Slender Masonry Research Articles

Time-history analysis of slender masonry towers: a parametric study on the reliability of a simplified Bouc and Wen approach

The assessment of existing masonry structures under seismic loading requires reliable and expedite numerical modelling approaches. These approaches should take into account both the specific non-linear behaviour of the material (f.i. the small tensile strength) and, in case of time-history analysis, the hereditary nature of the restoring forces that describe the masonry mechanical behaviour. The paper, considering the need of simplified but effective methods to assess the seismic response of masonry towers, proposes an expeditious approach based on an equivalent Bouc and Wen model. The model, that has been extensively employed to describe a wide range of hysteretic behaviours like degradation of stiffness and strength, has the advantage of the computational simplicity since only one auxiliary non-linear differential equation is needed to describe the hysteretic behaviour. As a prototype of masonry towers, a cantilever masonry beam is analysed and the non-linear Bouc and Wen model is employed to reproduce the system hysteretic response assuming that the first mode shape governs the dynamic behaviour. A two-steps identification procedure is proposed. Static non-linear analyses are employed to assess a few of the Bouc and Wen model parameters; remaining ones are assessed in order to minimize the error between the estimated displacement and the one obtained in a reference finite element model of the structure. Within the paper, the identification of the parameters needed to build the single-degree-of-freedom oscillator is analysed in depth analysing the effects of four different seismic natural records. The results of the identification procedure show a general trend concerning the values to be selected for the Bouc and Wen parameters.

Reliability assessment of vertically loaded masonry walls

For the safety assessment of vertically loaded masonry walls, the Eurocode 6 considers a linear limit state function with only one basic parameter for the compressive strength of masonry. This assumption disregards the contribution of the uncertainty in other material parameters, like the elastic modulus, which is more important than the compressive strength in slender masonry walls. Furthermore, Eurocode 0 gives no clear advice on how to deal with the partial safety factors for non-linear problems in general.A reliability assessment has been carried out for the vertically loaded masonry walls, in order to clearly understand the contribution of the uncertainty of different material parameters on the evaluation of safety. The limit state function of the problem has been calculated using the transfer-matrix method. The full probabilistic approach has been applied using Monte Carlo simulations which helped to propose a new approach for the use of the partial safety factors in the non-linear analysis.

Stability of Slender Masonry Columns with Circular Cross-Section under Their Own Weight and Eccentric Vertical Load

ABSTRACTThis work concerns the stability of unreinforced masonry slender circular cross-sectional columns subjected to their own weight and eccentric vertical load. Cantilever columns are examined, considering that the material has infinitely linear elastic behavior in compression and has no tensile strength. For the analysis, an existing numerical model and solution procedure developed for the stability analysis of masonry elements with rectangular cross-section are utilized and adapted to the circular columns. For the instability of the columns, an appropriate criterion that relates the top lateral deflection to the intensity of the applied eccentric vertical load is employed. By considering a reference column, critical buckling load is obtained, behavior of the column interpreted and efficiency of the numerical model emphasized. Performing a nonlinear buckling analysis using a general purpose software on this reference column, obtained results are compared with those of the adapted procedure of the present study. Implementing parametric analyses on reference column, effects of the column slenderness, eccentricity of vertical load, elastic modulus, and self-weight on the buckling load are investigated. Presented calculation procedure provides a useful tool in order to calculate the critical loads or to check the stability of masonry circular columns.

