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Architected porosity in masonry structures can be created by transforming stock materials into a lattice of interlocking units through an automated batch process. Porous masonry forms numerous enclosed cavities for thermal performance and reduces material usage while maintaining structural integrity. This work investigates the potential and limits of digital tectonics of porous masonry through a complete process of design, manufacturing, and construction. The confluence of digital fabrication with tectonic exploration opens new dimensions unattainable by traditional stereotomy. Interlocking materials inspired by Abeille vault and digital stereotomy have made rapid progress. Following the theory of poetic construction, this work proposes that masonry construction should evoke visual or haptic enhancement through the fulfillment of pragmatic functions. We formulated a design challenge for a confined dry masonry wall for the envelope of the 2226 building. It assumes batch-cutting bespoke units out of large blocks of high-strength foam. Through a process of cutting and reassembling, the stock material is topologically expanded into a porous structure. A series of prototypes were developed to explore novel articulation, structural and thermal performance, and economical manufacturing. One can perceive the logic of porous construction through visual and haptic empathy. The materialization process interacts with the design masonry units and the interlocking mechanism. For future practice in masonry, the porosity should be planned at multiple scales (molecular scale, aggerate scale, construction scale) across the life cycle of the material. [ABSTRACT FROM AUTHOR]

The present study investigates the relation between the optimal geometry (quantified via the minimum thickness) and the number of concurrent hinges at the masonry arch's limit state. The Heymanian assumptions regarding material behavior are adopted, and only constant thickness arches subject to static (i.e., self-weight) loading are considered. First, the only numerically verified completeness of the failure mode types (including 6 and even 7 hinges) of gothic arches is analytically proven. Next, it is investigated whether a higher number of hinges can concurrently occur for arbitrary, symmetric concave arches. A numerical procedure is presented which generates suitable arch geometries corresponding to a k-hinge mechanism, where k is an arbitrary odd integer not smaller than 5. For the generated class of arches, a higher number of concurrent hinges leads to lower minimum thickness values. However, it is explicitly proven that a higher number of hinges is not necessary for lower minimum thickness values. A small database about the geometry of the transversal arches of English and French medieval gothic cathedrals concludes the first part to allow comparison with the derived results. In the second part of the paper, existing literature results on the limit state analysis of gothic arches are extended by the effect of stereotomy on the failure mode type and minimum thickness value. [ABSTRACT FROM AUTHOR]

The stereotomy (bricklaying pattern) of masonry arches is not only a characteristic of the architecture of these structures, but also an important revealing element of mechanical safety when degradations appear in the complex material of masonry. This paper presents the effect of randomness of this parameter on the bearing capacity of masonry arch bridges based on reliability of structures. Different mechanical models that are classically used for the analysis of the bearing capacity of masonry arches can support a reliability analysis. In this paper, a rigid block model and finite-element model are presented and compared. Then, focusing on the rigid block method, stereotomy has been integrated as a geometrical parameter influencing the mechanical behavior. To this end, the stereotomy function is presented as a parameter that can be influenced by the possible degradations affecting the blocks and/or mortar joints, thus justifying its randomness and consequently integrating it in a reliability study. The reliability study carried out in this work focused on the case of a single-span masonry arch bridge located in Morocco. The reliability analysis demonstrated the importance of joints orientation and the possible perturbations that it can undergo around the classical radial configuration. The effect of these perturbations is shown for the failure multiplier, which represents the bearing capacity of the studied arch. Masonry arch bridges are a heritage of great architectural and economic importance for many countries worldwide. This is due to the historical value of these ancient constructions, but also to their durability that allowed them to still fulfil their economic role. Nevertheless, the preservation of the safety of masonry arch bridges depends on a good maintenance approach that takes into account the different hazards affecting these constructions. The uncertainties affecting the geometry are among the hazards to be taken into account by the roadway and railway managers. In this paper, the authors study the effects of uncertainties related to the bricklaying pattern of masonry blocks on the mechanical behavior of the arch bridge. For this purpose, probability-based methods are applied in conjunction with mechanical calculation techniques. The results obtained highlight the importance of considering the stereotomy parameter, which represents the bricklaying pattern of masonry blocks in the arch in maintenance operations. [ABSTRACT FROM AUTHOR]

