Analysis of shear transfer and gap opening in timber–concrete composite members with notched connections
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Abstract
In timber–concrete composite members with notched connections, the notches act as the shear connections between the timber and the concrete part, and have to carry the shear flow necessary for composite action. The shear transfer through the notches generates shear and tensile stresses in both parts of the composite member, which may lead to brittle failure and to an abrupt collapse of the structure. Although simplified design formulas already exist, some structural aspects are still not clear, and a reliable design model is missing. This paper summarizes current design approaches and presents analytical models to understand the shearcarrying mechanism, to estimate the shear stresses acting in the timber and concrete, and to predict failure. The analysis concentrates on three problems: the shearingoff failure of the timber close to the notch, the shear failure of the concrete, and the influence of the shear flow on the gap opening between the timber and concrete. Parts of the model calculations could be compared to experimental observations. The conclusions of this paper contribute to improving current design approaches.
Keywords
Timber–concrete composite Notched connection Shear failure Shearingoff failure Gap opening1 Introduction
Timber–concrete composite structures represent a convenient solution to refurbish old buildings and for new construction because they are able to offer several structural, economic and ecological advantages compared to reinforced concrete slabs and timber slabs [1]. In a timber–concrete composite member, the timber part is usually subjected to tension and the concrete part to compression. To ensure composite action, a shear connection between the two parts is needed. As shear connections markedly influence the structural behavior of the composite member, several research projects have focused on developing connection systems (e.g. screws [2], or notches cut from timber [3, 4]).
Notches represent easy to fabricate and hence, competitive timber–concrete connections. Notches act as shear keys. They minimize the relative displacement between the timber and concrete [3], and hence, they ensure a higher stiffness and a more efficient composite action than most of the other connection systems. However, a notch causes a reduction in timber crosssection. Furthermore, a notched connection implies shearcarrying mechanisms in both parts of the composite member, which may lead to critical stress states and brittle failure modes that should be prevented by means of appropriate design. The present paper focuses on this topic.

flexuralshear failure of the concrete

shearingoff failure of the timber close to the notch

shear failure of the timber part

gap opening
The most frequent questions relate to the shearcarrying mechanism in the concrete. In contrast to conventional reinforced concrete structures, where extensive studies on the shear behavior were conducted (e.g. [8]), in timber–concrete composite structures with notched connections, this topic needs further research. On the basis of truss models, some authors (e.g. [9]) suggested to equip the composite members with screws to ensure the shear transfer and to prevent gap opening. However, in practice, there is no general agreement in the method to design such fasteners. Further critical topics related to shear are the stress distribution in the timber close to the notch edges, the design approach to prevent brittle shearingoff failure of the timber, and the relationship between shear forces at the interface and gap opening.
2 Loadcarrying mechanism
This section presents an analytical approach to understand the shearcarrying mechanism in a timber–concrete composite member with a notched connection and to estimate the shear forces.
Figure 2a shows a timber–concrete composite member as onespan beam and subjected to fourpoint bending as an example. Figure 2b shows the composite crosssection and the axial stresses and strains in the case that the zerostrain layer is located in the concrete. The reason for this choice is that the models presented in this paper were developed in the frame of a research project about timber–concrete composite members made of 40 mm thick beech LVL plates and 160 mm thick concrete layers, where the zerostrain layer was located in the concrete [10]. Nevertheless, the presented approach allows to derive similar models for the case where the zerostrain layer is located in the timber too.
The timber part is subjected to tension and bending, and the concrete layer carries compression and bending. As shown in Fig. 2c, if the timber and concrete are glued together, the shear flow at the interface \(\tau _{12,xz}\) is distributed over its area. In contrast, if the shear connection is accomplished by means of notches cut in the timber part of the composite member, the shear flow between the timber and concrete is transferred through compression over the notch edges (Fig. 2d).

The two parts of the crosssection behave linearelastic.

The behavior of the shear connections are linearelastic.

The distribution of the axial strains is linear in each part of the crosssection.

The parts of the crosssection are perpendicular to the axis of the deformed beam.

