29 research outputs found
A novel analytical model for fiber reinforced cementitious matrix FRCM coupons subjected to tensile tests
No full textA much enhanced -with respect to existing literature- analytical model for FRCM coupons subjected to standard tensile tests is proposed. One fourth of the coupon is idealized considering two layers, matrix and fiber, subjected to a uniaxial stress state, mutually interacting at the interface through tangential stresses. The matrix is assumed elastic-perfectly fragile and the fiber linear elastic. The shear stress-slip relationship at the interface is tri-linear, with the first phase elastic, the second exhibiting linear softening followed by a third phase at possible non-null residual strength. The longitudinal equilibrium equations written for the two layers, suitably re-arranged, allow deducing a field problem governed in the three phases by a single second order linear differential equation where the independent variable is the interface slip, with solution retrievable analytically. Since the location of the points where the interface is in the different phases is not a-priori known, a discretization with small length elements is adopted. For each element the solution of the field problem is known in closed form and the only variables to determine are the integration constants coming from the solution of the differential equation. After a standard assemblage, all constants are derived imposing the boundary conditions at the extremes of the elements, which depend on the state of cracking of the matrix layer. The model is validated against two sets of experimental data on coupons tested in two different University laboratories in Italy. A satisfactory predictivity of both the global and local behavior is found
Simple Truss Finite Element to Model FRCM Strengthened Specimens in Single Lap Shear Tests
No full textA novel non-linear truss finite element specifically conceived to study an FRCM reinforcing package is presented. FRCM is modelled considering separately the central elastic fiber grid and the two upper and lower inelastic matrix layers; matrix and fiber are considered in a monoaxial state of stress, mutually exchanging shear stresses at the interface. The interface constitutive relationship assumed is trilinear with softening and residual strength; the element is thus constituted by three trusses (one elastic and two inelastic) linked with shear springs. The internal matrix layer exchanges also tangential stresses between reinforcement and substrate by means of elastic shear springs. The finite element is therefore characterized by 8 DOF, namely the longitudinal displacements of the three layers of the FRCM package plus that of the substrate, evaluated at the extremes of the element. The finite element performance is successfully validated against some available experimental datasets, relying into different FRCM strengthening packages bonded to rigid substrates and subjected to single lap shear tests
Non-linear 1D 16-DOF finite element for Fiber Reinforced Cementitious Matrix (FRCM) strengthening systems
No full textThe paper presents a novel non-linear one-dimensional finite element with 16 degrees of freedom aimed at modelling Fiber Reinforced Cementitious Matrix strengthening systems. Such composite is typically constituted by three superimposed layers −namely an outer matrix, a central fiber textile and an inner matrix- subjected to a prevailing longitudinal monoaxial stress state. They interact by means of interfaces exchanging both tangential and −when the reinforcing system is applied to curved substrates- traction/compression stresses. Matrix is made by mortar −possibly reinforced- exhibiting medium to high strength, whereas the fiber net can be aramid, carbon, glass, steel, basalt, etc. The reinforcing system is then connected to a substrate by means of a further interface. The finite element is a two-noded assemblage of three trusses representing matrix and fiber layers. Shear and normal springs are lumped at the nodes, mutually connecting contiguous trusses and the inner matrix to the substrate. They represent the interfaces and exchange normal and shear actions between contiguous layers or transfer them from the reinforcing system to the substrate. The degrees of freedom, 8 per node, are the longitudinal and transversal displacements of the three layers and of the substrate, evaluated at the nodes. Material non-linearity can be considered both for trusses and springs, giving the possibility to account for all the experimentally documented damaging cases that can be encountered in practice. Both softening and inelastic behavior are numerically tackled with a fully explicit algorithm where the elastic modulus of the layers and the stiffness of the interfaces are reduced at the new iteration if in the previous one the elastic limit is exceeded. The stiffness matrix is provided straightforwardly also in the inelastic case, showing the promising simplicity of the element when coupled with the non-linear solver. The performance of the novel finite element is validated against a comprehensive experimental dataset referring to curved masonry pillars reinforced with Fiber Reinforced Cementitious Matrix and tested in single lap shear
A New Analytical Model for FRCM Coupons
No full textAn analytical approach to describe FRCM coupons subjected to standard tensile tests is presented. The coupon is idealized assuming a mono-axial stress state and considering both matrix and fiber. Matrix and fiber interact at the common interface by means of tensile stresses. The fiber is supposed linear elastic, mortar is elastic perfectly brittle and the interface is characterized by a trilinear tau-slip law, where the first stage is elastic, the second involves linear softening and the third exhibits a constant tangential strength. A single second order linear differential equation - deduced from simple longitudinal equilibrium equations - governs the field problem in the three stages of the interface. The only independent variable is the slip at the interface and the solution can be obtained analytically. A priori it is not possible to know the position of the points where the interface exits one phase to enter into another and consequently a discretization with small elements is implemented. The closed-form solution is known for each element where the only variables to be defined are the integration constants of the differential equation solution of the differential equation. Depending on the state of cracking of the mortar, all the constants are derived by imposing suitable boundary conditions at the edges of the elements. The model is successfully validated against available experimental results and previously presented numerical models
