2.1. Strength Degradation Law of Concrete Slab

2.2. Strength Degradation Law of Steel Plate

2.3. Effective Cross-Sectional Area

For the profiled steel-concrete composite deck under fatigue load, cracks generally appeared in the pure bending section. In the early stage of the fatigue test, the crack initiated at the welding part between the shear connector and the steel plate and propagated along the transversal direction of the steel plate. With the increase of the cycle number, the crack penetrated through the lower flange of the steel plate and extended to the rib of the steel plate, which led to the failure of the composite deck, as shown in Figure 1.

2.4. Composite Deck with Partial Shear Connection

Usually, the shear connectors of the composite deck will be damaged due to the existence of cracks, and the composite deck is generally with a partial shear connection. Hence, the residual carrying capacity calculation of the composite deck can be divided into two cases based on the position of the neutral axis: (1) the neutral axis is inside the cross section of the steel plate and (2) the neutral axis is an outside cross section of the steel plate, as shown in Figure 4.

2.5. Composite Deck with Complete Shear Connection

For the composite deck under complete shear connection, its bearing capacity calculation can be divided into two cases as follows:

2.5.1. Case 1: Neutral Axis outside the Cross-Section of the Steel Plate

If the neutral axis is outside the cross section of the steel plate, as shown in Figure 5(a), then the equations can be formulated as follows:

$$ (19)

$$ (20)

$$ (21)

$$ (22)

The residual carrying capacity of the composite deck at the n-th load cycle can be calculated as follows:

$$ (23)

3.1. Experiments

The constant amplitude fatigue test has been conducted on three profiled steel-concrete composite decks to investigate their fatigue performance, as shown in Figure 6. The specimens are designated as SP-1, SP-2, and SP-3. The composite deck measures 3200 mm in length, 1000 mm in width, and 180 mm in height. The upper flange depth of the concrete slab is 115 mm. The steel plate measures 65 mm in height, with a 6 mm thickness. The shape of the cross section is shown in Figure 7. Table 1 lists the dimensions of the cross section of the composite deck. The MCL connector measures 3000 mm in length and 110 mm in height. It consists of steel dowels and a connector base. The connector base is 30 mm in height. The connectors are welded to the steel plate. Figure 8 displays the details of the composite deck. The spacing between the two steel dowels is 200 mm, as shown in Figure 9. Bottom bars with a diameter of 16 mm are symmetrically arranged on both sides of the steel dowels. The net distance between the bottom bar and the steel dowel is 22 mm.

The steel bar net of 16 mm diameter was arranged at a distance of 30 mm from the top of the concrete slab. The length of the longitudinal bar is 3000 mm, while for the transversal bar, it is 900 mm. The spacing between the bars is 100 mm. Table 2 displays the material properties of the composite deck.

3.2. Finite Element Analysis

To investigate the mechanical behavior of the composite deck with cracks under static load, the finite element method (FEM) was used for the analysis. Moreover, the results of the FEM were compared with the experimental ones to validate its accuracy.

One reference point (RP) was established to simulate the actual loading process in the static test. The distance between the point and the top surface of the concrete slab was 200 mm. The RP was coupled with the loading surface of the concrete slab in the model, as shown in Figure 10.

The solid elements were used for the simulation of the concrete slab, the steel plate, and the MCL connectors. The truss element was employed to simulate the bar net and the bottom bars. To conduct the mesh sensitivity analysis, the mesh size for the concrete slab was taken to be 60 mm, 50 mm, and 40 mm. The residual carrying capacities corresponding to different mesh sizes were 327.1 kN, 317.9 kN, and 319.3 kN, respectively. Considering the computation efficiency, the mesh size of 50 mm was used for the concrete slab simulation. The steel plate and MCL connectors were meshed with the element sizes of 30 mm and 10 mm, respectively, as shown in Figure 11(d). In the FE model, the regions where cracks appeared were cut out from the model.

The constraint “embedded” was used to simulate the interaction between the steel bars and concrete slab, and the constraint “tie” was employed to simulate the interaction between the MCL connectors and the steel plate. The hard contact was adopted to simulate the interaction between the concrete slab and the steel plate in the normal direction, while the penalty property with a friction coefficient of 0.4 was used to simulate the interaction in the tangential direction [14–16].

The ideal elastic-plastic constitutive relationship was employed for the steel components, as shown in Figure 12. The concrete damage plasticity model (CDP) according to the Mode Code 2010 was adopted to analyze the mechanical behavior of the concrete slab [17], as displayed in Figure 13. The compression strength f_c of the concrete slab at the n-th load cycle could be calculated through equation (1). Equation (2) was employed to calculate the tension strength of the steel plate at the n-th load cycle. The stress-strain relationship for concrete in compression could be divided into three stages. In the first stage, the stress increased linearly from 0 to 0.4 f_c. In the second stage, the stress-strain relationship curve was nonlinear with the stress ranging from 0.4 f_c to f_c. In the third stage, the stress descended linearly as the strain increased. For the concrete in tension, the stress-strain relationship could be defined using fracture energy.

