Fatigue Spectrum Analyzer guide

You pick a design code route — EN 1993-1-9, AISC 360-22 Appendix 3, DNV-RP-C203 or IIW-1823-07 — and classify your structural detail in that code's own system. You then supply stress ranges one of three ways: a typed binned spectrum, a single constant-amplitude block, or an uploaded CSV record that is rainflow-counted in your browser. The engine assesses the spectrum on the route's own design S–N curves, attributes the damage to the stress ranges that cause it, solves the remaining life and the required detail category, compares the configured codes side by side, and builds a report a checker can audit clause by clause.

Three scope facts protect you from wrong expectations. First, the tool starts from stress: there are no load models, influence lines or FE — the stress ranges are yours to bring, and the detail classification tells you exactly which stress that must be. Second, it works in nominal stress — the stress a classified detail category expects — not hot-spot FE or notch stress. Third, each assessment covers one channel and one crack site. A joint usually has several potential crack sites — each weld toe, the weld ends, the weld throat — so run one assessment per site, each with its own category.

The free tier runs the full counting pipeline and shows the signal charts, the spectrum histogram and the S–N overlay. The platform subscription unlocks the damage attribution, remaining life, route comparison and the report — one flat subscription across every Xarpis calculator.

Cycles and stress ranges

Fatigue cracks grow because stress cycles up and down, not because it is high. What matters is the stress range — the distance from a trough to a peak — and how many times each range occurs. The absolute stress level (the mean) mostly does not matter for welded details, because welding locks in residual stresses near yield; EN 1993-1-9 §7.2.1 grants a mean-stress benefit only for non-welded or stress-relieved details, and this tool applies it only there.

The S–N curve

An S–N curve says how many cycles N a detail survives at a given stress range Δσ. On EN 1993-1-9's curves the anchor is the detail category Δσ_C — the range the detail survives for exactly two million cycles. Above the knee the curve falls with slope m = 3: halve the stress and the life multiplies by eight. At five million cycles sits the constant-amplitude fatigue limit (CAFL) Δσ_D: constant-amplitude loading entirely below it never fails. For variable-amplitude spectra the curve continues below the CAFL at the shallower slope m = 5, down to the cut-off limit Δσ_L at 10⁸ cycles — ranges below the cut-off contribute exactly zero damage.

Detail categories

The geometry of the joint decides its fatigue strength. A plain rolled plate is category 160; a badly detailed cover-plate end is category 36. Because life scales with the cube of stress, that spread of 160/36 ≈ 4.4 in stress is a factor of roughly 80 in life. Classifying the detail correctly is therefore the highest-leverage decision in the whole assessment — which is why this tool makes you do it before anything else.

Miner's rule

Real spectra mix many ranges, so the codes add the damage up linearly: each range consumes the fraction n/N of the life, and when the fractions sum to the code's limit the design life is used up. That is the Palmgren-Miner rule (EN 1993-1-9 Annex A.5). Safety factors are applied before the sum — γ_Ff on your stress ranges, γ_Mf on the detail's strength.

Variable amplitude, and why counting exists

A measured stress history is not a list of cycles — it is a wiggly line. Before Miner's rule can add anything up, someone has to decide what counts as one cycle in that line. That is what rainflow counting does, and it is standardised (ASTM E1049) precisely so two engineers get the same spectrum from the same record. Section 7 shows how it works.

The detail category is not just a strength number — it comes with a stress specification. A bolted detail wants the stress on the net section, through the holes. A weld-root detail wants the stress computed on the weld throat, not in the plate. A lattice-node detail wants the stress in the brace, not the chord. Enter the stress first and you can silently bring the wrong one; classify first and the tool can tell you exactly what to bring.

If you come from an FE post-processor or a tool like IDEA StatiCa, this order can feel backwards — there, the stresses already exist, so upload comes first. Xarpis is the opposite: you supply the stress, so classification comes first and the stress request is precise.

1. 1

   Set the assessment basis

   Pick the design code route (EN 1993-1-9, AISC 360-22 Appendix 3, DNV-RP-C203 or IIW-1823-07), the assessment method and the partial factors.

2. 2

   Classify the structural detail

   Find the detail category with the finder, browse the tables, or enter the code's own class directly. The result tells you which stress to bring.

