Abstract
This paper presents a simplified analytical method for rectangular plates with edge beams, such as building slabs, under the validity of the Kirchhoff–Love hypotheses. The accuracy of the Galerkin method depends on the shape functions used. However, it is difficult to find out the suitable shape functions satisfying the boundary conditions of plates with edge beams. So, the plate supported with edge beams is replaced with the plate supported with edges elastically restrained against translation and rotation. From relationships between these different boundary conditions, the shape functions in the current plate use the shape functions of beams supported with equivalent translational stiffness and torsional stiffness. Approximate but accurate solutions for static and dynamic problems of a rectangular plate with edge beams are proposed by the use of the Galerkin method. The numerical results obtained from the proposed theory for an isotropic plate with edge beams show good agreement with results obtained from the finite element method (FEM) using FEM code MSC/NASTRAN.
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