show that the planes carrying principal stresses have zero shear stress
Answers
Answer:
This question is like, why is x=0x=0 on yy-axis or y=0y=0 on xx-axis. As y-axis is defined as the line, where x=0x=0, similarly, principal planes are defined as the planes on which shear force is zero. It is not the other way round.
To understand this, imagine a point(P)(P)in a given object(B)(B) under stress. Consider an imaginary plane passing through PP, of infinitesimal area δSδS. The plane’s orientation is described by its normal nn. In the figure, the plane is shown as a green patch, on the left portion of the object BB. The force tt exerted on this patch by the right portion (removed in the middle figure), will in general, not be normal to the plane. Actually, its direction varies, with the orientation nn. The beauty lies in the fact that there really exist some special planes, on which this force tt is actually normal. Those planes are called principal planes. Naturally, shear force (component || plane) is absent, when the force tt is normal.