for principal planes. Even though the idea for using the Mohr circle is to graphically find different stress components by actually measuring the coordinates for different points on the circle, it is more convenient to confirm the results analytically. Thus, the radius and the abscissa of the centre of the circle are and the principal stresses are The coordinates for both points H and G (Figure 8 and Figure 9) are the magnitudes of the minimum and maximum shear stresses, respectively; the abscissas for both points H and G are the magnitudes for the normal stresses acting on the same planes where the minimum and maximum shear stresses act, respectively. The magnitudes of the minimum and maximum shear stresses can be found analytically by and the normal stresses acting on the same planes where the minimum and maximum shear stresses act are equal to We can choose to either use the double angle approach (Figure 8) or the Pole approach (Figure 9) to find the orientation of the principal normal stresses and principal shear stresses. Using the double angle approach we measure the angles ∠BOC and ∠BOE in the Mohr Circle (Figure 8) to find double the angle the major principal stress and the minor principal stress make with plane B in the physical space. To obtain a more accurate value for these angles, instead of manually measuring the angles, we can use the analytical expression One solution is: . From inspection of Figure 8, this value corresponds to the angle ∠BOE. Thus, the minor principal angle is Then, the major principal angle is Remember that in this particular example and are angles with respect to the plane of action of (oriented in the -axis)and not angles with respect to the plane of action of (oriented in the -axis). Using the Pole approach, we first localize the Pole or origin of planes. For this, we draw through point A on the Mohr circle a line inclined 10° with the horizontal, or, in other words, a line parallel to plane A where acts. The Pole is where this line intersects the Mohr circle (Figure 9). To confirm the location of the Pole, we could draw a line through point B on the Mohr circle parallel to the plane B where acts. This line would also intersect the Mohr circle at the Pole (Figure 9). From the Pole, we draw lines to