EN 1993-1-8 Moment Connection Design — End Plate, T-Stub & Prying Action

Complete reference for EN 1993-1-8:2005 moment-resisting connection design. Covers extended end plate moment connections (Clause 6.2.7), the T-stub model for tension zone design (Clause 6.2.4), prying action and its influence on bolt forces, column web panel shear (Clause 6.2.6.1), transverse stiffener design (Clause 6.2.6.2), bolt row force distribution, and the component method. Includes comprehensive worked examples for a full-strength extended end plate, flush end plate comparison, and design tables for standard UK beam-to-column connections.

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Moment Connections — Classification and Design Philosophy

A moment connection must simultaneously resist bending moment, shear, and (often) axial force while maintaining sufficient stiffness to justify the global analysis assumptions. EN 1993-1-8 classifies connections on two independent axes:

By stiffness (Clause 5.2.2):

By strength (Clause 5.2.3):

For rigid, full-strength moment connections in multi-storey frames — the bread and butter of European steel design — the extended end plate (EEP) bolted connection is the default solution. It provides the stiffness, strength, and ductility that moment frames demand, and crucially, all fabrication is done in the shop (beam + end plate assembly) with only bolting on site. No site welding in the moment-resisting elements.

The Component Method — Clause 6.2

EN 1993-1-8 decomposes a moment connection into independent components. Each is checked individually; the weakest governs. The components for an EEP beam-to-column moment connection are:

Component Clause What It Resists
Column web panel in shear 6.2.6.1 Unbalanced horizontal forces across joint
Column web in transverse compression 6.2.6.2 Compression from beam bottom flange
Column web in transverse tension 6.2.6.3 Tension from bolt rows
Column flange in bending 6.2.6.4 Bending at bolt rows (T-stub model)
End plate in bending 6.2.6.5 Bending at bolt rows (T-stub model)
Bolts in tension Table 3.4 Tension failure of bolts
Beam flange and web in compression 6.2.6.7 Compression at bottom flange
Beam web in tension 6.2.6.8 Tension transfer from end plate to web

The moment resistance M_j,Rd is found by summing bolt row forces multiplied by their lever arms from the centre of compression:

M_j,Rd = Σ (F_tr,Rd,i × h_i)

Bolt rows are checked sequentially from the tension side. If row i + 1 cannot develop its full capacity because row i consumed it, the remaining capacity is capped.

The T-Stub Model — Foundation of Tension Zone Design

The T-stub model (Clause 6.2.4) is the analytical heart of EN 1993-1-8 moment connection design. It replaces the complex 3D stress state in a bolted end plate or column flange with an equivalent T-section in bending. The equivalence is not geometric — it is mechanical: the effective length l_eff of the T-stub flange matches the yield line pattern that would form in the actual plate.

Three Failure Modes

A T-stub under tension can fail in three ways, and the lowest resistance governs:

Mode 1 — Complete flange yielding (maximum prying): F_T,1,Rd = 4 × M_pl,1,Rd / m

Four plastic hinges form: two at the bolt line, two at the web-flange junction. The entire tension is transferred to the bolts through flange bending. Prying is maximum — the bolt sees up to 2-3× the applied tension because the plate edge bears against the connected surface and levers the bolt.

Mode 2 — Bolt failure with flange yielding (intermediate prying): F_T,2,Rd = (2 × M_pl,2,Rd + n × ΣF_t,Rd) / (m + n)

Two plastic hinges form at the web-flange junction. The remaining tension goes through bolts via prying action. n is the effective edge distance (≤ 1.25m).

Mode 3 — Bolt tension failure (zero prying): F_T,3,Rd = ΣF_t,Rd

The flange is so stiff that it does not bend — all tension goes directly to the bolts. No prying. This is ideal for bolt utilisation but requires uneconomically thick end plates.

Worked Example — T-Stub Parameters

Parameter definitions for a bolted end plate:

Symbol Definition Typical Value (EEP, M20, S355)
m Bolt centre to web/flange junction 35-50 mm
e Bolt centre to plate edge 35-60 mm
e_min Minimum edge distance (1.2d_0 for cut edge) 26 mm for M20 (d_0 = 22 mm)
n Effective edge distance, n = e but ≤ 1.25m 40-50 mm
t_p End plate thickness 15-30 mm
l_eff Effective T-stub length per bolt row 200-400 mm

The ratio n/m is the single most important geometric parameter for T-stub behaviour. When n/m is small (< 0.8), prying is moderate and Mode 2 governs. When n/m is large (> 1.0), prying is significant and Mode 1 may govern for thin plates. The UK NA limit n ≤ 1.25m controls prying to acceptable levels.