This paper explores the corner tower of the Anagni Cathedral, a Romanesque structure built in the eleventh and thirteenth centuries. The tower, located beneath the baptistery, was likely constructed to support a small chapel with a font. Through digital surveying and geometric analysis, this study examines the tower's structural element and speculates on the ideal stereotomic apparatus and reference models. The paper also delves into the mechanism responsible for maintaining the cantilevering structure's equilibrium. The tower and baptistery exemplify the role of stereotomy and friction in maintaining equilibrium, with internal tensile forces and unilateral contact between the structure's blocks. This study provides valuable insights into the Anagni Cathedral's structural elements and highlights the importance of understanding stereotomy and friction principles. [ABSTRACT FROM AUTHOR]

This research concerns the historical-geometric interpretation of the stereotomic apparatus of Château de la Rochefoucauld's staircase (1520), using a survey carried out with laser scanner technology. The analysis also extends to the roof structure, hypothesizing a design process that was enriched by exchanges between French and Spanish stonemasonry masters. [ABSTRACT FROM AUTHOR]

Among the most characteristic elements of the Béjar Ducal Palace courtyard is the magnificent staircase made up of a large linteled arch that rests on Ionic columns with skewed capitals following the slope of the lintel. One of the capitals shows a different shape as it is bent. It consists of two halves, one of them in the common shape and the other one in a skewed shape. We deduce that there was a first project of the staircase that had to be modified. Master stonemason Pedro de Marquina's (author of the first conditions of the Project) knowledge of stone stereotomy suggests he was; the project architect, the execution director and the architect that modified the project during the work. [ABSTRACT FROM AUTHOR]

Copyright of Quintana: Revista do Departamento de Historia da Arte USC is the property of Universidad de Santiago de Compostela, Servicio de Publicaciones and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Anales de Investigación en Arquitectura is the property of Universidad ORT Uruguay, Facultad de Arquitectura and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper investigates the principles that regulate complex stereotomic constructions as a starting point for the design of a new two-dimensional floor structure based on the principles of TIM (Topological Interlocking Materials). These interlocking systems use an assembly of identical Platonic solids which, due to the mutual bearing between adjacent units and the presence of a global peripheral constraint, lock together to form pure geometric shapes. This type of structure offers several advantages such as a high energy dissipation capacity and tolerance towards localised failure, which has made it a popular research topic over the last 30 years. The current research project includes a case study of an assembly of interlocking cubes to create a "flat vault". The resulting vault design features a striking appearance and its geometry may be manipulated to achieve different two-dimensional solutions, provided certain geometric conditions necessary for the stability of the system are followed. [ABSTRACT FROM AUTHOR]

Gothic architecture can be viewed from several perspectives, including stylistic aspects, architectural theory, and structural analysis. As Gothic architecture is a skeletal construction, it is essential to achieve an equilibrium with the multiple loads and forces. Medieval master masons' architectural knowledge was firmly based on empirical learning, which stimulated the dynamic development of structural innovations. This paper emphasises and describes a particular type of vault springer, one of the most complicated and sensitive parts of Gothic construction. Known as tas-de-charge, it became especially characteristic of high Gothic architecture. According to its principle, the springer's lower courses contain the merged vault nerves and are carved from one single stone block in each course. The beds of these courses are not radial as those of the average voussoirs, but horizontal. Without the concept of tas-de-charge, the development of late Gothic vaults could not be imaginable. This particular solution made possible the creation of elegantly narrow imposts supporting the vault ribs, the double arch and the formerets. So far, tas-de-charge has not been a focus of interest in the historiography of Hungarian medieval architecture; however, it appears that it was commonly applied in our late Romanesque and early Gothic monuments. [ABSTRACT FROM AUTHOR]

