aritulo seismic perfomance of concrete walls

8/13/2019 Aritulo Seismic Perfomance of Concrete Walls

1/10

Seismic performance of concrete walls for housing subjected to shaking

table excitations

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

a Departamento de Ingeniera Civil, Universidad Militar Nueva Granada, UMNG, Cra. 11, No. 101-80, Bogot, Colombiab Instituto de Ingeniera, Universidad Nacional Autnoma de Mxico, UNAM, Ciudad Universitaria, Coyoacn 04510, DF, Mexico

a r t i c l e i n f o

Article history:Received 29 August 2011

Revised 5 February 2012

Accepted 9 March 2012

Available online 25 April 2012

Keywords:

Concrete walls

Shear behavior

Low-rise housing

Shaking table tests

Lightweight concrete

Welded-wire mesh

a b s t r a c t

Aimed at better understanding the seismic behavior of reinforced concrete (RC) walls, typically used in

one-to-two stories housing in several Latin American countries, a large investigation project has beencar-

ried out. Previous experimental programs considered the behavior of walls subjected to monotonically

and cyclically increased loads. This paper compares and discusses displacement and shear strength

capacities, 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 dynamic

characteristics, such as changes in fundamental frequencies and damping factors of RC walls for low-rise

housing.

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 small

demands of lateral displacements and seismic forces. This phe-

nomenon has prompted housing designers and contractors to use

concrete compressive strengths of 1520 MPa, as well as 100-

mm thick walls. Also, in zones where seismic demands are low,

such that design controlled by vertical actions, the minimum

web 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 steel

reinforcement ratios smaller than the minimum ratio prescribed

by ACI-318 building code and web shear reinforcement made of

welded-wire meshes are frequently used. All these features are a

direct consequence of attaining speed of construction and econ-

omy in a very competitive housing market. However, the effect

and 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

with 50% of the minimum code-prescribed web shear reinforce-

ment[2,3], exhibited comparable shear strength capacity to that

of walls reinforced with 100% of the minimum steel reinforcement

ratio. Nevertheless, walls with 50% of the minimum code pre-

scribed web shear reinforcement and reinforced with welded-wire

mesh exhibited limited displacement capacity as compared to

walls reinforced with 100% of the minimum amount.

When correlating earthquake demand to structural capacity, it

is essential that capacity be evaluated under conditions closely

approximating 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 effects

of earthquakes on buildings, structures or components. Thus, this

study aims at evaluating the effect of wall geometry, type of con-

crete, web steel reinforcement ratio and type of web reinforcement

on the shear strength, displacement capacity, and dynamic charac-

teristics of RC walls for low-rise housing subjected to shaking table

excitations. Most representative wall models tested in previous

phases were selected for studying the structural behavior under

actual seismic actions. Dynamic tests included four solid walls

with height-to-length ratio equal to 1.0, as well as two walls with

door and window openings. Wall properties were those obtained

from current design and construction practice found in typical

low-rise housing in several Latin American countries. Walls were

designed to fail in shear to better understand the strength mecha-

nism that take place during shear failures observed in RC walls for

low-rise housing.

0141-0296/$ - see front matter 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engstruct.2012.03.025

Corresponding author at: Departamento de Ingeniera Civil, Universidad Militar

Nueva Granada, UMNG, Cra. 11, No. 101-80, Bogot, Colombia. Tel.: +57 1

6500000x1268; fax: +57 1 6370557.

E-mail address: [email protected](J. Carrillo).

Engineering Structures 41 (2012) 98107

Contents lists available at SciVerse ScienceDirect

Engineering Structures

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e n g s t r u c t


2/10

Wall models were subjected to a series of earthquake records

associated to three limit states. The initial period of vibration of

the isolated walls was established to agree with the fundamental

period of vibration of a prototype house. For estimating the period,

mathematical models were developed and calibrated through

ambient vibration testing. The test set-up was purposely designed

to carry the additional inertial mass outside the shaking table. Wall

performance, hysteresis curves as well as changes in fundamental

frequencies and damping will be compared and discussed.

