Factor of Safety and load/stress linearity

[Mykhalo P]

Why can we calculate factor of safety using Strain (fail)/ Strain (allow) only if the load applied is linearly related to the stress developed within the member? What happens if the two are not related?

Also, my textbook says factor of safety can also be calculated by stress (fail)/ stress (allow). Are the two ratios the same? Why?

 

[Orodruin]

Also, my textbook says factor of safety can also be calculated by stress (fail)/ stress (allow). Are the two ratios the same? Why?

The ratios are the same in the regime where stress and strain are linearly related (ie, by Hooke’s law).