FATIGUE (GOODMAN, SODERBERG, GERBER)

Cyclic loading at stresses below static yield can still cause failure by fatigue. The endurance limit Se is the stress amplitude below which steel survives infinite cycles; for non-ferrous metals there's no true endurance limit. Marin modifiers reduce Se for surface finish, size, loading type, temperature, and reliability. Mean stress σ_m raises the effective amplitude; Goodman, Soderberg, Gerber, and ASME-Elliptic lines plot allowable amplitude vs mean on a Haigh diagram.

• Se = ka·kb·kc·kd·ke·kf · 0.5·Sut
• Goodman: σ_a/Se + σ_m/Sut = 1/n
• Soderberg: σ_a/Se + σ_m/Sy = 1/n
• Gerber: n·σ_a/Se + (n·σ_m/Sut)² = 1
• ASME-Ell: (n·σ_a/Se)² + (n·σ_m/Sy)² = 1

References & StandardsShigley Ch. 6, Norton Ch. 6, MIL-HDBK-5

Apply fatigue analysis to any cyclically loaded component: rotating shafts under bending, springs in compression cycles, pressurized vessels with cyclic pressure, structural members in vibration. Identify mean and amplitude stress separately. Use Goodman for ductile materials with a conservative bias; Soderberg if you can't accept any yielding; Gerber for less conservative match with test data; ASME-Elliptic for combined yield + fatigue safety.