# Parameterized FE Model for Designing Rigid End Plate Joints

### Technical Article

Designing rigid end plate connections is difficult for four-row connection geometries and multi-axis bending stresses because there are no official design methods.

With the model shown here, you can design connections under realistic loadings quickly. In order to be able to verify the model with the DSTV guideline of typified connections [1], we selected the following system.

#### System

Typified connection: IH 2.1 A 26 20
Section: HEA 260
Material: Steel S235
Bolts: M20 of strength class 10.9

The created FE model is created by means of surface elements for the beam. The modeling of the end plate is carried out by surfaces, which are then connected to each other in order to create a so-called contact solid between them. It defines the exact contact properties between the two surfaces. In this specific case, there is a failure in the case of a vertical tensile stress. Steel S235 is also selected as the material for the two end plate surfaces, but with plastic material behavior. Openings are modeled in the surfaces to represent the holes. The screws of the connection are defined as tension members and are shown in simplified form without a nut. A tension member has only a longitudinal stiffness E ⋅ A and can only absorb tensile forces. Moment hinges are arranged at the member ends. The screws are connected in a simplified way by several rigid members with member end hinges on the respective end plate. By entering the desired bolt size, all calculation-relevant parameters of the bolts (strength class 10.9) are transferred. Thus, it is possible to imply the correct strain length as a formula in the model in order to obtain the most accurate bolt forces.

Formula 1

$$lb = 2 · tp + 2 · D + k2 + m2$$

 tp Thickness of the end plate [mm] D Slice thickness [mm] k Head height [mm] m Nut height [mm]

#### Application

After opening the model, you can adjust the cross-section in the Data Navigator. The model is parameterized for the HEA, HEB and HEM beams standardized according to DIN EN 1025. You can then display the parameters and enter the dimensions and thickness of the end plate. Enter the bolt size (M12, M16, M20, M22, M24, M27, M30, M36) and the desired bolt spacings. At the same time, all screw parameters that are important for the calculations are adjusted. Finally, it is possible to adjust the loads.

#### Structural Design

To determine the load-bearing capacity of the connection, an initial load My of 50 kNm is applied and calculated with the load increment method. Then, you can evaluate the bolt forces and the plastic strains. For this, you have to determine the maximum tension resistance as follows.

Formula 2

$$Ft,Rd = k2 · fub · AsγM2Ft,Rd = 0,9 · 1.000 Nmm2 · 245 mm21,25 = 176,4 kN$$

 k2 Factor of tensile strength [-] fub Tensile strength of screw material [N/mm²] As Stress cross-section [mm²] γM2 Partial factor of the bolt [-]

#### Evaluation and Comparison

When comparing the tension resistance with the bolt forces of the FE modeling, you can see that the failure of the bolts occurs if the load is increased by more than 2.1 times. The bolt forces are 175.43 kN with an acting moment of 105 kNm.

Thus, the load bearing capacity of the connection of 105 kNm results from 2.1 ⋅ 50 kNm.

Evaluating the plastic strains shows maximum values of approximately one percent, which does not exceed the allowable limit strain of five percent according to EC3. In addition, you can see when the material starts to yield when displaying the nonlinearity degrees.

The DSTV guideline [1] gives a load capacity of 112.9 kNm which differs only slightly from the created FE model.

This deviation reflects, among other things, the lack of modeling the welds, which results in a lower stiffness of the outer bolt row. As a result, the internal screws are subjected to more loading and thus tend to fail.

Download below also a model having a connection with an extending end plate.

#### Reference

 [1] Typisierte Anschlüsse im Stahlhochbau nach DIN EN 1993-1-8. Stahlbau Verlags- und Service GmbH, Düsseldorf, 2013.

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• Updated 27 November 2020

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