Some authors have downplayed the importance of complex vaulted systems in ashlar in Roman architecture. This has led them to seek the origins of Early Modern stonecutting in Christian Syria or Languedocian Romanesque. However, some examples in many regions of the Empire, including Lazio, argue for the existence of advanced stonecutting techniques in the Roman world. In this paper, we will study an interesting example of these structures, the Grotta dei Massacci in Osteria Nuova, now in the municipality of Frasso Sabino. Starting with a precise survey carried out by 3D laser scanning and automated photogrammetry, we will put forward some hypotheses about its measurement system, proportion, stonecutting technique and the hoisting systems used in its execution. [ABSTRACT FROM AUTHOR]

This paper discusses the use of scripting procedures and structural computation applied to the stonecutting of vaults. Starting from the conceptualization of trumpet squinches in various treatises, it offers an understanding of the parametric framework used. The operation is then replicated on Wallis's conical edge surface as described by Guarino Guarini, demonstrating how to create complex surfaces from the basic script. The second part concerns the structural behavior of a conical vault in the same coding environment, thanks to Thrust Network Analysis method. Configurative and geometric analysis of vaults is paired with structural integrity in order to better manage historical buildings. [ABSTRACT FROM AUTHOR]

This article focuses on analysing and modelling geometrically a complex vault typology known as single-row spherical dome, which was defined in several classic stereotomy treatises. The peculiarity of this kind of dome is that all their stone pieces are different, since there is a helical directrix defining the upper and lower edges of the pieces. Different solutions will be compared and analysed, both from a graphical and a mathematical point of view, by describing the spatial helixes. The accuracy of the different methods described in the treatises for tracing the stone templates will be also tested. To conclude, some examples of virtual 3D modellings and 3D printed models will be exposed. [ABSTRACT FROM AUTHOR]

An analysis of treatment results was made in 226 patients with multiple isolated intrapulmonary metastases of solid tumors. It appears that surgical removal of metastases was possible in patients with satisfactory functional resources and accurate evaluation in order to validate the indications for surgery. The operation shouldn’t result in considerable reduction of quality of life and didn’t prevent using other methods of treatment such as medicamental and radiation therapy. The indications to surgical intervention have to be set as individual in consideration of the number of metastases and potential of the patient to undergo the surgery.

The Spanish Renaissance architecture is structured, in a general way, from pieces that, depending on the design criteria and the spatial configuration defined in the project, are joined to generate one result or another; this is what we will call “components.” This is justified by the fact that each builder had to plan the pieces of the puzzle that had been assigned to him and, therefore, it is not uncommon that, sometimes, disagreements appear between complementary pieces of the same work. Thus, the architect’s organizational capacity, as a composer of the formal configuration and as director of the executive process, plays a fundamental role. To recover the unfinished geometry of the church of Cazorla we will rely on the individualized study of the components that make up the set, paying special attention to the definition of the wall box that defines the volumetric envelope of the construction. [ABSTRACT FROM AUTHOR]

This research refers to the study of an arch adjoining two rooms of the Pio Clementino Museum, in the Vatican (Rome). This arch was designed by the architect Michelangelo Simonetti (1724–1781) around 1780. The warped intrados of the arch is defined by a flat round arch placed on the wall of the square vestibule and by a hunched curve traced on the cylindrical surface of the next vestibule. The resulting warped surface is a portion of a ruled surface that can be considered a good example of the lathe art and multi-axial modeling. The digital clone analysis demonstrated a double kind of perspective: structural and optical. The first was influenced by the researches on the stereotomic connections of ruled surfaces explained in treatises published in the second half of the 18th century. The second reference can be identified with optical-perspective studies applied to correction of sight like the pictorial decoration by Father Andrea Pozzo (1642–1709) which is present in the Casa Professa's Chapel (Rome). [ABSTRACT FROM AUTHOR]

Vandelvira's work can be read through quality indicators, which allow us to explain the importance of the graphic protocols used by the architect to define the spatial corporeity of his achievements. It is characteristic that in his projects we can always recognize an idealized abstract space that is manifested in the heart of the building; and for whose construction, Vandelvira had to draw geometric articulation mechanisms signified by the ability for release from the scale, form or matter; because many of these solutions were used on a recurring solutions, regardless of the program, the design of the plant, the height dimension of the set or, even, the defined stereotomic cut. [ABSTRACT FROM AUTHOR]

