= Pure shear from opposite principal strains
{title2=$\gamma=2e,\quad\tau=2Ge$}
The infinitesimal strain tensor $\operatorname{diag}(-e,e)$ compresses one principal direction and stretches the perpendicular one by the same amount. Rotating the coordinate axes through $45^\circ$ turns it into a tensor with zero normal strains and off-diagonal entries of magnitude $e$. The engineering <shear strain> is twice the tensor shear component, so its shear angle has magnitude $\gamma=2e$. Likewise principal stresses $(-S,S)$ give zero normal stress and shear stress of magnitude $S$ on those rotated faces. The <shear modulus> law $S=G\gamma$ therefore gives $S=2Ge$.
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