Effective Lengths for Yield Line Patterns — Table 6.6

The effective length l_eff depends on the bolt row position and whether rows are considered individually or in groups. The circular pattern represents an axisymmetric yield line mechanism; the non-circular pattern represents a prismatic mechanism.

Individual bolt row (end plate extension, outside tension flange):

Individual bolt row (below tension flange, first inner row):

Grouped bolt rows (rows 1 and 2 combined):

For each failure mode, use the minimum of the circular and non-circular effective lengths for that row (individual) and for any row grouping that includes that row. The effective length for Mode 1 may differ from Mode 2 because Mode 1 uses l_eff,1 (minimum of all patterns) and Mode 2 uses l_eff,2 (only non-circular patterns, because Mode 2 requires the compression ring to close).

Full T-Stub Worked Example — Extended End Plate

Connection: UKB 457×191×67 beam (S355) to UKC 254×254×107 column (S355). Extended end plate 250×540×20 mm (S355). M20 Grade 8.8 bolts, 4 bolt rows (2 rows at extension, 2 rows below top flange). Bolt spacing p = 90 mm between rows 1-2, p = 100 mm between rows 2-3.

Row 1 (extension, above top flange):

M_pl,1,Rd = 0.25 × l_eff,1 × t_p² × f_y / γ_M0 = 0.25 × 190 × 400 × 355 / 1.00 = 6,745,000 N·mm = 6.745 kN·m

F_T,1,Rd (Mode 1) = 4 × 6.745 / 0.040 = 675 kN F_T,3,Rd (Mode 3) = 2 bolts × 141 kN = 282 kN (M20 Gr 8.8: F_t,Rd = 0.9 × 800 × 245 / 1.25 = 141 kN) F_T,2,Rd (Mode 2) with n = min(50, 1.25×40) = 50 mm: = (2 × 6.745 + 50 × 282) / (40 + 50) = (13.49 + 14,100) / 90 = 157 kN (per 2-bolt row in Mode 2, but this needs conversion: N·m + N·mm → need consistent units)

Correction — units: M_pl is in N·m, bolt force in N. Mode 2: (2 × 6,745,000 N·mm + 50 mm × 282,000 N) / (40 + 50) = (13,490,000 + 14,100,000) / 90 = 27,590,000 / 90 = 306,556 N = 307 kN

Row 1 T-stub resistance: min(675, 307, 282) = 282 kN — Mode 3 governs for this plate/bolt combination. The 20 mm plate is thick enough that bolt capacity governs the individual row. This is a desirable outcome — bolt failure is more predictable (ductile) than plate yielding.

Group Check — Rows 1+2 Combined

Rows 1 and 2 are at p = 90 mm spacing. Combined circular: l_eff,cp = 2π × 35 + 90 = 310 mm. Combined non-circular: l_eff,nc = 3 × 35 + 1.25 × 40 + 90 = 105 + 50 + 90 = 245 mm. l_eff = min(310, 245) = 245 mm.

M_pl,Rd,group = 0.25 × 245 × 400 × 355 = 8,697,500 N·mm.

F_T,1,Rd,group = 4 × 8.698 / 0.040 = 870 kN for the group. F_T,3,Rd,group = 4 × 141 = 564 kN for all 4 bolts. F_T,2,Rd,group = (2 × 8,697,500 + 50 × 564,000)/90 = (17,395,000 + 28,200,000)/90 = 506,611 N = 507 kN.

Group T-stub resistance = min(870, 507, 564) = 507 kN. Per bolt row in the group: 507/2 = 254 kN per row.

Comparison: Individual row 1 = 282 kN. Group rows 1+2 = 254 kN per row. The group pattern governs — rows 1 and 2 cannot both develop 282 kN because their combined yield line mechanism has lower capacity. Row 1 = 282 kN, row 2 = 507 - 282 = 225 kN (capped by group capacity).

Prying Action — The Hidden Bolt Force

Prying is the mechanism that makes bolt tension higher than the applied external tension. Understanding it is essential for correct bolt sizing.

The Physics of Prying

When tension is applied to a T-stub, the flange bends. As bending increases, the flange edge contacts the connected surface. Further tension cannot separate the edge — the contact point acts as a fulcrum, and the bolt force must overcome both:

  1. The applied tension (direct)
  2. The prying force Q at the flange edge (indirect, levered)

The total bolt force B = T + Q, where T is the applied tension per bolt and Q is the prying force. Q is self-limiting — once the flange yields (Mode 1 or 2), Q stabilises. In Mode 3 (bolt failure before yielding), Q = 0 because the flange never contacts the surface.

