About Fatigue Life Calculator (S-N & Miner)
The fatigue life calculator predicts the fatigue endurance of a structural detail under a variable-amplitude load spectrum using the S-N (Wohler) detail-category curves of Eurocode EN 1993-1-9 and Miner's linear cumulative-damage rule. For each block of constant-amplitude cycles it computes the allowable number of cycles, accumulates the partial damage, and reports whether the detail fails (D >= 1) along with the number of times the spectrum can be repeated before failure.
Enter the detail category dSigmaC (the reference fatigue strength at two million cycles, e.g. 90, 71, or 36 MPa), the S-N slope m (typically 3 for welded steel), and a load spectrum of stress-range and cycle-count blocks. The tool applies N = 2e6*(dSigmaC/dSigma)^m to each block, sums the damage, and compares the result against the constant-amplitude fatigue limit at five million cycles.
How It Works
- Pick the detail category dSigmaC (reference strength at 2e6 cycles) and the S-N slope m for the connection or member.
- For each stress-range block compute the allowable cycles N_i = 2e6 * (dSigmaC / dSigma_i)^m.
- Form the partial damage n_i / N_i for every block and sum them into Miner's damage D = sum(n_i / N_i).
- Compare D to 1.0: failure is predicted when D >= 1, and the spectrum can be repeated 1/D times; stress ranges at or below the CAFL = dSigmaC*(2/5)^(1/m) are flagged as non-damaging under constant amplitude.
Worked Example
A welded detail of category 90 (dSigmaC = 90 MPa at 2e6 cycles, slope m = 3) carries a spectrum of 1,000,000 cycles at a 60 MPa stress range. The allowable cycles are N = 2e6 * (90/60)^3 = 2e6 * 3.375 = 6,750,000. The partial (and total) Miner damage is D = 1,000,000 / 6,750,000 = 0.1481, well below 1.0, so the detail survives and the spectrum can be repeated 1/0.1481 = 6.75 times. The constant-amplitude fatigue limit is CAFL = 90*(2/5)^(1/3) = 66.3 MPa, so the 60 MPa range sits just below it. Doubling the stress range to 120 MPa cuts the life to one-eighth (N = 843,750) because life scales with dSigma^-3.
Formulas
- S-N curve (Basquin / detail category)
N = 2e6 * (dSigmaC / dSigma)^m- Constant S-N relation
N * dSigma^m = K = dSigmaC^m * 2e6- Miner's cumulative damage
D = sum(n_i / N_i) ; failure when D >= 1- Constant-amplitude fatigue limit
CAFL = dSigmaC * (2e6 / 5e6)^(1/m)- Spectrum life
repeats = 1 / D
Standards & References
- Eurocode EN 1993-1-9 Fatigue (detail categories 160..36)
- AISC Specification Appendix 3 fatigue design
- Palmgren-Miner linear cumulative-damage rule
- Basquin / Wohler S-N curve
Frequently Asked Questions
What is the detail category in fatigue design?
The detail category is the reference fatigue strength (stress range) of a structural detail at two million cycles, expressed in MPa. Eurocode EN 1993-1-9 tabulates categories from 160 down to 36 for different weld and connection geometries; a higher number means a more fatigue-resistant detail.
How does Miner's rule predict fatigue failure?
Miner's rule sums the fractional damage of each block of cycles, n_i / N_i, where N_i is the allowable life at that stress range. When the cumulative sum D reaches 1.0 the detail is predicted to fail. The spectrum can be repeated 1/D times before reaching that limit.
Why does doubling the stress range cut the life so dramatically?
For a slope m = 3 the S-N relation is N * dSigma^3 = constant, so life is inversely proportional to the cube of the stress range. Doubling the stress range therefore reduces the allowable cycles to one-eighth, which is why controlling stress range dominates fatigue design.
What is the constant-amplitude fatigue limit?
The CAFL is the stress range below which, under purely constant-amplitude loading, the detail can sustain effectively unlimited cycles without fatigue cracking. The calculator places it at five million cycles, CAFL = dSigmaC*(2/5)^(1/m), and flags any spectrum block at or below it.