Fatigue Spectrum Analyzer — methodology & traceability

Parsing and conditioning

The parser handles comma, semicolon and tab delimiters, quoted cells, header rows and decimal commas; the user maps which column is the stress. Conditioning is a short, fully disclosed list: missing or non-numeric samples are dropped or linearly interpolated; an optional detrend removes the mean or a linear drift; a multiplicative scale converts units (microstrain to MPa via the modulus). One step is off by default on purpose: despiking. In fatigue the largest range often dominates the damage, and an automatic outlier filter can silently delete the governing event. When the user enables it, every removed sample is recorded with its index and value, and the report carries the filter setting and the removal count. Every operation that alters the signal emits an audit token; a step that changed a fatigue answer without leaving a trace would be a defect.

Counting per ASTM E1049

The conditioned series is reduced to turning points and counted. The default counter is rainflow per ASTM E1049-85 (Reapproved 2011) §5.4.4, including its treatment of the residue — what cannot be paired into closed cycles is counted as half cycles per the standard's own steps, not by a convention of ours. Three alternatives are offered, each labelled with its clause: the §5.4.5 simplified rainflow for repeating histories (full cycles only), §5.4.3 range-pair counting, and the reservoir method of EN 1993-1-9 Figure A.1 c).

The reservoir counter doubles as a structural cross-check: it is an independent implementation (a watershed algorithm, not the rainflow stack in disguise), and the automated suite asserts that the two standard-sanctioned counters produce identical cycle multisets — ranges and means — to within 1×10⁻⁹ on a 5 001-point reference history. The suite also reproduces ASTM E1049's own worked example (Table X1.3) cell for cell at machine precision.

Binning, and the 1 % honesty bound

The counter is exact; what travels into the assessment is a binned spectrum of 16, 32 or 64 bins. The bin edges are logarithmic in range, because damage rises with roughly the cube of stress and resolution belongs where the damage lives. Each bin is represented by the single stress range that would cause the same damage as the cycles inside it, computed on the standard's primary slope (m = 3). Cycle counts round up, never down — rounding must never delete a damaging cycle. The residual error of the whole step is then measured, not assumed: at ingest the exact damage of the unbinned cycles is recorded, and the assessment compares its binned damage against that reference, noting agreement and warning whenever the difference exceeds 1 %. Because counting happens before binning, results can differ slightly from tools that bin the signal into levels first — pre-binning quantises turning points and can destroy small cycles. The difference is disclosed rather than hidden.

Provenance — proof without the data

The record itself never leaves the browser and never reaches Xarpis. What the assessment carries instead is a SHA-256 fingerprint of the file's bytes, the number of parsed rows, and the ordered audit tokens of every conditioning and counting step — each of which the report expands into a clause-cited sentence. A reviewer holding the original file can therefore verify exactly which record was assessed and reproduce the count; a reviewer without the file can verify the process but not reconstruct the data, which is the intended boundary. A shared link transports the binned spectrum and the provenance, never the record — a recipient sees an explicit statement to that effect.

EN 1993-1-9:2005

Curve family: the §7.1 two-slope curves, anchored at the detail category Δσ_C at 2×10⁶ cycles, falling at m = 3 to the constant-amplitude fatigue limit Δσ_D at 5×10⁶, then at m = 5 to the cut-off Δσ_L at 10⁸ cycles. Format: Palmgren-Miner damage accumulation per Annex A.5, D_d ≤ 1,0, with γ_Ff applied to every stress range and γ_Mf dividing the strength. Limits and factors: γ_Mf ships at the recommended Table 3.1 values (damage tolerant 1,00/1,15, safe life 1,15/1,35 by consequence); §8(1) caps the largest ranges at 1,5·f_y and 1,5·f_y/√3; §8(3) combines direct and shear.

Deliberately precise behaviours worth knowing. The CAFL trichotomy is the standard's own: a spectrum entirely below Δσ_D accumulates no damage (§7.1(2)); a spectrum with ranges above and below it is assessed on the extended two-slope curve (§7.1(3)); ranges below the cut-off contribute exactly zero. Asterisk details (Δσ_C*) default to their tabulated, already-reduced category, with §7.1 NOTE 3's alternative — one category up with the CAFL redefined at 10⁷ cycles — as an explicit option. The §7.2.2 size effect reduces the category via k_s. The §7.2.1 mean-stress benefit applies only to non-welded or stress-relieved details, and only in signal mode, because binned spectra carry no cycle means. Details whose table specifies a different slope (Table 8.7's m = 5 lattice-node categories; Table 8.5 detail 10's m = 8 stud per EN 1994-2) are assessed on single-slope curves with no invented fatigue limit or cut-off — the literal, conservative reading of tables that define nothing below the category.