3.3. Finite Element Result

To describe the stress distribution in the steel plate, the steel plate was divided into four parts: Plate A, Plate B, Plate C, and Plate D, as shown in Figure 14. For the Specimen SP-1 under ultimate load, if the crack length was less than the width of the lower flange of the steel plate, the stress near the crack in Plates A and B could still reach the yield strength. For Plate D, the stress near the crack decreased significantly due to the reason that the crack penetrated through the lower flange of the steel plate, as shown in Figure 15(a).

As illustrated in Figure 15(c), Plates B, C, and D were split into two parts by the cracks, respectively. Additionally, Plate A was uncracked. The maximum stress in Plate B reached the yield strength since it was adjacent to Plate A. Compared with the stress in Plate B, the stress in Plate C decreased significantly, and the stress in Plate D was negligible. Observing the stress distribution in the steel plate, it revealed that the stress in the steel plate was redistributed due to the existence of the cracks. The tensile stress was mainly borne by Plate A, Plate B, and Plate C.

Figure 16 shows the load-displacement curves of the FE model and experiment. The residual bearing capacity obtained from the FE model was close to the test results. However, for specimens SP-1 and SP-2, the maximum displacements obtained from FE models were different from the test results. The reason was that the static test was stopped when the stress in the midspan of the steel plate reached the yield strength.

3.4. Verification of the Theoretical Method

The ultimate vertical loads of the composite deck obtained from the theoretical method and FE model were compared with the test results, as displayed in Table 3. The maximum error between the test results and the theoretical calculation was 4%. It indicated that the theoretical method was reliable. Additionally, the maximum error between the test results and the FE model was 9%, which showed that the FE model was acceptable.

4.1. Influence of the Shear Span Length

The shear span length L_sp was set to be 400 mm, 500 mm, 600 mm, 800 mm, 1000 mm, and 12000 mm. Figure 18 shows the relationship between the shear span length L_sp and the residual carrying capacity F_{u, FE} obtained from the FE model. When L_sp increased from 400 mm to 800 mm (by 100%), F_{u, FE} decreased from 1260.8 kN to 572.3 kN (by 54.6%). When L_sp increased from 800 mm to 1200 mm (by 50%), F_{u, FE} decreased from 572.3 kN to 327 kN (by 42.9%). As the shear span length L_sp increased, the residual carrying capacity F_{u, FE} decreased rapidly in the initial stage and then tended to be stable. The relationship between L_sp and F_{u, FE} was exponential.

4.2. Influence of the MCL Connector Spacing

Figure 19 shows the influence of the MCL connector spacing L_mc on the residual carrying capacity of the composite deck. The spacing L_mc was taken as 200 mm, 300 mm, 400 mm, 500 mm, 600 mm, 1500 mm, and 3000 mm. The residual carrying capacity F_{u, FEA} decreased by 9.4% when L_mc increased from 200 mm to 300 mm (by 50%). When L_mc increased from 300 mm to 400 mm, F_{u, FEA} decreased from 296.1 kN to 276.2 kN (by 6.7%). When L_mc increased from 500 mm to 600 mm, F_{u, FEA} decreased from 253.4 kN to 239.7 kN (by 5.4%). With the increase of L_mc, F_{u, FEA} descended rapidly in the initial stage and then tended to be stable. The longitudinal shear resistance of the composite deck went down because of the decrease in the number of MCL connectors, which led to the decline of the residual carrying capacity of the composite decks.

4.3. Influence of the Upper Flange Depth of the Concrete Slab

Figure 20 shows the relationship between the upper flange depth of the concrete slab h_c and the residual carrying capacity of the composite deck. The depth h_c was set to be 115 mm, 145 mm, 175 mm, 205 mm, 235 mm, and 265 mm. When h_c increased from 115 mm to 145 mm, F_{u, FEA} went up from 327 kN to 451.8 kN (by 38.2%). When h_c increased from 145 mm to 175 mm, F_{u, FEA} went up from 451.8 kN to 565.6 kN (by 25.2%). When h_c increased from 205 mm to 235 mm, F_{u, FEA} went up from 650 kN to 768 kN (by 18.2%). When h_c increased from 235 mm to 265 mm, F_{u, FEA} went up from 768 kN to 826 kN (by 7.6%). The relationship between the h_c and F_{u, FEA} was linear, as shown in Figure 20. It indicated that the residual bearing capacity of the composite deck could be improved by increasing h_c appropriately. The increase in the depth of the concrete slab enhanced the inertial moment of the cross section of the composite deck, which improved the flexural performance of the composite deck.