Problem $03\mathrm{.}020-$ Find the principal normal and shear stresses and the maximum shear stress

The state of stress at a point is ${}_x=-1\mathrm{.}00k,{}_y=20\mathrm{.}00k,{}_z=-10\mathrm{.}00k,{}_{xy}=15\mathrm{.}00k,$

${}_{yx}=4\mathrm{.}000k,$ and ${}_{}=-10\mathrm{.}00k.$

Problem $03\mathrm{.}020.$a $-$ Find the principal normal and shear stresses

Determine the principal stresses.

The principal normal stress ${}_1$ is determined to be

kpsi.

The principal normal stress ${}_2$ is determined to be

kpsi. $($Round the final answer to three decimal places.$)$

The principal normal stress ${}_3$ is determined to be

kpsi. $($Include a minus sign if necessary.$)$

The principal shear stress ${}_{\frac{1}{2}}$ is determined to be

kpsi. $($Round the final answer to three decimal places.$)$

The principal shear stress ${}_2$ is determined to be

kpsi.

The principal shear stress ${}_{\frac{1}{3}}$ is determined to be $k.$