Force Equilibrium |

The equilibrium equations describe how the plate carries external pressure loads with its internal stresses. To enforce equilibrium, consider the balance of forces and moments acting on a small section of plate. There are six (6) equilibrium equations, three for the forces and three for the moments, that need to be satisfied. The equations of force equilibrium are x direction: y direction: z direction: where N, _{y}N, _{xy}N, _{yx}Q, and _{xz}Q are force resultants; _{yz}p, _{x}p, and _{y}p are distributed external forces applied on the plate.
_{z}The equations of moment equilibrium are x direction: y direction: z direction: where M, _{y}M, _{xy}M, _{yx}N, and _{xy}N are moment resultants; and _{yx}m, _{x}m, and _{y}m are distributed external moments applied on the plate.
_{z}Note that all second and higher order terms are neglected. |

Further Simplicification |

To further simplify the problem, consider a plate subjected to transverse loads. In other words, only p=_{x}p=_{y}m=_{x}m=_{y}m=0
_{z}The above six equations of equilibrium become Due to the lack of external force components other than This yields |