UK Fatigue Design -- EN 1993-1-9 Detail Categories, S-N Curves, and Damage Accumulation
Fatigue is the progressive and 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, and changes in section -- and propagate with each load cycle until the remaining cross-section can no longer sustain the peak load. BS EN 1993-1-9:2005 provides the fatigue assessment framework, based on nominal stress S-N curves (also known as Woehler curves) that relate the applied stress range to the number of cycles to failure for each structural detail category. This reference covers the fatigue design methodology, detail categories for UK structural connections, the Palmgren-Miner linear damage accumulation rule, and worked examples for crane gantry girders in S355 steel.
The Fatigue Design Framework
Fatigue assessment under EN 1993-1-9 proceeds in four stages:
Identify fatigue-susceptible details: Joints subject to repeated loading -- crane runway beams, bridge girders, wind-sensitive structures, vibrating machinery supports.
Determine the design stress range spectrum: From load history data, the number of cycles n_i at each stress range level Delta_sigma_i is determined. For simple assessments, the equivalent constant amplitude stress range Delta_sigma_E at 2 million cycles may be used.
Select the appropriate detail category: Each structural detail (weld type, bolt configuration, surface condition) is assigned a FAT class from Table 8.1-8.10 of EN 1993-1-9.
Perform the damage assessment: Using the S-N curve for the selected detail category, determine whether the cumulative damage D = Sigma (n_i / N_i) <= 1.0 (safe life) or satisfies the damage-tolerant criteria.
Detail Categories (FAT Classes)
The FAT class is the stress range in MPa at 2 million cycles that the detail can sustain at 97.7% survival probability (mean minus 2 standard deviations). A higher FAT number indicates better fatigue resistance.
| FAT Class | Delta_sigma_C (MPa) | Detail Description | UK Application |
|---|---|---|---|
| FAT160 | 160 | Parent metal, as-rolled, clean surface | Plain steel away from welds |
| FAT125 | 125 | Full-penetration butt weld, ground flush, 100% NDT | Critical bridge butt welds |
| FAT112 | 112 | Full-penetration butt weld, as-welded, NDT verified | Standard UK butt weld (good quality) |
| FAT100 | 100 | Butt weld on permanent backing bar | Beam flange splices with backing |
| FAT90 | 90 | Full-penetration T-butt joint, as-welded | Moment connection flange welds |
| FAT90 | 90 | Cruciform joint, K-butt weld, no lamellar tearing | Column flange-to-web joints |
| FAT80 | 80 | Non-load-carrying fillet weld, L < 50 mm | Transverse stiffener welds |
| FAT80 | 80 | Longitudinal fillet weld, attachment L < 100 mm | Fin plate connection welds |
| FAT71 | 71 | Load-carrying fillet weld, end of weld | Fin plate top and bottom |
| FAT63 | 63 | Transverse fillet weld attachment, L > 100 mm | Web stiffener end weld |
| FAT56 | 56 | Cover plate end, t > 20 mm | Bolted splice cover plate end |
| FAT50 | 50 | Cover plate end, t <= 20 mm | Reinforcing plate ends |
| FAT45 | 45 | Slotted hole in tension member | Erection slots |
| FAT36 | 36 | Shear stud base (fatigue of stud) | Composite beam shear connectors |
For bolted connections, the detail category applies to the net section of the connected plate, not to the bolt itself. Preloaded bolts (Category D/E) have higher fatigue resistance than non-preloaded bolts because the friction interface shields the bolt from the full stress range.
S-N Curves
The S-N curve for each detail category is defined by three regimes:
1. High-cycle fatigue (m = 3): For stress ranges Delta_sigma >= Delta_sigma_D (the constant amplitude fatigue limit at 5 million cycles): N = 2 x 10^6 x (Delta_sigma_C / Delta_sigma)^3
2. Cut-off limit regime (m = 5): For stress ranges Delta_sigma_L <= Delta_sigma < Delta_sigma_D: N = 5 x 10^6 x (Delta_sigma_D / Delta_sigma)^5
3. Infinite life: For stress ranges Delta_sigma < Delta_sigma_L (the cut-off limit at 100 million cycles), the stress range is assumed to cause zero fatigue damage and can be ignored in the accumulation.
The transition from slope m = 3 to m = 5 at 5 million cycles reflects the physical observation that fatigue crack propagation slows significantly at low stress ranges, and below a threshold stress intensity factor range Delta_K_th, fatigue cracks do not propagate.