2. Experimental program

The three-dimensional prototype was a two-story house built

with RC walls in the two principal directions.In this type of housing

construction, 100-mmthick solid slabs or slabs made of precast ele-

ments are frequently used. In the case of solid slabs, these are cast

monolithically with walls. Wall thickness and clear height are com-

monly 100 and 2400 mm, respectively, and house floor plan area

varies between 35 and 65 m2. Foundations are strip footings made

of RC 400-mm square beams that support a 100-mm thick floor

slab. Variables studied in the experimental program were wall

geometry (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 webreinforcement

(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 presented

inTable 1. Web reinforcement ratios in Table 1 were calculated

from 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 shaking

table testing. The size of models was almost equal to that of walls

in the prototype. The simple law of similitude was then chosen for

scaling specimens, as well as for calculating the prototype response

from 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 dimensions

of the models are altered[5]. Main scale factors for simple law of

similitude are shown inTable 2.

2.1. Geometry and reinforcement

Nominal geometry and reinforcement layout of specimens are

shown inFig. 1. As-built wall dimensions and reinforcement char-

acteristics are presented inTables 1 and 3, respectively. Web rein-

forcement ratios in Table 3 were calculated from as-built

dimensions. In order to prevent cracking during transportation of

the specimens in the lab, specimens were built on a RC stiff gradebeam. Foundation beam was also used to bolt the specimens to the

platform of the shaking table. Top slab was cast monolithically

with walls and was used to connect the mass-carrying load system

for testing (Fig. 4).

According to the scaling factors (i.e. 0.8), height and thickness of

walls 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. For

walls with openings, areas of door and window were equivalent

to 32% of the specimen area (length of specimen multiplied by

its 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 a

length to height ratio of 1.0 or larger. The behavior of these squat

walls is governed by shear deformations and hence the area of lon-

gitudinal reinforcement at boundary elements is almost always

controlled by minimum requirements. During testing, free top wall

rotation was allowed (section 0), thus exhibiting a maximum

bending moment at the base. To prevent a flexural failure prior

to achieving shear strength, the longitudinal reinforcement at the

boundary elements was purposely designed and detailed. If the

amount of longitudinal boundary reinforcement would have been

similar to that used in prototype walls, a flexural failure would

have been observed. Evidently, longitudinal reinforcement within

boundary 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 of

longitudinal reinforcement was small compared to other resisting

mechanisms 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 longitudinal

reinforcement was calculated so that the ratio between shear force

associated to flexural yielding and that associated to shear failure

of wall section was equal to 1.6 and was roughly constant for all

specimens.

Wall reinforcement was made of a single layer placed at wall

mid-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

Table 1

Main characteristics and as-built dimensions of specimens.

No. Wall Type of concrete Geometry tw (mm) lw (mm) hw (mm) Door (mm mm) Window (mm mm) Web reinforc.

qh,v (%) Type

1 MCN50m Normal Solid 83 1916 1923 0.11 D

2 MCN100 Normal Solid 84 1921 1924 0.28 W

3 MCL50m Light Solid 82 1917 1917 0.11 D

4 MCL100 Light Solid 82 1912 1918 0.28 W

5 MVN50m Normal Openings 83 3042 1924 1681 720 965 689 0.11 D

6 MVN100 Normal Openings 84 3042 1926 1681 721 959 689 0.28 W

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

Table 2

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

Quantity Equation Scale factor

Length (L) SL= LP/LM SL= 1.25

Stress (r) Sr=fP/fM 1Force (F) SF S

2L Sf S

2L 1:56

Time (t) and period (T) St= SL(ScSe/Sf)1/2 SL= 1.25

Displacement (d) Sd= SLSe SL= 1.25

Acceleration (a) Sa= Sf/SLSt 1/SL= 0.80Mass (m) Sm ScS

3L S

3L 1:95

J. Carrillo, S.M. Alcocer / Engineering Structures 41 (2012) 98107 99


3/10

320 mm. The amount of web reinforcement corresponded approx-

imately to the minimum web steel ratio prescribed by ACI-318

building code [1]. Specimens MCN50m, MCL50m and MVN50m

were reinforced in the web using a single mesh (66-8/8) of No.

