Mechanical analysis of timber connection using 3D finite element model

Mechanical analysis of timber connection using 3D finite element model Bohan XU Ph.D Student Civil Engineering Laboratory (CUST) Clermont-Ferrand, France Mustapha TAAZOUNT Dr-Ing Civil Engineering Laboratory (CUST) Clermont-Ferrand, France Patrick RACHER Dr-Ing Civil Engineering Laboratory (CUST) Clermont-Ferrand, France Summary Among the various structural components, the connections are often one of the weakest points in a timber structure. However, they govern the load-carrying capacity of structure. Thus, the knowledge of the mechanical behaviour of connection is particularly important for timber engineers. There are two approaches in the field of joint mechanics: experimental approach and numerical approach. The former is the global approach which considers the joint as whole object, but it is limited by cost, a low number of parameters and types of joints which it can represent. The later looks at the joints as an assembly of elementary components with their own mechanical behaviours. It is the local approach based on numerical analysis with limited experimental identifications and validations. This paper is focused on developing of the numerical model based on local experimental material identification and taking into account the mechanical contact and friction phenomenon between different components, with failure criterion in order to predict the mechanical behaviours of timbersteel-timber connections made with dowel-type-fasteners.. Introduction The dowelled connections are the main fastening technique used in timber structures. Facing the actual architectural trends and high requirements of mechanical strength, timber-to-timber connections are mainly replaced by connections using slotted-in steel plates. In this case, better aesthetical appearance and greater fire safety is obtained. Some experimental investigations on timber-steel-timber tension connections arranged with multiple blots were carried out [,,3,4,]. The mechanical behaviour of timber connections is very complex and is influenced by connection geometry, the plastic moment of the fastener and the embedding properties of the wood. However, to simplify the problem, most previous investigations have considered the effects of individual parameter on the mechanical behaviour of timber connections. It is difficult to undertake an analytical study due to interactions among parameters. Thus, 3D finite element model is proposed to investigate the mechanical performance of dowel-type timber connections. The nonlinear material model is crucial to the development of accurate load-slip behaviour for timber connections. In dowel-type timber connection, the timber hole introduces high localized stress concentrations. Macroscopic observations have revealed that these compressive stresses play an important role in the development of brittle failures around holes. Kharouf [5] proposed a plasticity based constitutive compressive material formulation to model wood as elasto-plastic orthotropic according to the Hill yield criterion. The model is implemented in a finite element code to carry out the analysis of bolted joints. Reasonable trends were found between numerical simulations and experimental measurements of local and global deformations for one-bolt connection. Furthermore, the predicted failure modes were found to be consistent with experimental observations. However, the numerical stiffness obtained by simulation is greater than the

experimental measurement ones. Laplanche [6] has developed a three-dimensional finite element modelling to analyse the behaviour of timber connections with multiple dowel type fastener. Material model is based on the orthotropic plasticity compression behaviour of the timber according to Hill yield criterion. The same phenomenon of greater stiffness in numerical simulations has also been found. Patton-Mallory and al. [7] have developed a three-dimensional numerical model of a bolted wood connection. The numerically obtained load-slip curves were generally stiffer than the experimental ones. It is showed that the weakness of experimental stiffness is due to local wood crushing under the fasteners. The progressive failure of timber in the process of loading causes the local crushing. However, the progressive failure of timber in the process of loading can not be modeled by the elasto-plastic orthotropic material model according to the Hill yield criterion. Thus, the improved material model including the progressive failure of timber needs to be developed. In this paper, a three-dimensional (3D) finite element model including a new material model is developed to predict behaviours of timber steel-timber connections loaded in parallel-to-grain tension. Timber is modelled as elasto-plastic transverse isotropic compression according to Hill yield criterion, and Hoffman failure criterion was applied to model the progressive failure of timber. Numerical results obtained by the finite element program using this constitutive model are compared to experimental ones and very good agreement is observed between them.. Experimental program Tests of timber-steel-timber connections were carried out at Civil Engineering Laboratory LGC in France [8]. Displacement transducers are mounted to record the movement of the timber member relative to the steel member. Their results are used for validation of modeling for timber-steel-timber connections (figure and table ). The connections had two rows of four fasteners with same diameter (, 6 or 0mm). The following part focuses on results for timber connection with fasteners of 6 mm and timber thickness of 75 mm. a a 3 a a 4 h t t Tightened bolts Dowels Fig. Geometry of the timber-steel-timber connections and test configuration Table Geometry of the timber-steel-timber connections (mm) d t t a a a 3 a 4 h 6 60 8 59 5 64 54 The parallel-to-grain loading was applied in the tests according to the European Norm NF-EN 689 technical protocol for determining the stiffness and strength of timber connection. The figure shows the experimental results. The plastic behaviour of the fastener was only obtained for

