Engineering Structures 41 (2012) 98–107

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Engineering Structures

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Seismic performance of concrete walls for housing subjected to shakingtable excitations

Julian Carrillo a,b,⇑, Sergio M. Alcocer b

a Departamento de Ingeniería Civil, Universidad Militar Nueva Granada, UMNG, Cra. 11, No. 101-80, Bogotá, Colombiab Instituto de Ingeniería, Universidad Nacional Autónoma de México, UNAM, Ciudad Universitaria, Coyoacán 04510, DF, Mexico

a r t i c l e i n f o a b s t r a c t

Article history:Received 29 August 2011Revised 5 February 2012Accepted 9 March 2012Available online 25 April 2012

Keywords:Concrete wallsShear behaviorLow-rise housingShaking table testsLightweight concreteWelded-wire mesh

0141-0296/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.engstruct.2012.03.025

⇑ Corresponding author at: Departamento de IngeniNueva Granada, UMNG, Cra. 11, No. 101-80, Bog6500000x1268; fax: +57 1 6370557.

E-mail address: wjcarrillo@gmail.com (J. Carrillo).

Aimed at better understanding the seismic behavior of reinforced concrete (RC) walls, typically used inone-to-two stories housing in several Latin American countries, a large investigation project has been car-ried out. Previous experimental programs considered the behavior of walls subjected to monotonicallyand cyclically increased loads. This paper compares and discusses displacement and shear strengthcapacities, as well as the dynamic characteristics of six RC walls tested under shaking table excitations.Variables studied were the wall geometry (solid walls and walls with openings), type of concrete (nor-malweight and lightweight), web steel reinforcement ratio (0.125% and 0.25%) and type of web reinforce-ment (deformed bars and welded-wire mesh). Shaking table tests were essential for assessing dynamiccharacteristics, such as changes in fundamental frequencies and damping factors of RC walls for low-risehousing.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Because of their potential lateral stiffness and strength, one-to-two stories high concrete wall structures are subjected to smalldemands of lateral displacements and seismic forces. This phe-nomenon has prompted housing designers and contractors to useconcrete compressive strengths of 15–20 MPa, as well as 100-mm thick walls. Also, in zones where seismic demands are low,such that design controlled by vertical actions, the minimumweb shear reinforcement prescribed by ACI-318 building code [1]appears to be excessive for controlling diagonal tension cracking.Moreover, application of such a code commonly leads to an unjus-tifiable excessive cost of the housing unit. As a result, web steelreinforcement ratios smaller than the minimum ratio prescribedby ACI-318 building code and web shear reinforcement made ofwelded-wire meshes are frequently used. All these features are adirect consequence of attaining speed of construction and econ-omy in a very competitive housing market. However, the effectand adequacy of such structural characteristics on seismic behav-ior have not been assessed experimentally.

In a first stage of the testing program, reinforced concrete (RC)walls tested under monotonic and cyclic loading, and reinforced

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ería Civil, Universidad Militarotá, Colombia. Tel.: +57 1

with 50% of the minimum code-prescribed web shear reinforce-ment [2,3], exhibited comparable shear strength capacity to thatof walls reinforced with 100% of the minimum steel reinforcementratio. Nevertheless, walls with 50% of the minimum code pre-scribed web shear reinforcement and reinforced with welded-wiremesh exhibited limited displacement capacity as compared towalls reinforced with 100% of the minimum amount.

When correlating earthquake demand to structural capacity, itis essential that capacity be evaluated under conditions closelyapproximating those representing the true dynamic conditions[4]. Up to date, shaking table testing is recognized as the most suit-able experimental method for reproducing the real dynamic effectsof earthquakes on buildings, structures or components. Thus, thisstudy aims at evaluating the effect of wall geometry, type of con-crete, web steel reinforcement ratio and type of web reinforcementon the shear strength, displacement capacity, and dynamic charac-teristics of RC walls for low-rise housing subjected to shaking tableexcitations. Most representative wall models tested in previousphases were selected for studying the structural behavior underactual seismic actions. Dynamic tests included four solid wallswith height-to-length ratio equal to 1.0, as well as two walls withdoor and window openings. Wall properties were those obtainedfrom current design and construction practice found in typicallow-rise housing in several Latin American countries. Walls weredesigned to fail in shear to better understand the strength mecha-nism that take place during shear failures observed in RC walls forlow-rise housing.

Table 2Main scale factors for the simple law of similitude [5].

Quantity Equation Scale factor

Length (L) SL = LP/LM SL = 1.25Stress (r) Sr = fP/fM 1Force (F) SF ¼ S2

L Sf S2L � 1:56

Time (t) and period (T) St = SL(ScSe/Sf)1/2 SL = 1.25Displacement (d) Sd = SLSe SL = 1.25Acceleration (a) Sa = Sf/SLSt 1/SL = 0.80Mass (m) 3 3

J. Carrillo, S.M. Alcocer / Engineering Structures 41 (2012) 98–107 99

Wall models were subjected to a series of earthquake recordsassociated to three limit states. The initial period of vibration ofthe isolated walls was established to agree with the fundamentalperiod of vibration of a prototype house. For estimating the period,mathematical models were developed and calibrated throughambient vibration testing. The test set-up was purposely designedto carry the additional inertial mass outside the shaking table. Wallperformance, hysteresis curves as well as changes in fundamentalfrequencies and damping will be compared and discussed.

Sm ¼ ScSL SL � 1:95

2. Experimental program

The three-dimensional prototype was a two-story house builtwith RC walls in the two principal directions. In this type of housingconstruction, 100-mm thick solid slabs or slabs made of precast ele-ments are frequently used. In the case of solid slabs, these are castmonolithically with walls. Wall thickness and clear height are com-monly 100 and 2400 mm, respectively, and house floor plan areavaries between 35 and 65 m2. Foundations are strip footings madeof RC 400-mm square beams that support a 100-mm thick floorslab. Variables studied in the experimental program were wallgeometry (solid walls and walls with door and window openings),type of concrete (normalweight and lightweight), web steel rein-forcement ratio (0.125% and 0.250%) and type of web reinforcement(mild-steel deformed bars and cold-drawn welded-wire mesh).These variables were chosen to be the most representative in hous-ing construction. Main characteristics of specimens are presentedin Table 1. Web reinforcement ratios in Table 1 were calculatedfrom design dimensions.

