The present paper aims to propose a frequency-domain formulation of a stress invariant based multiaxial fatigue criterion, called "Projection by Projection" (PbP) approach, suitable for estimating fatigue life in presence of complex multiaxial loadings. The new proposed spectral method is first validated with experimental data from the literature, concerning bending-torsion random loading, showing a general accuracy. Numerical simulations are next used to generate a wide set of bending-torsion random loading with different correlation degrees, variance ratios and frequency content, in order to further validate the new proposed method. Simulations confirm a general quite good accuracy for PbP spectral method and also emphasize its better precision compared to another spectral method, namely the equivalent von Mises stress approach, developed by Preumont and co-workers.