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When we talk about load spectra we often mean load-time histories, i.e. load as a function of time. So in fact, a load spectrum is nothing else than a set of loads acting on a structure during service. For fatigue, the relevant data for fatigue are maximum and minimum stress levels (peaks and troughs). All other stress levels in between are not relevant.
For fatigue analysis, the load-time history needs to be translated to a table with stress amplitudes, mean stress levels and corresponding number of occurences. Such a translation is usually done with the rainflow counting method.

An example of a load spectrum is the pressurization and de-pressurization of a pressure vessel. The spectrum is determined by number and severity of pressurization. From that data stress amplitudes and number of occurences can be determined.
Another example is the wing of an aircraft. During a flight the bending moment varies due grounds loads (taxiing), lift during flight, manoeuvres and touch down.

Two different load types can be distinguished: deterministic loads and stochastic loads. Deterministic loads are loads of which occurences and magnitude are known. On the other hand, stochastic loads are loads of which occurences and magnitude are not known. Very often those are random loads of which statistical data are gathered by long-term measurements.

Functional loads are very often deterministic loads. Due to the function of a structure we know what loads to expect. Pressurization cycles of pressure vessels are a clear example of deterministic functional loads.

Disturbances are often stochastic. Variations in wind speed, air turbulence and variations in wave height are examples of disturbances which are not predictable. Note that order and number of deterministic loads are often stochastic as well, for example manoeuvres of vehicles.

When we perform a fatigue analysis we mainly consider the functional loads. After all, those are the loads that follow from the function of the structure. However if disturbances are ignored or underestimated, you may easily overestimated the fatigue life of the structure. Often disturbances are superimposed on functional loads. This is shown in the figure below. That makes the spectrum more severe than you would expect just based on functional loads alone.

The effect of disturbances can become very critical when design is done for infinite life. If disturbance are properly accounted for, your infinite life can easily become finite….