Experimental Study of Infill Walls with Joint Reinforcement Subjected to In-Plane Lateral Load

Jesús Martin Leal-Graciano; Juan J. Pérez-Gavilán; Alfredo Reyes-Salazar; Federico Valenzuela-Beltrán; Edén Bojórquez; Juan Bojórquez

doi:10.3390/buildings12030259

Leal-Graciano, Jesús Martin;Pérez-Gavilán, Juan J.;Reyes-Salazar, Alfredo;Valenzuela-Beltrán, Federico;Bojórquez, Edén;Bojórquez, Juan

2022-02-23 00:00:00

buildings Article Experimental Study of Inﬁll Walls with Joint Reinforcement Subjected to In-Plane Lateral Load 1 , 2 1 1 Jesús Martin Leal-Graciano *, Juan J. Pérez-Gavilán , Alfredo Reyes-Salazar , Federico Valenzuela-Beltrán , 1 1 Edén Bojórquez and Juan Bojórquez Facultad de Ingeniería, Universidad Autónoma de Sinaloa, Calz. Las Americas Nte. S/N, CU, Culiacán de Rosales 80013, Mexico; reyes@uas.edu.mx (A.R.-S.); fvalenzuelab@uas.edu.mx (F.V.-B.); eden@uas.edu.mx (E.B.); juanbm@uas.edu.mx (J.B.) Instituto de Ingeniería, Universidad Nacional Autónoma de México, Av. Universidad 3000, CU, Ciudad de México 04510, Mexico; jperezgavilane@iingen.unam.mx * Correspondence: jesusleal@uas.edu.mx Abstract: The results of an experimental study of four inﬁlled frames with brick masonry walls subject to reversal cyclic lateral load are presented. The variables studied were the height to length aspect ratio of the wall and the use of joint reinforcement. The investigation was motivated by the fact that the Mexican code establishes the same speciﬁcations about the use of joint reinforce- ment for inﬁll walls as for conﬁned walls, because there is not enough experimental evidence on joint reinforced inﬁll walls. To investigate the possible interaction of the study variables in the seismic performance of the walls, two pairs of specimens, scaled 1:2, with different aspect ratios (H/L = 0.75, 0.41) were tested. The specimens in each pair were identical except that one of them included steel bars into the bed-joints as reinforcement leading to amount p f = 0.6 MPa. The h yh inﬁll walls with H/L = 0.41 were included from a previous study. The behavior of the specimens was deﬁned in terms of lateral strength, ductility, displacement capacity, deformation of the joint Citation: Leal-Graciano, J.M.; reinforcement and crack pattern. The results indicate that joint reinforcement increases the strength Pérez-Gavilán, J.J.; Reyes-Salazar, A.; of the system; however, the increase was more pronounced in longer walls. Ductility was reduced Valenzuela-Beltrán, F.; Bojórquez, E.; Bojórquez, J. Experimental Study of with horizontal reinforcement and this behavior was more important for longer walls. As occurred in Inﬁll Walls with Joint Reinforcement conﬁned walls, the joint reinforcement generates a more distributed cracking and reduces the width Subjected to In-Plane Lateral Load. of the cracks. The experiments are described and this and other results are discussed in detail. Buildings 2022, 12, 259. https:// doi.org/10.3390/buildings12030259 Keywords: inﬁll wall; joint reinforcement; inﬁlled frame; seismic behavior; RC frame structure Academic Editor: Alessandra Aprile Received: 18 January 2022 1. Introduction Accepted: 16 February 2022 Load-bearing walls are those that support both vertical and lateral loads. Usually, Published: 23 February 2022 when these type of walls are used, they constitute the main resisting elements in the Publisher’s Note: MDPI stays neutral system. Historically, unreinforced masonry was used for load-bearing walls around the with regard to jurisdictional claims in world; however, it is rarely used now a days in seismic zones where it has been replaced published maps and institutional afﬁl- by reinforced and/or conﬁned masonry walls. Reinforced masonry is seldom used in iations. developing countries, such as Mexico, mainly due to its high cost when compared to conﬁned masonry [1]. For this reason, we will restrict our presentation to conﬁned masonry walls. On the other hand, inﬁll walls are surrounded by beams and columns of a structural Copyright: © 2022 by the authors. frame, to which they provide rigidity against lateral loads [2]. Unreinforced masonry Licensee MDPI, Basel, Switzerland. is still the dominant masonry system for inﬁll walls. Only recently, conﬁned masonry This article is an open access article was proposed as an alternative system for inﬁll walls (Figure 1). It has been observed distributed under the terms and in experimental tests, that unreinforced masonry inﬁll walls can fail out of plane once conditions of the Creative Commons they have developed some type of cracking during an earthquake. Conﬁning elements Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ reduce the vulnerability of the wall to out-of-plane failure and improve the performance 4.0/). of in-plane walls [3]. The system was adopted in the Mexican code, while unreinforced Buildings 2022, 12, 259. https://doi.org/10.3390/buildings12030259 https://www.mdpi.com/journal/buildings Buildings 2022, 12, x FOR PEER REVIEW 2 of 21 Buildings 2022, 12, 259 2 of 19 plane walls [3]. The system was adopted in the Mexican code, while unreinforced ma- masonry for inﬁll walls is no longer allowed [2]. It is recognized that out-of-plane failure of sonry for infill walls is no longer allowed [2]. It is recognized that out-of-plane failure of inﬁll walls is common during seismic action. If this failure is not properly prevented, any infill walls is common during seismic action. If this failure is not properly prevented, any reinforcement for in-plane actions could be useless. However, only in-plane behavior of reinforcement for in-plane actions could be useless. However, only in-plane behavior of inﬁll walls is included in this paper. infill walls is included in this paper. Figure 1. Mexican construction practice of masonry infill walls. Figure 1. Mexican construction practice of masonry inﬁll walls. Although, in appearance, a confined masonry construction and a reinforced concrete Although, in appearance, a conﬁned masonry construction and a reinforced concrete (RC) frame infilled with masonry walls may look alike, structurally they perform quite (RC) frame inﬁlled with masonry walls may look alike, structurally they perform quite dif differentl ferentlyy [ [44] ]. . Figur Figure 2 e 2 shows shows the the main maindif difer fference ences,s,whi which a ch are rer elated related to tothe theconstr construct uction ion sequence sequence and andthe the manner manner in in which whichthey they support supportvertical vertical and and lateral lateral loads. loads. A Aconﬁned confined masonry masonrywall wall consists consists of of a a non nonr reinf einfor orce ced d mason masonry ry pan panel el surro surr und ounded ed by by con concr crete ete tie-tie- col- columns, umns, in in the the vert vertical ical direct direction, ion, and and tie-tie-beams, beams, in th inethe horiz horizontal ontal direct dir ion, ection, know known n as con- as conﬁning elements [5]. The masonry panel is built ﬁrst and the conﬁning elements are fining elements [5]. The masonry panel is built first and the confining elements are cast in cast in place afterwards against the panel rough sides (toothed or with dowells). This place afterwards against the panel rough sides (toothed or with dowells). This construc- construction sequence guaranties the full integration of the conﬁning elements and the tion sequence guaranties the full integration of the confining elements and the panel. The panel. The conﬁning elements provide additional lateral strength after diagonal cracking confining elements provide additional lateral strength after diagonal cracking and in- and increase the displacement capacity of the walls. However, conﬁning elements do crease the displacement capacity of the walls. However, confining elements do not pro- not provide an effective frame action and, consequently, masonry walls support gravity vide an effective frame action and, consequently, masonry walls support gravity loads [6]. loads [6]. Unlike confined masonry construction, in RC frame infilled with masonry walls, the Unlike conﬁned masonry construction, in RC frame inﬁlled with masonry walls, the columns and beams are built first and the wall later to fill the frame span. The result is columns and beams are built ﬁrst and the wall later to ﬁll the frame span. The result that there is a lack of bond between the masonry infill and the RC frame (Figure 2a), es- is that there is a lack of bond between the masonry inﬁll and the RC frame (Figure 2a), pecially when the wall is unreinforced and no confining elements are provided. When especially when the wall is unreinforced and no conﬁning elements are provided. When using confining elements and a careful construction process, full interaction between the using conﬁning elements and a careful construction process, full interaction between the frame and the infill wall could be achieved [3]. frame and the inﬁll wall could be achieved [3]. Other differences relative to confined masonry walls is that infill walls do not support Other differences relative to conﬁned masonry walls is that inﬁll walls do not support vertical loads. The main reason for this fact is that the axial stiffness of the columns is vertical loads. The main reason for this fact is that the axial stiffness of the columns is much much higher when compared to the axial stiffness of the infill walls (Figure 2b). Addition- higher when compared to the axial stiffness of the inﬁll walls (Figure 2b). Additionally, ally, in infill wall construction, it is not uncommon to have gaps between the panels and in inﬁll wall construction, it is not uncommon to have gaps between the panels and the the concrete beams. These gaps are created when the walls do not fit tightly to the under- concrete beams. These gaps are created when the walls do not ﬁt tightly to the underside side of the beams. These gaps allow the beams to deflect without transferring the gravity of the beams. These gaps allow the beams to deﬂect without transferring the gravity loads loads to the wall below [4]. to the wall below [4]. Buildings 2022, 12, x FOR PEER REVIEW 3 of 21 Buildings 2022, 12, 259 3 of 19 (a) (b) (c) Figure 2. A comparison of confined masonry construction and RC frames with masonry infills. (a) Figure 2. A comparison of conﬁned masonry construction and RC frames with masonry inﬁlls. Construction sequence, (b) Size of concrete elements, (c) Seismic response. (a) Construction sequence, (b) Size of concrete elements, (c) Seismic response. When subjected to lateral seismic loads, confined walls act as shear wall and