test, and brittle shear failures were observed for other two test. The theoretical reference loadcarrying capacity is calculated with different manner: Johansen theory, block shear formulations and EuroCode5 (Table). The mean value of the stiffness is 3kN/mm. Table Theoretical load-carrying capacity (kn) Test Johansen Block shear EC5. 335. 34 35 7 Fig. Load-slip behaviour and failure mode 3. Finite element modelling 3. Meshing and boundary conditions To describe the load-carrying capacity as well as the stiffness of the timber connections, a finite element approach is made using the MARC.MSC software package. Using symmetry, only one quarter of the connection geometry was modeled. The geometry of finite element model based on 8- noded hexahedral elements is showed in Fig3. All loading was applied using fixed displacement of the nodes. Load in parallel-to-grain tension was introduced by applying a prescribed displacement. F Wood member 0 displacement in parallel-to-grain Fig. 3 Finite element model geometry Dowel Bolt Steel member

3. Material properties The timber properties may be regarded as transverse isotropy, which assumes identical properties in radial and tangential directions. This combined direction is referred to as perpendicular to grain ( ) while the longitudinal direction is referred to as parallel to grain (//). The glued-laminated timber used for timber-steel-timber connection corresponds to resistance class GL8 according to EN 94. Its measured density ρ mean is equal to 450 kg/m 3 and the moisture content h mean is equal to 0%. The numerical values of the elastic parameters that have been used are given in Table 3 and Table 4. Table 3 Material parameters for the glulam GL8h used in the model Young s modulus (MPa) Poisson s ratio Shear modulus (MPa) E 0 600 ν TR ν LT 0.4 G mean 780 E 90 40 ν RL 0.0 The steel materials are modelled as being non-linear and isotropic. The young s modulus is set to 0GPa, the Poisson s ratio υ 0.3. The plasticity is considered using the Von Mises criterion. Table 4 Steel properties Steel plate t 8mm Steel dowel 3.3 Hill yield criterion f y (MPa) f u (MPa) f y (MPa) f u (MPa) 360 540 336 460 Hill was the first to conduct studies on anisotropic plasticity [9]. The Hill criterion is a generalized version of the von Mises yield criterion to consider the anisotropy of the materials. Its stress potential can be expressed as [0]: [ a ( σ σ ) + a ( σ σ ) + a ( σ σ ) + 3a τ + 3a τ 3a τ ] / / σ + a y z z x 3 x y 4 zx 5 yz 6 xy a a3 f c,90 f c,0 f c,0 Where σ i and τ ij are the timber stresses, a 4 a5 a6 3 f c,0 and f c,90 are the compressive strength parallel and perpendicular to the grain, f v is the shear strength of the timber. The compression strength and shear strength are determined experimentally: f c,0 50.64MPa, f c,90 3.4MPa and f v 0.98MPa. 3.4 Failure criterion Failure theories are functions of the stresses and strengths of the material. They are assumed to represent failure under all loading conditions without regard to failure mechanism or failure mode. For isotropic materials there are three well-known strength theories: maximum principal stress, maximum shear stress, and distortional energy. In each case a function of the stresses is equated with a single parameter, the tensile yield strength, or the fatigue strength of the material. The anisotropic materials that have more than one strength parameter have led to numerous proposals for failure theories. More than 40 such theories have been proposed for wood, reinforced plastics, etc. f v ()

