A point in the ground has a total vertical $($normal$)$ stress $($v$)$ of $200$ kPa, a total horizontal $($normal$)$ stress $($x$)$ of $120$

kPa, a horizontal shear stress $($xy$)$ of $0$ kPa, and a pore water pressure $($uo$)$ of $40$ kPa.

$($a$)$ Determine the shear and effective normal stresses that act on a plane oriented $30$ degrees clockwise from

horizontal. Sketch the plane and draw the stresses acting on it; make sure you have the correct sign

convention.

$($b$)$ Determine the shear and effective normal stresses that act on a plane oriented $30$ degrees counterclockwise

from horizontal. Sketch the plane and draw the stresses acting on it; make sure you have the correct sign

convention.

$($c$)$ Determine the maximum shear stress and the orientation of the planes on which it acts.