# Creep in steel-concrete composite beams bonded by adhesive and connected by studs

Alex Li, Ismail Yurtdas, Boussad Abbès

► To cite this version:

Alex Li, Ismail Yurtdas, Boussad Abbès. Creep in steel-concrete composite beams bonded by adhesive and connected by studs. Structures, 2025, 74, pp.108560. 10.1016/j.istruc.2025.108560. hal-05226712

HAL Id: hal-05226712

https://univ-reims.hal.science/hal-05226712v1

Submitted on 27 Aug 2025

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# Creep in steel-concrete composite beams bonded by adhesive and connected by studs

Alex Li*, Ismail Yurtdas, Boussad Abbes

Université de Reims Champagne-Ardenne, MATIM, Reims 51687, France

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

**Keywords:**

Creep
Composite beam
Shear stud
Steel
Adhesive
Finite element

## ABSTRACT

This study investigates the creep behavior of steel-concrete composite beams, comparing traditional shear stud connections with adhesive bonding. Unlike shear studs, adhesive bonding distributes stress more evenly along the interface, reducing stress concentrations and enhancing structural performance. It also eliminates the need for welding or bolting, significantly reducing construction time—an advantage particularly beneficial for prefabricated and modular structures. Flexural creep tests were conducted under constant loads for 120 days, with longitudinal deformations monitored. Three-dimensional finite element models incorporating linear viscoelastic theory were developed to analyze strain and stress evolution. Results highlight significant differences: adhesive-bonded beams exhibit lower creep strains and more uniform strain distribution compared to stud-connected beams. Creep strain follows a three-stage pattern: in the initial stage (0–9 days), adhesive bonding reduces the rate of creep increase by up to 39%; in the second stage (10–80 days), by up to 33%; and in the final stage, the creep stabilizes, with an overall reduction of up to 24%. Finite element simulations further demonstrate that adhesive bonding enhances stress redistribution and ensures a more uniform creep variation along the beam’s length, offering a promising alternative for long-term structural performance.

## 1. Introduction

Steel-concrete composite structures are widely employed in bridges and building construction due to their practical construction and high level of convenience. These structures combine the high tensile strength of steel with the high compressive strength of concrete. The performance of composite structures heavily relies on the connection between the steel beam and the concrete slab, traditionally achieved using steel connectors [1–3]. These shear connectors play a critical role in transferring longitudinal shear stresses at the interface between the steel beam and the concrete slab [4–6,24–28]. However, as this traditional steel connector technique has some drawbacks, including microcracks due to concrete shrinkage and stress concentration-induced cracks at the concrete-stud interface, the adhesive bonding technique has appeared as an alternative [7–9,11,29,30,34] (Fig. 1).

Steel-concrete composite structures connected by adhesive joints offer several advantages [7–9]:

* Speed of construction: Prefabricated concrete slabs eliminate the need for on-site concreting and welding stud groups.

* Uniform stress transfer: Adhesive joints ensure uniform and efficient stress transfer between the concrete slab and the steel beam surface.

* Homogeneous connection: The absence of steel studs creates a homogeneous surface connection, reducing shear stress concentrations.

* Crack prevention: Adhesive joints eliminate microcracks due to concrete shrinkage and stress concentration-induced cracks.

* Quality assurance: Adhesive joints allow for precast or prestressed concrete slabs, ensuring high-quality structural products.

* Mechanical strength: Adhesive connections offer high resistance and rigidity.

* Corrosion protection: Impermeable adhesive layers protect steel girders from corrosion.

* Vibration damping: Polymer-based adhesives can dampen vibrations.

* Safety: Adhesive connections simplify operations, reducing risks to workers.

Research into the mechanical performance of steel-concrete composite structures connected by bonding has spanned two decades

<footnote>* Corresponding author.
E-mail addresses: alex.li@univ-reims.fr (A. Li), ismail.yurtdas@univ-reims.fr (I. Yurtdas), boussad.abbes@univ-reims.fr (B. Abbes).</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 1. Steel beam and concrete slab connected by studs or adhesive.</figcaption></figure>

[9–11]. Experimental and analytical results confirm that it is feasible to create composite structures with multiple concrete slabs without altering the fundamental behavior of the composite beam: the steel beam supports tensile loads, and the concrete slab supports compressive loads. Rigid adhesive bonding enables the two materials, steel beam and concrete slab, to act as one. Consequently, the bonded steel-concrete composite beam's maximal stress occurs at the mid-span, decreasing towards the beam ends, similar to reinforced concrete beams.

For steel-concrete beams connected by shear studs, the following failure modes are observed under short-term loading [9,24]: concrete cracking due to local tensile stress, concrete crushing under compressive stress, and extensive yielding of the steel beam under global bending moments. When subjected to a sustained loading, concrete exhibits an additional deformation called creep, in addition to instantaneous deformation [31,32]. This time-dependent deformation is inevitable in reinforced concrete structures [33], even in bonded steel-concrete composite structures, and remains largely unexplored in the literature.

Creep is significantly impacting the long-term behavior and durability of reinforced concrete structures [31,33]. It is a gradual, often imperceptible deformation that develops over time when concrete sustains continuous or sustained loads. Excessive creep can lead to issues such as cracking, deflection, and reduced load-carrying capacity.

