Thick Plates in Bending and Shear

Abstract

A plate subjected to a load perpendicular to its plane is in a state of bending and transverse shear. If the plate is of concrete, it is called a slab. Plates are generalizations of beams. A beam spans one direction, but a plate is able to carry loads in two directions. Figure 3.1 shows an example of a plate on four supports under a point load Fz. The mid-plane of the plate is in the x-y plane and Fz is acting in z-direction perpendicular to the plate. The plate will undergo deflections, and moments and shear forces can be expected. The aim of of this chapter is to explain how these stress resultants can be determined. If both bending moments and shear forces occur, in general bending deformations and shear deformations have to be accounted for. For beams, it is known that shear deformation can be neglected only if the beam is slender. Similarly we must distinguish between thin plates and thick plates. We will start so that the theory applies for both categories. In Chapter 4 we reduce the complexity and restrict ourselves to the theory for thin plates and its application. An important reason for starting in a general way, including thick plates is, that many computer programs also offer options for thick plates.