Modelling of steel-timber composite connections: Validation of finite element model and parametric study

Engineering Structures 138 (2017) 35–49

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Modelling of steel-timber composite connections: Validation of finite element model and parametric study A. Hassanieh a, H.R. Valipour a,⇑, M.A. Bradford a, C. Sandhaas b a b

Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering UNSW Australia, UNSW Sydney, NSW 2052, Australia Institute for Timber Structures and Building Construction, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany

a r t i c l e

i n f o

Article history: Received 30 March 2016 Revised 28 November 2016 Accepted 3 February 2017

Keywords: Finite element Hybrid structure Load-slip Non-linearity Steel-timber composite Timber

a b s t r a c t This paper investigates the mechanical behaviour of lap steel-timber composite connections using a 3-D continuum-based finite element (FE) model. In the FE models developed, the non-linear behaviour and failure of the timber is captured by a stress-based failure criterion formulated in the framework of continuum-damage mechanics. Yielding of the steel plates and fasteners (i.e. coach screws and bolts) is captured by an elastic-hardening plastic constitutive law. These FE models are validated by experimental (push-out) tests conducted on laminated veneer lumber (LVL)-steel and cross-laminated timber (CLT)steel composite lap connections. It is shown that the FE models developed in the paper can replicate adequately the load-slip response and failure mode of the hybrid steel-timber composite connections tested. The validated FE model is used to undertake a parametric study that elucidates the influence of the yield strength and the length of the fasteners and the post-tensioning force in the bolts on the stiffness, load carrying capacity and load-slip behaviour of hybrid steel-timber composite connections. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction The structural performance of timber elements can be improved by hybridising timber with steel and/or reinforced concrete at different levels (i.e. members, structure). The timber-concrete and steel-concrete composite beams comprising of a reinforced concrete slab connected to timber or steel joists have been extensively investigated and used in the past few decades [1–14], however, the steel-timber composite floor comprising of a timber slab connected to steel girders is a relatively novel concept developed just in recent years. The steel-timber composite (STC) floors can reduce the self-weight of the structure and the need for craneage and rigging and increase the speed of construction dramatically. Moreover, the STC system can reduce the size of foundation, facilitate the construction on soft and problematic soils and improve the sustainability of buildings by lowering the self-weight of the structure and subsequently reducing the energy- and carbon-intensive construction materials (i.e. steel and concrete). The structural behaviour of hybrid (composite) steel-concrete, timber-concrete and steel-timber composite (STC) systems is significantly influenced by mechanical behaviour (stiffness and load carrying capacity) of connections the. The mechanical behaviour

⇑ Corresponding author. E-mail address: [email protected] (H.R. Valipour). http://dx.doi.org/10.1016/j.engstruct.2017.02.016 0141-0296/Ó 2017 Elsevier Ltd. All rights reserved.

and load-slip response of the fasteners in composite connections is usually characterised by the results of experimental push-out tests. The results from push-out tests conducted on steelconcrete composite connections with different types of fasteners have been widely reported in the literature [1–5]. Moreover, the tests have been used to evaluate the service stiffness and loadcarrying capacity and to characterise the load-slip behaviour of timber-timber [6] and timber-concrete composite connections [7–14]. In addition to laboratory push-out tests, finite element (FE) models have been used to simulate the load-slip response and to predict the stiffness and the peak load carrying capacity of fasteners and composite connections. The FE models used for the nonlinear analysis of composite connections can be classified to 1-D frame [15,16], 2-D [17] and 3-D continuum-based FE models [3,10,14,18–21]. The 1-D FE models take advantage of beam on elastic/inelastic foundation theory to capture the linear as well as the non-linear behaviour of dowel-type fasteners. For the 1-D FE models, the fasteners (e.g. nails, screws or bolts) are modelled by beam elements and linear/non-linear springs parallel and perpendicular to the axis of the dowels are used to model the behaviour of the foundation (i.e. timber or concrete). 1-D FE beams can represent the non-linear behaviour of the dowels adequately, as well as the load-slip response of hybrid timber-timber, timberconcrete and steel-timber composite connections with dowel-

