Considering that the fixed crack model by default of the general finite element software was unable to simulate the shear softening behavior of concrete in the actual situation, a rotational crack model based on the modified compression field theory developed by UMAT (user material) of ABAQUS software was proposed and applied to the nonlinear analysis, and a numerical simulated model for the steel-concrete composite slab was built for shear analysis. Experimental studies and numerical analyses were used to investigate the shear load-carrying capacity, deformation, and crack development in steel plate-concrete composite slab, as well as the effects of the shear span ratio and shear stud spacing on the shear performance and the contribution of the steel plate and the concrete to the shear performance. Shear capacity tests were conducted on three open sandwich steel plate-concrete composite slabs and one plain concrete slab without a steel plate. The results indicated that the shear-compression failure mode occurred primarily in the steel plate-concrete composite slab and that the steel plate sustained more than 50% of the total shear force. Because of the combination effect of steel plate, the actual shear force sustained by the concrete in the composite slab was 1.27 to 2.22 times greater than that of the calculated value through the Chinese Design Code for Concrete Structures (GB 50010-2010). Furthermore, the shear capacity of the specimen increases by 37% as the shear stud spacing decreases from 250 mm to 150 mm. By comparing the shear capacity, the overall process of load deformation development, and the failure mode, it was shown that the simulation results corresponded with the experimental results. Furthermore, the numerical simulation model was applied to analyze the influence of some factors on composite slab, and a formula of shear bearing capacity of slab was obtained. The results of the formula agreed with the test result, which could provide references to the design and application of steel plate-concrete composite slab.
A steel plate-concrete composite component is a combination of steel and concrete (Figure
Steel plate-concrete composite component.
Due to the simplicity of these structures, steel plate-concrete composite components, including composite beams, slabs, or shear walls, have been recently used for strengthening purposes [
Link and Elwi [
Some studies have focused on dual-layer steel plate-concrete composites. Yang et al. [
At present, common finite element software incorporates a fixed crack model in numerical simulations by default. Application of a rotating crack model, which is more practical, requires secondary analysis by the finite element software, and there are few systematic studies in this aspect.
In this study, an experimental evaluation of the shear resistance of a simply supported open sandwich steel plate-concrete composite slab was conducted, using three steel plate-concrete composite slabs and one concrete slab. The effects of the shear span ratio and shear stud spacing on the shear performance of the composite slab, the damage mode and the mechanism of the shear failure of the steel plate-concrete composite slab, and the shear sustained individually by the steel plate and concrete were analyzed. A secondary analysis using the UMAT subprogram of ABAQUS was conducted, and the modified compression field theory (MCFT) was applied to analyze the shear capacity of the concrete. The experimental results were compared with the results of the numerical simulation in order to validate the model. Furthermore, the influence of some factors on composite slab was analyzed by the numerical simulation model and a formula of shear bearing capacity of slab was obtained, which could provide references to the design and application of steel plate-concrete composite slab.
Three steel plate-concrete composite slabs, identified as SCS-1, SCS-2, and SCS-3, were designed as shown in Figure
Sectional dimensions of specimens.
Test matrix of steel plate-concrete composite deep slabs.
Specimens |
|
Span L0 (mm) |
|
bs (mm) | Stud spacing (mm) | Steel mesh (mm) |
---|---|---|---|---|---|---|
SCS-1 | 2.63 | 2100 | 1050 | 6 | 150 | Φ6-150 |
SCS-2 | 1.88 | 1500 | 750 | 6 | 150 | Φ6-150 |
SCS-3 | 1.88 | 1500 | 750 | 6 | 250 | Φ6-150 |
SCS-4 | 1.88 | 1500 | 750 | — | — | Φ6-150 |
The steel material used for the steel plate had the yield strength of 316.7 MPa, the ultimate strength of 448.8 MPa, and the percentage elongation of 28.8%. The concrete used in the composite samples had the averaged compression strength of 28.66 MPa based on three standard concrete cube specimens of 150 × 150 × 150 mm. Shear studs, made of ML-15 steel, had the diameter of 13 mm and the ultimate tensile strength of
Three-point static loading tests were conducted on the four specimens. The ends of the specimens were simply supported. Cushion blocks were established at the midspan loading zones of the composite slabs to ensure that the vertical displacement of the steel plate and concrete at the loading zone remained identical, to sustain the load and prevent local damage at the loading zone together. Step loading which was driven by displacement was used according to the predicted failure load in order to measure the displacement and collect the strain value when the deformation was fully developed. The test setup is shown in Figure
Test setup.
