Variable-Amplitude Loading & Load Spectra

Technical provenance

Applicable standards / specifications

• BS 7608 (2014+A1:2015) — Guide to fatigue design and assessment of steel products — Use only where the material/detail and project basis fall within scope.

References

• Schijve, J. — Fatigue of Structures and Materials — Background reference for fatigue mechanisms, S–N behaviour, mean-stress effects and variable-amplitude loading.
• BS 7608 — Guide to fatigue design and assessment of steel products — Applicable principally to fatigue assessment of steel products and welded details.

What Is It?

Variable-amplitude loading is the realistic representation of how structures are loaded in service. Unlike constant-amplitude fatigue testing, where every cycle is identical, real structures experience loads that vary from cycle to cycle, from mission to mission and from one period of service to another. A load spectrum is the organised representation of this variable loading for fatigue analysis.

Why It Matters

Fatigue life depends on the complete load history, not just a single load level. A structure designed against a single constant-amplitude load may fail prematurely in service because the real loading contains occasional high loads that accelerate damage. Conversely, a structure designed against the peak service load may be over-designed because the peak occurs rarely. A representative load spectrum is essential for predicting realistic fatigue life.

Fatigue life depends on how the structure is used, not just how it is designed. The same structure in different service roles can have very different fatigue lives.

Sources of Variable Loading

Load Spectrum Representation

A load spectrum can be represented in several ways, each useful for different purposes. The choice of representation depends on the analysis method and the available data.

• Time history — load as a function of time; most detailed; requires cycle counting for fatigue
• Cycle histogram — range-mean matrix of counted cycles; compact; standard for fatigue analysis
• Block spectrum — groups of constant-amplitude cycles at different levels; simplified representation
• Exceedance diagram — number of occurrences exceeding each load level; used in aerospace
• Mission profile — sequence of load events for a typical mission; used for sequence-dependent analysis

Mission Profiles

A mission profile defines the loading that occurs during a representative operational cycle — a flight, a lap, a day of operation. It includes all significant load events in sequence. Mission profiles are used to construct load spectra by repeating the mission for the required service life. The mission must be representative of actual usage — an overly severe mission over-predicts damage; an overly benign mission under-predicts it.

Sequence Effects

The order of loads in a variable-amplitude spectrum affects fatigue life. As discussed in the Cumulative Damage article, high loads can retard or accelerate subsequent damage. A spectrum that places high loads early (when the crack is short) may produce a different life from the same spectrum with high loads late (when the crack is long). For crack-growth analysis, the sequence is important. For S-N-based analysis with Miner's rule, the sequence is lost — only the cycle histogram matters.

Truncation of Small Cycles

A load spectrum typically contains many more small cycles than large ones. The smallest cycles may contribute negligible damage. Truncation — removing cycles below a certain amplitude — reduces the number of cycles and the computational effort. However, truncation must be applied carefully. If the truncation level is too high, cycles that contribute meaningful damage are removed. The truncation level should be justified — typically by showing that the removed cycles contribute a negligible fraction of total damage.

COMMON MISTAKE: Truncating small cycles from a load spectrum without checking that the removed cycles contribute negligible damage. Cycles that appear small individually can contribute significantly in aggregate.

Why Rare High Loads Matter Disproportionately

A single high load in a spectrum can contribute more damage than thousands of smaller loads. In the S-N method, damage per cycle is n_i/N_i, and N_i decreases rapidly with increasing stress. A load that is twice the amplitude of the typical cycle may have a life 100 times shorter, meaning one cycle contributes as much damage as 100 typical cycles. Furthermore, high loads can cause sequence effects — retardation or acceleration — that are not captured by Miner's rule. Rare high loads must be retained in the spectrum and their effect understood.

Spectrum Development

Developing a representative load spectrum is a critical engineering activity. It typically involves measuring service loads, analysing operational data, defining representative missions and constructing a spectrum that captures the significant loading events. The spectrum should be reviewed for plausibility — total cycles, maximum load, load distribution and mission variability. A spectrum that does not represent realistic service usage will produce a life prediction that is technically computed but engineeringly wrong.

• Measure or estimate service loads for representative operations
• Define mission profiles that capture significant loading events
• Process time histories through cycle counting to extract fatigue-relevant cycles
• Construct the spectrum — cycle histogram or exceedance diagram
• Check plausibility — total cycles, maximum load, distribution
• Document the basis and assumptions of the spectrum

Key Takeaways

• Real structures experience variable-amplitude loading, not constant-amplitude cycles
• A load spectrum is the organised representation of service loading for fatigue analysis
• Rare high loads can contribute disproportionately to total damage
• Small cycle truncation must be justified — truncated cycles must contribute negligible damage
• A spectrum that does not represent realistic service usage produces an engineeringly wrong prediction