Owing to limitations in the payload capacity of the shaking ta-ble equipment at UNAM, lightly-reduced scaled models were de-signed and built (i.e. geometry scale factor, SL = 1.25) for shakingtable testing. The size of models was almost equal to that of wallsin the prototype. The simple law of similitude was then chosen forscaling specimens, as well as for calculating the prototype responsefrom measured response in the wall models. For this type of simu-lation, models are built with the same materials of the prototype(i.e. materials properties are not changed) and only the dimensionsof the models are altered [5]. Main scale factors for simple law ofsimilitude are shown in Table 2.

2.1. Geometry and reinforcement

Nominal geometry and reinforcement layout of specimens areshown in Fig. 1. As-built wall dimensions and reinforcement char-acteristics are presented in Tables 1 and 3, respectively. Web rein-forcement ratios in Table 3 were calculated from as-builtdimensions. In order to prevent cracking during transportation ofthe specimens in the lab, specimens were built on a RC stiff gradebeam. Foundation beam was also used to bolt the specimens to theplatform of the shaking table. Top slab was cast monolithically

Table 1Main characteristics and as-built dimensions of specimens.

No. Wall Type of concrete Geometry tw (mm) lw (mm)

1 MCN50m Normal Solid 83 19162 MCN100 Normal Solid 84 19213 MCL50m Light Solid 82 19174 MCL100 Light Solid 82 19125 MVN50m Normal Openings 83 30426 MVN100 Normal Openings 84 3042

D = deformed bar, W = welded-wire mesh.

with walls and was used to connect the mass-carrying load systemfor testing (Fig. 4).

According to the scaling factors (i.e. 0.8), height and thickness ofwalls were 1920 and 80 mm, respectively. Walls were prismatic,that is, thickness of boundary elements was equal to the web thick-ness. For solid walls, height-to-length ratio was equal to 1.0. Forwalls with openings, areas of door and window were equivalentto 32% of the specimen area (length of specimen multiplied byits height). Opening size and configuration were typical of the pro-totype house.

In a prototype, all walls are connected to a RC solid slab, so that,top wall rotation is restrained. Due to their geometry, walls have alength to height ratio of 1.0 or larger. The behavior of these squatwalls is governed by shear deformations and hence the area of lon-gitudinal reinforcement at boundary elements is almost alwayscontrolled by minimum requirements. During testing, free top wallrotation was allowed (section 0), thus exhibiting a maximumbending moment at the base. To prevent a flexural failure priorto achieving shear strength, the longitudinal reinforcement at theboundary elements was purposely designed and detailed. If theamount of longitudinal boundary reinforcement would have beensimilar to that used in prototype walls, a flexural failure wouldhave been observed. Evidently, longitudinal reinforcement withinboundary elements contributed to shear strength. Such contribu-tion was assessed through strains measurement in the longitudinalreinforcement. Measured strains indicated an elastic behavior dur-ing all testing stages. Moreover, strain loops (in a lateral force vs.strain curves) were consistent with flexural demands and their cor-responding rotations. This indicated that contribution to shear oflongitudinal reinforcement was small compared to other resistingmechanisms developed in the wall web. In general, walls were de-signed to fail in shear to better understand the strength mecha-nism under this type of failure mode. Area of longitudinalreinforcement was calculated so that the ratio between shear forceassociated to flexural yielding and that associated to shear failureof wall section was equal to 1.6 and was roughly constant for allspecimens.

Wall reinforcement was made of a single layer placed at wallmid-thickness. Specimens MCN100, MCN100L and MVN100 werereinforced in the web using a single layer of No. 3 vertical and hor-izontal deformed bars (9.5 mm diameter = 3/8 in.) spaced at

hw (mm) Door (mm �mm) Window (mm �mm) Web reinforc.

qh,v (%) Type

1923 – – 0.11 D1924 – – 0.28 W1917 – – 0.11 D1918 – – 0.28 W1924 1681 � 720 965 � 689 0.11 D1926 1681 � 721 959 � 689 0.28 W

(a)

lw = 1920

2400

hw =

192

08

No.

5S

No.

2 @

180

No.

3 @

320

No. 3 @ 320

lw = 1920

tw = 80

600

200

2400600

400

(b)

6 N

o. 5

S N

o. 2

@ 1

80

mesh6x6-6/6

No. 3 @ 250

hw =

192

0

All dimensions in mm

1 No. 3

1 No. 31 No. 3

4 N

o. 4

S N

o. 2

@ 1

80

4 N

o. 4

S N

o. 2

@ 1

80

4 N

o. 4

S N

o. 2

@ 1

80

3500

96688896720640

1680

No. 3 @ 320

No.

3 @

320

(c)

mesh6x6-8/8

1 No. 3

1 No. 31 No. 3

4 N

o. 4

S N

o. 2

@ 1

80

4 N

o. 4

S N

o. 2

@ 1

80

4 N

o. 4

S N

o. 2

@ 1

80

3500

lw = 3040

960

hw =

192

0

2 N

o. 3

2 N

o. 3

1 N

o. 3

(d)

Fig. 1. Geometry and reinforcement layout of specimens: (a) MCN100, MCL100; (b) MCN50m, MCL50m; (c) MVN100, (d) MVN50m.

Table 3Reinforcement characteristics of specimens.

