seismic behaviour of structural walls with specific …earthquake.hanyang.ac.kr/journal/2002/2002,...

Seismic behaviour of structural walls with

specific details

S. W. Han!, Y.-H. Oh{ and L.-H. Lee!

Hanyang University

Bearing wall systems have been commonly used for low to mid-rise buildings particularly in low to moderateseismic zones. This study investigates the seismic performance of bearing walls with rectangular sectional shapeand specific details of reinforcements. Such details have been developed for 10- to 15-storey apartment buildings inKorea, and used most commonly in apartment building construction. To investigate seismic behaviour of such walls,experimental tests were carried out. Structural behaviour is expressed in terms of ductility, deformation, andstrength capacities. For this purpose, three full-scale test specimens were constructed having different shear-spanratios (2 and 3). The test results of this study are compared with those of other researchers. By this comparison,seismic performance of the walls with specific details is discussed. Also this study compares the responsemodification factor (R) for the bearing wall systems in different seismic design provisions.

Notation

A, Aa, Av zone factorAcv gross area of concrete section bounded by

web thickness and length of section in thedirection of shear force considered

A g gross area of a sectionC, Cs seismic coefficientdb diameter of a reinforcementf 9c concrete compressive strengthfy reinforcement yield stressI importance factorlw length of entire wall or of segment of wall

considered in the direction of shear forceM magnitude of an earthquakeR, Rw response modification factor (strength

reduction factor)S soil factorT fundamental period

Vcr shear force corresponding to first cracking(experimental)

Vmax maximum shear forceVy shear force corresponding to yielding˜max maximum displacement˜ y yield displacement!u maximum drift ratio"˜ ductility ratio

Introduction

Structural walls have been commonly used for resist-ing the lateral forces induced by winds and earthquakesbecause of their efficiency in resistance. Many low tomid-rise RC buildings have either interior or exteriorwalls. These walls are placed to resist lateral and grav-ity forces. This type of wall system is very common inlow to moderate seismic regions, which is classified asbearing wall system.

This system has been most commonly used for con-structing mid-rise (10–15 storeys) apartment buildingsin Korea, which is classified as a low and moderateseismic zone according to the Korean Seismic DesignProvisions.

1Since this system is used for residence

buildings, a rectangular sectional shape is preferred forproviding better interior space. Also, to secure theseismic resistance of walls in mid-rise apartment build-

Magazine of Concrete Research, 2002, 54, No. 5, October, 333–345

333

0024-9831 # 2002 Thomas Telford Ltd

! Department of Architectural Engineering, Hanyang University,

Seoul 133-791, Korea.

{ Advanced Structure Research Station (STRESS), Hanyang Univer-

sity, Seoul 133-791, Korea.

(MCR 971) Paper received 14 September 2001; last revised 27 March

2002; accepted 22 April 2002

ings against earthquakes, special reinforcement detailshave been provided.

This study investigates the structural behaviour ofwalls with a rectangular sectional shape and specialreinforcement details. For this purpose, three full-scalewall test specimens, which have different shear-spanratios of 2 and 3, were made. Since the size of thelaboratory is limited, the size of all specimens was thesame, but a special setting was made to simulate thedifferent shear-span ratios. In this study, strength, de-formation and ductility capacities are estimated basedon experimental results. The capacities of each speci-men are compared with the results of other re-searchers

2–6and the drift limit in seismic design

provisions (UBC, ATC3-06). Based on this comparison,the performance of walls with specific details is dis-cussed.

Also, this study compares the R factor of bearingwall systems in three different seismic design provi-sions such as UBC (1994), ATC 3-06,

7and Korean

Seismic Design Provisions (KSDP).1

KSDP has beendeveloped based on UBC and ATC 3-06. Thus, incalculation of design base shear according to KSDP, Rfactor is included in the formula for calculating designbase shear. The major role of R factor is to reduce theelastic design base shear whereby structures can behavein the inelastic range during design level earthquakeground motions (mean return period of 475 years). Rfactors are assigned according to material and structuralsystems. Based on the comparison of R factors in threedifferent provisions and the investigation of structuralbehaviours of the tested walls, the R factor for the wallswith specific details is discussed.

Design base shear and R factor

In current seismic design provisions, the lateral forcedemand by earthquakes is represented by seismic de-sign base shear. In general, the formula for calculatingdesign base shear is expressed as the following equa-tion

V " CsW

R(1)

where V denotes design base shear, and Cs, R, and Wdenote seismic coefficient, response modification factorand weight, respectively. Seismic coefficient Cs is theLinear Elastic Design Response Spectrum (LEDRS) ofdesign earthquake with mean return period of 475years. Thus, in equation (1), the numerator (Cs timesW ) is the seismic force demand of an elastic system.Since the design earthquake is a rare event, currentseismic design provisions introduce the R factor inorder to allow the structures to behave in the inelasticrange against design level earthquake. Consequently,Cs=R can be referred to as Inelastic Design ResponseSpectrum (IDRS). If structures are designed using the

elastic design base shear (CsW ), the structures maybehave elastically during design level earthquakeground motions.

