Reference: Principal stresses and strains in a two-dimensional stress field.
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ESDU 72013 gives curves from which the principal stresses and their direction can be found from a knowledge of the direct and shear stress components applied. The formulae on which the curves are based are given, together with formulae for the maximum shear stresses and shear strains. These formulae apply to any material and condition. For elastic isotropic materials, formulae for the principal direct strains and maximum shear strains are also given when the material is in either plane stress or plane strain.