Wall Web reinforcement Boundary elements

Longitudinal Stirrups (S)

Layout qh,v (%) Layout q (%) Layout qs (%)

MCN50m Mesh 6�6-8/8a 0.11 6 No. 5 0.81MCN100 No. 3 @ 320 mm 0.26 8 No. 5 1.08MCL50m Mesh 6 � 6-8/8 0.11 6 No. 5 0.81 No. 2 @ 0.43MCL100 No. 3 @ 320 mm 0.27 8 No. 5 1.08 180 mmMVN50m Mesh 6 � 6-8/8 0.11 4 No. 4 0.91MVN100 No. 3 @ 320 mm 0.26 4 No. 4 0.91

a First two digits (i.e. 6 � 6) indicate the horizontal and vertical spacing of wiresin the mesh, in inches. The second two digits (i.e. 8/8) correspond to the wire gage;gage 8 has a diameter of 4.1 mm.

100 J. Carrillo, S.M. Alcocer / Engineering Structures 41 (2012) 98–107

320 mm. The amount of web reinforcement corresponded approx-imately to the minimum web steel ratio prescribed by ACI-318building code [1]. Specimens MCN50m, MCL50m and MVN50mwere reinforced in the web using a single mesh (6�6-8/8) of No.8 wires (4.1 mm diameter) spaced at 150 mm (�6 in.). The websteel ratio was approximately 50% of the minimum ratioprescribed by ACI-318. These tests were aimed at examining the

performance of walls with a steel reinforcement smaller than theminimum prescribed by the code. A lower steel ratio is supportedby the fact that lower concrete compressive strengths and higheryield strengths of the web steel require, in theory, steel reinforce-ment ratios smaller than the 0.25% minimum prescribed ratio [6].

2.2. Mechanical properties of materials

Ready-mixed concrete was used for wall casting. Maximum sizeof coarse aggregate for normalweight and lightweight concretewas 10 mm. Design concrete compressive strength was 15 MPa,and nominal yield strength of bars and wire reinforcement were412 MPa (mild steel) and 491 MPa (cold-drawn wire reinforce-ment), respectively. Mean value and coefficient of variation ofthe measured mechanical properties of concrete and reinforce-ment are presented in Tables 4 and 5, respectively. For concrete,properties were obtained from cylinder tests at the time of shakingtable testing. Because of the small size of the coarse aggregate andthe measured slump, internal consolidation of fresh concrete wasnot needed. Form vibration was applied through a rubber hammeronly.

During tensile tests of coupon specimens, differences in thestress–strain behavior of deformed bars and welded-wiremeshes were readily apparent. ‘‘Yielding’’ was clearly defined for

Table 4Measured mechanical properties of concrete.

Mechanical property Normal Light

Slump (mm) 210 145Compressive strength, fc (MPa) 24.8 (5.3) 21.0 (6.8)Strain at compressive strength, e0 0.0031 (15.3) 0.0030 (9.5)Poisson’s ratio, m 0.16 (12.3) 0.16 (14.1)Elastic modulus, Ec (MPa) 14,760 (5.1) 9145 (4.7)Flexural strength, fr (MPa) 3.75 (9.0) 3.29 (9.5)Tensile splitting strength, ft (MPa) 2.09 (13.5) 1.44 (11.5)Specific dry weight, c (kN/m3) 20.3 (0.7) 16.8 (1.2)

(CV, %) = coefficient of variation, %.

Table 5Measured mechanical properties of steel reinforcement.

Mechanical property No. 5 No. 4 No. 3 No. 2 Cal. 8

Type D D D D WDiameter (nominal),

mm15.9 12.7 9.5 6.4 4.1

Yield strength, fy,MPa

411(0.6)

425(1.5)

435(1.2)

273(3.1)

630(3.5)

Yield strain, ey 0.0022(5.2)

0.0025(3.0)

0.0022(1.9)

0.0019(5.4)

0.0036(1.6)

Strain hardening, esh 0.0119(2.2)

0.0071(2.2)

0.0130(2.9)

0.0253(5.6)

–

Ultimate strength, fu,MPa

656(0.7)

677(0.8)

659(0.4)

388(1.3)

687(1.8)

Strain at ultimatestrength, esu

0.0789(4.2)

0.0695(4.3)

0.0730(6.6)

0.1426(3.4)

0.0082(3.5)

Elongation, % 12.2(5.2)

9.1 (4.1) 10.1(3.6)

19.2(10.1)

1.9(19.2)

D = deformed bar, W = welded-wire mesh, (CV, %) = coefficient of variation.

Table 6Characteristics of earthquake records for the prototype house.

Record Magnitude,MW

PGA(g)

PGD(mm)

IA

(m/s)Totalduration(s)

Intense phaseduration, IPD (s)

CA-71 7.1 0.38 7.8 2.02 29.5 13.4CA-77 7.7 0.72 16.6 8.81 36.1 16.3CA-83 8.3 1.30 30.5 41.63 99.8 40.7

PGA = peak ground acceleration, PGD = peak ground displacement, IA = arias inten-sity [8], IPD = time interval between 5% and 95% of IA.

J. Carrillo, S.M. Alcocer / Engineering Structures 41 (2012) 98–107 101

reinforcement made of mild-steel where an increment of tensilestrength is not observed until a well-defined yielding platform isdeveloped. In contrast, cold-drawn wire reinforcement used in thisstudy did not exhibit a specific yield point. Furthermore, in thistype of reinforcement, the loading branch between onset of plastic-ity and maximum deformation capacity (at fracture) was muchshorter than that of mild-steel reinforcement (see the elongationparameter in Table 5). The behavior of this type of material wascharacterized by fracture of material with a slight increment ofstrain. As a result, and as it will be shown below, the elongationcapacity of wires was a key parameter for displacement capacityof walls reinforced in the web using this type of reinforcement. Itis important to note that brittle behavior of reinforcement is unde-sirable and is, therefore, not allowed in modern construction codes.The inclusion of welded wire meshes as a variable in the testingprogram was decided because brittle reinforcement is used with-out knowing the actual effects on wall behavior. It is the authors’opinion that such reinforcement should not be allowed nor encour-aged, but while this occurs, limitations on their use should beindicated.