3. 3

   Bring the right stress

   Obtain the stress ranges the detail's stress specification asks for — nominal stress at the assessed section — from your own analysis, measurement or FE model.

4. 4

   Build the spectrum

   Type a binned stress-range spectrum, enter a constant-amplitude block, or upload a CSV record for rainflow counting in the browser.

5. 5

   Read the assessment

   Review the spectrum histogram, the S–N overlay, the damage attribution, the remaining life and the seven checks with their clause citations.

6. 6

   Issue the report

   Review the warnings and assumptions, then export the audit-grade report with the full provenance trail.

Not sure of the category yet? Screening mode runs the whole check at the safest category that could apply — if your spectrum passes at category 36, the exact classification never mattered and you are done. If you already know your detail, type it into the direct-entry box (“71”, “8.4.6”, “cover plate”) or browse the tables with search and filters. If you need to work it out, the finder asks plain-language questions about observable facts — “was the weld ground flush?”, “does the plate width change?” — never about code jargon. Every question has an “I'm not sure” answer that routes to the conservative branch, and no path is longer than six questions.

The result screen gives you four things: the category with the standard's own citation (“Table 8.4 detail 1”); the detail figure drawn at your dimensions; the stress specification — which stress, at which section, this category expects; and the detail's requirements, which flow into the report's assumptions so a checker sees what you accepted. If you stay unsure between two categories, the sensitivity note shows what the choice costs — the damage at category 71 versus category 90 — so you can decide whether the uncertainty is worth resolving.

On the other routes there is no finder, by design: you enter the code's own class directly — AISC stress category, DNV S-N curve and environment, IIW FAT class. Those codes publish their own catalogues, and the classification stays your judgement, attributed as such in the comparison and the report.

The spectrum's time base is explicit: the bins hold cycles per repetition of the spectrum, and a separate field says how many repetitions the design life demands. Give the optional repetitions-per-year rate and every life answer is also stated in years. This split keeps an annual load spectrum readable — the bins describe one year, the repetitions count the years.

Shear stress ranges have their own spectrum, because the codes treat shear separately. On the EN route shear is assessed once you set Δτ_C (100 or 80 per Figure 7.2), with the §8(3) combined check when both act together. On IIW you set a shear FAT class. On AISC shear on the weld throat is always category F. DNV assesses no pure shear at all — its classes are defined for the principal stress direction, and a supplied shear spectrum is flagged as unassessed rather than silently dropped.

The EN route also polices the boundary of high-cycle fatigue: §8(1) caps the largest direct range at 1,5·f_y and the largest shear range at 1,5·f_y/√3. Trip either ceiling and you are outside the regime these curves describe — the check fails and tells you so rather than extrapolating.

What conditioning does — and what it refuses to do

Parsing handles comma, semicolon and tab delimiters, decimal commas, and a header row; you map which column is the stress. Conditioning then handles missing samples (drop or interpolate), an optional detrend, and unit scaling — a strain record in microstrain becomes stress via your Young's modulus. One filter is deliberately OFF by default: despiking. In fatigue the largest range often dominates the damage, so an automatic despike can quietly delete the answer. If you switch it on, every removed sample is listed with its index and value for your review, and the report records the filter setting and the removal count.

What rainflow counting is

A stress history usually carries two scales at once: slow, large excursions with fast, small oscillations riding on them. Simple peak counting sees only the small wiggles and misses the big slow cycle — which is usually where the damage is. Rainflow counting pairs each small excursion into a closed loop, counts it as one full cycle, removes it, and lets the large underlying cycle emerge whole. What cannot be paired at the end — the residue — is settled by the standard, not by us: the default method counts it as half cycles per ASTM E1049 §5.4.4.

Four counting methods are offered, each labelled with its clause: rainflow per ASTM E1049 §5.4.4 (the default), the §5.4.5 simplified rainflow for repeating histories (full cycles only — right when your record is one duty block that repeats), §5.4.3 range-pair counting, and the EN 1993-1-9 Figure A.1 c) reservoir method as a same-standard cross-check. The repeating-history rainflow (§5.4.5) and reservoir counters are two independent implementations that must agree — the test suite holds them to equality within 1×10⁻⁹ (the §5.4.4 default differs from both only in how it counts the residue, as half cycles).

