Solution of Contact Problem for Supporting Node of Beam Hinged Plate

Abstract

The paper considers a solution of contact problem for hinged supporting node of beam floor slab (coating). The main goal is to determine a stress state of the area where a plate rests on the wall. In this case, a number of problems are solved: construction of reactive pressure diagrams in the area of direct plate and wall contact, clarification of the calculated plate span, influence of contact zone size on a value of maximum bending moment in the middle of the plate, determination of contact area at various indices of flexibility and comparison of the obtained results with the known solution of rigid stamp and elastic quarter-plane interaction. The calculation has been carried out by the Zhemochkin method, its implementation for the given task corresponds to a mixed method of structural mechanics. As an illustration, the calculation has been performed on a concentrated load applied in the middle of the plate span. In the course of the study, it has been established that when a reinforced concrete slab rests on concrete and brick walls, the contact zone reduces itself to two Zhemochkin sections. When a flexibility index is decreased that corresponds to slab support on a less rigid base, the contact area is increased, and that, in its turn, has an influence on an increase of the calculated slab span and the bending moment in the middle of the slab. In the case of an absolutely rigid plate support (flexibility index is equal to zero), the contact stresses reach their maximum value at the point of plate edge contact and elastic quarter-plane. The nature of the diagram is confirmed by an analytical dependence of contact stress distribution obtained by Aleksandrov V. M. when solving a problem of pressing a rigid stamp into an edge of an elastic wedge.