Effect of masonry joints on the behavior of infilled frames

Construction and Building Materials 189 (2018) 144–156

Contents lists available at ScienceDirect

Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Effect of masonry joints on the behavior of infilled frames Alex Brodsky a, Oded Rabinovitch b, David Z. Yankelevsky a,⇑ a b

Faculty of Civil and Environmental Engineering, Technion Israel Institute of Technology, Haifa 32000, Israel Abel Wolman Chair in Civil Engineering, Faculty of Civil and Environmental Engineering, Technion Israel Institute of Technology, Haifa 32000, Israel

h i g h l i g h t s
Failure of a supporting column triggering a progressive collapse is analyzed.
The effect of infill masonry wall interfaces on wall behavior is investigated.
Three large-scale identical walls with different joints’ properties are studied.
Joint properties strongly affect the ultimate load and the energy dissipation.
Contact zone size changes during loading and depends on joints characteristics.

a r t i c l e

i n f o

Article history: Received 29 April 2018 Received in revised form 27 August 2018 Accepted 30 August 2018

Keywords: Interaction Masonry infill wall Joint type Infilled frame structure Column loss Progressive collapse Experimental investigation Contact tractions Contact zone

a b s t r a c t The present paper investigates the behavior of masonry infill walls and the effect of the interfaces between the masonry wall units (joints), on the global behavior and on the local infill-frame interaction. The investigation focuses on the case of failure of a supporting column that may trigger a progressive collapse of the building. Experimental results of a new testing method are presented. The experimental technique enables analysis of the contact zone and the contact tractions, and their variations during the loading process. The purpose of this study is to explore and quantify the effect of the joints on the global and local behavior of the composite infill-frame structure. The study examines the contact zone between the infill wall and the frame and its variation with loading, and compares the new data with available expressions that are found in the literature. A comparative experimental study that includes three large-scale unreinforced masonry infill walls with identical geometry and identical Autoclaved Aerated Concrete (AAC) masonry units, but different joints’ properties is presented. The results show that the joint properties have a significant effect on the ultimate load, the initial stiffness and the energy dissipation with differences of about 50%, 85% and 70%, respectively. It is also shown that the length of the contact zone changes during loading in all three specimens and its size depends on the joints characteristics. The different contact lengths that are calculated by available simplified models are smaller than the experimentally measured contact region by more than 30%. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Masonry infill walls are commonly used in public and residential buildings around the world. In past design practices, the contribution of the infill walls to the structural system was commonly neglected. However, when the structure is exposed to extreme loads as in the cases of earthquake, blast, car collision etc., it develops large deformations and the infill walls interact with the structural skeleton and affect its response. The behavior of the infill wall depends on the geometry of the wall including the layout of the ⇑ Corresponding author. E-mail addresses: [email protected] (A. Brodsky), [email protected] (O. Rabinovitch), [email protected] (D.Z. Yankelevsky). https://doi.org/10.1016/j.conbuildmat.2018.08.209 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.

masonry units and their dimensions, the mechanical properties of the masonry units and the interfaces between the units (the joints), and the geometrical and mechanical properties of the surrounding frame. It also depends on the interaction between the frame and the infill wall. The characterization of the infill wall is commonly based on series of tests in which the stiffness, tensile strength, and compressive strength of the masonry units are determined, and friction coefficient as well as the shear, compressive and tensile strengths of the mortar-masonry unit interface are evaluated. The stiffness, compressive strength, and stress-strain relationship of the masonry units and mortar joints are usually assessed based on a masonry prism compressive test (e.g. [1]). Such mechanical properties tests are reported in many studies (e.g., [2–8]) and they

A. Brodsky et al. / Construction and Building Materials 189 (2018) 144–156

provide an inclusive assessment of the main masonry material. However, along with the assessment of the masonry material properties, the characterization of the involved interface is of major importance. The assessment of the interface properties is commonly conducted by relative normal and tangential displacement tests. The shear behavior that characterizes the commonly used mortar joints is assessed by direct shear tests or by testing triplets made of three masonry units connected by two joints [9–13]. The normal behavior is assessed by means of compressive and tensile tests (e.g. [14–16]). The aforementioned interface characterization tests naturally consider relatively small specimens that are composed of a small number of masonry units and mortar interfaces. The tests do not take into consideration the surrounding frame and particularly the interaction between that surrounding frame and the infill wall. This interaction is based on the contact regions between the infill wall and the frame and on the evolution of tractions along those contact regions. The formation of the contact regions directly affects the wall behavior, including its stiffness and load bearing capacity, which depend on the interaction. The complex behavior of the frame, the nonlinear behavior of the infill wall, and particularly, the nonlinear infill-frame interaction underline the complexity of the problem at hand and the need for experimental information regarding the contact phenomenon and its role in the infill wall’s response. Such information, which is essential for understanding the response of the structural system as well as its assessment using analytical or numerical tolls is still missing. A critical aspect of the infill-frame interaction comes into effect in the failure mechanism of the structural assembly. The combination of a relatively strong infill with a relatively weak of poorly detailed reinforce concrete (RC) frame may lead to failure of the latter. Column failures have been widely observed in RC structures subjected to recent earthquakes in L’Aquila and Lorca reported by Verderame et al. [17] and Hermanns et al. [18]. The frame failure mechanism may become even more dominant when the RC infilled frame is subjected to relative vertical deformation. This observation has been investigated and highlighted by Brodsky and Yankelevsky [19] where the response of infilled RC frame to loss of a supporting column was investigated. The experimental investigation in [19] shows that the RC frame failure may determine the overall resistance of the infilled frame. In addition, it points at the relationship between the failure characteristics and the interaction effects along the infill-column interface. These observations, as well as the ones made in Brodsky et al. [20,21], where the interaction with a sensory surrounding frame made of hinged steel frame, further emphasizes the importance of the contact effects and the interfacial tractions that develop between the infill wall and the surrounding frame. Naturally, the evolution of the interfacial tractions and the critical role they play draw the attention to the question of the impact of the masonry material as a whole and the properties of the individual masonry units and the interfaces in between them on the interaction phenomena. This question is in the focus of the present paper. In general, it is claimed that the strengths of the joints and the masonry units govern the cracking pattern of the infill wall. These parameters affect the response of the wall, dictate the interfacial behavior, govern the internal forces that develop along the frame elements, and influence the failure mechanism of the assembled wall. There is a broad spectrum of possible infill walls configurations, which differ in parameters such as the geometrical dimensions, the wall layout, type of masonry units, type of joints between the masonry units, properties of the joints, frame characteristics etc. The large number of possible combinations of different wall characteristics makes it difficult to determine the infill wall behavior and to come up with general concepts. Even for specific geometry, a given frame, and a well-defined type of

