002072

2026-08-12

Assessment of Ductility of Extended End-Plate Connections with Steel Joints for RFEM

Four extended end-plate beam-to-column connections (FS1–FS4, S355/S690 steel) were tested experimentally and evaluated with the Steel Joints add-on for RFEM 6 and with EN 1993-1-8 (Eurocode 3) hand calculation. The article compares moment resistance and initial rotational stiffness across all three methods and reports the underlying T-stub component equations.

This study evaluates the design of steel joints for RFEM by investigating the ductility characteristics and failure modes of extended endplate beam-to-column connections. The structural behaviour and load-bearing capacity of these connections are analysed in accordance with the design provisions specified in Eurocode 3 (EC3), and the resulting predictions are subsequently validated through comparison with a finite element model developed using Steel Joints for RFEM, as well as with corresponding experimental data.

Analytical Model

This study adopts the design criteria specified in EN 1993-1-8 for evaluating bolt resistance (shear and tension) and plate resistance (bearing and punching shear), utilizing the limit state formulations provided in Table 3.4.

The design resistance of the equivalent T-stub is evaluated independently for the endplate and the column flange components. For each component, the governing design resistance, F_T,Rd is defined as the minimum value derived from three potential failure mechanisms.

F_{T, R d} = m i n (F_{T 1, R d}, F_{T 2, R d}, F_{T 3, R d})

T-Stub Design Resistance (Governing Value of Three Failure Modes)

The individual resistance for each mode is calculated based on the plastic moment capacity of the flange (M_pl,1,Rd and M_pl,2,Rd) and the tension resistance of the bolt group (∑F_t,Rd). These modes account for complete flange yielding (Mode 1), bolt failure coupled with flange yielding (Mode 2), and pure bolt fracture (Mode 3).

Failure Modes:

F_{T, 1, Rd} = \frac{(8 n - 2 e_{w}) \cdot M_{pl, 1, Rd}}{2 mn - e_{w} (m + n)}

T-Stub Resistance – Failure Mode 1 (Complete Flange Yielding)

F_{T, 2, Rd} = \frac{2 \cdot M_{pl, 2, Rd} + n \cdot (\sum F_{t, Rd})}{(m + n)}

T-Stub Resistance – Failure Mode 2 (Bolt Failure with Flange Yielding)

F_{T, 3, Rd} = \sum F_{t, Rd}

T-Stub Resistance – Failure Mode 3 (Bolt Fracture)

Plastic Resistance Moments:

M_{pl, 1, Rd} = \frac{0.25 \cdot \sum l_{eff, 1} \cdot t_{f}^{2} \cdot f_{y}}{γ_{M 0}}

Plastic Moment Resistance of Flange (Failure Mode 1)

M_{pl, 2, Rd} = \frac{0.25 \cdot \sum l_{eff, 2} \cdot t_{f}^{2} \cdot f_{y}}{γ_{M 0}}

Plastic Moment Resistance of Flange (Failure Mode 2)

The initial stiffness of the connection is given by the formula:

S_{j, ini} = \frac{E \cdot z^{2}}{\sum_{i = 1}^{n} \frac{1}{k_{i}}}

Initial Rotational Stiffness of Connection

Where
E is the Young's modulus,
z is the lever arm,
K_i is the stiffness coefficient of the i_th component and
n is the number of basic joint components.

Geometric Details of Beam-to-Column Connection

All beam and column members were fabricated from S355 steel following standard construction practice. Endplates were made from either S355 & S690 steel. Geometric details—including endplate dimensions and bolt group layouts—are shown in Image 2, while the test matrix and measured material properties are presented in Table 1.

Specimens FS1 through FS4 used an HEM 340 column section paired with an IPE 300 beam section. This configuration was chosen to examine weak-column strong-beam behaviour. Across all four specimens, the beam section remained constant at IPE 300, with endplate thicknesses of 10, 15, 20, and 10 mm for FS1, FS2, FS3, and FS4, respectively.

Table 1: Geometric & Material Details of Tested Specimens
Specimens	Column	Steel grade	Beam	Steel Grade	Endplate Thickness, mm	Steel Grade
FS1	HEM340	S355	IPE300	S235	10	S355
FS2	HEM340	S355	IPE300	S235	15	S355
FS3	HEM340	S355	IPE300	S235	20	S355
FS4	HEM340	S690	IPE300	S235	10	S690

Technical drawing of a typical beam-column bolted connection showing an IPE300 beam connected to an HE340M column with detailed dimensions and plate thicknesses.

1 Typical Beam-Column Bolted Connection

Technical drawing of an extended endplate connection showing bolt arrangement and stiffener configuration for steel joint analysis.

