Parametric Finite Element Analyses of Demountable Shear Connection in Cold-Formed Steel–Concrete Composite Beams

Abstract

It is known that steel–concrete composite systems are very efficient. However, such steel–concrete composite systems can be optimised using cold-formed steel elements and innovative shear connections. In other words, by considering demountability and reusability, the negative impact of the built environment on the whole ecosystem can ultimately be reduced. This paper, therefore, presents a numerical study of an innovative solution for a composite floor system consisting of built-up cold-formed sections and concrete slabs. Through parametric numerical analysis, parameters such as the diameter and quality of bolts, the concrete class, the type of concrete slab, and the steel quality of sections and bolts were varied. The numerical analysis results show that the system with a solid concrete slab had a higher shear resistance and ductility than the system with a concrete slab made with profiled sheeting and showed different failure modes. The presented results form the basis for push-out tests for the proposed shear connection types.

1. Introduction

The combination of two different materials in one system is an increasingly common solution in the construction industry to achieve numerous advantages. This is also the case with steel–concrete composite systems, in which structural steel is characterised by high tensile strength and ductility, while concrete offers high stiffness and compressive strength. Therefore, despite numerous studies, steel–concrete composite structures are still the subject of research and continuous development, especially when new proposals for composite systems emerge. The system is a built-up system that combines cold-formed steel (CFS) corrugated web girders and concrete slabs using innovative shear connections, ultimately offering numerous advantages. In this sense, the shear connection is also an essential component of the structural behaviour of steel–concrete composite beams, as it allows the interaction of the individual parts.

This paper presents a preliminary numerical parametric study of an innovative construction system. This system integrates a built-up beam consisting of CFS C sections with a spot-welded corrugated web (CWB), as shown in Figure 1. This structural assembly is further enhanced by an additional concrete slab with profiled steel plates placed on top of the CWB. The connection between the CWB and the concrete slab is established through the application of a demountable shear connection, ensuring composite interaction. This system, called LWT-FLOOR, is the subject of investigation of the scientific project LWT-FLOOR [1], which is ongoing at the University of Zagreb at the Faculty of Civil Engineering, Croatia. As an integral component of the project, this work undertakes a preliminary analysis as the groundwork for future experimental research. The aim is to enhance our understanding of potential failure modes and enable predictions regarding shear resistance. As the project progresses, a comprehensive approach will be adopted, encompassing experimental, numerical, and probabilistic investigations. These multifaceted analyses will serve as the basis for establishing a reliable analytical calculation method for the resistance of the shear connection.

2. Overview of the Previous Research

As mentioned earlier, using CFS sections in steel–concrete floor systems offers numerous advantages, depending on the design solution adopted [2,3,4,5]. Furthermore, the advantages are even more apparent with the proposed new steel–concrete composite system, which includes a CWB and a concrete slab connected with a demountable shear connection. The CWB is a relatively new structural system developed for various applications. Among the most important advantages is undoubtedly its reduction in mass compared to hot-rolled or welded sections due to its low web thicknesses. The application of non-stiffened thinner webs also results in lower material costs compared to hot-rolled beams. However, the main advantage is the increase in stability of the beam against local and lateral torsional buckling due to the use of a corrugated web. These advantages can ensure a more efficient design from a technical and economic point of view. Looking at a CWB from a static point of view reveals that its behaviour is more like the behaviour of a lattice beam, in which moments and longitudinal forces are transmitted through the flanges, whereas, in this case, transverse forces would be transmitted through a corrugated web. It can be concluded that the beam flanges provide the bending resistance of the beam without the contribution of the corrugated web, which provides the shear resistance of the beam. In the proposed LWT-FLOOR system, the sections and the corrugated web were joined via spot welding, which achieved excellent ductility and load-bearing capacity. Spot-welded beams have a higher stiffness and load-bearing capacity compared to beams with self-drilling screws [6,7]. However, besides its satisfactory behaviour, spot welding also allows the standardisation of design and fabrication details and production process automation, which can ultimately lead to the faster fabrication of the designed CWB [8].

The shear connection is also an important component of the system that ensures the interaction between structural materials, and it can significantly influence the behaviour of the system. Nowadays, welded shear connectors are the most common form of shear connection; they are the only one standardised according to European standards [9]. In addition, various solutions for shear connections and new innovative types of shear connections are being further developed. However, as mentioned above, new types of shear connections have recently been developed, allowing a structural system to be dismantled when modifications, repairs or deconstruction are required [10].

