Principal Stresses

Principal stress can be explained as the most as well as the least value of regular normal stress on a plane wherein one cannot find shear stress. On the other hand, the principal plane can be described as the plane on which the principal stress is acting upon and the value of shear stress is found to be zero. The third point, that is the principal angle can be explained as the angle at which the orientation of the principal plane can be found regarding the original axis. 

Principal Stress

In physics, stress can be explained as the amount of the magnitude of the forces that lead to deformation. In basic terms, one can explain stress as force per unit area. Principal planes can be explained as the planes with the material such that the subsequent stresses across them are totally regular stresses or planes across whose none shearing stresses take place. In simple words, one can say that the principal stresses are the ones that act on the principal planes. The plane which has the most normal stress is popularly known as the major principal plane whereas the stress which acts on this plane is known as major principal stress. The plane which carries the least normal stress can be called a minor principal plane whereas the stress which acts upon this can be named minor principal stress. 

As observed from the above statements, it can be put into gist that stress in physics refers to the perpendicular force which acts on an object per unit area. The stress which is maximum, that is the most, is known as principal stress whereas the plane at which this supreme stress gets induced can be called the principal plane. Lastly, it can be said that the value of shear stress on the principal planes can be found as zero. 

Principal stress formula

Principal stress can also be explained using a formula. The figure can help in understanding the formula and its derivation in a better way. 

Now, as observed, one can take the angle formed in the triangle ABC as θ, Now as we can see from the below equation:

• The normal component of force, Pn is equal to P.Cosθ 

• The tangential component of force, Pt is equal to P.Sinθ 

• Normal stress is equal to σn is equal to σ.Cos2 θ 

• Tangential Stress σt is equal to σ. (Sin2θ/2)

• Thus, the resultant stress can be implied as σr = √ σ2n + σ2t

Lastly, from the given formula one can better learn about the concept of principal stress.

Conclusion

As we have reached the conclusion of this segment, the concepts regarding stress, principal plane, principal stress have become clear. One can understand that stress in physics refers to the value of the magnitude of the forces that lead to deformation. In simpler words, an individual can explain stress as force per unit area. It can be further brought to light that the principal stresses refer to those stresses which act on the principal planes. Now, as we moved forward, we also learnt about the plane which has the maximum amount of normal stress and it is popularly termed as the major principal plane whereas the stress which acts on this plane is popularly termed as major principal stress. Lastly, that plane that carries the lowest normal stress can be termed as minor principal plane whereas the stress which acts upon this can be named as minor principal stress.