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type fasteners [22,23]. However, the accuracy of such 1-D FE models depends strongly on the mechanical characteristics of the springs (representing the timber foundation modulus) that can be obtained from embedding tests. Accordingly, there have been attempts to develop 2-D and 3-D continuum-based FE models that can accurately capture the behaviour of dowel-type fasteners in steel-concrete, timber-timber and timber-concrete lap connections without the need of embedding test results; relying only on the basic mechanical properties (e.g. compressive, tensile and shear strength) of timber, concrete and steel. Nguyen and Kim [19] used ABAQUS software to develop a 3-D FE model of steel-concrete composite connections with headed stud shear connectors. In the model developed, damage and failure (being material nonlinearities) of the concrete, headed stud, steel beam and reinforcing were taken into account. More recently, Pavlovic´ et al. [21] reported 3-D FE models of steel-concrete composite joints with embedded high-strength bolted shear connectors and analysed the models using ABAQUS with its explicit solver. The strength, failure mode, ductility and the load–slip behaviour of the steelconcrete composite joints predicted by the 3-D FE models showed good correlation with push-out test data [19,21]. Similar numerical modelling has been reported by Liu et al. [24] for high-strength friction-grip bolts as shear connectors between precast concrete and steel composite beams. However, the development of detailed 3-D continuum-based FE models that can accurately predict the behaviour of timber lap connections with dowel-type fasteners has been hampered by strong geometrical and material nonlinearities associated with the anisotropic nature of timber (and engineered wood) and by the combination of different brittle and ductile failure modes in shear and compression, as well as scarcity of reliable experimental data on the behaviour and failure of timer under multi-axial stress states required for calibration of timber constitutive laws [25,26]. Moreover, the strain hardening behaviour and the strength gain associated with wood densification (due to compression) in the perpendicular to the grain direction can add another layer of complexity to the non-linear behaviour of timber under multiaxial stress states [27]. The constitutive laws used for modelling the behaviour of timber behaviour and for capturing timber failure under multiaxial stress states can be classified as (i) elasticity-based models, that take advantage of equivalent uniaxial and invariant-based models [27,28]; (ii) plasticity-based models, that employ a yield surface to represent the onset of yielding and the evolution of the yield strength [26,29–34]; (iii) models based on progressive damage and fracture mechanics [35,36]; (iv) continuum damage models, and (v) a combination of plasticity with damage and fracture models [37]. Amongst existing timber constitutive laws, the elasticitybased models are applied mainly for representing timber behaviour/failure under 2-D plane stress conditions [27,28]. The plasticity-based models tend to overestimate the strength and stiffness of the timber, owing to quasi-brittle and brittle nature of the behaviour of timber (associated with progressive damage and fracture) that cannot be accommodated in the framework of plasticity [38–40]. Furthermore, the plasticity-based models typically do not take account of the unequal tensile and compressive strengths of timber [33] and accordingly, the framework of continuum damage mechanics or a combination of continuum damage and plasticity appear to be one of the most accurate frameworks for formulating the non-linear behaviour of timber [41]. In this paper, 3-D FE models of STC connections with doweltype (i.e. coach screw and high-strength bolt) fasteners are developed and analysed using ABAQUS software. In the FE formulations developed, the timber is modelled by an eight-parameter stressbased failure criteria formulated in the framework of continuumdamage mechanics by Sandhaas [41]. The non-linearity of the steel plates, screws and bolts are represented by an elastic-hardening

plastic model. Moreover, geometrical non-linearities and the non-linearity of the interface between the timber, steel plate and dowel-type fasteners are considered in the FE models developed. The accuracy of the numerical models is verified against the results of push-out tests conducted on STC connections and a parametric study is carried out to determine the influence of different parameters (i.e. the length and yield strength of the fasteners, coefficient of friction and post-tensioning force in the high-strength bolts) on the load-slip, stiffness and peak load capacity of STC lap connections with dowel-type fasteners.

2. Outline of push-out tests The geometric outline of the symmetric STC connections used for validation of the FE models is shown in Fig. 1. The symmetric configuration of the push-out test provide a uniform shear stress distribution and minimise the parasitic stresses due to friction and imperfection at the interface between timber panels and steel profile and accordingly reduce the variability of push-out test results. Furthermore, symmetric configuration can significantly facilitate the testing. In the tested STC connections, either coach screws or high strength bolts were used to connect two LVL or CLT timber panels to the flanges of a 310UB32.0 steel beam [22]. The timber panels in the push-out specimens were 400 mm wide and 600 mm long. The LVL panels were 75 mm thick hySPAN manufactured from Radiata Pine by Carter Holt Harvey Australia and the CLT panels were 120 mm thick with 5 lamellas manufactured from European Spruce. The size of steel profiles (i.e. 310UB32.0) and thickness of CLT timber panels (120 mm thick with 5 lamellas) in the push-out test specimens were determined with respect to the preliminary design of a STC floor for a hypothetical 8-storey residential building with 6 m long steel girders and 1.2 m spaced steel joists. A 3D finite element model of the building was developed and analysed and accordingly the timber slab was designed to comply with minimum strength and serviceability limit state design requirements of AS1720.1 [42]. The 120 mm thick CLT slabs could provide up to two-hour fire rating based on a charring rate of 0.7 mm/min. Furthermore, the possible annoying vibration of the STC floor was addressed by limiting the maximum short-term deflection and maximum allowable impulse velocity of the timber slab to the values specified in EC5 [43] and ensuring that the first natural frequency of the STC floor is bigger than 8 Hz [43]. Details of the push-out test specimens including the type of timber slab and the diameter and type of fasteners are given in Table 1. In addition, the adopted mechanical properties of the LVL and Spruce wood (used for fabrication of the CLT panels) including their elastic moduli, compressive strength fc, tensile strength ft and shear strength fv are given in Tables 2–5, respectively. The coach screws were made of Grade 4.6 steel with a yield strength of 240 MPa and an ultimate tensile strength of 400 MPa, and the screws were AS/NZS 1393 [44] compliant. The high strength bolts complied with the minimum requirements of AS1110.1 [45] and AS1112.1 [46] and the bolts had a proof yield strength of 660 MPa and an ultimate tensile strength of 830 MPa. The variability of timber mechanical properties and fabrication methods can significantly affect the structural behaviour of steeltimber composite joints. Accordingly, three identical specimens were fabricated and tested for each type of STC joint to ensure the precision and repeatability of the push-out test results [22]. Four linear variable differential transformers (LVDTs) were mounted on each push-out specimen, to measure the relative slip between the timber slab and steel flange and also capture any possible twist in the specimens. The push-out test procedure and load protocol followed the EN 26891 [47] specifications. The specimens

