This research work provides a stability study for a double masonry dome during its construction process and, a consideration of the possible effects that the procedure followed for building the structure has on its current mechanical behaviour. In particular, the analysis is carried out on the Baroque dome of Santa Maria alla Sanita in Naples, a relatively small dome with a span of 12 m. The main contribution of the paper consists of making a hypothesis about the different phases of construction and demonstrating that the dome was in equilibrium during these different phases. This aspect has been rarely considered when analysing historical structures. The theoretical framework assumed refers to Limit Analysis in which the masonry is modelled as composed of rigid-unilateral material. To assess the stability of the dome, the study proposes an equilibrium analysis performed both graphically and analytically, by using the graphic statics and the membrane analysis. The results obtained from the two methods are also compared, at each stage of construction. Besides the classical graphical methodology based on the slicing technique, the membrane equilibrium solution provides a wider repertoire of equilibrium states, since it allows for biaxial stress fields and is here implemented with a new method for which the surface and the stress potential are both approximated through simplicial surfaces based on the same triangulation. This more refined analysis confirms the results obtained through graphic statics giving wider geometrical safety margins and a more detailed interpretation of the non-axisymmetric loading cases

The paper investigates the territorial layout of the fortified system of Naples that developed during the Spanish Vice Kingdom in the 16th-17th centuries. Both existing castles and towers, and constructions built for the purpose, were included in the system. The Tower of Nisida is one of the existing ancient towers that became part of the impressive 17th century defense system of Naples. The study focus is on the strategic importance acquired by Nisida and its Tower in those years, when it became a key location in the fortified system, both evidencing its cruciality through the study of the field of vision that widens from the location and dealing the issue with the point of view landscape and territorial defense, recalling the concept that the defense architecture is part of architectural heritage.

This study presents an assessment of the state of stress of the dome of San Francesco di Paola Basil Naples.The number of Finite Analyses of masonry structures proposed over the years is now uncountable, but most of the studies make reference to ideal geometries, even if based on actual measurements.The present work, on the contrary, does not rely upon any regular geometrical model but, instead, on what could be defined as a scan of the actual structure which accounts for both the original plan and on the inevitable construc�on imperfec�ons.It is found that these apparently negligible, but diffuse imperfec�on from an ideal modelling lead to a substan�ally different state of stress from what could be expected from a regular geometry.The findings are discussed and it is also shown that they give reason of the actual cracking paterns on the dome.

The present paper applies the Linear Arch Static Analysis (LASA), which models the masonry material as unilateral, i.e., No-Tension material in the sense of Heyman, and the Safe Theorem of the Limit Analysis to the study of masonry spiral stairs. A comparison is made with a refined FE analysis of the same problem, obtained by means of the ANSYS Parametric Design Language (APDL). The objective is to prove that LASA can be a valid alternative to other more complex numerical methods, such as FE, especially when the modeling parameters, such as the boundary conditions, cannot be exactly defined. The case study of a small spiral staircase placed in the tower of Nisida, a small island close to Naples, Italy is taken into consideration. The results show that the LASA analysis provides results that fall within two limit FE cases in terms of stress and overall thrust, providing at the same time a meaningful insight into the equilibrium state of the structure.

The staircases represent one of the most impressive architectural expressions of the building. Many authors presented a great deal of research over the years on this matter intending to understand how they are designed and laid out. This paper is concerned with a particular structural type of masonry staircase, known as stair with open well or roman staircase. It aims to demonstrate that in masonry-vaulted staircases, the close relationship between the shape and static behavior is particularly evident, and geometry and construction are essential for their stability. The authors have proved this statement by studying Palazzo Di Majo's open-well staircase in Naples, whose main structure consists of tuff vaults. The first part of the article is substantially descriptive and presents an in-depth description of the geometric and architectural features of the stair. The second part explains all the aspects concerning the equilibrium of this kind of stairways, within Heyman's theory of masonry.

Las escaleras representan una de las más imponentes expresiones arquitectónicas del edificio. Varios autores han presentado muchas publicaciones a lo largo de los años sobre este tema para entender cómo han sido diseñadas y cómo se sostienen. Este trabajo se trata sobre un tipo específico de escalera de albañilería, conocida como escalera “de ojo abierto” o “a la romana”. El objetivo es demostrar que en las escaleras con bóvedas de fábrica existe una estrecha relación entre la forma y su comportamiento estático. La geometría y la construcción son imprescindibles para su estabilidad. Los autores han demostrado esta tesis estudiando la escalera de ojo abierto del Palacio Di Majo en Nápoles, cuya estructura principal está constituida por bóvedas de toba. La primera parte del artículo presenta una descripción detallada de las características geométricas y arquitectónicas de la escalera. La segunda parte, explica el equilibrio de estas escaleras a partir de la teoría del equilibrio de estructuras de fábrica de Heyman.

