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Cross masonry vaults are common structural elements in historical buildings. They are largely diffused in all European countries, including those characterized by higher levels of seismicity. Although they have been constructed for centuries, they represent some of the most vulnerable elements of traditional architecture, especially with reference to horizontal loads. The understanding of their structural behaviour under seismic loading is a crucial aspect for the accurate assessment of the safety of historical buildings. In the present work, the seismic response of cross masonry vaults is analysed through the Finite Element Method (FEM) and static non-linear analyses considering the effect of different brick patterns and boundary conditions. A simplified micro-modelling approach is adopted for the generation of the FEM models and two different brick arrangements are considered, i.e., radial bricks and diagonal bricks, which are the most widespread in European cross vaults. Two different boundary conditions are assumed in order to simulate a vault with and without lateral confinement. Static non-linear analyses are performed by monotonically incrementing a lateral acceleration until collapse. Results are analysed in terms of maximum load factor, stiffness, ductility, crack pattern and damage mechanisms. The analysis of the results shows that not only boundary conditions, but also the brick pattern strongly influences the vault seismic response both in terms of stiffness and ductility as well as in terms of global capacity.

Zagreb Cathedral was severely damaged by the 5.4 magnitude earthquake on March 22, 2020. Thechurch had already been hit by a severe earthquake in 1880 and was restored in the neo-Gothic stylewith cross vaults and arches supported by slender columns. In the restoration, the spatial connectionbetween the load-bearing elements was poorly executed and the structural system for horizontal loadshas not been significantly improved, which resulted in serious damage from the new earthquake. Forthe purposes of a new reconstruction, a structural analysis of the Cathedral is currently being done usingthe distinct element method (DEM). This paper focuses on the geometry of blocks that form a crossvault. The available solutions for the automatic generation of masonry geometries developed inGrasshopper are mostly focused on the generation of walls [4] or barrel vaults. The vaults in ZagrebCathedral are non-standard cross vaults that are not square in plan, but strongly rectangular. The crownsof orthogonal barrel vaults that form a cross vault are not at the same height and some are not horizontal.Since the block arrangement in vaults (stereotomy) is of great influence on the behaviour of cross vaults(less depending on mechanical properties [5]), this paper proposes a different definition of groins ofuntypical cross vaults. Finally, results (failure mechanism) of a numerical model for the cross vault aftertime history analysis obtained with 3DEC software are shown.

This paper presents a parametric stability study of groin, or cross vaults, a structural element widely used in old masonry construction, particularly in Gothic architecture. The vaults’ stability is measured using the geometric safety factor (GSF), computed by evaluating the structure’s minimum thickness through a thrust network analysis (TNA). This minimum thickness is obtained by formulating and solving a specific constrained nonlinear optimisation problem. The constraints of this optimisation enforce the limit analysis’s admissibility criteria, and the equilibrium is calculated using independent force densities on a fixed horizontal projection of the thrust network. The parametric description of the vault’s geometry is defined with respect to the radius of curvature of the vault and its springing angle. This detailed parametric study allows identifying optimal parameters which improve the vaults’ stability, and a comprehensive comparison of these results was performed with known results available for two-dimensional pointed arches. Moreover, an investigation of different force flows represented by different form diagrams was performed, providing a better understanding of the vaults’ structural behaviour, and possible collapse mechanisms were studied by observing the points where the thrust network touches the structural envelope in the limit states. Beyond evaluating the GSF, the groin vault’s stability domain was described to give additional insights into the structural robustness. Finally, this paper shows how advances in equilibrium methods can be useful to understand and assess masonry groin vaults., Applied Sciences, 11 (8), ISSN:2076-3417