In reinforced concrete beams, creep is influenced by factors including concrete mix design, environmental conditions, loading duration, and the presence of reinforcing steel. Engineers employ empirical models and equations to predict and account for creep's effects in structural designs, ensuring the continued safety and functionality of structures over their intended service life.

This comprehensive exploration of creep in reinforced concrete beams will delve into its underlying mechanisms, factors influencing creep, prediction methods, and strategies for mitigating its effects. A profound understanding of creep behavior in concrete beams empowers engineers and construction professionals to make informed decisions, designing and constructing durable, safe, and reliable structures to meet the demands of our built environment. Creep, as a critical aspect of concrete's long-term performance, has consistently drawn researchers' attention. Its occurrence not only increases structural deformation and redistributes internal forces and sectional stresses but also impacts a structure's natural frequency and dynamic response.

According to research results [12–15], concrete creep is more pronounced at early ages, decreasing over time. The creep behavior of concrete structures depends on various parameters, including curing methods, concrete strength, composite admixtures, mineral powder content, loading duration, and other factors. A significant increase in deflection at long-term were reported for steel-concrete composites with shear connectors [2,16,28]. For bonded steel-concrete composite beams, which consist of precast reinforced concrete slabs and steel beams, the conditions differ from fresh concrete. However, there is still a lack of experimental investigation for this type of structure.

This study addresses a critical gap in existing literature by investigating adhesive bonding as a viable alternative to shear studs in steel-concrete composite beams, particularly focusing on creep behavior under sustained loading. By employing a dual approach that combines experimental testing and finite element modeling, this research provides

a comprehensive understanding of long-term performance, extending beyond the short-term assessments typically found in prior studies of traditional connection methods. Understanding creep behavior is vital to ensuring the long-term serviceability of composite structures, especially in modern construction applications such as prefabricated buildings and bridges. Adhesive bonding offers notable advantages, including faster assembly and improved structural efficiency, making it a promising solution for sustainable and innovative construction practices.

The study provides insights into how creep affects the structural performance of steel-concrete composite beams under sustained loading over time, filling a gap in long-term material behavior research. The findings can lead to better design guidelines for steel-concrete composite beams, ensuring their reliability and safety in real-world applications like bridges, high-rise buildings, and industrial structures.

While extensive research exists on the performance of shear stud connections, these studies frequently highlight challenges such as non-uniform strain distribution and stress concentrations. This research advances the field by comparing these challenges with the more uniform and stable creep behavior exhibited by adhesive-bonded beams. The primary objective of this study is to analyze the long-term creep behavior of adhesive-bonded steel-concrete composite beams relative to shear stud-connected beams.

This study investigates the creep behavior of steel-concrete composite beams, comparing traditional shear stud connections with adhesive bonding. Flexural creep tests were conducted under constant loads for 120 days, with longitudinal deformations monitored. Three-dimensional finite element models incorporating linear viscoelastic theory were developed to analyze strain and stress evolution. Results highlight significant differences: adhesive-bonded beams exhibit lower creep strains and more uniform strain distribution compared to stud-connected beams.

The creep strain exhibits a linear variation over time and can be divided into three distinct phases. In the first phase, it increases rapidly. In the second phase, the rate of increase slows but remains significant. In the final phase, the creep strain stabilizes, showing no substantial further changes. Notably, adhesive bonding significantly reduces both the rate of creep strain increase and the overall creep value. Finite element simulations further demonstrate that adhesive bonding enhances stress redistribution and ensures a more uniform creep variation along the beam's length, offering a promising alternative for long-term structural performance.

The following sections will illustrate the beam's geometry details, measurement positions, experimental results, the applied numerical analysis method, numerical results, and the comparison between experimental and numerical results.

## 2. Material and experimental methods

### 2.1. Steel-concrete composite beams

The experiments conducted in this study focused on characterizing the deformations of steel-concrete composite beams subjected to constant long-term loads. Long-term three-point bending tests were performed on beams with the geometry illustrated in Fig. 2. The composite beam, measuring 3.5 m in length and spanning 3.25 m, was loaded at its mid-span.

The steel beam used was an IPE-200 with a cross-sectional area of 28.5 cm². The concrete slab had a cross-section of 350 × 55 mm² with a network of reinforcement bars, each having a diameter of 6 mm. The distance between the two reinforcement bars was 300 mm in the longitudinal direction and 25 mm in the vertical direction.

This study tested two types of composite beams. Based on Eurocode 4 and the technical specifications of the adhesive used, 18 shear studs and a 4 mm adhesive layer were selected.

The first steel-concrete composite beam achieved full connection using 18 shear steel studs (Fig. 3). The second composite beam achieved
<figure><img src="image_5.png" /><figcaption>Fig. 2. Geometry of the steel-concrete composite beam under a 3-point long-term bending test.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. Geometry of the steel-concrete composite beam connected with 18-shear steel studs.</figcaption></figure>

full connection through a 4 mm adhesive layer (Fig. 4).

