Beam-to-column end-plate connection — CalculiX analysis

Beam-to-column connection with end plate and bolts

Analiză cu element finit solid (CalculiX) — plăci, profile, suduri și șuruburi. Model parametric: placă de capăt de 20 mm, rigidizări teșite, 8 șuruburi, stâlp încastrat sus și jos.

The model

A beam–column connection made with a 20 mm end plate welded to the beam and bolted with 8 bolts to the column flange, with tapered stiffeners on the beam (haunches with a straight edge) and continuity stiffeners in the column, in line with the beam flanges. The whole geometry is modelled with solid finite elements (C3D8I hexahedra): the welds as *TIE constraints, the bolts as axial springs, frictional contact between the plate and the column, and the elasto-plastic behaviour of the steel. The column is fixed at the top and bottom, so the moment from the connection loads its web panel.

🟦 Plates (20 mm end plate, beam + column stiffeners) 🟫 Profiles (beam + column) 🟨 Welds (*TIE) 🔩 8 bolts (axial spring + contact) ↔ Frictional contact ⚙ Plasticity (von Mises)

Deflected shape + von Mises stress at the service load (rotate with the mouse)

The field is shown at a service load (≈73% of the resistance): the connection holds and remains almost elastic (only ~1% of the material has yielded, at the corner concentrations). The curve below shows the full response, up to the resistance. The colour scale is capped at f_y = 275 MPa (red = yielding).

Summary of results

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Resistance F [kN] (at 5% plastic strain)

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σ von Mises max [MPa]

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max displacement [mm]

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max plastic strain [%]

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nodes (surface)

Force–displacement curve (CalculiX, solid FEA)

Force (the reaction at the beam tip) as a function of the imposed displacement. The pink diamond is the resistance F, read at the limit of 5% plastic strain (the CBFEM / EN 1993-1-5 Annex C convention) — the design resistance. The dotted portion beyond that limit is the uncredited pushover: the analysis continues, but no resistance is credited to it, so as to stay conservative relative to a real test (no bolt or weld rupture in the model).

How it works

Unlike the component method (CBFEM), here we model the connection directly, with solid FEA: every plate, profile and bolt is discretised into hexahedra. The welds are rigid ties between faces, the bolts are solid bodies with a pretension section (the real clamping force), and the contact with friction lets the plates separate and slide. The steel yields according to the von Mises criterion. The result needs no calibration — it is direct physics.

Tool information

What this calculator checks

The calculator analyses a complete beam-to-column connection by solid finite elements (CalculiX) — plates, profiles, welds and bolts modelled as 3D volumes. Unlike the component methods (T-stub) or the plate idealisation (end plate), here the whole node is meshed as a solid and loaded to failure.

The parametric model

The standard node is generated parametrically: a 20 mm end plate, chamfered stiffeners, 8 bolts, a column fixed at both ends. The nonlinear analysis increases the load and tracks the material yielding, giving the node capacity at a plastic-strain criterion — not just an elastic utilisation, but the behaviour up to failure.

The advantage of the solid analysis: it captures effects that analytical methods approximate or ignore — stress concentrations at the fillets, the interaction between plates and stiffeners, the progressive yielding of the column.

What the analysis returns

The stress distribution over the whole node, visualised in 3D
The capacity of the connection at the chosen plastic-strain criterion
The critical zones — where yielding starts and how it propagates

The parametric model deliberately differs from any specific experimental specimen, so it does not overlay a single test curve; it represents the family of nodes with the given geometry.

Input data

Node geometry — the plate and stiffener dimensions, the bolt positions.
The profiles of the column and beam.
The bolts — the class, diameter.
The loading — the moment and forces transmitted by the beam.
The material — with its nonlinear constitutive law.

Assumptions and limitations

A nonlinear solid finite-element analysis; the result depends on the mesh density and the material model.
It requires the computation agent connected (CalculiX runs externally); without it, the analysis cannot run.
The geometry is that of the parametric model; large deviations from it require remodelling.
The code check of the components (EN 1993-1-8) remains complementary — the solid analysis supports it, it does not formally replace it.

T-stub — the analytical component check (EN 1993-1-8)
End plate — the FEM idealisation of the end plate
Import from Tekla — bringing the real node geometry from Tekla
Bending and compression — checking the members entering the node