Binning, disclosed

The counter itself is exact. What travels into the assessment is a binned spectrum — 16, 32 or 64 bins (default 64) with logarithmic edges, because damage concentrates where stress is high. Each bin is represented by the single range that would cause the same damage as the cycles inside it (computed on the standard's primary slope, m = 3), and cycle counts round up, never down — rounding must never delete a damaging cycle. The tool then cross-checks the binned damage against the exact unbinned count and warns if the difference ever exceeds 1 %. Because Xarpis counts first and bins second, its answers can differ slightly from tools that bin the signal before counting — count-then-bin is the more accurate order, and the difference is disclosed rather than hidden.

1. The counted record (signal mode): the trace with its turning points, the reduction strip (samples → turning points → cycles), the rainflow matrix, and — if despiking was on — every removed sample listed for review.
2. The spectrum histogram, drawn the way EN 1993-1-9 Figure A.1 d) draws it: ranges descending, each band as wide as its share of the cumulative cycle count. A spectrum dominated by one giant band is visible at a glance.
3. The S–N overlay — the money chart. Your bins are plotted on the route's design curve at their own endurance. A point above the line is consuming life faster than the curve allows at that count; a point below it has margin. The ghost ladder shows the neighbouring categories, so you can see what one classification step is worth, and the toggle switches between the design curve (γ_Mf applied) and the unfactored one.
4. Damage attribution (subscription; Miner routes only — the AISC format defines no damage to attribute): the Pareto of damage by bin, and the single most useful sentence the tool produces — for Example 1 below, 84.0% of the damage comes from 6,037,500 of 6,080,750 cycles. What to do with it: chase the machine state, duty cycle or resonance that produces those few bins, because that is where the life is going.
5. Remaining life (subscription): allowable and remaining repetitions, in years when you gave a rate. Section 9 explains how to act on it.
6. Route comparison (subscription): each configured code's own verdict, with the non-commensurability caveats attached. The four results are not the same quantity — a damage-scale utilisation and a stress-scale ratio differ in kind — so bars are only comparable to each code's own 1.0. Unconfigured codes say so explicitly rather than showing a silently defaulted bar.

The seven checks

Two checks are deliberately informational — the equivalent-range format and the required-category solve carry no pass/fail of their own. Both express the same acceptance the damage sum already carries, on a stress scale; letting a stress-scale ratio compete for the governing slot would let it out-govern the damage sum whenever D is below 1 (because D^1/3 is larger than D there). The governing check and the overall status always come from the checks that carry the code's own verdict.

Interpreting the number

A damage sum is a used-up fraction of the stated design life — always of the stated life, never of forever. D_d = 0.3 means the spectrum, repeated as declared, consumes 30 % of the design life: real margin. D_d = 0.95 passes, but one revision of the load assumptions can flip it; treat it as a design at its limit. And D_d < 1 is not “safe forever” — it is “the declared repetitions fit”. Change the repetitions and the verdict changes with them.

When to distrust the answer: a utilisation near 1.0 (small modelling choices now decide the verdict); endurances below 10⁴ cycles (the tool warns — the curves are extrapolated there); a spectrum whose damage is dominated by one giant cycle (verify that cycle is real, not an instrumentation spike); and any despiked samples you did not personally review.

The life check divides the route's damage limit by the damage one repetition of your spectrum causes: that is the allowable number of repetitions. Subtract what the design life demands and the remainder is your reserve — in years, when you gave a repetitions-per-year rate. On the AISC route, which has no damage sum, the life is the point where the governing band meets its own allowable stress range instead.

The required-category solve is a failed check turned into a specification: the smallest detail category that would pass this exact spectrum, solved on the same curves with the same factors, then snapped to the standard's real ladder. In Example 1 below the solve reports that any category from 63 upward passes — so if the detail had classified one step worse, the design would still work.

The design levers, with honest arithmetic

On the m = 3 branch (the caveat: these ratios hold only there), damage scales with roughly the cube of stress. That cuts both ways: a 20 % stress reduction roughly doubles the life, and a 20 % life shortfall needs only about 6 % less stress. Improving the detail one category step (a factor ≈ 1,12 in strength) buys about 1.4× life. Moving from safe life to damage tolerant (γ_Mf 1,35 → 1,15, Table 3.1) is worth about 1.6× — but damage tolerant is an inspection commitment, not a preference: it is only valid where a prescribed inspection and maintenance regime will actually detect cracks before they matter.

