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Extreme Value Analysis and its Application to C.G. Vertical Accelerations Measured on Transport Airplanes of Type C-130

The static design of an aircraft structure is based on loads, which have been settled either by convention or by
experience and which have to be proved with a certain safety factor against ultimate load of the structure.
This design procedure, however, cannot" guarantee that no cracks or failures caused by fatigue will occur within-
the required life time.
Even if these static design loads would in fact occur during service operation, we first have to know how often
they will occur, before we can use them for the fatigue design. This has not only to be required for the design loads
but also for all smaller loads which occur more frequently.
Information about magnitude and frequency of loads can be obtained only by measurements under service
conditions. If it has been decided to count certain characteristic occurrences, e.g. level crossings or peaks (Refs.l ,2),
the choice of which may be supported by theoretical considerations or to some extent by experience about material
behaviour, then modern measurement and data processing techniques allow one to provide the so-called cumulative
frequency distribution (CFD). It is derived from the continuous history of the load P , see Figure 1.
For such an analysis we have to distinguish between the so-called basic load Pb , which is constant in the
example shown and which corresponds to the load in the undisturbed condition at the load factor n = l , and
super-imposed ascending and descending incremental loads AP, resulting, e.g., from gusts, maneuvers, or runway
roughness.
The CFD as used-for fatigue analysis is plotted normally in a semi-logarithmic grid. It says that there occur
load increments, which reach or exceed with a certain cumulative frequency Hi the corresponding maximum load
Pmax,i = Pb + APi and minimum load Pmin,i = Pb — APi.
In addition also the basic load can vary with time. As an example Figure 2 shows the stress time history as
measured at the lower wing spar boom of a transport airplane. It is necessary and reasonable to distinguish here
between so—called loading segments, which are characterized by a constant value of the basic load and which are
repeated in similar form during each flight. For each of those-loading segments a separate CFD has to be presented.
Such CFDs result in most cases from relatively short measurements if compared with the life of the structure.
Therefore they normally do not include those maximum loads, the occurrence of which during life has to be taken
into account and the knowledge of which is absolutely necessary for a reliable design.