In the past, different types of demountable shear connectors and different mechanisms for transmitting shear forces have been investigated. Experimental and numerical studies on proposed shear connection solutions were summarised chronologically in [11]. Pardeshi and Patil [12] also published a review of the current state of the art and the different types of shear connectors used in composite structures over the last decade. The review in [11] pointed out that the biggest problems of demountable shear connections are precisely the resistance and ductility of the connection itself, and it concluded that further research is needed. In line with this issue, research on detachable shear connectors has increased. For example, a push-out test of the steel–concrete composite system with a demountable shear connection was carried out and summarised in the paper [13]. The obtained results were compared with those of welded-headed bolts, from which it was concluded that beams with detachable shear connectors achieve similar stiffness but higher ductility. Dia et al. [14] also conducted experimental and numerical investigations to demonstrate the possible use of demountable shear connectors instead of welded shear studs. Patel et al. [15] conducted a numerical investigation of demountable steel–concrete composite beams, which were finally compared with the experimental test results and the results obtained when welded shear studs were used in composite beams. The results were also compared with values calculated according to Eurocode 3 [16], Eurocode 4 [9], and the Australian standard [17]. From this comparison, and according to Eurocode 3 [16], it can be stated that the resistance of bolted shear connectors is insufficient due to the additional resistance that the nut provides to the flange. Friction effects in bolts were investigated by [18]. In the study [19], it was found that the definition of the load-bearing capacity of the shear connection needs to be re-evaluated to apply the Eurocode 4 rules for beams with partial interaction. On the other hand, to fully understand the behaviour of the bolted shear connection in concrete slabs made within profiled sheeting, it is necessary to analyse the contribution of other components to the overall behaviour of the system. Such a numerical study was carried out by Arezoomand et al. [20], in which the overall behaviour of the model was observed through changing various parameters. Through the mentioned study, the influence of various parameters was observed, such as the effects of the strength of the concrete, the reinforcement frame, the diameter and height of the bolt head, the position of the bolt (strong or offset), the thickness and type of the profiled sheets, and some other parameters. From the results obtained, it can be concluded that increasing the strength of the concrete slabs leads to an increase in the stiffness and load-bearing capacity of the connectors. The possibility of increasing the strength of concrete slabs and preventing their earlier failure was realised using a modified reinforcement frame. Increasing the diameter of the bolted shear connectors also led to higher values in the load-bearing capacity and stiffness of the composite slabs. Even with a constant diameter, connections with a greater height in the concrete slab resulted in a higher load-bearing capacity and stiffness. The application of different types of profiled sheets was found to increase the stiffness and load-bearing capacity of shear connectors, while changing the thickness of the profiled sheets did not significantly affect the final behaviour.

It should be noted that, in the mentioned study [11], a demountable shear connection between the CFS elements and the concrete slab could not be found. The reason for this was the lack of research in this area. As a contribution to the study of the demountable shear connection between the CFS elements and the concrete slab, Hosseinpour et al. [21] experimentally investigated the behaviour of the shear connection in a composite CFS beam and concrete slab. They performed a parametric analysis considering three important parameters: the thickness of the CFS sections and the diameter and strength of the bolts. The obtained results indicated that, in the thinner CFS sections, there was a small bearing failure in the bolt hole of the CFS segment associated with the buckling of the flanges of the CFS beam flanges, which ultimately manifested as the failure mode of these models. Furthermore, for the specimens with thicker CFS sections, the main failure mode was bolt yielding associated with small elongations in the holes of the CFS sections. However, in some specimens, cracks in the concrete slabs and shear failure were also observed as accompanying failure modes. It is also worth noting that Hanaor [22] was one of the first to investigate the shear connection between CFS beams and concrete or composite slabs. That research was based on the study of two types of shear connections, i.e., embedded and dry solutions. The embedded solution consisted of channel sections as shear connectors connected to CFS beams by means of welds or screws. Lakkavali and You [23] conducted a study in which they observed the behaviour of four shear transfer mechanisms to join cold-formed C sections and concrete slabs. The shear transfer mechanisms observed included surface bonds, prefabricated bent-up tabs, pre-drilled holes, and self-drilling screws. From the results, it was concluded that, as expected, the specimens with surface bonds had the lowest strength and stiffness. In contrast, the specimens with bent-up tabs had the highest strength and the lowest deflections in terms of serviceability. Observing three specimens whose joint types used some form of shear transfer enhancement, the lowest increase in strength was found in the specimens with self-drilling screws. In the study by [4], the authors conducted experimental tests on the proposed shear transfer enhancement called the bent triangular shear transfer. The tests were conducted in two different phases. In the first phase, the objective was to gain the best possible knowledge of the behaviour of the curved triangular link during shear transfer. These tests were carried out to investigate the effects of various parameters, such as the type of shear transfer enhancement, the strength of the concrete, and the thickness of the CFS. In the second phase, specimens were tested to study the effects of various parameters, such as the shear transfer enhancement, as well as the dimensions and the angle of the bent triangular Table The failure mode of the specimen was controlled via the fracture and splitting of the concrete, and the ductility was below the limit of 6 mm specified in Eurocode 4 [9]. Based on the results of the experimental test, it could also be stated that the shear capacity of the connection could be increased by increasing the thickness of the CFS section or by increasing the angle and/or dimensions of the Table The bond behaviour between lipped C-channels and a ferrocement slab using 12 mm diameter bolts as shear connectors was studied by [24]. Recently, Bamaga et al. [25] proposed three innovative demountable shear connections between cold-formed beams and concrete slabs. The shear connections were implemented with either hot-rolled steel plates, single brackets, or double brackets connected with bolts between the CFS C sections. The results of the push-out tests for all three shear connections showed sufficient strength and ductile behaviour.

