The state of stress at a point is defined by the stresses on two perpendicular planes (for 2D). For example, for the x-y planes:
These two planes plot as the end points on a diameter of Mohr's Circle:
Note the sign convention: 1) on the x-face, a positive shear stress plots as negative on
Mohr's circle, or, equivalently, 2) a shear stress which causes CCW moment on the stress
cube plots as negative on Mohr's circle (CW moment plots as positive). When using
Mohr's circle to draw the stress cube, a negative shear stress on Mohr's circle plots so that
the shear stress on a cube causes a CW moment.
For an x'-y' plane where x' is rotated an angle  CCW from the x-axis, the stresses on
these two planes also plot as the end points on a diameter of Mohr's circle:
On Mohr's circle, note that the diameter for the x'-y' stresses is rotated by an angle 2
(also CCW) from the diameter for the x-y stresses.
The principal stresses are defined by those planes where the shear stress is zero. On
Mohr's circle, these are represented by horizontal diameter as shown below:
On Mohr's circle, the planes of max shear is always +/- 90 degrees from the planes of
principal stress, or +/- 45 degrees for the stress cube:
We conclude that the state of stress for any set of perpendicular planes is defined by the
end points of the corresponding diameter of Mohr's Circle. Note that the planes on a
cube are separated by 90 degrees but by 180 degrees on Mohr's circle.
Rule for plotting shear stresses: For the x-face, a positive value of shear stress (from
tensor, or stress cube) plots as a negative value on Mohr's circle. Alternative way to say
the same thing: If the shear stress on the face of a cube causes a CCW moment on the
cube, then it plots as a negative value on Mohr's circle.
Rule for drawing stress cube: For the rotated x-face, a negative value of shear stress from
Mohr's circle is shown as a positive value on the stress cube. Alternative way to say the
same thing: If the shear stress on Mohr's circle is negative, draw the shear stress on that
face so that it causes a CCW moment on the cube.
8
6
1
1
6
1 6 
Example:    

6 8
8
Generalized plane stress - add to book and notes
Lets go through this one more time. a) On generalized plane stress problems, you have
to start the problem with the plane stress part first (that plane which has shear stress in it).
So it can be the x-y plane, or the x-z or y-z plane. Look at the stress tensor and determine
which plane that is. The plane with plane stress on it, is the only one we have discussed
for which you can apply the stress transformation equations and for which you can
determine the Mohr's circle using both normal and shear stress. For this plane, you will
be able to determine two principal stresses and max shear stresses; and for this plane you
can show the rotated stress cubes.
b) The remainder of Mohr's circle calculations involve only the normal stress on the
plane where there is no shear stress (so on that plane the normal stress is by definition a
principal stress). Plotting this third principal stress gives you two additional Mohr's
circles and possible a large max shear stress.
Consider the following example:
 2 0 0 
    0 10 5
 0 5 20 
theta=67.5 deg CW from y-axis to P1 (22.07), prin=22.07,7.93, tmax=7.07 (y-z plane),
tmax =12.04