Analysis of Anchoring Attachments Using Finite Element Modeling
FEM is a general method commonly used for structural analysis. Usage of FEM for modeling of connections of any shapes seems to be ideal (Virdi 1999 ). An elastic- plastic analysis is required, as the steel ordinarily yields in the structure. In fact, the results of the linear analysis are useless for connection design when high loads are applied.
FEM model of a connection for research. It uses spatial 3D elements for both plates and anchors
The fasteners – anchors and welds – are the most difficult in the point of view of the analysis model. Modeling of such elements in general FEM programs is difficult because the programs do not offer required properties. Thus, special FEM components had to be developed to model the welds and anchors behavior in the connection.
In the case of connections, the geometrically nonlinear analysis is not necessary unless plates are very slender. Plate slenderness can be determined by eigenvalue (buckling) analysis. The geometrically nonlinear analysis is not implemented in the software.
Material model for steel
The most common material diagrams which are used in finite element modeling of structural steel are the ideal plastic or elastic model with strain hardening and the true stress-strain diagram.
The plates in Hilti PROFIS Engineering are modeled with elastic-plastic material with a nominal yielding plateau slope according to EN 1993-1-5 [2], App C, Part C.6. The material behavior is based on von Mises yield criterion. It is assumed to be elastic before reaching the yield strength, fy.
The ultimate limit state criterion for regions not susceptible to buckling is reaching the limiting value of the principal membrane strain. The value of 5% is recommended EN 1993-1-5 [2], App C, Part C.8 Note 1.The limit value of plastic strain is often discussed. In fact, the ultimate load has low sensitivity to the limit value of plastic strain when the ideal plastic model is used, [3].
Material diagrams of steel in numerical models distribution
Plate model
Shell elements are recommended for modeling of plates in FEA of structural connection. Four-node quadrangle shell elements with nodes at its corners are applied. Six degrees of freedom are considered in each node: 3 translations (ux, uy, uz) and 3 rotations (φx, φy, φz).
Rotations perpendicular to the plane of the element are considered. Complete 3D formulation of the element is provided. The out-of-plane shear deformations are considered in the formulation of the flexural behavior of an element based on Mindlin hypothesis. The MITC4 elements are applied, see Dvorkin (1984) [4]. The shell is divided into five integration layers through thickness of the plate at each integration point and plastic behavior is analyzed in each point.
It is called Gauss-Lobatto integration. The nonlinear elastic-plastic stage of material is analyzed in each layer based on the known strains.
Mesh Convergence
There are some criteria for the mesh generation in the connection model. The sensitivity analysis considering mesh discretization should be performed by the user for complicated geometries. In general, larger mesh size leads to faster calculation time but less accurate results, smaller mesh size lead to slower calculation but higher accuracy in results.
All plates of a steel-to-concrete connection have a common division into elements. The size of generated finite elements is limited. The minimal element size is set to 10 mm and the maximal element size to 50 mm (can be changed by the user in advanced settings). Meshes on flanges and webs are independent of each other. The default number of finite elements is set to 8 elements to the large profile dimension, as shown in the following figure. The user can modify the default values in advanced settings, [3].
The mesh on a column and baseplate with constraints between the web and the flange
The relation between the profile mesh and the plate mesh is defined as follows:
• Mesh in largest side of base plate =2∙number of profile mesh elements
• Then, default finite element size is set to 16 elements as shown in the figure below:
The mesh on a baseplate with 16 elements along its width
The following example of a concrete-to-base plate connection shows the influence of mesh size on the base plate stress. It is loaded by a bending moment as shown in the following figure, the number of the finite elements along the cross-section height varies from 8 to 40 (leading to a division of the larger plate size by a factor from 16 to 80) and the results are compared. It is recommended to subdivide the base plate length into 16 elements, as smaller elements only slow down the calculation but don’t improve accuracy. It is the responsibility of the user to define the mesh size for the application at hand.
Influence of mesh size of base plate stress
Anchors
Anchor material properties are based on experimental Hilti research for the product assessments. The anchor stiffness is a product specific characteristic which differs depending on the selected product, loading conditions, diameter, material and embedment depth.
Schematic load displacement
Anchors with stand-off
The CBFEM model described in this document is suitable for fastenings with a base plate on concrete and with stand-off in case of grouting under the plate. The grout should have at least the same resistance as the concrete base material.
It is assumed that the grout can resist the compressive stress while tensile stress is transmitted to the anchors. The internal load distribution is determined by finite element model.
PROFIS users must select, in this case, standoff with grout. If the compressive strength of the grout is smaller than the concrete under it, then PROFIS conservatively assumes that the grout cannot transmit compression forces into the concrete.
The anchor resistance verifications produced by PROFIS Engineering consider increase of shear load due to the lever arm of the shear load, as per the calculation example below.
Selection of standoff with grout Anchors with stand-off with grouting
Example of steel shear resistance of Hilti Anchor with lever arm
Concrete Block
Design model
In CBFEM, it is convenient to simplify the concrete block as 2D contact elements. The connection between the concrete and the base plate resists in compression only. Compression is transferred via Winkler-Pasternak subsoil model which represents deformations of the concrete block. The tension force between the base plate and concrete block is carried by the anchor bolts, [3].
Deformation Stiffness
The stiffness of the concrete block may be predicted for the design of column bases as an elastic hemisphere. A Winkler-Pasternak subsoil model is commonly used for a simplified calculation of foundations. The stiffness of subsoil is determined using modulus of elasticity of concrete and the effective height of a subsoil as, [3]:
where:
SI units must be used in the formula, the resulting units is N/m3.