Based on the presented investigations, which focused on the bolted shear connection, it is obvious that the overall behaviour of composite systems is still quite unknown. This is especially the case when the CFS elements are used, emphasising the need for further investigations within this field. Therefore, the main objective of this study is to preliminarily investigate the behaviour of the demountable bolted shear connection between built-up CFS CWB beams and concrete slabs with profiled steel sheets based on the developed nonlinear three-dimensional finite element models (FE) using the ABAQUS 2021 software [26]. For this purpose, a parametric study was carried out to observe the influence of certain parameters, such as the diameter and strength of the bolt, the geometry and strength of the concrete, and the steel grade of the CFS section. Furthermore, various failure modes were investigated, and the results were compared and evaluated with analytical values calculated using expressions from Eurocode 3 [16,27,28] and Eurocode 4 [9].

3. Theoretical Background of Shear Resistance

As previously mentioned, there are still no specific expressions or regulations for determining the resistance of bolted shear connections. The most common type of shear connection in composite steel–concrete beams is the one using welded-headed studs, which is also the only shear connection that has been standardised within the European standards [16,27,28], the Australian standard [29], and AISC 360-10 [30].

In this paper, thin CFS sections were used, unlike the usual sections used in steel–concrete composite structures. For this reason, it was necessary to check the CFS section’s hole-bearing resistance. EN 1993-1-3 [27] provides expressions for determining the resistances of the bolt and the CFS C section. Therefore, the characteristic value of the CFS section hole-bearing resistance can be calculated according to this expression:

$${\mathrm{F}}_{\mathrm{b},\mathrm{R}\mathrm{k}}={2.5·\mathrm{k}}_{\mathrm{t}}·{\mathsf{\alpha }}_{\mathrm{b}}·{\mathrm{f}}_{\mathrm{u}}·\mathrm{d}·\mathrm{t}$$

(1)

where k_t and α_b are the coefficients dependent on the load direction, f_u is the ultimate strength of the CFS C section, and d is the diameter of the bolt, while t is CFS C section thickness.

Due to the use of thin sections and cold-formed steel, there was a possibility of a loss of section stability. For simplification, the characteristic resistance of the cross-section to the axial compressive force can be assumed, i.e., calculated according to the expression given in EN 1993-1-1 [28]:

$${\mathrm{N}}_{\mathrm{R}\mathrm{k}}={\mathrm{f}}_{\mathrm{y}}·{\mathrm{A}}_{\mathrm{e}\mathrm{f}\mathrm{f}}$$

(2)

where f_y is the yield strength of the CFS C section, while A_eff represents the effective cross-section area.

Also, one of the possible failure modes was the shear failure of the bolt at the thread area. Therefore, the shear resistance of the connector could be calculated according to the expression given in EN 1993-1-8 [16]:

$${\mathrm{F}}_{\mathrm{v},\mathrm{R}\mathrm{k}}={\mathsf{\alpha }}_{\mathrm{v}}·{\mathrm{f}}_{\mathrm{u}\mathrm{b}}·{\mathrm{A}}_{\mathrm{s}}$$

(3)

where α_v is a factor defined in the relevant table which is taken with a value of 0.6 for bolts of quality 4.6 and 8.8, and f_ub represents the ultimate tensile strength, while A_s is the tensile stress area of the bolt when a shear plane passes through the threaded portion of the bolt.

In addition to the failure modes mentioned above related to steel elements, the failure modes of composite structures also had to be considered. The design resistance of shear connectors in solid slabs and concrete encasements according to EN 1994-1-1 [9] should be determined from the following equation:

$${\mathrm{P}}_{\mathrm{R}\mathrm{k}}=\mathrm{m}\mathrm{i}\mathrm{n}\left({\mathrm{P}}_{\mathrm{R}\mathrm{k},\mathrm{S}},{\mathrm{P}}_{\mathrm{R}\mathrm{k},\mathrm{C}}\right)$$

(4)

where P_Rk,S represents the resistance of the shear connection when the failure occurs through the steel shear connector, while P_Rk,C is the shear connection resistance when the failure occurs over the concrete surrounding the shear connector.

