Design Proposal for Masonry Infill Walls Subject to Seismic Actions
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applied sciences Article Design Proposal for Masonry Infill Walls Subject to Seismic Actions João Leite, Paulo B. Lourenço and Nuno Mendes * ISISE, Department of Civil Engineering, University of Minho, 4800 Guimarães, Portugal; jmcleite@gmail.com (J.L.); pbl@civil.uminho.pt (P.B.L.) * Correspondence: nunomendes@civil.uminho.pt Abstract: Several factors influence the behaviour of masonry infilled frames, which have been the subject of previous research with moderate success. The new generation of European design standards imposes the need to prevent the brittle collapse of infills and makes the structural engineer accountable for this requirement, yet it fails to provide sufficient information for masonry infill design. The present study aimed to compare experimental results with the provisions of the standard for the computation of the demand and capacity of infilled frames. Three reinforced concrete buildings with different infill solutions were constructed at a 1:1.5 scale. The infill walls were tested until collapse, or severe damage, using the shake table of the National Laboratory for Civil Engineering, Portugal, and their response was measured using accelerometers attached to the walls. The European normative standard provides results close to the experimental ones as far as demand and capacity are concerned. Based on the experiments, two design proposals for infill walls are presented here, one for the definition of the natural frequency of the infills, and another for a reduction factor to account for the presence of openings in the out-of-plane capacity of infills. Keywords: masonry infills; reinforced concrete frame; shake table tests; earthquake engineering; Citation: Leite, J.; Lourenço, P.B.; out-of-plane behaviour Mendes, N. Design Proposal for Masonry Infill Walls Subject to Seismic Actions. Appl. Sci. 2022, 12, 503. https://doi.org/10.3390/ app12010503 1. Introduction Even though the study of masonry infilled frames started several decades ago, there Academic Editors: Giuseppe Brando, remain many factors that influence their behaviour, such as mechanical properties of the Maria Giovanna Masciotta and materials, aspect ratio, boundary conditions, the presence of reinforcement or the presence Massimo Latour of openings. The role of infill walls in the global performance of frame structures subjected Received: 14 December 2021 to seismic action is well known, see e.g., [1], as well as the requirements to ensure that the Accepted: 3 January 2022 influence of the infill is either positive or neutral [2]. The demonstration that more studies Published: 5 January 2022 are needed is revealed by the behaviour observed during recent earthquakes, which can be Publisher’s Note: MDPI stays neutral analysed from a lifesaving (Ultimate Limit State), or economic perspective (Serviceability with regard to jurisdictional claims in Limit State). Infill walls often collapse out-of-plane, see Figure 1, even for structures published maps and institutional affil- designed using the recent design codes, and up to 80% of the full cost of buildings can be iations. needed to reconstruct non-structural elements [3]. The present study compares experimental results from shake table tests on reinforced and unreinforced clay brick masonry infills, built within reinforced concrete frames, us- ing the provisions of design standards and reference literature. For that purpose, three Copyright: © 2022 by the authors. buildings were tested on the shake table of the National Laboratory for Civil Engineering, Licensee MDPI, Basel, Switzerland. Portugal, at a scale of 1:1.5. The specimens were subjected to increasing levels of horizon- This article is an open access article tal accelerations in the two orthogonal main directions. The experimental demand and distributed under the terms and capacity were computed using accelerometers bolted to the infill walls. conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Appl. Sci. 2022, 12, 503. https://doi.org/10.3390/app12010503 https://www.mdpi.com/journal/applsci
Appl. Sci. Appl. Sci.2022, 12,x503 2022,12, FOR PEER REVIEW 2 2ofof27 26 Figure Figure 1. 1. Partial and complete Partial and completeout-of-plane out-of-planecollapses collapses of of infilled infilled walls walls during during the L’Aquila the L’Aquila earth- earthquake quake (2009), Italy. (2009), Italy. 2. 2. Out-of-Plane Out-of-PlaneBehaviour BehaviourofofMasonry Masonry Infill Infill Walls Walls 2.1. Experimental 2.1. ExperimentalResearch Research Studies Studies Theout-of-plane The out-of-planebehaviour behaviour of of an an infill infill wallwall is highly is highly dependent dependent on theon the arching arching effect effect due [4–6], [4–6],todue the to the confinement confinement provided provided by theby the frame. frame. Hence,Hence, the out-of-plane the out-of-plane capac- capacity is ity is greatly affected by the compressive strength of masonry greatly affected by the compressive strength of masonry and the stiffness of the RC ele- and the stiffness of the RC elements. ments. TheThe firstfirst analytical analytical models models calculated calculated the the out-of-planecapacity out-of-plane capacityofofinfill infillwalls walls[5,6] [5,6] and only considered this effect in one of the main directions. and only considered this effect in one of the main directions. This might not be realistic asThis might not be realistic as infill infill wallswalls can can be connected be connected to thetoframe the frameon allon all sides four four sides and, in and, thisincase, thisthe case, theeffect arch arch effect can develop in two directions. Given this, Dawe and Seah can develop in two directions. Given this, Dawe and Seah [7] proposed an analytical so- [7] proposed an analytical solution lution to to compute compute thethe out-of-plane out-of-plane capacityofofinfill capacity infillwalls wallsthat thatassumed assumedaa bi-directional bi-directional arch effect. Their tests included nine frames with concrete arch effect. Their tests included nine frames with concrete blocks, subjected to blocks, subjected to aa uniform uniform load on the surface of the infills using airbags, see Figure 2, with load on the surface of the infills using airbags, see Figure 2, with the objective of under- the objective of under- standing the out-of-plane behaviour and the maximum load standing the out-of-plane behaviour and the maximum load capacity of the infill walls. capacity of the infill walls. The authors concluded that the out-of-plane behaviour could be divided into four stages: The authors concluded that the out-of-plane behaviour could be divided into four stages: (i) linear elastic until the first crack; (ii) propagation of cracks and definition of a failure (i) linear elastic until the first crack; (ii) propagation of cracks and definition of a failure line; (iii) increment in the load capacity due to the arch effect; (iv) crushing of masonry, line; (iii) increment in the load capacity due to the arch effect; (iv) crushing of masonry, due to compression and collapse. The authors proposed that the out-of-plane capacity due to compression and collapse. The authors proposed that the out-of-plane capacity that that the panel can withstand, in the case of a panel supported on four sides, is given by q the panel can 2 ) as:withstand, in the case of a panel supported on four sides, is given by q (in (in kN/m kN/m2) as: α β 0.75 2 q = 4.50 f m0 t + (1) . l 2.5 h2.5 = 4.50 + . (1) 1 . ℎ0.25 2 ∝= EIc h + Gs Jc th < 50 (2) 1 h . ∝= ( 1 ℎ +2 ℎ) 0.25 < 50 (2) β ℎ= EIb l + Gs Jb tl < 50 (3) l 1 where, f m0 is the compressive =strength ) . (in
Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 of 27 Appl. Sci. Appl. 2022, Sci. 12,12,503 2022, x FOR PEER REVIEW 3 of 26 3 of 27 (a) (a) (b) (b) Figure 2. 2. Figure Figure Experimental design 2. Experimental Experimental [7]: design design (a) [7]: [7]:(a)geometry geometry (a) of tested ofof geometry frames; frames; tested (b)(b) (b) frames; test test setup. setup. test setup. InIn a alater In laterstudy, study,Flanagan study, Flanaganand Flanagan andBennett and Bennett[8,9] Bennett [8,9]proposed proposed proposed changing changing changing the thethe valuevalue value 4.50 4.50 4.50ininin Equation Equation Equation (1) (1)(1) to toto 4.10, 4.10, 4.10, and and and eliminating eliminating eliminating the the the term term term related related related to to to torsion torsion torsion in in Equations inEquations Equations (2) (2)(2)and andand(3),(3), (3), duedue duetotoitsits to lowlow influence influence influence andand and unnecessary unnecessary unnecessary complexity. complexity. complexity. The The The in-planedamage in-plane in-plane damage damage has hashas aaconsiderable aconsiderable considerable influence influence influence on onon the the out-of-plane the out-of-plane out-of-plane resistance resistance resistance ofofof an an infill wall, wall, asasshown shown by Angel by Angel [10], who [10], tested who eight tested full eight an infill wall, as shown by Angel [10], who tested eight full scale, one storey, one bay, RC scale, full one storey, scale, one one storey,bay, RC one bay, frames, RC frames, frames, with with brick brick withand and brick concrete and concrete concrete masonry, masonry, first masonry, in-plane and first in-plane first in-plane then and thenand out-of-plane, see then out-of-plane, out-of-plane, Figure see Figure see 3. The 3. Figure The in-plane 3. Thetest in-plane testconsisted in-planeconsisted test of ofthe theapplication consisted application of load, of the application of load, monotonically, until untila adisplace- of load, monotonically, monotonically, until a displace- ment value, equal displacement ment value, equal tototwice value, twice equal the the value tovalue needed twiceneededthe value for needed for the first for the first crack crack theto appear, tofirst crack appear, was to achieved. was appear, achieved. was Then, achieved. the walls Then, were the loaded walls out-of-plane were loaded using out-of-planeairbags until using the collapse airbags until of the the specimen. collapse of the Then, the walls were loaded out-of-plane using airbags until the collapse of the specimen. The conclusions specimen. The were: (i) thewere: conclusions out-of-plane (i) the capacity depends out-of-plane capacity on the slenderness depends on theand com- slenderness The conclusions were: (i) the out-of-plane capacity depends on the slenderness and com- pressive and strength of masonry; compressive (ii) the in-plane damage in-planedoes not affect the affect out-of-plane pressive strength ofstrengthmasonry; of masonry; (ii) the damage (ii) the in-plane damage does notdoes affectnot the out-of- the out-of-plane cracking plane pattern; cracking (iii) pattern; for high (iii) forslenderness high infills, slenderness in-plane infills, cracks in-plane lower cracks the maximum lower the out- maximum cracking pattern; of-plane capacity; (iii) for high (iv) vertical slenderness loading infills, increases in-plane the stiffness cracks lower but doesbut the notdoes maximum affect out- theaffect out- the out-of-plane of-plane capacity;capacity; (iv) vertical loading increases the stiffness (iv) vertical loading increases the stiffness but does not affect the out- not of-plane out-of-plane capacity. capacity. of-plane capacity. (a) (b) Figure 3. Figure 3. Testing Testing setup (a)(a)in-plane setup [10]: [10]:(a) in-planetest; test;(b) out-of-plane (b) test. out-of-plane test. (b) Figure 3. Testing setup [10]: (a) in-plane test; (b) out-of-plane test. Angel [10] Angel [10] also alsoproposed proposedan ananalytical analyticalsolution solution forfor thethe out-of-plane out-of-plane capacity capacity of infills of infills q, see q, see Equation Equation (4), (4), with with or or without without in-plane in-plane damage. damage. The reduction The reduction of the of out-of-plane the out-of-plane Angel [10] also proposed an analytical solution for the out-of-plane capacity of infills capacity is capacity is made made using aaparameter, R,1which can bebeobtained by,by, seesee[10]: (i) estimating q, see Equation (4),using with orparameter, without in-plane , which can damage. obtained The reduction of [10]: (i) estimating the out-of-plane the in-plane the in-plane displacement displacement due to cracking, due to cracking, using the using uncracked stiffness of the system; (ii) capacity visual is made inspection using and aclassification parameter, the of , which damage caninbethe the uncracked obtained infill. If by, the stiffness see [10]: infill wall (i)of is the system; estimating undam- (ii) visual inspection and classification of the damage in the infill. If the infill wall is theaged, in-plane displacement assumes duevalue. a unitary to cracking, using theisuncracked stiffness of theofsystem; (ii) undamaged, R1 assumes a unitaryThevalue.value Theof value related of R2 isto the related stiffness to the EI the most stiffness EI of the visual inspection flexible frameframeand element,classification see Equation of the damage in depends (5), and(5), the infill. If on the height the infill wall is undam- most flexible element, see Equation and λ depends on thehheight to thickness t ratio t h to thickness aged, of infill the assumes wall, a unitary see Equationvalue. (6). The value of is related to the stiffness EI of the most ratio of the infill wall, see Equation (6). flexible frame element, see Equation (5), and depends on the height h to thickness t ratio of the infill wall, see Equation (6). 2f0 q = m R1 R2 λ (4) h t
