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This paper presents the results of the blind test competition carried out within the scope of the European project SERA.ta "Seismic Response of Masonry Cross Vaults: Shaking table tests and numerical validations". The purpose of the competition was to predict the results of a set of tests carried out on an unstrengthened full-scale cross vault with mortar joints and solid bricks (then strengthened with textile reinforced mortar) subjected to a horizontal dynamic excitation. The paper offers an overview of the modelling approaches utilised, along with their corresponding predictions and post dictions. The findings are assessed based on both the damage mechanisms and predicted values for displacements and accelerations in both directions. The results are then compared with the experimental findings. Modelling approaches utilizing the Finite Element Method (FEM) yielded the most accurate predictions regarding displacements and crack patterns. Conversely, a submission employing a Discrete Element model provided the most accurate prediction of damage mechanisms. Nonetheless, the significant discrepancies in predicted displacements and accelerations underscore the necessity for continued efforts to establish consensus on appropriate modelling assumptions for masonry vaults. [ABSTRACT FROM AUTHOR]

The evaluation of the structural behaviour of a masonry Venetian church with a pointed barrel vault is presented in this paper through an analysis following the necessary steps of a monument study. With a detailed geometric model and material estimation, the finite-element method is used to investigate the influence of specific structural parts of the structure, like masonry buttresses and wall connections, on the structural behaviour. The operational modal analysis is used to identify the structure dynamically. The comparison of the eigenfrequencies, which are estimated by in situ measurements and finite-element modal analysis, is used to perform a model identification. The response spectrum analysis, the static analysis after the subsistence of some parts following strengthening proposals, and the transient analysis of specific seismic excitations are used for the evaluation of the structural behaviour. The purpose of the work is to highlight the need for an interdisciplinary approach to the study of a monumental complex structure, regardless of its scale. The coexistence of structural elements of different stiffnesses, such as vaults, elongated walls, buttresses, transverse walls with pediment and belfry, as well as the concha, affects the mechanical behaviour and the pathology of the structure, which is difficult to study with simplifying models. From the analysis, it is concluded that subsidence problems, combined with seismic actions, lead to the cracking of the masonry, while the existence of buttresses limits the extension of the damage and contributes to the stabilization of the structure. [ABSTRACT FROM AUTHOR]

Ancient masonry constructions and historical buildings, such as cathedrals, are exposed to considerable risks attributed to factors like ageing and long-term exposure to both dynamic and static variations in loading conditions. In this study, an innovative and promising monitoring approach was applied to assess the structural integrity of the vault in the central nave of the Turin Cathedral. Specifically, the outcomes obtained from Acoustic Emissions (AE) are correlated with the insights derived from the Thrust Network Analysis (TNA) conducted on the structure. This analysis considers the structural elements introduced early in the twentieth century to mitigate horizontal forces. Acoustic Emission (AE) is a commonly employed technique in structural monitoring to detect and analyze elastic waves generated by crack formation, providing valuable information about structural damage. The Thrust Network Analysis (TNA) is an approach that applies Heyman's principles to represent stress in masonry vaults. This method models the stresses as a discrete network of forces, achieving equilibrium with gravitational loads. In this context, the results obtained by TNA analysis are strictly correlated with AE localization results.

Thrust Network Analysis and Thrust Surface Analysis are two well-established methods for studying the stability of vaulted masonry structures. Working within the framework of limit analysis and adopting the well-known Heyman hypotheses, both methods search for generalized statically admissible stress fields in historical masonry constructions. Although these two methods are sometimes considered to be linked, it is still unclear how this link can effectively be exploited from a practical standpoint. In this paper, we focus our attention on the conditions that enable establishing a proper connection between the two methods, which are based on different structural models, and we apply them to a case study, the dome of Pisa Cathedral. The analogies and differences in the results obtained are highlighted, and the feasibility in practice of a possible method combining thrust network and thrust surface is checked. [ABSTRACT FROM AUTHOR]

