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TRANSCRIPT
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THE NONLINEAR RESPONSE OF
REINFORCED CONCRETE COUP LING SLABS IN
EARTHQUAKE-RESISTING SHEARWALL STRUCTURES' . ""
by
Thomas E. MalyszKo
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\ A thesis submitted to the Faculty of Graduate Studies
and Research in partia,l fulfilment of the requirements
for the degree of Master of Engineering
Department of Civil Engineering
and Applied Mechanics, ,
McGill University
Mon treal, Quebec .. Canada
A
--August 1986
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6 Permission has been granted to the National LiQrary of Canada to microfi lm thi s thesis and to lend or se11
f copies of the (fi,lm. '
The author (c~Pyright owner) has reserved other publication rights, and neither the thesis nor extensive extracts from i t may be printed or otherwis e reproduced wi thout his/her written permission.
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ISBN 0-315-38292-9
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ABSTRACT
The N9nIinear Response of Re:nforced Coupling Siabs 1n\Earthquake-ResistingrSh~arwal1 Structures
by
Thomas E. Malyszko
Department of Civil Engineering and App11ed Mechanies McGi11 University
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M. Eng". Thesis August -1986
Influence of stirrup spacing and conarete, strength 6n the
nonlinéar .- seismic response of coupled slàb-shearwall structures ls
reported • 1
Three 1/3-scale models were tested ta study the total response
under impo~ed deformati~ns ~ith progresslvely increaslns displacement o
ductilities. These specimens wer.e identicà'l in all respec ts except for
variations in the stirrup spacings. The _ force-dis placement
characteristics, reinforcement and concrete strains, and displacement 1
profiles are presented.
The behaviour of chese models compared favourably' with the
1/2-scale models tested by "Taylor ( 11 ) • The higher model concrete
strength, re~tive to the prototype concrete strength, increased the
model she~r eapacity proportionately. Dee~easing stirrup spacings ,
substantially enhanced ductility but not shear resistance. Stlffness
degredation in the inelastic response range was rapid and severe.
Thus, effective slab widths are only a fractioti of the overall slab
w1dth. These results are compared with previous studies in this area.
Design recommendations are presented for the placement of longitudinal
se1smic reinforcement, effective width and ultimate shear capacity of
the slab •
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RESUME Cl "
Le comportement non-Unéaire sous charge sei:smic . , ..
de dalles- jointe à des murs de cisaillement ,
Département de Genie Ci vil et~de Mécanique Appliqùee
,Université HcGill,
par Thomas E. 'Malyszko . \.
These de Ma!trise' Août 1986
Ce rapport présente les re3ultats' d'une etude expérimentale-- <.
s~r le comportemant non-l1ri'éaire sous charges ~i3miques de dalles
jointe à des murs de cisaillement. Leo effets des étriers dans les
dall4!s' et d ',une tésistance accrue du béton sur la ductilité et la
résistance -------au c:isaillement sont èxaminés. , Trois specimens de laboratoire avec different espacement
"" dt etriers ont été tes té jusQu t a la rupture sous l'effet de déformations
, imposées et avec l'amplitude croissante. Les relations ,
, , ,for"e-dé p~àcement,
tI.-que les profils de
béton et de ~ature, ainsi
déplacement on ét~ preséntés.
déformations les du
,
Le comportement P'~ ces modèles à 1 t échelle 1/3 etait similaire
au prototype. La résistance accrue du béton des specimens, relativeme r
fa résistance du prototype, a proporti~nellement augmenté.-±a capacité
de cisaillement du modèle. 1
L'espacement diminues ~ des étriers a
. amélioré la ductilité sans toutefois influencer la résistance aU v
cisaiUement. Une fois la limite elastique d~passée, la rigidité du
severement. Cependant, la largeur' specimen diminu\ rapidement et
réelle de 'la dall\ e3t seulem~nt une f'raction la largeur totale de la
dalle. Ces résultats· sont comparés aux études antérieures faiteJ9 dans
ce domaine. Le rapport présente des reco~dations sur placement de
l' armature si~mlque' longi,tudinale, le largeur réelle et la resistance'
ul time au cisaillement de la dalle.
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ACKNOWLEDGEMENTS \\
• The author wishes to express his sincere thanks to' the
\: • following individuals whose contributions led to the successful
completion ;"'of thi::} research progra:n:
Dr. M. S. ,Mirza, Professor, Department of" Civil Engineering and
Applied Mechanics, McGill University, as 'research advisor, for his .,
~ilvaluable advice, encouragement and patience throughout the author' s'
period of study.
'0- Dr. D. Mitchell, Professor, Department of Clvil Engineering and
Appll ed Met!hanlcs, McGill University, - for hlS useful advice and
knowledgeable explanatlOns throughout this study.
\ Particular thanks 1s due to my colleague HllllaIO Cook, for his
sug~e3tions on the loading system set-up and procedure, hlS guidance
concerning .the data acquisi tlon system, and generally for his help in ,
, ... ironing-out the countless problems arisl(îg throughout this study. ,
My colleague Charles Manatakos, for the extremely generous
contribution of his Ume and hlS effort to thlS experlmentai program.
His good humour made the testl',ng that much more enjoyable.
My eolleagues David Leblanc, Lionel Lemay, J .P. Landry, Jahlil ~ahn
and Alain Dandurand for their contributions to this study.
Mark Malyszko for his help during testing.
Mr. B. Cockayne, Ml". R. Sheppard, MI'. M. Pzykorski and the staff of
the Ci vil Engineering Structures Laboratory for ·their invaluable
technical, assistance. " ,The Civil Engineering Department! secretarial staff for their
cheerful encouragement J support and l1'elp.
The partial funding of the National Research Couneil 1s gratefully
acknow 1 edged •
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TABLE OF COtlTENTS
Page
ABS:rRACT i
ACKNOWLEDGEMENTS 1i1
T ABLE .. OF CONTENTS 1
1v
• LIST OF FIGURES vi
LIST OF TABLES xi
NOTATION xi1
. " CHAPTER
1 INTRODUCTION
1.1 The Prob1em
1.2 Brief Review of' Previous Wor.k
1.3 Scope of' Researeh
2 MATERIAL PROPERTIES AND TEST SET-UP
2. 1 The Modeling Pro cess
2. 1.1 Choice of Geometrie Scale
2.1.2 Materials Similitude
2.2 Description of the Madel
2.2.1 -Geometry
2.2.2 Material Properties
2.2.3 Design of Reinf'orcement , ~I 1 !
2.3 Ins~~umentation ,
2.3.1
2.3.2
Dia1 Gauges and LVDTs .
Load Cells . ~.3.3 SErain Gauges "
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1
19
19
21
26
26
30
36~
42
42
42
44
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2.3.4 0 Demec Gauges
2.4 Loading System
. ~ 2.5 Testing Procedure
2.6' Pr~plems Encountered During Set-up and Tes ting
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3 EXPERIMENTAL DATA AND DISCUSSION OF RESULTS
3.1' Crack Propagation
3.2 Force-Displacement Results •• 3.3 Slab Deflection Profiles
, 3.4 Longitudinal Steel Strains
3.5 Performance of Stirrups
4 . SUMMARY AND COMPARISONS
4.1. Summary of Exp'ei~imental Resul ts
4.2 Effective Width
4.3 Comparisons with Prev1~us'Work
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55
57
58
71
79
87
92
100
103
107
Recommendations of Paulay and Taylor 101 '7
Recommendations of Schwaighofer, and Collins 112
4d.} Recommendations of Qadeer and Stafford Smith 119
-r 5 RECOMMENDATIONS AND œNCLUSIONS
5.1 Design Recommendations 121
5.2 Conclusions
5.3 Suggestions for Future Research
LIST OF REFERENCES 128
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•• LIST OF FIGURES
1.1 - Types of Earthquake-Resisting Shearwalls ,
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1.2(a) - Plan of Slab and Cross-Wall Structure used by'Qadeer
and Stafford Smith
1.2(b) - Value of Slab Stiffness Number k and YelY as a ~
Function of LlX' for C/X = 0
1.2(c) - Value of Slab Stiffness Number k and YelY as a
Fl.\.nction of L/X for C/X = 117
1.2«(1) - Value of Slab Stiff~ss N,umber k and Ye/Y as a
Function of L/X for C/X = 1/16
1.3 - Variation of Slab Stiffness Factor and Efféo.ti v~ Width
, with Wall Spacing for Combinations of Plane and Flangèd
1:\ Walls
1.4 - 1~ Storey Prototype Structure Adopted by T~y~or (11) and , .
Schema tic View of a Typical !nterior Bay COrld±dered, in
this Study
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5
6
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8
10
12
1.5 Typical Plan View of Prototype Structure by Tay..lor 13
1.6 Dimensions and Reinforcing Details of Taylor's Test Units 14
1.1 - Cross-Section of Taylor 1 s Uni ts 1 - 4
1.8 - Scl1ematlc Illustration of Taylor's Test Model
2.1 - Similitude Requir~ments
2.2 - Dimensions of the Model 1
2.3 - Assembly of Pr'ecàst Wall Segments
2.4 Stress-Strain Curve for Cold FQ~~d D7 Deformed Wire
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17
24
27
29
32
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LIST OF FIGURES ( cont ' d)
2.5 - Hea t Trea tment o~ 07 De~ormed ~re lo/.
-2.6 - Stress-Strain Curve of Heat' Treated 07 Deformed' Wire
-- " 2.7 - Concrete Compr~s3ion Stress-Strain Curve (Typical)
\ 2~8 - Cross-Section of Units 1 , 2 and 3 '4 • 2.9 -~ Plan View of Flexural Reinforcement in Units 1, 2 and ,
2.10 - Slab Rcinf'orccmcnt tn Unit .... '4'I...1'i1J{~
2.11 - Slab Reinf'orcement in Unit 2 /
2.12 - -Sla b Reinf'orcemen t in Unit 3 l'
2.13 - Typical Shearwall Segment
2.14 - Enlarged Views of' Stirrup Cage
2.15 - Dial Gauge and L.V.D.T: Locations
2.16 - Stirrup Oimensions and Straln Gauge Locat1:ons l'
2.17 - Strain Gauge Protection o
2.18 - Demec Stud Locations 1.'
2.19 - Elevation of Loading Systl3m -2.20 - Plan View of Loading System
2.21 - End Vfew of' Support Structure and Specimen
2.22 - Side View of Set-Up Prior to Loading 0 J
2.23 - Rela tiye Mo '1ements of Shearwalls Subjected to' Lat~ral
Loading
2.24 - Illustrat ton of Forces Exerted on South Shearwall o
2.25 - I.ol.là.lng D~ t.ails
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40
40
41
43
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LIST' OF FIGURES (cont' d) Page ~_
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3.1 - Primary Yield Lines in Unit 1 • 59
3.2 - Formation of Secondary Yield Lines in Unit 1
(cycle 5, }l = 3) 59
3.3 - Torsion Cracking in Unit 1 (cycle 8, p = 3) 60
3.4 - Cracking at Toe of South Wall in Unit 1 (cycle 17, p = 7) 60
3.5 - C()n('reb~ Crush;lne; at Toe of North \-lnll in Unit 1 (cycle 21) 61
3.6 - First Signs of Tensile Membrane Action Near the South
Wall in Unit 1 (cycle 23, ~ = 9) !
3. 7 .. ;"~ltFan Type" Punching Shear Failure Around Each Wall' ,
in Unit 1 (cycle 35, p = 13)
3.8 - Unit 1 at End of Test .. 3.9 - Elevation View of North Wall Toe Punching into Slab
in Unit 1
3.10 - Primary Yield Lines in Unit 2
3.11 - Cracking at Cycle 5 (p = 3) in Unit 2
3.12 - Cracking at Cycle 8 (p = '3) in Unit 2
3.13 - First Signs of Tensile Membrane Action ln Unit 2 ,.'
(cycle 1 7, }l = 7 )
3.14 - Unit 2 at End of Test (cycle 23, p = 9)
3.15 - Close-up of Central Area of Unit 2 at Cycle 23
3.16 - Shear Fallure at Toe of South Wall in Unit 2
3. l7- - Y:1.eld Lines 1n Unit 3 (cycle 5, }l = 3)
3.18 - Shear Failure at Toe of South Wall in Unit 3
<~ycle 7, P = 3)
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62
63
64
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61
68
68
3.19 - Clpse-up of Shear Failure at Toe of South Wall in Unit 3 6~
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LIST OF F~GURES (cont'd) o Page
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72 3.20 Force-D~splacement Characteristics, Unit 1 \- .
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80 -
3.21 - Force-Displacement Characteristics 1 Unit 2 î
3.22 - Force-Displacement Characteristics, Unit 3.
3.23 - Long~tud~nal Displacement Profiles, Unit
3.24 - Long~tud~nal Displacement Prof~les, Unit 2 81
3.25 - Longitud~nal Dis placemen t Profiles, Un~t 3 82
J.26 - Transverse D~spla.cement t'roflles, Unit 84 r
3.27 Transverse D~splacement Proflles, Unlt 2 85 .' "
3.28 Transverse D~splacement Pràflles, Unit 3 86
3.29 Longitudinal Relnforcement and Concrete Strains
(F~rst Cycle to 60% Ult~mate) .88
3.30 - Longitudinal Re~nforcement and Concrete Strains •
(Cycle 5 (p = 3» 89
3.31 - Long~tudinal Reinforcement and Concrete Strains,
(Cycle 1~» •
3.32 - End View ,of Deep Column
3.33 - Punching Shear Failure at Foot of Deep Column
(view from west side)
3.34 - Punching Shear Fallure at Foot of Deep Column
(view from east s~de)
3.35 - The Spandrel Be2~ Between the Deep Columns 4-
3.36 - Strain Gauge Readings on Ver-tical Stirrup Legs
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LIST OF FIGURES (cont'd) Page
4.1 (a) - Cantilever Beam Subject:eQ" to a Vertical Point ·Load - 104
4.1(b) $hearwalls Subjected to Concentrated Vertical Loads 104
4.2(a) - Taylor's Unit 1 Force-Displacement Characteristics 108
4.2(b) - Taylor's Unit 2 Force-Displacement Characteristics 108
4.3(a) - Plan V~ew of Szalwin3k~ Model
4.3(b) - Elevation of Szalwin3k~ Model
4.4 - Load Displacement DiagrJ~ \...
4.5 - Strains in Top Steel Along L1ne K-K
4.6 Strains in Top Steel Along Line L-L
Critical Section for Shear Strength
4.8 - Flexural Reinforcing in Coupling Slab
to Resist Lateral Loading
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5.1 - Cross~Section Along the Wall Face Centrel~ne-or a Slab
Coupled ..3hearwall Speci~en with a Drop Panel
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115
116
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LIST OF TABLES
Page
2.1 Typical Scale Factors 20
" \ 2.2 - Possible Distdrtions in Reinforced Concrete Models 20
2.3 Similitude Requirements, Static Elastic Modeling 22
2.~ - Summary of Scale Factors for Reinforced Concrete Models 24a
2.5 - Summary of Scale Factors and Scaled Model Values
2.6 - Deformed Wire Properties
~eCim~n S~rengths at a Displacement Ductility ~ = 3
.~ 3.2- - Stiffness Values at Load Cycles to 60% of Ultimate Load
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4.1 - Effective Slab Widths
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18,
106
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S
S
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effective ~idth of slab
.Corridor opening
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NOTATION (
-distance from end of shearwall to transv~rse edge of 31ab
1 -
(in study by Qadeer and Stafford Smith): C = 0.0 in th13 study
effective depth of the 3la~
vertical displac,ement of cantllever
modulus of elastlcity
modulus of elasticity of concrete
modulus of elasticity of steel
y~eld strength of steel •
slab thickness
horizontal. loads ~in'study by Taylor)
moment of ~nertla
non-duD,enslonal slab 'stiffness ntimber (ln study by Qadeer and
Stafford Smith)
cornidor width (in study by 'Qadeer and Stafford Smith)
scale factor
strain scale factor
\ 1
f
modulus of elasticity.scale factôr
length scale factor
stress scale'factor
thickness of the shearwall
u~t1mate sheav st~ess (.3:ff~,) shear force carried by the lab
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tfOTATION
w
x
X
y
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{con,t 'd) .
wall depth (in study by Qadeer and Stafford Smith) ,<.
cantilever length
-= 2W + L (in study by Qadeer and Staffora Smith)
bay width (in study by Qadeer and Stafford Smith)
Y e effective slab width (in study by Qadeer and Stafford Smith)
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f
P
= 2dy ='relative vertical displacement ,of the shearwalls
~train
displ~ceme~t ductility
Pmin -' minimym reinforcement ratio for flexural sections ,
-v - 'poisson's ratio (value of .17:~sed in this study)
stress
e wall rotations (in study by Taylor)
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CHAPTER 1
INTRODUCTION
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1.1 TfIE PROBLEM
Multistorey structures are norrnally designed '0 resist lateral
loads p;'oduced by wind forces and earthquake forcen.
