Simulation of Load–Slip Capacity of Timber–Concrete Connections with Dowel-Type Fasteners

Abstract

Quality assessment of stiffness and load-carrying capacity of composite connections is of great importance when it comes to designing timber–concrete composite structures. The new European regulation intended explicitly for timber–concrete structures has made a significant contribution to this field, considering that until today there was no adequate design standard. Due to the proposed general expressions for determining the stiffness and load-carrying capacity of composite connections made with dowel-type fasteners, which are incapable of describing most of the commonly applied fasteners, engineering, and scientific practice remained deprived of a quality assessment of the essential mechanical properties of the connection. In order to overcome this problem, this paper proposes a numerical model of the connection suitable for determining the whole load–slip curve, allowing it to estimate the stiffness and load-carrying capacity of the connection. The model was developed by considering the non-linear behavior of timber and fasteners, which is determined through simple experimental tests. For the numerical model validation, experimental tests were carried out at the level of the applied materials and on the models of the composite connection. Through numerical simulations, analysis of obtained results, and comparison with experimental values, it can be confirmed that it is possible to simulate the pronounced non-linear behavior of the timber–concrete connection using the proposed model. The estimated values of stiffness and load-carrying capacity are in agreement with the conducted experimental testing. At the same time, the deviations are much less than the ones obtained from recommendations given by the new regulation. Additionally, apart from evaluating the value and the simulation of the complete curve, it is possible to determine local effects, such as the crushing depth in timber and concrete, the fastener’s rotation, and the participation of forces in the final capacity of the connection.

1. Introduction

In the last few decades, the worldwide interest in timber–concrete composite (TCC) structures has increased because of their structural benefits, i.e., more rational construction is obtained, where a high degree of utilization of both materials can be achieved [1]. It is an adequate solution for renovating old timber floors and is suitable for new structures, such as floors and walls in buildings and timber bridge decks [2]. TCC elements usually comprise thin concrete plates connected to timber beams with shear connectors (dowel-type fasteners, steel-punched metal plates, split rings and toothed plates, notches, glued-in plates, notches with dowel-type fasteners) [3]. The function of a shear connection is to transfer shear forces between timber and concrete and prevent transverse separation. Under bending action, when mechanical fasteners (dowel-type fasteners) are used, adjacent layers of composite systems slide relative to each other in a partially constrained manner, and only partial composite action is developed. The behavior of TCC structures is quite complex because their analysis requires the consideration of the slip between timber and concrete [4].

The design of timber–concrete composite structures is based on the assumptions of the elastic coupling theory, which takes into account the slip between two materials [5]. Displacement/slip in the connection, i.e., the flexibility of the fasteners (stiffness of the connection), is introduced into the calculation using the value of the slip modulus. The efficiency of TCC structures is related to the quality of the connection system (through the stiffness of the connection) because their behavior directly affects the distribution of internal forces and structural deformations. Additionally, apart from stiffness, the load-carrying capacity of the fasteners, which ensures the transfer of shear forces in the shear plane, plays an essential role in the composite connection.

Ideally, the analysis of composite beams should be based on experimental load–slip curves that describe the complete behavior of the composite connection. However, the behavior of the connection is usually represented by a limited number of properties based on experimental curves, which are expected to represent the actual behavior of the connection. These properties are stiffness and load-carrying capacity. Therefore, the behavior of connections is most often described by a bilinear load–slip relationship, defined by the slip modulus (initial part) and the load-carrying capacity of the fasteners (final part) [3].

Due to the lack and inadequacy of the provisions in the existing regulations used in this field, Eurocode 5 (EN 1995-1 [6] and EN 1995-2 [7]) and Eurocode 4 (EN 1994-1 [8]), there was a necessity for an adequate standard, which resulted in CEN/TS 19103 [9], explicitly intended for TCC structures. It made a significant contribution to this field, considering that, so far, there was no specific standard for TCC structures. Due to the proposed general assessments (for stiffness and load-carrying capacity), which are incapable of describing most of the frequently used dowel-type fasteners (nails, screws, bolts, dowels, and rods), only some observations that were not considered in the proposed expressions are given below. According to CEN/TS 19103, the evaluation of the connection stiffness (slip modulus K_ser) for all considered dowel-type fasteners is still determined as a double value of the slip modulus given by empirical expressions for steel-timber connections, neglecting deformations in concrete [1]. It should also be noted that CEN/TS 19103 expressions were developed for the ductile type of failure, i.e., only for the case where two plastic hinges are formed in the fastener, with an empirically based approximation of the instantaneous deformation at 40% of the load-carrying capacity of the nailed connection [10]. According to [11], the slip modulus is a function of the fastener embedment depth in timber. Different failure modes result in different values of the slip modulus for different embedment depths. When considering the different types of concrete, such as normal weight concrete (NC) and lightweight aggregate concrete (LWAC), in accordance with CEN/TS 19103, the proposed expressions for LWAC concrete may lead to an inaccurate estimation of the slip modulus value [12,13] since local failure effects in concrete are not considered. On the other hand, in expressions for the load-carrying capacity of connections (F_v,R), different types of mode failure are taken into account by using expressions for timber–timber connections, with the approximation of the deformation in concrete based on the local strength of the concrete through a coefficient β [3]. In this way, the influence of local failure effects on the concrete side on the load-carrying capacity of the connection (local crushing of concrete) was only partially assessed. In contrast, the effects of pull-out [13] and cone expulsion [14] for the fasteners with heads were not considered, which indicates that LWAC concretes are not fully covered. When determining the connection load-carrying capacity, the rope effect contribution is considered in increasing the connection load-carrying capacity through the timber withdrawal capacity, provided that the fasteners are anchored adequately in concrete and ensured respecting the provisions of EN 1992 [15]. The general assessment proposed through empirical expressions in CEN/TS 19103 cannot comprehensively describe the behavior of a wide range of timber–concrete connections when different types of dowel fasteners and types of concrete are used. Due to the observation mentioned above, it is reasonable to expect that, in the next generation of CEN/TS 19103, a division will be made for different types of fasteners and consideration of the influence of local failure effects in concrete, which will affect the innovation and expansion of expressions for evaluating stiffness and load-carrying capacity. In the lack of appropriate proposals, engineering practice is always left with the possibility of evaluating the properties of composite connections via experimental tests or consulting the available applicable literature.