3.4. Maximum stress criterion The most frequently used failure criterion for anisotropic brittle materials is the maximum normal stress criterion, which states that the material will fail when any one of the stresses in the principal material directions exceeds the material strength in that direction. This assumes that failure is independently controlled by each stress type and is not a function of interaction between stresses. The maximum stress criterion has been successfully used with wood to predict crack initiation due to perpendicular to grain tension or parallel to grain shear stresses. A Qualitative assessment of failure in bolted connections has been done by Patton-Mallory and al. []. The Maximum stress criterion is found to be useful for comparing numerically predicted stress distributions with failure modes observed experimentally. However, predictions of ultimate strength due to brittle failure were not performed. 3.4. Tsai-Wu stress criterion It has long been suspected that stresses in principal directions influence each other and therefore affect material failure. Especially for fibrous materials, stress interaction may change failure mode and failure stress. Tsai and Wu [] developed a tensor polynomial strength criterion for anisotropic materials. The Tsai-Wu failure criterion is an interactive failure theory that has been used mostly for fiber reinforced materials and was derived from the well known von Mises criterion for isotropic materials. Some numerical models including the Tsai-Wu failure criterion have been developed [3, 4]. A concern exists about using the Tsai-Wu criterion due to the need to evaluate the stress interaction coefficients that are sensitive to the test methods used to evaluate biaxial strength. No recommendations exist for selecting interaction coefficients for 3D wood failure [5]. 3.4.3 Hoffman stress criterion Although several failure criteria exist for wood and orthotropic materials, most are difficult to apply to 3-D stress fields. Hoffman criterion is essentially Hill criterion modified to allow unequal maximum allowable stresses in tension and compression. It is also an interactive failure theory that has been used for anisotropic materials, and no interaction coefficients need be selected. It can be expressed as [0]: [ C ( σ σ ) + C ( σ σ ) + C ( σ σ ) + C σ + C σ + C σ + C σ + C σ + C ]/ F 3 3 3 4 5 6 3 7 3 8 3 9σ With C C f t,90 f c,90 f f t,0 c,0 C C3 f t,0 f c,0 5 C6 C 7 C8 C9 f t,90 f c,90 f v C 4 f t,0 f c,0 () Where σ i and τ ij are the timber stresses, f t,0 and f t,90 are the tensile strength parallel and perpendicular to the grain f c,0 and f c,90 are the compressive strength parallel and perpendicular to the grain, f v is the shear strength of the timber. In this case, timber strength values are considered: f t,0 5.3MPa, f t,90 0.585MPa, f c,0 50.64MPa, f c,90 3.4MPa and f v 0.98MPa. 3.5 Contact description Contact was modelled using the direct constraint method in MSC.Marc. The method requires the definition of the contact body that potentially may come in contact with other. Contact bodies can simply be the physical bodies themselves (e.g. timber, fasteners and steel). For taking into account the contact and the friction effects on the timber stresses beneath the fastener, the Coulomb friction model that is the most popular friction model was chosen. Between fasteners and timber, the friction coefficient is set equal to 0.3, between fasteners and steel, the friction coefficient is set

equal to 0.00. In MSC.Marc, three different approximations of the step function can be implemented. The stick-slip model was applied to this case. The other issue with contact was the use of analytical contact rather than discrete contact in this case. 4. Simulation results and analysis To validate the numerical model, the load-slip curves given by the three-dimensional finite element model are compared with those from experiments (figure 4). Two models have been developed, the model is including Hill yield criterion considering timber elasto-plastic transverse isotropic behaviour, the model is including Hill yield criterion and Hoffman failure criterion to model the progressive failure of timber. Fig. 4 Comparison of experimental and numerical load-slip curves The results of comparison between tests and models have showed that the numerically obtained load-slip curve of model was stiffer than the experimental curves. The model presents an advantage than the model due to simulating the progressive failure of timber. The numerical results of model are in good agreement with experimental observations in stiffness and loadcarrying. The table 5 shows the comparison results. Table 5 Comparison results Stiffness (kn/mm) Load-carrying (kn) Test Model Model Test Model 3 75 07 335 347 The great initial stiffness in model is due to without considering the holes clearance. In the process of test, the contact area increases progressively when the load increases. At about 0kN, the fasteners fully embedded into timber. The model and the model have same initial stiffness, they are fully consistent with the experimental initial stiffness as they are reloaded (figure 5). An accurate estimation of the initial stiffness requires simulating the increasing progressively contact area. Fig. 5 Improved load-slip curve The numerically predicted stresses of interest are: parallel to gain compression and shear and perpendicular to grain tension. Parallel to gain compression stresses, exceeding the material capacity cause only non-catastrophic crushing failure of the wood near the fastener. However, parallel to gain shear and perpendicular to grain tension stresses cause the potential catastrophic failure. The figure 6 presents the parallel to grain shear stress distribution and the perpendicular to grain tension stress distribution in the timber at the yield level (F 70kN) and at the ultimate load. The position of failure is in accordance with the observed stress contours. The failure is caused by

