Hanging models

Hanging models are simulations of a weighted net under gravity, also called, (stereo-)funicular models. Its functioning, clearly described by Hooker in the seminal quote “as hangs the flexible line, so but inverted will stand the rigid arch”^[1], allows these kind of models to use flexible curves/ networks/fabrics that, using their own tension strength to carry a certain load, are morphologically vertically symmetrical to a solution strong in compression, successfully avoiding bending moments.

Before computation, architects such as Gaudi, Isler or Otto used this concept as a design tool for shells made of materials such as brick, concrete or wood. Computation tools^[2] were created for a more comprehensive usage of hanging models, allowing for complex realizations which take advantage of computation such as Voussoir Cloud (Figure 81[a]) or PreVault (Figure 81[b]).

Computational hanging models are always based in a polygon mesh (a finite element surface representation). This mesh topology might be implemented in different approaches: a) the mesh topology is equivalent to the desired tessellation topology and the resulting hanging model contains in itself the final tessellation; b) the mesh topology resolution is very high so that the resulting hanging model reflects the thrust surface^[3] as close as possible, which will serve as base for the ensuing stereotomic design.

[1] The original quote describing this catenary curve is the anagram ”abccc ddeeeee f gg iiiiiiii Ilmmmmnnnnnooprr sssttttttuuuuuuuux”, revealed only as “Ut pendet continuum fl exile, sic stabit contiguum rigidum inversum” after Hooke’s death by his will (Heyman, 1998, p. 79).

[2] See CADenary (A. Kilian et al., 2003) or Kangaroo (Piker, 2010).

[3] In an arch, the resultant of compressive forces lies within a line called the line of thrust. Stable structures contain this line within its mass. Similarly, in a three dimensional system, one can find a thrust surface where forces optimally flow.