EN 1993-1-9 Fatigue Assessment Calculator — S-N Curve & Miner Rule

Q: How does the Palmgren-Miner rule work?

For variable-amplitude loading, the cumulative damage sum D = Σ(n_i/N_i) must not exceed 1.0. Each band contributes n_i/N_i where n_i is the applied cycles and N_i is the allowable cycles from the S-N curve at that stress range. The γ_Mf factor is applied by dividing Δσ_C before computing N_i.

Q: What is γ_Mf and how do I choose it?

γ_Mf is the partial factor for fatigue strength per EN 1993-1-9 Table 3.1. Use 1.00 for damage-tolerant details (inspectable and repairable) with low failure consequence. Use 1.35 for safe-life design with high consequence of failure (e.g. primary bridge girder). Intermediate cases use 1.15.

Q: What is the CAFL (Δσ_D)?

The constant-amplitude fatigue limit (CAFL) Δσ_D = Δσ_C × (2/5)^(1/3) ≈ 0.737 × Δσ_C is the stress range below which constant-amplitude cycles cause no damage. For variable-amplitude loading, cycles between Δσ_L and Δσ_D use the shallower m=5 slope.

Q: What detail category should I use for a transverse butt weld?

Per EN 1993-1-9 Table 8.3: full penetration weld ground flush and NDT-OK → Δσ_C = 112 MPa; full penetration with reinforcement ≤10% → 100 MPa; backing strip removed → 90 MPa; backing strip left in → 80 MPa; partial penetration → 71 or 63 MPa. The crane gantry worked example on this page uses detail 80 (backing strip left in).

Q: How do I assess crane gantry runway beams?

For crane runway girders, use the λ-method (EN 1993-1-9 §6.2): Δσ_E,2 = λ × Δσ_p where Δσ_p is the stress range from a single crane passage and λ is a damage-equivalence factor from Annex F (or project specification). Then compare Δσ_E,2 ≤ Δσ_C/γ_Mf. Class Q1 cranes typically use λ ≈ 0.52, Class Q3 λ ≈ 0.79. The default worked example on this page illustrates this approach.

Assessment Inputs

Detail group

Select the structural category that best matches your detail (Tables 8.1–8.10).

Detail category

Δσ_C is the characteristic stress range at N = 2×10⁶ cycles. Higher Δσ_C = better fatigue class.

Partial safety factor γ_Mf (Table 3.1)

1.00 damage-tolerant/low; 1.15 damage-tolerant/high or safe-life/low; 1.35 safe-life/high.

Assessment approach

Constant amplitude: single Δσ + N_Ed cycles. Variable amplitude: up to 10 stress-range blocks, Palmgren-Miner Σ(n_i/N_i) ≤ 1.0.

Design stress range Δσ_Ed (MPa)

Constant-amplitude applied stress range. Include γ_Ff = 1.0 for steel (EN 1993-1-9 §3.2).

Applied cycles N_Ed

Number of stress-range cycles over the design life. Typical crane gantry 2×10⁶, highway bridge 2×10⁶.

Fatigue Results

412.0%

Utilisation η η

FAIL — fatigue limit exceeded

Δσ_C (MPa at 2×10⁶) 80 MPa

Δσ_D — CAFL at 5×10⁶ (MPa) 58.94 MPa

Δσ_L — cut-off at 10⁸ (MPa) 32.37 MPa

Allowable cycles N_R 485,450

S-N branch m3

Upgrade detail class, reduce stress range, or reduce cycle count.

① Detail category Δσ_C
Δσ_C = 80 MPa (detail T8.3-80)

② Design strength Δσ_C,d = Δσ_C / γ_Mf
Δσ_C,d = 80 / 1.35 = 59.26 MPa

③ CAFL Δσ_D (at N_D = 5×10⁶)
Δσ_D = 80 × (2/5)^1/3 = 58.94 MPa

④ Cut-off Δσ_L (at N_L = 10⁸)
Δσ_L = 58.94 × (5/100)^1/5 = 32.37 MPa

⑤ S-N branch selection
Slope m=3 (N ≤ 5×10⁶)

⑥ Allowable cycles N_R
N_R = 485,450 cycles

⑦ Utilisation η = N_Ed / N_R (or D for spectrum)
η = 2000000 / 485450 = 4.1199

⑧ Result
✗ FAIL — η = 4.1199 > 1.00

γ_Mf values from EN 1993-1-9 Table 3.1. National Annexes (NL, FR, IT) raise the damage-tolerant floor to 1.15.

Export Calculation Report

Receive a formatted fatigue calculation note (EN 1993-1-9) by email.

Frequently Asked Questions

What is the EN 1993-1-9 S-N curve?

The S-N (stress range vs. cycles) curve for a detail category Δσ_C has two log-linear branches: slope m=3 for N ≤ 5×10⁶ cycles and slope m=5 for 5×10⁶ < N ≤ 10⁸. The constant-amplitude fatigue limit Δσ_D occurs at N_D = 5×10⁶ and the cut-off limit Δσ_L at N_L = 10⁸. Below the cut-off, stress cycles cause no damage.

How does the Palmgren-Miner rule work?

For variable-amplitude loading, the cumulative damage sum D = Σ(n_i/N_i) must not exceed 1.0. Each band contributes n_i/N_i where n_i is the applied cycles and N_i is the allowable cycles from the S-N curve at that stress range. The γ_Mf factor is applied by dividing Δσ_C before computing N_i.

What is γ_Mf and how do I choose it?

γ_Mf is the partial factor for fatigue strength per EN 1993-1-9 Table 3.1. Use 1.00 for damage-tolerant details (inspectable and repairable) with low failure consequence. Use 1.35 for safe-life design with high consequence of failure (e.g. primary bridge girder). Intermediate cases use 1.15.

What is the CAFL (Δσ_D)?

The constant-amplitude fatigue limit (CAFL) Δσ_D = Δσ_C × (2/5)^(1/3) ≈ 0.737 × Δσ_C is the stress range below which constant-amplitude cycles cause no damage. For variable-amplitude loading, cycles between Δσ_L and Δσ_D use the shallower m=5 slope.

What detail category should I use for a transverse butt weld?

Per EN 1993-1-9 Table 8.3: full penetration weld ground flush and NDT-OK → Δσ_C = 112 MPa; full penetration with reinforcement ≤10% → 100 MPa; backing strip removed → 90 MPa; backing strip left in → 80 MPa; partial penetration → 71 or 63 MPa. The crane gantry worked example on this page uses detail 80 (backing strip left in).

How do I assess crane gantry runway beams?

For crane runway girders, use the λ-method (EN 1993-1-9 §6.2): Δσ_E,2 = λ × Δσ_p where Δσ_p is the stress range from a single crane passage and λ is a damage-equivalence factor from Annex F (or project specification). Then compare Δσ_E,2 ≤ Δσ_C/γ_Mf. Class Q1 cranes typically use λ ≈ 0.52, Class Q3 λ ≈ 0.79. The default worked example on this page illustrates this approach.