FINITE ELEMENT ANALYSIS OF A HYPERBOLIC PARABOLOID BOUNDED BY STRAIGHT LINES
DOI:
https://doi.org/10.51923/repae.v12i02.421Keywords:
Hyperbolic Paraboloid; Finite Element Analysis, Membrane, Shell.Abstract
Hyperbolic paraboloid roofs exhibit great versatility, as they can span large distances using a relatively small amount of material. Due to their shape, they also have a strong aesthetic appeal and allow the use of different materials, such as concrete, steel, and wood, in their construction. Structural analysis and design can be carried out using an analytical procedure in which only membrane effects are considered in the roof, that is, tangential stresses. However, the widespread use of numerical tools allows for the consideration of all forces acting on the roof when it is modeled as a shell. The objective of this work is to evaluate the differences in the analysis of a hyperbolic paraboloid bounded by straight lines when treated as a membrane and as a shell. To this end, a membrane simulation was performed and validated through comparison with analytical results. The same roof was also simulated considering shell effects, that is, bending, shear, and torsion in addition to tangential stresses. It was observed that considering shell behavior leads to a reduction in the forces in the beams supporting the roof, since the roof itself begins to actively contribute to absorbing these forces. Moreover, there are regions in the roof where stress concentrations occur and must be taken into account in the design of these structures. In general, replacing the analytical membrane method with computational methods that consider shell behavior can be recommended, as this approach results in safer and more economical structures, and there are currently various computational tools available for this purpose.
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Copyright (c) 2026 Vitor Rigueira de Godoy, Geraldo Donizetti de Paula, Flávio Teixeira de Souza (Autor)
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