145

masonry units there may be different layouts of joints. Within each layout, there may be different types of joints and different joint materials. The combined effect of the joints’ layout and the joint properties plays a major role on the infill cracking and resistance. Commonly the wall construction is based on staggered laying a block on two blocks underneath, where its vertical centerline is aligned with the vertical joint between the blocks below. With about the same layout, these are the mechanical characteristics of the joint that are the key parameter that governs the behavior of a wall, and specifically the infill-frame interaction. The effect of different masonry joints on the response to diagonal and vertical loadings has been widely investigated in the context of masonry walls without a confining frame (e.g. [22–24]). These studies showed that different joint parameters and particularly different mortar materials affect the masonry compressive strength. Sarangapani et al. [2] examined the brick-mortar bond effect on the masonry compressive strength. Four different mortars were examined consisting of different ratios of cement, sand, lime and soil (sand, silt and clay fractions). They found that an increase in bond strength, while keeping the mortar strength constant, leads to compressive strength increase of the masonry assembly. Alecci et al. [25] studied the effect of three different mortars (lime, cement and cement-lime based) on the shear strength of the masonry panel using a diagonal loading test. This study found that the mortar significantly affects the panel shear strength and the failure mode of the panel. Specimens with relatively lower mortar strength (the lime and the cement-lime based mortars) cracked along a non-diagonal direction (a step crack) while the crack in the cement based mortar specimen developed along the loaded diagonal. Zahra and Dhanasekar [26] summarized the effects of the mortar properties based on the different experimental results taken from the literature. This include the mortar compressive strength (see [27–29]), the joint thickness, and the ratio between the joint thickness and the height of the masonry units [30]. Accordingly, the European Standard EN 1996-1-1 [31] defines the characteristic compressive strength of masonry, f k , is expressed as function of the masonry unit’s and mortar’s strengths: a b

f k ¼ Kf b f m

ð1Þ

where K, a, and b are constants, f b is the mean masonry units compressive strength and f m is the mortar compressive strength. However, for AAC units, the compressive strength depends on the masonry unit strength only and therefore b = 0 according to 3.6.1.2(2). Despite the spectrum of studies on masonry without a confining frame, the effect of different mortar properties on the infilled frame behavior received considerably less attention. One of the few studies that addressed this question was presented by Gazic and Sigmund [32]. This investigation experimentally examined the effect of two different mortar types (made of lime and cement-lime) on the behavior of RC infilled frames during lateral cyclic loading. In both tests, hollow clay masonry units were used. It was found that the mortar type affects the strength, the energy dissipation capacity, and the mode of damage of the infilled frame. Sevil et al. [33] tested two stories infilled frames under reversed cyclic lateral loading with two different mortar mixtures, with and without steel fibers. It was found that the reinforced mortar dramatically changes the global load-displacement behavior. No further information is available on that aspect and the effect of different mortar properties on the infilled frame behavior remains an open question. This refers to the global (force-displacement) behavior of the infilled frame. With regard to the evolution of the contact effects between the infill and the frame no earlier works were found. Opposed to the case of lateral loading, which has gained

146

A. Brodsky et al. / Construction and Building Materials 189 (2018) 144–156

considerable attention, the critically important case of loss of a supporting column has gained considerably less attention. In light of the above knowledge gap, the objectives of this paper are twofold. First, it aims at exploring the effect of the joint bond material (mortar, adhesive, or none) on the physical behavior of the infill-frame structure. This behavior refers to a range of aspects, including the global load–displacement curve, the initial stiffness, the point of transition into the inelastic regime, the cracking pattern, the ultimate load, and the ultimate resisting mechanism. Along with those global aspects, the effect of the masonry joints on the local infill-frame contact interaction, the contact regions, the contact tractions and their evolution along the loading path are also looked at. The second goal of this study is to further look into the effect of the masonry joints with reference to design standards such as ASCE/SEI 41 [34] and FEMA 306 [35]. Those standards adopt the idea of replacing the infill wall with a single off-diagonal strut as means to assess the tractions in the frame elements. The compression strut concept is based on predefined points of contact that do not change during loading. More advanced strut models include several diagonal and off-diagonal struts see, for example, Chrysostomou et al. [36], El-Dakhakhni et al. [37], Farazman et al. [38] and Jeon and Park [39]. The locations of these struts are based on the estimated length of the contact region between the infill wall and the frame obtained by simplified analytical methods. In the context of such approaches, which are given in detail in Saneinejad and Hobbs [40], ASCE/SEI 41 [34] and Anderson and Brzev [41], the paper examines the size of the contact region and its location that is proposed in these models with the experimentally measured contact region size in the present research. The main methodology adopted for the investigation herein is a comparative experimental study. The responses of three walls with similar geometry and masonry units, placed in an identical frame and subjected to the same loading and supporting conditions but differ in the joints’ properties are compared. In all tests, the walls are subjected to a loading scenario that simulates the event of gradual (quasi-static) loss of a supporting column. This is achieved using the experimental setup and monitoring concept developed in Brodsky et al. [20] for the investigation of the monotonic response of such infilled frames and in Brodsky et al. [21] for its comparison with cyclic loading. More details about the setup that uses a stiff and strong hinged steel frame, which does not yield and hardly deforms during the experiment, are given there. The ability to

re-use the setup with different combinations of infill layout and materials supports the comparative study and allows to focus on the role of the masonry joints in the structural behavior. The remainder of this paper is organized as follows: The test setup and its instrumentation are outlined in Section 2. The material properties of the blocks, the properties of the three investigated joint configurations, and the wall’s construction method are described in Section 3. The test results and their discussion appear in Section 4 with emphasis on the effect of the joints on the load=displacement curves, cracking patterns, initial stiffness, ultimate load, energy dissipation, the evolution of force resultants and contact regions, and the evolution of contact tractions. The concluding remarks are presented in Section 5.

2. Test setup The test setup developed in Brodsky et al. [20] is illustrated in Fig. 1. The setup was designed in order to detect the global and local response of infill masonry walls in the scenario of loss of a supporting column. Emphasis is directed to the interaction between the infill and the frame. The loading scenario includes the removal of one of the supporting columns and then enforcing a prescribed displacement using a hydraulic jack that is located on top of that column (Fig. 1). The monitoring devices used in the experiments include a load cell, a LVDT, a position transducer, and a series of strain gauges. The surrounding frame serves as part of the tested specimen and, at the same time, as a sensory device. For that purpose, it is equipped with 126 strain gauges and rosettes mounted on the beams and the columns. The strain records enable to calculate the neutral axis location, the shear angle and the curvature. Then, by means of data-reduction tools the axial force, the shear force and the bending moment distributions along the frame’s elements may be calculated (see Appendix A – Force resultants and [20] for more details). This data is then used to assess the interaction forces and the contact regions at the infill-frame interfaces. To simplify the translation of the strain records to the above-mentioned resultants and, in turn, to the interfacial tractions, the frame was designed to respond in the elastic range and to eliminate the contribution of the frame action through moment resisting beam-column joints. Following these concepts, a steel frame with hinge joints was designed and built. An additional advantage of the elastic and hinged layout of the frame is the ability to reuse the surrounding steel frame

Fig. 1. Test setup.

