Fatigue spectrum assessment

Example project · Rev A

2026-09-12 05:48:37 UTC

SI (mm · kN · MPa)

EN 1993-1-9:2005 - cumulative damage (Annex A)

Assessment basis

Design code

EN 1993-1-9:2005

Assessment method

Safe life · high consequence of failure

$γ_{M} f$

1.35

$γ_{F} f$

1.00

$Δ σ_{C}$

71.0 MPa

$f_{y}$

355.0 MPa

Stress input

Binned spectrum · 8 bins

Cycles per spectrum repetition

263,000

Spectrum repetitions

Repetitions per year

Cycles over the assessed life

6,575,000

Schematic

The detail category was entered directly; no tabulated detail classification was selected, so no detail figure is shown. The classification is the user's responsibility (see Assumptions).

Governing summary

Governing check

Cumulative damage (Palmgren-Miner)

Utilisation

0.630 (63.0%)

Overall status

pass

FEA recommended

Checks

Check	Demand	Capacity	U	Status
Cumulative damage (Palmgren-Miner)	0.630	1.000	0.630	Pass
Direct stress: D_d = 0.630 from 6,575,000 cycles (25 repetitions of the spectrum). 80.9% of the damage comes from 1,800,000 of 6,575,000 cycles (4 of 8 bins); the top three bins alone cause 68.7%. 3,000,000 cycles fall below the cut-off limit and contribute exactly zero damage.
Equations used $D_{d} = \sum_{i} \frac{n _{E i}}{N _{R i}} \leq 1.0$ (EN 1993-1-9 Annex A.5 Eq. (A.1); A.6 Eq. (A.2)) $Δ σ_{R}^{m} N_{R} = Δ σ_{C}^{m} \cdot 2 \times 1 0^{6}$ (EN 1993-1-9 §7.1, Figures 7.1 & 7.2)
Equivalent stress range at 2×10⁶ cycles	48.0 MPa	52.6 MPa	-	Info
γ_Ff Δσ_E,2 = 48.0 MPa against Δσ_C/γ_Mf = 52.6 MPa - format ratio 0.912. Some cycles fall below the knee or cut-off, where the m = 3 equivalent-range format weighs them more heavily than the extended curve does. The format is conservative here; the damage accumulation of Annex A governs the verdict.
Equations used $Δ σ_{E, 2} = (\frac{\sum _{i} n _{i} Δ σ _{i}^{3}}{2 \times 1 0 ^{6}})^{1/3}$ (EN 1993-1-9 Annex A.6 (m = 3)) $\frac{γ _{F f} Δ σ _{E, 2}}{Δ σ _{C} / γ _{M f}} \leq 1.0$ (EN 1993-1-9 §8(2), Eq. (8.2))
Direct stress-range ceiling (1.5 f_y)	120.0 MPa	532.5 MPa	0.225	Pass
Largest supplied direct stress range 120.0 MPa against 1.5·f_y = 532.5 MPa. EN 1993-1-9 §8(1) applies this ceiling to nominal stress ranges due to frequent loads ψ₁·Q_k; the largest range of the supplied spectrum is taken as that value.
Equations used $Δ σ \leq 1.5 f_{y}$ (EN 1993-1-9 §8(1), Eq. (8.1))
Shear stress-range ceiling (1.5 f_y/√3)	-	-	-	Info
No shear stress ranges supplied - not applicable.
Combined direct + shear stress ranges	-	-	-	Info
Combined verification applies when direct and shear stress ranges act together (§8(3)); only one kind is supplied, and it is fully covered by the damage accumulation.
Equations used $(\frac{γ _{F f} Δ σ _{E, 2}}{Δ σ _{C} / γ _{M f}})^{3} + (\frac{γ _{F f} Δ τ _{E, 2}}{Δ τ _{C} / γ _{M f}})^{5} \leq 1.0$ (EN 1993-1-9 §8(3), Eq. (8.3))
Remaining fatigue life	-	-	0.630	Pass
The detail sustains 39.7 repetitions of the supplied spectrum before D_d = 1.0; 25 are demanded, leaving 14.7 in reserve. At 1 repetition per year: total life 39.7 years, remaining 14.7 years.
Equations used $R_{m a x} = \frac{D _{l i m}}{D _{d, rep}}$ (EN 1993-1-9 Annex A.5 (linear damage accumulation))
Required detail category	61.9 MPa	71.0 MPa	-	Info
The smallest detail category satisfying D_d ≤ D_lim is 61.9 MPa - category 63 is the nearest tabulated one at or above it. Passing tabulated categories: 160, 140, 125, 112, 100, 90, 80, 71, 63. Solved on the standard fatigue strength curves with the same γ_Mf and k_s as the assessment, for the direct-stress spectrum only.
Equations used $D_{d} (Δ σ_{C, req}) = D_{l i m}$ (EN 1993-1-9 §7.1 + Annex A.5 (inverse solve))

Data provenance

The stress-range spectrum was entered directly by the report author as binned ranges and counts; no measured record was processed. The derivation of the spectrum is the author's responsibility.