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Fig. 1. Configuration of push-out test specimens with (a) high-strength bolts and (b) coach screws (all in [mm]).

Table 1 Details of push-out test specimens. Fasteners

LVL (ts = 75 mm)

CLT (ts = 120 mm)

Diameter (mm)

Length (mm)

Diameter (mm)

Length (mm)

Coach screw

8, 12 16 20

65 75 100

12, 16, 20

100

Bolt

12

110

12 & 16

150

Table 2 Elastic modulus E, Poisson’s ratio m and shear modulus G of Spruce wood adopted for CLT plys in the FE models. Elastic modulus (MPa) [41]

Poisson’s ratio [46]

Shear modulus (MPa) [41]

E11

E22

E33

m12

m13

m23

G12

G13

G23

11000

370

370

0.48

0.48

0.22

690

690

50

Table 3 Compressive strength fc, tensile strength ft, shear strength fv of Spruce wood, and fracture energies Gf adopted for CLT plys in the FE models [41]. Parallel-to-grain (MPa)

Perpendicular-to-grain (MPa)

Shear strength (MPa)

Fracture energy (N/mm)

fc11

ft11

fc22

ft22

fv

fv

36

24

4.3

0.7

6.9

0.5

were loaded up to 0.4Fu (with Fu being the estimated ultimate load) and unloaded from 0.4Fu to 0.1Fu and then the load was maintained at 0.1Fu for 30 s. In the final stage, the reloading started from

roll

Gf,0 Gf,90 Gf,v Gf,roll 6 0.5 1.2 0.6

0.1Fu and continued until failure of the specimen. Further details on the loading procedure and push-out test setup can be found in Hassanieh et al. [22]. The load-slip response of the steel-LVL

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Table 4 Elastic modulus E, Poisson’s ratio m and shear modulus G of LVL adopted in the FE models [49]. Elastic modulus (MPa)

Poisson’s ratio

Shear modulus (MPa)

E11

E22

E33

m12

m13

m23

G12

G13

G23

13000

400

400

0.48

0.48

0.22

850

850

100

Table 5 Compressive strength fc, tensile strength ft and shear strength fv of LVL adopted in the FE models [22]. Parallel-to-grain (MPa)

Perpendicular-to-grain (MPa)

Shear strength (MPa)

fc11

ft11

fc22

ft22

fv

fv

60

55

12

7.0

6.9

3.2

and steel-CLT connections (with coach screw and bolt fasteners) obtained from push-out tests is shown in Fig. 2. 3. Finite element (FE) model 3.1. Geometry and boundary conditions A timber-steel-timber arrangement with two planes of symmetry was adopted for fabrication of the push-out specimens (see Fig. 1). Accordingly, in the FE models one quarter of the tested specimen was modelled to reduce the computational cost. The geometry and boundary conditions of the one-quarter FE model are shown in Fig. 3. 3.2. Constitutive material laws 3.2.1. Timber In this study, the failure of timber under a multiaxial stress sate is captured by a 3-D constitutive model formulated in the framework of continuum damage mechanics (CDM) by Sandhaas

roll

[41,48]. The constitutive law adopted is able to simulate ductile and brittle failure of timber material simultaneously by identifying different modes of failure, including compressive and tensile failure parallel and perpendicular to the grain and shear failure. In the constitutive law adopted, timber is treated as an orthotropic material, but the mechanical properties of the timber in the two directions perpendicular to the grain (namely radial and tangential directions) are assumed to be identical (Fig. 4). To simplify the damage-based equations in the main directions (parallel and perpendicular to the grain) for timber elements, a subscript ‘90’ denotes perpendicular to the grain and ‘0’ parallel to the grain. Accordingly, the stress tensor r is defined as

2

cccr11

3

2

3

cccr0 rv R rv T r12 r13 6 r¼6 r22 r23 7 r90R rroll 7 4 5¼4 5: Sym:: r33 Sym:: r90T

ð1Þ

3.2.1.1. Failure modes. The material models with a single-surface failure/damage criterion (e.g. Hill [33] and Hoffman [32]) cannot adequately simulate the combination of ductile and brittle failure modes in parallel and perpendicular to the grain directions. Accordingly, the constitutive law adopted takes advantage of a multi-surface failure criterion to adequately identify and capture the onset of the brittle and ductile modes of failure. The multisurface damage/failure criteria comprises of the followings equations/regions: Criterion I represents tensile failure in the direction parallel to the grain. This brittle mode of failure is caused by tension stress rL P 0 and it is independent of other stress components, being