A. Brodsky et al. / Construction and Building Materials 189 (2018) 144–156

with different infill materials. This allows testing and comparing different joint layouts or materials, which are in focus of the present investigation, with a high level of repeatability of all other aspects of the experiment. More details about the test setup, the monitoring system, and the data reduction methodology are given in Appendix Aand in Brodsky et al. [20]. 3. Material properties and wall construction 3.1. General The comparative investigation looks at three large-scale tests of masonry infill walls (1400 mm by 2045 mm) made of Autoclaved Aerated Concrete (AAC) blocks and three different joint types: (a) cement-based mortar joints, (b) dedicated AAC masonry adhesive joints and (c) dry joints, i.e. without any adhesive or mortar. The thickness of the head and bed joints was modified accordingly with 10 mm in joint type (a), 5 mm in type (b), and 0 mm in type (c). All other parameters including the type of blocks, their layout, the location of the head and the bed joints, the surrounding frame and the boundary/loading conditions were identical in all three tests. Cement-based (joint type a) represents the traditional joining material. Masonry adhesive (joint type b) is a rather modern form of masonry joining material that has gained relatively less attention compared with the cement-based mortar (joint type a) despite its expanding use, especially in AAC infills. The third alternative in the comparative study, the dry joints (joint type c), aims to eliminate the interface mechanical properties of the mortar/adhesive (stiffness, tensile behavior/strength, shear behavior/strength etc.) and examine the resistance that only depends on the dry contact and friction between AAC blocks and between the AAC blocks and the frame. 3.2. AAC blocks The AAC blocks are 250 mm wide, 100 mm thick and 150 mm high. The compressive strength of the AAC block was determined by uniaxial tests on a single block on its 250x100mm2 face. This uniaxial compressive strength equals to 3:1 MPa. 3.3. Head and bed joints In each configuration, the head and the bed joints were made of the same material and thickness. The mix proportion (in volume) of cement: lime: sand that was used for the cement-based mortar (type a) is 2:1:3. The relatively high content of cement in this mixture aimed at achieving relatively high compressive and tensile strengths with improved adhesion. The AAC ready-made adhesive composition (type b) is a C2T improved cementitious adhesive with reduced slip (<0.5 mm) according to the classification of the relevant standard [42]. This adhesive was provided by the AAC blocks manufacturer. The compressive and the flexural strengths of the mortar and the adhesive were obtained according to the European Standard EN 1015-11 [43]; 40x40x40 mm3 cubes were tested for the compression strength evaluation and 40x40x160 mm3 prisms for the flexural strength. The results are listed in Table 1.

Table 1 Properties of the joints. Joint type

Thickness [mm]

Mean compressive strength [MPa]

Mean flexural strength [MPa]

(a) Cement-based mortar (b) Adhesive

10

17.70

4.09

5

4.60

0.81

147

3.4. Wall construction During the construction process of a wall, the loaded column was supported in the vertical direction. Attention was given to ensure full and continuous contact of the infill wall with the surrounding frame. The height of the last masonry course was fitted to meet the wall’s height, which is 1400 mm in all three tests. In the construction of the last masonry course of infill walls with cement-based mortar and masonry adhesive, the upper beam was lifted up to allow mortar or adhesive application on the upper face of the top course. Then the beam was lowered down to its location and connected to the frame. This procedure assures full contact along all four frame-wall interfaces.

4. Results and discussion 4.1. Load-displacement response The experimental results in terms of the load-displacement relationships of the three tests appear in Fig. 2. The main events that occurred throughout each of the tests are discussed in the following.

4.1.1. Infill masonry wall with cement-based joints The first cracking of the infill wall was observed at a displacement of about 5 mm (point A in Fig. 2). That led to a sudden increase of the vertical displacement. Then, as the loading process continued, additional infill diagonal cracks and horizontal cracks developed along the bed joints. A detailed discussion of the cracking pattern appears in Section 4.2 but it is noted that the formation of these cracks gradually decreased the stiffness of the specimen. The experiment was terminated at the maximal actuator stroke of about 110 mm, which corresponds to a vertical drift (the vertical displacement over the beam’s length) of about 5.4%. At this large drift, the infill wall accumulated significant damage.

4.1.2. Infill masonry wall with adhesive joints Following an initial linear response, the first event was detected at a displacement of about 9 mm (point B in Fig. 2) where the vertical displacement suddenly increased by 1.0 mm with no change to the measured vertical load. After this event, the stiffness slightly decreased. The event designated by point B was not associated with any observable damage and it is attributed to sliding of the infill wall and changes to the contact zones with the frame. The first cracking of the infill wall occurred at point C designating a second global event, which is probably the most significant one. This cracking event occurred at a vertical load of about 39 kN and a displacement of 28 mm. A decrease in resistance to about 33 kN occurred right after the crack opening. Afterwards, additional infill cracking occurred at a displacement of 42 mm. Following those two events, the growth of the vertical displacement was quite stable, and the resistance remained rather constant over a considerably large range of displacements. The test was terminated when the maximum actuator stroke was reached, similarly to the first test. The behavior of this specimen may be divided into two main stages. The first stage is characterized by a linear loaddisplacement behavior as long as the infill is uncracked. After the formation of the major crack that divides the solid panel into two major sub-elements, a new resistance mechanism is developed. The two sub-elements are interacting along the common crack, thus developing a constant resistance at larger displacements.

148

A. Brodsky et al. / Construction and Building Materials 189 (2018) 144–156

Fig. 2. Load-displacement curves.

4.1.3. Infill masonry wall with dry joints The load-displacement pattern observed with the dry joints is fundamentally different from the other two cases. At the early stages of the test, sliding of the blocks along the bed joints and openings of the head joints occurred. The wall resistance increased almost linearly along the entire displacement range, compared to a roughly bi-linear load-displacement behavior that may characterize the previous two tests. In the progressive stages of this experiment, the AAC blocks started to spall off and diagonal cracks were observed in some of the blocks. The experiment was terminated at the same vertical displacement (110 mm) as the previous two. The load level detected here under this displacement is similar to the one measured in the wall with the adhesive based joints, (type b) and it is a about half of the one observed in the wall with the cement-based mortar joints (type a). The comparative observations on the three load-displacement responses underline that while all three infill walls are made of the same blocks and share identical geometry and loading, the behaviors are much different in terms of the initial stiffness, the energy dissipation, the ultimate load, and the displacement at any load level. These differences are solely attributed to the difference in the joints’ properties. 4.2. Cracking pattern Prior to testing, the infill wall surface had been whitewashed to provide better contrasting background to identify cracks. Fig. 3 shows a general view of the three damaged walls and illustrations of the cracking patterns for each wall at its final state. The figure reveals three completely different cracking patterns. In the cement-based specimen (type a), the loading process was involved with the development of many cracks. Most of them are horizontal cracks along the bed joints or diagonal cracks that cross the blocks and the head joints. Opposed to that, the infill wall with the adhesive joints behaves as a solid uncracked panel with no joints. Cracks along the head or the bed joints were not detected up to the stage where a horizontal-diagonal infill cracking occurred (point C) and separated the infill wall into two distinct parts. The second infill cracking occurred at a vertical displacement of about 42 mm, where the existing horizontal crack developed into an additional diagonal crack located above the first one (Fig. 3b). Then, the AAC blocks started to spall near that crack and near the contact

