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The IIW-Recommendation for fatigue design of welded joints and components presents two different evaluation approaches for multiaxial stress states under constant amplitude: an approach based on the maximum principal stress, which is only applicable under certain conditions, and the Gough-Pollard approach for the remaining cases. In the course of this work, this maximum principal stress-based approach is analyzed. It is examined in which cases the method is applicable, the advantages and disadvantages compared to the approach according to Gough-Pollard are discussed, and an evaluation according to the von Mises equivalent stress is presented as a third alternative. This is followed by a validation based on literature data on laser-welded steel joints using the nominal stress, hot spot stress, and effective notch stress concept.