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This paper aims to illustrate and compare different approaches for the limit analysis of masonry domes of revolution with an oculus at the top. It specifically focuses on the influence of the limited compressive and tensile strength of masonry on the bearing capacity of the dome. The first assessment is conducted through a semi-analytical formulation that revisits Durand-Claye's method within the framework of the lower bound theorem of limit analysis. The second investigation is performed using a kinematic approach, which allows for closed-form solutions by exploiting the upper bound theorem of limit analysis and the virtual work theorem. These approaches are applied to a case study that was experimentally tested, involving a hemispherical dome with an oculus. The dome is subjected to its self-weight and a vertical load at the crown. Parametric investigations are presented to compare the results obtained through the proposed methods with those derived from the classical limit analysis of masonry structures, based on Heyman's hypotheses. [ABSTRACT FROM AUTHOR]

Masonry domes have always represented one of the most fascinating and daring architectural structures, with great symbolic relevance. However, their structural behaviour under environmental actions, such as earthquakes, has not yet been thoroughly investigated. This paper defines an interdisciplinary methodological approach, based on advanced digital survey techniques to evaluate constructive, geometrical, and structural aspects of historical domes. The applied procedure comprises the study of archival documents and diagnostic reports, in-situ analyses and advanced three-dimensional surveys, the development of simplified discrete-element-based structural models, and the performing of pushover analyses. The procedure is applied to a case study represented by the dome of the 'Badia di Sant'Agata' church in Catania, an earthquake-prone town located in Eastern Sicily. This church was built after the devastating 1693 earthquake and its dome represents one of the most significant examples among hundreds of masonry domes built in Sicily. The historical and constructive investigation showed that the dome was built without supporting formworks, by laying 21 concentric courses of limestone voussoirs on a peculiar springing ring made of mortared rubble stones. The numerical simulations highlighted that this peculiar ring affects the dome's failure mechanism and limits its displacement capacity and the maximum shear transferred to the substructure. [ABSTRACT FROM AUTHOR]

A simple numerical approach to predict the efficacy of FRP hooping in historical masonry domes is presented. The dome is modelled with 8-noded elastic hexahedron elements connected by 1D trusses/springs on meridians and on parallels, where all the non-linearity takes place. The aim is to simulate the nonlinear behaviour of domes through every FE commercial software equipped only with non-linear 1D elements, namely point contacts and cutoff bars. The constitutive behaviour of the trusses is assumed to be either perfectly brittle or perfectly ductile. A possible orthotropic behaviour and the no-tension material case can be reproduced. External retrofitting is simulated using trusses with an elastic perfectly ductile behaviour, assuming a perfect bond between the substrate and the reinforcement and imposing an ultimate strength for the trusses, which takes into account the possible debonding/delamination from the substrate in a conventional way. The Italian code CNR DT200 and the existing specialized literature are used as references. The models are benchmarked on a masonry dome reinforced with three hooping FRP strips and experimentally tested at the University Architecture Institute of Venice IUAV, Italy. The procedure is validated through extensive comparisons with available experimental data and numerical results obtained in the literature with a variety of different models. Through the extensive comparisons that were made and discussed, the robustness and simplicity of the procedure are proven. [ABSTRACT FROM AUTHOR]

Historical masonry domes are an important part of the architectural and engineering heritage in the World. They have been extensively used to cover the spaces of temples, mausoleums, palaces, forts, baths, churches, mosques, etc. Damages and collapses of masonry domes occurred as a result of earthquakes or lack of maintenance. Therefore, many efforts have been devoted to clarifying the theoretical and experimental responses of masonry domes by researchers. In addition to traditional techniques, significant developments have been achieved on the strengthening of masonry domes using innovative techniques. The study firstly presents a complete review on the state of knowledge about theoretical and experimental responses and strengthening of masonry domes under static and dynamic loads. Then crack patterns and failure mechanisms of masonry domes are explained, and traditional and innovative strengthening techniques that can be rehabilitated the masonry dome without any harmful intervention or disagreement with conservation principles are introduced and evaluated in detail. [ABSTRACT FROM AUTHOR]

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 Sanità 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 [ABSTRACT FROM AUTHOR]

