Draft:Component-Based Finite Element Method

The Component-Based Finite Element Method (CBFEM) is a numerical approach to structural steel connection design that synthesises the component method of Eurocode 3 (EN 1993-1-8) with the finite element method. In CBFEM, steel plates are modelled with shell elements using materially nonlinear analysis, while individual connection components, such as bolts, anchor bolts, and welds, are represented by nonlinear springs whose stiffness and resistance are derived from design code provisions and laboratory test data. The method was developed within the R&D project of Czech Technical University in Prague, Brno University of Technology, and IDEA StatiCa supported by Technology Agency of the Czech Republic and has since been validated by independent research groups at institutions including ETH Zürich, the Ohio State University, the University of Tennessee, and the University of Illinois Chicago.

CBFEM removes many of the geometric restrictions inherent in the tabulated component method of EN 1993-1-8. Non-standard connection topologies that fall outside those procedures can therefore be analysed using CBFEM. The method has been implemented in several commercial structural engineering software packages, including IDEA StatiCa, Dlubal RFEM, and Hilti PROFIS Engineering.

Background

The component method

CBFEM is based on the component method of Eurocode 3, Part 1-8 (EN 1993-1-8). The component method represents a structural connection as an assembly of basic components, such as T-stubs in tension, column webs in compression, bolt rows in shear, and similar elements. Each of these is characterised by an individual stiffness and resistance. The component method was developed at Delft University of Technology by Zoetemeijer in the 1970s and 1980s, and extended to a general framework by Jaspart at the University of Liège in the 1990s.

The component method applies only to connection geometries explicitly addressed in EN 1993-1-8. Connections with non-standard topology or unusual loading fall outside the scope of its tabulated procedures.

Development of CBFEM

The method embeds the component method's spring models within a finite element framework, allowing analysis of connection geometries not covered by EN 1993-1-8. The method was first described in conference proceedings by Sabatka, Wald, Kabelac, Godrich, and Navratil at the 12th International Conference on Steel, Space and Composite Structures in 2014. A fuller treatment was published in the Journal of Civil Engineering and Architecture in 2015. Wald et al. set out the theoretical framework and validation in a monograph published by the Czech Technical University in Prague (2021).

Wald et al. (2020) reported validation cases for welded connections, bolted end-plate connections, and column bases in Wiley's Civil Engineering Design. In 2024, Denavit, Nassiri, Mahamid, Vild, Wald, and Sezen published Steel Connection Design by Inelastic Analysis through Wiley. The work verified CBFEM results against AISC 360 provisions for a range of connection types.

Theory

Modelling approach

Steel plates, including base plates, end plates, and stiffeners, are modelled as four-node shell elements with materially nonlinear constitutive models calibrated to the relevant design code. Bolts and welds are represented as nonlinear springs or constraint elements, with stiffness and resistance derived from component method formulations in EN 1993-1-8 or equivalent AISC provisions. Anchor bolts are modelled similarly, using spring properties based on anchor capacity models from EN 1992-4 or ACI 318 Chapter 17. Bearing of base plates on concrete is represented by compression-only Winkler springs.

Analysis procedure

The assembled model is solved using materially nonlinear analysis (MNA). The load is applied incrementally, and at each step the nonlinear spring properties and material plasticity are updated. The solution yields stress distributions in the plates and weld segments, forces in individual bolts and anchors, contact pressures at steel-to-concrete and steel-to-steel interfaces, and the deformed configuration of the connection.

Code checks yield utilisation ratios for each failure mode, including bolt tension, weld fracture, and plate yielding, rather than a single pass/fail result.

Applications

CBFEM is used in structural engineering practice for the design and code-checking of steel connections where standard procedures are insufficient or inapplicable. CBFEM has been applied to beam-to-column moment connections, column base plates, gusset plate connections, and hollow section joints, among other configurations. It is used where the connection geometry or loading falls outside the scope of the prescriptive tabulated procedures in EN 1993-1-8 or AISC 360.

Validation

CBFEM has been validated through several independent research programmes comparing its predictions with laboratory test results and advanced research-oriented finite element models.

