The probability density functions used to characterize the distribution of fatigue cycles in random loads are usually defined over an infinite domain. This means that they give a non-zero probability to count cycles with an infinitely large peak or valley, which however seems of less physical sense. Moreover, practically all the methods existing in the literature completely neglect the negative effect on fatigue strength produced by fatigue cycles with positive mean values. With theses premises, this work tries to further extending the probabilistic theory used by the frequency-domain methods by addressing to distinct problems. First, it tries to include in cycle distributions the effect of both a threshold level SL (representing a limit state of the system) and the ultimate static strength Su. Secondly, it uses the Goodman mean value correction to include the effect of mean values of counted cycles in the fatigue analysis of random loads by frequency-domain methods. The fatigue load is modeled as a stationary random process X(t) with constant mean value mc; two approaches of increasing complexity are presented: in the first one, only the effect of mc is considered, while in the second one also the effect of the random mean value mr, calculated with respect to mc, is added. The proposed theoretical formulae are applied to two frequency-domain methods, namely the narrow-band approximation and the TB method. Finally, a comparison of the proposed formulae with the results from preliminary numerical simulations is shown.