An evaluation of the seismic behavior of a massive masonry monument with vaults, namely, the Neoria complex at the old port of Chania, is presented here. The usage of modal response analysis requires the combination of many eigenmodes in order to capture the required amount of vibration energy. Alternatively, a number of earthquakes can be used within a time domain response analysis in order to evaluate the response and, subsequently, the strength of the structure. Results of linear analysis are compared here, since this is what is required from current seismic codes. A nonlinear analysis with adequate material models will also be presented in order to demonstrate a comparison with linear analysis and a prediction of damage appearance under ultimate conditions. From the present investigation, it is shown that the results of the modal analysis and the linear time-step analysis are comparable. Therefore, some confidence is gained towards using the results for the design of strengthening and rehabilitation studies. Nonlinear models are very sensitive with respect to design earthquakes and material models. Therefore, at this stage, their results are used for the identification of areas where interventions must be performed very carefully. [ABSTRACT FROM AUTHOR]

In this paper, the structural performance of masonry cross vaults is investigated with regard to the most common differential settlements occurring in historical constructions. Numerical parametric models are developed for vaults with different brick patterns and lateral constraints, in the presence/absence of infill. In particular, radial, diagonal and pitched brick patterns are taken into account and opening, shear and vertical settlements are analyzed. Moreover, the behaviour of laterally unconfined vaults is compared with the response of vaults restrained with rigid perimeter walls or with lateral masonry arches. The analyses highlight the strengths and weaknesses of each configuration, providing a scientific validation to some speculations found in historical technical literature on the most widespread use of some brick patterns. The outcomes of this research provide a deep knowledge of masonry vaults behaviour in view of more effective interventions on historical buildings, supplying the practitioners with a crack-pattern chart useful for better interpreting the damage pattern in historical vaults with different brick courses. [ABSTRACT FROM AUTHOR]

The evaluation of the structural behaviour of a masonry Venetian church with a pointed barrel vault is presented in this paper through an analysis following the necessary steps of a monument study. With a detailed geometric model and material estimation, the finite-element method is used to investigate the influence of specific structural parts of the structure, like masonry buttresses and wall connections, on the structural behaviour. The operational modal analysis is used to identify the structure dynamically. The comparison of the eigenfrequencies, which are estimated by in situ measurements and finite-element modal analysis, is used to perform a model identification. The response spectrum analysis, the static analysis after the subsistence of some parts following strengthening proposals, and the transient analysis of specific seismic excitations are used for the evaluation of the structural behaviour. The purpose of the work is to highlight the need for an interdisciplinary approach to the study of a monumental complex structure, regardless of its scale. The coexistence of structural elements of different stiffnesses, such as vaults, elongated walls, buttresses, transverse walls with pediment and belfry, as well as the concha, affects the mechanical behaviour and the pathology of the structure, which is difficult to study with simplifying models. From the analysis, it is concluded that subsidence problems, combined with seismic actions, lead to the cracking of the masonry, while the existence of buttresses limits the extension of the damage and contributes to the stabilization of the structure.

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]

A numerical method is implemented to cope with the funicular analysis of ribbed masonry vaults under self-weight. A two-layer spatial network with given plan geometry is adopted to account for the load path in the overlying vault and in the supporting ribs. The minimization of the horizontal thrusts is formulated in terms of an independent set of force densities, and in the vertical coordinates of the restrained nodes. Constraints are enforced on the height of the nodes and on the sign of the force densities, to seek anti-funicular networks in equilibrium with the loading that lie within the envelope of the ribbed vault. A stellar masonry vault originally built in the ancient church of Tereske (Hungary) is investigated, comparing results achieved by using either single-layer or two-layer spatial networks. [ABSTRACT FROM AUTHOR]

An evaluation of the seismic behavior of a massive masonry monument with vaults, namely, the Neoria complex at the old port of Chania, is presented here. The usage of modal response analysis requires the combination of many eigenmodes in order to capture the required amount of vibration energy. Alternatively, a number of earthquakes can be used within a time domain response analysis in order to evaluate the response and, subsequently, the strength of the structure. Results of linear analysis are compared here, since this is what is required from current seismic codes. A nonlinear analysis with adequate material models will also be presented in order to demonstrate a comparison with linear analysis and a prediction of damage appearance under ultimate conditions. From the present investigation, it is shown that the results of the modal analysis and the linear time-step analysis are comparable. Therefore, some confidence is gained towards using the results for the design of strengthening and rehabilitation studies. Nonlinear models are very sensitive with respect to design earthquakes and material models. Therefore, at this stage, their results are used for the identification of areas where interventions must be performed very carefully.

