Problem $8.$

An element in plane stress is subjected to stresses ${}_x=-150$MPa,${}_y=-210$MPa,

and ${}_{xy}=-16$MPa. The material is brass with modulus of elasticity $E=100$GPa

and $v=0\mathrm{.}34.$

Determine the following quantities: $($a$)$ the strains for an element oriented at angle $=$

$50,($b$)$ the principal strains, and $($c$)$ the maximum shear strains. Show the results on

sketches of properly oriented elements.