Numerical modelling of timber/timber–concrete composite frames with ductile jointed connection

Abstract

Due to the scarcity of experimental data, this article focuses on the application of detailed finite element models for evaluating structural behaviour of timber–concrete composite frames with post-tensioned beam-to-column joints. In the developed finite element models, nonlinear behaviour and failure mode of timber and concrete under biaxial stress state are captured by hypo-elastic constitutive laws based on the equivalent uniaxial strain concept. In addition to material nonlinearities, the effect of geometrical nonlinearities and nonlinearity of contacts at the concrete slab-to-beam, beam-to-column and slab-to-column interfaces are considered in the finite element models. The accuracy of developed finite element models is verified against available experimental data on post-tensioned timber frames, and the validated analytical tool is used to undertake a parametric study. It is shown that elastic modulus of timber and the details of concrete slab-to-column connection can significantly affect the drift response and failure mode, whereas the compressive strength of timber and stiffness of timber–concrete composite connection have only a minor influence on the drift and failure mode of the timber/timber–concrete composite frames with ductile jointed connections.

Keywords

contact damage model finite element post-tensioned timber–concrete composite

Introduction

Timber structures have found increased usage over the past decades because of the lower cost of construction and maintenance, as well as better sustainability compared with reinforced concrete (RC) and steel (Sathre and O’Connor, 2008). In particular, the engineered wood products (i.e. laminated veneer lumber (LVL) and glulam), with improved structural characteristics, have made it possible for structural engineers to construct large buildings that can be as robust as steel and RC but more sustainable. However, design and construction of timber frames, particularly beam-to-column connections, with adequate ductility to resist moderate to severe earthquake loads is still a challenging task. Accordingly, over the past two decades, a large number of studies have been devoted to response of timber structures subject to earthquake loads (Collins and Kasal, 2010; Fragiacomo et al., 2011; Loss et al., 2013). Studies covering various aspects of timber elements and frames, such as shake table testing of timber frames (Ceccotti et al., 2013; Heiduschke et al., 2009; Smith et al., 2014), development of design provisions for timber structures subject to seismic/cyclic loads (Fragiacomo et al., 2011; Loss et al., 2013; Sarti et al., 2012), theoretical and experimental investigations of cyclic and dynamic response of timber elements, connections and subassemblies (Kasal et al., 1994; Rinaldin et al., 2013; Schneider et al., 2015; Smith et al., 2012; Wu et al., 2015), have been conducted and reported. However, less attention has been paid to structural behaviour of timber–concrete composite (TCC) frames and the interaction between concrete slab and timber frame and its influence on the global response of the structure subjected to lateral seismic loads (Newcombe et al., 2010).

In response to the emerging need for developing high-performance structural systems, the concept of jointed ductile connections, originally developed for precast RC members (Palermo et al., 2005; Priestley, 1991; Priestley et al., 1999), has been incorporated into construction of steel and timber frames, and the efficiency of these connections for eliminating the inelastic and residual deformations in the event of an earthquake has been demonstrated through different studies (Buchanan et al., 2011; Newcombe, 2011; Pino, 2011; Ricles et al., 2001; Smith et al., 2014). However, the long-term behaviour of post-tensioned (PT) timber frames can be of concern and only a few studies have addressed this concern to date (Davies and Fragiacomo, 2011; Wanninger et al., 2014).

In jointed ductile connections, the inelastic demand is accommodated at the connection level, and energy is dissipated through controlled rocking mechanisms provided by elastic pre-tensioning of high-strength steel cables that clamp beam to the column. The structural performance of connections can be improved by adding energy dissipaters to the connection (Newcombe, 2011; Vasdravellis et al., 2013). In such high-performance hybrid connections, energy is dissipated by inelastic deformation or friction mechanisms within particular components (i.e. dissipaters) and hence seismic analysis of structures with such hybrid jointed connections requires accurate modelling of connecting members, as well as the energy dissipaters.

