What is the T-stub model for end plate connections?

The T-stub model treats each bolt row in the tension zone as an equivalent T-shaped flange welded to a rigid web. The flange represents the end plate, the web represents the beam flange, and the bolts represent the tension anchors. Three failure modes are checked: Mode 1 (complete flange yielding), Mode 2 (bolt failure with partial flange yielding), and Mode 3 (pure bolt failure). Mode 2 governs for well-designed end plate connections — the end plate yields moderately before the bolts reach their tension capacity.

How many bolt rows are typically used in UK end plate connections?

UK end plate connections typically use 2-4 bolt rows in the tension zone. For beam spans of 6-12 m, 8 bolts total (2 rows of 4) is the standard for 533UB and 610UB sections. For deeper sections or higher moments, 12 bolts (3 rows of 4) or 16 bolts (4 rows of 4) may be used. The number of effective rows is limited by the lever arm and the compression zone depth — rows near the neutral axis contribute little to moment resistance.

What is the standard UK end plate thickness for a moment connection?

The standard end plate thickness for a moment-resisting connection in UK practice is 15-25 mm depending on bolt size and moment demand. For M20 bolts: 15 mm (light moment), 20 mm (standard moment), 25 mm (heavy moment). For M24 bolts: 20-30 mm. The plate must be thick enough to avoid Mode 1 (complete flange yielding) failure — which requires FT,1,Rd ≥ FT,2,Rd. The UK Steel Construction Institute (SCI) design guides recommend end plate thicknesses between 0.7d and 1.2d (d = bolt diameter).

When are full-strength butt welds required for end plate connections?

Full-strength butt welds (complete joint penetration, CJP) are required when the weld must develop the full yield strength of the connected member — typically for moment-resisting frames in high-ductility demand situations. For end plate connections in simple frames (nominally pinned), fillet welds are adequate. The UK NA to BS EN 1993-1-8 requires CJP welds for beam flanges in moment connections designed for ductility (seismic or plastic hinge rotation). For standard braced frames, single-V butt welds with backing bars are standard for the tension flange fillet welds.

UK End Plate Connection Design -- EN 1993-1-8 Clause 6.2 with UK National Annex

The bolted end plate connection is the standard moment-resisting joint in UK multi-storey steel frames. It consists of a steel plate shop-welded to the beam end and site-bolted to the column flange. The connection transfers bending moment from the beam into the column through tension in the upper bolt rows and compression at the beam bottom flange. EN 1993-1-8 Clause 6.2 provides the component method for end plate design, anchored by the T-stub model for the tension zone. This reference covers the complete design procedure, including the T-stub failure modes, bolt row distribution, column web panel shear, and a full worked example for a 533UB beam to 254UC column moment connection in UK practice.

The Component Method Applied to End Plate Connections

The component method decomposes the end plate connection into three zones:

Tension Zone (Clause 6.2.6): Each bolt row above the neutral axis is modelled as an equivalent T-stub flange in tension. The effective T-stub comprises the end plate as the flange and the beam flange/web as the stiffener. For each bolt row, the design tension resistance is the minimum of three failure modes (Mode 1, 2, or 3).

Compression Zone (Clause 6.2.6.7): The beam bottom flange and a portion of the beam web act in compression, bearing against the column flange. The compression resistance is the minimum of the beam flange/web crushing resistance and the column web crushing resistance.

Shear Zone (Clause 6.2.6.1): The column web panel between the beam flanges (bounded by the column flanges and stiffeners) resists the shear force induced by the tension-compression couple. The shear resistance of the column web panel may be increased by supplementary web plates (doubler plates) if required.

The connection moment resistance M_j,Rd is:

M_j,Rd = Sigma (F_T,Rd,i x h_i)

Where F_T,Rd,i is the tension resistance of bolt row i and h_i is its lever arm from the centre of compression.

The T-Stub Model -- Failure Modes

Each bolt row in the tension zone is modelled as a T-stub: a flange plate of effective length l_eff, thickness t (the end plate thickness), connected by two circular bolts. The stem of the T represents the beam flange, providing stiff restraint at the bolt line. The T-stub flange (end plate) can fail in three modes:

Mode 1 -- Complete Flange Yielding

Two plastic hinges form in the flange at the weld toe (or at the bolt centreline if the bolts are close to the free edge). Four plastic hinges develop per bolt pair, allowing large deformations before failure.