2 a) Endplate/Bolt, b) Stiffener Configuration

Discussion

Steel Joints for RFEM Solution

Using the Steel Joints add-on for RFEM 6, the connection design was fully integrated within the primary structural model. This study presents an experimental and numerical investigation into the structural performance of four extended end-plate beam-to-column connections, with particular emphasis on ductility assessment. The investigation was complemented by targeted T-stub component characterization and high-fidelity finite element (FE) analysis. The developed FE models were validated against experimental measurements and verified against the Eurocode 3 (EC3) design framework, then employed to extract detailed insights into localized deformation behavior. Images 3 and 4, along with Tables 2 and 3, present comparisons of moment resistance and rotational stiffness among the experimental results, the Steel Joints for RFEM 6 predictions, and the EC3 analytical solutions.

A bar chart comparing the moment capacity of four steel joint specimens based on experimental results, RFEM simulations using the Steel Joints add-on, and Eurocode 3 calculations.

3 Comparison of Moment Resistance – Experimental vs. Steel Joints for RFEM and EC3

Bar chart comparing initial stiffness for four test cases, showing results from experiments, Steel Joints for RFEM, and EC3 calculations.

4 Comparison of Stiffness – Experimental vs. Steel Joints for RFEM and EC3

Table 2: Comparison of Moment Resistance – Experimental vs. Steel Joints for RFEM & EC-3-1-8 | Moment Capacity (kNm)
Specimens	Experiments	Steel Joints in RFEM	EC3
FS1	107.45	107.53	77.52
FS2	167.93	122.51	132.09
FS3	182.46	126.09	187.29
FS4	164.56	118.46	124.44

Table 3: Comparison of Stiffness – Experimental vs. Steel Joints for RFEM & EC-3-1-8 | Initial Stiffness S_j,ini (MNm/rad)
Specimens	Experiments	Steel Joints for RFEM	EC3
FS1	17.51	29.20	34.66
FS2	22.69	38.30	46.76
FS3	22.39	43.50	51.76
FS4	16.66	29.20	32.77

Finite element analysis results showing equivalent von Mises stresses and equivalent plastic strains for a steel joint model with 1 mm thickness.

5 Equivalent Stresses and Plastic Strain of FS-1mm Model

Finite element analysis of a steel joint showing equivalent von Mises stresses and plastic strains under load. The visualization displays stress distribution and deformation in the connection area.

6 Equivalent Stresses and Plastic Strain of FS-2mm Model

Finite element analysis of a steel joint showing equivalent von Mises stresses and equivalent plastic strains under applied loading conditions.

7 Equivalent Stresses and Plastic Strain of FS-3mm Model

Finite element analysis results showing equivalent von Mises stresses and equivalent plastic strains for a steel joint model.

8 Equivalent Stresses and Plastic Strain of FS-4mm Model

Table showing design check ratios for plate, bolt, and fillet weld components under ultimate limit state, alongside calculated rotational stiffness values for connected members.

9 Design Ratio and Rotational Stiffness of FS-1 Model

Table showing design check ratios for plates, bolts, and welds, alongside calculated rotational stiffness values for a steel connection joint.

10 Design Ratio and Rotational Stiffness of FS-2 Model

Table displaying design check ratios for plates, bolts, and fillet welds alongside calculated rotational stiffness values for joint members in a structural analysis.

11 Design Ratio and Rotational Stiffness of FS-3 Model

Table showing design check ratios for plates, bolts, and welds, alongside rotational stiffness values for joint members in a structural analysis.

12 Design Ratio and Rotational Stiffness of FS-4 Model

Conclusions

The comparison between experimental, Steel Joints for RFEM component-based, and EC-3-1-8 predictions shows that the RFEM model provides good overall agreement with test results for both moment resistance and initial stiffness, confirming its reliability for representing the actual joint behavior. EC-3-1-8 predictions for moment resistance vary across specimens (ratios of 0.72–1.49 relative to RFEM), reflecting the sensitivity of the analytical component method to specific geometric parameters such as plate thickness and bolt layout. The results demonstrate that Steel Joints for RFEM provides a notably more accurate prediction of initial joint stiffness than the EC-3 analytical method. This confirms RFEM's finite-element-based approach better captures the actual stiffness behaviour of the tested connections, making it a more reliable tool for practical design and analysis compared to the conservative, and often overly simplified, EC3 component method.

References

European Committee for Standardization (CEN). (1993). Eurocode 3. Design of Steel Structures Part 1–8: Design of Joints (EN 1993-1-8). Brussels, CEN.
Girão Coelho, A. M., Bijlaard, F. S. K., & Simões da Silva, L. (2004). Experimental assessment of the ductility of extended end plate connections. Engineering Structures, 26(9), 1185–1206. https://doi.org/10.1016/j.engstruct.2000.09.001

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