In a linear analysis of composite beams, stresses and deformations are usually calculated based on the linear elastic behavior of materials and connections. Based on these assumptions, for most practical problems, linear models offer sufficient accuracy and reliability, decreasing the need for more complex non-linear models. When timber–concrete connections are assembled with dowel-type fasteners, due to their pronounced non-linear behavior, assumptions about the linear elastic behavior of the connections and materials do not provide the possibility of including non-linear phenomena (the elastic non-linearity and the plastic deformation capacity of the joint) and can lead to non-conservative results. In order to overcome this problem, non-linear analyses have been increasingly used, taking into account the non-linear behavior of the connections and materials [16,17,18,19]. Therefore, the behavior of composite connections with dowel-type fasteners cannot be represented by a simple relation as an ideal elastoplastic behavior that is described only by the fastener’s slip modulus and load-carrying capacity. This problem is precisely the weakness of numerical models for non-linear analysis. It is essential to use more sophisticated models that could describe the non-linear behavior of the timber–concrete connection and define the whole load–slip curve (e.g., finite element (FE) models [20,21,22,23]).

Due to the necessity for numerical simulations of composite beams and considering the pronounced non-linear behavior of connections in relation to complex FE models, most research was based on the development of analytical models for determining complete load–slip curves [24]. These models are based on exponential functions, which were mainly developed to describe the behavior of timber [25], fasteners [26], and timber connections. However, due to their wide application in other fields, the possibility of their application in timber–concrete connections as descriptive models were also proposed [27,28,29,30,31]. The limitation of the models is the finite number of parameters (stiffness and load-carrying capacity), previously adjusted to experimental values, which describe the mechanical behavior of the composite connection. To overcome this problem and to reduce the extent of experimental tests, Dias [28] applied empirical expressions for K_ser and F_v,R from Eurocode 5 in the models and enabled a more comprehensive application of descriptive models for timber–concrete connections made with dowel-type fasteners. Based on the material and geometric properties of the connection, predictive models were mainly developed in the wooden connections field [32,33,34,35], while such models do not exist for timber–concrete connections. Researchers Heine and Dolan [36], Laszlo Erdodi [37], Dominguez [38], and Kobel [39] made outstanding contributions to the characterization of timber connections. They proposed numerical predictive models to determine the whole load–slip curve based on the European Yield Model (EYM), taking into account the non-linear behavior of the timber and the fastener (determined from experimental tests). These models have shown very good results and, with certain modifications, could also be suitable in the case of timber–concrete connections.

In order to adequately predict pronounced non-linear behavior and to evaluate the mechanical properties of the composite connection required for the calculation of the TCC structures, a novel approach is needed. Therefore, there is a need for a non-linear connection model that will cover most of the abovementioned problems. This paper presents a suitable numerical model for describing the complete load–slip curve. The model is based on the mechanical characteristics of timber, concrete, and fasteners and includes the non-linear behavior of composite connections. The proposed model describes the complete behavior of the composite connection. It was developed so that instead of the assumed idealized behavior of the applied materials, their non-linear behavior is taken into account, which was determined by simple experimental tests.

2. Proposed Numerical Model

Apart from the model proposed by Dias [28], which is descriptive, no model has been developed that predicts the load–slip relationship over the entire domain in timber–concrete connections based on the material and geometric characteristics of the connection. Therefore, those above-mentioned predictive numerical models [36,37,38,39] represent the basis for the formation of a new model.

2.1. Background Theory of the Numerical Model

The EYM is a commonly accepted procedure for determining the capacity of timber connections based on the yield theory assumptions that consider the rigid-plastic behavior of the fasteners and timber. It represents the equilibrium conditions on an isolated segment of the fastener for possible types of failure in the connection. It implies that the failure of the connection is ductile and caused by the yield of the fastener or timber failure. Requirements for minimum dimensions of timber elements as minimum edge and spacing distances of fasteners usually guarantee this condition. It should also be noted that the load-carrying capacity of the connection determined by the EYM represents the final value of the capacity of the connection at failure caused by the yield of the fastener and timber failure. This theory does not cover the gradual development of timber and fastener damage, so quantifying displacement is impossible.

Additionally, the EYM theory implies a specific state when a failure in the connection occurs, i.e., a condition in which the simultaneous formation of plastic hinges and yield of timber and crushing of concrete arise under the assumption shown in Figure 1a. For a particular type of connection failure (failure modes), the EYM determines the position of the maximum moments in the fastener, which also represents the location of the plastic hinges or the location of the fastener rotation. Based on the assumed development of the connection failure (Figure 1a), it is possible to determine the complete load–slip curve (F_v,R-δ) on the considered displacement domain (Figure 1b).

As the failure modes are correlated with the geometrical characteristics of the connection and the mechanical properties of the timber and the fastener, it is possible to predict the failure mode that will occur (Figure 2).

In the case when the connection is assembled with different materials (represented by the embedment strength of the materials f_h,t ≠ f_h,c), the transition from Mode II to Mode III must satisfy the requirements regarding the embedment depth of the screw in timber (l_t,req) and concrete (l_c,req) [40]:

$$l_t\ge l_{t,req}=1.15·\left(2·\sqrt{\frac{\beta }{1+\beta }}+2\right)·\sqrt{\frac{M_y}{f_{h,t}·d}}$$

(1)

$$l_c\ge l_{c,req}=1.15·\left(\frac{2}{\sqrt{1+\beta }}+2\right)·\sqrt{\frac{M_y}{f_{h,c}·d}}$$

(2)

By using timber screws, the effect of the screw thread in timber provides a certain degree of anchoring, which creates the rope effect (Figure 3), i.e., due to the slip in the connection and prevented extraction of the screw from timber, a tensioning force occurs in the screw. Prevented extraction of the screw leads to the adhesion of timber and concrete, and an additional normal force, H_t, occurs at the contact, where its horizontal component (μ·H_t) contributes to an increase in the load-carrying capacity of the connection. Due to the tension force in the screw F_ax(θ), its horizontal component also contributes to an increase in the load-carrying capacity of the connection by activating a larger timber crushing zone (outside the plastic hinges zone). In CEN/TS 19103, the contribution of the rope effect to an increase in the load capacity of fasteners (where anchoring is provided) is considered according to the recommendation given in Eurodoce 5 (8.2.2(2)), i.e., as an additional force F_rope (min{F_ax/4;100%·F_Joh}) in relation to the Johansen part (F_Joh), where F_ax is the withdrawal capacity in timber, and 1/4 represents the friction coefficient μ = 0.25 (corresponding to friction between two timber elements) [41]. In the timber–concrete connection, according to experimental tests, the coefficient of friction between concrete and timber is μ = 0.45–0.66 [42,43]. Using the simplified EYM model and based on the experimental tests, Hao Du et al. [44] concluded that the angle of rotation of the screw has a significant part in contributing to the load-carrying capacity due to the rope effect. The coefficient of friction is in the range of 0.35–0.50 (μ = sin(90 − θ)) for an angle θ that varies from 20 to 30 degrees (for the slip in connection up to 15 mm). According to previous experimental research [3], for a slight slip in the connection (below the yield load point), the contribution of the load-carrying capacity due to the rope effect on the connection load-carrying capacity is negligible. On the contrary, when large slips occur, the rope effect significantly increases the final load-carrying capacity. In the expressions according to Eurocode 5, as the rope effect is determined regardless of the angle of the screw rotation, the force contribution due to the rope effect and friction cannot be perceived and determined in the final load-carrying capacity of the connection.