2 = (4) ℎ Appl. Sci. 2022, 12, 503 4 of 26 = 0.357 + 2.49 × 10 ≤ 1.0 (5) R2 = 0.357 + 2.49 × 10−14 EI ≤ 1.0 (5) = 0.154 . (6) h λ = 0.154e−0.0985 t (6) Another analytical solution, based on the bi-directional arch effect allowed by the Another surrounding analytical frame, solution, was proposed bybased Klingner on ettheal.bi-directional [11]. This is in fact archaneffect allowed extension of theby the analytical surrounding solution frame, by was Cohen and Laing proposed by [12], whichetconsidered Klingner al. [11]. This only thefact is in archaneffect in oneof the extension ofanalytical the main solution directionsby ofCohen the frameandas: Laing [12], which considered only the arch effect in one of the main directions of the frame as: 8 = ( ( − ℎ) + ℎ (2) + ! (7) ℎ 8 xyv − ℎ 2 l !) q = 2 Myv [(l − h) + hln(2)] + Myh ln l (7) h l xyh l − 2h 0.85 = −0 (8) 4 0.85 f m 2 Myv = t − xyv (8) 4 = t f m0 xyv = ⎡ ⎤ # (9) ℎ " ⎢1 − ⎥ (9) 1.000 1.000E 1 − q 2⎥ h ⎢ ℎ 2 + ⎣ 2 2 ( 2 ) ⎦+t h 2 isxthe Here, Here, yv is the maximum maximum displacement displacement of the of the infill wallinfill wall in the in thedirection vertical vertical and direction and M yh is is obtainedobtained by replacing x by by replacing by yv in Equation x yh in Equation (8) and l by h (8) and by ℎ in Equation (9). in Equation (9). Withthe With theobjective objective of of comparing comparing thethe influence influence of reinforcement of reinforcement in theinin-plane the in-plane dam- dam- age of masonry infill walls and their out-of-plane-capacity, age of masonry infill walls and their out-of-plane-capacity, after initial in-plane damage, after initial in-plane damage, Calvietetal.al.[13] Calvi [13]andand Penna Penna et al. et al. [14][14] tested tested threethree full-scale full-scale RC frames RC frames with with different different infills,infills, seeFigure see Figure4:4: (i)(i) unreinforced; unreinforced; (ii)(ii) withwith bedbedjointjoint reinforcement; reinforcement; (iii) with (iii) with reinforced reinforced plaster. plaster. Theframes The frameswere weresubjected subjectedto toananin-plane in-planecyclic cyclicloadload with with aa constant constant vertical vertical load, load, and and then subjected then subjected to out-of-plane to out-of-plane loads applied loads applied ononfour four points pointsofofthe theinfill infillwall. wall. (a) (b) Figure Figure4.4.Models Models[13,14]: (a)(a) [13,14]: infill walls; infill (b) (b) walls; detail of the detail of reinforcement at theatinfills. the reinforcement the infills. The conclusions were that:were The conclusions (i) the that: presence of reinforcement (i) the presence oflowers the damagelowers reinforcement in the infill thewall damage in but only the reinforced plaster infill increases the in-plane stiffness, energy dissipation the infill wall but only the reinforced plaster infill increases the in-plane stiffness, energy capacity and maximum load; (ii) the in-plane damage drastically reduces the acceleration needed for the dissipation capacity and maximum load; (ii) the in-plane damage drastically reduces the out-of-plane collapse; (iii) both reinforced solutions improve the out-of-plane behaviour of the acceleration needed for the out-of-plane collapse; (iii) both reinforced solutions improve the infill walls, to the greatest extent in the reinforced plaster one. The authors also proposed analyti- out-of-plane cal behaviour solutions to calculate theof the infill walls, out-of-plane to thevibration fundamental greatest period extentofinthe theinfill reinforced wall, see plaster Equa- one. The authors also proposed analytical solutions to calculate the out-of-plane tion (10), and the in-plane capacity of infill masonry walls reinforced with bed joint reinforcement, fundamental vibration see Equationperiod (11). of the infill wall, see Equation (10), and the in-plane capacity of infill masonry walls reinforced with bed joint reinforcement, see Equation (11). r Et3 2 1 1 Tp = + 2 (10) π l2 h 12m f y Ash d0 VR = VR,M + VR,H = f v l 0 t + ≤ f v lt (11) s
. Sci. 2022, Appl. Sci. 2022, 12, x FOR PEER12, 503 REVIEW 5 of 27 5 of 26 Here, m and f v are the specific mass and shear resistance of masonry, respectively, l 0 is the length of the compressed 2 1zone1 of the wall, f y is the yield strength of steel, Ash is the area = in the of reinforcement applied + bed joint, s is the horizontal spacing of the (10) reinforcement 0 0 ℎ 12 and d is the lowest between l and h. An extensive study on the out-of-plane behaviour of reinforced and unreinforced infill walls, with previous = , +in-plane , = damage, + ≤ 5, was also performed(11) see Figure by Pereira [15]. He compared experimental results with available analytical solutions and codes, and Here, andconcluded are thethat specific mass andproposal the analytical shear resistance of masonry, capacity for the out-of-plane respectively, is [10] was the of Angel the length ofmost the compressed adequate, if zone of theaswall, modified shown inis Equation strength of steel, is the the yield (12). area of reinforcement applied in the bed joint, is thehorizontal spacing of the reinforce- 0 ment and is the lowest between q = andf ℎ. m R1 R2 λ 0.77C f h + 0.34C f (12) An extensive study on the out-of-planehbehaviour of reinforced l and unreinforced in- tw fill walls, with previous in-plane damage, see Figure 5, was also performed by Pereira [15]. He compared experimental results with available analytical i f x1 solutions and codes, and concluded that the analytical proposal for the out-of-plane C f = capacity of Angel [10] was the (13) f x1 most adequate, if modified as shown in Equation (12). 1—Reaction frame 2—Transverse beam 3—Structure for load application 4—Airbags 5—Airbag fixing panel 6—Horizontal actuator Out-of-plane Figure 5. test Figure 5. Out-of-plane setup [15].test setup [15]. Here, f x1i is the flexural strength in the direction parallel to the bed joints and f is the x1 flexural strength ′ in the direction ℎ to the bed joints for the unreinforced solution. parallel = 0.77 + 0.34 (12) Butenweg etℎ al. [16] carried out an experimental study on the behaviour of reinforced concrete frames filled with high thermal insulating clay bricks, applying cyclic in-plane and out-of-plane loading based on the three following methodologies: (1) application of only one type of loading; (2) both = of loading sequentially applied; (3) both (13) types types of loading sequentially in combination. In this experimental study, four specimens were tested: (1) a Here, is reinforced the flexural strength concrete in the frame direction without parallel infill under to the bedloading); in-plane joints and infilled (2) an is the frame with flexural strength in the direction parallel to the bed joints for the unreinforced solution. a small gap between the infill and a column under out-of-plane loading; (3) an infilled Butenweg et al.under frame [16] carried out an sequential experimental in-plane study on theloading; and out-of-plane behaviour(4)of anreinforced infilled frame under concrete frames filled in-plane combined with high andthermal insulating out-of-plane clayIn loading. bricks, these applying tests, two cyclic verticalin-plane hydraulic cylinders and out-of-plane loading based for application of theon the three forces from following methodologies: higher storeys, one hydraulic(1) application cylinder for ofapplication of only one type of loading; (2) both types of loading sequentially applied; (3) both types of loading sequentially in combination. In this experimental study, four specimens were
