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Finite element modelling of blind bolted composite joints
Journal of Constructional Steel Research 112 (2015) 339–353
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Journal of Constructional Steel Research
Finite element modelling of blind bolted composite joints Huu-Tai Thai ⁎, Brian Uy Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia
a r t i c l e
i n f o
Article history: Received 31 January 2015 Accepted 27 May 2015 Available online 19 June 2015 Keywords: Finite element model Analytical model Composite joint Concrete-filled steel column Blind bolt
a b s t r a c t This paper aims to develop a detailed three-dimensional finite element model to study the behaviour of blind bolted endplate composite joints that connect composite beams to a concrete filled steel tubular column. All connection components such as steel beam, profiled sheeting, shear stud, endplate, blind bolt, concrete infill, concrete slab, hollow steel column and reinforcing bars were separately modelled using shell, solid and truss elements. The obtained predictions of the moment–rotation curve and failure mode were compared with experimental results and a very good agreement was established. In addition, an analytical model for predicting the moment–rotation response of composite joints up to failure was also presented based on the component method. Finally, extensive parametric studies were carried out to investigate the influences of shear studs and reinforcement ratio, blind bolt types and diameters, column sections and thickness ratios on the joint performance. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Due to their excellent seismic performance such as high strength, high ductility and large energy absorption capability, concrete-filled steel tubular (CFST) structures have been increasingly used in multistorey buildings. In these framed building structures, the bolted endplate joints have been favourably used in construction practice to connect composite beams to a CFST column because of the simplicity and economy of their fabrication and assembly. These joints may be either flush or extended endplate types depending mainly on their strength and stiffness requirements. A typical bolted endplate joint consists of the endplate welded to the end of the steel beam. This assembly is then connected to either open section columns using standard bolts or CFST and hollow section columns using the blind bolts which can be installed from the outer side of the steel tube. The behaviour of bolted endplate composite joints has been extensively investigated via experimental tests [1–11], finite element (FE) simulations [10–12] and analytical approaches [5,7,13,14]. However, these studies were limited to conventional composite joints in which the standard bolts were used to connect the steel beams to the open section column. The studies on the behaviour of the composite joints connecting the steel beams to CFST columns using the blind bolting technique were still limited. Loh et al. [15] carried out a series of tests on flush endplate composite joints with Hollo-bolt to study the effects of partial shear connection and reinforcement ratio on composite joints. They concluded that the degree of shear connection has a significant effect on the behaviour and rotational capacity of composite joints. The behaviour of composite joints with oneside Ajax bolts subjected ⁎ Corresponding author. E-mail address: [email protected] (H.-T. Thai).
http://dx.doi.org/10.1016/j.jcsr.2015.05.011 0143-974X/© 2015 Elsevier Ltd. All rights reserved.
to low-probability, high-consequence loading was examined experimentally by Mirza et al. [16] and numerically by Mirza and Uy [17]. Numerical studies on the semi-rigid behaviour of blind bolted composite joints were recently conducted by Ataei et al. [18] to develop moment–rotation models that can be used in advanced analysis and design of composite framed structures. Although experimental and numerical studies involving blind bolted composite joints have been carried out [15–18], no effort has been devoted to investigating the influences of column sections and different types of blind bolts. Therefore, the main objective of this paper is to develop a reliable FE model to further investigate the effects of column sections and different types of blind bolts on the joint behaviour. All joint components and the interaction between them were taken into account in the modelling to achieve reliable results. Since the geometry of the tightened Hollo-bolt is quite different with that of the standard bolt and oneside Ajax bolt, the Hollo-bolt was carefully modelled as close to its real shape as possible. To avoid numerical convergence difficulties caused in large deformation and complex contact problems, the explicit solver provided by the general commercial code ABAQUS was used. The bolt pretension was also included using the initial temperature approach. The validity of the developed FE model was also verified. 2. Description of composite joints Four cruciform beam-to-column joints tested by Loh et al. [15] were considered in this study. The joints, which were designed to simulate the internal regions of a typical composite frame, consist of two composite beams connected to a CFST column using eight Hollo-bolts and two flush endplates. The detailed layout and geometric dimension of the specimens were shown in Fig. 1 and Table 1. All specimens are similar with respect to the steel beam, concrete slab, blind bolts,
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Fig. 1. Configuration details of specimen CJ1 tested by Loh et al. [15].
endplates and CFST columns. They were designed to vary the degree of shear connection and reinforcement ratio. The composite joints were inverted with the concrete slab facing down and the vertical load was Table 1 Summary of specimens tested by Loh et al. [15].
applied to the CFST column. The specimens were loaded using a hydraulic actuator of 500 kN with an available stroke of 250 mm. The loading rate was set to 0.4 mm/min in the linear elastic range and subsequently increased to 1.0 mm/min in the nonlinear range towards the failure [15]. 3. Finite element model
Specimens
CJ1
CJ2
CJ3
CJ4
Reinforcing bars (ratio, %) Number of stud Spacing of stud (mm) First stud from column face (mm) Degree of shear connection (%) Headed stud size Concrete slab thickness Hollo-bolt Bondek sheeting Steel column Steel beam Flush endplate
4ϕ16 (1.29) 5 265 100
4ϕ16 (1.29) 3 480 140
4ϕ16 (1.29) 2 800 300
2ϕ16 (0.65) 3 480 140
110
66
44
133
ϕ19 × 100 mm 120 mm M20 grade 8.8 3200 × 515 × 1 mm 200 × 200 × 9 mm 250UB25.7 (248 × 124 × 8 × 5 mm) 300 × 200 × 10 mm
Due to the symmetry of geometry and loading, only half of the joint was modelled. Unlike any other blind bolts, the geometries of the Hollobolt before and after tightening are completely different as shown in Fig. 2. This difference can provide more tensile resistances in the Hollo-bolted joints compared to other blind bolted joints if the tubular column was filled with concrete [19]. Therefore, the geometry of the Hollo-bolt was carefully modelled as in Fig. 2(c) to achieve an acceptable level of accuracy. An outline of the FE model of the CJ1 specimen was shown in Fig. 3. There are two different solution strategies in ABAQUS: the implicit and the explicit solvers. The comparison between the implicit and explicit solvers has been carried out by Van der Vegte and Makino
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(a) Hollo-bolt
(b) Tightened Hollo-bolt
341
(c) Modelled Hollo-bolt
Fig. 2. Hollo-bolt.
Fig. 3. FE model of half of specimen CJ1.
[20] and Hu et al. [21], and the explicit method was recommended for simulating bolted steel connections because it avoids numerical convergence difficulties caused by large deformation and complex contact problems. The implicit method was initially used in this study to simulate the blind bolted endplate composite joints, but it failed to find a convergent solution and ceased at a very low load level. The explicit method was therefore adopted.
time. Based on the mesh convergence studies, the finite element mesh adopted for all joint components is shown in Fig. 5 with the smallest and largest element sizes being 2.5 mm and 101.6 mm, respectively. The fine mesh was created at the region around the bolts and studs to
250
3.1. Element type and mesh
Moment (kNm)
200
A suitable type of element needs to be selected for the finite element model to obtain reliable results. In this study, eight-node linear brick elements with reduced integration and hourglass control (C3D8R) are used to model all joint components except for the reinforcing bars which were modelled by truss elements (T3D2). The steel beam was primarily modelled with the C3D8R elements, but it overestimated the strength and the post-buckling behaviour of the connections as indicated in Fig. 4 in which the FEM (beam-solid) and FEM (beam-shell) curves denote the predictions obtained by using the solid C3D8R and shell S4R elements, respectively. The shell S4R element was therefore used to model the steel beam to obtain better predictions of both the strength and post-buckling behaviour. Mesh convergence studies were also conducted to obtain a reasonable mesh which provided reliable results with less computational
150
Test [15]
100
FEM (beam-solid) FEM (beam-shell)
50
0 0
10
20
30
40
50
60
Rotation (mrad) Fig. 4. Comparison of shell (S4R) and solid (C3D8R) elements in beam modelling.