In general, timber structures can be analysed using continuum-based finite element (FE) models or one-dimensional (1D) beam elements (Dias et al., 2007; Fragiacomo and Ceccotti, 2006). The continuum-based FE models provide the versatility required for detailed analysis of the entire frame and the joints/connections (Dias et al., 2007; Kharouf et al., 2003), whereas 1D beam models can only capture the global response of members and to capture the behaviour of connections 1D beam elements rely on component-based lumped models (Kasal et al., 1994; Pampanin et al., 2001). In the component-based technique, response of connections is captured by hysteretic nonlinear multi-spring elements and dampers and mechanical characteristic (e.g. stiffness and viscosity) of components are determined with respect to experimental results (Ceccotti and Vignoli, 1989; Rinaldin et al., 2013). However, such an approach is time-consuming and costly because any changes in timber or connection characteristics (e.g. PT force) typically necessitate a new set of tests to be carried out for calibration of the model. Accordingly, over the past decade continuum-based FE models have replaced experiments and gained popularity for predicting behaviour of timber elements/joints by only relying on basic properties of material (Meghlat et al., 2013; Xu et al., 2009).

Given the attention focused on the behaviour of structures subjected to seismic action, reliable understanding of the structural behaviour and failure mode of TCC frames with PT timber beam-to-column joints is needed; however, the experimental data on such frames are non-existent or very scarce. Furthermore, the influence of concrete slab-to-column connection and effect of TCC connection stiffness on the drift response and failure mode of frames with ductile jointed connection remain largely unexplored. Accordingly, in this article, detailed continuum-based FE models of a TCC frame with ductile jointed connections are developed and analysed. The developed FE models can capture material nonlinearities including concrete cracking and crushing and nonlinear anisotropic behaviour of timber under biaxial stress states (Valipour et al., 2014). The accuracy of the proposed FE models for predicting failure mode and nonlinear load–deflection response is verified against available experimental data on PT timber subassemblies/frames. The validated FE model is employed to undertake a parametric study and evaluate the influence of timber compressive strength and modulus of elasticity, TCC connection stiffness, concrete slab thickness and construction details of concrete slab-to-column connection on the failure mode and load–deflection behaviour of TCC frames with PT beam-to-column connection.

Constitutive models

Timber

In this study, the anisotropic behaviour and failure of timber under biaxial stress state is formulated using concept of fibre reinforced composite materials (Valipour et al., 2014), in which, timber is treated as a composite material comprising a matrix with smeared reinforcing fibres in the main direction (parallel-to-grain) as shown in Figure 1(a). Assuming that subscripts X and Y denote the original axes of orthotropy for the representative element, the relationship between total stress $s_{XY} = [\begin{matrix} σ_{X} & σ_{Y} & τ_{XY} \end{matrix}]^{T}$ and total strain $e_{XY} = [\begin{matrix} ε_{X} & ε_{Y} & γ_{XY} \end{matrix}]^{T}$ can be obtained by superimposing the behaviour of matrix and the reinforcing fibres

s_{XY} = {D_{\sec (m)} + D_{\sec (r)}} e_{XY}

(1)

where $D_{\sec (m)}$ and $D_{\sec (r)}$ represent the secant stiffness matrices of the matrix (m) and the fictitious reinforcing fibres (r), respectively.

Figure 1.

Outline of the (a) modelling timber as a composite material comprising a matrix with smeared reinforcements parallel-to-grain direction and (b) equivalent uniaxial stress–strain relationship for the matrix.

For the matrix component, the relationship between principal 1–2 stress $s_{12} = [\begin{matrix} σ_{1} & σ_{2} & τ_{12} \end{matrix}]^{T}$ and strain vector $e_{12} = [\begin{matrix} ε_{1} & ε_{2} & γ_{12} \end{matrix}]^{T}$ takes the form

s_{12} = D_{\sec (m) - 12} e_{12}

(2)

where $D_{\sec (m) - 12}$ is the secant stiffness of the matrix in the local 1–2 coordinate system and it is related to $D_{\sec (m)}$ (stiffness in X–Y coordinate system) by

D_{\sec (m)} = T_{ε}^{T} D_{\sec (m) - 12} T_{ε}

(3)

where $T_{ε}$ is strain transformation matrix.