AISC 360-22 Appendix 3

Curve family: Eq. A-3-1M's allowable stress range, F_SR = 6900·(C_f/n_SR)^0,333 in MPa — and, in US units, the printed ksi form Eq. A-3-1, F_SR = 1000·(C_f/n_SR)^0,333, used exactly rather than converted, so the route is exact in both systems. Category constants C_f and thresholds F_TH come from Table A-3.1 (categories A–E′, plus G for bolts in tension per §3.4(b)); shear on the weld throat is always category F (Eq. A-3-2). Format: an allowable-STRESS-range verification — every band of the spectrum is checked against F_SR at its own lifetime cycle count, with F_TH as a per-band floor. Limits: no evaluation is required at or below 20 000 cycles, and §3.1 caps the stress due to peak cyclic loads at 0,66·F_y — a cap that cannot be derived from stress ranges and is therefore stated for separate verification, never silently assumed satisfied.

What is deliberately different: no damage sum is ever printed on this route. Appendix 3 defines no variable-amplitude accumulation rule, and the tool does not invent one — the verdict is the governing band against its F_SR, the remaining life is the inversion of Eq. A-3-1/A-3-1M for the governing band, and interaction between bands is stated as not covered by the code. The two formats genuinely disagree on some spectra (a spectrum can fail a Miner sum while every band passes its own F_SR); the automated suite asserts that divergence so a future “simplification” fails loudly.

DNV-RP-C203 (2011)

Curve family: the Tables 2-1/2-2/2-3 classes (B1…W3, plus T for tubular joints), kept in their native log-intercept form log N = log ā − m·log Δσ so reported intermediates match Eq. (2.4.1) as a checker reads it. The design curves are mean minus two standard deviations of the test data — 97,7 % probability of survival — and their inherent failure criterion is crack growth through the thickness: a “failure” on this route is a through-thickness crack, not a detectable surface crack. Format: Palmgren-Miner per §2.2, with the acceptance D ≤ 1/DFF — the Design Fatigue Factor scales the allowable damage down for consequence and inspectability.

What is deliberately different: the knee moves with the environment — the slope changes at 10⁷ cycles in air but at 10⁶ in seawater with cathodic protection, and free corrosion is a single m = 3 slope with no fatigue limit at all, so every cycle damages. The §2.11 omission criterion (analysis may be omitted below the fatigue limit at 10⁷) uses the TABLE's own fatigue-limit column, reduced by DFF^0,33 when DFF exceeds 1 — not a value re-derived from the curve, which differs in the last digits and would change verdicts at the boundary. The Eq. (2.4.3) thickness correction multiplies every stress range by (t/t_ref)^k on the stress side, with each class carrying its own exponent k. The route defines no pure-shear curves — details are classified for the principal stress direction per Appendix A — so a supplied shear spectrum is flagged as unassessed rather than silently dropped.

IIW-1823-07 (2008)

Curve family: FAT classes — the characteristic stress range at 2×10⁶ cycles — for welded details under normal stress (m = 3, knee at 10⁷), base material (m = 5, knee at 10⁷) and shear (m = 5, knee at 10⁸). Below the knee the variable-amplitude column of Table {4.3}-2 applies: the curve continues at m₂ = 2·m₁ − 1. Format: Palmgren-Miner with the recommended variable-amplitude limit D ≤ 0,5 (§4.3.1, Table {4.3}-1) — deliberately the strictest Miner acceptance here, because the recommendations themselves state D = 1 can be non-conservative. The Eq. (4.1) partial factors are taken as γ_F = γ_M = 1,0, disclosed in the assumptions; the recommendations' own alternative — stepping the FAT class down — remains available to the user.

What is deliberately different: the constant-amplitude column is unrepresentable. Table {4.3}-2 carries separate constant-amplitude (slopes up to m = 22) and variable-amplitude columns whose constants differ by up to roughly 32 orders of magnitude; a rainflow spectrum is variable amplitude by definition, so this route hardcodes the variable-amplitude slopes and the wrong-column mistake cannot be made. Knee stresses are recomputed from FAT·(2×10⁶/N_knee)^1/m rather than transcribed, which matches the tabulated ladder to its own 0,1 MPa rounding and defeats a known misprint in circulating copies. Combined normal and shear loading is verified by Eq. (4.6) against the comparison value CV = 1,0 (proportional) or 0,5 (non-proportional).

