$1\mathrm{.}4\mathrm{.}9.$ Example $4$

Given that:

$[{}_{ij}]=\left[\begin{array}{ccc}0& 0& 0\\ 0& 300& 100\sqrt[\phantom{2}]{3}\\ 0& 100\sqrt[\phantom{2}]{3}& 100\end{array}\right]$

Calculate:

A$.$ Principal stresses

B$.$ Normal and shear stresses

at a plane with $n=\{\frac{1}{2},\frac{1}{2},\frac{1}{1\mathrm{.}414}{\}}^T$

C$.$ Octahedral stresses

D$.$ Maximum shear stress

Solution: