COMPARATIVE ANALYSIS BETWEEN THE CLASSICAL ANALYTICAL METHODS AND THE FINITE ELEMENTS METHOD (FEM) IN OBTAINING EFFORTS ON SUPPORTED AND FREE STANDING STAIRS IN REINFORCED CONCRETE

Resumo

Free standing stairs in reinforced concrete are important structural elements that make up
the buildings. They are designed and executed to join, through successive steps, without intermediate
support, in a comfortable way the different levels of a building. In this context, the objective 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 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 [1] and (3) Knijnik & Tavares’ simplified method
[2]. In order to obtain FEM efforts, the free standing stair were modeled using the SAP2000® [3]
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. 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.