... decades the une of shearwalls ln rC31ntlng :Juch loade, and partlcularly
seisrnlc loads, has galned popularlty due to thelr lnh~rent cao~omy (1),
natural stlffne3s, and inelastlc r behaviour (2). Yet the b,l:Jic
understandlng of the3e fundamental phenomena remalns llmlted.
Not only do sheal".·lalls provlde efflclent lateral 3trcngth and
stablllty, but wi th propEl'r- detaillng of the relnforcernent' one obtain3
the added bonus of a ductlle wall renpon3C and- thU3 an overall
hysteretic dam'ping of the enUre structure (2). Therefore , ba3f~d on
industry standards,' shearwalls can provlde conslderable protectlon to
other structu'ral and non-structural component3 during mild to mO,derate ,
eart hquakes • ThlS in turn lncreases a bUildlng occupant's ~afety
during selsrnic ac~t1, WhlCh should be the ultimate concern 'of any
designer. The survivabllity of shearwall structures durlng large
earthquakes i3 also conside~ed to be reasonable.
A large, single, solid cantilever wall is ofte~ used in engineering
classroom examples, and rarely used otherwise. Cantilever shearwalls
are almost always pierced throughout with various openings in irregular
o patterns. This. paper deals with only a single row of such open!ngs as
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illustrated in Fig. 1.1. The illustration in Fig. 1.1(b) 1s gen~rally
ref~rr,ed -,to as a coupled shearwalJ. and can be considered ,as two
shearwalls jOined by deep coupl~ng (or 'link') beams. The focus here
is on thin link beam elements (Fig. l.l(cl) such as monolithic concrete
slabs. Such element,s are commonly utilized in high-rise apartment
buildings' because of ,
low ~to~ey height restrictions imposed by the
normal industry standards.
As ltentioned earlier, hysteretic damping of a shearwall
structure subjected t'o earJhquake forces 13 a desirable feature. In a
plain SOlld shearw~ll subJe~t to lateral load creatlng an overtu~ning
moment Mo (Fig. 1.1 (a», such energy dissipation takes place' when
'inelas,tlc deformations occur due to a single plastic. hil)ge in the ,
bottom stories of the wall. According to Paulay and Taylor (3),
'In a coupled shearwall, however, a very slgnificant part, if not aIL of the requlred energy'disslpation, can take Rlace in the coupling system. Thereby'the walls themselves may be ~rotected_ against "early" damage~ Prerequisites to such a desirable inelastic reponse are that: (a) the coupllng beams possess sufficient stiffness and strength sa as to contribute signif1cantly to Lateral load resistances, (~) the coupling beams are ducti~e and exhiblt stable hysteretic response,. and (c) the hierarchy of failure mechanism~ ,ls preferably such that the majority of COUpl1l1g beams J such as shown in Fig. 1 (b), will slgnificantly yield before the development of plastic ~inges at the base of the wal~s'.
p
Cons1dering the above, the following ~eneral aspects of-thin . -. link beams will be studied -fierein: energy absorbing capacity, ability
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to transfer shear forces, ductility, crack pattern~, ultimate strength,
and failure mode under cYOlic loading.
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FIGURE 1.1 TYPES OF EARTHQUAKE-RESISTING SHEARWALLS. (Ref. 3) (a) CANTILEVER WALLS (b) !WO WALLS COUPLED BY BEAMS (c) !WO WALLS COUPLED BY FLOOR SLABS
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1.2 BRIEF REVIEW OF,PREVIOUS WORK
The behaviour of coupled slab-shearwall structures has
attracted . a limited amount of research in the pa~t, 'hence relative1y
1ittle information relating to this subject i$ available. A brief
chronologica1 summary of the previous work in this area is presented.
In 1967, Barnard and Schwaighofer (4) presented the results of
tests donc on three 1/64-sc~~e epoxy models of 22 storey shea~a11
struqtures inter-connected with floor slabs. They found that the
entire bay width must be considered as the effective
Qadeer ~d Stafford smi~ (5) presented
'significant analytical investi ation involving . , computer ana1ysis of walls and slabs in cross-wall
slab w~dth.
the resul ts of a'
~in1te difference
structures. The
graphs, presenbed in Figures 1.2(a) through (ct), could be used to
obtain the nondimensiona1 slab stiffness, or effective width, based on
certain parameters such as bay width, corridor width and wall depth.
Howe~~r, no account was taken, of the wall's finite thickness, nor was
any information provided on the slab bending moments and shear streYs'
concentrations at the toe of the wall.
Later ln the same year, Chang (6) recommended that slab .&'
reinforcemen~ which is placed parallel to a shearwall should extend a y
distance of at least,one corridor width beyond the shearwal1 toe. His
findings were also based on a ffnite difference parametriè study.
In 1971, Mirza and Jaeger (7) reported on tests performed on
1/10-scale, 2 storey reinforced microconcrete coupled shearwall-slab
models. The specimens were subjected to monotoni~ally increasing
static loads until 'failure. No reversed loading.~n either the linear
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FIGURE 1.2(a}
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. 1 S f-R --------- -.
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• A
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0 ----+- c - - -,
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y
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PL~ OF SLAB AND CROSS-WALL STRUCTURE USED Bt QADEER AND STAFFORD SMITH (Ref. 5)
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1- C~RVES FOIl, k - - .
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lIê l "'<7\ ~ . 1 1 ; i 1~ ~~
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/'\1 V'~ 1 r ...... ~ __ J...~ .~
/ 't 1 1./ ~ '..< ' 1""/ .--- "'"
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// '--. .t' M ' " ~ - , ./::;;,........ , CURVES FOII !c.
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/ 03 04 Or: QO Q1 Qa
Vaille ot - . X· -
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Q) t :J 0
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01
t FIGURE 1.2(b) VALUE OF SLAB STIFFNESS NUMBER k AND Y IY ~ A
FUNCTION OF L/X ~OR C/X = 0 . (Ref. 5) e ( where El = kDL ~6{L+W)2 ahd y IY = (kL/(L~W) /6( 1- -v 2)(Y/L» ) e .
, ,
------------------~--~~-_ .. _.--
o
.'
•
- ->
o
to Il
Il
'7
Il
l
0 0
0
a ' f=
o~ 1= ,
01-f-
A= 01-
~ 1--
O~ ~ ~ 1=
2 0 ~ 1= 1-l-I-l-I-1-1-
~ 10 E
cU ::l C
>
§
§ ~ i ~
• 7
CI i= t: l-
~ 1-
~ l
~
2 1-
~ 1- i
1-
~
t 0.1
1
-,-
- 1 -
i 1 1
t _= 1 X
~\' 7
~'- VCURVES FOR k
\ 1 ' 1
~~ -~
~ ~ ,
~ '\ O~~ ~ . '1'\ 1'.' ~
\ , ~
1'\ "-~ :.,..._.-1-...
~-> --' ~ ~ "-~-~~9'" ., '\ I~ ~ K-~
V .. ~ "'-~ // \ v· .... .-/ ~ ./ .. ....-- -" l' ,
~ 1-
1/ ~ o,.y V' 1--' /- -' l// ~ < ./,.- ,,~
. ' .,'> • ,A' / r
/ ~'- CURVES FOR {t-
/
L/ 1/ ~ .' -/ ~/ lI'/ '/ /
/ 0.% 0.4 0.7
Value 01 ~ X
' '
la 0.9'
0,4 '
0,7
00
0:1
0-4
0-3 "1>-.... 0 cu :J'
O~ g
, o .•
FIGURE 1.2(c) VALUE OF, ~LAB'STIFFNESS NUMBER k AND Y IY AS A FUNCTION OF L/X FOR C/X = 1/7 (Ref. 51.
..
( where El = kDL3/b(L~W)2 and y Il = (kL/(L+W)2/6( 1- ~2)(Y/L» )
e ,
"
.. -'-
:
, \
(
'. -
. -
10
• • 7
0 0
0
0
0 ~
01-1-
01-
l-3 0
1-2 0
o~ E ~
;;
~ r
1-'
2
1 1
/
1- /
1 0.1
- 8
-
~
I~ 1
e 1 . -:-
'\--CtlRVF:S FOR k X 16
I
.' 1
/ V
III
/
~ ~ ~ ~ ,
~ ,,-" 0-
--~ " '-..::r--.... J.. ~" ~~" 1-
.1-..... "" ,~ ~t---~ i'\ v·' K K
, ... 1 ~
v< ./ ~ -- f).... ~";
1 ".., ./ ""./ ./ ~ r;'Y ~ lo--/ k -"-/ V" "'"
......... ~ .... l/ ,,". 1:';<
r-CURVES FOR !.f. 0/ V""" 1/
y
l;/ ' / f ... "
[//
0.:1 04 00 0.1
VQlue o1l X
-
-
0
\
. 0.7_.. oa
10
.0.0
0.8
0.7
0.0
, ,
-03 0 Q) ::J 0"
g 02
0.1
, J" ~
FIGURE 1.2(d) VALUE OF SLAB STIFFNESS ~UMBER k AND Y IY AS A FUNÇT10N"OF L/X ~OR C/X = 1/16 (Ref. 5) , , where El = kDL ~6(L+W)2 and
, \
y ri = (kL/( L ... W) /6( 1- -v 2)(Y/L» ) e
, "-
...
o . .
. .
'. r'
o
..
- 9 -
or non-linear ranges was performed. The shean.talls were found to ,
behave as individual deep beams, and failure occurred ln a
'shear-compression' mode àt the toes of the shearwalls. The authors
concluded that:
a) "With improved reinforcing details, the shear-compression mode
of failure can be,either delayed or eliminated to obtain a more ducttle
flexural fallure" ;and ., b) "A graduaI transition is noted in behaviour of coupled sh~ar
wall-slab structUres from cantilever action to frame action '!epeqdl'ng
on the relative stiffness ~ the connecting slabs"(7).
In 1975, Coull and E)_Hag (8) presented ~raphs similar to
those of Qadeer and Stafford Sm.ith (5) to Gletermi'nè the e ffect! ve
bending stit'fness of floor slabs coupllng shearwalls. The
force-displacement relationships were used to deterruine the relative
influence of wall dimensions and shapes (plane or flanged walls, and
box cores) on effective widths (Fig. 1.3). Wall thicknèss was.Qot a
parameter.
In 1976, Black et al (9) used the finite element method ta
improve on the results of Qadeer and Stafford Smith. The research
results showed large stress concentrations at the toe of the
shearwall. They included ~he wall thickness as a~parameter, and as a
result slab stiffnesses were generally 33% higher than thdse predlcted
by Qadeer and Stafford Smith's methods.
Schwaighofer and Collins (1) presented ln 1976 some design
recomm~ndations based on a theoretical and experimental study done by "
«;,,;,...:; Szalwinski (10) using the flnite element method and a, 1/4-scale
reinforced concrete model which was loaded through Its plas~ic range to
. '
c
l
, , ,
. - 10 -
2
~
1 1 X ) ~
IV r or r ---! z :-. ." ° •
1 1 • t c '-' l- I.! C
~ , tM FLAI;Crs )
lt ~
~
\ V f\ /
~ "'0 on ~ ~ 1&.
\ 1/
I Î\ 1/ !!r ... CIl ~
0He:1WU ,_ / X NO IUllCE:S
sa
g
o (H
f " / X ~ 1 >< If :;-~ ~
/i V ""--17
Î T T
~.o "l
~ -O!l
~ .Ob z: ~
V /
/ -
V ~t!'~}/
1/ IlOn.A~ v-/f
/~ • DATA Ç"OR K
" DATA FOR Yel'(
'" ~, '\ ~
"-'- '" "--.......; ~ t::
" '
III o
,.. o
N o
ô
0.5 Oô -
, .
.' '. (
VARIATION OF SLAB STIFFNESS FACTOR AND EFFECTIVE WIDTH WITH 'WALL 'SPACING FOR COHBINATIONS OF PLANE AND
FLANGED WALLS' (Ref. -8) , ,
, --
(
, l
/
•
0,
'\ - - 11 -
t'ailure. The stUdy was aimed at determitning the force-displ-acement, \ '
,r~lati~nshi~, 'braèkc patterns and steel strains in order to establish ~
both the effective ,width and the dis.tr~bution of stress couples 'ln the
'" slab. It should loadfng was mondt'onic, "\
&..:Id special CI>
t'lexuf'al or shéar re' nforcement 'Was not pla'ced acr"oss the door
'. opening. Th~ recormnendations stemmtng from this research will be
considered in grea detail in Section 4.3.2.
1
The mo comprehensi ve s tudy to da te was ~eported by
Taylor (11) in 1977 ,and' presented by Paulay and Taylor (3) in 1981. A
~ 15-storey prototype structure (Fig. 1,.4) of typ~ca.l plan (Fig. 1.5) was
chosen to study the impact of earthquake loads on such slab coupled,'
shearwall buildings. Although the prototype dimensions were
arbitrarily chosen, they are considered typical of New Zealand ~
condHions (for the purposes of this study, the prototype is ,also
considered typical of No~~h American conditions). Four 1/2-scale test
speCimens, similar' to the one shown in the Fig. 1.4 schematic view,
W'êre buil t with. various arrangements 'of longitudinal and transver3e \
slab reinforcement, embedded transversè' structural 'steel beams, slab
, stirrups, and composi te ,longitudinal beams. 'The dimensions >'and )
reinforcfng details of the test Uni ts are shawn in Figur,éS 1.6 and
l" 1.7. Special slab reinforcément was placed in the vicinity of the door
'r 1 ~ , ___ • ~opening based on the suggestions of Qadeer and Stafford Smi th (5) for'
equival~Il~ slab 'width. The first three slabs were reinforced
identicall~ excepting for the {einforcement in the wall toe region.
The fourth specimen incorporated a 'shallow coupI1.~g beam caat
~onolithically W'ith the slab. Of particular importance 1s Unit 1, on'
o whlch thia atudy is-based, where,~he, special longitudinal reinforcement , \
"
/ /
'/
'"
~
~
, 1
....
r-P-. ~l~
1 I-~~~~~~~U 1 J- .L '~~~~U l' ~
"r-~ , J
II~~~
o o o (\j
'It
1 ~ g~~ ~ ~~ .. ~
1
"
~~F==~====~~======~
\ 7000 11 S.O 7000 1 ~ "I~ ·loC .,...
<1
l
FfGURE 1.4
. ,
t-\
;-,
r
~
15 STOREY PROTOTYPE STRUCTURE ADOPTED 'V •
BY TAYLOB (11) AND SCHEMATIC VIEW OF A
TYPICAL INTERIOR BA y SECTION CONSIDERED
.. FPR' THI~ .STUDY. '
\ ,
fi,
.... N
i '
n
Q.
•
o
13 -
..
FIGURE 1.5 TYPIC.AL PLAN VIEW OF PROlO TYPE STRUCTURE
SY TAYLOR (Ret. 11)
..
