 30 % or more while that of the second failure mode can only reach 26%, which indicating the good energy dissipating capability of the proposed semi-rigid connection.
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3.4 Conclusions from experimental investigation The results of experimental investigation can be summarized as follows:
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(1) By a proper design, the damage of the frame with EDP connections can be restricted to the EDP while the other parts of the connection, the beam and column of the frame, can be free of damage. The hysteresis loops of the connections exhibit limited pinching and provide a high damping ratio, indicating that the connection has good energy dissipation capability. The ductility ratio and damping ratio of the connections can reach more than 3.0 and 30%, respectively. (2) The failure mode of connection depends on the length-to-thickness ratio of the EDP. For the connections with large EDP length-to-thickness ratio, the failure was ductile and occurred in the middle of EDP after some reversed cyclic loading action. For the connections with small EDP length-to-thickness ratio, the failure occurred prematurely at the weld joint between EDP and base plate, and virtually no post-peak strength degradation was 10
ACCEPTED MANUSCRIPT observed in their envelop profiles. Since the length-to-thickness ratio plays a key role in dictating the mode of failure, it should be possible to detail the connection to avoid weld failure and achieve the more desirable ductile failure mode. This issue will be addressed in Section 4.
Table 3. Experimental results Hysteretic loops 80
Hysteretic loop Envelope curve
60 40
M /kN·m
Yield moment: 68.66 / -69.35 kNm
20
Ultimate moment: 62.05 / -63.17 kNm
0
-20
Yield Rotation: 0.000460/ -0.000496 rad
-40
Ultimate rotation: 0.001390 /-0.001431 rad
-60 -0.02
100 60
M /kN·m
0.00
θ /rad
0.01
0.02
Hysteretic loop Envelope curve
80
J-8
-0.01
40
Yield Rotation: 0.000521/ -0.000592 rad
-40
Ultimate rotation: 0.001800/ -0.001855 rad
-0.02
-0.01
0.00
θ /rad
0.01
0.02
100
Hysteretic loop Envelope curve
80 40
Yield Rotation:0.000595 / -0.000535 rad
-40
0.269
2.1/1.9
0.264
Ultimate rotation:0.001226/ -0.001215 rad
-60
Elastic stiffness: 135781 / 152317 kNm /rad
-80 -0.010
-0.005
0.000
θ /rad
100
0.005
0.010
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Hysteretic loop Envelope curve
80 60 40 20 0 -20
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M /kN·m
2.3/2.2
Ultimate moment: 88.63 / -90.90 kNm
0
-20
-40
-0.005
0.000
θ /rad
0.005
Ultimate moment: 88.18 / -85.79 kN.m Yield Rotation:0.000489/ -0.000565 rad Elastic stiffness: 154212 / 137168 kNm /rad
-80
-0.010
Yield moment: 75.41/-77.50 kNm
Ultimate rotation:0.001049/ -0.001059 rad
-60
-100
0.331
Yield moment: 80.79/-81.49 kNm
20
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M /kN·m
60
J-12
3.5/3.1
Elastic stiffness: 149846 / 137719 kNm /rad
-80
-100
0.311
Ultimate moment: 69.61/ -72.02 kNm
0 -20 -60
J-10
3.0 / 2.9
Yield moment: 78.07/-81.53 kNm
20
-100
Damping ratio
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Elastic stiffness: 149130 / 139819 kNm/rad
-80
Ductility ratio
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J-6
Mechanical Parameters*
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Tested sample
0.010
*Values are given for positive and negative side of the response.
4. Simplified modeling 4.1 Assumptions The objective of this section is to develop a manual calculation procedure to predict the load-carrying capacity 11
ACCEPTED MANUSCRIPT of the proposed semi-rigid connection. As presented above, the desirable failure mode is the one with failure in the middle of EDP and which exhibits good ductile and energy dissipating capability. For this reason, a manual calculation procedure for predicting load-carrying capacity is developed based on this failure mode. On the basis of experimental results, the following assumptions are adopted to develop manual calculation procedure for
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design: (1) the deformations of steel column, EBP beam, and the jointed panel of the brackets can be omitted; (2) the friction of the hinge is ignored; and (3) the first yield of EDP is induced by buckling of the panel while the load-carrying capacity depends on the partial yielding of the EDP.