The equivalent uniaxial stress–strain diagram adopted for the matrix is shown in Figure 1(b) and the equivalent tensile strength $X_{m, eq}^{T}$ and the equivalent compressive strength $X_{m, eq}^{C}$ of the matrix are obtained from the piecewise continuous failure envelop shown in Figure 2.

Figure 2.

Failure envelop for the matrix.

In this study, the fictitious fibres are assumed to be only in X-direction, accordingly

D_{\sec (r)} = D_{\sec (rX)} = ρ_{X} E_{(rX)} [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{matrix}]

(4)

where $D_{\sec (r X)}$ and $ρ_{X}$ , respectively, denote the stiffness matrix and proportions of fictitious reinforcements in X-direction and $E_{(r X)}$ is the secant modulus (Figure 3) of the fibres in X-direction.

Figure 3.

Uniaxial stress–strain relationship adopted for the fictitious fibres.

In essence, timber is a fully orthotropic material with different material properties in longitudinal, transverse and radial directions. However, when biaxial stress states such as two-dimensional (2D) cases are concerned, the behaviour of timber can be considered as transversely isotropic and accordingly, timber can be characterised by six material properties, that is, compressive strength parallel-to-grain $X^{C}$ , tensile strength parallel-to-grain $X^{T}$ , compressive strength perpendicular-to-grain $Y^{C}$ , tensile strength perpendicular-to-grain $Y^{T}$ , modulus of elasticity parallel-to-grain $E_{X}$ and perpendicular-to-grain $E_{Y}$ (AS/NZS4063.1:2010, 2010; ASTM-D143-09:2009, 2009; BS-EN-408:2010, 2010). Accordingly, the adopted timber model is calibrated against these six mechanical properties, assuming perfect bond between the fibres and matrix in conjunction with equilibrium and compatibility equations

X_{m}^{T} = Y^{T}, X_{m}^{C} = Y^{C} : Matrix

(5a)

X_{r}^{T} = \frac{X^{T} - Y^{T}}{ρ_{X}}, X_{r}^{C} = \frac{X^{C} - Y^{C}}{ρ_{X}} : fibres in X - direction

(5b)

Similarly, equation (5) establishes the relationship between the modulus of elasticity of timber, matrix and fibres. Further details on computer implementation and calibration of timber constitutive law can be found in Valipour et al. (2014).

Concrete

In the FE models, the concrete is modelled using a 2D hypo-elastic constitutive law recast in the framework of a total secant damage formulation and equivalent uniaxial stress–strain concept. This concrete constitutive law is similar to so-called SBETA model incorporated to commercial software ATENA (2012) and validated in previous studies (Valipour and Foster, 2010). A piecewise continuous failure envelop, as shown in Figure 2, is employed to calculate the equivalent uniaxial compressive and tensile strength and failure of concrete under biaxial stress states and the equivalent uniaxial strain (in the i-direction), $ε_{i, eq}$ , is calculated from (Valipour and Foster, 2010)

ε_{i, e q} = \frac{1}{1 - υ^{2}} (ε_{i} + υ \sqrt{\frac{E_{j}}{E_{i}}} ε_{j}), (i \neq j) i, j = 1, 2

(6)

where $E_{i (j)}$ and $ε_{i (j)}$ are the secant moduli of elasticity and strains corresponding with directions $i (j)$ , respectively; υ is the Poisson’s ratio and it is taken as υ₀ = 0.2, for the compression–compression state (third quadrant in Figure 2) and for the other states it is reduced by

v = {\begin{matrix} v_{0} (1 - ε_{1 (2), eq} / ε_{ut}) & ε_{t} \leq ε_{1 (2)} \leq ε_{ut} \\ 0 & ε_{ut} \leq ε_{1 (2)} \end{matrix}

(7)

The equivalent uniaxial stress–strain diagram adopted for concrete is shown in Figure 1(b) (tensile strains taken as positive). The details on formulation and computer implementation of the adopted concrete constitutive law can be found in Valipour and Foster (2010).

