Estudo comparativo analítico e numérico via Método dos Elementos Finitos (MEF) de escada reta autoportante em concreto armado

Abstract

The aim of this research is to realize a comparative study of internal forces of the bending moment, shearing and torsion in free standing stairs considering two methodologies: (a) one using classical analytical methods for obtaining efforts in stairs (CAM) and (b) other using Finite Element Method (FEM). In the analytical modeling, the free standing stairs were treated as structures composed of: (1) isolated slabs through the Plate Theory with resolution of Lagrange's non-homogeneous fourth-order differential equation, (2) simplified method proposed by Araújo (2014) and (3) Knijinik's simplified method (1977). In order to obtain FEM efforts, the free standing stair were modeled using the SAP2000® program, using frame elements, both individual and in grid structures, and shell elements. The structures were made considering discretized finite element meshes with dimensions varying from 20 cm to 25 cm, sufficient to obtain the satisfactory efforts and with low computational cost. The results showed that on average the analytical models overestimated the values of internal forces (bending moments in the transversal direction in the landing and in the longitudinal direction of the stair), mainly by the fact of not considering the three-dimensionality of the stairs, redistribution of efforts and the consequent interaction among the bending and torsion efforts. It was also observed that shell element modeling, when compared to the frame elements, presented results closer to the analytical models considering the supported stairs. In the case of free standing stair, the settling moments between the landing-ladder links were similar to the numerical models and diverged when compared to the simplified models of Araújo (2014) and Knijinik (1977). Finally, the conclusions of the research indicated that although free standing stairs present much greater efforts and require higher thicknesses of bids and levels than ladders supported in beams, however, the lack of intermediate and adjacent structural elements results in a much more accelerated constructive process.