How is the safety factor calculated using the modified Goodman criterion?

The modified Goodman criterion defines the failure boundary as σa/Se + σm/Su = 1. The safety factor n is calculated as n = 1/(σa/Se + σm/Su), representing how far the operating point lies from the failure line along the load line from the origin. A safety factor of n ≥ 2 is generally targeted in design; n < 1 indicates the operating point is in the failure region.

When should I use the Goodman criterion versus the Gerber parabola?

The modified Goodman criterion is preferred for conservative engineering design, particularly for pressure vessels, structural components, and safety-critical parts, because it envelopes experimental data on the safe side. The Gerber parabola fits experimental data more accurately for ductile materials but can be non-conservative in some cases. When maximum design efficiency is needed and material ductility is well characterized, the Gerber criterion may be applied.

How do I determine the modified endurance limit Se for a real component?

For steel, the specimen endurance limit is Se' ≈ 0.5·Su for Su ≤ 1400 MPa. The modified endurance limit for a real component is Se = ka·kb·kc·Se', where ka is the surface finish factor (0.5–1.0 depending on roughness), kb is the size factor (decreases with diameter), and kc is the reliability factor (0.868 at 99% reliability). This tool lets you set Se directly or use the Se = 0.5·Su approximation.

What engineering actions can I take when the operating point falls outside the Goodman line?

When the safety factor n < 1, four main approaches are available: (1) material upgrade to a higher-strength steel to increase Su and Se; (2) geometry change to reduce stress concentration factor Kt, such as adding fillets or reducing notch depth; (3) surface treatment like shot peening to introduce compressive residual stress; (4) load reduction by redesigning operating conditions or adding vibration damping. Reducing tensile residual stresses through stress-relief heat treatment is also effective when mean stress is the dominant factor.

/ Fatigue Life & Goodman Diagram Tool Tool List

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Fatigue Analysis Tool

Fatigue Life & Goodman Diagram Tool

Draw the modified Goodman line, Gerber parabola, and Soderberg line in real time. Instantly calculate the safety factor and predicted fatigue life for your operating stress point.

$$\frac{\sigma_a}{S_e} + \frac{\sigma_m}{S_u} = 1 \quad \text{(Modified Goodman)}$$

Material & Loading Parameters

Ultimate Tensile Strength S_u 800 MPa

Ultimate tensile strength of the material

Endurance Limit S_e 400 MPa

Modified endurance limit (after stress concentration & surface factors)

Se = 0.5·Su (auto)

Mean Stress σ_mean 300 MPa

Alternating Stress Amplitude σ_alt 200 MPa

Show Gerber Parabola

Show Soderberg Line

Safety Factor n

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Goodman criterion

Goodman Index

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σa/Se + σm/Su (< 1: safe)

Predicted Life N_f

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cycles

Failure Mode

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prediction

Goodman Diagram

S-N Curve (Life Estimate at Current Stress Amplitude)

Theory — Comparison of Fatigue Criteria

Modified Goodman Line (Most Widely Used)

$$\frac{\sigma_a}{S_e}+\frac{\sigma_m}{S_u}=1$$

Provides a safe-side envelope of experimental data. Standard in design practice.

Gerber Parabola (Closer to Experiments)

$$\frac{\sigma_a}{S_e}+\left(\frac{\sigma_m}{S_u}\right)^2=1$$

Better fit to test data, but may be non-conservative in some cases.

Soderberg Line (Most Conservative)

$$\frac{\sigma_a}{S_e}+\frac{\sigma_m}{S_y}=1$$

Uses yield strength Sy (≈ 0.6·Su). The most conservative criterion.

Basquin's Law (S-N)

$$N_f=\left(\frac{\sigma_a}{C}\right)^{1/b}$$

C = 1.62·Su, b = −0.085 (typical for steel).
Below the endurance limit, infinite life is assumed.