Resumen
AbstractThere is a set of Romanesque churches at Valle de Aran that were built between the eleventh and thirteenth centuries; these churches have suffered large deformations and geometrical displacements. These deformations have provoked, in some cases, convex shapes to appear, in relation to the generatrix of the vaults, which have the inverted shape of an arch. Geometrical assessment of the least rigid elements, the pillars, makes it possible to analyse the displacements, which have been the cause of funicular shapes on some vaults. It is possible to deduce the regression plane of the displacements of the pillars of the central nave and to define the deformation vectors over it. Thus, these data reveal the directions of the deformations of vaults and pillars to be determined. The deformations of the pillars are not perpendicular to the directrix of the central vault, so the methodology and results can be very useful to understand the nature of the displacements and to maintain these masonry structures.