Their characteristic values can be calculated according to the following expressions:

$${\mathrm{P}}_{\mathrm{R}\mathrm{k},\mathrm{S}}=\frac{0.8·{\mathrm{f}}_{\mathrm{u}}·\mathsf{\pi }·{\mathrm{d}}^2}{4}$$

(5)

$${\mathrm{P}}_{\mathrm{R}\mathrm{k},\mathrm{C}}=0.29·\mathsf{\alpha }·{\mathrm{d}}^2\sqrt{{\mathrm{f}}_{\mathrm{c}\mathrm{k}}·{\mathrm{E}}_{\mathrm{c}\mathrm{m}}}$$

(6)

where d is the diameter of the shank of the stud (16 mm ≤ d ≤ 25 mm), while f_u is the ultimate tensile strength of the material of the shear connector but not greater than 500 N/mm².

α was calculated as follows:

$$\mathsf{\alpha }=\left\{\begin{array}{c}0.2\left(\frac{{\mathrm{h}}_{\mathrm{s}\mathrm{c}}}{\mathrm{d}}+1\right)\hspace{1em} \mathrm{f}\mathrm{o}\mathrm{r} 3\le {\mathrm{h}}_{\mathrm{s}\mathrm{c}}/\mathrm{d}\le 4\\ 1 \mathrm{f}\mathrm{o}\mathrm{r} {\mathrm{h}}_{\mathrm{s}\mathrm{c}}/\mathrm{d}>4\end{array}\right.$$

(7)

If profiled steel sheeting is used in a composite steel–concrete structure, it is necessary to reduce the shear connection strength by considering the reduction factor.

Considering that the ribs of the sheeting are placed transversely to the supporting beam, as in Figure 2, the reduction factor k_t was calculated as follows:

$${\mathrm{k}}_{\mathrm{t}}=\frac{0.7}{\sqrt{{\mathrm{n}}_{\mathrm{r}}}}\frac{{\mathrm{b}}_{\mathrm{o}}}{{\mathrm{h}}_{\mathrm{p}}}\left(\frac{{\mathrm{h}}_{\mathrm{s}\mathrm{c}}}{{\mathrm{h}}_{\mathrm{p}}}-1\right)$$

(8)

where n_r is the number of stud connectors in one rib, while the other symbols are defined in Figure 2.

Considering that, in the research, the ribs of the sheet were placed perpendicular to the CFS section, it was necessary to additionally reduce the calculated shear connection resistances by the reduction factor k_t. For the chosen geometry of the PSS panel with b₀ = 120 mm, h_p = 60 mm, two connectors per rib, and the height of the shear connector h_sc = 95 mm, the reduction factor was 0.58, which was less than the permissible upper limit value of 0.7 provided by EN 1994-1-1 [9].

The Australian standard, AS2327.1-2003 [29], defines the design rules for the resistance of welded-headed studs in a solid slab based on two possible failure modes, expressed in the following equation:

$${\mathrm{f}}_{\mathrm{v}\mathrm{s}}=\min \left\{\begin{array}{c}0.63·{\mathrm{d}}_{\mathrm{b}\mathrm{s}}^2·{\mathrm{f}}_{\mathrm{u}\mathrm{c}} \mathrm{The\; shear\; failure\; of\; the\; headed\; stud}\\ 0.31·{\mathrm{d}}_{\mathrm{b}\mathrm{s}}^2\sqrt{{\mathrm{f}}_{\mathrm{c}\mathrm{j}}^{\prime }·{\mathrm{E}}_{\mathrm{c}}} \mathrm{The\; concrete\; cone\; failure\; around\; the\; stud}\end{array}\right.$$

(9)

where d_bs is the diameter of a shear connector, f_uc represents the ultimate strength of the bolt material, and f′_cj is the concrete characteristic cylinder strength, while E_c represents the modulus of elasticity of the concrete. While welded-headed studs were not utilised in this study, the objective was to assess the applicability of this expression to demountable shear connectors.

AISC 360-10 [30] also provides an equation for determining the shear capacity of headed studs and channel shear connectors. Therefore, this study assessed the viability of employing this procedure to determine the shear resistance of a demountable shear connector, as expressed below:

$${\mathrm{Q}}_{\mathrm{n}}=\mathrm{m}\mathrm{i}\mathrm{n}\left\{\begin{array}{c}0.5·{\mathrm{A}}_{\mathrm{s}\mathrm{a}}\sqrt{{\mathrm{f}}_{\mathrm{C}}^{\prime }·{\mathrm{E}}_{\mathrm{C}}}\\ {\mathrm{R}}_{\mathrm{g}}·{\mathrm{R}}_{\mathrm{p}}·{\mathrm{A}}_{\mathrm{s}\mathrm{a}}·{\mathrm{F}}_{\mathrm{u}}\end{array}\right.$$

(10)

where A_sa represents the cross-section area of a connector, f′_C is the compressive strength of concrete, E_C is the modulus of elasticity of the concrete, and F_u represents the ultimate strength of the connector, while R_g and R_p are corrective factors.