F t;0 ¼

rL f t;0

6 1 Criterion I

ð2Þ

where ft,0 is the tensile strength of timber in the direction parallel to the grain. Criterion II represents compressive failure in the direction parallel to the grain. This ductile mode of failure is caused by the compressive stress rL 6 0 and it is independent of other stress components, being

F c;0 ¼

Fig. 2. Experimental load-slip response of (a) steel-LVL and (b) steel-CLT composite connections with coach screws and bolts.

rL 6 1 Criterion II f c;0

ð3Þ

where fc,0 is the compressive strength of timber in the direction parallel to the grain. In the adopted multi-surface damage criteria, the transverse tension modes and shear modes of failure are dependent and hence they should be considered together. Criteria III and IV represent a brittle failure mode associated with tensile failure in the direction perpendicular to the grain and splitting in the LT-plane and/or in the LR-plane. These modes of failure are caused by the tensile stress rR/T in the radial/tangen-

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Timber panel

Steel flange Fig. 3. Outline and boundary conditions of one-quarter FE model of STC connections (with coach screws).

rij ¼ ð1  dÞDijkl ekl

where ekl and rij are the strain and stress tensors respectively, d 2 [0,1] is the damage index (d = 0 indicates no damage and d = 1 represents a fully damaged state). Due to the anisotropic behaviour of timber, several damage indices associated with different modes of failure are defined, i.e. Criterion I dt,0, Criterion II dc,0, Criteria III and IV dt,90R/T and dvR/T, droll and Criteria V to VIII dc,90R/T and dvR/T, droll. In a case where two damage indices depend on the same stress component, the Macaulay operator :=(a + |a|)/2 is used. With regard to the ductile and brittle modes (Fig. 5) considered for timber under compression and tension/shear respectively, two functions are used for damage evolution, being

Perpendicular to grain Parallel to grain

Fig. 4. Definition of material directions.

dðjÞ ¼ 1  tial direction, the longitudinal shear stress rLR/LT in the LR/LT-plane or rolling shear stress rRT, being

rR=T

F t;90R=T ¼

!2

f t;90



rLR=LT

þ

fv

2

 þ

rRT f roll

2 6 1 Criterion III  IV: ð4Þ

Criteria V–VIII represent two pairs of pure transverse compression and/or shear failure. The compressive failure perpendicular in the direction perpendicular to the grain is a ductile failure mode caused by the compressive stress rR/T in the radial/tangential direction, and the shear failure mode is brittle and it is caused by compressive stresses that create high shear stress components in the LT/LR planes:

rR=T 6 1 Criterion V=VIII  Transverse compression; f c;90

F c;90R=T ¼

ð5Þ  F v R=T ¼

rLT=LR fv

2

 þ

rRT f roll

2 6 1 Criterion V=VIII  Shear:

ð7Þ

ð6Þ

The stress-strain behaviours adopted for ductile and brittle failure modes under a uniaxial stress state are shown in Fig. 5. More specifically, the linear elastic-perfectly plastic (Fig. 5a) behaviour adopted for the ductile mode of failure is used to determine the behaviour under compression, and the brittle behaviour of timber under shear and tension is represented by a linear elastic-softening model (Fig. 5b). 3.2.1.2. Damage evolution. The 3-D stress-strain relationships in the constitutive law adopted have been recast in the framework of damage mechanics, and the material non-linearity is captured by modifying the material stiffness tensor Dijkl as

dðjÞ ¼ 1 

1

j

1 2

ð8Þ

Damage evolution in compression;

f max  2Gf E

  2Gf E 2 f max 

j

 Damage evolution in tension and shear;

ð9Þ

where fmax is the maximum strength, E the modulus of elasticity and Gf denotes fracture energy and j is the history parameter [48]. Rearranging Eq. (7) leads to the relationship between the strain and stress matrices as

e ¼ C dam r

ð10Þ

where Cdam is compliance matrix of the damaged material [48]. 3.2.1.3. Cross-laminated timber (CLT) modelling. The CLT panels comprise of five layers of Spruce wood. The approximate thickness of each layer is either 20 mm or 40 mm. The first, third and fifth layers are loaded parallel to the grain, while the second and fourth layers are loaded perpendicular to the grain. In the FE analysis, each layer was considered separately and the mechanical properties of the Spruce wood provided in Tables 2 and 3 were assigned to the layers with respect to their orientations. Furthermore, it was assumed that the bond (glue) between different layers and laminates is perfect and stronger than the Spruce wood itself. 3.2.1.4. Laminated veneer lumber (LVL) modelling. The LVL panels consist of 3 mm thick laminated veneers compressed and glued together. Considering the small thickness of the laminates, the layer-wise nature of LVL panels was not considered in the FE models and the LVL panels were treated as one homogenous layer. The mechanical properties of the LVL panels adopted in FE analysis are provided in Tables 4 and 5 [22,49].