regions with the frame. Even at the final stages of this test, cracks along the joints were not detected. In the dry joints case (type c), where sliding along the bed joints has already occurred at a very low load level. When the load increased, the cracks started to grow into the AAC blocks as well. However, those diagonal cracks were limited to the local block scale, i.e. they did not propagate from one block to its neighboring blocks. This cracking localization is due to the unique contact conditions between adjacent blocks. The interface between such two blocks are in contact and transfer compression and friction-based shear but the material discontinuity and the lack of bonding arrests the cracks and confine them to a single block. The differences in cracking pattern also affect the infill-frame separation, which is shown in Fig. 3 by dashed lines (only observed separation is illustrated). This aspect of separation will be discussed in detail in Section 4.6. The cracking patterns observed in Fig. 3 provide further insight into the structural mechanisms that govern the response of the examined joint layouts. In particular, they throw some light on the events along the response curves and the levels of displacement that characterize them. The relative vertical displacement observed at the ultimate load in the adhesive joint wall (1.8%) is considerably smaller than the ones observed in the mortar or the dry joints (about 5.4%). This difference is attributed to the different cracking patterns and cracking mechanisms and their impact on the load-displacement curves. In the mortar joints, small cracks and relative displacements start to evolve at the very early stages of the response and they gradually grow until the ultimate load is achieved. Correspondingly, the slope of the load-displacement curve gradually decreases up to the limit point at the ultimate load. In the dry joints, the relative deformations at the joints also start very early but since there is no bond material, the evolution curve is almost linear. Opposed to that, the pre-cracking behavior of the adhesive joints wall is rather linear, excluding a single change of slope that is attributed to changes in the contact pattern. The quasi-linear behavior is associated with accumulation of energy that eventually leads to the formation of a single major crack. In that sense, the lack of a mechanism that allows for energy dissipation yields a more brittle pre-cracking phase that reaches its end under a lower level of vertical drift. From this point and on, the adhesive joint wall behaves as a two body mechanism with contact and friction along the mutual cracked interface, a structural form that yields the plateau observed in the load displacement response.

149

A. Brodsky et al. / Construction and Building Materials 189 (2018) 144–156

(a) Cement-based mortar

(b) Adhesive

(c) Dry

1 2 1

Infill crushing

Observed infill-frame opening

Infill cracking

Fig. 3. Cracking patterns at the final stage of the tests (displacement = 110 mm).

Opposed to that, the behavior of the mortar joint wall in the deep nonlinear regime is associated with a further gradual decrease of the load-deflection slope as the cracking at the joints develops.

4.3. Initial stiffness and ultimate load The initial stiffness values (K i ) in each test are listed in Table 2. While the initial stiffness of the wall with the cement-based mortar (joint type a) is higher than the stiffness of the one with the adhesive (joint type b) by about 20%, the stiffness of the specimen with dry joints (joint type c) is about 5 times smaller than that. The sliding along the joints in the infill wall with the dry joints has started at an early stage of the loading process and provided a deformation mechanism with an overall smaller initial stiffness. The ultimate loads (P u ) in each of these tests are also listed in Table 2. The ultimate loads of the specimens with the dry joints (c) and of the adhesive joints (b) are rather similar. In contrast to that, the ultimate load of the cement-based mortar specimen (a) is almost twice larger. The infill cracking of the adhesive specimen (point C in Fig. 2) defines its ultimate load, while in the other two cases there was no specific event that clearly defines the ultimate

load. The limited failure that was observed in the blocks in the cases of dry joints and cement-based joints mortar, implies that it is possible that further increase of the prescribed vertical displacement beyond the actuator’s stroke limit and the 5% vertical drift would correspond to further increase in load. It may however be noted that such a large drift is beyond the scope of interest, because failure of real frame components occurs at smaller drifts and determine the ultimate drift of the system.

4.4. Energy dissipation The load-displacement curves that are shown in Fig. 2, ended by an almost vertical unloading curve without a real recovering displacement. Therefore, the energy dissipation of the system may be defined as the area under the load-displacement curve up to R 110 the maximal displacement of 110 mm, i.e. 0 PðdÞdd as illustrated in Fig. 4. The relative compliance of the specimen with the dry joints dictates that the energy absorption of this specimen is significantly lower than the other two. Comparing the energy dissipation of the cement-based joints (type a) wall and of the adhesive joints (type b) wall clearly shows a larger energy dissipation in the

Table 2 Major parameter of test results.

1

Specimen

(a) Cement-based mortar

(b) Adhesive1

(c) Dry1

K i Initial stiffness (kN/mm) P u Ultimate load (kN) Du Deflection at ultimate load (mm) EDEnergy dissipation (kN.mm)

2.5 67.3 112.2 6.0E + 03

2.0 (20%) 39.8 (40%) 36.0 (68%) 3.6E+3 (40%)

0.4 (84%) 32.4 (52%) 111.9 (0.3%) 1.9E+3 (69%)

Values in brackets denote the difference with respect to type (a) results.

150

A. Brodsky et al. / Construction and Building Materials 189 (2018) 144–156

4.5. Force resultants

Pu Ki

ED Du

110 mm

Fig. 4. Typical test load-displacement curve.

cement-based wall. This is likely due to the failure mechanism of this wall, which is characterized by many cracks rather than a single crack and by a higher ultimate load as a result. The results of the three tests show a significantly different global behavior, which is expressed in terms of the cracking patterns and the load-displacement curves. The next sections focus on the local behavior: the shear force and the bending moment diagrams along the frame elements, the evolution of the infill-frame contact regions during the loading process, and the interfacial tractions along those contact regions.

Loaded column

The strains that were measured at various cross sections along the frame elements were translated into sets of force resultants (axial force, shear force, bending moment) in each monitored cross-section. The procedure is developed and explained in detail in Brodsky et al. [20] and, for the sake of completeness, it is briefly outlined in Appendix A. The shear force and the bending moment resultants along the frame’s elements at the ultimate load of each test are presented in Figs. 5 and 6, respectively. The values are calculated at the monitored cross sections and for clarity, dashed lines connect these points. The results reveal the impact of the joint type on the shear force and the bending moment magnitudes. The cement-based joint is associated with the largest bending moments and shear forces, compared to the other joint types. The distribution function and the location of the maximum values along the frame element axis also depend on the joint type. This indicates that the design of the frame, on the one hand, or the assessment of its capacity (see [19]), on the other hand, may depend not only on the masonry unit’s material but also on the joint type.

