Principal Stresses and Principal Planes:

In previous Section, we have seen that for a given state of stress at a point, the magnitude of normal stress and shear stress might vary with respect to the inclination of planes. If we are concerned with the safety of solids under stress, we are needed to find on which planes extreme values of normal & shear stress components are present. Therefore, it is necessary to know :

1.      Maximum tensile stress,

2.      Maximum compressive stress, and

3.      Maximum shear stress.

Additionally, we might also have to know the planes on which these values occur.

The extreme values of normal stresses are called as the Principal Stresses and the planes on which the principal stresses work are called as the principal planes. In two-dimensional problems, there are two principal stresses, like as the major principal stress and the minor principal stress which is defined as the maximum & minimum values of the normal stresses respectively. Here, the maximum or minimum is to be let algebraically. For instance, if the principal stresses happen to be 20 N/mm² tensile and 75 N/mm² compressive, the tensile stress of 20 N/mm² is to be taken like the major principal stress mention by the symbol σ ₁ and the compressive stress of 75 N/mm² is to be taken as the minor principal stress (algebraically - 75 N/mm²) and mention by the symbol σ ₂. The corresponding planes are described as major and minor principal planes.