"
(-
, 1
-
\
- 14 -
/ 1 UNIT t/
, . ,laD
1 UNITS 2 & 31
FIGURE 1.6
125
. ~ .... ~' DIMENSIONS AND R'EINFORCING' DETAILS OF TAYLOR' S TEST UNITS (Rer. 3)
.'
o
11
-
(, tZ
Xl
305 ~
rno~ 5:0 -:n30 DO~S50 -151)
~
3160
XF.J 25 ,
R6·5 st Jrrup5 <Cù 37crs tht 1 :D as uNis 2 &-3
morfCT \ D'X) speoal lransva-se steel o:ross 'MJII toes
"
Ca) Unl.ts 1-,3 cross-sections_ at wall eâge.' -
1
1475 150~ ~75
• Il ~ 0106120 1f.8) 000 5:0-3)6.)
010 in SJme ~f. p16 p:>sIh:ns oZ o_lxNe .=~Kl CDYer b strrrups
OD6lSSa -J060~ structural s.feel./ ITOrtr ------- - \ \ Rb·5 s1Jrrups, 6l ~ Dnfi) 5:D - 1520 1 '220 2-D 1 0
1 T 3100
(b) Unl.t 4 cross-sectl.on at wall edge.
Flgure_ 1.7 CROS~-SECTION OF TAYLOR'S U~ITS 1 - ~
,:
... -(\)
~ ?
.... ~ u o r-
'0
3,1-
3J
-, 1
~
III N ..-
s \ 1
~
~
U1
1
"
...-
- 16 -1
in the vicinity of the door opening was confined by stirrups ~paced' at
c 37 mm centres (Flg.' 1.7a).
Accordlng to Taylor (11), the purpo3e of the stirrups was to
"provide transverse flexural reinforcement as weIl as shear
reinforcement with respect to seismic actions". They were meant to
control "deformations and damage in the central region, punching shear,
buckling of the flexural relnforcemen t and dlagonal cracklng", and
enhanced slab ductl~ity.
The test speClmens were subjected to reversed cyclïc loading
wlth gradually increaslng deformatlons. Equal Jack forces were applied
horizontally at the top of each( shearwall, and the shearwalls were free
to rotate about the plnS shown in Flg. 1.8. The first tnree test
speclmens failed in puncl:\lng shear mode3, and the fourth Îailed in a
horizontal slidlng shear mode at the beam-slab junction. However, i t
was not clear from the .resul ts whether the stlrrups dld actually
, ' . , enhance the punching shear strength, ctuctility and deformatlOn to such
" an extent which would warrant theïr use in practical si tuations .
... 1 Taylor' s study lS, referred to throughout thlS report, and the
recommenda tions are dlscussed in d~tail in Section 4.3. 1.
1.3 SCOPE OF THE RESEARCH
This expevimental Invest1gation i3 the first in a series of
tests planned to study the behaviour of coupled shearwalls subjected to o
reversed cyclic loading in the non-linear ranges. This investigation' s
ultimate Objective 13 . to establish sorne design recommendations and
useful observations for the engineering profession pursuant ta slab
c coupl ing" of shearwalls.
o \
'000
~ ~ precast 125 thlck
- 17 -
1000 ' 580 1000
, ~ t t
wolls , 1
~
KEY
--..;"_'" jack forc.es
® loteral support
dose to(erance pin
prestress rcxj forces
o
----- mortar Jomt
1
1000
" t'
-
G> 0 .-.....
. -0
o o .....
0 ~
FIGURE '.8 SCHEHATIC Il.LUSTRATION OF TAYLOR'S TEST MODEL (Rer. 11)
c
- 18 -
This objectiva was pursued by testing three 1/3-scale,
reinforced' con crete models (the prototype being Taylor f s 15-storey
prototype struc ture) bas\d on the de:3ign of the 1 /2-scale m~del3 tes~ed
by Taylor. The only notable difference between the three mode ls in
this study was the, spacin~ of the stirrups wi thin the slab. \ r.
Thus l the primary concerns of' this investigation are: -'
1 i) To determine ,the effectiveness of stirrups within the slab r
corridor width in improving ·the per-formance of the- slab
coupled shearwall structures ......
. 11) To compare li theoretical (yield Hne theàry) strength
predictions with tes t resul ts.
Iii) To establish a procedûre for predicting the effective width
of a slab.
Iv) To Compare the hysteretic response of the' three specimens.
v) Ta determine' the effect of increased concrete strength on the
failure mode and the overall - response of a slab-shearwall
system.
m «
.'
o.
o
..; 19 -
"
r CHAPTER' 2
MATERIAL PROP8RTIES A~D TEST SET-Ur
This chapter describes the design of the model and Hs "limi tation!3 ,
similitude requirements, material propertles for the model steel and , ,
èoncrete, ,i,nstrumentation, the loadwg system and the specimen load lng
, history.
" .
2. 1 • THE MODELING P ROCESS ( ,
2.1.1 Choiee of _Glpmetr~c ,Scale
Typlcal scale factrJrs for several clas3es of struct.'ure3 are
presented ~n Table, 2.1 (15'). The appropriate range of OC..ll'c fJ,ctors
for a strength model of. a sLlb coupled shearwall structure l'j suggc:J tcd ,
as being between 1/10-scale and lILI-scale. However, "any glvcn modSl . . . be~ng bull t in a given laboratory has an optimUr.i geometric scale
factor" (15). Accordingly, the following'cnteria were considered in
chosing the 113-scale, test models for th13 study (the prototypè 13 .
shown in Fisures 1.4 and 1.5):
c The amount of laboratory space available. for such a . o
comprehensi ve, long-term test, and the lifting capac1 ty of laboratoty ,
li
cranes (1820 kg., 4000 lbs.) to maneuver the specill!en during" a!3sembly;
li) 11;
The displac.ement li('li ts of the load jacks (152 mm, 6 in.);
111) The mass densi ty distortions in such a test;
Iv) Inelastic stresses and displacements were to be observed.
If
c
, .
, ,
'. 1 •
,
"
Type or Structure
Shell roof Hi~way bndge Rcactor vesse! Slab structures Dams Wind elfccts
-20
. -. Elastic Modèls~
-1 \ .
Strength Models
TABLE 2.1 , ,
TYPICAL MODEL SCALE FACTORS (Réf. 15)
.. 0
fÎ
Concrcte Rcin{orcement
CAse S, $, Ss S~ S~ St
*1 Sr 1 ~ S, S, 1 2 *1 ! IlS, S, 1 lIS, 3 *1 *1 *1 S, Sr 1 4 ;*1 * 1- *1 S, s,,, *Se
. .
·TABLE 2.2 ~O;5SIaI.;E: DISTORTION~ IN REINfORCED .-CONCRETE MODElS (Ref. 15)
-~-'
. '
o
. ",
o
, , ~
... ---_ .... _._-~---"
21 ,-
Because the design of the three 1/3-scale models was based on
Taylor' S fU'st 1/2-scale test specimen, the actual scaling factor, for
c9mparative purpos'es between this study and Taylor',s report J is 2/3.
Thus it is submitted that the balance between r?inimizing deviations
from complete similarity in ordér to obtain the highest possible "
accuracy for research purposes and staying wl.thin the constraints
l'lsted above was achieved.
'2.1.2 Material Slmilltude // /-
"Any structural model must be de::ngned,' loaded and " lnterpre,t.ed
according to a . set of slml.litude requlrernents that relate the mod8'1 to \,
the prototype structurel! ( 15) . The requirement.s vary accordlng' to the
degree of simllan. ty bet;.{een the model and prototype boundary and
ini tial èOndl. tlons, geometry, and material propert les. Departures from
-complete similarity are frequently met ln 'modeling. Such deviations.
W'hether accidentaI, _ deliberate or necessary (when requued' modèling
méÎterials are not available, as in this st udy) are pe\mi t ted q.s long as 'l. ' "
thei~ , influenc~ ca n' be determiried.
Whife geornetrJ.c distortions must be minimlzed as explal.ned in \
the pl"evious section, "of greater:- importance to the structural engineer
iB the POSSJ. bility of permi t,ting 'dlstort.l,on in the reproduction of . the
prototype stress-strain char'acte-!" istics" ( 15) . For s:tatic, elastic
inod~ling, the similitude requirernents are summarlzed in Table 2.3. Ail
the scaling factors are functlons of the two inde pendent scaling
factors SE and SL and were derived using a dimensional analysis.
Such static, elastic. mQdeling may be used a.s iong a3 the model material
remains elastio within the model loading
\, , 1
...
'. , .. , - '
22
c 1 -. ;
~ Quanllties Dimensions Scala Factor
Matcrial-rclatèd propertics Stress FL-l SI! 'Modulus of elasticity FL-a S6 Poisson 's ratio 1 ,Mus densll>, FL-J Sil/S, " Sirain l
ûeometry " Lincar dimension L S,
Lincar displacement L S, Angular displacemeni 1 A~ L" Sr Moment of inertia L~ st <.
Loadins 1 \
Conccntrated load Q_' F S~Sr Lino load w FL-l S.s, ... <> Pressure or umformly --
distributed load q FL-" Sil Moment M or torque T FL SES' Shear force V F SI!S, .
'-
..
, \
, . TABLE 2.3 SIMILITUDE REQUIREHENTS,STATIC ELASTIC HODEI;ING (Ref. 15) -
,. . •
..
. .
m •
. \
o
o J"
"". ... ", ~
23
range and the Poisson' s ratio 15 the same as the prototype' s.
However, the above similitude requHements do not apply in a
,study of the t'ailure mode 1 capàci ty and inelastic behaviour of.a
reinforced concret'e structure. Ideally 1 the fallure crlterla for the
model concrete subjected to multiaxlal stresses should be identical ta
the prototype's concrete. Since this failure criterion is not weIL ~)
defined, the resulting requirements' are sbown ln Flg. 2.1{a) and column
4 of Table' 2.4.
When the model mate"'"!.als do not respond as ShOWh in the above
figure, vari'ous other distorted models must be consldered (see
Table 2.2) (only Cases 1 and 3 are shown ln Flgure3 2.1(b) & (c) and in
columns 6 & 7 of Table 2. tt Slnce Cases 2 and 4 requlre re1nforcement
made of material other than steel (15». As stated by Sabnls et al
(15) "it is necessary to utilize a distortt::d model approach when the ri
aval:lable concrete does not ha v"e Scr = Sc: = 1". Accordingly 1 the Case 3
scale factors were considered appropriate for th'lS study because the
model concrete strength Uft MPa) was significantly higher than the ~.'>..
prototype concrete str'ength (25 MPa): A summary of the scale factors
and the scaled model materlal values is contalned in Table 2.5.
Factors influencing similitude but not appearing in Table 2.5
are bond and maS3 densi ty • Bond has be~n shawn by Mlrza (14) to model
weIl as long as the selecUon of 'modeling materials 1 construction and
testi?g is êlone prudently. '1 t is submi~tte? that the3e criteria havr been met for thi:;! series of tests. Secondly 1 the maS3 density scale
factor in this study is Sq/SL = 1.711.5 = 1.13, Keeping in mind the
nature and relative magnitude of the loading exerted" on the speclmen3,
such a distortion 1s considered negligi ble.
/ (
\
-.
. "
c
., .
'" '---..
(b)
'ù
(0)
- 2/J -
/1 /1
~---~p
_--__ m
~~------~----~,
(., Concrtt. lbl R.lnforeement
-. "- --
/1 ----- ------------------------ /1
---p p
m
1'1
t trlft frp
tco-S,tem
(., Confrtt. (bl R.lnforeement
/1 )
_----m m I------p"
-~~----L.. __ --L_ c ___ ~ , f
,., Concret. Ibl RIlRforcem,nt
FIGURE 2.1 SIHILITUDE REQUIREMENTS (Ref. 15) (a) SIMILITUDE REQUIREMENTS
...
e
(b) CASE 1 :DISTORTION -SIMILITUDE REQUIREHENT (0) CASE 3:DISTORTED MODELS
-'--
...
Il
r .. ~
r;/, - 2!Ja ~
0 ~
, ,(. . \ i,
-/
••
, ~
~ Distorled Distorlct!
Praclical Model, Modcl. Tru!) Truc C,se 1 'Ca\e J
Quatllity Dimensio!, Model Model (Fig. 2.7) (Fig, 2.8) (1) (2) (3) . (4) (5) (6) (7)
! -----Concrete 51["(:56, cr. FL-l S. 1 S" S.,
oc Conérele slrain, f. t 1 S. S, t> Modulus or concrele. Ec FL-2 S" 1 S.,IS, S.IS , ;:; ->. Poisson's ralio:V. 1 1 1 ' 1 t>_ p: .. ..:.8- Mass dcnsity. P. FL-l S"IS, lIS, S.IS, S.ISL .~ e Rcinforcing stress, rlr FL-l S. ] S .. S. ,,~
;:; Reinforcing strain, f, 1 1 S. s. ::E' Modulus or rein forcing. Er FL-l S" 1 1 1
Bond stress, U FL-l S. 1 S • • ..1a
~ Linear dimension, 1 L S, SI, .\t S, Ü Displaccmcnt. 0 L S, S, S,SI S,S, E 'Angular displaccm~nt, p 1 1
S; J s. 0 u
Area of rcinforcement, A, L2 sI sI S.S1l5. ' 0 .-,
tIC) Concentratcd load, Q F s"sl si s"sl s.~l c Line load, IV FL-I S"s, S, S.S, S,,5, :a n Pressure, q FL-l S" 1 S" s • .3 Moment, M FL s.sl s7 S.S? s.sl
), -Function or choice of dislorted reinforcing nrea.
TABLE 2.4 SUMM4RY OF SCALE FACTORS FOR REINFORCED CONCRETE MODELS ( Ref. 15) ~
o
/
Tl)
Quantity
25 -
(2) (3)
Distorted Taylor's
Hodel" Unit 1
Case 3 Values
~ Scale
Factors
, (4) (S)
Corresponding Unit 1
'Olstorted Actual
( 6)
per-cent~ D~fference r?
Model, Case 3 Values Between,
Values Col. 4 & 5
--
.
Concrete stress 1.7
Concrete stra in 2.0
M0dulus of concrete 0.85
Reinforclng ~ tress, 1.7
Reinfor<? ~ng stra'in 2. a
Modulus of reinf. 1.0
Linear dimension
Displacement
Area ôf reinf. 1 .,9
. Concentrated load 3.8
25 MPa
.• 003*
15 MPa
.0015
27,500* 32,350
345 MPa 205 MPa
.002*
200000*
.001 ,
200,000
• assumed value:;
36 MPa 140
.003 100 ,
25,.000, -23
205 MPa o
.001 o ,
200,000 o
45 mm2 . 10
** based on information from Figures 1. fi and 1.7
Table 2.5 SUHMARY OF SCALE FACTORS AND SCALED MODEl VALUES
•
26
. ' " ,
In 'order t~ compare the results of this study to tha t
raylor's, the differences in the methods of load applic~tion and
specimen displaceme~ts must be dealt ·with. To convert Taylor's wall
.. "
rotations (9) to the rel<;ftive vertical wall. displacème,n\<,)l (~) (sce '
Figure 2.23), each 1- RAD of rotation is equivalent to a relativ,e
vertical displacement' of 2580 mm. Simlldrly, each 1 kN horizontal jack ,
load on ,appÙed at each shearwall in Taylor's test is ~quivalent t.o'
1.18 kN net vertical fOr'ce (V) in this stydy (see Fig. 2.24).
...
