Review of strength models for masonry spandrels

Many older unreinforced masonry (URM) buildings feature timber floors and solid brick masonry. Simple equivalent frame models can help predicting the expected failure mechanism and estimating the strength of a URM wall. When modelling a URM wall with an equivalent frame model rather than, for example, a more detailed simplified micro-model, the strengths of the piers and spandrels need to be estimated from mechanical or empirical models. Such models are readily available for URM piers, which have been tested in many different configurations. On the contrary, only few models for spandrel strength have been developed. This paper reviews these models, discusses their merits, faults and compares the predicted strength values to the results of recent experimental tests on masonry spandrels. Based on this assessment, the paper outlines recommendations for a new set of strength equations for masonry spandrels.     

Observed failure modes of unreinforced masonry buildings during the 2015 Hindu Kush earthquake

On 26 th October 2015, an Mw 7.5 earthquake struck northern Pakistan, with its epicenter located 45 km southwest of Jarm in the Hindu Kush region of Afghanistan. The earthquake resulted from reverse faulting at a depth of 210 km, resulting in 280 fatalities and substantial damage to some 109,123 buildings. Regional seismicity, characteristics of recorded strong motions, damage statistics, and building performance observations are presented. Earthquake damage was mostly constrained to seismic-deficient unreinforced masonry(URM) buildings. Typical failure modes included toppled minarets, partial or complete out of plane collapse of URM walls, diagonal shear cracking in piers, flexural cracking in spandrels, corner damage, pounding damage, and damage due to ground settlement. The majority of human loss resulted due to failure of URM walls and subsequent roof collapse. URM buildings located in rural hilly areas closer to the epicenter suffered more intense and frequent damage than urban URM buildings located farther away in larger cities.     

Nonlinear analysis of masonry structures using fiber-section line elements

For seismic analysis of unreinforced masonry (URM) buildings characterized by a box-like behavior, a widely accepted model is based on the equivalent frame idealization of walls. The equivalent frame model uses 1D elements to represent the vertical piers and horizontal spandrels which are connected by rigid nodes. The mechanical characterization of the elements is one of the crucial aspects to predict reasonably the building seismic behavior. Through the comparison with pseudo-static and dynamic experimental tests performed on two-story full-scale buildings, this paper validates the frame modeling in the OpenSees framework, which includes a fiber-section force-based beam element for the axial-flexural behavior, coupled with a cyclic shear-deformation phenomenological law.     

A macro‐model with nonlinear springs for seismic analysis of URM buildings

Seismic assessment of existing unreinforced masonry buildings represents a current challenge in structural engineering. Many historical masonry buildings in earthquake regions were not designed to withstand seismic loading; thus, these structures often do not meet the basic safety requirements recommended by current seismic codes and need to be strengthened considering the results from realistic structural analysis. This paper presents an efficient modelling strategy for representing the nonlinear response of unreinforced masonry components under in‐plane cyclic loading, which can be used for practical and accurate seismic assessment of masonry buildings. According to the proposed strategy, generic masonry perforated walls are modelled using an equivalent frame approach, where each masonry component is described utilising multi‐spring nonlinear elements connected by rigid links. When modelling piers and spandrels, nonlinear springs are placed at the two ends of the masonry element for describing the flexural behaviour and in the middle for representing the response in shear. Specific hysteretic rules allowing for degradation of stiffness and strength are then used for modelling the member response under cyclic loading. The accuracy and the significant potential of the proposed modelling approach are shown in several numerical examples, including comparisons against experimental results and the nonlinear dynamic analysis of a building structure. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic behaviour of masonry buildings built of low compressive strength units

Seismic behaviour of masonry buildings, built of low compressive strength units, is discussed. Although such materials have already been tested and approved for use from mechanical and thermal insulation point of view, the knowledge regarding their structural behaviour is still lacking. In order to investigate the resistance and deformation capacity of this particular type of masonry construction in seismic conditions, a series of eight walls and model of a two-storey full scale confined masonry building have been tested by subjecting the specimens to cyclic shear loads. All tests were conducted under a combination of constant vertical load and quasi static, cyclically imposed horizontal load. The behaviour of tested specimens was of typical shear type. Compared with the behaviour of plain masonry walls, the presence of tie-columns resulted into higher resistance and displacement capacity, as well as smaller lateral resistance degradation. The response of the model was determined by storey mechanism with predominant shear behaviour of the walls and failure mechanism of the same type as in the case of individual confined masonry walls. Adequate seismic behaviour of this particular masonry structural type can be expected under the condition that the buildings are built as confined masonry system with limited number of stories.     