The geometry of the composite beams was designed to induce the maximum shear stress in the adhesive layer. The dimensions of the composite beams are provided in Table 1.

## 2.2. Materials

For a steel-concrete composite structure, the strength of the assembly depends significantly on the construction materials, including concrete, steel, and adhesive, as well as the interfaces between steel, adhesive, and concrete. It is evident that concrete exhibits a brittle behavior, while steel demonstrates an elastic-plastic response. The choice of adhesive type is contingent upon the materials being joined and the required ultimate strength of the composite structure. In this study, we selected a two-component epoxy adhesive consisting of resin and hardener. The mechanical properties of the adhesive are as follows: compressive strength = 55 MPa, flexural strength = 32 MPa, elastic modulus = 12,300 MPa, shearing tensile strength = 15 MPa, and Poisson's ratio = 0.34.

In a steel-concrete composite structure connected via an adhesive system, it is well-known that shearing failure can occur either at the steel-adhesive-concrete interface or within the concrete itself [9]. Among the three materials used, both interfaces and the concrete are particularly susceptible to shear failure. To achieve the required shear strength for the concrete, its compressive strength was set at 70 MPa, and its measured elastic modulus was 36,600 MPa. The steel beam used was an IPE200 with a yield stress of 365 MPa and an elastic modulus of 205,000 MPa.

For a hybrid steel-concrete structure, the bonding process demands meticulous care and special attention due to the critical importance of assembly quality. In this study, the surfaces of steel and concrete intended for bonding were sanded and subsequently cleaned with a solvent.

<table><caption>**Table 1**
Dimensions of the composite beams.</caption><thead><tr><th>L (m)</th><th>a (m)</th><th>h<sub>s</sub> (cm)</th><th>b<sub>s</sub> (cm)</th><th>t<sub>w</sub> (mm)</th><th>b<sub>c</sub> (cm)</th><th>h<sub>c</sub> (cm)</th><th>t<sub>f</sub> (mm)</th><th>t<sub>a</sub> (mm)</th></tr></thead><tbody><tr><td>3.30</td><td>0.125</td><td>20</td><td>10</td><td>5.6</td><td>35</td><td>5.5</td><td>8.5</td><td>4</td></tr></tbody></table>

## 2.3. Loading and measurements

A mixed steel-concrete beam assembled using an adhesive joint was tested to failure. The ultimate load capacity of this beam was used as a reference for subsequent experimental tests.

Preliminary tests determined the ultimate load for both composite beams to be $F_u = 160$ kN. During the long-term testing phase, a sustained force of $F = 48$ kN (equivalent to 30 % of the ultimate load) was applied.

To minimize the potential impact of manual measurement errors, several precautions were taken:

* The beams were stored in a controlled laboratory environment maintained at a constant temperature of $20 \pm 2^{\circ}$C.

* All measurements were conducted by the same operator using the same measuring device throughout the experiment.

* Before each measurement, the applied load was thoroughly checked to ensure that it was consistent and accurate.

Creep monitoring is conducted at 18 designated positions, as illustrated in Fig. 5. Each measured section has an initial length of 10 cm. These positions are categorized as follows:

### i. Surface of the concrete slab

Ten measurement points are located on the surface of the concrete slab.

Positions labeled $P_1$, $P_2$, $P_3$, $P_4$ and $P_5$ correspond to points situated 1 cm below the upper surface of the concrete slab.

Positions labeled $P'_1$, $P'_2$, $P'_3$, $P'_4$ and $P'_5$ indicate measurement points located 1 cm above the bottom surface of the concrete slab.

<figure><img src="image_7.png" /><figcaption>Fig. 4. Geometry of the steel-concrete composite beam connected with adhesive.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig. 5. Creep monitoring positions for the two beams (dimensions in cm).</figcaption></figure>

## ii. Concrete-steel interface

Three measurement points are positioned at the interface between the concrete slab and the steel beam, labeled as $P_{C-S1}$, $P_{C-S2}$, and $P_{C-S3}$.

## iii. Bottom surface of the steel beam

Five measurement positions are designated on the bottom surface of the steel beam, labeled $P_{S1}$, $P_{S2}$, $P_{S3}$, $P_{S4}$ and $P_{S5}$.

Manual measurements are taken every two to four days, with the initial measurements performed after 28 days of concrete hardening. The measured elongations are used to calculate the creep longitudinal deformation at each position using the formula:

$$Creep = (l_p(t) - l_p(t_0))/l_p(t_0) \qquad (1)$$

Where, $l_p(t)$ represents the length at position i at time t, and $l_p(t_0)$ represents the length immediately after applying the sustained load at the start of the long-term experiments.

The measurement of creep was stopped at 120 days because the creep values had stabilized, indicating no significant additional deformation over time.

# 3. Finite element modeling

## 3.1. Constitutive models

The state of stress in the steel beam and shear stud connectors is modeled using linear elasticity. Both the steel beam and the shear connectors do not exhibit time-dependent behavior and remain elastic during the serviceability stage.