infill When subjected to lateral seismic loads, conﬁned walls act as shear wall and inﬁll walls act as diagonal strut (Figure 2c). In the case of infill walls, the masonry wall separates walls act as diagonal strut (Figure 2c). In the case of inﬁll walls, the masonry wall separates from the surrounding frame due to their different deformation characteristics and to a from the surrounding frame due to their different deformation characteristics and to a relative lack of bond. Separation occurs in two diagonally opposite corners while in the relative lack of bond. Separation occurs in two diagonally opposite corners while in the other two corners the masonry wall reacts against the frame over a certain length of con- other two corners the masonry wall reacts against the frame over a certain length of contact tact extending extendin frg om from the th loaded e loadcorners. ed corners. Consequently Consequently , the , th system e system behaves behaves appr approx oximately imatel as y a as braced a brace frame d fra[ me 7–15 [7 ]. –15] When . When the dir the ection directof ion the of lateral the later load al load is reversed, is rever the sed, braced the braced frame mechanism is developed along the direction of the other diagonal [16]. frame mechanism is developed along the direction of the other diagonal [16]. For mid-rise masonry constructions under seismic loading, the shear strength of the For mid-rise masonry constructions under seismic loading, the shear strength of the walls wallsis is com commonly monly excee exceeded. ded. In Inth that at case, case,stee steel l bbars ars with within in th the e m mortar ortar bed bed-joints -joints may maybe be provided as shear reinforcement. Another use of the joint reinforcement is for cracking provided as shear reinforcement. Another use of the joint reinforcement is for cracking control against volumetric changes in masonry walls or bonding of multiple wythes. control against volumetric changes in masonry walls or bonding of multiple wythes. In Mexico, joint reinforcement consists of cold drawn steel wires with diameters of In Mexico, joint reinforcement consists of cold drawn steel wires with diameters of 5/32-in (3.97 mm), 3/16-in (4.76 mm) and 1/4-in (6.35 mm). The yield strength of this steel 5/32-in (3.97 mm), 3/16-in (4.76 mm) and 1/4-in (6.35 mm). The yield strength of this steel wires is 588 MPa. The wires should be properly anchored in RC elements or internal cells. wires is 588 MPa. The wires should be properly anchored in RC elements or internal cells. Lapping is not allowed because the bond between the wire and mortar, and between the Lapping is not allowed because the bond between the wire and mortar, and between the mortar and masonry units, gradually degrades with cracking [6]. mortar and masonry units, gradually degrades with cracking [6]. For load-bearing walls, the use of reinforcement within bed-joints normally improves For load-bearing walls, the use of reinforcement within bed-joints normally improves their behavior when they are subjected to lateral loads. Joint reinforcement signiﬁcantly their behavior when they are subjected to lateral loads. Joint reinforcement significantly increases the lateral strength and displacement capacity of the walls. increases the lateral strength and displacement capacity of the walls. It is generally accepted that the horizontal reinforcement does not affect the initial It is generally accepted that the horizontal reinforcement does not affect the initial stiffness and cracking strength of masonry walls, since it is argued that the reinforcement is stiffness and cracking strength of masonry walls, since it is argued that the reinforcement activated after the ﬁrst diagonal crack appears. The reinforcement produces a distributed is activated after the first diagonal crack appears. The reinforcement produces a distrib- cracking and the crack width is smaller than in walls without joint reinforcement. In uted cracking and the crack width is smaller than in walls without joint reinforcement. In addition, it retards the shear strength degradation of the wall and increases its lateral addition, it retards the shear strength degradation of the wall and increases its lateral de- deformation capacity [17–19]. In the 2004 edition of the Mexican code [20], Equation (1) formation capacity [17–19]. In the 2004 edition of the Mexican code [20], Equation (1) to estimate the contribution of the joint reinforcement to the shear strength of confined ma- sonry walls was included, for the first time: Buildings 2022, 12, 259 4 of 19 to estimate the contribution of the joint reinforcement to the shear strength of conﬁned masonry walls was included, for the ﬁrst time: V = F h p f A (1) sR R h yh T In such equation, F is the strength reduction factor, A is the cross-section area of the R T wall, f is the yield strength of joint reinforcement, p = A /(s t) is the percent of steel yh h reinforcement, s is the vertical spacing, t is the thickness of the wall and h is an efﬁciency factor which depended only on the amount of joint reinforcement given by p f . h yh In the 2017 version of the Mexican code [2], the expression for h calculation was updated to include several new concepts. The contribution of the joint reinforcement was limited by the masonry compressive strength and the net area of the masonry units, while the masonry component was reduced by the percent ratio of joint reinforcement [6,21]. The efﬁciency factor was deﬁned as in Equation (2): mR h = (k k 1) + h (2) 0 1 s F p f A R h yh T where k depends on the aspect ratio (H/L) of the wall Equation (3), k is a factor to take into 0 1 account the reduction of efﬁciency with the product p f Equation (4), a is a reduction rate h yh and h is an efﬁciency factor depending on the compressive masonry strength Equation (5): 1.3 i f H/L 1.0 k = (3) 1.0 i f H/L 1.5 k = 1 aP f (4) 1 h yh 0.75 i f f 9 MPa h = (5) 0.55 i f f 6 MPa It is important to say that few information is found in the existing literature about the effects of joint reinforcement on the seismic behavior of inﬁll masonry walls. Consequently, the Mexican code [2] establishes the same equations to estimate the contribution of joint reinforcement for both conﬁned walls and inﬁll walls. Leal et al. [3] tested six inﬁll walls subjected to cyclic lateral load, of which four included conﬁning elements and the rest were of unreinforced masonry. All the walls had the same aspect ratio. Additional variables were wall/frame stiffness using different column sizes and the use of joint reinforcement. It was concluded that the contribution of horizontal reinforcement to the lateral load resistance of the system depends on the wall/frame stiffness ratio. For the specimens with smaller columns, the contribution of the reinforcement was greater. This result was attributed to the fact that in the specimens with larger columns, the failure in the wall was predominantly due to sliding shear along the bed-joints, preventing the proliferation of diagonal cracks needed for the activation of the joint reinforcement. Due to the evident differences among conﬁned walls and inﬁll walls (for example, inﬁll walls do not support vertical loads, and when subjected to lateral loads the wall separates from the concrete elements), and that in the RC inﬁlled frame system includes variables that are not included in conﬁned walls, such as the relative wall/frame stiffness, it is suggested that the contribution of the joint reinforcement is different than in the case of conﬁned walls. It is generally accepted that the shear strength of masonry walls increases with decreas- ing aspect ratio. To take into account this fact, several construction codes for reinforced masonry include a modiﬁcation factor as a function of aspect ratio [22]. Based on experi- mental evidence from several authors, Alvarez and Meli [23] argued that aspect ratio affects the strength due to stress distribution changes in comparison with square walls (H/L = 1). Buildings 2022, 12, 259 5 of 19 Later, this idea was conﬁrmed for conﬁned masonry walls in an experimental study in which seven walls with aspect ratios from 0.3 to 2.2 were tested [5]. In addition, it could be observed that for slender walls, diagonal tension was the main failure mode, while a combination of diagonal tension and sliding dominated as the aspect ratio decreased. Cruz and Pérez-Gavilán [24] conﬁrmed that sliding is a mechanism that frequently appears in long walls after signiﬁcant cracking due to tension. Consequently, joint reinforcement can be effective. However, once sliding appears, this inhibits the production of new inclined cracks, which are necessary to deform the joint reinforcement. In this paper, new experimental evidence is presented about the contribution of the joint reinforcement on the behavior of RC frame inﬁlled with masonry walls subject to in plane lateral load for different aspect ratios. For the analysis, two new specimens were tested and the results were complemented with previous tests using the same type of material presented by Leal et al. [3]. The hysteretic behavior of the walls is evaluated through standard structural parameters, such as the cracking strength, peak strength, displacement capacity, ductility and cracking patterns. In addition, the contribution of the joint reinforcement to the shear strength of the walls is analyzed in detail. For that purpose, stress in the wires was estimated using measurements of strain gauges from which the forces in the steel bars were calculated using classical plasticity theory. The importance of this investigation is attributed to the fact that there is not enough experimental evidence about the use of joint reinforcement on inﬁll walls; consequently, the Mexican code [2] establishes the same speciﬁcations as those of conﬁned walls. The test results here presented contribute to verify the Mexican code considerations on the topic. 2. Experimental Program An overview of the specimens and tests is presented below. Detailed information regarding the design of the specimens, material properties, construction sequence, test setup, instrumentation and load sequence can be found on Leal et al. [3]. 