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Great part of the existing buildings in seismic areas and in particular in developing countries is represented by masonry buildings, diffused also in the major part of historical centres in Europe. Damages due to seismic events have evidenced the large demand of rehabilitation together with suitable assessment methods for these structures. When out of plane mechanism can be avoided, the contribution of in-plane shear resistance of the masonry walls is a key aspect to consider in the vulnerability analysis of the whole structure. Based on this last consideration, this paper presents an approach to the analysis of in-plane behaviour of masonry walls, involving a minimum energy strategy. The results of the numerical analyses presented are compared with those obtained by laboratory tests on brick masonry panels. © Patron Editore S.r.l. Gran parte del patrimonio edilizio esistente in zona sismica, soprattutto nei paesi in via di sviluppo, è costituito da edifici in muratura, largamente diffusi anche in tutti i centri storici europei. I collassi e i danni rilevati a seguito di eventi sismici hanno evidenziato la necessità di interventi e soprattutto di tecniche di analisi idonee. In un edificio in muratura ben progettato e realizzato, ove i meccanismi di collasso per azioni fuori piano possono essere esclusi, il comportamento nel piano delle pareti in muratura diventa un aspetto chiave da esaminare nelle valutazioni di vulnerabilità sismica. Partendo da quest'ultima considerazione, questo lavoro presenta un approccio per la l'analisi del comportamento nel piano di pareti murarie sottoposte a compressione e taglio. La procedura utilizzata considera la muratura come un materiale elastico non resistente a trazione, definisce pertanto una sagoma reagente contenuta nell'ambito del pannello murario soggetta a soli sforzi di compressione e risolve una procedura numerica la cui soluzione corrisponde al minimo dell'energia potenziale per il pannello. Vengono presentati confronti fra i risultati numerici e alcune prove sperimentali presenti in letteratura per diverse geometrie di pannello. © Patron Editore S.r.l.

Seismic capacity assessment of existing buildings is of paramount importance for mitigating the seismic risk in earthquake-prone areas. In Europe, the next version of Eurocode 8 and the current version of the Italian standards suggest the adoption of both linear and nonlinear approaches to perform seismic analyses of existing masonry buildings. This paper discusses with the main issues concerning linear and nonlinear analyses methodologies provided by the Italian standards for existing unreinforced masonry buildings. An historical building located in Southern Italy, representative of the Mediterranean basin buildings, has been chosen as a case study and modelled through the equivalent frame model. According to the Italian standards, the influence of in-plane stiffness of floors and spandrels on the overall seismic capacity of the structure has been considered in the analyses. Beyond the code prescriptions, the effect of different ultimate drifts values assumed for the spandrels on nonlinear behavior of the structure has been analysed. The results of two types of linear analyses (lateral static force method and modal response spectrum analysis) have been compared among them and with those provided by the nonlinear static method. Conclusions show that either behavior and overstrength factors provided by the Italian standards are conservative than those estimated through the nonlinear static analyses. Moreover, it has been remarked that the value of ultimate drift adopted for the spandrel can affect significantly the nonlinear response of the structures, although this topic still represents an open issue.

This paper presents a benchmark exercise for the seismic assessment of unreinforced masonry (URM) buildings as a follow-up of a blind prediction test organized in the context of the European Conference of Earthquake Engineering Series. The blind prediction exercise was aimed at better defining the open issues in current procedures for modeling and performing seismic analysis of URM buildings, by highlighting the uncertainty that can influence the results. This work presents an overview of the approaches used by different research teams and the scope of predictions. The benchmark structure was a three-story building with traditional European architecture from which two Cases were considered: A) stone masonry walls and flexible horizontal diaphragms and B) brick masonry walls and rigid horizontal diaphragms. A wide range of approaches was used by the participating teams concerning modeling strategies, methods of analysis and criteria for the attainment of limit states, which are here addressed as potential sources for the dispersion of predictions. The results were compared in terms of capacity curves, predicted failure mechanisms compatible with the fulfillment of limit states of near collapse and damage limitation, and related minimum values of peak ground acceleration (PGA). The results show an overall good agreement for damage patterns and collapse mechanisms in both benchmark structures, presenting some differences in the type of failure mode and its extent. However, the scatter of predicted capacity curves and critical PGAs is very high, especially for the Case with brick masonry and rigid diaphragms, indicating that clearer procedures in the building codes are required for professionals., This work was partly financed by FCT/MCTES through national funds (PIDDAC) under the R&D Unit Institute for Sustainability and Innovation in Structural Engineering (ISISE), under reference UIDB/04029/2020.

