Structural analysis of Félix Candela's hexagonal hyperbolic paraboloidal umbrellas

Félix Candela was a celebrated builder of thin concrete hyperbolic paraboloidal (hypar) shells with a lasting legacy on the rationalist architectural movement of the 20th century. The iconic 4-edged square hypar umbrella became one of Candela most defining works due to its structural efficiency, economical constructability, and striking elegance. Yet, Candela's propensity for geometric experimentation led to the development of hexagonal 6-edged umbrellas capable of supporting parabolic discontinuities bisecting each tympan into two separate leaves for projects such as the Villahermosa Cathedral. Despite their artistic appearance, the structural performance of such topologies has never been subjected to rigorous analysis. In response, this paper presents a parametric investigation into the behaviour of 6-edged umbrellas, with and without parabolic bisectors, based on the proposed Villahermosa Cathedral. Finite element modelling revealed that hexagonal umbrellas exhibit markedly reduced deflections and stresses relative to equivalent square and triangular geometries, which are inversely related to the rise-to-area ratio. Unlike square umbrellas, critical bending moments are not sensitive to the edge rise for hexagonal 6-leaved variants with a constant projected area. However, 12-leaved hexagonal umbrellas adopting parabolic discontinuities suffer from disruptions in the flow of internal forces which ultimately yield a less efficient design.