2.1. Specimens Four specimens, scaled 1:2, were built and tested. A summary of characteristics of the specimens is presented in Table 1. All the specimens included tie-columns and tie- beams on the inﬁll wall perimeter. The dimensions of these concrete conﬁnement elements were 65 100 mm. The main reason to use conﬁnement elements is to anchor the joint reinforcement. Table 1. Description of the specimens. Joint Reinforcement Pairs Specimens H/L of the Inﬁll Wall ( p f ) h yh MD3N_L75 - 0.75 MD3NRH_L75 0.6 MPa 0.75 MD3N_L41 - 0.41 MD3NRH_L41 0.6 MPa 0.41 These specimens were presented in Leal et al. (2017), and they were denominated MD3N and MD3NRH. 2.2. Material Properties Mechanical properties of the material were investigated through the corresponding standard Mexican tests, similar to the ASTM tests. The average values for the compressive strength of masonry units ( f ), compressive strength of mortar ( f ), concrete strength ( f ) p c and elastic modulus (E ), compressive strength of masonry ( f ) and diagonal compressive c m strength (v ) are shown in Table 2. m Buildings 2022, 12, 259 6 of 19 Buildings 2022, 12, x FOR PEER REVIEW 6 of 21 Table 2. Material properties (MPa). Table 2. Material properties (MPa). Units Mortar Concrete of Frame Concrete Concrete of of Tie-Elements Concrete of Masonry Units Mortar Masonry Specimens Specimens Frame Tie-Elements f f f E f E f v E c c m m p j c c m 𝒇 𝒇 𝒇 𝑬 𝒇 𝑬 𝒇 𝒗 𝑬 𝒑 𝒋 𝒄 𝒄 𝒄 𝒄 𝒎 𝒎 𝒎 MD3N_L75 9.36 12.80 32.51 24773 22.62 21998 1.6 0.29 - MD3N_L75 9.36 12.80 32.51 24773 22.62 21998 1.6 0.29 - MD3NRH_L75 9.36 12.80 32.51 24773 22.62 21998 1.6 0.29 - MD3N_L41 9.36 15.01 MD3NRH_L 19.03 75 9.36 19490 12.80 15.07 32.51 24773 17220 22.62 219983.40 1.6 0.53 0.29 703 - MD3NRH_L41 9.36 8.01 19.95 19719 13.30 15661 3.34 0.59 693 MD3N_L41 9.36 15.01 19.03 19490 15.07 17220 3.40 0.53 703 MD3NRH_L41 9.36 8.01 19.95 19719 13.30 15661 3.34 0.59 693 In all cases, the inﬁll walls were made of brick units with nominal dimensions of 25 65 125 mm. All the units were obtained from the same production batch. 2.3. Reinforcement 2.3.1. Reinforcement in Reinforced Concrete Elements 2.3. Reinforcement The longitudinal reinforcement in columns and beams consisted of rebars of 12.7 mm 2.3.1. Reinforcement in Reinforced Concrete Elements (1/2″) and 9.5 mm (3/8″) diameter with a nominal yielding stress 𝑓 = 412 MPa. Trans- The longitudinal reinforcement in columns and beams consisted of rebars of 12.7 mm verse reinforcement consisted of rebars with 6.3 mm (1/4″) diameter stirrups with 𝑓 (1/2”) and 9.5 mm (3/8”) diameter with a nominal yielding stress f = 412 MPa. Transverse equal to 230 MPa. In the case of confining elements, 4 mm diameter bars were used for reinforcement consisted of rebars with 6.3 mm (1/4”) diameter stirrups with f equal to longitudinal reinforcement (𝑓 = 588 MPa) and tie wire for transversal reinforcement. Fig- 230 MPa. In the case of conﬁning elements, 4 mm diameter bars were used for longitudinal ure 3 shows the details of the reinforcement in columns and beams, as well as tie-columns reinforcement ( f = 588 MPa) and tie wire for transversal reinforcement. Figure 3 shows the and tie-beams. details of the reinforcement in columns and beams, as well as tie-columns and tie-beams. (b) (c) (d) (a) Figure 3. Dimensions (in millimeters) and reinforcing details of specimens. (a) elevation view, (b) Figure 3. Dimensions (in millimeters) and reinforcing details of specimens. (a) elevation view, columns, (c) tie-columns and tie-beams, (d) beams. (b) columns, (c) tie-columns and tie-beams, (d) beams. 2.3.2. Reinforcement in Bed-Joints 2.3.2. Reinforcement in Bed-Joints Joint reinforcement consisted of 4 mm (5/32”) diameter bars, which were investigated Joint reinforcement consisted of 4 mm (5/32″) diameter bars, which were investigated through three samples tested in tension (Figure 4a). The average values for yield stress ( f ) through three samples tested in tension (Figure 4a). The average values for yield stress and elastic modulus (E ) were 691 MPa and 188,494 MPa, respectively. The reinforcing bars (𝑓 ) and elastic moduluss (𝐸 ) were 691 MPa and 188,494 MPa, respectively. The reinforcing 𝑦 𝑠 were located every six courses, corresponding to a value for p f = 0.6 MPa. The diameter h yh bars were located every six courses, corresponding to a value for 𝑝 𝑓 = 0.6 MPa. The ℎ 𝑦 ℎ and spacing of joint reinforcement were selected in concordance with the requirements of diameter and spacing of joint reinforcement were selected in concordance with the re- the Mexican code [2] relative to the use of steel bars with smaller diameter than 0.75 thick quirements of the Mexican code [2] relative to the use of steel bars with smaller diameter bed-joint and spacing no larger than six courses. Details of the joint reinforcement are than 0.75 thick bed-joint and spacing no larger than six courses. Details of the joint rein- shown in Figure 3. forcement are shown in Figure 3. In order to estimate the contribution of the joint reinforcement to the shear strength of the walls, an average stress–strain curve was obtained to characterize the reinforcing bars. This average curve was approximated to an elastoplastic curve (Figure 4b). Buildings 2022, 12, x FOR PEER REVIEW 7 of 21 Buildings 2022, 12, 259 7 of 19 Buildings 2022, 12, x FOR PEER REVIEW 7 of 21 800 800 600 600 500 500 800 800 𝜎 = 691 MPa 400 𝑦 B1 700 700 𝐸 = 188,494 MPa 300 300 B2 B3 500 500 𝜎 = 691 MPa 400 𝑦 B1 𝐸 = 188,494 MPa B2 0.0% 0.5% 1.0% 1.5% 2.0% 0.0% 0.5% 1.0% 1.5% 2.0% B3 (a) (b) 0.0% 0.5% 1.0% 1.5% 2.0% 0.0% 0.5% 1.0% 1.5% 2.0% Figure 4. Stress–strain curve of joint reinforcement. (a) curves of samples tested, (b) average curve. Figure 4. Stress–strain curve of joint reinforcement. (a) curves of samples tested, (b) average curve. 2.4. Test Setup and Load S (a equence ) (b) In order to estimate the contribution of the joint reinforcement to the shear strength of the walls, an average stress–strain curve was obtained to characterize the reinforcing bars. Figure 5 shows the test setup used to apply loads to the specimens. To simulate the Figure 4. Stress–strain curve of joint reinforcement. (a) curves of samples tested, (b) average curve. This average curve was approximated to an elastoplastic curve (Figure 4b). gravity loads, vertical load was applied on the top of the columns. The vertical load was maintained constant during each test, equal to 120.17 kN, leading to a vertical stress on 2.4. Test Setup and Load Sequence 2.4. Test Setup and Load Sequence columns of 3.92 MPa. The specimens were subjected to cycles of quasi-statics alternated Figure 5 shows the test setup used to apply loads to the specimens. To simulate the Figure 5 shows the test setup used to apply loads to the specimens. To simulate the lateral load, simulating seismic action. The application of the lateral load followed the test gravity loads, vertical load was applied on the top of the columns. The vertical load was gravity loads, vertical load was applied on the top of the columns. The vertical load was procedure described in the Appendix A of Mexican code [2]. The first two cycles were maintained constant during each test, equal to 120.17 kN, leading to a vertical stress on maintained constant during each test, equal to 120.17 kN, leading to a vertical stress on load controlled up to 25% of the estimated cracking load, and the next two cycles up to columns of 3.92 MPa. The specimens were subjected to cycles of quasi-statics alternated columns of 3.92 MPa. The specimens were subjected to cycles of quasi-statics alternated 50% of the estimated cracking load. The estimated cracking lateral loads were 32.31 kN lateral load, simulating seismic action. The application of the lateral load followed the test lateral load, simulating seismic action. The application of the lateral load followed the test and 58.86 kN for specimens with H/L equal to 0.75 and 0.41, respectively. The sequence procedure described in the Appendix A of Mexican code [2]. The first two cycles were procedure described in the Appendix A of Mexican code [2]. The ﬁrst two cycles were continued with displacement controlled cycles starting with deformations of 0.001 and load controlled up to 25% of the estimated cracking load, and the next two cycles up to load controlled up to 25% of the estimated cracking load, and the next two cycles up to 0.002. After that, drifts with increments of 0.002 were applied considering two cycles for 50% of the estimated cracking load. The estimated cracking lateral loads were 32.31 kN 50% of the estimated cracking load. The estimated cracking lateral loads were 32.31 kN each increment. When the specimen reached a deformation of 0.02, the drift increment and 58.86 kN for specimens with H/L equal to 0.75 and 0.41, respectively. The sequence and 58.86 kN for specimens with H/L equal to 0.75 and 0.41, respectively. The sequence changed to 0.004 (Figure 6). continued with displacement controlled cycles starting with deformations of 0.001 and continued with displacement controlled cycles starting with deformations of 0.001 and 0.002. After that, drifts with increments of 0.002 were applied considering two cycles for 0.002. After that, drifts with increments of 0.002 were applied considering two cycles for each increment. When the specimen reached a deformation of 0.02, the drift increment each increment. When the specimen reached a deformation of 0.02, the drift increment changed to 0.004 (Figure 6). changed to 0.004 (Figure 6). (a) (b) Figure 5. Test setup. (a) transverse view, (b) elevation view. (a) (b) Figure 5. Test setup. (a) transverse view, (b) elevation view. Figure 5. Test setup. (a) transverse view, (b) elevation view. (MPa) (MPa) (MPa) (MPa) Buildings 2022, 12, 259 8 of 19 Buildings 2022, 12, x FOR PEER REVIEW 8 of 21 Buildings 2022, 12, x FOR PEER REVIEW 8 of 21 Figure 6. Lateral load sequence. Figure 6. Lateral load sequence. Figure 6. Lateral load sequence. 2.5. Instrumentation 2.5. Instrumentation 2.5. Instrumentation The The applied applied loads loads and and displacements displacements i inneach each specimen specimen wer were e measur measured ed during during tests. tests. The applied loads and displacements in each specimen were measured during tests. Strain gauges were installed in the joint reinforcement, following a diagonal trajectory on Strain gauges were installed in the joint reinforcement, following a diagonal trajectory on Strain gauges were installed in the joint reinforcement, following a diagonal trajectory on the the wall wall (Figur (Figure e 7a). 7a). Due Due to tothe the symmetry symmetry of ofthe the wall, wall,for for MD3NRH_L41, MD3NRH_L41,strain strain gauges gauges the wall (Figure 7a). Due to the symmetry of the wall, for MD3NRH_L41, strain gauges wer were con e concentrated centrated in in one one panel panel (F (Figur igure e 7 7 b). b). were concentrated in one panel (Figure 7b). (a) (b) (a) (b) Figure 7. Internal instrumentation. (a) specimens MD3NRH_L75, (b) specimens MD3NRH_L41. Figure Figure7. 