The R factor is related to reserve strength, ductility,and viscous damping.

8,9The response modification fac-

tor may be calculated as the product of three factors9

R " R" 3 Rs 3 R# (2)

where Rs is a period-dependent strength factor, R" is aperiod-dependent ductility factor, and R# is a dampingfactor. Fig. 1 shows the relationship between LEDRSand IDRS. Also this figure shows IDRSs for ultimatestrength and working strength levels. According to theinvestigations by many researchers

8–14there are several

weaknesses in R factor used in current seismic designprovisions. Detail discussion can be found in ATC 19.

9

However, this study does not attempt to solve theweaknesses in R factor. This is beyond the scope of thisstudy. Instead, this study compares design base shearforces for bearing wall systems in UBC (1994), ATC3-06,

7and KSDP.

1

Comparison of seismic design base shearin different provisions

The design base shear formula has been developedbased on either a working stress or ultimate strengthbasis. For example, the design base shear in UBC(1994) is on a working stress basis, but both NEHRPProvisions

15and ATC 3-06

7have an ultimate strength

design base shear.KSDP was established in 1988 and revised in 2000.

The design base shear in this provision is workingstress level. Table 1 shows the design base shear for-mulas in UBC, ATC 3-06

7and KSDP.

1Assigned values

for R factor in these provisions are also shown in Table2.

Figure 2 is the plot for comparison of design baseshears in ATC 3-06, UBC and KSDP. The R factor inthis plot is the value for bearing wall system withreinforced concrete shear walls. For this comparison,the zone factor, importance factor, and soil factor areset to be 0·12 (A = 0·12, Z = 0·12, Aa = Av = 0·12), 1·0

LEDRS (Cs)

IDRSw (Cs/Rw)

IDRS (Cs/R)

Period: s

1

0Nor

mal

ised

spe

ctra

l acc

eler

atio

n

Fig. 1. LEDRS and IDRS

Han et al.

334 Magazine of Concrete Research, 2002, 54, No. 5

and 1·0, respectively. A zone factor of 0·12 is theassigned value for the Seoul area in Korea. Thesefigures show that design base shear in KSPD is largerthan that in UBC (1994) throughout the whole period

range. Also, the design base shear in KSDP exceedsthat of ATC 3-06 when the fundamental period be-comes either less than 0·2 s or larger than 0·7 s.

By simply comparing design base shear for thebearing wall system, it is concluded that the designbased shear used in KSDP is the highest. If it isassumed that the values for design base shear in ATC3-06 and UBC are reasonable, the R factor in KSPDneeds to be calibrated to reduce the design baseshear. This study assumes that R factors provided inATC 3-06 and UBC are accurate. Thus, R factor iscalibrated to make the design base shear in KSDPsimilar to that in UBC (1994). However, in calibra-ting R factor, both structural details and structuralperformance are important since R factor is relatedto those. Details of walls and experimental tests forinvestigating their structural performance are explain-ed in the following section.

Table 1. Comparisons of base shear formulation in each seismic provision

Korea Seismic Design

Provisions (2000)

UBC (1994) ATC 3-06 (1978)

Design base shearV =

AIC

RW V =

ZIC

RwW V = CsW

C =S

1:2!!!!

Tp , 1·75 C =

1:25

T23

, 2·75 Cs =1:2 AvS

RT23

,2:5 Aa

R

Notation A: zone factor Z: zone factor Av, Aa: zone factor

I: importance factor I: importance factor

S: soil factor S: soil factor S: soil factor

Design method to

be considered

Working stress

design

Working stress

design

Ultimate strength

design

Table 2. Comparison of response modification factors in each seismic provision

Structural systems Earthquake resisting

systems

R

(ATC, 1978)

R

(ICBO, 1994)

R

(Korea, 1988)

R

(Korea, 2000)

Bearing wall system Reinforced concrete

shear walls

4·5 6 3

Reinforced masonry

shear walls

3·5 6

Unreinforced masonry shear walls,

Partially reinforced

masonry shear walls

1·25 - 3

Reinforced concrete

shear walls having

boundary elements

like tied columns

- - 3·5

Frame system Reinforced concrete

shear walls

5·5 8 - 4

Korea 2000 (R ! 3)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Period: s

ICBO 1994 (Rw ! 6)

ATC 3-06 (R ! 4.5)

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

Des

ign

base

she

ar: V

/W

Fig. 2. Normalised design base shear for bearing wall system

Seismic behaviour of structural walls

Magazine of Concrete Research, 2002, 54, No. 5 335

Provisions for structural wall details

Requirements for the design of structural walls areintroduced in chapter 11 (shear and torsion), chapter 14(walls), and chapter 21 (special provisions for seismicdesign) in ACI 318.

15The design code of Korean Con-

crete Institute (2000, referred to as KCI hereafter) hasbeen basically developed based on ACI 318 (BuildingCode and Commentary, 1995 and 1999).