The design of brick masonry vaults has frequently been one of the main topics of historical construction handbooks, where also the orientation of the blocks was an examined issue. However, the influence of brick-texture has not yet been thoroughly investigated computationally. In the present paper the static behavior of masonry vaults of different shapes (barrel, pavilion, and cross vaults), was studied by analyzing and integrating two points of view: one historical and the other computational. First, the instructions provided by ancient documents were described. Then, a Non-Smooth Contact Dynamics Software was used to model vaults with different brick patterns suggested in the past. The vaults were studied with self-weight to observe load descent. Then, a concentrated force was added up to collapse. The analyses show how the load descent and load-bearing capacity are influenced by the brick pattern. Finally, the results of the various analyses were compared with the insights of the past. [ABSTRACT FROM AUTHOR]

The assessment of the equilibrium and the safety of masonry vaults is of high relevance for the conservation and restoration of historical heritage. In the literature many approaches have been proposed for this tasks, starting from the 17th century. In this work we focus on the Membrane Equilibrium Analysis, developed under the Heyman's theory of Limit Analysis. Within this theory, the equilibrium of a vault is assessed if it is possible to find at least one membrane surface, between the volume of the vaults, being in equilibrium under the given loads through a purely compressive stress field. The equilibrium of membranes is described by a second order partial differential equation, which is definitely elliptic only when a negative semidefinite stress is assigned, and the shape is the unknown of the problem. The proposed algorithm aims at finding membrane shapes, entirely comprised between the geometry of the vault, in equilibrium with admissible stress fields, through the minimization of an error function with respect to shape parameters of the stress potential, and then, with respect to the boundary values of the membrane shape. The application to two test cases shows the viability of this tool for the assessment of the equilibrium of existing masonry vaults. [ABSTRACT FROM AUTHOR]

The behavior of Prussian vaults of brick aggregate concrete differs both from the behavior of brick vaults and classical flat slabs. Such vaults are particularly susceptible to physical damage and deterioration. To determine the real bearing capacity of the vaults, the authors not only performed the insitu determination on several sections with deflection control, but also numerical simulations of the multispan system of Prussian vaults in the program complex Abaqus. Moreover, experimental comparisons between damaged and not damaged vaults were also performed in the historical building of the New Holland complex. Obtained results show that, the vaults adjacent to the loaded one exhibit opposite behavior and significant damages caused by the loaded one, both of which are useful outcomes for evaluation of this vaulting type.

The evaluation of the seismic safety of ancient masonry buildings usually requires compounding the need of preservation of the historical values with the need of achieving a proper level of knowledge of the parameters influencing their structural behaviour. To this aim, non-destructive techniques of instrumental investigation have lately attracted increasing attention, although the provided data are frequently not exhaustive and require to be integrated with different sources of information, such as historical documents and hypotheses of critical interpretation. Therefore, the management of this multi-source information is a crucial aspect in defining a methodological approach to the structural evaluation of the cultural heritage. This paper describes an integrated approach developed in the framework of the Project on the seismic evaluation of the Museum of Capodimonte in Naples (Italy) with reference to the typological identification of the horizontal structures upon the first level of the building. The management of the data derived from the application of the infrared thermography, integrated with the information from the visual inspections, the architectural survey and the historic analysis, has allowed obtaining a complete characterization of the structures under study.

Masonry vaults are able to withstand their dead load and external forces thanks to their curved surface, therefore geometry plays a major role in their structural behaviour. Besides the well-known effects of the macro-geometry (overall shape and dimensions), micro-geometry (details of the masonry apparatus) is also expected to play a key role. The study seeks to determine the advantages (constructional and structural) that a specific masonry apparatus offered for simple forms like barrel vaults and more complex forms like cross vaults. It is carried out, firstly, through a critical review of the European technical literature concerning vault construction with particular focus on brick laying techniques; then, numerical approach is adopted to scientifically investigate the role of micro-geometry on the static behaviour of barrel and cross vaults subjected to self-weight. Comparison of results allows observing different structural behaviour (displacement field, elastic stiffness, reaction forces) for different brick patterns and provides a scientific validation to some speculations found in historical technical literature. [ABSTRACT FROM AUTHOR]

Brick masonry is a very widely used building method. A specific example of use of this masonry is the thin-tile vault. This is characterised by the format of several layers joined together with mortar and in which the position of the bricks means that they bear the load on edges. The main objective of this study is an assessment, based on experimental results, of clay brick masonry behavior when the load is applied parallel to the face of the bricks instead of perpendicular thereto. This study compares the stress-strain behavior, failure modes, compressive strength, and Young's modulus of this type of masonry with data obtained from scientific literature. [ABSTRACT FROM AUTHOR]