Simple non-linear numerical modelling of masonry arches reinforced with SRG using elasto-fragile and elasto-ductile truss finite elements
No full textA general and simple numerical strategy that can be used in common practice even by unexperienced users is proposed to analyze masonry arches reinforced with Steel Reinforced Grout (SRG). The reinforcement pack is modeled with elastic steel elements interacting with the substrate by means of non-linear interfaces. Bricks are meshed with elastic quadrilateral elements, whereas mortar joints and interface between substrate and reinforcement steel are modeled with trusses assumed either elastic perfectly brittle or elastic perfectly ductile (cutoff bars). The aim is to reproduce the non-linear behavior of mortar under both a mode 1 and mode 2 deformation and the possible debonding of SRG. The dependance of the ultimate tangential resistance of the joints upon the acting compressive stress is accounted for simply updating the strength value of the shear cutoff bars at the end of each iteration step, considering the normal stresses calculated in post processing at the previous iteration and using a Mohr Coulomb cohesive frictional relationship. For the interface between steel and substrate, three different non-linear models are considered, the first relying in a fragile cutoff bar interposed between reinforcement and substrate, the second constituted by two in parallel fragile cutoff bars and the third characterized by the presence of three in parallel cutoff bars (two fragile and one ductile). The procedure is benchmarked on a masonry arch reinforced with SRG and tested in place, for which experimental data and a variety of previously presented results obtained through numerical models characterized by different levels of complexity are available. From the thorough analysis carried out on the global force displacement curves so obtained and a detailed observation of the non-linearity developing in the structural model, the reliability and simplicity of the approach proposed are assessed
Full 3D CAD procedure for the speedy evaluation of the seismic vulnerability of masonry towers
No full textA very straightforward 3D CAD approach for the speedy evaluation of the seismic vulnerability of existing masonry towers is presented. The procedure requires only the detailed 3D geometric model of the structure and automatically calculates the collapse acceleration on a user defined failure mechanism. In this paper, few pre-assigned mechanisms are tested, as for instance vertical splitting, simple overturning at the base, rocking with inclined yield lines and combined rocking and vertical splitting. The restriction of the possible tower failure within such a few mechanisms grounds on previous numerical research in the field and post-earthquake surveys experience. In any case, any user can define his own mechanisms according to the specificity of the case-study under consideration, directly shaping distinct volumes inside the CAD software. The procedure is automatized and the direct application of the principle of virtual works-assuming that masonry behaves as a no-tension material-allows the immediate evaluation of the horizontal acceleration at collapse. The mechanism associated to the minimum acceleration, in agreement with the kinematic theorem of limit analysis, is that most probably would occur in reality during a seismic event. The approach allows a straightforward evaluation of the seismic vulnerability of a tower and can be used even by practitioners not familiar with advanced FE computations and limit analysis concepts, so adapting well to the heterogeneous community involved in cultural heritage preservation. The automatized procedure is applied in this paper to a historical tower located in central Italy, to show the capabilities of the approach. © 2019 Author(s)
On the Nonlinear Behaviour of Domes Subjected to Point Loads on the Crown
No full textA new model for nonlinear static analysis of masonry domes subjected to point loads on the crown is presented. Its simplicity makes it usable in common practise by unexperienced users. Masonry is modelled with elastic hexahedral elements connected by 1D elements representing mortar joints, both meridian and horizontal, on which nonlinearities are concentrated. The aim is to simulate the nonlinear behaviour of domes under vertical loads by using a Finite Element commercial software equipped only with the simplest finite elements, namely point contacts and cutoff bars. The mortar joints nonlinearity is reproduced by two different models. The first of which accounts for elastic perfectly brittle point contacts under Heyman’s hypothesis of no-tension material. Whereas the second exploits elastic perfectly ductile cutoff bars, by which different tensile strengths and masonry orthotropy are considered. In this last model, to evaluate the increase in load carrying capacity, Fibre Reinforced Polymers (FRP) strips are applied. While in the first model, the position of plastic hinge is well defined at the expense of the ultimate load, in the second model, the plastic hinge is smeared in favour of a major precision and accuracy in the computation of collapse load. The models are benchmarked on a masonry dome experimentally tested. The procedure is validated by comparison of results with a wide range of Finite Elements, numerical approaches and limit analysis available in the literature for the same dome. By the analysis of nonlinear behaviour emerging from load-displacement curves, the robustness and simplicity of the procedure is proven
Una compleja misión diplomática : Leonardo Donà en la corte española de Filipo II (1570-1573).