No gap opening and no vertical stresses at the interface occur. Thus, the timber and concrete bend with the same deflection and the same curvature.
If the connections are ductile (e.g. ductile steel fasteners or notches designed to fail due to plastic timber compressive deformations) and have an adequate deformation capacity, they can redistribute the shear forces. This means that, in a onespan beam, the maximal axial force in the parts of the composite member is equal to the sum of the shear resistance of the connectors between the support and the critical crosssection [11]. If the connections may exhibit elastic–brittle behaviour, this assumption is not valid.
3 Shearingoff failure of the timber
In a timber–concrete composite member with a notched connection subjected to positive bending moment, the shear force, which occurs between the two parts, is transferred through the notch edges. Similar to step joints, this causes local shear and tensile stresses in the timber next to the notch edge (Fig. 3), which may lead to shearingoff failure. As observed in several tests (e.g. [4, 7, 14]), this failure mode is characterized by a sudden detachment of a timber piece next to the notch, and usually causes collapse of the composite member.
However, the assumption of a constant shear stress distribution is a rough approximation of reality. In elastic conditions, the shear stress distribution is nonlinear and shows a peak close to the notch edge [4, 7, 16] (Fig. 3). In theory, this is valid for low stress only, where the material is still elastic. According to the fracture mechanics theories presented by Smith et al. [18], timber is a quasibrittle material and hence activates complex energy dissipation mechanisms, which imply softening in the stress–strain relationship. Thus, if the shear force reaches a significant level, it can be supposed that the shear stresses redistribute along the shear area. Nevertheless, additional theoretic and experimental research is needed to identify how the different zones of the timber close to the notch participate to the shearcarrying mechanism at the ultimate limit state.
The interaction between shear and tensile stresses perpendicular to the shear plane is a critical issue in timber structures, because a tensile stress decreases the shear strength [20]. Hence, in respect of shearingoff failure, the critical element is located close to the notch edge because in this point the perpendicular tensile stress is maximal (\(x = l_{N}\) and \(z = t_{N}\) according to Fig. 3). As summarized by Steiger and Gehri [20], several analytical and experimental studies allowed to develop models to quantify the influence of perpendicular stresses on the shear strength of timber. The first type of models base on fracture mechanics (e.g. [21]) and ask for the introduction of a critical stress intensity factor (fracture toughness), which depends on the test setup and the material. The second type of models belong to the stressbased strength approach. In engineering, this approach is usually preferred to fracture mechanics because the concepts of stress, strain and strength are well established in the current analysis techniques. The material strengths are usually determined in standard tests. Special attention should be paid to the shear strength, because it is strongly dependent on the volume of the test specimen and on the test configuration [22]. It is suggested to derive the shear strength of timber from tests performed with a static system and dimensions similar to the investigated structure.
A family of failure criteria, which belong to the stressbased strength approach, are the phenomenological strength criteria, which are usually represented by mathematical expressions describing a strength surface [23]. One phenomenological strength criterion, which aroused great interest in timber engineering, is the tensor polynomial model presented by Tsai and Wu [24]. This approach considers orthotropic materials such as wood, in which tensile and compressive strengths are different. Although, as shown by Van der Put [25, 26], the tensor polynomial model can be used to represent the failure surface of wood, several aspects of these models are still matter of discussion [23]. Thus, in structural engineering, a stress analysis made by means of this model should be interpreted carefully.
As shown in Fig. 4, in the case of LVL made of European beech wood, both Eqs. 15 and 16 exhibit that a tensile stress (\(\sigma _{z} > 0\)) has a negative influence on the shear stress. In the case studied, Eqs. 15 and 16 give nearly the same result.
4 Shear failure of the concrete
4.1 Introduction
In a timber–concrete composite member with a notched connection, the stress transfer from the concrete layer to the notch edges causes shear and tensile stresses in the concrete. The shearcarrying mechanisms in the concrete were mostly studied in the context of modeling and designing of conventional reinforced structures (e.g. [8, 28]).
The loadcarrying mechanism in timber–concrete composite members with notched connections involves several analogies with conventional reinforced concrete structures. However, the most important difference is that, in a reinforced concrete member, the force is usually transferred in a continuous way along the reinforcing bars, whereas, in a timber–concrete composite member, the load transfer occurs locally through the notch edges. This aspect influences the position, the distribution and the width of the cracks.
If a conventional reinforced concrete member is provided with vertical reinforcement, after cracks develop, the vertical tensile stresses are carried by the steel reinforcement, and the composite member can be designed with stress fields and truss models [29], which ensure a predictable behavior at ultimate limit state.
In contrast, the modeling and the design of concrete members without shear reinforcement is more difficult. Several authors (e.g. [8, 30, 31, 32]) noticed that, after bending cracks develop, the loadcarrying mechanism begins to change, and analyzed the various shearcarrying mechanisms. An example is the cantilever action: because of cracks, the tension zone is divided up into separate concrete elements, which can be visualized as cantilever beams fixed in the upper compression zone. All these mechanisms cause tensile stresses in the concrete near the crack tip and close to the reinforcement, which may provoke crack propagation. Nevertheless, after the propagation of a shear crack, an arching action may develop to carry the shear, which is governed by the location of the critical shear crack, its width, and the aggregate size [8]. This approach is supported by several experiments (e.g. [33, 34]).
