Fatigue Limit — Endurance Limit, S-N Curve & AISC Appendix 3
The fatigue limit (or endurance limit) is the stress range below which a steel structural detail can theoretically sustain an unlimited number of load cycles without fatigue crack initiation. Steel is unique among most engineering materials in possessing a true endurance limit — aluminum and other non-ferrous metals do not, meaning every stress cycle causes cumulative damage.
Fatigue design condition: Δf ≤ CAFT → infinite life
Δf > CAFT → finite life, calculate N from S-N curve
PRELIMINARY — NOT FOR CONSTRUCTION. All content is for educational and reference use only. Must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any project.
S-N Curve (Wöhler Curve)
The S-N curve relates the applied cyclic stress range S (or Δf in AISC notation) to the number of cycles N to failure:
For N ≤ N_TH (CAFT threshold): Δf × N^(1/m) = C_F
For N > N_TH: Δf = CAFT (constant — infinite life)
Typical values (AISC Appendix 3): m = 3 (slope), N_TH ≈ 2×10⁶ cycles.
On a log-log plot:
- The curve is a straight line with slope −1/m from ~10⁴ to 2×10⁶ cycles
- At N = 2×10⁶, the curve flattens to horizontal — this is the CAFT
- Below CAFT, the material never fails regardless of cycles
AISC 360 Appendix 3 — Fatigue Design
AISC categorizes steel details by their fatigue sensitivity. Each category has a unique S-N curve defined by the constant CF:
| Category | CF (×10⁸) | CAFT (ksi) | Typical Details |
|---|---|---|---|
| A | 250 | 24.0 | Plain base metal, rolled surfaces, no attachments |
| B | 120 | 16.0 | Continuous full-penetration groove welds, ground flush |
| B′ | 61 | 12.0 | Continuous full-penetration groove welds, as-welded |
| C | 44 | 10.0 | Transverse groove welds with reinforcement removed |
| D | 22 | 7.0 | Fillet-welded attachments parallel to stress |
| E | 11 | 4.5 | Cover-plated beams, transverse stiffeners, cope holes |
| E′ | 3.9 | 2.6 | A514 steel with transverse attachments > 2 in long |
Key insight: A Category E detail (e.g., a welded transverse stiffener on a girder web) has only ~19% of the fatigue strength of plain rolled base metal (Category A). The drop from A (24 ksi) to E (4.5 ksi) demonstrates how severely welding attachments degrade fatigue performance.
Stress Range Design Approach
Fatigue is governed by stress range Δf = f_max − f_min — not by maximum stress alone. AISC uses the stress range approach:
Δf = f_max − f_min (for cycles where tension component governs)
For load combinations involving fatigue, the required strength is:
(Δf)_required ≤ (ΔF)_n where (ΔF)_n = (C_F / N)^(1/3) ≥ CAFT
Worked example — Crane runway girder, Category D:
A simply supported W24x55 crane girder has a bottom flange stress range of Δf = 8.0 ksi under the maximum wheel load (live load only, per AISC fatigue load combination). The flange has continuously welded rail clips (Category D: CF = 22 × 10⁸, CAFT = 7.0 ksi). Crane operates 50 cycles/day × 250 days/year × 30 years = 375,000 cycles.
(ΔF)_n = (22 × 10⁸ / 375,000)^(1/3) = (5,867)^(1/3) = 18.0 ksi
But (ΔF)_n ≥ CAFT = 7.0 ksi, so check: 8.0 ≤ 18.0? YES.
The design is adequate — the required strength is well below the allowable stress range at 375,000 cycles. For 30-year service with only 375,000 cycles, fatigue is not limiting.
If the same detail were subjected to 2 million cycles: (ΔF)_n = (22×10⁸/2×10⁶)^(1/3) = (1,100)^(1/3) = 10.3 ksi. But CAFT = 7.0 ksi governs for N > 2×10⁶ — so ΔF_n = 7.0 ksi, and 8.0 > 7.0 → FAIL.
High-Cycle vs Low-Cycle Fatigue
| Type | Cycles (N) | Stress Level | Strain Type | AISC Coverage |
|---|---|---|---|---|
| High-cycle (HCF) | > 10,000 | Below Fy (elastic) | Elastic | Appendix 3 |
| Low-cycle (LCF) | < 10,000 | May exceed Fy | Plastic | AISC 341 (seismic) |
AISC Appendix 3 addresses high-cycle fatigue only (N ≥ 10,000 cycles). Seismic applications (fewer than 100 large cycles into the plastic range) are governed by AISC 341's ductility and connection qualification requirements — a fundamentally different failure mechanism driven by plastic strain amplitude.
Frequently Asked Questions
Why does steel have a fatigue limit but aluminum does not?
Steel's body-centered cubic (BCC) crystal structure develops persistent slip bands that arrest crack growth below a threshold stress intensity. Aluminum (FCC) does not exhibit this arrest mechanism — microcracks continue to grow at any positive stress range, albeit very slowly. This is why aircraft structures (aluminum) require mandatory inspections and retirement lives, while steel bridges can be designed for infinite life.
How are variable-amplitude loads handled in fatigue design?
Miner's rule of linear cumulative damage: D = Σ(n_i/N_i), where n_i is the number of cycles at stress range level i, and N_i is the allowable cycles at that stress range. Failure is predicted when D = 1.0. AISC provides rainflow counting methods and simplified spectrum approaches for variable-amplitude loading (e.g., crane runway beams with different load magnitudes).
Does corrosion affect fatigue life?
Severely. Corrosion pits act as stress raisers (notch effect), reducing the effective CF constant by 30-50%. AISC Appendix 3 does not explicitly cover corroded members — for bridges and offshore structures, fatigue-sensitive details must be protected from corrosion (painting, galvanizing) and regularly inspected.
Related Terms and Pages
- Tensile Strength (Fu) — Definition & Values
- Yield Strength (Fy) — Definition & Values
- Notch Toughness — Charpy V-Notch & Temperature Effects
- Ductility — Elongation, R-Value & Seismic Performance
- AISC 360 Steel Design Code — Complete Guide
- Connection Design Workflow
Educational reference only. Fatigue design must follow AISC 360 Appendix 3 or the governing bridge code (AASHTO LRFD Bridge Design Specifications). Crane runway and machine-support structures require site-specific loading spectra. All designs must be independently verified by a licensed Professional Engineer.
Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.