Bending of Multilayer Slabs Lying on Elastic Half-Space, Considering Shear Stresses

Abstract

This article is devoted to the development of models and methods for solving contact problems of a structure with a foundation. The study of internal force factors in multilayer slab-strips lying on an elastic half-space, taking into account shear stresses, is an urgent task. In this study, a mathematical model is developed and an analytical method for solving contact problems is proposed to determine the internal force factors of multilayer slab-strips interacting with a half-space, taking into account the shear stresses in the structure-foundation contact. The problem, using orthogonal Chebyshev polynomials, is reduced to solving infinite systems of algebraic equations. To obtain a result with satisfactory accuracy, the required number of terms of the Chebyshev polynomial is established. From the result of numerical examples, the influence of the filler on the internal forces of the slab-strip is determined. At the same time, the internal forces of layered slabs-strips are compared, corresponding to different stiffness characteristics of the aggregate. An increase in the numerical values of the stiffness coefficients of the filler leads to a convergence of the values of bending moments. Based on the comparison, theoretical conclusions about the effect of the aggregate on the force factor of layer slabs, which is important for the designer when calculating projects of multilayer slabs, are presented. An analytical method for solving the problem was proposed to assess the internal force factors of multilayer slab-strips, based on the approximation of the orthogonal Chebyshev polynomials. An account for the shear stresses arising in the contact of multilayer slabs with the foundation leads to a decrease in the force factors in the slab-strips.