Principal Stresses and Principal Planes:

Here, we have seen that for a given state of stress at a point, the magnitude of normal stress and shear stress might vary along with respect to the inclination of planes. If we are concerned within the safety of solids under stress, we are needed to find on that planes extreme values of normal and shear stress elements are present. Hence, it is necessary to know:

(a) Maximum tensile stress,

(b) Maximum compressive stress, and

(c) Maximum shear stress.

Further, we might also need knowing the planes on that these values occur.

The extreme values of general stresses are known as the Principal Stresses and the planes on that the principal stresses act are known as the principal planes. In two-dimensional problems, there are two principal stresses, namely the major principal stress and the minor principal stress that is described as the maximum and minimum values of the general stresses respectively. Here, the maximum or minimum is to be considered 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 as the major principal stress denoted by the symbol σ₁ and the compressive stress of 75 N/mm² is to be taken as the minor principal stress (algebraically - 75 N/mm²) and denoted by the symbol σ₂. The corresponding planes are defined as major and minor principal planes.