In this study, the time-dependent behavior of concrete is approached using an isotropic linear model of a viscoelastic material, with shrinkage being neglected. Under conditions of small deformations, the constitutive behavior of such a material, based on the Boltzmann superposition principle, can be represented in the form of an integral equation, as described by [17]:

$$\sigma(t) = \int_{0}^{t} G(t - \tau) \frac{\partial \varepsilon(\tau)}{\partial \tau} d\tau \qquad (2)$$

where $\sigma(t)$ is the time-dependent stress, $\varepsilon(\tau)$ is the time-dependent strain and $G(t)$ is the time-dependent relaxation function that characterizes the material's response.

The relaxation modulus can be written in the following dimensionless form:

$$g(t) = G(t)/G_0 \qquad (3)$$

where $G_0 = G(0) = \frac{E_0}{2(1+\nu_0)}$ is the instantaneous shear modulus, $E_0$ is the instantaneous elastic modulus and $\nu_0$ is the instantaneous Poisson's ratio.

In ABAQUS software the viscoelastic material is defined by a Prony series expansion of the dimensionless relaxation modulus [18]:

$$g(t) = 1 - \sum_{i=1}^{N} g_i (1 - e^{-t/\tau_i}) \qquad (4)$$

where $N$, $g_i$, and $\tau_i = \eta_i/g_i$, $i = 1, 2, \dots, N$, are material constants.

The viscoelastic model consists of elastic and viscous elements combined into multiple networks connected in parallel (Fig. 6). The viscoelastic networks are represented by Maxwell elements, i.e., a combination of spring and damper elements. The number of viscoelastic networks is arbitrary (1 to N).

The bonded joint of the hybrid beam is assumed to consist of a viscoelastic material, and the model mentioned earlier can be applied. It is noteworthy that the epoxy used for bonding the steel I-beam to the concrete beam may exhibit shear creep behavior. Its creep properties can have an impact on the distribution and magnitudes of interfacial adhesive stresses, both in shear and peeling. Several studies conducted on the long-term behavior of FRP-strengthened concrete beams [19–21] have highlighted the significance of the rate of creep in epoxy adhesives.

For the calibration of the model defined by Eq. (4), experimental creep results are extracted from the literature for the concrete [22] and the adhesive [23]. These experimental datasets are used in a nonlinear least-squares fit to determine the Prony series parameters ($g_i$, $\tau_i$) for the concrete and the adhesive. In this study, the number of viscoelastic networks is defined as $N = 2$. This was found enough to fit the experimental datasets. Fig. 7 shows the comparison between the experimental creep curves and the fitted models for concrete and adhesive. Tables 2 and 3 present the values of the elastic properties and the determined Prony series parameters, respectively. These properties are then used as input data for the finite element simulations of the creep of the steel-composite beams under three-point bending test.

## 3.2. Simulation setup

A numerical model has been developed to conduct the creep study

<figure><img src="image_9.png" /><figcaption>Fig. 6. Linear viscoelastic model with multiple parallel networks.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig. 7. Comparison between the experimental creep curves and the fitted models: (a) Concrete, (b) Adhesive.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Table 2**

Elastic properties of materials.</figcaption></figure>

<table><caption>**Table 3**

Prony series parameters.</caption><thead><tr><td>Material</td><td>Elastic Modulus (MPa)</td><td>Poisson's ratio</td></tr></thead><tbody><tr><td>Steel</td><td>205000</td><td>0.3</td></tr><tr><td>Concrete</td><td>36600</td><td>0.28</td></tr><tr><td>Epoxy resin</td><td>12300</td><td>0.34</td></tr></tbody></table>

<table><thead><tr><th rowspan="2">i</th><th colspan="2">Concrete</th><th colspan="2">Adhesive</th></tr><tr><th>g<sub>i</sub></th><th>τ<sub>i</sub> (s)</th><th>g<sub>i</sub></th><th>τ<sub>i</sub> (s)</th></tr></thead><tbody><tr><td>1</td><td>0.4937</td><td>6.1898E+06</td><td>0.6100</td><td>532.8</td></tr><tr><td>2</td><td>0.1319</td><td>5.0841E+07</td><td>0.1400</td><td>3.3468E+06</td></tr></tbody></table>

using the finite element software ABAQUS. The numerical representation of the steel-concrete composite beams is depicted in Fig. 8.

To reduce computational time, only half of the composite beam is modeled, thanks to its inherent symmetry. These composite beams consist of three components: a steel beam, a concrete slab, and either shear studs or an adhesive layer. All these parts are represented using 3D, 8-node, linear, brick (C3D8R) elements with reduced integration and hourglass control.

The test setup involves applying a load at the mid-span of the composite beam. A simple support condition is applied at a distance of 12.5 cm from the end of the I-beam by constraining the translation in the y direction (U<sub>y</sub>), as shown in Fig. 9.

The solution to the model is computed using a transient, static,

<figure><img src="image_12.png" /><figcaption>Fig. 8. Finite element models of the steel-composite beams.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 9. Finite element boundary conditions.</figcaption></figure>

stress/displacement analysis with a time-dependent material response approach available in ABAQUS Standard software.