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(a) Concrete slab (C3D8R)
(b) Hollo-bolt and stud (C3D8R)
(c) Reinforcing bar (T3D2)
(d) Endplate (C3D8R)
(e) Profiled sheeting (S4R)
(f) Steel tube (C3D8R)
(g) Steel beam (S4R)
(h) Concrete infill (C3D8R)
Fig. 5. FE mesh of individual components.
achieve reliable results. The finite element mesh of each specimen contains approximately 12,500 nodes. 3.2. Material models 3.2.1. Steels A multi-linear elastic–plastic model was used to simulate the inelastic behaviour of the structural steel, profiled sheeting, reinforcing bar, blind bolt and headed shear studs. Fig. 6 shows the stress–strain curves of steel materials which were approximated from the actual stress– strain curves obtained from the tensile tests carried out by Loh et al. [15]. To simulate the failure of the shear studs, both ductile damage and shear damage criterion were used. Once the damage criterion is
reached, the stiffness of the material degrades following the softening law. The element will be removed from the mesh when the stiffness at all integration points reaches the maximum degradation. In this study, the damage parameters of headed shear studs were taken from Nguyen and Kim [22]. 3.2.2. Concrete The 28 day compressive strength and tensile strength of concrete were 17.5 MPa and 1.7 MPa, respectively [15]. The concrete damaged plasticity model was used for the concrete slab and concrete infill. The compressive behaviour was modelled by the uniaxial stress–strain model given by Tao et al. [23]. The tensile behaviour is assumed to increase linearly up to concrete cracking at the tensile strength, and
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Flange, box and endplate Web
1200
Stress (MPa)
There are several tension stiffening models proposed by Kim and Nguyen [24], and the model based on the cubic Bezier curve is the best among them. Therefore, it was adopted in this study. Fig. 7(a) shows the tensile stress–displacement relationship of concrete based on the cubic Bezier curve with the cracking opening of 2 mm calibrated from the present model. Accordingly, the tensile damage caused by tensile failure (i.e. concrete cracking) is assumed as in Fig. 7(b). The compressive damage was not included in the analysis since the failure mode observed in the experiment was due to the concrete cracking around the connection region rather than the concrete crushing.
Stud Sheeting Rebar
1000 800
343
Hollo-bolt
600 400 200
3.3. Contact interaction and constraint conditions 0 0
50
100
150
200
Strain (10-3) Fig. 6. Stress–strain curves for steel materials.
decrease to zero with the tension stiffening effect. The tension stiffening can be expressed by means of a post-failure stress–strain curve or a fracture energy cracking criterion. As stated in the ABAQUS manual, the post-failure stress–strain approach is sensitive to the mesh for small reinforcement percentages. Therefore, the fracture energy cracking criterion was used in this study. In this approach, the brittle behaviour of concrete is represented by a stress–displacement curve rather than a stress–strain relationship.
1.8
Tensile stress (MPa)
1.5 1.2 0.9 0.6 0.3 0 0
0.5
1
1.5
2
3.4. Boundary and loading conditions
Cracking openning (mm)
(a) Post-failure model
Tensile damage parameter
1
0.8
0.6
0.4
0.2
0 0
0.5
1
The general contact algorithm available in ABAQUS/Explicit was used to enforce the contact between the contacting surfaces in all joint components. This contact algorithm which is based on the finitesliding formulation allows for arbitrary translations and rotations between interacting surfaces. To improve the time analysis, the contact surfaces in each contact pair should have almost identical meshes [25]. It is worth noting that the careful choice of master or slave surface in each contact pair is not required for the ABAQUS/Explicit model [26]. In this analysis, eight contact pairs were defined in the model: (1) steel column and concrete infill, (2) steel column and concrete slab, (3) steel column and endplate, (4) steel column and Holl-bolt, (5) steel beam and profiled sheeting, (6) endplate and concrete slab, (7) Hollo-bolt and endplate and (8) Hollo-bolt and concrete infill. Fig. 8 illustrates the contacting surfaces between the Hollo-bolts, endplates and CFST column. The embedded constraints were applied to the reinforcing bars, headed studs and concrete slab. In these constraints, the translational degree of freedom (DOF) of the nodes on the reinforcing bar and headed stud elements was constrained to the interpolated values of the corresponding DOF of the concrete slab elements. The slip and debonding of the reinforcing bars and headed studs were therefore ignored. Since the headed studs and the top flange were welded together, they were tied to each other using the Tie constraint. The Tie constraint was also used to model the interaction between the profiled sheeting and concrete slab. Although the steel beam and endplate were also welded together, the Tie constraint cannot be applied to them since they were modelled by different types of element (i.e. shell for the beam and solid for the endplate). Therefore, the shell-to-solid coupling constraint was used instead of the tie constraint.
1.5
2
Cracking openning (mm)
The simply supported boundary condition (BC) was applied to the upper face of the concrete slab. Due to the symmetry of the specimen, the symmetric boundary conditions were also applied to the surfaces at the symmetric planes of the specimen as shown in Fig. 3. The axial loading was applied vertically through the reference point located at the centre of the end section of the CFST column via the displacement control method. The applied load was then calculated as the total reaction acting on the reference point. Since the initial stable time increment in the explicit analysis was 6 × 10−7s, it would lead to an unacceptably large number of increments if the experimental loading rate was used. To reduce the computational time, the simulation was sped up by increasing the loading rate accompanying with the use of the smooth step amplitude as shown in Fig. 9. Different loading rates were assessed, and the most appropriate one was determined to be 375 mm/s. 3.5. Pretension in the bolt
(b) Tensile damage model Fig. 7. Tension stiffening and tensile damage model based on the cubic Bezier curve.
Since the bolt load tool is currently not available in the explicit dynamics solver, the initial temperature was used to create the bolt
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Fig. 8. Contacting surfaces between the Hollo-bolt, endplate and CFST column.
pretension. Similar approaches were taken by Tanlak et al. [25] and Egan et al. [26]. In this approach, a coefficient of thermal contraction was given to the bolt material. A reference temperature was then assigned to the bolt shank in a step created before the load step by using the predefined field option. A temperature increase induces the shrinkage of the bolt shank in the through-thickness direction and consequently induces the desired bolt prestress.
Dispacement control (mm)
75
60
45
30
4. Analytical model The analytical model developed by Aribert and Dinga [5] for predicting the moment–rotation curve of composite joints up to failure was extended herein to account for the effect of concrete filled into the hollow steel column. The basic principle of this model is based on the component method which has been introduced in the Eurocode 4 [27] for composite joints. The present model shown in Fig. 10 consists of four important components modelled by the translational springs Kr (the reinforcement), Ksc (the shear connection), Kp (the bending of the endplate region located between the upper bolt row and the tensile steel flange) and Kb (the bolt row). The present model is based on the assumptions that only the top bolt row is in tension and the joint is rotated about the bottom flange. It is noted that the column flange and web in compression components are omitted in the present model because of the presence of concrete infill. From Fig. 10, the compatibility conditions of the joint are Δr þ s−Δp
15
zr ¼ bzr H
Δb ¼ bzb
0 0
0.05
0.1
0.15
Time (s) Fig. 9. Smooth step amplitude of displacement control.
0.2
ð1Þ ð2Þ
where Δr, s, Δp and Δb are respectively the deformations of the reinforcement, shear connection, endplate in bending and bolt row. The equilibrium conditions of the joint lead to the following equations F r ¼ F sc
Fig. 10. Component model for the composite joint used in this study.
ð3Þ
H.-T. Thai, B. Uy / Journal of Constructional Steel Research 112 (2015) 339–353
F p ¼ K p Δp
345
ð9Þ
where F and K are the forces and stiffnesses of the related components, respectively. Substituting Eqs. (6) and (7) into Eqs. (3), and Eqs. (8) and (9) into Eq. (4), the following equations are obtained s¼
Kr Δr K sc
Δp ¼
ð10Þ
K b Δb zb : Kp H
ð11Þ
The displacements of the reinforcement, shear connection and endplate in bending are obtained by substituting Eqs. (10) and (11) into Eq. (1) Δr ¼ C e bzr s¼
ð12Þ
Kr C e bzr K sc
Δp ¼
1þ
ð13Þ
Kr C e −1 bH K sc
ð14Þ
where K b zb 2 Kp H Kr 1þ K sc
1þ Ce ¼
ð15Þ
Finally, the rotation of the joint is obtained as ϕ¼bþ
Δp ¼ H
1þ
Kr C e b: K sc
ð16Þ
Once the force–deformation relationships of the individual components in Eqs. (6)–(9) are known, the joint rotation ϕ for each incremental increase of the externally applied moment ΔM can be determined from the iterative procedure illustrated in Fig. 11. In this procedure, the increase of the applied moment ΔM will stop if the failure of the joint is detected. The failure conditions of the joint used in this study are [5]: Δbj N Δbu and Δrj N Δru ¼ lr εru and s j N su
where Δbu, Δru and su are the deformation capacities of the bolt row, reinforcement and shear connector, respectively. In this study, Δbu is taken as 6 mm [5] whilst su is taken as 10 mm [27]. The ultimate deformation of the reinforcement Δru is computed from the ultimate strain εru which is usually taken as 0.08 [5]. The force–deformation relationships of the individual components are successively discussed hereafter.
Fig. 11. Flow chart of the present model.