Appl. Sci. 2022, 12, x FOR PEER REVIEW 6 of 27 tested: (1) a reinforced concrete frame without infill under in-plane loading); (2) an infilled Appl. Sci. 2022, 12, 503 frame with a small gap between the infill and a column under out-of-plane loading; (3) an 6 of 26 infilled frame under sequential in-plane and out-of-plane loading; (4) an infilled frame under combined in-plane and out-of-plane loading. In these tests, two vertical hydraulic cylinders for application of the forces from higher storeys, one hydraulic cylinder for ap- the in-plane loading and airbags for the application of the out-of-plane loading were used plication of the in-plane loading and airbags for the application of the out-of-plane load- (Figure 6). ing were used (Figure 6). Figure6.6. Test Figure Test setup setup for for the the in-plane in-planeand andout-of-plane out-of-planetests testscarried out carried byby out Butenweg et al. Butenweg et [16]. al. [16]. Fromthe From the results results of of the the tests, tests, itit was was concluded concluded that that boundary boundary conditions conditions at at the the con- connec- nection area between the masonry infill and the reinforced concrete tion area between the masonry infill and the reinforced concrete frame are a crucial frame are a crucial aspect aspect for the for the out-of-plane out-of-plane behaviour. behaviour. Moreover, Moreover, the infilled the infilled frame frame withwith a small a small gapgap be- between tween the the infill infill and and a column a column under under out-of-plane out-of-plane loading loading presented presented an out-of-plane an out-of-plane ca- q capacity pacity q in agreement with the analytical approach proposed by Dawe in agreement with the analytical approach proposed by Dawe and Seah [7] for a panel and Seah [7] for a panel supported on supported on three sides:three sides: 4.50.f m0 t2 β 0.75 4.50 =q = (14)(14) ℎ . h2.5 where, 0 isisthe where, f m thecompressive compressivestrength strengthofofmasonry, and masonry,t and ℎ are h are the the thickness andand thickness the the height ofheight of the the infill infillrespectively. wall, wall, respectively. For more For more information information on onexperimental experimentalstudies onon studies thethe out-of-plane out-of-planebehaviour of ma- behaviour of ma- sonry infill walls, sonry infill walls, see [17–19]. [17–19]. 2.2. 2.2.Code Code Proposals Proposals In InNorth NorthAmerica, America, Annex Annex BB of of M.S.J.C. M.S.J.C. [20] [20] determines determines that for the out-of-plane de- design of participating sign infill infill of participating walls, the use walls, the of useconnectors of connectors spaced at aatmaximum spaced a maximum of 1.22 m along of 1.22 m the along the supported perimeter of the infill is mandatory, and the out-of-plane capacity of the supported perimeter of the infill is mandatory, and the out-of-plane capacity of walls havehave the walls to betocomputed be computed using Equation using Equation(1) (1) [7].[7]. FEMA FEMA 273 273[21] defines [21] definesthe themaximum maxi- slenderness mum slenderness valuesvalues in Tablein 1, while Table the capacity 1, while should the capacity be computed should usingusing be computed Equation Equa-(15), iftion the (15), arch ifeffect can effect the arch be taken caninto account, be taken into otherwise the out-of-plane account, otherwise capacitycapacity the out-of-plane is assumed asis the maximum assumed as theflexural maximum capacity flexuralofcapacity the wall.of the wall. Table 1. λ2 values for the computation of the out-of-plane capacity of infill walls (FEMA 273 [21]). Slenderness λ2 5 0.129 10 0.030 15 0.034 35 0.013
Appl. Sci. 2022, 12, 503 7 of 26 0.7 f 0 m λ2 q= × 144 (15) h t FEMA 306 [22] does not impose a limit drift. Nonetheless, it mentions that the limit is about 1.5% for clay brick masonry, and assumes the analytical proposal of [10,23], see Equation (4), for the out-of-plane capacity of the infills. Regarding the seismic loads to be used in the out-of-plane design, which cannot be higher than the capacity computed using the methods mentioned, FEMA 302 [24] prescribes Equation (16) in the case of new buildings with rigid diaphragms, within the limits obtained by Equations (17) and (18): 0.4a p SDS Wp z Fp = Rp 1+2 (16) h Ip Fp < 1.6SDS I p Wp (17) Fp > 0.3SDS I p Wp (18) Here, a p is the amplification factor, SDS is the spectral acceleration, Wp is the weight of the wall, z is the height of the highest point of the infill wall, h is the height of the building, R p is the response modification factor and I p is the importance factor. Another proposal is made by FEMA 356 [25], see Equation (19), in which the perfor- mance level is taken into consideration through a specific parameter that varies according to the desired performance level (Table 2). Here, SXS is the spectral acceleration and W is the weight of the wall. Fp = χSXS W (19) Table 2. Coefficient χ 1 for calculation of the out-of-plane all forces. Structural Performance Level Flexible Diaphragms Other Diaphragms Collapse prevention 0.9 0.3 Life safety 1.2 0.4 Immediate occupancy 1.8 0.6 1 Values of χ for flexible diaphragms need not be applied to out-of-plane strength of walls in Sections 2.6.7.2 of the FEMA 356 [25]. The NZS 1170.5 [26] standard provides a design methodology for infill masonry walls identical to the North American code. Infill walls have a considerable contribution to the lateral load resistant structure, except in situations when the infill wall is separated from the frame, the infill wall is constructed with a flexible and light material, or it has a fragile behaviour such that it will collapse in the event of a very low seismic action. The out-of-plane capacity follows FEMA 306 [22]. The seismic force to be used in the seismic design of infill walls should be computed using Equation (20), which includes the influence of the vertical position of the element in the structure as well as an amplification of the acceleration, when compared to the maximum acceleration at the floor height: Fph = C p Tp C ph R p Wp < 3.6Wp (20) C p Tp = C (0)CHi Ci Tp (21) hi 1 + 6 , hi ≤ 12m CHi = h i (22) 1 + 10 hn , hi < 0.5hn 3.0, hi ≥ 0.2hn
Appl. Sci. 2022, 12, 503 8 of 26 2.0, hi ≤ 12m Ci Tp = 0.5, hi < 0.5hn (23) 2.0 1.75 − Tp hi ≥ 0.2hn Here, C p Tp is the horizontal load design coefficient, R p is the risk factor, Wp is the weight of the element, C (0) is the site hazard coefficient for T = 0, CHi is the floor height coefficient for level i, Tp is the period of the element, Ci Tp is the spectral shape factor at level i, hi is the height of the element and hn is the height from the base of the structure to the uppermost seismic weight or mass. For the European regulations EC8 [27], the infill walls have to be considered if their presence influences the lateral stiffness of the structure. Independently of their influence on the lateral resistance system, appropriate measures should be taken to avoid brittle failure and premature disintegration of the infill walls, and their partial or total out-of-plane collapse. The out-of-plane design load is given by: Sa Wa γa Fa = (24) qa z 3 1+ Sa = ∝ S H 2 − 0.5 (25) Ta 1+ 1− T1 where Sa is the seismic coefficient applicable to non-structural elements, Wa is the weight of the element, γa is the importance factor of the element, q a is the behaviour factor, ∝ is the ratio of the design ground acceleration on type A ground, a g is the acceleration of gravity, S is the soil factor, Ta is the fundamental vibration period of the non-structural element, T1 is the fundamental vibration period of the building in the relevant direction, z is the height of the non-structural element above the level of application of the seismic action and H is the building height measured from the foundation or from the top of a rigid basement. EC8 [27] does not provide any analytical solution for the fundamental vibration period of an infill wall. EC6 [28] proposes two methods for the design