According to ACI 318, structural walls are classifiedas ordinary and special reinforcement concrete structur-al walls. Ordinary reinforced concrete structural wallsmust satisfy the requirements from chapter 1 to 18 inACI 318 and special reinforcement concrete structuralwalls must satisfy the requirements of chapter 21 (21·6)in ACI 318 in addition to the requirements for ordinaryreinforcement concrete structural walls. In the case ofspecial reinforced concrete structural wall design,boundary element or details of a wall should satisfy therequirements in chapter 21 (21·6·6·3).

Details of structural walls commonly used for bear-ing wall systems in Korea are quite different from thoseused in the USA. Fig. 3 shows wall details commonlyused in Korean construction practice for mid-rise resi-dence buildings. The sectional shape is rectangularrather than barbell shape with boundary elements. Arectangular shape provides more usable interior space.Flexural reinforcement is concentrated at the wallboundary (the end region with 10% of wall length, lw)as shown in Fig. 3.

U-type transverse reinforcements and tie bars areplaced. The spacing of U-type transverse reinforce-ments and tie bars is determined from the code require-ment for column in KCI and ACI 318. Tie spacing incolumns should not determine more than the minimumvalue among: (a) 16 longitudinal bar diameters; (b) 48tie diameters; and (c) least dimension of a column. Incase of walls considered in this study, the minimumdimension requirement governs. The wall thicknesscommonly used in Korea is 200 mm so that the thick-ness can easily place the longitudinal and transversereinforcements at the ends of a wall. U-type transversereinforcements are extended into the wall web with thelength of 20db (db: diameter of reinforcement). This isalso determined based on the development length inKCI. The ends of ties are anchored by a 908 or 1358bend around a bar (see Fig. 3). This study investigatesthe structural behaviours of these walls, which arerepresented in terms of strength, ductility and deforma-tion capacities.

Former studies of structural walls

In this section, researches related to structural wallsare introduced. Cardenas and Magura

16tested rectangu-

lar shape walls with different arrangements of long-itudinal reinforcement. According to their study,

flexural, deformation and energy absorption capacity ofshear walls are enhanced when vertical reinforcementis concentrated at the end of a wall. Thus, walls havinguniformly distributed longitudinal reinforcement haveless deformation capacity. This is an important con-clusion, since deformation capacity has an influence ondetermining the R factor (see R" in equation (2)).Experimental tests by PCA researchers were carried outfor walls having various section-shapes (rectangular,barbell, flanged) and different failure modes.

2Test re-

sults showed that all specimens have displacement duc-tilities larger than 3·0 and have drift ratios larger than1·5%.

Wallace and Moehle17

investigated the level ofdamaged buildings in the city of Vina del Mar due toChile’s earthquake (M = 7·8) occurring in 1985. Theyreported that in the city of Vina del Mar there wereabout 400 modern reinforced concrete buildings, whichcontained numerous shear walls and had been designedfor lateral forces comparable to those used in regionsof high seismicity in the USA. Seismic design provi-sions in Chile do not require boundary element like inthe USA. Also, reinforcement details, according to theirpaper, are less stringent than those commonly used inthe USA. However, they reported that these walls per-formed well with little or no apparent damage in themajority of buildings during the earthquake.

Figures 4 and 5 show drift and ductility capacitiesversus maximum observed shear stress of various wallstested by many researchers.

2,4–6,18–20Detailed informa-

tion for each specimen in this figure is in Table 3. Thetest parameters of these structural walls were sectionalshapes (rectangular, barbell, and flange shape), detailsof reinforcement distribution (concentrated or uniformdistribution of longitudinal vertical reinforcement, anddistribution of horizontal reinforcement), shear spanratio, existence of boundary element, ratio of axial load,etc.

It is considered that deformation and ductility capa-cities of walls depend on the level of maximum shearstress and/or failure mode because the level of maxi-mum shear stress is related to the failure mode ofstructural walls. Figure 4 shows that all specimens havea drift capacity of over 1·5% except for one specimengoverned by shear.

A drift ratio of 1·5% is the allowable limit valueagainst a design earthquake in seismic provisions.

8

Thus, it is judged that most structural walls have satis-factory deformation capacities irrespective of the testvariables.

When maximum shear stress is lower than 0·1 MPa,all specimens have a ductility capacity larger than 3·0(see Fig. 5). It is prescribed in the UBC (1994) provi-sions that the R factor for a shear wall system is 8·0(see Table 2). Expected maximum displacements ac-cording to the 1994 UBC can be calculated by multi-plying the design displacement by 3=8 Rw. Thisimplicitly indicates that the displacement ductility ca-

Han et al.


pacity of a wall should be larger than 3·0. Thus driftcapacity of 1·5% and displacement ductility ratio of 3can be treated as the limit values of deformation andductility capacities, which structural tests shall verify.According to Figs 4 and 5, most walls have satisfactorycapacities in ductility and deformation.

