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Masonry buildings are the main part of the Architectural heritage in the World. The need of preservation for the historical memory, together with the exigence of fruition and use, has evidenced the need of appropriate analysis tools. In general, the stresses in masonry structures are usually considerably lower than those required for their material failure, so that the stability is mainly due to their shape and self weight. These aspects allowed in the past the simple realization of construction models in a reduced scale in order to assess the stability. As the history has pointed out, the behaviour of constructions is strongly linked to the workmanship and the good realization of the construction details. Local or global collapse can occur in fact due to pathologies arising during the construction or to bad realization of construction details. This paper deals with this last aspect, examining three different masonry buildings: the first one is a brick masonry building in Bologna: San Barbaziano Church, the others are two Roman domus in two different archaelogical sites in Campania: Villa Regina (Boscoreale, Napoli) and Villa dei Misteri (Pompeii, Napoli). The defects have been divided into two classes: structural defects and non structural ones. It is shown that structural defects can cause a global damage and could involve significant interventions.

A method is presented for evaluating the axial critical loads and deformed shapes of a Vierendeel periodic girder. They are obtained by solving the large-deflections equilibrium problem of a micro-polar equivalent model. The elastic properties of this model have been derived from those of an ideal girder whose cells may deform only according to the inner forces transferring modes of the unit cell. In particular, the strain energy density of the equivalent medium is obtained by evaluating the limit of the girder elastic energy for the cell to girder size ratio tending to zero. To solve Engesser/Haringx discord, the large deflections equilibrium equations are deduced by the virtual work principle, without any a priori assumption on the shear force. For this aim, also the external work of the substitute medium is evaluated by the same procedure as the strain energy density. Actually, it is first written for the ideal girder under the assumption of negligibility of the axial effects at the cell-scale, then specialized for the continuous medium by examining the limit value for cell to girder size ratio going to zero. Closed form solutions for the critical deformed shapes are given, together with an accurate formula for the girder buckling load

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)

In many seismically active regions of the world there are large numbers of masonry buildings. Most of these buildings have not been designed for seismic loads. Recent earthquakes have shown that many of these buildings are seismically vulnerable and should be considered for retrofitting. Different conventional and unconventional retrofitting techniques are available to increase the strength and/or ductility of unreinforced masonry (URM) walls. This paper reviews and discusses seismic retrofitting of masonry walls with emphasis on the conventional techniques. Retrofitting procedures are discussed with regard to a case study: a stone masonry building in Irpinia region, damaged by the 1980 earthquake. The interventions are evaluated by means of finite elements with a macroelement obtained with an homogenization technique. Linear and nonlinear procedures are compared, and peculiarities of each procedure are shown

In the present paper, we propose the Continuous Displacement for Fracture (CDF) method, a continuous energy-based numerical approach to find mechanisms and crack patterns exhibited by 2D masonry structures subjected to given loads and settlements. The structure is modelled through the normal, rigid, no-tension material, and the equilibrium problem is solved as the minimum of the total potential energy (TPE). With the CDF method the solution is sought in the space of continuous functions. The CDF performances are compared and illustrated against the PRD approach that finds the TPE minimum in the space of small, piecewise-rigid displacements. The CDF method is displacement-based approach, allowing for a direct control of the effects of foundation settlements. Some problems are proposed to benchmark the methodology against both PRD and analytical solutions to also clearly illustrate its peculiarities. Finally, its use and potentials are benchmarked and compared on a case study. CDF provides results in good agreement with both the PRD approach and another more sophisticated model. The main outcome is that, although more computationally cumbersome, CDF is mesh independent and perfectly captures a clear subdivision of the structural domain into macro-regions behaving as rigid or quasi-rigid bodies.

The archaeological site of Pompeii has been subjected to restoration interventions since the beginning of its excavation. After the second World War concrete structures replaced the old wooden roofs erected in the late XIX. A systematic study of these structures is lacking, despite the number and the significant role they play in the stress state of the ancient masonry. In particular, the structural role of atriums roofing structures in the Pompeii buildings is examined. The impact of the restoration interventions actually present in the archaeological area of Pompeii is analyzed. A dynamic analysis has been performed to assess the seismic vulnerability of the ancient buildings in their actual state. The paper shows that maintenance of the existing interventions is a fundamental topic and substitution of r.c. roofs with timber structures cannot be justified by structural reasons. As a case study the entire Domus of the Tragic Poet is analyzed. A simulation involving a wooden roof is compared with the actual structure of concrete roof building. © 2020 European Association for Structural Dynamics.

This paper deals with a mechanical model for the analysis of the railway track behaviour built by exploiting the periodicity of the track-structure. The starting point of this study is the analysis of the inner forces transferring modes. They have been determined by the unit principal vectors analysis of the base cell transfer matrix. The proposed model is able to reproduce accurately the track behaviour in transferring its inner forces. However, solutions that are equilibrated but not kinematically admissible are obtained from it when transversal loads are applied. In additions, only boundary conditions compatibles with the track transferring modes can be satisfied. This inconsistency is eliminated by superposition of a corrective deformed shape. This is derived from the eigenvectors of the transfer matrix pertaining to self-equilibrated systems of bending moments decaying along the track. The application field of the proposed track model is also discussed and the results of a validation study carried out by F.E. analysis are finally presented.