Prying Force Calculation

From EN 1993-1-8, the prying force can be derived from the Mode 2 equation:

Q = (2 × M_pl,Rd − T × m) / n

For a T-stub with M_pl,Rd = 6.745 kN·m, T = 141 kN (applied per bolt), m = 40 mm, n = 50 mm:

Q = (2 × 6,745,000 - 141,000 × 40) / 50 = (13,490,000 - 5,640,000) / 50 = 7,850,000/50 = 157,000 N = 157 kN per bolt

Total bolt force B = T + Q = 141 + 157 = 298 kN. But F_t,Rd = 141 kN — so the bolt fails. This is why Mode 2 governs: the combined direct + prying force exceeds bolt capacity.

Controlling Prying

Three strategies reduce prying:

  1. Increase end plate thickness. t_p ↑ → M_pl,Rd ↑ → Mode 2 capacity increases. A 25 mm plate instead of 20 mm increases M_pl,Rd by (25/20)² = 1.56×.
  2. Reduce edge distance e. Smaller n reduces the prying lever arm. But e is constrained by minimum edge distance for bolt holes.
  3. Increase bolt diameter. Higher F_t,Rd shifts the governing mode from Mode 2/3 toward Mode 1.

In practice, UK design offices size the end plate thickness such that Mode 2 governs but with adequate margin — typically t_p ≈ d (bolt diameter) for M20, t_p ≈ 1.2d for M24.

Column Web Panel Shear — Clause 6.2.6.1

The column web between beam flanges must transfer the shear from the unbalanced moment. For a single-sided connection:

V_wp,Ed = M_b1,Ed / z - V_c1,Ed

Where z is the lever arm between bolt tension and compression centroids. The shear resistance:

V_wp,Rd = 0.9 × f_y,wc × A_vc / (√3 × γ_M0)

Worked Example — UKC 254×254×107, S355:

A_vc = A - 2bt_f + (t_w + 2r)t_f = 13,700 - 2×258.8×20.5 + (12.8 + 2×12.7)×20.5 = 13,700 - 10,611 + 783 = 3,872 mm².

V_wp,Rd = 0.9 × 355 × 3,872 / (1.732 × 1.00) = 714 kN.

If V_wp,Ed > 714 kN, add a doubler plate (supplementary web panel) or diagonal stiffeners.

Transformation Parameter β

β accounts for the moment distribution in double-sided connections. EN 1993-1-8 Table 5.4:

| Configuration | β | Notes | | ------------------------------------------- | ----------- | --------------------------------------- | ------ | --------------------------------- | | Single-sided, M_b1 only | 1.0 | Conservative for design | | Double-sided, M_b1 = -M_b2 (equal/opposite) | 0.0 | Zero panel shear — beams balance | | Double-sided, M_b1 = M_b2 (same sign) | 2.0 | Worst case, panel shear from both sides | | General: β = | M_b1 - M_b2 | / max(M_b1, M_b2) | Varies | Intermediate linear interpolation |

For interior columns in braced frames where beams deliver opposing moments (gravity loading), β < 1.0 — the panel shear is less than the worst-case single-sided assumption. However, for seismic or wind load cases with same-sign moments, β can approach 2.0.

Continuity Plates — Column Web Stiffeners

When the unstiffened column web cannot resist the compression from the beam flange or the tension from bolt rows, continuity plates (full-depth transverse stiffeners) are welded into the column. The decision is driven by three checks:

1. Compression Check (F_c,wc,Rd)

F_c,wc,Rd = ω × k_wc × b_eff,c,wc × t_wc × f_y,wc / γ_M0 (if λ_p_bar ≤ 0.72)

Where b_eff,c,wc = t_fb + 2√2 × a_f + 5(t_fc + r_c) + s_p (force dispersion at 45° through end plate).

2. Tension Check (F_t,wc,Rd)

F_t,wc,Rd = ω × b_eff,t,wc × t_wc × f_y,wc / γ_M0

b_eff,t,wc = l_eff of the equivalent T-stub for the column flange (limited by the bolt geometry).

3. Practical Rule

If t_fb (beam flange) > 0.5 × t_fc (column flange), continuity plates are recommended regardless of calculation outcome. The column flange bending is the weak link — continuity plates bypass it entirely by transferring beam flange force directly into the column web.

