Factor of Safety Calculator: Yield, Stress Concentration and Fatigue (Goodman) Safety Factor
Check a loaded part for yielding and for fatigue.
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How this calculator works
Enter the yield strength, the ultimate strength, the endurance limit of the part, the highest and lowest nominal stress in the cycle, the stress concentration factor and the notch sensitivity.
The calculator gives the factor of safety against yielding, the peak stress at the notch, and the fatigue stress concentration factor Kf = 1 + q (Kt - 1).
It finds the alternating and mean stress, and the Goodman factor of safety, which says how far the cycle is below the fatigue failure line.
Formulas used
- n_y = \frac{S_y}{\sigma_{max}}
- K_f = 1 + q(K_t - 1)
- \sigma_a = \frac{\sigma_{max} - \sigma_{min}}{2},\ \sigma_m = \frac{\sigma_{max} + \sigma_{min}}{2}
- \frac{1}{n_f} = \frac{K_f\sigma_a}{S_e} + \frac{\sigma_m}{S_u}
Worked example
With the default numbers in the calculator above:
- Factor of safety against yielding, from the nominal stress: 2.50
- Local peak stress at the notch (stress concentration): 200.00 MPa
- Factor of safety if the notch peak were to be taken against yield (a conservative check; a ductile part yields locally and redistributes): 1.25
- Fatigue stress concentration factor: 1.80
- Alternating and mean stress of the cycle: 50.00 MPa alternating and 50.00 MPa mean
- Fatigue factor of safety by the Goodman line: 1.45
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
What is a stress concentration factor?
The ratio of the highest stress at a hole, notch or fillet to the nominal stress. A circular hole in a wide plate has a factor of 3.
What factor of safety should I use?
Typical values are 1.5 to 2 for well known loads and materials, and 3 or more when they are uncertain. The standards often set their own.
What is the Goodman line?
A straight line on a graph of alternating against mean stress from the endurance limit to the ultimate strength. A point under the line will not fail in fatigue.
What is notch sensitivity?
How much of the theoretical stress concentration a material actually feels in fatigue. It is 0 for no effect and 1 for the full effect.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Shigley and Mischke, Mechanical Engineering Design (fatigue and stress concentration); Peterson, Stress Concentration Factors.
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