of masonry walls subjected to out-of- plane loads, based on: (i) the assumption that the wall is supported along the boundaries; (ii) the arch effect between the supports. The first method considers that the wall is supported along three or four edges, and assumes that failure can occur parallel to the bed joints, see Equation (26), or perpendicular to the bed joints, see Equation (27): MEd1 = ∝1 WEd l 2 (26) MEd2 = ∝2 WEd l 2 (27) where ∝1 and ∝2 are bending moment coefficients accounting for the degree of fixity at the edges of the walls, the height to length ratio values of the walls, as described in Annex E [28], l is the length of the wall and WEd is the design lateral load per unit area. The load needs to be equal to or smaller than the capacity of the wall, which is computed using: MRd = f xd Z (28) where f xd is the flexural capacity of the infill wall in the desired direction and Z is the flexural modulus of the wall. The second method is applicable when the wall is constructed between supports capable of inducing an arch effect horizontally or vertically when the wall is subjected to out-of-plane loads. The capacity of the infill is then computed as: 2 t qlat,d = f d (29) la
Appl. Sci. 2022, 12, 503 9 of 26 Here, f d is the design compressive strength of the masonry in the direction of the arch thrust, t is the thickness of the wall and la is the length or height of the wall between supports capable of resisting the arch thrust. 3. Shake Table Tests 3.1. Building Models Three different models were idealized at a scale of 1:1.5 (Figure 7 and Table 3), with dimensions of 4.30 × 3.80 × 4.00 m. See [29] for details. Model 1 represents the built heritage of the last three decades in Portugal, while models 2 and 3 represent likely future solutions. The chosen class for concrete and rebar reflects this distinction, as lower classes were used in model 1 (C20/25 and S400) and higher classes in models 2 and 3 (C30/37 and S500). The mortar used for the bed joints and plaster was pre-batched (M5 class). Further Appl. Sci. 2022, 12, x FOR PEER REVIEW 10 of 27 details on mechanical properties can be found in [15]. The loads were reduced using the similitude law relations. Figure 7. Geometry Figure of the 7. Geometry openings of the in each openings facade: in each (a) North; facade: (b) West; (a) North; (c) East; (b) West; (c) (d) South. East; (d) South. The 3.2. Shake infills Table of and Input model 1 were Setup Acquisition unreinforced double-leaf clay brick walls with a cavity. Horizontally perforated Eight artificial units were accelerograms wereused, and the generated outer using leaf was partially a LNEC-SPA hanging [30] to obtain thethe RC frame. four The stages of inner leaf table the shake had atests, gypsum with plaster, increasingwhile the outer amplitude, seeleaf had4.aThe Table mortar rendering. accelero- The infills grams of the of model first three2stages were awere single leaf clay adapted brick to the wall with response a bed spectra joint reinforcement (damping ratio equal every tosecond bed joint. 5%) of each damageThelimit leaf was statecompletely withininthe that was defined RC3frame part of EC8,plane (as an external see Figure 8 Damage thermal insulation(DL Limitation system will beSignificant 225 YRP); required) with an internal Damage (SD 475gypsum plaster YRP); Near and an (NC Collapse external 2475mortar rendering. YRP): here, YRPAgain, equalshorizontally Years of theperforated unitsAwere Return Period. used.was last stage The bed joint defined reinforcement as the maxi- mumwascapacity a truss Bekaert Murfor of the table RND.4/100, in terms of velocity,with given4 mm diameter the size and masslongitudinal bars of the model, 100 mm and it apart. corresponds The bed to joint 4574 YRP. reinforcement was connected to the RC frame through steel bars at both Table 4. Adopted shake table test sequence of inputs. Stage Identification Description DI 0 Initial dynamic identification test
Appl. Sci. 2022, 12, 503 10 of 26 ends. The infills of model 3 were similar to those of model 2 but a reinforced plaster was used on both wall faces, with a grid Bekaert Armanet φ1.05 mm 12.7 × 12.7 mm attached to the RC frame using Hilti X-M8H10-37-P8 nails. Table 3. Description of the tested models. Model Design Concrete Rebar Class Infill Solution Number Standards Class Double leaf clay brick 1 RSA/REBAP C20/25 S400 unreinforced wall Single leaf clay brick wall 2 EC2/EC8 C30/37 S500 with bed joint reinforcement every two joints Single leaf clay brick wall 3 EC2/EC8 C30/37 S500 with reinforced plaster on both sides 3.2. Shake Table Input and Acquisition Setup Eight artificial accelerograms were generated using a LNEC-SPA [30] to obtain the four stages of the shake table tests, with increasing amplitude, see Table 4. The accelerograms of the first three stages were adapted to the response spectra (damping ratio equal to 5%) of each damage limit state that was defined in part 3 of EC8, see Figure 8 Damage Limitation (DL 225 YRP); Significant Damage (SD 475 YRP); Near Collapse (NC 2475 YRP): here, YRP equals Years of the Return Period. A last stage was defined as the maximum capacity of the table in terms of velocity, given the size and mass of the model, and it corresponds to 4574 YRP. One signal was introduced for each horizontal direction for the shake table, namely North-South (N-S), or longitudinal, and East-West (E-W), or transversal. Before the first stage and after each stage, the model was subjected to two white-noise small amplitude inputs, again orthogonal, horizontal, and uncorrelated, specifically generated to obtain the dynamic properties of the model (natural frequencies, mode shapes and damping ratios) and their evolution during the experiment. The out-of-plane behaviours of the infill walls were captured by a set of accelerometers (ACC) distributed on the surface of the walls, see Figure 9. In the solid walls of the South façade, three ACC were placed at mid-height, one in the centre and the other two at half the distance to the RC columns. The West facade had one ACC in each infill of the lower storey, under the midpoint of the opening. The same occurred in the lower storey of the East facade. The North facade had three ACC in each infill, below the openings at the centre. In model 1, due to the existence of two leaves, the ACC had to be placed in the inner and outer leaves at the same position. This scheme can be seen in the outer leaf and was repeated in the inner leaf at the same position, totalling thirty-eight ACC. Models 2 and 3 followed a similar scheme, which did not repeat itself on the inside, as these models had single leaf infill walls. Except for the infill wall on the upper storey of the North facade, all the positions for the ACC in the outer leaf of model 1 were repeated in models 2 and 3. The ACC that were not used inside the model were applied outside, increasing the number of measurement points considerably. Each solid wall on the South facade received two extra rows of ACC, directly above and below the ones in model 1, at the upper and lower third of the height. The West facade had the same setup in all three models and the East facade received four extra ACC. The lower infill of the North facade received two extra ACC, totalling thirty-four ACC on the infill walls.