The paper deals with the seismic vulnerability of masonry vaults: a review of the results of an experimental campaign recently performed by the authors and a numerical study are presented. In particular, the effectiveness of a strengthening technique based on the application, at the vault extrados or intrados, of a 30 mm thick mortar coating with glass fiber-reinforced polymer meshes embedded is discussed, referring to vaults carrying their self-weight and subjected to a lateral transversal load. The role of the connection of the vault with its abutments is particularly emphasised in this review of the experimental results, evidencing how slides and/or uplifts at the spring sections can reduce the strengthening effectiveness. The numerical study, based on non-linear static analysis, allowed to investigate in depth into the effects of an inadequate skewback configuration: it was found that a ductile connection, which allows plastic rotation at the spring section while maintaining the bending resistance and avoiding shear slip and uplift, is the optimal solution. Moreover, the results of a sensitivity study are also presented, as this permits to evaluate the incidence of the different mechanical and geometrical parameters on the behavior of the vaults and provides useful indications towards a proper design and optimization of the strengthening intervention. [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]

Abstract In many engineering applications the limit analysis theorems can be used to estimate the ultimate capacity of several structures. However, the limit analysis can be applied on structures with an adequate plastic capacity. When the goal is to evaluate the ultimate capacity of masonry structures, they could show some drawbacks. For this reason, the incremental analysis represents a valid alternative to estimate the ultimate capacity of masonry structures. These structures could show brittle failures before the hinge mechanism. It is a key aspect especially for curved masonry elements like as arches and vaults. The work focuses on the incremental analysis of masonry barrel vaults without backfill. An analytical model in the framework of the incremental analysis has been proposed. The analytical model allows to assess both the ultimate capacity and the ductility of the masonry barrel vaults. In the first part, the proposed model has been discussed. Then, parametric analysis was performed to assess the impact of physical, geometrical and mechanical parameters on the ultimate behaviour. The numerical results allow to identify some structural examples where the brittle behaviour becomes crucial. Finally, the proposed model was validated with experimental results on a full-scale masonry barrel vault. Highlights • The work focuses on the incremental analysis of masonry barrel vaults without backfill, accounting for tensile strength. • The analytical model allows to assess both the ultimate capacity and the ductility of the structure incrementally. • The numerical results allow to identify some structural examples where the brittle behaviour becomes crucial. • The proposed model was validated by using the experimental tests of a masonry barrel vault actually tested. [ABSTRACT FROM AUTHOR]

The assessment of the equilibrium and the safety of masonry vaults is of high relevance for the conservation and restoration of historical heritage. In the literature many approaches have been proposed for this tasks, starting from the 17th century. In this work we focus on the Membrane Equilibrium Analysis, developed under the Heyman’s theory of Limit Analysis. Within this theory, the equilibrium of a vault is assessed if it is possible to find at least one membrane surface, between the volume of the vaults, being in equilibrium under the given loads through a purely compressive stress field. The equilibrium of membranes is described by a second order partial differential equation, which is definitely elliptic only when a negative semidefinite stress is assigned, and the shape is the unknown of the problem. The proposed algorithm aims at finding membrane shapes, entirely comprised between the geometry of the vault, in equilibrium with admissible stress fields, through the minimization of an error function with respect to shape parameters of the stress potential, and then, with respect to the boundary values of the membrane shape. The application to two test cases shows the viability of this tool for the assessment of the equilibrium of existing masonry vaults.

The evaluation of the seismic safety of ancient masonry buildings usually requires compounding the need of preservation of the historical values with the need of achieving a proper level of knowledge of the parameters influencing their structural behaviour. To this aim, non-destructive techniques of instrumental investigation have lately attracted increasing attention, although the provided data are frequently not exhaustive and require to be integrated with different sources of information, such as historical documents and hypotheses of critical interpretation. Therefore, the management of this multi-source information is a crucial aspect in defining a methodological approach to the structural evaluation of the cultural heritage. This paper describes an integrated approach developed in the framework of the Project on the seismic evaluation of the Museum of Capodimonte in Naples (Italy) with reference to the typological identification of the horizontal structures at the first level of the building. The management of the data derived from the application of the infrared thermography, integrated with the information from the visual inspections, the architectural survey and the historic analysis, has allowed obtaining a complete characterization of the structures under study.