For the model formulation, the following assumptions and approximations were introduced:

• Timber and concrete may be considered deformable bodies into which the fastener is pressed. The fastener rests on a deformable elastic foundation in timber and concrete and can be represented as a beam on which embedded stresses act (f_h,t and f_h,c);
• The gradual development of the position of plastic hinges or the location of rotation of the fastener can be estimated by the EYM model for Mode III, i.e., considering the condition of equilibrium on an isolated screw segment, as shown in Figure 4c;
• It is assumed that the embedment stresses (f_h,t and f_h,c) are uniformly distributed in the zone between the plastic hinges;
• When pressed into timber and concrete, the fastener behaves like a rigid body, except for an infinitesimally small region where plasticization of the fastener (plastic hinge) occurs, around which rotation is achieved. This assumption results in a linear function of displacement in timber and concrete [36,39];
• In the zones outside plastic hinges, the fastener remains in its initial position since, according to EYM, the fastener outside plastic hinges is balanced, while the deformations perpendicular to the axis of the fastener can be ignored;
• The mechanical characteristics of timber (embedment strength in timber → f_h − Δ) and the fastener (fastener yield moment → M_y − θ) are presented through non-linear behavior, i.e., determined experimentally. These characteristics are required to describe the behaviors of timber and the fastener as a function of slip in the shear plane;
• Deformation in concrete is idealized through the ratio β = f_h,c/f_h,t, i.e., through the function of displacement in timber δ_c = δ_t/β, taking into account the deformations in concrete (concrete crushing as a local failure effect adopted as f_h,c = 4·f_c [45]);
• The withdrawal capacity in timber was introduced through a sine function of the angle of rotation of the fastener θ (Equation (3), Figure 3). The withdrawal capacity F_ax,max is determined via experimental testing or obtained using empirical expressions according to Eurocode 5. It only applies to failure modes involving fastener deformation (plastic hinges);

  $$F_{ax}\left(\theta \right)=F_{ax,max}·\sin \left(\theta \right)$$

  (3)
• The fastener is perpendicular to the shear plane;
• Although a plastic barrier (plastic sheet) was placed in order to minimize the effects of friction on the response of the connection and to protect the timber from the influence of moisture from concrete, the effect of friction in the connection (due to rope effect) was introduced into the calculation [43]. The coefficient of friction between timber and concrete adopted in this paper was assumed as μ = 0.45, for the case of applying plastic sheet, according to the suggestion from [43].

2.2. Analytical Procedure and Calculation Technique

The analytical procedure for determining the load-carrying capacity of a connection is divided into four phases:

Phase I—Determination of the failure mode of connection:

Applying Equations (1) and (2) determines the failure mode depending on the required embedment depth l_req. Expressions for the required embedment depth were derived based on the two considered failure modes (Mode II and Mode III), demonstrating the transition from one failure mode to another (Figure 2).

Phase II—Determination of the embedment depth in timber and concrete:

For the obtained failure mode determined in Phase I and using the EYM (taking into account the above simplifications and the equilibrium state on an isolated segment of the fastener), the positions of the maximum bending moments in the fastener are obtained, i.e., the crushing depth in timber b_t (Equation (4)) and concrete b_c = b_t/β, Figure 4. Under the assumption of the rigid-to-plastic behavior of timber and the fastener, the first estimation of the position was determined for the maximum values of the embedment strength (f_h,t,max) and yield moment of the fastener (M_y,max), which should be determined through experimental tests or calculated using the available empirical expressions given in Eurocode 5.

$$b_t=\sqrt{\frac{2·M_y+F_{v,ax}\left(\theta \right)·S}{f_{h,t}·d_{eff}}}·\sqrt{\frac{2·\beta }{1+\beta }}$$

(4)

Phase III—Determination of the angle of rotation of the fastener:

For a given displacement S of the connection, the indentations in timber and concrete (δ_t and δ_c) are determined, as shown in Figure 4a. Based on the calculated indentation values and estimated crushing depths (b_t and b_c from Phase II) in timber and concrete, the angle θ is determined from the geometry of the considered deformed screw and according to the expression given for the angle θ shown in Figure 4a.

Phase IV—Determination of load-carrying capacity of a connection:

As the first estimation for b_t and b_c in Phase II was carried out based on f_h,t,max and M_y,max, in order to estimate the angle θ, the final crushing depths b_tk and b_ck, which are used in Equation (6), must be iteratively determined using experimentally determined functions f_h − Δ and M_y − θ. The final crushing depths b_tk and b_ck are determined using Equation (4) and applying the values determined in Phases II and III. If b_tk and b_ck values differ by more than 1% from the estimated b_t and b_c from Phase II, it is necessary to repeat the determination of the rotation angle, taking the recently calculated values (b_tk and b_ck) as input data for Phase III. Due to the impossibility of including the share of force F_h,ax(θ) in the model due to the unknown displacement in timber outside the plastic hinge, to satisfy the equilibrium condition (Figure 4c), F_h,ax(θ) is added to F_y,R afterward. As tension force occurs in the screw from the beginning, the force at the shear plane F_μ = μ·F_v,ax(θ) represents the share of friction in the connection. The friction force does not affect the moment equilibrium, which implies that F_μ can be added to F_y,R afterward. The load-carrying capacity of the connection is determined according to Equations (5) and (6).

$$F_{v,R}=F_{y,R}+\mu ·F_{v,ax}\left(\theta \right)+F_{h,ax}\left(\theta \right)$$

(5)

$$F_{y,R}=b_{tk}·f_{h,t}·d_{eff}=b_{ck}·\beta ·f_{h,t}·d_{eff}$$

(6)

The above equations represent the algorithm for calculating the load-carrying capacity of a connection for one screw. For obtaining the complete load–slip curve on the entire domain, an iterative procedure must be carried out for predefined displacements S in connection. The maximum displacement δ_max on the considered domain in the proposed model in the amount of 15 mm was adopted according to Dias [28], which stated that for this slip, the maximum load is always reached, and the assumption is only valid for the TCC connection made with dowel-type fasteners. For a more straightforward interpretation of the proposed procedure, a summary of the calculation process can be seen on the flow chart in Figure 5.

3. Materials and Methods

3.1. Material Properties

The first step required to obtain the complete load–slip curve of the connection with the proposed numerical model is the determination of the mechanical properties of applied materials. Based on the proposed algorithm, two sets of material properties are needed for the analysis. The first set of material properties refers to the determination of mechanical properties of materials, i.e., the ultimate strength of screw f_u, the withdrawal capacity in timber F_ax, and the compressive strength of concrete f_c. The second set involves determining the non-linear relationship of the embedment in timber (f_h − Δ) and yield bending moment in screw (M_y − θ).