Contact/interface

In the FE modelling of TCC floors, the discrete connections between timber beams and concrete slabs can be modelled by nonlinear lumped springs (Khorsandnia et al., 2014b); however, this approach can lead to numerical instability and premature failure of connections due to stress concentrations at the location of lumped springs. Accordingly, in this study, the connection between timber beam and concrete slab (Figure 4(a)) is modelled by nonlinear contact elements (distributed springs) with idealised rigid–elastic–perfect plastic behaviour (Figure 4(b)) in the tangential direction and linear elastic springs with K_nn = 2 × 10⁸ MN/m³ in the direction normal to the slab-to-timber beam interface. Assuming that the push-out test results for the TCC connection are available and the spacing between the connectors is s, the value for τ₀ and τ_y in Figure 4(b) can be obtained by dividing the corresponding shear force from the push-out test results by the spacing of connectors, s.

Figure 4.

(a) Schematic outline of the location of contacts/interfaces, (b) idealised shear force versus slip for tangential contact springs representing concrete slab-to-timber beam (TCC) connections and (c) contact law for ductile jointed timber beam-to-column and column-to-footing connection in the normal and tangential to the interface directions.

In the developed FE models, behaviour of ductile jointed beam-to-column and column-to-foundation connections is modelled by interface (contact) elements. The contact elements used for modelling ductile jointed connection (see Figure 4(c)) are characterised by three parameters including a coefficient of friction µ, the normal stiffness of interface K_nn and tangential stiffness of interface K_tt. The normal and tangential stiffness of interface elements are linear elastic (Figure 4(c); however, in the tangential direction, a cut-off shear resistance (τ = µσ) based on Coulomb friction law is introduced to capture the possible shear sliding along the interface (Figure 4(c)). The coefficient of friction typically depends on applied load, velocity and direction of motion (Newcombe, 2007); however, in the absence of reliable experimental data, a constant coefficient of friction is considered in this study. For timber–steel and timber–timber iinterfaces a value of µ = 0.4 (Meng et al., 2008) and for timber–concrete interface a value of µ = 0.6 (Dias, 2004) are assumed in this study.

Element formulation

The commercial software ATENA is employed for implementing all the FE models in this article. Nine-node quadrilateral isoparametric Lagrangian elements with reduced Gauss integration scheme are employed to model timber beam, concrete slab, steel plates and other planar structural components. The reinforcing bars and PT cables are modelled by three-node truss element with quadratic interpolation and Gauss two-point integration scheme (Zienkiewicz and Taylor, 2000). The interface element used for modelling contact is also a three-node quadratic element derived from the corresponding isoparametric elements, and a penalty method is employed for contact analysis and determining the opening/closing states of the interface. Moreover, the effect of geometrical nonlinearities is incorporated into the FE formulation using Update Lagrangian approach (Belytschko et al., 2000).

In the FE models, the mesh sensitivity and lack of objectivity associated with softening of timber and concrete are treated by preserving the constant fracture energy G_f and subsequently adjusting the softening part of the stress–strain relationship with respect to element sizes (Bazant and Oh, 1983; Valipour et al., 2014).

Validation of FE models

FE analysis of ductile jointed timber subassemblies

The proposed FE model is employed to evaluate the behaviour of PT structural LVL timber elements. Two different types of PT members including box column and beam–column subassemblies are analysed to demonstrate the adequacy of the proposed continuum-based FE models for capturing the response of PT timber frames. The members considered herein have been tested by Newcombe (2007) and evaluated using section analysis procedures (Newcombe et al., 2008).