DI 4 Dynamic identification test after the fourth stage Transversal direction (East-West) Longitudinal direction (North-South) 20 20 18 Generated 1.5xNC 4574yrp 18 Generated 1.5xNC 4574yrp input input Appl. Sci. 2022, 12, 503 16 16 11 of 26 EC8 EC8 14 Acceleration (m/s ) 14 Acceleration (m/s ) 2 2 NC 2475yrp NC 2475yrp 12 12 10 10 8 8 6 4. Adopted shake table test sequence Table of inputs. 6 SD 475 yrp SD 475 yrp 4 4 2Stage Identification 2 Description DL 225yrp DL 225yrp 0 0 0.01 0.1 DI 0 1 0.01 Initial dynamic 0.1 test 1 identification Period (s) DL Period Seismic test based on (s) Damage Limitation—225 YRP 1 DI 1 Dynamic identification test after the first stage Figure 8. Comparison between the pseudo-acceleration response spectra of the accelerograms gen- SD erated and the response spectra obtained Seismic test based on Significant Damage—475 YRP from EC8 (scaled). 2 DI 2 Dynamic identification test after the second stage One signal was introduced NC for each horizontal direction Seismic for theonshake test based Neartable, namely YRP Collapse—2475 North-South 3 (N-S), or longitudinal, and East-West (E-W), or transversal. Before the first Appl. Sci. 2022, 12, x FOR PEER REVIEW DI 3 Dynamic identification test after the third stage 11 of 27 stage and after each stage, the model was subjected to two white-noise small amplitude Seismic test with an amplitude of 1.5 times the inputs, again orthogonal, horizontal, 1.5xNC and uncorrelated, specifically generated to obtain 4 previous stage—4574 YRP the dynamic properties of the model (natural frequencies, mode shapes and damping ra- DI 4 Dynamic identification test after the fourth stage tios) and their evolution DI during 4 the experiment. Dynamic identification test after the fourth stage The out-of-plane behaviours of the infill walls were captured by a set of accelerome- ters (ACC) distributed on the surface of the walls, see Figure 9. In the solid walls of the Transversal direction (East-West) Longitudinal direction (North-South) South façade, three ACC were placed at mid-height, one in the centre and the other two at half the20 distance to the RC columns. The West facade had 20 one ACC in each infill of the 18 Generated 1.5xNC 4574yrp 18 occurredGenerated 1.5xNC 4574yrp lower storey, under input the midpoint of the opening. The same input in the lower storey 16 16 of the East facade. EC8The North facade had three ACC in each infill, EC8 below the openings at 14 Acceleration (m/s ) 14 Acceleration (m/s ) 2 2 the centre.12 In model 1, dueNC to 2475yrp the existence of two leaves, the 12 ACC had to beNCplaced 2475yrp in the inner and10outer leaves at the same position. This scheme can 10 be seen in the outer leaf and was repeated8 in the inner leaf at the same position, totalling 8 thirty-eight ACC. Models 2 6 and 3 followed a similar scheme, which did not repeat 6 on the inside, as these models itself SD 475 yrp SD 475 yrp had single4 leaf infill walls. Except for the infill wall on the4 upper storey of the North fa- 2 2 cade, all the positions for the DLACC 225yrp in the outer leaf of model 1 were repeated DLin models 2 225yrp 0 0 and 3. The0.01ACC that were0.1not used inside1 the model were applied 0.01 outside,0.1increasing the 1 number of measurement points Period (s)considerably. Each solid wall on the South facade Period (s) received two extra rows of ACC, directly above and below the ones in model 1, at the upper and Figure lower Figure third 8. Comparison of the 8. Comparisonheight. Thebetween between West the pseudo-acceleration thefacade had the same setup pseudo-acceleration response response in threespectra allspectra models of andthe theaccelerograms of the accelerograms gen- Eastgenerated facade erated and the and receivedthe response response fourspectra spectra extra ACC. obtained Thefrom obtained from lowerEC8infillEC8 (scaled). of the North facade received two (scaled). extra ACC, totalling thirty-four ACC on the infill walls. One signal was introduced for each horizontal direction for the shake table, namely North-South (N-S), or longitudinal, and East-West (E-W), or transversal. Before the first stage and after each stage, the model was subjected to two white-noise small amplitude inputs, again orthogonal, horizontal, and uncorrelated, specifically generated to obtain the dynamic properties of the model (natural frequencies, mode shapes and damping ra- tios) and their evolution during the experiment. The out-of-plane behaviours of the infill walls were captured by a set of accelerome- Appl. Sci. 2022, 12, x FOR PEER REVIEW ters (ACC) distributed on the surface of the walls, see Figure 9. In the 12 ofsolid 27 walls of the South façade, three ACC were placed at mid-height, one in the centre and the other two at half the distance(a) to the RC columns. The West facade had (b) one ACC in each infill of the lower storey, under the midpoint of the opening. The same occurred in the lower storey of the East facade. The North facade had three ACC in each infill, below the openings at the centre. In model 1, due to the existence of two leaves, the ACC had to be placed in the inner and outer leaves at the same position. This scheme can be seen in the outer leaf and was repeated in the inner leaf at the same position, totalling thirty-eight ACC. Models 2 and 3 followed a similar scheme, which did not repeat itself on the inside, as these models had single leaf infill walls. Except for the infill wall on the upper storey of the North fa- cade, all the positions for the ACC in the outer leaf of model 1 were repeated in models 2 and 3. The ACC that were not used inside the model were applied outside, increasing the number of measurement points considerably. Each solid wall on the South facade received two extra rows of ACC, directly (c) above and below the ones in model 1, at the upper and lower Figure 9. Model third Figure1:9. of the (a)Model height. construction The West offacade of the RC structure; 1: (a) construction the(b) had RCmodel the same on the structure; setup shake (b) in(c)the table; model on all three table; accelerom- shake models(c) and the accelerome- East eters setup. facade ters setup. received four extra ACC. The lower infill of the North facade received two extra ACC, totalling thirty-four ACC on the infill walls. 4. Comparison of the Experimental Results with Design Standards Next, comparisons between the experimental results and different design standard provisions are presented, based on two parameters: (i) the out-of-plane demand to which the infill walls were subjected; (ii) the out-of-plane capacity of the infill walls.