In this paper, shear test specimens were made of timber lag screws 10 mm × 150 mm (DIN 571 hexagon head timber screws, Grade 5.6, as specified by the manufacturer), lightweight aggregate concrete LWAC LC45/50 (density class D1.8) and glulam GL24 h (ρ_m = 477 kg/m³). The structural lightweight concrete was made with a combination of riverbed aggregate (size 0/4 and 8/16 mm) and Liapor HD 1/8 lightweight aggregate incorporating 40% (by volume) of fresh concrete. The hardened concrete had a dry density of 1740 kg/m³, compressive strength of f_c = 55 MPa and modulus of elasticity E = 25.3 GPa. The timber test specimens were tested after conditioning at relative humidity of 65 ± 5% at a constant temperature of 20 ± 2 °C, leading to a timber moisture content of around 12%. Experimental tests were carried out for the first set of material properties, and in

Table 1. Mechanical properties of the first set of materials.

Materials	Properties	Mean Value	No. of Tests	Applied Standard
Glulam GL24h	Axial withdrawal capacity Fax	15,525 N	3	EN 1382 [46]
Concrete LC45/50	Cubic compressive strength fc	55 MPa	3	EN 12390-3 [47]
Screw Φ10/150 mm	Ultimate tensile strength fu	695 MPa	5	EN ISO 6892-1 [48]

, the mechanical characteristics of the materials and the applied test standards are shown.

For the second set of material properties, in order to determine the non-linear relationship between the timber embedment strength f_h − Δ and the yield bending moment of the screw M_y − θ, experimental tests were carried out according to EN 383 [49] and ISO 10984-1 [50], respectively. The test setups are presented in Figure 6a and Figure 7a, respectively.

To determine the embedment strength of timber parallel to grain, according to EN 383, the dimensions of the timber specimens were 30 × 60 × 140 mm, where the thickness t = 30 mm was adopted to minimize the effect of screw bending during the test. Five specimens were made for this test (Figure 6b). After processing the timber specimens, holes with a diameter d_in of 7 mm were drilled, and screws were inserted into the timber specimens using a wrench. This ensured a direct contact between the core diameter of the screw and timber, as will be achieved in a composite connection.

All timber specimens were monotonically loaded parallel to grain with a preloading cycle, while the load was adjusted following the loading procedure given in EN 383. The load increased or decreased at a constant rate of loading-head movement through a universal hydraulic press with a capacity of 2000 kN (P-250, Milaform-Service, Neftekamsk, Russia). The applied load was controlled using a 50 kN compression load cell with a measurement accuracy of 0.01 kN (CZL312A-5t, SAH Electronics, Belgrade, Serbia). Indentation of screws in timber specimens is measured using a Linear Variable Differential Transformer (LVDT) with a maximum deflection range of 10 mm and an accuracy of 0.01 mm (NOVOTECHNIK TR-0010). The measurement was made at half the timber specimen height, i.e., LVDTs were attached to the external steel arm while its tip rested on a small steel L profile screwed into the timber specimen at the level of the center line of the screw. Simultaneous data acquisition from LVDTs and load cells was conducted at a rate of 10 Hz using the “SPIDER 8” acquisition system. The test was stopped either when the maximum load was reached or when the deformation was 5 mm.

The embedment–slip curves (with labels FH1Z to FH5Z, the same as the name of the tested timber specimens) were obtained from the recorded measurements (load and indentation) and presented in Figure 6c. For the purpose of the proposed numerical model, for all tested embedment–slip curves, the initial slips and preload cycles (from 0.4·F_max,est to 0.1·F_max,est) were cut out from the curves presented in Figure 6c. In this paper, the effective diameter of the screw d_eff = 7.7 mm (d_eff = 1.1·d_in) was used to determine the embedment strength. The reason for taking the effective diameter of the screw arrived from the suggestion given in Eurodoce 5, i.e., in the case of screws, it is necessary to consider the thread’s positive effect using the effective diameter of the screw [51]. When the effective diameter of the screw is considered in the proposed expression for f_h in Eurocode 5 (f_h,EC5 = 36.1 MPa), a better agreement with the experimentally determined mean value of the embedment strength f_h,mean = 35.3 MPa is obtained. Additionally, the same reference diameter of the screw must be used to derive the embedment strength of timber and load-carrying capacity given with Johansen’s expressions [51].

In ISO 10984-1, two suggested methods (Method A and B) are given to determine the yield moment and noted that the choice is left to the user to choose the method, whichever is most relevant. The experimental study conducted in [34] shows significant differences between the two test methods. These differences are reflected in terms of the test setup and determination of the load necessary to determine the yield moment. Within the EN rules of safety, which avoids reaching the actual collapse of connection, the determination of yield moment according to suggested methods leads to the yield moment that lies between the elastic and plastic moment according to the mechanical relationship [52]. This fact indicates that only the outer areas of the cross-section of the screw are under plastic deformation, and the plastic bending moment is only partially utilized in real connections, i.e., the plastic bending capacity of the screw in connection will never reach its maximum values. As mentioned above, for the proposed model, it is essential to determine the real behavior of the yielding moment of the screw in the connection, i.e., the relationship M_y − θ cannot be calculated using a simple empirical expression. Nevertheless, it must be determined in a bending test. For this purpose, both methods can be applied. Depending on the slenderness of the fasteners and the method of estimating the rotation angle, Method B was applied in this paper.

The procedure in accordance with ISO 10984-1 (Method B) was applied to determine the yield bending moment of the screw, via three-point bending test, with a distance of supports equal to L₀ = 80 mm (Figure 7b). The test was carried out on 5 specimens, where the force was applied at a speed of 2 mm/min. Using recorded data of the screw displacement in the middle of the span u and the applied force P, the relationships M_y − θ (with labels My1 to My5, for all tested screws, Figure 7c) were determined according to Equation (7) for the yield moment, and Equation (8) for the rotation angle.