8 wires (4.1 mm diameter) spaced at 150 mm (6 in.). The web

steel 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 the

minimum prescribed by the code. A lower steel ratio is supported

by the fact that lower concrete compressive strengths and higher

yield 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 concrete

was 10 mm. Design concrete compressive strength was 15 MPa,

and nominal yield strength of bars and wire reinforcement were

412 MPa (mild steel) and 491 MPa (cold-drawn wire reinforce-

ment), respectively. Mean value and coefficient of variation of

the measured mechanical properties of concrete and reinforce-

ment are presented inTables 4 and 5, respectively. For concrete,

properties were obtained from cylinder tests at the time of shaking

table testing. Because of the small size of the coarse aggregate and

the measured slump, internal consolidation of fresh concrete was

not needed. Form vibration was applied through a rubber hammer

only.

During tensile tests of coupon specimens, differences in the

stressstrain behavior of deformed bars and welded-wiremeshes were readily apparent. Yielding was clearly defined for

(a)

lw = 1920

2400

hw=1920

8No.5

SNo.2@1

80

No.3@3

20

No. 3 @ 320

lw = 1920

tw = 80

600

200

2400600

400

(b)

6No.5

SNo.2@1

80

mesh

6x6-6/6

No. 3 @ 250

hw=1920

All dimensions in mm

1 No. 3

1 No. 31 No. 3

4No.4

SNo.2@1

80

4No.4

SNo.2@1

80

4No.4

SNo.2@1

80

3500

96688896720640

1680

No. 3 @ 320

No.3@3

20

(c)

mesh

6x6-8/8

1 No. 3

1 No. 31 No. 3

4No.4

SNo.2@1

80

4No.4

SNo.2@1

80

4No.4

SNo.2@1

80

3500

lw = 3040

960

hw=1920

2

No.3

2No.3

1No.3

(d)

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

Table 3

Reinforcement characteristics of specimens.

Wall Web reinforcement Boundary elements

Longitudinal Stirrups (S)

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

MCN50m Mesh 66-8/8a 0.11 6 No. 5 0.81

MCN100 No. 3 @ 320 m m 0.26 8 No. 5 1.08

MCL50m Mesh 6 6-8/8 0.11 6 No. 5 0.81 No. 2 @ 0.43

MCL100 No. 3 @ 320 m m 0.27 8 No. 5 1.08 180 m m

MVN50m Mesh 6 6-8/8 0.11 4 No. 4 0.91

MVN100 No. 3 @ 320 m m 0.26 4 No. 4 0.91

a First two digits (i.e. 6 6) indicate the horizontal and vertical spacing of wires

in 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) 98107


4/10

reinforcement made of mild-steel where an increment of tensile

strength is not observed until a well-defined yielding platform is

developed. In contrast, cold-drawn wire reinforcement used in thisstudy did not exhibit a specific yield point. Furthermore, in this

type of reinforcement, the loading branch between onset of plastic-

ity and maximum deformation capacity (at fracture) was much

shorter than that of mild-steel reinforcement (see the elongation

parameter inTable 5). The behavior of this type of material was

characterized by fracture of material with a slight increment of

strain. As a result, and as it will be shown below, the elongation

capacity of wires was a key parameter for displacement capacity

of walls reinforced in the web using this type of reinforcement. It

is 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 testing

program 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 be

indicated.

2.3. Loading histories

To assess wall performance under earthquake records, models

were subjected to real and numerically simulated acceleration re-

cords. Records were associated to different limit states (from onset

of cracking to collapse), and therefore, three earthquake hazard

levels were selected. The earthquake recorded in Caleta de Campos

station, Mexico, in January 11, 1997 (MW= 7.1, CA-71) was used for

the seismic demand representing the diagonal cracking limit state.

