Standards such as EN 1992-4 and ACI 318-19 generally require that anchors subjected to shear load must be assessed for several failure mechanisms.
- Steel failure of a fastener without or with a lever arm
- Concrete pry-out failure
- Concrete edge failure
- Failure of supplementary reinforcement
The IDEA StatiCa Connection application includes checks for the first three failure modes for plain concrete. In the case of reinforced concrete, it is possible to export the model to the IDEA StatiCa Detail application and, in addition, perform an analysis and code-check of the reinforced concrete, and thus cover the fourth failure mode. It should be noted here that the failure mode names listed may slightly differ in various standards. In particular, in the context of this article, we consider the fourth failure mode to be the failure of any reinforcement in a concrete block. (anchor and supplementary reinforcement as stated in ACI 318-19 chapter 17.5, supplementary reinforcement as defined in EN 1992-4 chapter 7.2.2, and all other reinforcement in the model)
In the Detail application, which has 3D CSFM implemented for the 3D modeling environment, it is therefore possible to model even heavily reinforced elements with anchors that can be subjected to shear loads. Such elements will certainly not fail in the second and third failure modes. However, it is necessary for them to verify the first and fourth failure modes, plus the situation where concrete in contact with the surface of an anchor subjected to shear stress begins to crush.
The first mode is directly checked using formulas from the selected standard; the fourth failure mode is verified by comparing the results on the reinforcement elements from 3D CSFM and the standard load-bearing capacity of the reinforcement bars. The remaining question is how to determine the limit load value (bearing capacity) for the case of concrete crushing at the anchor–concrete interface.
From the available standards and literature, we can take as a reference the approach described in EN 1994-1-1 Chapter 6.6.3, formula 6.19. This formula is designed to assess the effect of concrete crushing in contact with anchors for headed studs of concrete-steel composite slabs and beams and is based on research papers [5] [6].
\[P_{Rd}=\frac{0.29\alpha d^{2}\sqrt{f_{ck}E_{cm}}}{\gamma_{V}}\]
However, the standard specifies that this approach is limited to anchors with a diameter of 16-25 mm and, in section 6.6.3.2, restricts its scope in terms of the interaction of tensile and shear forces.
We can also get inspiration from AISC 360-22 Chapter I8 Steel Anchors, Equation I8-1.
\[Q_{n}=0.5A_{sa}\sqrt{f'_{c}E_{c}}\le R_{g}R_{p}A_{sa}F_{u}\]
The first part of the equation expresses the same effect as equation 6.19 mentioned above in an analogous way. We can only observe differently determined empirical coefficients.
Verification of shear capacity using only the above-mentioned formulas is therefore insufficient due to the aforementioned limitations of the diameter and type of anchors (only headed studs), which is also demonstrated by the range of tested samples in [5] [6]. Another limitation when assessing using only the aforementioned formulas is the method of attaching the anchors to the base plate. These anchors are welded to the base plate, so it is assumed that rotation is fixed in the anchor-plate connection. Therefore, these formulas do not cover anchors that are secured with a single nut from above and cannot be considered fixed to the base plate.
For the reasons mentioned above, we performed a series of simulations in ABAQUS, where we first modeled examples corresponding to the scope of EN 1994-1-1. We calibrated the models so that the determined load-bearing capacity corresponded to the load-bearing capacity determined using the methodology in EN 1994-1-1. Subsequently, under the same assumptions, we modeled a wider series of examples to cover the needs of 3D CSFM and the Detail application. The determined load-bearing capacities are then directly implemented as a stop criterion in 3D CSFM.
ABAQUS models
Concrete blocks with anchors of 8, 12, 16, 25, and 50 mm in diameter were modeled. For each diameter, a model with concrete strengths of 16, 30, and 50 MPa was used. Finally, each anchor was modeled with a free end (hinged) and with rotational support at the point of load application (fixed). A total of 5 * 3 * 2 = 30 models were created. It is also important to mention that the bond between the anchor and the concrete is considered the same in all models. Before defining the test set, we verified that varying the bond strength has a negligible effect on the load-bearing capacity under investigation.
Obrázek celkového modelu
Geometry
The floor plan of the model is shown in the following figure. It is the same for all models. The height of the model is set at 200 mm for anchors with diameters of 8, 12, and 16 mm. For anchors with a diameter of 25 mm, the height of the model is 250 mm, and for anchors with a diameter of 50 mm, the height is 400 mm.