The test measurements included deflection at the midspan and 350 mm around it, transverse and side displacement of the support, and strain of each section. A labelled layout of the measuring points is provided in Figure
Layout of displacement gauges and strain gauges. (a) Layout of displacement gauges. (b) Layout of strain gauges on steel plate. (c) Layout of strain gauges on concrete slabs.
Vertical cracks were first observed at midspan when the loading force approached 40%
Crack pattern of steel plate-concrete composite slabs. (a) Crack pattern diagram for SCS-1 (
As is evident from the damage to SCS-2 and SCS-3 when
The load-displacement relations of the three composite slabs and the plain concrete slab are shown in Figure Elastic stage: the stage lasted from the start of loading until the elastic shear capacity stage. All parts of the specimen were in the elastic state, and the relationship between the shear stress and midspan deflection was essentially linear for all specimens. Elastoplastic stage: when cracks appeared on the concrete, the stiffness of the specimen decreased and deflection development was accelerated. The load-displacement curve of the composite slab was nonlinear. Vertical cracks appeared on the concrete at the midspan and the cracks widened as the load increased. Descending stage: as the load was continually increased, once a certain load-carrying capacity of the steel plate-concrete composite slab was reached, diagonal cracks appeared in the concrete. At this point, the load-carrying capacity was at its maximum and shear failure occurred at the side of the concrete. Due to the increase in shear span ratio and decrease in shear stud spacing, the descending branch of the curve was smooth. The three composite slabs demonstrated outstanding ductility compared to SCS-4.
Load-displacement diagrams: (a) SCS-1, (b) SCS-2, (c) SCS-3, and (d) SCS-4.
In the Chinese Design Code for Concrete Structures (GB 50010-2010)), the reinforced concrete shear capacity,
All data, as well as test results, are summarized in Table
Experimental load value (kN).
Specimens |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
SCS-1 | 2.63 | 344.3 | 155.3 | 189.0 | 0.45 | 87.7 | 1.77 |
SCS-2 | 1.88 | 416.9 | 195.0 | 221.9 | 0.47 | 87.7 | 2.22 |
SCS-3 | 1.88 | 304.4 | 111.7 | 192.7 | 0.37 | 87.7 | 1.27 |
SCS-4 | 1.88 | 71.9 | 71.9 | 0 | 1.0 | 87.7 | — |
The ultimate load sustained by the steel plate
According to the von Mises yield condition, when the material equivalent stress
Table
Numerical simulation using finite element analysis (FEA) was conducted to further explore the shear capacity of the composite. The commercially available FEA software ABAQUS was used in this study.
A shell element, S4R, was used to simulate the steel plate, and a rectangular beam section element, B32, was used to simulate the concrete. Twenty-five integral points were placed in the beam section, and modified compression field theory was applied to each integral point. The constitutional relationship was defined by a bilinear elastic hardening model (bilinear model). The yield strength and elastic modulus were given according to the experimental results given in Section
Here, two models were used to simulate the concrete cracking: (a) the rotation crack model using the developed UMAT subprogram of the concrete rotation crack model (denoted as RCM) and (b) a fixed crack model (denoted as FCM), which is presented in the next section.