7. Inter Internal nal inst instr ru umentation. mentation. (( aa )) spe specimens cimens MD3NR MD3NRH_L75, H_L75, ((b b)) spe specimens cimens MD3 MD3NRH_L41. NRH_L41. 3. Experimental Results 3. Experimental Results 3. Experimental Results 3.1. Hysteretic Curves and Crack Patterns 3.1. Hysteretic Curves and Crack Patterns 3.1. Hysteretic Curves and Crack Patterns The lateral load–drift hysteretic curves of each specimen are presented in Figure 8. The lateral load–drift hysteretic curves of each specimen are presented in Figure 8. The lateral load–drift hysteretic curves of each specimen are presented in Figure 8. The drift is deﬁned as the lateral displacement divided by the height of the wall. The The drift is defined as the lateral displacement divided by the height of the wall. The final The drift is defined as the lateral displacement divided by the height of the wall. The final ﬁnal cracking patterns are shown in Figure 9. Both hysteretic curves and crack patterns cracking patterns are shown in Figure 9. Both hysteretic curves and crack patterns evolu- cracking patterns are shown in Figure 9. Both hysteretic curves and crack patterns evolu- evolution of each inﬁll wall are described below. For a better understanding, it is important tion of each infill wall are described below. For a better understanding, it is important to tion of each infill wall are described below. For a better understanding, it is important to to note that positive lateral load occurred when the specimen was pulled towards the note that positive lateral load occurred when the specimen was pulled towards the strong note that positive lateral load occurred when the specimen was pulled towards the strong strong wall, and negative load occurred when the inﬁll wall was pushed (Figure 5b). wall, and negative load occurred when the infill wall was pushed (Figure 5b). wall, and negative load occurred when the infill wall was pushed (Figure 5b). In the case of the specimen MD3N_L75, the ﬁrst diagonal cracking was registered In the case of the specimen MD3N_L75, the first diagonal cracking was registered in In the case of the specimen MD3N_L75, the first diagonal cracking was registered in in cycle 5 for a lateral load of V = 28.8 kN and a drift level of g = 0.0006. This crack cycle 5 for a lateral load of 𝑉 = 28.8 kN and a drift level of 𝛾 = 0.0006. This crack started cycle 5 for a lateral load of 𝑉 = 28.8 kN and a drift level of 𝛾 = 0.0006. This crack started started near the center top and descended towards the right tie-column with an angle of near the center top and descended towards the right tie-column with an angle of approx- near the center top and descended towards the right tie-column with an angle of approx- approximately 30 degrees from the horizontal (Figure 9a). In the same cycle, when the imately 30 degrees from the horizontal (Figure 9a). In the same cycle, when the lateral load imately 30 degrees from the horizontal (Figure 9a). In the same cycle, when the lateral load lateral load was negative, diagonal cracking occurred at the upper left corner of the wall. was negative, diagonal cracking occurred at the upper left corner of the wall. This second was negative, diagonal cracking occurred at the upper left corner of the wall. This second This second diagonal crack had a direction approximately orthogonal than the ﬁrst one. diagonal crack had a direction approximately orthogonal than the first one. The first crack- diagonal crack had a direction approximately orthogonal than the first one. The first crack- The ﬁrst cracking is usually associated with a change in the slope of the hysteretic curve; ing is usually associated with a change in the slope of the hysteretic curve; however, in ing is usually associated with a change in the slope of the hysteretic curve; however, in however, in these tests, the ﬁrst cracking had no apparent effect on the load–drift curve. these tests, the first cracking had no apparent effect on the load–drift curve. The first crack these tests, the first cracking had no apparent effect on the load–drift curve. The first crack The ﬁrst crack in the frame occurred in cycle 7 at the left end of the beam for V = 53.8 kN in the frame occurred in cycle 7 at the left end of the beam for 𝑉 = 53.8 kN and 𝛾 = in the frame occurred in cycle 7 at the left end of the beam for 𝑉 = 53.8 kN and 𝛾 = and g = 0.0016. When the lateral load acted upon the negative direction, the right end 0.0016. When the lateral load acted upon the negative direction, the right end of the beam 0.0016. When the lateral load acted upon the negative direction, the right end of the beam of the beam cracked. Cracking on the beam occurred when the wall and frame were in cracked. Cracking on the beam occurred when the wall and frame were in contact at that cracked. Cracking on the beam occurred when the wall and frame were in contact at that contact at that zone. In the same cycle, diagonal cracks forming an “X” at the central zone zone. In the same cycle, diagonal cracks forming an “X” at the central zone of the wall zone. In the same cycle, diagonal cracks forming an “X” at the central zone of the wall Buildings 2022, 12, 259 9 of 19 Buildings 2022, 12, x FOR PEER REVIEW 11 of 21 of the wall were registered. In cycle 9, corresponding to a lateral load of V = 88.8 kN and The effect of aspect ratio was much more important. Walls with H/L = 0.41 had more a drift of g = 0.0040, the ﬁrst ﬂexural crack appeared at the bottom of the right column. than twice the residual drift after cracking than walls with H/L = 0.75 (2.19 without rein- At the same time, a diagonal crack arose in the right beam–column connection. Change forcement and 2.16 with reinforcement). At peak strength, the residual drift was also sig- in the slope of the hysteretic curve (yielding) was reached at cycle 11 for a lateral load of nificantly larger. The residual drift in walls with H/L = 0.41 compared to those with H/L = V = 103.7 kN and a drift level of g = 0.0060. At this level of deformation, the damage of 0.75 was 1.42 and 1.31 times larger for the cases without and with reinforcement, respec- the specimen consisted of well-deﬁned diagonal cracks on the inﬁll wall, ﬂexural cracks tively. at both ends of beam and at the bottom of columns, and diagonal cracking at both beam– column connection. As the test progressed, some new diagonal cracks appeared in the Table 3. Residual drift after unloading and reloading/loading ratio. wall and width of the old cracks increased signiﬁcantly; new cracks at the beam did not appear; ﬂexural cracking in the columns extended towards the center of the members; and Cycle of First Cracking Cycle of Peak Strength Cycle of Failure Specimen damage at beam-column connections increased. The maximum strength of the specimen, 𝜸 𝑽 ⁄𝑽 𝜸 𝑽 ⁄𝑽 𝜸 𝑽 ⁄𝑽 𝑷 𝒓𝒆𝒍 𝒍 𝑷 𝒓𝒆𝒍 𝒍 𝑷 𝒓𝒆𝒍 𝒍 V = 130.1 kN, was reached in cycle 27 for a drift of g = 0.0240. At this stage of the test, all MD3N_L75 0.00042 0.906 0.0064 0.908 0.0160 0.963 the cracks on the specimen had already appeared, including crushing of the concrete at the MD3NRH_L75 0.00045 0.928 0.0054 0.907 0.0153 0.907 bottom of the columns. In the descending part of the curve, the width of cracks increased MD3N_L41 0.00092 0.891 0.0091 0.747 0.0154 0.925 and total separation of some portions of the wall occurred. Failure of the specimen occurred MD3NRH_L41 0.00097 0.913 0.0071 0.881 0.0149 0.882 in cycle 37, reaching a lateral load of V = 97.1 kN and a drift of g = 0.0440. 200 200 100 100 50 50 0 0 -50 -50 -100 -100 -150 -150 -200 -200 -0.05 -0.03 -0.01 0.01 0.03 0.05 -0.05 -0.03 -0.01 0.01 0.03 0.05 Drift Drift MD3N_L75 MD3NRH_L75 200 200 150 150 100 100 50 50 -50 -50 -100 -100 -150 -150 -200 -200 -0.05 -0.03 -0.01 0.01 0.03 0.05 -0.05 -0.03 -0.01 0.01 0.03 0.05 Drift Drift MD3N_L41 MD3NRH_L41 Figure 8. Lateral load–drift hysteretic curves. Figure 8. Lateral load–drift hysteretic curves. Lateral load (kN) Lateral Load (kN) Lateral load (kN) Lateral Load (kN) Buildings 2022, 12, 259 10 of 19 Buildings 2022, 12, x FOR PEER REVIEW 12 of 21 (a) (b) (c) (d) Figure 9. Crack pattern. (a) MD3N_L75; (b) MD3NRH_L75; (c) MD3N_L41; (d) MD3NRH_L41. Figure 9. Crack pattern. (a) MD3N_L75; (b) MD3NRH_L75; (c) MD3N_L41; (d) MD3NRH_L41. The inﬁll wall MD3NRH_L75 had the ﬁrst diagonal cracks in cycle 5 for a lateral 3.2. Envelope Curves load of V = 31.5 kN and a drift of g = 0.0006. Unlike to MD3N_L75, the ﬁrst cracking For each specimen, the envelope curve was obtained connecting the peak points of consisted of a set of three thin cracks distributed at the central zone of the wall. In this early the hysteretic cycles. In Figure 10, the envelope curve corresponding to specimen stage of the test, new ﬁne cracks appeared in each drift increment. Flexural cracking in MD3N_L75 is presented. The global behavior of the walls is described by four critical the frame started in cycle 9 for V = 90.1 kN and g = 0.0040, located at the left end of the events, which are included in the envelope curves: first cracking ( 𝛾 , 𝑉 ), yielding 𝑐𝑟 𝑐𝑟 beam and the bottom of the left column. When lateral load acted in a negative direction, strength (𝛾 , 𝑉 ), peak strength (𝛾 , 𝑉 ) and failure (𝛾 , 𝑉 ). In addition, the equiv- both beam and column cracked at the opposite zones. In𝑈 cycle 11, corresponding to a alent elastoplastic model is included in this figure, which was determined according with lateral load of V = 107.5 kN and a drift of g = 0.0060, a vertical crack arose at the left the procedure described by the Mexican code [2], similar to the one established in ASCE- bonding surface of beam–column, which represented the most signiﬁcant damage in the SEI frame 41at -13 the [25 last ], with stage out of co the nsider test. ing Yielding hardening of the or load–drift strengthcurve degrad occurr ation. ed Th inecycle equi13 valto ena t model has the same area under the curve as the experimental envelope and its first branch lateral load of V = 120.1 kN and a drift level of g = 0.0080. At this point, damage of the specimen consisted of distributed diagonal cracks on the inﬁll wall, cracks at both ends of intersects the experimental envelope at 0.6𝑉 , where 𝑉 is the resistance of the elasto- 𝑦 𝑦 beam, ﬂexural cracking at both ends of the columns and vertical cracks at both interphase plastic model. beam–column surface. From yielding to maximum strength (cycle 27, V = 148.3 kN and g = 0.0240), ﬂexural cracking in the columns extended towards the central zone, diagonal cracks at beam-column