Force Equilibrium |

The equilibrium equations describe how the plate carries pressure loads with its internal stresses.
Consider balancing of the forces and moments acting on a small section of a 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, whereas _{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}Notice that all second and higher order terms are neglected. |

Pressure Load |

In most practical cases, the external loading is limited to a distributed pressure. In other words, only p, _{x}p, _{y}m, _{x}m and _{y}m) are zero.
_{z}The six equations of equilibrium become Due to the lack of external force components other than This yields |