Stress-range spectrum and damage summation

All 8 bands are printed, including the zero-damage bands, so the cycle count reconciles with the counting record: 6,575,000 cycles over the assessed life. Each row restates the branch its endurance was computed on, so it can be re-derived from the clause with a calculator.

Δσᵢ	nᵢ (life)	N_Ri (branch)	dᵢ	Share
120.0 MPa	5,000	1.68×10⁵ (m = 3)	0.0297	4.7%
95.0 MPa	20,000	3.39×10⁵ (m = 3)	0.0589	9.4%
75.0 MPa	75,000	6.90×10⁵ (m = 3)	0.1088	17.3%
60.0 MPa	225,000	1.35×10⁶ (m = 3)	0.1670	26.5%
45.0 MPa	500,000	3.19×10⁶ (m = 3)	0.1566	24.9%
32.0 MPa	1,000,000	1.30×10⁷ (m = 5)	0.0768	12.2%
24.0 MPa	1,750,000	5.49×10⁷ (m = 5)	0.0319	5.1%
16.0 MPa	3,000,000	∞ (below cut-off)	0	0%
Σ	6,575,000		D_d = 0.6297	100%

Stress-range spectrum (EN 1993-1-9 Figure A.1 d))

Ranges descending against cumulative cycles over the assessed life. Ranges below the cut-off contribute no damage.

S–N curve and spectrum overlay

Design fatigue strength curve with the assessed spectrum

Design curve Δσ_C/γ_Mf
Spectrum bins (area ∝ cycles; darker = larger damage share)

Curve regenerated from the parametric constants of EN 1993-1-9 §7.1 (Δσ_D (CAFL) = 38.8 MPa; Δσ_L (cut-off) = 21.3 MPa). 1 band lies below the cut-off with no finite endurance and is not plotted.

Damage attribution

80.9% of the calculated damage arises from 4 of 8 stress bands, totalling 1,800,000 cycles out of 6,575,000 counted. The governing band is 60.0 MPa (26.5%). 3,000,000 cycles - 45.6% of the count - fall below the cut-off limit Δσ_L = 21.3 MPa and contribute no damage.

Damage Pareto

Damage share per band
Cumulative share

4 of 8 bands carry 81% of the damage. Both series share one axis: per cent of the total damage.

Remaining life and required detail category

Linear damage accumulation (EN 1993-1-9 Annex A.5): the allowable repetitions scale the supplied spectrum until the damage sum reaches the limit. The inverse solve reports the smallest detail category for which the spectrum passes, on the standard curves with the same γ_Mf and k_s.

$D_{d}$

0.6297 of 1.0

Allowable spectrum repetitions

39.7

Remaining repetitions

14.7

Total / remaining service life

39.7 / 14.7 years

$Δ σ_{C}, r e q$

≥ 61.9 MPa - smallest passing tabulated category: 63

Multi-code comparison

These results are not the same quantity. EN 1993-1-9 is a partial-factor format (γ_Ff on the ranges, γ_Mf on the strength); DNV-RP-C203's design curves are mean-minus-two-standard-deviation curves with 97,7 % probability of survival whose inherent failure criterion is crack growth through the thickness; IIW-1823-07 is characteristic with its own knee and a recommended Miner limit of 0,5 for variable amplitude; and AISC 360-22 Appendix 3 is an allowable-stress format with a threshold rather than a damage sum - its row reports the governing band against F_SR, not a D_d. A damage-scale utilisation and a stress-scale ratio also differ in kind (damage grows with roughly the cube of stress), so bar lengths are comparable only against each code's own acceptance at 1,0 - never against each other. The classifications are equivalent, not identical. Each code's class (EN detail category, AISC stress category, DNV S-N curve, IIW FAT class) was selected separately by the report author; mapping a detail across the taxonomies is an engineering judgement this comparison attributes to the author rather than asserts. Codes without a selected class are shown as not configured - they were not run on a silently assumed equivalent.