The present paper concerns an approach to the structural identification of tall buildings. The identification is based on a large number of experimental data obtained on a scaled model. The procedure consists in steps of system identification by means of a refined finite element model which is the base for the evaluation of a simplified one dimensional scheme. The parameters accuracy of this last one has been determined with reference to a refined schematization. The approach is model updating, based on the first three experimental natural frequencies and modes. The case study is a structure in Naples, made by two reinforced concrete towers, linked at the top by a steel girder with suspended storeys, while the foundation slab is based on a reinforced concrete piled group.

In this paper an homogenization procedure of a Vierendeel girders with elastic joints is shown. The method is based on the Stephen transfer matrix analysis and employs as substitute continuum a polar Timoshenko beam. The polar character of the equivalent beam arises quite naturally from the analysis of the pure bending eigenvector components of the girder force transfer matrix. Through the girder unit cell, two bending moments are transmitted: one is generated by the couple of axial forces acting on each nodal section of the beam, the other is produced by the moments applied at the nodes of every ones by the adjacent cells and is modelled as the resultant of the micro-polar moments. Transfer force eigenvector analysis reveals that the unit cell bends maintaining the webs undeformed, a property that allows evaluating both the bending stiffnesses and the equivalent material micro-polar scale parameter by means of straightforward equations. The accuracy of the proposed method is verified by comparing the predictions of the homogenized model with literature data and with the results of the analysis of a series of girders carried out by the finite element method.

The recent diffusion of wind turbines has evidenced problems about their vulnerability in different site conditions, as shown by recent collapse of wind towers after severe actions. The analysis of structures subjected to variable actions can be carried out by means of several methods with different levels of accuracy, among which the nonlinear dynamics is generally recognized as the most reliable one. This paper develops a numerical procedure to obtain approximate solutions for rigid-plastic response of structures subjected to base harmonic pulse. The model is applied to a wind turbine tower subjected to inertia forces generated by an harmonic ground acceleration, in which the failure is assumed depending on the formation of shear hinges. The approach presents the advantages of rigid-plastic procedures, in particular an efficient representation of the post-elastic behaviour of the structure, low computational competence and limited number of mechanical parameters.

The objective of the present work is to develop an automated numerical method for the analysis of thin masonry shells. The material model for masonry that we adopt is the so-called "normal rigid no-tension" (NRNT) material; and for such a material, the kinematical and the safe theorems of limit analysis are valid. The present study focuses on the application of the second theorem to masonry vaults and domes, being devoted to the determination of a class of purely compressive stress regimes, which are balanced with the load. The mere existence of such a class is a proof that the structure is safe, and members of this class may be used to assess the geometric degree of safety of the structure and to estimate bounds on the thrust forces exerted by the structure on its boundary. The problem is reduced to the equilibrium of a membrane S and can be formulated in terms of projected stresses defined on the planform Ω of S. The search of the stress reduces to the solution of a second-order pde, in terms of the stress potential F. In order that the membrane stress on S be compressive, the potential F must be concave. As for the thrust line in an arch, the surface S is not fixed and may be changed, given that it remains inside the masonry. Under these simplifying assumptions, the whole class of equilibrated stress regimes for a masonry shell is obtained by moving and deforming S inside the masonry, and also, for any fixed shape, by changing the boundary data for F, that is the distribution of thrust forces along the boundary. The search for a feasible stress state on a convenient membrane surface, to be chosen with a trial and error procedure, requires a substantial effort and may be unrewarded. Then, the main object of the present work, is to produce a computer code that can handle numerically the interplay of the shape controlled by a function f, and of the stress potential F, by developing a convergent optimization scheme able to give a safe state under the given material and geometrical constraints, namely the concavity of F and the inclusion of f within the masonry. Two simple cases, are exposed in detail to illustrate the method.

The equilibrium of cloister masonry vaults, treated as composed of unilateral material in the sense of Heyman, is the topic of the present work. For such a material, the safe and the kinematic theorems of limit analysis can be employed to detect equilibrium and nonequilibrium. In the spirit of the safe theorem, the structure is stable if a statically admissible stress field can be detected. On allowing for singular stresses, here we consider statically admissible stress fields concentrated on surfaces or lines lying inside the masonry vault. Such structures are unilateral membranes, whose geometry is described a la Monge, and the equilibrium of them is formulated in Pucher form, that is, in terms of the so-called projected stresses over the planform Ω. The problem, under purely parallel loads, is reduced to a single partial differential equation of the second-order, in two space variables, where the shape function f and the stress function F appear symmetrically. The unilateral restrictions require that the membrane surface S lies in between the extrados and intrados surfaces of the vault and that the stress function be concave. In the present work, by starting with a sensible choice of a concave stress function F, the transverse equilibrium equation is solved for f by imposing suitable boundary conditions. A cloister vault of Palazzo Caracciolo di Avellino, a XIV century building located along via dell'Anticaglia in Naples, is the case study. For two load conditions, membrane surfaces and geometrical safety factors are identified.

The analysis of rocking behaviour is a key aspect of safety assessment the maintenance of artifacts, like statues vases, since the rocking itself can be the cause of damage at the base of the object, due to impact with the support. By seismic excitation, a freestanding object may in fact enter a rocking state which would cause overturning, so that often the sliding is desirable, given the possibility of evaluating relative displacements to avoid collisions. In the majority of cases, museum exhibitions are not equipped with isolation devices for every single contained object. This paper presents the theoretical numerical bases of a simple low cost isolation system to protect small art objects. Smaller artifacts are in fact the more prone to overturning since the rocking response is highly influenced by the size of the object. The insertion of a further rigid body between the moving base the statue can reduce the effect of base motion due to earthquakes. The case study is a real marble statue by Donatello, placed in the Museo dell’Opera del Duomo in Florence.

Within the frame of parametric design, in the present work we focus on a very special objective, namely parametrically generating families of purely compressed shells. A similar task can be pursued by adopting for the equilibrium analysis the so-called Thrust Network Analysis for which the shell structure is condensed into a network of bars. Here instead, we adopt a continuum approach, namely the so-called Membrane Equilibrium Analysis. With this continuum approach, a purely compressed membrane equilibrium solution is searched by solving a scalar second-order partial differential equation representing the transverse equilibrium equation of the membrane. The shell is compressed if the membrane surface is contained within the volume of the shell and if the stress potential is concave. For a given shell, the main difficulty is represented by the fulfillment of the concavity constraint for the stress potential. In the present study, this difficulty is overcome by assigning families of convenient concave stress potentials and considering the shape as the unknown. By considering stress potentials or boundary data controlled by a few parameters, such variable parameters can be manipulated in order to alter the end result. Other methods tackling the stress function with the help of a computer, exist in the literature, but the main contribution of the present paper is the shape analysis of compression-only shells with the help of finite element apparatus. A few illustrative examples are presented to demonstrate the method.

The collapse factor is a significant parameter in the framework of the safety assessment and economical design of ductile structures. This fact draws attention to the necessity of a careful assessment of the limit analysis approaches. The kinematics in these structures arises in fact from the actual rotation of the plastic hinges under axial force and bending moment. It can be shown that it is possible to obtain a reliable tool capable of competing with computationally expensive methodologies. The application of the methods of limit analysis involves a simplified and idealised model of the structure and, notwithstanding the fact that hundreds of papers have been devoted to the topic, some consequences of apparently unimportant simplifications still seem to have not been properly and firmly highlighted. This paper investigates the ultimate load and collapse modes of steel frames under combined vertical and horizontal forces through limit analysis.

The methodical study of seismic safeguard of artistic heritage has considerably spreaded in the last years, thus increasing researchers’ interest in problems concerning monumental buildings. In particular, the seismic safety of art objects, that are the objects generally contained within Museums, is a research field of great interest, being part of research and policy in the more general field of Cultural Heritage, with contribution of several local government and European research grants. It must be noted, in fact, that buildings of historical and cultural significance may contain objects of inestimable value, for which there is no assessment of their effective vulnerability related to how they are displayed or stored. The case of statues and ceramics placed on pedestals, not equipped with any isolation system capable of mitigating the oscillations induced by possible earthquakes can be just considered as an example. This paper focuses the attention on this last problem, i.e. objects that can be considered as rigid bodies simply supported on the main structure, leaving out of account the filter’s effect due to the action of structure on the show-case or furniture. This problem is the same of a large class of non-structural components, such as mechanical and electrical hospital and laboratory equipment that can lose their functionality because of earthquake motions, and structural problem, such as isolated constructions made of superimposed rigid blocks in archaeological areas. The results of a numerical analysis on the rocking behaviour of rigid bodies are compared with experimental dynamic tests performed on simple shaped objects made of different materials and simply supported on a shaking table.

The global interest in renewable energy sources has increased the attention to the manufacturing of wind turbine towers, since they are largely diffused in seismic areas too. Different types of towers have been produced in recent years. Among them, the truss structures assure a reduced mass and the modular characteristics necessary for easy transportation. Reduced costs of production, installation and maintenance are typical of these structures. Nonlinear dynamics is an efficient framework to analyze structures subjected to variable actions, i.e. to assess the seismic safety of wind turbine towers in case of earthquake actions. This study outlines a procedure to evaluate the post-elastic behavior of truss towers for wind turbines. Rigid-plastic behaviour is taken into account to develop approximate solutions for the problem of a tower modeled as a vertical cantilever beam and subjected to harmonic base motion. A comparison with the results of a finite element model is proposed.

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.

