Fatigue Design Research on Notch–Stud Connectors of Timber–Concrete Composite Structures

Abstract

To investigate the mechanical behavior and damage mechanism of notch–stud connectors in timber–concrete composites under fatigue loading, fifteen push-out specimens in five groups were designed with load cycles as the key variable. Fatigue failure modes and mechanisms were analyzed to examine fatigue life, stiffness degradation, and cumulative damage laws of connectors. Numerical simulations with up to 100 load cycles explored timber/concrete damage effects on stud fatigue performance. Based on the results, an S-N curve was established, a fatigue damage model developed, and a fatigue design method proposed for such connectors. Primary failure modes were stud fracture and local concrete crushing in notches. Stiffness degradation followed an inverted “S”-shaped “fast–slow–fast” pattern. Using residual slip as the damage variable, a two-stage fatigue damage evolution model was constructed from the damage–cycle ratio relationship, offering a new method for shear connector fatigue damage calculation in timber–concrete composites and enabling remaining life prediction for similar composite beam connectors. Finite element simulations of push-out specimens showed high consistency between calculated and experimental fatigue life/damage results, validating the conclusions.

1. Introduction

Modern timber structures offer advantages, such as green eco-friendliness, excellent seismic performance, high industrialization, and healthy livability, aligning with national strategies for sustainable development. Over the past decade, research on modern timber structures in China has developed rapidly, with comprehensive advancements in materials, components, connections, structural systems, fire resistance, and durability. The standard specification system has become nearly complete, supported by a maturing industrial chain and increasing engineering applications. Timber–concrete composite (TCC) structures integrate existing or new timber beams with concrete slabs through shear connectors to form monolithic structural components, leveraging timber’s tensile strength and concrete’s compressive strength [1,2]. Attaching concrete slabs to timber beams not only significantly enhances the beam load-carrying capacity and stiffness but also improves fire resistance, sound insulation, and vibration performance, making TCC beams suitable for multi-story, high-rise, and long-span timber buildings. However, shear connector deformation under longitudinal shear induces interfacial slip, invalidating the traditional plane section assumption for TCC structures. Thus, the mechanical behavior of shear connectors has become a key research focus, with substantial achievements reported by domestic and international scholars [3,4,5,6,7,8,9,10,11,12,13]. Regarding fatigue research, Kuhlmann and Balogh et al. [14,15,16,17] conducted fatigue failure tests on TCC connectors, established S-N curves, and demonstrated that repeated loading reduces structural strength and stiffness.

Although progress has been made in studying the mechanical behavior of TCC structures, research on connector fatigue remains insufficient. Key issues include (1) inadequate investigation into the fatigue failure mechanisms of shear connectors, (2) unclear summarization of cumulative damage laws under cyclic loading, (3) incomplete establishment of relationships between fatigue load amplitude and fatigue life, and (4) absence of specific fatigue design procedures for TCC connectors.

Shear connection methods in TCC structures primarily include dowel-type connectors, notched connections, and plate-type connections. Notched connections exhibit superior strength and stiffness performance [18,19,20]. To address these gaps, this study conducts static and cyclic push-out tests on 15 stud-connected specimens to analyze the fatigue life, stiffness degradation, and cumulative damage laws of notch–stud connectors under varying fatigue loads. Based on the test results, an S-N curve and fatigue damage model are developed, followed by a fatigue design method tailored for TCC notch–stud connectors. Finite element analysis is finally employed to validate the accuracy of the experimental results and conclusions.

Through experimental validation, theoretical analysis, numerical simulation, and case studies, this study addresses previous gaps in understanding fatigue life, stiffness degradation, cumulative damage laws, and fatigue design of shear connectors under cyclic loading. It provides a reference for TCC fatigue research. With advancing studies, TCC structures hold broad application prospects.

2. Experimental Study

Experimental studies can accurately reveal the mechanical behavior of notch–stud connectors, primarily using two methods: push-out tests and bending tests [21,22]. The push-out specimen model is shown in Figure 1.

2.1. Specimen Design and Fabrication

To investigate the fatigue failure mechanism of notch–stud connectors in TCC structures, this study designed 5 groups of 15 specimens: 1 group for static testing to determine the upper fatigue load limit, and 4 groups for fatigue testing. Following standard push-out specimen configurations and existing research, the concrete slab used C30 concrete with 5–30 mm continuously graded crushed stone as coarse aggregate and medium sand as fine aggregate. Its measured strength was obtained after 28 days of standard curing. The timber beams were made of Larix gmelinii glulam from northeastern China (the water content was 10–12%). Studs with dimensions Φ12 mm × 130 mm were used for connection, with an embedment depth of 80 mm into the timber. Specific specimen dimensions are shown in Figure 2. Mechanical property tests of relevant materials were conducted prior to push-out tests, with results listed in

Table 1. Characteristic values of each material.

Specimen ID	Number	Compressive Strength of Concrete (MPa)	Elastic Modulus of Concrete (MPa)	Compressive Strength of Timber (Parallel to Grain, MPa)	Elastic Modulus of Timber (Parallel to Grain, GPa)	Yield Strength of Bolts (MPa)	Ultimate Tensile Strength of Bolts (MPa)
N-F1	3	34.3	30,000	40.34	11.02	391.97	505.67
N-F2	3
N-F3	3
N-F4	3
N-S	3

.

