Fluctuating-Stress Fatigue Safety Factor (Goodman/Soderberg/Gerber)

The fatigue safety factor for a rotating shaft, spring.

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Details, formula, and sources

The fatigue safety factor for a rotating shaft, spring, or fastener under a fluctuating load - how such parts actually fail, which a static stress check misses. From the alternating stress sigma_a and the mean sigma_m, the infinite-life safety factor on the standard failure lines: modified Goodman 1/n = sa/Se + sm/Sut (the design standard), Soderberg 1/n = sa/Se + sm/Sy (never yields, most conservative), or Gerber n sa/Se + (n sm/Sut)^2 = 1 (best data fit), plus the Langer first-cycle-yield line ny = Sy/(sa + sm); the governing factor is the smaller. Se is the CORRECTED endurance limit (an input, so no Marin tables). sigma_a 25, sigma_m 30 ksi with Se 40, Sut 100, Sy 80 ksi gives Goodman n = 1.08 (fatigue governs, 8% margin), Soderberg 1.00, Gerber 1.34, Langer 1.45; fully reverse the load and all give n = Se/sa. Building Se from the Marin factors, notch Kf, finite-life S-N, and multiaxial combination are separate. A design aid; Shigley / Juvinall and the engineer of record govern.

Goodman 1/n = sa/Se + sm/Sut; Soderberg 1/n = sa/Se + sm/Sy; Gerber n sa/Se + (n sm/Sut)^2 = 1; Langer ny = Sy/(sa + sm); governing = min(n, ny).

The modified-Goodman, Soderberg, and Gerber fluctuating-stress fatigue criteria with the Langer first-cycle-yield line (Shigley, Mechanical Engineering Design; Juvinall, Engineering Considerations of Stress, Strain, and Strength), by name.

The three fatigue criteria and the Langer line are standard published machine-design results; the corrected endurance limit Se, the strengths, and the stresses are the designer's inputs.

Estimate. AHJ and licensed professional govern.

Field names used by the API: alternating_stress_psi, mean_stress_psi, endurance_limit_psi, ultimate_strength_psi, yield_strength_psi, criterion, fatigue_n, langer_ny

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