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_{x}, N_{y}, N_{xy}, N_{yx}, Q_{xz}, and Q_{yz} are force resultants; p_{x}, p_{y}, and p_{z} are distributed external forces applied on the plate.
The equations of moment equilibrium are
x direction:
y direction:
z direction:
where M_{x}, M_{y}, M_{xy}, M_{yx}, N_{xy}, and N_{yx} are moment resultants; and m_{x}, m_{y}, and m_{z} are distributed external moments applied on the plate.
Note that all second and higher order terms are neglected.