Such record was measured in the epicentral region nearby

Acapulco. In this study, the diagonal cracking limit state is reached

when the initial inclined web cracking was observed. Owing to the

potential 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 prototype

house are relatively low. Therefore, the PGA of the earthquake re-

cord representing the diagonal cracking limit state is higher than

that used for medium- and high-rise structures with larger vibra-

tion periods. The CA-71 record was considered as a Green function

to simulate larger-magnitude events, i.e. with larger instrumental

intensity and duration[7]. Two earthquakes with magnitudes MW7.7 (CA-77) and 8.3 (CA-83) were numerically simulated for the

strength and ultimate limit states, respectively. Main earthquake

characteristics and time history accelerations for the prototype

house are presented in Table 6 and Fig. 2, respectively. Pseudo-

acceleration, displacement and velocity response spectra for 5%

damping are shown inFig. 3.

According to the simple law of similitude, acceleration and time

scale 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 the

value of peak acceleration as the reference factor until the final

damage stage was attained. Walls were tested in the in-plane

direction only. Target PGA and the sequence of input motion used

in the tests are described in Table 7. To evaluate the level of friction

of the mass-carrying load system, tests started with sine-curve

(SN) and ramp signals (RP) (see Fig. 4). At the beginning and at

the 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 of

models. Mean value of peak accelerations measured in the table

Table 4

Measured mechanical properties of concrete.

Mechanical property Normal Light

Slump (mm) 210 145

Compressive strength,fc(MPa) 24.8 (5.3) 21.0 (6.8)

Strain at compressive strength,e0 0.0031 (15.3) 0.0030 (9.5)Poissons 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 5

Measured mechanical properties of steel reinforcement.

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

Type D D D D W

Diameter (nominal),

mm

15.9 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 ultimate

strength,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 6

Characteristics of earthquake records for the prototype house.

Record Magnitude,

MW

PGA

(g)

PGD

(mm)

IA(m/s)

Total

duration

(s)

Intense phase

duration, IPD (s)

CA-71 7.1 0.38 7.8 2.02 29.5 13.4

CA-77 7.7 0.72 16.6 8.81 36.1 16.3

CA-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% ofIA.

-1.4

-0.7

0.0

0.7

1.4

0 20 40 60 80 100

t (s)

acceleration(

g)

(a)0 20 40 60 80 100

t (s)

(b)0 20 40 60 80 100

t (s)

(c)

Fig. 2. Time history accelerations for prototype house: (a) CA-71, (b) CA-77, (c) CA-83.



5/10

platform during testing models are included in Table 7. The accel-

eration scale factor (Sa= 0.80, Table 2) was applied to the records to

compare with target values for prototype house.

2.4. Design for dynamic similitude

For adequately extrapolating specimens response to a proto-

types response, isolated wall models were designed considering

the fundamental period of vibration of the prototype house. For

establishing such dynamic characteristic, mathematical models

were developed and calibrated through ambient vibration testing.

Hence, the fundamental period of vibration of the two-story house

was estimated to be equal to 0.12 s[10]. Taking into account the

scale 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 that

walls would behave as a single degree of freedom system. The dy-namic weight,Wd(mass gravity acceleration), needed to achieve

the desired design period, Te, was computed as KeT2e=4p

2g; where

Ke is the in-plane stiffness of the wall that was calculated from

measured mechanical properties of materials. To account for

early-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 for

high-rise walls whose behavior is controlled by flexural deforma-

tions. The dynamic weight used for achieving the desired design

periods for each specimen are presented inTable 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 it

was indicated, for adequate dynamic simulation, it is necessary

to add some mass (dynamic weight) to the specimens. If such dy-

namic weight were to rest at the top of models, the risk of lateral

instability would have been a major concern. Therefore, an alterna-

tive method for supporting the mass and transmitting the inertia

forces was required. An external device with a mass-carrying load

system was designed and installed outside the shaking table. The

device 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 linear

motion guide system (LMGS) with very low friction (Fig. 4).