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Fig. 5. Stress-strain relationships for material with (a) ductile failure represented by linear elastic-perfectly plastic behaviour and (b) brittle failure represented by linear elastic-softening behaviour [41].

3.2.2. Steel plates and fasteners There are four steel components in the FE models, i.e. the steel beam flange, fasteners (coach screw and bolt), square washer (used in conjunction with bolts) and base block (support). The steel profile used for fabrication of the benchmark push-out specimens was a hot-rolled section of Grade-300PLUS steel. Accordingly, a yield strength of 320 MPa and an ultimate strength of 440 MPa were adopted for the steel beam flange in the validation study for the FE models. The coach screw shear fasteners were made of Grade 4.6 steel with a yield strength of 240 MPa and an ultimate strength of 400 MPa, while a yield strength of 640 MPa and an ultimate strength of 800 MPa for the high-strength 8.8 bolts were used in the validation study. The stress-strain relationships adopted for the steel components are shown in Fig. 6. In the FE models, an isotropic hardening plastic material model was employed to simulate the non-linear behaviour of steel flange, coach screws and bolts [50]. Possion’s ratio for the steel components was assumed to be 0.3 for all steel components, and the elastic modulus of steel was taken as 200 GPa. The bolts were post-tensioned to approximately 0.4fy and 0.1fy, in steel-LVL and steel-CLT composite connections respectively. To distribute the post-tensioning force induced in the bolts over an area to prevent local crushing of timber, a 50  50  4 mm square washer was used in conjunction with the bolt (Fig. 1).

3.3. Contact/Interface In the FE models, the behaviour of the contact interface between different components (Fig. 7) was modelled by a surface-to-surface discretisation method [50]. The behaviour of the contact interface is characterised in the normal and tangential directions. The behaviour of the contact elements in the tangential

Fig. 6. Piecewise linear stress-strain relationship adopted for steel plates, coach screws and bolts.

Timber panel-Support Timber panel-flange

Timber panel-Fastener Steel flange-Fastener Fig. 7. Outline of the contact interface considered in the FE models.

direction was incorporated into the FE models by a penalty friction formulation in which a coefficient of fiction is assigned to the contact surfaces, being 0.4 for steel-to-steel contact 0.25 for steel-toCLT and 0.3 for steel-to-LVL [20,51]. The contact behaviour in the normal direction for the steel-tosteel interface was modelled by ‘‘Hard Contact” with the ‘‘Allow separation after contact” option in the ABAQUS software which is quite straightforward. However, modelling the steel-to-timber contact behaviour, particularly the contact between the dowel-type fasteners and timber, is not straightforward. Recent FE simulations have shown that the numerical models tend to consistently overestimate the initial stiffness of timber connections with dowel-type fasteners [41,52], because the installation of dowel-type fasteners can cause some damage in the timber (in the vicinity of doweltype fasteners) and this pre-existing damage is not typically considered in the numerical simulations. In addition, some slip is caused by imperfect drilling especially in bolts connections. A simple strategy to take account of this pre-existing damage (induced following installation of the dowel-type fasteners) is to reduce the elastic modulus (and sometimes strength) of the timber material in the vicinity of the dowels [53,54]. Recently, the behaviour of the contact between timber and steel parts has been investigated thoroughly by Dorn [52]. An optical surface measurement method was used to characterise parameters that affect the elastic modulus of the cut or drilled timber surface. The measurements showed that the stiffness of the timber surface can be significantly less than the stiffness of the bulk timber, especially when it is cut or drilled [55]. Furthermore, a non-linear relation between contact pressure and displacement in the direction normal to the interface was found. This observation was consistent with weak boundary layer (WBL) interpretation that was provided by Good [56] and applied to the wood material by Stehr and Johansson [57]. A generalised Lame function (Fig. 8) has been proposed by Dorn [55] to take

A. Hassanieh et al. / Engineering Structures 138 (2017) 35–49

gf ¼

Fig. 8. Lamé function representing normal contact pressure-deformation relationship [51].

account of the WBL and non-linear behaviour of normal pressure versus contact over-closure, so that