The effective stiffness of modern unreinforced masonry walls

Code design of unreinforced masonry (URM) buildings is based on elastic analysis, which requires as input parameter the effective stiffness of URM walls. Eurocode estimates the effective stiffness as 50% of the gross sectional elastic stiffness, but comparisons with experimental results have shown that this may not yield accurate predictions. In this paper, 79 shear‐compression tests of modern URM walls of different masonry typologies from the literature are investigated. It shows that both the initial and the effective stiffness increase with increasing axial load ratio and that the effective‐to‐initial stiffness ratios are approximately 75% rather than the stipulated 50%. An empirical relationship that estimates the E‐modulus as a function of the axial load and the masonry compressive strength is proposed, yielding better estimates of the elastic modulus than the provision in Eurocode 6, which calculates the E‐modulus as a multiple of the compressive strength. For computing the ratio of the effective to initial stiffness, a mechanics‐based formulation is built on a recently developed analytical model for the force‐displacement response of URM walls. The model attributes the loss in stiffness to diagonal cracking and brick crushing, both of which are taken into account using mechanical considerations. The obtained results of the effective‐to‐initial stiffness ratio agree well with the test data. A sensitivity analysis using the validated model shows that the ratio of effective‐to‐initial stiffness is for most axial load ratios and wall geometries around 75%. Therefore, a modification of the fixed ratio of effective‐to‐initial stiffness from 50% to 75% is suggested.     

Distinct element modelling of the in-plane cyclic response of URM walls subjected to shear-compression

The in-plane capacity of unreinforced masonry (URM) elements may vary considerably depending on several factors, including boundary conditions, aspect ratio, vertical overburden, and masonry texture. Since the overall system resistance mainly relies on the in-plane lateral capacity of URM components when out-of-plane modes are adequately prevented, the structural assessment of URM structures could benefit from advanced numerical approaches able to account for these factors simultaneously. This paper aims at enhancing and optimising the employment of the distinct element method, currently confined to the analysis of local mechanisms of reduced-scale dry-joint blocky assemblies, with a view to simulate the experimentally observed responses of a series of URM full-scale specimens with mortared joints subjected to quasi-static in-plane cyclic loading. To this end, a mesoscale modelling approach is proposed that employs a simplified microscale modelling approach to effectively capture macroscale behaviour. Dynamic relaxation schemes are employed, in combination with time, size, and mass-scaling procedures, to decrease computational demand. A new methodology for numerically describing both unit, mortar and hybrid failure modes, also including masonry crushing due to high-compression stresses, is proposed. Empirical and homogenisation formulae for inferring the elastic properties of interface between elements are also verified, enabling the proposed approach to be applied more broadly. Using this modelling strategy, the interaction between stiffness degradation and energy dissipation rate was accounted for numerically. Although the models marginally underestimate the energy dissipation in the case of slender piers, a good agreement was obtained in terms of lateral strength, hysteretic response, and crack pattern.     

Shake‐table experiment on reinforced concrete structure containing masonry infill wall

A hypothetical 5‐storey prototype structure with reinforced concrete (RC) frame and unreinforced masonry (URM) wall is considered. The paper focuses on a shake‐table experiment conducted on a substructure of this prototype consisting of the middle bays of its first storey. A test structure is constructed to represent the selected substructure and the relationship between demand parameters of the test structure and those of the prototype structure is established using computational modelling. The dynamic properties of the test structure are determined using a number of preliminary tests before performing the shake‐table experiments. Based on these tests and results obtained from computational modelling of the test structure, the test ground motions and the sequence of shakings are determined. The results of the shake‐table tests in terms of the global and local responses and the effects of the URM infill wall on the structural behaviour and the dynamic properties of the RC test structure are presented. Finally, the test results are compared to analytical ones obtained from further computational modelling of the test structure subjected to the measured shake‐table accelerations. Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic behavior and strength capacity of steel tube‐reinforced concrete composite columns

The steel tube‐reinforced concrete (ST‐RC) composite column is a novel type of composite column, which consists of a steel tube embedded in RC. In this paper, the seismic behavior of ST‐RC columns is examined through a series of experiments in which 10 one‐third scale column specimens were subjected to axial forces and lateral cyclic loading. The test variables include the axial force ratio applied to the columns and the amount of transverse reinforcement. All specimens failed in a flexural mode, showing stable hysteresis loops. Thanks to the steel tube and the high‐strength concrete it is filled with, the ST‐RC column specimens had approximately 30% lower axial force ratios and 22% higher maximum bending moments relative to the comparable RC columns when subjected to identical axial compressive loads. The amount of transverse reinforcement made only a small difference to the lateral load‐carrying capacity but significantly affected the deformation and energy dissipation capacity of the ST‐RC columns. The specimens that satisfied the requirements for transverse reinforcement adopted for medium ductile RC columns as specified by the Chinese Code for Seismic Design of Buildings (GB 50011‐2010) and EuroCode 8 achieved an ultimate drift ratio of around 0.03 and a displacement ductility ratio of approximately 5. The design formulas used to evaluate the strength capacity of the ST‐RC columns were developed on the basis of the superposition method. The predictions from the formulas showed good agreement with the test results, with errors no greater than 10%. Copyright © 2013 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.     