In this study, for the comparison with Eurocode 5, the yield bending moment of the screw was obtained using both methods. According to Method B, the yield bending moment M_y,0.05% = 41,369 Nmm was obtained using the yield force P_0.05% = 2.04 kN, determined by the 5% offset method, which uses the core diameter of the screw (d_in = 7 mm) [51]. According to Method A, yield moment M_y,max = 46,613 Nmm was determined based on the maximum force P_max = 2.33 kN. Using the empirical expression (8.14), given in Eurocode 5, the yield moment is M_y,EC5 = 42,071 Nmm (with d_eff = 7.7 mm and f_u = 695 MPa). The deviation of −9.7% in relation to M_y,max is a consequence of the adopted assumption of ultimate strength in bending f_ub = 0.8·f_u used for bolts and dowels in Eurocode 5 [26], while a deviation of −1.7% to M_y,0.05% shows good agreement with experimental one. Based on the yield moment M_y,max, the ultimate strength of the screw from the bending test can be estimated with Equation (9), based on the plastic moment according to the mechanical relationship via assuming full plastification of the screw cross-sections. In Equation (9), the effective screw diameter d_eff is applied [53]. The ultimate strength of the screw in bending was f_ub,max = 612 MPa (~0.9·f_u). The ultimate strength in bending is in the range of the yield strength in tension f_y and ultimate tensile strength f_u. In order to allow a more realistic estimation of the maximum yield moment, if the recommendation according to [54] was adopted (f_ub,eff = 0.9·f_u = 625 MPa, for f_u > 450 MPa), the yield moment M_y,eff = 47,593 Nmm would have a deviation of +2.1%, which is in the interval of the experimentally obtained yield moment (M_y,min = 45,954 Nmm and M_y,max = 47,425 Nmm). The ultimate effective strength of the screw in bending f_ub,eff ≈ f_ub,max agrees with experimental values.

$$M_y=\left(P·L_0\right)/4$$

(7)

$$\theta =2·{\tan }^{-1}\left(\frac{2·u}{L_0}\right)$$

(8)

$$M_{pl}=\left(f_{ub}·d_{eff}{}^3\right)/6 \to f_{ub}=\left(6·M_y\right)/d_{eff}{}^3$$

(9)

3.2. Push-Out Test Specimens, Loading Procedure, and Results

3.2.1. Description of Shear Test Specimens

For the proposed model validation, all push-out composite connection specimens were made according to the materials mentioned in Section 3.1 (Table 1). According to CEN/TS 19103, the suggestion of the specimen configuration, testing protocol, and determination of mechanical properties of the TCC connection is given in Annex C. The suggestion that test specimen dimensions can be defined based on a minimum admissible edge and spacing distances allowed for each specific fastener according to Eurocode 5 is unsuitable for TCC connections. As there are no specific criteria regarding the influence of test specimens on the experimental characterization of a TCC connection, the author of [55] proposed two configurations of the symmetrical type of connection (concrete–timber–concrete and timber–concrete–timber), as well as minimum dimensions of the specimens from the requirements of ductile behavior of the connection. Considering the mentioned problems, in this paper, the dimensions of the timber part of the specimens were derived from the criteria of minimum screw distances according to Eurocode 5, adopted as double the minimum value prescribed for timber connections. The screw distance of at least 150 mm (a₁ ≥ 13·d_eff·n^0.4 = 131 mm) was adopted based on the criterion of the effective number of fasteners in 1 row to provide that n_eff = n = 2 [56]. Doubling the value of minimum distances was adopted in order to ensure that the influence of the group of fasteners, the uneven redistribution of the shear force between the fasteners, and the possible splitting of timber perpendicular to the fibers is avoided, which is implicitly contained by the effective number of fasteners according to Eurocode 5. To ensure the ductile-type failure mode in the connection and the development of two plastic hinges, the embedment depth of the screw in timber must be at least l_t = 9·d_in [11]. Considering the embedment depth of the screw in concrete, the minimum depth must be l_c = 3·d_s [9,57]. According to the recommended values, the screw (Φ10/150 mm) satisfies the minimum installation criteria since the depth in timber was l_t = 100 mm and concrete l_c = 50 mm.

In this study, double shear test specimens were adopted (concrete–timber–concrete), consisting of 1 central timber (160 × 240 × 400 mm) and 2 side concrete (160 × 100 × 400 mm) members connected with 2 timber screws 10 × 150 mm in each shear plane at a distance of 150 mm (Figure 8a). Concrete was reinforced with steel mesh reinforcement Φ4/50 mm in the bottom zone at 20 mm from the timber member (Figure 8b). Three shear test specimens were made for this study (Figure 8c). Before forming the test specimens and placing them in the formwork, the timber member was conditioned at 20 °C/65%, and during the shear test, the timber humidity was 10.9%. After pre-drilling the holes with a core diameter of 7 mm (d_in) in timber, the screws were installed manually with a wrench. A plastic sheet was placed between timber and concrete, which reduces the effects of friction and prevents water penetration into the wood from concrete.

3.2.2. Test Setup and Loading Procedure

Short-term push-out tests were conducted according to EN 26891 [58]. In Figure 9a, the shear test setup is shown. The force was applied to a timber member through a universal hydraulic press with a capacity of 2000 kN (P-250, Milaform-Service, Neftekamsk, Russia). The applied force was controlled using a 200 kN compression load cell with a measurement accuracy of 0.01 kN (CZL110D, SAH Electronics, Belgrade, Serbia). Displacements between timber and concrete were measured using a Linear Variable Differential Transformer (LVDT) with a maximum deflection range of 50 mm and an accuracy of 0.01 mm (SHTSEIKO KTR-50 mm). For each test specimen, two LVDTs were placed near the shear plane to register the displacements as precisely as possible and to observe any uneven movements. The measurement was made at half the model height, i.e., at half the distance between the screws. LVDTs were attached to the timber member of the test specimen, while its tip rested on a small steel L profile screwed into the concrete. Simultaneous data acquisition from LVDTs and load cells was conducted at a rate of 10 Hz using the “SPIDER 8” acquisition system.

The shear tests were conducted based on the loading protocol from EN 26891 (Figure 9b). At first, the test specimens were loaded up to 40% of the estimated ultimate load (F_est). The applied load was kept constant for 30 s. After that, the load was reduced to 10% F_est and kept constant for 30 s. The load was increased to 70% F_est with a rate of 20% F_est per minute. Finally, the displacement control mode was adopted to apply the further load until the occurrence of either failure or a 15 mm displacement.

3.2.3. Push-Out Test Results

Shear test specimens were tested according to a protocol given in EN 26891 that requires the estimated maximum load F_max,est based on which the loading is carried out. In this study, the first test specimen was tested to accurately assess the maximum load (F_max). The other two test specimens were tested according to the adopted loading procedure in Figure 9b. Although the first test specimen was used for a more accurate estimation of the maximum load, using Johansen’s expression for Mode III and experimental values of the mechanical characteristics of the material, the calculated estimated load (in the interval of 40.7 to 55.6 kN) was in agreement with the first tested specimen. As EN 26891 prescribes that the test should be carried out when the ultimate load is reached or when the slip is 15 mm, the first test specimen was tested up to a slip of ~30 mm, while the remaining 2 test specimens were tested up to the slip of 15 mm. This ensures that the maximum capacity is reached and shows the composite connection behavior beyond the proposed slip. The experimentally obtained load–slip curves for all tested specimens (with labels LWAC-1 to LWAC-3) are shown in Figure 10.