The outline of geometry, dimensions and cross-section of tested members (i.e. column and beam–column subassemblies) are shown in Figure 5. The beam–column subassemblies were made of HySpan LVL, but column subassemblies were made of Hy90 LVL (all produced in New Zealand). The material characteristics of dry HySpan and Hy90 LVL according to manufacturer technical note are given in Table 1. The stress–strain relationships of HySpan LVL obtained from direct compression test in the direction parallel-to-grain are shown in Figure 6(a) which clearly demonstrates the sensitivity of the compression test results with respect to gauge length (i.e. end effect (Newcombe, 2007)). Accordingly, in the FE analysis, an idealised stress–strain relationship (Figure 6(a)) for timber under compression was considered and calibrated against experimental data. In the idealised model, compressive strength of HySpan LVL in the direction parallel-to-grain was taken 48 MPa (slightly higher than 45 MPa given in Table 1) and strain corresponding with the compressive strength in the direction parallel-to-grain was taken ε_c₀ = 0007. The maximum size of the elements in the developed FE model was limited to 20 mm.

Figure 5.

Outline of geometry, cross-sectional view and test set up for (a) column and (b) beam–column subassemblies tested by Newcombe (2007).

Table 1.

Material characteristics of dry HySpan and Hy90 LVL according to manufacturer technical note.

LVL type	Direction	Compressive strength (MPa)	Tensile strength (MPa)	Modulus of elasticity (GPa)	Modulus of rigidity (MPa)
HySpan	Parallel-to-grain	45 (48)^a	33	13.2	660
HySpan	Perpendicular-to-grain	12	–	–	660
Hy90	Parallel-to-grain	28	19	9.0	475
Hy90	Perpendicular-to-grain	10	–	–	475

Adopted value in the FE analysis which obtained from calibration of an idealised stress–strain relationship against experimental data.

Figure 6.

Comparison between experimental and idealised stress–strain relationships for (a) HySpan LVL under compression parallel-to-grain and (b) internal energy dissipater (mild steel bar).

PT cables used in these type of beams are made of high-strength steel with estimated yield strength of f_py = 1530 MPa. The area and location of PT cables and stress induced in the PT cables for all specimens are given in Table 2. In addition, a rocking mechanism was installed in beam–column subassembly no. 6, consisting of an epoxy glued internal energy dissipater made of mild steel bars. The energy dissipaters had characteristic yield strength of 300 MPa. In Figure 6(b), the experimental stress–strain relationship of mild steel bars obtained from a direct tension test is compared with idealised linear elastic–plastic hardening material model that adopted in the FE analyses. A model developed by Menegotto and Pinto (1973) is used for modelling the behaviour of energy dissipaters (embedded mild steel bars) under cyclic loading and in the absence of a reliable cyclic bond model, the bond between embedded steel bars and timber is assumed to be perfect.

Table 2.

Characteristics of post-tensioning cables and internal energy dissipaters.

Specimen type	No.	Post-tensioning cables^a			Internal energy dissipater^b
Specimen type	No.	Stress (MPa)	Area (mm²)	e (mm)	Area (mm²)	x_d (mm)
Column subassembly	1	550	2 × 99	168	–	–
Column subassembly	2	735	2 × 99	168	–	–
Beam–column subassembly	3	918	1 × 99	Centroid of beam	–	–
Beam–column subassembly	6	1209	1 × 99	Centroid of beam	78.6	50

Post-tensioning strands were made of high-strength steel with E = 197 GPa (modulus of elasticity) and f_py = 1530 MPa (conservatively estimated initial yield strength).

Internal energy dissipaters were made of mild steel bars with characteristic yield strength of f_y = 300 MPa.

The lateral load versus drift and the axial load in the PT cables versus drift for the column and beam–column subassemblies are, respectively, shown in Figures 7 and 8. Overall, the numerically predicted results are in good agreement with experimental data for self-centring subassemblies with and without internal energy dissipaters. For beam–column no. 6 with internal energy dissipaters, the size of hysteresis loops for axial PT load versus drift has been slightly overestimated by the FE model and in part, this can be attributed to the assumption of perfect bond between mild steel bars (dissipaters) and timber as well as adopted material model for mild steel under cyclic load. In addition, normalised neutral axis (NA) depth (depth of NA over beam depth) versus drift for beam–column subassemblies 2 and 3 is shown in Figure 9 and it was observed that the depth of NA predicted by the FE model at drifts larger than 2% correlates reasonably well with the depth of NA estimated from experimental data. The overestimation of location of NA at drifts less than 2% (Figure 9) could be attributed to stiffness of contact/interface as well as adopted values for elastic modulus of timber in the direction perpendicular-to-grain.

