Question $4$: $[25$ Marks$]-40$ minutes

The $\backslash (\backslash$mathbf$\{45\}\{\}^\{\backslash$circ$\}\backslash )$ strain rosette with $\backslash (\backslash$mathbf$\{$G$\}=\backslash$mathbf$\{75\}\backslash$mathbf$\{$~ G P a$\}\backslash )$ is mounted on the surface of a pressure vessel. Using Mohr's Circle, determine.

a$)$ The in$-$plane principal strains.

b$)$ The maximum in$-$plane shear shear strains in the $\backslash ($ x$-$y $\backslash )$ plane and associated average normal strain.

c$)$ The absolute maximum shear strain.

d$)$ The associated in$-$plane normal stresses.