Santiago Huerta

The structural behavior of tile vaults remains challenging to evaluate accurately through numerical models, due to their geometry, the heterogeneity of its mechanical properties, and its boundary conditions. This study presents an experimental investigation carried out as part of a teaching innovation project aimed at deepening the understanding of masonry behavior through hands-on construction and collapse testing. Scaled vaults were built using traditional methods, employing thin bricks and fast-setting gypsum, materials typically selected for their accessibility and compatibility with heritage-inspired craftsmanship. The models were incrementally loaded until failure, enabling direct observation of collapse mechanisms. Plastic limit analysis was used to estimate structural capacity, with a focus on verifying the compatibility conditions of hinge formation. The vaults were documented using photogrammetric reconstruction (Structure-from-Motion) to generate accurate 3D models, and the evolution of collapse mechanisms was analyzed through digital motion tracking of observed hinges. Experimental loading reached values up to 4 kN/m² without collapse, confirming that even thin-tile vaults exhibit considerable reserve capacity. While these values should be understood as conservative lower-bound estimates due to the workshop conditions, results also highlight the significant influence of construction imperfections and boundary conditions. This work reinforces the educational value of physical experimentation and offers empirical insights into tile masonry behavior that cannot be captured through purely digital or parametric models.

El análisis gráfico de equilibrio se remonta a los inicios de la teoría de arcos. Visto en retrospectiva, parece obvio pues sólo hay que emplear la ley de composición de las fuerzas, descubierta por Stevin a fines del siglo xvii. Sin embargo, tuvieron que pasar dos siglos y medio hasta que, a mediados del siglo xix, la combinación del concepto de línea de empujes con las herramientas gráficas, permitió a arquitectos e ingenieros analizar, primero arcos, y luego cúpulas, bóvedas espaciales, y edificios complejos. Estos métodos gráficos fueron considerados entonces aproximados o incorrectos por la concentración en el análisis elástico. El profesor Heyman demostró en los años 1960 que el empleo de métodos de equilibrio, con una condición de resistencia del material (la fábrica tiene que trabajar a compresión), conduce a soluciones seguras. Hoy día el análisis de equilibrio es “moderno” y la teoría clásica elástica es “antigua”, aunque se formalice con complicados programas de ordenador. La historia es interesante en sí misma, pero quizá también arroje luz sobre la resistencia que existe hoy día contra el empleo de estos métodos de equilibrio.

La columnata del Louvre es la obra maestra de Claude Perrault, no sólo por su atractivo estético, sino también por la solución técnica que adoptó. Perrault puede considerarse el inventor de la fábrica armada, en la que la piedra resiste las fuerzas de compresión y el hierro las de tracción. Este artículo examina el proyecto, la construcción y el comportamiento estructural de la columnata del Louvre, y evalúa su seguridad mediante un análisis de equilibrio dentro del marco del Análisis Límite de Heyman. La columnata es estable, bien proyectada, y los únicos problemas que ha sufrido a lo largo de su historia se deben a la corrosión de los elementos de hierro.

Gothic architecture, while it looks frail and unstable, has survived for centuries. Some 17th- and 18th-century architects and engineers praised its robustness, but gave no explanation for it. Only Viollet-le-Duc tried to resolve this contradiction. For decades he inspected, surveyed and studied countless Gothic buildings and observed that the stone skeleton, this charpente de pierre, was capable of suffering deformations and maintaining equilibrium without collapsing. Viollet-le-Duc called this property élasticité: Gothic construction in stone was “elastic”, flexible. Viollet-le-Duc’s theory was accepted by the next two generations. By the 1920s, several authors strongly criticized its vagueness and contradictions. But it turns out that Viollet-le-Duc’s intuition was right. The limit analysis of masonry, developed by Professor Heyman in the 1960s, explains the robustness of the Gothic structure, which can crack and deform safely, finding always a state of stable, safe equilibrium.

The vault of Villaviciosa is one of the oldest existing examples of a true ribbed vault, and is the first of the crossed-arch type. Although its perfection suggests earlier trials, none has been found so far. It predates the oldest Romanesque ribbed vaults by more than a century. Notwithstanding its importance, no construction and structural study has ever been done; neither has an accurate survey been published. The purpose of this article is to fill this gap in the history of vault construction. A detailed survey has been made, providing the first accurate drawings of the vault. A close inspection of the extrados, completed with a visual inspection of interior damages, has allowed ascertaining the main construction features. With the geometry and the material data a structural analysis has been carried out. This analysis explains the fundamental structural behavior of the vault and throws new light into some historical issues; for example, it leads to discarding the widespread belief that the ribs are decorative: they are supporting the weight of the vault.