Fp ¼
F b zb H
M ¼ F b zb þ F r zr :
ð17Þ
ð4Þ
ð5Þ
The constitutive relationships of four components are expressed as follows: F r ¼ K r Δr
ð6Þ
F sc ¼ K sc s
ð7Þ
F b ¼ K b Δb
ð8Þ
4.1. The reinforcement To account for the tension stiffening effect, a simplified stress–strain relationship for the embedded reinforcement given by CEB-FIP Model Code [28] as shown in Fig. 12(a) was used. The stiffness Kr of the reinforcement for four different phases as shown in Fig. 12(b) is obtained as follows: (a) Uncracked E c Ac f kc ð1 þ ρnr Þ for F r b F r1 ¼ σ sr1 Ar ¼ ct ð1 þ ρnr ÞAr ð18Þ lr ρ ¼ F r1
Kr ¼
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Fig. 12. Reinforcement curves.
(b) Crack information phase
(d) Post-yielding
Er Ar 3ρnr þ 3 for F r1 ≤ F r b F rn ¼ σ srn Ar ¼ 1:3 F r1 ð19Þ lr 3ρ nr þ 13−10 βr ¼ F rn
Kr ¼
(c) Stabilized cracking Kr ¼
E r Ar for F rn ≤ F r b F ry ¼ f ry Ar lr
Kr ¼
E r Ar 1 for F ry ≤ F r b F ru ¼ f ru Ar lr δ 1− F r1 =F ry
with
ð21Þ
nr ¼ Er =Ec ; ρ ¼ Ar =Ac ; kc ¼ 1=ð1 þ d=2z0 Þ ð22Þ
ð20Þ where d is the thickness of the concrete slab and z0 is the vertical distance between the centroids of the uncracked, unreinforced concrete slab and the uncracked, unreinforced composite section; βr is taken as 0.4 for short term loading and δ is taken as 0.8 for high ductility bars; fct and Ec are respectively the elastic modulus and the tensile strength of concrete; Ac and Ar denote the areas of the concrete slab and the reinforcement, respectively; Er, fry and fru are respectively Young's modulus, yield stress and ultimate stress of the reinforcement. The effective length of the reinforcement lr is determined based on the formulae proposed by Anderson et al. [29] as follows:
Fig. 13. Force–deformation of shear connection [5].
lr ¼ 2Lt if ρ b 0:8%
ð23aÞ
lr ¼ hc =2 þ Lt if ρ ≥ 0:8% and ac b Lt
ð23bÞ
lr ¼ hc =2 þ ac if ρ ≥ 0:8% and ac ≥ Lt
ð23cÞ
250
250
200
200
Moment (kNm)
Moment (kNm)
H.-T. Thai, B. Uy / Journal of Constructional Steel Research 112 (2015) 339–353
150
100
Test [15]
150
100
Test [15] FEM [18] FEM (Present) Analytical model
FEM [18] 50
50
FEM (Present) Analytical model
0
0 0
10
20
30
40
50
0
60
10
20
30
(a) CJ1
50
60
50
60
(b) CJ2 250
200
200
Moment (kNm)
250
150
100
Test [15] FEM [18] FEM (Present) Analytical model
50
40
Rotation (mrad)
Rotation (mrad)
Moment (kNm)
347
150
100
Test [15] FEM [18] FEM (Present) Analytical model
50
0
0 0
10
20
30
40
50
60
0
10
20
30
40
Rotation (mrad)
Rotation (mrad)
(d) CJ4
(c) CJ3 Fig. 14. Comparison of moment–rotation curves of four composite specimens.
where ac is the distance from the face of the column to the first shear connector along the beam, hc is the depth of the column section in the direction parallel to the longitudinal reinforcement, and Lt is the ‘transmission’ length given by Hanswille [30] as follows kc f ct ϕr 4τρ
Lt ¼
ð24Þ
where ϕr is the diameter of the reinforcement and τ is the average bond stress along the transmission length which can be taken as 1.8fct [28].
where N is the number of shear connectors distributed over the length ls of the beam in hogging bending which may be assumed to be 15% of the span, ksc is the stiffness of one shear connector determined by test or taken as 100 kN/mm for a 19 mm diameter headed stud if the test result is not available, EI denotes the bending stiffness of the steel beam, and dr is the distance between the centroids of the steel beam and the reinforcement. Fig. 13 shows the relationship between the interaction force Fsc and the slip s at the steel–concrete interface. The slip and force at the initial yielding are 0:7P R ksc
4.2. The shear connection
sel ¼
Based on a theoretical approach established by Aribert [31,32], the elastic stiffness of the shear connection Ksc is given by the following expressions
F scel ¼ K sc sel
K sc ¼
Nksc β−1 zr β− 1 þ α dr
ð25Þ
α¼
spl ¼ ψsel EI 2
E r Ar d r
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð1 þ α ÞNksc ls dr and β ¼ EI
ð26Þ
ð28Þ
where PR is plastic resistance of one shear connector which is equal to 106 kN for a 19 mm diameter headed stud based on the test conducted by Loh et al. [15]. The force and slip at the ultimate state are [5] F scu ¼ NP R
with
ð27Þ
F scu F scel
ð29Þ ð30Þ
where ψ may be taken as 2 or 3 depending on whether the shear connection is full or partial, respectively.
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(a) Crack of concrete slab
(b) Plastic strain and local buckling of the flanges and web of steel beam Fig. 15. Comparison of the failure modes of specimen CJ1.
respectively, and lp is the distance between the tension flange and the upper bolt row as indicated in Fig. 10.
4.3. Bending of the upper part of the endplate The stiffness Kp of the endplate which is assumed to be constant was derived by Aribert and Dinga [5] as follows
Kp ¼
3Dp 3
lp
¼
3Ep bp t 3p 3 12 1−ν2 lp
ð31Þ
where Ep and v are respectively Young's modulus and Poisson's ratio of the endplate, bp and tp denote the width and thickness of the endplate,
The components contributed to the stiffness of a bolt row include the column web in tension (k3), column flange in bending (k4), endplate in bending (k5) and bolt in tension (k10). For the joints with CFST columns, the test results reported by Wang et al. [33] confirmed the assumption of an infinite stiffness for the column web in tension (k3 = ∞). Therefore, the stiffness of a bolt row is calculated as 1 1 1 1 ¼ þ þ K b k4 k5 k10
250
ð32Þ
and the deformation of each component is related to the total deformation Δb and stiffness Kb of the bolt row by
200
Moment (kNm)
4.4. Bolt row
150
100
δ4 ¼
K b Δb k4
ð33Þ
δ5 ¼
K b Δb k5
ð34Þ
110% shear connection (5 studs) 66% shear connection (3 studs) 44% shear connection (2 studs)
50
δ10 ¼
0 0
10
20
30
40
50
60
K b Δb : k10
ð35Þ
Rotation (mrad) Fig. 16. Effect of degree of shear connection on behaviour of composite joints.
The deformation of each component in a bolt row obtained in Eqs. (33)–(35) is used to trace the current stiffness of each component
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(a) Five studs (110%) (3) Three studs (66%)
349
(c) Two studs (44%)
Fig. 17. Deformation and von Mises stress of shear studs at ultimate loads.
based on its force–deformation relations, and consequently, the equivalent stiffness of a bolt row Kb can be updated using Eq. (32). The detailed formulae of each component in a bolt row can be found in Aribert et al. [34]. It should be noted that the column flange in bending component (k4) given in [34] is applied for the open section column only. For the joint with hollow section or CFST columns as in this study, the analytical model developed by Neves and Gomes [35] and Gomes et al. [36] will be used to predict the force–deformation relationship of the column flange in bending component (k4). 5. Verifications of the present models The FE and analytical models developed in this study were verified against the experimental results reported by Loh et al. [15]. In addition, the FE solutions generated by Ataei et al. [18] were also used in the
verification to illustrate the accuracy of the developed FE model. The obtained moment–rotation curves of four specimens were compared with the experimental results [15] and those predicted by FE method [18] in Fig. 14. It can be seen that the present FE model predicts very well the initial stiffness, ultimate moment capacity as well as the postbuckling behaviour of all connections. As shown in Fig. 15, the present model also reasonably predicts the failure mode of the joint due to cracking of concrete slab around the connection region and the local buckling of the bottom flange and the web of the steel beam. In general, the analytical model predicts rather well the initial stiffness, moment resistance and of rotation capacity composite joints except for the case of the specimen CJ4 in which the present analytical model underestimates the ultimate moment capacity. 6. Parametric studies 6.1. Effect of shear studs and reinforcement ratio
250
Moment (kNm)
200
150
N28 (3.98 %)
100
N24 (2.93 %) N20 (2.03 %) N16 (1.30 %)
50
N12 (0.73 %)
0 0
10
20
30
40
50
Rotation (mrad) Fig. 18. Effect of reinforcement ratio on behaviour of composite joint CJ1.
