Out-of-plane seismic response of masonry façades using discrete macro-element and rigid block models

This paper investigates the out-of-plane response of masonry façades under earthquakes by means of two different approaches. A discrete macro-element approach, based on modelling the structure by means of spatial deformable macro-elements interacting through nonlinear zero-thickness interfaces, and the classical approach in which the masonry façade is assumed as a rigid block subjected to earthquake loading. The latter method neglects the elasticity of the masonry element and contemplates the energy dissipation only at each impact by means of a coefficient of restitution. The results of dynamic non-linear analyses, performed with the two methods on a real case of a church façade, provide a first comparison between the two ap-proaches highlighting some limits of application of the simplified rigid block model

Numerical Modelling of Masonry Arches Strengthened with SFRM

The adoption of effective strengthening techniques of historical constructions is one of the most widely debated aspects in structural engineering. Within this topic, the application of steel fiber reinforced mortar (SFRM) has been recently proposed as a low invasive and effective way to obtain a considerable structural benefit in the safety of existing masonry structure. To this purpose, in this paper the experimental results obtained on a circular masonry arches are presented. The considered specimens, subjected to a vertical increasing static load, is tested in the unstrengthened and strengthened configurations, and is part of a wider experimental campaign. After presenting and discussing the experimental results, they are compared with those relative to numerical simulations conducted by means of a discrete macro-element (DME) strategy, based on a simple mechanical scheme, able to model the nonlinear behavior of masonry structures with a limited computational effort. Such an approach is here extended to model the SFRM strengthening technique accounting for the main failure mechanisms associated to the combined presence existing masonry and the additional strengthening layer applied at the intrados of the arch. Numerical and experimental results demonstrate the efficacy of the proposed retrofitting strategy both in terms of bearing capacity and increase of ductility

Multi-cracked Euler-Bernoulli beams: Mathematical modeling and exact solutions

Localized flexibility models of cracks enable one for simple and effective representation of the behavior of damaged beams and frames. Important applications, such as the determination of closed-form solutions and the development of diagnostic methods of analysis have attracted the interest of many researchers in recent years. Nevertheless, certain fundamental questions have not been completely clarified yet. One of these issues concerns with the mechanical justification of the macroscopic model of rotational elastic spring commonly used to describe the presence of an open crack in a beam under bending deformation. Two main analytical formulations have been recently proposed to take into account the singularity generated by the crack. The crack is represented by suitable Dirac\u2019s delta functions either in the beam\u2019s flexural rigidity or in the beam\u2019s flexural flexibility. Both approaches require some caution due to mathematical subtleties of the analysis. Motivated by these considerations, in this paper we propose a justification of the rotational elastic spring model of an open crack in a beam in bending deformation. We show that this localized flexibility model of a crack is the variational limit of a family of one-dimensional beams when the flexural stiffness of these beams tends to zero in an interval centered at the cracked cross-section and, simultaneously, the length of the interval vanishes in a suitable way. We also show that the static and dynamic problem for the flexibility model of cracked beam can be formulated within the classical context of the theory of distributions, avoiding the hindrances encountered in previous approaches to the problem. In addition, the proposed treatment leads to a simple and efficient determination of exact closed form solutions of both static and dynamic problems for beams with multiple cracks

Detecting damage in a beam by static tests

This paper presents a constructive procedure for the identification of a single crack in a beam based on the knowledge of the damage-induced variations in the static deflection of the beam. The crack is simulated by an equivalent rotational spring connecting the two adjacent segments of the beam. The analysis is based on an explicit expression of the crack-induced variation in the deflection of the beam under a given load distribution. The theoretical results are confirmed by a comparison with static measurements on steel beams with a crack

A Procedure for Multiple Damage Identification in Elastic Beams

This paper concerns with the identification of multiple cracks in a beam by measurements of the damage-induced variations in the static deflection of the beam under a prescribed load condition. Each crack is simulated by an equivalent linear elastic rotational spring connecting the two adjacent segments of the beam. Sufficient conditions on the static measurements which allow for the unique identification of the damage are presented and discussed for beams under various sets of boundary conditions. The analysis is based on an explicit expression of the crack-induced variation in the static deflection of the beam. The present results are obtained by non trivial extension of recent results given by the authors regarding the identification of a single crack in a beam by static tests

Detecting Multiple Open Cracks in Elastic Beams by Static Tests

This paper concerns with the identification of multiple open cracks in a beam by measurements of the damage-induced variations in the static deflection of the beam under a prescribed load condition. Each crack is simulated by an equivalent linear spring connecting the two adjacent segments of beam. Sufficient conditions on the static measurements which allow for the unique identification of the damage are presented and discussed for nonuniform beams under some ideal boundary conditions. The inverse analysis is based on an explicit expression of the crack-induced variation in the deflection of the beam under a given load distribution and it provides exact closed-form expressions of position and severity of the cracks in terms of the measured data. The theoretical results are confirmed by a comparison with static tests carried out on a steel beam with localized damages

Crack detection in elastic beams by static measurements

This paper deals with the identification of a single crack in a beam based on the knowledge of the damage-induced variations in the static deflection of the beam. The crack is simulated by an equivalent linear spring connecting the two adjacent segments of the beam. Sufficient conditions on static measurements which allow for the unique identification of the crack are presented and discussed. The inverse analysis provides exact closed-form expressions of position and severity of the crack as functions of deflection measurements for different boundary conditions. The theoretical results are confirmed by a comparison with static measurements on steel beams with a crack. Extension of the presented analysis to multiple cracks is briefly discussed