UK Steel Fatigue Assessment -- BS EN 1993-1-9 Detail Categories & Damage Accumulation
Fatigue governs the design of steel structures subjected to repeated loading -- cranes, bridges, wind-sensitive structures, and machinery supports. Unlike static strength, fatigue resistance depends on the geometry of the detail (not the parent metal grade) and the stress range (not the maximum stress). BS EN 1993-1-9 provides the framework for fatigue verification using S-N curves, detail categories, and cumulative damage analysis. This reference covers the detail category system, S-N curve construction, the Palmgren-Miner rule for variable amplitude loading, and a crane runway fatigue assessment.
The Detail Category System
The detail category Delta_sigma_C (or Delta_tau_C for shear) is the characteristic fatigue strength at 2 million cycles for a constant amplitude stress range, expressed in MPa. It is the fundamental parameter that captures the effect of local geometry, welding process, and inspection standard on fatigue resistance. A higher category number indicates superior fatigue performance.
UK Typical Details -- EN 1993-1-9 Tables 8.1-8.10 Summary
Rolled Sections and Plates (Table 8.1)
| Detail | Category | Condition |
|---|---|---|
| Rolled sections, as-rolled surface | 160 | No welded attachments in fatigue zone |
| Flame-cut edges, shallow drag lines < 1000 MPa | 140 | Free edges of plate girders |
| Flame-cut edges, sharp drag lines | 125 | Machine-quality cut required for higher |
| Punched holes, reamed to remove burrs | 125 | Reaming must remove full HAZ |
Transverse Butt Welds (Table 8.2)
| Detail | Category | Condition |
|---|---|---|
| Full penetration, ground flush, NDT | 125 | Weld toe ground smooth, UT/RT verified |
| Full penetration, as-welded, NDT | 100 | Weld cap left in place, UT/RT verified |
| Full penetration, as-welded | 90 | No NDT, weld profile conforms to EN 1090-2 |
| Partial penetration butt weld | 71 | Permanent backing, root gap verified |
| Transverse fillet weld at cope hole | 71 | Web penetration at cope -- UK fin plate detail |
Longitudinal Welds (Table 8.3)
| Detail | Category | Condition |
|---|---|---|
| Longitudinal fillet weld, automatic, no stops | 100 | Plate girder web-to-flange, submerged arc |
| Longitudinal fillet weld, manual, stops | 80 | Manual welder qualification required |
| Intermittent longitudinal fillet weld | 63 | Weld terminations create stress raisers |
| Longitudinal fillet at cope hole | 56 | Where weld terminates within 10 mm of cope |
Welded Attachments (Tables 8.4-8.6)
| Detail | Category | UK Example |
|---|---|---|
| Transverse stiffener, full penetration, ground | 90 | Column web stiffener, ground toes |
| Transverse stiffener, fillet weld, as-welded | 80 | Standard stiffener to flange |
| Gusset plate on beam flange, end < 50 mm from edge | 71 | Bracing gusset on beam top flange |
| Shear stud on tension flange | 80 | Composite beam in hogging |
| Tack weld (temporary attachment) in tension zone | 56 | Removal and grinding required for higher |
Bolted Connections (Table 8.7)
| Detail | Category | Condition |
|---|---|---|
| Preloaded bolt, friction grip, double cover | 112 | No slip, Category C connection |
| Bolt in bearing, single shear | 90 | Standard hole clearance |
| Bolt in tension (T-stub) | 90 | M20 preloaded |
| Countersunk bolt in shear | 71 | Reduced bearing area |
Hollow Section Joints (Tables 8.9-8.10)
| Detail | Category | Condition |
|---|---|---|
| RHS brace to RHS chord, gap | 45 | beta <= 0.85, 2gamma = chord width/thickness |
| CHS brace to CHS chord, gap | 36 | beta <= 0.80, theta >= 30 degrees |
| RHS brace to RHS chord, overlap | 50 | Full overlap joint, overlap > 80% |
Selecting the Governing Detail
For any potential fatigue-critical location, examine ALL possible failure modes:
- Base metal at the toe of the weld (the heat-affected zone)
- Weld throat (fillet weld in shear, butt weld in tension)
- Bolt in tension or shear
- Net section at a bolt hole
- Weld root (partial penetration, fillet weld root in tension)
The lowest category governs. A single cope hole (Category 71) on an otherwise Category 100 beam reduces the fatigue life by a factor of (100/71)^3 = 2.8 times. This is why UK beam end connections (fin plates, partial-depth end plates) often govern the fatigue assessment -- the coped web detail is the weak link.
