Simulation of masonry out-of-plane failure modes by multi-body dynamics

The seismic assessment of the local failure modes in existing masonry buildings is currently based on the identification of the so-called local mechanisms, often associated with the out-of-plane wall behavior, whose stability is evaluated by static force-based approaches and, more recently, by some displacement-based proposals. Local mechanisms consist of kinematic chains of masonry portions, often regarded as rigid bodies, with geometric nonlinearity and concentrated nonlinearity in predefined contact regions (unilateral no-tension behavior, possible sliding with friction). In this work, the dynamic behavior of local mechanisms is simulated through multi-body dynamics, to obtain the nonlinear response with efficient time history analyses that directly take into account the characteristics of the ground motion. The amplification/filtering effects of the structure are considered within the input motion. The proposed approach is validated with experimental results of two full-scale shaking-table tests on stone masonry buildings: a sacco-stone masonry façade tested at Laboratório Nacional de Engenharia Civil and a two-storey double-leaf masonry building tested at European Centre for Training and Research in Earthquake Engineering (EUCENTRE).

Assessment of overlay masonry strengthening system under in-plane monotonic and cyclic loading using the diagonal tensile test

The development of novel strengthening techniques to address the seismic vulnerability of masonry elements is gradually leading to simpler, faster and more effective strengthening strategies. In particular, the use of fabric reinforced cementitious matrix systems is considered of great potential, given the increase of ductility achieved with simple and economic strengthening procedures. To assess the effectiveness of these strengthening systems, and considering that the seismic action is involved, one important component of the structural behaviour is the in-plane cyclic response. In this work is discussed the applicability of the diagonal tensile test for the assessment of the cyclic response of strengthened masonry. The results obtained allowed to assess the contribution of the strengthening system to the increase of the load carrying capacity of masonry elements, as well as to evaluate the damage evolution and the stiffness degradation mechanisms developing under cyclic loading.

In-plane stiffness of timber floors strengthened with CLT

Five full-scale timber floors were tested in order to analyse the in-plane behaviour of these structural systems. The main objective was an assessment of the effectiveness of in-plane strengthening using cross-laminated timber (CLT). To this end, one unstrengthened specimen (original), one specimen strengthened with a second layer of floorboards, two specimens strengthened with three CLT panels, and one specimen strengthened with two CLT panels, were tested. A numerical analysis was then performed in order to analyse the composite behaviour of the timber floors in more detail. Due to its importance as regards composite behaviour, the first phase of the experimental programme was composed of push-out tests on specimens representing the shear connection between the timber beams and the CLT panels. This paper describes the tests performed and the numerical modelling applied to evaluate the composite behaviour of the strengthened timber floors. The use of CLT panels is revealed to be an effective way to increase the in-plane stiffness of timber floors, through which the behaviour of the composite structure can be significantly changed, depending on the connection applied, or modified as required.

Numerical Assessment of the out-of-plane response of a brick masonry structure without box behaviour

This paper presents the assessment of the out-of-plane response due to seismic loading of a masonry structure without rigid diaphragm. This structure corresponds to real scale brick masonry specimen with a main façade connected to two return walls. Two modelling approaches were defined for this evaluation. The first one consisted on macro modelling, whereas the second one on simplified micro modelling. As a first step of this study, static nonlinear analyses were conducted to the macro model aiming at evaluating the out-of-plane response and failure mechanism of the masonry structure. A sensibility analyses was performed in order to assess the mesh size and material model dependency. In addition, the macro models were subjected to dynamic nonlinear analyses with time integration in order to assess the collapse mechanism. Finally, these analyses were also applied to a simplified micro model of the masonry structure. Furthermore, these results were compared to experimental response from shaking table tests. It was observed that these numerical techniques simulate correctly the in-plane behaviour of masonry structures. However, the

Out-of-plane behavior of masonry infill walls

In order to investigate the out-of-plane behaviour of masonry infill walls, quasi-static testing was performed on a masonry infill walls built inside a reinforced concrete frame by means of an airbag system to apply the uniform out-of-plane load to each component of the infill. The main advantage of this testing setup is that the out-of-plane loading can be applied more uniformly in the walls, contrarily to point load configuration. The test was performed under displacement control by selecting the mid-point of the infill as control point. Input and output air in the airbag was controlled by using a software to apply a specific displacement in the control point of the infill wall. The effect of the distance between the reaction frame of the airbag and the masonry infill on the effective contact area was previously analysed. Four load cells were attached to the reaction frame to measure the out-of-plane force. The effective contact area of the airbag was calculated by dividing the load measured in load cells by the pressure inside the airbag. When the distance between the reaction walls and the masonry infill wall is smaller, the effective area is closer to the nominal area of the airbag. Deformation and crack patterns of the infill confirm the formation of arching mechanism and two-way bending of the masonry infill. Until collapse of the horizontal interface between infill and upper beam in RC frame, the infill bends in two directions but the failure of that interface which is known as weakest interface due to difficulties in filling the mortar between bricks of last row and upper beam results in the crack opening trough a well-defined path and the consequent collapse of the infill.