Upper beam

Supported column

Lower beam

Fig. 5. Shear force diagrams along the frame elements at the ultimate load level.

Loaded column

Upper beam

Lower beam

Fig. 6. Bending moment diagrams along the frame elements at the ultimate load level.

Supported column

A. Brodsky et al. / Construction and Building Materials 189 (2018) 144–156

The experimental investigation reported in Brodsky and Yankelevsky [19] showed that column’s shear failure and the column’s tension failure accompanied with yielding of the longitudinal reinforcement commonly determine the ultimate load of infilled RC frames in case of loss of supporting column. Therefore, determination of these force and moment diagrams is essential to determine the mode of damage in any of the frame elements, its location and the load level at which it occurs thus determining the ultimate load of the entire infill frame. 4.6. Frame-infill contact The contact length calculation is based on the fact that the interfacial tractions between the infill and the frame elements vanish when the two components separate. As a result, the bending moment diagram along the detached regions of the frame element becomes a linear function of the element’s axial coordinate. A detailed explanation of the procedure developed for the detection of those regions is found in Brodsky et al. [20] and it is briefly outlined in Appendix B. In this section, the discussion focuses on the variation of the contact region along the loaded column versus the vertical displacement during the loading process. The results for joint types (a) to (c) appear

151

in Figs. 7–9. Each point along the curve indicates the transition between the detached region below that point and the contact region area above the point. The contact region may include one or more contact regions, as explained in Section 4.7. For coordination with the load-displacement results (Fig. 2), the vertical load variation is also shown by a dashed curve. The most prominent observation reflected by Figs. 7–9 is that the contact regions vary considerably with loading. Comparison of these figures further reveals the impact of the different masonry joints on the size of the contact region under similar levels of load. There is little information in the literature regarding the contact zone, and in most cases, it is related to lateral loading action on the frame. Information regarding the contact zone under vertical loading is limited to Brodsky et al. [20,21] whereas additional sources were not found. Nevertheless, it is interesting to compare the data available regarding lateral action with the new experimental results of the present study. The contact length is used in the equivalent strut model for the assessment of the traction forces in the frame elements. Table 3 summarizes several models assessing the wall contact length at the upper part of the column of a frame with the beam (Lb Þ and the column ðLc Þ given by (1) Saneinejad and Hobbs [40], (2) Anderson and Brzev [41] and (3) ASCE/SEI 41-06 [34].

Fig. 7. Contact length evolution in the infill wall with cement-based mortar joints (Joint type a).

Fig. 8. Contact length evolution in the infill wall with adhesive joints (Joint type b).

152

A. Brodsky et al. / Construction and Building Materials 189 (2018) 144–156

Fig. 9. Contact length evolution in the infill wall with dry joints (Joint type c).

Table 3 Different suggested contact lengths.

Saneinejad and Hobbs [40]

The contact length rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ðMpj þ0:2Mpc Þ Lc ¼ tf 0m0 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ðMpj þ0:2Mpb Þ Lb ¼ 0 tf

(2) (3)

m90

ASCE/SEI 41-06 [34]

w Lc ¼ cosh c

(4)

w Lb ¼ sinh b

(5) 0:4

Anderson and Brzev [41]

w ¼ 0:175ðkhcol Þ p Lc ¼ 2k Lb ¼ pk rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 Em t inf sin2h k¼ 4Ec Ic hinf

d

(6) (7) (8) (9)

In the given expressions, M pj is the minimum value out of the three plastic moment capacities: the column (M pc ), the beam 0 0 (Mpb ) and the joint (M pj ); tf m0 and tf m90 are the compressive strengths of the masonry panel parallel and normal to the bed joint, respectively; Ec and Em are the elastic moduli of the frame and the infill material respectively; Ic is the moment of inertia of the columns; hinf and tinf are the infill wall height and thickness; and his the angle between the wall diagonal and the horizon    h h ¼ tan1 Linf : The relative stiffness parameter k that was suginf

gested by Stafford Smith [44] is based on the beam on elastic foundation analogy. The equivalent strut width (w) is calculated using a semi-empirical equation proposed by Mainstone and Mainstone and Weeks [45,46] on the basis of experimental and analytical data, where hcol is the story height. The evolution of the contact regions in the cement-based mortar joints (type a) wall in the present research (Fig. 7) is compared with the assessment of Eqs. (2), (4) and (7). The expression proposed by Anderson and Brzev [41] gives a contact size that is longer than the wall height, therefore it is not presented in the figure. Also, note that the vertical axis represents the column height (0–1640 mm) rather than the infill wall height. The infill wall is located between 120 mm and 1520 mm and its height ishinf ¼ 1400 mm. The experimental curve for the cement-based mortar joints (type a) in Fig. 7 indicates that at the beginning of the test and up to Point A, the infill masonry wall is in contact with the frame along its entire height. At Point A, where the first infill cracking

occurs, the contact region reduces to 375 mm that is about 27% of the infill wall height. Afterward, the contact region stabilizes with minor changes at displacements of about 26 and 32 mm. At a vertical displacement of 40 mm, the size of the contact region changes and stabilizes again at 655 mm (about 47% of the infill wall height). This transition point does not change until the end of the experiment. The evolution of the contact regions in the specimen built with adhesive joints (type b) is studied in Fig. 8. Similar to the case of the cement-based mortar joints, the test started with full contact along the interface of the infill wall and the loaded column. Then, after a vertical deflection of about 5 mm, which is also similar to the case of the cement-based mortar specimen, the contact region decreases to about 255 mm (18% of the infill wall height). Afterward, the infill cracking at Point C significantly changes the contact region. Quantitatively, the contact length of 375 mm (27%) that was detected prior to the infill cracking increases to 780 mm (56%) after cracking. The contact region size stabilizes at about 655 mm at a vertical displacement of about 55 mm and does not change any further at larger displacements until the end of the experiment. The evolution of contact zone at the infill-frame interface in the case of dry joints (type c) is shown in Fig. 9. Opposed to the two previous cases, here up to a displacement of about 65 mm the contact length fluctuates between two contact states. The first is a full contact along the entire interface and the second is a 655 mm high contact region that is about half of the infill height. These changes are observed at vertical displacements of about 27, 31, 35, 37, 48, 51, 52, 57, 59 and 64 mm and they are attributed to sliding along the joints. For relatively large displacements beyond about 65 mm, the contact region size stabilizes at about 655 mm (about 47% of the height of the infill wall) until the end of the experiment. The contact length is one of the most important parameters that affects the tractions in the frame elements. The suggested contact length that was proposed by Anderson and Brzev [41] is not physical since it is longer than the wall height. The contact lengths proposed by Saneinejad and Hobbs [40] and by ASCE 41 [34] show better results. It should be mentioned that these suggested values are intended for lateral loading, whereas the present study examines the contact length in the case of vertical loading. The suggested expressions yield results that are lower than the experimentally measured contact region by 33% and 36%, respectively. Moreover, the proposed contact zone size is constant and

