Closed form analytical expressions have been derived and are proposed for use to predict accumulated fatigue damage and fatigue life of structural elements subjected to a combination of fully reversed narrow-band Gaussian random and static mean stresses. Such mean stresses can significantly alter fatigue life. The proposed method of combining random alternating and mean stresses shows excellent agreement with published experimental data for a steel alloy. Reasonable agreement is maintained, surprisingly, even for static tensile stress values up to near the material's yield stress where the failure mode shifts from that of typical brittle fatigue to that of stress rupture (i.c.,creep). Numerical examples are provided to illustratc the application.

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