Check a part under fluctuating load against the modified Goodman line. Enter the alternating and mean stresses together with the endurance limit and ultimate strength to get the fatigue factor of safety, the Goodman utilisation, and the maximum alternating stress allowed at the current mean stress.
Most structural failures are fatigue failures: parts break under fluctuating loads at stresses well below their static strength, after many cycles. The modified Goodman criterion is the classic, conservative way to design against this by accounting for both the swinging (alternating) part of the stress and the steady (mean) part. This calculator evaluates the Goodman line for you, returning the fatigue factor of safety, the utilisation, and how much more alternating stress the part can tolerate.
Fatigue behaviour is mapped on an S-N curve: alternating stress amplitude (S) plotted against the number of cycles to failure (N), usually on log axes. Higher stress means fewer cycles to failure.
For steels and a few other materials the curve flattens to a horizontal asymptote, the endurance (or fatigue) limit Se: below this stress the part theoretically survives indefinitely (>10βΆβ10β· cycles). Many non-ferrous metals like aluminium have no true endurance limit, so a fatigue strength at a specified life is used instead. Se is the cornerstone input for any infinite-life design.
A fluctuating stress is split into a mean (steady) component Οβ = (Οmax + Οmin)/2 and an alternating (amplitude) component Οβ = (Οmax β Οmin)/2. The endurance limit Se is measured under fully-reversed loading where Οβ = 0.
A tensile mean stress is damaging: it holds cracks open and reduces the alternating stress the part can survive. So a design with Οβ = 0 may be safe while the same Οβ added to a large tensile Οβ fails. Mean-stress criteria like Goodman quantify exactly this penalty.
The modified Goodman criterion draws a straight failure line on the ΟββΟβ diagram from Se on the alternating axis to Sut on the mean axis. Points below the line are safe; on or above it, fatigue failure is predicted. Algebraically: Οβ/Se + Οβ/Sut = 1/n.
The fatigue factor of safety n is the reciprocal of the utilisation Οβ/Se + Οβ/Sut. n β₯ 1 means the stress state lies on or inside the line (infinite life predicted); n < 1 means it lies outside (finite life or failure). The maximum alternating stress permitted at a given mean is Οβ,max = SeΒ·(1 β Οβ/Sut).
Three common mean-stress criteria trade conservatism against fit. Soderberg draws the line to the yield strength Sy instead of Sut, making it the most conservative and the only one that also guards against yielding. Goodman draws it to the ultimate strength Sut β a straight line that is moderately conservative and the most widely used in design. Gerber uses a parabola to Sut that best fits experimental data for ductile materials but is non-conservative for brittle ones and on the safe side only with care.
This tool implements the modified Goodman line; for a yield check, compare separately against Sy, and use Gerber when you have test data and need a less penalising estimate.
The endurance limit Se is the alternating stress below which a material can endure essentially infinite cycles without fatigue failure. Ferrous metals (steels) and titanium typically show a true endurance limit, often roughly half the ultimate strength for steels. Aluminium, copper, and many non-ferrous alloys have no true limit β their S-N curve keeps sloping down β so a fatigue strength at a specified life (e.g. 5Γ10βΈ cycles) is used.
From the maximum and minimum stresses in the cycle: mean stress Οβ = (Οmax + Οmin)/2 and alternating stress Οβ = (Οmax β Οmin)/2. For fully-reversed loading Οmin = βΟmax, giving Οβ = 0 and Οβ = Οmax. For a repeated (zero-to-max) load, Οβ = Οβ = Οmax/2.
It means the stress state plots outside the Goodman line, so infinite life is not predicted β the part is expected to fail by fatigue within a finite number of cycles. Reduce the alternating stress, the mean stress, or both (lower load, larger section, smoother surface, residual compressive stress) until n rises above 1, with margin for scatter.
Comparing Οβ to Se alone is only valid for fully-reversed loading with zero mean stress. Real components usually carry a steady mean stress (from preload, weight, or pressure) that erodes the available fatigue strength. The Goodman line combines the alternating and mean components into a single check, so it captures the mean-stress penalty that a bare endurance-limit comparison misses.
Yes, in practice. Handbook endurance limits come from polished lab specimens. The Marin factors adjust Se for surface finish, size, loading type, temperature, reliability, and stress concentration, often reducing it substantially. Enter the corrected (de-rated) endurance limit as Se here so the Goodman result reflects the real part, not an idealised test bar.