, ,
2.2 ,DESCRIPTION OF THE MODEL
2.2.~ Geometr1
, The 1/3-scale reinforèed conorete (test) model used in -thl ~ , ,
study is shown in Fig. 2.2., The prototype was Taylor,' ~ first 1/2-;;3cale\
model (unit 1). 1
Certain assumptions put forth by Taylor will also ap(:ily to U\i3
1 experimentai study (11):
'The use of precas t wall segments, which were mode'ra te 1 y
/
stress'ed ' during the test, instead of ca3t-in-p]~ce
construction' is unlikely' to af.fect slab perfor~an('c
significahtly. '
(U) 'Failure to accurately model dead and live load actions h2.:,J
- only minor effects on" the failure mechanism and the ult~ate
moments due to laterai loading. Th~ use of a longit~dinal'
.J
lipe of symmetry is therefore reasonable in the-model.'
, ,
o , .
"
. , .
c ,1 .. 1332
, \
, -
" 0 0 0 0
,
duet / 'post-te'nsloning
~
\ FIGUA~ 2.2
c
- 27-;
~I"' 386 ~!"' 1332
Elevation
3050
1
-
- , . .
. ,
J 1 o· 0 0
13~_ 354 l 354 l , J J J J
J
,
Plan
l DIMENSIONS OF THE MODEL
-
,
0
354 ES 1
1
.
o M ,...
lT
o 0) 0)'
o 0)
01
LO co
..
. ,
o
- 28 -
, ,
,qii) 'The' model is of sufflcHmt length so that the free end
boundary condltions of the model slab are, 0 f minimal
importance. '
, Uv) "-forces in the slab are gen8rated as. 'Insignif.lcant separatlon
a consequence of small dlfferences in yield moments at wall
,1 faces. ' "
(v) In deslgning the slab, moment red1strlbution red~ced the
negatlve support,moments by 20%.
-(Vl) For the lateral lQad analysis, the crJ.cked ,slab stlfrne~l:J
. value was assumed ta be 50% ot tne uncracked stiffnc33.
It must be noted that unllke Taylor's experlmenthl program'
where the Jack loads were applled horlzontally (hence the reference to
'lateru.l loadwg' ln .asswnption- Cu) above), the load was appJ,.led
vertlcally io thlS 'stud~ (reter' to Sect~on 2.4). Nevertheless, the ~s~
of the'bay çentrellne . \ ' .
(Flg. 1.5), as a longlt~dlnal 11ne of symmetry for
làtéral loati resistlOg' actlon:;; lS reé}.30nable, "as i3 shown in
Section 3.3(f).
, ,
Each model tested was a comblnatlon of f1ve separate, element3:
a 3050 x 2065 mm slab and four seperate 730 x 1332 mm wall segments.
The model walls were pr~cast an~ reused for aIL three tests in a manner
·similar to that used by Taylor. For each test', the' spec1men wa3
assembled . .-as 'shawn in Fig. 2.3. The walls and the slab were clamped
snugly tog~ther by t~gh~ening the nuts on elth~r end of each 19 mm
diameter bhreaded rod which pas3ed through dUCt3 placed in the wall.s·'
and through small openings in the slab. Each rod wa3 then 3ubjected' to \
an averag~ postteosioning force Qf 33 kN by having the out rotated one
\
l
'.
~
....
~ 5mm
~
",
r
--nut a
.'
19 mm ~ threaded rod
/ ~ - L--
~ 1-. ~
° t
;
\ \
'--
lortar 1
01"\ ..--f-..
/0 25mm ~ hole for
lifting purposes
. ,
'1P' /fi \
~
/'
'---
. .
P"
.
25 mm ~
135 ~~
alumlnum duet (ungrauted)
• .
,
~
1
76.2x 16.2x4. 7 a mm. H.S.S.
354 354 354 ~ ..... -- 135
~~
1
76x76x9mm platè -'.
n~~ (/th 25mm ~ hale
.-Lb..... _
° .
.
:.-. t----
0 .
1
\ \ ',1'"
152.4x101.6x6.35 mm H.S.S.
FIGURE 2.3 ASSEMBL y OF PRECAST WAll SEGMENTS
.'" r
-~
'.
"
~
f'
./
N <0
\
\ \
\
- 30 -
full turn af~er the "snug" position. This insured not only a tight fit
between each wall and slab, but it also simulated the structural dead
loads that would be experienced by the walls in an actual building , ,
i
structure. Overall, thl3 metWbd of assembly led to significant economy
and greatly facilitated the construction and handling of cach test
specimen.
2.2.2 Material Properties
Three sizes of deformed steel wir,e were used; theH
specifications are given in Table 2.6. 07 deformed Wlres werc used as f~
longitudinal and transverse flexural reinfcrcement,~ .03 deformed ~irc5
as slab stirrups, and 08.5 deformed wir~s w~re USèd as wall
reinforcement. AlI deformed wlres were originally cold-worked and
Bar Oesig~ation Oiameter Weight
(mm) (g/m) 1
, 03 4.95 152.3
----
D7 7.57 354.8
~
D8.5 8.35 IUO.6
Table 2.6 DEFORHED WIRE PROPERTIES
o .. "\ ,
- 31 -
exhibited brittle behaviour as shown in Fig. 2.4. The D7 deformed
c wires were subsequently heat treated at 650 degrees Centigrade
(1200 OF) for one hour and thirty minutes (Fig. 2.5) and then air
cooled to obtain the desired ductil~ty and yleld strength (F~g. 2.6).
The D3 deformed wlres, after being bent into the desired stirrup shape
(Flg. 2.16), were heat treated at 800 Oc for one ho~r and flfteert
minutes and then alr coolèd. The D8.5 deformed wires were not heat
treated. ,
The cancre te was pro Jlded by a local ready-mlx supplier and
conformed to the following speciflcatlons:
1) Hlgh early 'strength Portland Type III cement
,2) 35 MPa speclfled strength at age 28 days
3) 100 mm slump
4) maxlmum aggregate Slze of 10 mm
5) 4 to 6 percent alr entralnment
Although a lower maximum aggregate size would have been
desirable due to the 7 mm specified slab clear cover, the smallest size
available was 10 mm.
'. A typical concrète compression stress-strain curve appears ln
Fig'~ 2.7. Included with the figure are th~ concrete properties
obtained from tests performed on the twelve 100 x 200 mm size and 150 x
300 mm size con~r~te cylinders cast wlth each specimen. " \~: l "
... . "
'-"-. "~ ..... ",
"
"
- 32-
i.
600
500
/ /
400 \ fS
300
(MP'a>
200
100
.001 .005 .010 .020
C concrete (mm/mm)
FIGURE 2.4 STRESS-STRAIN CURVE FOR
'0 COLO FOR~EO 07 OEFORMEO WIRE:
"
c
.,
c
1300 ,
1200
1100
TEMPERATURE
1000
(:±25 ·F)
900
800
700
o
heatlng rate of
400 "F/hr.
oven preheated
to 800 oF :,-1
1 2
TIME (hrs.)
cooling rate of
400 "F/hr.
air cooled to
room temperature
3
FIGURé 2.5 HEAJI TREA TMENT OF 07 OEFORMEO WIRE
"
[,
0-'
'., \. 250 -
200 -
150 -
fy .
(MPa)
100 -
50 -
, '
.'
...
~ Long.Steel
fy
(MPa)
unit 1 Il 204.8
unit 2
Il
214.3
1 unit 3 213.6
.001- .003 .005
Csteel
J v
Stlrrups . f
(M:a~ ,
242.8
234.3
(mm/mm)
. ---"
'allure v n
-.lIIo. ~
.040
·0
1 \
FIGURE ~ 6 SïRESS-STRAIN ClJRY1= OF rlEAT TREATEf? 07 :JEFORMEO WIRE , t' ~ __ ~_~J __ ' ~
\
,
. 1 (.J ~
1
..
(
. "
40
so
fi -C
(MPa)
20
10
. '.
. - .
.001
"- 35-
;
unit
unit
unit
f: concrete
f' c ft (MPa) (MPa)
1.1 . 1 36~4 2.8 -
2 36.6 2.3
3 37.3 2,3
.002 .003
(mm/mm)
FIGURE 2.1 CONCRETE COMPRESSION STAESS-STRAIN CURVE (typicat)
o i
o
JI
o
- 36 -
" Design of Reinforcement
~
'The configuration and the type of reinforcement used for each
specimen is shown in Figures 2.8 to 2.14. Thè main differe~ce between
the three units was the spacing of the shear reinforcement. Stirrups
in Unit were spaced at a distance - of 0/2 (23 mm), normally the
maximum spacing for any regularly reinforced concrete beam. Units 2
and 3 had no stirrups and a stirrup' spacing of d (46 mm) respectivelY.
The longitudinal and transverse flexural reinforcement was
identical in aIl the slabs. The quantity of the longit~pinal
(j>
reinforcement was based on the lateral seismic load analysis of the
15-storey prototype building by Taylor and on the recommendat~ons by
Qadeer and Stafford Smith (5) .. The SAP IV (Structural Analysis
Program) ~as used for computer analysis of the prototype structure,
bas éd on Zone 3 seis61ic loading' (13), to verify the design of the
specimen. Within the stirrup cage 2.07~ longitudinal reinforcement was
provided, 0.44% was used outside the oage area, and 0.76% was the
average when considering the entire s'lab width. A minimum of 0.65~
reinforcement for flexural sections P min = 1.4ff y) is suggested
by the Canadian Standards Association (G.S.A.) (12).
Using C.S.A. procedures, each wall segment (Fig. 2.13), was
designed to wi thstand the 'anticipated maximum shear and flexural
capacities of the slab. Since the performanoe of the walls did not
comprise part of this investigation, they were overdesigned to ensure J c'
their structural integrlty throughout,the experimental program. ::
1 .. j
'''' ....
(
" f
, --~~--- ,;;
~. ~
\
2065
205 205 205 205 8 at 50mm 205 205 205 205 p 1
~
1 ~ -.. , 13.5 13.5 1
49: d l -1-:, : - : : t: e: ! ~J : J-03 ~tlrrups: : t : 1 } 7 '\
o
..
~
transverse relnforcement 7 mm'clear caver
07 lon~ItUdln.' salsmlc ralnlorc.m~(j .-, J "
d
shear watt ~
~
" '-
Unit 1 : stlrrups al. 23 mm (d/2) c;lc
Unit 2 no stlrrups
'" Unit 3 : stirrups at 46 mm (d) c;tt::
... ,
.FIGU~E 2.8 CROSS-SECTION OF UNITS 1, 2 AND 3 [/
.'
.-
o
"
(..)
..... 1
• 0
.j,
'.'
- 38-
. .. 07 bars 07 bars 07 bars -
st 335 mm <;A: a 335 mm c;..i: at 335 mm ~ ,
bottom only / tv & bottom,/ top only t 17.5 '\ / '
) " :0
1 ! t' "
1 / 1
[ 1
" r 1
! 1 .0 1
1 J <
1/7 . f 1
0 . , r
! 1
o
1
,QI "
LI J
700
~ 1 .... '1 ,
.' 1 (, (
Q1 1
r-- ,
" 1 )
1 1
OJ , 1 1 .. 1
, 1 1 \~
. rOI
\ 1
1 l l, .1
1°1 1
1 1 1 1 l ..
• seismic remforcement
stratn gauge locations , '
o FIGURE 2.9· PLA~ VIE~ OF FLEXURAl ·REINFORCEMENT IN UNITS "J. ,2, AND ~ { , ,
(
, "
--'.
:
c.
. FIGURE 2.10 ,
FIGURE 2.11 1 -.,
o
" 39
SLA~ REINFORCEMENT IN UNIt 1
":-SLAB REINFORCEHENT IN UNIT 2
o
.. ' - 110'-
l'
, .
FIGURE 2.12 SLAB REINFORCEMENT IN 'uNIT ~ 1
,0
0-, -FIGURE 2.13 TYPICAL SHEARWALL SEGMENT - REINFORCEHENT AND POST-TENSIONING DueTS
(
c
'.
, .'"'•
~
.' ,
r i, ! 1 1 .'
F!GURE 2.14
41
,-
'.
'.
'ENLARGEO VIEWS OF STIRRUP CAGE IN JJ1i~T, 1
. ,
-:l
o • 1
· .... -----
, ' , '
, -
, 2: 3- INSTRUMENTATION ,
The instrumentation used ,
for Unit 1 was modified for' Units 2
.and 3 for two specific reasons: 1) the slab transverse deflection
pro,f~le in Uni t was symmetrical about the shearwall centre) ine (reCel'
to Fig. 3.26); 2) some electronic strain gauge data collected from the
lqngitudinal flexural reinforcement w~s not satisfactory. Thesc changes
will be discussed below. Note that the, ac?uracy of aIl measurements 13
mueh higher than plot resolut-ion in the figures used' to ' represent the
test results.
il. '" •
2.3.1 D~al Gaugcs and Linear Variable DifferentiaI' Transformers
Due to the ~nusually large qua'nti ty' of itlstrument?ion needed'
'J for this experiment, a combination of dial gauges and Linear Variable
DifferentiaI Tragsformers (LVDT) were used to obtain the displacemenL
profiles and the ,,'
forc~-displacemen~. relationships: Figure 2.15
illustra tes the location of slab instrumentation. As mentioned
previously, the instrumentation layout was cha~ged for Units 2 and J
because' of the symmetry of the transverse deflection profile. Other 1
dia~ , gauges monitoring wall movements were, removed ,when the wa]"]
co'uP.ling system functioned . as expected in ·Unrt 1. D~al gauges 3 and II
remaineq oeneath the north wall'to monitor ariy rotations. , ,
2.3.2' Load Cell~
6ne 333.6 kN, (75,OO'b 'ib.) load cell above each load jack was ~ ~ r
us~d ta determine the app~ied load (Fig. 2~19).
.,
..... 43-
a 0
"
~
l<I4 a 0
,
0 0
650 ./.
650
"'" dlal gaugo under wall
o LVOT
a a Q 0
,
.
0 0 0 0
000 0 0 0
3~1 ..... 0 0 0 0
1 4
0 a 0 0
D D D 0
0 0 0 0
--l' 1 1 o dial gauge
linè E F G H 1 t 1 1
0 c 0 D C 0
" 0 0 0 0
0- 0 0 0
,
_D- o 0 0 D 0
!'IC _oorth, .. , ~ 0 0 0 <>
'.
, ,
, ,
, 0 ,.
1
t"'I.
,
-
, ,
-
0 5
, -unit 1
0
650 650
C ,
il ~< [l
-
. unlts 2 & 3
.: ,
0
~ c
6
c
20
610
315
135 -lino A
3'15 -' B
315
-c ,315
20-0
-II·T 32
0 *20-0 315 ' ,
i -t- - C-----
315
-- -8 315
o I-~ line A , -~ 135
! -t-
945
o !=r= 20
FIGURE 2.15 DlAl GAUGE AND l.V.o.T. LOCATIONS
m -
'.
II
"'i>' .. ' -------------
. - 44 -
2.3.3 Strain Gauges
Electrical resi-stance t'oil strain gauges (5 mm 'gauge .length)
on both the longitudinal ·ô
from the s train
slab relnforcement and the
, st~rrups. The wiring gauges to the Optilog data
'processlng unit was placed beneath the slab in order ta leave the top
surface unobstructed. 1
Fort y s train gauges were used in Uni t 1 aiong the wall cen~re
lines on both the top and bot tom layers of the slab rein forcement where
yield lines 'were anticipated (Fig. 2.9). ... . The da ta obtained for th<,
longitudinal reinforcement was gen.erally acceptable up t6 yielding.
Due to the l1mited reli<.ibility of the gauges, which' depended on crack
loca ttion and size, demec gauges (see Sec tion 2.3.4) were used Ins tead )
in Units 2 and 3.
Strain - gauges were installed on the vertical and horizontal
,
'legs of selected stirrups (see Fig. 2.16) in an effort to determine the
participation and effectiveness of each stirrup in resiBting shear.
The lIle'th~d of protecting each strain gauge from electrical
leak::- and mechanical damage is illustra ted in Figure 2.17. This .method.
meri ts mention since less than 5 percent of aU gauges werè damaged
prior to the initial loading of Unit' 1, much below the initial
expectation of 30% based on previous experimental tests using such
gauges. The majority continued to function well. beyond first yield,
albeit inconsistently.
