Factor of Safety
It is defined, in general, as the ratio of the maximum stress to the working stress.
Factor of safety = Maximum stress/ Working or design stress
In case of ductile materials e.g. mild steel, where the yield point is clearly defined, the factor of safety is based upon the yield point stress. In such cases,
Factor of safety = Yield point stress/ Working or design stress
In case of brittle materials e.g. cast iron, the yield point is not well defined as for ductile materials. Therefore, the factor of safety for brittle materials is based on ultimate stress.
Factor of safety = Ultimate stress/ Working or design stress
This relation may also be used for ductile materials.
The above relations for factor of safety are for static loading.