Figure 7.

Lateral load versus drift and axial load of the post-tensioning cables versus drift for column subassemblies (a) no. 1 and (b) no. 2.

Figure 8.

Lateral load versus drift and axial load of the post-tensioning cables versus drift for beam–column subassemblies (a) no. 3 and (b) no. 6.

Figure 9.

Normalised neutral axis depth versus drift for beam–column subassembly (a) no. 2 and (b) no. 3.

FE analysis of ductile jointed timber frames

In this example, a two-bay three-storey frame tested by Pino (2011) is analysed. The frame has been tested three times corresponding with different levels of PT force, P = 17, 29 and 44 kN. The outline of geometry, dimensions and cross-section of beams and columns is shown in Figure 10. The entire frame was made of LVL with specifications given in Table 3. Furthermore, in the FE models, strain corresponding with the compressive strength in the direction parallel-to-grain was taken ε_c₀ = 0.007. The timber frame is modelled and analysed using quadrilateral elements. Since the frame has smaller size (i.e. scaled-down specimen) than the full-scale subassemblies tested by Newcombe (2007), a smaller mesh size with maximum 15 mm elements is considered.

Figure 10.

Outline of geometry, dimensions, cross-sectional view and test set up for the post-tensioned timber frame tested by Pino (2011).

Table 3.

Material characteristics of LVL used in Pino’s (2011) test.

Direction	Compressive strength (MPa)	Tensile strength (MPa)	Modulus of elasticity (GPa)	Modulus of rigidity (MPa)
Parallel-to-grain	35	22	10.7	500
Perpendicular-to-grain	12	–	1.5	500

The lateral load versus drift and the axial load in the PT cables versus drift for the tested frame with 29 kN and 44 kN PT force are shown in Figure 11. It is observed that FE model results are in good agreement with experimental data. Furthermore, the contour of σ_xx stresses and pattern of damage (due to crushing) on the column surface at 4.5% drift is shown in Figure 12. The small damaged zone at the beam–column interface predicted by FE model is consistent with experimental observations (Newcombe, 2007). It is noteworthy that in the FE model, the first sign of damage in the column was observed at 4.4%–4.5% drift and no sign of timber crushing was observed in the column at lower drift levels. These two examples demonstrate the accuracy of the adopted FE models for capturing nonlinear local and global response of the timber frames with ductile jointed connections.

Figure 11.

Lateral load versus drift and axial load of the post-tensioning cables versus drift for the frame with (a) P = 29 kN and (b) P = 44 kN initial post-tensioning force.

Figure 12.

Contour of σ_xx stress (MPa) and crushing damage in the column at the beam–column interface (drift = 4.5%).

FE analysis of TCC beam

The developed FE model is also employed to analyse beam B-NS tested earlier under service loads (Khorsandnia et al., 2012). The beam is a simply supported TCC beam with the low composite efficiency provided by normal screws as the connection between timber joist and concrete slab. The ultimate response of the beam was predicted by application of Hashin’s failure criteria and plastic-damage constitutive law for timber and concrete, respectively (Khorsandnia et al., 2014a). For the developed model in this study, the strain corresponding with the compressive strength was taken as 0.008 and 0.003 for timber and concrete, respectively. The maximum mesh size of 20 mm with quadrilateral elements was used for both timber joist and concrete slab.

The load versus mid-span deflection of the beam is shown in Figure 13. It is seen that the developed model in this study not only has a good agreement with the test results under service loads, but also correlates very well with other FE model predictions (Khorsandnia et al., 2014a). This example demonstrates the accuracy of proposed modelling strategy and material models for capturing the global response of TCC beams up to failure loads.

