Constraints for equivalence of hydrostatic stress and Normal Principal stress

Manjeel Kumar

Volume : VII, Issue : III, March - 2018

Constraints for equivalence of hydrostatic stress and Normal Principal stress

Manjeel Kumar

Abstract :

Hydrostatic stress be the one kind of average of the normal stress components of any stress tensor while Principal stress is one kind of maximum or minimum normal stress when the corresponding shear stresses are zero and the plane on which principal stress act is known as principal plane. As we know that there are infinite numbers of planes passing through the given point and the normal stress on each plane will be different from the other. Therefore If we know all the stress components σx,σy,σz,τxy,τyz,τzx,τyx,τzy and τxz for a particular plane then the principal stresses are the roots of the characteristic equation whose coefficients are stress invaiants I1,I2 and I3 Major aspect of this paper is to discuss the condition in terms of stress in–variants of equivalence of hydrostatic stress and principal stresses along the co–ordinate axes by taking principal axes as the axes of reference.