BUCKLING DELAMINATION IN COMPRESSED NO-TENSION HOMOGENEOUS BRITTLE BEAM-COLUMNS REINFORCED WITH FRP

The main issue of this paper is the instability of no-tension structural members reinforced with FRP. This study concerns the instability of FRP reinforcement. The primary instability problem of a compressed element involves the partialization of the inflex section. In particular, in the case of a compressed slender element reinforced on both tense and compressed side FRP delamination phaenomenon could occur on the latter. This entails the loss of the reinforcement effectiveness in the compressed area for nominal load values much lower than material effective strength. Therefore, structural elements or portions thereof which absorb axial components in the direction of the reinforcement may exhibit relatively modest performance with respect to the unreinforced configuration. By employing a no-tension material linear in compression, an analytical solution for FRP buckling delamination length is provided. The main objective of this paper is to provide a simplified tool that allows to evaluate the critical load of the reinforced beam-column and to predict the tension at which delamination and the loss of effectiveness of reinforcement in the compressed area could occur.

Out-of-plane local mechanism analysis with finite element method

The stability check of masonry structures is a debated problem in Italy that poses serious problems for its extensive use. Indeed, the danger of out of plane collapse of masonry walls, which is one of the more challenging to evaluate, is traditionally addressed not using finite element models (FEM). The power of FEM is not properly used and some simplified method are preferred. In this paper the use of the thrust surface is suggested. This concept allows to to evaluate the eccentricity of the membrane stresses using the FEM method. For this purpose a sophisticated, layered, finite element with a no-tension material is used. To model a no-tension material we used the smeared crack method as it is not mesh-dependent and it is well known since the early ’80 in an ASCE Report [1]. The described element has been implemented by the author in the program Nòlian by Softing.

Assessment of 3D Linear Elastic Masonry-Like Vaulted Structures

A novel approach is adopted to assess the static behavior of vaulted structures, such as cantilevered masonry stairs, assuming a linear elastic no-tension material model. Masonry is substituted by an equivalent orthotropic material whose elastic properties vary locally and with a negligible stiffness where tensile strain occurs. In order to recover a tension-free state of stress, an energy-based minimization procedure is carried out to establish the distribution and the orientation of the equivalent material for a given compatible load. The capability of the approach in defining purely compressive stress solutions in masonry walls under dead load and both in-plane and out-of-plane live loads has already been assessed. A meaningful application to a cantilevered masonry stair is here presented; the results are in good agreement with those available in the technical literature on historical masonry constructions.

Static Analysis of Cross Vaults: The Case of the Cathedral of Casertavecchia

In the present paper, on assuming that the material has infinite friction and no cohesion,i.e. it is No-Tension in the sense of Heyman, we study the equilibrium of cross vaults of unequal rise, such as those of some Romanesque and Gothic churches. In particular the case study of the lateral cross vaults of the Cathedral of the old town of Caserta is analyzed. The scope of the paper is not to study in detail and quantitatively any particular vault, rather we give a compressive equilibrium solution (compatible with the unilateral material assumption) for the general case of cross vaults, constructed on arches of unequal rise, and loaded by a uniform load.For the purpose of the structural analysis, the vault is modelled as a thin shell made of Rigid No-Tension material. The webs of the vault that we consider, are supported on two crossing ribs. To obtain the axial force inside the ribs, equilibrated and singular stress fields (that is stress fields concentrated on curves and balanced with the loads) are constructed.An estimate of the thrust forces transmitted by the vault to the peripheral arches and walls is also obtained, so that the stability of these structures can be checked.

Modeling Approaches for Masonry Structures

Different scale approaches, micromechanical, multiscale and macromechanical or phenomenological, are presented to study the structural response of masonry elements. First, a micromechanical model is introduced and the masonry is considered to be a heterogeneous material, made of mortar and bricks joined by interfaces, where the mortarbrick decohesion mechanisms occur. To this end, a special interface model combining damage and friction is proposed. Then, two multiscale procedures are presented, that consider regular arrangements of bricks and mortar, modeled by nonlinear constitutive laws which account for damage and friction effects. A homogenization technique is developed to derive two different equivalent continuum models at the macro-level, a micropolar Cosserat continuum and a nonlocal Cauchy model. Finally, a macromechanical model, based on the adoption of a classical No-Tension Material (NTM) model, and on the presence of irreversible crushing strains, is proposed. A zero tensile strength is assumed, thus fracture strains arise when the stress is zero. Moreover, an elastoplastic model is considered for the material response in compression. Numerical applications are performed on a masonry arch and two masonry panels, by adopting the three approaches presented. Comparisons with experimental outcomes, published elsewhere, are performed.

Computational Methods for Masonry Vaults: A Review of Recent Results

The present paper makes a critical review of some methods and models, now available in the technical litera-ture and commonly used in the analysis of masonry vaults up to their collapse, by highlighting advantages and drawbacks of each approach. All methods adopted to describe the mechanical behavior of masonry structures, in order to be reliable, must take into account the distinctive aspects of masonry, namely the scarce (or zero) tensile strength, the good resistance in compression and the occurrence of failure mechanisms through rotation-translation of rigid macro-blocks. Classic no-tension material models disregard the small existing tensile strength and make the assumption of (1) infinitely elastic be-havior in compression and (2) isotropy, giving thus the possibility to deal with either semi-analytical approaches (espe-cially for arches) or robust numerical procedures. More advanced but rather complex models are nowadays able to deal al-so with anisotropy induced by texture, small tensile strength and softening in tension, as well as by finite strength in com-pression. Traditionally – and nowadays it is still an opinion commonly accepted, in contrast with step by step complex procedures, Limit Analysis has proved to be the most effective Method for a fast and reliable evaluation of the load bear-ing capacity of vaulted masonry structures: classic lower and upper bound theorems recall respectively the concepts of equilibrium and occurrence of failure mechanisms with rigid elements. The so-called Thrust Network Method moves its steps from lower bound theorems, whereas FE limit analysis approaches with infinitely resistant elements and dissipation on interfaces take inspiration from the upper bound point of view. An alternative to Limit Analysis is represented by tradi-tional FEM combined with either elastic-plastic or damaging models with softening, commonly used for other materials but recently adapted also to masonry. They are able to provide a large set of output numerical information but further studies are still needed to ensure their proper application.

Additional Results to the Structural Analysis of Eccentrically Compressed Cross-Section Made of no Tension Material

The mechanical behaviour of eccentrically compressed stocky bars of rectangular cross section, having no-tension material is well known. The aim of the structural analysis is to determine the distribution of the stresses arisen from the effect of an eccentrically compressive force, i.e. to describe the shape of the stress block, and to calculate the compressive resistance of the bar. Some important details of the phenomenon could not be found in the technical literature. In our paper we study these details. We evaluate the analytical functions of the curves, bounding areas lain around the kern or the point of gravity, on which areas the eccentric force acts a pentagonal compressed zone arisen. Furthermore, we determine the resistance of the stocky bar in the cases of triangular and rectangular compressive zone.