CAFL and Cut-Off Limits for Standard Detail Categories
| FAT Class | Delta_sigma_D at 5e6 cycles (MPa) | Delta_sigma_L at 1e8 cycles (MPa) |
|---|---|---|
| 160 | 117 | 64 |
| 125 | 91 | 50 |
| 112 | 82 | 45 |
| 100 | 73 | 40 |
| 90 | 66 | 36 |
| 80 | 59 | 32 |
| 71 | 52 | 29 |
| 63 | 46 | 25 |
| 56 | 41 | 22 |
| 50 | 37 | 20 |
| 45 | 33 | 18 |
| 36 | 26 | 14 |
For a FAT90 detail (typical as-welded butt weld): stress ranges below 36 MPa cause no measurable fatigue damage, stress ranges between 36 and 66 MPa cause damage at the reduced m = 5 rate, and stress ranges above 66 MPa cause damage at the full m = 3 rate.
Palmgren-Miner Linear Damage Accumulation
For variable amplitude loading, the Palmgren-Miner rule sums the damage fractions from each stress range level:
D = Sigma (n_i / N_i) <= 1.0
Where n_i is the number of applied cycles at stress range Delta_sigma_i, and N_i is the number of cycles to failure at that stress range from the S-N curve.
The linear damage rule is simple but has known limitations: it ignores load sequence effects (an overload cycle that causes crack tip plasticity can retard subsequent crack growth, while underloads can accelerate it), and it does not account for the mean stress effect. Despite these limitations, it remains the standard method for variable amplitude fatigue assessment in EN 1993-1-9.
Equivalent Constant Amplitude Stress Range
For design purposes, the variable amplitude spectrum is often represented by a single equivalent constant amplitude stress range Delta_sigma_E at 2 million cycles:
Delta_sigma_E = [Sigma (n_i x Delta_sigma_i^m) / 2 x 10^6]^(1/m)
Where m = 3 for Delta_sigma_i >= Delta_sigma_D, and m = 5 for stress ranges below this threshold.
The fatigue check then reduces to: Delta_sigma_E <= Delta_sigma_C / gamma_Mf, where gamma_Mf is the fatigue partial factor.
Worked Example -- Crane Gantry Girder
Given:
- Girder: 610 x 229 x 101 UB in S355
- Critical detail: Full-penetration butt weld in the bottom (tension) flange at a flange splice, as-welded, NDT verified
- Detail category: FAT112 (as-welded full-penetration butt weld, NDT verified)
- Crane capacity: 20 tonnes, class Q3 (heavy), 250,000 load cycles per year
- Design life: 25 years
- Stress range spectrum derived from influence line analysis:
| Stress Range Delta_sigma (MPa) | Cycles per year n_i |
|---|---|
| 120 | 2,500 |
| 90 | 12,500 |
| 65 | 50,000 |
| 40 | 125,000 |
| 25 | 60,000 |
| Total per year: | 250,000 |
Step 1 -- CAFL and cut-off for FAT112: Delta_sigma_D = 82 MPa (at 5 x 10^6 cycles) Delta_sigma_L = 45 MPa (at 1 x 10^8 cycles)
Step 2 -- Cycles to failure for each stress range:
Delta_sigma = 120 MPa (>= 82, m = 3): N = 2 x 10^6 x (112/120)^3 = 2 x 10^6 x 0.814 = 1.628 x 10^6
Delta_sigma = 90 MPa (>= 82, m = 3): N = 2 x 10^6 x (112/90)^3 = 2 x 10^6 x 1.923 = 3.846 x 10^6
Delta_sigma = 65 MPa (< 82 but >= 45, m = 5): N = 5 x 10^6 x (82/65)^5 = 5 x 10^6 x 3.338 = 16.69 x 10^6
Delta_sigma = 40 MPa (< 45): Below cut-off -- ZERO damage.
Delta_sigma = 25 MPa (< 45): Below cut-off -- ZERO damage.
Step 3 -- Annual damage: D_annual = 2,500/1.628e6 + 12,500/3.846e6 + 50,000/16.69e6 + 0 + 0 = 0.00154 + 0.00325 + 0.00300 = 0.00779
Step 4 -- Design life damage: D_25yr = 25 x 0.00779 = 0.195 < 1.0. OK.
The detail has a comfortable fatigue life with only 19.5% of the Palmgren-Miner damage limit used in 25 years. The life could be extended to approximately 128 years at the current loading rate.
Step 5 -- What if the weld quality is reduced to as-welded, no NDT (FAT90)? Delta_sigma_D = 66 MPa, Delta_sigma_L = 36 MPa.