The fabrication process of the push-out specimens is illustrated in Figure 2.

2.2. Loading Protocol and Test Configuration

The fatigue tests were conducted using an MTS810 material (MTS Systems Corporation in the Eden Prairie, MN, USA) testing system, which has a maximum static/dynamic load capacity of ±100 kN, loading accuracy better than 0.5%, and a maximum actuator displacement of ±150 mm, as shown in Figure 3. A steel plate was placed on the timber surface to ensure uniform force distribution during loading. To prevent lateral displacement and tilting, the bottom end of the specimen was moderately constrained using screws and straps. Mechanical dial gauges were used for measurement, with four measurement points positioned near the studs on the timber surface, and the average value of these four points was taken as the final relative slip value, as shown in Figure 4.

The test loading was divided into five groups: the N-S group was a static failure test, the N-F1 to N-F3 groups were complete fatigue failure tests, and the N-F4 group was an incomplete fatigue failure test. Static and fatigue test parameters and loading cycles for each specimen are listed in

Table 2. Parameters of fatigue loading.

Speci-men ID	Static Ultimate Load Capacity, Pu (kN)	Fatigue Loading Lower Bound, Pmin (kN)	Fatigue Loading Upper Bound, Pmax (kN)	Load Amplitude, ΔP (kN)	Load Ratio, η	Shear Stress Amplitude, Δτ (MPa)	Fatigue Cycles, TT (×104)	Loading Condition
N-F1-1		3.4	34.1	30.7	0.50	135.8	48	Fatigue
N-F1-2		3.4	34.1	30.7	0.50	135.8	87
N-F1-3		3.4	34.1	30.7	0.50	135.8	83
N-F2-1		3.1	30.6	27.5	0.45	121.7	90	Fatigue
N-F2-2		3.1	30.6	27.5	0.45	121.7	153
N-F2-3		3.1	30.6	27.5	0.45	121.7	126
N-F3-1		2.7	27.2	24.5	0.40	108.4	144	Fatigue
N-F3-2		2.7	27.2	24.5	0.40	108.4	183
N-F3-3		2.7	27.2	24.5	0.40	108.4	177
N-F4-1	61.8	2.4	23.8	21.4	0.35	94.7	200	Post-Fatigue Static Load
N-F4-2		2.4	23.8	21.4	0.35	94.7	200
N-F4-3		2.4	23.8	21.4	0.35	94.7	200
N-S1	68.1	-	-	-	-	-	-	Static Load
N-S2		-	-	-	-	-	-
S3

$\eta =P_{\max }/P_u$.

.

(1)

Static Loading Failure Test

The static loading process comprised two stages: preliminary testing and main testing [23]. A preloading procedure was implemented before formal loading. During the preliminary stage, an incremental stepwise loading strategy was adopted, with the load level increased in two stages from the initial zero-load state. Following preloading, the main static loading commenced. The load–relative slip curve of the push-out specimen is depicted in Figure 5. The ultimate bearing capacity, Pu, of the specimen was defined as the average ultimate load of the three specimens in the N-S group, amounting to 68.1 kN.

(2)

Complete Fatigue Failure Test

As indicated in Ref. [24], the fatigue life of studs primarily depends on the stress amplitude or load amplitude. Typically, the upper fatigue load limit, Pmax, is determined based on the ultimate bearing capacity, Pu, of the stud from static tests, ensuring that the notch–stud connectors remain in the elastic stage (with a load ratio below approximately 0.5). The loading limits and amplitude are listed in Table 2. The preloading method for specimens was consistent with that of the static loading test. Fatigue loading employed an 8 Hz constant-amplitude sinusoidal wave. The test series included nine specimens in Groups N-F1 to N-F3. To better capture the initial damage accumulation and slip stabilization trends while balancing test efficiency and data integrity, during fatigue testing, after every 200,000 loading cycles, the machine was stopped for unloading, followed by a static load application up to the fatigue upper limit, Pmax, to monitor changes in specimen stiffness and slip behavior with the number of cycles. Residual slip, defined as the irreversible displacement of the specimen after unloading to zero load, was recorded at the timber–concrete interface during fatigue loading pauses.

(3)

Incomplete Fatigue Failure Test

GB 50010-2010 specifies 2 × 10⁶ cycles as the fatigue limit for reinforced concrete. U.S. timber design manuals and studies [25,26] adopt 2 × 10⁶ cycles as the fatigue limit for wood bending tests. AASHTO defines 2 × 10⁶ cycles as the baseline life threshold. Specimens surviving 2 × 10⁶ cycles are considered to have ‘infinite life’ or minimal failure probability under constant-amplitude loading—critical for long-life structures like bridges. Thus, 2 × 10⁶ cycles was set as the fatigue limit for push-out specimens.

After completing the prescribed 2 million fatigue cycles without fatigue failure, static loading was immediately applied until specimen failure, using the same loading protocol as in the first two groups. This series included three specimens in Group N-F4, with loading parameters detailed in Table 2.

