Plate Membrane Theory

Abstract

The word plate is a collective term for systems in which transfer of forces occurs in two directions; walls, deep beams, floors and bridge slabs are all plates. We distinguish two main categories, plates that are loaded in their plane, and plates loaded perpendicularly to their plane. For both categories we give an approach with differential equations, such that a basic understanding is provided and for certain characteristic cases an exact solution can be determined. We follow the displacement method, working with differential equations. In plates that are loaded in their plane, the plane stress state is called the membrane state. All stress components are parallel to the mid- plane of the plate. In special cases we can simply determine the stresses.