To show the failure mode of the screw and the damage to timber and concrete, parts of the timber and concrete were removed after the test. All tested specimens showed ductile behavior, i.e., during the screw indentation in the timber, a maximum embedment strength was reached, and two plastic hinges were formed in the screw (Figure 11a), as was expected at the given outset in the design of specimens to ensure a ductile-type failure of the connection. Although the first specimen was tested for slips beyond 15 mm (Figure 11b), it can be observed that there is no crushing in concrete around the screw, shear failure of the screw, or timber splitting. Figure 11c shows that the screw is pressed into the concrete and that the proposed approximation of neglecting the deformations in concrete is inappropriate. This fact implies that attention should be paid to this assumption, especially when LWAC with lower density classes than D1.6 are applied [12].

4. Validation of the Proposed Numerical Model

4.1. Numerical Simulations

In order to determine and evaluate the behavior of the composite connection using the proposed numerical model, a code was written in MATLAB according to the given algorithm. Based on the experimental curves for the embedment strength of timber and yield moment of the screw, numerical curves for simulations of the TCC connection were formed. Numerical curves for embedment strength f_h − Δ (with labels fh1z to fh5z) were obtained based on the assumption that hardening after the yielding was negligible for the indentations above 5 mm, i.e., the horizontal branch of the curve was added to the experimentally determined curves (Figure 12a). As the experimentally obtained yield moment curves M_y − θ (My1 to My5) are uniform in behavior, the mean curve My-NUM (Figure 12b), with a horizontal branch after the maximum moment, was adopted for the numerical curve of the screw yield moment. Five numerical simulations (with names SIM(fh1z) to SIM(fh5z)) were carried out to validate the proposed model, in which the numerical embedment curves f_h − Δ (fh1z to fh5z) were varied, while the mean curve of the yield moment of the screw M_y − θ (My-NUM) was the same for all simulations. All simulations were carried out up to the slip of 15 mm, and Figure 12c shows superimposed experimentally (LWAC-1 to LWAC-3) and numerically (SIM(fh1z) to SIM(fh5z)) obtained load–slip curves F_v,R − δ to compare the results.

In addition to the numerically determined curves shown in Figure 12c, the following diagrams for simulation 3 (SIM(fh3z)) are superimposed and shown in Figure 13a: b_t (crushing depth in timber), b_c (crushing depth in concrete), θ (screw rotation angle), M_y (yield moment of the screw), and f_h,t (embedment strength in timber) as functions of the connection displacement δ in the shear plane. To perceive the contribution of forces to the increase in the load-carrying capacity of the connection (in addition to the final value F_v,R, and Johansen’s part F_Joh without rope effect), the following contributions of forces are shown in Figure 13b:

• The influence of the axial force in the screw F_ax,f = F_rope′ + F_rope″, where F_rope′ = F_y,R − F_Joh is the force that increases the indentation zone in timber when withdrawal capacity is activated (increasing b_t), while F_rope″ = F_h,ax(θ) is the force that represents a further expansion of the indentation zone beyond the plastic hinge in timber;
• The effect of friction force F_μ = μ·F_v,ax(θ);
• The combined effect of axial and friction forces F_rope = F_ax,f + F_μ, i.e., the “rope effect”.

Observing the local effects in the connection behavior (Figure 13a), it can be seen that after 4 mm of slip, the crushing depth in timber b_t rapidly increases due to the rope effect. In contrast, the crushing depth in concrete is approximately constant b_c = 5 mm (see Figure 12c). The crushing depth b_t, derived from the equilibrium condition, shows the activation of a larger zone of timber that resists the movement/rotation of the screw due to the activation of the axial force and the change in the position of the plastic hinge in timber. In reality, changing the position of the plastic hinge is not possible, and this can be interpreted in a way that the plasticization and the moment increase in the screw spreads in a larger zone around the plastic hinge, which can be seen in Figure 11a,b. Additionally, Figure 11a,b show that even for displacements larger than 15 mm, the position of the plastic hinge remains unchanged and corresponds to a length of 25–35 mm obtained within the numerical simulation. The assumption that the fastener remains in its initial position in the zones outside the plastic hinge was experimentally confirmed for displacements up to 15 mm (Figure 11a). It can be noticed that for a displacement of δ = 15 mm, considering all simulations, the angle of rotation is θ ≈ 21°, and in agreement with the experimentally measured value of θ ≈ 22° (Figure 11a). It can also be seen that plastification of the screw was achieved with the formation of two plastic hinges, where the maximum value of yield moment M_y,max is reached. From Figure 13a, it can be seen that for a slip greater than 2 mm, due to the formation of the second plastic hinge in timber and to reaching the yield point of the screw M_y and timber f_h,y, the connection shows a pronounced non-linear behavior, which is expected for these fasteners.

In Figure 13b, a significant increase in the load-carrying capacity of the connection due to the rope effect can be observed. Due to the slip increase in the connection and activation of the withdrawal capacity in timber, the gradual development of the rope force contribution F_ax,f can be observed. It can be noted that this contribution gradually develops before the yield point of the connection is reached and that their further increase is approximately linear. As the friction force F_μ is the function of F_v,ax(θ) and friction coefficient μ (which has been adopted as constant), its contribution is developed from the very beginning and follows the trend of axial force in the screw F_ax(θ). For the maximum rotation angle of screw θ = 22°, the contribution of the rope effect to the increase in the bearing capacity of the connection according to the numerical simulation is F_rope = 6593 N (Figure 13b, purple dashed curve), which corresponds to the force that represents the limit in Johansen’s expression for the rope effect F_rope = min{100%·F_Joh = 6438 N; μ·F_ax,max = 0.45 · 15,525 = 6986 N} = 6438 N. Based on the results, the rope effect significantly contributes to the connection’s load-carrying capacity. The proposed approximation of axial force in the screw as a function of the rotation angle θ (sine function) shows a good agreement with experimental results and assumptions from Eurocode 5. For a slip of δ ≈ 19 mm (Figure 10), the maximum load-carrying capacity of the connection occurs, followed by a decrease in load capacity due to the screw being pulled out of timber, as well as the formation of plastic hinges in the screw (Figure 11b). Due to the unknown axial tension force in the screw, as a relationship between the withdrawal force in timber and slip in the shear plane, as well as due to the impossibility of taking it into account through a kinematic relation [39], for displacements above 15 mm, the numerical model would continue to increase the force. This fact represents one of the limitations of the proposed numerical model. This issue is noted as one of the crucial problems in the design of timber connections with configurations that use fasteners with threads, i.e., when the contribution of the rope effect is essential to determining the connection resistance [59]. By comparing numerical and experimental curves, numerical simulations showed that if the material characteristics of timber and the fastener are known (represented in the form of f_h − Δ and M_y − θ), it is possible to simulate the non-linear behavior of the timber–concrete connection on the whole domain (δ = 0–15 mm) by using the proposed numerical model.