Fatigue cycles for Groups N-F1 to N-F3 represented complete fatigue failure stop points. Fatigue cycles for Group N-F4 represented the designated test stop point.

N-F1-1 data showed significant scatter. Fractography revealed tear morphology in N-F1-1 studs versus planar fractures in N-F1-2/N-F1-3, indicating complex stress concentration or microstructural defects in N-F1-1.

3. Experimental Results and Analysis

3.1. Failure Modes

The final failure mode of the static test was splitting failure of the concrete slab, as shown in Figure 6. No obvious phenomena were observed at the start of the test. When the load exceeded 50 kN, initial cracks initiated on the outer side of the concrete slab. As the load increased, these cracks gradually propagated, and new cracks emerged. When the load reached approximately 65 kN, vertical cracks in the concrete slab penetrated through the entire section. After a slight load increase (less than 5 kN), brittle splitting failure occurred. Upon disassembly of the specimen for observation, the stud exhibited a double plastic hinge failure mode, indirectly confirming the conclusion [27] that when the thickness-to-diameter ratio (ratio of timber thickness to bolt diameter) exceeds 6.56, the primary failure is double plastic hinge yielding of the bolt. The notched concrete separated from the concrete slab, but no fragmentation was observed.

The fatigue failure modes of the specimens in Groups N-F1, N-F2, and N-F3 were similar but significantly different from those under static loading, as shown in Figure 7. Under fatigue loading, fatigue brittle fractures occurred in the bolts of the push-out specimens. Fatigue cracks emerged in the bolts under repeated loading. When the fatigue cracks propagated to a sufficient size such that the net cross-section of the bolt was unable to resist the maximum fatigue load, the bolt fractured instantaneously, forming a fresh and rough fracture surface, as shown in Figure 8. Under repeated loading, local damage in the concrete slab accumulated continuously. However, unlike in static loading failure, there were no overall cracks or crushing failures in the concrete slab. Instead, local crushing occurred at the bolt connections. The concrete inside the notch was crushed under repeated loading, while there was no obvious damage to the wood around the notch. Therefore, for the wood–concrete composite structure, the influence of local damage to the concrete slab and wood on the fatigue life of the shear connectors can be ignored. The failure modes considered were the brittle fracture of the studs and the crushing of the concrete inside the notch.

Group N-F4 specimens survived 2 × 10⁶ cycles without fatigue failure. Subsequent static loading induced failure modes identical to static tests. At η ≤ 0.35, the load amplitude was below the fatigue crack initiation threshold. Damage manifested as interfacial slip accumulation, with studs remaining elastic and fracture-free. Here, fatigue life was governed by ‘slip deformation limits’ rather than crack propagation, explaining the reversion to concrete splitting failure linked to timber–concrete bond degradation.

3.2. S-N Curve

Statistical analysis based on the test data in Table 2 indicated a significant negative correlation between the fatigue life cycles of notch–stud connectors and the applied fatigue load amplitude. The experimental results revealed that in the higher load level range (load ratio > 40% Pu), minor load fluctuations triggered accelerated propagation of fatigue cracks, leading to an exponential decay in fatigue life. When the load ratio increased from 45% to 50%, the corresponding average fatigue life decreased significantly. The shear stress amplitude of studs was calculated using the cross-sectional area of the stud shank, a method also adopted in current domestic and international codes, with specific values listed in Table 2.

To quantitatively characterize fatigue performance parameters, this study established a bi-logarithmic coordinate system for fatigue life and shear stress amplitude to model damage evolution (Figure 9). Through regression analysis based on the least squares method with a 95% confidence level, the fitted fatigue S-N curve was obtained as:

$$\lg N=-2.98\lg \Delta \tau +8.29$$

(1)

In this test, the specimens in Group N-F4 did not undergo fatigue failure after 2 million cycles of fatigue loading and were directly subjected to static failure tests thereafter. Therefore, further experimental analysis is still needed for the fatigue life relationship when the fatigue load amplitude is controlled below 35% of the ultimate bearing capacity. Formula (1) is applicable for load ratios in the approximate range of 0.35 to 0.5.

3.3. Analysis of Slip Magnitude and Stiffness Degradation

Figure 10 reveals the evolution law of interfacial slip in stud-connected specimens during fatigue loading. In the initial loading stage, the slip curve exhibited nonlinear characteristics, which originated from the initial voids between different materials. When fatigue loading entered the stable development stage, the slope of the slip curve tended to stabilize, indicating that the compaction effect of interfacial micro-voids was basically completed. At this stage, the slip increment exhibited a linear relationship with the number of load cycles. However, in the latter stage of fatigue loading, fatigue damage began to occur in the studs, accelerating their stiffness degradation process. This caused the load–slip curve to re-exhibit nonlinear characteristics.

