EN 1993 Bolt Group Capacity — Eccentric Load per Eurocode 3

Complete guide to bolt group analysis under eccentric loading per EN 1993-1-8:2005. Elastic (vector) and instantaneous center of rotation (ICR) methods for bolt groups subjected to combined shear and torsion/moment. Worked examples with M20 8.8 bolts.

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Elastic (Vector) Method

The elastic method assumes linear-elastic behavior:

  1. The applied load P is resolved into direct shear plus moment about the bolt group centroid
  2. Direct shear per bolt: F_i = P / n (equal distribution)
  3. Torsional shear component: F_M,i = M × r_i / Σ(r_j²)

Where M = P × e (eccentric moment), n = number of bolts, r_i = distance from bolt to centroid.

For each bolt: F_resultant,i = √((F_x + F_M,xi)² + (F_y + F_M,yi)²)

The design check: F_resultant,max ≤ F_b,Rd and F_resultant,max ≤ F_v,Rd.

Worked Example — 4-Bolt Bracket, M20 8.8

Geometry:

Centroid properties:

Property Value
Bolt group centroid Centered
r_max (corner bolt) √(50² + 50²) = 70.7 mm
Σ(r_j²) 4 × (50² + 50²) = 20000 mm²
Direct shear per bolt (vertical) 100 / 4 = 25.0 kN
Moment 100 × 200 = 20000 kN·mm
Torsional shear at corner (horizontal) 20000 × 50 / 20000 = 50.0 kN
Torsional shear at corner (vertical) 20000 × 50 / 20000 = 50.0 kN

Resultant at critical bolt (corner, vertical component):

F_resultant = √(50.0² + (25.0 + 50.0)²) = √(2500 + 5625) = 90.1 kN

Check:

Utilization: 90.1 / 94.1 = 0.96 — OK, but close to capacity.

Instantaneous Center of Rotation (ICR) Method

For a more accurate (less conservative) analysis, the ICR method considers:

  1. The bolt group rotates about an instantaneous center (not the centroid)
  2. Bolt forces are proportional to distance from the ICR, but limited by bolt deformation capacity
  3. The ICR location is found iteratively by satisfying equilibrium

The ICR method typically gives 10-30% higher capacity than the elastic vector method for eccentric connections with significant rotation.

Method Max Bolt Force Utilization Conservatism
Elastic vector 90.1 kN 0.96 Conservative
ICR method ~78 kN ~0.83 More accurate

Bolt Group Capacity Tables — M20 8.8 in S355 (12 mm plate)

4-Bolt Group (2×2), Vertical Load

Eccentricity e (mm) Elastic Capacity (kN) ICR Capacity (kN)
0 (concentric) 376 376
50 240 275
100 160 190
150 120 145
200 96 120
300 68 88

6-Bolt Group (3×2), Vertical Load

Eccentricity e (mm) Elastic Capacity (kN) ICR Capacity (kN)
0 (concentric) 564 564
100 300 360
200 184 228
300 130 164

Bolt Shear Resistance per EN 1993-1-8

Shear per Bolt (Threads in Shear Plane — Category A)

F_v,Rd = α_v × f_ub × A_s / γ_M2

Where α_v = 0.6 for 8.8 and 10.9, γ_M2 = 1.25.

Bearing per Bolt

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

See the bearing and tearout guide for detailed factor calculations.

Frequently Asked Questions

Should I use the elastic or ICR method for bolt group design?

The elastic (vector) method is simpler, conservative, and acceptable for most connections per EN 1993-1-8. The ICR method gives a more accurate capacity assessment and is recommended for heavily loaded connections or when the elastic method gives utilization > 0.90. Some national annexes require the ICR method for specific connection types.

What is the maximum eccentricity for bolt groups in EN 1993?

EN 1993-1-8 does not specify a maximum eccentricity limit. However, as eccentricity increases, the connection becomes increasingly inefficient (one bolt carries most of the load). Practical limits are e ≤ 3 × bolt group depth. For larger eccentricities, consider a moment connection (end plate with stiffeners) instead of a simple bracket connection.

Related Pages

Educational reference only. Design per EN 1993-1-8:2005. γ_M2 = 1.25. Elastic method is conservative for eccentric groups. ICR method requires iterative analysis per EN 1993-1-8 Annex A. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent verification.

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