Gaudi's models

Why Gaudi realized one of Viollet le Duc's ideals

Viollet le Duc thought that shape (i.e. structure) should be adapted to the materials used. He appraciated gothic architecture as the most effective technic ever found to build stone cathedrals (large, high and lighty building). Gaudi founded a way even more effective for stone constructions. His way can be considered as the most effective way using some physical properties (it minimizes the shearing forces which are the causes of collapses). He found the way not using math as I will to demonstrate what I do assess but models that took naturally the optimum shape by putting them upside down. As you know it, Gaudi was very fond of nature and nature inspires his work very much. Once again natural shapes have proven to be effective and tightly linked to efficient structures.

Gaudi used models in several buildings including the Colegio Teresiano, The Guell crypt, the Sagrada Familia (only towers have been built so the "parabolic" structure is not visible). The "parabolic" archs are used in almost every building by Gaudi.

Comparison between stone works and chains

Gaudi's models

How can a "pseudo parabolic" arch be a "naturally efficient" structure for stone work

Generalization to take into account filling walls

The former calculus took into account only the structure. It is possible to take into account also the filling walls. It is to change the link mass from ml g dl into ml g dl+mwy where mw is the mass per surface unit of the wall. This modifies (1) into

(1') y'(x)=dy/dx=C2*mlgl/C1+C2*mwy/C1

I do not know how to solve simply those kind of differential equation but Gaudi knew how to do it without math: he evaluated the mass of the wall and then hang some little masses to the links to simulate the weight of the walls.

I hope you had fun in reading this.

©1993-2006 Frank Derville
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