The reinforcement of existing masonry vaults against seismic actions is an extremely timing issue and it has already involved many researchers in experimental testing and numerical modelling. However, up to now, the results of the research have been expressed and compared in terms of load-displacement capacity curves. But the designers, in the practice, need to assess the resisting peak ground acceleration of the vault (PGA), so to compare it with the seismic demand. In the paper, a strategy to evaluate this parameter, based on the modified Capacity Spectrum Method and accounting for the level of the vault in the building is proposed. The procedure is applied to a case study of a masonry building with barrel vaults, comparing the performances of plain vaults and vaults strengthened with a GFRP (Glass Fiber Reinforced Polymer) reinforced mortar coating. The results evidenced significant improvements in terms of PGA after the reinforcement, attaining to values from 3.1 to 3.3 times that of the unreinforced vault. [ABSTRACT FROM AUTHOR]

The paper collects the results of an innovative experimental campaign carried out on full-scale, non-structural masonry barrel vaults, so to assess, by means of quasi-static cyclic tests, the lateral performances of a strengthening technique based on the application, at the extrados or the intrados, of a 30 mm thick mortar layer with Glass Fiber-Reinforced Polymer meshes embedded. The samples were made of solid bricks, with a radius of 2060 mm and are 770 mm wide and 120 mm thick; three vaults have a span of 3980 mm and other three of 3575 mm. It emerged that the presence of the composite mesh contrasted the collapse mechanism, leading to resistance increases ranging from 2 to 4 times that of plain masonry and increasing considerably the ultimate horizontal displacements at crown section. A simplified analytical approach is also presented in the paper, to quantify the samples lateral resistance for assigned geometry and mechanical characteristics of materials. [ABSTRACT FROM AUTHOR]

The evaluation of the seismic safety of ancient masonry buildings usually requires compounding the need of preservation of the historical values with the need of achieving a proper level of knowledge of the parameters influencing their structural behaviour. To this aim, non-destructive techniques of instrumental investigation have lately attracted increasing attention, although the provided data are frequently not exhaustive and require to be integrated with different sources of information, such as historical documents and hypotheses of critical interpretation. Therefore, the management of this multi-source information is a crucial aspect in defining a methodological approach to the structural evaluation of the cultural heritage. This paper describes an integrated approach developed in the framework of the Project on the seismic evaluation of the Museum of Capodimonte in Naples (Italy) with reference to the typological identification of the horizontal structures upon the first level of the building. The management of the data derived from the application of the infrared thermography, integrated with the information from the visual inspections, the architectural survey and the historic analysis, has allowed obtaining a complete characterization of the structures under study. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the dynamic and static three-dimensional behavior of a dry-assembled masonry cross vault, through the comparison of Distinct Element Modeling results and laboratory tests’ results on a physical model obtained by mean of 3D printing. The work consists of two phases: the first one compares two numerical models of a cross vault built with different masonry patterns (parallel, orthogonal); the second phase deals with a comparison between the static behavior of the computational and the real scaled models (1 m × 1 m) of the same cross vault, tested at one support collapse. The study focuses on three principal aspects: (i) to evaluate the three-dimensional mechanism of the cross vault, (ii) to determine the support displacement’s magnitude that leads to its collapse and (iii) to evaluate the ability of computational methods to predict the experimental results. The results obtained from the numerical and the experimental tests have been compared in order to give general specifications on the behavior of these types of vaults. [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]

The damages occurred during recent seismic events have emphasised the vulnerability of vaulted masonry structures, one of the most representative elements of worldwide cultural heritage. Although a certain consensus has been reached regarding the static behaviour of masonry arches, still more efforts are requested to investigate their dynamic behaviour. In this regard, the present paper aims to investigate the performance of a scaled dry-joint arch undergoing windowed sine pulses. A feature tracking based measuring technique was employed to evaluate the displacement of selected points, shading light on the failure mechanisms and gathering data for the calibration of the numerical model. This was built according to a micro-modelling approach of the finite element method, with voussoirs assumed very stiff and friction interface elements. Comparisons with existing literature are also stressed, together with comments about scale effects. [ABSTRACT FROM AUTHOR]

