End Plate Connection Design Theory (EN 1993-1-8)

The theory behind this end plate calculator: how a plate welded to the beam end and bolted to its support is verified to Eurocode 3 (EN 1993-1-8) with the SCI P358/P398 rules, for both a simple (shear) end plate and a moment end plate. We cover the weld group, the supported beam web shear, the bolt group (shear with the long-joint reduction and bearing), the end plate gross/net/block shear, and the equivalent tension-zone T-stub (Mode 1 plate yielding, Mode 2 bolt-plus-yield, Mode 3 bolt failure) with the combined bolt shear-tension interaction.

An end plate connection joins a steel beam to its support through a plate welded to the end of the beam and bolted to the supporting member - a primary beam web or a column. It is one of the most versatile steel connections: a partial-depth or flush end plate acts as a simple (shear) connection, while a deeper flush or extended end plate carries a moment as well. This page explains the mechanics and every formula behind the checks this calculator performs to Eurocode 3 (EN 1993-1-8) with the supplementary rules of SCI Publications P358 and P398.

An end plate is welded to the beam end and bolted to the support; the bolts pass through the plate into the support, mostly in shear (simple) or in tension (moment).

The verification framework

Every potential failure mode is verified - in the weld, the supported beam web, the bolt group, the end plate and (for a moment connection) the tension zone. For each, the design action must not exceed the design resistance, i.e. the utilisation must not exceed 1.0.

Weld group and beam web

The fillet welds between the beam web and the end plate carry the beam reaction in shear. The applied stress per unit length is $\tau_{Ed} = V_{Ed}/(2 l_w)$ over the two weld runs, and it must not exceed the fillet weld longitudinal resistance $F_{w,L,Rd}$. The supported beam web is then checked for shear over the rolled-section shear area:

Bolt group

The shear resistance of a single bolt is $F_{v,Rd} = \alpha_v f_{ub} A_s / \gamma_{M2}$ ($\alpha_v = 0.6$ for classes 4.6 / 8.8, $0.5$ for 10.9), reduced by the long-joint factor $\beta_{Lj}$ when the joint exceeds $15 d$. Because tension is present in the bolts of a moment end plate, the group shear resistance carries the SCI P358 reduction factor of 0.8:

Bolt bearing on the end plate, $F_{b,Rd} = k_1\alpha_b f_{u,p} d t_p / \gamma_{M2}$, is checked in parallel and may govern for a thin plate.

End plate resistance

The end plate is checked for three shear modes, each over its two vertical shear planes:

• Gross-section shear - $V_{Rd,g} = (2 h_p t_p/1.27)\,f_{y,p}/(\sqrt3\gamma_{M0})$.
• Net-section shear through the bolt holes - $V_{Rd,n} = A_{v,net} f_{u,p}/(\sqrt3\gamma_{M2})$.
• Block shear (tearing) - a concentric block tears out along the bolt lines, $V_{Rd,b} = 2(f_u A_{nt}/\gamma_{M2} + f_y A_{nv}/(\sqrt3\gamma_{M0}))$ (EN 1993-1-8 §3.10.2).

Tension zone - the equivalent T-stub

For a moment connection, the applied moment is resolved into a tension force on the top bolt rows, $F_{t,Ed} = M / r$, where $r$ is the lever arm between the beam flanges. The end plate around the tension bolts behaves as an equivalent T-stub (EN 1993-1-8 §6.2.4) and can fail in three modes:

The tension bolt row plus the end plate around it form an equivalent T-stub. Mode 1 = complete plate yielding with prying; Mode 2 = bolt failure with plate yielding; Mode 3 = bolt tension failure.

• Mode 1 (plate yielding) - $F_{T,1,Rd} = (8n - 2e_w)M_{pl,1,Rd}/(2mn - e_w(m+n))$.
• Mode 2 (bolt + plate yielding) - $F_{T,2,Rd} = (2M_{pl,2,Rd} + n\sum F_{t,Rd})/(m+n)$.
• Mode 3 (bolt failure) - $F_{T,3,Rd} = \sum F_{t,Rd}$, with $F_{t,Rd} = 0.9 f_{ub} A_s/\gamma_{M2}$.

The end plate tension resistance is the minimum, $F_{t,ep,Rd} = \min(F_{T,1,Rd}; F_{T,2,Rd}; F_{T,3,Rd}) \ge F_{t,Ed}$. The plastic moment uses the effective length $l_{eff}$ of the T-stub:$M_{pl,Rd} = 0.25\,l_{eff}\,t_p^{2} f_{y,p}/\gamma_{M0}$, with $m = (p_3 - t_{wc} - 1.6 r_c)/2$ the bolt-to-web distance.

Combined shear and tension

The tension bolts also carry their share of the shear, so each is checked for the combined action (EN 1993-1-8 Table 3.4):

Detailing rules (SCI P358)

• for a simple (shear) end plate keep the plate thin ($t_p \le 12$ mm typically) so it can rotate as a pin;
• use M20 grade 8.8 bolts in 22 mm holes as the standard detail;
• edge and end distances $\ge 1.2 d_0$; pitch and gauge within the EN 1993-1-8 limits;
• for a moment end plate, an extended plate with bolts outside the flange increases the lever arm and the moment capacity.

Frequently asked questions

Ready to check your connection? Run the full EN 1993-1-8 / SCI P358 verification for an end plate connection in 3D, with step-by-step derivations for every check.