Ivo Caliò

Passive control of the seismic rocking response of art objects

The present paper deals with the passive control of the vibrations of art objects subjected to base excitations. The art object is modelled as a rigid block simply supported on a pedestal which is connected to a visco-elastic device in order to obtain a passive control system. If subjected to seismic excitation, the art object may tilt over the movable supporting mass and eventually overturn, while the sliding is prevented by means of seismic restraints. The nonlinear dynamic equilibrium equations of the structural model for each phase of the motion have been derived for large displacements. The transition conditions between the phases of the motion that may occur have also been defined. Extensive numerical investigations under impulsive and seismic excitations have been carried out in order to both verify the efficiency of the passive control and to evaluate the values of the characteristic parameters of the isolation device which provide the best performance. The results show that the investigated isolation device may be easily and successfully applied for the mitigation of the seismic damage of art objects.

CLOSED-FORM TRIGONOMETRIC SOLUTIONS FOR INHOMOGENEOUS BEAM-COLUMNS ON ELASTIC FOUNDATION

In this study, a special class of closed-form solutions for inhomogeneous beam-columns on elastic foundations is investigated. Namely the following problem is considered: find the distribution of the material density and the flexural rigidity of an inhomogeneous beam resting on a variable elastic foundation so that the postulated trigonometric mode shape serves both as vibration and buckling modes. Specifically, for a simply-supported beam on elastic foundation, the harmonically varying vibration mode is postulated and the associated semi-inverse problem is solved that result in the distributions of flexural rigidity that together with a specific law of material density, an axial load distribution and a particular variability of elastic foundation characteristics satisfy the governing eigenvalue problem. The analytical expression for the natural frequencies of the corresponding homogeneous beam-column with a constant characteristic elastic foundation is obtained as a particular case. For comparison the obtained closed-form solution is contrasted with an approximate solution based on an appropriate polynomial shape, serving as trial function in an energy method.

A Discrete Element for Modeling Masonry Vaults

The assessment of the seismic response of historical masonry buildings represents a subject of considerable importance but, at the same time, of very difficult task. Refined finite element numerical models, able to predict the non-linear dynamic mechanical behavior and the degradation of the masonry media, require sophisticated constitutive law and a huge computational cost that makes these methods nowadays not suitable for practical application. In the past many authors developed simplified or alternative methodologies that, with a reduced computational effort, should be able to provide numerical results that can be considered sufficiently accurate for engineering practice purposes. However most of these methods are based on simplified hypotheses that make these approaches inappropriate for monumental buildings. In this paper a three dimensional discrete element model, able to predict the nonlinear behaviour of masonry shell elements, is presented as an extension of a previously introduced spatial discrete-element conceived for the simulation of both the in-plane and the out-of-plane behavior of masonry plane elements. The new macro-element enriches a larger computational framework, based on macro-element approach, devoted to the numerical simulation of the seismic behaviour of historical masonry structures.

Can a Trigonometric Function Serve Both as the Vibration and the Buckling Mode of an Axially Graded Structure

Abstract It is well known that for homogeneous beams that have simply supported or guided ends a trigonometric function serves both as a vibration and a buckling mode. The research in this paper shows that, remarkably, the same result is valid for some axially graded beams. Specifically, three cases of harmonically varying vibration modes are postulated and the associated semi-inverse problems that result in the distributions of elastic modulus that together with a specific variation of material density and axial load distribution satisfy the governing eigenvalue problem for the inhomogeneous Bernoulli-Euler beam are solved. In all cases the closed-form solutions are obtained for the natural frequency. Those closed-form solutions are contrasted with approximate solutions based on appropriate polynomial functions, serving as trial functions in an energy method.

Free vibrations of Timoshenko beam-columns on Pasternak foundations

In this paper the free vibration and the stability of axially loaded Timoshenko beams on elastic foundation are analyzed through the dynamic stiffness matrix method. The study is carried out considering a two–parameter elastic soil which contains the characteristics of both the Winkler and the Pasternak foundations. The equation of motion and the exact dynamic stiffness matrix of a beam–column including the effect of shear deformation and rotatory inertia is derived. The eigenproblem of the beam–column is therefore solved through the application of the general Wittrick and Williams algorithm. The effects of soil characteristics as well as shear deformations and rotatory inertia on the natural frequencies of the beam-column are investigated. An extensive parametric study highlights the main parameters that characterize the dynamical behavior of the considered beam–column.