4. Numerical Analysis

4.1. Specimens’ Geometry and Finite Element Types

As mentioned before, the ABAQUS software was used to develop a nonlinear FE model to demonstrate the behaviour and failure modes of the demountable bolted shear connection between the CFS section and the concrete slab. Due to the complex geometry and non-linearities included in the model, the ABAQUS Explicit [26] solver was used. The model represents a system which contains a built-up CWB connected using a spot welding technique, with the shear connection to the concrete slabs made using demountable bolted connectors, as shown in Figure 3. Bolts with embedded nuts in the concrete slabs were used in the models (a single nut was used on the concrete side). The bolts used in the model are shown schematically in Figure 4. This shows that the bolt diameter between the two nuts decreased due to the threads. Based on the surface of the bolt core, the reduced bolt diameter in the thread area was calculated [31]. The reason for using bolts with a diameter of 16 mm was the provision given in EN 1994-1-1 [9], which states that 16 mm is the minimum shank diameter of a headed stud. On the other hand, diameters of 12 mm and 14 mm have been used as bolts, which are considered structural bolt diameters, according to EN 1090-2 [32]. However, smaller diameters are also permissible for thin components and metal sheets. Therefore, 8 mm and 10 mm diameters were also included in the model to evaluate their behaviour in the proposed composite system.

One of the main objectives of this paper was to evaluate the behaviour of shear connections using demountable bolts, also including the diameters of the connectors that are not covered in EN 1994-1-1 [9]. Two different bolt grades, 4.6 and 8.8, were used to observe the behaviour of the composite connection. Grade 8.8 was chosen because it is most commonly used for structural bolting, while 4.6 was chosen to fulfil the requirement of EN 1994-1-1 [9], which allows the use of shear connectors whose strength is less than 500 N/mm². For the height of the bolts, it was necessary to fulfil the condition prescribed in EN 1994-1-1 [9] that the nominal height of a connector should extend at least 2d above the top of the steel deck. Accordingly, for the maximum used bolt diameter of d = 16 mm, a connector height of h_sc = 95 mm within the concrete was assumed in the models. As mentioned above, the connection between the CFS section and the CW was made using the spot welding technique. Although the shear force between the slab and the CWB is transmitted via a bolted connection, sufficient resistance of the spot welds must be ensured. As experimental tests on their resistance are not available yet, the spot welds in these numerical models were modelled using constraints to simulate rigid points and avoid any undesirable behaviour or failure.

Table 1. Summary of the parameters used in the study.

Bolts	Concrete Class	Steel Grade	Bolt Quality
M8	C20/25 C30/37 C40/50	S350GD S460NL	4.6 8.8
M10
M12
M14
M16

summarises the parameters whose effects were observed in this study. The geometry of the model itself consists of CFS C sections with dimensions of 120 × 47 × 3.0 mm made of steel grades S350GD and S460NL, while the CW connecting the C section has dimensions of 780 × 240 × 1.25 mm and is made of steel grade S350GD. The concrete slabs used in the model have dimensions in the plan of 720 × 600 × 120 mm with profiled sheets of the same dimensions in the plan and a thickness of 1 mm. The reinforcement of the concrete slab is Q524 mesh, with bars of 10 mm diameter spaced 150 mm apart in each direction.

For meshing concrete slabs, CFS C sections and connectors with eight-node brick elements with reduced linear integration (C3D8R) were used. Profiled steel sheeting was meshed using the four-node shell element with reduced integration (S4R), while for the reinforcement, a two-node 3D truss element (T3D2) was adopted. To maintain the accuracy of the simulation, mesh sensitivity analysis was performed. Therefore, the adopted sizes of meshing were 10 mm for the concrete slab, profiled steel sheeting, and corrugated web, 2 mm for the bolts, 3 mm for the CFS sections, and 25 mm for the reinforcement mesh.

4.2. Constitutive Models

4.2.1. Steel

The behaviour of steel materials is defined through a bilinear stress–strain curve according to EN 1993-1-5, Appendix C [33]. For all steel elements, the modulus of elasticity, Poisson’s ratio, and density values were assumed to be 210 GPa, 0.3, and 7850 kg/m³, respectively. As mentioned above, the steel used was S350GD; its yield and ultimate stress values are 350 MPa and 420 MPa, respectively, while values of 460 MPa and 550 MPa were assumed for S460NL steel. The FE models contain bolts listed in Table 1 of grade 8.8, giving the yield and ultimate stress values of 640 MPa and 800 MPa, respectively, while for grade 4.6, the yield and ultimate stress values are 240 MPa and 400 MPa, respectively. The ultimate strain value, εus, was assumed to be 15% for the S350GD and S460NL steels and 12% for the bolts. The reinforcement material was defined without strain hardening, i.e., the yield and ultimate stresses were assumed to be equal, corresponding to a value of 500 MPa.

