Plane Stress

Plane stress refers to a state of stress in which two faces of a cubic element are free of stress, such that stress is zero across one of the dimensions. This simplifies analysis to an $xy$ plane.

• In the above, the stresses that exist are ${\sigma }_x,{\sigma }_y,{\tau }_{xy}$. Note that ${\tau }_{yx}={\tau }_{xy}$ (for equilibrium)!
• The stresses acting on the faces perpendicular to the thickness ($z$-direction) are assumed to be zero, such that ${\sigma }_z={\tau }_{zx}={\tau }_{zy}=0$.

The state of plane stress occurs in a thin plate subjected to forces acting in the midplane of the plate.