60
The effect of the degree of shear connection on the moment–rotation responses of composite joints was shown in Fig. 16. It can be seen that the ultimate moment capacity of composite joints slightly increases with the increase of the degree of shear connection because of the reduction in the slip between steel beam and concrete slab as indicated in Fig. 17. Fig. 18 shows the effect of the reinforcement ratio on the moment– rotation responses of the joint CJ1. Five different diameters of reinforcing bars of N12, N16, N20, N24 and N28 corresponding to the reinforcement ratios of 0.73, 1.30, 2.03, 2.93 and 3.98% were considered. It can be observed that the ultimate moment capacity of composite joints increases by increasing the reinforcement ratio, and this increase is not significant when the reinforcement ratio is greater than 3%. The failure mode of composite joints is also influenced by the reinforcement ratio as shown in Fig. 19. The effect of reinforcement ratio on the cracking of the concrete slab was also illustrated in Fig. 20. As expected, the greater the reinforcement ratio used, the lesser the cracking observed in the concrete slab.
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(a) N12
(b) N16, N20, N24, N28
Fig. 19. Effect of reinforcement ratio on the failure modes of composite joint CJ1.
(a) N12
(b) N16
(c) N20 Fig. 20. Effect of reinforcement ratio on the damage of concrete slab at ultimate loads.
60
60
50
50
Moment (kNm)
Moment (kNm)
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40
30 Ajax bolt Hollo-bolt
20
351
40
30 M16 20
M20
10
10 0 0
0 0
20
40
60
80
100
20
40
60
80
100
120
40
50
60
Rotation (mrad)
120
Rotation (mrad)
(a) Steel joint
(a) Steel joint
160
160 140
140 120
Moment (kNm)
Moment (kNm)
120 100 Ajax bolt
80
Hollo-bolt
100 M16
80
M20 60
60 40
40 20
20 0 0
0 0
10
20
30
40
50
10
20
30
Rotation (mrad)
60
(b) Composite joint CJ4
Rotation (mrad)
(b) Composite joint CJ4 Fig. 22. Effect of blind bolt diameter on moment–rotation responses. Fig. 21. Effect of different types of blind bolts on moment–rotation responses.
7. Discussion 6.2. Effect of different types of blind bolts and bolt diameters The effects of the blind bolt types (e.g. Hollo-bolt versus oneside Ajax bolt) and the bolt diameters (e.g. M16 versus M20) on the moment– rotation responses of steel and composite joints were shown in Figs. 21 and 22, respectively. It can be seen that these effects can be negligible in composite joints and insignificant in the case of the steel joint. This might be due to the fact that the composite joints used in this study were designed to fail by cracking of the concrete slab and buckling of the steel beam rather than failure of the bolt.
6.3. Effect of width-to-thickness ratio and column sections Figs. 23 and 24 show the effects of the width-to-thickness ratios and column sections on the moment–rotation behaviour of bare steel and composite joints. Two values of thickness ratio of 22 and 40 corresponding to the column thickness of 9 mm and 5 mm were examined. The circular section ϕ219.1 × 9 mm was chosen since it has approximate area of the square section 200 × 9 mm. Again, the composite joint is not sensitive to the change of the thickness ratio and section type of the column since its behaviour is governed by the concrete slab and reinforcing bars. However, for the bare steel joints, the circular section provides greater strength than the square section as confirmed by experimental observation reported by Wang et al. [33].
The FE model developed by Ataei et al. [18] cannot fully captured the flange local buckling which is the dominant failure mode in the specimens CJ1, CJ2 and CJ3 [15]. This was clearly indicated in Fig. 14(a)–(c) in which the descending branch of the moment–rotation curves predicted by Ataei et al. [18] does not exist. This is due to the fact that the solid C3D8R elements used by Ataei et al. [18] cannot accurately predict the local bucking of the beam when compared with the shell S4R elements used in this study. It is also observed from Fig. 14 that the FE model developed by Ataei et al. [18] cannot predict well the initial stiffness as well as the stiffness degradation of all specimens when compared with the present one. This might be due to the inappropriate modelling of the Hollo-bolt as well as its contact interactions with the endplates and the CFST column. In the FE model developed by Ataei et al. [18], the Hollo-bolt was modelled as a standard bolt and the interaction between the bolt, endplates and CFST column was modelled by TIE constraints instead of CONTACT interaction as in the present model. Since the present analytical model is based on the component method, the accuracy of its predictions is strongly dependent on the force–deformation curve of each component of the composite joint which is assumed as multi-linear curves in this study. Therefore, it is incapable of accurately capturing the stiffness degradation of composite joints when compared with the FE model as shown in Fig. 14. However, the present analytical model is very useful for the design purpose as it predicts rather well the initial stiffness, moment resistance and rotation
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60
70
50
60 50
40
Moment (kNm)
Moment (kNm)
352
30 20
b/t=22
40 30
Square column Circular column
20
b/t=40
10 10 0 0
20
40
60
80
100
0
120
0
Rotation (mrad)
20
40
80
100
120
50
60
(a) Steel joint 250
200
200
Moment (kNm)
Moment (kNm)
(a) Steel joint 250
150 b/t=22
100
60
Rotation (mrad)
b/t=40
150
100
Square column Circular column
50
50
0 0
10
20
30
40
50
60
0 0
10
20
30
40
Rotation (mrad)
Rotation (mrad)
(b) Composite joint CJ1
(b) Composite joint CJ1 Fig. 24. Effect of column section on moment–rotation responses.
Fig. 23. Effect of column thickness ratio on moment–rotation responses.
capacity which are the key structural properties of a joint in framed structures.
been studied. Further research therefore needs to be carried out to investigate these effects on the seismic performance of blind bolted endplate composite joints.
8. Conclusions
Acknowledgements
A reliable FE model has been developed for blind bolted endplate composite joints that connect the composite beams to a CFST column. The validity of the present model was verified by comparing the obtained predictions with experimental results and those predicted by the existing FE model. The verification study demonstrates that the present FE model is capable of accurately predicting the moment–rotation response of composite joints including the initial stiffness, the ultimate moment capacity and the post-buckling behaviour. In addition, the present model also reasonably predicts the failure modes of composite joints. The analytical model proposed in this study based on the component method predicts rather well the initial stiffness, moment resistance and rotation capacity which are the key structural properties of a joint in framed structures. Unlike the bare steel joints, the bending behaviour of composite joints is dominated by the concrete slab and reinforcing bars. Therefore, the behaviour of composite joints is not sensitive to the blind bolt type and diameter as well as the section type and thickness ratio of the column as clearly shown in the numerical results. The FE model developed in this paper is limited to blind bolted endplate composite joints subjected to static loading. The influences of different types of blind bolts and column sections on cyclic behaviour of these joints have not
This work was supported by the Australian Research Council under its Discovery Early Career Researcher Award scheme (Project No: DECRA140100747). This financial support is gratefully acknowledged. References [1] Y. Xiao, B.S. Choo, D.A. Nethercot, Composite connections in steel and concrete. I. Experimental behaviour of composite beam–column connections, J. Constr. Steel Res. 31 (1) (1994) 3–30. [2] D. Anderson, A.A. Najafi, Performance of composite connections: major axis end plate joints, J. Constr. Steel Res. 31 (1) (1994) 31–57. [3] T.Q. Li, D.A. Nethercot, B.S. Choo, Behaviour of flush end-plate composite connections with unbalanced moment and variable shear/moment ratios—I. Experimental behaviour, J. Constr. Steel Res. 38 (2) (1996) 125–164. [4] J.Y.R. Liew, T.H. Teo, N.E. Shanmugam, C.H. Yu, Testing of steel–concrete composite connections and appraisal of results, J. Constr. Steel Res. 56 (2) (2000) 117–150. [5] J.M. Aribert, O.N. Dinga, Modeling and experimental investigation of bolted flush endplate composite beam-to-column joints, Composite Construction in Steel and Concrete IV2000. 711–724. [6] L.S. da Silva, R.D. Simoes, P.J.S. Cruz, Experimental behaviour of end-plate beam-tocolumn composite joints under monotonical loading, Eng. Struct. 23 (11) (2001) 1383–1409. [7] N.D. Brown, D. Anderson, Structural properties of composite major axis end plate connections, J. Constr. Steel Res. 57 (3) (2001) 327–349. [8] E.A. Sumner, T.M. Murray, Behavior of extended end-plate moment connections subject to cyclic loading, J. Struct. Eng. 128 (4) (2002) 501–508.
