UK Bolt Bearing and Tear-Out Resistance — EN 1993-1-8 Clause 3.6 with UK National Annex

Bolt bearing and tear-out failures are ductile limit states that govern the plate-side resistance of bolted connections. Unlike bolt shear fracture, which is a sudden failure, bearing deformation provides visible warning before the ultimate load is reached. EN 1993-1-8 Clause 3.6 provides the design formula for Fb,Rd -- the design bearing resistance per bolt -- which captures both bearing (plate crushing around the hole) and tear-out (shear rupture from hole to plate edge). This reference covers the complete derivation, tabulated values for standard UK spacings, and worked examples for common UK connection configurations.

The Bearing Resistance Formula

The design bearing resistance per bolt on a connected plate, per EN 1993-1-8 Table 3.4, is:

Fb,Rd = (k1 x alpha_b x fu x d x t) / gamma_M2

Where each term carries a specific physical meaning:

• k1: Factor accounting for the beneficial effect of edge distance perpendicular to the direction of force. A larger edge distance develops a fuller bearing stress block, increasing k1 up to the upper bound of 2.5.

• alpha_b: Factor accounting for end distance parallel to the force direction, bolt pitch, and the ratio of bolt to plate tensile strength. This factor determines whether the connection is limited by end tear-out, bolt interaction, or bearing crushing.

• fu: Ultimate tensile strength of the connected plate. For S275: fu = 410 MPa. For S355: fu = 470 MPa. These values derive from EN 10025-2:2019.

• d: Nominal bolt diameter, not the hole diameter.

• t: Thickness of the plate being checked (the thinner of the connected plies where multiple plates are present).

• gamma_M2: Partial factor for bolted connections in bearing. The UK NA confirms gamma_M2 = 1.25, which is the recommended value.

The k1 Factor -- Edge Distance Perpendicular to Load

For edge bolts (nearest the plate edge perpendicular to the force), the k1 factor accounts for the distance e2 from the bolt centre to the edge of the plate:

k1 = min(2.8 x e2/d0 - 1.7, 2.5)

For inner bolts (not adjacent to a perpendicular edge), the gauge spacing p2 replaces edge distance:

k1 = min(1.4 x p2/d0 - 1.7, 2.5)

The cap of 2.5 prevents unrealistically high bearing resistance when edge distances are large. For standard UK detailing with e2 = 30 mm and d0 = 22 mm (M20 bolt): k1_edge = min(2.8 x 30/22 - 1.7, 2.5) = min(2.118, 2.5) = 2.118. To achieve k1 = 2.5, the edge distance must satisfy e2 >= (2.5 + 1.7) x d0 / 2.8 = 1.5 x d0 x 22 = 33 mm for M20.

k1 Values for Standard UK Edge Distances

The table reveals that M12-M16 achieve full k1 = 2.5 easily with standard edge distances. For M24 and larger, the edge distance must increase to realise the full bearing capacity, or the reduced k1 must be explicitly accounted for.

The alpha_b Factor -- End Distance and Pitch Parallel to Load

The alpha_b factor is the minimum of four terms:

For End Bolts (adjacent to plate end):

alpha_b = min(e1/(3d0), p1/(3d0) - 0.25, fub/fu, 1.0)

For Inner Bolts (not adjacent to plate end):

alpha_b = min(p1/(3d0) - 0.25, fub/fu, 1.0)

The four terms represent different failure modes:

1. e1/(3d0): End tear-out -- shear rupture from hole to plate end. Governs for small end distances.
2. p1/(3d0) - 0.25: Bolt interaction -- overlapping bearing stress fields between adjacent bolts. Governs for tight pitches.
3. fub/fu: Bearing crushing -- the plate's bearing strength relative to the bolt's tensile strength. Governs for strong bolts in weak plate.
4. 1.0: Upper bound -- alpha_b cannot exceed unity under any circumstances.

For Class 8.8 bolts (fub = 800 MPa) in S355 plate (fu = 470 MPa): fub/fu = 800/470 = 1.70, which exceeds 1.0, so the upper bound governs in the absence of tight spacing. For Class 4.6 bolts (fub = 400 MPa) in S355 plate: fub/fu = 400/470 = 0.851, which governs for inner bolts with generous pitch.