This article deals with the survey and representation of the dome of Santa Maria della Sanità in Naples (Italy). The survey led to a geometric analysis of the spatial configuration of the dome, the drawing of its majolica decoration and its structural behavior. The overall objectives of this research can be briefly outlined as follows. First, the study focuses on defining the correct geometry of the dome obtained through accurate surveys. Finally, the study performs a simplified structural analysis of the compound dome-buttress system set within the theoretical framework of the Limit Analysis through the graphical statics.

This paper presents the structural assessment of a portion of 'Giovanni Vinciguerra' School, located in the municipality of Anagni, Italy. In 2009, the presence of some cracks in the vaults of the basement led the authorities to close the building and declare it not usable. In this work, firstly a proper knowledge of the history, geometry and structural configuration of the school was achieved by means of bibliographic research, laser-scanner survey and visual inspections. During onsite inspections, the damage observed was also surveyed and mapped in detail. Then, structural analysis applying graphic statics and inverse piecewise rigid displacement (PRD) analysis was carried out with the aim to identify the causes of damage and evaluate the residual structural safety of the building. The results obtained allowed to prove that the structure is safe despite the occurrence of some damage in the basement.

This contribution is part of a larger study on the island of Nisida (Naples) and its architectures, that has been conducted by the authors for several years now in collaboration with a research group at the Department of Architecture of University of Campania "Luigi Vanvitelli". The work previously proposed constitutes a state of progress of the current knowledge on the architectures present on the island, in particular on the cylindrical tower (with the original paths to access it) and on the buildings of the Institute for Juvenile Justice (IPM). By comparing the data taken from the historical iconographic sources with those derived from the architectural and structural surveys, it has been possible to advance a number of hypotheses on the modifications of the cylindrical tower (placed on the highest part of the island) and of the buildings that belong to IPM. The small spiral staircase found in the inner back side of the circular tower is part of this study. This spiral staircase can be seen as an unrolled ribbon of extreme proportionality and architectural accuracy despite its small size, and its helical movement shows the ability reached by masters of stonemasonry in the realization of one of the main elements in the building composition of space. The research focuses on studying the structural behavior of the spiral-shaped masonry stair of the Tower of Nisida, with a circular plan and a central circle, in the framework of Limit Analysis. Garcia Ares (2007) demonstrates for the first time the static equilibrium of this type of constructions (helical-shaped stairs) from the point of view of Limit Analysis and, some years later, Block (2009) analyses them by using the Thrust Network Analysis. Through the equilibrium approach, which can be considered the more suitable for the study of masonry structures, one of the equilibrium solutions of this construction has been found analytically. The analysis also demonstrated that the geometry and proportion of the spiral stairs play a fundamental role in their structural behavior by deepening the conceiving process that allowed to the construction of such splendid artefacts.

Masonry domes constitute a large part of the international architectural heritage. The issue of its conservation has long been a challenge both for architects and engineers. To limit any problems related to degradation, arising from structural damage or external factors, historical buildings are continuously restored and strengthened. Reliable tools are therefore needed to assess their structural safety. The present work discusses how modern methods can be used to understand ancient structures addressing the comparison between different methods of structural analysis, exploring the range of applications of limit analysis and finite element analysis in the stability assessment of masonry domes, focusing on the pros and cons of each approach. By applying equilibrium approaches and deformation-based models (finite element method), this paper provides two demonstration examples to compare the utility of each of them within a longstanding debate on the most proper way to evaluate traditional structures in masonry.

This article deals with the survey and representation of the dome of Santa Maria della Sanita in Naples (Italy). The survey led to a geometric analysis of the spatial configuration of the dome, the drawing of its majolica decoration and its structural behavior. The overall objectives of this research can be briefly outlined as follows. First, the study focuses on defining the correct geometry of the dome obtained through accurate surveys. Finally, the study performs a simplified structural analysis of the compound dome-buttress system set within the theoretical framework of the Limit Analysis through the graphical statics.

