$3\mathrm{.}3-3.$ Consider the following three states of principal stresses, in MPa:

$(1){}_1=8,{}_2=3,{}_3=1$; $(2){}_1=6,{}_2=0,{}_3=-1$; $(3){}_1=7\mathrm{.}5,{}_2=1,{}_3=0.$

Using the following failure criteria, rank these states of stress, from most dangerous to least.

$($a$)$ Maximum normal stress criterion.

$($b$)$ Mohr criterion, with ${}_{tf}=10$MPa and ${}_{cf}=180$MPa.

$($c$)$ Maximum shear stress criterion.

$($d$)$ Von Mises criterion.