F_T,1,Rd = (4 x M_pl,1,Rd) / m

Where M_pl,1,Rd = 0.25 x Sigma l_eff,1 x t_f^2 x fy / gamma_M0.

This mode is ductile and desirable, but it requires a relatively thin end plate. In UK practice, end plates are usually thick enough that Mode 1 does not govern.

Mode 2 -- Bolt Failure with Partial Flange Yielding

Two plastic hinges form in the flange, and the bolts fail in tension. The prying force (additional bolt tension induced by flange bending at the bolt line, beyond the applied tension) is explicitly captured in this mode.

F_T,2,Rd = (2 x M_pl,2,Rd + n x Sigma F_t,Rd) / (m + n)

Where:

M_pl,2,Rd = 0.25 x Sigma l_eff,2 x t_f^2 x fy / gamma_M0
Sigma F_t,Rd = total tension resistance of the bolts in the row (two bolts typically)
n = e_min (distance from bolt centre to free edge) but n <= 1.25m

This is the most common governing mode for properly proportioned UK end plate connections.

Mode 3 -- Bolt Failure Only

The end plate is so thick that it acts as a rigid body. The bolts fail in pure tension without any flange yielding.

F_T,3,Rd = Sigma F_t,Rd = n_b x (0.9 x f_ub x As / gamma_M2)

This is a brittle failure mode and is avoided in UK design. It can be identified when the end plate thickness is significantly greater than the bolt diameter.

Effective Lengths for T-Stubs

The effective length l_eff of the T-stub flange depends on the bolt row position:

Bolt Row Adjacent to a Stiffener (e.g., beam flange):

Circular pattern: l_eff,cp = 2 x pi x m
Non-circular pattern: l_eff,nc = 4m + 1.25e

Bolt Row at the End of the Plate (end bolt row):

Circular pattern: l_eff,cp = min(2 x pi x m, pi x m + 2e_1)
Non-circular pattern: l_eff,nc = min(4m + 1.25e, 2m + 0.625e + e_1)

Inner Bolt Row (between two other rows):

Circular pattern: l_eff,cp = 2 x pi x m
Non-circular pattern: l_eff,nc = 4m + 1.25e

The minimum of the circular and non-circular patterns governs, per EN 1993-1-8 Table 6.6. For Mode 1, either pattern may be used. For Mode 2, the non-circular pattern governs.

Prying Forces

Prying occurs when the end plate deforms under bolt tension, levering against the column flange at the toe of the weld and developing additional tension in the bolts beyond the applied load. The T-stub model captures prying implicitly through the Mode 2 formula. If Mode 1 or Mode 3 governs, prying is either fully developed (Mode 1) or absent (Mode 3).

The prying force Q per bolt can be calculated as: Q = F_T,2,Rd / n_b - F_t,Ed / n_b (approximately)

For a well-designed connection, the bolts should not be excessively stressed by prying. Adequate end plate thickness and appropriate bolt edge distance n minimise prying effects.

Column Web Panel Shear

The column web panel between the beam tension and compression flanges resists a shear force equal to the sum of the tension forces in the bolt rows (or the compression force). The design shear resistance is:

V_wp,Rd = 0.9 x f_y,wc x A_vc / (sqrt(3) x gamma_M0)

Where A_vc is the shear area of the column (for a rolled I-section: A_vc = A - 2 x b x t_f + (t_w + 2r) x t_f). If V_wp,Rd is insufficient, a supplementary web plate (doubler plate) is welded to the column web to increase A_vc. The additional shear area is the doubler plate area, but limited by the column flange width.

Worked Example -- 533UB to 254UC Moment Connection

Given:

Beam: 533 x 210 x 92 UB, S355
- h_b = 533.1 mm, b_fb = 209.3 mm, t_fb = 15.6 mm, t_wb = 10.1 mm
Column: 254 x 254 x 89 UC, S355
- h_c = 260.4 mm, b_fc = 256.3 mm, t_fc = 17.3 mm, t_wc = 10.5 mm
End plate: 200 x 460 mm, t_p = 20 mm, S355
Bolts: 8 x M20 Class 8.8, two columns of four rows
Design moment: M_Ed = 250 kN.m (at the face of the column)

Geometry:

Bolt gauge (p2): 110 mm (centre-to-centre between bolt columns)
Top bolt row to top of plate: e_1 = 50 mm
Bolt pitch (p1): 100 mm between rows
m (bolt centre to weld toe): 40 mm (horizontal distance)
e (bolt centre to edge): 45 mm
n = min(e, 1.25m) = min(45, 50) = 45 mm

Tension Zone -- Bolt Row 1 (Top Row)

T-stub effective lengths: Row 1 is an end bolt row (at the top of the plate). Circular: l_eff,cp = min(2 x pi x 40, pi x 40 + 2 x 50) = min(251.3, 225.7) = 225.7 mm Non-circular: l_eff,nc = min(4 x 40 + 1.25 x 45, 2 x 40 + 0.625 x 45 + 50) = min(216.3, 158.1) = 158.1 mm

For Mode 1: M_pl,1,Rd = 0.25 x min(225.7, 158.1) x 20^2 x 355 / 1.0 = 0.25 x 158.1 x 400 x 355 / 1.0 = 5,614,000 N.mm = 5.61 kN.m

F_T,1,Rd = 4 x 5.61 / 0.040 = 561 kN (two bolts)

For Mode 2: l_eff,nc = 158.1 mm governs. M_pl,2,Rd = M_pl,1,Rd = 5.61 kN.m Sigma F_t,Rd = 2 x (0.9 x 800 x 245 / 1.25) = 2 x 141.1 = 282.2 kN

F_T,2,Rd = (2 x 5.61 + 0.045 x 282.2) / (0.040 + 0.045) = (11.22 + 12.70) / 0.085 = 23.92 / 0.085 = 281.4 kN

For Mode 3: F_T,3,Rd = 282.2 kN

Row 1 resistance: F_T,Rd,1 = min(561, 281.4, 282.2) = 281.4 kN

Commentary: Mode 2 governs (bolt failure with flange yielding). The resistance is very close to Mode 3 (pure bolt failure), indicating that the end plate at 20 mm is appropriately proportioned -- thick enough that Mode 1 is avoided, but not so thick that the bolts govern without any plate yielding.

Bolt Row 2 (Inner Row)

Row 2 is an inner bolt row: l_eff,cp = 2 x pi x 40 = 251.3 mm l_eff,nc = 4 x 40 + 1.25 x 45 = 216.3 mm

For Mode 2 (using l_eff,nc = 216.3 mm): M_pl,2,Rd = 0.25 x 216.3 x 400 x 355 / 1.0 = 7.68 kN.m F_T,2,Rd = (2 x 7.68 + 0.045 x 282.2) / 0.085 = (15.36 + 12.70)/0.085 = 330.1 kN

Row 2 resistance: F_T,Rd,2 = min( ... , 330.1, 282.2) = 282.2 kN (Mode 3 governs)

Compression Zone

Beam flange in compression: F_c,fb,Rd = M_c,Rd / (h_b - t_fb) approximately. This check is typically satisfied by inspection for the beam compression flange bearing against the column.

Column web in compression: F_c,wc,Rd = omega x k_wc x b_eff,c,wc x t_wc x f_y,wc / gamma_M0 where omega = 1.0 (reduction factor for interaction with shear), and b_eff,c,wc = t_fb + t_p + 17.3 = 15.6 + 20 + 17.3 = 52.9 mm.

F_c,wc,Rd = 1.0 x 1.0 x 52.9 x 10.5 x 355 / 1.0 = 197.3 kN -- this check is for the flange bearing load. In a moment connection, the compression zone force is the sum of the tension bolt row forces. If the column web compression governs, a local stiffener or web doubler may be required.

Column Web Panel Shear

A_vc = 12,300 - 2 x 256.3 x 17.3 + (10.5 + 2 x 15.2) x 17.3 = 12,300 - 8,868 + 40.9 x 17.3 = 12,300 - 8,868 + 708 = 4,140 mm^2

V_wp,Rd = 0.9 x 355 x 4,140 / (1.732 x 1.0) = 1,322,000 / 1.732 = 763.0 kN

The shear force in the column web panel = Sigma F_T,Rd = 281.4 + 282.2 = 563.6 kN (assuming the first two rows in tension, with the third near the neutral axis contributing less).

V_wp,Rd = 763.0 kN > 563.6 kN. OK. Column web panel shear does not govern.

