Bending of Simply Supported Rectangular Plates

Abstract

Many structures such as powerplant duct assemblies (Fig. 1–1), submarine bulkheads, ship and barge hulls, building slabs, (Fig. 1–2), and machine parts are designed in accordance with the bending theory of plates. The analysis of most plate configurations consists of solving a differential equation that is a function of deflection, applied loads, and stiffness of the plate. The solution of this differential equation results in an expression for the deflection of the plate. Other quantities such as forces and moments must then be determined from the calculated deflection. In this chapter, equations that express moments and forces in terms of deflection are developed first. Next, the basic differential equation for the bending of rectangular plates is established together with corresponding boundary conditions. These expressions are then used to solve various plate configurations and loading conditions.