No full textThis research article studies through a qualitative methodology perspective the period between 1570 and 1573, when Leonardo Donà was ambassador of the Serenissima to the court of Philip II. In Madrid, the future Doge carried out a delicate and complex diplomatic assignment. The duration of his ambassadorship coincided exactly with the years of the Cyprus War and the circumstances of his mission all gravitated into the orbit of those events. In the three years he spent at the court he maintained constant relations with the sovereign and his entourage. Between the formation of the Holy League, the battle of Lepanto and the peace stipulated by Venice with the Ottoman Empire, without the knowledge of the “Confederates” Leonardo Donà exercised his diplomatic mission in an exemplary manner: he put the interests of the Serenissima before any personal considerations and, with prudence and shrewdness, he was able to face the difficult mission of justifying to Philip II the peace reached between Venice and the Sublime Porte. The correspondence of the Venetian ambassador from Madrid addressed to the Venetian Senate is full of political considerations of high moral value, inspired by a high sense of duty towards the Signoria and, above all, guided by a refined knowledge of the art of diplomacy. Donà remained in Madrid until September 17th 1573.El presente artículo de investigación analiza mediante una metodología cualitativa la etapa entre 1570 y 1573, cuando Leonardo Donà fue embajador de la Serenissima en la corte de Felipe II. En Madrid, el futuro Doge llevó a cabo una acción diplomática delicada y compleja. La duración de su embajada coincidió exactamente con los años de la guerra de Chipre y las circunstancias de su misión gravitaron en la órbita de esos eventos. En los tres años que pasó en la corte mantuvo relaciones constantes con el Soberano y su entourage. Entre la constitución de la Liga Santa, la batalla de Lepanto y la paz estipulada por Venecia con el Imperio Otomano sin el conocimiento de los “confederados”, Leonardo Donà ejerció su misión diplomática de manera ejemplar: colocó los intereses de la Serenissima antes de cualquier consideración de naturaleza personal y, con prudencia y astucia, pudo enfrentar la difícil misión de justificar a Filippo II la paz estipulada entre Venecia y la Sublime Puerta. La correspondencia del embajador veneciano de Madrid y dirigida al Senado veneciano está llena de consideraciones políticas de alto valor moral, inspiradas en un alto sentido del deber hacia el Signoria y, sobre todo, dictadas por un conocimiento refinado del arte de la diplomacia. Donà permaneció en Madrid hasta el 17 de septiembre de 1573
Simple Nonlinear Numerical Modeling for Unreinforced and FRP-Reinforced Masonry Domes
No full textThis paper presents a new method to model the nonlinear behavior of double-curvature masonry structures, possibly reinforced by composite materials, by means of conventional elasto-plastic analyses. The method is meant to be used in professional design, especially for assessment and retrofitting purposes, based on the exploitation of the simplest nonlinear finite elements available in commercial software, namely, trusses with elasto-fragile and elasto-ductile behavior (Cutoff Bars, according for instance to the definition provided by Strand7 R3.1.3a). Numerical static nonlinear analyses are carried out by considering elastic hexahedral elements for bricks and by lumping nonlinearities on joints. These are assumed, in turn, to be elastic–brittle and elastic–plastic by using 1D elements, namely, Point Contacts, under the No-Tension Material hypothesis, and Cutoff Bars, respectively, assigning a small tensile resistance to the material. The reinforcement, realized with FRP hooping strips, is successfully modeled in a similar fashion, i.e., by applying perfectly bonded elastic–plastic Cutoff Bars at the extrados of the dome, where debonding is accounted for in a conventional way, limiting the tensile strength according to Italian Standards’ indications. The procedure is validated against benchmark models with the same geometry, using experimental data and more refined structural model results for comparison. After an in-depth analysis of the obtained results, in terms of capacity curves, the robustness and accuracy of the proposed approach are assessed
Automatic CAD kinematic limit analysis approach for the limit analysis of masonry towers
No full textIn this paper, a simple and fast 3D CAD approach to estimate the seismic vulnerability of existing masonry toweers is presented The procedure consists in a 3D detailed geometnc model of the tower made in CAD, where the structure is obtained by means of the assemblage of different 3D volumes having complex shape. The choice of the different volumes is not only related to the need of distinguishing between different matenals/weights/loads, but is primarily made to identify specific failure mechamsms activating at the interfaces between contiguous volumes. The collapse acceleration isthenautomatically evaluated applying the kinematic theorem oflimitanalysisfornotensionmatenalsonmepre-assigned failure mechanism chosen in the pre-procession phase. Some few mechamsms are tested in the paper, considering L s e occurring most frequently in past seismic events, as for instance vertical splitting, simple overturning at the base, rocking with inclined yield lines and combined rocking and vertical splitting. The inclusion of different mechamsms is very straightforward, simply requmng an updating of the number and shape of the volumes directly in the CAD software by means of the cutting plane command The mechanism associated to the minimum acceleration, in agreement with the kinematic theorem of limit analysis, is that activating most probably in reality during a seismic event The automatized procedure is fast and straightforward, being applicable also by all those technicians not familiar with Limit Analysis concepts. Two examples of technical relevance on two historical masonry towers in Italy are discussed to show the capabilities of the approach