Okotovaný půdorys
The embended depths of anchors are: D8 - 100 mm, D12 - 150 mm, D16 - 170 mm, D25 - 220 mm, D50 - 350 mm. The length above the surface was always set to 10 mm. The model also features 2 (only for the 8 mm anchor) or 3 layers of U-shaped reinforcement bars. They have a 25 mm cover from the upper surface for all models. The diameters of the reinforcement for the individual anchors are as follows: D8 - 10 mm, D12 - 10 mm, D16 - 14 mm, D25 - 20 mm, and D50 - 28 mm. The distance between layers was D8, 12 - 40 mm D16 - 50 mm D25 - 60mm, and D50 - 75 mm.
Okotovana výztuž
Boundary conditions and load
The Displacement/Rotation surface support, with all translations and rotations turned on, was applied on the side surfaces of the wider part of the model to capture forces in Y direction and on the small surfaces to capture forces in X direction.
Podpory
Next, a point was defined on the upper surface of the anchors, which was connected to the entire upper surface of the anchors using RBE2 (123456) constraints. This point was used to apply a deformation load of up to 3 mm to the model. A rotational support was also placed on this point for models simulating an anchor welded to the base plate. In the case of a hinged connection, the rotational support was removed from the model.
Finite elements types and meshing
The basic geometry of the concrete is meshed according to the following figure. However, it is important to focus on meshing around the anchors. For each anchor diameter, two concentric circles were defined, where a refined mesh was enforced.
The anchors were also modeled using solid elements, with each quadrant of the circular cross-section of the anchor containing four surface finite elements.
C3D8R (An 8-node linear brick, reduced integration, hourglass control) elements were used as solid elements. The reinforcement was modeled from T3D2 elements.
Material models
For concrete, the Concrete Dapage Plasticity Model (CDP) developed by Lubliner was selected based on recommendations in the program documentation. In Abaqus, it is necessary to define the course of the uniaxial material curve in compression and tension. For the concrete model in compression, the definition according to Mandera was used. The post-cracking tensile response of concrete was described using a linear tension softening law, where the tensile stress decreases linearly from the tensile strength to zero with increasing cracking strain.
Graf mdoelu betonu
Anchors and reinforcement were modeled as a linear elastic material without plasticity. The material behaviour was defined using Young’s modulus and Poisson’s ratio, assuming no yielding or strain hardening. In the case of anchors, this was intentional, so that they would not become plasticized, and only the effect of concrete crushing in contact with the anchor would be examined.
Interactions
The interaction between concrete and reinforcement was modeled using the embedded element constraint available in Abaqus. This formulation assumes a perfect bond between concrete and reinforcement, i.e. no slip occurs at the interface.
interactions - reinf vs mesh, contacts
35.4.1 Embedded elements
[1] AMERICAN CONCRETE INSTITUTE (ACI). Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19). Farmington Hills, MI: American Concrete Institute, 2019.
[2] AMERICAN INSTITUTE OF STEEL CONSTRUCTION (AISC). Specification for Structural Steel Buildings. ANSI/AISC 360-22. Chicago, IL: American Institute of Steel Construction, 2022.
[3] CEN. EN 1992-4: Eurocode 2 – Design of concrete structures – Part 4: Design of fastenings for use in concrete. Brussels: European Committee for Standardization, 2018.
[4] CEN. EN 1994-1-1: Eurocode 4 – Design of composite steel and concrete structures – Part 1-1: General rules and rules for buildings. Brussels: European Committee for Standardization, 2004 (incl. Amendment A1:2014, pokud cituješ konsolidované znění).
[5] STARK, J. W. B. a van HOVE, B. W. E. M. Statistical analysis of push-out tests on stud connectors in composite steel and concrete structures. Part 1: Method and recommendations (Technical Paper S84, Part 1). Delft (NL): TNO Building and Construction Research, 1991. Report no. BI-91-163.
[6] STARK, J. W. B. a van HOVE, B. W. E. M. Statistical analysis of push-out tests on stud connectors in composite steel and concrete structures. Part 2: Solid concrete slabs (Technical Paper S84, Part 2). Delft (NL): TNO Building and Construction Research, 1991. Report no. BI-91-163.