Welds
Several options how to treat welds in numerical models exist. It is possible to use different mesh descriptions, different kinetic and kinematic variables and constitutive models. The different types of geometric 2D and 3D models and thereby finite elements with their applicability for different accuracy levels are generally used. Most often used material model is the common rate-independent plasticity model based on von Mises yield criterion. Two approaches which are used for welds are described, [3].
Direct connection of plates
This first option of weld model between plates is rigid connection by links between meshes of connected plates. The connection is called multi point constraint (MPC) and relates the finite element nodes of one plate edge to another plate. The finite element nodes are not connected directly. The advantage of this approach is the ability to connect meshes with different densities. The constraint allows to model midline surface of the connected plates with the offset, which respects the real plate thickness. This type of connection is used for full penetration butt welds, [3].
Constraint between weld element and mesh nodes, source [3]
Weld with plastic redistribution of stress
The load distribution in weld is derived from the MPC, so the stresses are calculated in the throat section. This is important for the stress distribution in plate under the weld and for modelling of T-stubs. This model does not respect the stiffness of the weld and the stress distribution is conservative. Stress peaks, which appear at the end of plate edges, in corners and rounding, govern the resistance along the whole length of the weld. To express the weld behaviour an improved weld model is applied. A special elastoplastic element is added between the plates. The element respects the weld throat thickness, position and orientation. The equivalent weld solid is inserted with the corresponding weld dimensions. The nonlinear material analysis is applied and elastoplastic behaviour in equivalent weld solid is considered. [3].
Steel material and lamellar tearing
PROFIS Engineering does the connection verification in terms of design. Lamellar tearing is related to the choice of the structural steel materials – depending on the weld, a higher ‘Z’ value may be needed for the involved components (profile, plate and stiffeners).The consideration of the steel Z-value to prevent lamellar tearing, is not determined by PROFIS Engineering. Users can input yield strength and ultimate strength of the main steel, from other structural steel information like ‘Z’. To fully define the features of the steel more information would be needed, e.g. next image.
Designation of the steel grade according to EN 10025 (2004). Source: The right choice of steel [5]
Point of applied shear loads
The shear load at the base plate is transferred to the anchors according to EN1992-4 section 6.2.2.3. Fastenings are considered to act without lever arm, if all conditions below are satisfied:
• The fixture is made from steel and is in contact with the fastener over a length of 0.5tfix.
• Using a levelling mortar with thickness tgrout≤0.5d under at least the full dimensions of the fixture on a rough concrete surface as an intermediate layer. The strength of the mortar shall be that of the base concrete, but not less than 30N/mm2.
When the above is not satisfied, then the shear force on the fastenings is assumed to act with lever arm. The considered point of applied load for shear with lever arm is the center of the plate.
Point of applied load for shear with lever arm
National Annexes of the Eurocode considered in design
The national annexes of EC3 & EC2 affect the advanced base plate (ABP) default values for γM0, γM1, γM2 and concrete factor αcc.
Most countries in Europe have published a National Annex which provides guidance to engineers regarding which safety factors should be used for design. The default values in PROFIS Engineering are according to the national annex for each region used in design. However, the user can also edit these values in the advanced settings (check the image below).
Advanced settings to change safety factors
CBFEM application in case of seismic design
Earthquake resistance steel buildings shall be designed in accordance with one of the following dissipative behavior:
• Low dissipative behavior (concept a)
• Medium or high dissipative behavior (concept b)
Requirements on cross sectional class of dissipative elements depending on ductility class (medium and high)
and reference to behavior factor q (Table 6.3, EN1998-1)
In PROFIS Engineering Load Type Seismic should be selected to prove earthquake load combinations. The value of q should be determined by the user outside of PROFIS. Based on the value of q and Table 1, elastic or capacity design should be selected.
Capacity and elastic design
The CBFEM design described in this document is applicable for concept a), and the resistance of the members and of the connections should be evaluated in accordance with EN 1993 without any additional requirements.
In this case, PROFIS Engineering proceeds to connection design for seismic load combinations, as described below.
CBFEM details in case of seismic (DCL, q<1.5-2)
CBFEM application in case of seismic design has been investigated and assessed by Hilti, [6].
If you would like to start using PROFIS Engineering and start design as per EC2 visit our webpage clicking here
You are also welcome to ask us for support: simply leave a comment or post your question in the community, or improve your knowledge and skills via our Webinars or training sessions.
For the latest news in engineering solutions and innovations follow us on: LinkedIn, Instagram and Twitter
To view further articles on PROFIS Engineering please click here
References
[1] Numerical Simulation of Semi Rigid Connection by the Finite Element Method, Report of Working Group 6 Numerical, Brussels Luxembourg, 1999.
[2] Technical Commitee CEN/TC 250, Eurocode 3: Design of steel structures - Part 1-5: Desing of steel structures, 2006.
[3] IDEA StatiCa, General theoretical background; https://resources.ideastatica. com/Content/02_Steel/Theoretical_background/1_General.htm, Version used 10/2018.
[4] Dvorkin E. N. and Bathe K. J., Mechanics Based Four Node Shell Element for General Nonlinear Analysis, 1984.
[5] Oliver Hechler, Georges Axmann & Boris Donnay, The right choice of steel - according to the Eurocode, 2015
[6] Hilti investigations and assessments for the use of CBFEM method under seismic loading, Schaan: Not published, 2019.
No comments yet
Be the first to comment on this article!