Stereotomy, the art of cutting stones into particular shapes for the construction of vaulted structures, is an ancient art that has been practiced over a wide chronological and geographical span, from Hellenistic Greece to contemporary Apulia and across the Mediterranean Basin. Yet the history of ancient and medieval stereotomy is little understood, and nineteenth- century theories about the art’s Syrian origins, its introduction into Europe via France and the crusaders, and the intrinsic Frenchness of medieval stereotomy are still largely accepted. In this essay, I question these theories with the help of a work-in-progress database and database-driven maps that consolidate evidence of stereotomic practice from the third century BCE through the eleventh century CE and across the Mediterranean region. I argue that the history of stereotomy is far more complex than what historians have assumed so far and that, for the most part, it has yet to be written.

The use of construction techniques in cloister vaults in noble buildings, as covering elements for square or rectangular rooms, is widespread across Europe. The geometric continuity at the intrados makes generally possible the execution all over the span of frescoes, stucco and decorations, with a great diffusion of a great variety of solutions. The construction of brick vaults, from the late Middle Age, was sped up by limiting the centring to the wooden planks arches that were instrumental in the profile determination. Starting from laser scanning, photogrammetric and thermographic techniques, the punctual reconstruction of the geometry and construction techniques allowed to recognise and understand the constructive richness, the multiplicity and unicity of each vaulted element, made of recurrent elements and specific features, thus sketching a mixed pattern of workers and highlighting the constructive knowledge of ‘stereotomy’ applied to the brick block vaults. Nowadays, the availability of several BIM-based modelling procedures and tools based on high detailed surveys allows to identify and reconstruct the shape, drawing reliable assumptions about the construction methods and the execution time. The research methodology here proposed intends to tackle an updatable geographic catalogue, able to transfer the construction richness, inheriting the historic lesson of French ‘repertoires’ to generate modern HBIM vault libraries (abaci). The paper focuses on a well-documented case, the Magio Grasselli palace in Cremona in which the cloister vaults of two main rooms, and others, show different construction systems embodied by the geometry. The methodology has shown how the cloister vault typology can be turned to a dome construction in the same vault, and how ‘stereotomy’, the capacity of skilled workers to control the space, modified the typical geometry, made by the ‘generative’ construction process used for the cloister vault (intended as the intersection of 2 barrel vaults), turning it into a dome in the upper part, giving back a sort of morphing, merging the two different generative rules (dome and vault) as described hereafter and creating unexpected scenic effect. [ABSTRACT FROM AUTHOR]

The past 15 years have been characterised by constant technological and digital innovations, and, as a consequence, computer science has evolved past its academic and elitist status to become the common language adopted by professionals in many fields, revolutionising the methods and tools, and even creating new industries and markets. This shift permeated the architectural and construction industry, dramatically influencing the form and function of modern buildings. Stereotomy, one of the most fascinating and complex techniques in the history of pre-modern architecture, captures best the potential of being able to use digital design to integrate architectural form, structural integrity and environmental performance in a single multi-performative “skin”. The intention of the following text is to highlight some application of new digital technologies in real life projects that fundamentally have a close link to the traditional stereotomic principles of “solid cutting” (Fallacara and Barberio in Handbook of research on form and morphogenesis in modern architectural contexts. IGI Global, Hershey, 2017). [ABSTRACT FROM AUTHOR]

The aim of the article is to describe the historical background and the birth of a relatively new discipline consisting in the digital evolution of classical stereotomy. “Stereotomy 1.0” comprises the early development of the discipline primarily related to stonecutting. The new discipline, “Stereotomy 2.0” goes beyond this early concept to embrace contemporary design paradigms and materials. It is described in an “Unfinished Manifesto”, which describes its fundamental theoretical principles, understood as a new didactic comprehensive approach for the schools of architecture and a new design process useful for contemporary architectural design. Each point of the Manifesto is described in a short paragraph and shows the most important theoretical nodes of the renewed discipline. The various points are then exemplified by the experimental projects presented in the final part of the article. [ABSTRACT FROM AUTHOR]

