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This routine computes the principal stresses, maximum shear stresses and direction cosines for a set of normal and shear stresses in a solid body. The basic theory is described here, you should familiarise yourself with both of these monographs and their referenced documents:
You can use any system of units as long as it's consistent, i.e, use the same units of stress for all stresses. The routine can calculate results either for the full stress set or the deviatoric one, but you must input the full stresses.