connections 𝛾 ,appear 𝑉 ed on both directions forming an “X” and 𝑚𝑎𝑥 𝑚𝑎𝑥 𝛾 , 𝑉 𝑦 𝑦 crushing of masonry occurred on dispersed zones of the wall. In the last stage of the test, 𝛾 , 𝑉 which is characterized by the descending part of 𝑈 the 𝑈 hysteric curve, the vertical crack at 𝛾 , 𝑉 interphases beam–column 𝑦𝑠 𝑦𝑠 surface increased in width signiﬁcantly, detachment of a portion Envelope curve of the left column occurred due to the diagonal cracking on beam–column connection Elastoplastic model and crushing on the inﬁll wall was widespread (Figure 9b). Failure occurred in cycle 37, First cracking reaching a lateral load of V = 113.1 kN and a drift of g = 0.0440. Yielding The ﬁrst diagonal crack on specimen MD3N_L41 occurred at cycle 5 for V = 47.8 kN Peak strength and g = 0.0006. It developed on the central zone of the left masonry panel. When lateral 𝛾 , 𝑉 𝑐𝑟 𝑐𝑟 Failure load changed direction (V =49.9 kN and g =0.0006), a second diagonal crack appeared in the right panel. These two cracks did not cross each other. In the same cycle, a vertical crack between masonry and the right tie-column occurred. Cracking in the frame started 0.00 0.01 0.02 0.03 0.04 0.05 in cycle 7 for a lateral load of V = 66.4 kN and a drift of g = 0.0012, located at the left Drift (mm/mm) end of the beam. In the same cycle, when load was negative, cracking appeared in the opposite end of the beam. Flexural cracks at the bottom of the left column appeared in Figure 10. Envelope curve and critical points. Lateral load (kN) 𝑚𝑎𝑥 𝑦𝑠 𝑚𝑎𝑥 𝑦𝑠 Buildings 2022, 12, 259 11 of 19 cycle 9, corresponding to V = 119.4 kN and g = 0.0040. Additionally, other damages in the specimen consisted of new diagonal cracking in the wall, the previous diagonal cracks widened and their length increased towards the opposite panel, so they crossed each other and the cracks in the beam extended about 500 mm from the ends. In this point of the test, yielding of the hysteretic curve can be observed. Diagonal cracking at left beam–column connection was registered in cycle 11 for V = 133.7 kN and g = 0.0060. However, in cycle 16 (g = 0.010), a shear cracking appeared near the upper part of the column, which absorbed the deformation of the frame in the last stage of the test. Flexural cracking on beam and columns extended towards the center of the members as the tests progressed. Unlike specimens with H/L = 0.75, the MD3N_L41 developed cracking along the complete beam. From yield point onward, a combination of inclined cracks and horizontal sliding developed on the wall. As the tests continued, horizontal sliding was predominant, meaning that few additional inclined cracks developed. The maximum strength, V = 148.2 kN, was reached in cycle 27 for a drift of g = 0.0240. At this point of the test, shear failure of the central tie-column occurred. The descending part of the curve was characterized by a combination of sliding and well-deﬁned diagonal cracks in the wall, while in the frame, a shear damage produced failure of the left column (Figure 9c). In cycle 33, failure was registered. This cycle reached a lateral load of V = 115.6 kN and a drift of g = 0.0360. For the specimen MD3NRH_L41, it was difﬁcult to detect the ﬁrst diagonal cracking on the wall. In cycle 6 for V = 39.2 kN and g = 0.0006, three thin cracks appeared on units located at the central zone of the right panel. However, apparently they were not connected. Two cracks with more deﬁned diagonal trajectories appeared in cycle 7 (V = 68.6 kN and g = 0.0014), although they had a small width and were distributed in both masonry panels. The ﬁrst crack in the frame, located at the right end of the beam, occurred in cycle 7 for V = 80.9 kN and g = 0.0014. Change in the slope of the hysteretic curve (yielding) was deﬁned at cycle 11 for a lateral load of V = 150.9 kN and a drift of g = 0.0060. Unlike specimen MD3N_L41, at this point of the test, diagonal cracking on the inﬁll wall were of smaller width and distributed around the wall, and ﬂexural cracks on the columns had not appeared yet. In cycle 13, for a lateral load of V = 165.2 kN and g = 0.0080, the ﬁrst ﬂexural crack at the bottom of the left column was registered. In the same cycle, when lateral load was V = 152.6 kN and drift g = 0.0080, a diagonal cracking at right beam–column connection occurred. As the test progressed, damage on the wall consisted of new thin diagonal cracks distributed in the panel. It was observed that the previous diagonal cracks did not increase in width. Sliding on bed-joints occurred approximately every six courses, which did not coincide with the courses where the horizontal reinforcement was placed and crushing of masonry developed on dispersed zones of the wall. Damage on the frame consisted of cracking at the ends of the beam located at an approximate length of 700 mm, ﬂexural cracking extended towards the center of the columns and diagonal cracks at the beam–column connections increased. The maximum strength, V = 194.0 kN, was reached in cycle 27 for a drift of g = 0.0240. In the descending part of the hysteretic curve, crushing and sliding on the wall were predominant, while in the frame, crushing at the ends of the beam and diagonal cracking at the beam–column connection occurred when its zone was in contact with the wall (Figure 9d). Failure occurred in cycle 35, for a lateral load of V = 147.3 kN and a drift of g = 0.040. In all cases, separation between the wall and the frame occurred early through cracks in the interface of these elements. This fact is due to the natural construction sequence of the system, in which the inﬁll wall is built after the frame producing a cold joint between them. To avoid this early separation, integral inﬁlled frames can be considered, where wall–frame separation is expected for lateral loads higher than 50% of the ultimate strength [16]. As the test progressed, separation between the wall and the column increased signiﬁcantly, reaching a maximum of 18 mm. According to the lateral load, a diagonal strut developed, while separation of the wall and frame occurred at the opposite corners. Buildings 2022, 12, x FOR PEER REVIEW 12 of 21 Buildings 2022, 12, 259 12 of 19 The hysteretic behavior of the specimens is investigated through the residual drift (g ) after unloading in each cycle and the reloading/loading ratio (V /V ) of two repeated rel l cycles. Table 3 shows values for g and V /V corresponding to the cycles of ﬁrst diagonal rel l cracking, peak strength and failure. Table 3. Residual drift after unloading and reloading/loading ratio. Cycle of First Cracking Cycle of Peak Strength Cycle of Failure Specimen g V /V g V /V g V /V P P P rel l rel l rel l MD3N_L75 0.00042 0.906 0.0064 0.908 0.0160 0.963 (a) (b) MD3NRH_L75 0.00045 0.928 0.0054 0.907 0.0153 0.907 MD3N_L41 0.00092 0.891 0.0091 0.747 0.0154 0.925 MD3NRH_L41 0.00097 0.913 0.0071 0.881 0.0149 0.882 The joint reinforcement signiﬁcantly reduced the residual drift at peak strength, reduc- tions of 15.6% and 22% were observed for H/L = 0.75 and H/L = 0.41, respectively. In the walls with H/L = 0.41, the repeat cycle at peak strength reduced signiﬁcantly less in the case with reinforcement (17.9% less). The effect of aspect ratio was much more important. Walls with H/L = 0.41 had more than twice the residual drift after cracking than walls with H/L = 0.75 (2.19 without (c) (d) reinforcement and 2.16 with reinforcement). At peak strength, the residual drift was also Figure 9. Crack pattern. (a) MD3N_L75; (b) MD3NRH_L75; (c) MD3N_L41; (d) MD3NRH_L41. signiﬁcantly larger. The residual drift in walls with H/L = 0.41 compared to those with H/L = 0.75 was 1.42 and 1.31 times larger for the cases without and with reinforcement, 3.2. Envelope Curves respectively. For each specimen, the envelope curve was obtained connecting the peak points of 3.2. Envelope Curves the hysteretic cycles. In Figure 10, the envelope curve corresponding to specimen MD3N_L75 is presented. The global behavior of the walls is described by four critical For each specimen, the envelope curve was obtained connecting the peak points of the events, which are included in the envelope curves: first cracking ( 𝛾 , 𝑉 ), yielding hysteretic cycles. In Figure 10, the envelope curve corresponding to specimen MD3N_L75 𝑐𝑟 𝑐𝑟 is presented. The global behavior of the walls is described by four critical events, which strength (𝛾 , 𝑉 ), peak strength (𝛾 , 𝑉 ) and failure (𝛾 , 𝑉 ). In addition, the equiv- are included in the envelope curves: ﬁrst cracking (g , V ), yielding strength (g , V ), cr cr ys ys alent elastoplastic model is included in this figure, which was determined according with peak strength (g , V ) and failure (g , V ). In addition, the equivalent elastoplastic max max U U the procedure described by the Mexican code [2], similar to the one established in ASCE- model is included in this ﬁgure, which was determined according with the procedure SEI 41-13 [25], without considering hardening or strength degradation. The equivalent described by the Mexican code [2], similar to the one established in ASCE-SEI 41-13 [25], model has the same area under the curve as the experimental envelope and its first branch without considering hardening or strength degradation. The equivalent model has the intersects the experimental envelope at 0.6𝑉 , where 𝑉 is the resistance of the elasto- 𝑦 𝑦 same area under the curve as the experimental envelope and its ﬁrst branch intersects the plastic model. experimental envelope at 0.6V , where V is the resistance of the elastoplastic model. y y 𝛾 , 𝑉 𝑚𝑎𝑥 𝑚𝑎𝑥 𝛾 , 𝑉 𝑦 𝑦 𝛾 , 𝑉 𝑈 𝑈 𝛾 , 𝑉 𝑦𝑠 𝑦𝑠 Envelope curve Elastoplastic model First cracking Yielding Peak strength 𝛾 , 𝑉 𝑐𝑟 𝑐𝑟 Failure 0.00 0.01 0.02 0.03 0.04 0.05 Drift (mm/mm) Figure 10. Envelope curve and critical points. Figure 10. Envelope curve and critical points. Lateral load (kN) 𝑚𝑎𝑥 𝑦𝑠 𝑚𝑎𝑥 𝑦𝑠 Buildings 2022, 12, 259 13 of 19 3.2.1. Cracking Strength The joint reinforcement did not have a significant effect on the cracking strength. Such an effect varies from one model to another. For the first pair (MD3N_L75 and MD3NRH_L75), the cracking strength of specimen with reinforced joints was 1.09 times that of the specimen without reinforcement. For the second pair (MD3N_L41 and MD3NRH_L41), the corresponding value was 0.89. Hence, on average, the specimens with steel bars in bed-joints had a value of V equal to 0.99 times that of the non-reinforced specimen cr (Table 4). These results are consistent with those presented by Leal el at. [3] for inﬁlled frames with larger size columns (denominated as MD6N and MD6NRH). The