$6\mathrm{.}6-2$ Solve the preceding problem if the element is steel $)=200$GPa,

$u=(0\mathrm{.}30$ with dimensions $a=300mm,b=150$ mm $,$ and $c=150mm$ and the stresses are ${}_x=-60$MPa,${}_y=-40$MPa, and ${}_z=-40$MPa.

$6\mathrm{.}6-3$ A cube of cast iron with sides of length $a=4\mathrm{.}0in.($see figure$)$ is tested in a laboratory under triaxial stress. Gages mounted on the testing machine show that the compressive strains in the material are $lo{n}_x=-225{10}^{-6}$ and $lo{n}_y=lo{n}_z=-37\mathrm{.}5{10}^{-6}.$

Determine the following quantities: $($a$)$ the normal stresses ${}_x,{}_y,$ and ${}_z$ acting on the $x,y,$ and $z$ faces of the cube; $($b$)$ the maximum shear stress ${}_{\text{m}\text{a}\text{x}}$ in the material; $($c$)$ the change $V$ in the volume of the cube; $($Assume $E=14,000$ ksi and

$u=0\mathrm{.}25.)$