FEM Modeling Approaches of Rigid Connections

Technical Article

Especially when the adjacent area of connection points should be analyzed, the geometry or load of the connection does not correspond to the standard specifications and/or a structure should be analyzed with an FE model (for example in plant engineering), it is necessary to evaluate the connections in detail on the FE model.

To obtain significant results about the choice of the selected modeling aproach, it may be helpful to generate a structure first which can be compared with the classical methods.

In a previous article, the design resistance of a rigid end plate connection was calculated with the formula according to EN 1993-1-8 [1]. In this example, the design resistance of the end plate should be loaded by means of an FEM modeling approach with the determined design resistance of 324.95 kNm.

Figure 01 - Calculation example

Surface Model

The beam HEB 400 was entered with a length of 500 mm and divided into surfaces. Assuming that the end plate has a rigid behavior under the solid bolt heads, a rigid surface with the diameter of the washer of 44 mm was generated. To simulate the elasticity of the bolts under tensile stress, they werde defined with a diameter of 24 mm and a length of 29 mm (= thickness of end plate + thickness of washer). To ensure that the load is introduced equally into the beam, a rigid end plate was used at the load application location.

Since a rigid support in the z-axis of the end plate can lead to convergence problems, a surface eleastic foundation with 2 ∙ 108 kN/m³ was assumed and at the locations where no deformation can take place due to the symmetry conditions of a beam joint or where the largest contact forces are expected, a line support was additionally designed. Both supports should fail in case of positive support reaction. Since EN 1993-1-8 [1] performs a plastic design, the material model "Isotropic Plastic 2D/3D" with the yielding criterion 23.5 kN/cm² was selected. As soon as the yield criterion is reached in the FE element, it cannot absorb further forces and a stress redistribution takes place.

Figure 02 - Surface model

Results

The failure criterion "Bolt failure with yielding of the flange" of the manual calculation can be validated.

When using the nonlinear material model "Isotropic Plastic 2D/3D", the area of the elements in plastic state has to be evaluated. It has to be considered that the elements in plastic state correspond to remaining damages. The FEM model shows too large plastic areas. This means that the connection is overloaded when considering it using the surface model. The determined bolt tension force with 279 and 288 kN also exceed the allowable limit tension force.

Figure 03 - Results

With an additional modeling, where beam, end plate, bolts and welds have been displayed with solids and the force introduction from the beam to the end plate takes place across the welds (=larger load surface), similar-sized plastic areas were determined. 

Reference

[1]   Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings; EN 1993-1-1:2010-12

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