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4.2 Initial yield load and stiffness
The initial yielding is the point when the stress of EDP reaches the yield strength of steel, f y . Thus the tensile
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or compressive force in EDP must be FEDP = f y bt when initial yielding takes place; hence the initial yield moment can be calculated by M y = f ybt ( h + t )
(4)
The initial moment stiffness of the connection can be calculated by K y = f ybt ( h + t ) / θ y , where, θ y represents
be calculated by Ebt ( h + t )
2
2l
(5)
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Ky =
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the rotation of connection, which can be calculated by θ y = 2 f yl / E ( h + t ) . Thus the initial rotational stiffness can
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where, b and t are width and thickness of EDP respectively, l represents length of EDP; h stands for the clear distance between the two EDPs.
4.3 Load-carrying capacity
According to assumption (3), the maximum force of EDP at the ultimate limit state can be expressed as FEDP = η f u bt , where f u is the ultimate strength of the EDP steel. Therefore, the failure moment of the connection can be expressed as M u = η f ubt ( h + t )
(6)
12
ACCEPTED MANUSCRIPT where, η is partial yield coefficient, that represents the degree of which depends on the EDP length-to-thickness ratio. In this study, finite element analyses were performed to estimate the partial yield coefficient. As illustrated in Fig. 8, the bracket of the connection is divided into two segments, the EDP and joint panel, respectively. Obviously, the EDP can be freely deformed out of its own plane leading to large nonlinear
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deformation. On the other hand, the out-of-plane movement of the joint panel is restricted by the beam and the stub, which means it performs as a rigid panel to apply tensile or compressive force to the EDP. For this reason, in the finite element (FE) modeling, the out-of-plane movement of the joint panel was restricted and the compressive load was applied to EDP through the joint panel. The end of EDP is assumed to be rigid to simulate welding
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boundary. Therefore, the simplified model as shown in Fig. 8(c) was used in the finite element analyses.
In total, three groups of EDPs with cross sectional sizes of 6mm × 100mm, 8mm × 75mm and 10mm × 60mm
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respectively were numerically investigated. The lengths of the EDPs were varied to achieve length-to-thickness ratio between 6 and 16 for each group. Material properties input into the FE model were obtained by testing the same batch steel used to fabricate experimental connections as presented in Table 1. Monotonic loading regime was chosen in the numerical simulation.
The numerical analysis was implemented by using ABAQUS software. Nominal stress and strain were
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transferred to true stress and strain by the formulas
σ tru = σ nom (1 + ε nom ) and ε tru = ln (1 + ε nom ) specified by
ABAQUS code, where, the subscripts, tru and nom, stand for the actual and nominal quantity, respectively. The
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correspondence of the true stress and strain with the nominal stress and strain is presented in Table 4.
Table 4. The correspondence of true and nominal stress and strain in FE model Nominal stress (MPa)
Nominal strain
Actual stress (MPa)
True strain
Plastic strain
0.0015
314.5
0.0015
0
315
0.003
315.9
0.003
0.0015
445
0.15
511.75
0.139
0.137
445
0.40
580.0
0.340
0.337
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314
Solid element C3D8R was selected to model the EDP. The “element depth” technique provided by ABAQUS was employed to simulate the crack growth of EDP. Fig. 8(d) presents the distribution of compressive stress in EDP. It can be observed that the stress in the mid-EDP reaches maximum value due to global buckling, which approximately equals to the actual yield stress.
13
ACCEPTED MANUSCRIPT (b)
(d)
(c)
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(a)
Fig. 8 Simplified model to estimate the load-carrying capacity of EDP. (a) top view; (b) side view; (c) model for FE analysis; (d) compressive stress in EDP calculated using FE analysis.
Considering the fact that the cross section of EDP cannot fully yield when connection failed, a coefficient
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η =σ u / f u is used to quantify the partial yielding effect, where σ u is the ultimate compressive stress obtained from
FE analysis, which was estimated by σ u = Fu, FE / AEDP , where, Fu, FE and AEDP are the ultimate load calculated by
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FE model and the cross-section area of EDP, respectively; f u is the ultimate strength of the steel which is obtained through test and is presented in Table 1. Fig. 9 presents how the partial yielding coefficient varies with the length-to-thickness ratio, λ = l / t , of EDP. An empirical relationship between η and λ can be obtained by data fitting which is expressed as follows
6.6 ≤ λ ≤ 7.2
0.978
η =
−
(7)
7.2<λ ≤ 16.0
1.897
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0.749 + 1.150e
λ
Furthermore, the load-carrying capacity of the connection can be calculated by Eq. (6). Table 5 compares the
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ultimate moments computed by Eq. (6) with that obtained by testing for groups J-6 and J-8. Good agreements can be observed between the two results.
