Mechanics of Masonry Structures Strengthened with Composite Materials II

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Authors: Daniele Baraldi, Antonella Cecchi
Abstract: A discrete model with rigid blocks and elastic-plastic interfaces is adopted for studying the collapse behavior of in-plane loaded masonry panels with random texture. An existing random discrete model, originally developed in the elastic field, is here extended to the field of material nonlinearity by adopting a Mohr-Coulomb yield criterion for restraining actions at joint level. The resulting model turns out to be simple and effective in determining collapse loads and mechanisms of rectangular masonry panels, also accounting for a further perturbation parameter able to vary the height of each course of blocks into the masonry panel. The collapse loads turn out to be slightly smaller than those typical of regular assemblages, whereas mechanisms turn out to be influenced by local arrangement and size of blocks.
Authors: Giancarlo Ramaglia, Gian Piero Lignola, Francesco Fabbrocino, Andrea Prota
Abstract: Among masonry buildings characterized by a complex architecture, a significant portion is represented by heritage buildings. A significant seismic vulnerability is due to the presence of thrusting elements like as arches and vaults. Their ultimate capacity can be improved by means of several strengthening techniques. However the advantages of using Textile Reinforced Mortars (TRM) are well highlighted in the scientific literature.The present work focuses on ultimate behaviour of masonry barrel vaults, in the framework of incremental analysis, including the strengthening effect. The analytical model is compared in terms of ultimate capacity and failure mode with a full scale masonry barrel vault dynamically tested. After the first tests, the vault has been strengthened with Textile Reinforced Mortar (TRM) and tested again.
Authors: Massimiliano Lucchesi, Barbara Pintucchi, Nicola Zani
Abstract: This paper deals with non linear elastic materials for which not all the stresses are admis-sible but only those which belong to the stress range, i.e. a closed and convex subset of the spaceof all symmetric tensors. The constitutive equation that has been formulated and explicitly solved issufficiently general to include, besides the so-called masonry-like materials, many others whose stressrange is obtained experimentally or is theoretically defined. The model, implemented into the finiteelement code MADY, has been used to analyze a masonry panel under a bi-directional monotonicallyincremental load and the obtained numerical results have been discussed.
Authors: Marco Piedigrossi, Simona Coccia, Fabio di Carlo
Abstract: Unreinforced masonry (URM) structures represent most of the world architectural heritage, whose vulnerability has been also highlighted by damages and collapses occurred after recent seismic events. Numerous studies regarding the seismic capacity of masonry walls, arches and portals have been carried out by applying the so-called equivalent static analysis method, neglecting their dynamic behaviour. A proper evaluation of the dynamic response of masonry elements can be done analytically considering the dynamic equation of rigid bodies not resistant to the tensile stresses. Some studies are available in literature regarding the dynamic behaviour of walls and arches. In this framework, the paper aims to develop an analytical model, able to describe the dynamic behaviour of portals with circular arches, subjected to a base motion. Starting point of the analysis is the evaluation of the mechanism (local, semi-global or global) governing the activation of the motion of the structure, performed in the context of Limit Analysis. Subsequently the equation of motion of the system of rigid bodies is derived applying the Lagrange Equation. Finally a numerical application is carried out.
Authors: Matteo Bruggi, Alberto Taliercio
Abstract: An innovative approach is proposed to define the optimal fiber-reinforcement of in-plane loaded masonry walls, modeled as linear elastic no-tension (NT) bodies. A topology optimization formulation is presented, which aims at distributing a prescribed amount of reinforcement over the wall, so as to minimize the overall elastic energy of the strengthened element. Perfect bonding is assumed at the wall-reinforcement interface. To account for the negligible tensile strength of brickwork, the material is replaced by an equivalent orthotropic material with negligible stiffness along the direction (s) undergoing tensile principal stress (es). Compressive principal stresses in the reinforcement are not allowed. A single constrained optimization problem allows both the equilibrium of the NT body to be enforced, and the optimal reinforcing layout to be spotted out, without any demanding incremental approach. Some preliminary numerical examples are shown to assess the capabilities of the proposed procedure and to identify the optimal reinforcement patterns for common types of masonry walls with openings.