To further investigate the stiffness variation of specimens, a stiffness–cycle curve was established (Figure 11), where the abscissa is the ratio of the number of loading cycles to the fatigue life, N/Nf. The secant slope of the load–slip curve, defined as the shear stiffness K of the specimen [28], was obtained from Figure 10, K = Pmax/δmax, where δmax is the slip increment corresponding to the upper fatigue load limit, Pmax. Figure 11 shows that the stiffness of specimens degraded in an inverted “S” shape with a “fast–slow–fast” pattern: stiffness decreased significantly at the start and end of cycling, with only a slight reduction during the intermediate stage. By normalizing the stiffness with its initial value, the relative stiffness was obtained. The stiffness of N-F1, N-F2, and N-F3 specimens decreased by 20.59%, 19.34%, and 19.85%, respectively, prior to fatigue failure. The larger the loading amplitude, the faster the stiffness degraded in the final stage of cyclic loading. By contrast, the stiffness of N-F4 decreased by 11.03% after 2 million loading cycles. The stiffness degradation rate (11%) of the N-F4 group was significantly lower than that of the failure groups (19–20%), as its low stress amplitude inhibited plastic deformation of the studs. Therefore, specimens are considered to approach fatigue failure when stiffness degradation exceeds 20%.

Figure 12 presents the load–slip curve of Group N-F4 after 2 million fatigue cycles followed by static loading, and

Table 3. Comparison of ultimate shear capacity.

Specimen ID	Ultimate Shear Capacity		Error % (①②)
	S ①	F4 ②
N-S/N-F	68.1	61.8	−9.25

compares the ultimate shear capacity of N-F4 with that of Group N-S. Results showed that when the fatigue load peak was controlled within 0.35 times the ultimate bearing capacity, the specimen fatigue life reached 2 million cycles with no significant surface damage. The ultimate shear capacity decreased by approximately 9.25%, and the overall load–slip curve was consistent with that of Group N-S. This indicates that at lower load ratios, damage to each component was negligible, fatigue loading had minimal effect on specimens, and the reduction in bearing capacity was slight.

3.4. Analysis of Residual Slip and Cumulative Damage

Figure 13 illustrates the relationship between residual slip and the number of load cycles for selected specimens, where the abscissa represents the ratio of the number of loading cycles to the fatigue life, N/Nf. The curves show that the residual slip evolution of N-F1, N-F2, and N-F3 specimens followed a consistent pattern: rapid growth in the early stage of fatigue loading, stable and slow growth in the middle stage, and a sharp increase in slip magnitude in the later stage, leading to specimen failure within a short number of cycles. For Group N-F4, due to the lower fatigue load level, no fatigue failure occurred—even after millions of load cycles, the slip magnitude did not increase significantly.

Based on the residual slip–load cycle curve, the fatigue cumulative damage process of notch–stud connectors could be divided into the initial fatigue damage stage, fatigue damage development stage, and fatigue failure stage, as shown in Figure 14. In the initial fatigue damage stage (accounting for 20% of the fatigue life), the residual slip of notch–stud connectors increased rapidly due to the presence of micro-voids between wood, concrete, and bolts, as well as the influence of plastic damage deformation of wood [29] under the action of cyclic load, leading to rapid slip accumulation in specimens [30]. In the fatigue damage development stage (accounting for 70% of the fatigue life), local crushing of concrete inside the notch caused the force-bearing mode of studs to shift from pure shear to bending shear, resulting in increasing bolt stress—residual slip accumulated slowly at this stage, primarily from the plastic deformation of bolts. In the fatigue failure stage (accounting for 10% of the fatigue life), fatigue cracks initiated and propagated at stress-concentrated areas of bolts, leading to complete fracture within a short period, during which the residual slip of specimens increased rapidly.

3.5. Remaining Life Analysis

The third stage of the specimen occupies a very small proportion of the fatigue life. When this stage is reached, the residual slip of the notch–stud connector has already become significant and exceeds the normal service range. Therefore, it is sufficient to study the initial and progressive stages of fatigue damage. There are three main theoretical frameworks for fatigue cumulative damage development: the Palmgren–Miner linear cumulative fatigue damage theory [31], the bilinear cumulative fatigue damage theory proposed by Grover [32] and Manson [33], and the nonlinear cumulative fatigue damage theory proposed by Starkey et al. [34]. The linear cumulative fatigue damage theory assumes that each stress cycle causes an equal amount of damage during cyclic loading, with total damage being the linear summation of individual cycle damages, neglecting the stage-dependent nature of fatigue damage. The bilinear theory improves upon this, while the nonlinear theory accounts for fatigue damage patterns under non-constant-amplitude loading.

Calculations showed that the coefficient of determination (R²) of the test data for Groups N-F1, N-F2, and N-F3 exceeded 0.9, with the coefficient of variation (COV) less than 10%. Through R² and COV analysis, despite the limited sample size, the two-stage linear model demonstrated strong explanatory power for the test data, with dispersion within a reasonable range. Based on experimental results, the residual slip development in the first two stages approximately followed a linear growth trend, which can be analyzed using the bilinear cumulative fatigue damage theory. Experimental analysis indicated that the residual slip (δ₂) before fatigue failure onset tended toward a constant value, which can be defined as the fatigue failure criterion for notch–stud connections, with the damage variable expressed as:

$$\mathrm{D} = {\delta }_{\mathrm{N}}/{\delta }_2$$

(2)