2.3.4 Demec Gauses
In this study, brass demec studs were ·used to monitor elastie
and plastic strains in the longi tudina). '~~rection on the top and bot tom
o
C
.'
"
c
~ ...
,
corridor ~ 1
1 ...
1
1
S1
,
. s ymmotrical
......
... 1 po 1
1 f 1
1
,
1 ..
-
S2 ~~ 1
1
unit ,
~S1 S2
tS9
unIt 3
'\
- 45-
23 mm c/c 140 c/c ~I'" ..
, t l t t , ,
, ' , i l" nqrth wat' <
, , t l' , '
S4 S5 S6 , sl7 S8 "'::. ~
i l' 'f 1 ,
, , r
* 1 ,
l' 1
• strain ,gaug'o
46 mm G/c --, 'r '" ,
l ,
~dud 1 t '.1
JO t 1 ,
~3 ~S4 S5 S6 S7 ~S8 ~"-
,1 1 , " l • 1 . , ,. 1
1 t 1
• S9 on horiz,?ntal log of stirrup
, 308 ~I
03 stirrup
FIGURE 2.16 STIRRUP DIMENSIONS AND STRAIN GAUGE LOCATIONS
o
........ _. __ .. _._-----------'~-----------------------------
; ,
"
"
- 46-
.'
M-Coat ,G -mochanlcal protectiom , , '. ,. .. "
-also Pfotocts agalnst
, ,watEH, olls, solvants, etc.
, '
M-Coat B -primer to Împrove
M:"èoat 0 -m0istllre .barrier oond batwacn vlnyl
"
-prevents' ~Iectrical leakage and M-Coat G
-2 conts apphed
lead WJrc to Optllog
: / (vlnyl co~tCd) , ,,- . :::;:::~~
'\ termmal
Condltioner A (acld)
Neutralizer 5 (base)
07, 03 .de1ormed wlre.
" 1
used to prepàre reinforcing surface
, (Reference: Intertechnology, Ltd .. Montreal, Canada)
FIGÙRE 2.17 STRAIN GAUGE PROTECTION
(
c
- 47
slab surfaces, and on the bot"tom layer or the longitudinal slab
'reinforcement (Fig. 2.18). The targets were not placed on the top ,
layer due to placement aifficulties. A 100 mm demo,untable lIleéhanical
strain"gauge, with an equivalent strain apcuracy of .0001 mm/mm, was
used to measure the change in ,the distance between these targets. A
, typ1cal strain prof'ile 1s given in Fig. 3.29.
, 2-.4 LOADING SYSTEM
The elevation and plélo v1ew of the loading sys~em are sl)own iri
Figures 2.19 and 2.20 respectively. The entire specimen was, ele~ated
'appr?ximâtely a half meter above the strong floor to ensure" adèquate
. space for the load cells and jacks underneat~ the sou~h w~ll, and to
'provide a convenient access to the ins trumentation' directly' underneath '1
the slab~ •
The north wall was fixed to the stron~ floor while the south
wall was fTee to move vertlcally. Lateral stability for the fmti re
unit was providea by small S75x8 structural steel beams (liS Shapes")
clamped to the north wal1 both above and below the slab. A 2 mm gap
was provided between the south, wall and each S Shape to minimize the
sliding friction. The S Shapes were designed to carry a conèentrated
horizontal force at the corridor centrefine equi valent to 10~ of the
anticipated maximum vertical shear force (V), with the maximum
transverse horizontal deflection restricted to 5 mm.
The south wall was moved in a direction parallel to the north
wall by means of three load jacks. Two of the load jacks were placed
along the corridor centreline to apply the shear force (V), load
.'
o
o • J
48-
a demec gauge on bottom relnforce'ment .
o demec gauge on concrete, top and bottom l 1332
north wall
, ,
CI o
a o
, Q, o
1
~ ·1
o a
, a o
Q • 0
Q
o
Q
o
o Q
slab edge
1-50150 l 0
a 0
Q
o
CI o
o o
"
0
0 0
'II o
o o
o CI
FIGURE 2.18 DEMEC STUD LOCATIONS
_935 -920
_a~5
-a:zo
"
Omm
"
q
J
"
north wall
corridor
~
1
" 1
1·
S75x8 ./
~I---r~--~------r=r=r===~======~==~ , I~
l' H.S.S.
load cali 1
load Jack
( floor
19 mm ~ threaded rod
FIGURE 2.19 ELEVATION OF LOADING SYSTEM
•
fI\
9 mm 590
.-
'/
~ <0 J
r
o
,
ij.
base plate \
W310x118 L
01 I~ f
7-' 1
55x~5x6 an lIa
.
"'
.",
, .
-1 .
. ,
/
(.
~
t. ,.fi
-...:
, , , -
r
.' , ' . , . ~ -
" - . , . ' ,
. 2 mm plate ' . "- ~mm gap
....... .t -....,
f!orthwall 1 , l - .\..
"
S75X( . ,
" :
,
" ,
- " . , -, û ,
\,
FIGURE 2.20 PLAN VIEW'OF LOADING SYSTEM .of
§
o 500 1 mm 1
1
,
~!J. '1
l ' ~~ Ire
r 1)
spacars
~~
. )
.~
Ct
"'--~ . \ "-.
(Il
o 1
'.
-- 51 -
c ..
(
FIGUR~ 2.21 END VIEW OF SUPPORT STRUCTURE AND SPECIMEN (tf:.
1 •
)
•
..
c FIGURE 2.22 SIDE VIEW OF SET-UP PRIOR TO LOADING
:
, ~l
. 0
-
, - 52
"
f /,
\ jack 1 below the holloN structural section and la ad jack 2 directly
beneath the strong floor. For upward displacement, load .Jack' 2 wa,s
disengaged and load jack 1 was utilized. For dawnward d~~placement,
load jack 1 was disengaged and load jack 2 pulled o~ the 19 mm diameter
threaded ~od which passed through load jaCk 1 ta the hollow ~tructural ,
section. Load j'ack 3 carriéd the unit' s partial self -weig~t only, which
13 approximately 25 percent (5.1 kN) of the specimen's total weight.
The vertical ?~splace~ent of the walls, as opposed to the
rotation method used by Taylor; doe~' not alter the type of forces
exerted on the slab. As iIIustrated ih fig. 2.23, thd' relative
movement of the two shear wall toes (polnts 8, and 82 ) is the same,
whether both waiis are rotated thro~gh an angl'e e about points Al, ~~d .
A2' or s'imply displaced by ile in' the longi tud~nal direction of the
wa11s. 'While both methods of loading are acceptable, the chances of
introducing unequal horizontal forces within the siab arE! red,UÇ!ed I;>y. , "
the vertical dis placement method.
The net force, or shear forpe (V) as mentioned in the p~eviou3
sect~on, was used as the 'force' in the force-dis placement graphs in .h
Section 3.2. 'T'ho ...... - positive (upw~rd) net force was,obtained by
SUb~~~cting fh~ uni~'s partial self~weight (~.1 kN) from the reading in
load cell 1 (Fig~ 2.24) •. Conversely, 5.1 kN had to be added to Lhe
reading in load,cell 2 to obtain the negative (downward) net force.
The 1 relative vertical' rooyement of the north and south
shearwall toes constituted 'cjisplacement' (il) (le. the reading of LVDT',
4. minus that of LVDT 1, see Fig~ 2.15) •
, .'
"
0.
, ,
c
-
1
.' 1 '
,~.. f
-,53 -"
.~
" . "
, ' 1 wall 1
1 . f <>
"
t , 1
J . 1
wall 2 "
-
,
. 0,
f
f 1
J
"
'0
FIGURE 2.23' RELA'tlVE MOVEMENTS' OF'SHEARWALLS
SUBJECTED TO LATERAL LOADING . , \ '
1 l, i
,1
.. ,
, ,
o
'.
. ! •
. '
"
" ,
- "
-~. - - -1.
1
, -1
north wall ,
,
, .
, ,
'/I/(''''''''' / /""" / / // / // / / /.1
l '
. -• r 1 ,
,
, j
1, (flxed) '/"" / /"',( /" /" / / / / / / / /",
, , , ,
-'-
, ,
- 54-
1 -~
s!luth waH
-~
\ , , ,
L_
~
1
,
t v = fo~ce exorted by
Iqad Jack 1 -
dead load (O.L.)
\ ,
-'/
,
-
, "
,~ If V· = force e~erted by
load Jack 2 + D.L.
,
,
-
, • 0
,
t O,L.
t D. L. .
,
. " o FIGURE 2.24 ILLUSTRATION OF FORCES EXERTED ON SOUTH SHEARWALL "
~-------~ -~---- - - . - -
(: /
) -
c
55 , ,
2.5 TESTING PROCEDURE
(
Taylor's loadlng progedurej ri 11 us trated in Flg .. 2.25, was
followed for aIl thr~~ specim~ns to facllitate the comparison of
re3ults between this study and Taylor's findlngs. The procedure
, consi.'s ~3 of a seri~s of' impo~ed, deformations with progressi ve'ly
increasing dis placement ductilities. The intermediate 'elastic' load
cycles were included to" observe the effect, of each displacement cycle ' ,
on the slab ooupling st1ffn,ess. The 20 kN peak va.l-ue fDr these "Cycles
ta 60% Ultlmate" is nbt 60% of the ultlmate load predlcted by yield
line theory (46.8 kN). The 20 kN value was chosen as follow3: the .. equlvalent vertlcal load to the 24 kN horizontal peak load \used in
Taylor's "Cycles to 60% Ultimate" 13 42.8 kN· , then, uSlng an elastic
2 2 . . scale factor of .444 (SESL = 1.0 ( .667 ) = .444, ,Sée
Table 2.3), the required load is calculated as 19.02 kN· , thlS value,
for simpliclty, wa~ rounded-off to 20.0 kN.
A d.i,splacement ductility of 1 corresponds to a relati~e ~ ,
verticaf dis placement ( il ) of 2.8 mm. 1
The following test sequence was used for each 'load step: - - --
1) a parall~l displacement of the south wall with respect to the
north wall was selected;
2) then the load jacks were adJusted so that thi~ new dlsplacement
was achieved;
3) the load cell, LVDT and strain gauge readings were recorded
electronically using an Apple IIe personal computer, and the
Optilog data acquisition system;
{Steps 4, 5 and 6 were,perf9rmed ortly at selécted load steps)
• 4) all dial gauge readings were recorded; , .
,
o
13
11 1
9
"7
5
3
DISPLACEMENT
DUCTILITY
-3
'-5 1
-7
-9
-11
113
~~\
'-23 25
cycle number ---------17 19
11 13
5 7
12 14
18 20
24 26 - - - -Ioad controlled cycles to 60%
of thecrellcal ultlmàte load
F!GU~E 2.25 LOADING DETA~LS
,..
35 37
:29 31
",
30 32
36 38
.0
:.1
<n 0)
1
. .,.
c
- 57 -
, "
5) the demec target readlngs were recorded manuallYi
6) crack patterns were marked and photogràphed.
2.6 PROBLEMS ENCOUNTERED DURING SET-UP AND TESTING ,
The following minor problems were enoountered during the
preparation J lnstrumentation and t.estlng of' the specimens:
il, The concrete supplied by the local ready-mix company for Unit 1
bontained aggregates whlch were up to· 50% larger. than the stipulated
maximum Slze of 10 mm. The problem was rectlfled for Units 2 ar.d 3.
b) The n6vth ~hearwall exhiblted mLnor rota~ions durlng testing~
Since the relatl ve movement 'of the north' and sout,h shearwall toes
constituted 'dlsplacemen~', the rotation effeét was insigniflcant on
the force-dlsplacement'results. Howeyer" the movement was accounted
for in th~ longitudLnal and transverse displacement proflles. , 1
c) , The force exerted by load jack 3 (Fig. 2.19) to keep the south
'shearw~ll horizontal as load was applied ln load Jacks 1 or 2 was not
constant throughout each test. A 20'" • fO ~hscrepancy was encountered
du~ing the init~al load;ng cycles. The value decreased to 5% in •
, 1
subseque~t cycles as the specimen stiffness decreased.
\
T
' ... ~ 1
, -~ ... - .. 1 \
, .
-J'
o
..... __ ._--_._-----
CHAPTER 3
EXPERIMENTAL DATA AND DISCUSSION OF RESULTS
, "
\ 3 ,deals with data from the experimental program and i3
subdivided into the following five sections: crack propaga t ion,
force-displacement results, slab deflection pro'files, longJ.tud'wal 3te~'1
strains and performance of stirrups.
The first 1/2-scale model tested by Taylor (11), de3Lgnat~d b~
Tayl~r as Unit 1, 1s the prototype for the three specimens an~ly~cd Ir
this rep~rt and will simply be referred to as 'Taylor's Unit 1'. "
3.1 CRACK PROPAGATION' , .
1 The series of photcigraphs in Figures 3.1 to 3.19 ill~strate the
cracking sequence'in each unit from initial loading to tailure.
The cracking pattern in Unit 1 and Taylor's Unit are nearly
ldentical, though there we~e fewer c~acks in Unit 1 (the smafler scale . (
model)' as expected. Such decr.eases in the total number and width of
cracks as the model size diminishes have been reported by Mirza (lit) and
discussed by Sabnis et al (15).
:Primary yield 1ine cracking (le. the yleld lines along Whlch the
" largest slab rotations would occur) first appeared near the shearwall toe
area and propagated toward the slab ~dse3 and paraI leI to the wall face
céntre11ne as anticipated (arrow- in Flg. 3.1). ,
However, the paths were
" influenced by the location of transverse reinforcement
\
c'
c
, \
i'
- 59 -
\,
FIGURE '3.1 PRIMARY YIELD LINES IN UNIT
FIGURE 3.2 fORMATION OF SECONDARY YIELp LINES IN UNIT l .(cycle 5, p = 3>
\. 1
o
\ \
60
FIGURE 3.3 TORSION CRACKING IN UNIT (c y c le 8, }l -:: r 3)
FIGURE 3.4 CRACKING AT TOE OF SOUTH WALL IN UNIT " (cycle 17, il :: 7) ,
o
c
- 61 --'-
FIGURE 3.5 CON CRETE CRUSHING AT TOE OF NORTH WALL IN UNIT 1 (cycle 21)
FIGURE 3.6 FIRST SIGNS OF TENSILE MEMBRANE ACTION NEAR THE SOUTH WALL IN UNIT 1 (cycle 23, p = 9)
"
l ,
o
'.
62
"
II\. FIGURE 3.7 "FAN TYPE" PUNCHING SHEAR FAlLU RE AROUND EACH WALL
IN UNIT 1 (èycle 35, P = 13)
, '
FIGURE 3.8 UNIT 1 AT END OF TEST \,
o
1.
. '
:,
, .
) . ~
63 ..:
"
FIGURE 3.9 ELEVATION VIEW OF NORTH WALL TOE PUNCHING INTO SLAB.IN UNIT
-'
. ,
"
m
•
"
"
~
0,
/-') /
f )-
~ 64
, 1
• • .. 1.- ~P1 .. "-.
'. , FIGURE 3.10 ,PRIMARY YIËLD LINES IN UNIT 2
\ ---
, -
, . - cl ,
1 /'
:,~
.. , le ~ \ ,
1-J ,/ ~
J \ \ ) 1
\
J. ( (1\ /
l' .. f.I.II' IINI' .' ~ CYLll " ~l Il " ., "
,'010/ W
FIGURE 3.11 CRACKING 'AT CYètE 5 (~ ~ 3) IN UNIT 2
(
FIGURE 3.12
.rI
( r
FIGURE 3.13
.:. 65
M{:'\..\\ ... L UNI"T "2-CYC\...E U S'TEt> fiH) S'Ol:. ''N ...... "'-.... _ ....