Collapse analysis of slender masonry barrel vaults

Significant part of the world cultural heritage is represented by masonry buildings. Many of them are characterised by a complex architecture like as the religious buildings and need to be preserved, from a structural point of view, especially in high seismic risk areas. The recent earthquakes showed that the Historical and Monumental buildings are often characterised by high seismic vulnerability. The lowest seismic performances are associated with the presence of thrusting elements like as arches and vaults. In this background, the numerical analyses and experimental simulations provide important information about the structural behaviour of such elements. The structural behaviour of curved elements can be complex to simulate and to predict exclusively by numerical analyses. Indeed, the experimental tests can provide an efficient contribution to the calibration and interpretation of the numerical models.The present work focuses on a particular typology of vaults generally used as roofs in religious buildings. These vaults typically do not include any backfill and are slender. These typologies of masonry vaults cannot be analysed with classical approaches where no-tension is assumed. In fact, the tensile strength must be included in order to assess the seismic capacity of these masonry elements. A simplified analytical model, which includes the tensile strength, was proposed. Validation of the analytical model is provided by comparing predictions of the load capacity and the failure mode with those obtained from previous shaking table test series on two full scale masonry vaults. The proposed method represents a useful modelling tool in order to design dynamic tests on masonry vaults and to assess their vulnerability.

A simplified procedure for the seismic safety of large and slender rigid masonry blocks

This paper aims at finding the features of an artificial accelerogram which can be used to assess the seismic safety of large and slender rigid masonry blocks. The most important feature derives from a simple observation: well-known uncertainties on time variations of seismic actions imply that seismic risks analyses must be developed without privileging any detailed description of expected accelerograms. It follows that the best choice to build an artificial accelerogram is to represent it with sequences of instantaneous Dirac impulses and to look at its worst effects. A multiple impulse input is herein proposed, with impulses all applied right after the impact of the generic block on the ground. Intermediate impulses are then introduced to reduce the resonance effects and to cover a broad range of conditions. Approximate equations of block motion are proposed and numerical analyses are performed to highlight the most significant aspects of the proposed approach.

A preliminary approach of dynamic identification of slender buildings by neuronal networks

The study of the dynamic behavior of slender masonry structures is usually related to the preservation of the historic heritage. This study, for bell towers and industrial masonry chimneys, is particularly relevant in areas with an important seismic hazard. The analysis of the dynamic behavior of masonry structures is particularly complex due to the multiple effects that can affect the variation of its main frequencies along the seasons of the year: temperature and humidity. Moreover, these dynamic properties also vary considerably in structures built in areas where land subsidence due to the variation of the phreatic level along the year is particularly evident: the stiffness of the soil–structure interaction also varies. This paper presents a study to evaluate the possibility of detecting the variation of groundwater level based on the readings obtained using accelerometers in different positions on the structure. To do this a general case study was considered: a 3D numerical model of a bellower. The variation of the phreatic level was evaluated between 0 and −20m, and 81 cases studies were developed modifying the rigidity of the soil–structure interaction associated to a position of the phreatic level. To simulate the dispositions of accelerometers on a real construction, 16 points of the numerical model were selected along the structure to obtain modal displacements in two orthogonal directions. Through an adjustment by using neural networks, a good correlation has been observed between the predicted position of the water table and acceleration readings obtained from the numerical model. It is possible to conclude that with a discrete register of accelerations on the tower it is possible to predict the water table depth.

The debate on the strengthening of two slender masonry structures in early XX century: A contribution to the history of wind engineering

In this paper, the debates and the studies carried out in the first half of the XX century on the dynamic response of two slender masonry structures to wind actions are presented. The two buildings are the St. Gaudenzio Basilica in Novara and the Mole Antonelliana in Turin, both designed by the Italian Architect Alessandro Antonelli at the end of XIX century. Their exceptional audacity (121 and 167.5m high, respectively) raised many doubts on their structural safety, leading between 1930 and 1954 to many consolidation interventions. In the case of St. Gaudenzio, these works apparently produced new damage, in an impressive sequence of failure and interventions. For this reason, a heated debate concerning the dynamic response of the structure to wind action was aroused between 1939 and 1942. In the case of Mole Antonelliana, wind action was only marginally considered until the collapse of the spire in 1953, but its reconstruction was undertaken through a number of experimental tests carried out in the wind tunnel of the Aeronautics Laboratory of Turin Polytechnic in 1954. These experiments were among the first pioneering wind tunnel tests on civil structures in Europe.