153

A. Brodsky et al. / Construction and Building Materials 189 (2018) 144–156

obviously cannot represent the measured variable contact length along the loading process. The comparison of the three tested cases indicates the different evolution of the contact zone during loading and different contact zone sizes. Furthermore, it indicates that the contact behavior clearly depends on the joint type. While in the cases of mortar and adhesive joints the behavior is somewhat similar, the dry joints layout exhibits a significantly different mechanism. The implication of these observations on the contact evolution is twofold. First it reflects two different mechanisms that eventually lead to a different global behavior and expected to lead to different tractions at the interface. Second, even in the case of similar contact lengths, the differences observed in the load levels associated with the two responses (Fig. 2, Table 2) and the different cracking patterns (Fig. 3) are expected to yield different interfacial tractions. This aspect is studied in the following section.

4.7. Interfacial tractions Two different tractions are calculated at the frame-infill wall interface for every record: the tangential tractions (T t ) and the nor-

Infill wall

tinfTt(x)dx

tinfTn(x)dx

x Fig. 10. Frame-infill interfacial tractions.

(a) Cement-based mortar

mal traction (T n ) as illustrated in Fig. 10. The contact tractions are assumed to be uniformly distributed across the masonry wall width (t inf ). A detailed explanation of the traction assessment procedure is found in Brodsky et al. [20], and it is briefly outlined in Appendix C. Fig. 11 illustrates the interfacial normal and the tangential tractions along the contact region of the loaded column in each of the three tests at its ultimate load levels. The normal tractions are connected by dashed lines for convenience. Fig. 12 links the examined tractions to the cracking pattern of the infill masonry wall and reveals the strong coupling of the two phenomena. The regions where the tractions vanish are determined by the analysis, but at the examined high levels of displacement, they can also be identified visually. The visually detected regions are marked with dashed lines in Fig. 12 and they are in good agreement with the results obtained by the monitoring system and the analysis. At an advanced stage of loading, the cracking of the masonry infill in the adhesive joints specimen (b) splits the infill wall into two distinct parts. Each of the parts is in contact with the column, the lower of which is shown in Fig. 8 above. The spalling of the AAC blocks at these regions (Fig. 12) supports the claim of two contact regions. By means of the traction analysis, it is possible to follow the infill wall-frame contact state in more detail and to point at the number and the location of the second contact region. Similarly, it allows to handle the general case of multiple contact zones. The normal compressive tractions at the two contact regions detected in the adhesive joints specimen are about 4.1 and 4.5 MPa. The peak compressive contact traction obtained in the cement-based specimen is about 6.2 MPa. These values are higher than the average uniaxial compressive strength of the masonry blocks, and it may be attributed to the local compressive strength and biaxial state of stress that evolves at the local contact region. The effect of the discrete distribution of gauges along the frame and the finite spaces between them may also be a factor. This is particularly meaningful where the contact area is short.

(b) Adhesive

Fig. 11. Interfacial tractions on the loaded column at the ultimate load.

(c) Dry

154

A. Brodsky et al. / Construction and Building Materials 189 (2018) 144–156

(a) Cement-based

(b) Adhesive

(c) Dry

Fig. 12. The cracking pattern and the interfacial tractions on the loaded column.

Considering the fact that the tractions are calculated by numerical derivatives which are based on a limited number of points. When the region is short this number may be small, this limitation plays a role in the assessment of the compressive tractions as well as the assessment of the detached regions. 5. Conclusions The results of a comparative experimental study that investigates the effect of the joint type on the response of an infill wall in the case of loss of a supporting column has been presented. Three AAC walls with different joint types: (a) cement-based mortar joints, (b) AAC masonry adhesive joints and (c) dry joints have been examined. All three walls were similar in the geometry and were built with identical AAC masonry units. In all the tests the walls were subjected to a vertical loading acting on a column to simulate the event of gradual (quasi-static) loss of a supporting column. The effect of the masonry joints on the global behavior and on the local infill-frame interaction has been investigated using a specially tailored experimental methodology. The major findings and the conclusions of the investigation are: 1. The joint properties have a significant effect on the global behavior of the infill wall. The ultimate load of the wall built with cement-based mortar joints is almost double the ones of the adhesive joints and the dry joints walls. The ultimate load acting on the adhesive joints wall develops at a relatively small vertical displacement upon the infill wall major crack formation. The ultimate load of the mortar joint configuration develops at about three times larger displacements. This fundamental difference is due to the fact that until a major single crack is developed, the infill wall with the adhesive joints behaves as a solid uncracked panel and lacks the ability of gradually dissipating energy through cracking or sliding at the joints. This type of behavior is attributed to the high bond strength between the blocks provided by the adhesive based joint. The behavior of the other two infill walls is characterized by such gradual cracks development, sliding along the joints, and dissipating the accumulated energy already at low load levels. These differences reflect of the fundamental mechanics of the different layouts as well as the analysis and constitutive modeling of the infill material

2. The failure mechanism of the cement-based joint layout, which includes many cracks rather than a single crack, and is characterized by a higher ultimate load, enables a significantly more effective energy dissipation mechanism compared with the adhesive joints specimen. 3. Different joint properties lead to different cracking patterns, different load-bearing mechanisms and different frame-infill contact states. All these aspects affect the shear forces and the bending moments along the frame elements and, as such, may become major players in its failure mode. 4. The length of the contact zone is a critical feature that constantly changes during loading in all three examined layouts. The pattern of change depends on the joint type and the one attributed to dry joints is significantly different from those observed with mortar or adhesive joints. 5. The closed form expressions found in the literature for the assessment of the contact region lengths in laterally loaded infilled frames yield values that are generally smaller than the experimentally measured ones by more than 30%. The reference expressions refer to lateral loading rather than vertical loading which is investigated here, but they all refer to a constant contact length. The variation of the contact length and its depending on the joint type are beyond the scope of the simplified compressed diagonal approach that is the basis of such models. The experimental results presented in this study highlight the importance of the type and properties of the joints on the global behavior and especially on the infill-frame interaction. These results and particularly the ones that refer to the infill-frame interaction may serve as a calibration source for analytical and numerical tools.

Acknowledgement The research was supported by The Israeli Ministry of Science, Space and Technology (MOST), grant no. 2021954.

