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

Determine the plane stresses for:

a$.$ the $\backslash ([$A$-$B$]\backslash )-$oriented line.

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, linked to the $[$A$-$B$]-$oriented line. $\backslash \{$Plane stresses: stresses along$/$upon its plane$\backslash \}$

$\backslash (\backslash$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.

Figure: External load on cube in $2$D $($and line $[$A$-$B$]).$

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, linked to the $\backslash ([\backslash$mathrm$\{$A$\}\backslash )-$ B$\backslash (]\backslash )-$oriented line.

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