the timber stress interactions (perpendicular to grain tension stress and parallel to gain shear) in the joint area. They govern the load-carrying capacity and mode of failure. (a) Fig. 6 (a) Parallel to grain shear stress distribution at the yield level (left) and at the ultimate load(right) (b) perpendicular to grain tension stress distribution at the yield level (left) and at the ultimate load(right) The experiences have also presented that the appropriate fastener distance can increase loadcarrying capacity and also change the mode failure. When a 3 08mm and other connection geometry was unchanged, the mean value of the load-carrying capacity was equal to 374kN. The connection shows a good ductile behaviour and the failure of connection is caused by the plastic behaviour of the fasteners. No splitting failure due to the shear has been observed. 5. Conclusion In this paper, a three-dimensional finite element approach is proposed to evaluate the performance of dowelled timber connections. The proposed material model including Hill yield criterion and Hoffman failure criterion for anisotropic timber material was shown to perform well for timbersteel-timber connections with multiple fasteners. Wood exhibits a progressive failure process as they are loaded. The progressive failure of timber begins significantly when the fasteners fully are embedded into timber. The progressively decreasing stiffness can be simulated using the presented model. The 3D finite element model is reliable and efficient method to predict load-slip, ultimate strength, stress distributions and mode of failure in multiple fasteners connection. Moreover, the research is going on to introduce the increasing progressively contact area into the current model for simulating the initial stiffness. References [] Mohammad M., and Quenneville J. H. P., Behaviour of wood-steel-wood bolted glulam connections, CIB-W8, Graz, Austria, 999, Paper 3-7-. [] Uhre Pedersen M., and Odin Clorius C., Dowel Type Connections with Slotted-in Steel Plates, CIB-W8, Graz, Austria, 999, Paper 3-7-8. [3] Mischler A., Prion H., and Lam F., Load-carrying behaviour of steel-to-timber dowel connections Proceedings. World Conference of Timber Engineering 000, British Columbia, Canada, 000, p. 8. (b)

[4] Gattesco N., and Toffolo I., Experimental study on multiple-bolt steel-to-timber tension joints, Materials and structures, Vol.37, 004, pp.9-38. [5] Kharouf N., McClure G., and Smith I., Elasto-plastic modelling of wood bolted connections, Computer Structures, Vol.8, 003, pp. 747 754. [6] Laplanche K., Etude du comportement au feu des assemblages de structures bois : approche expérimentale et modélisation, Thèse de docteur, Blaise Pascal University, 006, p.40. [7] Patton-Mallory M., Cramer S.M., Smith F.W., and Pellicane P.J., Nonlinear material models for analysis of bolted wood connections, Journal of Structural Engineering, Vol. 3, No. 8, 997, pp. 063 070. [8] Racher P., Comportement à froid des assemblages bois-métal, Rapport d étude, 00.55. MSGC-CUST, 00, p8. [9] Hill R., The mathematical theory of plasticity, Oxford University Press, 950. [0] MSC.MARC (005) User s Manual, vol. A: theory and user information. MSC.Software Corporation. [] Patton-Mallory M., Pellicane P.J., and Smith F.W., Qualitative assessment of failure in bolted connections: Maximum stress criterion, Journal of Testing and Evaluation, Vol. 6, No. 5, 998, pp. 489-496. [] Tsai S.W., and Wu E.M., A general theory of strength for anisotropic materials, J.Compos.Mat, Vol. 5, 97, pp. 58-80. [3] Patton-Mallory M., Pellicane P.J., and Smith F.W., Qualitative assessment of failure in bolted connections: Tsai-Wu stress criterion, Journal of Testing and Evaluation, Vol. 6, No. 5, 998, pp. 497-505. [4] Carradine D.M., Dolan J.D., Heine C.P., Development of the "Displaced Volume Model" to Predict Failure for Multiple-Bolt Timber Joints CIB-W8, 004, Paper 37-7-. [5] Patton-Mallory M., Pellicane P.J., and Smith F.W., Modeling Bolted Connections in Wood: Review, Journal of Structural Engineering, Vol. 3, No. 8, 997, pp. 054-06.