Principal Planes and Principal Stresses:

Define the Principal Planes and Principal Stresses.
Sol.: When an element in strained body is under action of plane stresses, it is found that there exist 2 mutually perpendicular planes of element on which normal stresses are maximum and minimum and no shear stress is acting on these planes. These planes are called as principal planes.

From the figure given below; the principle planes is determined by
 
As shear stress on these plane is zero, thus they are also called as shear free plane.

The maximum and minimum principal stresses which are acting on principal planes are called as principal stress.
 
The principal stress which is having maximum value is called as "major principal stress" and principal stress having minimum value is called as "minor principal stress".
 
Where  σ_x,  σ_y be direct stresses in  x and y direction and   σ_xy be the shear stress normal to xy plane.

Resultant stress can be given as follows