Masonry structural modelling needs of a completely different methodology from the ones adopted for ductile structures. In fact, the concepts of strength, stiffness and elastic stability, fundamental for the latter structures, play a marginal role in masonry mechanics. In this respect, Heyman's theory, gives a modern turn to the old methods of masonry design, adopting a set of very simple and clear mechanical hypotheses. In these papers, the basic ingredients of a new method based on unilateral equilibrium and rigid block kinematics, which may allow the implementation of Heyman's model for masonry on a computer, is introduced. In particular a simple method based on energy minimisation, with the possibility of combining the effects of loads and settlements on real masonry structures, is developed.

To homogenize lattice beam-like structures, a direct approach based on the matrix eigen- and principal vectors of the state transfer matrix is proposed and discussed. The Timoshenko couple-stress beam is the equivalent continuum medium adopted in the homogenization process. The girders unit cell transmits two kinds of bending moments: the first is generated by the couple of the axial forces acting on the section nodes, the other one is due to the moments directly applied at the node sections by the adjacent cells. This latter moment is modelled as the resultant of couple-stress. The main advantage of the method consists in to operate directly on the sub-partitions of the unit cell stiffness matrix. Closed form solutions for the transmission principal vectors of the Pratt and X-braced girders are also attained and employed to calculate the stiffnesses of the related equivalent beams. Unit cells having more complex geometries are analysed numerically. As a result, the principal vector problem is always reduced to the inversion of a well-conditioned ( 3 × 3 ) matrix employing the direct approach. Hence, no ill-conditioning problems, affecting all the known transfer methods, are present in the proposed method. Finally, comparing the predictions of the homogenized models with the finite element (f.e.) results of a series of girder, a validation of the homogenization method is performed.

The seismic protection of objects contained within museums is a topic of great interest, especially with reference to how they are displayed or stored. This problem is the same as that of a large class of non-structural components, such as mechanical and electrical hospital and laboratory equipment that could lose their functionality because of earthquakes. Statues and ceramics simply supported on the floor represent a significant set of case. In some cases, like the Bronzes of Riace, isolation systems have been developed. However, in general museum exhibits are not equipped with devices capable of mitigating the oscillations induced by possible earthquakes. The case study of a marble statue placed on a freestanding squat rigid pedestal is examined. The system of algebraic differential equations governing the problem has been derived and included in an ad-hoc numerical procedure. It is shown that the insertion of a squat rigid body with low frictional resistance at the lower interface with the floor, and high frictional resistance at the upper interface with the artifact significantly reduces the amplitude of the rocking response. As a result the artifact rocks without sliding on the rigid base that slides without rocking with respect to the floor. The numerical analysis performed can be a tool to help in the choice of the optimal friction values in the surfaces of the flat block, designed as a simple isolation system.

The broad topic of the present work is Statics and Kinematics of masonry structures, made of monolithic blocks, modelled a la Heyman, that is rigid bodies loaded by external forces, submitted to unilateral constraints, and undergoing small displacements, under the simplifying assumption that sliding on rough interfaces is prevented. Specifically, in this work, we study the effect, in terms of internal forces, of specified loads, by using given settlements/eigenstrains to trigger special regimes of the internal forces. Although our scope here is the analysis of masonry structures composed by monolithic pieces, and whose blocks are not likely to break at their inside, the method we propose can also be applied to generic masonry structures, such as those made of bricks or small stones. Heyman’s assumptions translate, for unilateral continua, into a normality assumption which allows to employ the two theorems of Limit Analysis. These continuous structures may actually fracture everywhere at their inside, forming rigid blocks in relative displacement among each other. Such piecewise rigid-body displacements in masonry are physiological, and rather than the result of over-loading, are most likely the direct product of small changes of the displacement type boundary conditions. However, when in a part of the structure a specific piecewise rigid-body displacement nucleates, that part of the structure exhibits a one degree of freedom mechanism, and becomes statically determined. Therefore, the internal forces can be computed, despite the original uncracked structure being abundantly overdetermined, and then admitting infinite many statically admissible stress regimes. With these assumptions, in the present paper we study the equilibrium and the effect of settlements in a masonry structure made of monolithic blocks. In particular, the triple helical stair of the convent of San Domingos de Bonaval, located in the Bonaval district of Santiago de Compostela, is considered as case study.

A homogenization method for periodic beam-like structures that is based on the unit cell force transmission modes is presented. Its main advantage is that to identify the principal vectors of the state transfer matrix corresponding to the transmission modes it operates directly on the sub-partitions of the unit cell stiffness matrix and allows to overcome the problems due to ill-conditioning of the transfer matrix. As case study, the Pratt girder is considered. Closed form solutions for the transmission modes of this girder are achieved and used into homogenization. Since the pure bending mode shows that the Pratt unit cell transmits two kinds of bending moments, one given by the axial forces and the other originated by nodal moments, the Timoshenko couple-stress beam is employed as substitute continuum. Finally, a validation of the proposed procedure is carried out comparing the predictions of the homogenized models with the results of a series of girder f.e. analyses.