Which checks carry the verdict

The fatigue verification, the two stress ceilings, the combined criterion and the remaining-life check carry pass/fail verdicts and compete for the governing slot; the overall status is Pass only when every verdict-carrying check passes. Two checks are deliberately informational. The equivalent-stress-range check is the §8(2) format — the same acceptance as the damage sum, expressed on a stress scale — and the required-category check is an inverse solve of that same acceptance. Neither may carry a utilisation of its own, because a stress-scale ratio would out-govern the damage-scale sum whenever D is below 1 (D^1/3 exceeds D there): the governing check would then flatter every passing design. Where the two formats must agree — every bin on the equivalence slope — the engine verifies that they do, to 1×10⁻⁹, as a free internal-consistency check (Annex A.6, Eq. (A.3)).

A verdict from nothing is also refused: with zero stress ranges supplied, the verification checks report no result at all rather than a vacuous pass, and the overall status reads indeterminate until there is something to assess.

Unpacked: the four codes differ in safety format (partial factors, characteristic values, survival probability, allowable stress), in failure criterion (EN's design curves and DNV's through-thickness crack are not the same event), and in acceptance limit (1,0 · 1/DFF · 0,5 · a stress ratio). A bar at 0,8 on one route and a bar at 0,8 on another describe different quantities that happen to share a scale — each is meaningful only against its own code's acceptance at 1,0. And a code the user never classified the detail for is shown as “not configured” rather than run on a silently assumed equivalent class, because mapping a detail between taxonomies is an engineering judgement the tool attributes to its author instead of asserting.

The flagship cases, in words

• The anchor: category 71 loaded at exactly 71 MPa for exactly 2×10⁶ cycles with unit factors must give D_d = 1,0 exactly — the definition of a detail category, asserted with no tolerance.
• The factor chain: raising γ_Mf to 1,35 must scale that damage by exactly 1,35³ = 2,460375, because the factor enters the strength side of an m = 3 curve.
• The DNV moving knee: curve D in seawater with cathodic protection must change slope at 10⁶ cycles, not 10⁷ — a module that left the knee in the air position would miss by a factor of about 1,9 and fail the case.
• The IIW column guard: a mixed spectrum on FAT 80 must be assessed on the variable-amplitude column (m = 5 below the knee); the constant-amplitude m = 22 column would understate the case's damage sum by roughly a factor of ten (the below-knee term itself by three orders of magnitude), and the case fails loudly on it.
• The binning bound: a 1 500-cycle pseudo-random spectrum binned to 32 bins must reproduce the exact unbinned damage within 1 % — the transport-loss contract the signal pipeline is held to.

Beyond the validation registry, the automated test suite asserts the counting layer against the standards' own material: ASTM E1049's Table X1.3 rainflow example is reproduced to machine precision, the independent repeating-history rainflow (§5.4.5) and reservoir implementations must agree on identical cycle multisets to 1×10⁻⁹, the AISC-versus-Miner format divergence is pinned so the two can never be “unified”, and every pack input survives an SI↔US round trip with the engine result unchanged.

Automatic out-of-scope rules

Consolidated limitations

The tool starts from stress: it contains no load models, influence lines or finite-element analysis, and the supplied ranges are assumed to be the nominal (or modified nominal) stress at the assessed detail. It carries no stress-concentration-factor library and no hot-spot FE integration — EN Annex B's hot-spot categories are a category set, not an FE method. One stress channel and one crack-initiation site are assessed at a time. Damage accumulation is linear and order-independent: load-sequence and overload-retardation effects are outside the model. There is no fracture mechanics — the tool cannot assess a detected crack. Binned spectra are an approximation bounded at 1 % and disclosed. The codes' own scope limits apply and are stated in the assumptions: EN 1993-1-9 excludes seawater corrosion and member temperatures above 150 °C; AISC Appendix 3 assumes mild atmospheres and the same temperature bound. Detail figures are schematics with exaggerated thickness — never to scale.

Cycle counting is additionally traceable to ASTM E1049-85 (Reapproved 2011) — §5.4.4 and §5.4.5 rainflow, §5.4.3 range-pair — and to EN 1993-1-9 Figure A.1 c) for the reservoir method; those clauses are cited by the counting layer and by every conditioning-trail sentence in the report. Table 8.5 detail 10's stud shear curve is EN 1994-2's (Δτ_C = 90 at m = 8), cited where it is applied.