End Plate Connection Design Calculator

What it checks

An end plate connection welds a plate to the beam end and bolts it to the supporting column or beam. This calculator verifies the whole set to EN 1993-1-8: the weld group and beam web, the bolt group in shear and bearing, the end plate in gross shear, net shear and block tearing, and the tension zone through the equivalent T-stub model.

A partial-depth end plate is a shear connection; a full-depth or extended plate carries moment as well, and the tension zone then governs the design. The tool reports every mode so you can see which one is actually controlling rather than assuming.

The equivalent T-stub usually governs

The tension zone is modelled as an equivalent T-stub, and EN 1993-1-8 requires three failure modes: mode 1 is complete flange yielding, mode 2 is bolt failure with flange yielding, and mode 3 is bolt failure alone. The lowest governs, and which one it is tells you what to change.

Running the tool against the published example gives these values, and the pattern is characteristic:

T-stub mode 1 (flange yielding)

252.0 kN

T-stub mode 2 (bolt + flange yielding)

202.5 kN - GOVERNS

Bolt shear, single bolt

90.6 kN

Bolt bearing

178.2 kN

Bolt group, 0.8 n Fv

869.3 kN

End plate gross shear

1961.2 kN

End plate block tearing

2132.9 kN

End plate net shear

2152.8 kN

Beam web shear

1462.5 kN

Mode 2 governs at 202.5 kN. That is the mixed mode - the plate yields and the bolts fail together - and it is the most common outcome for a normally proportioned end plate. Mode 1 means the plate is too thin relative to the bolts; mode 3 means the plate is too thick and the bolts are the sole weak point, giving a brittle failure with no warning.

Designing for mode 1 or mode 2 rather than mode 3 is a ductility requirement, not just an economy one: a connection that fails by plate yielding deforms visibly first, which is why EN 1993-1-8 makes the distinction at all.

Formula reference

T-stub mode 1

$F_{T,1,Rd} = \dfrac{4 M_{pl,1,Rd}}{m}$

T-stub mode 2

$F_{T,2,Rd} = \dfrac{2 M_{pl,2,Rd} + n \sum F_{t,Rd}}{m+n}$

T-stub mode 3

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

Plastic moment of the flange

$M_{pl,Rd} = \dfrac{0.25 \sum \ell_{eff}\, t_f^{2} f_y}{\gamma_{M0}}$

Bolt tension

$F_{t,Rd} = \dfrac{0.9 f_{ub} A_s}{\gamma_{M2}}$

Bolt shear

$F_{v,Rd} = \dfrac{\alpha_v f_{ub} A_s}{\gamma_{M2}}$

Block tearing

$V_{eff,Rd} = \dfrac{f_u A_{nt}}{2\gamma_{M2}} + \dfrac{f_y A_{nv}}{\sqrt3\,\gamma_{M0}}$

Assumptions and limits

The tool checks the connection, not the members. Column web panel shear, web crushing, web buckling and the need for stiffeners are separate checks - a strong end plate on an unstiffened column web will fail in the column, not the connection, and that mode is outside this tool.

Prying force is accounted for inside the T-stub model rather than reported separately. The model assumes the bolts sit inside the plate edge with enough edge distance for prying to develop as the code assumes; a very wide or very narrow bolt spacing falls outside the tabulated effective lengths.

Static persistent design situation, non-preloaded bolts in normal clearance holes. Rotational stiffness and joint classification, fatigue, fire and seismic detailing are not covered.

FAQ