This paper deals with the analysis of fracture identification of a generic masonry structure subjected to loads and to kinematical actions (settlements, distorsions). The masonry is composed of normal rigid no-tension material (NRNT), that is a Heyman’s material treated as a continuous body. An energy minimum criterion is used to solve the equilibrium problem, using continuous (C°) displacement fields and adopting a classical Finite Element approximation for the geometrical description. Some examples illustrate the way in which our approximate method detects crack patterns in some simple cases. The C° method, though more cumbersome form the numerical point of view, exhibits great efficiency in the identification of the exact location and orientation of the crack system, compared to methods based on discontinuous displacement fields.

The methodical study of safeguard of artistic heritage and other devices subjected to earthquake and, in general, to time-dependent forces has considerably spreaded in the last years, thus increasing researchers’ interest in problems concerning motions of rigid objects simply supported on a base plane. The behaviour of piece of equipments, statues, storage tanks, or even tall buildings has been in fact studied as that of rigid bodies with relation to different base excitations. In some cases, the possibility of influencing the quality of motion can be a strong tool to reduce vulnerability, like in the cases in which rocking motion is to be avoided and sliding motion is welcome. This paper focuses the attention on this last problem. This is the same large class of both non-structural and structural elements that can lose their functionality because of earthquake motions. The results of numerical modelling of sliding and rocking motion in presence of both different excitations and mechanical parameters are presented and compared with experimental data performed by the authors. The results developed are in good agreement with the laboratory tests, and this assures the reliability of both the analytical procedure and the determination of the parameters involved.

The structural restoration interventions in the archaeological site of Pompeii have been performed since the beginning of excavation in the area. In the last century the old wooden roofs erected in the late 1800s were replaced with concrete structures similar to the old ones, realized after the Second World War. A systematic study of these structures is lacking, despite the number and the significant role they play in the stress state of the ancient masonry. The structural role of these roofing structures in the Pompeii buildings and atriums and in the suburban Villas is examined. Starting from a detailed geometrical and historical analysis of the roof, the impact of the restoration interventions actually present in the archaeological area of Pompeii is analyzed in order to assess the seismic vulnerability of the buildings and the key aspects in case of restoration or maintenance. The paper shows that maintenance of the existing interventions is a fundamental topic and substitution of r.c. roofs with timber structures cannot be justified with structural reasons. As a case study the entire structure of the Domus of the Tragic Poet (masonry walls and concrete roof) is investigated.

This paper deals with a mechanical model for the analysis of the railway track behaviour built by exploiting the periodicity of the track-structure. The starting point of this study are the inner forces transferring modes. They have been determined by the unit principal vectors analysis of the base cell transfer matrix. The main outcome on bending moments is that they are transferred through the track without deforming the sleepers and fasteners and are composed of two parts: the first one, referred as primary bending moment, is generated by the couple of axial forces acting on each nodal section while the second is due to the curvature changes of the rails. Shear forces are engendered by two independent mechanisms that are associated respectively with the unit changes of the total and primary bending moments. The constitutive properties of the equivalent medium are derived by an averaging and limiting process of the transferring modes strain energies, avoiding any a priori assumption on the kinematics of the substitute medium. Finally, the equilibrium equations are achieved by the virtual work principle. The proposed model is able to reproduce accurately the track behaviour in transferring its inner forces. However, solutions that are equilibrated but not kinematically admissible are obtained from it when transversal loads are applied. In additions, only boundary conditions compatibles with the track transferring modes can be satisfied. This inconsistency is eliminated by superposition of some corrective deformed shapes. These are derived by the eigenvectors of the transfer matrix pertaining to self-equilibrated systems of bending moments decaying along the track. The application field of the proposed track model is also discussed, and the results of a validation study carried out by F.E. analysis are finally presented.

The analysis of structures subjected to earthquake actions can be carried out by means of several methods with different levels of accuracy, among which the nonlinear dynamics is generally recognized as the most reliable one. This paper presents a general treatment to develop approximate solutions for rigid-plastic response of structures subjected to base harmonic pulse, by means of a numerical procedure on-purpose developed. The case study is a vertical cantilever beam, with base support, constant mass, and inertia distribution, subjected to only ground acceleration. The failure is assumed depending on the formation of a single shear hinge and the results are expressed in general terms. As a result, the motion proceeds through successive spreading and contractions of the plastic front and related elastic returns. Possible applications of the method to real structures can be envisaged.

The paper deals with a direct approach to homogenize lattice beam-like structures via eigen- and principal vectors of the state transfer matrix. Since the girders unit cells transmit two bending moments, one given by the axial forces, the other originated by nodal moments, the Timoshenko couple-stress beam is employed as substitute continuum. The main advantage of the method is the possibility of operating directly on the sub-partitions of the unit cell stiffness matrix. Closed form solutions for the Pratt and X-braced girders are achieved and used into the homogenization. Unit cells with more complex geometries are numerically addressed with direct approach, showing that the principal vector problem corresponds to the inversion of a well-conditioned matrix. Finally, a validation of the procedure is carried out comparing the predictions of the homogenized models with the outcomes of f.e. analyses performed on a series of girders.

