different points on the Mohr circle. The coordinates of the points where these lines intersect the Mohr circle indicate the stress components acting on a plane in the physical space having the same inclination as the line. For instance, the line from the Pole to point C in the circle has the same inclination as the plane in the physical space where acts. This plane makes an angle of 63.435° with plane B, both in the Mohr-circle space and in the physical space. In the same way, lines are traced from the Pole to points E, D, F, G and H to find the stress components on planes with the same orientation. Mohr's circle for a general three-dimensional state of stresses To construct the Mohr circle for a general three-dimensional case of stresses at a point, the values of the principal stresses and their principal directions must be first evaluated. Considering the principal axes as the coordinate system, instead of the general , , coordinate system, and assuming that , then the normal and shear components of the stress vector , for a given plane with unit vector , satisfy the following equations Knowing that , we can solve for , , , using the Gauss elimination method which yields Since , and is non-negative, the numerators from these equations satisfy as the denominator and as the denominator and as the denominator and These expressions can be rewritten as which are the equations of the three Mohr's circles for stress , , and , with radii , , and , and their centres with coordinates , , , respectively. These equations for the Mohr circles show that all admissible stress points lie on these circles or within the shaded area enclosed by them (see Figure 10). Stress points satisfying the equation for circle lie on, or outside circle . Stress points satisfying the equation for circle lie on, or inside circle . And finally, stress points satisfying the equation for circle lie on, or outside circle . See also Critical plane analysis References Bibliography External links Mohr's Circle and more circles by Rebecca Brannon DoITPoMS Teaching and Learning Package- "Stress Analysis and Mohr's Circle" Classical mechanics Elasticity (physics) Solid mechanics Mechanics