Example 1 — EN route, typed spectrum

A category 71 welded attachment on a safe-life, high-consequence basis (recommended γ_Mf = 1,35, Table 3.1), carrying an annual four-band spectrum for a 25-year design life. The inputs, in full:

Walk the numbers. The design curve is anchored at Δσ_C/γ_Mf = 71/1,35 = 52.59 MPa, with the CAFL at 38.75 MPa and the cut-off at 21.28 MPa. The three largest bands (110, 78 and 52 MPa) sit on the m = 3 branch; the 30 MPa band falls below the CAFL and is assessed on the extended m = 5 branch. Over 25 years the damage fractions add to D_d = 0.546 — the design passes with visible margin, and the damage sum is the governing check.

The attribution is the lesson: the smallest band — 30 MPa, 5,750,000 cycles over the life — carries 58.6% of the damage, because sheer count beats amplitude once every band is above the cut-off. The remaining life confirms it: 45.8 allowable years against 25 demanded leaves 20.8 in reserve. And the required-category solve reports 61.6 MPa as the smallest passing category — tabulated category 63 or better works.

Example 2 — signal mode, end to end

This example runs the actual downloadable sample record through the actual pipeline at render time — parsing, counting, binning and assessment are the same code the browser runs. To reproduce it, download the sample file from the dropzone and upload it back.

1. Parse: 400 data rows with columns time_s and stress_MPa; the stress column is mapped automatically.
2. Condition: nothing to fix — no missing samples, no detrend, no scaling, despike off. The audit trail records only the counting step.
3. Reduce and count: 400 samples become 89 turning points; rainflow per ASTM E1049 §5.4.4 extracts 44 cycles (half cycles at 0,5), the largest with a range of 138.2 MPa.
4. Bin: the counted cycles fill 24 logarithmic bins (64 requested; short records need fewer), transporting 46 cycles with damage-equivalent representative ranges.
5. Assess: category 90, safe life, high consequence (γ_Mf = 1,35); the record is one duty block, repeated 80,000 times over the life at 10,000 blocks per year — an 8-year demanded life.

The verdict is D_d = 0.683 — a pass, with 3.7 years of reserve beyond the demanded 8. The attribution tells the two-scale story from Section 7 in damage terms: 99.8% of the damage comes from just 160,000 of the 3,680,000 lifetime cycles — the big slow cycles in every block — while 3,440,000 small cycles fall below the cut-off and contribute exactly zero. The binning honesty check compares the binned damage against the exact unbinned count recorded at ingest (D = 0.6824) and finds them 0.12% apart — far inside the 1 % bound the pack holds itself to.

Provenance: the report for this assessment would carry the record's SHA-256 fingerprint _ptLguCDqzh-N4kWdq0Iqp5gQsbYv56cxT9LUjsfPaY and the audit trail — enough for a reviewer to verify which file was assessed, without the file.

Example 3 — the same spectrum on the AISC route

Example 1's spectrum again, now assessed as AISC 360-22 Appendix 3 stress category C. The point is the format difference: Appendix 3 has no damage sum. Each band is verified against the allowable stress range F_SR at its own lifetime cycle count, with the threshold F_TH as a floor — and no D_d appears anywhere.

The governing band is the smallest range: 30 MPa over 5,750,000 cycles, where the curve value falls below the threshold and F_SR is floored at F_TH = 69 MPa — ratio 0.435. Both routes happen to pass this spectrum, but the two verdicts are different kinds of number: EN's 0.546 is a damage fraction on factored curves, AISC's 0.435 is a stress ratio on unfactored service ranges. They are not comparable — and spectra exist that fail one format while passing the other, which is exactly why the tool never converts between them.

Two disclosures apply everywhere: binned spectra are an approximation bounded at 1 % and cross-checked against the exact count, and detail figures are schematics with exaggerated thickness — never to scale.

See a complete one before subscribing: open the demo report — the full document for the calculator's built-in example. The report supports engineering review; it is not a certification, and it does not replace the engineer who signs the design.