According to the bilinear cumulative fatigue damage theory, it is further expressed as:

$$\mathrm{D}=\left\{\begin{array}{ll}{\mathsf{\lambda }}_1{\displaystyle \frac{\mathrm{N}}{{\mathrm{N}}_{\mathrm{f}}}}& 0 \le \mathrm{N} \le {\mathrm{N}}_1\\ {\mathsf{\lambda }}_1{\displaystyle \frac{\mathrm{N}-{\mathrm{N}}_1}{{\mathrm{N}}_{\mathrm{f}}}}+{\mathrm{D}}_1& {\mathrm{N}}_1 \le \mathrm{N} \le {\mathrm{N}}_2\end{array}\right.$$

(3)

In Equations (2) and (3), δ_N represents the residual slip of the specimen after the N-th load cycle, N1 and N2 are the number of cycles at the end of the initial and progressive damage stages, respectively, Nf is the fatigue life, λ1 and λ2 are the damage growth rates in the two stages, and D1 is the damage value at the end of the first stage. In this test, the cycle ratios N1/Nf and N2/Nf approached 0.2 and 0.9, respectively.

When the number of loading cycles equaled the fatigue life, the damage variable D > 1. To ensure a safety margin for the structure, it is reasonable to approximate the damage value D as 1 when the number of cycles reaches N2, as illustrated in Figure 15. D1 can be determined by referring to the three-stage fatigue deformation model for concrete proposed by Huang et al. [35]:

$${\mathrm{D}}_1 = \mathrm{B}{[- \ln (1 - {\displaystyle \frac{{\mathrm{N}}_1}{{\mathrm{N}}_{\mathrm{f}}}}\left)\right]}^{{\displaystyle \frac{1}{\mathrm{K}}}}$$

(4)

Based on the research of Oehlers et al. [36], under constant-amplitude fatigue loading, the residual slip per cycle of notch–stud connections remained constant. Fitting the experimental data from this study yielded:

$${\mathsf{\lambda }}_1={\displaystyle \frac{{\mathrm{D}}_1}{{\mathrm{N}}_1}}{\mathrm{N}}_{\mathrm{f}}$$

(5)

$${\mathsf{\lambda }}_2={\displaystyle \frac{1 - {\mathrm{D}}_1}{{\mathrm{N}}_2 - {\mathrm{N}}_1}}{\mathrm{N}}_{\mathrm{f}}$$

(6)

Simultaneously solving Equations (2)–(6) provided the expression for the fatigue damage accumulation model of notch–stud connections:

$$\mathrm{D}=\left\{\begin{array}{ll}\mathrm{B}{\left[-\ln (1-{\displaystyle \frac{{\mathrm{N}}_1}{{\mathrm{N}}_{\mathrm{f}}}})\right]}^{{\displaystyle \frac{1}{\mathrm{K}}}}{\displaystyle \frac{\mathrm{N}}{{\mathrm{N}}_1}}& 0 \le \mathrm{N} \le {\mathrm{N}}_1\\ {\displaystyle \frac{\mathrm{N}-{\mathrm{N}}_1}{{\mathrm{N}}_2-{\mathrm{N}}_1}}+{\displaystyle \frac{{\mathrm{N}}_2-\mathrm{N}}{{\mathrm{N}}_2-{\mathrm{N}}_1}}\mathrm{B}{\left[-\ln (1-{\displaystyle \frac{{\mathrm{N}}_1}{{\mathrm{N}}_{\mathrm{f}}}})\right]}^{{\displaystyle \frac{1}{\mathrm{K}}}}& {\mathrm{N}}_1 < \mathrm{N} \le {\mathrm{N}}_2\end{array}\right.$$

(7)

Among them, B and K are coefficients. Based on experimental data (notch–stud connectors), B = 2.637(Fmax/Fu), where Fmax is the maximum shear force applied to a single bolt, and Fu is the ultimate shear capacity of a single bolt. K = 1.825, and N1/Nf and N2/Nf can be approximately 0.2 and 0.9, respectively.

With a sufficient number of test samples, the residual slip of the stud connector before the onset of the fatigue failure stage can be statistically determined and used as an indicator for judging the fatigue failure of such connectors. Once this value is determined, the damage degree of the connector can be assessed by measuring changes in residual slip, and the remaining fatigue life of the connector can be estimated. In practical engineering, the residual slip δ₂ before the start of fatigue failure can be obtained through numerical analysis, thereby calculating the damage value D and deriving the remaining fatigue life Nf using Equation (7).

The above formula was proposed based on the results of constant-amplitude fatigue tests, and further research is required for the case of multilevel fatigue loading.

The model derivation assumed constant amplitude and idealized conditions. Future work will include (1) variable-amplitude validation (e.g., random spectra) considering load-sequence effects and (2) environmental coupling (hygrothermal/freeze–thaw cycles) to develop coupled damage models.