This paper addresses the structural safety assessment of the Chapel of the Würzburg Residence (Germany), one of the most important churches of the Central European Baroque. It was declared as World Heritage Site by UNESCO in 1981, one of its most unique and distinctive characteristics is the geometry of its complex vaults. Intersections between vaults are warped and vaults surfaces were built using only one layer of brick masonry. In this work, a nonlinear finite elements (FE) model has been developed and used to assess the structural safety of the building. In order to update the model by identifying the dynamic response of the building, experimental ambient vibration tests have been previously subsequently carried out. Operational Modal Analysis (OMA) has been used to experimentally identify both modal displacements and natural frequencies. The numerical FE model is them adjusted using genetic algorithms until its dynamic response resembles that experimentally observed, thus providing a valid model to further analyse the structural behaviour of the building. After briefly descripting the Chapel, the methodology followed to update the numerical model and the obtained results from a non-linear analysis on this over-complex vaulted structure are the main goals of the paper. [ABSTRACT FROM AUTHOR]

We address the Thrust Network Analysis (TNA), i.e. the methodology for modeling masonry vaults as a discrete network of forces in equilibrium with gravitational loads, first contributed by O’Dwyer and fully developed by Block and coworkers. Reducing the bias by the quoted authors in favor of a graphical interpretation of the method, we reformulate the original version of the TNA by discarding the dual grid and focusing only on the primal grid, thus significantly enhancing the computational performances. The proposed reformulation of the TNA is also extended by including horizontal forces in the analysis as well as holes or free edges in the vault. Furthermore, the coefficient matrices entering the solution scheme are obtained by assembling the separate contribution of each branch, thus avoiding the ad hoc node numbering and branch orientation required by alternative implementations. Numerical examples, some of which referred to vaults having a particularly complex geometry, show the effectiveness and robustness of the proposed approach in assessing the safety conditions of existing masonry vaults or in designing new ones. [ABSTRACT FROM AUTHOR]

The present paper proposes a new Genetic Algorithm NURBS-based approach for the limit analysis of masonry vaults based on an upper bound formulation. A given masonry vault geometry can be represented by a NURBS (Non-Uniform Rational B-Spline) parametric surface and a NURBS mesh of the given surface can be generated. Each element of the mesh is a NURBS surface itself and can be idealized as a rigid body. An upper bound limit analysis formulation, which takes into account the main characteristics of masonry material is deduced, with internal dissipation allowed exclusively along element edges. The approach is capable of well predicting the load bearing capacity of any masonry vault of generic shape. It is proved that, even by using a mesh constituted by very few elements, a good estimate of the collapse load multiplier is obtained provided that the initial mesh is adjusted by means of a meta-heuristic approach (i.e. a Genetic Algorithm, GA) in order to enforce that element edges accurately represent the actual failure mechanism. The proposed method turns out to be both accurate and much less computationally expensive than existing methods for the limit analysis of masonry vaults. [ABSTRACT FROM AUTHOR]

Since cross masonry vaults represent one of the more widespread types of horizontal structural elements in historical constructions, understanding their behaviour is a crucial precondition for the accurate assessment of the global response of buildings to earthquakes. In spite of the importance of this topic, the complexity of evaluation three-dimensional response of vaults still represents a challenge for researchers. Experimental investigations can be a valid tool to analyse this difficult problem, as they provide useful results that can validate the reliability of the numerical and analytical tools developed for analysis. In this paper, the results of an experimental campaign on 1:5 scale model of a masonry cross vault are presented. The main aim was to evaluate the response of the vaults in the context of a global analysis of historic masonry buildings by determining their ultimate in-plane seismic capacity (diaphragm effect) in terms of stiffness, strength, and ultimate displacements. Their three-dimensional damage mechanisms on the vaults was also described. The model, made of 3D printed plastic blocks with dry joints, was tested by statically applying different horizontal displacements settings to the abutments in order to simulate differential displacements of the supports (walls or pillars). In particular, in-plane horizontal shear distortions and longitudinal opening/closing of the abutments, as they are the most common seismic damage mechanisms seen in masonry vault buildings, were applied. [ABSTRACT FROM AUTHOR]