Conflict of interest The authors declare that they have no conflict of interest.

A. Brodsky et al. / Construction and Building Materials 189 (2018) 144–156

Appendix A. – Force resultants The sensing system provides strain readings at specific points 2;i along the frame. e1;i xx ; exx are the axial strains measured at two th

distinct points in the i cross section as illustrated in Fig. 13. The translation of the strain readings into stress resultants is given by:

M ixx

¼ v  EIi ¼ i

Nixx ¼ ei0  EAi ¼

2;i e1;i xx  exx

zi1  zi2

 EIi

i 1;i i e2;i xx  z1  exx  z2

zi1  zi2

ð10Þ

 EAi

ð11Þ th

where Nixx and M ixx are the axial and bending resultants in the i cross section, zi1 and zi2 are the vertical coordinates of the strain gauges on the section, Ii and Ai are the geometrical moment of iner-

155

This procedure includes a linear function curve fitting procedure starting from the known (equal to zero) bending moment at the hinge. In every analysis cycle, a first order polynomial curve is fitted to the calculated bending moment values along the element axis over a longer length, where one more calculated value at a cross section is added to the curve fitting procedure. At every cycle, the degree of linearity is examined by calculating the coefficient of determination (R2 ) of the fitted linear function. The point where the coefficient of determination starts to drop reflects the shift from a no-contact region to a contact region. Fig. 14 illustrates this linear function curve fitting procedure for the moment values along the loaded column. This example refers to an infill wall with cement-based joints at the ultimate load level. The coefficient of determination values are greater than 0.98 (98%) up to point 7. The R2 drops significantly from point 7 to point 8 ðR28 ¼ 0:93), and therefore, the contact change is between these two points.

th

tia and area of the i cross section, ei0 and vi are the axial strain at the neutral axis and the curvature and E is the elastic modulus. Appendix B. – Contact regions In a region where the infill wall is detached from the frame, the interfacial tractions vanish and therefore the distribution of the bending moment diagram reduces to a first-order polynomial along the axial coordinate of the frame element (beam or column). A repeating type of calculation procedure is performed.

Infill -z2

2 xx

C.G. r

Appendix C. – Interfacial tractions The tangential tractions (T t ) at the frame-infill wall interface and normal traction (T n ) are calculated in every record. These tractions are calculated based on equilibrium of an infinitesimal segment between every two monitored cross sections:

Ni;x  T t i t ¼ 0

ð12Þ

Mi;xx  T in t þ T it;x td ¼ 0

ð13Þ

where t is the width of the contact surface (the thickness of the infill wall), d is the distance between the interface and the neutral axis of the frame element (half of the beam’s/column’s height for symmetric elements) and the notations ( ),x, and ( ),x x stands for first and second derivatives with respect to the local longitudinal coordinate x. The first derivatives can be approximated using a central difference expression and the second derivatives can be approximated using the Lagrange’s interpolation formula for unequal spacing:

z1 1 xx

Fig. 13. Strain distribution in typical monitored cross section.

Ni;x ¼

Niþ1  Ni1 xiþ1  xi1

Mi;xx ¼

2½ðxiþ1  xi ÞM i1  ðxiþ1  xi1 ÞMi þ ðxi  xi1 ÞM iþ1  ðxi  xi1 Þðxiþ1  xi Þðxiþ1  xi1 Þ

Fig. 14. Contact region determination at the ultimate load in the cement-based test.

ð14Þ ð15Þ

156

A. Brodsky et al. / Construction and Building Materials 189 (2018) 144–156

References [1] C1314  16: Standard Test Method for Compressive Strength of masonry prisms, 2016. [2] G. Sarangapani, B.V. Venkatarama Reddy, K.S. Jagadish, Brick-mortar bond and masonry compressive strength, J. Mater. Civ. Eng. 17 (2005) 229–237, https:// doi.org/10.1061/(ASCE)0899-1561(2005) 17:2(229). [3] B.D. Ewing, M.J. Kowalsky, Compressive behavior of unconfined and confined clay brick masonry, J. Struct. Eng. 130 (2004) 650–661, https://doi.org/ 10.1061/(ASCE)0733-9445(2004) 130:4(650). [4] M. Tomazˇevicˇ, Earthquake-resistant Design of Masonry Buildings, 1999. [5] H.B. Kaushik, D.C. Rai, S.K. Jain, Effectiveness of some strengthening options for masonry-infilled RC frames with open first story, J. Struct. Eng. 135 (2009) 925–937, https://doi.org/10.1061/(ASCE)0733-9445(2009) 135:8(925). [6] K. Naraine, S. Sinha, Behavior of brick masonry under cyclic compressive loading, J. Struct. Eng. 115 (1989) 1432–1445, https://doi.org/10.1061/(ASCE) 0733-9445(1989) 115:6(1432). [7] L. Binda, A. Fontana, G. Frigerio, Mechanical behaviour of brick masonries derived from unit and mortar characteristics. Brick Block Mason (8 Th IBMAC) London, Elsevier Appl Sci 1 205–216, 1988. [8] W.S. McNary, D.P. Abrams, Mechanics of masonry in compression, J. Struct. Eng. 111 (1985) 857–870, https://doi.org/10.1061/(ASCE)0733-9445(1985) 111:4(857). [9] R.H. Atkinson, B.P. Amadei, S. Saeb, S. Sture, Response of masonry bed joints in direct shear, J. Struct. Eng. 115 (1989) 2276–2296, https://doi.org/10.1061/ (ASCE)0733-9445(1989) 115:9(2276). [10] B. Amadei, S. Sture, S. Saeb, R.H. Atkinson, An Evaluation of Masonry Joint Shear Strength in Existing Buildings, Dept Civil Environ Archit Eng Rep, 1989. [11] A.B. Mehrabi, P.B. Shing, M. Schuller, J. Noland, Performance of Masonryinfilled RC Frames Under in-plane Lateral Loads, 1994. [12] T. Manzouri, Nonlinear Finite Element Analysis and Experimental Evaluation of Retrofitting Techniques for Unreinforced Masonry Structures, 1997. [13] R.G. Drysdale, A.A. Hamid, L.R. Baker, Masonry Structures: Behavior and Design, Prentice Hall, 1994. [14] E. Jung, Binding between mortar and brick. Brick block mason (8 Th IBMAC) London, Elsevier Appl Sci 1988;1:182–93. [15] P. Jukes, J.R. Riddington, Review of masonry tensile bond strength test methods, Mason Int. 12 (1998) 51–57. [16] J.C. Almeida, P.B. Lourenço, J.A. Barros, Characterization of brick and brick – mortar interface under uniaxial tension. VII Int Semin Struct Mason Dev Countries, Belo Horizonte, Brazil, 2002. [17] G.M. Verderame, F. De Luca, P. Ricci, G. Manfredi, Preliminary analysis of a soft storey mechanism after the 2009 L’Aquila earthquake, Earthq. Eng. Struct. Dyn. 40 (2011) 925–944, https://doi.org/10.1002/eqe.1069. [18] L. Hermanns, A. Fraile, E. Alarcón, R. Álvarez, Performance of buildings with masonry infill walls during the 2011 Lorca earthquake, Bull. Earthq. Eng. 12 (2014) 1977–1997, https://doi.org/10.1007/s10518-013-9499-3. [19] A. Brodsky, D.Z. Yankelevsky, Resistance of reinforced concrete frames with masonry infill walls to in-plane gravity loading due to loss of a supporting column, Eng. Struct. 140 (2017) 134–150, https://doi.org/10.1016/j. engstruct.2017.02.061. [20] A. Brodsky, O. Rabinovitch, D.Z. Yankelevsky, Experimental evaluation of the interaction between an infill wall and the surrounding frame, Strain 53 (2017) e12250, https://doi.org/10.1111/str.12250. [21] A. Brodsky, O. Rabinovitch, D.Z. Yankelevsky, Determination of the interaction between a masonry wall and a confining frame, Eng. Struct. 167 (2018) 214– 226, https://doi.org/10.1016/j.engstruct.2018.04.001. [22] B. Ozsayin, E. Yilmaz, M. Ispir, H. Ozkaynak, E. Yuksel, A. Ilki, Characteristics of CFRP retrofitted hollow brick infill walls of reinforced concrete frames, Constr. Build. Mater. 25 (2011) 4017–4024, https://doi.org/10.1016/ j.conbuildmat.2011.04.036. [23] M.F. Ghazy, Effect of using mortar interface and overlays on masonry behavior by using Taguchi method, ACI Mater. J. 109 (2012) 509–516.