The event “Stereotomy 2.0 and Digital Construction Tools” was held in New York from April 16th to April 29th, 2018 at the School of Architecture and Design (SoAD) of the New York Institute of Technology. The event included a workshop and an exhibition of the students’ work, that was followed by a symposium with international academics and professional speakers. Finally, an exhibition held in the Par Excellence Gallery in New York has shown some of the state-of-the-art research on digital stereotomy through physical models, prototypes and posters. [ABSTRACT FROM AUTHOR]

NNJ guest editors Giuseppe Fallacara and Maurizio Barberio introduce the papers in the special issue of the Nexus Network Journal dedicated to Stereotomy 2.0. [ABSTRACT FROM AUTHOR]

Contemporary innovations in structural form-finding and fabrication techniques are leading to design of freeform masonry architecture. These new forms create new challenges in laying out tessellation patterns, especially if structural, fabrication and construction requirements as well as aesthetical considerations are taken into account. Addressing these challenges, we review historic stone-cutting strategies and their geometric principles, forming the base for the development of two new discretisation approaches for given thrust surfaces, allowing for various degrees of user control. First, we introduce a tessellation approach based on primal, anisotropic triangular meshes and their dual counterparts. Second, an alternative tessellation approach based on transverse cutting curves is presented. Using a simple set of geometric rules, both methods enable the design of rigid, staggered bonds with locally force-flow aligned block configurations to avoid sliding failures. For this research, the tessellation design of the Armadillo Vault, an unreinforced, dry-assembled, cut-stone stone shell, served as a case study to demonstrate the feasibility of our methods in the context of a full-scale architectural project. [ABSTRACT FROM AUTHOR]

From a historical analysis of hemispherical domes and from the rigorous study of geometric methods to divide a sphere, this study presents innovative solutions for bonding a hemispherical stereotomic dome in cut stone, solutions that optimize its construction compared to traditional methods. This result is achieved through a five-fold structural geometry of bonding that reduces the number of invariant-ashlars to be produced in relation to maintaining their reduced dimensions and increasing the diameter of the dome they constitute, respecting static laws and improving aesthetic expressivity, and through modern technologies for designing and cutting building elements, thus simplifying the production process. [ABSTRACT FROM AUTHOR]

This paper describes the adaptation of the Exquisite Corpse to the design of a vault, cut using only ruled surfaces. The Surrealist process of the Exquisite Corpse, where a group of artists work collectively on a single drawing, without seeing the work of their collaborators, Salvador Dalí called working in “semi-darkness”. This method succeeds however in producing complex combinations of forms that rarely emerge from solo designers. When a project arose for a vault in a remote environment, the Exquisite Corpse was chosen to generate complimentary and juxtaposing forms from which an architectural language could be later assembled. A model of the vault was fabricated using a robotic arm with a custom built nichrome wire foam cutting end effector from 107 billets of expanded polystyrene. The discussion notes the stereotomic challenges, the differences between the modelled outcome and its stone version, and reflects on maintaining “semi-darkness” during early stages of form design. [ABSTRACT FROM AUTHOR]

For centuries, stereotomy has been the instrument for building arches, staircases and complex vaulted systems using stone as load-bearing material. Its constructive principles, codified in the classical treatises of few historical figures as Alonso de Vandelvira and Philibert de L’Orme, have found new applications in contemporary architectures, although the carrier is no longer stone, but pre-cast or fabricated components, and the technologies to materialise the whole process have profoundly changed. To demonstrate the great potential that the stereotomic process retains even in a deeply transformed context, the analogies between the stereotomy principles and some of the projects designed by Foster + Partners are outlined. The challenges faced by the builders of the Gothic cathedrals and the great constructions of the Renaissance remain unchanged. [ABSTRACT FROM AUTHOR]