CRACKING AT CYCLE 8 (p = 3) IN UNIT 2 '\
FIRST SIGNS OF TENSILE MEMBRANE ACTION IN UNIT 2 (cycle 11, il = 1>
,.- '1
.,
o
1 1 .
:~ , '.1
·1 J
) i j
~ . : 11
- 66 -
, f l
5
.. \
\ . l' J. '.
J .
FIGURE 3.14 UNIT 2 AT END OF TEST (cycle 23, ~ = 9)
.
",7 ... 1'1 \. '".'
'v,' :"
-~=-.---- • ,(
, "- .. \
, , \
" .
\
FIGURE 3.15 CLOSE-UP OF CENTRAL AREA OF UNIT 2 AT CYCLE 23
67 '-.'
"
..
. ,
- ." .1 ' ..
FIGURE 3 .16 SHEAR FAILURE AT ~OE OF SOU~ WALL IN UNIT 2
.'
c \
68
FIGURE 3.17 YIELD UNES IN UNIT 3 (cycle 5, f.l = 3)
•
., , 1' .. , .. ' , ',l, • ,1
dt if IN
, FIGURE 3.18 SHEAR FAILURE AT TOE OF SOUTH W(lLL
IN UNIT 3 (cycle 7. f.l = 3)
•
(
- 69 -
.J
FIGUR'E 3.19 CLOSE-UP OF SHEAR FAILURE AT TOE OF SOUTH WALL IN UNIT 3
detatl
/ ' south wall
slab
s lab
- 70 -
in the immediate vic ini ty. Concurrently, small cracks progress~d
behind each wall toe which indicated sorne distress in tho~e locations.
The cracks then propagated toward the slab edges forming secondary
yield lines (arrow. Fig. 3.2) (' second ary' signifies smaller rotat ions
than at the primary yield line locations). Other secondary Yield lines
propagated transversely from the slab edges toward the shearwall
centreline and changed directiç-n toward the wall toes as they
approached the wall centreline due to the rotational restrictions of
the flexurally stiff walls.
The next identifiable type of cracking was the .diagonal
'torsion' type, clearly visible in Fig. 3.3 (arrow), which commenced in
the wall toe area and propagat~d diagcnally te the yield line along the c::J
opposite wall face centreline. This torsion ls created by the change
in moment between the shearwall toe and slab edge along each yield line
(elaborated ln Ch,apter 3.3) . There were'fewer diagonal cracks ln Unlt
1 • The decrease is attributable to the ccnfining effect of the
stirrups, and to the reduction in the slope of the transverse
deflection profiles by virtue of the horizontal stirrup legs acting as
transverse rein forcement
The first indications of concrete crushing were at the foot of
the north wall in cycle 21 (Fig. 3.5). This crushing rapidly
intensified in susequent cy'cles as large concrete pieces spalled and
chipped away on both the top and bottom surfaces of the slab.
In the peak displacement cycles immediately followlng the
onset of crushing, tensile membrane action first appeared (Fig. 3.6) ln
cycle 23 ( P = 9). It eventually developed into a 'fan type' punching
shear faLlurel around each wall at cycle 35 ( P = 13) (Fig. 3.7). At
- 71
-c this stage sliding shear de formations became apparent at the wall toes.
There was . no cracking evident in 'the shearwalls themeselves,
except for sorne minor chipping and spalllng at the wal,l ·toe corners at , 1
véry high wall displacements which was repaired before each subsequent
test,
In Uni ts 2 and 3 the the cracking sequence was very similar to
tha t of Uni t 1, wi th notablè exceptions. The crack pa t tern in Unit 2
progressed at an accelerated pace with respect to the other ~\oIo
specimens. Comparing the patterns of the three Units at a dis placement
ductilityof three (compare Fig. 3.11 with Figures 3.2 and 3.17, and
Fig. 3.12 wlth Figures 3.3 and 3.18), the cracking 1s more extensive in
Unit 2, with a unique longitudinal crack propogating directly between
both shearwalls. Tensile 'membrane action f1rst appeared in this Unlt
. at cycle 17 às opposed to cycle 23 in Unit 1, and developed lnto a
punching _shear failure at cycle 23 as opposed to cycle 35 in Unit :.
The accelerated cracking was expected since there were no stirrups in
Unit 2 to control such crack1ng through confinement of the concrete or
by acting ,
transverse reinforcement to decrease the slope of' the \ as
.slab' s transverse deflection profile in the vicinity of the door
opening (see Section 3.3).
\ \,
3.2 FORCE-DISPLACEMENT RESULTS . \
The net force (V) plottéd against the l'elat1 ve vertica.l
1 \ shearwall displacement consti tute the force-d1splaèement d1agrams shoHn
in Figures 3.20 to 3.22. It must be clea~ly noted that the 20 kN
c maximum load used in the intermediate load "Cycles to 60~) Ultimate"
\
é-
t:)
CYCLES TO
60% ULTIMATE
v (kN)
JL1
27 ~ ,L2
1 V (kN)
40
... , ';?ji? '7 ~.c:1b"! · · ''-DISPLACEMENT (mm)
34 28 -(2,-20 20
Jo
-40
t
/
L3 /
/
/
'"
t·.)
/L4
/
DISPLACEMENT (qlm)
PEAK DISPLACEMENT CYCLES
FIGURE 3.20 FORCE-OIS PLACEMENT CHARACTERISTICS, UNIT t
--.l l'V
~
CYCLES TO ' 60% ULTIMATE
22
i /
16 10
,L1
v (kN) l l ' 20 ~.~ 9 15 21 .,.
10 DISPlACEMENT (mm)
42,-20 ,
L 12
L 6
v (kN>t
40~
-40
\
,L2 >L3 5 -,
L4 /--,
/ .; / -, 11
./ /L5
20
DISPLACEMENT (mm)
PEAK DISPLACEMENT CYCLES
FIGURE 3.21 FORCE-DISPLACEMENT C.HARACTERISTlCS, UNIT 2
/
""" (..)
1
~~
CYCLES TO
60% UL TIMATE
-10
.L -10
. c:..
,l1
9 ,l2 /L3 /L4 1
V (kN) T 5 /
40t 1 /:J 11 / -, l /'1/
--I....à... / -10
DISPLACEMENT (mm)
~/!;11//1 I~~ 20
4,2 -Pro /'"
-20 -10 ..; /r 1 AI 1 VI I~ -...j
20 :.. ~ VI Y 1 -Tl 7 10 DISPLACEMENT (mm) 1
L -40 PEAK DISPLACEMENT CYCLES
~
FIGURE 3.22 FORCE-DISPLACEMENT CHARACTERISTlCS, UNIT 3
- 75 -
( (ln the upper left hand corner of Figures 3.20 to 3.22) is not in
actual fact 60~ of the ultimate load capacity of each specimen. The
method of chosing this 20 kN value for the intermediate cycles 1s
) discussed in Chapter 2.5.
a) Assuming the partie ipation of the seismic (longitudinal)
- reinforcement across the entire width of the slab, ultimate forces
attained during the tests were somewhat lower than those predicted by
the yield li ne theory. A comparison of the test values from the three
units with the theoretical ultimate value of 46.8 kN yields an average ,
difference of 7.0~. This insignificant difference may be due. to
variat ions in actual distances between top and bottom layers of the
longitudinal reinforcement. Since great care was excercised to ensure
a clear cover of at least 7 mm, it can be assumed that generally the,
layers were slightly less than 48 mm apart (Fig. 2.1), thereby slightly
reducing each slab's moment capacity. The effect of straln hardening )
'\
in i~creasing the flexural capacity of the specimens in the early
loading stages, as proposed by Taylor (11), is ce'ns idered te' be
negligible sin ce tenstle reinforcement strain values were not h,igh
enough for signifiqant strain hardening to have occurred (refer to
Chapter 3.5).
b) Table 3.1 lists the specimen strengths at a displacêment
ductility of 3.
Unit was the only specimen to demonstrate a small increase
in load capaci ty from the peak displacement in cycle 5 te' cycle 6.
However, the strength dropped gradually at cycles 1, 11 and 17,' and
C· "
then increased again in subsequent cycles to the end of testing. This
decrease i3 attributed to the cracking and general deterioration of the
76 -
-'
o concrete, while the increase at larger deformations can be attributed
to straln hardening as large strains were imposed on the relnforcement.
~
The event
11 failure mode was flexural, and occurred in
cycle 23 (p = 9) wi h\fhe onset cf con crete crushing. However; testing
, con t inuEld untU /uns,ile membrane action developed into a notiqeable
punching shear fal ure.
" Despite the higher strength o,f Unit 2 in cycle 5 as cC'mpared 1
with Unit 1, the load capacity dropped substantially in subsequent
cycles. The sharp 28% decrease (Table 3.1) 1s attributed ta ct vlSlble
vertical sliding shear deformatlOn at the toe of the south wall. ThlS
was therefore ccnsidered to be the primary fallure mode. No
appreciable increase in peak loads occurred thereafter.
'''.
1 .
NET FORCE CV) , ~ CkN)
absolute values
CYCLE UNIT UNIT UNIT <p=+3) 1 2 3
5 42.5 43.6 43.4
6 44.6 35.1 38.8
7 37.1 31.4 32.1
% diff. between +4.9 -18.0 -10.6 5 and 6
% diff. between -12.7 -28.0 -26.0 5 and 7
TABLE 3.1 SPECH1EN STRENGTHS AT A DISPLACEMENT DUCTILITY OF 3
C <3
The
similar sharp
7, and again
behaviour of
drop of 26.0%'
- 77
~
\
Unit! 3 was comparflble
(Table 3.1) occurred
a vertical sliding shear deformation
to that of Uni t 2. A
between cycles 5 and
was noticed at the
south wall toe. How~ver, the 10.6% decrease betweeI~ cycles 5 and 6 was
an improvement over the 18.0% strength decrease in Unit 2.
c) Table 3.2 lists tangent stiffness valuee obtained at a
value of V = + 15 kN on each dis placement cycle to 60 % of the ul timate
load (Figures, 3.20 to 3.22).
The largest stiffness decreases occurred wi thin the first 9
load cycles, wi th ,Unit exhiblting the lowest ràte of stiffness
det~rioration. Beyond cycle 9 the rate of stiffness detenoratlOn
decreases. Nonetheless, Unit 1 slab stJ.ffness . reduces to on~y 6% of its
initial value of 12.55 kN/mm, demonstrating the severe .slab stiffness
degradation produced by the 'repeated cyclic loadJ.ng of a specimen
beyond the elastic limi t.
Thé stJ.ffness losses to cycle 9 ln Units 2 and 3 were nearly
twice that of Unit 1, and may have, been caused by the early local
slidi~g shear failures at the wall toes ~ However, the extent of the
. stiffness deterioration at higher ductilities is almost identical in
Units and 2, indica ting the ineffecti veness of slab stirrups in
significantly enhancing the specimen stiffness at dis placement
ductilities greater than 3.
-'
o - 78 -
,
UNIT 1 UNIT 2 UNIT 3 ,
, 0
r CYCLE STIFF'. ,.
OF 1 st STIFF. % OF lst STIFF. :t OF 1 st p
, (kN/mm) , CYCLE (kN/mm) CYCLE (kN/mm) CYCLE {
1
1 112.55 100 12.70 100 12. 14 100 -
-9 4 .. 91 39 2.57 20 3.25 27
15 1.36 15 1.60 13 --- ---
./ 21 1.26 10 1.06 8 --- ---
1
-, 27 .94 8 --- -- --- ----
--
33 .70 6 --- --- --- ---\ ,
1
. Note: stiffness = tangent stiffness at V = + 15 kN
TABLE 3.2 STIFFNESS VALUES AT LOAD CYCLES. TO 60~ OF ULTIMATE LOAD
j
-1
o
-
" -'
- 79 ..:
-• -'-3.3" SLAB DEFLECTION PROFILES 6
Longi tud 1nal ,
and trans'verse deflection profiles for eacb
specimen, Figures 3.23 to 3.28; we'ré obtained from the dial gauge and
L.V.D.T. instrumentation shown in Fig. 2.15 (The displacement values • 1
for line A profiles in Fig. 3.23 correspond to the réadings taken from~
the L.V.D.T.s and cHa'!' gauges along' line A of Unit 1 in Fig. 2~15.
Thus J,~nts Y5 and Y6 in Fig. 3.23 correspond with L.V.D.T. and 4
, in Unit , of Fig. 2.' 5, ltnd points Y7 and Ya correspond to dial
gauges 5 and respective-ly) • Among the most prominent ., ,
characteristics of each longitudinal 'Slab deflection profile are the >1 • ., .......
,'~harP-Èis.co~tinuities occurri~g B:t points 'Y" Y2 , Y5 and Y6' t
Thése discontinuities ièentify the appro~~at~~cations_bf the Iargest
rotations and strain~ within each specimen, and hènce indicate the , ,
location where transverse primary yie,ld lineso
formed:
'a) Between the primary yield .lines (ie. between points Y,
and Y2 for example) the deflection profiles are nearly 'linear,.
refl~c~ing the virtual absence of tra~sversé crac~ing in that area. "
The smaller yet sfgnificant secondary yield li~ rotations are
" represented by the difference in slope between the line segment profile
Y2-Y3 and the nearly horizontal pr:ofile Y6-Y7' . This, indicates
that up ~to 800" mm from the--corridor centreline along line D,
longitudinal reinforcement was being strained. However, the linearity .. of profile
.. reflecting
( the minimal straining of the
longitudinal- steel due to the influence of the flexurally stiff
shearwalls on the 1mmediate slab area, indicate that curtailment of the
concentrated longitudinal seism1c reinforcement 700 mm from the
'"
corridor centrel1ne (Fig. 2.9) (ie. 143 mm before po~nt Y7 on prol1le '
."
r ~-
..
o. ,-
"
. ~ ,
"
o
. ,
- 80-
DISPlACEMENT (mm) 10
CYCLE es Cp: 3)
-1000
CYCLE 6 Cf:-3)
*refer to Une A in Fig. 2.20
CYCLE 17 (fJ:7)
-1000
l
CYCLE 18 (J'=~7)
Y6
-10
corridor ~
20
, . , corridor opening
DISPlACEMENT (mm)
Y7 Y3
1000
. , 1
YB Y4
LONGITUOINAl OIST ANCE (mm)
LONGITUDINAL DISTANCE (mm)
1000
.. -l- ')
A
FIGURE 3.23 LONGITUDINAL DISPLACEMENT PROFILES. UNIT i •
' ...
r
..
Y1
> •
"
.'
o
. - 81-
DISPLACEMENT (mm) IIne A
Y'1 . 10 D
CYCLE 5 <JJ=3}
-1000 Y13 1000
LONGITUDINAL DISTANCE (mm)
CYCLE 6 <JJ=-3) , ,,-_0
-10 A
corridor <l
A
c/ o
, CYCLE 17 <JJ= 7}
LONGITUDINAL DISTANCE (mm) "
1 •
-1000 1000
CYCLE 18 <p=-7)
-20 , DISPLACEMENT (mm)
o •
FIGURE 3.24 LONGITUDINAL DISPLACEMENT PROFILES, UNIT 2
'.~ . , . , 'i' ,
'- J.t~
'"
- _. -.. ~ .......
o
-'82 .:.