In Fig. 4, the scattering of drift capacities of structur-al walls is large with respect to maximum shear stress.It is worthwhile noting that there is a relationshipbetween maximum shear stress and drift capacity.Ductility capacity decreases as maximum shearstress increases. As maximum shear stress increases,

700

350

7-D25

7-D25

40

!25@500

30

D10

D10@250

200

250250

!70@500

D13@1507- D25

7- D25

500

700

SECTION

200

150

D10@200 D10@220

D10@2503050 50

1500 300

D10@200

4-D13

800

150

50

30

300

D10@200

200

50

130D10@250

200

D10 D10@200

100 100 50

200

300D10@200

(b) WF2 specimen

SECTION A-A!

(a) W2 and W3 specimen

ELEVATION

100

D13@150

125 100

250 D10@250

7-D25

A

D13

125 100

7-D25

100 40 5007-D25

D13@150

500

A! 2000

D13

D10@200

D13

500

7-D25

(unit ! mm)

200

220

50

150

300

BOUNDARY DETAILS for W2, W3 and WF2

4-D13

Fig. 3. Wall configuration and specific wall details



structural walls become more likely to be shear-criticalmembers. From Figs 4 and 5, the relationship betweenmaximum shear stress and ductility, deformation capa-cities can be derived as follows

$u

Hw" 1:5% if

Vmax!!!!!!!!!!!!

f 9c Acv

p , 0:2MPa (3a)

$u

Hw" 1:0% if

Vmax!!!!!!!!!!!!

f 9c Acv

p $ 0:2MPa (3b)

"$ " 10# 80Vmax!!!!!!!!!!!!

f 9c Acv

p ifVmax!!!!!!!!!!!!

f 9c Acv

p , 0:1MPa

(4a)

"$ " 2:0 ifVmax!!!!!!!!!!!!

f 9c Acv

p $ 0:1MPa (4b)

But, this is limited since it considers only isolated wallsrather than an entire structural system.

PCA (flexure failure)Northwestern (flexure failure)Michigan (flexure failure)Clarkson (flexure failure)This Study (flexure failure)PCA (shear failure)Northwestern (shear failure)

Michigan (shear failure)Clarkson (shear failure)

Berkeley (shear failure)

Monotonic loading

Monotonic loading

Shear failuredrift ratio ! 1%

Flexure-shear failure:drift ratio ! 1.5%

Flexure failuredrift ratio ! 1.5%

0.300.00 0.05 0.10 0.15 0.20 0.25

Maximum shear stress: (Vmax/!f !cAcv, MPa)

7

6

5

4

3

2

1

0

Drif

t rat

io: "

u/H

w (

%)

Fig. 4. Maximum shear stress versus drift ratio

PCA (flexure failure)Northwestern (flexure failure)Michigan (flexure failure)Clarkson (flexure failure)This Study (flexure failure)PCA (shear failure)Northwestern (shear failure)

Michigan (shear failure)Berkeley (shear failure)

Clarkson (shear failure)

Monotonic loading

Monotonic loading

Shear failureµ ! 2

Flexure–shear failureµ ! 2

Flexure failure:µ ! "80 Vmax # 10

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Maximum shear stress (Vmax/!f !cAcv, MPa)

16

14

12

10

8

6

4

2

0

Dis

plac

emen

t duc

tility

rat

io: µ

Fig. 5. Maximum shear stress versus displacement ductility ratio

Han et al.


Table 3. Test parameters and performance of wall specimens by other researchers

Specimen Sectional Loadinga Dimension H wb

Lw

Reinforcmentc P

A g f 9c

Ref. f 9ce Vmax!!!!!

f 9cp

Acv

$ yf $u

g "$h $u

Hw

Failure

shape No. mode

Length Boundary Thickness rbe rv rh rs

(cm) (cm) (%) (%) (%) (%) (%) (MPa) (MPa) (cm) (cm) (%)

(cm) (cm)

PCA-R1 Rectangular IC 190·5 19·1 10·2 10·2 2·4 1·47 0·25 0·31 0 0·4 11 44·7 0·03 1·35 10·31 7·66 2·26 Flexure

PCA-R2 Rectangular IC 190·5 19·1 10·2 10·2 2·4 4·00 0·25 0·31 2·07 0·4 11 46·4 0·05 2·16 13·34 6·18 2·92 Flexure

PCA-R3 Rectangular MC 190·5 38·1 10·2 10·2 2·4 6·00 0·22 0·42 1·33 7·0 21 24·4 0·19 3·43 7·62 2·22 1·67 Shear

PCA-R4 Rectangular IC 190·5 27·9 10·2 10·2 2·4 3·50 0·28 0·31 1·07 7·5 21 22·7 0·10 2·24 7·62 3·41 1·67 Flexure

PCA-B1 Barbell IC 190·5 30·5 30·5 10·2 2·4 1·11 0·29 0·31 0 0·3 11 53·0 0·06 1·78 13·23 7·44 2·89 Flexure