Figure 13.

Load versus mid-span deflection of TCC beam B-NS (Khorsandnia et al., 2014a).

Parametric study

The frame tested by Pino (2011) with 44 kN PT force (Figure 10) is used in the parametric study. First, the sensitivity of the failure mode and global response of the ductile jointed timber frame with respect to timber modulus of elasticity and compressive strength in the direction perpendicular-to-grain is studied. The frame tested by Pino (2011) (Figure 10) was analysed assuming three different values for parallel-to-grain elastic modulus (i.e. 9.0, 10.7 and 12.0 GPa), perpendicular-to-grain compressive strength (i.e. 10, 12 and 14 MPa) and perpendicular-to-grain modulus of elasticity (i.e. E₀, 1.2 E₀ and 1.4 E₀, where E₀ = 1.5 GPa) of timber. The load versus drift response and extent of damage within the beam–column joint are shown in Figures 14 and 15, respectively. It is seen that parallel-to-grain modulus of elasticity of timber can directly affect the load–drift response, whereas perpendicular-to-grain compressive strength and modulus of elasticity of timber have minor influence on the load–drift response. Furthermore, as shown in Figure 15, the extent of damage within the beam–column joint can be influenced by the compressive strength of timber in the direction perpendicular-to-grain.

Figure 14.

Sensitivity of lateral load versus drift response with respect to (a) parallel-to-grain modulus of elasticity, (b) perpendicular-to-grain compressive strength and (c) perpendicular-to-grain modulus of elasticity.

Figure 15.

Crushing damage in the column at the beam–column interface assuming compressive strength perpendicular-to-grain: (a) 10 MPa and (b) 14 MPa.

The experimental data on the structural behaviour of TCC and timber–timber composite (TTC) frames with PT beam-to-column joints are scarce (Moroder et al., 2013). Accordingly, in the second part of the parametric study, the influence of concrete slab and its thickness, the effects of TCC connection stiffness (i.e. partial and full composite action) and concrete slab-to-column construction details (see Figure 16) on the lateral load–drift response and failure mode of the TCC frames with ductile jointed connection are investigated. The scaled frame tested by Pino (2011) is used in this parametric study and the adopted thickness of the concrete slab was also scaled with respect to the size of the adopted timber frame (Pino, 2011).

Figure 16.

Different types of concrete slab-to-column connection considered in the parametric study (reinforcing proportion in the slab ρ = 0.4%).

A 30-mm thick RC slab with reinforcing proportion of ρ = 0.4% was assumed to be attached to the timber beams of the frame tested by Pino (2011) (Figure 10). Based on the results obtained from earlier push-out test on normal screw connections (Khorsandnia et al., 2012), the initial shear strength and the yield strength of connection are assumed as τ₀ = 10 and τ_y = 20 N/mm, respectively (Figures 4(b) and 17). A sensitivity analysis showed that the overall response of the TCC beam is not significantly influenced by the yield strength (τ_y) and a value between 20 and 30 N/mm can be adopted. Furthermore, the slip corresponding with the yield strength of the connection was taken δ_y = 6 mm (Figures 4(b) and 17). The adopted values for τ₀, τ_y and δ_y in conjunction with the rigid-elastic-perfectly plastic model can adequately represent the behaviour of TCC joints with normal screws and weak partial shear interaction (Khorsandnia et al., 2012). The lateral load versus drift response of the TCC frame, assuming different types of details for slab-to-column connection (Figure 16), was obtained from the developed FE models, and the results for TCC frames with full, medium to strong partial interaction and weak partial composite action are shown in Figure 18. It is seen that the construction details of concrete slab-to-column connection (Figure 16) can significantly affect the lateral load versus drift response of the frames with PT beam-to-column joints. However, the stiffness of TCC connection has negligible influence on the drift response of the frames when a medium to strong composite action between concrete slab and timber beams has been provided (Figure 18(a) and (b)).

Figure 17.

