EN 1993-1-9 Fatigue Design — Detail Categories, S-N Curves, Palmgren-Miner Cumulative Damage

Quick Reference: This guide covers structural fatigue design of steel members to EN 1993-1-9:2005. We explain the family of S-N curves with slopes m=3 and m=5, how to select a detail category from Tables 8.1–8.10 based on constructional detail, the Palmgren-Miner linear damage accumulation rule for variable amplitude loading, the λ damage equivalent factor method from Annex A, and a complete crane runway girder worked example. All clauses reference EN 1993-1-9.

PRELIMINARY — NOT FOR CONSTRUCTION. All calculations are illustrative educational examples. Results must be verified by a licensed Professional Engineer before use in any design project.

1. When Is Fatigue Design Required?

Fatigue is the progressive, localised structural damage that occurs when a material is subjected to cyclic loading. In steel structures, fatigue cracks initiate at stress concentrations — weld toes, bolt holes, cope holes, sharp re-entrant corners — and grow with each load cycle until fracture occurs at stress levels far below the static yield strength.

EN 1993-1-9 fatigue assessment is mandatory when:

• The structure experiences frequent cyclic loading (typically >10,000 cycles over its design life).
• The stress range exceeds 25% of the constant amplitude fatigue limit for the relevant detail category.
• The structure is classified as Consequence Class 2 or 3 (failure would risk life safety or major economic loss — see EN 1990 Annex B).

Common fatigue-governed structures:

• Crane runway girders and their support brackets.
• Highway and railway bridge girders, cross-frames, and orthotropic decks.
• Industrial structures with vibrating machinery (crushers, screens, hammer mills).
• Wind-sensitive slender structures (chimneys, masts, cable-stayed bridge stays).
• Offshore structures subject to wave loading.

2. The S-N Curve Family

EN 1993-1-9 defines fatigue resistance through a family of parallel S-N curves on a log-log scale. Each curve represents a distinct detail category, identified by its reference fatigue strength ΔσC in N/mm² at 2 million cycles.

2.1 Two-Slope Curve Model

An S-N curve has three regimes:

The key inflection points for any detail category:

Constant amplitude fatigue limit (CAFL): ΔσD = 0.737 × ΔσC at ND = 5 × 10⁶ cycles. Cut-off limit: ΔσL = 0.404 × ΔσC at NL = 1 × 10⁸ cycles.

2.2 Reference Fatigue Strengths

For a detail with category ΔσC = X, the fatigue strength at any number of cycles N is:

ΔσR = ΔσC × (2 × 10⁶ / N)^(1/m)

Where m = 3 for the primary branch (N ≤ 5×10⁶) and m = 5 for the secondary branch (N > 5×10⁶).

For Detail 80 (ΔσC = 80 N/mm²):

• At N = 2×10⁶: ΔσR = 80 MPa (definition point)
• At N = 5×10⁶: ΔσD = 0.737 × 80 = 58.9 MPa (CAFL)
• At N = 10⁷: ΔσR = 58.9 × (5×10⁶/10⁷)^(1/5) = 58.9 × 0.871 = 51.3 MPa
• At N = 1×10⁸: ΔσL = 0.404 × 80 = 32.3 MPa (cut-off)

3. Detail Categories — Tables 8.1 to 8.10

The hardest part of fatigue design is correctly identifying the detail category. EN 1993-1-9 provides ten tables covering all common constructional details. Selection errors are the most common cause of fatigue failures in practice.

3.1 Key Detail Categories

3.2 Detail Selection Workflow

1. Identify the critical stress-raising feature (weld, cope hole, bolt hole, abrupt section change).
2. Find the matching geometry in Tables 8.1–8.10. Match the exact detail — "similar" is not sufficient.
3. The lower the number, the worse the fatigue performance. Improvement may be possible by:
   • Grinding weld toes to remove undercut and improve the transition radius.
   • Specifying full penetration welds instead of fillet welds.
   • Using NDT to verify weld quality (allows higher category for butt welds).
   • Hammer peening or TIG dressing to introduce compressive residual stress at the weld toe.

4. Palmgren-Miner Linear Damage Rule

For variable amplitude loading, EN 1993-1-9 Cl. 5(2) requires a cumulative damage assessment using the Palmgren-Miner rule:

Dd = Σ (ni / Ni)

Where:

• ni = number of applied cycles at stress range Δσi
• Ni = number of cycles to failure at stress range Δσi from the S-N curve

Fatigue failure is deemed to occur when Dd ≥ 1.0 over the design life.

4.1 Worked Example — Crane Runway Girder

Crane runway girders are the most fatigue-intensive structures in industrial buildings. Consider a simply supported girder with the following stress range histogram obtained from rainflow counting of 20 years' crane operations:

Given:

• Beam: built-up welded I-girder, S355 steel
• Detail at bottom flange-to-web weld: Detail 100 (automatic fillet weld, start/stop ground, NDT verified) from Table 8.2
• ΔσC = 100 N/mm²
• Design life: 50 years
• γMf = 1.15 (safe-life assessment, low consequence of failure)
• γFf = 1.00 (fatigue load factor)

Stress Range Histogram (annual cycles):

4.2 Determining Ni for Each Bin

For ΔσC = 100 MPa, m = 3 for N ≤ 5×10⁶, m = 5 for N > 5×10⁶.

