The use of structural analysis programs for the determination of the geometrical configurations of an artwork


Acad. Ms. Arq. Silvia Lenyra Meirelles Campos Titotto

Department of Design and Architecture, Faculty of Architecture and Town Planning, University of São Paulo



Associate Professor  Ruy Marcelo de Oliveira Pauletti

Department of Structures, Faculty of Civil Engineering, Polytechnic School, University of São Paulo






The sculpture “Monument to the Futile Form II” (“Monumento à Forma Fútil II”, MFF2) is composed of a textile membrane, anchored to a tensegrity simplex module. This paper reports the main ideas behind its conception, and the processes adopted for its design and construction.

The motivation for the MFF2 Project was to expose the geometric and structural peculiarities of taut membranes and tensegrities, realizing an art object of notable scale, and trying to intrigue observers through of the oddity of the shape. Even if underlying principles are well known to researcher in the field, a novel and remarkable artwork was resulted, as suggested by comparison with other works reported on the specialized literature.

The geometrical configurations of the tensegrity module and of the membrane composing the sculpture were determined both empirically and numerically, with the aid of adequate structural analysis programs (although the geometry of the tensegrity module was already well known, since the original studies of Snelson e Füller).



Tensegrity structures (“tension + integrity”) constitute a spatial structural system where compressed bars (struts), disconnected from one another, are connected by tensioned cables.

The stiffness of the structure is intrinsically geometric, meaning, in the terminology of structural engineering, that it depends on the intensity of the traction applied to the cables, the structure becoming hypostatic, in the cables go slack1.

Structures of this type were first conceived during the decades of 1950 and 1960, by architecture researchers and artists like Buckminster Füller, David Georges Emmerich, Keneth Snelson, Marc Mimram e Robert Le Ricolais. It is well known the dispute between Fuller and Snelson, regarding authorship of tensegrities, but it appears that also Emmerich and a few others could claim their discovery, so a communal authorship seems more appropriate.


Among the pioneering works, it can be cited the “Needle Tower” built by Snelson New York, in 1948. The title of the present work celebrates another historical oeuvre, the “Monument to the Futile Form”, built near Ramboiuillet, France (cited by Emmerich, 1996). It is a 6 bars tensegrity simplex module, different to the 3 bars, prismatic simplex module of the present work.

The use of membranes, by its turn, goes back to antiquity, but its architectonic use was popularized by architect Frei Otto, starting from the end of the decade of 1950. The artistic exploration, with very light and flexible fabrics, started during the decade of 1960, by designers like Bruno Munari, and took momentum in the decades of 1970 and 1980, mainly with the works of artist Aleksandra Kasuba. More recently, relevant works have been produced by interior designer Gisela Stromeyer, the architect Allan Parkinson, and artist Ernesto Neto.

In the present work, it is explored the possibility to fulfill the irregular space generated by the disposition of the bars of the tensegrity module with a stressed membrane, which insinuates through the bars, without touching them, and thus establishing instigating nuances of tension and dialog between these elements, whose geometry, highlighted by strong, primary colors, try to defy the common sense of the observer.



The geometrical configurations of the tensegrity module and of the membrane composing the sculpture were determined both empirically and numerically, with the aid of adequate structural analysis programs (although the geometry of the tensegrity module was already well known, since the original studies of Snelson e Füller).

Exhibition view I: FAU-USP, 2003.


The simulation of the assembling process of the tensegrity module was simulated with the aid of the PEFSYS finite element program by Delmo Deifeld, a PhD researcher in Structural Engineering of the Polytechnic School – University of São Paulo. Adjusting the length of only one cable, depicted in red in the figure, the whole structure can be erected. Several steps of the assembling sequence are show in the figure.

The tensegrity module was built from PVC hydraulic pipes, as well as steel cables, caps and fasteners, according to dimensions numerically determined by the PEFSYS program. Feasibility of stretching a membrane in-between the bars of the tensegrity module, without touching them, was initially guessed through sketches, then physically tested on the real module, with a piece of white Elanca fabric. It was concluded that the idea was feasible, but a more flexible and isotropic material should be used.


Exhibition view II: FAU-USP, 2003.


The final form of the membrane was then determined both in a 1:4 scale mock-up, using pantyhose fabric, and numerically, by means of nonlinear static analysis, using the Ansys finite element code.

In the 1:4 mock-up, some cables were substituted by rigid bars in order to enable easy manipulation. Once a satisfactory form was obtained for the membrane, size measurements made on the 1:4 pantyhose pattern were transferred to a 1:1 pattern, made of red Suplex fabric.






(Deifeld, 2002) Deifeld, T.E.C.; Pauletti, R.M.O. “Um Breve Estudo Sobre as Estruturas Tensegrity”. I Simpósio Nacional sobre Tensoestruturas, 2002, São Paulo.

(Emmerich, 1999) Emmerich D. G., “Structures tendues et autotendantes”. Monographies de geometrie constructive. La Villette: Editions de l’Ecole d’Architecture de Paris, 1999.

(Fuller, 1975) Fuller, R. B. Synergetics, Explorations in the Geometry of Thinking. Macmillan Publishing Co. Inc., Vol. 1, 1975.

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(Pauletti, 2002) Pauletti, R.M.O. “Análise de Estruturas Retesadas (Tensoestruturas),

empregando Programas Generalistas”. I Simpósio Nacional sobre Tensoestruturas, 2002, São Paulo.

(Pugh, 1976) Pugh, A. An Introduction To Tensegrity. Berkeley, U.S.A, Ed. University of California Press, 1976.

(Snelson, 1996) Snelson, K. “Snelson on the tensegrity invention”. International Journal of Space Structures. vol.11, p.43–48, 1996.

(Titotto, 2004) Titotto, S.L.M.C.; Pauletti, R.M.O. “Spatiality in Membrane Structures”. IASS 2004 Symposium – Shell and Spatial Structures: from Models to Realization, 2004, Montpellier.

(Titotto, 2003) Titotto, S.L.M.C.; Pauletti, R.M.O.; Brasil, R.M.L.R.F. “Tensile Structures: Form and Function Relationships”. International Conference of Textile Composites and Inflatable Structures, 2003, Barcelona.