# 4. Results and discussion

## 4.1. Experimental results

Figs. 10 to 13 illustrate the measured creep values at eighteen designated positions (as shown in Fig. 5) for both shear stud-connected and bonded steel-concrete composite beams. Moreover, the creep values at the end of creep tests for the two steel-concrete composite beams are reported in Table 4 as a function of monitoring position.

The experimental results reveal typical creep behavior on both the upper (Fig. 10) and lower (Fig. 11) surfaces of the reinforced concrete slab (designated as P<sub>i</sub> and P<sub>i</sub>, respectively, where i ranges from 1 to 5). Initially, the creep strains escalate rapidly within the first few days of the experiment before stabilizing. As anticipated, the strain on the upper surface (Fig. 10) is greater than that on the lower surface (Fig. 11) also detailed in Table 4. Additionally, the creep strain tends to increase more rapidly and to higher levels at a measurement position closer to the middle of the beam (i.e., P<sub>5</sub>) compared to a position nearer to the beam's end (i.e., P<sub>1</sub>).

Although the evolutions of strains in reinforced concrete slab for the bonded steel-concrete composite beam (Figs. 10(b) and 11(b)) are comparable to those for the shear stud-connected composites beam (Figs. 10(a) and 11(a)), they increase with a slower rate and reach lower values by about 25–67% (Table 4). Recall that the concrete slab was directly poured on the shear stud connect while the precast concrete was bonded on the I-beam after 28 days of concrete curing. It is reported that the in-situ casting of concrete accentuates the shrinkage-induced micro-cracking compared to precast concrete [11,29]. Therefore, it is thought that a part of the difference in strain could come from the occurrence of a
<figure><img src="image_14.png" /><figcaption>Fig. 10. Creep on the upper surface of SCCBS18 (a) SCCBA (b) beams.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 11. Creep on the lower surface of SCCBS18 (a) SCCBA (b) beams.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 12. Creep at the concrete-steel interface of SCCBS18 (a) SCCBA (b) beams.</figcaption></figure>

higher shrinkage-induced micro-cracking in the shear stud-connected composite beam compared to that in the bonded steel-concrete composite beam. The shrinkage-induced micro-cracking probably accentuates the strains under creep for the first beam. Another part of this difference could come from the fact that the adhesive ensures a stronger connection compared to shear studs, enhancing the composite structure's resistance to creep deformation under bending. This behavior is attributed to structural interactions rather than solely material properties. This improves the opposing force of the composite structure to concrete creep.

Fig. 12 shows the measurement of slip at different positions between the surface of the reinforced concrete slab and the I-beam. For a given composite beam, the strain increases slightly with time of creep test in

particular for the interface positions of $P_{C-S2}$ and $P_{C-S3}$ then tend to stabilization. The difference in the evolution of strain is observed mainly after 30–40 days. The closest is the measurement position to the loading applied point the higher is the strain value, even if this one remains relatively low in the absolute. This would mean that the slip does not only depends on the shear force distribution as it is constant between the support and the load applied point for the present study. A slip value between the support and the load applied point is also reported in the case of a four-point short-term mechanical test where the shear force is null [6]. The measured creep values at the concrete-steel interface positions $P_{C-S1}$ and $P_{C-S2}$ for the SCCBA beam closely resemble those for the SCCBS18 beam (Fig. 12). However, for position $P_{C-S3}$, the SCCBS18 beam registers a slightly lower value compared to the SCCBA beam. This
<figure><img src="image_17.png" /><figcaption>Fig. 13. Creep on the bottom face (I profile) of SCCBS18 (a) SCCBA (b) beams.</figcaption></figure>

<table><caption>**Table 4**
Comparison of creep values.</caption><thead><tr><th>Position</th><th>SCCBS18<br>(μm/m)</th><th>SCCBA (μm/m)</th><th>(SCCBS18/ SCCBA) (%)</th></tr></thead><tbody><tr><td>P<sub>1</sub></td><td>100</td><td>80</td><td>25</td></tr><tr><td>P<sub>2</sub></td><td>130</td><td>90</td><td>44</td></tr><tr><td>P<sub>3</sub></td><td>150</td><td>90</td><td>67</td></tr><tr><td>P<sub>4</sub></td><td>160</td><td>110</td><td>45</td></tr><tr><td>P<sub>5</sub></td><td>170</td><td>130</td><td>31</td></tr><tr><td>P'<sub>1</sub></td><td>90</td><td>60</td><td>50</td></tr><tr><td>P'<sub>2</sub></td><td>100</td><td>60</td><td>67</td></tr><tr><td>P'<sub>3</sub></td><td>110</td><td>70</td><td>57</td></tr><tr><td>P'<sub>4</sub></td><td>120</td><td>90</td><td>33</td></tr><tr><td>P'<sub>5</sub></td><td>130</td><td>100</td><td>30</td></tr><tr><td>P<sub>S1</sub></td><td>-30</td><td>-40</td><td>-25</td></tr><tr><td>P<sub>S2</sub></td><td>-40</td><td>-50</td><td>-20</td></tr><tr><td>P<sub>S3</sub></td><td>-50</td><td>-70</td><td>-29</td></tr><tr><td>P<sub>S4</sub></td><td>-70</td><td>-80</td><td>-12</td></tr><tr><td>P<sub>S5</sub></td><td>-90</td><td>-90</td><td>0</td></tr><tr><td>P<sub>C-S1</sub></td><td>10</td><td>10</td><td>0</td></tr><tr><td>P<sub>C-S2</sub></td><td>30</td><td>30</td><td>-0</td></tr><tr><td>P<sub>C-S3</sub></td><td>40</td><td>50</td><td>-20</td></tr></tbody></table>