A simple numerical approach to predict the efficacy of FRP hooping in historical masonry domes is presented. The dome is modelled with 8-noded elastic hexahedron elements connected by 1D trusses/springs on meridians and on parallels, where all the non-linearity takes place. The aim is to simulate the nonlinear behaviour of domes through every FE commercial software equipped only with non-linear 1D elements, namely point contacts and cutoff bars. The constitutive behaviour of the trusses is assumed to be either perfectly brittle or perfectly ductile. A possible orthotropic behaviour and the no-tension material case can be reproduced. External retrofitting is simulated using trusses with an elastic perfectly ductile behaviour, assuming a perfect bond between the substrate and the reinforcement and imposing an ultimate strength for the trusses, which takes into account the possible debonding/delamination from the substrate in a conventional way. The Italian code CNR DT200 and the existing specialized literature are used as references. The models are benchmarked on a masonry dome reinforced with three hooping FRP strips and experimentally tested at the University Architecture Institute of Venice IUAV, Italy. The procedure is validated through extensive comparisons with available experimental data and numerical results obtained in the literature with a variety of different models. Through the extensive comparisons that were made and discussed, the robustness and simplicity of the procedure are proven.

The research starts from an analogy found between two apparently very different structural solutions: the double spiral pattern of the herringbone brick courses in the domes built by Antonio da Sangallo the Younger (1484-1546) during the Renaissance, and the particular pattern of a wooden floor ‘à la Serlio’, described by Amand Rose Emy in his Treatise at the beginning of 19th century, made by diagonal beams reciprocally sustained. The diagonal pattern of the floor has a geometrical relationship with the cross-herringbone pattern, so that the latter can be obtained by some geometrical transformations of the former. This pattern was also used in thin shells built by Nervi, from the destroyed airplane hangars in Tuscany to the Palazzetto dello sport in Rome, and even by Piacentini in 1936 and earlier in some neoclassical domes. Thus the construction tool, useful for building domes without expensive scaffolding, could have a structural role at the completed construction stage. Within the research different structures were investigated, in order to observe the relevance of this peculiar structural scheme particularly in the construction of modern domes.

This study focuses on historical rotational domes, whose surface is obtained by the rotation of a profile around a vertical axis. The recognition of the geometrical rules underlying the dome design is fundamental to correctly interpret its initial conception, the project and construction phases and all the changes over time. To this aim, the paper proposes two different procedures of Best Fit Analysis (BFA) applied on the inner surfaces of domes, which are obtained geometrically and analytically, respectively. Starting from a 3D survey, the objective is to determine the best approximating geometric shape of a dome and the existing point-to-point deviations between the geometric and the surveyed shape. In particular, the proposed analytical BFA uses all the 3D surveyed points as input data to obtain the geometric model. The BFA procedures were applied to seven examples of Sicilian domes built between the eighteenth and nineteenth centuries. [ABSTRACT FROM AUTHOR]

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.

Starting from funicular models, chain models and hanging membranes, the role of 3D physical models in optimized shape research is the basis of form-finding strategies. Advances in structural optimized shape design derive from the wide spread of special digital form-finding tools. The goal of this paper is to test and evaluate interdisciplinary approaches based on computational tools useful in the form finding of efficient structural systems. This work is aimed at designing an inverse hanging shape subdivided into polygonal voussoirs (Voronoi patterns) by relaxing a planar discrete and elastic system, loaded at each point and anchored along its boundary. The workflow involves shaping, discretization (from pre-shaped paneling to digital stereotomy) and structural analysis carried out using two modeling approaches, finite element and rigid block modeling, using an in-house software tool, LiABlock_3D (MATLAB®), to check the stress state and to evaluate the equilibrium stability of the final shell. [ABSTRACT FROM AUTHOR]

The behaviour of axisymmetric masonry shells can be simulated by a system of forces constituted by meridian forces acting in the vertical planes, and by hoop forces acting circumferentially. A crucial component for the assessment of these structures using the Modified Thrust Line Method (MTLM) is the determination of hoop forces, whose computation is strenuous, limiting the practical application of MTLM. Working around this limitation, the current research introduces a strategy to manipulate the hoop forces by graphically implementing a function describing their distribution. The adaptiveness of this distribution function not only allows the application of MTLM for the analysis of a range of geometries, but also enables the simulation of membrane behaviour, arch behaviour and their combination, for considering partially cracked structures. Taking this into account, the approach is applied in the case studies illustrated within the current research. [ABSTRACT FROM AUTHOR]