PCA-B2 Barbell IC 190·5 30·5 30·5 10·2 2·4 3·67 0·29 0·63 0 0·3 11 53·6 0·15 2·54 10·39 4·09 2·27 Shear

PCA-B3 Barbell IC 190·5 30·5 30·5 10·2 2·4 1·11 0·29 0·31 1·28 0·3 11 47·3 0·07 1·78 17·96 10·10 3·93 Flexure

PCA-B4 Barbell M 190·5 30·5 30·5 10·2 2·4 1·11 0·29 0·31 1·28 0·3 11 45·0 0·08 2·03 31·75 15·63 6·94 Flexure

PCA-B5 Barbell IC 190·5 30·5 30·5 10·2 2·4 3·67 0·29 0·63 1·35 0·3 11 45·3 0·18 2·79 12·67 4·54 2·77 Shear




PCA-B9 Barbell MC 190·5 30·5 30·5 10·2 2·4 3·67 0·29 0·63 1·35 8·9 11 44·1 0·24 3·45 13·79 3·99 3·02 Shear

PCA-B10 Barbell MC 190·5 30·5 30·5 10·2 2·4 1·97 0·29 0·63 1·35 8·6 11 45·6 0·17 2·97 12·67 4·26 2·77 Shear

PCA-F1 Flanged IC 190·5 10·2 91·4 10·2 2·4 3·89 0·30 0·71 0 0·4 11 38·5 0·22 2·54 5·05 1·99 1·11 Shear

PCA-F2 Flanged IC 190·5 10·2 91·4 10·2 2·4 4·35 0·31 0·63 1·43 7·6 11 45·5 0·21 2·87 10·16 3·54 2·22 Shear

PCA-CI-1 Rectangular MC 190·5 31·8 10·2 10·2 2·88 2·40 0·28 0·42 1·07 1·0 27 23·3 0·11 3·68 12·70 3·45 2·31 Shear

PCA-USJP Rectangular IC 157·5 14·2 5·7 5·7 2·78 1·26 0·37 0·37 0·75 4·9 20 31·7 0·07 1·14 6·60 5·78 1·51 Flexure

UCB-SW1 Barbell MC 238·8 25·4 25·4 10·2 1·28 3·52 0·83 0·83 1·42 7·9 32 34·5 0·24 1·78 10·67 6·00 3·50 Shear

UCB-SW2 Barbell IC 238·8 25·4 25·4 10·2 1·28 3·52 0·83 0·83 1·42 7·6 32 35·6 0·24 1·78 5·08 2·86 1·67 Shear

UCB-SW3 Barbell M 238·8 25·4 25·4 10·2 1·28 3·52 0·83 0·83 1·39 7·8 30 34·8 0·24 1·98 17·27 8·72 5·67 Shear

(continued overleaf )

Seism

icb

eha

viou

ro

fstru

ctura

lw

alls

Ma

gazin

eo

fC

on

creteR

esearch,

20

02

,5

4,

No

.5

33

9

Table 3. (continued)

Specimen Sectional Loadinga Dimension H wb

Lw

Reinforcmentc P

A g f 9c

Ref. f 9ce Vmax!!!!!

f 9cp

Acv

$ yf $u

g "$h $u

Hw

Failure

shape No. mode

Length Boundary Thickness rbe rv rh rs

(cm) (cm) (%) (%) (%) (%) (%) (MPa) (MPa) (cm) (cm) (%)

(cm) (cm)

UCB-SW4 Barbell IC 238·8 25·4 25·4 10·2 1·28 3·52 0·83 0·83 1·39 7·5 30 35·9 0·22 1·93 6·86 3·55 2·25 Shear

UCB-SW5 Rectangular M 241·3 27·9 27·9 10·2 1·28 6·34 0·63 0·63 1·79 7·3 30 33·4 0·20 1·47 7·37 5·00 2·42 Shear

UCB-SW6 Rectangular IC 241·3 27·9 27·9 10·2 1·28 6·34 0·63 0·63 1·79 7·0 30 34·5 0·19 1·63 7·11 4·38 2·33 Shear

NWU-B11 Barbell MC 190·5 30·5 30·5 10·2 2·4 3·67 0·29 0·63 1·35 0·3 21 53·7 0·16 2·92 12·70 4·35 2·78 Shear

NWU-B12 Barbell MC 190·5 30·5 30·5 10·2 2·4 3·67 0·29 0·63 1·35 0·4 21 41·7 0·20 2·90 10·16 3·51 2·22 Shear

NWU-F3 Flanged IC 190·5 10·2 91·4 10·2 2·4 2·29 0·25 0·31 0·85 5·9 21 27·9 0·13 2·21 10·16 4·60 2·22 Shear

UM-W1 Barbell IC 122·0 12·7 12·7 7·6 2·9 3·00 0·30 0·30 0·40 8·0 1 34·5 0·08 2·65 10·41 3·93 2·94 Flexure

UM-W3d Barbell IC 122·0 12·7 12·7 7·6 2·9 3·00 0·30 0·30 0·40 8·0 1 34·5 0·10 2·71 5·31 1·96 1·50 Shear

