114x

002074

2026-08-24

Parametric Analysis of End Plate Connections with Steel Joints for RFEM

This study evaluates the influence of bolt diameter and end plate thickness on the capacity and failure modes of nine extended end-plate beam-to-column connections. Moment resistances and failure modes obtained with the Steel Joints add-on for RFEM are compared against a detailed finite element model (ROFEM) and the Eurocode 3 (EN 1993-1-8) component method. The Steel Joints add-on for RFEM reproduces the governing failure mode in every model, while the EC-3 hand calculation method underestimates the capacity for thin end plates and instead identifies the bolt as the weak component.

This study validates the Steel Joints add-on for RFEM by investigating the influence of bolt diameter and end-plate thickness on the capacity and failure modes of end-plated beam-to-column connections. The structural behavior and load-bearing performance of these joints are evaluated according to the design provisions of Eurocode 3 (EC-3), and the results are then compared with predictions from a finite element model developed using RFEM and the research-oriented finite element method (ROFEM).

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 and Failure Modes per EN 1993-1-8

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 (ΣF_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:

\begin{matrix} \begin{matrix} M_{p l, 1, R d} = \begin{array}{c} 0.25 \sum l_{e f f, 1} t_{f}^{2} f_{y} \\ γ_{M 0} \end{array}, \\ M_{p l, 2, R d} = \begin{array}{c} 0.25 \sum l_{e f f, 2} t_{f}^{2} f_{y} \\ γ_{M 0} \end{array} . \end{matrix} \end{matrix}

Plastic Resistance Moments of Equivalent T-Stub for Modes 1 and 2

1 Fig. 1 - Failure modes of T-Stub

Geometric details of beam to column connection

The rigid flange was modeled as an elastic element. Material models S275 and S420 were assigned to the end plate and beam, respectively. For the parametric study, the beam was chosen to represent a typical European profile section with dimensions approximately corresponding to an IPE300 section, while the column was modeled as an HEA300 section, in accordance with the Eurocode provisions being evaluated. The dimensions of the beam and end plate are shown in Fig. 2. The variables considered in the study were bolt diameters of 16 mm (M16), 20 mm (M20), and 24 mm (M24), together with end plate thicknesses (t_p) of 10 mm, 15 mm, and 20 mm.

2 Fig. 2 - Endplate/Bolt configuration

Discussion

Steel Joints Add-on for RFEM Solution

This study presents a numerical investigation into the effects of bolt diameter and end plate thickness on the capacity and failure modes of extended steel end plate beam-to-column connections. The structural performance of nine such connections was examined.

The results of the parametric study are summarized in Table 1, and the corresponding moment resistances are shown in Fig. 3. Increasing the end plate thickness produced higher plastic and ultimate moment capacities. However, once the bending moment capacity of the beam fell below that of the connection, further increases in end plate thickness had no effect on the overall capacity. The same trend was observed for bolt diameter. Table 2 shows the failure modes.

3 Fig. 3 - Comparison of moment resistance – Steel Joints for RFEM and EC-3

Table 1: Comparison of moment resistance - Steel Joints add-on for RFEM & EC-3 | Moment Capacity (kNm)
Specimens	ROFEM	Steel Joints add-on in RFEM	EC-3	EC-3/RFEM
M16-tp=10mm	87.00	85.35	65.00	0.76
M16-tp=15mm	147.00	123.12	105.00	0.85
M16-tp=20mm	153.00	132.23	143.00	1.08
M20-tp=10mm	114.00	95.85	73.00	0.76
M20-tp=15mm	186.00	167.40	129.00	0.77
M20-tp=20mm	223.00	183.33	186.00	1.01
M24-tp=10mm	128.00	102.60	73.00	0.71
M24-tp=15mm	195.00	132.30	155.00	1.17
M24-tp=20mm	283.00	175.50	211.00	1.20

Table 2: Failure modes
Specimens	ROFEM	Steel Joints add-on in RFEM	EC-3
M16-tp=10mm	Mode 1	Mode 1	Mode 1
M16-tp=15mm	Mode 1	Mode 1	Mode 1&2
M16-tp=20mm	Mode 2	Mode 2	Mode 2&3
M20-tp=10mm	Mode 1	Mode 1	Mode 1
M20-tp=15mm	Mode 1	Mode 1	Mode 1&2
M20-tp=20mm	Mode 2	Mode 2	Mode 1&2
M24-tp=10mm	Mode 1	Mode 1	Mode 1
M24-tp=15mm	Mode 1	Mode 1	Mode 1
M24-tp=20mm	Mode 1	Mode 1	Mode 1&2

4 Fig. 4 - Equivalent Stresses and Plastic strain of M16-tp-10mm model and design check

5 Fig. 5 - Equivalent Stresses and Plastic strain of M16-tp-15mm model and design check.

6 Fig. 6 - Equivalent Stresses and Plastic strain of M16-tp-20mm model and design check.

7 Fig. 7 - Equivalent Stresses and Plastic strain of M20-tp-10mm model and design check.

8 Fig. 8 - Equivalent Stresses and Plastic strain of M20-tp-15mm model and design check.

9 Fig. 9 - Equivalent Stresses and Plastic strain of M20-tp-20mm model and design check.

10 Fig. 10 - Equivalent Stresses and Plastic strain of M24-tp-10mm model and design check.

11 Fig. 11 - Equivalent Stresses and Plastic strain of M24-tp-15mm model and design check.

12 Fig. 12 - Equivalent Stresses and Plastic strain of M24-tp-20mm model and design check.

Conclusions

Three methods—a detailed FE model (ROFEM), the component-based Steel Joints add-on in RFEM, and the EC-3 (EN 1993-1-8) component method—were compared across nine bolted end plate connections (M16/M20/M24 bolts × 10/15/20 mm plates).

The EC-3/RFEM ratio is governed by plate thickness, rising monotonically within each bolt group: EC-3 substantially underestimates the resistance for 10 mm plates (0.71-0.76) but overtakes the RFEM for 20 mm plates (1.01-1.20). The reason is mechanical—thin plates fail by ductile plate yielding (Mode 1), whereas the FE methods capture the membrane action and strain hardening that the EC-3 T-stub model omits.

As the plate thickens and the bolt becomes the weak component, that margin disappears. On failure modes, ROFEM and RFEM agree in every specimen; EC-3 agrees on the governing component but tends to flag combined modes (1&2, 2&3). The pattern follows the classic T-stub theory: thicker plates shift failure toward bolt control, while larger bolts keep the joint in ductile Mode 1.

The initial stiffness of an end plate connection rises with increasing bolt diameter or end plate thickness. The Eurocode predicts the failure modes of such connections with a high degree of accuracy.

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.
Ozkilic YO. Investigation of the effects of bolt diameter and end-plate thickness on the capacity and failure modes of end-plated beam-to-column connections. Res. Eng. Struct. Mater., 2021; 7(3) 445-463.

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