$1-$ The stress tensor$($matrix$)$ at a critical point of a Ductile material is

given by:

$\left[\begin{array}{ccc}3& 1& 1\\ 1& 0& 2\\ 1& 2& 0\end{array}\right]$

Determine the safety factor using Tresca and Von Mises theories.

Sy $=200$Mpa.

$2-$For a special experiment, a thin$-$walled vessel has been made of a

brittle material with Sut $=$A and Suc$=2A.$ The inside diameter of the

vessel is $($d$)$ and the thickness is $($t$).$ Calculate the magnitude of inside

pressure $($ P $)$ according to Coulomb$-$Mohr theory for safety factor of $n=1.$

Note: As diameter of the vessel is bigger than the thickness, therefore

$d+td$