002060

2026-06-23

Analysis of High-Strength Steel Section and End Plate Connections with Steel Joints Add-on for RFEM

This study presents the design of a steel joint as implemented in RFEM for the analysis of high-strength steel connections comprising profile sections and end plates. The structural behavior and load-bearing performance of these joints are evaluated against the design provisions of Eurocode 3 (EC3) and subsequently compared with the predictions of a finite element model developed in RFEM, the latter having been validated against experimental test data in prior work.

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})

Governing Design Resistance

The individual resistance for each mode is calculated on the basis of 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, R d} = \frac{(8 n - 2 e_{w}) * M_{p l, 1, R d}}{2 m n - e_{w} * (m + n)}

Complete Flange Yielding

F_{T 2, R d} = \frac{2 M_{p l, 2, R d} + n (\sum F_{t, R d})}{(m + n)}

Bolt Failure Coupled with Flange Yielding

F_{T 3, R d} = \sum F_{t, R d}

Pure Bolt Fracture

Plastic Resistance Moments:

M_{p l, 1, R d} = \frac{0.25 \sum l_{e f f, 1} * t_{f}^{2} * f_{y}}{γ_{M O}}

Plastic Resistance Moments. Part 1

M_{p l, 2, R d} = \frac{0.25 \sum l_{e f f, 2} * t_{f}^{2} * f_{y}}{γ_{M O}}

Plastic Resistance Moments. Part 2

Schematic diagram illustrating the three failure modes of a T-stub connection: Mode 1 complete flange yielding, Mode 2 combined bolt failure and flange yielding, and Mode 3 pure bolt failure.

1 Failure Modes of T-Stub

Geometric Details of Beam-to-Column Connection

In line with standard construction practice, all beam and column members were fabricated from S355, Q690, and Q960 steel, whereas the endplates used the higher-strength Q690 and Q960 grades. The geometric configurations, including the end plate and bolt-group arrangements, are shown in Images 2 & 3 and the corresponding experimental test matrix.

Specimen JD1 (S355) used an HEM 300 column section. To assess the performance of a weak-column/strong-beam hierarchy, a uniform HEA 320 beam section together with 10 mm thick S690 end plates was retained. JD2 was fabricated from Q690 steel and JD3 from Q960 steel. The beam and column sections were H300×180×10×12 and H340×200×10×12 for JD2, and H250×180×10×12 and H300×200×10×12 for JD3. M24 grade 8.8 and M27 grade 10.9 bolts were used.

Technical diagram illustrating the end plate and bolt configuration for connection JD1, showing bolt positions, dimensions, and spacing for structural steel design.

2 End Plate/Bolt Configuration of JD1

Technical drawing showing the end plate and bolt configuration for connections JD2 and JD3, detailing dimensions, bolt grades, and row arrangements.

3 End Plate/Bolt Configuration of JD2 & JD3

Discussion

Steel Joints for RFEM Solution

This study presents an experimental and numerical investigation into the structural performance of three extended high-strength steel end plate beam-to-column connections.

The experimental program was augmented by targeted T-stub characterization and high-fidelity finite element (FE) analysis. The connection design was fully integrated into the primary structural model using the FE-based Steel Joints add-on for RFEM 6. After validation against the experimental data and verification within the Eurocode 3 (EC3) framework, the FE models were employed to extract granular insight into localized deformation mechanics. Images 4 and 5 and Tables 1 and 2 present the comparison of moment resistance and stiffness across the experimental results, the Steel Joints add-on in RFEM, and EC3, while Table 3 summarizes the observed failure modes.

A bar chart compares the moment capacity in kNm for three steel joint configurations (JD1, JD2, JD3) based on experimental data, RFEM Steel Joints analysis, and EC3 design standards.

4 Comparison of Moment Resistance – Experimental vs. Steel Joints in RFEM and EC3

Bar chart comparing initial stiffness values from experiments, RFEM steel joint analysis, and EC3 calculations across three different joint configurations.