(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. [ABSTRACT FROM AUTHOR]

• 3D no-tension masonry-like structures are analysed using an energy-based approach. • The solving algorithm iteratively calls a finite element software for orthotropic solids. • A limited number of iterations is needed to solve the equilibrium for any compatible load. • Load paths are shown in cracked solids of general shapes, such as masonry vaults and domes. • The collapse load multiplier is computed with no a priori assumption on the mechanism. A new numerical procedure is presented to perform the analysis of three-dimensional linear elastic no-tension structures exploiting the application programming interface of a general purpose finite element analysis software. Masonry is replaced by an equivalent orthotropic material with spatially varying elastic properties and negligible stiffness in the case of cracking strain. A non-incremental algorithm is implemented to define the distribution of the equivalent material, minimizing the strain energy so as to achieve a compression-only state of stress for any given compatible load. Applications are shown for masonry-like solids of general shape visualizing load paths in walls subject to dead loads and out-of-plane live loads, circular domes under self-weight and a groin vault acted upon by both vertical and horizontal seismic loading. [ABSTRACT FROM AUTHOR]

(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.

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]

The present paper aims to contribute to the knowledge concerning the seismic assessment of load bearing masonry buildings with reinforced concrete slabs. The final goal of the present research was to propose a simple, yet accurate, methodology to assess the seismic safety of existing masonry buildings. The methodology here presented was based on the so-called ICIST/ACSS methodology with major improvements such as the extension to load bearing masonry wall buildings and the consideration of the effects of one of the most common strengthening solutions for masonry walls, here referred to as reinforced plastering mortar, as well as the possibility of considering four levels of increasing refinement: global, by alignment, by wall panel and by wall element. An extended research was performed on the existing methodologies to evaluate the seismic structural risk of load bearing masonry buildings, briefly describing methodologies similar to the one proposed, namely all of those that have in common the fact that they are based in the physical comparison between the resisting and acting shear forces at all storeys and along the two orthogonal horizontal directions. A case study is presented to check the applicability of the proposed methodology. The case study showed that the proposed methodology is relatively simple to apply and has a sufficiently good accuracy when compared with alternative methodologies. The degree of refinement of the analysis (global, by alignment, by wall panel and by wall element) must be taken into consideration and successively more complex analyses may be required when the results of simpler analyses are inconclusive. [ABSTRACT FROM AUTHOR]

That tensile hoop stresses will cause an un-chained masonry dome to burst is well known, but the stabilizing influence of hoop-wise compression is rarely discussed. An arch cannot exhibit hoop stresses of any kind, so freestanding masonry arches must fit their own funiculars. But hoop compression does arise in some domes, such as those designed on shallow circular arcs. And as long as the hoop stresses they develop are exclusively compressive (except, of course, at the base), masonry domes are free to take certain non-funicular forms. To explore this design freedom, the author and his students built an unusual array of domes of un-bound and un-mortared masonry. Notable examples include the anticlastic or bell-shaped roofs we call pseudomes, some antidomes that descend from their foundation ring to form basins, and a hemi-toroidal ambidome that rises conventionally from its foundation to a circular crown whence it descends to a pendant oculus. To the best of our knowledge, the anti- and ambidomes are unprecedented in the history and theory of structures. The material success of these counterintuitive structures advanced our understanding of masonry, it raised some questions about the natural and the artificial in structural form-finding, and it challenged our preconceptions about the optimal, the ideal, and the free in structural form. [ABSTRACT FROM AUTHOR]

