2006-2 adaptable leonardo

Adaptables2006, TU/e, International Conference On Adaptable Building Structures Eindhoven The Netherlands 03-05 July 2006

Adaptable Leonardo. José Sánchez and Félix Escrig

Adaptable Leonardo.

J, Sánchez; F. Escrig. Seville University, School of Architecture, Avda. Reina Mercedes 2 Seville. Spain [email protected]

KEYWORDS Historic structures, rapidly erected structures, bridges . ABSTRACT. It is a topic to refer Leonardo when we introduce any branch of the art, science o technique because his manuscripts ever contains news that before him never where explored, nor profited even later. This can be understood because these manuscripts never where published till five centuries later. Observations referred to design of structures are the less known and otherwise the less studied. Really the most important problems about this subject are contained in the Codex I of Madrid, some in the Codex Atlantic, and less in the Codex II of Madrid. Other books do not refer these questions. 1. Two designs to span great distances with short pieces. One of the objectives of Leonardo who obsessively made research in the field was to achieve structural solutions to cover great spans with short pieces. We find a lot of drawings researching different solutions, mainly for bridges and roofs. Probably he never build it, but he solved the details as if they where to be realized. We want to introduce some of his applications to the architecture and engineering. 2. Bridge to be assembled rapid and easily.

Figure 1 Villard de Honnecourt Notebook (Folio 20) and Figure 2. Idem in Folio 23.



In the Codex Atlantic (Folio 22 recto) we can show a bridge build with trunks with which Leonardo suppose than he can build a path over obstacles rapid and easily (Figure 3). This is a clever idea based in other studies about braced girders as known from medieval writings (Figures 1 and 2). It is a precedent in China in the XII Century, the Rainbow Bridge, really build based in the same idea (Figure 4) with a lot of replicas along next centuries and the present days. In the Leonardo drawing we can find a lot of interest in construction process and less in the structural analysis, that is logic because the form is very efficient and the only really difficult is the construction.

Figure 3. Drawing in Folio 22 recto in the Codex Atlantic. Figure 4. Chinese Rainbow Bridge. The recent attempts of reproduce Leonardo’s bridge or the Chinese’s one are based in a physical connection by means of screws, that is not the spirit of the invention which did not require any connection nor tying except the necessaries to avoid sliding. Nevertheless sliding is avoided by self-weight. We can think that Leonardo’s idea was conceived without precedents that do not means that he did not know oriental technical advances published and explained by travelers who spoke about wonderful seen in other countries, mainly in China. But the Rainbow bridge from Song Dynasty was an aisled case that we know thanks to the drawing of the Silk museum of Beijing with the name “Quingming Festival in the Pien river”(Figure 4) The figure 3 contains the most advanced proposal and it describes completely the construction process that we reproduce in the figure 5. Previously he drew other models to improve the solution (Figures 6 to 8)

Figure 5. Different steps to erect the bridge (J. Sánchez). Figure 6. Bridge drawn in the Folio 45 recto of the Madrid I Notebook

Figure 7 Bridge drawn in the Folio 46 recto of the Madrid I Notebook. Figure 8 Bridge drawn in the Folio 183 recto of the Codex Atlanticus.



The difficulty of assembling the trunks decided Leonardo to prefer the solution of figure 3. He never made an analysis of these structures in part because he does not know very much about vectorial calculus and in part because construction was more important. We have analyzed the Leonardo Bridge and have found great difficulties to reproduce the real conditions of geometry and joints. Only a second order analysis has permitted to arrive to coherent solutions that we show in the figures 9 and 10 for symmetric and non symmetric loads.

Figures 9 and 10 Bendig moments for symmetric and non symmetric loads. 3. Roofs and Floors. An other subject in which Leonardo took great interest is in the problem of roofing. His first designs where elemental (Figures 11 and 12).

Figures 11 drawn in the Folio 50 verso of the Madrid I Notebooks and 12 Studies on the bracing of bars and the model.

Figure 13 Codex Atlanticus Fol 328 verso where we can find different patterns of braced roofs.



From a structural point of view it seems that the stability is not possible for so many extensions made with so short pieces. But the physical and analytical model confirms that they work with great efficiency (Figures 14 to 17). If we compare the bending moments with a conventional reticulated roof the difference is about 30% in the bending moments and 25 % in deflections. That means that in the practice these structures are optimal.

Figures 14 and 15 The model of the Figure 11 and the results in bending moments obtained by Finite element Methods.

Figures 16 and 17. The model of the Figure 13 A1 and the results in bending moments obtained by Finite element Methods.

Figures 18 and 19. Represents the bending moments produced in conventional reticulated roofs with the same span. For triangular meshes (Figure 13 B1) the results leads to the same conclusions. In the Figures 20 and 21 we show the physical model and the analytical model.



Figures 20 and 21 The model of the Figure 13 B1 and the results in bending moments obtained by Finite element Methods. In the figure 22 we show a device invented by Leonardo as a platform with great stiffness. Is the same design used in the figure 3 that if build with curved bars grows plain as shown. The advantage is that can be continued as desired as a cantilever. Leonardo proposed it also as a wall.

Figure 22. Rigid platform device invented by Leonardo. 4. Conclusions. May be Leonardo was a frustrated researcher who did not build any of his devices but the reality is that this can not be true because he the perfection of each detail of his proposals and the perfection of his drawings. May be his inventions have been lost and not known till the fifties of XX Century, but at the presents it is a lot of knowledge that we must profit. This is the objective of the research in which is based this paper. 2. References Leonardo Da Vinci .Códice Atlantico. Biblioteca Ambrosiana. Milán. Leonardo Da Vinci. Códice Madrid I y II. Biblioteca Nacional. Madrid. Duhem, Pierre “Etudes sur Léonard de Vinci. Ceux qu´il a lus et ceux qui l´ont lu » Librairie Scientifique A. Hermann. Paris 1906. Escrig, F., Sánchez, J. La geometría de las estructuras I. STAR 12. Sevilla. 2005. Pedretti, Carlo. Leonardo architetto. Electa 1988. ISBN 8843525190. Truesdell,C. Ensayos de Historia de la Mecánica. Ed Tecnos 1975. ISBN 84-309-0597-9. pp 17 a 88.

2006-2 adaptable leonardo

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