For an element in pure shear (+τxy), the principal stresses will be given as

1
\({\sigma _{1.2}} = 0,\; + {\tau _{xy}}\)
2
\({\sigma _{1,\;2}} = \pm {\tau _{xy}}\)
3
\({\sigma _{1,2}} = \pm {\tau _{xy}}\sqrt 2 \)
4
\({\sigma _{1,2}} = \pm {\tau _{xy}}/\sqrt 2 \)

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