Calculation of the strength of the plate, reinforced by the ribs of rigidity on the elastic base by the reverse method
Abstract
Calculation of the strength of the plate, reinforced by the ribs of rigidity on the elastic base by the reverse method
Incoming article date: 22.12.2017In this paper we consider the bending of a plate on an elastic base. Plate in plan has a rectangular outline. The plate material is isotropic. The plate is supported by ribs of rigidity directed parallel to the sides of the plate. It is taken into account that ry-bra, rigidities parallel to different sides, have different rigidity for bending and torsion. The calculation scheme assumes an orthotropic plate having various cylindrical stiffnesses in two mutually perpendicular directions parallel to the reinforcing ribs. The elastic foundation is adopted by Winkler, ie. it is believed that the reaction of the base is directly proportional to the deflection of the plate at each point. The plate rests on an elastic base and is loaded with a distributed load according to the following law q=q_0*sin〖2πx/a*cos〖πy/2b〗 〗. The problem is solved by the inverse method. Function of deflections of the plate are: w=C*sin〖2πx/a*cos〖πy/2b〗 〗.The stress state is studied and the load-carrying capacity is calculated for various parameters of the plate and the base.
Keywords: ribs, plate, elastic base, inverse method, thin, orthonormal, bending, load-carrying capacity, strength