Stresses and deflections in thin rectangular plates using Navier's, Levy's, and energy methods are considered in this chapter. As observed previously, the rectangular-plate element is an excellent model for development of the basic relationships in Cartesian coordinates. However, for most rectangular-plate problems, there is no exact solution to the governing equations. Instead solutions for deflections and moments are obtained by using various infinite series formulations. The method of superposition is also applied to determine stresses and deflections. The numerical values are much easier to determine with the aid of a computer.
Rectangular plates are mostly classified in accordance with the types of support used and loading. Here the bending of simply supported plates, clamped or built-in plates, plates having mixed support conditions, plates on an elastic foundation, and continuous plates are considered. Rectangular plates subject to uniform and nonuniform loadings are analyzed. Continuous plates consisting of a single plate supported by intermediate beams or columns are also discussed. All cases are treated using relationships derived in Chapter 3. The strip method represents an examination of the bending of rectangular plates based on elementary beam theory.