## 27 Jun 2019 Factor of Safety

To assess if a structure is suitable for the intended purpose, the results of a FE analysis have to be compared to acceptance criteria, also called allowables.

For a stress analysis, allowables could be e.g. equivalent stresses (see https://www.fea-solutions.co.uk/equivalent-stress/) or deflections.

The Factor of Safety (FoS) is then the ratio of (Allowable/FEA Result).

The design is acceptable (passes), if the minimum FoS is greater than a certain value. This value might come from an engineering code or the design authority.

It is very common in many disciplines of mechanical engineering to calculate the FoS from the Yield Strength of the material and the Von Mises stress of the FEA. The minimum FoS should then be greater than 1.5. That means, the maximum Von Mises stress result from the FEA is by a factor of at least 1.5 less than the Yield Strength of the material, hence permanent (plastic) deformation will definitely not occur.

Depending on the industry, other factors might be used, such as:

- Safety Margin (SM) = FoS – 1
- Reserve Factor (RF) = (Proof Strength / Proof Load) or (Ultimate Strength / Ultimate Load).

There might be several acceptance criteria that a structure has to satisfy simultaneously, e.g. strength, stiffness, stability, and hence there would be a FoS for each of them.

For all cases, the FoS is a convenient result as it directly indicates the suitability of a design.

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