specimen with joint reinforcement had a cracking strength of 0.99 times that of the specimen without reinforcement. Table 4. Shear strength for the critical points of the envelope and elastoplastic model. Specimen V (kN) V (kN) V (kN) V (kN) V (kN) V /V V /V y cr ys max U ys cr max ys MD3N_L75 118.9 28.8 103.7 130.1 104.1 3.60 1.26 MD3NRH_L75 135.0 31.5 120.1 148.3 118.7 3.81 1.24 MD3N_L41 137.1 76.9 119.4 148.2 118.6 1.55 1.24 MD3NRH_L41 178.4 68.6 150.9 194.0 155.2 2.20 1.29 3.2.2. Yielding Strength In each pair, the yielding strength of the specimen with joint reinforcement was larger than that of specimen without reinforcement. The most signiﬁcant increase was found for the pair with H/L = 0.41, which was 26.4%; for the pair with H/L = 0.75, it was 15.8% (Table 4). Similarly, for the specimens with larger size columns (MD6N and MD6NRH), reported by Leal et al. [3], the joint reinforcement increased the yielding strength (10.0% increase). Yielding of the load–drift curve did not occur when the ﬁrst diagonal cracking was detected. Yielding strength was, on average, 2.79 times that of the cracking strength. The use of steel bars in bed-joints signiﬁcantly affect the quotient V /V . Pairwise comparison ys cr shows that the inﬁll wall with joint reinforcement had, on average, a value of this quotient 19.5% larger than that of the non-reinforced specimen. However, this increase was not consistent. For the ﬁrst pair, the effect of joint reinforcement was unimportant (only 5.8% increase); for the second pair, horizontal reinforcement had a strong impact (41.8% increase). In the case of specimens with larger size columns presented by Leal et al. [3], the joint reinforcement increased 11.1% the value of this quotient. 3.2.3. Peak Strength In general, the use of horizontal reinforcement increased the maximum strength of the inﬁll wall (Table 4). The specimen MD3NRH_L75 had a value of V 14% larger than max that of MD3N_L75; for the wall MD3NRH_L41, V was substantially larger than for max MD3N_L41, with a 30.9% increase. However, for specimens with larger size columns (MD6N and MD6NRH) reported in the literature [3], the joint reinforcement had no effect on the maximum strength. In all cases, the lateral load continued increasing after achieving yielding strength, although at a rate substantially lower. On average, the maximum strength was 1.25 times that of the yielding strength. However, neither the joint reinforcement nor the aspect ratio had a signiﬁcant effect on the quotient V /V . For the ﬁrst pair of specimens, the wall max ys with reinforced bed-joints had a value of V /V 1.6% smaller than the non-reinforced max ys wall; for the second pair, the quotient was 3.6% larger. In the case of specimens with larger size columns presented by Leal et al. [3], the joint reinforcement decreased 8.5% the value of this quotient. Buildings 2022, 12, 259 14 of 19 3.2.4. Failure The ultimate strength of each specimen corresponds to 0.8 V . Consequently, in each max pair of specimens, the joint reinforcement contributed to the ultimate strength on the same level than it increased the maximum strength. 3.2.5. Displacement Capacity and Ductility The displacement capacity of each specimen was evaluated through the drift at failure (Table 5). For the specimens with H/L = 0.41, the joint reinforcement had a slight effect on the displacement capacity (10% increase). In the case of inﬁll walls with H/L = 0.75, the use of steel bars in the bed-joint was not signiﬁcant on this parameter. Table 5. Drift at critical points and ductility. Specimen g g g g g m m y cr ys max U max U MD3N_L75 0.0050 0.0006 0.006 0.024 0.042 4.8 8.3 MD3NRH_L75 0.0057 0.0006 0.008 0.024 0.041 4.2 7.2 MD3N_L41 0.0030 0.0014 0.004 0.024 0.034 8.0 11.4 MD3NRH_L41 0.0050 0.0014 0.006 0.024 0.038 4.8 7.5 The ductility developed by each specimen at peak strength (m ) and at failure (m ) max u was calculated as the ratio of the corresponding drift to that reached at the yield point of the elastoplastic model (g ). Ductility at peak strength had an average value of 5.48 and at failure it was 8.61 (Table 5). In both pairs of specimens, the joint reinforcement consistently decreased the value of m and m . The quotients of ductility of specimens MD3N_L75 and MD3NRH_L75 max u at peak strength and at failure were 0.88 and 0.86, respectively; while for MD3N_L41 and MD3NRH_L41, the quotients were 0.60 and 0.66, respectively. The reason for this is that the specimen with joint reinforcement had a value for g signiﬁcantly larger than that of the unreinforced specimen. 3.3. Contribution of Joint Reinforcement and Inﬁlled Frame to Lateral Load It is considered that the applied lateral load (V) to the specimen is resisted by the joint reinforcement and the inﬁlled frame. The contributions of each component are presented below. 3.3.1. Contribution of the Joint Reinforcement As an indicator of the contribution of the joint reinforcement to the shear strength, the sum of the forces developed in the steel bars (V ) was calculated. In a given course, the force in the rebar is obtained by multiplying the maximum calculated stress by the rebar area. The maximum stress is calculated from strain gauges installed in the joint reinforcement. To convert the measured strain by strain gauges to stresses, the average stress–strain curve of the joint reinforcement (Figure 4b) and the deformation history of each rebar were considered. For this purpose, the constitutive model of one-dimensional rate-independent plasticity was used, which is described in detail by Simo and Hughes [26]. In the case of MD3NRH_L41, only a panel was instrumented (Figure 7b). The total force in the joint reinforcement was obtained as the force in the instrumented panel multiplied by 2. The variation of V with drift for each specimen with joint reinforcement is shown in Figure 11. In both cases, it was observed that in the ﬁrst stage of the test, the total force in the rebars was negligible and the shape of the cycle was undeﬁned. It was until the ﬁrst inclined cracking that the value of V increased signiﬁcantly and from the next cycle the loops adopted their typical asymmetric “U” shape. The shape of the cycles shows that the horizontal reinforcement works in tension during the test and the force in it is larger when drift is positive. Good repeatability of the cycles is observed until the maximum value for V is reached, which indicates that cycles were stable. S Buildings 2022, 12, x FOR PEER REVIEW 16 of 21 𝛾 = 0.028. The descending part of the curve was stable, judging by the repeatability of the cycles. The largest force in the joint reinforcement was found for the specimen MD3NRH_L41. The maximum value for 𝑉 = 69.6 kN was registered in the cycle 29 for a lateral load of 𝑉 = 190.3 kN and a drift of 𝛾 = 0.028. In the next drift increment (𝛾 = 0.032), 𝑉 practically kept its maximum value, reaching a value equal to 69.4 kN. How- ever, in the cycle 33 corresponding to a maximum drift of 0.036, 𝑉 decreased suddenly its value from 61.6 kN to 30.8 kN. After this cycle the strain gauges measurements were significantly smaller and unstable, so the curve was cut at this point. A reduction in the Buildings 2022, 12, 259 maximum value of 𝑉 is observed to a drift equal to 0.02. This fact is consistent with 15 th ofe 19 decrease of the lateral load observed in the hysteretic curve (Figure 8) for the same drift. 70 70 60 60 50 50 40 40 30 30 20 20 10 10 0 0 -0.05 -0.03 -0.01 0.01 0.03 0.05 -0.05 -0.03 -0.01 0.01 0.03 0.05 Drift (mm/mm) Drift (mm/mm) MD3NRH_L75 MD3NRH_L41 Figure 11. Contribution of joint reinforcement (𝑉 )—drift curves Figure 11. Contribution of joint reinforcement (V )—drift curves. For the specimen MD3NRH_L75, the maximum force in the joint reinforcement of Figure 12 shows the contribution of joint reinforcement versus drift for each rein- V = 49.5 kN was registered in cycle 29 for a lateral load of V = 147.6 kN and a drift of forced specimen. Similar to the envelope curve, this one connects the positive peak points g = 0.028. The descending part of the curve was stable, judging by the repeatability of the of the cycles plotted in Figure 11. In addition, the values of 𝑉 at first cracking (𝑉 ) and 𝑆 𝑆 ,𝑐𝑟 cycles. at peak strength (𝑉 ) are indicated. 𝑆 , The largest force in the joint reinforcement was found for the specimen MD3NRH_L41. Consistently, it is observed that the force contributed by joint reinforcement is negli- The maximum value for V = 69.6 kN was registered in the cycle 29 for a lateral load gible before first cracking (𝑉 ≈ 0); after that, 𝑉 increases with drift until maximum 𝑆 ,𝑐𝑟 𝑆 of V = 190.3 kN and a drift of g = 0.028. In the next drift increment (g = 0.032), V force is reached. In both cases (MD3NRH_L75 and MD3NRH_L41), the maximum contri- practically kept its maximum value, reaching a value equal to 69.4 kN. However, in the bution of the joint reinforcement was reached for a larger drift than 𝛾 , although the cycle 33 corresponding to a maximum drift of 0.036, V decreased suddenly its value from value of 𝑉 corresponding to drift at maximum strength was very close to 𝑉 (98% 61.6 kN to 𝑆 30.8 kN. After this cycle the strain gauges measurements were signiﬁcantly 𝑆 , on average). smaller and unstable, so the curve was cut at this point. A reduction in the maximum value of V is observed to a drift equal to 0.02. This fact is consistent with the decrease of the lateral load observed in the hysteretic curve (Figure 8) for the same drift. Figure 12 shows the contribution of joint reinforcement versus drift for each reinforced specimen. Similar to the envelope curve, this one connects the positive peak points of the Buildings 2022, 12, x FOR PEER REVIEW 17 of 21 cycles plotted in Figure 11. In addition, the values of V at ﬁrst cracking (V ) and at peak S S,cr strength (V ) are indicated. S,max MD3NRH_L75 MD3NRH_L41 First inclined crack 30 Peak strength 0.00 0.01 0.02 0.03 0.04 0.05 Drift (mm/mm) Figure 12. Contribution of joint reinforcement. Figure 12. Contribution of joint reinforcement. Consistently, it is observed that the force contributed by joint reinforcement is negligi- 3.3.2. Contribution of Infilled Frame ble before ﬁrst cracking (V 0); after that, V increases with drift until maximum force S,cr S The contribution of infilled frame to lateral load (𝑉 ) was calculated as the difference is reached. In both cases (MD3NRH_L75 and MD3NRH_L41), the maximum contribution between the applied lateral load (𝑉 ) and the force of the joint reinforcement (𝑉 ). The value of 𝑉 versus drift at peak of each cycle is plotted in Figure 13. In addition, for each reinforced specimen, the envelope curve of the corresponding non-reinforced infill wall is included for comparison purposes. The envelope curves of the non-reinforced speci- mens are presented by continue lines, while the contribution of the infilled frames in re- inforced specimens by discontinue lines. In Figure 13, it is observed that all cases presented a reduction of the contribution of infilled frame relative to the shear strength of non-reinforced specimen. This result is con- sistent with that reported in the literature for masonry load-bearing walls [24,27]. It is argued that the reason of this fact is that once the diagonal crack appears, the horizontal steel goes into tension at the points of intersection with the crack, causing the masonry across to lessen its resistance. For the specimen MD3NRH_L75, the infilled frame contribution to the peak strength was equal to 76.9% of the lateral load reached by MD3N_L75 at the same drift (𝛾 = 0.024), and in the case of MD3NRH_L41 was 84.5% of the applied load to MD3N_L41. MD3N_L75 (MD3NRH_L75) MD3N_L41 𝑉 (MD3NRH_L41) 0.00 0.01 0.02 0.03 0.04 Drift (mm/mm) Figure 13. Contribution of infilled frame. (kN) (kN) Lateral load (kN) (kN) 𝐼𝐹 𝐼𝐹 𝑚𝑎𝑥 𝐼𝐹 𝐼𝐹 𝑚𝑎𝑥 𝑚𝑎𝑥 𝑚𝑎𝑥 Buildings 2022, 12, x FOR PEER REVIEW 17 of 21 MD3NRH_L75 MD3NRH_L41 First inclined crack Peak strength 0.00 0.01 0.02 0.03 0.04 0.05 Drift (mm/mm) Figure 12. Contribution of joint reinforcement. 