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The fatigue life assessment under multiaxial loadings is a rather complex task. There is a largenumber of criteria for such an assessment. Many of them are formulated for a constantamplitude loading. In the case of variable amplitudes an application of fatigue assessmentcriteria becomes more difficult. For many criteria there are no well-known detaileddescriptions of such an application.Therefore a simple algorithm which allows an application of critical plane and integral stressbasedmethods to variable proportional and non-proportional loadings is proposed. With thisalgorithm the well-known stress-based multiaxial fatigue hypotheses according to Findley [1,2] and also the shear stress intensity hypothesis SIH [3, 4] (both originally proposed forestimation of the fatigue limit) are used for the evaluation of spectrum loadings. Thesehypotheses were applied to the finite fatigue strength assessment of thin-walled, overlappedlaserbeam-welded aluminium joints made of the artificially hardened aluminium alloyAlSi1MgMn T6 (EN AW 6082 T6) and of the self-hardening alloy AlMg3.5Mn(EN AW 5042) [5]. Additionally, the fatigue strength evaluation of multiaxial spectrumloading was carried out by a modified Gough-Pollard algorithm as it is proposed in the IIWrecommendationsfor fatigue assessment of welds [6]. Since fatigue is a local process the usedstress components are local stresses in the critical area at the weld root which are calculatedby applying the notch stress concept with a reference radius of rref = 0.05 mm [7, 8, 9].Fatigue life calculations using the criteria SSCH [10, 11] and EESH [12] were alreadyperformed in [5]. These two methods do not require computation of stress values in arbitrarycutting planes and hence the algorithm presented in this paper cannot be applied to them.Further it is discussed if the hypotheses are suitable to describe the fatigue behaviour withsufficient precision and if some modifications are required.