The present work is concerned with the prediction of the crack pattern produced by given kinematical data (settlements/distortions) in masonry constructions. By adopting the simplified model of Heyman, extending it to masonry structures treated as continuous bodies, we restrict the analysis to the search of displacement fields which are piecewise rigid. Restricting to small strains and displacements we look for the solution of the kinematical problem by minimizing the potential energy of the structure. A variational approximation of the minimum problem is obtained by considering a fixed finite element subdivision of the structure into rigid blocks. Two case studies are presented to illustrate the way in which a particular fracture pattern can be identified as the one associated to the minimum of the energy in this restricted class of piecewise rigid displacements.

In this paper the lower bound theorem of limit analysis for No-Tension materials is applied to study the equilibrium of spiral vaults, modeled as continuous unilateral membranes. The most efficient approach to the equilibrium of a thin shell is the covariant representation proposed by Pucher and adopted in the present study. Statically admissible singular stresses in the form of line or surface Dirac deltas and lying inside the masonry, are taken into account. The unilateral restrictions require that the Airy stress function representing the stress, be concave. The case study is a helical stair with a central pillar in Sanfelice Palace in Naples, whose structure is a tuff masonry spiral vault. The maps of the stress corresponding to two different stress functions and the safety factors in the two cases are provided.

The safeguard of museum exhibits like vases and statues, laboratory equipments, storage tanks, or even tall buildings and other structural elements subjected to earthquake and in general to time-dependent forces has been in the last years a topic focus. The classical mechanical problem of the motions of rigid objects simply supported on a base plane, developed in the first year of sixties, thanks to the seminal paper by Housner on the inverted pendulum, can be now take advance due to the development of calculation tools. In some cases the quality of motion can be determined varying the material parameters involved. This is a strong tool to reduce vulnerability, especially when rocking motion should be avoided and sliding motion is welcome, as in the case of artistic heritage. This paper focuses the attention on this last problem, common to a large class of both non-structural and structural elements that can lose their functionality because of earthquake motions. The results of a numerical modelling of sliding and rocking motion in presence of both different excitations and mechanical parameters are presented and compared with experimental data performed by the authors. The results developed are in good agreement with the laboratory tests and this assures the reliability of both the analytical procedure and the determination of the parameters involved. A model for a safeguard proposal is provided.

This paper is devoted to the application of unilateral models to the stress analysis of masonry structures. Some 2d applications of what we can call the simplified masonry-like model for masonry, are discussed and studied. The results here presented demonstrate that the unilateral model for masonry can be a useful tool for modeling real masonry structures. The main technique here employed for applying the No-Tension model to structures is the systematic use of singular stress and strain fields within the frame set by the theorems of Limit Analysis. A number of simple examples is discussed to illustrate the method.

This paper concerns the structural identification of an innovative manufacturing and assembling building technology system allowing fast times to build up. The building has been subjected to an experimental investigation and to an accurate FEM modeling. The experimental investigation has been carried out using a vibrodyne. The comparison between the experimental evidences with the results of finite element models allowed us the dynamic identification of the structure. The experimental modal analysis is a kind of test in which input forces and structural responses are known. It is important to note that the dynamic behavior is a kind of "fingerprint", in fact it depends only by intrinsic characteristics (mass, stiffness, damping, boundaries, degree of freedom, etc.) and not by the applied loads. Therefore, the structural response still remains unchanged in absence of modification (structural damage, etc.), otherwise a variation of frequencies and vibration modes occurs. The dynamic structural identification is a non-destructive technique, so that it can be applied to new structures (for monitoring the construction phases), to existing and even historical buildings (for checking the health) and to innovative structures (where there is not well defined design criteria).

A new type of sensor for distributed strain or temperature readings on structures, based on the use of Optical Fibres (OF) utilising the Brillouin scattering effect, has been recently proposed. The use of this new sensor has been successfully carried out not only in laboratory, but also in field tests on bridges and dams. As a matter of fact, several authors have shown that, by means of distributed experimental strain readings, it is easy the safety monitoring and assessment of large structures as bridges, pipes, high rise buildings, dams and tunnels. Moreover, the greatest utility of this new sensors is demonstrated by the present Authors to detect the raising of defects in large structures, and accuracy and reliability of measurements are discussed. Some uncertainties of this kind of measure related both to mechanical aspects of the sensor response and to the optical signal processing are still present. In particular, the mechanical response of optical fibre, when bonded on a straining structure was deeply addressed by some of the present Authors. The sensors were modelled in the framework of elastic Functionally Graded Material Cylinders (FGMCs), under symmetrical load conditions. Analytical closed form solutions both for the decaying and for non-decaying cases were already found and also assessed from the experimental point of view. In particular, for the application of these sensors to the interesting case of rods and wires, which constitute elements widely present in many types of bridge structures, the theoretical mechanical response of the sensors connected to the elements to be monitored, was already obtained. The base theoretical results already carried out, have shown that thanks to the embedding technique of the bonding of the sensor to the rod element, a non-decaying response of the optical sensor should be expected. Indeed, in this case, the axial strain transmitted by the deforming rod to the central glass core of the optical fibre, should equate with the supporting one. With the aim to show consistency and accuracy of the proposed theory concerning the mechanical response of the couple rod-OF-sensor (OFS), in the present work laboratory tests are carried out on aluminium large rods in extension, equipped with embedded-type optic fibre sensors. Experimental strains read by means of embedded OFS, showed very good agreement with the forecasts obtained by means of the above cited theory. This result confirms, from the experimental point of view, the reliability of the theoretical provisions. In particular, the adopted measuring technique, which utilises embedded OFS, shows great consistency and accuracy for a class of important problems related to rod structures. Rods are commonly used in several structural systems, such as trusses, suspension or cable-stayed bridges. Currently, some experiments are under preparation for the detection of surface deficiencies on high strength steel bridge wire surface, using the new Optical Fibre Sensors. The work on the bridge wire application is a joint research effort between the University of Naples Federico II and Bridge Technology Consulting in the United States. Finally, the characterization of the mechanical response of optical fibres, joined with some new solutions obtained for FGMCs, leads to a very accurate calibration of the sensors when they are utilised for strain distributed readings.