-1.4

-0.7

0.0

0.7

1.4

0 20 40 60 80 100

t (s)

acce

lera

tion

(g)

(a)0 20 40

t

Fig. 2. Time history accelerations for prototyp

2.3. Loading histories

To assess wall performance under earthquake records, modelswere subjected to real and numerically simulated acceleration re-cords. Records were associated to different limit states (from onsetof cracking to collapse), and therefore, three earthquake hazardlevels were selected. The earthquake recorded in Caleta de Camposstation, Mexico, in January 11, 1997 (MW = 7.1, CA-71) was used forthe seismic demand representing the diagonal cracking limit state.Such record was measured in the epicentral region nearbyAcapulco. In this study, the diagonal cracking limit state is reachedwhen the initial inclined web cracking was observed. Owing to thepotential lateral stiffness and strength of concrete wall structures,demands of lateral displacements and seismic induced forces asso-ciated to the fundamental period of vibration of the prototypehouse are relatively low. Therefore, the PGA of the earthquake re-cord representing the diagonal cracking limit state is higher thanthat used for medium- and high-rise structures with larger vibra-tion periods. The CA-71 record was considered as a Green functionto simulate larger-magnitude events, i.e. with larger instrumentalintensity and duration [7]. Two earthquakes with magnitudes MW

7.7 (CA-77) and 8.3 (CA-83) were numerically simulated for thestrength and ultimate limit states, respectively. Main earthquakecharacteristics and time history accelerations for the prototypehouse are presented in Table 6 and Fig. 2, respectively. Pseudo-acceleration, displacement and velocity response spectra for 5%damping are shown in Fig. 3.

According to the simple law of similitude, acceleration and timescale factors (Sa = 0.80, St = 1.25, Table 2) were applied to the re-cords for testing of models. Specimens were tested under progres-sively more severe earthquake actions, scaled up considering thevalue of peak acceleration as the reference factor until the finaldamage stage was attained. Walls were tested in the in-planedirection only. Target PGA and the sequence of input motion usedin the tests are described in Table 7. To evaluate the level of frictionof the mass-carrying load system, tests started with sine-curve(SN) and ramp signals (RP) (see Fig. 4). At the beginning and atthe end of the tests, a random acceleration signal (white noise,WN) at 10 cm/s2 (0.01 g) root mean square (RMS) was also appliedto identify the periods of vibration and the damping factors ofmodels. Mean value of peak accelerations measured in the table

60 80 100

(s)

(b)0 20 40 60 80 100

t (s)

(c)

e house: (a) CA-71, (b) CA-77, (c) CA-83.

0.0

1.6

3.2

4.8

T (s)

Sa (

g)

CA-71

CA-77

CA-83

0

50

100

150

T (s)

Sd (m

m)

0

800

1600

2400

0.0 0.3 0.6 0.9 1.2 0.0 0.3 0.6 0.9 1.2 0.0 0.3 0.6 0.9 1.2

T (s)

Sv (

mm

)

Fig. 3. Response spectra for prototype house, n = 5%: (a) pseudo-acceleration, (b) displacement, (c) velocity.

Table 7Testing stages for prototype house.

Stage Record PGA Total duration (s)

% g

Target Measured: Mean(CV, %)

0 SN – – – 30.01 RP – – – 150.0

2 WN – 0.01 0.01 (5.3) 120.0

3CA-71

50 0.19 0.12 (10.5) 29.54 100 0.38 0.28 (2.8)

5CA-77

75 0.54 0.45 (1.8) 36.16 100 0.72 0.60 (4.0)

7CA-83

75 0.98 0.77 (2.0) 99.88 100 1.30 a

9 WN – 0.01 0.02 (10.8) 120.0

a Failure of models was observed at previous earthquake records.

102 J. Carrillo, S.M. Alcocer / Engineering Structures 41 (2012) 98–107

platform during testing models are included in Table 7. The accel-eration scale factor (Sa = 0.80, Table 2) was applied to the records tocompare with target values for prototype house.

2.4. Design for dynamic similitude

For adequately extrapolating specimen’s response to a proto-type’s response, isolated wall models were designed consideringthe fundamental period of vibration of the prototype house. Forestablishing such dynamic characteristic, mathematical modelswere developed and calibrated through ambient vibration testing.Hence, the fundamental period of vibration of the two-story housewas estimated to be equal to 0.12 s [10]. Taking into account thescale factors of the simple law of similitude (St = 1.25, Table 2), iso-lated wall models were designed to achieve an initial in-plane per-iod of vibration close to 0.10 s. In design, it was supposed thatwalls would behave as a single degree of freedom system. The dy-namic weight, Wd (mass � gravity acceleration), needed to achievethe desired design period, Te, was computed as ðKeT2

e=4p2Þg; whereKe is the in-plane stiffness of the wall that was calculated frommeasured mechanical properties of materials. To account forearly-age shrinkage cracking observed in the specimens, the mo-ment of inertia of the wall section was reduced by 25%. The reduc-tion factor was selected as half the reduction typically assumed forhigh-rise walls whose behavior is controlled by flexural deforma-tions. The dynamic weight used for achieving the desired designperiods for each specimen are presented in Table 8.

2.5. Test setup and instrumentation

Models were subjected to a series of base excitations repre-sented by selected earthquake records. Records were applied

through a shaking table over which models were bolted. As itwas indicated, for adequate dynamic simulation, it is necessaryto add some mass (dynamic weight) to the specimens. If such dy-namic weight were to rest at the top of models, the risk of lateralinstability would have been a major concern. Therefore, an alterna-tive method for supporting the mass and transmitting the inertiaforces was required. An external device with a mass-carrying loadsystem was designed and installed outside the shaking table. Thedevice allows guided horizontal sliding of the mass within a fixedsupporting structure [9]. Additional mass blocks (dynamic weight)were placed in a steel box which is, in turn, supported by a linearmotion guide system (LMGS) with very low friction (Fig. 4).