Wald et al. published benchmark cases covering welded connections, bolted end-plate connections, and column bases, with CBFEM results compared against analytical design models and experimental data. Results were benchmarked against both code-based analytical calculations and validated research FEM models developed in software such as ABAQUS.

In 2024, a team from the Ohio State University (Nassiri, Sezen), the University of Tennessee (Denavit), and the University of Illinois Chicago (Mahamid), together with Vild and Wald, published approximately 250 verification examples comparing CBFEM results with AISC 360 analytical calculations and ABAQUS research models for connection types including T-stub connections, end-plate moment connections, bolted wide-flange splices, and chevron brace connections.

The method has also been extended to elevated temperature conditions. Der et al. (2024) applied CBFEM to predict the resistance of steel beams, columns, spliced and T-stub bolted connections at elevated temperatures. Results were consistent with analytical fire design models.

Comparison with other methods

Method	Scope	Basis	Standard reference
Component method (EN 1993-1-8)	Predefined connection types with tabulated mechanical models	Analytical springs assembled per codified rules	Eurocode 3, Part 1-8
AISC direct analysis (AISC 360)	Standard connections per design guide procedures	Prescriptive equations from experimental databases	AISC 360-22, AISC Design Guides
Research-oriented FEM (ABAQUS, ANSYS)	Any geometry, any loading	Continuum finite elements with detailed material models	No specific design standard; requires expert judgement
CBFEM	Any geometry, design-oriented	Shell elements for plates, code-based springs for components	EN 1993-1-8 or AISC 360 component properties
Generalised Component Method (GCM)	Frame-level analysis with connection behaviour	Multi-spring joint models integrated into frame FE models	Research framework (Yan and Rasmussen, 2021)

CBFEM sits between the traditional component method and research-oriented FEM in terms of both fidelity and scope. It retains the design code basis that makes results directly comparable to hand calculations, while using finite elements to remove geometric restrictions. Research-oriented FEM models bolt threads, contact mechanics, and residual stresses explicitly; CBFEM instead relies on the component abstractions of EN 1993-1-8, accepting lower fidelity in exchange for faster analysis suitable for design practice.

Limitations

The accuracy of CBFEM results is bounded by the accuracy of the underlying component models — bolt springs, weld models, and bearing models derived from EN 1993-1-8. Where those models carry known simplifications, such as the approximate treatment of prying action or group effects in multi-row bolt arrangements, the same simplifications propagate into CBFEM results. Plate buckling is not captured directly by the materially nonlinear shell analysis; buckling checks are therefore performed separately using code-based procedures.

Validation to date has focused primarily on static, monotonic loading, and the method's performance under cyclic or dynamic loading has not been systematically verified. Results are also sensitive to mesh density, and convergence checks are required to confirm that conclusions are mesh-independent.

Software implementations

Several commercial software packages implement CBFEM for structural connection design:

• IDEA StatiCa Connection implements CBFEM for steel connections, base plates, and anchoring, with code checks per EN 1993-1-8, AISC 360, CSA S16, AS 4100, and other national standards.
• Dlubal RFEM 6 includes a Steel Joints add-on that uses CBFEM and integrates connection design with global structural analysis of the complete building model.
• Hilti PROFIS Engineering applies CBFEM to base plate and anchor design, combining steel plate analysis with anchor component models based on Hilti's product test data.

See also

• Finite element method
• Structural engineering
• Eurocode 3
• Structural steel
• Bolted joint
• Nonlinear finite element analysis

Further reading

• Wald, F.; Sabatka, L.; Bajer, M.; Jehlicka, P.; Kabelac, J.; Kozich, M.; Kurikova, M.; Vild, M. (2021). Component-based Finite Element Design of Steel Connections. Czech Technical University in Prague. ISBN 978-80-01-06861-8.
• Denavit, M. D.; Nassiri, A.; Mahamid, M.; Vild, M.; Wald, F.; Sezen, H. (2024). Steel Connection Design by Inelastic Analysis. Wiley. ISBN 978-1-394-22215-5.
• "CBFEM – Component-Based Finite Element Method". cbfem.com. Retrieved 2026-03-26.

External links

• cbfem.com – dedicated resource site for the CBFEM method