The 19th century graphic method of Eddy-Lévy is analyzed and proposed in an analytical form as an assessment tool for masonry domes. The method determines the neutral hoop that separates the upper part of the dome that behaves as a compressed membrane from and the bottom that behaves as independent arches, due to the presence of vertical cracks. This method allows determining a no-tension equilibrated solution, accounting for the natural behavior of masonry domes of fracturing along meridian planes. Six case studies were investigated, considering spherical and pointed dome, complete, with hole and with hole and lantern. A modified version has been studied to model the biaxial stress of upper part properly through the membrane theory, and compared to the solution obtained by a numeric discrete block model. Limit thickness-to-radius ratio was identified, and a parametric analysis was carried out to investigate the extension of meridian fracture varying dome shape and thickness. [ABSTRACT FROM PUBLISHER]

• Safety assessment of masonry domes. The solution method is based on the static theorem of limit analysis. • Domes are modelled as thin shells. Membrane forces and bending moments are suitably combined to find statically admissible internal forces. • The internal force distribution that maximizes the safety factor is searched by means of a constrained optimization method. The solution is pursued numerically by means of an expressly developed procedure that uses the collocation method. • The paper illustrates application of the method to the dome of Pisa cathedral. The present paper illustrates a methodology for the safety assessment of masonry domes. The dome is modelled as a thin shell made of a material satisfying Heyman's hypotheses. Based on the static theorem of limit analysis, the method searches for statically admissible distributions of internal forces within the shell, suitably combining membrane forces and bending moments, by solving a convex optimisation problem. The solution is pursued numerically by means of an expressly developed collocation method that enables obtaining the analytical expressions for each internal force component. In its present formulation the method can be applied to domes of any shape, as well as to arbitrary load distributions. After validation against the benchmark case of the spherical dome under its self-weight, the paper illustrates application of the method to the dome of Pisa Cathedral under vertical loads as a first real case study. [ABSTRACT FROM AUTHOR]

A masonry dome cracks when the tension stresses in the hoop rings near the springing reach the masonry's weak tensile strength. These meridional cracks arrive and spread along the dome. In this condition, the pressure surface with zero hoop stresses represents the extension to the three-dimensional case of the problem of the catenary. This analytical approach is adopted in the paper first to develop an accurate description of the minimum thrust state for the hemispherical masonry dome and the corresponding configuration of the pressure surface. Furthermore, the minimum thickness state is studied. Contributions of the paper are either an analytical formulation of the minimum thrust, depending on the geometrical thickness-radius ratio, or a modification of the minimum thickness-radius ratio with respect to the commonly accepted value. In this last geometrical configuration, the pressure surface has to touch the intrados of the dome at the crown, instead of passing through the extrados at the springing. [ABSTRACT FROM AUTHOR]

This paper presents the results of an interdisciplinary study carried out on Brunelleschi's Cupola of Santa Maria del Fiore in Florence, Italy, one of the most emblematic masonry domes in the world. The cupola has been affected since the beginning of its construction by a widespread cracking phenomenon, and several studies were done over the centuries to clarify its safety conditions. To have a direct and indirect record of the cracks opening or closing, a complex monitoring system was installed on the monument during the last century. An accurate analysis of crack widths and global displacements, performed considering both historical and recent monitoring data, has allowed for the identification of the movements developed in the monument, evaluating their relationship with environmental and seismic events. In line with the interdisciplinary approach strongly recommended in the field of assessment and conservation of monumental heritage, this paper reconsiders some issues concerning the causes of the actual damage to the cupola. In particular, in light of the obtained results, the famous seventeenth century Viviani's conclusions about the cupola's damage, confirmed by Chiarugi in the 1980s, are compared with other hypotheses, such as the differential settlement of pillars (Cecchini in 1698 and Ximenes in 1757) and the influence of temperature variations (Nervi in 1934). The large amount of measured data and the results of the last numerical models of the cupola, combined with recent dynamic measurements, allowed the updating of some previous conclusions on damage causes and trends. Starting from these conclusions, a more reliable forecasting model of the monument can be set up that could be useful in identifying effective conservation strategy for this outstanding monument. [ABSTRACT FROM AUTHOR]

