PROBLEM $3(20$ Points$)$

The stress conditions on Plane A inside a soil specimen is given by: ${}_A=10$kPa and ${}_A=+2$kPa. The stress conditions on another Plane $B$ are given by: ${}_B=9$kPa and ${}_B=-3$kPa. Plane A makes an angle $15$ degrees with the horizontal.

$($a$)$ Draw Mohr's Circle with the help of these given stress conditions $($hint: the circle must have the center on the X axis$).$

$($b$)$ Find the major and minor Principal Stresses

$($c$)$ Find the pole

$($d$)$ Find the stresses on a horizontal plane

$($e$)$ Determine the angle between the Planes A and $B$