NOTE: For this problem, I want you to do your work by hand, on graph paper. Most of this can be done using Excel features, but I

want to see your ability to do hand$-$plotted analysis. Do this neatly and precisely! See my example in the last tab of this file.

Stress measurements at depth give the following results for stresses acting on planes C$1$ and C$2.$

C$1$ and C$2$ are mutually perpendicular, but they are not horizontal and vertical.

Graph these two stresses on a Mohr circle plot, and draw the circle that includes both points and lies symmetrically on the $$ axis.

A$.$ What is the magnitude of the maximum shear stress ${}_{\text{m}\text{a}\text{x}}($in psi$),$ and what is its orientation relative to $C1$ and $C2($expressed as the angle $$ in the ground$)?$

B$.$ What are the magnitudes of the Principal Stresses? These are the maximum $({}_1)$ and minimum $({}_3)$

normal stresses, and occur on the Mohr Circle where the circle crosses the $$ axis where $=0.$

C$.$ Assuming that the Principal Stresses act in the vertical and horizontal directions $($i$.$e$.{}_1$ is the vertical

overburden stress acting on a horizontal plane and ${}_2$ is the lateral stress acting on a vertical plane$),$ and a

bulk density for the ground of $2600kg{m}^{-3},$ at what depth $z$ in the ground would ${}_1$ occur?

D$.$ What orientations in the ground do the principle stresses act on$?$