The endurance at any Δσ: If Δσ ≥ 0.737×100 = 73.7 MPa → m = 3: Ni = 2×10⁶ × (100/Δσi)³ If 0.404×100 ≤ Δσ < 73.7 MPa → m = 5: Ni = 5×10⁶ × (73.7/Δσi)⁵ If Δσ < 40.4 MPa → Ni = ∞ (below cut-off, no damage)

Bin calculations:

1. Δσ = 120 MPa, m = 3: N1 = 2×10⁶ × (100/120)³ = 2×10⁶ × 0.579 = 1.158×10⁶ cycles
2. Δσ = 90 MPa, m = 3: N2 = 2×10⁶ × (100/90)³ = 2×10⁶ × 1.372 = 2.743×10⁶ cycles
3. Δσ = 65 MPa → < 73.7, m = 5: N3 = 5×10⁶ × (73.7/65)⁵ = 5×10⁶ × 1.476⁵ = 5×10⁶ × 7.00 = 35.0×10⁶ cycles
4. Δσ = 45 MPa, m = 5: N4 = 5×10⁶ × (73.7/45)⁵ = 5×10⁶ × 1.638⁵ = 5×10⁶ × 11.79 = 59.0×10⁶ cycles
5. Δσ = 30 MPa → < 40.4 MPa → below cut-off → N5 = ∞, damage = 0
6. Δσ = 20 MPa → below cut-off → N6 = ∞, damage = 0

4.3 Damage Accumulation

Total damage Dd = Σ ni/Ni = 0.00648 + 0.01458 + 0.00500 + 0.01017 = 0.0362

Fatigue verification: Dd = 0.0362 < 1.0 → PASS with substantial margin.

This result shows the beam has only 3.6% fatigue damage after 50 years — equivalent to a theoretical fatigue life of 50/0.0362 ≈ 1380 years. The design could tolerate significantly higher load cycles (e.g., a heavier crane duty class) without fatigue becoming the governing limit state.

5. The λ Damage Equivalent Factor Method (Annex A)

For routine design, the full Palmgren-Miner summation over a histogram is time-consuming. EN 1993-1-9 Annex A provides a simplified method using damage equivalent factors:

ΔσE,2 = λ × Δσ(γFf × Qk)

Where:

• ΔσE,2 = damage equivalent stress range at 2×10⁶ cycles
• λ = λ1 × λ2 × λ3 × λ4 × λ5 × ... (as many λi factors as needed per Annex A)
• Δσ(γFf × Qk) = stress range from the fatigue load model

The verification then becomes a single-check comparison against the detail category:

γFf × ΔσE,2 / (ΔσC / γMf) ≤ 1.0

Or equivalently: ΔσE,2 ≤ ΔσC / (γFf × γMf) = 100 / (1.0 × 1.15) = 87.0 MPa for Detail 100.

5.1 Key λ Factors

For our crane girder, the equivalent stress range can be back-calculated from the Palmgren-Miner result:

ΔσE,2 = ΔσC × Dd^(1/3) at 2×10⁶ cycles (assuming m=3 equivalence) = 100 × (0.0362)^(1/3) = 100 × 0.331 = 33.1 MPa

Then λ = ΔσE,2 / Δσ(γFf × Qk) = 33.1 / 120 = 0.276 (crane-specific λ factor).

This λ captures the effect of the stress spectrum: even though peak stress ranges reach 120 MPa, the infrequency of heavy lifts means the damage-equivalent constant-amplitude stress range is only 33.1 MPa.

6. Fatigue Improvement Techniques

Where fatigue verification fails (Dd > 1.0), improvement techniques can increase the detail category by 1–2 classes:

These treatments must be specified on engineering drawings and verified by inspection. Each has a defined surface finish requirement (e.g., burr grinding to a depth of 0.5 mm below the surface, with a minimum radius of 5.0 mm or one-quarter of the plate thickness).

7. Design Recommendations

• Avoid fatigue details in tension zones. Wherever possible, locate fillet-welded attachments, stiffeners, and shear studs in compression zones of the member, where crack propagation is suppressed.
• Specify cope holes at stiffener-to-flange intersections with a radius ≥ 35 mm (or 1.5× the web thickness) to reduce the stress concentration factor from ≈ 2.5 to ≈ 1.5.
• For crane girders, use class D or higher cranes only where fatigue has been explicitly checked. Class A–C cranes (light/medium service) rarely require fatigue design — but always verify against EN 1991-3 crane load models.
• Consider the fabrication sequence. Fatigue-critical welds should be accessible for NDT and improvement treatment. Back-gouged and re-welded butt joints achieve better fatigue performance than permanent backing bar details.
• Residual stresses matter. As-welded details have tensile residual stresses at the weld toe approaching fy, which means the effective stress ratio R is near 0 regardless of the applied minimum stress. EN 1993-1-9 S-N curves already account for high tensile residual stress — do not apply a mean stress correction unless the component has been post-weld heat treated or peened.

Related Pages

• EN 1993-1-1 Beam Design — IPE 300 Worked Example, χLT
• EN 1993-1-1 Column Design — HEA 200 Example, Buckling Curves
• EN 1993-1-2 Fire Design — Section Factor, Critical Temperature
• EN 1993-1-8 Weld Design — Directional Method, βw Factors
• EN 1993-1-8 Base Plate Design — T-Stub, Concrete Bearing