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[22] H.T. Nguyen, S.E. Kim, Finite element modeling of push-out tests for large stud shear connectors, J. Constr. Steel Res. 65 (10–11) (2009) 1909–1920. [23] Z. Tao, Z.-B. Wang, Q. Yu, Finite element modelling of concrete-filled steel stub columns under axial compression, J. Constr. Steel Res. 89 (2013) 121–131. [24] S.E. Kim, H.T. Nguyen, Finite element modeling and analysis of a hybrid steel–PSC beam connection, Eng. Struct. 32 (9) (2010) 2557–2569. [25] N. Tanlak, F. Sonmez, E. Talay, Detailed and simplified models of bolted joints under impact loading, J. Strain Anal. Eng. Des. 46 (3) (2011) 213–225. [26] B. Egan, C.T. McCarthy, M.A. McCarthy, P.J. Gray, R.M. Frizzell, Modelling a single-bolt countersunk composite joint using implicit and explicit finite element analysis, Comput. Mater. Sci. 64 (2012) 203–208. [27] ENV, Eurocode 4: design of composite steel and concrete structures—part 1–1: general rules and rules for buildings, 1994. [28] CEB-FIP Model Code, Design Guide 1990: Thomas Telford, 1991. [29] D. Anderson, J.M. Aribert, H. Bode, H.J. Kronenburger, Design rotation capacity of composite joints, Struct. Eng. 78 (6) (2000) 25–29. [30] G. Hanswille, Cracking of concrete mechanical models of the design rules in Eurocode 4, Composite Construction in Steel and Concrete, ASCE, 1997. 421–433. [31] J.M. Aribert, Influence of slip of the shear connection on composite joint behavior, 3rd International Workshop on Connections in Steel Structures, Pergamon, Trento, 1995. 11–22. [32] J.M. Aribert, Theoretical solutions relating to partial shear connection of steel– concrete composite beams and joints, Proceedings of the International Conference on, Steel and Composite Structures, 1999 (7.1–7.16). [33] J.F. Wang, L.H. Han, B. Uy, Behaviour of flush end plate joints to concrete-filled steel tubular columns, J. Constr. Steel Res. 65 (4) (2009) 925–939. [34] J.M. Aribert, A. Lachal, O.N. Dinga, Modélisation du compteur d'assemblages metalliques semi-rigides de type poutre-poteau boulonnes par platine dextremite, Constr. Met. 1 (1999) 25–46. [35] L.C. Neves, F. Gomes, Semi-rigid behaviour of beam-to-column minor-axis joints, IABSE Colloquium on Semi-Rigid Structural Connections1996. 207–218. [36] F. Gomes, J.P. Jaspart, R. Maquoi, Moment capacity of beam-to-column minor-axis joints, IABSE Colloquium on Semi-Rigid Structural Connections1996. 319–326.
Contents lists available at ScienceDirect
Journal of Constructional Steel Research
Finite element modelling of blind bolted composite joints Huu-Tai Thai ⁎, Brian Uy Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia
a r t i c l e
i n f o
Article history: Received 31 January 2015 Accepted 27 May 2015 Available online 19 June 2015 Keywords: Finite element model Analytical model Composite joint Concrete-filled steel column Blind bolt
a b s t r a c t This paper aims to develop a detailed three-dimensional finite element model to study the behaviour of blind bolted endplate composite joints that connect composite beams to a concrete filled steel tubular column. All connection components such as steel beam, profiled sheeting, shear stud, endplate, blind bolt, concrete infill, concrete slab, hollow steel column and reinforcing bars were separately modelled using shell, solid and truss elements. The obtained predictions of the moment–rotation curve and failure mode were compared with experimental results and a very good agreement was established. In addition, an analytical model for predicting the moment–rotation response of composite joints up to failure was also presented based on the component method. Finally, extensive parametric studies were carried out to investigate the influences of shear studs and reinforcement ratio, blind bolt types and diameters, column sections and thickness ratios on the joint performance. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Due to their excellent seismic performance such as high strength, high ductility and large energy absorption capability, concrete-filled steel tubular (CFST) structures have been increasingly used in multistorey buildings. In these framed building structures, the bolted endplate joints have been favourably used in construction practice to connect composite beams to a CFST column because of the simplicity and economy of their fabrication and assembly. These joints may be either flush or extended endplate types depending mainly on their strength and stiffness requirements. A typical bolted endplate joint consists of the endplate welded to the end of the steel beam. This assembly is then connected to either open section columns using standard bolts or CFST and hollow section columns using the blind bolts which can be installed from the outer side of the steel tube. The behaviour of bolted endplate composite joints has been extensively investigated via experimental tests [1–11], finite element (FE) simulations [10–12] and analytical approaches [5,7,13,14]. However, these studies were limited to conventional composite joints in which the standard bolts were used to connect the steel beams to the open section column. The studies on the behaviour of the composite joints connecting the steel beams to CFST columns using the blind bolting technique were still limited. Loh et al. [15] carried out a series of tests on flush endplate composite joints with Hollo-bolt to study the effects of partial shear connection and reinforcement ratio on composite joints. They concluded that the degree of shear connection has a significant effect on the behaviour and rotational capacity of composite joints. The behaviour of composite joints with oneside Ajax bolts subjected ⁎ Corresponding author. E-mail address: [email protected] (H.-T. Thai).
http://dx.doi.org/10.1016/j.jcsr.2015.05.011 0143-974X/© 2015 Elsevier Ltd. All rights reserved.
to low-probability, high-consequence loading was examined experimentally by Mirza et al. [16] and numerically by Mirza and Uy [17]. Numerical studies on the semi-rigid behaviour of blind bolted composite joints were recently conducted by Ataei et al. [18] to develop moment–rotation models that can be used in advanced analysis and design of composite framed structures. Although experimental and numerical studies involving blind bolted composite joints have been carried out [15–18], no effort has been devoted to investigating the influences of column sections and different types of blind bolts. Therefore, the main objective of this paper is to develop a reliable FE model to further investigate the effects of column sections and different types of blind bolts on the joint behaviour. All joint components and the interaction between them were taken into account in the modelling to achieve reliable results. Since the geometry of the tightened Hollo-bolt is quite different with that of the standard bolt and oneside Ajax bolt, the Hollo-bolt was carefully modelled as close to its real shape as possible. To avoid numerical convergence difficulties caused in large deformation and complex contact problems, the explicit solver provided by the general commercial code ABAQUS was used. The bolt pretension was also included using the initial temperature approach. The validity of the developed FE model was also verified. 2. Description of composite joints Four cruciform beam-to-column joints tested by Loh et al. [15] were considered in this study. The joints, which were designed to simulate the internal regions of a typical composite frame, consist of two composite beams connected to a CFST column using eight Hollo-bolts and two flush endplates. The detailed layout and geometric dimension of the specimens were shown in Fig. 1 and Table 1. All specimens are similar with respect to the steel beam, concrete slab, blind bolts,
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Fig. 1. Configuration details of specimen CJ1 tested by Loh et al. [15].
endplates and CFST columns. They were designed to vary the degree of shear connection and reinforcement ratio. The composite joints were inverted with the concrete slab facing down and the vertical load was Table 1 Summary of specimens tested by Loh et al. [15].
applied to the CFST column. The specimens were loaded using a hydraulic actuator of 500 kN with an available stroke of 250 mm. The loading rate was set to 0.4 mm/min in the linear elastic range and subsequently increased to 1.0 mm/min in the nonlinear range towards the failure [15]. 3. Finite element model
Specimens
CJ1
CJ2
CJ3
CJ4
Reinforcing bars (ratio, %) Number of stud Spacing of stud (mm) First stud from column face (mm) Degree of shear connection (%) Headed stud size Concrete slab thickness Hollo-bolt Bondek sheeting Steel column Steel beam Flush endplate
4ϕ16 (1.29) 5 265 100
4ϕ16 (1.29) 3 480 140
4ϕ16 (1.29) 2 800 300
2ϕ16 (0.65) 3 480 140
110
66
44
133
ϕ19 × 100 mm 120 mm M20 grade 8.8 3200 × 515 × 1 mm 200 × 200 × 9 mm 250UB25.7 (248 × 124 × 8 × 5 mm) 300 × 200 × 10 mm
Due to the symmetry of geometry and loading, only half of the joint was modelled. Unlike any other blind bolts, the geometries of the Hollobolt before and after tightening are completely different as shown in Fig. 2. This difference can provide more tensile resistances in the Hollo-bolted joints compared to other blind bolted joints if the tubular column was filled with concrete [19]. Therefore, the geometry of the Hollo-bolt was carefully modelled as in Fig. 2(c) to achieve an acceptable level of accuracy. An outline of the FE model of the CJ1 specimen was shown in Fig. 3. There are two different solution strategies in ABAQUS: the implicit and the explicit solvers. The comparison between the implicit and explicit solvers has been carried out by Van der Vegte and Makino
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(a) Hollo-bolt
(b) Tightened Hollo-bolt
341
(c) Modelled Hollo-bolt
Fig. 2. Hollo-bolt.
Fig. 3. FE model of half of specimen CJ1.
