Bidirectional behavior of unreinforced masonry walls

Most of the studies related to the modeling of masonry structures have by far investigated either the in‐plane (IP) or the out‐of‐plane (OP) behavior of walls. However, seismic loads mostly impose simultaneous IP and OP demands on load‐bearing or shear masonry walls. Thus, there is a need to reconsider design equations of unreinforced masonry walls by taking into account bidirectional effects. The intent of this study is to investigate the bidirectional behavior of an unreinforced masonry wall with a typical aspect ratio under different displacement‐controlled loading directions making use of finite element analysis. For this purpose, the numerical procedure is first validated against the results of the tests on walls with different failure modes conducted by the authors. Afterward, the response of the wall systems is evaluated with increasing top displacement having different orientations. A set of 19 monotonic and three cyclic loading analyses are performed, and the results are discussed in terms of the variation of failure modes and load–displacement diagrams. Moreover, the results of wall capacity in each loading condition are compared with those of the ASCE41‐06 formulations. The results indicate that the direction of the resultant force, vectorial summation of IP and OP forces, of the wall is initially proportional to the ratio of stiffness in the IP and the OP directions. However, with the increase of damage, the resultant force direction inclines towards the wall's longitudinal direction regardless of the direction of the imposed displacement. Finally, recommendations are made for applicability of ASCE41‐06 formulations under different bidirectional loading conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Out‐of‐plane seismic response of vertically spanning URM walls connected to flexible diaphragms

A simplified numerical model was used to investigate the out‐of‐plane seismic response of vertically spanning unreinforced masonry (URM) wall strips. The URM wall strips were assumed to span between two flexible diaphragms and to develop a horizontal crack above the wall mid‐height. Three degrees of freedom were used to accommodate the wall displacement at the crack height and at the diaphragm connections, and the wall dynamic stability was studied. The equations of dynamic motion were obtained using principles of rocking mechanics of rigid bodies, and the formulae were modified to include semi‐rigid wall behaviour. Parametric studies were conducted that included calculation of the wall response for different values of diaphragm stiffness, wall properties, applied overburden, wall geometry and earthquake ground motions. The results of the study suggest that stiffening the horizontal diaphragms of typical low‐rise URM buildings will amplify the out‐of‐plane acceleration demand imposed on the wall and especially on the wall–diaphragm connections. It was found that upper‐storey walls connected to two flexible diaphragms had reduced stability for applied earthquake accelerograms having dominant frequency content that was comparable with the frequency of the diaphragms. It was also found that the applied overburden reduced wall stability by reducing the allowable wall rotations. The results of this study suggest that the existing American Society of Civil Engineers recommendations for assessment of vertically spanning walls overestimate the stability of top‐storey walls in multi‐storey buildings in high‐seismic regions or for walls connected to larger period (less stiff) diaphragms. Copyright © 2015 John Wiley & Sons, Ltd.     

In‐plane and out‐of‐plane behavior of confined masonry walls for various toothing and openings details and prediction of their strength and stiffness

Eight half‐scale brick masonry walls were tested to study two important aspects of confined masonry (CM) walls related to its seismic behavior under in‐plane and out‐of‐plane loads. Four solid wall specimens tested to investigate the role of type of interface between the masonry and tie‐columns, such as toothing varying from none to every course. The other four specimens with openings were tested to study the effectiveness of various strengthening options around opening to mitigate their negative influence. In the set of four walls, one wall was infilled frame while the other three were CM walls of different configurations. The experimental results were further used to determine the accuracy of various existing models in predicting the in‐plane response quantities of CM walls. Confined masonry walls maintained structural integrity even when severely damaged and performed much better than infill frames. No significant effect of toothing details was noticed although toothing at every brick course was preferred for better post‐peak response. For perforated walls, provision of vertical elements along with continuous horizontal bands around openings was more effective in improving the overall response. Several empirical and semi‐empirical equations are available to estimate the lateral strength and stiffness of CM walls, but those including the contribution of longitudinal reinforcement in tie‐columns provided better predictions. The available equations along with reduction factors proposed for infills could not provide good estimates of strength and stiffness for perforated CM walls. However, recently proposed relations correlating strength/stiffness with the degree of confinement provided reasonable predictions for all wall specimens. Copyright © 2016 John Wiley & Sons, Ltd.     