Seismic performance evaluation of slender masonry towers: a case study

Summary Historical structures and preserving their cultural values are crucial issues for humanity, not only because of their link to important certain periods in the past, but also their unique architectural features. Although many historical structures continue to offer services while keeping their historical values, some of them are at high risk in seismic prone regions. Therefore, the understanding of their structural performance under strong ground motions has been of significant importance to the civil societies as well as engineering community. The structural systems of historical buildings, generally, consist of masonry walls or piers. The behavior of such walls is controlled by either deformation or force. Seismic performance evaluation of historical structures can be carried out within the framework of performance-based evaluation principles. This paper mainly discusses the basic principles to be considered in performance-based seismic evaluation of historical structures. Proposed seismic hazard levels, evaluation of existing seismic hazard, selection of earthquake ground motions as well as site geology, geological and tectonic settings of the area, seismic activity of the region and local soil conditions are needed for a thorough performance evaluation. Seismic performance evaluation of a clock tower located in eastern Turkey was accomplished based on the proposed principles. Copyright © 2015 John Wiley & Sons, Ltd.

Limit equilibrium analysis of masonry buttresses and towers under lateral and gravity loads

This paper revisits the fracturing of masonry buttresses and towers when subjected either to a concentrated oblique force at their head or to lateral inertial loading due to ground shaking and presents the corresponding failure criteria in elongation and shear. The loading configurations examined result either from the thrust that an elevated arch exerts on its supporting buttresses or from earthquake shaking on soli- tary masonry towers. At their limit state, tall, slender masonry buttresses and towers collapse by pivoting about their base corner, whereas less slender masonry structures may collapse by developing a shear fail- ure. Because of the unilateral behavior of masonry, at the initiation of collapse of a slender buttress, the compression-free region separates from the rest of the buttress and reduces the stabilizing moment. As the ratio, base/height or the gravity load, increases, masonry buttresses and towers may fail in shear; therefore, the paper presents envelopes of their limit lateral capacity depending on the aspect ratio, the mechanical properties of masonry and the level of vertical loading. The equivalent static analysis adopted in this paper concludes that in most cases under lateral inertial loading, elongation failure is the lower failure mechanism of a tall masonry tower; nevertheless, a subsequent initiation of rocking that engages the large rotational iner- tia of the detached portion of the tower attracts additional inertia forces that may induce a follower shear failure.

Empirical Formulation for Estimating the Fundamental Frequency of Slender Masonry Structures

ABSTRACTThe fundamental frequency of a structure enables better assessment of its seismic demand for an efficient design and planning of its maintenance and retrofit strategy. The frequency is independent of the type of external loads, however, depends on structural stiffness, mass, damping and boundary conditions. In the case of slender masonry structures such as towers, minarets chimneys, and pagoda temples, it is influenced by mass and stiffness distribution, connection to adjacent structures, material properties, aspect ratio and slenderness ratio. In this present article, the data collected from various literature reviews on the slender masonry structures regarding dynamic, geometrical, and mechanical characteristics have been correlated to identify the major parameters influencing the fundamental frequency of such structures. The database has been used for developing an empirical formulation for predicting the fundamental frequency of such structures. The comparison between the experimental fundamental frequencies and the estimated fundamental frequencies are carried out in order to define reliability and accuracy of these empirical formulae.

On the dynamics of viscous masonry beams

In this paper, we consider the longitudinal and transversal vibrations of the masonry beams and arches. The basic motivation is the seismic vulnerability analysis of masonry structures that can be modeled as monodimensional elements. The Euler–Bernoulli hypothesis is employed for the system of forces in the beam. The axial force and the bending moment are assumed to consist of the elastic and viscous parts. The elastic part is described by the no-tension material, i.e., the material with no resistance to tension and which accounts for the cases of limitless, as well as bounded compressive strength. The adaptation of this material to beams has been developed in Orlandi (Analisi non lineare di strutture ad arco in muratura. Thesis, 1999) and Zani (Eur J Mech A/Solids 23:467–484, 2004). The viscous part amounts to the Kelvin–Voigt damping depending linearly on the time derivatives of the linearized strain and curvature. The dynamical equations are formulated, and a mathematical analysis of them is presented. Specifically, following Gajewski et al. (Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie-Verlag, Berlin, 1974), the theorems of existence, uniqueness and regularity of the solution of the dynamical equations are recapitulated and specialized for our purposes, to support the numerical analysis applied previously in Lucchesi and Pintucchi (Eur J Mech A/Solids 26:88–105, 2007 ). As usual, for that the Galerkin method has been used. As an illustration, two numerical examples (slender masonry tower and masonry arch) are presented in this paper with the applied forces corresponding to the acceleration in the earthquake in Emilia Romagna in May 29, 2012.