An axial compressive stress of 0.25 MPa was uniformly appliedto the walls and was kept constant during testing. This value cor-responds to 2% of the nominal concrete compressive strength. Todetermine the average axial stress at service loads in first storywalls of the housing prototype, finite element models of two-storyhouses were carried out [10]. The axial load was exerted throughthe weight of the load and connection beams, and lead ingotsbolted to the load beam. Although lead ingots resulted in a triangu-lar load distribution, the addition of the weight of the connectionbeam provided for a uniform distribution of the axial load on thewalls.

To measure the specimens’ response, walls were instrumentedinternally and externally. Internal instrumentation was designedto acquire data on the local response of steel reinforcementthrough strain-gages at selected locations, specifically aimed atevaluating strength contribution of steel reinforcement. Externalinstrumentation was planned for measuring the global responsethrough displacement, acceleration and load transducers. The loadcell was placed in the connection beam to measure the load ex-erted on specimens by the moving mass of the external device(Fig. 4). Also, an optical displacement measurement system withLight Emitting Diodes (LEDs) was used. In the tests, 41 strain-gagesand 36 external transducers were used for solid walls, as well as 59and 64, respectively, for wall with openings.

3. Test results and discussion

Wall response was assessed through crack patterns and failuremodes, changes in fundamental frequencies and damping factors,strength-to-displacement hysteresis curves, as well as the contri-bution of each mode of deformation on the total displacement ofwall specimens.

3.1. Crack patterns and failure modes

Prior to testing, walls exhibited early-age shrinkage cracking sothat it can be argued that their initial stiffness was affected. Wallsreinforced in the web using welded-wire mesh and with 50% of theminimum code prescribed web steel reinforcement ratio exhibited

LMGS

Shaking table

Pinnedconnection

Lead ingots

Load cell

Connectionbeam

Supporting frame

Vertical load

Storingbox

oadingbeam

Fig. 4. Test setup for walls with openings.

Table 8Main parameters of measured hysteresis curves.

Limit state Parameter Welded-wire mesh Deformed-bars

1 2 3 Mean (CV, %) 4 5 6 Mean (CV, %)

Cracking Dynamic weight, Wd (kN) 243.4 208.1 184.0 – 243.4 208.1 184.0 –Shear strength, Vcr (kN) 148.4 134.3 115.2 132.7 (10.2) 150.0 133.8 116.2 133.3 (10.4)Drift ratio, Rcr (%) 0.09 0.14 0.05 0.10 (36.9) 0.09 0.14 0.05 0.10 (37.5)

Peak strength Shear strength, Vmax (kN) 233.8 240.3 184.4 219.5 (11.4) 273.6 249.8 226.2 249.9 (7.7)Seismic coefficient, Cs (g) 0.96 1.15 1.00 1.04 (8.0) 1.12 1.20 1.23 1.18 (3.7)Shear stress (MPa) 1.47 1.53 1.44 1.48 (2.6) 1.70 1.60 1.75 1.68 (3.8)Drift ratio, Rmax (%) 0.44 0.62 0.40 0.49 (19.5) 0.53 0.50 0.49 0.50 (3.3)

Ultimate Shear strength, Vu (kN) 187.1 192.2 147.5 175.6 (11.4) 218.9 199.8 181.0 199.9 (7.7)Drift ratio, Ru (%) 0.54 0.65 0.44 0.55 (15.6) 0.58 0.73 0.82 0.71 (14.2)Ratio Ru/Rmax 1.23 1.05 1.09 1.12 (7.0) 1.10 1.47 1.68 1.42 (17.2)

Failure mode Diagonal tension, DT Mixed DT-DC

1 = MCN50m, 2 = MCL50m, 3 = MVN50m, 4 = MCN100, 5 = MCL100, 6 = MVN100.

J. Carrillo, S.M. Alcocer / Engineering Structures 41 (2012) 98–107 103

a diagonal tension failure, DT. Failure of the three specimens wasobserved during CA-77 earthquake record at 100% of PGA (CA-77-100). Failure mode was governed by web inclined cracking atapproximately 45� angle, plastic yielding of most of web shearreinforcement, and subsequent fracture of wires. Failure was brit-tle because of the limited elongation capacity of the wire mesh it-self (Table 5). Final crack patterns of walls are shown in Fig. 5.

In contrast, walls reinforced using deformed bars and with theminimum web steel ratio exhibited a mixed failure mode, wherediagonal tension and diagonal compression, DT-DC, were observed(i.e. yielding of most web steel reinforcement and noticeable webcrushing of concrete). Failure of the three specimens was observedduring CA-83 earthquake record at 75% of PGA (CA-83-75). Finalcrack patterns of walls are shown in Fig. 6.

3.2. Frequencies of vibration and damping factors

The period of vibration of a RC structural system is a crucialparameter for earthquake-resistant design. Model frequencies (in-verse of the period) and damping factors were estimated from theratios of spectral amplitude of acceleration recorded at the top ofspecimens to that recorded at the base (shaking table), particularlyin the vicinity of the peak at the fundamental frequency of vibra-tion of the specimen. Ratios of spectral amplitudes for walls thatexhibited DT and DT-DC failure modes are shown in Figs. 7 and8, respectively. For comparison purposes, spectral amplitudes werenormalized by the peak spectral amplitude (A/Amax). At the initial

testing stage, acceleration records were measured during whitenoise excitation. To identify the frequency and damping factorfrom curves in Figs. 7 and 8, the procedure proposed by Rinawiand Clough [11] was followed. In this approach, the theoreticaltransfer function of a single degree of freedom system is fitted tothe experimental shape of a similar transfer function; the identifi-cation of the equivalent damping factor is then based on the ampli-tude of the function for the vibration mode under consideration.