Influence of boundary conditions on the out‐of‐plane response of brick masonry walls in buildings with RC slabs

In modern unreinforced masonry buildings with stiff RC slabs, walls of the top floor are most susceptible to out‐of‐plane failure. The out‐of‐plane response depends not only on the acceleration demand and wall geometry but also on the static and kinematic boundary conditions of the walls. This paper discusses the influence of these boundary conditions on the out‐of‐plane response through evaluation of shake table test results and numerical modelling. As a novum, it shows that the in‐plane response of flanking elements, which are orthogonal to the wall whose out‐of‐plane response is studied, has a significant influence on the vertical restraint at the top of the walls. The most critical configuration exists if the flanking elements are unreinforced masonry walls that rock. In this case, the floor slabs can uplift, and the out‐of‐plane load‐bearing walls loose the vertical restraint at the top. Numerical modelling confirms this experimentally observed behaviour and shows that slab uplift and the difference in base and top excitation have a strong influence on the out‐of‐plane response of the walls analysed. Copyright © 2016 John Wiley & Sons, Ltd.     

Out‐of‐plane strength reduction of unreinforced masonry walls because of in‐plane damages

There are numerous studies on the behavior of Unreinforced Masonry (URM) walls in both in‐plane (IP) and out‐of‐plane (OP) directions; however, few aimed at understanding the simultaneous contribution of these intrinsic responses during earthquakes. Undoubtedly, even a strong URM wall shows weakened capacity in the OP direction because of minor cracks and other damages in the IP direction, and this capacity reduction has not yet been accounted for in seismic codes. In this study, performance of three URM walls is evaluated by several numerical analyses in terms of the OP capacity reduction because of IP displacements and failure modes. Several parameters influencing the OP capacity have been studied including aspect ratio, roof boundary condition, IP displacement and IP loading patterns. The results indicate that reduction in the OP capacity of URM walls varies from negligible to very high depending on boundary conditions, IP failure mode and IP damage severity. Moreover, IP loading pattern is more important in walls with higher aspect ratios because of their IP failure modes. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical study on factors that influence the in‐plane drift capacity of unreinforced masonry walls

Displacement‐based assessment procedures require as input reliable estimates of the deformation capacity of all structural elements. For unreinforced masonry (URM) walls, current design codes specify the in‐plane deformation capacity as empirical equations of interstory drift. National codes differ with regard to the parameters that are considered in these empirical drift capacity equations, but the inhomogeneity of datasets on URM wall tests renders it difficult to validate the hypotheses with the currently available experimental data. This paper contributes to the future development of such empirical relationships by investigating the sensitivity of the drift capacity to the shear span, the aspect ratio, the axial load ratio, and the size of the wall. For this purpose, finite element models of URM walls are developed in Abaqus/Explicit and validated against a set of experimental results. The results show that the axial load ratio, the shear span, and the wall size are among the factors that influence the drift capacity the most. Empirical equations are mainly derived from test results on small walls, and the numerical results suggest that this can lead to a significant overestimation of the drift capacity for larger walls.     

Implications of the spandrel type on the lateral behavior of unreinforced masonry walls

Seismic response of unreinforced masonry (URM) buildings is largely influenced by nonlinear behavior of spandrels, which provide coupling between piers under in‐plane lateral actions. Seismic codes do not appropriately address modeling and strength verification of spandrels, adapting procedures originally proposed for piers. Therefore, research on spandrels has received significant attention in some earthquake‐prone countries, such as Italy and New Zealand. In the last years, the authors of this paper have performed both monotonic and cyclic in‐plane lateral loading tests on full‐scale masonry walls with single opening and different spandrel types. Those tests were carried out in a static fashion and with displacement control. In this paper, experimental outcomes for two as‐built specimens are presented and compared with those obtained in the past for another as‐built specimen with a wooden lintel above the opening. In both newly tested specimens, the masonry above the opening was supported by a shallow masonry arch. In one of those specimens, a reinforced concrete (RC) bond beam was realized on top of the spandrel, resulting in a composite URM‐RC spandrel. Then, the influence of spandrel type is analyzed in terms of observed damage, force–drift curves, and their bilinear idealizations, which allowed to compare displacement ductility and overstrength of wall specimens. Furthermore, effects of rocking behavior of piers are identified, highlighting their relationship with hysteretic damping and residual drifts. Copyright © 2014 John Wiley & Sons, Ltd.     