Effectiveness of nonlinear static procedures for slender masonry towers

This paper investigates the accuracy of pushover-based methods in predicting the seismic response of slender masonry towers, through comparison with the results from a large number of nonlinear time-history dynamic analyses. In particular, conventional pushover analyses, in both their force- and displacement-based variants, are considered, and seismic assessment through the well-established N2 method is also addressed. The study is conducted by applying a simple non-linear elastic model recently developed and implemented in the computational code MADY to represent slender masonry structures. The model enables both pushover analyses and non-linear dynamic analyses to be performed with a minimum of effort. A multi-record incremental dynamic analysis carried out for a quite large number of structural cases, each of which is subjected to a comprehensive set of dynamic nonlinear analyses, is used to evaluate the accuracy of pushover methods in predicting the global structural response, as represented by the usual capacity curve together with a damage curve, both of which are compared with dynamic envelopes. Local responses, in terms of lateral displacements and the distribution of damage along the tower height are also compared. The results reveal that the key issue in the accuracy of pushover methods is the nature of the lateral load applied, that is, whether it is a force or a displacement. Different ranges of expected deformation are suggested for adopting each type of lateral load to better represent the actual behaviour of masonry towers and their damage under seismic events through pushover methods.

Seismic improvement of slender masonry tower by using hysteretic devices and partial prestressing technique

An innovative system for seismic improvement of slender masonry towers by using hysteretic devices and partial prestressing technique was developed and applied to a case study. The proposed technique consists in a low level of prestressing of the upper part of the tower in order to localize in the un-prestressed lower part of the tower, i.e. a limited zone near the basement, the vertical displacements due to the cracking of masonry under seismic action. The positioning of dissipative devices, such as the Buckling-Restrained Axial Dampers, across the localization zone allows a significant contribution in terms of damping for hysteretic dissipation. The main effect of such an intervention is the reduction of the seismic demand to the tower and consequently the reduction of the top displacement as well as of the level of damage of the masonry. Both numerical analyses and experimental tests on a scale model of a Venetian bell tower were carried out showing the efficiency and reliability of the proposed technique.

Dynamic Investigation of an Ancient Masonry Bell Tower with Operational Modal Analysis - A Non-Destructive Experimental Technique to Obtain the Dynamic Characteristics of a Structure

This paper shows the results of an experimental analysis on the bell tower of Chiesa della Maddalena (Mola di Bari, Italy), to better understand the structural behavior of slender masonry structures. The research aims to calibrate a numerical model by means of the Operational Modal Analysis (OMA) method. In this way realistic conclusions about the dynamic behavior of the structure are obtained. The choice of using an OMA derives from the necessity to know the mo- dal parameters of a structure with a non-destructive testing, especially in case of cultural-historical value structures. Therefore by means of an easy and accurate process, it is possible to acquire in-situ environmental vibrations. The data collected are very important to estimate the mode shapes, the natural frequencies and the damping ratios of the structure. To analyze the data obtained from the monitoring, the Peak Picking method has been applied to the Fast Fourier Trans- forms (FFT) of the signals in order to identify the values of the effective natural frequencies and damping factors of the structure. The main frequencies and the damping ratios have been determined from measurements at some relevant loca- tions. The responses have been then extrapolated and extended to the entire tower through a 3-D Finite Element Model. In this way, knowing the modes of vibration, it has been possible to understand the overall dynamic behavior of the struc- ture.

