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• Mean stress pushing factor to fatigue damage. • Consideration of intrinsic and extrinsic mean stress. • Definition of three second-order fatigue effects. • Development of a 12-storey building as case study. • Proposition of a simple experimental setup. A fatigue process due to random loading that is progressively damaging a certain structural detail will vary in the presence of mean stresses. The variations are already considered in crack propagation laws and by applying equivalent 0-mean stress ranges from the Palmgren–Miner linear rule. Nevertheless, if the mean stress is intrinsic, instead of a direct consequence of the random loading, other second-order effects will have to be taken into account. Those effects are cycle quasi-ordering, histogram variations, and apparent mean tension, which are identified and defined in this study and, finally, developed in a case study for demonstrative purposes. [ABSTRACT FROM AUTHOR]