This paper presents a probability distribution of stress ranges and a spectral fatigue damage calculation of offshore structures subjected to non-narrow banded Gaussian stress processes. The stress range probability distribution is empirically formulated on the base of a number of stress range probability histograms obtained from the rainflow cycle counting algorithm using the Monte-Carlo procedure. Although the probability distribution introduced is general for both linear and nonlinear damage accumulations, in the paper the linear damage accumulation (Palmgren-Miner's rule) is used with a multi-linear SoN fatigue model. This model can also be used for a nonlinear fatigue model applying a piecewise linear approximation. Formulation of the mean damages in short-term and long-term sea states are presented in general. For a linear SoN model the customarily known damage correction factor is constructed. It is worked out that an empirical stress range probability distribution can be more generally used in the damage calculation than an empirical damage correction factor.
In practical fatigue analysis of offshore structures it is often assumed that the stress process is narrow banded. Under further restriction of the process as to be Gaussian the mean fatigue damage can be calculated precisely from the stress range distribution which becomes Rayleigh. In this approach, the stress range is assumed reasonably to be double of the stress amplitude. This approach is appropriate if the stress spectrum has a single peak which may be observed under certain conditions e.g. a) when the wave frequency and the natural frequency of the structure lie within close proximity of each other or b) assumption of a quasi-static response of the structure neglecting the effect of the natural vibration which is applicable only in sever sea states and if the structure is not dynamically sensitive.
