Problem $3(30$ Points$)$:

The state of strain at the point on the spanner wrench has components of $lo{n}_x=-260({10}^{-6}),lo{n}_y=320({10}^{-6}),$ and ${}_{xy}=180({10}^{-6}).$

Use the strain transformation equations to determine a$)$ the in$-$plane principal strains and b$)$ the maximum in$-$plane shear strain and average normal strain.

Use the Mohr's circle determine c$)$ the principal strains and d$)$ the absolute max in$-$plane shear strains.

e$)$ Determine the corresponding orientation of each state.