Q$\mathrm{.}2)$ The measured strains on the outer surface of a structural member by using rosette $($shown below$)$ are: $lo{n}_a=+900,lo{n}_b=-450,$ and $lo{n}_c=+400$

Determine

$($a$)$ The strain components $lo{n}_x,lo{n}_y$ and ${}_{xy}.$

$($b$)$ The magnitudes and orientations of the principal strains. Sketch the deformations and distortions.

$($c$)$ The maximum in$-$plane shear strain

$($d$)$ The absolute maximum shear strain $($use $v=0\mathrm{.}3)$