This study focuses on domes the ground plan of which, instead of the more common circular shape, is an oval, and aims at finding the minimally necessary uniform wall thickness for domes of different geometries loaded by their selfweight. The discrete element code 3DEC was applied because of its capability of simulating the collapse mechanisms of masonry structures. Results on the minimal wall thickness, corresponding masonry volume and failure mechanisms for different dome geometries are presented. Three ranges of the friction coefficient were found. For very low frictional resistance collapse happens with pure frictional sliding, for any arbitrarily large wall thickness. In the range of relatively high (i.e., realistic) friction coefficients the structure collapses without any sliding if the wall is not sufficiently thick, and in the observed range of the friction coefficient the necessary wall thickness is nearly insensitive to its value (collapse initiates with hinging cracks only). Between the two domains an intermediate behavior was found: combined cracking and sliding collapse modes occur for insufficient wall thickness, and the minimal thickness strongly depends on the friction coefficient. The critical and transitional friction coefficients separating the failure modes were determined for different eccentricities of the groundplan. [ABSTRACT FROM AUTHOR]

This paper aims to determine the dynamic characteristics, such as natural frequencies, mode shapes and damping ratios, of two different domed structures, namely Hamza Paşa Mausoleum and Kavak Meydan Fountain, built in the sixteenth century by experimental methods. The experimental dynamic characteristics are used to develop initial analytical models and update these models. Analytical models of the structures are constituted using finite element theoretical software, and dynamic characteristics are determined analytically. The experimental measurements are carried out by operational modal testing under environmental loads, which are wind and traffic loads, and the dynamic characteristics are identified experimentally. Vibration responses are collected from the dome's outer surface for Hamza Pas¸a Mausoleum and the dome pulley's inner surface for Kavak Meydan Fountain. Measurement time, frequency span, and effective mode number are determined by considering pretest measurement results. At the end of the study, analytical and experimental dynamic characteristics are compared with each other and the finite element models of these domed structures are updated by changing material properties and boundary conditions. [ABSTRACT FROM AUTHOR]

• Static and seismic behaviors of masonry domes with circular and octagonal drum and buttress. • Failure behaviours of masonry domes with circular and octagonal drum and buttress under strong earthquake shaking. • Failure angles of masonry domes with thickness-to-span ratios t/R = 0.092 under strong ground motions. General stability and failure behaviors of masonry domes under static loads have been investigated extensively in literature. However, a few studies have been done on the seismic failure behavior of masonry domes under strong ground shaking. This study aims to investigate the seismic failure behaviors and failure angles of masonry domes with support system including drum and buttresses using advanced 3D nonlinear numerical simulations. Four types of masonry domes with thickness-to-span ratios t/R = 0.092, such as a dome with circular drum (Dome A), a dome with circular drum and buttress (Dome B), a dome with dodecagon drum (Dome C), a dome with dodecagon drum and buttress (Dome D), built on historical structures are selected. Three-dimensional solid finite element models of the selected masonry domes are created using isotropic continuum macro modelling technique with homogenized properties. The finite element models are utilized to simulate the seismic behaviors of the masonry domes under three different strong ground motion acceleration records matched according to the target response spectrum with a return period of 475 years in the Turkish Building Earthquake Code. The seismic failure behaviors of four masonry dome models are evaluated by comparing mode shapes, displacements, maximum principal stresses, damage propagation patterns and failure angles. It is determined that the average angle intervals of hoop tension failure regions of Dome A, Dome B, Dome C and Dome D models under strong ground motions vary between 39, 25, 35 and 26 degrees, respectively. [ABSTRACT FROM AUTHOR]

The insertion of metal tie rods all around masonry domes, in order to hoop them and to absorb their horizontal thrusts, is the most ancient traditional strengthening technique for these fascinating structures. This article presents some general considerations for this primeval remedy, starting from the historical and structural analysis of the large 16th-century octagonal dome of Madonna dell’Umiltà in Pistoia (Italy). Several hooping systems had been inserted around this dome in different periods and with different techniques in order to reinforce this weak masonry structure, and their tensile stresses have been measured by means of dynamic tests. The results have shown the large differences in the tensile stresses among the different ties, allowing an understanding of the real contribution of each hooping systems. These data were then used to calibrate a finite element model, which allowed researchers to retrace and quantify from a structural point of view the passage through the centuries of this daring construction and to understand the efforts made to preserve it up to now. The final results presented here are new suggestions on the most efficient way to ensure, once again with hooping ties, the preservation of this monument for the future, starting from empiricism. [ABSTRACT FROM PUBLISHER]