[ES] La arquitectura valenciana del siglo XIII tiene, en el Real Monasterio de Santa María del Puig, una de las construcciones más icónicas en la reconquista de Jaume I. En conmemoración de la batalla del Puig, en 1238, el rey mandó edificar un primer santuario que en el siglo XIV se transformó en uno de estilo gótico, el que ha llegado hasta nosotros tras una serie de intervenciones realizadas en siglos posteriores. De ellas destacamos la del monasterio, realizada a fines del siglo XVI y la construcción de un coro en el siglo XVII, en estilo renacentista, a los pies de la iglesia. Dicho coro, derribado en 1964 debido a su mal estado, fue reconstruido posteriormente imitando el estilo gótico, siendo sus bóvedas el objeto de estudio de este Trabajo Final de Grado. El objetivo principal del presente trabajo es la determinación de la geometría espacial de los dos tramos de la bóveda reconstruida del coro a través del análisis de todos los elementos que las integran (elementos de sustentación, arranques, perfil de los nervios, curvatura de los arcos, claves, plementería, ...), haciendo un análisis comparativo con la geometría de las bóvedas de crucería gótica. Ello será desarrollado mediante un trabajo de campo consistente en la elaboración de croquis con mediciones utilizando los instrumentos de precisión métrica oportunos, completado con toma de puntos mediante estación total y fotografías para el empleo de la fotogrametría digital con el fin de realizar un levantamiento gráfico completo de las bóvedas de crucería del coro que permita el desarrollo del análisis geométrico de las mismas y de los elementos que las integran., [EN] The Valencian architecture of the 13th century has, in the Royal Monastery of Santa María del Puig, one of the most iconic buildings after the reconquest of Jaume I. In commemoration of the battle of Puig, in 1238, the king ordered the construction of a first sanctuary. In the 14th century it was transformed into a Gothic style, which has reached us after a series of interventions made in later centuries. Of these we highlight the one of the monastery, realized at the end of the 16th century and the construction of a choir in the 17th century, in Renaissance style, at the foot of the church. This choir, demolished in 1964 due to its poor condition, was rebuilt later imitating the Gothic style, with its vaults being the object of study of this Final Degree Project. The main objective of the present work is the determination of the spatial geometry of the two sections of the reconstructed vault of the choir through the analysis of all the elements that integrate them (support elements, starts, profile of the nerves, curvature of the arches, keys, severies, ...), making a comparative analysis with the geometry of the Gothic ribbed vaults. This will be developed through a fieldwork consisting of the preparation of sketches with measurements using timely metric precision instruments, completed with points taken by total station and photographs for the use of digital photogrammetry in order to perform a complete graphic survey of the ribbed vaults of the choir that allows the development of the geometric analysis of the same and of the elements that integrate them.

Masonry cross vaults had been used for centuries in the roofing of European buildings, palaces and churches, representing nowadays an integral part of national cultural heritage. In this regard, a sound knowledge of the structural response of cross vaults under vertical and horizontal loads is fundamental for planning accurate and compatible conservation programs. Whereas a certain consensus on the static behavior of the cross vault under gravitational loads has been reached, still more efforts are requested for assessing its seismic capacity. In the present work, the finite element approach has been implemented with a particular attention to the block interlocking and interface elements. On the one hand, an appreciable accommodation between the real block arrangement and computational effort is shown. On the other hand, modelling the blocks with rigid-infinitely resistant elements leads the interface as the only source of physical nonlinearities. Paralleling recent works on the seismic behavior of masonry arches, the influence of the mechanical parameters of the interface elements is discussed. Comparisons between numerical and experimental results available in literature are presented in terms of ultimate strength capacity and failure mechanisms., (undefined)