Appl. Sci. 2022, 12, 503 12 of 26 4. Comparison of the Experimental Results with Design Standards Next, comparisons between the experimental results and different design standard provisions are presented, based on two parameters: (i) the out-of-plane demand to which the infill walls were subjected; (ii) the out-of-plane capacity of the infill walls. 4.1. Demand In order to compute the design out-of-plane load according to the standards in Table 5 the maximum seismic input acceleration that is associated with the infill location on the structure must be considered, among other parameters. Given the fact that the PGA varied during the test, the PGA was not the same for each tested model, and that the measurements for the reinforced plaster infill seem to be unreliable, the value used in the equations proposed by each standard, see Table 5, was the maximum recorded acceleration at the foundation, for each tested model and each stage. This might not be necessarily the case for taller buildings, where more research seems to be needed. The out-of-plane design load variation, for each standard, was then plotted against the values recorded experimentally in each stage of the tested models, see Figures 10–12. Table 5. Analytical solutions used to compute the out-of-plane demand of the infill walls. Standard Analytical Solution 0.4a p SDS Wp FEMA 302 [24] and 306 [22] 1 + 2 hz Fp = Rp Ip EC8 [27] Fa = Sa W qa a γa FEMA 356 [25] Fp = χSXS W NZS 1170.5 [26] Fph = C p Tp C ph R p Wp < 3.6Wp As far as model 1 is concerned, see Figure 10, FEMA 302 [24], 306 [22] and 356 [25] presented a lower load than the experimental values during all the stages. FEMA 302 [24] and 306 [22] presented a load 46% and 60% lower on average, than the experimental values for the longitudinal and transversal infill walls, respectively, and FEMA 356 [25] presented design loads 48% and 62% lower in the same situation. As for NZS 1170.5 [26], in the longitudinal direction and until the second stage, the standard presented loads slightly higher than the experimental values for the exterior walls and lower values for the interior ones. In the last two stages, the standard presented loads 12% lower, on average for all infills, than the experimental values. In the transversal direction, the standard loads were lower in all stages, and 38% lower on average for all infills, in the last stage. EC8 [27], in the longitudinal direction presented design loads always higher than the experimental ones for the infill walls on the second floor (30% on stage 4) and always lower for the ground floor (20% on stage 4). In the transversal direction, the design loads were the same, on average, for all the infill walls on the second floor and always lower for the ground floor (46% on stage 4). As for model 1, FEMA 302 [24], 306 [22] and 356 [25] presented the highest differences in model 2, see Figure 11. In the longitudinal direction, FEMA 302 [24] and 306 [22] presented a load, on average (for all infills), 50% lower than the experimental results, in stage 3 and 267% lower in stage 4, while FEMA 356 [25] presented loads 74% lower in stage 3 and 87% lower in stage 4.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 13 of 27 Appl. Sci. 2022, 12, 503 13 of 26 Longitudinal Transversal 4 4 FEMA 302 and 306 3 3 Stage Stage 2 Expe Code 2 Expe Code P1Int P1Int P1Int P1Int P1Ext P1Ext P1Ext P1Ext P2Int P2Int P2Int P2Int P2Ext P2Ext P2Ext P2Ext 1 1 0 2 4 6 8 10 12 14 0 1 2 3 4 5 6 Force (KN) Force (KN) 4 4 3 3 Stage Stage EC8 2 Expe Code 2 Expe Code P1Int P1Int P1Int P1Int P1Ext P1Ext P1Ext P1Ext P2Int P2Int P2Int P2Int P2Ext P2Ext P2Ext P2Ext 1 1 0 2 4 6 8 10 12 14 0 1 2 3 4 5 6 Force (KN) Force (KN) 4 4 3 3 FEMA 356 Stage Stage 2 2 Expe Code Expe Code Int Int Int Int Ext Ext Ext Ext 1 1 0 2 4 6 8 10 12 14 0 1 2 3 4 5 6 Force (KN) Force (KN) 4 4 3 3 NZS 1170.5 Stage Stage 2 2 Expe Code Expe Code Int Int Int Int Ext Ext Ext Ext 1 1 0 2 4 6 8 10 12 14 0 1 2 3 4 5 6 Force (KN) Force (KN) Figure10. Figure Standardand 10.Standard and experimental experimental out-of-plane out-of-plane load load comparison comparison forfor model model 1. 1.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 14 of 27 Appl. Sci. 2022, 12, 503 14 of 26 Longitudinal Transversal 4 4 FEMA 302 and 306 3 3 Stage Stage 2 2 Expe Code Expe Code P1 P1 P1 P2 P2 P2 P2 P2 1 1 0 5 10 15 20 25 30 35 40 45 0 1 2 3 4 5 6 7 8 9 10 Force (KN) Force (KN) 4 4 3 3 Stage Stage EC8 2 2 Expe Code Expe Code P1 P1 P1 P2 P2 P2 P2 P2 1 1 0 5 10 15 20 25 30 35 40 45 0 1 2 3 4 5 6 7 8 9 10 Force (KN) Force (KN) 4 4 3 3 FEMA 356 Stage Stage 2 2 Expe Code Expe Code NZS NZS FEMA 356 FEMA 356 1 1 0 5 10 15 20 25 30 35 40 45 0 1 2 3 4 5 6 7 8 9 10 Force (KN) Force (KN) Figure11. Figure Standardand 11.Standard andexperimental experimental out-of-plane out-of-plane load load comparison comparison forfor model model 2. 2. A similar situation was found in the transversal direction. NZS 1170.5 [26] presented veryAs goodfar as modeluntil results 1 is the concerned, see Figure third stage, with load10, FEMA 14% and 3029% [24], 306 [22] lower and in the 356 [25] longitudinal presented a lower load than the experimental values during all the stages. and transversal direction, respectively, but in stage 4, the load proposed by this standard FEMA 302 [24] is and 306 [22] presented a load 46% and 60% lower on average, than low, 57% and 23% for the longitudinal and transversal direction, respectively. This may the experimental val- be ues for the longitudinal and transversal infill walls, respectively, due to the nonlinear evolution of the experimental load due to damage accumulation in and FEMA 356 [25] pre- sented the infilldesign walls loads and 48% and 62% lower RC structure. As forinthetheEC8same situation. [27], until theAsthird for NZS stage1170.5 [26], in the differences the longitudinal between direction the demand andand until the second experimental load wasstage, the standard negligible presented (3% and 6% for loads slightly the longitudinal higher than the experimental values for the exterior walls and lower values and transversal directions, respectively, in stage 3), but in the last stage the load was 57% for the interior ones. and 23%In the last two stages, the standard presented loads 12% lower, on average for all lower. infills,The thanresults the experimental of the designvalues. In the standards transversal were not as gooddirection, as for the the standard previous loads modelswere in the lower in all stages, and 38% lower on average for all infills, in the last case of model 3, possibly due to the separation of the plaster from the walls, particularly stage. EC8 [27], in on the longitudinal direction presented design loads always higher the transversal direction where higher experimental loads were recorded. The attaching than the experimental ones for theused technique infillfor walls the on the second floor accelerometers, (30% bolted to on thestage 4) and plaster and always lowertofor not directly thethe infill ground wall, mightfloor have (20% onledstage 4).reliable to less In the transversal results. direction, the design loads were the same, on average, for all the Nonetheless, infill walls on a comparison the second is made floor12, in Figure andand always FEMA lower 302 for [24]the andground 306 [22] floor (46% on stage 4). presented loads 79% and 65% lower in the longitudinal direction than the experimental values for stages 2 and 3, respectively, and 63% and 57% lower in the transversal direction for stage 2 and 3, respectively. As for FEMA 356 [25], a similar situation was found with
