R-funicularity of analytical shells

Francesco Marmo, Stefano Gabriele, Valerio Varano, Sigrid Adriaenssens

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


Between the ’50s and the ’70s of the last century a class of analytical forms, the so called parabolic velaroid surfaces, were widely used to design thin reinforced concrete shells due to their ability to equi-librate design loads by pure membrane actions. These forms are obtained as an approximate analytical solution to the differential equation corresponding to a compressed membrane subjected to a uniformly distributed vertical load. The same equation furnishes an analytical solution in the form of a series. The membrane equation is also solved numerically by an iterative implementation of the finite difference method. These numerical solutions are compared in terms of funicular efficiency by evaluating the generalized eccentricity and estimating their R-funicularity.

Original languageEnglish (US)
Title of host publicationProceedings of 24th AIMETA Conference 2019
EditorsAntonio Carcaterra, Giorgio Graziani, Achille Paolone
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages11
ISBN (Print)9783030410568
StatePublished - 2020
Event24th Conference of the Italian Association of Theoretical and Applied Mechanics, AIMETA 2019 - Rome, Italy
Duration: Sep 15 2019Sep 19 2019

Publication series

NameLecture Notes in Mechanical Engineering
ISSN (Print)2195-4356
ISSN (Electronic)2195-4364


Conference24th Conference of the Italian Association of Theoretical and Applied Mechanics, AIMETA 2019

All Science Journal Classification (ASJC) codes

  • Automotive Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


  • Analytical shells
  • Form finding
  • Funicular analysis


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