PSI - Issue 77

Miloslav Kepka et al. / Procedia Structural Integrity 77 (2026) 272–278

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unpredictability. Fortunately, the consequences of external and internal forces or forced vibrations of structures can be analysed and eliminated based on measurements performed directly in real operations, Kepka and Kepka jr. (2022). The measured stress processes are key to understanding fatigue damage, which manifests itself as a consequence of the stress-strain response of the material in critical places (areas, nodes) of the structure. To assess the fatigue life, it is necessary to know the load spectra of the structure, or rather its important structural nodes, to which they are exposed during their operation. In the field of fatigue, a load spectrum is a histogram of the frequency of load cycles with different amplitudes (or ranges), or even their mean values. Knowledge of load spectra has different meanings in different phases of the life cycle of a structure. In the early design phase, load spectra allow engineers to identify critical points in a structure where fatigue failure could occur, and thus design structures that are sufficiently robust and resistant to fatigue loading. During operation, load spectra can be the output of continuous monitoring of the structure, which can prevent its premature failure or serve as information for maintenance planning, timely replacement of "fatigued" parts, etc. Finally, in the event of operational failures (occurrence of fatigue cracks or fatigue fractures), they provide valuable information that helps determine the cause of such failures and, in feedback, contributes to the improved design of critical structural nodes and new generation components. Load spectra can thus be divided into two main categories: operational load spectra and design (typical, standardised) load spectra. 2. Service load spectra Operational load spectra are most often derived directly from measurements in real operating conditions and are the basis for testing and computational verification of structures and their critical structural nodes. Measurement of operational load, or rather the response of the structure to this load, is performed on prototypes or on older generations of structures. The determination of operational spectra is typically performed by strain gauge measurement, in which the deformation or mechanical stress is measured during operation at a specific point (cross-section) of the structure or by using accelerometers that record acceleration in one or more directions. Since measured loading processes tend to be complex, careful processing is required before they can be converted into operational spectra usable for calculations or laboratory experiments. The rainflow method, also known as the rain runoff method, is currently the leading technique used for the analysis and decomposition of random loading processes. This method allows the transformation of measured operational load patterns into harmonic cycles that are independent of the time order of their occurrence. The rainflow method is based on the identification and classification of load cycles in a signal. The cycles are sorted according to their “size” and frequency of occurrence, which allows the creation of a histogram of the frequency of cycles. This histogram can be one-parameter, where only the amplitude (or range) of the identified cycles is taken into account, or two-parameter, where the mean value of the cycle is also taken into account. An example of a measured signal from a strain gauge placed on the bus body, with examples of one-parameter and two parameter histograms of cycles created in the nCode software, is shown in Fig. 1.

Fig. 1. Stress-time history measured on bus bodywork and examples of one-parameter and two-parameter histograms of cycles.