Appl. Sci. 2022, 12, 503 15 of 26 loads 85% and 66% lower, for stages 2 and 3 respectively, in the longitudinal direction and 64% and 55% lower, for stage 2 and 3 respectively. NZS 1170.5 [26], unlike models 1 and 2, did not present a good agreement with the experimental values, proposing loads 63% and 43% lower, for stages 2 and 3 respectively, in the longitudinal direction and 27% and 25% lower, for stages 2 and 3 respectively, in the transversal direction, even though the results were better than the ones obtained using the North American standards. EC8 [27] also presented results with a poor agreement with the experimental values, in contrast to the very good results in the two previous models, with design loads 59% and 43% lower, for stages 2 and 3 respectively, in the longitudinal direction and 25% and 59% lower, for stage Appl. Sci. 2022, 12, x FOR PEER REVIEW 15 of 27the 2 and 3, respectively, in the transversal direction. Still, and overall, EC8 [27] presented best results, when compared to the other design standards. Longitudinal Transversal 3 3 FEMA 302 and 306 2 2 Stage Stage Expe Code Expe Code P1 P1 P1 P1 P2 P2 P2 P2 1 1 0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 4 5 6 7 8 9 10 Force (KN) Force (KN) 3 3 2 2 Stage Stage EC8 Expe Code Expe Code P1 P1 P1 P1 P2 P2 P2 P2 1 1 0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 4 5 6 7 8 9 10 Force (KN) Force (KN) 3 3 FEMA 356 2 2 Stage Stage Expe Code Expe Code NZS NZS FEMA 356 FEMA 356 1 1 0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 4 5 6 7 8 9 10 Force (KN) Force (KN) Figure Figure12. 12.Standard Standardand andexperimental experimentalout-of-plane out-of-planeload comparison load forfor comparison model 3. 3. model 4.2. As Capacity for model 1, FEMA 302 [24], 306 [22] and 356 [25] presented the highest differences in model 2, 6see Table Figure shows 11. In the analytical longitudinal solutions direction, that compute theFEMA 302 [24] out-of-plane and 306 capacity of[22] infillpre- walls. sented a load, In Figures 13 on andaverage (forsolutions 14, these all infills), are50% lower than compared withthe theexperimental experimental results, resultsinobtained stage 3using and 267% lower the three in stage tested 4, while models. TheFEMA 356 [25] presented reinforcement loads in the infills 74% lower of model 2 (bedin joint) stage and 3 and 87%3lower model in stage (plaster) were4.not taken into consideration because their percentage was very A similar situation was found in the transversal direction. NZS 1170.5 [26] presented very good results until the third stage, with load 14% and 9% lower in the longitudinal and transversal direction, respectively, but in stage 4, the load proposed by this standard is low, 57% and 23% for the longitudinal and transversal direction, respectively. This may be due to the nonlinear evolution of the experimental load due to damage accumulation
Appl. Sci. 2022, 12, 503 16 of 26 low and defined only for crack control. The infill walls were separated into walls without openings (South infill walls in the longitudinal direction) and walls with openings (North walls in the longitudinal direction, and East and West walls in the transversal direction), but the walls with openings were computed as if they were solid, considering their actual weight. The load obtained experimentally, for each wall during the four stages of the tests, was calculated by adding the product of the acceleration in each accelerometer and the mass associated with it, and then plotted against the analytical values for that set. Table 6. Analytical solutions used to compute the out-of-plane capacity of the infill walls. Standard Analytical Solution 0.7 f 0 m λ2 FEMA 273 [21] qin = hin f × 144 tin f 0.75 2 q = 4.50 f m0 MSJC [20]/Seah and Dawe [7] α β t l 2.5 + h2.5 FEMA 306 [22] and Angel [10] 2f0 m q= R R λ ( ht ) 1 2 q= Klingner et al. [11] xyv 8 l h2 l Myv [(l − h) + hln(2)] + Myh xyh ln h l l− 2 h i f cmw Pereira [15] q = h R1 R2 λ 0.77C f hl + 0.34C f ( tw ) 2 EC6 [28] qlat,d = f d lta It was considered that the maximum load value obtained experimentally was the capacity of the wall, as all the infill walls of the ground floor in model 1 collapsed during the last stage, and the infill walls of model 2 were damaged beyond repair and were unable to sustain any more load. In model 3, the experimental load curve is only presented until stage 3 for the sake of comparison with the other two models, as the model had to be re-tested due to technical problems [29]. It is important to keep in mind that the out-of-plane capacity is influenced by other parameters, such as the in-plane displacements and subsequent damage, vertical loads and even the presence of reinforcement, and that infill walls have damage accumulation from one stage to the next. The infill walls with openings in the longitudinal direction presented the highest experimental force value during stage 3, which is associated with damage and loss of connection between the wall and the surrounding RC frame. Walls of higher slenderness, as the interior leaves of model 1 (thickness/height equal to 24.3), do not seem to be affected by the presence of openings, and EC6 [24] provided a very good agreement for the estimate of capacity, with only 7% error on average for all interior leaves, with and without openings. As for the exterior leaves (thickness/height equal to 18.9), EC6 [28] overestimated the capacity of the infills, on average by 46% and, as with the interior leaves, the presence of openings did not seem to affect the results. FEMA 273 (1997) presented an average error of 17% for the interior leaves and 52% for the exterior ones, while FEMA 306 (1998) presented an error of 40% and 11% for the interior and exterior leaves, respectively. All other analytical solutions presented out-of-plane capacity values with higher dif- ferences than the experimental values. Regarding the solid infill walls, MSJC [20] presented the highest values, with an error of 70% and 58% for the interior and exterior walls, re- spectively. The analytical solution proposed by Klingner et al. [11] also overestimated the experimental values by 37% and 138% for the interior and exterior infills, respectively. The recommendations from Pereira [15] were acceptable in the case of exterior infills, under- estimating the capacity by 17%, but considerably underestimating the capacity by 56% in the case of the interior infill walls. Regarding the infill walls with openings, MSJC [20] presented the highest overestimation, 150% and 199% for interior and exterior infill walls, respectively, followed by Klingner et al. [11] with 47% and 171% for the interior and ex- terior infills walls, respectively. Pereira [15] presented the lowest underestimations for
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