The geometry of timber–concrete composite members with notched connection suggests that the concrete layer carries shear by means of cantilever action.
4.2 Simplified model for notches without reinforcement
This model is suitable to understand the stress state of concrete and the influence of some parameters. However, a failure prediction is unsure because the model is based on the assumption of simplified crack configurations and stress distributions. A problem can be that internal stresses (which are very difficult to predict), or punching loads, may cause modifications of the crack layout as well as the growth of new cracks.
Whatever model is applied, a design of timber–concrete notched connections without vertical reinforcement may be critical because of several reasons. The crack width can become larger than in a conventional reinforced concrete structure. The fact that the position of the flexuralshear cracks in a composite member with a notched connection is usually given and corresponds to the notch edges, implies that, in contrast to conventional reinforced concrete members, the number of cracks is smaller and they become larger. Thus, the risk of flexuralshear failures increases because there is no interlocking action which can contribute to the shearcarrying mechanism. In addition, the fact that the concrete is stiffer than the timber, and is brittle when subjected to tension, may compromise the shearcarrying mechanism. Timber deformations within the notches, in particular when the timber develops plastic compressive deformations, may cause enlargement of the existing flexuralshear cracks in the concrete. If two notches close to each other develop different timber deformations (\(u_{i} < u_{i1}\)), the concrete cracks may enlarge, leading to an interruption of the shearcarrying mechanism.
This situation makes a reliable design without shear reinforcement more difficult than in conventional reinforced concrete structures. Because of the brittle behavior of concrete, a reliable failure prediction is not possible. The installation of vertical reinforcement is a possible solution to ensure a robust and consistent structural behavior.
4.3 Simplified model for notches with reinforcement
As soon as a flexuralshear crack opens in the concrete, vertical reinforcement should carry the tensile stresses and prevent crack propagation. This section presents a method to design such reinforcement under the assumption that, when the vertical reinforcement activates, the loadcarrying mechanism in the concrete part of the composite member approaches to a truss (Fig. 5b). The model refers to a composite member where the concrete cracks grow starting from the notch edges and the reinforcement is accomplished by means of vertical steel rods with anchorage plates on the top and bottom edge of the composite member (Fig. 5b). For different conditions (e.g. if the vertical reinforcement is made of screws), specific models can be developed using a similar procedure.
The first issue to solve is the position of the vertical reinforcement. As explained previously, the concrete layer can be divided up into a series of cantilevers fixed in the compression zone (Fig. 5a). Therefore, the impact of a vertical steel reinforcement in the notch can be compared to the effect of a longitudinal tensile reinforcement in a concrete console. Hence, the tensile reinforcement should be installed close to the notch edge where the tensile stress is maximal, so that it is able to carry the tensile stress as soon as horizontal cracks open. In the literature, other truss models can be found for timber–concrete composite members, which lead to different possible positions for the vertical reinforcement. This means that the installation of a reinforcement in a different position does not necessarily mean premature failure, but it can be that the cracks enlarge more before the reinforcement activates.
At the ultimate limit state, the presence of an adequate reinforcement in zdirection generates a direct bracing, which can be described by means of a truss model (Fig. 5b). The horizontal component of the diagonal concrete strut corresponds to the horizontal notch force \(T_{{\mathrm{Ni}}}\) and is transferred to the timber part through compression in the notch edge. The vertical component of the diagonal strut is transferred to the timber thanks to compression in vertical direction, is taken by the anchorage plate on bottom edge, and is carried by the vertical reinforcement in tension.
However, it must be taken into account that vertical reinforcement such as screws and dowels may participate in carrying the horizontal shear flow between timber and concrete as well, thus influencing the loadcarrying mechanism [15].
4.4 Minimum amount of reinforcement
Reinforced concrete structures should be provided with a minimum amount of reinforcement. The most important reason is to prevent brittle failure as soon as the concrete cracks. When a crack occurs, the reinforcement should not yield. Otherwise, since the reinforcement would be in plastic conditions, it would not be able to carry the necessary tensile force, and hence, a brittle failure would occur.
For conventional reinforced concrete structures subjected to bending, analytical models to asses the minimum reinforcement are well established [36]. For vertical shear reinforcement, due to the high complexity of the shearcarrying mechanism, semiempirical equations are used (e.g. [37]).
For timber–concrete notched connections with vertical reinforcement, the same principle should be valid. In this section, a simplified analytical model to understand the most important factors which influence the minimum vertical reinforcement is presented. It is assumed that a horizontal crack opens when the tensile stress exceeds the tensile strength of the concrete according to the cantilever model shown in Fig 5a.
In the presented approach, some assumptions are strongly simplified. First of all, the crack position and the effective part of the concrete, which carries the stresses, are unknown and must be assumed. Secondly, the interaction between tensile stresses in the concrete and shear stresses is neglected. In reality, as previously described by means of the Mohr–Coulomb failure criterion, shear stresses acting in the critical zone facilitate crack opening. However, in any case, a calculation neglecting the shear stresses leads to a safe design of the minimum reinforcement.
