A Simplified Approach for Bending Analysis of Beams Resting on a Two-Parameter Elastic Foundation

Abstract

This paper presents a simplified method for analyzing beams interacting with two-parameter elastic foundations. The study develops and examines a refined mathematical model that captures the mechanical interaction between the beam and the elastic foundation, providing an accurate description of the beam’s stress-strain state. The scientific novelty and practical significance lie in deriving analytical expressions for vertical displacements, bending moments, shear forces, and the distributions of normal and shear stresses along the beam. The methodology is based on theoretical analysis using an enhanced model of the two-parameter elastic foundation. As a result, analytical solutions are obtained, enabling evaluation of how the foundation’s stiffness parameters influence structural behavior. The study establishes that the distributions of deflection and bending moment are symmetric about the midspan, whereas the distributions of shear forces and shear stresses are antisymmetric. Findings indicate that increasing foundation stiffness reduces deflections but maintains the overall pattern of internal force distribution. Special attention is given to the case where α < 1, revealing unique features in the beam’s stress-strain state. The results confirm the effectiveness of the proposed method and demonstrate its applicability for analyzing beam structures on two-parameter elastic foundations