Seismic capacity of irregular unreinforced masonry walls with openings

Masonry buildings are often characterized by geometric irregularities. In many cases, such buildings meet global regularity requirements provided by seismic codes, but they are composed by irregular walls with openings. The latter are masonry walls characterized by (i) openings of different sizes, (ii) openings misaligned in the horizontal and/or vertical direction, or (iii) a variable number of openings per story. An irregular layout of openings can induce not only a nonuniform distribution of gravity loads among masonry piers but also unfavorable damage localizations resulting in a premature collapse of the wall and hence a higher seismic vulnerability. This paper is aimed at providing a simplified methodology to assess the effects of irregularities on the in‐plane seismic capacity of unreinforced masonry (URM) walls with openings. To this end, a macroelement method was developed and validated through experimental results available in the literature. The proposed methodology was based on the quantification of wall irregularities by means of geometric indices and their effects on seismic capacity of URM walls with openings through both sensitivity and regression analyses. Sensitivity analysis was based on a high number of static pushover analyses and allowed to assess variations in key seismic capacity parameters. Regression analysis let to describe each capacity parameter under varying irregularity index, providing empirical models for seismic assessment of irregular URM walls with openings. The in‐plane seismic capacity was found to be significantly affected by wall irregularities, especially in the case of openings with different heights. Copyright © 2012 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.     

Force–displacement response of in‐plane‐loaded URM walls with a dominating flexural mode

This article presents a new mechanical model for the non‐linear force–displacement response of unreinforced masonry (URM) walls developing a flexural rocking mode including their displacement capacity. The model is based on the plane‐section hypothesis and a constitutive law for the masonry with zero tensile strength and linear elastic behaviour in compression. It is assumed that only the compressed part of the wall contributes to the stiffness of the wall and therefore the model accounts for a softening of the response due the reduction of the effective area. Stress conditions for limit states are proposed that characterise the flexural failure. The new model allows therefore linking local performance levels to global displacement capacities. The limit states criteria describe the behaviour of modern URM walls with cement mortar of normal thickness and clay bricks. The model is validated through comparison of local and global engineering demand parameters with experimental results. It provides good prediction of the effective stiffness, the force capacity and the displacement capacity of URM walls at different limit states. Copyright © 2015 John Wiley & Sons, Ltd.     

Masonry infill walls in reinforced concrete frames as a source of structural damping

This paper presents the results of an experimental study on the determination of damping characteristics of bare, masonry infilled, and carbon fiber reinforced polymer retrofitted infilled reinforced concrete (RC) frames. It is well known that the masonry infills are used as partitioning walls having significant effect on the damping characteristics of structures as well as contribution to the lateral stiffness and strength. The main portion of the input energy imparted to the structure during earthquakes is dissipated through hysteretic and damping energies. The equivalent damping definition is used to reflect various damping mechanisms globally. In this study, the equivalent damping ratio of carbon fiber reinforced polymer retrofitted infilled RC systems is quantified through a series of 1/3‐scaled, one‐bay, one‐story frames. Quasi‐static tests are carried out on eight specimens with two different loading patterns: one‐cycled and three‐cycled displacement histories and the pseudo‐dynamic tests performed on eight specimens for selected acceleration record scaled at three different PGA levels with two inertia mass conditions. The results of the experimental studies are evaluated in two phases: (i) equivalent damping is determined for experimentally obtained cycles from quasi‐static and pseudo‐dynamic tests; and (ii) an iterative procedure is developed on the basis of the energy balance formulation to determine the equivalent damping ratio. On the basis of the results of these evaluations, equivalent damping of levels of 5%, 12%, and 14% can be used for bare, infilled, and retrofitted infilled RC frames, respectively. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimation of load reduction factors for clay masonry walls

The in‐plane cyclic behaviour of three types of unreinforced clay masonry was characterized by means of laboratory tests on full‐scale specimens. The masonry walls were assembled with various bonding arrangements (head joints made with mortar pockets, dry head joints with mechanical interlocking, thin‐layer mortar bed joints), which are not yet inserted in seismic codes. Experimental behaviour was modelled with an analytical hysteretic model able to predict lateral load–displacement curves in case of shear failure of the unreinforced walls. According to the experimental results and those of the selected analytical model, parametric study to evaluate the reduction in lateral strength demand produced by non‐linear behaviour in masonry walls, i.e. the load reduction factor was carried out by non‐linear dynamic analyses. The calculated values of the load reduction factor were modest. The differences in values found for the three masonry types, although consistent with them, were not great. This may indicate that, in the ultimate limit state, the type of masonry cannot significantly affect the behaviour of an entire building. Copyright © 2009 John Wiley & Sons, Ltd.     