The project for an acoustic shell in the Italian city of Matera was looked as an opportunity to explore an alternative stereotomic approach. The semi-vaulted space was initially thought to be built with discrete blocks of stone following a structural system in compression bounded by tie-rods, but practical and economic sustainability issues led to a different approach to that of classic cutting and carving raw stone. The collaboration between two different research teams led to the incorporation of a reusable mold technology; with the help of robotic technology and flexible moulding, it became possible to create customized heavy blocks discarding the need for disposable one-off moulds for casting voussoirs. By surveying stereotomy as a classic discipline within the scope of this project, this paper extrapolates and reflects on the validation of a different production process facing the classic ones that have defined stereotomy in architecture and construction. [ABSTRACT FROM AUTHOR]

Stereotomy is historically synonymous with stone construction and solid architectural poché. Yet stereotomy need not be limited to dense materials and compression-only structural forms. With the aim of developing stereotomic architecture that employs parts that are exceptionally expressive—rather than exceptionally heavy—this paper explores constructions made from glass-fiber reinforced plastic, a contemporary lightweight material. The research also recognizes that the volumetric parts and networks of joints employed for stereotomy have important visual as well as physical consequences. By focusing on creative applications of descriptive geometry, the projects presented in this paper seek to make explicit stereotomy’s unique combination of graphic and constructional qualities. Using a novel system of tessellations derived from digital simulations, the research puts computational techniques in service of stereotomy’s formal questions, developing visually animated assemblies of parts. The architectural qualities of these assemblies as well as the constructional feasibility of lightweight stereotomic parts were tested through a series of designs that culminated in large architectural constructions, including a free-standing wall, a pavilion prototype and a free-standing interior pavilion employing lightweight, free-form Cyclopean masonry. [ABSTRACT FROM AUTHOR]

The funicular analysis of curved masonry structures is addressed, considering the stereotomy of the voussoirs, a limited compressive strength, and a limited friction coefficient. The force density method is used to handle the equilibrium of the loaded nodes of the network, whose vertices lie along vertical lines passing through the centroids of the blocks. For the resulting grid with fixed plan projection, the minimization of the horizontal thrusts is formulated in terms of the height of the restrained nodes and of any set of independent force densities. Anti-funicular networks are sought by enforcing compression-only branches of the network. Local constraints are stated at each joint addressing the hypothesis of a limited compressive strength and a finite value of the friction coefficient between two adjacent voussoirs. To enforce no-tension blocks, lower and upper bounds for the vertical coordinates of the unrestrained vertices of the network are prescribed, as well. Sequential convex programming is used to solve the arising multi-constrained minimization problem. The algorithm, which can handle networks with general topology, is assessed by comparisons with results achieved with the Durand–Claye method, a semi-analytical method for the equilibrium analysis of symmetric masonry arches and domes that accounts for the limited compressive strength of masonry, the friction coefficient and the stereotomy of the voussoirs. Numerical examples concern arches, domes and a cloister vault, considering varying mechanical parameters. • Minimum thrust funicular networks are sought accounting for stereotomy aspects. • Joints with finite compressive strength and finite friction are dealt with in arches and vaults. • Statically admissible solutions are retrieved that are fully feasible with failure constraints. • An updated version of the stability area method is employed for algorithm validation. • Networks are remarkably sensitive to geometry and mechanical properties of the joints. [ABSTRACT FROM AUTHOR]

This article presents a study that preceded a lesson for the Department of Architecture of Bologna held to children between eight and fourteen years of age, , as part of an initiative by the University for the dissemination of science. The study presents some experiences of perspective and stereotomy. Among the objectives of the research is to explain to children, through playing, the illusory power of perspective and, therefore, the deceptions to which the human perception of space is subjected. For this purpose a small Ames room was built, studying its decomposition in parts, in a sort of contemporary stereotomy. In the first part of the article, the lesson given to the children is briefly presented, as well as some insights on the theoretical issues addressed, which obviously could not be included in the lesson. In the second part, of the study, design and construction of the Ames room are described.