Analytical model for the out‐of‐plane response of vertically spanning unreinforced masonry walls

An analytical model describing the flexural response of vertically spanning out‐of‐plane loaded unreinforced masonry walls is presented in this paper. The model is based on the second‐order Euler‐Bernoulli beam theory and captures important characteristics of the out‐of‐plane response of masonry walls that have been observed in experimental tests and from numerical studies but for which an analytical solution was still lacking: the onset and the evolution of cracking, the peak strength of the out‐of‐plane loaded walls, and the softening of the response due to P ?Δ effects. The model is validated against experimental results, and the comparison shows that the model captures both the prepeak and postpeak response of the walls. From the analytical model of the force‐displacement curve, a formula for the maximum out‐of‐plane strength of the walls is derived, which can be directly applied in engineering practice.     

Assessment of the dynamic response of unreinforced masonry structures using a macroelement modeling approach

The seismic performance of unreinforced masonry structures is strongly associated with the interaction between in‐plane and out‐of‐plane mechanisms. The seismic response of these structures has been thoroughly investigated by means of experimental testing, analytical procedures, and computational approaches. Within the framework of the numerical simulations, models based on the finite element method provide a good prediction of the seismic performance of unreinforced masonry structures. However, they usually require a high computational cost and advanced user expertise to define appropriate mechanical properties and to interpret the numerical results. Because of these limitations, simplified models for practical applications have been developed during the last decades. Despite this, a great number of these models focus mostly on the evaluation of the in‐plane response, assuming box (or integral) behavior of the structure. In this paper, a simplified macroelement modeling approach is used to simulate the seismic response of 2 masonry prototypes taking into consideration the combined in‐plane and out‐of‐plane action. The numerical investigations were performed in the static and dynamic fields by using pushover analyses and nonlinear dynamic analyses respectively. The latter is a novel implementation of a model previously developed for static analysis. The results obtained from this study are in good agreement with those provided by a detailed nonlinear continuum FE approach, demonstrating the applicability of this macroelement model with a significant reduction of the computational cost.     

Effectiveness of superelastic bars for seismic rehabilitation of clay‐unit masonry walls

This paper presents the results on shaking table tests of half‐scale brick walls performed to investigate the effectiveness of newly developed Cu–Al–Mn superelastic alloy (SEA) bars in retrofitting of historical masonry constructions. Problems associated with conventional steel reinforcing bars lie in degradation of stiffness and strength, or pinching phenomena, under cyclic loading, and presence of large residual cracks in structures during and after intense earthquakes. This paper attempts to resolve the problems by applying newly developed Cu–Al–Mn SEA bars, characterized by large recovery strain, low material cost, and high machinability, as partial replacements for steel bars. Sets of unreinforced, steel reinforced, and SEA‐reinforced specimens are subjected to scaled earthquake excitations in out‐of‐plane direction. Whereas steel‐reinforced specimens showed large residual inclinations, SEA‐reinforced specimens resulted in stable rocking response with slight residual inclinations. Corresponding nonlinear finite element (FE) models are developed to simulate the experimental observations. The FE models are further used to examine the sensitivity of the response with respect to the variations in experimental conditions. Both the experimental and numerical results demonstrate the superiority of Cu–Al–Mn SEA bars to conventional steel reinforcing bars in avoiding pinching phenomena. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic behavior and modeling of steel reinforced concrete (SRC) walls

The steel reinforced concrete (SRC) wall consists of structural steel embedded at the boundary elements of a reinforced concrete (RC) wall. The use of SRC walls has gained popularity in the construction of high‐rise buildings because of their superior performance over conventional RC walls. This paper presents a series of quasi‐static tests used to examine the behavior of SRC walls subjected to high axial force and lateral cyclic loading. The SRC wall specimens showed increased flexural strength and deformation capacity relative to their RC wall counterpart. The flexural strength of SRC walls was found to increase with increasing area ratio of embedded structural steel, while the section type of embedded steel did not affect the wall's strength. The SRC walls under high axial force ratio had an ultimate lateral drift ratio of approximately 1.4%. In addition, a multi‐layer shell element model was developed for the SRC walls and was implemented in the OpenSees program. The numerical model was validated through comparison with the test data. The model was able to predict the lateral stiffness, strength and deformation capacities of SRC walls with a reasonable level of accuracy. Finally, a number of issues for the design of SRC walls are discussed, along with a collection and analysis of the test data, including (1) evaluation of flexural strength, (2) calculation of effective flexural stiffness, and (3) inelastic deformation capacity of SRC walls. Copyright © 2014 John Wiley & Sons, Ltd.     