5 Comparison of Stiffness – Experimental vs. Steel Joints in RFEM and EC3

Table 1: Comparison of Moment Resistance – Experimental vs. Steel Joints in RFEM & EC-3 | Moment Capacity (kNm)
Specimens	Experiment	Steel Joints in RFEM	EC3	EC3/RFEM
JD1	188.00	199.60	184.00	0.92
JD2	313.89	310.26	292.03	0.94
JD3	267.82	263.25	280.40	1.07

Table 2: Comparison of Stiffness – Experimental vs. Steel Joints in RFEM & EC3 | Initial Stiffness Sj,ini (MNm/rad)
Specimens	Experiment	Steel Joints in RFEM	EC3	EC3/RFEM
JD1	19.90	10.00	34.30	1.72
JD2	26.27	29.00	68.82	2.37
JD3	17.36	20.60	47.46	2.30

Table 3: Failure Modes
Specimens	EC-3	Steel Joints in RFEM	Experiment
JD1	End plate and bolt	End plate and bolts row 1 & 2	End plate and bolts row 1 & 2
JD2	End plate and bolt	End plate and bolts row 1 & 2	End plate and bolts row 1 & 2
JD3	End plate and bolt	End plate and bolts row 1 & 2	End plate and bolts row 1 & 2

Analysis results showing equivalent von Mises stresses and equivalent plastic strains for a steel joint model, visualized using color-coded surface plots.

6 Equivalent Stresses and Plastic Strain of JD1 Model

Finite element analysis results showing equivalent von Mises stresses and plastic strains for a steel joint model. The visualization displays stress distribution and localized plastic deformation in the connection area under applied loading.

7 Equivalent Stresses and Plastic Strain of JD2 Model

Finite element analysis results showing equivalent von Mises stresses and plastic strains for a steel joint model, visualizing stress distribution and material behavior under load.

8 Equivalent Stresses and Plastic Strain of JD3 Model

Table showing design check ratios for plate, bolt, and weld components alongside calculated rotational stiffness values for a structural joint connection.

9 Design Ratio and Rotational Stiffness of JD1 Model

Table showing ultimate limit state design checks for plate, bolt, and weld components, including calculated rotational stiffness values for connected members.

10 Design Ratio and Rotational Stiffness of JD2 Model

Table showing 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 JD3 Model

Conclusions

Three bolted end plate joints (JD1–JD3) were studied by comparing experiments with the RFEM Steel Joints model and the EC3 hand calculation. For moment resistance, all three methods agreed well. RFEM matched the test results closely (within about 6%), and EC3 gave safe, slightly conservative values. EC3 can, therefore, be trusted for strength design.

The main difference was in initial stiffness. RFEM gave reasonable values, but EC3 greatly overestimated the stiffness of every joint — roughly 1.7 to 2.7 times the measured values. EC3 stiffness should, therefore, be used with care, especially in serviceability and deflection checks.

For failure modes, RFEM correctly predicted what was seen in the tests (end plate yielding with both bolt rows failing), while EC3 predicted a simpler single-bolt mode. In short, RFEM is a reliable tool for predicting joint resistance, stiffness, and failure, and can reduce the need for testing. EC3 is safe for strength but tends to overestimate stiffness.

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.
Qiang, X., Wu, N., Luo, Y., Jiang, X., & Bijlaard, F. (2018). Experimental and Theoretical Study on High Strength Steel Extended Endplate Connections After Fire. International Journal of Steel Structures, 18(2), 609–634. https://doi.org/10.1007/s13296-018-0020-3
Girão Coelho, A. M., & Bijlaard, F. S. K. (2007). Experimental behaviour of high strength steel end-plate connections. Journal of Constructional Steel Research, 63(9), 1228–1240. https://doi.org/10.1016/j.jcsr.2006.11.010

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