4.2. Validation of the Proposed Model via an Example from the Literature

In order to additionally validate the proposed numerical model, an experimental study of TCC connections conducted by Stevanović in his Ph.D. thesis [60] was selected. All available input data required for the numerical model were taken from the [60]. The double-shear push-out test specimens were used. Test specimens were formed of 1 central timber (100 × 200 × 350 mm) and 2 side concrete (70 × 300 × 350 mm) members connected with 2 timber screws Φ10 × 150 mm in each shear plane at a distance of 100 mm (see Figure 3.10 in [60]). Three replicants of the shear test specimen were made and tested according to EN 26891. Based on the conducted experimental tests, the load-carrying capacity of the connection was F_v,R,mean = 10.65 kN (F_v,R,min = 10.47 kN and F_v,R,max = 10.78 kN), while the slip modulus was K_s,mean = 2580 N/mm (K_s,min = 2140 N/mm and K_s,max = 2860 N/mm). For details of experimental research conducted by Stevanović, see Figure 4.4 for F_v,R − δ curves (test specimens Z1–Z3) and Table 4.1 for values F_v,R and K_s in [60].

Since experimental tests for embedment strength in timber f_h − Δ and yield moment of the screw M_y − θ were not conducted, they were reconstructed by using exponential functions [33], as shown in Figure 14a,b. The input data (f_h,t and K_f) for the exponential function f_h − Δ were determined according to the suggestions from [61], i.e., using the expression from Figures 6 and 7 provided in [61], Equations (10) and (11), which was based on timber density ρ_m. Input data (M_y and K_b) for the exponential function M_y − θ were determined according to the suggestions from this paper based on conducted tests on the screws. Yield moment M_y was determined as the effective value according to the expression in

Table 2. Mechanical properties of materials of TCC connection according to [60].

Materials	Properties	Mean Value
Glulam (approx. GL24h)	Axial withdrawal capacity Fax	13,090 N
	Density of timber ρm	476 kg/m3
	Embedment strength fh,t *	36.1 MPa
	Foundation modulus Kf *	43.4 N/mm3
Concrete MB30 (approx. C25/30)	Cubic compressive strength fc	46 MPa
Screw Φ10/150 mm	Ultimate tensile strength fu	590 MPa
	Yield moment My **	My,eff = 0.9·fu·deff3/6 = 40,403 Nmm
	Initial slope of yield moment function Kb **	13,867 Nmm/deg

* f_h,t and K_f were calculated according to Equations (10) and (11). ** M_y and K_b were estimated according to the suggestions from this paper.

, and K_b was determined as the mean value of the initial slope of the M_y − θ curves from Figure 7c. The withdrawal capacity in timber F_ax was estimated according to expression (8.3), given in Eurocode 5. The coefficient of friction was adopted as μ = 0.45. The input data are summarized in Table 2.

$$f_{h,t}=0.0936·{\rho }_m-8.454$$

(10)

$$K_f=0.2183·{\rho }_m-60.513$$

(11)

The numerical simulation results are shown in Figure 14 and Figure 15. In order to compare numerical load–slip curves with experimental ones, Figure 14c shows superimposed experimental (black lines for experimentally tested specimens ZP1 to ZP3 [60]) and numerical (red lines, for F_v,R and F_v,eff,R(n_eff)) load–slip curves F_v,R − δ. It should be noted that in Figure 14c, the red line (F_v,R) represents the F_v,R − δ curve of the connection without the influence of the group effects (effective number of fasteners in a line parallel to the grain on the load-carrying capacity of the connection), while the dashed line (F_v,eff,R(n_eff)) takes into account the spacing between the screws through the effective number of screws, n_eff = 0.93, reducing the load-carrying capacity of the connection. With this simple suggestion from Eurocode 5, as well as observations and conclusions reported in [53], in the proposed numerical model, an attempt was made to consider the reduction in the load-carrying capacity of the connection through the effective number of screws. This recommendation refers to the final value of the load-carrying capacity and that further investigation of this influence on the complete F_v,R − δ curve is necessary to improve the prediction by the proposed numerical model. Comparing the numerical results with the deformation of the screw (see Figure 4.8 in [60]), the distance of plastic hinges b_t,NUM = 20–30 mm, and the maximum angle of rotation of the screw θ = 22.6° follows the experimental values (b_t,EXP ≈ 30 mm and θ ≈ 24°, according to [60]). Based on results from the presented numerical simulation, it can be concluded that the numerical model can sufficiently accurately capture the load–slip response, although not all experimental data were available, i.e., embedment strength in timber f_h − Δ, the yield bending moment of the screw M_y − θ, and the withdrawal capacity in timber F_ax.

4.3. Discussion of Results—Load-Carrying Capacity and Slip Modulus of the TCC Connection

In order to compare the numerical, theoretical, and experimental values of the load-carrying capacity and slip modulus of the TCC connection,

Table 3. Comparison of the load-carrying capacity and slip modulus of the TCC connection.

	Method		Mean Values 1	Deviations [%]	Mean Values 2	Deviations [%]
Load-carrying capacity Fv,R [N]	Experimental (δ = 15 mm)		13,240	-	10,650	-
	Numerical (δ = 15 mm)		13,400	1.2	11,560/12,390 f	8.5/16.4
	Theoretical	CEN/TS 19103 a	10,491	−20.8	8773/9400 f	−17.6/−11.7
		Fv,R,corr b	13,218	−0.2	11,217/12,019 f	5.3/12.9
Slip modulus K [N/mm]	Experimental		2889	-	2580	-
	Numerical	Ks (EN 26891)	2670	−7.6	2732/2980 f	5.9/15.5
		Ks,0.4Fmax c	2825	−2.2	3058/3279 f	18.5/27.1
	Theoretical	Kser,TTC d	3488	20.7	3477	34.8
		Kser,TCC = 2·Kser,TTC e	6975	141.4	6954	169.5

¹ Experiment from this study: d_eff = 7.7 mm, ρ_m = 477 kg/m³, f_h,t,mean = 35.3 MPa, F_ax = 15,525 N, f_h,c = 220 MPa, M_y = 46,613 Nmm, μ = 0.45. ² Experiment from [60]: d_eff = 7.7 mm, ρ_m = 476 kg/m³, f_h,t = 36.1 MPa, F_ax = 13,089 N, f_h,c = 184 MPa, M_y = 40,403 Nmm, μ = 0.45. ^a F_v,R = F_Joh + F_ax/4; ^b F_v,R,corr = F_Joh + F_rope, where F_Joh = $\sqrt{\left(\left(2·\beta \right)/\left(1+\beta \right)\right)}·\sqrt{2·M_y·f_{h,t}·d_{eff}}$ and F_rope = min{100%·F_Joh; μ·F_ax}. ^c Secant value determined from the load–slip curve at 40% of the ultimate load at slip δ = 15 mm. ^d For timber-timber connection (TTC): K_ser,TTC = ρ_m^1.5·d/23; ^e For TCC connections: K_ser,TCC = 2·ρ_m^1.5·d/23 (where d = d_eff). ^f With or without effective number of fasteners n_eff = 0.93, F_v,eff,R/F_v,R, where F_v,eff,R = n_eff · F_v,R.

shows the estimations of the proposed model compared to theoretical values (CEN/TS 19103) and the experimentally determined values considering the mean values. Based on the comparison presented in Table 3, the load-carrying capacity of the connection obtained by the numerical model gives a better estimation compared to the recommendations by CEN/TS 19103. This deviation is a consequence of the proposal for the rope effect in CEN/TS 19103 given in the form F_ax/4. This effect should be revised or taken in the form of μ·F_ax, where if there is a plastic sheet or if timber is in direct contact with concrete, the coefficient of friction between timber and concrete should be experimentally obtained or taken according to the recommendation from [43]. If the value μ = 0.45 was adopted, then the load-carrying capacity of the connection according to Eurocode 5 would have been estimated better F_v,R,corr compared to the experimental one. It should be noted that in the case of Stevanović, the load-carrying capacity of the connection should include the influence of the group effects in order to take into account the reduction in the load-carrying capacity of the connection through the effective number of screws.