Free rocking response of a regular stone masonry wall with equivalent block approach: experimental and analytical evaluation

The evaluation of the dynamic behaviour of rocking elements is directly correlated to the energy dissipated because of the impacts at the base interface, which can be represented by means of a coefficient of restitution. This schematization is commonly accepted as representative of the out‐of‐plane response of stone masonry walls. An experimental campaign (in a lab environment) aiming at assessing the value of this coefficient for a sacco granite masonry wall is presented in this work. The rocking motion at a predefined bed joint level was induced in the tested specimens in order to validate a novel test setup designed to assess the coefficient of restitution value by means of a realistic reproduction of the rocking behaviour of a single element, under the hypothesis of an infinitely stiff system above the bed joint level. As the main objective of the work was to assess the rocking behaviour of a masonry wall that looses energy at the impacts at a certain joint level, the flexural behaviour was not desirable and had to be avoided. For this purpose, a test setup based on the equivalent block approach was developed. In the final section of this work, comparisons between experimental and numerical results are presented together with some preliminary conclusions on the appropriate modelling strategy and the values of the coefficient of restitution to be used for the seismic assessment of the out‐of‐plane rocking behaviour of this type of sacco stone masonry walls. Copyright © 2013 John Wiley & Sons, Ltd.     

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). Copyright © 2015 John Wiley & Sons, Ltd.     

Softening effects of RC nonstructural flat walls on ductile concrete buildings

Nonstructural reinforced concrete flat walls architecturally designed as exterior/partition walls in concrete buildings were severely damaged by the 2011 earthquake off the Pacific coast of Tohoku. This damage was observed in the monolithic nonstructural flat walls of relatively old ductile concrete buildings. Although these flat walls might affect the overall seismic performance and behavior of a building, the nonstructural wall effects have not been clarified because of the complex interactions among the structural components. To understand these effects, this paper conducts an experimental and numerical investigation of the nonstructural wall effects, focusing on a typical residential building damaged by the 2011 earthquake. A single‐story, one‐bay moment‐resisting frame model of the building with a nonstructural flat wall was tested to clarify the fundamental behavior. The results reveal that the wall significantly contributed to the seismic performance of the overall frame until it failed in shear, subsequently losing structural effectiveness. Such experimental wall behavior could be simulated by the isoparametric element model. Moreover, the structural effects of the nonstructural flat walls on the global seismic performance and behavior of the investigated building were discussed through earthquake response analyses using ground motions recorded near the building site and pushover analyses. Consequently, the building damage could be simulated in an analytical case considering the nonstructural flat walls, showing larger inter‐story drifts in the lower stories due to softening of the walls. The analytical results also indicated that the softening of the nonstructural flat walls decreased the building ductility, as defined by ultimate inter‐story drifts. Copyright © 2017 John Wiley & Sons, Ltd.     

Coupled shear‐bending formulation for seismic analysis of stacked wood shear wall systems

A summary of the development of a new coupled shear‐bending model for analysis of stacked wood shear walls and multi‐story wood‐frame buildings is presented in this paper. The model focuses on dynamic response of light‐frame wood structures under seismic excitation. The formulation is intended to provide a more versatile option than present pure shear models in that the new model is capable of accurately capturing the overall lateral response of each story diaphragm and separates the inter‐story shear deformation and the deformation associated with rotation of the diaphragm due to rod elongation, which is an analogue to the bending deformation in an Euler–Bernoulli beam model. Modeling the coupling of bending and shear deformation is shown to provide more accurate representation of stacked shear wall system behavior than a pure shear model, particularly for the upper stories in the assembly. The formulation is coupled with the newly developed evolutionary parameter hysteretic model for wood shear walls. Existing data from a shake table test of an isolated three‐story wood shear wall were used to verify the accuracy of the model prediction. The numerical results agreed very well with shake table test measurements. The influence of a continuous rod hold‐down system on the dynamic behavior of the three‐story stacked wood shear wall was also successfully simulated. Copyright © 2009 John Wiley & Sons, Ltd.     

