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:

• 4 bolts in a 150 × 200 mm pattern (p₁ = 100 mm, p₂ = 100 mm)
• Bracket load: P = 100 kN at e = 200 mm eccentricity
• Bolt grade: M20 8.8 (F_v,Rd = 94.1 kN per bolt, F_b,Rd = 137.3 kN for 12 mm S355)
• d₀ = 22 mm

Centroid properties:

Resultant at critical bolt (corner, vertical component):

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

Check:

• Shear: 90.1 kN ≤ 94.1 kN ✓ (F_v,Rd governs)
• Bearing: 90.1 kN ≤ 137.3 kN ✓

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.

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

4-Bolt Group (2×2), Vertical Load

6-Bolt Group (3×2), Vertical Load

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 0.5 for 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.

Design Applications

Common Design Scenarios

This reference covers structural design scenarios commonly encountered in structural steel design practice:

• Strength verification: Check member or connection capacity against factored loads per the applicable design code
• Serviceability checks: Verify deflections, vibrations, and other serviceability criteria
• Code compliance: Ensure design meets all provisions of the governing standard
• Connection detailing: Verify weld sizes, bolt quantities, and edge distances

Related Design Considerations

• System behavior: consider the interaction between members and connections
• Load paths: verify that forces can be transferred through the structure to the foundations
• Constructability: check that the design can be fabricated and erected practically
• Cost optimisation: evaluate alternative sections or connection types for economy

Worked Example

Problem: Verify a typical steel member for the following conditions:

Typical span: 6.0 m | Load: service loads per applicable code | Section: common section in this category

Design Check:

1. Determine governing load combination (ULS or SLS per EN 1990)
2. Calculate maximum internal forces (moment, shear, axial)
3. Compute nominal capacity per code provisions
4. Apply resistance/safety factors
5. Verify interaction if combined forces exist

Result: Use the results from the Steel Calculator tool to verify design adequacy.

Frequently Asked Questions

What European Standard governs structural steel design?

EN 1993 (Eurocode 3: Design of Steel Structures) is the primary standard for structural steel design in Europe. EN 1993-1-1 covers general rules for buildings, EN 1993-1-8 addresses connection design, and EN 1993-1-2 covers fire design. The standard uses limit state design with partial safety factors (γM). National Annexes adapt parameters to each member state. Companion standards include EN 10025 for hot-rolled products, EN 1090 for execution, and EN 1994 for composite design.

What are the common steel grades used in European construction?

The most common steel grades for European construction are S235, S275, S355, S420, and S460 per EN 10025-2. S355 (minimum yield 355 MPa for t ≤ 16 mm) is the most widely used for structural applications. S275 is used for secondary members. S420 and S460 are quenched and tempered high-strength steels for weight-critical applications. Weathering steel (S355J2W) and fine-grain structural steels (EN 10025-3 and -4) are also available.

How does EN 1993 compare to other international steel design codes?

EN 1993, AISC 360 (US), AS 4100 (Australia), and CSA S16 (Canada) all use limit states design principles but differ in key details. EN 1993 uses partial safety factors (γM0 = 1.00, γM1 = 1.00, γM2 = 1.25) rather than resistance factors (φ). Buckling curves in EN 1993 follow the European Column Curve system (a0 to d) with 5 distinct curves, compared to AISC's single curve. EN 1993-1-8 has comprehensive connection design provisions including the component method for moment connections.

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 utilisation > 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

• Bolt Bearing & Tearout — Bearing per EN 1993-1-8 Clause 3.6
• Bolt Torque Chart — Torque-tension values
• Bolt Spacing — EN 1993-1-8 Table 3.3
• End Plate Connection — Moment connection design
• All European References

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.

Design Resources

Calculator tools

• Bolt Torque Calculator
• Bolted Connection Calculator
• Splice Connection Calculator
• Steel Bolted Connection Calculator

Design guides

• Bolt Torque Worked Example
• Bolted Connection Checklist
• Bolted Connection Worked Example
• AISC Shear Tab Example
• EN 1993-1-8 Bolted Connection Worked Example