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The investigation of masonry structures behaviour, considered as Normal Rigid No-Tension material (NRNT) and subjected to loads and settlements, is the principal purpose of the present work. The equilibrated solution is a minimum of the energy and, adopting piecewise-rigid (PR) displacement, a minimization strategy procedure is proposed. Some cases will be analysed to illustrate the numerical performances of the PR approach, pointing out the subdivision into macro-blocks arises naturally in solving these minimization problems, and that the subdivisions into macro-blocks predicted by the proposed approximation procedure, are in good agreement with the ones expected and seen in real masonry structures. In particular two applications on masonry panels with irregular openings are exposed simulating the effect of an earthquake, so that variable horizontal forces are applied to the floor levels. The examples shown that the PR strategy appears efficient in reproducing both the location of cracks and the horizontal collapse load multipliers as well as the related collapse mechanisms.

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)

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.

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 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.

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 masonry structures as composed by Normal Rigid No-Tension (NRNT) material. With the NRNT model the material is rigid in compression, but extensional deformations, allowed at zero energy price, can be either regular or singular; then extensional deformation can appear as either diffuse (smeared cracks) or concentrated (macroscopic cracks), and there is not any reason to prefer one upon another, on an energy ground. The fact that rigid block deformation seems to be the preferred failure mode for real masonry structures stems from mechanical characteristics, such as toughness and cohesion, that are not inherent to the simplified NRNT continuum model. So, it is interesting to see if rigid block mechanisms can arise naturally in solving the equilibrium problem, and if there is any legitimate way to force rigid block mechanisms over diffuse cracking. We formulate the equilibrium problem as an energy minimum search and propose two methods for approximating the solution. With the first one we minimize the energy in the set of piecewise-rigid (PR) displacements. With the second method, we explore the possibility to restrict the search of the minimum to continuous (C°) displacement fields, by adopting some classical Finite Element (FE) approximation.

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.