In the framework of classical plasticity, even when limit multipliers and collapse mechanisms associated with different loads independently acting on a solid or structure are known, not much can be inferred on the limit multiplier of the combined loading. Frame structures under the action of dead loads and seismic forces, soil–foundation interaction problems, tunnels under a variety of loads, deepwater pipelines subject to bending and pressure constitute only a few selected examples for which some sort of superposition rule, as well as bounding techniques, would be extremely useful. The present paper introduces a set of theorems for bounding limit multipliers for combined loads. In particular, ranging from a minimum knowledge about the critical state under a particular loading to a reasonable guess of the kinematics of the problem under combined loads, more and more refined bounds for the overall limit multiplier are derived. The results, to the best of the authors’ knowledge, are novel and a few examples showing their practical value are presented and discussed.

This paper presents an approach to a constitutive model for anisotropic quasi-brittle materials, developed in the framework of rate independent softening plasticity, involving a yield criterion in which an anisotropic friction tensor is involved. It turns out to be useful for materials characterized by ultimate behaviour which varies according to the direction, such as composite materials, anisotropic rocks, textiles, masonry. A geometrical representation of the limit domain in the case of plane stress, together with the results of laboratory tests is presented and discussed.

This paper provides a criterion for the proportioning of a steel frame for the retrofit of an unreinforced masonry building. A standard model to parametrize the values of the seismic forces absorbed by the masonry structure and steel frame is defined. The main aspect of the paper concerns the proportioning of the stiffness of the steel frame and the size of the anchor under shear force that the masonry panel provides for the steel frame. The interactions between the masonry building and the steel frame are analyzed by means of a commercial finite element code.

The ultimate load and collapsing modes of steel frames under combined vertical and horizontal forces are investigated through finite element (FE) modelling and limit analysis. Consideration is given to a frequently overlooked problem which is the kinematics arising from the actual rotation of the plastic hinges under axial force and bending moment. This fact draws attention to the necessity of a careful assessment of the limit analysis approaches, a fact that might be seen as somewhat in line with the outcome from famous paradoxes, such as the one by Stussi and Kollbrunner (1935), which can only be solved by making reference to both elastic and plastic deformations. As a result, it can be shown that in such a manner, it is possible to obtain a handy tool capable of competing with much more computationally expensive methodologies. The approach may be relevant to practising engineers dealing with code prescriptions and standardization committees.

The problem of reducing the seismic risk for art objects, that are the objects generally contained within Museums, is of great interest. The first studies were performed in Japan and were successively organized in a general framework by a research program performed at Southern California University and sponsored by the Getty Museum at Malibu, California. In these papers and in the following Italian studies, the theoretical models for the problem concerning vases and statues are based on the dynamic behavior of rigid blocks and have been deeply developed. Unfortunately, because of the great lack of experimental data, determinant parameters for the problem characterization (like the friction between two superimposed blocks or between the art object and the support plane) are often assumed without reference to real values derived from laboratory tests. This paper presents the results of a research program containing the experimental determination of the friction coefficient between the art object and the support (by means of a testing apparatus on purpose realized) together with dynamic tests performed on simple-shaped objects made of different materials. The dynamic tests were performed using an unidirectional shaking table and different supporting surfaces, so that the influence of different friction coefficients has been analyzed. © 2014 Springer Science+Business Media Dordrecht.