, , 1.,
'-,
"
DISPLACEMENT (mm)
• "
. -1000 1000 \
LONGITUDINAL DISTANCE (mm) 1
~YCLE 6 (p=-3) o lJ
A
corridor t
•
0, ,FIGURE 3.25 LONGITUDINAL OI~PLACEMENT PROFILES. UNIT 3
-', ,~. or.!~lZ
-,0
• j
o
.1
, 1
7 ' .. 4
- 83
A) was reas~nable. This applies t~higher ductilities as'well:
'b) The participation of . the . longi tudinal seismic , ...
reinforcement ~n carrying the.applied cyelic loa~ alons eae~ yield line
i5 greatly reduced at the slab -edges as indicated by the decreased
. displaCement of point Y2 with respect to point Y6'
increases at higher displacement ductilities. Furthermore,
This
transverse
defleotion profiles (Figures 3.26 ~o 3.28) indioate that the greatest _ .1' \. .. -
transverse slab rotations oceur close to the shearwall cen~reline, and ~
'hat in , '
general the transverse. profile tends to flatten out beyond
point T, (Fig. 3.26). Theret;.ore, it seems that the Most aet1 ve . ., longitudinal seismlc reinfo'~eement ;,s confined to a maximum area
extending approximately 350 mm on ei ther side of the ~hearwall
èentreline.
e) The transverse displacement profiles aid in visualizing
the formation of diagonal torsion" cracks first- men t ioned ,il1)
Section 3. 1 •
longitudinal
rotated in ,
Torsional stresses within each ~pecimen arise when
slab strips si tuated between f ~
primary yield ~.
Unes are
opposite ~enses, such as the clockwise twist which oocurs )'
between segment'T3-T4 on profile E and segment T,-T2 on profile
H in Fig. 3.26.
d) the' der~eétion profiles pro vide . As stated by Taylor,
\... ft ••• evidence of concentràted shear deformation in J;.he wall toe region \
in that substantial departures from (antisymmetry) of the longitudinal
. deflection prof1les May be observed. 'Considering shear forces
o
qoneentrat1ng in the two wall toe regions as loading progresses:'at the
upward ~oving wall toe dead load sbears"red1stributed' as cracking and
y1eldi~g 1n the slab. <?ccurs, are addit1've -to"ee~smic shears; at the
, .
" .. ,qw:
f
o f
"
1
,
. 1
• "
, '
, .
• :Oi: .........
, .. DISPLACEMENT (mm)
20
, r
----- 10
.'
- 84-
.'
. " \ .
1
. \
, , Cycle.Ductllity
--~~--~~----~ 6,3
. 500
E .';
E·,-----~;;--
6,3 1000
18-,-7
fi" --'.... t ---:-~~_--L=-__ J._-.-:'----=----~ 8,-3
H--------------~ " __ ------ 18,-7
l· ahaar wall ~
. * ratar to lin, H ln Fig. 2.20
FIGURE 3.28 TRANSVERSE DISPLACEMENT PROFILES, UNIT 1
. , .. , ,
1 '.
"
, !
';
1 1
/
. ,
" .. ~ .' ---..... ~ .....
0 \
• \,
-'
,
• •
- 85.,.
" -.. # ..
DtSPLACEMENT (mm)
Llne H Cycle,Ouctlllty
5,3
1t '0
'5,3 r E 1000
" 6,-3 .1'
TRANSVERSE DISTANCE (mm) E----!-, ...--..~
_.L_-------..:s:r::s::~6, -3 H . 18,-7 -10
, '.
" ~ __ ---18,-7 -20
H-...... --
shear wall ct
fieURE 3.27 , \
TRANSVERSE OISPLACEMENT PROFILES, UNIT 2 ' , .
, .
, ,
•
-0 •
\
'; ,
, J
•
\' .. - - 86- \\
..
DISPLACEMENT (mm) ~
10-:...
Cycle,ouctllltYl
i Llne
H~T-----______________ ~~
.'" F- •. 5.3 •
10PO ..
TRANSVERSE DISTANCE (mm) E .
- ,_ ...
H~---------------/ . -10-1-
, shear wall ct
"
-- 1 ,.
. -
, ,
FIGURE 3.28 TRANSVERSe D~SPLACEMENT PROFILES. UNIT 3
, .
~~_._-_.-
..
~
rf,('~:'; O'··· ,'.
1·
, '
o
-.... - ... _._.~. _. "'., . ~:J1tA
,
...
downward moving wall tee shéar
seismic shears •• :" •
, • 81
t'orces are
-of the opposite sign~o
. Since specimens were not rotated but displaced vertically in 1
this study, concentrated' shear deformations May be observed by 1
comparing the perpendicular distance between point [Y9 t'and the
'se1nent ~10-Y 11 (1.2 mm) and th~perpendicUlar extension 'of
distance between point and segment Y13-Y14 (0.9 mm) in -, . "
Fig. 3.24. The diff'erence (0.3 mm), which 1ncreases at higher
displacement ductilities, indicates tHe existence of these shear
deformations.
e) The effects of dead load, cracking and yielding, ànd . . redistribution of the dead load transfer .mechanism (11) May be observed
1
on each ~itts ,long1tudinal displacement profiles by the' indrsection ~ .
of .profile D and pr~f11e A (point X in Fig. 3.24) alternating about the
vertical axis for upward and downward peak dis placements • This
suggests that had the test specimens weighed less, been very stif.f and ..
remained uncracked, point X would bave coincided wit9 the vertical axis
at all times'.
f) The 'Use of' the. bay centrelil'Je as a longitudinal line of
symmetry for lateral lc>ad l'esisUng actions 15 reasonable sinee the
. transverse dis placement profiles '. are nearly hol'izo~taf at e~ slab
eçlge. ,
" '
3.4' LONGI~UDINAL SEISMIC'REINFORÇE~NT AND gpNCRETE STRAINS . , -, , -
The lons~ tudinal seismio reint'orcement and boncrete strain , • 1"
data in F1~res 3.29 to 3.31 was obtained trom electrical resistance
.. ~ ... ~ --~ .. -,--.:".
. .
' .
o
"-
"
-v
.' • , tl
,- ! ~1 .. ~ Ii'..! , -da'
\" "r·"i -"~. . . .. , l'o •... . . ... 88-
(a) (top of slab) bar! t· ahear' wall Ci."
0.0
,... J:I ca üJ -0
CD CI '0 CD ....
(b)
----.----- -
'unit 1, ·cycl'8 5 (,.,=1) ~step 65 •
. ---.' ~ ',;'
..--
--"'7' • ,r. . _-4\1:1 - ... ------...,J--.. . ---.. '_----:r ..... ~--_._._.<
TOP CONCftETE STRAINS
&c (x 10·S) ,
-60P Compression
Jey 1000 Tension
BOTTOM
REINFORCEMENT
.,STRAINS
, &s Cx10·S)
--:"~ . L=;:;:::=a!!:.~=::::~7 -===-=:...~'--.----.,......:~-,----tO.O
. "6'00 J. 900 1032
Unit 1-.
Unit 2 ---
Unit 3 ----~ ,
300 TRANSVERSE DISTANCE (mm)
.. ," ,"
"
" ." ," " , ,,'
.. ' ... ' , .. "
," " ...... '
• j ,.-
2000
SOTTOM CONCRETE
STRAINS
. ,
. & ex 10-S)' c·
, JOOO Tension
" .--~N9 __ ----~~r-~~ o ~'(C) ......... , .- ...........
(boUom of slab)
0.0
. RRST CYCLE!Q !2..,Ul TIMATE
: FIGUF\E 3.29 LONGITUDINAL AEINFORCEMÉNT AND CONCRETE STRAfNS •. , '
...
\ -
, .'
~,-' -
"',
~
'0
. • ' 1 - .. ,
\ .. -.... , .; ---~- - .... ..-:;;;;::. ""'."""',-Vi'~',~\;~,~''?'''' .... ~j .:>""+lJ·"'I:F~.~f6%~, ~,""'!,"!"'~5!'!!'!~Î7ft11~-.... ~. .. h~, - 89':" 1
• ,1
. , . ahear wall
(a)
STRAINS
Cc (x 10-8)
-3aOO 'Compresslon'
'. /
.. ..1----," ,
_~"'.J
S'lOO Tension
~ - ...... --- --:.:,-::-". -----p.-..... ,...----... --------_ ... - .---- --*.
BOTTOM
REINFORCEMENT --.---,~
• ,-------- -----STRAINS
(
- & Cs (x 10-8 ) , .Y
(b)~-----~-------~-----~----~ _____ ~---.---~-----~QO 300 600
TRANSVERSE DISTANCE (mm)
Unit 1
Unit 2
900 1032 -
1 1 -
1
10,000
.BOTTOM CPNCRETE
STRAINS
... UnU 3
1,,- Cc (x 10-0)
5000 Tension
- __ --'f
----.,::,,: .. :.:~=-. --. --~----:.,.", .
------ *'" ----------_.--- ~ ....... "... ..... --~_.-.-(
(c)~ __________________________________ ~o._o ____ '._~ ...
CYCLE 5~
FIGURE '3.30 LONGITUDINAL REINFOACEMEN1'- AND CONCRETE STR'AINS .
r .,
• ..
)
" r . , '. '
'T-"··..,. '.
o ..
•
,'#
"
, ' If. r:X - -, • -. - '-"!!;::'!i~
(b)
--
.. ,
.. 90- \ . ahear wall
Unit 1
Unit 2 _._~
Unl13
. ,
," "
.... ..... ," .... . "'-------.. _-- .. _--- , .,.,..,,--.. --_._----._-~-_ .. ,. /
""" --_. _ .. _.-. _. -, _. ~.-' _.
1 2
300 600
TRAt-tsVER~E DISTANCe (mm)
.- .. ----II'
/
900
.. .... --- ~ • __________ ... ____ ~ _______ -----.----- 1
_.- . -- . .....- -' .-" /
..... _. - 1 _ • .,- • - • _. - .-"
1
STRAINS ,
C ' ex 10-8 ) c
•
-4000 Compression
10,000 Tension
BOTTOM
REINFORCEMENT.
STRAINS
, 20,000
OTTOM CONCRETE
STRAINS f
Cc (x 1.0~)
10,000 Tension
./
(c)L-~ ____________________________ ~~o~.O~~r~~~
F.IG!JRE 3.31 LONGITUDINAL REINFORCEMENT AND CONCRETE STRAINS
( \..
.. _ .... ~ .. [ ... -~
"
. '
•
. C'
.. ~ ~-h~
, , ,
1
'7': '
0,
. ~: .) ,:".;, ,~
.' ", .. strain gauge and demec gauge instumentation described in Sections 2.3.3
and 2. 3.4 res pecti vely • In Many cases, surprislngly, the electrical
resistanee strain gauges contlnued to perform beyond the range of • 18,000 microstrains. Exceptlng for the first five loading cycles when
1 concrete dlsturbance was minimal, strain data was adversely affected by
the proximi ty of cracks to the strain gauge loca Mons. On the bot tom
reinforcement in Fig. 3.31(b) for example, the strain readings ltt the
first three strain sauges from the' free edge of Unit 1 are too low
sinee .~rack1ng took· place some distance, away from these gauges. The
reading for the fourth gauge 'increases dramatically to a much higher
value due to the openlng of a crack dlrectly above 1 t. The firth
gauge, closest to' the wall, was no longer functional. The demec gauge
readings were more consistent.
a) In a11 cases, as expected, the stralns near the shearwaU.
1. centreline were high.er than at the slab edges. At the peak of the
first "Cycle to 60S Ulimate" (Fig. 3.29 (b) and (c», MOSt of the load
transfer between the north and south walls took place between th~
shearwall centreline and the- f: bay centreline, the remainder of the slab
being relatiyely inactive. However, ab higher ductil1ties the • fi •
longltuginal reinforcement in the outer haif of the slab was observed
ta carry strains well above fi ve times the yleld value of 1030
micros trains • This ls contrary to Taylor's observation that fi ••• no ,
longitudinal 'bars outside the stirrup cage (of T~ylor' s Unit 1) gave
mea~ured strains greater. than 1.8 t1aies yield" (11). -~ . ,
, '
~-1
~ . .Ji, • l ,.,~, 1. f ..
" 't "
\ ..
·0
.'
!
.-
... ~._--------------..,~
- 92
. The longitud.inal reinforcement and concrete
\.,...
(no. stirrups) are concentrated~ JJ1 the central .
strains of Unit 2 \'
slab region (wi thlA'
200 mm of the shearwall centrellne) to a higher degree than those of J
Units and 3. At both low and high ductilities, the slopes of the .'
Unit 2 strain profiles o closest to the shearwall centr~l1ne are
consistently the steepest, indicating the" greatest transverse strains
in this aree. for this specimen. This accounts for the unique
-longi tudinal crack extending between the' Unit 2 shearwalls. In
comparison, the presence of stirrups in Uni ts - 1 and 3 acting as
transverse reinforcement enhanced the strain distribution from the
shearwall centreline to the middle slab regions (ie. within 600 mm of 1
the shèarwall centreline).
(b) The bot tom reinforcement strains in Unit 1 at load st~p
65 (Fig. 3.20) are plotted in Fig. 3.29(b). The 0 .tensile slab
reinforcement f1rst reached yield at this load step. Hence, the
relative vertical displacement of the shearwalls at this load step
( 6 = 2.8 mm) was uded as the value for· "displacement ductility of -one!'
in all SUbsequent experimentation.
3-.5 Performance of Stirrups • J
Taylor (11) states tha t ,, __ p the f~s t important function of the ",
stirrups ,.
_. - was 1if;> prevent a total punching ~hear failure by the r
horizontal legs acting as part of a shear friction mechanism. The .
horizontal portion of the stirrups provides a normal clamping force to ~ - .
enhanoe aggregate interlock and resist shear in an identical manner to ,
the secondary transverse reinforcement •• _ Stirrups within the central
... ..,---~ . c.
" ,
o
l
o
)
" - 93 -
slab region were JrOVided as conventional beam-type shear reinforcement
and for confinement of the flexural reinforcement to pre vent buckling --, when compressive yield occurred ••• ". It was also speculated that the
vertical stirrup legs would resist seismic shear forces, as doea
conventional shear reinforcement in a regular reinforced cqncerete ,..
beam. Howaver, the vertical height restrictions of the slab greatly
reduced their effectiveness.
a) The potential , ... '
of these stirrups and transverse
reinforcement i~ resisting total punching shear failure in an actual
structure through the functions listed above can be clearly illustrated • 1
by considering the damage which occurred from a disastero~s explosion
in a "real life" -modern highrise apartment building. A.lthough these
explosive forces and the earthquake forces simulated herein are not !
identical, the type of damage around the deep.column-slab jun2tJons in
th~ apartment building was similar to that encountered in this testing
pro gram and hence merits s9~e consideration.
" -The fIat slab (125 mm thick) structure contained evenl..y ....
deep, c()1umns resemb1lng smaii shear spaced, rectangu1ar, exterior ~ - )
walls. A shallow spandrel beam was situa::ted betweEm these columns
'" approximate1y 250' mm from their interior faces. Besides the large
def1ection and yield 1ine cracking in the damaged slab, severe and
unrestricted punching around the column toes occurred. There was a -l
distinct lack of flexural and shear. reinforcement irl- thls area, tnu5 \ '
the concrete was completely unconfined (only on~ reinfo!"cing bar
extended approxlmatelY 300 mm from the column rac~ into the siab). . Sorne of the damage is shown ln ~igures 3.32 through 3.,35. If 1t were
.... .' not for the spandrel beam which resisted large shear rorces . , .
, ,
' ..
:
- 94 --
- _.~
-;, .... -",
•
FIGuliE 3.32 END VIEW OF DEEP COLUHN,
.-.~"
-. ': FIGURE 3.33 PUNCHING SHEAR FA IL uRE A~,FOO~ OF DEEP COLuMN~ (vlaw trom west sida) ,
, " '"
o
o
, .
o
·'
,'"
- 95 -(
•
FIGURE 3.34 PUNCH1NG SH~AR FAILURE AT FOOT ,OF DEEP COLUMN (view from east side)
li. -'/
c 'FIGURE',3.35 THE SPANDREL BEAH BETWEEN l'HE DEEP COLUHNS
"
..
0,'
,
, 1
96
..