difference in behavior can be due to the location in the SCCBS18 beam of the shear studs which are situated outside of the measurement span, while the studs are nearly at the middle of the first two measurement spans, effectively acting as supports. This distinction is depicted in Fig. 14. Thus, these results on the slip at the concrete-steel interface under creep clearly depend on the type of connection even if the difference in strains between the two type of connection is small for the creep loading of the present study.

The strains observed on the bottom face of the I-beam (Fig. 13) exhibit a similar pattern of evolution, albeit in the opposite direction to those observed on the reinforced concrete slab. These strains are generally lower than those observed on the upper face of the concrete. This is mainly due to higher elastic modulus of steel compared to the effective elastic modulus of concrete, leading to register lower strains on the bottom face of the I-beam. The development of micro-cracks in the concrete induced by shrinkage and creep [11] can probably accentuate the difference in strains between the upper and lower faces of steel-concrete composite beam. The deformation in the steel, which

experiences no creep, counteracts the creep deformation observed in the concrete slab, effectively equilibrating it. Additionally, it appears that the creep experienced by the I-beam is marginally more pronounced in the bonded composite beam compared to the shear steel stud composite beam (as outlined in Table 4). This observation underscores the influence of the connection mode between the steel beam and the concrete slab on the phenomenon of creep.

The experimental investigation of creep variation in the concrete slab over time reveals three distinct linear stages. Fig. 15 and Table 5 illustrate the behavior of the concrete's upper surface.

In the initial stage (0–9 days), the creep strain in the composite beam SCCBS18 follows a linear trend described by the equation $y = 9.45x$, where y represents the creep strain (in µm/m) and x denotes time (in days). The rate of creep increase is 9.45, leading to a rise from 0 to 90 µm/m. In comparison, the composite beam SCCBA follows a linear equation $y = 5.80x$, with a lower creep rate of 5.80. This indicates that adhesive bonding reduces the rate of creep increase by up to 39%, resulting in a creep strain increase from 0 to 60 µm/m. The creep progression in SCCBA is 1.6 times slower than in SCCBS18, likely due to the uniform and homogeneous bond between the steel section and the concrete slab, ensuring a well-integrated connection.

In the second stage (9–80 days), the creep strain in SCCBS18 follows the equation $y = 1.29x + 74$, with a rate of increase of 1.29. The slope is 7.3 times lower than in the first stage, and the creep strain rises from 90 to 170 µm/m. In SCCBA, the creep strain variation is represented by $y = 0.87x + 47$, with a rate of increase of 0.87–6.6 times lower than in the first stage. At this stage, adhesive bonding reduces the rate of creep increase by up to 33%, with the creep value rising from 60 to 130 µm/m. The increase in creep is 1.5 times slower compared to SCCBS18, and the final creep strain is 1.3 times lower, decreasing from 170 to 130 µm/m.

In the final stage (beyond 80 days), the creep strain stabilizes, with an overall reduction of up to 24%. For SCCBS18, the ultimate creep strain reaches 170 µm/m, whereas in SCCBA, it is limited to 130 µm/m, confirming the effectiveness of adhesive bonding in reducing long-term deformation.

Experimental results clearly demonstrate that composite beams bonded with adhesive exhibit significantly lower creep strain compared to those assembled with shear steel studs. This highlights the potential of adhesive bonding as an effective alternative for minimizing long-term

<figure><img src="image_18.png" /><figcaption>Fig. 14. Position of the measurement span at the concrete-steel interface in the beam.</figcaption></figure>
<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /><figcaption>Fig. 15. Creep trend curve of composite beams SCCBS18 (left) and SCCBA (right) at mi-span.</figcaption></figure>

<table><caption>**Table 5**
Variation of creep strain as a function of time.</caption><thead><tr><th>Level</th><th></th><th>Stage 1</th><th>Stage 2</th><th>Stage 3</th></tr></thead><tbody><tr><td>Time (day)</td><td></td><td>0-9</td><td>9-80</td><td>80-108</td></tr><tr><td rowspan="2">Creep strain (μm/m)</td><td>SCCBS18</td><td>y = 9.45x</td><td>y = 1.29x+74</td><td>170</td></tr><tr><td>SCCBA</td><td>y = 5.80x</td><td>y = 0.87x+47</td><td>130</td></tr><tr><td>Ratio of slope (SCCBS18/ SCCBA)</td><td></td><td>1.6</td><td>1.5</td><td>—</td></tr></tbody></table>

creep in steel-concrete composite structures.