Coefficient of partial yield
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1.00 0.95
η = 0.978 λ − η = 0.749 + 1.150e 1.897
0.90 0.85 0.80 0.75 6
7
8
9
10
11
12
13
14
15
16
Length-to-thickness ratio
Fig. 9 Variation of partial yield coefficient with EDP length-to-thickness
14
ACCEPTED MANUSCRIPT Table 5. Comparing the load-carrying capacity between calculation and experiments Peak moment Specimen J-6-1
J-8-3
Elastic stiffness
Experiments*
Error*
Calculation
Experiments*
Error*
Calculation
Experiments*
Error*
(kNm)
(kNm)
(%)
(kNm)
(kNm)
(%)
(kNm/rad)
(kNm/rad)
(%)
81.30
76.81 / -78.96
5.85 / 2.96
76.73
68.66 / -69.35
11.41 / 9.55
129810
149130 / 139819
13.06 / 7.16
87.11 / -87.41
8.60 / 5.91
77.94 /-78.33
4.50 / 1.52
87.01/ -90.02
5.49 / 8.65
78.07/ -81.53
2.0 / 5.42
79.21 /-81.79
3.81 / 5.40
72.83/ -76.04
5.46 / 1.23
J-8-1 J-8-2
Moment of initial yielding
Calculation
82.23
77.11
131090
133680 / 128830
1.94 / 1.75
149846 / 137719
12.52 / 4.81
123231 / 124656
6.38 / 5.16
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*Values are given for positive and negative side of the response.
5. Summary and discussions
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The semi-rigid connection proposed in this study uses a hinge and a pair of brackets to carry shear force and moment, respectively. The structure of the connection provides a possible way to control the damage mechanism
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and failure mode of connections, i.e. to restrict damage to the two EDPs by controlling its length-to-thickness ratio to force a specific failure mode. Based on the results of experiments and numerical analysis, it can be concluded that the suitable length-to-thickness ratio is in the range of 8 - 16. This is because within this range, the failure mode of the EDP is ductile, thereby providing not only adequate load-carrying capacity but energy dissipating capability to resist seismic loads.
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The load-carrying capacity of the connection was found to be dependent on the compressive strength of EDP. Theoretically, the compressive strength of EDP must be determined by the fatigue strength of steel. Although there are models available to predict the fatigue strength of steel, to determine the stress level for each loading cycle in
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damage process would require a substantial amount of work, which is beyond the scope of the current project. Instead, the present work provides an approximate formula to predict the moment capacity of the connection
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based on use of a partial yielding coefficient. The partial yielding coefficient was obtained from finite element analyses and is expressed as a function of the length-to-thickness ratio of the EDP. Comparison of predicted moment capacity with the measured capacity reveals a good agreement between the two. On the basis of this study, suggestions for the connection design are as follows: (1) the strength of EBP beam-to-stub connection and the column-to-base panel connection should be designed to fail first; (2) the length-to-thickness ratio of EDP should be in the range of 8 to 16; (3) the damage and failure of the weld should be avoided; and (4) the yield moment and initial stiffness can be calculated by Eqs. (4) and (5), and the ultimate moment capacity can be calculated by Eq. (6). A further study for the engineered bamboo-steel frame with the proposed connection is need and results will 15
ACCEPTED MANUSCRIPT be reported in another paper in near future.
Acknowledgements
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The study was supported by National Intensive Research Project, 2017YFC0703500, which was provided by the Ministry of Science and Technology, China. Their support is gratefully acknowledged.
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19
ACCEPTED MANUSCRIPT Highlights
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We innovated a semi-rigid connection for mid- and high-rise bamboo-steel hybrid structures. The connection can be used as not only a moment-frame joint, but also an energy dissipation device. The performances, damage and failure mode of the connection can be well controlled as expected. Formulas for predicting the stiffness and strength of the connection are provided. Suggestions for the design of connection were proposed.
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1. 2. 3. 4. 5.