The change of fundamental frequency and effective dampingfactors with drift ratio is shown in Fig. 9. The effective dampingfactor was calculated by subtracting the value of damping gener-ated in the LMGS of the mass-carrying load system, from the equiv-alent viscous damping involved in the measured response of thespecimen. Carrillo and Alcocer [9] have demonstrated that theLMGS of the mass-carrying load system did not add any significantamount of damping into the specimen response. For instance, thehighest value of the damping added by LMGS was equal to 0.20%,which was equivalent to 2% of the damping developed in the spec-imens’ response. Drift ratio, R, was obtained by dividing the rela-tive displacement measured at mid-thickness of the top slab bythe height at which such displacement was measured. Drift ratiocorresponded to the average of the peak drift ratio for the twodirections of in-plane displacement measured during each earth-quake record. Although scatter of damping factors was higher thanthat associated to frequency of vibration, the fitted curves show asuitable agreement with test data as can be concluded from thecorrelation coefficient, r.

(a) MCN50mD (b) MCL50mD (c) MVN50mD

Fig. 5. Final cracks patterns of walls that failed in DT.

(a) MCN100D (b) MCL100D (c) MVN100D

Fig. 6. Final cracks patterns of walls that failed in DT-DC.

0.0

0.4

0.8

1.2

Frequency (Hz)

A /

A m

ax

Initial

CA-71-50

CA-71-100

CA-77-75

CA-77-100

CA-83-75

(a)

0.0

0.4

0.8

1.2

Frequency (Hz)

A /

A m

ax

(b)

0.0

0.4

0.8

1.2

1 3 5 7 9 11 1 3 5 7 9 11 1 3 5 7 9 11

Frequency (Hz)

A /

A m

ax

(c)Fig. 7. Ratios of spectral amplitudes of acceleration for walls that failed in DT: (a) MCN50m, (b) MCL50m, (c) MVN50m.

0.0

0.4

0.8

1.2

Frequency (Hz)

A /

A m

ax

Initial

CA-71-50

CA-71-100

CA-77-75

CA-77-100

(a)

0.0

0.4

0.8

1.2

Frequency (Hz)

A /

A m

ax

(b)

0.0

0.4

0.8

1.2

1 3 5 7 9 11 1 3 5 7 9 11 1 3 5 7 9 11

Frequency (Hz)

A /

A m

ax

(c)Fig. 8. Ratios of spectral amplitudes of acceleration for walls that failed in DT-DC: (a) MCN100, (b) MCL100, (c) MVN100.

104 J. Carrillo, S.M. Alcocer / Engineering Structures 41 (2012) 98–107

It is significant to note in Fig. 9a that mean value of measuredfrequencies was 7.5 Hz (i.e. 0.13 s), which was 25% lower thanthe target frequency of 10 Hz (0.10 s). Early-age shrinkage crackingwas the main reason attributed to this fact. As expected, a key

characteristic of test specimens was the change in measured fre-quency with the reduction in stiffness caused by the seismic exci-tations. Small amounts of damage significantly reduced thefundamental frequency of each specimen, as may be observed in

f / finitial = -0.12Ln(x) + 0.47

1

3

5

7

9

11

Drift ratio, R (%)

f (H

z)

0.1

0.4

0.7

1.0

1.3

f / f

initi

al

Target (initial)

Achieved (initial) = finitial

r = 0.97

(a)

Damping factor (%) = 8.58 R0.08

1

3

5

7

9

11

0.0 0.4 0.8 1.2 1.6 0.0 0.4 0.8 1.2 1.6

Drift ratio, R (%)

Dam

ping

fac

tor

(%)

DT failure

DT-DC failure

r = 0.81

(b)Fig. 9. Frequencies of vibration and damping factors.

-1.8

-1.2

-0.6

0.0

0.6

1.2

1.8

Drift ratio, R (%)

Shea

r st

ress

(MP

a)

-287

-191

-96

0

96

191

287CA-71-50

CA-71-100

CA-77-75

CA-77-100

MCN50m-1.8

-1.2

-0.6

0.0

0.6

1.2

1.8

Drift ratio, R (%)

-282

-188

-94

0

94

188

282

MCL50m-1.8

-1.2

-0.6

0.0

0.6

1.2

1.8

-0.9 -0.6 -0.3 0.0 0.3 0.6 0.9 -0.9 -0.6 -0.3 0.0 0.3 0.6 0.9 -0.9 -0.6 -0.3 0.0 0.3 0.6 0.9

Drift ratio, R (%)

-230

-154

-77

0

77

154

230

F la

tera

l (k

N)

MVN50m

Fig. 10. Hysteresis curves of walls that failed in DT.

-1.8

-1.2

-0.6

0.0

0.6

1.2

1.8

-1.8 -1.2 -0.6 0.0 0.6 1.2 1.8 -1.8 -1.2 -0.6 0.0 0.6 1.2 1.8

Drift ratio, R (%)

Shea

r st

ress

(MP

a)

-290

-194

-97

0

97

194

290CA-71-50

CA-71-100

CA-77-75

CA-77-100

CA-83-75

MCN100-1.8

-1.2

-0.6

0.0

0.6

1.2

1.8

Drift ratio, R (%)

-281

-187

-94

0

94

187

281

MCL100-1.8

-1.2

-0.6

0.0

0.6

1.2

1.8

Drift ratio, R (%)

-232

-155

-77

0

77

155

232

F lat

eral

(kN

)

MVN100

-1.8 -1.2 -0.6 0.0 0.6 1.2 1.8

Fig. 11. Hysteresis curves of walls that failed in DT-DC.

J. Carrillo, S.M. Alcocer / Engineering Structures 41 (2012) 98–107 105

Fig. 9a. For instance, frequency of vibration associated to the meandrift ratio at peak shear strength of specimens (Rmax � 0.5%, Table8) was equivalent to 55% of the initial frequency of vibration.

As it may be observed in Fig. 9b, the damping factor slightlyaugmented with drift ratio; for example, damping factors associ-ated to the initial loading stage were roughly equal to 6%, but in-creased to 9% at failure. Damping factors measured at the initialstage were related to very small amplitudes applied during whitenoise excitation. It should be also noted that damping of an RCbuilding would be dependent on the damping of the structural sys-tem and of nonstructural elements (if they are present), as well ason friction between different elements [12]. Considering thatdamping factors associated to the ‘‘undamaged’’ stage were closeto 6%, the 5% damping factor commonly used for code-based de-sign is consistent with that measured.