[20] and Hu et al. [21], and the explicit method was recommended for simulating bolted steel connections because it avoids numerical convergence difficulties caused by large deformation and complex contact problems. The implicit method was initially used in this study to simulate the blind bolted endplate composite joints, but it failed to find a convergent solution and ceased at a very low load level. The explicit method was therefore adopted.
time. Based on the mesh convergence studies, the finite element mesh adopted for all joint components is shown in Fig. 5 with the smallest and largest element sizes being 2.5 mm and 101.6 mm, respectively. The fine mesh was created at the region around the bolts and studs to
250
3.1. Element type and mesh
Moment (kNm)
200
A suitable type of element needs to be selected for the finite element model to obtain reliable results. In this study, eight-node linear brick elements with reduced integration and hourglass control (C3D8R) are used to model all joint components except for the reinforcing bars which were modelled by truss elements (T3D2). The steel beam was primarily modelled with the C3D8R elements, but it overestimated the strength and the post-buckling behaviour of the connections as indicated in Fig. 4 in which the FEM (beam-solid) and FEM (beam-shell) curves denote the predictions obtained by using the solid C3D8R and shell S4R elements, respectively. The shell S4R element was therefore used to model the steel beam to obtain better predictions of both the strength and post-buckling behaviour. Mesh convergence studies were also conducted to obtain a reasonable mesh which provided reliable results with less computational
150
Test [15]
100
FEM (beam-solid) FEM (beam-shell)
50
0 0
10
20
30
40
50
60
Rotation (mrad) Fig. 4. Comparison of shell (S4R) and solid (C3D8R) elements in beam modelling.
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(a) Concrete slab (C3D8R)
(b) Hollo-bolt and stud (C3D8R)
(c) Reinforcing bar (T3D2)
(d) Endplate (C3D8R)
(e) Profiled sheeting (S4R)
(f) Steel tube (C3D8R)
(g) Steel beam (S4R)
(h) Concrete infill (C3D8R)
Fig. 5. FE mesh of individual components.
achieve reliable results. The finite element mesh of each specimen contains approximately 12,500 nodes. 3.2. Material models 3.2.1. Steels A multi-linear elastic–plastic model was used to simulate the inelastic behaviour of the structural steel, profiled sheeting, reinforcing bar, blind bolt and headed shear studs. Fig. 6 shows the stress–strain curves of steel materials which were approximated from the actual stress– strain curves obtained from the tensile tests carried out by Loh et al. [15]. To simulate the failure of the shear studs, both ductile damage and shear damage criterion were used. Once the damage criterion is
reached, the stiffness of the material degrades following the softening law. The element will be removed from the mesh when the stiffness at all integration points reaches the maximum degradation. In this study, the damage parameters of headed shear studs were taken from Nguyen and Kim [22]. 3.2.2. Concrete The 28 day compressive strength and tensile strength of concrete were 17.5 MPa and 1.7 MPa, respectively [15]. The concrete damaged plasticity model was used for the concrete slab and concrete infill. The compressive behaviour was modelled by the uniaxial stress–strain model given by Tao et al. [23]. The tensile behaviour is assumed to increase linearly up to concrete cracking at the tensile strength, and
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Flange, box and endplate Web
1200
Stress (MPa)
There are several tension stiffening models proposed by Kim and Nguyen [24], and the model based on the cubic Bezier curve is the best among them. Therefore, it was adopted in this study. Fig. 7(a) shows the tensile stress–displacement relationship of concrete based on the cubic Bezier curve with the cracking opening of 2 mm calibrated from the present model. Accordingly, the tensile damage caused by tensile failure (i.e. concrete cracking) is assumed as in Fig. 7(b). The compressive damage was not included in the analysis since the failure mode observed in the experiment was due to the concrete cracking around the connection region rather than the concrete crushing.
Stud Sheeting Rebar
1000 800
343
Hollo-bolt
600 400 200
3.3. Contact interaction and constraint conditions 0 0
50
100
150
200
Strain (10-3) Fig. 6. Stress–strain curves for steel materials.
decrease to zero with the tension stiffening effect. The tension stiffening can be expressed by means of a post-failure stress–strain curve or a fracture energy cracking criterion. As stated in the ABAQUS manual, the post-failure stress–strain approach is sensitive to the mesh for small reinforcement percentages. Therefore, the fracture energy cracking criterion was used in this study. In this approach, the brittle behaviour of concrete is represented by a stress–displacement curve rather than a stress–strain relationship.
1.8
Tensile stress (MPa)
1.5 1.2 0.9 0.6 0.3 0 0
0.5
1
1.5
2
3.4. Boundary and loading conditions
Cracking openning (mm)
(a) Post-failure model
Tensile damage parameter
1
0.8
0.6
0.4
0.2
0 0
0.5
1
The general contact algorithm available in ABAQUS/Explicit was used to enforce the contact between the contacting surfaces in all joint components. This contact algorithm which is based on the finitesliding formulation allows for arbitrary translations and rotations between interacting surfaces. To improve the time analysis, the contact surfaces in each contact pair should have almost identical meshes [25]. It is worth noting that the careful choice of master or slave surface in each contact pair is not required for the ABAQUS/Explicit model [26]. In this analysis, eight contact pairs were defined in the model: (1) steel column and concrete infill, (2) steel column and concrete slab, (3) steel column and endplate, (4) steel column and Holl-bolt, (5) steel beam and profiled sheeting, (6) endplate and concrete slab, (7) Hollo-bolt and endplate and (8) Hollo-bolt and concrete infill. Fig. 8 illustrates the contacting surfaces between the Hollo-bolts, endplates and CFST column. The embedded constraints were applied to the reinforcing bars, headed studs and concrete slab. In these constraints, the translational degree of freedom (DOF) of the nodes on the reinforcing bar and headed stud elements was constrained to the interpolated values of the corresponding DOF of the concrete slab elements. The slip and debonding of the reinforcing bars and headed studs were therefore ignored. Since the headed studs and the top flange were welded together, they were tied to each other using the Tie constraint. The Tie constraint was also used to model the interaction between the profiled sheeting and concrete slab. Although the steel beam and endplate were also welded together, the Tie constraint cannot be applied to them since they were modelled by different types of element (i.e. shell for the beam and solid for the endplate). Therefore, the shell-to-solid coupling constraint was used instead of the tie constraint.
1.5
2
Cracking openning (mm)
The simply supported boundary condition (BC) was applied to the upper face of the concrete slab. Due to the symmetry of the specimen, the symmetric boundary conditions were also applied to the surfaces at the symmetric planes of the specimen as shown in Fig. 3. The axial loading was applied vertically through the reference point located at the centre of the end section of the CFST column via the displacement control method. The applied load was then calculated as the total reaction acting on the reference point. Since the initial stable time increment in the explicit analysis was 6 × 10−7s, it would lead to an unacceptably large number of increments if the experimental loading rate was used. To reduce the computational time, the simulation was sped up by increasing the loading rate accompanying with the use of the smooth step amplitude as shown in Fig. 9. Different loading rates were assessed, and the most appropriate one was determined to be 375 mm/s. 3.5. Pretension in the bolt
(b) Tensile damage model Fig. 7. Tension stiffening and tensile damage model based on the cubic Bezier curve.
Since the bolt load tool is currently not available in the explicit dynamics solver, the initial temperature was used to create the bolt
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Fig. 8. Contacting surfaces between the Hollo-bolt, endplate and CFST column.
pretension. Similar approaches were taken by Tanlak et al. [25] and Egan et al. [26]. In this approach, a coefficient of thermal contraction was given to the bolt material. A reference temperature was then assigned to the bolt shank in a step created before the load step by using the predefined field option. A temperature increase induces the shrinkage of the bolt shank in the through-thickness direction and consequently induces the desired bolt prestress.
Dispacement control (mm)
75
60
45
30
4. Analytical model The analytical model developed by Aribert and Dinga [5] for predicting the moment–rotation curve of composite joints up to failure was extended herein to account for the effect of concrete filled into the hollow steel column. The basic principle of this model is based on the component method which has been introduced in the Eurocode 4 [27] for composite joints. The present model shown in Fig. 10 consists of four important components modelled by the translational springs Kr (the reinforcement), Ksc (the shear connection), Kp (the bending of the endplate region located between the upper bolt row and the tensile steel flange) and Kb (the bolt row). The present model is based on the assumptions that only the top bolt row is in tension and the joint is rotated about the bottom flange. It is noted that the column flange and web in compression components are omitted in the present model because of the presence of concrete infill. From Fig. 10, the compatibility conditions of the joint are Δr þ s−Δp
15
zr ¼ bzr H
Δb ¼ bzb
0 0
0.05
0.1
0.15
Time (s) Fig. 9. Smooth step amplitude of displacement control.
0.2
ð1Þ ð2Þ
where Δr, s, Δp and Δb are respectively the deformations of the reinforcement, shear connection, endplate in bending and bolt row. The equilibrium conditions of the joint lead to the following equations F r ¼ F sc
Fig. 10. Component model for the composite joint used in this study.