4.2.2. Concrete

Cracking and crushing damage phenomena can occur in concrete, which must be considered in FE models to accurately describe the behaviour of concrete components. Therefore, the concrete damage plasticity (CDP) approach available in ABAQUS [26] was used in this study. The CDP approach is primarily intended to describe the behaviour of reinforced concrete members under cyclic or dynamic loading [34]. Two main mechanisms of concrete failure have been observed in the models, namely fracture in compression and cracking in tension. The CDP model, Figure 5, was adopted in accordance with publications [18,35], with adjustments made according to EN 1992-1-1 [36].

4.3. Interaction Conditions

Correctly defining the interaction conditions between elements that interact with each other ensures the correct transfer of horizontal and vertical forces. Appropriate constraints were used to define these interactions, such as surface-to-surface and general contact options in ABAQUS. The contact surfaces considered are those between bolts and steel elements, bolts and concrete slabs, and concrete slabs with PSS in models with a profiled slab, whereas with a solid concrete slab, the concrete slab is in contact with the CFS section. The same contact properties were defined for all contact surfaces, including a normal and a tangential behaviour that allows the correct force transmission between the elements. Normal behaviour defines ‘hard contact’ that minimises the penetration of the slave surface into the master surface and prevents the transfer of tensile stresses across the interface [26]. The tangential behaviour allows horizontal contact between the surfaces, and these contacts are considered to be a penalty formulation with a friction coefficient of 0.3, which is in the range of values adopted by a previous study [37]. Previous studies have investigated how the value of the friction coefficient affects the behaviour of this type of model, considering friction coefficients of 0.3–0.5 [20,38,39,40]. Also, the study described in the paper [20] compared the influence of different friction coefficient values on the connectors’ behaviour. The results showed that the friction coefficient did not significantly influence the connection’s behaviour.

Reinforcement mesh was embedded in the concrete slab, so the relative slip and debonding of the reinforcement were ignored. The interaction between the nut and bolt during tightening was also not considered, i.e., the nut and bolt were modelled as a single element. As mentioned above, the CFS C sections are connected to the corrugated web via spot welds. In this case, where the specimens contain a bolted shear connection, the shear force is transferred directly from the concrete slab to the CFS C sections via the bolts. Therefore, spot welds have no significant influence on the shear force transfer, so their actual resistance values were not considered. In this study, spot welds in the models were modelled as rigid points, using MPC-Link-type wire constraints to avoid undesirable behaviour or failure. In the future, the actual resistance values of the individual spot welds will be determined and integrated into FE models.

4.4. Boundary and Loading Conditions

Symmetrical boundary conditions were applied to the plane orthogonal to the X-axis, preventing displacement along the X direction and rotation around the Y and Z axes, in accordance with Figure 6. The bottom plane of the concrete slab was modelled as a support in which displacements in all directions were prevented to avoid movement of the concrete slab during the translation of the CFS beam. Following planned experimental tests, rotations and displacements in the horizontal X and Z directions were prevented at the top of the CFS beam, where the vertical displacement due to loading occurs, to avoid undesired local instability. Since the Abaqus Explicit Solver was used, it was necessary to keep the kinetic energy of the model under 10% of the total internal energy. Therefore, a uniform displacement of 10 mm in the vertical direction (Y-direction) was applied to the top of the CFS beam within a total time of 0.1 s.

5. Results and Discussion of the Parametric Numerical Study

5.1. Review of Failure Modes

A detailed review of the numerical model results revealed three main failure modes, as shown in Figure 7. The first failure mode manifested in the elongation of the bolt hole, i.e., when the bearing resistance of the bolt hole within the CFS section was reached. This mode of failure was usually followed by an inclination of the nut through the stretched holes. The second failure mode was related to concrete failure, where either cracking or crushing of the concrete around the shear connector occurred. In some models, failure of the concrete cone also occurred without the tearing of the shear connectors. This type of failure was caused by crushing the concrete around the shear connector, where cracks spread into the depth of the concrete slab in the form of a cone. This type of cracking was more noticeable in models with a lower concrete strength. The third failure mode was the shear failure of the shear connector at the area of the thread between the nuts, where the reduced radius was defined.

5.2. Bolted Shear Connection with a Profiled Concrete Slab

In this section, the results related to models containing a profiled concrete slab are presented. Here, cold-formed steel S350GD was used for all steel elements. Various parameters, such as the effect of the shear connector diameter, bolt quality, and concrete strength, were varied in the models in order to show their influence on the behaviour of the shear connection of the observed system.

5.2.1. The Effect of the Bolt Diameter

Here, the effect of the shear connector diameter on the behaviour of the model was investigated. It can be seen in Figure 8 that increasing the diameter of the bolt led to an increase in the bearing capacity, as well as the stiffness of the shear connector. From the obtained shapes of the force-displacement curves, it can be concluded that different failure modes occurred. Therefore, in the models with bolts M8 and M10, shear failure of the shear connector was observed at the thread between the two nuts. This failure mode was also characterised by the force plateau of the curves, after which almost no reduction of the bearing force occurred. This behaviour resulted from the fact that the failure of steel or the development of steel damage is not explicitly defined in ABAQUS. On the other hand, the models with M12, M14, and M16 bolts showed similar failure modes, i.e., concrete failure in tension and compression. In these cases, the bearing capacity decreased after reaching the ultimate strength, which was a consequence of the concrete failure.