Pregledno se i uz kritičke napomene donosi prikaz i povijesne okolnosti pojave likovne umjetnosti na prostoru današnjega Makarskog primorja, donjeg toka lijeve strane Cetine, Zabiokovlja i donjoneretvanskoga pojasa u 15. st., kojom se prezentira gotički stil. Osim arhitekture crkava, skulpture i slikarstva, obuhvaćene su i utvrde, u prvom redu naznakom njihove uloge u razdoblju vladavine hercega Stjepana Vukčića Kosače. Istaknute su i one gradnje koje za hercega Stjepana vezuje predaja, te su kao takve i toponimijski posvjedočene., Gothic art in Primorje (Krajina), Gorska Zupa and Radobilja was emphasized during the rule of the Herzog Stjepan Vukcic Kosaca over the territories between Cetina and Neretva, around 1440-1416. Churches with rectangular shrine, mostly with partitions, mentioned in the Ottoman 16th-17th c. prove that they were built in the 15th century. The buildings were erected according to the model of the Franciscan churches of Our Lady in Makarska and Zaostrog from the 15th century. The Makarska church even after the destruction in the 16th and 17th c., preserved the aisle with a rectangular shrine. Such is St. Nicholas' church in Gornja Brela and reconstructed St. Cosmas and Damian church in Rogoznica, mentioned in 1461. In the church of St. Luke in Kucici the foundations of an earlier church with a rectangular apse were discovered. During Stjepan Kosaca's rule in the Omis hinterland there were built other churches, mentioned in the list from 1625. In Gorska Zupa worth mentioning is St. Peter in Dusina from 1585. In Lower Neretva area, St. Stjepan in Slivno Ravno has preserved only a sanctuary, while the foundations of St. Nichola's in Borovci prove its Gothic construction. The inscription with the name of the Herzog Stjepan from 1466 indicates that he constructed the church in Drasnice to honor the saint of the same name. The top door reliefs with relief crosses in Tucepi and Borovci belong to the churches from the 15th century, as well as the aspersorium of St. Luke's church in Kucici. At the beginning of the 15th century, St. Juraj in Tucepi and St. Ivan in Podaca were painted with dedicated crosses, inside squares and decorated circles. Their tombstones and plaques are also worth mentioning. The tombstones were related to Vlachs, and plaques with heraldic features to the local ethnic groups. The number of Vlachs was significant at the time of the Herzog Stjepan, when most of the tombstones were made. In the Omis fortress of Pec, according to tradition, the Herzog had a residence, but he also owned Starigrad and Visuc up the river. In Radobilja he intended to raise the bridge across the river and a fortress, which the Venetians in 1457 were seeking to destruct. He also owned Vrgorac in Gorska Zupa, whose wall had a Gothic crown and towers at the bottom. Additionally, there is Vratar on the right side of the Neretva, and Brstanik near Opuzen, important in the war with Dubrovnik from 1451 to 1454. The Herzog's Tower was preserved in Gornja Brela. It is an indication of the rule of Kosacas, as well as the Erceg's hill above Makarska, erected as a part of town fortification plan. Ermitage along the Cetina river from 5th- 6th c. is linked to the Herzog, as a remembrance of his rule (1440-1444) in Omis, as well as the interpretation of the Venetian coat of arms from the 17th century as his. The tradition was indirectly linked to the Herzog Stjepan in the name of the Illyrian fortress Matijasevica in Zivogosce, relating it to the Croat- Hungarian king Matija Korvin. Both rulers were allies in 1463 in the battles to return Bosnia from the Ottomans.

Cross vaults can be easily destabilised when their thrusts are not sufficiently contained by the stiffness of their lateral walls or systems of buttresses. A quarter-scale model from the aisles of Holyrood Abbey church in Edinburgh, which collapsed in 1768 due to excessive load from diaphragm walls that substituted the original roof trusses, demonstrated earlier the pattern of cracks that leads to failure under horizontal spread of supports. A recent model of this vault aimed to study the effects of applying Aramid fibre reinforcement against such failure exactly at the critical cracks, compared to other tests that studied arches or vaults under point load, reinforced continuously. The paper presents how the quality of certain areas of the fabric diverted failure from the longitudinal vertex merging with the detachment of the ribs, as originally observed. Moreover, the repair allowed the vault to resist 50% more spread of its supports, and failure occurred ultimately when new cracks formed in parallel to the repaired ones. The tests and repairs validate qualitative observations on crack patterns and failure of real cases and highlight the benefits and limitations when specific repairs are made instead of wholesome application of a reinforcing mesh at the extrados of vaults.