According to the fixed crack model, the direction of the cracks that appeared after the first was identical to that of the first. In other words, the shear stress at the crack surface increased until shear locking occurred. In practice, crack direction angles vary as the load increases, and the shear stress at the crack surface remains steady or even decreases. However, the fixed crack model cannot simulate the shear softening problem of concrete in practical situations and it overestimates the analytical result of shear capacity. The rotation crack model can demonstrate the variation in angle direction, as presented in the next section. The stiffness matrix can vary at any time under different crack directions, and the shear stress at the crack surface can be better simulated.
Vecchio and Collins proposed the MCFT [
The UMAT in ABAQUS was used to define the subroutine of the MCFT for describing the rotation crack model for the concrete. When the state variant and strain increment were input by the main program, the UMAT solved the stress increment according to the strain variant, solved and returned the Jacobian matrix to develop the global stiffness matrix, and then temporarily stored the state variant for the next increment. The key was to solve the Jacobian matrix.
Because the coordinates and positive direction were different before and after the appearance of cracks in the concrete, the Jacobian matrix was also different. When
The detailed framework of the program is shown in Figure
Flowchart of the rotation crack modeling using ABAQUS subroutine.
In accordance with the MCFT, the cracked concrete was treated as a new type of material. The reinforcement and cracks were smeared within the material so that no crack existed. The MCFT model used in this study required modification in order to cancel crack detection. The constitutional relationship of the MCFT was used as the compressive constitutional relationship of the concrete; the tensile constitutional relationship is represented by equations (
The tensile stress-strain relationship of concrete is written as
The stud was the connecting element between steel plate and concrete. The relative slippage of the steel plate and concrete should be taken into account when modeling with ABAQUS software. Therefore, a nonlinear spring element was used to simulate the role of studs. The spring element adopted the shear slip formula for the slip curve proposed by Ollgaard et al. [
The steel plate-concrete composite slabs were modeled, and the boundary condition was established as a simple support at both ends. Loading was controlled through displacement. The finite element model of the composite slab is shown in Figure
FEM model of composite slab.
The results of simulation and the experimental data are listed in Table
Comparisons of shear capacity.
Specimens |
|
|
|
|
|
|
---|---|---|---|---|---|---|
SCS-1 | 2.63 | 344.3 | 336.6 | 374.4 | 0.98 | 1.09 |
SCS-2 | 1.88 | 416.9 | 408.6 | 456.6 | 0.98 | 1.10 |
SCS-3 | 1.88 | 304.4 | 299.4 | 350.8 | 0.98 | 1.15 |
SCS-4 | 1.88 | 71.9 | 67.2 | 100.8 | 0.93 | 1.40 |
Figure
Comparison of experimental load-displacement curve to that of FEM: (a) SCS-1, (b) SCS-2, (c) SCS-3, and (d) SCS-4.
From test analysis of Section
The shear span ratio
Relationship between shear span ratio and shear capacity. (a) Length of shear span. (b) Section height.
From Figure
Based on the parameters in Section
Relationship between steel plate thickness and shear capacity.
As mentioned above, the shear bearing capacity of steel plate-concrete composite slabs was similar to combination of the respective shear resistance of steel plate and concrete, so concrete thickness
Relationship between concrete thickness and shear capacity.
In model test, the difference between SCS-2 and SCS-3 was the shear stud spacing
Relationship between shear stud spacing and shear capacity.
In the finite element analysis, considering the slip effect between steel plate and concrete slab, the nonlinear springs were used to simulate the stud. Figure
Deformation figure of composite slab under different stud spacings: (a) 150 mm, (b) 250 mm, and (d) 500 mm.
Through the parameter analysis of steel plate-concrete composite slab, the main factors of shear capacity were steel plate thickness
The parameters of the example.
|
|
|
|
|
|
---|---|---|---|---|---|
400 | 6 | 20.1 | 235 | 150 | 335.63 |
140 | 321.86 | ||||
130 | 295.65 | ||||
120 | 287.34 | ||||
110 | 273.21 | ||||
100 | 256.39 |
Fitting curve of concrete combination coefficient.
