Chapter 14, Problem 5RP

In the case of plane stress, where the in-plane principal strains are given by ${ϵ}_1$, and , show-that the third principal strain can he obtained from

${ϵ}_3=\frac{-v\left({ϵ}_1+{ϵ}_2\right)}{\left(1-v\right)}$

where v is Poisson’s ratio for the material.