5.2.2. The Effect of Different Bolt Qualities

To determine the influence of bolt quality on the behaviour of the shear connection, models were made using two bolt qualities, 8.8 and 4.6. Figure 9 shows the difference in the bearing capacity, as well as the stiffness of the shear connection for two bolt grades. In addition to the expected bearing strength difference for the various bolt material grades, different failure modes were also observed. Particularly, concrete failure occurred in the models with grade 8.8 bolts (M12, M14, and M16), while shear failure occurred in the area of the thread of the connector in models with bolt grade 4.6. The M8 and M10 bolts showed the same failure mode for both grades, 8.8 and 4.6.

5.2.3. The Effect of Concrete Strength

Models with various concrete strengths for each connector diameter were compared. From Figure 10, it can be observed that, with an increase in concrete strength, the maximum shear capacity of the connection also increased. It can also be seen from the shape of the curves that different failure modes occurred. Considering that, in the models where M8 and M10 bolts were used, concrete cone failure did not occur in low-strength concrete, it was expected that increasing the concrete strength would not change the resistance of the shear connection or the shape of the curve. Based on the shape of these curves and a detailed review of the numerical models, it is clear that shear failure of the connector occurred (Figure 7c). However, looking at the curves of the M12, M14, and M16 bolts showed that an increase in concrete strength led to an increase in the resistance of the shear connection and its ductility. All models with the M12, M14, and M16 bolts showed the same type of failure, namely failure of the concrete cone.

5.3. Bolted Shear Connection with a Solid Concrete Slab

5.3.1. The Effect of Bolt Diameter

Expectedly, through the observation of the obtained curves in Figure 11, it is evident that an increase in the bolt diameter led to an increase in the resistance of the shear connection, as well as its stiffness. From the shape of the obtained curve, it cannot be concluded that two failure modes occurred within the models. However, a detailed examination of the numerical models revealed two different failure modes. The first was a shear failure at the threaded area in models with M8, M10, and M12 bolts. In models with M14 or M16 bolts, the failure mode manifested in reaching the bearing resistance of the bolt hole in the CFS section, whereupon the nut was tilted through the stretched holes, which ultimately caused the deformation of the bolt in the threaded area.

5.3.2. The Effect of Different Bolt Quality

As previously mentioned, the use of the lower bolt quality of 4.6 led to an expected decrease in the value of the resistance and stiffness of the shear connection compared to models with bolts of 8.8 quality. It is also evident from the shape of the curves from Figure 12 that the failure modes were the same for all models, i.e., shear failure occurred at the thread area, and the bearing resistance of the bolt hole in the CFS section was reached. This occurred regardless of the change in the quality of the connector material.

5.3.3. The Effect of Concrete Strength

From Figure 13, it can be seen that increasing the strength of the concrete did not increase the resistance of the shear connection, as was the case when the profiled concrete slab was used. In other words, in models with a solid concrete slab, the shear resistance of the concrete was greater than the shear resistance of the connector at the thread area, which always led to the shear failure of the connector.

5.4. A Comparison of Shear Connection Behaviours with Solid and Profiled Concrete Slab

In this section, a comparison was made between models using profiled and solid concrete slabs, and their effects on the behaviour of the shear connection were observed. In both models, CFS C sections of the same thickness (3 mm) were used, for which S460NL steel was used, and the concrete class was C20/25, while the shear connection was made with M12 and M16 bolts of grade 8.8.

Looking at the curves from Figure 14 demonstrates that the models with a solid concrete slab (SS) achieved greater resistance and ductility of the shear connection, as well as a different failure mode. In the case of a solid concrete slab (SS), shear failure of the connector occurred in the area of the thread, as in the previous models, while the failure mode in models with a profiled concrete slab (PS) was a failure of the concrete cone. Indeed, the different failure modes, as well as the different resistances, were consequences of the application of profiled steel sheeting in the PS models; i.e., due to the profiled sheeting, it was necessary to consider the reduction factor according to EN 1994-1-1 [9], which reduces the ultimate resistance of the shear connection. For this very reason, it was expected that the SS models would achieve a higher shear strength value.

6. Comparison of Numerical and Analytical Results

In this section, the characteristic resistance values related to the models with varying bolt diameters defined in Section 5.2.1 and Section 5.3.1 are presented and compared with the numerically obtained resistance values.

Table 2. Comparison of numerically and analytically calculated results in kN.

