Designing End Plate Connection of Hollow Sections Under Tension According to the CIDECT Method and by Means of the FEM Model

Technical Article

A site joint consisting of hollow sections with end plates will be designed. It is the bottom chord of a truss which has to be divided for transport reasons.

This example is described in [1]. The design according to Section 6.2 of DIN EN 1993-1-8 applies to I and H sections and is not applicable in this case. Therefore, the CIDECT method described in [2] as well as an FEM model are used.

Structural System

Section: HE-A 180
End plate: tp = 35 mm
Material: Steel S355 according to DIN EN 1993-1-1, Table 3.1
Bolts: M 30x85 - 10.9/10 - HV

Figure 01 - Dimensions of the End Plate

Figure 02 - Surface Thicknesses and Loads

The FEM model is modeled by means of surface elements, member elements for the bolts, and a solid to represent the contact of the two end plates. Nonlinearities are defined for the contact solid. "Isotropic plastic 2D/3D" is selected as material model for the end plates (requires the RF-MAT NL add-on module). This material model shows an isotropic material behavior in the elastic zone. The plastic zone is based on the yielding according to the distortion hypotheses according to von Mises with a defined yield strength of the equivalent stress of 35.5 kN/cm².

Internal Forces

The governing design force in the bottom chord resulting from the determination of internal forces is NEd = 1,491.5 kN (tension). If this is converted to the perimeter of the hollow cross-section (center line), the line load is 2,211.60 kN/m.


The design should include the partial design of the ultimate limit state of the end plate and the calculation of the loading of oen bolt (including contact force).

  • Ultimate limit state of the end plate

    The resistance of the end plate under bending is determined according to Equation 8.6 with the CIDECT method:

    ${\mathrm N}_{\mathrm{Rd}}\;=\;\frac{\mathrm t_{\mathrm p}^2\;\cdot\;(1\;+\;\mathrm\delta\;\cdot\;{\mathrm\alpha}_1)\;\cdot\;\mathrm n}{\mathrm K\;\cdot\;{\mathrm\gamma}_{\mathrm M2}}$

    With Equation 8.5

    ${\mathrm\alpha}_1\;=\;\left(\frac{\mathrm K\;\cdot\;{\mathrm F}_{\mathrm t,\mathrm{Rd}}}{\mathrm t_{\mathrm p}^2}\;-\;1\right)\;\cdot\;\left(\frac{{\mathrm a}_{\mathrm{eff}}\;+\;{\displaystyle\frac{\mathrm d}2}}{\mathrm\delta\;\cdot\;({\mathrm a}_{\mathrm{eff}}\;+\;\mathrm b\;+\;{\mathrm t}_0}\right)\;=\;0.88$

    this results in:

    ${\mathrm N}_{\mathrm{Rd}}\;=\;\frac{35\;\mathrm{mm}^2\;\cdot\;(1\;+\;0.63\;\cdot\;0.88)\;\cdot\;6}{5.92\;{\displaystyle\frac{\mathrm{mm}²}{\mathrm{kN}}}\;\cdot\;1.25}\;=\;1,543\;\mathrm{kN}$

    Thus, it results in a ratio of:

    $\mathrm\eta\;=\;\frac{{\mathrm N}_{\mathrm{Ed}}}{{\mathrm N}_{\mathrm{Rd}}}\;=\;\frac{1,491.5\;\mathrm{kN}}{1,543.9\;\mathrm{kN}}\;=\;0.966\;<\;1.0$

    The evaluation of the stresses in the end plate on the FEA model with the RF-STEEL Surfaces add-on module results in an adequate result.

    Figure 03 - Stress Analysis of the End Plate According to the Hypothesis of von Mises with RF-STEEL Surfaces

  • Bolt Resistance

    For the bolt design, it is essential to determine the resistance including the contact forces. It is calculated according to Equation 8.7 with the CIDECT method as follows:

    ${\mathrm F}_{\mathrm t,\mathrm{ED}}\;=\;{\mathrm P}_{\mathrm f}\;\cdot\;\left(1\;+\;\frac{\mathrm b'}{\mathrm a'}\;\cdot\;\frac{\mathrm\delta\;\cdot\;{\mathrm\alpha}_2}{1\;+\;\mathrm\delta\;\cdot\;{\mathrm\alpha}_2}\right)$

    With Equation 8.9

    ${\mathrm\alpha}_2\;=\;\left(\frac{\mathrm K\;\cdot\;{\mathrm F}_{\mathrm t,\mathrm{Rd}}}{\mathrm t_{\mathrm p}^2}\;-\;1\right)\;\cdot\;\frac1{\mathrm\delta}\;=\;1.53$

    this results in:

    ${\mathrm F}_{\mathrm t,\mathrm{ED}}\;=\;248.6\;\cdot\;\left(1\;+\;\frac{43}{60}\;\cdot\;\frac{0.63\;\cdot\;1.53}{1\;+\;0.63\;\cdot\;1.53}\right)\;=\;335\;\mathrm{kN}$

    Thus, it results in a ratio of:

    $\mathrm\eta=\frac{{\mathrm F}_{\mathrm t,\mathrm{Ed}}}{{\mathrm F}_{\mathrm t,\mathrm{Rd}}}\;=\;\frac{335\;\mathrm{kN}}{403,6\;\mathrm{kN}}\;=\;0.83\;<\;1.0$

    The evaluation of the member internal force N in the FEM model results in a maximum bolt force of 343 kN in the central bolts and is therefore slightly higher than the analytical result.

    Figure 04 - Bolt Forces F,t,Ed (Including Contact Forces) for e = 45 mm

    In [2], the validity of the design criterion is linked to the fact that the outer bolt axes in the top plate connection are not located outside the corners of the hollow section. Figure 8.5 in [2] does not show the axis of the bolt, but the bolt hole as lying within the dimensions of the hollow section.

    Increasing the edge distance to e = 55 mm results in a redistribution of the bolt forces towards the outer bolts and a homogeneous distribution in terms of the process.

    Figure 05 - Bolt Forces F,t,Ed (Including Contact Forces) for e = 55 mm


CIDECT End plate joint Hollow section Tension joint


[1]   bauforumstahl e.V.: Beispiele zur Bemessung von Stahltragwerken nach DIN EN 1993 - Eurocode 3. Berlin: Ernst & Sohn, 2011
[2]   Packer, J. A.; Wardenier, J.; Zhao, X.-L.; van der Vegte, G. J.; Kurobane, Y.: Nr. 3 - Knotenverbindungen aus rechteckigen Hohlprofilen unter vorwiegend ruhender Beanspruchung - CIDECT-Handbuch Reihe "Konstruieren mit Hohlprofilen", 2. Auflage. Köln: TÜV Rheinland, 2009



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