ð3Þ
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F p ¼ K p Δp
345
ð9Þ
where F and K are the forces and stiffnesses of the related components, respectively. Substituting Eqs. (6) and (7) into Eqs. (3), and Eqs. (8) and (9) into Eq. (4), the following equations are obtained s¼
Kr Δr K sc
Δp ¼
ð10Þ
K b Δb zb : Kp H
ð11Þ
The displacements of the reinforcement, shear connection and endplate in bending are obtained by substituting Eqs. (10) and (11) into Eq. (1) Δr ¼ C e bzr s¼
ð12Þ
Kr C e bzr K sc
Δp ¼
1þ
ð13Þ
Kr C e −1 bH K sc
ð14Þ
where K b zb 2 Kp H Kr 1þ K sc
1þ Ce ¼
ð15Þ
Finally, the rotation of the joint is obtained as ϕ¼bþ
Δp ¼ H
1þ
Kr C e b: K sc
ð16Þ
Once the force–deformation relationships of the individual components in Eqs. (6)–(9) are known, the joint rotation ϕ for each incremental increase of the externally applied moment ΔM can be determined from the iterative procedure illustrated in Fig. 11. In this procedure, the increase of the applied moment ΔM will stop if the failure of the joint is detected. The failure conditions of the joint used in this study are [5]: Δbj N Δbu and Δrj N Δru ¼ lr εru and s j N su
where Δbu, Δru and su are the deformation capacities of the bolt row, reinforcement and shear connector, respectively. In this study, Δbu is taken as 6 mm [5] whilst su is taken as 10 mm [27]. The ultimate deformation of the reinforcement Δru is computed from the ultimate strain εru which is usually taken as 0.08 [5]. The force–deformation relationships of the individual components are successively discussed hereafter.
Fig. 11. Flow chart of the present model.
Fp ¼
F b zb H
M ¼ F b zb þ F r zr :
ð17Þ
ð4Þ
ð5Þ
The constitutive relationships of four components are expressed as follows: F r ¼ K r Δr
ð6Þ
F sc ¼ K sc s
ð7Þ
F b ¼ K b Δb
ð8Þ
4.1. The reinforcement To account for the tension stiffening effect, a simplified stress–strain relationship for the embedded reinforcement given by CEB-FIP Model Code [28] as shown in Fig. 12(a) was used. The stiffness Kr of the reinforcement for four different phases as shown in Fig. 12(b) is obtained as follows: (a) Uncracked E c Ac f kc ð1 þ ρnr Þ for F r b F r1 ¼ σ sr1 Ar ¼ ct ð1 þ ρnr ÞAr ð18Þ lr ρ ¼ F r1
Kr ¼
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Fig. 12. Reinforcement curves.
(b) Crack information phase
(d) Post-yielding
Er Ar 3ρnr þ 3 for F r1 ≤ F r b F rn ¼ σ srn Ar ¼ 1:3 F r1 ð19Þ lr 3ρ nr þ 13−10 βr ¼ F rn
Kr ¼
(c) Stabilized cracking Kr ¼
E r Ar for F rn ≤ F r b F ry ¼ f ry Ar lr
Kr ¼
E r Ar 1 for F ry ≤ F r b F ru ¼ f ru Ar lr δ 1− F r1 =F ry
with
ð21Þ
nr ¼ Er =Ec ; ρ ¼ Ar =Ac ; kc ¼ 1=ð1 þ d=2z0 Þ ð22Þ
ð20Þ where d is the thickness of the concrete slab and z0 is the vertical distance between the centroids of the uncracked, unreinforced concrete slab and the uncracked, unreinforced composite section; βr is taken as 0.4 for short term loading and δ is taken as 0.8 for high ductility bars; fct and Ec are respectively the elastic modulus and the tensile strength of concrete; Ac and Ar denote the areas of the concrete slab and the reinforcement, respectively; Er, fry and fru are respectively Young's modulus, yield stress and ultimate stress of the reinforcement. The effective length of the reinforcement lr is determined based on the formulae proposed by Anderson et al. [29] as follows:
Fig. 13. Force–deformation of shear connection [5].
lr ¼ 2Lt if ρ b 0:8%
ð23aÞ
lr ¼ hc =2 þ Lt if ρ ≥ 0:8% and ac b Lt
ð23bÞ
lr ¼ hc =2 þ ac if ρ ≥ 0:8% and ac ≥ Lt
ð23cÞ
250
250
200
200
Moment (kNm)
Moment (kNm)
H.-T. Thai, B. Uy / Journal of Constructional Steel Research 112 (2015) 339–353
150
100
Test [15]
150
100
Test [15] FEM [18] FEM (Present) Analytical model
FEM [18] 50
50
FEM (Present) Analytical model
0
0 0
10
20
30
40
50
0
60
10
20
30
(a) CJ1
50
60
50
60
(b) CJ2 250
200
200
Moment (kNm)
250
150
100
Test [15] FEM [18] FEM (Present) Analytical model
50
40
Rotation (mrad)
Rotation (mrad)
Moment (kNm)
347
150
100
Test [15] FEM [18] FEM (Present) Analytical model
50
0
0 0
10
20
30
40
50
60
0
10
20
30
40
Rotation (mrad)
Rotation (mrad)
(d) CJ4
(c) CJ3 Fig. 14. Comparison of moment–rotation curves of four composite specimens.
where ac is the distance from the face of the column to the first shear connector along the beam, hc is the depth of the column section in the direction parallel to the longitudinal reinforcement, and Lt is the ‘transmission’ length given by Hanswille [30] as follows kc f ct ϕr 4τρ
Lt ¼
ð24Þ
where ϕr is the diameter of the reinforcement and τ is the average bond stress along the transmission length which can be taken as 1.8fct [28].
where N is the number of shear connectors distributed over the length ls of the beam in hogging bending which may be assumed to be 15% of the span, ksc is the stiffness of one shear connector determined by test or taken as 100 kN/mm for a 19 mm diameter headed stud if the test result is not available, EI denotes the bending stiffness of the steel beam, and dr is the distance between the centroids of the steel beam and the reinforcement. Fig. 13 shows the relationship between the interaction force Fsc and the slip s at the steel–concrete interface. The slip and force at the initial yielding are 0:7P R ksc
4.2. The shear connection
sel ¼
Based on a theoretical approach established by Aribert [31,32], the elastic stiffness of the shear connection Ksc is given by the following expressions
F scel ¼ K sc sel
K sc ¼
Nksc β−1 zr β− 1 þ α dr
ð25Þ
α¼
spl ¼ ψsel EI 2
E r Ar d r
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð1 þ α ÞNksc ls dr and β ¼ EI
ð26Þ
ð28Þ
where PR is plastic resistance of one shear connector which is equal to 106 kN for a 19 mm diameter headed stud based on the test conducted by Loh et al. [15]. The force and slip at the ultimate state are [5] F scu ¼ NP R
with
ð27Þ
F scu F scel
ð29Þ ð30Þ
where ψ may be taken as 2 or 3 depending on whether the shear connection is full or partial, respectively.
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(a) Crack of concrete slab
(b) Plastic strain and local buckling of the flanges and web of steel beam Fig. 15. Comparison of the failure modes of specimen CJ1.
respectively, and lp is the distance between the tension flange and the upper bolt row as indicated in Fig. 10.
4.3. Bending of the upper part of the endplate The stiffness Kp of the endplate which is assumed to be constant was derived by Aribert and Dinga [5] as follows
Kp ¼
3Dp 3
lp
¼
3Ep bp t 3p 3 12 1−ν2 lp
ð31Þ
where Ep and v are respectively Young's modulus and Poisson's ratio of the endplate, bp and tp denote the width and thickness of the endplate,
The components contributed to the stiffness of a bolt row include the column web in tension (k3), column flange in bending (k4), endplate in bending (k5) and bolt in tension (k10). For the joints with CFST columns, the test results reported by Wang et al. [33] confirmed the assumption of an infinite stiffness for the column web in tension (k3 = ∞). Therefore, the stiffness of a bolt row is calculated as 1 1 1 1 ¼ þ þ K b k4 k5 k10
250
ð32Þ
and the deformation of each component is related to the total deformation Δb and stiffness Kb of the bolt row by
200
Moment (kNm)
4.4. Bolt row
150
100
δ4 ¼
K b Δb k4
ð33Þ
δ5 ¼
K b Δb k5
ð34Þ
110% shear connection (5 studs) 66% shear connection (3 studs) 44% shear connection (2 studs)
50
δ10 ¼
0 0
10
20
30
40
50
60
K b Δb : k10
ð35Þ
Rotation (mrad) Fig. 16. Effect of degree of shear connection on behaviour of composite joints.