This paper provides a comphrensive review of the critical aspects of nonlinear modeling for evaluating the seismic response of masonry structures, emphasizing the issues relevant to engineering practice. Currently, the specialized technical community shares the opinion that, for a performance-based approach, numerical models are the only tools sufficiently effective to support the seismic assessment of existing buildings. However, their potential often falls short when attempting to accurately describe the behavior of masonry structures. In fact, these structures feature highly complex architectural configurations, different masonry types, and various structural solutions, meaning that extra care is required in numerical modeling. This is especially true when the modelers do not have a solid background in the software chosen and may not be practiced using the vast variety of options offered by the software houses. They are often unaware of the consequences that questionable modeling choices may have on the results obtained by the models. These extremely complex topics are treated in the paper from an engineering practice perspective, providing an in-depth overview of the challenging issues related to the use of different modeling strategies. The paper covers strategies ranging from the Equivalent Frame approach (widelyused in common engineering practice) to more refined techniques like 2D and 3D FiniteElement procedures based on continuous, discrete, and micro-mechanical approaches. Critical aspects in the modeling of both in- and out-of-plane responses of masonry, as well as the critical issues in wall-to-wall connections and diaphragm roles are investigated. All the examined issues are clarified through numerical examples highlighting also how a consistent and integrated use of different procedures may be beneficial. Finally, some of most relevant challenging issues concerning the use of numerical models in seismic assessment with the nonlinear static approach are presented and discussed.

This paper investigates the potentials of inter-story isolation systems (IIS) for retrofitting irregular masonry buildings by means of an isolated vertical addition realised on the roof of the existing structure. By assuming a case study, a wide parametric analysis is firstly carried out on lumped-masses model for identifying the dynamic properties of the isolated superstructure that minimizes the global seismic response. Hence, a 3D FE model is adopted for the detailed design and analysis of the IIS structure, with different solutions, in order to regularize the global seismic response of the IIS complex. Finally, some general design criteria are suggested.

Unreinforced masonry is the most diffused construction material in the major part of historical centers in Europe. In a building subjected to earthquake forces the contribution of in-plane shear resistance of the masonry walls is a determinant factor for the stability of the whole structure. In particular, the masonry piers are the structural elements subjected to the combination of normal and shear forces. In general, ductile tools to model the in plane behaviour of masonry are always welcome in order to evaluate the capacity of walls subjected to vertical and horizontal actions. In this framework, two no-tension approaches to model the behaviour of masonry walls loaded with in-plane forces, involving a minimum energy procedure, are presented. Both the procedures allow the representation of the stress maps in the panel in case of monotonic increase of shear load. The results of the numerical analyses are compared and discussed., Frattura ed Integrità Strutturale, 14 (51)

This paper presents the results of an experimental program conducted on H-shaped reduced-scale reinforced masonry spandrels subjected to monotonic loadings. It summarized tests units, test set-up and experimental results relative to seventeen samples reinforced by thin-steel stripes arranged with different configurations, and compared with those unreinforced. The first configuration comprised masonry spandrels strengthened by unbonded horizontal and diagonal steel stripes (i.e., stripes connected by means of threaded rods to the nodal area of the panel), while the second masonry spandrels reinforced by bonded horizontal stripes (i.e., stripes connected with 5 or 13 threaded rods over the spandrel length). For each reinforcement configuration, slender, intermediate and squat slenderness ratios have been considered for the samples. The conducted research investigated the effectiveness of the reinforcement to enhance the seismic response of the spandrels. Test results demonstrated that the application of steel stripes is beneficial in changing the failure modes from shear-dominated into flexural-dominated, especially for intermediate and squat panels prone to brittle shear mechanisms. Despite that increases of strength are reduced with respect to unreinforced samples, when reinforced the post-peak response changes significantly being it characterized by a remarkable ductile response for whatever spandrels’ slenderness ratios.