4. Finite Element Analysis

4.1. Finite Element Modeling and Validation

To perform fatigue calculations using nCode software (2024.0), the results file from static tests is required. To obtain finite element calculation results, a static analysis was conducted on the push-out specimens using Abaqus finite element software (2022). Due to the symmetry of the loading method and geometric model, only a 1/2 model was established in the finite element numerical analysis. All parts of the specimen were simulated using 8-node solid elements (C3D8R), with the mesh division shown in Figure 16. The 1/2 section of the numerical model was applied with symmetric constraints, and the bottom of the concrete was fixed. Surface-to-surface contact was used to simulate the combined action at the bolt–concrete, bolt–wood, and concrete–wood interfaces. The bolt was treated as an ideal elastoplastic material, while wood was considered an orthogonal anisotropic material in the elastic stage and simplified as an isotropic ideal elastoplastic material in the plastic stage [37]. The wood constitutive relationship adopted a three-segment stress–strain model [27], the concrete constitutive relationship was derived from the compression constitutive calculation formulas in the GB 50010-2010 Code for Design of Concrete Structures combined with material performance test results, and the bolt constitutive relationship used a bilinear kinematic hardening model.

(1)

The destruction mode

Figure 17, Figure 18 and Figure 19 show the finite element numerical simulation results of the notch–stud connection specimens. The results indicated that stress concentration occurred at the two plastic hinges of the stud, with stress values reaching the yield strength and causing significant bending deformation. Unlike stud connection specimens, the bending degree of the plastic hinge on the timber side was smaller. Concrete damage was concentrated at the interface between the notch and the concrete slab, as well as the contact surface with the stud, reaching the ultimate value and eventually triggering crushing failure of the entire concrete slab. The plastic strain in the timber was mainly distributed at the contact surface with the notch concrete.

(2)

Load–slip curve

The load–relative slip curve obtained from the static analysis is shown in Figure 20. The finite element calculation results showed good agreement with the test-derived load–relative slip curve. Additionally, the comparison of bearing capacity calculation results also demonstrated excellent consistency (

Table 4. Result comparison.

Specimen ID	Experimental ①	FEA Result ②	Error % (①②)
S1–S3	68.1	72.6	6.61

), indicating that the finite element model was accurate and applicable for fatigue analysis.

4.2. Fatigue Analysis

There is little literature addressing the influence of concrete and wood damage on the fatigue performance of shear connectors at present. Considering finite element calculation time and computational efficiency, this study used nCode DesignLife analysis software (2024.0) to conduct a numerical simulation of 100-cycle loading (load ratio = 0.5) on the push-out model test, focusing on the effect of concrete and wood fatigue damage on the fatigue performance of studs, and put forward relevant conclusions. A constant-amplitude load mapping was adopted, with material parameters consistent with those in the static analysis. The S-N curve of the bolt was selected from the standard material library. Considering the consistency of test conditions and material types, the S-N curves for concrete and wood refer to the research results of Miarka et al. [38] and Cao Lei et al. [39], respectively. The stress distribution of studs, concrete damage, and wood equivalent plastic strain in the notch–stud connection specimens under the first and 100th cycle loadings are shown in Figure 21.

Numerical analysis results showed that after 100 cycles of cyclic loading, the equivalent plastic strain of timber increased from 0.006 to 0.009, with a growth rate of 50%, indicating a significant increase, while the concrete strain increased from 0.445 to 0.520, with a growth rate of 17%, showing a moderate increase. Thus, it can be extrapolated that timber fatigue damage had a greater impact on the fatigue performance of studs. Compared with stud connectors, cutting notches around studs and filling them with concrete can improve the stiffness of the connector, reduce the bending deformation of studs under cyclic loading, and effectively delay the initiation of fatigue cracks.

Additionally, the nCode DesignLife analysis software (2024.0) was used to simulate and analyze the fatigue damage and life of the specimens. To verify the consistency of fatigue life among test data, finite element analysis, and theoretical formula calculations, fatigue analysis was performed on each group of specimens, with the number of loading cycles specified as the average fatigue life obtained from actual tests. The fatigue life from actual tests was compared with that from finite element simulation and theoretical formula calculations, as shown in

Table 5. Analysis results of fatigue life.

Specimen ID	Fatigue Life/×104			Error % (① vs. ②)	Error % (② vs. ③)	Error % (① vs. ③)
	Experimental (Avg.) ①	FEA Result ②	Theoretical ③
N-F1	72	83.5	86.1	16.0	3.1	19.6
N-F2	123	122.4	119.0	0.4	−2.8	3.3
N-F3	168	170.1	168.5	1.3	−0.9	0.3

. It can be seen from Table 5 that except for N-F1, where the large dispersion of test results for fatigue life led to a significant deviation between the calculated and actual values, the theoretical fatigue life of the remaining specimens showed good agreement with the measured fatigue life, with an error within 15%.

To verify the accuracy of Equation (7), the actual damage values (D = 0.67/0.65/0.62) from test data were used to calculate the remaining life from test values, finite element analysis, and theoretical formulas, with specific comparison values listed in

Table 6. Analysis results of remaining life.

Specimen ID	Remaining Fatigue Life/×104				Error % (① vs. ②)	Error % (② vs. ③)	Error % (① vs. ③)
	D	Experimental ①	FEA Result ②	Theoretical ③
N-F1	0.67	32.4	41.5	43.4	28	4.6	34.0
N-F2	0.65	55.4	60.3	63	8.8	4.4	13.7
N-F3	0.62	67.2	71.6	73.8	6.5	3.0	9.8

. Due to the large deviation in the test data of Group N-F1, the error rate was higher, while the error rates of the other two groups were relatively small. Group N-F4 was not included in the comparison data, as it did not undergo fatigue failure tests.

