$[20$p$]$ Problem $4.$

Determine the:

a$.$ 'plane stresses' acting along$/$perpendicular to the sides of the cube, in case it has rotated $\backslash (\backslash$mathbf$\{30\}\backslash )$ degrees clockwise about the z $-$axis. Check the line in blue $\backslash ([$A$-$B$]\backslash ).$

$($The $2-$axis is pointing outwards of the paper, according the right$-$hand rule$)$

b$.$ the 'principal stresses' and belonging angle of the rotated cube.

$\backslash (\backslash$checkmark $\backslash )$ Carefully check the figure.

$\backslash (\backslash$checkmark $\backslash )$ Draw Mohr's circle.

$\backslash (\backslash$checkmark $\backslash )$ Make a clear sketch of the rotated cube incl. of arrow and values for the plane stresses. $\backslash \{$Plane stresses: Stresses acting along$/$perpendicular to the side$-$faces of the cube; the front and rear face are free of any stress$\backslash \}$

$\backslash (\backslash$checkmark $\backslash )$ Make a clear sketch of the rotated cube incl. of arrow and values for the principal stresses. $\backslash \{$principle stresses: main stresses$\backslash \}$

$\backslash (\backslash$checkmark $\backslash )$ Notice, the set$-$up for the $2$D Mohr circle can be found in the appendix.

Distribution of credits:

$[10$p$]$ Proper execution of the $2$D Mohr's circle method inclusive of the values for: $\backslash (\backslash$tau $\backslash )$ and $\backslash (\backslash$sigma $\backslash ).$

$[5$p$]$ Clear sketch of the rotated cube inclusive of arrows and values for the plane stresses.

$[5$p$]$ Clear sketch of the rotated cube, inclusive of arrows and values for the principal stresses.