In-plane and out-of plane experimental characterization of rc masonry infilled frames

Seismic investigations of typical south European masonry infilled frames were performed by testing two reduced scale specimens: one in the in-plane direction and another in the out-ofplane direction. Information about geometry and reinforcement scheme of those structures constructed in 1980s were obtained by [1]. The specimen to be tested in the in-plane direction was constructed as double leaf masonry while the specimen for testing in the out-of-plane direction is constructed with only its exterior leaf since the recent earthquakes have highlighted the vulnerability of the external leaf of the infills in out-of-plane direction [2]. The tests were performed by applying the pre-defined values of displacements in the in-plane and out-of-plane directions in the control points. For in-plane testing it was done by hydraulic actuator and for out-of-plane testing through the application of an airbag. Input and output air in the airbag was controlled by using a software to apply a specific displacement in the control point of the infill wall. Mid-point of the infill was assumed as a control point for outof- plane testing. Deformation and crack patterns of the infill confirm the formation of two-way arching mechanism of the masonry infill until collapse of the upper horizontal interface between infill and frame which is known as weakest interface due to difficulties in filling the mortar between bricks of last row and upper beam. This results in the crack opening through a welldefined path and the consequent collapse of the infill.

Dynamic interface model for masonry walls subjected to high strain rate out-of-plane loads

The present study proposes a dynamic constitutive material interface model that includes non-associated flow rule and high strain rate effects, implemented in the finite element code ABAQUS as a user subroutine. First, the model capability is validated with numerical simulations of unreinforced block work masonry walls subjected to low velocity impact. The results obtained are compared with field test data and good agreement is found. Subsequently, a comprehensive parametric analysis is accomplished with different joint tensile strengths and cohesion, and wall thickness to evaluate the effect of the parameter variations on the impact response of masonry walls.

Mixed Hodge structures and vector bundles on the projective Plane I

We describe an equivalence of categories between the category of mixed Hodge structures and a category of vector bundles on the toric complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalises the notion of R-split mixed Hodge structure and compute extensions in the category of mixed Hodge structures in terms of extensions of the corresponding vector bundles. We also give a relative version of this correspondence and apply it to define stratifications of the bases of the variations of mixed Hodge structure.

On Hyperbolic once-punctured-torus bundles II. Fractal tessellations of the plane

We describe fractal tessellations of the complex plane that arise naturally from Cannon-Thurston maps associated to complete, hyperbolic, once-punctured-torus bundles. We determine the symmetry groups of these tessellations.

Non compact euclidean cone 3-manifolds with cone angles less than 2∏

We study of noncompact Euclidean cone manifolds with cone angles less than c&2π and singular locus a submanifold. More precisely, we describe its structure outside a compact set. As a corol lary we classify those with cone angles & 2π/3 and those with cone angles = 2π/3.

Intersected Plane

Combined media on photographic paper. 55” x 63¾”

Euclidean geometric invariant of framed knots in manifolds

We present an invariant of a three dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. An important feature of our work is that we are not using any nontrivial representation of the manifold fundamental group or knot group.

Counting polygon dissections in the projective plane

"Vegeu el resum a l'inici del document del fitxer adjunt."

Geometria integral i convexitat en espais de curvatura holomorfa constant

En aquest treball es tracten qüestions de la geometria integral clàssica a l'espai hiperbòlic i projectiu complex i a l'espai hermític estàndard, els anomenats espais de curvatura holomorfa constant. La geometria integral clàssica estudia, entre d'altres, l'expressió en termes geomètrics de la mesura de plans que tallen un domini convex fixat de l'espai euclidià. Aquesta expressió es dóna en termes de les integrals de curvatura mitja. Un dels resultats principals d'aquest treball expressa la mesura de plans complexos que tallen un domini fixat a l'espai hiperbòlic complex, en termes del que definim com volums intrínsecs hermítics, que generalitzen les integrals de curvatura mitja. Una altra de les preguntes que tracta la geometria integral clàssica és: donat un domini convex i l'espai de plans, com s'expressa la integral de la s-èssima integral de curvatura mitja del convex intersecció entre un pla i el convex fixat? A l'espai euclidià, a l'espai projectiu i hiperbòlic reals, aquesta integral correspon amb la s-èssima integral de curvatura mitja del convex inicial: se satisfà una propietat de reproductibitat, que no es té en els espais de curvatura holomorfa constant. En el treball donem l'expressió explícita de la integral de la curvatura mitja quan integrem sobre l'espai de plans complexos. L'expressem en termes de la integral de curvatura mitja del domini inicial i de la integral de la curvatura normal en una direcció especial: l'obtinguda en aplicar l'estructura complexa al vector normal. La motivació per estudiar els espais de curvatura holomorfa constant i, en particular, l'espai hiperbòlic complex, es troba en l'estudi del següent problema clàssic en geometria. Quin valor pren el quocient entre l'àrea i el perímetre per a successions de figures convexes del pla que creixen tendint a omplir-lo? Fins ara es coneixia el comportament d'aquest quocient en els espais de curvatura seccional negativa i que a l'espai hiperbòlic real les fites obtingudes són òptimes. Aquí provem que a l'espai hiperbòlic complex, les cotes generals no són òptimes i optimitzem la superior.

Quasiconformal distortion of Riesz capacities and Hausdorff measures in the plane

In this paper we prove the sharp distortion estimates for the quasiconformal mappings in the plane, both in terms of the Riesz capacities from non linear potential theory and in terms of the Hausdorff measures.