Bolt Group Analysis Methods

Two methods are used for bolt group design under eccentric loading:

UK NA Guidance

The UK NA to BS EN 1993-1-8 does not explicitly specify which bolt group method to use. UK practice:

• Elastic method is standard for simple connections (fin plates, partial-depth end plates)
• ICR method is used for heavily loaded groups and moment connections
• Both methods are acceptable provided the assumptions are clearly stated

Elastic (Vector) Method

The elastic method treats the bolt group as a cross-section with the following properties:

Direct shear per bolt: Fv,Ed (direct) = VEd / n (where n = number of bolts)

Torsional (rotational) shear per bolt: Fv,Ed (torsion) = VEd × e × ri / Ip

Where:

• e = eccentricity from centroid of bolt group to load line
• ri = distance from bolt group centroid to bolt i
• Ip = polar moment of inertia of the bolt group = Σ(xi² + yi²)

Resultant shear on critical bolt:

Fv,Ed (resultant) = √(Fv,Ed(direct)² + Fv,Ed(torsion)² + 2 × Fv,Ed(direct) × Fv,Ed(torsion) × cos θi)

Worked Example — Bracket Connection

Problem: A UK bracket connection has 6 × M20 Class 8.8 bolts in a 2×3 pattern (2 rows, 3 columns). The vertical load VEd = 200 kN acts at eccentricity e = 200 mm from the bolt group centroid. Determine bolt group capacity.

Bolt Group Geometry

Bolt pitch: p = 70 mm (horizontal), gauge: g = 60 mm (vertical) Columns: 3 (n₁ = 3), Rows: 2 (n₂ = 2) Total bolts: n = 6

Bolt group centroid at centre of rectangle (0, 0). r_i² for corner bolt: x = 70 mm, y = 30 mm → r² = 70² + 30² = 4,900 + 900 = 5,800 mm²

Ip = Σ(x_i² + y_i²) = 6 × (70² + 30²) — only for all equal distances? No, each position differs.

Full calculation:

• Inner bolts (2): x = 0, y = ±30 mm → r² = 0 + 900 = 900 mm² each
• Outer bolts (4): x = ±70 mm, y = ±30 mm → r² = 4,900 + 900 = 5,800 mm² each

Ip = 2 × 900 + 4 × 5,800 = 1,800 + 23,200 = 25,000 mm²

Direct Shear per Bolt

Fv,direct = 200 / 6 = 33.3 kN (downwards)

Torsional Shear on Critical Bolt

Critical bolt = furthest from centroid (corner bolt at x = 70 mm, y = 30 mm) r = √(70² + 30²) = √5,800 = 76.2 mm

Torsional moment: T = VEd × e = 200 × 200 = 40,000 kN·mm = 40 kN·m

Fv,torsion = T × r / Ip = 40,000 × 76.2 / 25,000 = 122.0 kN

Direction: perpendicular to radius, so at corner bolt the angle between direct shear and torsional shear must be determined.

Angle θ between direct (vertical) and torsional (perpendicular to radius) vectors at corner bolt:

cos θ = (direction) = vertical component of torsional force / total torsional = 30/76.2 = 0.394

Fv,resultant = √(33.3² + 122.0² + 2 × 33.3 × 122.0 × 0.394)

= √(1,109 + 14,884 + 3,199) = √19,192 = 138.5 kN

Bolt Check

M20 Class 8.8, single shear, threads in plane: Fv,Rd = 47.0 kN

Utilisation: 138.5 / 47.0 = 2.95 >> 1.0 — FAIL

Conclusion: The bolt group is inadequate. Six M20 bolts cannot resist a 200 kN eccentric load at 200 mm eccentricity. Options:

1. Increase number of bolts (e.g., 4×4 = 16 bolts)
2. Increase bolt size (M24 or M30 Class 8.8)
3. Reduce eccentricity (move load closer to group centroid)
4. Use Class 10.9 bolts (minor improvement — Fv,Rd = 49.0 kN for threads)
5. Redesign connection type (e.g., use a stiffer connection with reduced eccentricity)

Design Resources

• UK Steel Grades Reference — EN 10025-2 grade selection for UK projects
• UK Steel Mechanical Properties — fy, fu, and elongation tables
• UK Universal Beam and Column Sizes — UB/UC section dimensions and properties
• 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

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Frequently Asked Questions

What is the instantaneous centre of rotation method for bolt groups?

The ICR method finds the point about which the bolt group rotates under eccentric load. Each bolt deforms proportionally to its distance from the ICR, and the bolt force is determined from the load-deformation curve for the bolt type. The internal resistance of the bolt group must equal the applied load. This method typically gives 15-30 % higher capacity than the elastic vector method for ductile connections. The ICR method is implemented in design software and is the basis for the AISC and AS 4100 bolt group tables.

When should I use the elastic vector method vs the ICR method?

Use the elastic vector method for: (1) simple shear connections where bolt ductility is uncertain, (2) Class 10.9 bolts (brittle, limited ductility for redistribution), (3) connections where bolt deformation must be minimised (serviceability-critical). Use the ICR method for: (1) ductile Class 8.8 or 4.6 bolt groups, (2) heavily loaded connections where every kN of capacity matters, (3) connections with large eccentricity where the elastic method is overly conservative. In UK practice, the elastic method is the default for design offices, with ICR used only in specialist software.

What bolt pitch and gauge are standard for UK bolt groups?

Standard UK bolt spacing per BS EN 1090-2 and SCI guidance: pitch p1 = 70 mm (2.5-3d), gauge p2 = 60 mm (2.5d for M20). Minimum pitch is 2.2d0 (≈ 48 mm for M20). Maximum pitch in compression is 14t (stiffness requirement). Maximum pitch in tension is 28t (for corrosion protection). For moment end plate connections, the gauge is typically 90 mm for M20 (to clear the column web fillet).

How does the UK NA affect bolt group capacity calculations?

The UK NA to BS EN 1993-1-8 does not modify the bolt group analysis method. It confirms γM2 = 1.25 for bolt shear resistance. UK practice follows the standard elastic or ICR method per EN 1993-1-8. The UK NA also confirms the bolt spacing and edge distance minimums from Table 3.3. The main UK-specific consideration is the use of standard UK spacings (70 mm pitch, 60 mm gauge) rather than metric module spacings.

Related Pages

• EN 1993 Steel Design Overview
• European Steel Properties
• EN 1993 Beam Design Guide
• EN 1993 Column Buckling
• EN 1990 Load Combinations
• UK Steel Chemical Composition
• UK Steel Charpy Values

Educational reference only. All design values are per BS EN 1993-1-1:2005 + 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.