Recalculate with FAT90: Delta_sigma = 120: N = 2e6 x (90/120)^3 = 2e6 x 0.422 = 0.844e6 Delta_sigma = 90: N = 2e6 x (90/90)^3 = 2.000e6 Delta_sigma = 65: N = 5e6 x (66/65)^5 = 5e6 x 1.079 = 5.395e6 Delta_sigma = 40: N = 5e6 x (66/40)^5 = 5e6 x 10.18 = 50.9e6
D_annual = 2,500/0.844e6 + 12,500/2.0e6 + 50,000/5.395e6 + 125,000/50.9e6 = 0.00296 + 0.00625 + 0.00927 + 0.00246 = 0.02094
D_25yr = 25 x 0.02094 = 0.524 < 1.0. Still adequate but with less margin.
This demonstrates the sensitivity of fatigue life to weld quality -- the FAT90 detail uses 52.4% of its fatigue life at 25 years, compared with 19.5% for FAT112. The higher stress range cycles (120 and 90 MPa) dominate the damage despite their low frequency.
Damage-Equivalent Factor Method (Simplified)
For simpler assessments, EN 1993-1-9 provides damage-equivalent factors lambda that convert the variable amplitude spectrum to an equivalent constant amplitude stress range at 2 million cycles:
Delta_sigma_E2 = lambda x Delta_sigma_max
Where lambda is selected based on the type of structure and loading (bridges: lambda_1 to lambda_4, crane girders: specific lambda values per EN 1993-1-9 Annex A).
The fatigue check then becomes: gamma_Ff x Delta_sigma_E2 <= Delta_sigma_C / gamma_Mf
UK National Annex Provisions
The UK NA to BS EN 1993-1-9 confirms:
- The detail categories and S-N curves are adopted without modification.
- gamma_Mf = 1.00 for the safe life method (high consequence of fatigue failure).
- gamma_Mf = 1.15 for the damage tolerant method (low consequence with inspection regime).
- For UK highway bridges to BS EN 1993-2, the UK NA specifies more onerous detail categories for specific details and requires mandatory NDT for all Category >= 100 details.
- The UK NA permits the use of the hot-spot stress method (Annex B) for details not covered by the standard FAT classes, with specific guidance on the extrapolation path for stress measurement.
Design Resources
- UK Steel Grades Reference -- EN 10025-2 grades and Charpy requirements
- UK Connection Design Guide -- EN 1993-1-8 welded and bolted joints
- UK Steel Properties -- fy, fu, Charpy toughness
- UK Beam Design Guide -- Flexure, shear, LTB
- All UK Steel Design References -- complete library
Frequently Asked Questions
What detail category applies to a standard UK fin plate welded connection?
The fin plate-to-column weld (fillet weld, longitudinal, non-load-carrying attachment): FAT80 when the attachment length L <= 100 mm. The top and bottom of the fin plate (load-carrying fillet weld ends): FAT71. For fatigue-critical connections (crane girders, bridges), fin plate connections should be avoided or the end of the weld should be ground to a smooth profile to upgrade the detail category to FAT90-100.
How does the UK NA modify fatigue design compared with the standard EN 1993-1-9?
The UK NA adopts the recommended S-N curves and detail categories without modification. It confirms gamma_Mf = 1.00 (safe life) and 1.15 (damage tolerant). For highway bridges, the UK NA to BS EN 1993-2 imposes stricter requirements: mandatory NDT for details with FAT >= 100, additional detail categories for UK-specific bridge details, and a requirement for Charpy toughness verification at the minimum bridge service temperature.
What is the Palmgren-Miner rule and when does it apply?
The Palmgren-Miner rule sums the linear damage fractions from each stress range level in a variable amplitude spectrum: D = Sigma(n_i/N_i) <= 1.0. It applies whenever the loading spectrum is not a constant amplitude and multiple stress range levels contribute to fatigue damage. The rule assumes that damage is linear and independent of load sequence, which is a simplification but is conservative in most practical cases. EN 1993-1-9 requires the Miner summation for all variable amplitude fatigue assessments.
What stress ranges can be ignored in a fatigue assessment?
Stress ranges below the cut-off limit Delta_sigma_L (at 1 x 10^8 cycles) may be ignored as they cause negligible fatigue damage. For FAT90, Delta_sigma_L = 36 MPa. For FAT160 (parent metal), Delta_sigma_L = 64 MPa. Additionally, if the total number of cycles at all stress ranges is less than approximately 10,000 (for building structures not subject to significant cyclic loading), fatigue assessment may be waived entirely per EN 1993-1-9 Clause 2(3).
Educational reference only. All design values are per BS EN 1993-1-9:2005 + 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.