Modeling of masonry buildings subjected to seismic actions still represents an open problem in structural engineering. The equivalent frame model is the most used approach to analyze the seismic behavior of both existing and new masonry constructions but, despite this, several aspects are being researched to improve its effectiveness. Among these, modeling of spandrel panels plays a key role to correctly analyze the in-plane seismic response of unreinforced masonry walls. Actually, horizontal mono-dimensional beam-like elements provided of both strength and displacement capacity are used to schematize the spandrel panels, also according with the most of current national and international codes. In this paper an alternative strut and tie scheme to model the spandrel panels, suitable to be used within the equivalent frame approach, is presented: the compressed masonry material is schematized with an equivalent diagonal no-tension truss, whose length and effective compressed area are obtained with limit equilibrium conditions, while tensile-resistant element is represented by no-compression truss. Such model allows a more realistic representation of the mechanical behavior of spandrels because both amount of axial force within the spandrel and the reduced elastic flexural and shear stiffness due to progressive cracking of material are taken into account. Moreover, the local failures of both compressed masonry and/or tensile-resistant elements are better identified and, consequently, also the failure mechanisms of the whole equivalent frame are better detailed. The proposed schematization has been used to simulate the seismic behavior of some reference case studies of existing masonry walls, strengthened with different steel ties arrangement. These walls have been modelled with a hybrid equivalent frame model which consists of mono-dimensional beam-like element for piers, fully rigid offsets for the nodal panels and a strut and tie scheme for spandrels.

This paper deals with the experimental monotonic and cyclic behavior of masonry spandrels reinforced with Fiber Reinforced Polymers (FRP). The research is a part of a wider program, started by the authors in the last decade, regarding the analysis of the seismic behavior of masonry spandrels in historical buildings of the Mediterranean area. The paper summarizes the properties of the test units, the test set-up and the results of the experimental monotonic and cyclic behavior conducted on twenty-four scaled down H-shaped spandrels made with homogeneous material (e.g. mortar with low tensile strength). Both unreinforced and FRP-reinforced specimens with three different slenderness ratios – e.g. slender, intermediate and squat – and three different arrangements of FRP laminates have been considered for the tests. The main objective has been to verify the possibility of preventing brittle failure modes, typical of spandrels subjected to in-plane seismic actions (e.g. diagonal cracking), and of increasing their strength by applying specific reinforcement systems, so encouraging more ductile behavior characterized by toe-crushing at the ends of the spandrels itself.

The whole Mediterranean area historical heritage is mostly constituted by 'ancient' unreinforced masonry constructions which are particularly vulnerable to earthquakes. Due to the particular attitude to out-of-plane collapse mechanisms, 'ancient' constructions largely contribute to increase the seismic risk. In this paper, a methodology for retrofitting unreinforced masonry buildings, aimed to gradually transforms the 'ancient' masonry building into a 'modern' code-conforming building, is proposed. This approach has been applied to an existing masonry building located near L'Aquila (Italy) and damaged during the 2009 earthquake. The results demonstrate the usefulness of a methodological approach to implement retrofitting actions. Thus, appears more easily to calibrate the interventions as a function of the structural weakness and to quantify the role of each intervention in terms of capacity-to-demand ratio. Moreover, a gradual control of the seismic performance enhancement with respect to the original capacity can be achieved, avoiding high economic costs related to unnecessary interventions.

The interest of the scientific community for the seismic behaviour of existing masonry buildings has largely increased in recent years, due to the fact that the seismic events have evidenced a great need of rehabilitation. Masonry structures, and especially low rise buildings, are in fact the most diffused all over the world and in particular in seismic areas in developing countries because of their ease in construction and economy. Moreover unreinforced masonry is the most diffused construction material in the major part of historical centrers in Europe. In a well engineered and constructed masonry building subjected to earthquake forces, in which out of plane mechanisms can be avoided, the contribution of in-plane shear resistance of the masonry walls is a determinant factor for the stability of the whole structure. Based on this last consideration, this paper presents an approach for the analysis of masonry walls loaded with in-plane forces, involving a minimum energy procedure. The results of the numerical analyses presented are compared with those obtained by laboratory tests on brick masonry panels.