S-N Curves (Fatigue Strength Curves)
The relationship between stress range and cycles to failure is represented by S-N curves on a log-log plot. EN 1993-1-9 defines the S-N curve for each detail category as follows:
Constant Amplitude Fatigue Limit (CAFL) Region
For N <= 5 x 10^6 cycles (m = 3):
Delta_sigma_R^m x N_R = Delta_sigma_C^m x 2 x 10^6
Thus: N_R = 2 x 10^6 x (Delta_sigma_C / Delta_sigma_R)^3
For 5 x 10^6 < N <= 10^8 cycles (m = 5):
Delta_sigma_R^5 x N_R = Delta_sigma_D^5 x 5 x 10^6
Where Delta_sigma_D = (2/5)^(1/3) x Delta_sigma_C = 0.737 x Delta_sigma_C
The cut-off limit at N = 10^8 cycles: Delta_sigma_L = (5/100)^(1/5) x Delta_sigma_D = 0.549 x 0.737 x Delta_sigma_C = 0.404 x Delta_sigma_C
S-N Curve Worked Values
For a Category 80 detail (transverse fillet weld, as-welded):
| Stress Range (MPa) | Cycles to Failure | Region |
|---|---|---|
| 160 | 250,000 | m = 3 |
| 120 | 592,000 | m = 3 |
| 80 | 2,000,000 | Delta_sigma_C exactly |
| 59 | 5,000,000 | CAFL |
| 45 | 16,190,000 | m = 5 |
| 32 | 40,370,000 | m = 5 |
| 24 | 100,000,000 | Cut-off -- no further damage |
For stress ranges below the cut-off limit, fatigue damage is considered zero for constant amplitude loading. However, for variable amplitude loading, the CAFL does not apply -- damage continues to accumulate per the m = 3 curve for all stress cycles (the cumulative damage rule in Clause 5(4)).
Palmgren-Miner Linear Damage Accumulation
When a structure is subjected to variable amplitude loading (the real-world case), fatigue damage from each stress range block accumulates linearly:
D_d = SUM (n_i / N_i) <= 1.0
Where:
- n_i = number of applied cycles at stress range Delta_sigma_i
- N_i = number of cycles to failure at Delta_sigma_i from the S-N curve
- D_d = total damage sum -- must not exceed 1.0 at the end of the design life
Equivalent Constant Amplitude Stress Range
In practice, the variable amplitude stress spectrum is converted to an equivalent constant amplitude stress range at 2 million cycles using the damage equivalent factor lambda:
Delta_sigma_E,2 = lambda x Delta_sigma_max
Where lambda encapsulates the effects of:
- The stress spectrum shape (distribution of stress ranges)
- The S-N curve slope (m = 3 for damage calculation)
- The total number of cycles N over the design life
- The fatigue strength curve details
EN 1993-1-9 Annex A provides lambda values for cranes (Table A.1) and bridges (Table A.2).
For crane runway beams (EN 1993-6), the damage equivalent factor lambda is expressed as:
lambda = lambda_1 x lambda_2 x lambda_3 x ... x lambda_i
Where lambda_1 accounts for the crane classification (S0-S9), lambda_2 for the number of stress cycles, and lambda_3 for the stress spectrum shape.
