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.

Quick access: Bolt Bearing & Tearout → | Bolt Pretension → | Bolt Spacing →

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 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 optimization: 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 (LRFD or ASD per applicable code)
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 Australian Standard governs structural steel design?

AS 4100-2020 (Steel Structures) is the primary standard for structural steel design in Australia. It covers all aspects of design including member capacity, connections, serviceability, and fire resistance. The standard uses a limit states design philosophy with resistance factors (φ) applied to nominal capacities. Companion standards include AS/NZS 3679.1 for hot-rolled sections, AS/NZS 1554 for welding, and AS/NZS 4600 for cold-formed steel.

What are the common steel grades used in Australian construction?

The most common steel grades for Australian construction are Grade 300 and Grade 350 per AS/NZS 3679.1. Grade 300 (minimum yield 300 MPa for sections > 12 mm thick) is the standard for general structural applications. Grade 350 (minimum yield 340 MPa for sections > 12 mm) is used where higher strength reduces weight. Grade 400 and Grade 450 are available for specialized applications requiring higher strength-to-weight ratios.

How does AS 4100 compare to AISC 360?

Both AS 4100 and AISC 360 use limit states design (LRFD) principles. Key differences include: AS 4100 uses a single "capacity factor" φ approach rather than separate φ for different failure modes; AS 4100 specifies distinct buckling curves for hot-rolled and welded sections; the moment capacity formula in AS 4100 uses αm factor directly rather than Cb; and AS 4100 has more detailed provisions for slender sections and combined actions. Despite philosophical differences, both codes produce similar results for typical members.

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

• 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