 n   uinter u r0  rL nr þ ¼ 1; u0 r0

ð11Þ

where nu and nr are positive numbers that control the curvature of the function, r0 is the maximum compressive strength of the timber and u0 is the contact deformation. In the FE models, the normal contact between timber and steel fasteners is defined by means of the ‘‘Tabular” option available in ABAQUS. This option allows a piecewise curve to be defined for the contact pressure versus normal deformation. In this study, u0 was taken as 0.35 mm for screw connections and as 0.45 mm for bolted connections, and nr and nu were taken 1.1 and 3.9 respectively, as recommended by Dorn [52]. Furthermore, r0 was taken 60 MPa and 30 MPa for LVL and CLT contact surfaces respectively. 3.4. Loading and analysis procedure The loading and analysis of the FE models were conducted using a displacement-controlled procedure, with the prescribed displacement being applied on the edge of the flange of the steel beam. The FE models were loaded and analysed following a step by step procedure. To reduce the effect of the contact initiation on convergence of the results, a contact loading was considered in the first loading step, where a small displacement (less than 0.05 mm) was applied on the surface of steel flange to bring the steel flange and timber panels into full contact. In the case of bolted connections, the post-tensioning force induced in the bolts was applied in the second step and in the final step, the prescribed displacement was applied on the edge of the steel flange. 3.5. Finite element mesh The beam flange and connection parts were meshed by quadratic block (C3D20R) elements (Fig. 9) with the reduced integration scheme available in ABAQUS [50] that can capture the high plasticity deformation better than linear elements [20]. The CLT and LVL panels were meshed by 8-node linear block (C3D8) elements and some regions of the screw fasteners, particularly the core, were meshed by higher-order wedge (C3D15) elements to minimise mesh transitions. 3.5.1. Mesh sensitivity The mesh size and geometry can have significant influences on the FE results, particularly for materials having softening behaviour [41]. This spurious mesh sensitivity associated with softening of the material can be treated by regularisation techniques such as nonlocal formulations or crack band approaches [58] implemented in the ABAQUS subroutines. The main idea behind crack band regularisation is to adjust the fracture energy Gf of the material with respect to finite element mesh size h according to [41,48],

Gf : h

41

ð12Þ

The characteristic fracture energy gf which depends on the mesh size can restore the objectivity of the FE results to some extent. However, the mesh sensitivity associated with mesh orientation and configuration cannot be alleviated by the crack band approach [59]. Furthermore, the crack band approach works only when one failure mode is dominant. Despite using a crack band approach in the ABAQUS software to restore the objectivity of the FE results, a mesh sensitivity analysis was carried out to demonstrate the influence of the mesh size on the FE predictions and the adequacy of the implemented regularisation method in the ABAQUS material subroutines. Three different mesh sizes, i.e. coarse, medium and fine, were considered (Fig. 10) and the load-slip responses of the steel-LVL composite connection with 12 mm coach screw fasteners predicted by different FE mesh sizes are shown in Fig. 11. It is observable that the peak load capacity of the STC connection is slightly sensitive to the mesh size, but the initial stiffness of the STC connection is independent of the mesh size. The medium mesh size can provide a good compromise between the accuracy and computational efficiency and, accordingly, the medium mesh size was used for the validation and parametric studies.

4. Validation of FE models The adequacy of the adopted constitutive laws for the materials and the modelling strategies for determining the load-slip response, peak load capacity and failure mode of STC connections with dowel-type fasteners (Fig. 1) has been verified against the available push-out test results.

4.1. Steel-LVL connections The load-slip response for the steel-LVL connections with coach screws and bolt fasteners (Fig. 1) obtained from the FE models are compared with the experimental load-slip results in Figs. 12 and 13 respectively. In addition to the FE and experimental results, the peak load capacity of the STC connections were calculated by the method of Eurocode 5 and the results are shown in Figs. 12 and 13. The FE model predictions show a reasonably good agreement with the experimental data. In particular, the peak loading capacity and ultimate stages of load-slip response have been adequately captured by the FE models. However, the FE models have overestimated the load and stiffness at slips within the range of 2–4 mm (Fig. 12b–d). The overestimation of load-slip response can be attributed to adopted elastic-perfectly plastic behaviour for timber in compression (see Fig. 5a) that cannot adequately represent the crushing and yielding/softening of timber in compression. It is observable that the difference between the FE and experimental results increases as the diameter of the screw increases (see Fig. 12), owing to larger size of timber crushing zone around the screws, when the failure mode II (associated with timber crushing/softening) is dominating the behaviour of STC joints [22]. The permanent deformations of the 8 and 12 mm coach screws and the 12 mm bolt fasteners observed in the tests are compared with the deformation of the fasteners predicted by the FE models in Figs. 14 and 15. In addition, the deformation of the LVL panel beneath the washer and crushing of the LVL (close to the surface of the timber element and around the fastener hole) captured by the FE models shows a good correlation with the experimental results (see Figs. 16 and 17).

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Fig. 9. FE mesh for (a) timber slab, (b) steel beam flange, (c) coach screws and (d) high strength bolts.

Fig. 10. Outline of the (a) coarse (b) medium and (c) fine FE mesh used in the sensitivity analysis.

4.2. Steel-CLT connections

Fig. 11. Load-slip response of steel-LVL connections (with 12 mm coach screws) obtained from different mesh sizes.

The numerically-predicted load-slip response of the steel-CLT connections with coach screws and bolt fasteners (Fig. 1) are compared with the experimental load-slip curves in Figs. 18 and 19. The peak load capacity of the steel-CLT connections (with coach screw fasteners) obtained according to Eurocode 5 is also shown in Fig. 18. It can be seen that load-slip and peak loading capacity of the steel-CLT connections predicted by the numerical models agree reasonably well with the laboratory tests results. Moreover, the permanent deformation of the 12 mm coach screw and bolt fasteners (Fig. 20) and the deformation of the CLT panel close to the surface of the timber element and around the fastener hole (Fig. 21) determined by the FE models shows good agreement with the experiments.