[24] N. Gattesco, I. Boem, Experimental and analytical study to evaluate the effectiveness of an in-plane reinforcement for masonry walls using GFRP meshes, Constr. Build. Mater. 88 (2015) 94–104, https://doi.org/10.1016/ j.conbuildmat.2015.04.014. [25] V. Alecci, M. Fagone, T. Rotunno, M. De Stefano, Shear strength of brick masonry walls assembled with different types of mortar, Constr. Build. Mater. 40 (2013) 1038–1045, https://doi.org/10.1016/j.conbuildmat.2012.11.107. [26] T. Zahra, M. Dhanasekar, Prediction of masonry compressive behaviour using a damage mechanics inspired modelling method, Constr. Build. Mater. 109 (2016) 128–138, https://doi.org/10.1016/j.conbuildmat.2016.01.048. [27] F.M. Khalaf, A.W. Hendry, D.R. Fairbairn, Study of the compressive strength of blockwork masonry, ACI Struct. J. 91 (1994) 367–375. [28] K. Ramamurthy, V. Sathish, R. Ambalavanan, Compressive strength prediction of hollow concrete block masonry prisms, ACI Struct. J. 97 (2001) 61–67. [29] Vladimir G. Haach, Graça Vasconcelos, Paulo B. Lourenço, Assessment of compressive behavior of concrete masonry prisms partially filled by general mortar, J. Mater. Civ. Eng. 26 (2014) 1239–1247, https://doi.org/10.1061/ (ASCE)MT. [30] B.V. Venkatarama Reddy, R. Lal, K.S.N. Rao, Influence of joint thickness and mortar-block elastic properties on the strength and stresses developed in soilcement block masonry, J. Mater. Civ. Eng. 21 (2009) 535–542, https://doi.org/ 10.1061/(ASCE)0899-1561(2009) 21:10(535). [31] European Committe for Standardization. Eurocode 6 – Design of masonry structures – Part 1-1: General rules for reinforced and unreinforced masonry structures, 2005. [32] G. Gazic´, V. Sigmund, Cyclic testing of single-span weak frames with masonry infill, J. Croat. Assoc. Civ. Eng. 68 (2016) 617–633, https://doi.org/10.14256/ JCE.1614.2016. [33] T. Sevil, M. Baran, T. Bilir, E. Canbay, Use of steel fiber reinforced mortar for seismic strengthening, Constr. Build. Mater. 25 (2011) 892–899, https://doi. org/10.1016/j.conbuildmat.2010.06.096. [34] ASCE/SEI 41-06. ASCE/SEI 41-06 Seismic Rehabilitation of Existing Buildings. 2007. [35] Applied Technology Council (ATC-43 Project). FEMA 306 – Evaluation of Earthquake Damaged Concrete and Masonry Wall Buildings – Basic Procedures Manual, 1998. [36] C.Z. Chrysostomou, P. Gergely, J.F. Abel, A six-strut model for nonlinear dynamic analysis of steel infilled frames, Int. J. Struct. Stab. Dyn. 2 (2002) 335– 353. [37] W.W. El-Dakhakhni, M. Elgaaly, A.A. Hamid, Three-strut model for concrete masonry-infilled steel frames, J. Struct. Eng. 129 (2003) 177–185, https://doi. org/10.1061/(ASCE)0733-9445(2003) 129:2(177). [38] S. Farazman, B.A. Izzuddin, D. Cormie, Influence of unreinforced masonry infill panels on the robustness of multistory buildings, J. Perform Constr. Facil. 27 (2013) 673–682, https://doi.org/10.1061/(ASCE)CF.1943-5509.0000392. [39] Jong-Su Jeon, R.D. Ji-Hun Park, Seismic fragility of lightly reinforced concrete frames with masonry infill, Earthq. Eng. Struct. Dyn. 41 (2015) 1549–1568, https://doi.org/10.1002/eqe. [40] A. Saneinejad, B. Hobbs, Inelastic design of infilled frames, J. Struct. Eng. 121 (1995) 634–650, https://doi.org/10.1061/(ASCE)0733-9445(1995) 121:4(634). [41] D. Anderson, S. Brzev, Sesmic Design Guide for Masonry Buildings, 2009. [42] Standard IS 4004-1. SI 4004 – Part 1. Adhesives for tiles. Definitions and specifications, 2013. [43] EN BS. 1015-11, Methods of Test for Mortar for Masonry – Part 11: Determination of Flexural and Compressive Strength of Hardened Mortar. Eur Comm Stand Brussels, 1999. [44] Smith B. Stafford, Methods for predicting the lateral stiffness and strength of multi-storey infilled frames, Build. Sci. 2 (1967) 247–257, https://doi.org/ 10.1016/0007-3628(67)90027-8. [45] R.J. Mainstone, On the stiffness and strengths of infilled frames, Proc. Inst. Civ. Eng. (Supplement) (1971) 57–90, https://doi.org/10.1680/iicep.1971.6267. [46] R.J. Mainstone, G.A. Weeks, The influence of bounding frame on the racking stiffness and strength of brick walls, Proc. Int. Brick Mason. Conf. (1970) 165– 171.