Tear-Out Failure Mechanism

Tear-out is a shear rupture of the plate material between the bolt hole and the plate end, along planes parallel to the loading direction. The length of the shear planes is governed by the end distance e1. The critical term e1/(3d0) in the alpha_b formula arises from equating the shear stress on the tear-out planes to the ultimate shear strength of the plate.

For standard UK end distance of 40 mm and M20 bolt (d0 = 22 mm): e1/(3d0) = 40/(3 x 22) = 0.606. This value typically governs for end bolts, meaning the connection is limited by tear-out rather than bearing crushing. To increase the tear-out resistance, the end distance can be increased, but practical plate geometries and connection proportions impose constraints.

Block Shear Interaction

When bolt groups are subject to combined shear and tension, or when the bolt group configuration creates overlapping shear and tension zones in the connected plate, the block shear check per EN 1993-1-8 Clause 3.10.2 must be performed in addition to the individual bolt bearing checks. Block shear is a rupture of a block of plate material defined by the bolt hole perimeter and the plate edges. The design resistance Veff,Rd accounts for the relative contributions of shear yield, shear rupture, and tension rupture on the respective planes.

For a fin plate connection with three M20 bolts at 70 mm pitch and 40 mm end distance in a 220 mm wide plate, the block shear tension face is bounded by the top bolt hole and the plate top edge. The shear faces extend from the plate edges to the top bolt. The resulting Veff,Rd is compared with the applied shear to ensure that block shear does not precede bolt bearing failure.

Fb,Rd Tables for UK Practice

The following tables present Fb,Rd per millimetre of plate thickness for standard UK edge distances (e1 = 40 mm, e2 = 30 mm) in S355 plate. Multiply by plate thickness for the design value.

S355 Plate (fu = 470 MPa), Class 8.8 Bolts, e1 = 40 mm, e2 = 30 mm

S275 Plate (fu = 410 MPa), Class 8.8 Bolts, e1 = 40 mm, e2 = 30 mm

For a 10 mm thick S355 end plate with M20 end bolts: Fb,Rd = 48.4 x 10 = 484 kN per bolt. This typically exceeds the bolt shear resistance (Fv,Rd = 94.1 kN for M20 Class 8.8 with threads in the shear plane), confirming that the bolt shear governs for standard UK detailing -- the intended design outcome.

Worked Example -- Beam Splice Connection

Consider a 610x229x101 UB beam splice using external cover plates 12 mm thick in S355, with 8 M20 Class 8.8 bolts in two columns of four rows, e1 = 50 mm, e2 = 40 mm, p1 = 90 mm, p2 = 80 mm.

Alpha_b values: End bolt: alpha_b = min(50/(3 x 22), 90/(3 x 22) - 0.25, 800/470, 1.0) = min(0.758, 1.114, 1.702, 1.0) = 0.758 Inner bolt: alpha_b = min(1.114, 1.702, 1.0) = 1.0 (capped)

k1 values: Edge bolt: k1 = min(2.8 x 40/22 - 1.7, 2.5) = min(3.391, 2.5) = 2.5 Inner bolt: k1 = min(1.4 x 80/22 - 1.7, 2.5) = min(3.391, 2.5) = 2.5

Fb,Rd calculation: End bolt: Fb,Rd = 2.5 x 0.758 x 470 x 20 x 12 / 1.25 = 170.9 kN Inner bolt: Fb,Rd = 2.5 x 1.0 x 470 x 20 x 12 / 1.25 = 225.6 kN

Comparison with bolt shear: Fv,Rd = 0.6 x 800 x 245 x 0.8 / 1.25 = 94.1 kN (threads in shear plane, Class 8.8).

The bolt shear resistance of 94.1 kN governs for all bolts. The bearing resistance is more than adequate.

UK National Annex Provisions

The UK NA to BS EN 1993-1-8 confirms the following for bearing checks:

1. gamma_M2 = 1.25 for bearing resistance of bolted connections, consistent with the recommended value. This value applies uniformly to all steel grades and bolt classes.