Compared to the experimental values, the mean value of the slip modulus determined from the numerical curves, according to EN 26891, shows a good prediction compared to overestimated theoretical values according to CEN/TS 19103 (Table 3). It should be noted that the diameter of the screw is not precisely defined in CEN/TS 19103, which may result in an overestimation of the K_ser value. According to suggestions from the literature, effective diameter d_eff is used to estimate the slip modulus in this paper. Analyzing the expression given in CEN/TS 19103, for TCC connections K_ser,TCC, as well as the case for timber-timber connection (TTC) K_ser,TTC, the slip modulus for TCC connection has large deviations to the experimental values in comparison to the slip modulus for the TTC connection. Although in the case of concrete with a higher strength class that was used in this paper, based on the experimental results, the recommendation by CEN/TS 19103 to double the value of the slip modulus is not justified. Using numerical curves, slip modulus should be determined for 40% of the ultimate load, as in codes and standards, slip modulus for serviceability limit state design K_ser is derived as the ratio of the respective load (0.4·F_v,R) and the instantaneous deformation (v_40%) [10]. Compared to the EN 26891 methodology for determining K_s, in this study, the slip modulus was determined as a secant value at 40% of the ultimate load (K_s,0.4Fmax). This determination method is adopted because there is no initial slip, i.e., all initial slips have already been removed from the embedment curves when the numerical curves were formed, while EN 26891 takes this into account when determining the slip modulus. It should be noted that the load–slip curves show a pronounced non-linear behavior, which significantly affects the determination of the slip modulus value. As discussed in the paper [62], it can be concluded that a limit of 0.4·F_v,R is a sensitive parameter to obtaining the slip modulus of the connections. Thus, the evaluation of the slip modulus should be performed with caution. It was shown that the proposed numerical model has advantages in determining and evaluating the slip modulus of the TCC connection, so it is recommended that for TCC connections with screws, the slip modulus should be determined using the proposed numerical model. The load-carrying capacity and stiffness values of the TCC connection, determined by the proposed numerical model, agree with the experimental values, and maximum deviations are within acceptable limits according to [24].

5. Conclusions

To improve the prediction and assessment of the stiffness and load-carrying capacity of the TCC connection, in this paper, a numerical model of the connection suitable for determining the complete load–slip curve is proposed. The model was developed to consider the real non-linear behavior of timber and fasteners, which is determined via simple experimental tests. Since there are no detailed criteria in the CEN/TS 19103 regarding the geometry of test specimens and their influence on the response of TCC connections, all recommendations and observations were considered based on a literature review from the field of composite connections. Suggestions of minimum dimensions of shear test specimens, the optimal spacing between screws, and its effect on the load-carrying capacity of the connection, as well as the occurrence of a possible failure mode of the screw in the connection, are discussed in the paper. According to these suggestions, shear test specimens in this study were made. For the numerical model validation, experimental tests were carried out at the level of the applied materials, as well as on the specimens of the composite connection. For additional validation of the proposed model, experimental research of the TCC connection taken from the available literature was used.

Through numerical simulations, analysis of the obtained results, and comparison with experimental and theoretical values, it was shown that it is possible to simulate the non-linear behavior of the TCC connection using the proposed numerical model. It can be concluded that the numerical simulation carried out on the TCC specimen adopted from [60] proved to be successful, although all the experimental data needed for the numerical model was not available. This proves that in the absence of experimental tests, it is possible to use the generic functions for f_h − Δ and M_y − θ, i.e., using exponential functions in which the input parameters are determined empirically [61,63], or to evaluate the material behavior better through experimental testing. This aspect is of great importance in order to extend the application of the proposed numerical model, which requires simple experimental tests at the material level. The stiffness and load-carrying capacity values of the connection estimated with the numerical model agree with the experimental ones, and the deviations are minor compared to the recommendations and overestimated values given by the CEN/TS 19103. Investigating and updating the recommendations related to slip modulus is necessary because it overestimates the experimental values by more than +140%. These large deviations result from the adopted assumptions of negligible deformation in concrete, the unclear diameter of the fastener with threads, and the significant influence of timber properties. It can be noted that the connection response strongly depends on the adopted embedment f_h − Δ curve and that the foundation modulus significantly influences the initial slope of the F_v,R − δ curve, i.e., slip modulus. For the load-carrying capacity of the connection, the proposed expression in Eurocode 5 is in reasonable agreement with the experimental values, with a deviation of about −20%. The difference in these values is due to the rope effect behavior based on a simple relationship between timber withdrawal capacity and friction coefficient, where μ is assumed to be 0.25 or 1/4 of the maximum withdrawal capacity in timber. In these situations, where the prediction and evaluation of the stiffness and load-carrying capacity of the TCC connection are essential, as well as there is a need for a complete curve in the case of non-linear analysis of TCC structures, it is suggested to use the proposed numerical model. Additionally, in addition to the simulation of the complete curve, the numerical model can determine local effects such as the crushing depth in timber and concrete, the rotation angle of the screw, and the participation of forces in the load-carrying of the connection for any displacements in the connection.

In addition to the mentioned possibilities, it should be noted that there are certain limitations in the proposed model. They are related to the adopted assumptions about the axial force F_ax(θ) in the screw approximated by a sinusoidal function, constant friction coefficient, and the influence of the group effect of the screw (through the effective number n_eff) on the reduction in the load-carrying capacity of the connection. Additionally, this paper presents a numerical approach that solves the problem of the ductile failure of a composite connection with two plastic hinges when a fastener is placed perpendicular to the shear plane. The possibility is left to upgrade the model in order to cover other failure modes of the connection, as well as to take into account the behavior of LWAC with lower strengths that have a brittle behavior, i.e., the effects such as cone expulsion and pull-out. Future investigation should focus on more extensive experimental and theoretical research considering these limitations to improve the predictions of the proposed numerical model and to extend it in order to cover other dowel-type fasteners and types of concrete.