Principal Stresses

24 Regardless of the state of stress (as long as the stress tensor is symmetric), at a given point, it is always possible to choose a special set of axis through the point so that the shear stress components vanish when the stress components are referred to this system of axis. these special axes are called principal axes of the principal stresses.

25 To determine the principal directions at any point, we consider n to be a unit vector in one of the unknown directions. It has components n^. Let A represent the principal-stress component on the plane whose normal is n (note both n and A are yet unknown). Since we know that there is no shear stress component on the plane perpendicular to n, the stress vector on this plane must be parallel to n and t.

26 From Eq. 2.10 and denoting the stress tensor by a we get

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