CU-RW2 Rectangular IC 122·0 19·0 10·2 10·2 3·13 2·89 0·33 0·33 1·58 7·0 28 43·7 0·08 2·29 8·38 3·66 2·19 Flexure

CU-RW3Od Rectangular IC 122·0 19·0 10·2 10·2 3·13 2·89 0·33 0·33 2·05 10·0 28 31·0 0·10 2·86 8·26 2·89 2·16 Shear

Notes: a IC = cyclic loading with incremental displacement amplitude

MC = cyclic loading with different displacement amplitude

M = monotonic loadingb Aspect ratio where Hw = wall height from the base to applied load line, Lw = wall lengthc rbe = the ratio of boundary longitudinal reinforcement to boundary element area

rv = the ratio of web horizontal reinforcement to vertical cross section

rh = the ratio of web vertical reinforcement to horizontal cross section

rs = the volumetric ratio of transverse reinforcement at the boundary elementd Specimen with openinge actual concrete compressive strength obtained at testingf displacement when all boundary longitudinal reinforcement yieldgdisplacement corresponding to 80 percent of maximum strengthh displacement ductility ratio calculated from dividing the maximum displacement by the yield displacement.

Ha

net

al.

34

0M

aga

zine

of

Co

ncrete

Resea

rch,

20

02

,5

4,

No

.5

Structural behaviour of walls with specificdetails

In order to investigate the structural behaviour of awall with specific details (rectangular in sectionalshape and specific arrangement of reinforcements),three full-scale test specimens were made. Variables forthese specimens were shear-span ratio (2 and 3). Table4 shows sectional shape and reinforcement details.Also, Fig. 3 shows model dimension. Since the size ofthe laboratory is limited both specimens were made thesame size, but a special setting was made for simulat-ing a shear-span ratio. As shown in Figs 6 and 7, this isfeasible when two vertical actuators are controlled togive axial force to produce additional moment in addi-tion to vertical axial force. If the ratio of moment toshear is 2, it did not require the additional moment bythe two vertical actuators.

The specimens were cast monolithically in thehorizontal direction. The maximum size of aggregatein the concrete mix was 19 mm. At least 3 cylindertests were carried out at 3, 7, 28 days, and testingday. Average concrete compressive strengths for spe-cimens W2, WF2 and W3 obtained before the testwere 34·2, 34·5 and 36·9 MPa, respectively. Reinfor-cement was deformed bars with three different dia-meters: 10 mm (D10), 13 mm (D13) and 25 mm(D25). Table 5 shows the measured material proper-ties of the reinforcement.

Figure 6 shows the experiment test setup and Fig.7 shows the displacement history and loadingscheme. Incremental pseudo static cyclic loads con-trolled by deformation were applied to each speci-men. To keep a constant shear span ratio, the forcesproduced by three actuators were calculated at eachloading step as shown in Figure 7. Axial loads due

to gravity were kept constant (0·1 A g f 9c) throughoutthe test.

Test results and discussion

Figure 8 shows the hysteretic behaviour of eachspecimen. The important values of these figures areshown in the box in Fig. 8. According to Fig. 8, everyspecimen has a deformation capacity larger than 1·5%and has a displacement ductility ratio larger than 3·0.Displacement and ductility capacity are measured whenthe applied load is reduced by 20% of maximumstrength. Yield displacements were measured when alllongitudinal bars at the end (10% of lw) have yielded.Also, in Figs 4 and 5, the deformation capacities anddisplacement ductility ratios of the specimens areplotted with those of other experimental results shownin Table 3.

Table 4. Test parameters of specimens

Specimen Section shape Shear span

ratio

(M=VD)

Axial load

(N=A g f 9c)

f9ca

(MPa)

fyb

(MPa)

rbc

(%)

rhd

(%)

rve

(%)

rsf

(%)

W2 2·0 0·10 27·6 357·1 4-D13

(1·27)

D10

@250

(0·28)

D10

@220

(0·32)

D10

@200

(0·99)

WF2 2·0 0·10 27·6 357·1 4-D13

(1·27)

D10

@250

(0·28)

D10

@220

(0·32)

D10

@200

(0·99)

W3 3·0 0·10 27·6 357·1 4-D13

(1·27)

D10

@250

(0·28)

D10

@220

(0·32)

D10

@200

(0·99)

Notes: a Design compressive strength of concretebDesign strength of reinforcementcRatio of boundary longitudinal reinforcement to boundary element areadRatio of web horizontal reinforcement to vertical cross sectioneRatio of web vertical reinforcement to horizontal cross sectionf Volumetric ratio of transverse reinforcement at the boundary element

Fig. 6. Test setup for varying moment-to-shear depth ratio



Figure 9 also shows the cracks at the final stage ofthe test specimen. Specimen W2 has more shear cracksthan specimen W3. At the final stage both specimenslost their strength due to the crushing of concrete inlower end part of the wall.