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Eurocode 5 Eurocode 5

f k h = 28.6 kN

f k h = 12.7 kN

(a)

(b)

Eurocode 5

Eurocode 5

f k h = 50.8 kN

f k h = 79.4 kN

(c)

(d)

Fig. 12. Load-slip response of steel-LVL connections with (a) 8 mm (b) 12 mm (c) 16 mm and (d) 20 mm coach screws.

Fig. 13. Load-slip response of steel-LVL connection with 12 mm bolts.

5. Parametric study The FE models have been used to conduct a parametric study, in which the influence of the coach screw length and the yield strength, post-tensioning force in the bolt fasteners, thickness of the LVL timber slab, thickness of the steel flange and magnitude of the coefficient of friction on the load-slip behaviour, initial stiffness and peak load capacity of STC connections were investigated. 5.1. Length of coach screw fasteners One of the influential parameters on the load-slip behaviour and failure mode of STC connections with dowel-type fasteners is the ratio l/d (l being the penetration length of the screws in the

timber and d the diameter of screws) [60]. According to Aune and Patton-Mallory [60], the yield strength and failure mode of p timber connections can be characterised by the ratio t/ c, where t is the penetration length of fasteners into the timber and c = My/fe, where My = ry  p d3/32 is the yield moment of the fastener and fe = fembedding  d is the wood embedding strength. Substituting ry = 240 MPa and fembedding = 60 MPa into these equations p and assuming t  l produces t / c = 1.6l/d. The load-slip plots for STC connections with 90, 65 and 40 mm long coach screws (d = 12 mm and penetration lengths t of 75, 55 p and 32 mm) are shown in Fig. 22a. The ratio t/ c for the coach screws analysed is 10.0, 8.66 and 5.33 (corresponding to 90, 65, p and 45 mm long coach screws respectively). Since the t/ c is greater than 4, it can be concluded that STC connections within the range of the fasteners’ lengths (40 mm to 90 mm long) should have the same yield strength [60]. This conclusion is consistent with the peak load capacity of the STC connections predicted by the FE models (see Fig. 22a). 5.2. Yield strength of coach screw fasteners The load-slip response of STC connections with different yield strengths of the coach screw fasteners ry (ranging from 120 MPa to 360 MPa with d = 12 mm) are shown in Fig. 22b. It can be seen that the ultimate strength Fu of the coach screws is proportional to the square root of the yield strength ry of the fasteners, i.e. Fu p / ry. This observation is confirmed by the formula proposed by Aune and Patton-Mallory [60] that

Fu ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 2f e M y ¼ 0:25 f e ðp d Þ  ry :

ð13Þ

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A. Hassanieh et al. / Engineering Structures 138 (2017) 35–49

Fig. 14. Deformation and plastic strain (PE) of (a) 8 mm and (b) 12 mm coach screws in steel-LVL connection.

Fig. 15. Deformation and plastic strain (PE) of 12 mm bolts in steel-LVL connections.

Fig. 16. Deformation (mm) (U) of LVL panel beneath washer due to axial force induced in bolts.

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Fig. 17. Deformation (mm) U, and Crushing of LVL in STC connections with 12 mm bolts.

Eurocode 5 Eurocode 5

f k h = 37.5 kN

f k h = 21 kN

(a)

(b)

Eurocode 5 f k h = 58 kN

(c) Fig. 18. Load-slip response of steel-CLT connections with (a) 12 mm, (b) 16 mm and (c) 20 mm coach screws.

Fig. 19. Load-slip response of steel-CLT connections with (a) 12 mm and (b) 16 mm bolts.

It is noteworthy that Eq. (13) can only provide an approximate value of the ultimate strength Fu of the fastener, owing to the simplistic assumptions made in its derivation. In particular, the influence of the method of installation and the size effect on the peak load capacity of the fasteners have not been considered in Eq. (13).

5.3. Post-tensioning force in the bolt fasteners The FE models of bolted steel-LVL composite connections were developed and analysed assuming three different levels of the post-tensioning force (i.e. 17%, 35% and 50% of the bolt ulti-

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Fig. 20. Deformation and plastic strain (PE) of (a) 12 mm coach screw and (b) 12 mm bolts in steel-CLT connection.

Fig. 21. Maximum Principal Strain (E, Max, Principal) and Crushing of CLT in steel-CLT connection with 12 mm coach screws.

mate strength). The load-slip plots for bolted STC connections are compared in Fig. 23, which shows the negligible influence of bolt post-tensioning on the peak load capacity. However, the

level of the post-tensioning force induced in the bolts can significantly increase the initial stiffness of STC connections and the load required for initial slip in the STC connection (Fig. 23). It

A. Hassanieh et al. / Engineering Structures 138 (2017) 35–49

47

Fig. 22. Effect of (a) length and (b) yield strength of coach screws (d = 12 mm) on load-slip behaviour of steel-LVL connections.

can change the force corresponding to the initial slip in the STC connections, but the coefficient of friction has minor impact on the rest of load-slip response (Fig. 24a). The coefficient of friction has minor influence on the initial stiffness (pre-yield) and a major impact on the post-yield behaviour of STC connections with screw fasteners (Fig. 24b). 5.5. Effect of LVL timber panel thickness in bolted connections

Fig. 23. Effect of post-tensioning force induced in bolts on load-slip behaviour of STC connections with bolts.

is noteworthy that the post-tensioning force in the bolts cannot exceed a certain limit imposed by the bearing strength of the timber, and this bearing strength in wood-based materials is a rather small (typically less than 10 MPa) in the direction perpendicular to the grain. Furthermore, the large post-tensioning force can be lost over time due to creep and mechano-sorptive effects in the timber.