• Lower Bound 3D limit analysis code for masonry double curvature structures. • Hexahedral rigid 3D elements with dissipation on interfaces. • Possibility to analyze no-tension material models and masonry with orthotropy. • Validation on several different structural examples of major importance. • Detection of the failure mechanism from safe side by means of the solution of the dual problem. A new Lower Bound LB plate and shell limit analysis Finite Element FE model for the analysis at collapse of masonry double curvature structures is presented. The discretization relies into hexahedrons assumed infinitely resistant and quadrilateral interfaces where all plastic dissipation occurs. On such interfaces, the flexural behavior is ruled by the interaction between bending moment and axial load, whereas the shear and torsional behavior are modeled by means of an in-plane tangential force, out-of-plane shear and a plate torque. The resultant limit analysis problem obtained by such a formulation is particularly straightforward and the number of variables to deal with very limited. Equilibrium is indeed imposed only on hexahedrons and admissibility on interfaces between adjoining elements. Masonry can be modeled obeying a classic no-tension material or with more complex linearized failure surfaces, for example derived from suitable homogenization techniques. A simple Linear Programming LP problem is so derived, where the actual thickness of the structure is accurately accounted for, a key feature to assess the stability of a vault in case of the no-tension material assumption. The numerical model is validated by means of several meaningful structural examples. A detailed comparison with numerical data available in the literature, obtained for the same examples with alternative numerical approaches shows the accuracy of the method proposed and its usefulness for a fast and reliable prediction of the load carrying capacity of masonry double curvature structures. [ABSTRACT FROM AUTHOR]

Highlights: [•] The proposed strengthening system gives back a greater dissipation capacity. [•] The composite reinforcement well works also in compression without buckling effect. [•] The collapse mechanism avoids the vault local crash even in the case of earthquake. [•] The Ω-Wrap system triples the resistance than the traditional CFRP reinforcement. [•] No more fiber amount is required in respect to the traditional system. [ABSTRACT FROM AUTHOR]

Abstract: Knowledge of the functional and conservation state of a structure is a fundamental aspect in order to achieve its maintenance and preservation. Having adequate techniques for reaching this purpose is one of the most important aspects for professionals working about built-up structures. Geometry usually plays an important role in the diagnosis of these structures, and for masonry arches particularly. The most common software packages focused on the stability analysis of masonry arches use rigid blocks assuming masonry as plastic material into the context of Limit Analysis Theory. This paper presents the first results of a novel methodology for the analysis of arch bridge stability based on the construction of integral 3D models of entire vaults. This geometric reconstruction is achieved thanks to the employment of non-destructive techniques such as photogrammetry and Ground Penetrating Radar. Then, stability of vaults is evaluated through a tool specifically developed using Matlab software. [Copyright &y& Elsevier]

A second-order equilibrium analysis is developed for the calculation of the collapse load of an eccentrically compressed beam with an annular cross section in the presence of a no-tension material. Unlike the case of a rectangular cross section, extensively treated in the literature, no rigorous closed-form solution is possible, in this case, but semianalytical results can be obtained, which may be useful for engineering applications. [ABSTRACT FROM AUTHOR]

Abstract: The assessment of the load-carrying capacity of old masonry vaults loaded in longitudinal compression by pre-tensioned reinforcing bars, accounting for both material and geometrical nonlinearities, appears to be a difficult task, so far unattempted. Here, we consider a real case, both analytically and by means of the Finite Element Method (FEM), studying the effects of several factors on the maximum applicable compression: description of the material nonlinearity, self-weight, structural reinforcements such as extradossal ribs and internal buttresses, boundary conditions, geometrical imperfections. [Copyright &y& Elsevier]

Brick masonry vaults for the approach structures of the Brooklyn Bridge were instrumented for remote monitoring. The objective of the project was to monitor and quantify safety of the structure, because of the longitudinal cracks at the crown of the double span vaults. A fiber optic sensor system was installed in the Brooklyn Bridge to monitor the crack opening displacements, wall rotations, temperature fluctuations, and vibrations. To quantify safety, a scaled model of the masonry vault was also tested in the laboratory in order to determine the failure crack opening displacement limits of the vaulted structure. Fiber optic crack sensors were mounted on the test vault to record the crack opening displacements under a range of base movements. Correlation of the in-service and failure crack opening displacements from the field measurements and laboratory tests provided the basis for the quantification of safety. This article provides a synopsis of activities to achieve these goals in terms of monitoring plans, instrumentation, and analysis of remote field data, laboratory experimental results and formulation of the safety assessment strategies. [ABSTRACT FROM AUTHOR]