From Figs 4 and 5, the walls with specific details(rectangular in sectional shape and specific reinforce-ment arrangements) have satisfactory displacement andductility capacities compared to the walls tested byother researchers. This may be due to the fact thatsatisfactory capacities of tested walls were obtaineddue to the arrangement of longitudinal bars (concentra-tion at the ends of a wall) and lateral reinforcement (Ustirrup and tie reinforcement). This investigation is verysimilar to the study by Cardenas and Magura.

21Build-

ing using the walls considered in this study can have anR factor equivalent to those used in UBC or ATC 3-06even if those details are somewhat different. Such aconclusion requires the assumption that the R factorused in UBC and ATC 3-06 is appropriate for wallsystems.

Deformation capacities are important even to struc-tures located in low to moderate seismic zones sincerare seismic events should be considered in design.Also, the observed maximum strength of both walls ishigher than the calculated strength, as shown in Table6. In Table 6, calculated maximum strengths (Vmax(cal))were determined as the minimum value between nom-inal shear strength by ACI 318-95 and shear strengthcorresponding to maximum flexural strength obtainedfrom sectional analysis. Flexural strengths were calcu-lated by assuming a linear strain distribution across

the section and a peak compressive strain of 0·003 inthe concrete. Strain hardening of the longitudinal re-inforcement and actual material strengths were consid-ered. For all specimens, maximum strengths weregoverned by shear strength corresponding to maximumflexural strength obtained from sectional analysis.Also, these values correspond well with maximumshear strength observed from the test of each speci-men.

Conclusions

This study investigates the seismic behaviour ofstructural walls with specific details and rectangularsections. This experimental study was carried out forthis purpose. Three full-scale wall test specimens weremade. The conclusions obtained from this study are asfollows.

(a) All specimens have ductility and deformation capa-cities greater than 3·0 and 1·5% of height, respec-tively. Thus, the walls considered in this study havesatisfactory deformation and ductility capacities.

(b) The maximum observed strength of each specimenwas well estimated by the calculated maximumstrength which was determined by comparing thenominal shear strength by ACI 318 and the shearstrength corresponding to maximum flexuralstrength obtained from sectional analysis.

(c) The design base shear for bearing walls in KSDPis higher than that of ATC 3-06 in the period range

MVD

VH # PLVD

PV

! ! 2 # 3

V

H"P

N2

N2

P

DL

Loading scheme to vary M/VM

# ! 1/600 # ! 1/400 # ! 1/300 # ! 1/200# ! 1/150# ! 1/100

# ! 1/75

# ! 1/50

0 3 6 9 12 15 18 21 24 27

Cycle number

0.03

0.02

0.01

0.00

"0.01

"0.02

"0.03

Top

sto

rey

drift

rat

io: "

/hw

Fig. 7. Displacement history and loading scheme for varying M/VD

Table 5. Mechanical properties of reinforcement

Rebar

no.

Nominal

area

(mm2)

Yield

strength

(N=mm2)

Yield

strain

(3 10#6)

Elastic

modulus

(N=mm2)

Ultimate

strength

(N=mm2)

Elongation

(%)

D10 71·3 335 2004 1·83 3 105 443 17·6

D13 126·7 395 2206 1·82 3 105 601 14·4

D25 506·7 400 2035 2·17 3 105 610 15·0

Han et al.


Fig. 8. Hysteresis loops for (a) W2, (b) WF2 and (c) W3 specimens

Vcr: 186.2 kN

Vy: 348.9 kN

Vn: 448.9 kN

Vmax: 386.1 kN

!y: 12.4 mm

!max: 80.9 mm

µ!: 6.5

"u: 2.7%

Vcr: "197.9 kN

Vy: "332.2 kN

Vn: "448.9 kN

Vmax: "442.9 kN

!y: "9.2 mm

!max: "53.4 mm

µ!: 5.8

"u: 1.8%

Vy

Vcr

!y

# ! 1.5% # ! 2.0%500

400

300

200

100

0

"500

"400

"300

"200

"100

Late

ral l

oad:

kN

"100 "80 "60 "40 "20 0 10080604020

Top displacement: mm

(a)

Vcr: 268.5 kN

Vy: 355.7 kN

Vn: 437.1 kN

Vmax: 444.6 kN

!y: 5.6 mm

!max: 55.9 mm

µ!: 9.98

"u: 1.86%

Vcr: "252.8 kN

Vy: "467.5 kN

Vn: "515.5 kN

Vmax: "573.3 kN

!y: "9.6 mm

!max: "49.7 mm

µ!: 5.18

"u: 1.66%

Vy

Vcr

!y

# ! 1.5% # ! 2.0%500

400

300

200

100

0

"500

"400

"300

"200

"100

Late

ral l

oad:

kN

"100 "80 "60 "40 "20 0 10080604020


(b)