Authors: Daniel Meloni, Barbara de Nicolo
Abstract: Countries like Italy have to face the constant issue of preserving and renewing existing buildings, both for the sake of conservation of the architectural and monumental heritage and due to the need of requalification and reuse. Considering the seismic hazard of most of Italian regions, structural interventions need to be carefully evaluated since National Codes don’t allow any sort of weakening of buildings and conversely regard any structural intervention as an opportunity to improve existing building safety. Most of existing and historical buildings in Italy are masonry structures, whose functional and architectonical requalification usually consists of new openings in masonry walls, but, according to the above mentioned principles, these modifications need to be designed at least without significantly affecting the pre-existent structural behavior. Thus, steel or reinforced concrete frames are to be designed in order to restore the previous conditions of masonry integrity. In this paper FEM analyses are performed and discussed in order to achieve this goal.
Authors: Daniele Ferretti, Eva Coisson, Marco Rozzi
Abstract: The present paper concentrates on the numerical modelling of masonry vaults, adopting a type of analysis first developed at the University of Parma for applied mechanics, based on the use of non-smooth dynamics software, through a Differential Variational Inequalities (DVI) formulation specifically developed for the 3D discrete elements method. It allows to follow large displacements and the opening and closure of cracks in dynamic field, typical of the masonry vaulted structures. Once the modelling instrument was calibrated, thanks to the comparison with the recurrent damage mechanisms previously analysed, it was also applied to foresee the behavior of the same structure with different actions and with different types of strengthening. The development of damage mechanisms, both in quasi-static cases (for insufficient lateral confinement or for possible soil settlements) and in the occurrence of seismic events, make this type of structures very difficult to be modelled precisely with other methods. Given the three-dimensional CAD model of a vault modeled with a great number of masonry units with specific positions and pattern, the method proved to be able to reproduce the behavior of the structure under both static and seismic loads, showing the mechanism of collapse, the network of contact forces, the displacements and other useful data. The aim is to inspect the possible influences in the structural behavior given by the discrete geometry and the changes in the mechanisms development given by different strengthening interventions. Once the modeling instrument will be calibrated, also through the comparison with real cases and with the results obtained through limit analysis, it will be possible to adopt it as a base also for the prevision of the future behavior of the vaults subjected to strengthening, avoiding uncalibrated and uncritical applications of materials based more on trends rather than on a thorough analysis for the specific case.
Authors: Gemma Mininno, Bahman Ghiassi, Daniel V. Oliveira
Abstract: Tensile Reinforced Mortars (TRMs) are promising composites that address the compatibility demands required for strengthening of masonry and historical constructions. Although many recent studies have been devoted to the use of these materials for strengthening purposes, several issues such as efficiency for improving the structural performance are clearly open. The aim of this paper is to numerically investigate the effectiveness of TRM systems on the in-plane and out-of-plane response of masonry walls. Numerical models are adopted to describe the nonlinear behaviour and the failure mechanisms of unreinforced and strengthened walls. It is shown that the implementation of TRM layers improve largely the performance of the masonry walls both in terms of strength and displacement capacity.
Authors: Erasmo Viola, Francesco Tornabene, Nicholas Fantuzzi, Michele Bacciocchi
Abstract: The present study aims to show a novel numerical approach for investigating composite structures wherein inclusions and discontinuities are present. This numerical approach, termed Strong Formulation Finite Element Method (SFEM), implements a domain decomposition technique in which the governing partial differential system of equations is solved in a strong form. The provided numerical solutions are compared with the ones of the classic Finite Element Method (FEM). It is pointed out that the stress and strain components of the investigated model can be computed more accurately and with less degrees of freedom with respect to standard weak form procedures. The SFEM lies within the general framework of the so-called pseudo-spectral or collocation methods. The Differential Quadrature (DQ) method is one specific application of the previously cited ones and it is applied for discretizing all the partial differential equations that govern the physical problem. The main drawback of the DQ method is that it cannot be applied to irregular domains. In converting the differential problem into a system of algebraic equations, the derivative calculation is direct so that the problem can be solved in its strong form. However, such problem can be overcome by introducing a mapping transformation to convert the equations in the physical coordinate system into a computational space. It is important to note that the assemblage among the elements is given by compatibility conditions, which enforce the connection with displacements and stresses along the boundary edges. Several computational aspects and numerical applications will be presented for the aforementioned problems related to composite materials with discontinuities and inclusions.

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