The deformation of each component in a bolt row obtained in Eqs. (33)–(35) is used to trace the current stiffness of each component
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(a) Five studs (110%) (3) Three studs (66%)
349
(c) Two studs (44%)
Fig. 17. Deformation and von Mises stress of shear studs at ultimate loads.
based on its force–deformation relations, and consequently, the equivalent stiffness of a bolt row Kb can be updated using Eq. (32). The detailed formulae of each component in a bolt row can be found in Aribert et al. [34]. It should be noted that the column flange in bending component (k4) given in [34] is applied for the open section column only. For the joint with hollow section or CFST columns as in this study, the analytical model developed by Neves and Gomes [35] and Gomes et al. [36] will be used to predict the force–deformation relationship of the column flange in bending component (k4). 5. Verifications of the present models The FE and analytical models developed in this study were verified against the experimental results reported by Loh et al. [15]. In addition, the FE solutions generated by Ataei et al. [18] were also used in the
verification to illustrate the accuracy of the developed FE model. The obtained moment–rotation curves of four specimens were compared with the experimental results [15] and those predicted by FE method [18] in Fig. 14. It can be seen that the present FE model predicts very well the initial stiffness, ultimate moment capacity as well as the postbuckling behaviour of all connections. As shown in Fig. 15, the present model also reasonably predicts the failure mode of the joint due to cracking of concrete slab around the connection region and the local buckling of the bottom flange and the web of the steel beam. In general, the analytical model predicts rather well the initial stiffness, moment resistance and of rotation capacity composite joints except for the case of the specimen CJ4 in which the present analytical model underestimates the ultimate moment capacity. 6. Parametric studies 6.1. Effect of shear studs and reinforcement ratio
250
Moment (kNm)
200
150
N28 (3.98 %)
100
N24 (2.93 %) N20 (2.03 %) N16 (1.30 %)
50
N12 (0.73 %)
0 0
10
20
30
40
50
Rotation (mrad) Fig. 18. Effect of reinforcement ratio on behaviour of composite joint CJ1.
60
The effect of the degree of shear connection on the moment–rotation responses of composite joints was shown in Fig. 16. It can be seen that the ultimate moment capacity of composite joints slightly increases with the increase of the degree of shear connection because of the reduction in the slip between steel beam and concrete slab as indicated in Fig. 17. Fig. 18 shows the effect of the reinforcement ratio on the moment– rotation responses of the joint CJ1. Five different diameters of reinforcing bars of N12, N16, N20, N24 and N28 corresponding to the reinforcement ratios of 0.73, 1.30, 2.03, 2.93 and 3.98% were considered. It can be observed that the ultimate moment capacity of composite joints increases by increasing the reinforcement ratio, and this increase is not significant when the reinforcement ratio is greater than 3%. The failure mode of composite joints is also influenced by the reinforcement ratio as shown in Fig. 19. The effect of reinforcement ratio on the cracking of the concrete slab was also illustrated in Fig. 20. As expected, the greater the reinforcement ratio used, the lesser the cracking observed in the concrete slab.
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(a) N12
(b) N16, N20, N24, N28
Fig. 19. Effect of reinforcement ratio on the failure modes of composite joint CJ1.
(a) N12
(b) N16
(c) N20 Fig. 20. Effect of reinforcement ratio on the damage of concrete slab at ultimate loads.
60
60
50
50
Moment (kNm)
Moment (kNm)
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40
30 Ajax bolt Hollo-bolt
20
351
40
30 M16 20
M20
10
10 0 0
0 0
20
40
60
80
100
20
40
60
80
100
120
40
50
60
Rotation (mrad)
120
Rotation (mrad)
(a) Steel joint
(a) Steel joint
160
160 140
140 120
Moment (kNm)
Moment (kNm)
120 100 Ajax bolt
80
Hollo-bolt
100 M16
80
M20 60
60 40
40 20
20 0 0
0 0
10
20
30
40
50
10
20
30
Rotation (mrad)
60
(b) Composite joint CJ4
Rotation (mrad)
(b) Composite joint CJ4 Fig. 22. Effect of blind bolt diameter on moment–rotation responses. Fig. 21. Effect of different types of blind bolts on moment–rotation responses.
7. Discussion 6.2. Effect of different types of blind bolts and bolt diameters The effects of the blind bolt types (e.g. Hollo-bolt versus oneside Ajax bolt) and the bolt diameters (e.g. M16 versus M20) on the moment– rotation responses of steel and composite joints were shown in Figs. 21 and 22, respectively. It can be seen that these effects can be negligible in composite joints and insignificant in the case of the steel joint. This might be due to the fact that the composite joints used in this study were designed to fail by cracking of the concrete slab and buckling of the steel beam rather than failure of the bolt.
6.3. Effect of width-to-thickness ratio and column sections Figs. 23 and 24 show the effects of the width-to-thickness ratios and column sections on the moment–rotation behaviour of bare steel and composite joints. Two values of thickness ratio of 22 and 40 corresponding to the column thickness of 9 mm and 5 mm were examined. The circular section ϕ219.1 × 9 mm was chosen since it has approximate area of the square section 200 × 9 mm. Again, the composite joint is not sensitive to the change of the thickness ratio and section type of the column since its behaviour is governed by the concrete slab and reinforcing bars. However, for the bare steel joints, the circular section provides greater strength than the square section as confirmed by experimental observation reported by Wang et al. [33].
The FE model developed by Ataei et al. [18] cannot fully captured the flange local buckling which is the dominant failure mode in the specimens CJ1, CJ2 and CJ3 [15]. This was clearly indicated in Fig. 14(a)–(c) in which the descending branch of the moment–rotation curves predicted by Ataei et al. [18] does not exist. This is due to the fact that the solid C3D8R elements used by Ataei et al. [18] cannot accurately predict the local bucking of the beam when compared with the shell S4R elements used in this study. It is also observed from Fig. 14 that the FE model developed by Ataei et al. [18] cannot predict well the initial stiffness as well as the stiffness degradation of all specimens when compared with the present one. This might be due to the inappropriate modelling of the Hollo-bolt as well as its contact interactions with the endplates and the CFST column. In the FE model developed by Ataei et al. [18], the Hollo-bolt was modelled as a standard bolt and the interaction between the bolt, endplates and CFST column was modelled by TIE constraints instead of CONTACT interaction as in the present model. Since the present analytical model is based on the component method, the accuracy of its predictions is strongly dependent on the force–deformation curve of each component of the composite joint which is assumed as multi-linear curves in this study. Therefore, it is incapable of accurately capturing the stiffness degradation of composite joints when compared with the FE model as shown in Fig. 14. However, the present analytical model is very useful for the design purpose as it predicts rather well the initial stiffness, moment resistance and rotation
H.-T. Thai, B. Uy / Journal of Constructional Steel Research 112 (2015) 339–353
60
70
50
60 50
40
Moment (kNm)
Moment (kNm)
352
30 20
b/t=22
40 30
Square column Circular column
20
b/t=40
10 10 0 0
20
40
60
80
100
0
120
0
Rotation (mrad)
20
40
80
100
120
50
60
(a) Steel joint 250
200
200
Moment (kNm)
Moment (kNm)
(a) Steel joint 250
150 b/t=22
100
60
Rotation (mrad)
b/t=40
150
100
Square column Circular column
50
50
0 0
10
20
30
40
50
60
0 0
10
20
30
40
Rotation (mrad)
Rotation (mrad)
(b) Composite joint CJ1
(b) Composite joint CJ1 Fig. 24. Effect of column section on moment–rotation responses.
Fig. 23. Effect of column thickness ratio on moment–rotation responses.
capacity which are the key structural properties of a joint in framed structures.
been studied. Further research therefore needs to be carried out to investigate these effects on the seismic performance of blind bolted endplate composite joints.
8. Conclusions
Acknowledgements
A reliable FE model has been developed for blind bolted endplate composite joints that connect the composite beams to a CFST column. The validity of the present model was verified by comparing the obtained predictions with experimental results and those predicted by the existing FE model. The verification study demonstrates that the present FE model is capable of accurately predicting the moment–rotation response of composite joints including the initial stiffness, the ultimate moment capacity and the post-buckling behaviour. In addition, the present model also reasonably predicts the failure modes of composite joints. The analytical model proposed in this study based on the component method predicts rather well the initial stiffness, moment resistance and rotation capacity which are the key structural properties of a joint in framed structures. Unlike the bare steel joints, the bending behaviour of composite joints is dominated by the concrete slab and reinforcing bars. Therefore, the behaviour of composite joints is not sensitive to the blind bolt type and diameter as well as the section type and thickness ratio of the column as clearly shown in the numerical results. The FE model developed in this paper is limited to blind bolted endplate composite joints subjected to static loading. The influences of different types of blind bolts and column sections on cyclic behaviour of these joints have not
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