Bearing Resistance Formula — Clause 3.6.1

The design bearing resistance for each bolt is:

F_b,Rd = (k₁ × α_b × f_u × d × t) / γ_M2

Where:

Edge Distance Factor k₁

For bolts at a loaded edge (perpendicular to force direction):

k₁ = min(2.8 × e₂/d₀ - 1.7, 2.5)

For inner bolts (not at loaded edge):

k₁ = min(1.4 × p₂/d₀ - 1.7, 2.5)

Where:

k₁ Values for Standard Edge Distances (M20, d₀ = 22 mm)

e₂ (mm) e₂/d₀ k₁ Condition
30 1.36 2.12 Minimum edge distance
35 1.59 2.50 Reached limit
40 1.82 2.50 Spaced beyond critical
50 2.27 2.50 Adequate

End Distance Factor α_b

α_b is the minimum of three values:

α_d = e₁ / (3 × d₀) — for end bolts (loaded toward end) α_d = p₁ / (3 × d₀) - 1/4 — for inner bolts α_b = f_ub / f_u

Therefore: α_b = min(α_d, f_ub / f_u, 1.0)

Where:

α_b Values — End Bolts (M20 in S355, f_u = 470 MPa, f_ub = 800 MPa for 8.8)

e₁ (mm) e₁/(3d₀) f_ub/f_u Min α_b
30 0.45 1.70 0.45
35 0.53 1.70 0.53
40 0.61 1.70 0.61
50 0.76 1.70 0.76
60 0.91 1.70 0.91
70 1.00 1.70 1.00

The end distance governs for e₁ < 3 × d₀ × (f_ub/f_u), which for M20 in S355 means e₁ < 112 mm.

Bearing Capacity Table — M20 8.8 in S355

e₁ (mm) α_b k₁ t = 8 mm t = 10 mm t = 12 mm t = 16 mm t = 20 mm
30 0.45 2.12 57.4 kN 71.7 kN 86.1 kN 114.8 kN 143.5 kN
40 0.61 2.50 91.7 kN 114.7 kN 137.6 kN 183.5 kN 229.4 kN
50 0.76 2.50 114.3 kN 142.9 kN 171.5 kN 228.6 kN 285.8 kN
60 0.91 2.50 136.9 kN 171.1 kN 205.3 kN 273.7 kN 342.2 kN
70 1.00 2.50 150.4 kN 188.0 kN 225.6 kN 300.8 kN 376.0 kN

For inner bolts, use α_b based on p₁/(3d₀) - 1/4 and the same k₁ = 2.5.

Worked Example — M20 8.8 Bolt in 12 mm S355 Plate

Parameter Value
Bolt M20 8.8 (f_ub = 800 MPa)
Plate S355 (f_u = 470 MPa), t = 12 mm
e₁ 40 mm
e₂ 35 mm
d₀ 22 mm

Calculation:

Factor Value
k₁ = min(2.8 × 35/22 - 1.7, 2.5) min(2.75, 2.5) = 2.50
α_d = e₁ / (3 × 22) 40 / 66 = 0.61
f_ub / f_u 800 / 470 = 1.70
α_b = min(0.61, 1.70, 1.0) 0.61
F_b,Rd = (2.50 × 0.61 × 470 × 20 × 12) / 1.25 137.6 kN

Check against shear resistance of M20 8.8:

Minimum Edge and End Distances

Per EN 1993-1-8 Table 3.3:

Frequently Asked Questions

What is the difference between bearing and tearout in EN 1993-1-8?

Bearing (F_b,Rd) per Clause 3.6 covers the combined effect of hole elongation (bearing stress) and tearout (shearing of the plate from the bolt to the edge). The k₁ and α_b factors in the bearing formula account for both failure modes. Tearout is implicitly covered through the end distance term e₁/(3d₀) in α_b, with shorter end distances reducing the bearing resistance to reflect the tearout risk.

How does the EN 1993 bearing formula compare to AISC 360?

AISC 360 uses separate checks for bearing (2.4 × d × t × f_u) and tearout (1.5 × L_c × t × f_u). EN 1993-1-8 uses a single formula F_b,Rd = (k₁ × α_b × f_u × d × t) / γ_M2 with α_b accounting for end distance. The Eurocode approach typically gives slightly lower bearing capacities due to γ_M2 = 1.25 versus the AISC resistance factor φ = 0.75.

Related Pages

Educational reference only. Design per EN 1993-1-8:2005 Clause 3.6. γ_M2 = 1.25 per EN 1993-1-1 Clause 6.1. Verify actual hole diameters and plate f_u values. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent verification.

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