2. The k1 and alpha_b formulations are adopted without modification. The upper bound of k1 = 2.5 and alpha_b = 1.0 remain in force.

3. For slotted holes with the slot perpendicular to the load direction, the UK NA requires that the bearing check use a reduced k1 factor of 0.75 x k1_round to account for the reduced contact area between the bolt shank and the plate.

4. For oversized holes, bearing checks use the standard formula but with a cap on alpha_b at 0.8 to limit bearing deformation in the oversized configuration.

5. For countersunk bolts, the bearing area is reduced and a factor of 0.63 is applied to the calculated Fb,Rd per the UK NA guidance.

The UK NA also references BS EN 1090-2 for execution requirements affecting bearing resistance, including limits on hole out-of-roundness and burr removal that influence the effective contact area.

Interaction with Net Section Checks

Bearing checks must be accompanied by net section tension checks per EN 1993-1-1 Clause 6.2.2.2 for plates in tension. The net section resistance Nu,Rd = 0.9 x Anet x fu / gamma_M2, where Anet is the gross area less the total deduction for bolt holes on the critical failure path.

For a plate with staggered bolt holes, the effective net area deduction accounts for the stagger pitch s using the Cochrane formula: effective deduction = d0 - s^2/(4g), where g is the gauge between staggered rows. This formula provides a more favourable net area than simply subtracting all hole areas, because the stagger forces a longer and therefore stronger failure path.

In well-proportioned UK connections, the net section resistance typically exceeds the bearing resistance for the bolt group as a whole, meaning bearing governs the plate-side design. However, for thin plates with large bolts (high d/t ratio), the net section may become critical.

Design Resources

• UK Steel Grades Reference -- EN 10025-2 grade selection for UK projects
• UK Steel Mechanical Properties -- fy, fu, and elongation tables
• UK Bolt Capacity Tables -- Class 8.8 and 10.9 bolt resistance
• UK Beam Design Guide -- EN 1993-1-1 flexure, shear, and LTB
• UK Connection Design Guide -- EN 1993-1-8 bolted and welded joints
• All UK Steel Design References -- complete library

Frequently Asked Questions

What governs bearing resistance in a standard UK end plate connection?

For standard UK end plate connections with e1 = 40 mm, e2 = 30 mm and M20 Class 8.8 bolts in S355 plate, the bolt shear resistance Fv,Rd = 94.1 kN governs before bearing. The bearing resistance per bolt (Fb,Rd = 484 kN for a 10 mm plate) substantially exceeds the shear resistance. This is the intended design hierarchy -- the bolt fails in shear before the plate fails in bearing, providing a ductile and predictable failure mode.

How does the UK NA modify the EN 1993-1-8 bearing resistance formula?

The UK National Annex adopts the Clause 3.6 bearing formula without modification. The gamma_M2 value of 1.25 is confirmed. The UK NA provides supplementary guidance for slotted holes (reduced k1), oversized holes (alpha_b cap of 0.8), and countersunk bolts (0.63 reduction factor), which represent UK-specific clarifications rather than changes to the core formula.

What is the difference between bearing failure and tear-out failure?

Bearing failure involves localised crushing and plastic deformation of the plate material around the bolt hole under the bolt shank, resulting in hole elongation. It is a ductile failure mode. Tear-out is shear rupture of the plate from the bolt hole to the free edge along planes parallel to the load direction. Both are captured by the same Fb,Rd formula, with alpha_b distinguishing between the two: the e1/(3d0) term controls tear-out, while the fub/fu term controls bearing crushing. For UK standard detailing, e1/(3d0) typically governs for end bolts.

What k1 value should be used for an inner bolt with large gauge spacing?

The k1 factor for inner bolts is k1 = min(1.4 x p2/d0 - 1.7, 2.5). For large gauge spacings, k1 reaches its cap of 2.5. For M20 bolts with standard 22 mm holes: p2 = (2.5 + 1.7) x 22 / 1.4 = 66 mm to achieve the full k1 = 2.5. Standard UK gauge of 60 mm gives k1 = 1.4 x 60/22 - 1.7 = 2.118, which is below the cap but adequate for typical design.

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.