Model Name	${\mathbf{F}}_{\mathbf{N}\mathbf{U}\mathbf{M}}$	Failure Mode	${\mathbf{F}}_{\mathbf{C}\mathbf{A}\mathbf{L}\mathbf{C}}$	${\mathbf{F}}_{\mathbf{C}\mathbf{A}\mathbf{L}\mathbf{C}}/{\mathbf{F}}_{\mathbf{N}\mathbf{U}\mathbf{M}}$	${\mathbf{k}}_{\mathbf{t}}·{\mathbf{F}}_{\mathbf{C}\mathbf{A}\mathbf{L}\mathbf{C}}$	${{\mathbf{k}}_{\mathbf{t}}·\mathbf{F}}_{\mathbf{C}\mathbf{A}\mathbf{L}\mathbf{C}}/{\mathbf{F}}_{\mathbf{N}\mathbf{U}\mathbf{M}}$
PS1_M8	164	S.F.C.	140	0.85	-	-
PS2_M10	254	S.F.C.	218	0.86	-	-
PS3_M12	306	C.F.	258	0.84	150	0.49
PS4_M14	340	C.F.	352	1.04	204	0.60
PS5_M16	368	C.F.	460	1.25	266	0.73
SS1_M8	166	S.F.C.	140	0.84	-	-
SS2_M10	280	S.F.C.	218	0.78	-	-
SS3_M12	374	H.B.F./S.F.C.	326	0.88	-	-
SS4_M14	400	H.B.F./S.F.C.	304	0.76	-	-
SS5_M16	428	H.B.F./S.F.C.	356	0.83	-	-

Note: S.F.C.—shear failure of the connector; C.F.—concrete cone failure; H.B.F.—hole bearing failure.

also shows the failure modes for each model, which have already been commented on in Section 5.2.1 and Section 5.3.1.

From the obtained results for models with a concrete slab made within profiled sheeting, it can be observed that, for smaller bolt diameters, the reduction factor k_t could be completely omitted or modified values could be used, whereas it must be considered for bolts M16. However, it should also be noted that the value of the reduction factor calculated according to EN 1994-1-1 [9] is too conservative for the analysed models. Despite these results, it should be noted that the use of the expressions given in EN 1994-1-1 [9] is questionable since the material characteristics and the connector diameters are out of the scope of the mentioned standard, as well as the type of shear connector used.

As can be noticed, the numerical values for models SS1_M8, SS2_M10, and SS3_M12 were higher than the calculated values for the shear failure of the bolt, which was ultimately to be expected, considering that the values calculated using standards must always be on the safe side. Similarly, in the SS4_M14 and SS5_M16 models, the numerical bearing capacity of the hole was also higher than the calculated value.

7. Conclusions

In this preliminary study, a parametric numerical analysis of 60 FE shear connection push-out models was carried out. The influences of various parameters, such as bolt diameter, bolt quality, and concrete strength, were investigated. In addition to varying the above parameters, two types of concrete slabs were used—a concrete slab made within profiled sheeting and solid concrete slabs—to determine their influence on the overall behaviour of the composite structure. By investigating the models in the present study, the following conclusions are provided, which need to be further confirmed via experimental tests:

• Increasing the diameter of the bolt results in an increase in the bearing capacity and stiffness of the shear connection. Different failure modes were also observed, depending on the diameter of the bolt and the type of concrete slab. Increasing the connector’s strength results in the expected increase in bearing capacity and stiffness if shear failure of the bolt occurs.
• Increasing the strength of the connector results in the expected increase in bearing capacity and stiffness when the shear failure of the bolt occurs.
• Increasing the strength of the concrete also increases the bearing capacity and stiffness of the shear connection. However, it should be noted that with a solid concrete slab, the resistance of the concrete (i.e., the failure of the concrete cone surrounding the shear connector) is much higher than the characteristic value according to the Eurocode, which ultimately leads to a different failure mode compared to a concrete slab made within profiled sheeting.
• The effect of the bolt diameter on the behaviour of different types of concrete slabs was investigated and compared with the equations according to the Eurocode. In the case of a concrete slab made within profiled sheeting, where the ribs are arranged transversely to the beam, it was necessary to consider a reduction factor. The results indicate that the reduction factor can be increased for higher diameters and can even be omitted entirely or used with modified values for smaller bolt diameters. In the case of a solid concrete slab, it was not necessary to apply the reduction factor due to the absence of profiled steel sheeting. However, it should be noted that the numerical values are much higher than the analytical values.
• Furthermore, the application of the reduction factor for steel strengths greater than 450 N/mm² and for shear connectors with diameters less than 16 mm must be confirmed through future experimental investigations.

Further laboratory and numerical research will provide greater insights into the overall behaviour of the analysed system. The laboratory research will provide more knowledge about the materials used (concrete, metal sheets, and shear joints), the spot welds, and the behaviour of the demountable shear connection in the analysed system. This will lead to the development of calibrated numerical models that will serve as benchmark models for future parametric and probabilistic analyses.