Surface and curves: A dialogue between nature and structural analysis

Abstract

The Geometry and Graphics have a fundamental role in the progress of the structural Engineering and buildings. The mission of modern representation for structural Engineering was basically dedicated to mastering the relationships between shape finding (and shape definition) and statics prediction (and statics calculation) (Ugo V in Fondamenti della rappresentazione architettonica, 1994) [1]. Build with ingenuity to simplify construction processes, dematerialize the masses to establish simple compositional rules, these principles on which the world of tensile structures is based, where ingenuity and form interpenetrate to produce results that challenge physics and science for a form at the limit of perfection. The geometry, at the centre of the design process from the concept phase to the construction is the control tool through which spatial intuition becomes a feasible project. The nature provides extraordinary examples of relationship between geometry, drawing and statics as like the spider’s web, a unique case of perfect interpenetration between harmonious design and advanced engineering. The analysis of the Geometry of Curves and Surfaces started from the first century after Christ with empirical experiments of the ancient Romans in the covers of theatres and arenas. The connections between ambient, nature and shape were studied in the “De Oratore” of Cicerone 55–54 B.C. and again from Vitruvio in De Architectura 15 B.C. The mission of modern representation for structural Engineering was basic basically dedicated to mastering the relationship between shape finding (and shape concept) and static ideas (and static studios) from the nature to the calculation. The aim of this paper is to discuss about the dialogue between this double geometrical approach and about its development over time. Proceeding over the centuries, first example of a roof tensile structure, which marks the start date of the tensile architecture, are the four-folds in steel, designed by the engineer V. G. Shukhov for the All-Russian Exhibition in Nijny-Novgorod, inspired by the architecture of nomad tents with the emblematic example of “Oval Pavilion”. The four pavilions for a few years remained the only example of tensile architecture, while succeeding fifty years, the projects mostly turned to experimentation of structures linked to International Exhibitions. It was in the following century, precisely in 1952, which took place the true beginning of the high season of tensile architecture, with the construction of the Dorton Arena, in Raleigh, USA. For the first time the concept of “tense surface, double curvature, pre-stressed” was introduced. A double curvature structure that presents itself with the form of a hyperbolic paraboloid. In this perspective is the natural world and its laws that must be investigated for the application to architectures, through the search for constructions that show natural processes with particular clarity the natural processes that create objects, with the search for the essential. Artificial mesh work like natural ones, the supporting function is guaranteed by the central curved “saddle” shape supported a series of rods. The natural model for pneumatic structures is instead traced to the minimal surfaces of soap bubbles. on this last the first study models of the structures are founded. Remarkable principles have been learned: from their working, to their possible aggregations and subdivisions. In this paper we want to emphasize at the duality between the kinematic graphics drawing (direct consequence of Cremona’s diagrams in the mid-19th century) and stress-strain shapes with predictions trough the 2D e 3D Finite Element Model (F.E.M.) analysis. Two cases of study are analysed the “Olympiastadion” in Monaco (Germany) by Otto Frei and the “Jesolo Magica”—Venice, Jesolo (Italy) one of the last design of Zaha Hadid.