(1) Methods for checking the condition of monumental masonry structures can still be considered understudied. Among the different approaches available in the literature, the graphical ones have a special role, due to their simplicity and effectiveness. (2) In this work, a 2D method (Thrust Line Analysis (TLA)), the Modified Thrust Line Method (MTLM), and the 3D Membrane Equilibrium Analysis (MEA) method are compared. All methods have the same starting concept: no tensile strength, no sliding between the stone blocks, infinite compressive strength. (3) The methods are compared in terms of stress distribution (for the same-or similar-thrust line), and in terms of the Geometrical Safety Factor ensured. (4) The work shows that these theories, if properly conveyed in a scientific methodology (as many authors are doing currently and have done in the past) demonstrate the effectiveness and the advantages of graphical methods for simple structures.

This article focuses on the study of the so-called “Roman Masonry Stairways” which represent a rather common typology in historical buildings particularly in the Neapolitan area. The vaulted system of the numerous examples of Neapolitan open staircases consists of the use of the main elements of structural support, such as arches and vaults, underlining the close dialectical relationship between form and structure. Therefore, the analysis of the vaulted space is carried out in relation to functional requirements, materials and construction techniques within the articulation of the architectural figure. This research proposes an interpretation of the static behavior of this type of staircase through simplifications that facilitate its analysis. In this paper reference is made to the case study of the stairway of Palazzo Persico in Naples, whose structural analysis is carried out in the theoretical framework of the Limit Analysis as applied by Heyman to masonries. The main objective of the investigation is to demonstrate the static equilibrium of this structure and to understand its mechanical behavior. Before dealing with the analysis, the structural process was defined from different points of view, by interlocking formal, material and spatial aspects. The formal definition concerns its geometric configuration, while the material and spatial one concerns the elements that compose it and the relationship existing between them. Specifically, the staircase in issue is characterized by a cantilevered structural system with a planimetric scheme consisting of a 45° rotated square. Its vertices are rounded off by arches of circumference along the sides of which are placed the flights. The flights are cantilevered from the walls and connected by small vaults constituting the landings, as common for these masonry vaulted staircases. The aim of the work is to obtain an equilibrium solution that, being compatible with the loads, does not violate the limit condition of the material. In other words, a solution for which there is no traction and where the compressive stresses are contained within the masonry. The structural analysis was performed taking into account the principles of limit analysis and by applying the Safe Theorem. Ultimately a static graphic analysis has been conducted.

Introduction: Walking through the streets of the historic center of Naples and taking a glance at the sky, you may notice that its skyline is determined by the countless peculiar architectural elements, the domes precisely, that stand out from the context. Purpose of the study: The study aims to investigate the Neapolitan domes of the 16th and 17th centuries, focusing on the role of geometry and the close relationship between form and stability in the construction of this type of vaulted structures. Methods: Geometric surveys and in-situ investigations are used to define the shape of the domes. The study of the constructive solutions is based on the analysis of the original documents describing the works carried out as well as the analysis of several structural components that constitute the domes. This is related to ancient treatises and comparison, as far as possible, with similar buildings. Finally, to describe the mechanical behavior of these constructions, reference is made to the Modern Limit Analysis Theory developed by J. Heyman and applied to masonry structures in order to determine their degree of safety. Results: The approach set out can help to avoid improper restoration interventions on such historical artefacts. For good restoration work, it is absolutely indispensable to deeply investigate the geometrical and constructive aspects of a building, as well as its mechanical properties, in order to avoid approaches and methods of structural analyses far from the real behavior of these masonry structures.

The object of the present study is the basilica of San Francesco di Paola, an historical structure that well lends itself to use the graphic method of statics to analyse its stability for a two-fold reason: on the one hand, it is an interesting structure being dominated by a dome of considerable size with a solid appearance, and on the other, it is an entirely masonry structure for which no consolidation interventions with different materials have been necessary so far. This paper applies limit analysis based on the geometric equilibrium of the dome starting from detailed surveys of the church, from the knowledge of its history construction to the comprehension of the entire building. The study carried out enriches previous researches developed around the same case study, and the new contribution is integrated by the analysis of stability of the buttress system that completes the work on the vertical loads, providing a more detailed assessment of the safety level of the structure.