Typical UK Crane Classifications
| Crane Class | Cycles in 50 Years | Typical UK Application | lambda (approx) |
|---|---|---|---|
| S0-S2 | < 100,000 | Light workshop, occasional lift | 0.40 - 0.55 |
| S3 | ~250,000 | Warehouse, stockholder, light ind | 0.60 - 0.75 |
| S4-S5 | ~500,000 | Heavy warehouse, production line | 0.75 - 0.85 |
| S6-S7 | ~1,000,000 | Heavy production, steel stockyard | 0.85 - 0.95 |
| S8-S9 | > 2,000,000 | Steelworks, continuous process | 0.95 - 1.00 |
Fatigue Verification Procedure
The standard verification per EN 1993-1-9 Clause 8:
For normal stresses: gamma_Ff x Delta_sigma_E,2 / (Delta_sigma_C / gamma_Mf) <= 1.0
For shear stresses: gamma_Ff x Delta_tau_E,2 / (Delta_tau_C / gamma_Mf) <= 1.0
For combined normal + shear (Clause 8(4)): (D_d,sigma)^3 + (D_d,tau)^5 <= 1.0
Where:
- gamma_Ff = partial factor for equivalent constant amplitude stress range (1.0 per UK NA)
- gamma_Mf = partial factor for fatigue strength (1.00 safe-life low consequence, 1.15 safe-life high consequence, 1.35 damage-tolerant)
The damage-tolerant method's higher gamma_Mf = 1.35 is NOT a penalty -- it is the price of not providing redundancy. The safe-life method with gamma_Mf = 1.00 is only permitted when failure of the single element would have low consequences (ductile failure mode, load redistribution possible).
Worked Example -- UK Crane Runway Beam
A Class S4 overhead crane runway beam in a UK heavy engineering workshop:
Parameters:
- Crane class S4 (500,000 stress cycles in 50 years per EN 1991-3)
- Crane capacity: 200 kN, self-weight + crab: 220 kN
- Runway beam: 610 x 229 x 101 UB in S355J2, simply supported span 9.0 m
- Rail: A65 (65 kg/m) clipped to top flange, discontinuous fillet welds at 500 mm spacing
- Maximum static bending moment per wheel: 495 kN.m (from influence line analysis)
- Section modulus Wy = 2,880 x 10^3 mm^3
Step 1 -- Frequent load for fatigue: Frequent wheel load: Q_fat = (220 + 200) / 4 = 105 kN per wheel (crab positioned for maximum bending) Frequent bending moment M_fat = 105 / 220 x 495 = 0.477 x 495 = 236.2 kN.m
Step 2 -- Stress range: Delta_sigma = M_fat / Wy = 236.2 x 10^6 / (2,880 x 10^3) = 82.0 MPa
This is the stress range per crane passage. Note that for Class S4, the crane is assumed to cross the beam approximately 20 times per working day, 250 days per year, for 50 years = 250,000 passages. However, the total number of stress cycles includes all stress ranges (not just the maximum range) -- the stress spectrum includes partial-load passages, unladen crane returns, and crab traverses.
Step 3 -- Damage equivalent factor: From EN 1993-6 (EN 1993-1-9 Annex A for cranes), for Class S4 with a typical stress spectrum: lambda approximately 0.80 (this is an indicative value -- the actual lambda must be determined from the crane classification and the specific stress spectrum)
Delta_sigma_E,2 = 0.80 x 82.0 = 65.6 MPa
Step 4 -- Fatigue verification at critical details:
Detail 1 -- Bottom flange at mid-span (Category 160, plain rolled surface): gamma_Ff x Delta_sigma_E,2 / (Delta_sigma_C / gamma_Mf) = 1.0 x 65.6 / (160 / 1.00) = 65.6 / 160 = 0.41 << 1.0 -- OK.
Detail 2 -- Rail attachment weld (Category 80, discontinuous fillet weld): 65.6 / (80 / 1.00) = 65.6 / 80 = 0.82 < 1.0 -- OK but governing. This detail has 34% utilisation remaining, which is adequate for the 50-year design life.
Detail 3 -- Beam end cope at connection (Category 71): Stress range at end of beam (shear governs, but check stress at cope): At the cope location, the bending stress is approximately 10% of mid-span = 8.2 MPa (elastic moment distribution for UDL). 8.2 / (71 / 1.00) = 0.12 -- OK.