5. Fatigue Design

In the study of the fatigue performance of the timber–concrete composite (TCC) structural system, the shear fatigue failure mechanism of notch–stud connectors played a critical controlling role. As previously analyzed, when push-out specimens suffered fatigue failure, only local damage occurred in the timber and concrete without overall failure, while the bolts fractured, causing the entire component to lose its load-bearing capacity. Therefore, it is essential to conduct shear fatigue verification for notch–stud connectors in TCC structures.

5.1. Basic Assumptions

(1)

The load ratio η ≤ 0.5 (η = Pmax/Pu) to ensure that all components of the TCC structure remain in the elastic state.

(2)

Timber and concrete are ideal elastic materials.

(3)

The timber beam and concrete slab each conform to the plane section assumption and exhibit the same curvature, respectively.

5.2. Fatigue Calculation

In the study of the fatigue performance of TCC structural systems, the shear fatigue failure mechanism of notch–stud connectors plays a critical controlling role. As analyzed earlier, when the push-out specimens underwent fatigue failure, wood and concrete only experienced local damage without overall failure, while the bolt fractured, causing the entire component to lose its load-bearing capacity. Therefore, it is essential to conduct shear fatigue verification for notch–stud connectors in TCC structures. The main methods were as follows:

(1) First, the shear force on the bolt under fatigue loading needs to be calculated. Since each component of the composite structure remained in the elastic state under fatigue loading, the elastic design method was adopted to calculate the bolt shear force [40]. Under the elastic design method, the shear stress amplitude per unit length at the interface between the timber beam and concrete slab was:

$$\mathsf{\Delta }{\mathrm{V}}_h={\displaystyle \frac{\mathsf{\Delta }\mathrm{V}{\mathrm{S}}_0}{{\mathrm{I}}_{\mathrm{e}\mathrm{q}}}}$$

(8)

where $\mathsf{\Delta }$V (MPa) = the maximum vertical shear stress range in the composite cross-section, S₀ (mm³) = the first moment of area of the transformed section above the composite structure’s interface about the elastic neutral axis, and Ieq (mm⁴) = the equivalent moment of inertia of the transformed composite section.

(2) After determining the shear stress range per unit length at the timber–concrete interface, the average shear force range, $\mathsf{\Delta }$Q (MPa), per bolt within the shear span could be calculated:

$$\mathsf{\Delta }Q={\displaystyle \frac{V_{h}a}{n_f}}$$

(9)

where a (mm) = the shear span length and n_k = the number of bolts within the shear span.

(3) The shear stress range, Δτ (MPa), in the bolt was derived from the shear force and bolt cross-sectional area:

$$\mathsf{\Delta }\mathsf{\tau }={\displaystyle \frac{\mathsf{\Delta }Q(1-R)}{As}}$$

(10)

where As (mm²) = the cross-sectional area of the bolt shank.

Finally, fatigue life verification was performed using Equations (1) and (7).

5.3. Example Analysis

The following demonstrates the fatigue design process for a 25 m-span simply supported timber–concrete composite beam bridge. The bridge deck was designed for two-way two-lane traffic with a 50-year service life (calculations are omitted for brevity).

(1) Basic Design Parameters

Single-span simply supported beam: span = 25 m, deck width = 8 m (2 × 3.5 m lanes + 2 × 0.5 m barriers), glulam timber beams: cross-section = 400 mm × 800 mm, elastic modulus Ew = 11 GPa, Ew = 11 GPa, C40 concrete deck: thickness = 200 mm, full width = 8 m, notch–stud connectors: stainless-steel bolts in double rows (diameter = 30 mm, Fu = 132 kN), longitudinal spacing = 300 mm, load standard: Highway-II vehicle load, and fatigue load modeled as equivalent lane load.

(2) Load Distribution Factor Calculation

Lever method used to determine transverse load distribution factor: m = 0.6.

(3) Single-Beam Fatigue Load Spectrum

Fatigue vehicle model: equivalent axle load per the General Specifications for Design of Highway Bridges and Culverts (JTG D60): total weight = 300 kN (rear axle = 210 kN), axle spacing = 4 m, wheel spacing = 1.8 m, equivalent cycles per beam: equivalent daily fatigue vehicles = 300 vehicles/day, and Neq = 300 × 365 × 50 × 0.6 = 3.29 million cycles.

(4) Theoretical Stress Analysis

Equivalent moment of inertia Ieq = 4.7 × 10¹⁰ mm⁴, interface shear force per unit length (Formula (7)): Vh = 324 N/mm (live load only, Vmin = 0), average shear force per bolt in shear span (Formula (8)): ΔP = 48.6 kN, and bolt shear stress range (Formula (9)): Δτ = 68.8 MPa.

(5) Fatigue Life Assessment

S-N curve life prediction: substituting Δτ = 68.8 MPa into Formula (1): bolt fatigue life N = 6.35 million cycles.