Stiffener detailing:

Full Worked Example — 4-Row Extended End Plate, Full-Strength

Beam: UKB 533×210×92, S355. M_pl,Rd = 721 kN·m. Depth = 533.1 mm. t_fb = 15.6 mm. Column: UKC 305×305×137, S355. b_fc = 309.2 mm, t_fc = 21.7 mm, t_wc = 13.8 mm. End plate: 320×650×25 mm (S355). 4 bolt rows: Row 1 at +80 mm above top flange (extension), Row 2 at top flange, Row 3 at 110 mm below Row 2, Row 4 at 110 mm below Row 3. Bolts: M24 Grade 10.9, 2 per row. F_t,Rd = 0.9 × 1000 × 353 / 1.25 = 254 kN per bolt. Compression centroid: centre of beam bottom flange.

Step 1 — Lever Arms

Row 1: h_1 = 533.1/2 + 80 + 15.6/2 = 266.6 + 80 + 7.8 = 354 mm from compression centre. Row 2: h_2 = 266.6 mm. Row 3: h_3 = 266.6 - 110 = 156.6 mm. Row 4: h_4 = 156.6 - 110 = 46.6 mm.

Step 2 — Row 1 T-Stub (Extension)

m = 45 mm, e = 55 mm, m_x = 40 mm, e_x = 45 mm. l_eff,cp = 2π × 40 = 251 mm. l_eff,nc = 4 × 40 + 1.25 × 45 = 160 + 56 = 216 mm. l_eff,1 = 216 mm.

M_pl,1,Rd = 0.25 × 216 × 625 × 355 / 1.00 = 11,981,250 N·mm = 11.98 kN·m.

Mode 1: F_T,1,Rd = 4 × 11.98 / 0.045 = 1,065 kN. Mode 3: F_T,3,Rd = 2 × 254 = 508 kN. Mode 2, n = min(55, 1.25 × 45) = 55 mm: = (2 × 11,981,250 + 55 × 508,000) / (45 + 55) = (23,962,500 + 27,940,000) / 100 = 519 kN.

Row 1: min(1065, 519, 508) = 508 kN (Mode 3 governs for thick plate).

Step 3 — Rows 1+2 Group Check

p = 90 mm. l_eff,cp = 2π × 40 + 90 = 341 mm. l_eff,nc = 3 × 40 + 1.25 × 45 + 90 = 120 + 56 + 90 = 266 mm. l_eff = 266 mm.

M_pl,Rd,group = 0.25 × 266 × 625 × 355 = 14,759,375 N·mm. Mode 1: 4 × 14.76 / 0.045 = 1,312 kN. Mode 3: 4 × 254 = 1,016 kN. Mode 2: (2 × 14,759,375 + 55 × 1,016,000)/100 = (29,518,750 + 55,880,000)/100 = 854 kN.

Group: 854 kN. Per row: 427 kN. Row 1 = 508 kN, so Row 2 = 854 - 508 = 346 kN.

Step 4 — Row 3 (Inner, Below Flange)

m = 45, e = 55. l_eff,cp = π × 45 + 2 × 55 = 141 + 110 = 251 mm. l_eff,nc = 4 × 45 + 1.25 × 55 = 180 + 69 = 249 mm. Similar capacity calculations → ~500 kN. Row 3 contributes ≈ 346 kN (limited by equilibrium with Row 2, or group with Rows 2+3).

Step 5 — Row 4 (Lowest Row, Near Compression)

Row 4 is near the compression centroid. Its contribution to moment capacity is small (h_4 = 46.6 mm). Typically, Row 4 is omitted or conservatively capped at 50% of Row 3 capacity. Assume F_tr,Rd,4 = 173 kN.

Step 6 — Moment Resistance

M_j,Rd = 508 × 0.354 + 346 × 0.267 + 346 × 0.157 + 173 × 0.047 = 180 + 92 + 54 + 8 = 334 kN·m

This is significantly below the full-strength requirement of M_j,Rd ≥ 1.2 × 721 = 865 kN·m. The 4-row configuration with 25 mm plate is partial-strength.

Step 7 — Increasing to Full-Strength

To achieve full-strength, options include:

  1. Haunch the connection to increase lever arm (haunch depth ~300 mm below beam flange, h_row1 ≈ 650 mm, M_j,Rd ≈ 500+ kN·m — still insufficient).
  2. Use 6 bolt rows (3 rows in extension, 3 below). Triples the tension zone lever arm. With 6 rows at 354, 267, 157, 354, 267, 157 mm, M_j,Rd ≈ 2 × 334 = 668 kN·m — getting closer.
  3. Increase bolt grade to 12.9 (F_t,Rd = 305 kN per M24). 20% more bolt capacity → ~20% more M_j,Rd.
  4. Use deeper beam — UKB 610×229×113 (M_pl,Rd = 1,027 kN·m but bigger lever arm). Lever arm increases ~15%, M_j,Rd increases proportionally.