Modeling of Out-of-Plane Behavior of Masonry Walls

The flexural behavior of rectangular masonry sections is investigated by considering nonlinear stress-strain in compression and limited-tension material. A preliminary analysis shows that, with variation in the parameters specializing with the adopted conventional constitutive law, the experimentally observed behavior of different kinds of masonry materials can be approximated. Subsequently, moment-curvature dimensionless curves are derived numerically by satisfying the equilibrium equations of the section. In the case of negligible tensile strength these curves exhibit a typical shape that can be approximated by analytical expressions; consequently, suitable functions are proposed that are governed by only a few parameters which depend on the compression level of the section and the available ductility of the material. The reliability of the proposed modeling procedure is also verified by using the experimental results of a previous study, where masonry elements subjected to an increasing eccentric normal load were considered. Therefore, the analytically defined flexural behavior is transferred to the characteristic sections of a discrete model of slender masonry column, in order to reproduce the experimental results of full-scale tests on bearing masonry walls subjected to increasing lateral deflections for stability analyses. Comments on the results obtained with this model would be useful for further investigations.

A numerical model for non-linear dynamic analysis of slender masonry structures

A numerical model is presented to enable performing non-linear dynamic analysis of slender masonry structures and elements, such as towers and columns or masonry walls in out-of-plane flexure. Such structures are represented via a continuous one-dimensional model. The main mechanical characteristics of the material in all sections along the height of such structures are taken into account by means of a non-linear elastic constitutive law formulated in terms of generalized stress and strain, under the assumption that the material has no resistance to tension and limited compressive strength. The relations defined herein for the general case of hollow rectangular cross-sections are also aimed at enabling study of towers, bell-towers and similar slender structures.

The Stability Of Slender Masonry Millions

During the building of the great cathedrals of Europe. masons endeavoured to produce larger windows with more slender mullions? so as to flood the building with natural light. These were later glazed with stained glass, giving rich colours to the interiors. There is limited anecdotal reference to window collapse: however, one of the larger windows in Durham Cathedral has an internal masonry frame which appears to have been constructed to provide added resistance of the window to inward collapse under severe wind loading. This curious architectural detail is the reason for this study into window stability. Two windows in Durham Cathedral have been studied to consider their factors of safety against mullion instability.

SIGNIFICANT GROUND MOTION PARAMETERS FOR EVALUATION OF THE SEISMIC PERFORMANCE OF SLENDER MASONRY TOWERS

The evaluation of seismic risk of masonry monuments requires to study the combination of vulnerability and hazard. In the present work, the global seismic response of slender masonry towers has been studied by means of a specific 3-D fibre model. Accounting for the particular behaviour of such structures, the hazard should also be described by a suitable measure of intensity of the seismic action. A variety of different parameters relating with the ground acceleration recordings have been investigated for what regards their correlation with the damage indicators of the model. The combination of the peak ground velocity of the horizontal component and of the significant duration is an effective measure of intensity. This measure can be improved by considering the accord of the frequency content of the ground motion with the dynamical characteristics of the tower. Since in some cases the effect of the vertical component proved to be important, a further improvement can be obtained by taking into account also the vertical ground motion intensity.

A THREE-DIMENSIONAL MODEL FOR VULNERABILITY ANALYSIS OF SLENDER MEDIEVAL MASONRY TOWERS

A fibre model to describe the global dynamic response of slender masonry towers is presented for use in deterministic vulnerability analysis. The main stresses are axial in this type of structure, and coupling between flexural and axial modes in the inelastic region may be critical. The model accounts for the three-dimensional response of the structure and the relations between coupling effects and masonry characteristics. An exhaustive parametric study revealed that compression strength and height are the most important parameters determining global response to seismic excitation, and that the response is often very sensitive to the vertical component of the ground motion. The combination of flexural and axial vibrations can induce serious additional damage that should be considered in seismic risk analysis.

A Three Dimensional Model for Vulnerability Analyses of Slender Masonry Medieval Towers

A Three Dimensional Model for Vulnerability Analyses of Slender Masonry Medieval Towers