3.3.2. Contribution of Infilled Frame The contribution of infilled frame to lateral load (𝑉 ) was calculated as the difference between the applied lateral load (𝑉 ) and the force of the joint reinforcement (𝑉 ). The value of 𝑉 versus drift at peak of each cycle is plotted in Figure 13. In addition, for each Buildings 2022, 12, 259 16 of 19 reinforced specimen, the envelope curve of the corresponding non-reinforced infill wall is included for comparison purposes. The envelope curves of the non-reinforced speci- mens are presented by continue lines, while the contribution of the infilled frames in re- of the joint reinforcement was reached for a larger drift than g , although the value of V max S inforced specimens by discontinue lines. corresponding to drift at maximum strength was very close to V (98% on average). S,max In Figure 13, it is observed that all cases presented a reduction of the contribution of infilled frame relative to the shear strength of non-reinforced specimen. This result is con- 3.3.2. Contribution of Inﬁlled Frame sistent with that reported in the literature for masonry load-bearing walls [24,27]. It is The contribution of inﬁlled frame to lateral load (V ) was calculated as the difference I F argued that the reason of this fact is that once the diagonal crack appears, the horizontal between the applied lateral load (V) and the force of the joint reinforcement (V ). The steel goes into tension at the points of intersection with the crack, causing the masonry value of V versus drift at peak of each cycle is plotted in Figure 13. In addition, for each I F across to lessen its resistance. reinforced specimen, the envelope curve of the corresponding non-reinforced inﬁll wall is For the specimen MD3NRH_L75, the infilled frame contribution to the peak strength included for comparison purposes. The envelope curves of the non-reinforced specimens was equal to 76.9% of the lateral load reached by MD3N_L75 at the same drift (𝛾 = are presented by continue lines, while the contribution of the inﬁlled frames in reinforced 0.024), and in the case of MD3NRH_L41 was 84.5% of the applied load to MD3N_L41. specimens by discontinue lines. MD3N_L75 (MD3NRH_L75) MD3N_L41 (MD3NRH_L41) 0.00 0.01 0.02 0.03 0.04 Drift (mm/mm) Figure 13. Contribution of inﬁlled frame. Figure 13. Contribution of infilled frame. In Figure 13, it is observed that all cases presented a reduction of the contribution of inﬁlled frame relative to the shear strength of non-reinforced specimen. This result is consistent with that reported in the literature for masonry load-bearing walls [24,27]. It is argued that the reason of this fact is that once the diagonal crack appears, the horizontal steel goes into tension at the points of intersection with the crack, causing the masonry across to lessen its resistance. For the specimen MD3NRH_L75, the inﬁlled frame contribution to the peak strength was equal to 76.9% of the lateral load reached by MD3N_L75 at the same drift (g = 0.024), max and in the case of MD3NRH_L41 was 84.5% of the applied load to MD3N_L41. 4. Discussion 4.1. Cracking The initial cracking in the MD3N_L75 wall was due to local interaction of the wall and the conﬁnement elements and cannot be attributed to shear, which is probably the reason why it did not have an effect on the load–deformation curve. Considering each pair of specimens, the joint reinforcement had no effect on the cracking strength. This result is consistent with the fact that the strain in the rebars was negligible before the ﬁrst inclined crack appears. As in conﬁned masonry walls, the use of joint reinforcement in inﬁll walls produces a more distributed cracking and a reduction of the width of the cracks. It was consistently observed in each pair of specimens that joint reinforcement inhibits cracking between tie- columns and masonry panel. The non-reinforced inﬁll walls developed separation between these elements in the ﬁnal stage of the tests. The facts mentioned before are attributed to the lateral conﬁnement produced by the joint reinforcement, which is similar to a belt activated after ﬁrst cracking appears. (kN) Lateral load (kN) 𝐼𝐹 𝐼𝐹 𝑚𝑎𝑥 𝐼𝐹 𝐼𝐹 Buildings 2022, 12, 259 17 of 19 In the case of the specimens with joint reinforcement, it is considered that the observed damage at peak strength is repairable through standard retroﬁt procedures. However, this remark is not relevant due to, in practice, inﬁll walls of an ediﬁcation are replaceable. 4.2. Strength The joint reinforcement did not affect the cracking strength of the inﬁll walls. As reported in the literature for load-bearing walls [17–19], this result is attributed to the fact that joint reinforcement is activated after inclined cracks cross it. Judging by the load difference between the envelope curves of Figure 14, the contribu- tion of the joint reinforcement started at drifts of 0.006 and 0.004 for the specimens with Buildings 2022, 12, x FOR PEER REVIEW 19 of 21 H/L = 0.75 and 0.41, respectively. Although the force in the steel bars (V ) was already signiﬁcant for these levels of deformation (approximately 50% of V ), the differences S,max between the envelope curves were not relevant yet. 200 200 150 150 100 100 MD3N_L41 MD3N_L75 50 50 MD3NRH_L41 MD3NRH_L75 0 0 0.00 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04 0.05 Drift (mm/mm) Drift (mm/mm) (a) (b) Figure 14. Envelope curves comparison. (a) Specimens with H/L = 0.75, (b) specimens with Figure 14. Envelope curves comparison. (a) Specimens with H/L = 0.75, (b) specimens with H/L = 0.41.H/L = 0.41. For both cases, the largest load difference between envelope curves was for g = 0.028, 4.3. Capacity of Deformation and Ductility which coincides with the drift of the maximum force in the joint reinforcement. For the Regardless of the aspect ratio (H/L), the joint reinforcement did not have a significant two pairs of specimens, the maximum contribution of the joint reinforcement occurred at a effect on the displacement capacity of the system. This result is different than that ob- drift larger than g . The maximum contributions of the joint reinforcement were equal to max served for load-bearing confined masonry walls. For such walls, typically, it can be ob- 22.8 kN (46.1% of V ) and 62.8 kN (90.2% of V ) for specimens MD3NRH_L75 and S,max S,max served that the deformation at failure changes from 0.4% without reinforcement to nearly MD3NRH_L41, respectively. 1% [6]. Infill walls may undergo large deformations due to the frame that prevents the The specimen MD3NRH_L41 developed a larger force in the joint reinforcement than wall disintegration; however, for such large drifts, the infill wall may be considered that the MD3NRH_L75 one, which is consistent with the larger increment in the maximum have already failed. Consequently, the beneficial effect of the reinforcement cannot be ob- strength. This fact is attributed to a larger cross-section area of the wall. served for such large deformations. According to the Mexican code [2], the contribution of joint reinforcement to shear For both cases of H/L, the use of joint reinforcement reduced the ductility of the sys- strength (V ) of masonry walls must be included only if diagonal tension failure dominates. sR tem. Ductility depends on the displacement capacity (𝛾 ) and the drift at yielding of the For all specimens, the Mexican code predicts sliding failure in the inﬁll wall; however, elastoplastic model (𝛾 ). The reduction of ductility is attributed to the fact that, in each experimental results show that diagonal tension occurred ﬁrst and sliding appeared on the descending part of the envelope curve. The increment of shear strength estimated pair, the specimen with joint reinforcement had a value for 𝛾 significantly larger than by the Mexican code due to joint reinforcement (V ) was 37.69 kN and 68.24 kN, for the sR that of the unreinforced specimen. specimens with H/L = 0.75 and H/L = 0.41, respectively. Experimental results showed Even though the use of joint reinforcement increases the lateral strength, it could be an increment of 18.2 kN and 45.8 kN, which is 48.3% and 67.0% of the analytical results, detrimental to the seismic behavior of infill walls because it reduces the ductility of the respectively. system. A larger ductility leads to a better load redistribution and larger deformations after yielding. It allows people to exit the building and decrease the number of fatalities 4.3. Capacity of Deformation and Ductility in case of collapse. Regardless of the aspect ratio (H/L), the joint reinforcement did not have a signiﬁcant effect on the displacement capacity of the system. This result is different than that observed 5. Conclusions for load-bearing conﬁned masonry walls. For such walls, typically, it can be observed Based on the experimental results of four reinforced concrete infilled frames with that the deformation at failure changes from 0.4% without reinforcement to nearly 1% [6]. brick masonry walls, with the variables of the joint reinforcement and the aspect ratio of the wall, the following conclusion can be drawn: (1) As occurs in confined