We present a tensegrity approach to the strengthening of masonry vaults and domes performed by bonding grids of fiber reinforced composites to the masonry substrate. A topology optimization of such a reinforcement technique is formulated, on accounting for a tensegrity model of the reinforced structure; a minimal mass design strategy; different yield strengths of the masonry struts and tensile composite reinforcements; and multiple loading conditions. We show that the given optimization strategy can be profitably employed to rationally design fiber-reinforced composite material reinforcements of existing or new masonry vaults and domes, making use of the safe theorem of limit analysis. A wide collection of numerical examples dealing with real-life masonry domes and vaults highlight the technical potential of the proposed approach. [ABSTRACT FROM AUTHOR]

We employ a r -adaptive finite element model to search for a ‘safe’ thrust surface of a masonry dome, which minimizes the maximum tensile stress carried by the unreinforced portion of the material. A numerical procedure based on a Breeder Genetic Algorithm is employed to drive the movement of the nodes of a membrane model within a suitable design domain, which coincides with the region comprised in between the intrados and extrados of the dome in correspondence with the unreinforced portion of the structure. The presence of externally bonded Fiber Reinforced Polymer and/or Fabric Reinforced Cementitious Mortar reinforcements is accounted for by allowing the thrust surface to move outside the physical domain of the structure in correspondence with the reinforced regions. A benchmark example shows that the proposed procedure leads to detect if a masonry dome is safe or not, according to the master ‘safe’ theorem of the masonry vault theory. In addition it allows to optimally design reinforcement strategies that are aimed at preventing or mitigating crack damage, and increasing the load carrying capacity of the structure. [ABSTRACT FROM AUTHOR]

This study presents the results of the static and dynamic assessment of the dome of the Basilica of Santa Maria degli Angeli in Assisi, designed by Galeazzo Alessi. The first section is devoted to an overview of the masonry domes designed by the Italian architect and focuses on the structural solutions adopted in the several cases described to better understand Alessi’s designing skills. In the second part, the drum-dome system is analyzed in order to attain a structural assessment. The static assessment is performed by means of limit analysis and finite element model approaches with non-linear mechanical behavior. The obtained results are consistent with the detected crack pattern and confirm the suitability of the reinforcement steel rings applied to the drum. The seismic assessment has been performed by response spectrum analysis. Due to the lack of specific information, a probabilistic approach for the material mechanical properties was used. The results obtained highlight an adequate seismic response of the structure that can be attributed to the dynamic properties of the slender drum-dome system. This finding justifies the good performance of the structure during the seismic events of 1832 and 1997. [ABSTRACT FROM PUBLISHER]

The research synthesized in this paper focused on ultimate strength, structural safety assessment, and collapse of masonry domes. Activity was directed at analyzing the relationships between safety factor and geometry, and carrying out research targeted at reducing the incidence and severity of structural failures in cultural buildings. This paper shows that the resisting system of a masonry dome is not the two-dimensional shell, but a one-dimensional mechanism that derives from the splitting of the shell and drum. The resisting system, whose geometry depends on the dome shape and brick or stone pattern, may include the lantern and/or the masonry constructions around the drum. Well-known domes taken from architectural cultural heritage are used to exemplify the pivotal role of geometry and construction techniques in providing ultimate strength. These examples also show the importance of considering the architectural design of the time, in structural analyses. The results found in the paper suggest how to provide masonry domes with adequate safety, using the minimal level of structural intervention; in particular, without altering the way the building reacts to applied loads. Hence, the paper helps understand how to reduce the amount of structural work, which, in turn, guarantees conservation and restoration, as well as safeguarding. The conclusions are devoted to analyzing which observations are valid for seismic assessment and how the other observations have to be modified for seismic actions. [ABSTRACT FROM AUTHOR]

Highlights: [•] Assessment of masonry domes through: Limit Analysis more readable than FEM models. [•] Dome and drum are a structural system. [•] Hoop ties increase safety of the dome, may be used as retrofitting tools. [•] Cracks in domes are unlikely to be related foundation settlement or material creep. [Copyright &y& Elsevier]