Seismic response of multi-storey buildings base-isolated by friction devices with restoring properties

This paper investigates the seismic behaviour of multi-storey buildings base-isolated by friction pendulum systems. The non-linear equations of motion have been expressed in an original simple form through the use of appropriate Lagrangian parameters. The dynamic response of the system has been evaluated numerically by means of a Fast Non-linear Analysis based on a co-ordinate Ritz transformation. The adopted Ritz vector basis is represented by the undamped eigenvectors of the structure on a fixed base. Extensive parametric investigations have been performed in order to investigate the non-linear behaviour of multi-storey buildings subjected to harmonic and earthquake excitations. The results, expressed in the frequency domain and in the form of response spectra, allow to compare the dynamic response of the sliding system with the corresponding response of the same structural system on a fixed base.

Numerical and Experimental Validation of a 3D Macro-Model for the In-Plane and Out-Of-Plane Behavior of Unreinforced Masonry Walls

ABSTRACT The behavior of historical UnReinforced Masonry (URM) buildings subjected to earthquake loading is usually governed by a complex interaction between the in-plane and out-of-plane response of masonry walls. In modern masonry building, the in-plane behavior of masonry walls is generally guaranteed in the structural design, but thin non-structural masonry infills are often vulnerable to out-of-plane actions. A reliable prediction of the combined in-plane and out-of-plane behavior of URM walls requires rigorous nonlinear finite element models, whose complexity and computational cost are generally unsuitable for current engineering applications, motivating the research of alternative numerical approaches. This article presents a study for validation of a 3D macro-model intended to simulate the combined in-plane and out-of-plane behavior of unreinforced masonry walls, against experimental results available in the literature and FEM simulations. The model is based on a three-dimensional macro-element whose kinematics is governed by seven degrees of freedom only. The mechanical behavior of the element is based on a fiber discretization approach that adopts basic material parameters. The performance of the proposed macro-element strategy is assessed by means of nonlinear static analyses performed on masonry walls, for which both numerical and experimental results are available in the literature.

A new discrete‐element approach for the assessment of the seismic resistance of composite reinforced concrete‐masonry buildings

In the present study a new discrete‐element approach for the evaluation of the seismic resistance of composite reinforced concrete‐masonry structures is presented. In the proposed model, unreinforced masonry panels are modelled by means of two‐dimensional discrete‐elements, conceived by the authors for modelling masonry structures, whereas the reinforced concrete elements are modelled by lumped plasticity elements interacting with the masonry panels through nonlinear interface elements. The proposed procedure was adopted for the assessment of the seismic response of a case study confined‐masonry building which was conceived to be a typical representative of a wide class of residential buildings designed to the requirements of the 1909 issue of the Italian seismic code and widely adopted in the aftermath of the 1908 earthquake for the reconstruction of the cities of Messina and Reggio Calabria.

Seismic safety evaluation of reinforced concrete masonry infilled frames using macro modelling approach

Many reinforced concrete buildings have been built with masonry infill walls for architectural needs without considering their mechanical contribution. However, ignoring the structural influence of infills may lead to significant inaccuracies in the prediction of the actual seismic capabilities of the structure. Aiming at providing numerical tools suitable for engineering practice, simplified methodologies for predicting the nonlinear seismic behaviour of infilled frame structures (IFS) have been proposed, mostly considering the contribution of the infill as an equivalent diagonal strut element. In this paper, an alternative plane macro-element approach for the seismic assessment of IFS is proposed, validated and applied to a benchmark prototype building. The model validation is focused on recent experimental and numerical results that investigate the influence of non-structural infills, also in the presence of different openings layouts. As a benchmark investigation, a multi-storey plane frame prototype, for which the results of pseudo-dynamic tests are available, is investigated and compared to the results obtained by using a commonly adopted single-strut model. The merits and drawbacks of the considered numerical approaches are highlighted.

Advances in dynamic instability: can a beam-column undergo tensile flutter?:

Tensile instability in beam-like structures has been highlighted in very few papers; the studies reported in the specific literature are limited to beam-columns characterised either by high shear deformation or by the presence of a single structural junction allowing a transversal displacement discontinuity. Moreover, to the authors’ knowledge, the flutter instability associated to tensile axial load has not yet been disclosed. This work aims to offer further contribution to the knowledge of tensile instability of beam-columns by considering the dynamic instability of an Euler Bernoulli beam in presence of an arbitrary number of internal sliders endowed with translational elastic springs. The use of the generalised functions allows an exact evaluation of the eigensolution, provided in closed form, both for conservative and nonconservative axial load. In particular, the following relevant question is posed: Can a beam-column undergo tensile flutter instability? A comprehensive parametric analysis conducted in this work gives an affirmative answer to the asked question.