Aim of the present paper is the analysis of a series of existing masonry cross vaults exhibiting meaningful structural deterioration and diffused crack patterns, by means of an advanced non-linear and limit analysis software. The approach utilized is a non-standard and non-commercial one and bases both for the non-linear and limit analysis procedure on a FE discretization of the domain by means of rigid infinitely resistant wedges, where all the non-linearity is concentrated on interfaces between adjoining elements. When dealing with the non-linear code, a sequential quadratic programming scheme is used at each iteration in order to deal with the deterioration of mechanical properties of interfaces, provided that the actual non-linear behavior is approximated by means of a linear piecewise constant function. Several numerical simulations are performed varying constraint conditions, material properties, infill modeling and presence of FRP strips as reinforcement devices, comparing and discussing in detail the results obtained. From simulations results, it is found that the approach commonly used in practice to study cross vaults by means of the assemblage of single arches is not always reliable, providing failure loads and mechanism quite different from the real ones. Furthermore, similarly to what occurs for masonry arch bridges, it is found that the role played by the infill is crucial and that, depending on the actual mechanical properties of the infill, both the failure mechanisms and the collapse load may vary significantly.

[ES] En esta comunicación se hace un breve recorrido por el color en las bóvedas de crucería a través de algunas representaciones pictóricas, relacionándolas con algún ejemplo de edificaciones existentes que han llegado hasta nosotros prácticamente intactas. Se pretende asimismo, aportar un nuevo punto de vista al tratar de relacionar el empleo del color con aspectos geométricos. Se incluye también en la presente comunicación algún ejemplo que demuestra la presencia de decoración pictórica en las bóvedas de algunos edificios valencianos a partir de los restos de policromía localizados en algunos elementos de las mismas (nervios, claves o plementos) que permanecen en pie. También se incluye alguna muestra de restos de color en piezas halladas en excavaciones arqueológicas. En concreto, adjuntamos imágenes de las bóvedas del monasterio de la Trinidad y de la catedral de Valencia, de la iglesia de Santa María de Sagunto y una clave del monasterio de Santa María de la Valldigna (Simat de Valldigna, Valencia), con el fin de mostrar alguna relación entre los colores de dichos elementos y los ejemplos de decoraciones pictóricas analizados. ENGLISH: In this paper we do a brief tour of the color in the cross vaults through some pictorial representations, relating them with some examples of existing buildings that have come down to us practically intact. We also intended to bring a new point of view to try to relate the use of color with geometric aspects. There is also included in this communication an example which shows the presence of decorative paintings in the vaults of some Valencian buildings from the remains of polychromy in some elements of them (ribs, keys, or severies) that remain standing. There is also some sample paint in pieces found in archaeological excavations. In particular, we enclose images of the vaults of the Trinity monastery and the Valencia Cathedral, off the Santa Maria Church (Sagunto, Valencia), and a key of the “Santa María de la Valldigna” monastery (Simat de Valldigna, Valencia), in order to find any relationship between the colors of these elements and analyzed examples of pictorial decorations.

Umeå kommun har sedan 1995, med varierande intensitet, planerat för en ny simhall som ska ersätta den gamla från 1970. Det nu liggande förslaget har mötts med skiftande åsikter och de många kritiska handlar om både förslagets placering (mitt i centrala staden på en all- deles för trång tomt) och programmets omfattning (för lite). Eftersom jag delar dessa kritiska åsikter så har detta gett mig ett ypperligt tillfälle att som mitt examensarbete titta på hur jag anser att placeringen, omfattningen och gestaltningen av ett nytt badhus i Umeå ska se ut. Mina huvudsakliga frågeställningar har varit just placeringen, programmets omfattning samt naturligtvis även gestaltningen av ett badhus för Umeå kommun med sina 110 000 invånare. Jag har utvärderat de alternativa placeringar som föreslagits och samtliga platser har naturligtvis både sina för- och nackdelar men jag har kommit fram till att jag vill placera ett nytt badhus på samma plats som den nuvarande simhallen som planeras att rivas. Det som fick min jämförelse att väga över för min valda plats är att det ligger på randen av Gam- mliaskogen, ett rekreationsområde helt omgivet av stad men där det finns flera skid- och joggingspår. Detta är en möjlighet som är för bra för att försitta. Umeå municipality have, since 1995, at varying intensity, been planning for a new bath house to replace the existing from 1970. The current proposal has been met with mixed critique and the more critical ones fokus on both the placement (in the city centre on a too narrow lot) and the extent of the programme (too small). Since I share these critical opinions it has given me an excellent opportunity for this thesis work to examine the placement, extent and figuration of a new bath house in Umeå.