Route	Basis	Classification	Result	Verdict
EN 1993-1-9:2005 (active route)	partial factor, γ_Mf = 1.35	Cat. 71	D = 0.630 of 1.0	PASS
IIW-1823-07 (2008)	characteristic, variable amplitude, D ≤ 0,5	-	not configured - not run	-
DNV-RP-C203 (2011)	mean − 2σ (97,7 % survival), in air	-	not configured - not run	-
AISC 360-22 Appendix 3	allowable stress range with threshold F_TH	-	not configured - not run	-

Assumptions

The assessment assumes conditions inside EN 1993-1-9 §1.1 scope: structural steel to the EN 1993 series, no seawater-corrosion environment, and member temperatures not above 150 °C.
Supplied stress ranges are nominal (or modified nominal) stress ranges at the assessed detail per EN 1993-1-9 §6 - stress concentration factors for geometry not covered by the detail category are already included.
Damage accumulates linearly (Palmgren-Miner, EN 1993-1-9 Annex A); load-sequence and interaction effects are neglected.
The assessment addresses one crack-initiation site. Joints with several potential sites (each weld toe, weld ends, the weld throat) need one assessment per site, each with its own detail category.
The detail category (and any k_s size-effect parameters) are selected by the user from the standard's tables; the tool does not verify the classification against the actual joint geometry.
The assessment operates on the binned stress-range spectrum as supplied. For spectra entered directly, the fidelity of the binning (bin widths, counting method) is the responsibility of whoever produced the spectrum; for records counted in this tool, the binned damage is cross-checked against the unbinned count.

Source traceability

EN 1993-1-9 · 2005 (incl. corrigenda 2005/2009) · §7.1(2), §7.1(3), Figures 7.1 & 7.2
Fatigue strength curves: m = 3 to 5×10⁶ anchored at Δσ_C (2×10⁶); Δσ_D = (2/5)^1/3·Δσ_C; extended m = 5 branch to 10⁸ with Δσ_L = (5/100)^1/5·Δσ_D. Shear: m = 5 anchored at Δτ_C with Δτ_L = (2/100)^1/5·Δτ_C.
EN 1993-1-9 · 2005 (incl. corrigenda 2005/2009) · §7.1 NOTE 3, Figure 7.3
Δσ_C* details: tabulated one category lower; alternatively raised one category with the CAFL defined as the strength at 10⁷ cycles for m = 3.
EN 1993-1-9 · 2005 (incl. corrigenda 2005/2009) · §7.2.1, Figure 7.4
Mean-stress modification for non-welded / stress-relieved details: effective range = tensile portion + 0,6 × compressive portion.
EN 1993-1-9 · 2005 (incl. corrigenda 2005/2009) · §7.2.2, Eq. (7.1)
Size effect: Δσ_C,red = k_s·Δσ_C with k_s per the detail's row in Tables 8.1–8.10.
EN 1993-1-9 · 2005 (incl. corrigenda 2005/2009) · §3(7) NOTE, Table 3.1
Recommended γ_Mf: damage tolerant 1,00/1,15; safe life 1,15/1,35 (low/high consequence). NDP - recommended values shipped, user-overridable.
EN 1993-1-9 · 2005 (incl. corrigenda 2005/2009) · §8(1), Eq. (8.1)
Stress-range ceilings under frequent loads: Δσ ≤ 1,5·f_y and Δτ ≤ 1,5·f_y/√3.
EN 1993-1-9 · 2005 (incl. corrigenda 2005/2009) · §8(2), Eq. (8.2)
Equivalent-range verification format: γ_Ff·Δσ_E,2 / (Δσ_C/γ_Mf) ≤ 1,0 (and the shear analogue).
EN 1993-1-9 · 2005 (incl. corrigenda 2005/2009) · §8(3), Eq. (8.3)
Combined direct + shear ranges: cube of the direct utilisation plus fifth power of the shear utilisation ≤ 1,0.
EN 1993-1-9 · 2005 (incl. corrigenda 2005/2009) · Table 8.7; Table 8.5 detail 10
Table-specified curve slopes: the lattice-girder node categories of Table 8.7 are all assessed on m = 5 direct-stress curves; Table 8.5 detail 10 (welded stud shear connector) is assessed on Δτ over the stud's nominal cross section at category 90 with m = 8, per EN 1994-2. Neither table defines a CAFL or cut-off for these slopes - the single-slope lines are applied over the whole range.
EN 1993-1-9 · 2005 (incl. corrigenda 2005/2009) · Annex A.4 [normative]
Stress-range spectrum presented in descending order; peaks below 1 % of total damage and ranges below the cut-off may be neglected.
EN 1993-1-9 · 2005 (incl. corrigenda 2005/2009) · Annex A.5, Eq. (A.1)
Palmgren–Miner damage D_d = Σ n_Ei/N_Ri with applied ranges × γ_Ff and strength ÷ γ_Mf.
EN 1993-1-9 · 2005 (incl. corrigenda 2005/2009) · Annex A.6, Eqs. (A.2) & (A.3)
Verification formats: D_d ≤ 1,0, or γ_Ff·Δσ_E,2 ≤ ᵐ√D_d·Δσ_C/γ_Mf with m = 3.

Fatigue assessment of one structural detail from user-supplied stress ranges and detail classification. The detail classification, stress derivation and load history are inputs; the engine does not verify them.