An axial compressive stress of 0.25 MPa was uniformly applied

to the walls and was kept constant during testing. This value cor-

responds to 2% of the nominal concrete compressive strength. To

determine the average axial stress at service loads in first story

walls of the housing prototype, finite element models of two-story

houses were carried out[10]. The axial load was exerted through

the weight of the load and connection beams, and lead ingots

bolted to the load beam. Although lead ingots resulted in a triangu-

lar load distribution, the addition of the weight of the connection

beam provided for a uniform distribution of the axial load on the

walls.To measure the specimens response, walls were instrumented

internally and externally. Internal instrumentation was designed

to acquire data on the local response of steel reinforcement

through strain-gages at selected locations, specifically aimed at

evaluating strength contribution of steel reinforcement. External

instrumentation was planned for measuring the global response

through displacement, acceleration and load transducers. The load

cell 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 with

Light Emitting Diodes (LEDs) was used. In the tests, 41 strain-gages

and 36 external transducers were used for solid walls, as well as 59

and 64, respectively, for wall with openings.

3. Test results and discussion

Wall response was assessed through crack patterns and failure

modes, 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 of

wall specimens.

3.1. Crack patterns and failure modes

Prior to testing, walls exhibited early-age shrinkage cracking so

that it can be argued that their initial stiffness was affected. Walls

reinforced in the web using welded-wire mesh and with 50% of theminimum code prescribed web steel reinforcement ratio exhibited

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(mm)

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 7

Testing stages for prototype house.

Stage Record PGA Total duration (s)

% g

Target Measured: Mean

(CV, %)

0 SN 30.0

1 RP 150.0

2 WN 0.01 0.01 (5.3) 120.0

3CA-71

50 0.19 0.12 (10.5) 29.5

4 100 0.38 0.28 (2.8)

5CA-77

75 0.54 0.45 (1.8) 36.1

6 100 0.72 0.60 (4.0)

7CA-83

75 0.98 0.77 (2.0) 99.8

8 100 1.30 a

9 WN 0.01 0.02 (10.8) 120.0

a Failure of models was observed at previous earthquake records.



6/10

a diagonal tension failure, DT. Failure of the three specimens was

observed during CA-77 earthquake record at 100% of PGA (CA-

77-100). Failure mode was governed by web inclined cracking at

approximately 45 angle, plastic yielding of most of web shear

reinforcement, 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 inFig. 5.

In contrast, walls reinforced using deformed bars and with the

minimum web steel ratio exhibited a mixed failure mode, where

diagonal tension and diagonal compression, DT-DC, were observed

(i.e. yielding of most web steel reinforcement and noticeable web

crushing of concrete). Failure of the three specimens was observedduring CA-83 earthquake record at 75% of PGA (CA-83-75). Final

crack 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 crucial

parameter for earthquake-resistant design. Model frequencies (in-

verse of the period) and damping factors were estimated from the

ratios of spectral amplitude of acceleration recorded at the top of

specimens to that recorded at the base (shaking table), particularly

in the vicinity of the peak at the fundamental frequency of vibra-

tion of the specimen. Ratios of spectral amplitudes for walls that

exhibited DT and DT-DC failure modes are shown in Figs. 7 and

8, respectively. For comparison purposes, spectral amplitudes werenormalized by the peak spectral amplitude (A/Amax). At the initial

testing stage, acceleration records were measured during white

noise excitation. To identify the frequency and damping factor

from curves in Figs. 7 and 8, the procedure proposed by Rinawi

and Clough [11] was followed. In this approach, the theoretical

transfer function of a single degree of freedom system is fitted to

the experimental shape of a similar transfer function; the identifi-

cationof 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 damping

factors with drift ratio is shown inFig. 9. The effective damping

factor was calculated by subtracting the value of damping gener-

ated in the LMGS of the mass-carryingload system, from the equiv-alent viscous damping involved in the measured response of the

specimen. Carrillo and Alcocer [9] have demonstrated that the

LMGS of the mass-carrying load system did not add any significant

amount of damping into the specimen response. For instance, the

highest 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 by

the height at which such displacement was measured. Drift ratio

corresponded to the average of the peak drift ratio for the two

directions of in-plane displacement measured during each earth-

quake record. Although scatter of damping factors was higher than

that associated to frequency of vibration, the fitted curves show a

suitable agreement with test data as can be concluded from thecorrelation coefficient, r.

