9 - Continuous Rectangular Plates

Abstract

In beam theories, we have for continuous beams the equation of three moments, which connects the bending moments above any three successive supports. Generally we have the following three cases: continuous beams under transverse loads, continuous beams under transverse loads togather with either tensile or compressive axial forces, and continuous beams on elastic foundation. Analogous to the continuous beams in beam theories, we have, in the theories of bending of plates, the three moments equation for the continuous rectangular plates under the loads normal to the plate. It was Galerkin (B. F. rajrepjara) who developed that equation. In this paper is discussed the bending of continuous rectangular plates under the loads normal to the plate together with the tensile or compressive forces acting in the plane of the plate, and the continuous plates on the elastic foundation. For example, for the case of the plates on elastic foundation, we have to solve:for the Fourier coefficients in calculating the bending moments. The symbols in the above equation are respectively as follows : An1=Bn1 =Cn1 =an1 =