Verify shear fatigue: For shear stress from crane passage, the shear fatigue detail category for the web at the cope is Category 80 (plain web away from welds). Delta_tau_E,2 approximately 0.80 x 30 = 24 MPa (shear range) 24 / (80 / 1.00) = 0.30 -- OK.
Conclusion: The runway beam has adequate fatigue life for the 50-year design period. The governing detail is the rail attachment weld at Category 80 with 82% utilisation. If the crane classification were S6-S7 (twice the cycles), the utilisation would be 82% x (2)^0.333 = 103% and the beam would require a higher detail category or cross-section upgrade.
Design Resources
- UK Fatigue Assessment Guide -- Code overview and safe-life vs damage-tolerant
- UK Crane Runway Beam Design -- Complete crane beam to EN 1993-6
- UK Weld Design Guide -- Weld sizing and detail categories
- UK Weld Inspection Guide -- NDT requirements for fatigue-critical details
- UK Bolt Capacity Tables -- Bolted connection fatigue (Category F bolts)
- All UK Steel Design References -- complete library
Frequently Asked Questions
When does fatigue govern instead of static strength in UK design?
Fatigue governs when the stress range from repeated loading exceeds the CAFL of the governing detail over a sufficient number of cycles. As a rule of thumb: if the number of design cycles exceeds 10,000 and the maximum stress range exceeds 26 MPa (the cut-off limit for Category 160), fatigue should be checked. For building structures without cranes, fatigue rarely governs because the number of full load-unload cycles from imposed loads over a 50-year life is below 10,000. Warehouses, factories, and industrial buildings with overhead cranes are the primary building applications requiring fatigue assessment.
What is the most effective way to improve fatigue life at the design stage?
Improving the detail category is the single most effective measure because fatigue strength enters as the cube (m = 3). Upgrading a detail from Category 71 to Category 100 improves fatigue life by (100/71)^3 = 2.8 times. Practical upgrades include: grinding weld toes smooth (upgrades 1-2 categories), specifying automatic welding with no stops (longitudinal fillets from 80 to 100), moving the attachment away from the tension zone, eliminating unnecessary welded attachments, and reaming drilled holes to remove the HAZ. Post-weld treatment (TIG dressing, hammer peening, UIT) can upgrade by 2-3 categories for details loaded in tension.
How does EN 1993-1-9 handle multi-axial fatigue?
EN 1993-1-9 Clause 8(4) provides a combined damage check for normal and shear stress ranges. The normal stress damage D_d,sigma is cubed (reflecting m = 3 slope) and the shear stress damage D_d,tau is raised to the fifth power (reflecting m = 5 slope for shear). The sum must not exceed 1.0. In practice, for most UK crane runway beams, either normal stress damage entirely governs (at mid-span) or shear damage entirely governs (at supports). Combined damage checks are typically required only for complex details such as hollow section joints and welded stiffener intersections.
Do I need to consider fatigue for wind loading on UK buildings?
For most UK buildings, no. Wind-induced fatigue is only a consideration for structures that are sensitive to wind-induced vibration -- tall slender structures (h/d > 8), guyed masts, chimneys, lighting columns, and sign gantries. The UK NA to EN 1991-1-4 provides guidance on vortex shedding and galloping. If the building is a standard braced or moment-resisting frame with natural frequency above 1 Hz (almost all multi-storey buildings satisfy this), wind-induced fatigue can be deemed satisfied without calculation. Portal frame buildings in exposed locations may require a fatigue check of the eaves haunch and apex connections if vortex shedding from the cladding rails is a concern.
Educational reference only. All design values are per BS EN 1993-1-9:2005 + UK National Annex and BS EN 1993-6:2007 (crane supporting structures). Fatigue assessment must be based on the actual stress spectrum and crane classification for the specific project, not generic values. Designs must be independently verified by a Chartered Structural Engineer registered with IStructE or ICE. Results are PRELIMINARY -- NOT FOR CONSTRUCTION without independent professional verification.