Mohr's Circle for the Analysis of State of Stress:

Mohr's circle is a graphical method of discovering normal, tangential & resultant stresses on an oblique plane. Mohr's circle will be drawn for the below cases :

1. A body subjected into two mutually perpendicular principal tensile stresses of unequal intensities.

2. A body subjected into two mutually perpendicular principal stresses that are unequal & unlike (that means one is tensile & other is compressive).

3. A body subjected into two mutually perpendicular principal tensile stresses accompanied though a simple shear stress.

The circle in Figure is called as the Mohr's Circle of stress. Mohr's circle is extremely useful in graphical analysis of state of stress at a point.        

Given the state of stress (defined by s_x, s_y and t_xy), the process for making of the Mohr's circle was explained in previous Section. The determination of principal stresses & principal planes from the Mohr's circle was also mention. In this section let us study a few applications of stress analysis having the help of the Mohr's circle.

Assume we ought to discover the normal & shear stress components on a plane whose inclination to x plane is q_D. We require only drawing a radial line OD making an angle 2q_D with the radial line OX. The coordinates (s_D, t_D) of the point D shall give the normal & shear stress components on the plane. Therefore, once the Mohr's circle is made, the stress components on any plane might be readily achieved.