The parameters of the example.
|
|
|
|
|
|
---|---|---|---|---|---|
20.1 | 150 | 400 | 235 | 6 | 335.63 |
8 | 366.83 | ||||
10 | 385.78 | ||||
12 | 396.35 | ||||
14 | 412.68 | ||||
16 | 438.32 |
Fitting curve of steel plate combination coefficient.
Based on the fitting curve of the above parameters, the general formula of shear bearing capacity of steel plate-concrete composite slabs proposed in this paper is shown in the following equation:
The limitation of formula (
Considering the influence on practical engineering application, the general formula of shear bearing capacity of steel plate-concrete composite slabs obtained in the preceding section needed to be validated on the basis of test data. Based on the test data of three composite slabs, the results of model test and the results obtained by the shear capacity formula (equation (
Comparison of formula in this paper with test results.
Specimens |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
SCS-1 | 150 | 6 | 344.32 | 343.61 | 336.55 | 1.0 | 0.98 |
SCS-2 | 165 | 6 | 416.88 | 416.18 | 408.57 | 1.0 | 0.98 |
SCS-3 | 150 | 6 | 304.36 | 303.74 | 299.43 | 0.98 | 0.98 |
Experimental studies and numerical analyses were used to investigate the shear load-carrying capacity, deformation, and crack development in steel plate-concrete composite slab, as well as the effects of the shear span ratio and shear stud spacing on the shear performance and the contribution of the steel plate and the concrete to the shear performance. A rotational crack model based on the modified compression field theory developed by UMAT (user material) of ABAQUS software was proposed and applied to the nonlinear analysis, and a numerical simulated model for the steel-concrete composite slab was built for shear analysis. The following main conclusions can be obtained: The failure modes of the steel plate-concrete composite slabs in shear included bending failure and shear-compression failure. Bending failure was primarily witnessed in the shear span ratio of equal or greater than 2.63, whereas shear-compression failure was the main mode of shear failure for the composite slabs. The shear force sustained by the concrete ranged from approximately 37% to 47%, and the steel plate contributed more than 50% of the shear capacity. As shown by comparison of SCS-1 and SCS-2, the ultimate shear capacity decreased by 21% as the shear span ratio increased from 1.88 to 2.63. Furthermore, as shown by comparison of SCS-2 and SCS-3, the ultimate shear capacity decreased by 27% as the shear stud spacing increased from 150 mm to 250 mm. The actual shear force sustained by the concrete in the composite slab was 1.27 to 2.22 times greater than that of the calculated value through the Chinese Design Code for Concrete Structures (GB 50010-2010). Moreover, the load-carrying capacity of the concrete with smaller shear stud spacing was 1.75 times higher than that of the concrete with 250 mm shear stud spacing, but the shear stud spacing did not significantly affect the failure mode of the specimen. Bending failure was witnessed in the plain concrete slab specimen. After the combination of the steel plate and the resultant formation of the composite slab, the mode of failure changed to shear failure. The shear force sustained by the steel plate in the composite slab comprised more than 50% of the ultimate shear capacity, and the shear force sustained by the concrete doubled more than the calculated shear value according to the Chinese standard, suggesting that the presence of the steel plate significantly improved the shear capacity of the member. The modified compression field theory was used for the secondary development and establishment of the numerical model for shear analysis. The ultimate shear capacity of the composite slab acquired through the numerical analysis corresponded with the experimental values and surpassed the performance of the traditional fixed crack model. Thus, the proposed finite element numerical model for shear analysis would be capable of simulating the practical shear softening of concrete. The shear capacity of steel plate-concrete composite slabs was mainly affected by three factors: steel plate thickness
The data used to support the findings of this study are included within the article.
The authors declare that they have no conflicts of interest.
The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (nos. 51278488 and 51678564) and open projects of State Key Laboratory of Coal Resources and Safe Mining, China University of Mining (no. SKLCRSM14KFB05).