Structural evaluation of Félix Candela's 8-sided hyperbolic paraboloidal umbrellas

Shengzhe Wang, Annie Levine, Maria Garlock, José Antonio Contreras-Jiménez, Juan José Jorquera-Lucerga

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Structural artist Félix Candela pioneered the 8-sided hyperbolic paraboloidal (hypar) umbrella by introducing a parabolic discontinuity bisecting each quadrant of the classical 4-sided form. While artistically striking, such structures have never been rigorously examined from a structural engineering perspective. This paper formulates equations governing the geometry of 8-sided hypars, facilitating the in-depth analysis and comparison against their more common 4-sided variants via finite element modeling. A parametric investigation based on two historical case studies identified that 8-sided umbrellas exhibit larger deflections and stresses relative to 4-sided renditions, thus rebuking Candela's hypothesis concerning the improvement to structural efficiency offered by the parabolic fold. While corner deflections and principal stresses generally decrease with increasing curvature, the discontinuity present in 8-sided forms disrupt the flow of internal forces, resulting in stress concentrations at the parabolic apex manifesting as large moment demands. However, it was demonstrated that 8-sided hypars exhibit increased resistance to shell buckling over 4-sided variants as revealed through a simplified analytical approach.

Original languageEnglish (US)
Article number111156
JournalEngineering Structures
StatePublished - Nov 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering


  • 8-sided umbrella
  • Finite element modeling
  • Félix Candela
  • Hyperbolic paraboloid


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