After concrete cracking, measured damping was primarily cred-ited to yielding (of deformed bars) or plasticity (of welded-wiremesh) of steel reinforcement, as well as to the energy dissipatedby friction between crack surfaces and by crushing of concrete.As it is shown in Fig. 9b, for drift ratios lower than 0.8%, damping

factors of walls with DT failure were roughly 8% higher than thoseof walls with a mixed DT-DC failure mode. The observed variationsin the damping factors are related essentially with the effect oflow-cycle fatigue on the strength mechanisms, in turn associatedto different failure modes. For instance, when the failure modewas governed by concrete crushing (i.e. DT-DC failures), pinchingof hysteresis loops became more significant and thus, damping fac-tors were smaller than those of walls failing by diagonal tension.

3.3. Hysteresis curves

The overall performance of walls was assessed through hyster-esis curves expressed in terms of shear stress, lateral force (Flateral),and drift ratio, R. Lateral force was obtained using the equationsproposed by Carrillo and Alcocer [9], which are applicable whenthe mass-carrying load system is that shown in Fig. 4. In the com-puting procedure, the lateral force is calculated from the forcemeasured in the load cell and from the additional inertial forcegenerated by the mass located between the load cell and the spec-imen (Fig. 4). Shear stress was computed as the ratio of measured

106 J. Carrillo, S.M. Alcocer / Engineering Structures 41 (2012) 98–107

shear force to gross area of wall concrete; as-built wall thicknessand effective wall length were used (Table 1). The hysteresis curvesof walls that exhibited DT and DT-DC failure modes are shown inFigs. 10 and 11, respectively. The hysteresis loops were typical oflow-rise concrete walls controlled by shear deformations.

As it is shown in Figs. 10 and 11, significant differences may beobserved between the hysteresis curves of walls reinforced withwelded-wire meshes (DT failure) and with deformed bars (DT-DCfailures). For solid walls and web shear reinforcement made ofwelded-wire mesh, the inelastic portion of the hysteresis curvewas almost nonexistent because of the limited elongation capacityof the cold-drawn reinforcement used (see Table 4). For thesewalls, ultimate displacement capacity was nearly equal to that atpeak shear strength. Although pinching of hysteresis loops was evi-dent, loops were nearly stable and symmetric during all testingstages. In contrast, for solid walls and web shear reinforcementmade of deformed bars, hysteresis curves evidenced a more ductileresponse. Strength degradation began as soon as the peak shearwas reached; indeed, peak shear significantly dropped at drift de-mands larger than 0.5%.

Comparable trends were observed in walls having door andwindow openings. However, because of the arrangement of thetwo wall segments generated by openings, hysteresis loops werenot symmetrical. Unlike solid walls reinforced using welded-wiremeshes, walls with openings and welded-wire meshes exhibiteda well-defined unloading branch. This phenomenon is explainedby the different times in which the sudden fracture of the wirestook place in the two wall segments. For the wall specimen withopenings and web shear reinforcement made of deformed bars,strength degradation rate was lower than that observed in solidwalls. Interaction of shear and flexural deformations observed dur-ing testing of walls with openings (section 0) supported this find-ing. As it is commonly observed during testing of components

0%

25%

50%

75%

100%

Earthquake record

Con

trib

utio

n

0.11 0.25 0.44 0.54Drift ratio, %

(a)

0%

25%

50%

75%

100%

Earthquak

0.11 0.31Drift ra

(b

71-50 71-100 77-75 77-100 71-50 71-100

Fig. 12. Contribution of various deformation modes to drift ratio of w

0%

25%

50%

75%

100%

71-50 71-100 77-75 77-100 83-75

Earthquake record

Con

trib

utio

n

0.10 0.23 0.38 0.59 1.51

Drift ratio, %

(a)

0%

25%

50%

75%

100%

Earthquake

0.09 0.23 0.39Drift rat

(b

71-50 71-100 77-7

Fig. 13. Contribution of various deformation modes to drift ratio of w

subjected to earthquake loads, strength degradation of a compo-nent with flexural dominated behavior is lower than that observedin a component with a shear dominated response.

Most important parameters measured during tests are summa-rized in Table 8. Values presented correspond to the average of val-ues measured in the two directions of testing (i.e. ‘‘push’’ and‘‘pull’’ directions). Seismic shear coefficient was calculated as theratio of peak shear force to the dynamic weight (Vmax/Wd). In thisstudy, ultimate displacement capacity limit state was definedeither when a 20% drop of the peak shear strength was observed,or when web shear reinforcement fractured. As it was noted ear-lier, the 20%-reduction criterion was applied to the specimens rein-forced with deformed bars, whereas the second criterion wasapplicable for solid walls reinforced with welded-wire meshes.

As it is shown in Table 8, ultimate displacement capacity wassmaller in walls reinforced with welded-wire meshes. For instance,the mean value of the Ru/Rmax ratio was equal to 1.12, that is, ulti-mate displacement capacity was very close to the displacementcapacity at peak shear strength. In contrast, for walls with de-formed bars, mean Ru/Rmax ratio was equal to 1.42. As it was indi-cated before, welded-wire meshes exhibit a very limitedelongation capacity. Therefore, it would be safe to design suchwalls so that strains in reinforcement stay well below the plasticitythreshold.