walls, the joint reinforcement produces a more distributed cracking and a reduction of the cracking wide. In addition, the joint reinforcement had no effect on the initial lateral stiffness; (2) The joint reinforcement consistently increases the lateral strength of the system. However, this increase depends on the size of the wall as considered by the Mexican Code; (3) The joint reinforcement had no significant effect on the displacement capacity of the system. This result does not depend on the aspect ratio of the wall; (4) Ductility of the system is reduced with the use of joint reinforcement due to the fact that the drift at yielding of the elastoplastic model (𝛾 ) increases with the reinforce- ment; Lateral Load (kN) Lateral Load (kN) Buildings 2022, 12, 259 18 of 19 Inﬁll walls may undergo large deformations due to the frame that prevents the wall disintegration; however, for such large drifts, the inﬁll wall may be considered that have already failed. Consequently, the beneﬁcial effect of the reinforcement cannot be observed for such large deformations. For both cases of H/L, the use of joint reinforcement reduced the ductility of the system. Ductility depends on the displacement capacity (g ) and the drift at yielding of the elastoplastic model (g ). The reduction of ductility is attributed to the fact that, in each pair, the specimen with joint reinforcement had a value for g signiﬁcantly larger than that of the unreinforced specimen. Even though the use of joint reinforcement increases the lateral strength, it could be detrimental to the seismic behavior of inﬁll walls because it reduces the ductility of the system. A larger ductility leads to a better load redistribution and larger deformations after yielding. It allows people to exit the building and decrease the number of fatalities in case of collapse. 5. Conclusions Based on the experimental results of four reinforced concrete inﬁlled frames with brick masonry walls, with the variables of the joint reinforcement and the aspect ratio of the wall, the following conclusion can be drawn: (1) As occurs in conﬁned walls, the joint reinforcement produces a more distributed cracking and a reduction of the cracking wide. In addition, the joint reinforcement had no effect on the initial lateral stiffness; (2) The joint reinforcement consistently increases the lateral strength of the system. How- ever, this increase depends on the size of the wall as considered by the Mexican Code; (3) The joint reinforcement had no signiﬁcant effect on the displacement capacity of the system. This result does not depend on the aspect ratio of the wall; (4) Ductility of the system is reduced with the use of joint reinforcement due to the fact that the drift at yielding of the elastoplastic model (g ) increases with the reinforce- ment; (5) Sliding failure occurred after the inclined cracking. Consequently, the joint reinforce- ment is active, even if sliding is the dominant failure mode. A larger aspect ratio produces a greater inclined cracking; (6) The Mexican Code overestimates the join reinforcement contribution to shear strength of inﬁll walls. For walls with H/L = 0.75 and 0.41, the prediction of the code was 2.07 and 1.49 times, respectively, larger than that of experimental results; (7) Results show that the estimation of the contribution of joint reinforcement to the shear strength in multiple panel inﬁll walls is consistent with the current practice where the reinforcement in each panel is considered, although no previous evidence have been provided. Author Contributions: J.M.L.-G.: Conceptualization, Methodology, Investigation, Formal analysis, Funding acquisition, Writing—original draft, Writing—review & editing. J.J.P.-G.: Conceptualization, Formal analysis, Writing—original. A.R.-S.: Formal analysis, Writing—review & editing. F.V.-B.: Investigation, Writing—review & editing. E.B.: Visualization, Writing—review & editing. J.B.: Formal analysis, Writing—review & editing. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Consejo Nacional de Ciencia y Tecnología (CONACYT) under Grant CB 2017-2018/A1-S-36643. The ﬁnancial support given by the Universidad Autónoma de Sinaloa under Grant PROFAPI 2022 is appreciated. Data Availability Statement: The data used to support the ﬁndings of this study are available from the corresponding author upon request. Buildings 2022, 12, 259 19 of 19 Acknowledgments: Construction and testing of specimens were carried out at the Laboratory of Structures of the Autonomous University of Sinaloa. Many thanks are given to the students that participated during construction, instrumenting and testing: Yakiro Álvarez, Héctor Aispuro, Miguel Aispuro, Cuitláhuac Mendoza and Jazmín Campista. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. Marques, R.; Lourenço, P.B. Structural behavior and design rules of conﬁned masonry walls: Review and proposals. Constr. Build. Mater. 2019, 217, 137–155. [CrossRef] 2. NTCM. Normas Técnicas Complementarias para el Diseño y Construcción de Estructuras de Mampostería del Gobierno de la Ciudad de México; Gaceta Oﬁcial de la Ciudad de México: Ciudad de México, Mexico, 2017. (In Spanish) 3. Leal, G.J.M.; Pérez Gavilán, J.J.; Castorena, G.J.H.; Velázquez, D.J.I. Inﬁll walls with conﬁning elements and horizontal reinforce- ment: An experimental study. Eng. Struct. 2017, 150, 153–165. [CrossRef] 4. Meli, R.; Brzev, S.; Astroza, M.; Beon, T.; Crisafulli, F.J.; Farsi, M.; Hart, T.; Mebarki, A.; Moghadam, A.; Quiun, D.; et al. Seismic Design Guide for Low-Rise Conﬁned Masonry Buildings; EERI Conﬁned Masonry Network: Oakland, CA, USA, 2011. 5. Pérez Gavilán, J.J.; Flores, L.E.; Alcocer, S.M. An experimental study of conﬁned masonry walls with varying aspect ratio. Earthq. Spectra 2015, 31, 945–968. [CrossRef] 6. Cruz, O.A.I.; Perez Gavilan, J.J.; Flores, C.L. Experimental study of in-plane shear strength of conﬁned concrete masonry walls with joint reinforcement. Eng. Struct. 2019, 182, 213–226. [CrossRef] 7. Polyakov. Masonry in Framed Buildings (Godsudarstvenoe Isdatel’stvo Literatury Po Stroidal Stvui Architecture. Moscow, 1956); Cairns, G.L., Eds.; National Lending Library for Science and Technology: Boston, MA, USA, 1956. 8. Holmes, M. Steel frames with brickwork and concrete inﬁlling. Proc. Inst. Civ. Eng. 1961, 19, 473–478. [CrossRef] 9. Stafford-Smith, B. Lateral stiffness of inﬁlled frames. ASCE J. Struct. Div. 1962, 88, 183–199. [CrossRef] 10. Stafford-Smith, B. Behavior of square inﬁlled frames. ASCE J. Struct. Div. 1966, 92, 381–403. [CrossRef] 11. Stafford-Smith, B. Methods for predicting the lateral stiffness and strength of multi-storey inﬁlled frames. Build. Sci. 1967, 2, 247–257. [CrossRef] 12. Stafford-Smith, B.; Carter, C. A method of analysis for inﬁlled frames. Proc. Inst. Civ. Eng. 1969, 44, 31–48. [CrossRef] 13. Mainstone, R.J. Supplementary Note on the Stiffness and Strengths of Inﬁlled Frames; Building Research Station: Garston, UK, 1974. 14. Bazán, Z.T.E. Muros de Mampostería ante Cargas Laterales. Ph.D. Thesis, National Autonomous University of Mexico, Ciudad de México, Mexico, 1980. 15. Flanagan, R.D.; Bennett, R.M. In plane analysis of masonry inﬁlls material. J. Struc. Eng. 1990, 125, 590–599. [CrossRef] 16. Crisafulli, F.J. Seismic Behavior of Reinforced Concrete Structures with Masonry Inﬁlls. Ph.D. Thesis, University of Carterbury, Christchurch, New Zealand, 1997. 17. Aguilar, G.; Alcocer, S.M. Efecto del Refuerzo Horizontal en el Comportamiento de Muros de Mampostería Conﬁnada ante Cargas Laterales; Universidad Nacional Autónoma de México: Mexico City, Mexico, 2001. (In Spanish) 18. Pineda, C.J.; Alcocer, S.M. Comportamiento Ante Cargas Laterales de Muros de Mampostería Conﬁnada Reforzada con Malla Electrosoldada; Technical Report; Centro Nacional de Prevención de Desastres (CENAPRED): Ciudad de México, Mexico, 2004. (In Spanish) 19. Alcocer, S.M.; Zepeda, J.A. Behavior of multi-perforated clay brick walls under earthquake-type loading. In Proceedings of the 8th North American Masonry Conference, Austin, TX, USA, 6–9 June 1999. 20. NTCM. Normas Técnicas Complementarias para Diseño y Construcción de Estructuras de Mampostería; Gaceta Oﬁcial del Distrito Federal: Ciudad de México, Mexico, 2004. (In Spanish) 21. Rubio, P.L. Contribución del Refuerzo Horizontal a la Resistencia a Corte de Muros Conﬁnados de Piezas de Arcilla Extruida. Master ’s Thesis, National Autonomous University of Mexico, Ciudad de México, Mexico, 2017. (In Spanish) 22. Davis, C.L. Evaluation of Design Provisions for In-Plane Shear in Masonry Walls. Master ’s Thesis, Washington State University, Washington, DC, USA, 2008. 23. Aguilar, G.; Meli, R.; Díaz, R.; del Mercado, A.R.V. Inﬂuence of horizontal reinforcement on the behavior of conﬁned masonry walls. In Proceedings of the 11th World Conference Earthquake Engineering, Acapulco, Mexico, 23–28 June 1996. 24. Cruz, O.A.I.; Perez Gavilan, J.J. Seismic performance of conﬁned masonry walls with joint reinforcement and aspect ratio: An experimental study. Eng. Struct. 2021, 242, 112484. [CrossRef] 25. ASCE/SEI 41-13. Seismic Evaluation and Retroﬁt of Existing Buildings; ASCE: Reston, VA, USA, 2014. 26. Simo, J.C.; Hughes, T.J.R. Motivation. One-dimensional plasticity and viscoplasticity. In Computational Inelasticity; Marsden, J.E., Sirovich, L., Wiggins, S., Eds.; Springer: New York, NY, USA, 1997; Volume 7, pp. 1–70. 27. Anderson, D.; Priestley, M. In Plane Shear Strength of Masonry Walls. In Proceedings of the 6th Canadian Masonry Symposium, Sasketoon, SK, Canada, 15–17 June 1992.

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Experimental Study of Infill Walls with Joint Reinforcement Subjected to In-Plane Lateral Load

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DOI: 10.3390/buildings12030259
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Buildings – Multidisciplinary Digital Publishing Institute

Published: Feb 23, 2022

Keywords: infill wall; joint reinforcement; infilled frame; seismic behavior; RC frame structure

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Experimental Study of Infill Walls with Joint Reinforcement Subjected to In-Plane Lateral Load

Experimental Study of Infill Walls with Joint Reinforcement Subjected to In-Plane Lateral Load

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Experimental Study of Infill Walls with Joint Reinforcement Subjected to In-Plane Lateral Load

Experimental Study of Infill Walls with Joint Reinforcement Subjected to In-Plane Lateral Load

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