## 4.2. Finite element results

This study aims to deepen our understanding of how the distribution of shear stress is affected by the creep behavior of constituent materials in composite structures, as well as to explore stress redistribution. Figs. 16 and 17 present a comparison between the experimental

longitudinal creep deformation obtained through experiments and numerical simulations for the two composite beams SCCBS18 and SCCBA, respectively. Upon evaluating the consistency of creep behavior between the measured experimental data and simulation curves, some differences were noted. However, overall, the predictions of the proposed model are satisfactory and effectively capture the experimentally observed increases in longitudinal deformations.

The first factor concerns the omission of reinforcement steel bars in the numerical model. In fact, steel is a ductile material, and it has more capacity to strengthen in terms of shear and tension [35]. Another factor is related to the concrete behavior that is considered as linear elastic but is in fact nonlinear and is modeled using the concrete damaged plasticity (CDP) model accounting for damage and cracks propagation in the concrete slab during loading [36,37] available in Abaqus software. However, these nonlinear models cannot be combined with the visco-elastic model given in Eq. (3-5) in Abaqus software. The shrinkage effect is not available in Abaqus software and needs the development of a

<figure><img src="image_21.png" /><figcaption>Fig. 16. Comparison of experimental and FEM creep results for SCCBS18 beam.</figcaption></figure>

<figure><img src="image_22.png" /></figure>
<figure><img src="image_23.png" /><figcaption>Fig. 17. Comparison of experimental and FEM creep results for SCCBA beam.</figcaption></figure>

specific program like the one recently developed by Zhu et al. [38] using the subroutine interface program UMAT provided by Abaqus software.

Additionally, some other model assumptions, such as perfect adhesive bonding and the ideal connection of shear steel studs, may also contribute to these differences. Indeed, shear studs cause stress concentration in the concrete and may exhibit significant slip, which results in partial interaction [29]. The stress concentration around the shear studs is clearly shown in Fig. 18(b).

Numerical analyses using finite element methods allow for the evaluation of local strain and stress distribution by varying the applied loads. Fig. 17 shows the stress distribution at three load levels equivalent to 30 %, 60 %, and 80 % of the ultimate loads. As seen in Fig. 17, the

stress distribution in the concrete slab differs between the two composite beams.

For the SCCBS18 beam (Fig. 16), the von Mises stress is concentrated around the steel studs at the midpoint of the composite beam. Outside this area, the von Mises stresses are minimal and almost negligible. As the load increases from 30 % to 80 % of the ultimate load, the von Mises stress around the middle stud zone also increases, clearly indicating significant creep in this local area around the middle steel stud. Conversely, in other regions, the creep value remains small and negligible.

For the SCCBA beam (Fig. 17), the maximum von Mises stress is concentrated around the middle of the composite beam. The stress value in the concrete slab exceeds that in the steel beam and decreases along the longitudinal direction of the beam. Fig. 17 indicates that the stress variation is homogeneous in the transverse direction, with the stress variation illustrated in several zones. This implies that the creep value linearly decreases in the longitudinal direction. These results are consistent with those obtained from experimental tests.

At load levels corresponding to 30 % and 60 % of the ultimate loads, the creep value increases near the middle steel stud zone while remaining small in other regions. At 60 % of the ultimate load, numerical results indicate that the concrete near the middle steel stud is damaged, with initial microcracks recorded. The connection provided by the stud between the concrete slab and the steel beam has deteriorated, causing a considerable increase in creep in this area.

Numerical analyses using finite element methods enable the evaluation of local strain and stress distribution under varying applied loads. Fig. 18 presents the finite element stress distribution at three load levels: 30 %, 60 %, and 80 % of the ultimate load. The results highlight notable differences in stress distribution between the two composite beams.

For the SCCBA beam (Fig. 18a), the maximum von Mises stress is concentrated around the mid-span of the beam, where the bending load is applied. The stress within the concrete slab remains below its compressive strength of 70 MPa and gradually decreases along the

<figure><img src="image_24.png" /><figcaption>Fig. 18. Von Mises stress distribution on concrete slab: (a) SCCBA beam, (b) SCCBS18 beam.</figcaption></figure>
longitudinal direction of the beam. Additionally, the stress distribution appears homogeneous in the transverse direction, indicating a uniform transfer of load. This consistency aligns with experimental observations, where creep values also exhibit a linear decrease along the beam's length.

In contrast, the SCCBS18 beam (Fig. 18b) exhibits localized stress concentrations around the steel studs at the mid-span. Outside this region, the von Mises stress remains minimal and nearly negligible. As the applied load increases from 30% to 80% of the ultimate load, stress intensifies around the middle stud, signifying significant creep development in this localized zone. In other areas, however, the creep remains relatively low and negligible.

At a load level of 30% of the ultimate load, the von Mises stress in the concrete slab near the studs exceeds its compressive strength of 70 MPa, suggesting that concrete in this region is undergoing damage. As the load increases to 60% and 80%, the damaged zone expands further. These findings indicate that, in the early stages of loading, the connection between the concrete slab and the steel beam—provided by shear studs—begins to deteriorate. This deterioration leads to a considerable increase in localized creep around the middle steel stud, ultimately affecting the structural integrity of the composite beam.