This paper focuses on large domes’ building techniques and use of geometric rules in the design and construction of religious structures. A quick excursus on the cultural heritage in Italy and abroad highlights how domes have been used almost exclusively in sacred architecture, rather than in civic buildings, for most of history. Born of the need to cover large spaces without facing with the encumbrance of vertical elements, the domed cover, ideal for places of worship crowded by hundreds of faithful, has assumed, over the centuries, a symbolic meaning to every religion. In fact, identifying the shape of a large dome in the urban landscape immediately means to recognize the sacredness of that place. The ancient Romans who believed in the gods, Christians, Hindus and Muslims, all used this very peculiar architectural element in churches or mosques to express a kind of spiritual symbolism and, as mentioned, the fact that the shape of the dome arises from a functional reason, it has over time got pushed aside. Furthermore, the circle is a geometric form that possesses a great symbolic force, generated by the idea that, having no beginning and no end, reflected perfection, the eternal, and also the heavens. In this perspective, drawing a circle both in the horizontal and vertical section, the ultimate paradigm for all monumental domes was the Roman Pantheon which, with its centrally placed "oculus" or “eye of heaven” proved to be a model for all other domes after it, retaining its position as the most ancient and well preserved dome in the world. Therefore, this article concentrates on the study of the Pantheon as an emblem and reference model for all monumental domes. By analyzing the “meaning” of its architectural design and its structural and geometric characteristics, the research dissects a comparison between similar large domes, similar to each other, such as that of St. Francesco di Paola in Naples and the Mosta Dome in Malta. The comprehension of these valuable architectural artifacts lies between the search for their original geometry and the identification of structural models through which their shape was defined, namely the geometric and proportional rules of the past.

Masonry constructions represent an important part of the Italian Architectural Heritage, to be preserved. As well known, the analysis of masonry buildings presents some peculiarities mainly related to the nature of the material, being a heterogeneous type of material, characterized by different textures and sizes, which means that it behaves anisotropically. Moreover, the fragile behavior of its constituents makes the response of the material highly non-linear. In this context, the development of an accurate and efficient computational model becomes significant not only for the evaluation of the stability of these kind of constructions, but also for the design of appropriate maintenance interventions. The present research takes care the mechanics of historical masonries through the case study of the Main Cloister of the Abbey of San Lorenzo ad Septimum in Aversa. There are many historical and survey studies on the cloister, but so far there has not been a structural study with this methodology, so by analyzing, of the entire complex, only the most damaged part to date. In order to understand the mechanical behavior of the whole complex of the cloister, the structural analysis is carried out with reference to the modern theory of Limit Analysis applied by Heyman to masonry structures. In addition, the study features an interdisciplinary character, taking into account three different aspects which, in the case of masonry constructions, are closely interconnected: geometry, construction and stability.

In this work, a simplified structural analysis of the main dome of San Francesco di Paola in Naples is performed by adopting both analytical and graphical approaches. The analytical process is based on the simplified membrane theory and the graphical methodology on the slicing technique. Both methods are used to determine the safety of the dome design under vertical and horizontal loads. We explore the effects of earthquakes by introducing horizontal forces proportional to the weight. Since the slicing technique does not consider the hoop compressive stresses building up in the upper part of the cap, the geometrical safety factor obtained by combining the analytical with the graphical method for the sole dome is lower than the one obtained with the analytical method. The estimate of the alg factor for the dome-buttress structural system obtained with the graphical method is greater than the level accepted for the seismic area of Naples.

The work aims to describe the issue of the approach related to structural problems, both for valuable and minor manufacts existing in the Italian historical town centers. The heterogeneity shown by these constructive typologies should coincide with some heterogeneity of the structural approach, but this is not always feasible, so computational processes and a strict application of the norms are often used in automatically. A representative case, as an example of the above-mentioned kinds of buildings (which are valuable, but not so much as to require a tailored intervention that takes into account the whole constructive history and the changes over the time), is shown. Ricciardelli palace (or Palazzo Ricciardelli) presents a great difficulty as to the structural intervention, but the approach used was a "classical engineer approach", formulated on the basis of the new computing tools and the new constructive norms. The restoration and the consolidation of this artifact have been well conducted by technicians, but the result is an invasive intervention that doesn't respect the original structural configuration of the construction. So the paper explains and discusses some investigation methodologies, alternative to an elastic analysis, which could be used in these cases, with the awareness that they are not completely exhaustive and far far away from the determination of a general formulation for a “unique model”, which can be representative of the masonry material, as well as from a definition that catalogues all its several features.