Cumulative damage index: calculated via Formula (3): D = 0.86 > 0.65 [41], so design optimization required (e.g., increase bolt quantity) until fatigue criteria are met.

(6) Key Workflow Summary

Determine equivalent cycles per beam (Neq) → calculate transformed section parameters (Ieq) → compute bolt shear stress range (Δτ) → verify fatigue life via S-N curve and cumulative damage (D) → optimize design iteratively.

5.4. Engineering Design Guide

Based on experimental and theoretical analyses, the following engineering recommendations are proposed:

(1) Critical load ratio control: When the peak fatigue load is controlled within 0.35 times the ultimate bearing capacity, the fatigue life of connectors can exceed 2 million cycles. In practical engineering with high requirements, the load ratio η can be controlled to ≤0.35 to avoid early fatigue failure, though this will increase corresponding costs.

(2) Stiffness degradation threshold: When the stiffness degradation of specimens exceeds 20%, they are close to fatigue failure. The relative stiffness of 0.8 and residual slip can be used as critical values for engineering monitoring. Damage can be assessed and remaining life calculated by periodically measuring interfacial slip.

(3) Optimization of connector arrangement: Reduce the force per stud by increasing the number of studs until fatigue checking conditions are met. Additionally, notch-filled concrete can enhance connector stiffness and effectively delay the initiation of fatigue cracks. This construction form is recommended for priority adoption in bridges and multi-story composite beams.

6. Conclusions

(1)

Under fatigue loading, the failure mode of all push-out specimens was stud fracture, with the fracture position consistent with the double plastic hinge yielding observed in static failure. Local crushing of the notch concrete was evident, and slight spalling occurred on the concrete slab, but no obvious cracks were found in other areas.

(2)

As the peak fatigue load increased, the fatigue life of the specimens showed a decreasing trend. When the peak fatigue load was controlled within 0.35 times the ultimate bearing capacity, the fatigue life of the specimens could reach 2 million cycles. The fatigue failure mechanism of the specimens transitioned from “stud fracture” to “dominated by interfacial slip accumulation”, with no significant surface damage occurring in the specimens and minimal reduction in ultimate bearing capacity. An S-N curve relationship between stress amplitude (ordinate) and the logarithmic value of fatigue life (abscissa) was established. Finite element analysis results showed good agreement with test results, verifying the reliability of this functional relationship.

(3)

The stiffness of the specimens degraded in an inverted S-shaped “fast–slow–fast” pattern with increasing cycles, decreasing significantly at the start and end of loading and only slightly during the intermediate stage. Specimens approached fatigue failure when stiffness degradation exceeded 20%.

(4)

Numerical analysis indicated that fatigue damage in wood had a more significant impact on the fatigue performance of studs. Compared with pure stud connectors, cutting notches around studs and filling them with concrete improved connector stiffness, reduced stud bending deformation under cyclic loading, and effectively delayed the initiation of fatigue cracks.

(5)

Residual slip, reflecting the plastic deformation of specimens macroscopically, can serve as an indicator for measuring the fatigue damage of notch–stud connectors. Based on the evolution of residual slip, the fatigue failure process of notch–stud connectors was divided into three stages: initial fatigue damage, fatigue damage development, and fatigue failure. A fatigue cumulative damage model was established according to the failure mechanism, enabling a quantitative description of fatigue damage and prediction of the remaining fatigue life for similar composite structure connectors.

(6)

The ABAQUS/nCode model achieved 93% accuracy in static load–slip curves. Fatigue life predictions aligned well with tests and theoretical values, capturing the full mechanical behavior, from elasticity to fatigue fracture.

(7)

A fatigue design methodology for timber–concrete composite structures was established, providing a reference for fatigue design and refining the design process for timber–concrete composite systems.

The originality of this study lies not only in the innovation of models and methods but also in the first comprehensive and systematic investigation into the fatigue performance of notch–stud connectors. The two-stage fatigue damage evolution model proposed in this study, which uses residual slip as the damage variable, better fit the inverted “S”-shaped stiffness degradation law observed in tests. It can directly assess the damage degree of connectors through residual slip, providing a quantifiable physical indicator for engineering monitoring. For the first time, this study quantified that stiffness degradation exceeding 20% was set as the critical value for fatigue failure, incorporated residual slip into damage assessment, and formed a design process of “equivalent cycle calculation–stress amplitude calculation–fatigue life assessment”. This fills the gaps in existing literature regarding insufficient research on the fatigue mechanism of notch–stud connectors, unclear damage laws, and the absence of design methods, providing theoretical support and technical pathways for the engineering application of timber–concrete composite structures.

This study focused on a single stud type and constant-amplitude loading conditions, without considering the effects of variable-amplitude loads, multi-material combinations, or environmental factors, and the test data were relatively limited. Therefore, the conclusions have certain limitations. Future research should conduct multi-parameter coupling experiments and refined modeling, expand the diversity of stud types and load spectra, increase the number of test samples, and explore the fatigue mechanism under environmental–mechanical coupling to promote the engineering application of fatigue design for timber–concrete composite (TCC) structures.