Connection Moment Resistance

Lever arms from centre of compression (beam bottom flange centre): h_1 = 533.1 - 15.6/2 - 50 = 475.3 mm (Row 1 from compression flange centre) h_2 = 475.3 - 100 = 375.3 mm

M_j,Rd = F_T,Rd,1 x h_1 + F_T,Rd,2 x h_2 = 281.4 x 0.4753 + 282.2 x 0.3753 = 133.8 + 105.9 = 239.7 kN.m

M_j,Rd = 239.7 kN.m < M_Ed = 250 kN.m. The connection fails by a small margin (4%). Options:

Increase end plate thickness to 25 mm: improves Mode 2 resistance and may allow Mode 1 resistance to increase.
Increase bolt diameter to M24: F_t,Rd per bolt increases to 203.3 kN, Sigma F_t,Rd per row = 406.6 kN.
Add a third bolt row in tension: effectively doubles the tension bolt area.
Accept 4% overload (not recommended -- the design check is pass/fail at 1.0 utilisation).

Chosen solution: Increase to M24 Class 8.8 bolts. Recalculate Row 1: Sigma F_t,Rd = 2 x 203.3 = 406.6 kN F_T,2,Rd = (11.22 + 0.045 x 406.6)/0.085 = (11.22 + 18.30)/0.085 = 347.3 kN Mode 3: 406.6 kN F_T,Rd,1 = min(561, 347.3, 406.6) = 347.3 kN M_j,Rd = 347.3 x 0.4753 + 282.2 x 0.3753 = 165.1 + 105.9 = 271.0 kN.m > 250 kN.m. OK.

Alternatively, keep M20 bolts but increase end plate to 25 mm.

UK National Annex Provisions

The UK NA to BS EN 1993-1-8 confirms:

gamma_M0 = 1.00, gamma_M2 = 1.25.
The T-stub model and effective length formulae are adopted without modification.
For nominally pinned end plate connections (partial-depth end plates), the UK NA confirms that the connection must satisfy the ductility criteria of Clause 5.2.3.4 to be classified as pinned.
The UK NA references SCI P358 for standard UK end plate details and SCI P398 for moment-resisting end plate connections.

Design Resources

UK Bolt Capacity Tables -- Fv,Rd and Ft,Rd
UK Steel Grades Reference -- EN 10025-2
UK Connection Design Guide -- General connection provisions
UK UC and UB Section Properties -- Section dimensions
All UK Steel Design References -- complete library

Frequently Asked Questions

What is the T-stub model and when is it used?

The T-stub model represents a bolt row in the tension zone of an end plate or column flange as an equivalent T-shaped member. The flange of the T represents the end plate (or column flange), the stem represents the beam flange (or stiffener), and the two bolts represent the tension anchors. The T-stub capacity is the minimum of three failure modes: Mode 1 (complete flange yielding, most ductile), Mode 2 (bolt failure with partial flange yielding, most common for UK connections), and Mode 3 (pure bolt failure, avoided in UK practice).

What end plate thickness is standard for UK moment connections?

For M20 bolts, the standard UK end plate thickness is 15-20 mm in S355. For M24 bolts, 20-25 mm. The thickness should be sufficient to ensure Mode 2 governs (not Mode 1), but not so thick that Mode 3 governs (brittle failure). A well-proportioned end plate has t_p approximately 0.8-1.2 times the bolt diameter. SCI P398 provides standardised end plate geometries for UK beam-to-column moment connections.

How are prying forces accounted for in end plate design?

Prying forces are implicitly accounted for in the T-stub model through the Mode 2 formula. The term (2 x M_pl,2,Rd + n x Sigma F_t,Rd) captures the moment equilibrium of the flange, where the bolt tension acts at the bolt line plus the prying force at the flange tip. The prying force is the difference between the total bolt tension and the applied tension. For a well-designed connection, the prying force should not exceed approximately 30% of the bolt design tension resistance.

Educational reference only. All design values are per BS EN 1993-1-8:2005 + UK National Annex and BS EN 10025-2:2019. Verify all values against the current editions of the standards and the applicable National Annex for your project jurisdiction. Designs must be independently verified by a Chartered Structural Engineer registered with the Institution of Structural Engineers (IStructE) or the Institution of Civil Engineers (ICE). Results are PRELIMINARY -- NOT FOR CONSTRUCTION without independent professional verification.