Most practical: combination of (1) haunch + (2) 6 rows 10.9 bolts. This is the standard UK portal frame eaves connection solution — haunched with multiple bolt rows.

Design Tables — Quick Reference for Standard UK Sections

Full-strength EEP moment connections, S355, Grade 10.9 bolts, 25 mm end plate:

Beam Column Bolts per Row Rows Approx. M_j,Rd (kN·m) % Beam M_pl
UKB 457×191×67 UKC 254×254×107 M20 × 2 4 320 60%
UKB 457×191×82 UKC 254×254×107 M24 × 2 4 480 70%
UKB 533×210×82 UKC 305×305×137 M24 × 2 6 680 82%
UKB 533×210×92 UKC 305×305×137 M24 × 2 6 760 88%
UKB 610×229×101 UKC 305×305×198 M27 × 2 6 1,050 91%
UKB 610×229×113 UKC 356×368×202 M27 × 2 6 1,250 93%
UKB 610×229×125 UKC 356×368×202 M30 × 2 6 1,480 95%
UKB 686×254×140 UKC 356×406×287 M30 × 2 8 2,150 98%

Note: Full-strength requires M_j,Rd ≥ 1.2 M_pl,Rd,beam. These values approximate from SCI P398. Always verify with connection design software for specific geometries. Haunches may be required for the larger sections.

Where the table shows < 100% of beam M_pl, the connection is partial-strength. Partial-strength connections are acceptable when the global analysis explicitly models connection flexibility and the reduced resistance is accounted for in the member forces.

Practical Connection Detailing

End Plate Dimensions

Parameter Minimum Typical (UK Practice)
Plate width b_bf + 2a_w b_bf + 40-50 mm
Plate height beam depth + 300-500 mm beam depth + 400 mm
Bolt edge distance 1.2d_0 1.5-2.0d_0
Bolt gauge (horizontal) 90-120 mm 100-110 mm
Bolt pitch (vertical) 2.2d_0 80-120 mm
Weld size (beam web) ≥ 0.7t_w 5-6 mm FW
Weld size (beam flanges) ≥ 0.7t_f 8-12 mm FW or PJP

Weld Design Between Beam and End Plate

The welded connection between the beam and end plate transfers the full beam moment. Key rules:

  1. Flange welds: Design for the beam flange force F_f = M_Ed / z. Fillet weld throat a_w ≥ F_f × γ_M2 / (2l_w × f_u / √3). For a UKB 457×191×67 (flange = 189.9 × 12.7 mm, S355, M_Ed = 522 kN·m): F_f = 522 / 0.440 = 1,186 kN. Weld length per flange = 2 × 190 = 380 mm. a_w ≥ 1,186,000 × 1.25 / (2 × 380 × 490/1.732) = 1,482,500 / 214,900 = 6.9 mm → specify 8 mm FW.

  2. Web welds: Design for shear V_Ed plus any moment transferred through the web (conservatively: yield capacity of the web). Minimum a_w = 0.7t_w = 0.7 × 8.5 = 6.0 mm → specify 6 mm FW both sides.

  3. Weld access: The end plate must extend beyond the beam flanges by at least the fillet weld leg length plus 5 mm for the welder to see and access the joint.

Comparison: EN 1993-1-8 vs AISC 360 Moment Connections

Aspect EN 1993-1-8 AISC 360 (Chapter J)
Design approach Component method (decompose joint) Unified method (flange force)
Tension zone analysis T-stub model, 3 failure modes prying action model (Manual Part 9)
Prying Implicit in T-stub Modes 1-2 Explicit Q calculation with α'
Bolt pretension Partial safety γ_M3 for slip-resistant Fully pretensioned for slip-critical
Weld design Directional method (β_w) Instantaneous centre (IC) method
Partial factors γ_M0=1.00, γ_M2=1.25 φ=0.75 (bolts), φ=0.90 (base metal)
Column stiffeners Continuity plates (full depth) Continuity plates + doubler plates

The T-stub model is the most distinctive feature of EN 1993-1-8 — it has no direct equivalent in AISC 360, which uses prying action models from the AISC Steel Construction Manual Part 9. The T-stub model is more systematic (three modes, clear boundaries) but the AISC prying model is better supported by US testing data for standard configurations. Both produce similar outcomes when calibrated to the same reliability index.

Related Pages

Educational reference only. Verify all design values against the current EN 1993-1-8 and the applicable National Annex for your jurisdiction. Moment connection design is project-specific — the component method is systematic but sensitive to geometric assumptions. Always check the latest SCI/BCSA guidance. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent verification by a qualified structural engineer.