📉 Fatigue Analysis (Goodman)

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · A documented rule of thumb, pinned by automated tests · how PhDino checks its numbers

Checking whether a fluctuating (cyclic) stress will cause fatigue failure well before a single overload would.

A part loaded far below its static strength can still fail after enough load cycles — this is fatigue, and it's a completely different failure mode from a single static overload. Fatigue behavior is usually described by a mean stress (the average of the cycle) and an alternating stress (half the peak-to-peak swing); a part can tolerate less alternating stress as the mean stress rises toward the material's ultimate strength.

The (modified) Goodman relation is a simple, commonly used way to combine mean and alternating stress into a single safety factor against fatigue, using the material's endurance limit and ultimate strength as the two anchor points of a straight line.

Key formula

σ_mean = (σ_max + σ_min)/2
σ_alt = (σ_max − σ_min)/2
1/SF = σ_alt/S_e + σ_mean/S_u

Variables

S_e

endurance limit (stress below which fatigue life is effectively infinite)

S_u

ultimate tensile strength

Notes & limitations

• This calculator estimates S_e as roughly half of S_u, a common rule of thumb for steel — real endurance limits depend on surface finish, size, loading type, and reliability requirements, and are reduced from the ideal lab-specimen value by several correction factors in a full analysis.
• The Goodman line is one of several fatigue failure criteria (Gerber and Soderberg are others); Goodman is generally conservative, which is part of why it's widely used for design.