One of the objectives stated for this investigation was to assessthe effect of the amount of web shear reinforcement on wall shearstrength capacity. As may be noted in Table 8, mean values of peakshear stress and of seismic shear coefficient of walls reinforcedwith the minimum code-prescribed wall reinforcement was just13% higher than those of walls reinforced with 50% of theminimum amount. This finding support the use of a web steel ratiolower than the minimum prescribed in design codes, when appliedto walls with characteristics similar to those of walls tested.

e record

0.47 0.65

tio, %

)

0%

25%

50%

75%

100%

77-75 77-100 71-50 71-100 77-75 77-100

Earthquake record

0.08 0.19 0.38 0.72Drift ratio, %

(c)

Flexural

Sliding

Shear

alls that failed in DT: (a) MCN50m, (b) MCL50m, (c) MVN50m.

record

0.52 1.46

io, %

)

0%

25%

50%

75%

100%

5 77-100 83-75 71-50 71-100 77-75 77-100 83-75

Earthquake record

0.09 0.24 0.40 0.84 1.40Drift ratio, %

(c)

Flexural

Sliding

Shear

alls that failed in DT-DC: (a) MCN100, (b) MCL100, (c) MVN100.

J. Carrillo, S.M. Alcocer / Engineering Structures 41 (2012) 98–107 107

Additionally, hysteresis curves and measured parameters revealedthat performance of walls with normalweight and lightweight con-crete was readily comparable. This finding is only applicable forconcretes with the characteristics shown in Table 4.

3.4. Deformation analysis

An attempt was made to determine the effect of each mode ofdeformation on the total displacement of wall specimens. Webshear deformations, flexural deformations and horizontal slidingat the base were obtained from measurements of external trans-ducers. The total error in the estimation of each mode of contribu-tion (discrepancy between measured and calculated totaldisplacement) was evaluated. This error never exceeded 10% andwas distributed proportionally among the three deformation com-ponents. The contribution of deformation modes to total drift ratioof walls that exhibited DT and a mixed DT-DC failure mode, areshown in Figs. 12 and 13, respectively. For walls with openings,contribution was computed from the individual contributions ofthe two wall segments generated by the door and windowopenings.

It is clear from Figs. 12 and 13 that behavior of specimens wasalways controlled by web shear deformations. It is also evidentthat the relative contribution of each mode varied with drift ratio,particularly for walls that exhibited a DT-DC failure mode. As itwas expected, because of the aspect ratio of walls, specimens withopenings exhibited a higher contribution of flexural deformations,see Figs. 12c and 13c. This is particularly the case of the wall seg-ment located at the left side of the door opening, see Fig. 1c.

During the first earthquake record, contribution of flexuraldeformations played an important role in the response, reachinga contribution of 36% of total displacement. At higher drift de-mands, such contribution decreased to 16%. As it was mentioned,the contribution of wall sliding was also considered. Such contribu-tion accounted for about 11% during the first record, but decreasedto roughly 4% near failure. In contrast, web shear deformations sig-nificantly increased with drift ratio; in effect, contribution of sheardeformations varied between 53% during the first earthquake re-cord and 80% close to failure. When the peak shear strength wasattained, the mean values of web shear, flexural and sliding defor-mations were equal to 71%, 23% and 6%, respectively.

4. Conclusions

Form the analysis of results of an experimental study on RCwalls for low-rise housing subjected to shaking table excitations,the following conclusions can be drawn:

– Early-age shrinkage of walls caused means value of measuredfrequencies to be 25% lower than the design value.

– Frequency of vibration at peak shear strength of specimens wasequivalent to 55%, on the average, of the initial frequency ofvibration.

– It was corroborated that the 5% damping factor commonly usedfor code-based design was consistent with values measured inthis testing program.

– Measured response revealed that performance of walls withnormalweight and lightweight concrete was comparable.

– The type of web reinforcement (welded-wire meshes anddeformed bars) significantly affected the displacement capacityof specimens.

– Failure mode of walls with web shear reinforcement made ofwelded-wire mesh was brittle because of the limited elongationcapacity of the wire mesh itself. Then, for design purposes ofwalls with this type of web shear reinforcement, ultimate driftcapacity should be considered equal to drift capacity at peakshear strength. It is recommended that such walls be designedso that strains in the welded-wire mesh are within the elasticrange of behavior.

– Because of concrete design strengths (between 15 and 20 MPa)and nominal plasticity stress of reinforcement, walls may bereinforced with 50% of the minimum code prescribed wall steelreinforcement ratio. When welded-wire meshes are used, shearstrength capacity was comparable to that of walls reinforcedwith 100% of the minimum amount. Hence, walls with 50% ofthe minimum reinforcement ratio and welded-wire meshesmay be in concrete housing located in low hazard seismiczones. For this case, the prescribed allowable story drift ratiosshould be smaller than 0.4%.

Acknowledgments

The authors gratefully acknowledge the financial support fromGrupo CEMEX and the extensive assistance in the experimentaltesting from staff and students of the Shaking Table Laboratoryof the Instituto de Ingeniería at UNAM.

References

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[2] Flores L, Alcocer S, Carrillo J, Sánchez A, Uribe R, Ponce A. Tests of concretewalls with various aspect ratios and small steel ratios, to be used for housing.In: Proceeding of XVI national conference on earthquake engineering,Guerrero, Mexico; 2007. Paper 11-02 [in Spanish].

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[4] Derecho A, Iqbal M, Dintel M, Corley W. Loading history for use in quasi-staticsimulated earthquake loading tests. In: Reinforced concrete structuressubjected to wind and earthquake forces. Publication SP-63, AmericanConcrete Institute, Detroit; 1980. p. 329–57.

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[7] Ordaz M, Arboleda J, Singh S. A scheme of random summation of an empiricalGreen’s function to estimate ground motions from future larger earthquakes.Bull Seismol Soc Am 1995;85(6):1635–47.

[8] Arias A. A measure of earthquake intensity. In: Hansen RJ, editor. Seismicdesign for nuclear power plants. MIT Pres; 1970. p. 438–83.

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[10] Carrillo J. Evaluation of shear behavior of concrete walls for housing usingdynamic testing. PhD thesis. National University of Mexico, UNAM, Mexico;2010 [in Spanish].

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[12] Aristizabal-Ochoa J. Cracking and shear effects on structural walls. J Struct Eng,ASCE 1983;109(5):1267–77.