Question $1$

$(30$ Marks$)$

Three principal stresses and $\{$:${}_3=-80$MPa$)$ which are mutually

perpendicular to one another are applied to a cube of aluminum metal. The modulus of elasticity

of aluminum is $E=69$GPa and its Poisson's ratio is $v=0\mathrm{.}3.$

$($A$)$ Calculate the magnitudes of the principal strains.

$[15$ marks$]$

$($B$)$ Calculate the strain energy per unit volume.

$[15$ marks$]$