Simplified macro‐model for infill masonry walls considering the out‐of‐plane behaviour

One of the main challenges in earthquake risk mitigation is the assessment of existing buildings not designed according to modern codes and the development of effective techniques to strengthen these structures. Particular attention should be given to RC frame structures with masonry infill panels, as demonstrated by their poor performance in recent earthquakes in Europe. Understanding the seismic behaviour of masonry‐infilled RC frames presents one of the most difficult problems in structural engineering. Analytical tools to evaluate infill–frame interaction and the failure mechanisms need to be further studied. This research intends to develop a simplified macro‐model that takes into account the out‐of‐plane behaviour of the infill panels and the corresponding in‐plane and out‐of‐plane interaction when subjected to seismic loadings. Finally, a vulnerability assessment of an RC building will be performed in order to evaluate the influence of the out‐of‐plane consideration in the building response. 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.     

Application of an in-plane/out-of-plane interaction model for URM infill walls to dynamic seismic analysis of RC frame buildings

Experimental tests have shown that unreinforced masonry (URM) infill walls are affected by simultaneous loading in their in-plane and out-of-plane directions, but there have been few attempts to represent this interaction in nonlinear time history analysis of reinforced concrete (RC) buildings with URM infill walls. In this paper, a recently proposed macro-model that accounts for this interaction is applied to the seismic analysis of RC framed structures with URM infill walls representative of Mediterranean building stock and practices. Two RC framed structures that are representative of low and mid-rise residential buildings are analysed with a suite of a bidirectional ground motions, scaled to three different intensities. During the analyses, the in-plane/out-of-plane interaction is monitored, showing that cracking of the infills occurs predominantly by in-plane actions, while failure occurs due to a combination of in-plane and out-of-plane displacements, with the out-of-plane component usually playing the dominant role. Along the frame height, the bottom storeys are generally the most damaged, especially where thin infill walls are used. These results are consistent with observations of damage to URM infill walls in similar buildings during recent earthquakes.     

In situ cyclic tests on existing stone masonry walls and strengthening solutions

The present work reports on an in situ experimental test campaign carried out on abandoned traditional masonry houses after the 9th July 1998 earthquake that seriously hit the Faial island of Azores. For the testing purposes, an experimental test setup was developed based on a self‐equilibrated scheme, which is herein described reporting on the advantages and drawbacks of this in situ test setup. Five specimens were tested aiming at characterizing the out‐of‐plane behavior of stone masonry walls and strengthening solutions recommended for post‐earthquake interventions. A detailed comparison between solutions' efficiency is presented including a cost vs benefit analysis. In order to assess the efficiency of the developed test setup for other applications on stone masonry walls, an in‐plane test on an existing URM panel is also presented. Several related issues are discussed, namely the advantages of dealing with the real boundary conditions and the capacity of providing valuable information of the response, as well as a detailed analysis of the obtained results. The authors believe that this work provides an increase in knowledge on the seismic behavior of the existing masonry constructions, resulting from the development of an in situ test setup and the efficiency quantification of strengthening solutions. Therefore, the work is thought to positively contribute for the preservation of architectural heritage and for its seismic vulnerability reduction. Copyright © 2010 John Wiley & Sons, Ltd.     

基于等效框架模型的砌体结构抗震模拟及验证

等效框架模型采用宏观模型来模拟砌体墙在平面内的抗震性能。砌体墙的墙柱和墙梁采用同时考虑轴向弯曲和剪切变形的基于力法的纤维截面进行模拟,且两者的连接视为刚性区域。轴向压缩及弯曲效应在截面纤维模型中考虑,而剪切效应由V-γ剪切恢复力模型表达,弯曲和剪切在单元层面进行耦合。通过统计和分析,确定骨架曲线的计算方法,并基于Ibarra-Krawinkler模型提出剪切恢复力模型。通过算例得出:该模型在单调加载和循环加载下的数值计算结果与试验结果均吻合较好。