To understand the effect of the type of connection between the concrete slab and the steel surface on creep, the numerical axial strain and stress distributions over the midspan section of beams are plotted at four different times in Figs. 19 and 20, respectively. As shown in the Fig. 19(a), in the SCCBS18 beam, the steel IPE200 beam experiences both tensile and compressive stresses, while the concrete slab primarily undergoes compressive stresses, except for a small portion near the interface. Over time, the redistribution of stresses at the midspan section is influenced by concrete creep.

In this simulation, only the concrete slab undergoes creep. The model assumes a perfect connection only between the concrete slab and the studs, leading to discontinuities in axial strain distribution between the concrete slab and the steel stud surface as shown in Fig. 20(a).

In the SCCBA beam, the concrete slab experiences compressive stresses (Fig. 19(b)), while the steel beam undergoes both tensile and compressive stresses due to the presence of adhesive. Over time, the stresses at the midspan section redistribute because of the combined effects of concrete and adhesive creep. Additionally, the depth of the neutral axis in the concrete slab increases compared to its initial value. The presence of the adhesive reduces the strain discontinuity at the interface as shown in Fig. 20(b). It is very low and almost constant over time (0.001%) for the SCCBA beam, whereas it increases from 0.023% to 0.026% for the SCCBS18 beam.

Finally, numerical analyses confirm that the creep value for the composite beam connected by adhesive is less than that for the beam connected by shear studs.

## 5. Conclusions

This study investigated the long-term creep behavior of two types of steel-concrete composite beams: one with shear steel studs and the other bonded via an adhesive joint. Laboratory-scale flexural creep tests and numerical analyses using linear viscoelastic theory were conducted to evaluate strain distribution and stress redistribution under sustained loading. The key findings are as follows:

* In the first nine days of loading, creep strain increases rapidly, with higher values observed on the upper surface of the composite beam compared to the lower surface. Additionally, creep strain also escales more significantly at positions closer to the beam's mid-span than at its ends.

* Creep strain variation follows three distinct phases. In the first phase (0–9 days), the shear stud-connected beam exhibits higher creep values than the adhesive bonded beam. Adhesive bonding ensures a more uniform and stable connection, reducing early-stage deformation and improving structural performance. During the second phase (9–80 days), creep strain continues to increase but at a slower rate. In the final phase (beyond 80 days), creep strain stabilizes at approximately 170 µm/m for the shear stud-connected beam and 130 µm/m for the adhesive bonded beam.

* Differences in creep strain between the two beam types are influenced by micro-cracking, stress distribution, and connection efficiency. Shear stud connections are more susceptible to micro-cracking due to shrinkage, while adhesive bonding provides a continuous and homogeneous connection, leading to a more uniform stress distribution and lower overall creep strain.

* Strains on the bottom face of the steel beam are consistently lower than those on the upper face of the concrete. A part of this occurrence can be attributed to the development of micro-cracks within the concrete, induced by both shrinkage and creep. Moreover, it becomes evident that the level of creep experienced by the I-beam is slightly more pronounced in the bonded composite beam when compared to the shear steel stud composite beam.

* Numerical results demonstrate that creep due to loading varies depending on the type of connection (shear studs or adhesive). Up to a load level of 60% of the ultimate load, creep develops rapidly around the middle steel stud, leading to the appearance of initial cracks in the concrete slab. In contrast, for the composite beam connected by adhesive bonding, the distribution of strain and creep is homogeneous and linear.

This study is based on laboratory-scale experiments, which may not fully capture real-world complexities, such as environmental effects, dynamic loads, and large-scale structures. Future studies should

<figure><img src="image_25.png" /><figcaption>Fig. 19. Numerical evolution with time of axial stress distribution across the midspan section: (a) SCCBS18 beam, (b) SCCBA beam.</figcaption></figure>

<figure><img src="image_26.png" /></figure>
<figure><img src="image_27.png" /><figcaption>Fig. 20. Numerical evolution with time of axial strain distribution across the midspan section: (a) SCCBS18 beam, (b) SCCBA beam.</figcaption></figure>

investigate full-scale composite beams under realistic construction and loading conditions, exploring various adhesive thicknesses. The 120-day monitoring period under sustained loading captures the creep behavior but does not enough to reveal long-term deformation, which can develop over years. Extended testing is needed to understand long-term creep over such long periods. The finite element models relied on simplified assumptions, such as idealized material properties and linear viscoelasticity, which may not accurately reflect real behavior. Incorporating advanced modelling techniques, like non-linear viscoelasticity or cohesive zone modelling, could improve accuracy.

## CRediT authorship contribution statement

**ABBES Boussad:** Writing – review & editing, Visualization, Software, Data curation. **YURTDAS Ismail:** Writing – review & editing, Validation, Methodology. **LI Alex:** Writing – review & editing, Writing – original draft, Validation, Methodology, Formal analysis, Conceptualization.

## Declaration of Competing Interest

The authors, Alex LI, Ismail YURTDAS, Boussad ABBES, declare that there are no conflicts of interest related to this work. This research was conducted independently, and no external parties influenced the study design, data collection, analysis, or interpretation of results. The authors confirm that the results presented in this article are an objective and impartial representation of the findings. No financial or personal relationships exist that could have appeared to affect the research presented in this paper.

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