LMGS

Shaking table

Pinnedconnection

Leadingots

Loadcell

Connection

beam

Supporting

frame

Verticalload

Storing

box

oadingbeam

Fig. 4. Test setup for walls with openings.

Table 8

Main 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)

RatioRu/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.



7/10


8/10

Fig. 9a. For instance, frequency of vibration associated to the mean

drift ratio at peak shear strength of specimens (Rmax 0.5%,Table

8) was equivalent to 55% of the initial frequency of vibration.

As it may be observed in Fig. 9b, the damping factor slightly

augmented 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 initial

stage were related to very small amplitudes applied during white

noise excitation. It should be also noted that damping of an RC

building would be dependent on the damping of the structural sys-

tem and of nonstructural elements (if they are present), as well as

on friction between different elements [12]. Considering that

damping factors associated to the undamaged stage were close

to 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-wire

mesh) of steel reinforcement, as well as to the energy dissipated

by friction between crack surfaces and by crushing of concrete.

As it is shown inFig. 9b, for drift ratios lower than 0.8%, damping

factors of walls with DT failure were roughly 8% higher than those

of walls with a mixed DT-DC failure mode. The observed variations

in the damping factors are related essentially with the effect of

low-cycle fatigue on the strength mechanisms, in turn associated

to different failure modes. For instance, when the failure modewas governed by concrete crushing (i.e. DT-DC failures), pinching

of 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 equations

proposed by Carrillo and Alcocer [9], which are applicable when

the mass-carrying load system is that shown inFig. 4. In the com-

puting procedure, the lateral force is calculated from the force

measured in the load cell and from the additional inertial force

generated by the mass located between the load cell and the spec-imen (Fig. 4). Shear stress was computed as the ratio of measured

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

1

3

5

7

9

11

Drift ratio, R (%)

f(Hz)

0.1

0.4

0.7

1.0

1.3

f/finitial

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 (%)

Dampingfactor(%)

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 (%)

Shearstres

s(MPa)

-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

Flateral(kN)

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 (%)

Shearstress

(MPa)

-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

Flateral(

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.



9/10

shear force to gross area of wall concrete; as-built wall thickness

and effective wall length were used (Table 1). The hysteresis curves

of walls that exhibited DT and DT-DC failure modes are shown in

Figs. 10 and 11, respectively. The hysteresis loops were typical of

low-rise concrete walls controlled by shear deformations.

As it is shown inFigs. 10 and 11, significant differences may be

observed between the hysteresis curves of walls reinforced with

welded-wire meshes (DT failure) and with deformed bars (DT-DC

failures). For solid walls and web shear reinforcement made of

welded-wire mesh, the inelastic portion of the hysteresis curve

was almost nonexistent because of the limited elongation capacity

of the cold-drawn reinforcement used (see Table 4). For these

walls, ultimate displacement capacity was nearly equal to that at

peak shear strength. Although pinching of hysteresis loops was evi-

dent, loops were nearly stable and symmetric during all testing

stages. In contrast, for solid walls and web shear reinforcement

made of deformed bars, hysteresis curves evidenced a more ductile

response. Strength degradation began as soon as the peak shear

was reached; indeed, peak shear significantly dropped at drift de-

mands larger than 0.5%.

