Problem # $1(60$ Points$)$

The state of stress at a point $"$ P $"$ in a dry soil mass is described by a vertical stress $($acting on a horizontal plane through $"$ P $")$ of $25$ psi and a horizontal stress $($acting on a vertical plane through $"$P$")$ of $10$ psi. It is desired to perform the following tasks:

$1.)$ Plot the Mohr circle describing the state of stress at point $"$P$"$;

$2.)$ Identify the "Pole" on the Mohr circle at $"$P$"$;

$3.)$ Find the maximum shear stress acting on a plane passing through $"$ P $"$;

$4.)$ Show the orientation of the plane with the maximum shear stress;

$5.)$ Indicate the normal stress acting on the plane with maximum shear stress; and

$6.)$ Indicate the normal and shear stresses acting on a plane forming an angle of $22$ degrees $($clockwise$)$ from the vertical plane at $"$P$".$

$*$PLEASE DRAW FBD$*$