Analysis of RC beams on Elastic Foundations Based on Analytical Interpolation Functions

Resumo

Reinforced concrete beams resting on an elastic basis represent a typical problem of structural foundations. Although analytical solutions exist, the analysis of such structures is generally carried out using the Finite Element Method (FEM) due to the complexity introduced by different types of loading, support conditions and geometries. The classical FEM approach typically requires a refined discretization of the beam to accurately capture the elastic behavior of the supporting soil. Thus, the soil-structure interaction is simulated using springs along the nodes of the discretized model. However, when FEM interpolation functions are derived directly from the governing differential equations, these functions are analytical, and the discretization is not essential. This study employs an Euler-Bernoulli beam element formulation based on analytical interpolation functions considering the soil-structure interaction. This formulation is capable of modeling and simulating reinforced concrete beams with the minimum number of elements required to accurately describe geometry, or variation in soil properties. The numerical application demonstrates the capacity of the element in the design process of reinforced concrete beams on elastic foundation considering just a single element to model the structure.