Shear-slip behaviour of normal screw connection tested by Khorsandnia et al. (2012): (a) fitted model based on push-out test results and (b) adopted model in this study.

Figure 18.

Sensitivity of lateral load versus drift response with respect to details of slab-to-column connection for post-tensioned TCC frame with (a) full, (b) medium partial and (c) weak partial composite action.

The extent and pattern of damage and failure mode in the column at the beam–column interface of the TCC frame with partial composite action (at a drift = 4.5%) is shown in Figure 19. With regard to the FE predictions, it can be concluded that the construction details of concrete slab-to-column connection can dramatically affect the mode of failure and extent of damage in the beam-to-column joint region of the ductile jointed TCC frames. More specifically, when the slab is connected to (or in contact with) the timber column (i.e. Details-1 and Details-2 in Figure 16), the extent of damage in the beam-to-column joint (at the drift of 4.5%) will be greater than the case in which there is a gap between concrete slab and timber column.

Figure 19.

Pattern of damage in the column at the beam–column interface for the post-tensioned TCC frame with partial composite action and different slab-to-column connection details (drift = 4.5%).

The lateral load versus drift and cable axial force versus drift response of the partial composite TCC frame with Detail-2 for slab-to-column connection and assuming three different thicknesses for the concrete slab (i.e. 30, 50 and 70 mm) are shown in Figure 20. Since the analysed frame is a scaled-down specimen, the adopted concrete slab depths, that is, 30, 50 and 70 mm, represent normal, thick and extremely thick slabs in real structures, respectively. It is seen that the slab to timber beam depth ratio (i.e. h_s/h_b) can significantly affect the drift response of PT TCC frames (Figure 20(a)), where the slab has interaction with timber column through direct contact (see Detail-2 in Figure 16). Moreover, it is seen that the presence and thickness of slab have negligible influence on the axial force induced in the PT cables at different drift levels (Figure 20(b)).

Figure 20.

(a) Lateral load versus drift response and (b) cable axial force versus drift, with respect to concrete slab over timber beam depth ratio (h_s/h_b), assuming direct interaction between slab and column through contact (namely Detail-2) for the TCC frame with partial composite action.

Conclusion and discussions

In the absence of reliable experimental data on local and global behaviour of ductile jointed TCC frames subjected to lateral loads, this article focuses on development and application of nonlinear 2D (plane stress) continuum-based FE models to investigate the behaviour and failure mode of TCC frames with PT beam-to-column connections. The adopted constitutive laws for modelling nonlinear behaviour and failure of timber and concrete under biaxial stress states are briefly discussed, and outline of the FE models such as contact properties, element types and formulations is provided. The developed FE models are verified against available experimental results of PT timber frames (without concrete slab) and the validated analytical tool is employed to undertake a parametric study and predict the response of timber and TCC frame with ductile jointed connections. The following conclusions are drawn from the results of FE analyses:

The modulus of elasticity and compressive strength of timber can affect the response of the frame at both local and global levels; particularly, the extent of damage within the beam–column joint is sensitive to compressive strength of timber in the direction perpendicular-to-grain.

The details of concrete slab-to-timber column connection can dramatically affect the lateral load versus drift response and failure mode. In particular, direct contact/connection between concrete slab and timber column can significantly increase the lateral stiffness of PT frames and lead to unpredicted damage in the beam-to-column joint zone.

The stiffness (i.e. partial or full composite action) of TCC connection has minor influence on the lateral load–drift response of the TCC frames with PT beam-to-column connections, when a medium to strong composite action between the concrete slab and timber beam has been provided. This observation is in marked contrast to the common perception about the significant influence of TCC connection stiffness on the load–deflection response of TCC beams subject to gravity loads.

The lateral stiffness and drift of the TCC frame are sensitive to the thickness of concrete slab when the slabs have direct contact (or connection) with the timber columns. However, the influence of slab thickness on the axial force induced in the PT cables is negligible (less than 5% difference for the cases considered in this study, with concrete slab over timber beam depth ratio of h_s/h_b = 0.2–0.5).

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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