Stress Transformation Mohr Circle

Stress transformation rules

Let us consider an arbitrary plane inside an infinitesimal element. Let this plane be inclined at an angle to the vertical face of the element. A free body diagram of the region to the left of this plane is shown in the figure below.

 
Stress transformation


We get
 

 
Now let us look at a section that is perpendicular to the one we have looked at. This situation is shown in the figure below.
 


Or,
 

 
From equations (2) and (4) we see that the shear stresses are equal. However the normal stresses on the two planes are different as you can see from equations (1) and (3).