Comparable trends were observed in walls having door and

window openings. However, because of the arrangement of the

two wall segments generated by openings, hysteresis loops were

not symmetrical. Unlike solid walls reinforced using welded-wire

meshes, walls with openings and welded-wire meshes exhibited

a well-defined unloading branch. This phenomenon is explained

by the different times in which the sudden fracture of the wires

took place in the two wall segments. For the wall specimen with

openings and web shear reinforcement made of deformed bars,

strength degradation rate was lower than that observed in solid

walls. 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

subjected to earthquake loads, strength degradation of a compo-

nent with flexural dominated behavior is lower than that observed

in 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 the

ratio of peak shear force to the dynamic weight (Vmax

/Wd

). In this

study, ultimate displacement capacity limit state was defined

either 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 was

applicable for solid walls reinforced with welded-wire meshes.

As it is shown in Table 8, ultimate displacement capacity was

smaller in walls reinforced with welded-wire meshes. For instance,

the mean value of theRu/Rmaxratio was equal to 1.12, that is, ulti-

mate displacement capacity was very close to the displacement

capacity at peak shear strength. In contrast, for walls with de-

formed bars, meanRu/Rmaxratio was equal to 1.42. As it was indi-

cated before, welded-wire meshes exhibit a very limited

elongation capacity. Therefore, it would be safe to design such

walls so that strains in reinforcement stay well below the plasticity

threshold.

One of the objectives stated for this investigation was to assess

the effect of the amount of web shear reinforcement on wall shear

strength capacity. As may be noted in Table 8, mean values of peak

shear stress and of seismic shear coefficient of walls reinforced

with the minimum code-prescribed wall reinforcement was just

13% higher than those of walls reinforced with 50% of the

minimum amount. This finding support the use of a web steel ratio

lower than the minimum prescribed in design codes, when applied

to walls with characteristics similar to those of walls tested.

0%

25%

50%

75%

100%

Earthquake record

Contribution

0.11 0.25 0 .44 0.54

Drift ratio, %

(a)

0%

25%

50%

75%

100%

Earthquake record

0.11 0.31 0.47 0.65

Drift ratio, %

(b)

0%

25%

50%

75%

100%

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

Earthquake record

0.08 0.19 0.38 0.72

Drift ratio, %

(c)

Flexural

Sliding

Shear

Fig. 12. Contribution of various deformation modes to drift ratio of walls that failed in DT: (a) MCN50m, (b) MCL50m, (c) MVN50m.

0%

25%

50%

75%

100%

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

Earthquake record

Contribution

0.10 0.23 0.38 0.59 1.51

Drift ratio, %

(a)

0%

25%

50%

75%

100%

Earthquake record

0.09 0.23 0.39 0.52 1.46

Drift ratio, %

(b)

0%

25%

50%

75%

100%

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

Earthquake record

0.09 0.24 0.40 0.84 1.40

Drift ratio, %

(c)

Flexural

Sliding

Shear

Fig. 13. Contribution of various deformation modes to drift ratio of walls that failed in DT-DC: (a) MCN100, (b) MCL100, (c) MVN100.



10/10

Additionally, hysteresis curves and measured parameters revealed

that performance of walls with normalweight and lightweight con-

crete was readily comparable. This finding is only applicable for

concretes with the characteristics shown in Table 4.

3.4. Deformation analysis

An attempt was made to determine the effect of each mode of

deformation on the total displacement of wall specimens. Web

shear deformations, flexural deformations and horizontal sliding

at 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 total

displacement) was evaluated. This error never exceeded 10% and

was distributed proportionally among the three deformation com-

ponents. The contribution of deformation modes to total drift ratio

of walls that exhibited DT and a mixed DT-DC failure mode, are

shown in Figs. 12 and 13, respectively. For walls with openings,

contribution was computed from the individual contributions of

the two wall segments generated by the door and window

openings.

It is clear fromFigs. 12 and 13that behavior of specimens was

always controlled by web shear deformations. It is also evident

that the relative contribution of each mode varied with drift ratio,

particularly for walls that exhibited a DT-DC failure mode. As it

was expected, because of the aspect ratio of walls, specimens with

openings exhibited a higher contribution of flexural deformations,

see Figs.12c and13c. This is particularly the case of the wall seg-

ment located at the left side of the door opening, seeFig. 1c.

