Development of Calculation Theory for Hinged-Connected Beams on Elastic Base

The paper provides a brief review of the literature on the theory and methods of calculating hinged-connected or articulated structures on an elastic base. The author refers to the works of B. G. Korenev, G. Ya. Popov, I. A. Simvulidi, R. V. Serebryany, A. G. Yuriev, in which, using various approaches, studies have been carried out to calculate hinged-connected beams and slabs on an elastic base. From the analysis of  scientific literature on the topic under consideration, it can be concluded that there is no general approach to solving this problem, which is valid for any hinged-connected beams and plates lying on any model of an elastic base under the action of an arbitrary external load.  In addition, a similar problem for this type of engineering calculations is observed in the normative documents. In the Republic of Belarus, a number of industry documents have been used to calculate pavement bearing elements for various highways and track transverse structures, in which road pavements with a load-bearing element and the connection of elements between themselves (hinged or rigid) are considered in an incoherent formulation. The paper proposes a universal approach for calculating hinged-connected beams on an elastic foundation, based on the mixed method of structural mechanics, taking into account the Zhemochkin ratios for functions of the elastic medium effects. The following hypotheses and assumptions are taken into account: only normal stresses act on  the  contact  of  the  beam  with the base, hypotheses  of  the bending  theory are valid  for beams,  hinges  between  the beams are cylindrical, and the distribution of contact stresses along the width of the beams is uniform. As a result of the proposed calculation, the stress-strain state of a system of hinged-connected beams on an elastic foundation has been investigated, namely: distribution of contact stresses under beams, internal forces in the beams and hinged joints, as well as settlements of the elastic foundation under them. The numerical implementation of this approach has been performed using the mathematical package Mathematica 10.4. Examples of calculation are given for different versions of hinged-connected beams and an elastic base: for three hinged-connected beams based on Winkler and seven – on an elastic half-space.