Estudo comparativo de deslocamentos em lajes de concreto armado: Teoria de Kirchhoff e Método dos Elementos Finitos

Abstract

This study aims to compare the maximum displacements of reinforced concrete slabs using two distinct approaches: the classical Kirchhoff-Love plate theory and numerical modeling based on the Finite Element Method (FEM). Rectangular slabs subjected to uniformly distributed loads were analyzed under different boundary conditions, geometric aspect ratios, and varying thicknesses, in order to assess the validity of the plate assumption. Analytical solutions derived from Kirchhoff-Love theory were obtained through classical series formulations, while numerical analyses were carried out using the COMSOL Multiphysics software under a linear elastic framework. The results demonstrated excellent agreement between analytical and numerical solutions for slabs with high span-to-thickness ratios, confirming the applicability of plate theory within this regime. As slab thickness increases, progressive discrepancies between the analytical results and FEM predictions were observed, mainly due to the influence of transverse shear effects and the formulation of the finite element employed. It is concluded that Kirchhoff Love theory is suitable for displacement estimation in slabs, whereas the Finite Element Method provides greater flexibility and accuracy when classical assumptions are no longer valid.