During the first earthquake record, contribution of flexural

deformations played an important role in the response, reaching

a 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 decreased

to 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 was

attained, 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 RC

walls for low-rise housing subjected to shaking table excitations,

the following conclusions can be drawn:

Early-age shrinkage of walls caused means value of measured

frequencies 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 of

vibration.

It was corroborated that the 5% damping factor commonly used

for code-based design was consistent with values measured in

this testing program.

Measured response revealed that performance of walls with

normalweight and lightweight concrete was comparable.

The type of web reinforcement (welded-wire meshes and

deformed bars) significantly affected the displacement capacity

of specimens.

Failure mode of walls with web shear reinforcement made of

welded-wire mesh was brittle because of the limited elongation

capacity of the wire mesh itself. Then, for design purposes of

walls with this type of web shear reinforcement, ultimate drift

capacity should be considered equal to drift capacity at peak

shear strength. It is recommended that such walls be designed

so that strains in the welded-wire mesh are within the elastic

range of behavior.

Because of concrete design strengths (between 15 and 20 MPa)

and nominal plasticity stress of reinforcement, walls may be

reinforced with 50% of the minimum code prescribed wall steel

reinforcement ratio. When welded-wire meshes are used, shear

strength capacity was comparable to that of walls reinforced

with 100% of the minimum amount. Hence, walls with 50% of

the minimum reinforcement ratio and welded-wire meshes

may be in concrete housing located in low hazard seismic

zones. For this case, the prescribed allowable story drift ratios

should be smaller than 0.4%.

Acknowledgments

The authors gratefully acknowledge the financial support from

Grupo CEMEX and the extensive assistance in the experimental

testing from staff and students of the Shaking Table Laboratory

of the Instituto de Ingeniera at UNAM.

References

[1] ACI Committee 318. Building code requirements for structural concrete (ACI-

318) and commentary (ACI-318R). American Concrete Institute, Farmington

Hills, MI; 2008.

[2] Flores L, Alcocer S, Carrillo J, Snchez A, Uribe R, Ponce A. Tests of concrete

walls 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].

[3] Snchez A. Seismic behavior of housing with concrete walls. Technical report.

Institute of Engineering, National University of Mexico, UNAM; 2010 [in

Spanish].

[4] Derecho A, Iqbal M, Dintel M, Corley W. Loading history for use in quasi-static

simulated earthquake loading tests. In: Reinforced concrete structures

subjected to wind and earthquake forces. Publication SP-63, American

Concrete Institute, Detroit; 1980. p. 32957.

[5] Tomazevic M, Velechovsky T. Some aspects of testing small-scale masonry

building model on simple earthquake simulator. J Earthq Eng Struct Dynam

1992;21(11):94563.

[6] Bresler B, Scordelis A. Shear strength of reinforced concrete beams. J Am Concr

Inst 1963;60(1):5174.

[7] Ordaz M, Arboleda J, Singh S. A scheme of random summation of an empirical

Greens function to estimate ground motions from future larger earthquakes.

Bull Seismol Soc Am 1995;85(6):163547.

[8] Arias A. A measure of earthquake intensity. In: Hansen RJ, editor. Seismic

design for nuclear power plants. MIT Pres; 1970. p. 43883.

[9] Carrillo J, Alcocer S. Improved external device for a mass-carrying slidingsystem for shaking table testing. J Earthq Eng Struct Dynam

2011;40(4):393411.

[10] Carrillo J. Evaluation of shear behavior of concrete walls for housing using

dynamic testing. PhD thesis. National University of Mexico, UNAM, Mexico;

2010 [in Spanish].

[11] Rinawi A, Clough R. Improved amplitude fitting for frequency and damping

estimation. In: Proceeding of the 10th international modal analysis conference

society for experimental mechanics, Bethel, CT; 1992. p. 8938.

[12] Aristizabal-Ochoa J. Cracking andsheareffects on structural walls. J StructEng,

ASCE 1983;109(5):126777.


aritulo seismic perfomance of concrete walls

Documents