!max

"600

Vcr: 94.1 kN

Vy: 191.1 kN

Vn: 449.5 kN

Vmax: 311.6 kN

!y: 9.8 mm

!max: 59.6 mm

µ!: 6.1

"u: 2.0%

Vcr: "107.8 kN

Vy: "172.5 kN

Vn: "449.5 kN

Vmax: "321.4 kN

!y: "8.9 mm

!max: "59.3 mm

µ!: 6.7

"u: 2.0%

Vy

Vcr

!y

# ! 1.5% # ! 2.0%400

300

200

100

0

"400

"300

"200

"100Late

ral l

oad:

kN

"100 "80 "60 "40 "20 0 10080604020


(c)

!max



shorter than 0·2 s and longer than 0·7 s. Also it ishigher than UBC in the whole range of period. It isnoted that design base shear in Korean SeismicDesign Provisions (KSDP) and UBC are workingstress level whereas that in ATC 3-06 is strengthlevel.

(d ) Since the elastic design shear forces in UBC andKSDP are almost identical, it is concluded thatKSDP assigned a lower value of R factor for bear-ing wall systems, which causes a higher value ofdesign base shear. Considering the performance ofthe test walls it is conservative to assign a lower

value of the R factor in KSDP. If it is assumed thatthe value assigned for R factor in UBC is appro-priate the R factor used in KSDP needs to becalibrated.

Acknowledgements

The support of the advanced Structural ResearchStation (STRESS) of the Korean Science and Engineer-ing Foundation (KOSEF) at Hanyang University isgreatly acknowledged.

Fig. 9. Crack pattern at the loading stage, specimens: (a) W2 and (b) WF2

Vcr: 186.2 kN

Vy: 348.9 kN

Vn: 448.9 kN

Vmax: 386.1 kN

!y: 12.4 mm

!max: 80.9 mm

µ!: 6.5

"u: 2.7%

Vcr: "197.9 kN

Vy: "332.2 kN

Vn: "448.9 kN

Vmax: "442.9 kN

!y: "9.2 mm

!max: "53.4 mm

µ!: 5.8

"u: 1.8%

Vy

Vcr

!y

# ! 1.5% # ! 2.0%500

400

300

200

100

0

"500

"400

"300

"200

"100

Late

ral l

oad:

kN

"100 "80 "60 "40 "20 0 10080604020


(a)

Vcr: 268.5 kN

Vy: 355.7 kN

Vn: 437.1 kN

Vmax: 444.6 kN

!y: 5.6 mm

!max: 55.9 mm

µ!: 9.98

"u: 1.86%

Vcr: "252.8 kN

Vy: "467.5 kN

Vn: "515.5 kN

Vmax: "573.3 kN

!y: "9.6 mm

!max: "49.7 mm

µ!: 5.18

"u: 1.66%

Vy

Vcr

!y

# ! 1.5% # ! 2.0%500

400

300

200

100

0

"500

"400

"300

"200

"100

Late

ral l

oad:

kN

"100 "80 "60 "40 "20 0 10080604020


(b)

!max

"600

Han et al.


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al performance of the slender structural walls with different de-

tails. Proceedings of Advances in Structural Engineering and

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15. BUILDING SEISMIC SAFETY COUNCIL (BSSC). NEHRP recom-

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1994 Edition FEMA 222A, FEMA 223A, Washington DC 1995.

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Discussion contributions on this paper should reach the editor by

1 April 2003

Table 6. Observed strengths and deformability of wall specimens

Specimen Loading

direction

fc,test(28)a

(MPa)

Vcrb

(kN)

Vyc

(kN)

Vmax(test)d

(kN)

Vmax(cal)e

(kN)

Vmax( test)

Vmax(cal:)

f $ yg

(mm)

$maxh

(mm)

"$ i !uj

(%)

W2 positive 34·2

(29·4)

186·2 348·9 386·1 378·3 1·02 12·4 80·9 6·5 2·7

negative 198·0 332·2 442·9 1·18 9·2 53·4 5·8 1·8

WF2 positive 34·5

(28·6)

268·5 355·7 446·6 501·8 0·89 5·6 55·9 10·0 1·9

negative 252·8 467·5 573·3 544·9 1·05 9·6 49·7 5·2 1·7

W3 positive 36·9

(29·8)

94·1 191·1 311·6 252·8 1·23 9·8 59·6 6·1 2·0

negative 107·8 172·5 321·4 1·27 8·9 59·3 6·7 2·0

Notes: a Concrete compressive strength at test (and at 28th day)b Observed shear strength at first crackingc Observed shear strength when all boundary longitudinal reinforcement yieldd Maximum observed shear strength during the testeMaximum strength calculated as a minimum value between nominal shear strength by ACI 318-95 and shear strength corresponding to

maximum flexural strength obtained from sectional analysisf The ratio of maximum observed shear strength to maximum calculated strengthg Displacement when all boundary longitudinal reinforcement yieldh Displacement corresponding to 80 percent of maximum strengthi Displacement ductility calculated from dividing the maximum displacement by the yield displacementj drift ratio calculated from dividing the maximum displacement by wall height



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