Seismic response of three‐dimensional r/c multi‐storey frame building under uni‐ and bi‐directional input ground motion

This paper deals with seismic analysis of plan‐asymmetric r/c frame multi‐storey buildings. Non‐linear numerical analyses are carried out by using a lumped plasticity model for beams and a multi‐spring model for columns, the latter one introduced to account for axial force–biaxial bending moment interaction. A comparison between numerical analyses and experimental test results is reported in order to calibrate the numerical model, showing that the adopted model is very suitable. In order to study the effects of the earthquake orthogonal component, the seismic response of the modelled structure under uni‐directional excitation is compared to the one under bi‐directional excitation. Such comparison shows that the maximum base shear and the top displacement are not very sensitive to the presence of the orthogonal component, which, conversely, leads to large increase in the column plastic excursions. Copyright © 2007 John Wiley & Sons, Ltd.     

Seismic performance of masonry walls retrofitted with steel reinforced grout

An innovative solution for the seismic protection of existing masonry structures is proposed and investigated through shake table tests on a natural scale wall assemblage. After a former test series carried out without reinforcement, the specimen was retrofitted using Steel Reinforced Grout. The strengthening system comprises horizontal strips of ultra‐high strength steel cords, externally bonded to the masonry with hydraulic lime mortar, and connectors to transversal walls, applied within the thickness of the plaster layer. In order to assess the seismic performance of the retrofitted wall, natural accelerograms were applied with increasing intensity up to failure. Test results provide a deep understanding of the effectiveness of mortar‐based composites for improving the out‐of‐plane seismic capacity of masonry walls, in comparison with traditional reinforcements with steel tie‐bars. The structural implications of the proposed solution in terms of dynamic properties and damage development under earthquake loads are also discussed.Copyright © 2015 John Wiley & Sons, Ltd.     

Numerically based proposals for the stiffness and strength of masonry infills with openings in reinforced concrete frames

Aimed at investigating the effect of openings on the in‐plane behaviour of masonry infills in reinforced concrete frames, a parametric study is presented based on model calibration via experimental tests. Two types of openings are investigated: central window openings and different combinations of door and window openings based on the typologies of southern European countries. First, a finite element model of the structure is made using the DIANA software program. Then, after calibration with experimental results, a parametric analysis is carried out to investigate the effect of the presence and location of the different types of openings on the in‐plane behaviour of the infilled frame. Finally, different equations for predicting the initial stiffness and lateral strength of infilled frames with any types of openings were obtained. An α factor related to the geometry of the piers between openings is proposed to take into account the location of the openings in the developed equations. Subsequently, the masonry infill panel is replaced by a diagonal strut. An empirical equation is also proposed for the width of an equivalent strut to replace a masonry infill panel with openings in such a way that they possess the same initial stiffness. Copyright © 2015 John Wiley & Sons, Ltd.     

In‐plane quasi‐static cyclic tests of nonstructural lightweight steel drywall partitions for seismic performance evaluation

An experimental program was performed for evaluating the seismic response and fragilities of nonstructural lightweight steel drywall partitions, also considering the interaction with structural elements and other nonstructural building components, ie, outdoor façade walls. Therefore, in‐plane quasi‐static reversed cyclic tests were carried out on 8 specimens of indoor partition walls infilled in a frame and on 4 specimens of indoor partition walls connected at its ends with transversal outdoor façade walls. Constructive parameters under investigation include type of connections used for connecting the indoor partition walls to the surrounding elements, stud spacing, type of sheathing panels, and type of jointing finishing. The effect of the constructive parameters on the lateral response in secant stiffness and strength is examined. Furthermore, the main damage phenomena observed during the tests are reported and associated to 3 damage limit states distinguished for the required repair level for the tested partition walls. Fragility curves are used for the experimental assessment of seismic fragility of the tested specimens, in accordance with the interstorey drift limits required by the European code. Finally, the quantitative estimation of the repair action costs starting from the damage observation is also developed. The obtained results could be considered a starting point for developing the in‐plane seismic design assisted by testing of lightweight steel drywall partition walls.