Dans de nombreuses cavites produites par l'erosion naturelle ou par l'activite humaine, le phenomene de chutes de blocs du plafond comporte de graves risques pour la securite, et donc pour l'utilisation de ces lieux a des fins d'activites humaines. Les auteurs ont deja propose une methode pour calculer, au moyen du theoreme de la limite superieure de la theorie de plasticite, la forme et les dimensions des blocs qui peuvent s'effondrer. Le materiau forme de roche molle a ete modelise au moyen du critere limite de Mohr-Coulomb, et la loi d'ecoulement associe a ete utilisee pour la vitesse de deformation plastique. Le critere limite de deformation elastique a ete convenablement regularise au moyen d'un cercle dans la zone de traction. La frontiere du bloc qui s'effondre est decrite par une surface paraboloide. Dans cet article, on formule une procedure d'optimisation dans la forme standard de Kuhn-Tucker et on obtient une solution analytique. L'algorithme mentionne ci-haut a ete applique avec succes a des sols frequemment rencontres dans le sud de l'Italie. Pour valider la formulation theorique, plusieurs essais numeriques ont ete effectues dans cet article. Ces essais montrent une concordance optimale avec la solution exacte mentionnee. En consequence, la modelisation proposee peut etre utilisee comme guide utile pour le calcul de confortement des cavites.

In many seismically active regions of the world there are large numbers of masonry buildings. Most of these buildings have not been designed for seismic loads. Recent earthquakes have shown that many of these buildings are seismically vulnerable and should be considered for retrofitting. Different conventional and unconventional retrofitting techniques are available to increase the strength and/or ductility of unreinforced masonry (URM) walls. This paper reviews and discusses seismic retrofitting of masonry walls with emphasis on the conventional techniques. Retrofitting procedures are discussed with regard to a case study: a stone masonry building in Irpinia region, damaged by the 1980 earthquake. The interventions are evaluated by means of finite elements with a macroelement obtained with a homogenization technique. Linear and nonlinear procedures are compared, and peculiarities of each procedure are shown.

Masory arch bridges are an important part of both Italian cultural heritage and transportation network. Many of them have been built since the Roma age, and several of these bridges remain in service, despite having been subjected for centuries to a heavy regime of environmental conditions and loadings.Very few masonry arch bridges have been built in modern times, and knowledge of the related design methods is no longer part of a civil engineer’s training. In the meantime, because of their fundamental role, it is frequently necessary to strengthen existing bridge or part of them. Recent advances in retrofit technology have extended the application of advanced rehabilitation, retrofitting, stregthnening and field monitoring technologies to ageing infrastructures, expecially in the case of structures in seismic areas. This paper deals with the relia-bility of these interventions, considering that several of these interventions, made in recent years, have shown their limits. Old masonry structures require specific approach: strengthening techniques must not be influenced by the load bearing capacity only, since historic structures contribute to a sustainable future

This paper examines an interesting problem of soil engineering: the collapse of blocks from the ceiling of cavities in soft rock banks. The Mohr-Coulomb yield state with the associated flow rule is assumed for the soil. The kinematic theorem of limit analysis based on the choice of paraboloidal collapse surface supplies the total dissipation function; the equilibrium equations and a solving procedure based on Kuhn-Tucker conditions yield a closed form for the solution. This solution is applied to common soils in southern Italy and it agrees with the real situation in cavities known to the writers. Several examples are listed reporting the dimensions and the weight of the collapsing block depending on the variability of mechanical properties of different soils. Finally a method for the design of the reinforcement of the cavities roof based on the proposed calculation is reported.

In civil engineering, Experimental Modal Analysis (EMA) dynamic tests are powerful aids to the seismic design of new structures, and useful tools for the structural identification of existing structures. EMA tests require to accurately evaluate the harmonic forcing function that is applied to the structure under testing, in order to correctly apply "model updating" procedures. The present work experimentally investigates on the nature of the forcing function applied by a vibrodyne, and its influence on the results of simulations on the dynamics of a single degree of freedom system. By using wireless accelerometers attached to a vibrodyne, we were able to measure the applied accelerations in the time domain, and the applied forcing function under different frequencies. Such an identification procedure was applied both in presence of 3+3 keyed masses, and in presence of 5+5 keyed masses, considering different angular speeds. In both cases, the forcing function applied by the vibro-dyne was accurately determined as a function of time. We found out that the actual forcing function is slightly different from the theoretical sinusoidal profile, featuring marked oscillations. The work is completed by the analysis of the dynamic response a simple degree of freedom system under the action of smooth and oscillating sinusoidal forcing functions. A comparison between the results of the analyzed systems highlights marked mismatches in terms of predicted displacements, velocities, and accelerations. We therefore conclude that an accurate knowledge of the applied forcing function in EMA tests is essential in order to correctly identify the properties of the tested structures.

The equilibrium problem for masonry-like materials in the Heyman sense can be formulated looking for a minimum of the complementary energy functional defined in the field of admissible stress tensors, belonging to the class of negative semi-definite tensors. The classical mixed boundary problem for a masonry panel is developed assuming that the stress is uniaxial so it is possible to express the complementary energy as a function of the slope of compressive rays which characterise the uniaxiality of the stress field. In this work, a family of proximity curves defined starting from a Bézier curve with three control points to model the slope function is employed. Two structural cases are solved, pure shear displacements and shear-flexural-tensile ones, showing the usefulness of the method when applied to the analysis of masonry piers.