4.5 Experimental observations
In [14], experimental observations made during bending tests on timber–concrete composite members made of European beech laminated veneer lumber performed by Boccadoro and Frangi are described. These tests evidenced the cantilever mechanism occurring in the concrete part of the composite member, the influence of timber deformations within the notches on the concrete crack propagation and the beneficial influence of the vertical reinforcement.
During a series of preliminary fourpoint bending tests on LVLconcrete composite members without vertical reinforcement, flexuralshear failure of the concrete layer was observed [14]. Starting from the beginning of the test, cracks grew from the edges of the notches. This experimental observation fits with the assumption made in the model for members without reinforcement. Then, one crack propagated suddenly in longitudinal direction, causing a brittle collapse of the specimen. The observed failure put in evidence the formation of consoles subjected to bending and shear, but a good agreement between the prediction made with the cantilever model and the test result could not be found [10]. However, a quantitative comparison between model and reality is not possible yet. This would require more experimental results.
Another series of bending tests on LVLconcrete composite members with a ductile notched connection was performed with vertical reinforcement designed to carry only vertical forces. During these tests, no flexuralshear failure of the concrete occurred, and the specimen failed after large deformations due to compressive failure of the LVL in the notches [14]. It was observed that, in the parts of the composite member subjected to shear, flexuralshear cracks tended to develop, but remained closed until the end of the experiment because the vertical tension was carried by the reinforcement. In contrast, in the zone close to the midspan, the cracks were vertical.
This mechanism showed that the reinforcement fulfilled the minimal requirements. Otherwise, a sudden opening of the flexuralshear cracks would have occurred.
5 Gap opening
5.1 Causes
5.2 Experimental observations
Boccadoro and Frangi [14] observed gap opening phenomena during several bending tests on European beech LVLconcrete composite members with notched connections. Two categories of gap opening were observed: elastic gap opening (due to the mechanism shown in Fig. 7), and gap opening provoked by plastic compressive deformations of the LVL in the notches and crack propagation.
The design procedure of this type of LVLconcrete composite member with notched connections was optimized so that the behavior was governed by plastic deformations of the LVL in the notches in order to develop ductility [10]. To validate the model, several specimens were tested with a uniformly distributed vertical load, and the influence of vertical reinforcement was investigated. Due to the test configuration with distributed load, the gap opening in elastic conditions was smaller than that observed in the specimens subjected to fourpoint bending. However, the issue of gap opening was emphasized by plastic compressive LVL failure within the notches. The specimens without vertical reinforcement, starting from the beginning of the plastic compressive deformations of the LVL within the notches, showed a marked tendency to gap opening. This phenomenon always occurred in different zones. At the same time, it was observed that some concrete cracks enlarged. These two phenomena compromised the loadcarrying capacity of the specimens and determined the end of the test (e.g. Fig. 6). Some specimens were provided with vertical endtoend reinforcement to hold the LVL and the concrete together. These reinforcements prevented gap opening and crack opening.
The marked increase of the gap opening during plastic deformations of the timber in the notches is due to several phenomena that influence themselves. Elevated plastic compressive deformations of the timber within the notches facilitated a sliding out of the concrete layer and thus caused gap opening. Moreover, isolated cracks in the concrete with large dimensions had the effect of hinges in the concrete layer, and so the concrete tended to bend in an angled way. As explained in Fig. 6, also the enlargement of the concrete cracks is influenced by the plastic deformations of the timber within the notches.
5.3 Design of reinforcement to prevent gap opening
Since gap opening compromises the structural behavior, the composite member should be designed to prevent this phenomenon. As observed experimentally, vertical reinforcement which connects the timber and concrete prevents gap opening. In addition, as explained previously, vertical reinforcement has a beneficial influence on the shear resistance of the concrete. Thus, the design of a vertical reinforcement which achieves both these objectives is a possible solution.
6 Conclusions

Several current design approaches show that a shearingoff failure of the timber next to the notch is facilitated by local tensile stresses. This failure should be prevented by choosing a suitable notch geometry. However, the modeling of the critical zone of the timber part needs additional research.

The load transfer from the compressive concrete zone to the notch edge develops a cantilever action which implies combinations of shear and tensile stresses and can lead to failure. This finds agreement with experimental observations. Since this failure is influenced by several uncertain parameters, it is suggested to provide the composite member with an adequate vertical reinforcement in order to develop a controllable and robust loadcarrying mechanism.

The vertical opening of a gap between the timber and concrete has several mechanical reasons, some of them difficult to quantify. This paper discusses the influence of shear transfer at the interface on gap opening and suggests a simplified method to design vertical reinforcement to prevent this phenomenon
Notes
Acknowledgements
The Swiss National Science Foundation SNSF (NRP 66) and ClimateKIC are gratefully acknowledged for financing and supporting the project.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
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