ANALYTICAL METHOD FOR CALCULATING BENDING OF BEAMS OF VARIABLESTIFFNESS ON A NON-UNIFORM ELASTIC FOUNDATION

Abstract

An analytical method for calculating beams of arbitrary continuous variable stiffness supported on a non-uniform
continuous elastic Winkler foundation has been developed. The classical problem of calculating the bending of beams of
constant stiffness supported on a constant elastic Winkler foundation is well studied. However, the assumption of the
homogeneity of the foundation is far from reality and for more qualitative studies it is necessary to take into account the
heterogeneity (variability) of the foundation. In this case, the bed coefficient will be variable along the beam axis, which
significantly complicates the solution of the corresponding differential equation. The problem becomes even more complicated
when not only the bed coefficient, but also the stiffness of the beam is variable. This is the case that this article is devoted to.
The heterogeneity of the foundation is characterized by a variable linear bed coefficient, which can be any continuous function.
The method is based on the exact solution of the corresponding differential equation with variable coefficients. In closed form,
calculation formulas for the parameters of the stress-strain state of the beam are given. The calculation for the bending of a
concrete beam in the form of a truncated wedge resting on an exponentially varying elastic base is given.