Plates with Boundary Conditions of Elastic Support

A solution for the deflections, moments, and reactions in a rectangular plate under transverse load, supported at the corners, and with or without supporting beams at the panel boundaries, is presented in this paper. This solution can be classified as a unified one, since it is adaptable to most of the specific problems for which particular solutions have been developed. Provision is made for other classes of particular solutions for additional cases. The solutions for specific problems, expressed in a general form, differ only in the arbitrary constants appearing in the general form. These constants are evaluated by means of operational formulas, with dependence on parameters that are defined by the ratios of the flexural and torsional rigidities of the beams to the flexural rigidity of the plate, and by the proportions of the plate. To illustrate the procedure, the arbitrary constants are obtained for a rectangular plate under uniform load that is simply Supported on beams of finite flexural rigidity on four sides. A particular value of the parameter of relative flexural rigidity for which the expressions for moment reduce to simple exact formulas also exists. Moment and reaction coefficients are evaluated at positions along the axes of symmetry and the boundaries of the simply supported plate for several values of the parameter of relative flexural rigidity. Experimental verification is obtained by use of introductory tests made on panels supported on beams of arbitrarily reduced flexural rigidity.