Q$1/$

$=\left[\begin{array}{ccc}7& 3& 0\\ 3& 7& 4\\ 0& 4& 7\end{array}\right]$

Determine: $$

$1-$ The principal stress values and principal stress directions?

$2-$ The maximum shear stress values?

$3-$ Draw the Mohr's circles for maximum shear stress values?

Note:

${}_i^{\text{'}}=2(-\frac{1}{3}{I}_2^{\text{'}}{)}^{\frac{1}{2}}cos{}_i,i=1,2,3,$

where

${}_1=\frac{1}{3}\{co{s}^{-1}[\frac{I_3^{\text{'}}}{2}(-\frac{3}{I_2^{\text{'}}}{)}^{\frac{3}{2}}]\},{}_2={}_1+\frac{2}{3},{}_3={}_1-\frac{2}{3}$