(77)

Plane-strain conditions are used in the analysis of structures that are very thick in the *z*-direction. The *z-*direction strain is assumed zero $({\epsilon}_{zz}=0)$. Also zero are the shear strains ${\epsilon}_{yz}=0$ and ${\epsilon}_{zx}=0$. Hence, the 3-D elasticity relations (39) that express stresses in terms of strains are reduced to

$\begin{array}{l}{\sigma}_{xx}=\frac{E}{(1+\nu )}\hfill \end{array}$

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