Plane strain problems: In many situations, physical constraints prevent strain from occurring

in a given direction. For example, $\backslash$epsi $\_($z$)=0$ in the case shown, where longitudinal movement of

the long prism is prevented at every point. Plane sections perpendicular to the longitudinal

axis remain plane and the same distance apart. For this situation, which is known as a plane

strain problem, how can the components $\backslash$sigma $\_($z$),\backslash$epsi $\_($x$),$ and $\backslash$epsi $\_($y$)$ be expressed as a function of $\backslash$sigma $\_($x$)$ and

$\backslash$sigma $\_($y$).$ Hints: set $\backslash$epsi $\_($z$)=0$ in generalized Hooke's law equation.