5.4. Coefficient of friction between timber and steel flange The friction between the steel plate and timber panel can affect the load-slip behaviour of STC connections with dowel-type fasteners. Accordingly, the effect of coefficient of friction ranging from l = 0.2–0.4 on the load-slip response of STC connections (Fig. 24) was investigated by the FE models. As observed in FE models, in the STC connections with bolts, the coefficient of friction

Effect of the timber slab thickness (bolt length) on the load-slip behaviour of bolted steel-LVL composite connections was studied through an FE analysis of three bolted STC connections with LVL slab thickness of 45, 75 and 90 mm that are available in the Australian timber market. The load-slip behaviour of the STC joins with two 12 mm high-strength bolts are shown in Fig. 25a, which demonstrates the minor influence of timber the slab (or bolt length) on the load-slip behaviour of STC connections with bolts. 5.6. Effect of screw fastener diameter (ds) to steel flange thickness (ts) The ratio of the fastener diameter (ds) to the steel flange thickness (ts) may alter the mode of failure (changing from a plastic hinge in the screws to plastic deforming in the steel plate/flange). Accordingly, FE models of STC connections with 12 mm diameter coach screw fasteners and three different steel flange thickness (4, 6 and 8 mm) were analysed and the load-slip results of connections with ds/ts = 1.5, 2.0 and 3.0 are shown in Fig. 25b. It is seen that the parameter ds/ts has a minor effect on the initial stiffness of STC connections, but the peak load capacities of STC connections with coach screw fasteners start to decrease slightly as the ds/ts ratio exceeds 2.0, because localised plastic strains and crushing around the fasteners holes in the steel flange start to dominate the failure mode of STC connections for large ds/ts ratios.

Fig. 24. Effect of friction coefficient on load-slip response of STC connections with (a) bolts and (b) screws.

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Fig. 25. (a) Effect of timber slab thickness in bolted connection and (b) effect of coach screws diameter (ds) to steel flange thickness (tf) on load-slip behaviour of steel-LVL composite connections.

6. Conclusions

Acknowledgement

In this paper, non-linear finite elements (FE) models of steeltimber composite (STC) connections have been developed and analysed using ABAQUS software. The effects of geometrical and material non-linearities including steel yielding and plastic hardening, the anisotropic behaviour of engineered wood products (laminated veneer lumber LVL and cross laminated timber (CLT)) and combinations of brittle and ductile failure modes of the timber were considered in the FE models by adopting appropriate constitutive laws for the consistent materials. Moreover, non-linear behaviour of the contact interface between the steel and timber components were incorporated adequately into the FE models. The FE models developed were verified against available experimental push-out tests conducted on steel-LVL and steel-CLT composite connections, and it was shown that the FE models can adequately capture the loadslip, initial stiffness, peak load capacity and failure mode of fasteners and timber panels in STC connection. A parametric study was conducted using the validated FE models and the following conclusions can be drawn from the results of FE analyses.

The work in this paper was supported by a Discovery Project (DP160104092) awarded to the second and third authors by the Australian Research Council.

 The yield strength ry of the coach screw fasteners has a major influence on the peak load capacity Fu of STC connections.  The peak load capacity of STC connections with coach screw fasteners is proportional to square root of the yield strength of fasp teners, i.e. Fu / ry.  The length to diameter ratio (l/d) of coach screw fasteners was found to have minor influence on the peak load capacity and load-slip response of STC connections, as long as the ratio l/d exceeds 4.  The post-tensioning force induced in bolt fasteners has minor influence on peak load capacity of bolted STC connections. The magnitude of the post-tensioning force in the bolt fasteners can affect the shear force corresponding to the first slip in the STC connection.  The coefficient of friction (l 2 [0.2,0.4]) adopted for the steelto-timber contact surfaces can affect the peak load capacity of STC connections with coach screw fasteners, but it has negligible influence on the load-slip behaviour of STC connections with bolt fasteners.  The thickness of the timber slab (the length of bolt fasteners) in the range of 45 to 90 mm has minor influence on the peak load capacity and initial stiffness of steel-LVL connections with bolted fasteners.  The peak load capacity of STC connections starts to decrease slightly as the fastener diameter (ds) to steel flange thickness (ts) ratio exceeds 2.0. However, the initial stiffness of STC connections with coach screw fasteners is not sensitive to ds/ts ratios less than 3.0.

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