(~s '1ndloated by the diagonal shear oraoking 1n Fig. 3.35) the slab " ,. ! ... ), ,
pupp~lng oould have been much more severe and disasterous. ,
b) Electrical strain gauges placed on the ~e~tical stirrup
legs in Units 1 and 3 provided limlted but useful data. At low
- . displacement ductilities, when shear deformations were n&gligable, the
shear force carried by each stirrup 'across the door' opening. between
shearwalls was relatively uniform~, as' expect~d . theoretically (Fig. }
3.36.., Units 1 and 3 at cycle 5). As • vertical sliding. shear
deformations took place, a limited rlUmber of' stirrups showed signs of (
aotively.partlc~pating i~ carrying somë of the. applied ~hear force
(sttrrup S3 in Unrt 3, cycle Q) •. ;'Their part~cipat:J.on increased to the
yielding -point only after significant shear deformations had occured ,. -
(stlrrup S3, Unit 3, cycle 12). A more genera1 straining of stirrups
above yield values in the vicinity of 'the wall toe 'occured on1y wlth f
severe slab degredation, such as toward the end of t'esting ,for Unit 1
st cycle 35.
c) As she:ring'strains l~come, ~maller furthèr back from the
face of the shearwall, so shou1d t e need to place stirrups to resist
these - !1:.rains. . However this cut-Ot'f point .ts not well defined. In'
Unit 1, at oy~l~ 35, the straindecre~sed ~teadily behind t~e wall toe,
diminlsning tà 850 microst~ains at sti~rup S8. , .. ,was an 'inadequate- number- of stirrups placed at a sufficient1y
( large
distance away from the wall toe to make, a preci~e prediction of the
- c~t-off length, but an estimàte of 250 mm can be s'uggest~d through .....
'.
extrapolation. ,
In Unit 3, the strains were virtually ~il at stirrup S6, and
lnoreased unexpeotedly at Stlrrup'S7. Thè 1ncrease vas apparently due
=
"
. \'
Co.
.'
,l,'
o
1 _
'Sl 1 1 1 corridor ~
'wall face t
S~ stralns: 0 (~).
- ~P=-5)
cycle 5 (P.~3) ----.:.~---J...L
cyc;:~~ 12 (jJ=-S) ~~==.y ~ cycl~ 6 (p=-3)
. Si
-,
S2 S9
\
- 97;"
2000
UNIT 1 S"l'RA1NS
UNLT ~ STRAINS , r' •
\.
S4 55
190 -,
cycle tS (p=13)
" extrapolated'
" -'-cycle 5 Cp=3)
S7 - S8
STRAIN GAUGE LOCATIONS
o 50 1 (mm) 1
Scalè
. .
S6 S7 S8
stRAIN' GAUGE LOCATIONS , .
. "
FIGURE 3.36 STRAIN GAUGE ~Ë~DINGS ON VERTICAL STIRRUP LEGS
---------------"~~~~. ~.~_.-_.~--
.. ~~. "-L;~~;, •• rj
"
,
..'
~~: -.~l~
o
o
, .
,
,
98 -
,to the yield line ln. the vlelni ty of stlrrups S7 and. S8. Nonetheless,
" based on the assumption' that no major stirrup straihs oeeur beyond
-sti~rup S8, the eut-otf length estlmate ot
in tbe previous pàragraph seems reasonable.
250 mm behïnd the wal~·toe
, .
d) Unit 1: The changes in st;i.rrup spacings altered the ~
response ot each slab du ring testing. While all three spedimens
exhibited concentrated shear deformations at low displacement
d~çtilities in the immediate wall toe regions; only .in Unit 1 did the . ' '\
shear friction and clamping actions ot the stirrups control the- shear' ..,
detormation. Hende, flexural tailure preceded shear t~ilure in cyole . -
2~ <p=9) as descrfbed i~ Section 3.2. ,Testing 'progressed .until sig~s c
of punohing shear tailure occ~rred, similàr ~o the~one in Taylor's ,
Unit .1, where a tailure line'co1ncldeq with th~ outer edge of the
,stirrup cage approx!mately 200,,~ trom the shearwali centreline. 8y
this stage, large concentra~ed shear d~t6rmations had .""
already occurred
at the shearwall toes (Fig. 3~9), but con~inement 'of th~ longitudinal
-~eintorcement within the stirrup çage was such that the load carrying
eapacity ot the specimen did not decrease. If, not for the limitations
of the loading system (the available travel or the loading.jacks was , ,
exhausted) ~'" testing could' have been continued further. However, the
specimen was considered to have fa1led completely due .to the severe
spall1ng and cracking ()'f the siab b'eyond the, stirrup cage. , '
Unit 2: In the absence of any speoial shear reinforcement in , .
Unit 2, a slidlng, shear fa il ure occurred in eycle 7.' Without the .'
beneflt 'of shear friotion and the confining effect provided , ' . , stirrups, tensile membrane action and subsequent total "tan type" 4
punohing shear tailure oeeurred' eariier ln comparlson ~lth Unit 1.
.
1
"
o
. \
'.
,.
O"
"
~~~.k~~'..-.",,_.~ ~. ~ ~~
99 -
t ) Unit 3: 'A stlrrup spacing of 46 mm was not adequate ln ;,f,
restrictlng the same type. of early sli'~lrig shear failure whlch took
place 1n Un.lt 2. A difference ln the slab elevat1pns on. e1ther side of
the crack 111ustrates the presence of th1s concentrated Shear
deform~t1on (Fig. 3.19).
,
... . '
, > , ,
\ -"
-l,
- '
..
~ "'" ','
·0
'.
, '. ,.-" .:
I~~_"";" " ... "" t'''-",/ ". Y'"
- 100 .:.
CHAPTER II
SUMMARY AND COMPAR!SONS
,. ,'" p
4.1 SUMMARY OF BtPERlMENTAL RÉS'ULTS , " .
a) As predicted by yield 1ine th~ory, primary yield lines
form~d at the toe of each shearwall and progre~sed to the edge o~ the y •
slab i~'a direction parallel to the wall face centreline.
, , b) THe Most èxt~nsi ' cracking occùrred in- Unit ~ (with no .'
st~rrups) .as compared with Units 1 and 3 which contained stirrups. As.
an,ticipated, there were fèwer craCKS in J these 1/3-scale speci~ens
cOlDpared to Taylor' s 1/'2-scale specimens.
c) klong with flexuré,and shear, torsion. was one of' the load
transferrlng mèchanisms between' the shearwalls. Its prese~e' was
lndlcated by th~' diagonal cracking in the corridor opèning on either
side of 'the shearwall centreline.
d) Unit - 1 . . 4'
fal1ed in a f'lexural mode in cyole 23 Cp ~ 9}.
Thereafter, 10ad1ng continued-mltll" punch1ng shear failure occurred -a~
'cycle 35' (p =.13) •
U~lts 2 an~ 3 failed in s11d~rlg shear at a dis placement , {
ductility of 3 at which polnt their,load carrying capac1ties ~ecreased
bY 28J 'and 26~ ,respeètively. , -
Tbe~e shear failures occurred at the toes
of the 8hearw~l1s a~ong .~Yertical planes formed by the pr~mary. yield'
-( ,
-lines. The units.' con~lnued to carry substantlal. loads at' high-er----
\
dlsplaoement ductilities in ~ubsequent cycles. Only at theae ~lgher
l,
-
. , • 1
.-
f!'~:'-_ .. "'"1 ,.-.... ,.
. ~
o
• j
displacement ductllities t'>
reinfor~ement signif1cant
capacity.
: ;
... 101 -
..
strain hardening of the
in increasing ,.,.
the specimens' load carry1hg,
'\
e) The ultimate loads resisted by aIl three specimens were on
the ave~age ~ 1~ lower than the value predicted using the yield 11ne-
theory, assuming participation, of the full sla~ widths. This
dis cre pancy is not 3ignificant, and therefore the predictions using the "
yield 1ine theory are in reasonable agreement with the experimen{tal,
, resuits.
f) The,largest' reductions in st1ffness' occurred in the :first
sét of peak dis~lace~ent cycles to a displa~ement ductild.ty .. p = 3 for'
all 3 units. Stiffness reductions ranged from 61~ to 80~ in' Units 1
and 2 respeç.tivel:y. Stiffness \ reduc,tions of over 90~ at displacement
yductilities of 7 and beyond were ~bserved. At-displacement ductilïties· , . ,
. above 3, provision of stirruPs,in the slab did not enhance specimen-
s,tiffnesses.
~) Curtailment of the concentrated' longitudinal seismic~
flexural reinfdFcement at a distance 507 mm (approximately one and one
qùarter corridor openings) behind the shearwa11 toes (see Fig. 2.10),
was round to b~ reasonable. Th~ observation i3' ba3ed 6n th~
.6 ,
characteristics of the lQngitudin~l displaoement profiTes closest to / .
the shearwa~l centrel!nes (Lines A in Figures 3.23 to 3.~5) and on the -
siknificànt amount of 'cracking behind the toes of the shearwalls.
slab
, ,h) The 10ngi~udina1 reinforcement at the outer edges' of the ,
was not as "
effective as the iongitHdinal relnforcement ,in the
Q?rridor area des~ite the' fact that 'aIl 8uch reintoroement aeroes the
. rull width of the ~lab, had '.11èld~d at a displacement' 'ductility ot , "
..
i~~;;~~ ; , , .. \ .. \
, ,
'.
. ,
8-
, '. "~";" .... _, -; .. -.," 't,""
, -- 102 -
,- -
i) The horizontal legs ot the stirrups, acting as transverse
reintorcement, en~nc~d the distribution o~ strain in the,longitudi~~
seismic reinforcemknt from the shearwall- eentreline to th~ bay
centreline, as reflected in the longitudinal 'reinforcement strain
'profiles along the wall face centrel1ne for qnfts 1 and 3 (~igures 3.29
to 3.31). Nonetheless, the longitudinal reinfDreing strains in al1
th~ëe specimens exh1bited strains 'well above the yield values across
the entire slab widths at displacement ducti11t1es of 3 and above.
--,j) The vert1cal stirrup legs were not ~ffective -in resist1ng
shear forces at lOw displacement ductilities'~eeause: ~
1) the sliding shear failure plan,es were :v.ertical;
',' 2) the required, development lëngths could not be provided due-"to
the ve~tical height restrictions of the slab. "
Oo1y at h!gher dlsplacement ,dudtilitïes (p ~~) did these st1rrup legs , ,
. !mmediately in front of the shearwall toes ,and closest to the yield
lines yield because of the ,large shear deformati~ns" Gener~l strain1ng
above yield 'values, occurred only w1th the, onset of severe slab
d~gred~ti~n •
The stirrups were more effective in resi~ting s.lid1ng shear
fa~lures I;t, displacement ductil~t!es (~S, 3) through. a shear
frict n mechanism created by 'the clampin~ aotions of the horizontal
stirrup ,legs". This 'clamping àction confined the concrete and 'the
~gltudlnal selsm10 reinforceme~t, thereby improv1ng the aggregate .. interlock. t~is behavlour was obser-ved in Units 1 and 3, only , Although
~n the former speoimèn (Wi~h a stir~up spaolng of d/2) was the shear
friotion meohanism sufflclent to resist the vertical shear failure. , ,
". • , .... -: ~""- '"'" "''- " .... ' . .y.
-,
, , , '
l'
~;;:.:' ;. "
o.
..... "', , , ',' ,.,' ,f
103
4.2 EFFECTIVE WIDTH
The simplest way of express1ng a slab's ooup11ng stiffness 1s
in t~ms Or an effective slab w1dth. The relat10nshlp between
stiffness and effeotive width 1s deterDiined by cons1dering' a cantilever
beam sUbjected to a vertical concentrated load V appl1ed at ~ts ~~e
edge -(-pig. 4. na». The free edge deflecti()n dy 1s:
, where
\'
3(~I)'
x = cantilever length
E = modulus of elastioity \ \
l = mQment of inertia for a rectangular
= b efr(h:3') /12
where beff = ~ffect1ve sl~b width_
h =·thickness of slab
Hence, the,d~rlection of one shearWall
same vertical point load~ (F1g. 4.(b» 15 g1ven by:
section
). where o = the corridor w1dth between'shearwall races.
A = 2~y = relativ~ verrical displacemen~ ot_ the walls
T~~.refore thé slab st1ffness (VI ,,') can be expresse~ as:, .;
. .
"
( 1 )
•
,.<'
...... ;. ... ) ; .... .
. ,
,
'"
, .
. .;. .. , -
a)
~ b) t'
! ,
.. .
~ , _ .. ~ J ~';f·!'~ ~~, ~~. _~/~~ ~~.~_ . ~~, ".
- 104-'- .> -
--, -< ,
,
1 - 1
J ,
~Y "
V . , , .L
" '~ .~ ,;
.x
" 1 l' • "
i . - - ... -
~y >- -~
vt " . tV- :. td 'r
. y , -'-
, '1
'~ 1 »1 ~ .. x x
~ ·1 ~ 'C .. ,1 1-
~ , .
-~
- '
FIGURE 4.1 (".) CANTILEVER BEAM SUBJEC'l'ED TO A
, .
VERTICAL POINT LOAD' , (b) r $HEARWALLS:SUBJEèTED TO CONCENTRATED
~RTIC~LOADS
1
•
\.
..
.-, ..
>,
'fh':." '.
. . . •
- 105 --.
bettE(h3) V = = 3EI (3) Ll
8«1/2)c)3' 2 « 1/2) c ) 3 '
or the effectlvè width can be expressed in terms of'stiffness:
(4 )
For the dimensions used in this study, equation 4 l'esul ts-· in
beft ,= .00765 • v. ( 5)
Ll
Experimental slab tangent stiffness values obtained at
selected load cycles are listed in Table 3.2. The cor~esponding
értective slab widths, calculated using equat10n 5, are l1sted ln ......
Table 4.1. Also presented are the slab w1dths taken as a percentage of
the, s€irrup cage width (400 ~), wh1ch corresponds closely to ~he
corridor wldth (386 mm).
In order to ~ relate these effective w1dths and the
·correspond1ng.slab stiffnesses w1th the load deflect10n re~ponse of the
test units, flnes L1 through L5, wlth vary1ng slopes representlng
d1fferent. s;tffnesses,
defined as:
. (
were 1ntroduced 1n F1gures 3.20 to 3.22 and are
'1) Line L1 represent~ the ) ,
slab st1ffness based on a slab wldth of
400 mm, whièh 1s the widtt ~t the stirrup cage and which corresponds ",
âpproximate+y to the width of the' corridor opening (386 mm) and to 20J Y.<I &
'~
. .
i'
, <;
'. ,
, . 106 -
of the full sla~ w1dth (2065 mm). .
Ll 1s equivalent to the expression
'V/~ , ln equat10n 3, and was calculated uS1ng 50% of t~e homogeneous;
uncracked moment of 1nert1a of that 400 mm slab width (20Q' mm).
2) - Line L2 was based on 25% of the ~~irrup ~~ge w1d.th ( 100 mm),
wh1ch 13 5% of the fuld slab width.
3) L1~es L3,,.. LIJ and L5 were based on lOS (40 1IlDl), 5S (20 mm) and p-
o
2% (8 mm) of the st1rrup cage, respect1vely, which are only 2S, 1% and
.4% of the full slab width. ~ \~
.'
- . ~
CYCLE UNIT 1 UNIT 2 UNIT 3 . , ,
berf S of c~ge berf .... S of cage beff· S of cage •
(mm) width (mm) width (mm) width
( . ..
1 95.9 24 97.2 24 . 92.9 23 r: • -
9 37.5 9 19.7 5 24.9 6 ,
15 10.4 3 12.2 3 , ----- -- • • '-.21 9.6 2 8.1 2 --- -
\ 27 7.2 2 -- --- - ---- -
0 33 5.3 1 ---,. - ----- -- f'
, -~ . .
TABLE 4. l EFFECTIVE SLAB W~DTHS
•
~ •• '~.~.:"'~ ____________ ~ ________ ~~'~,-~ _______ -L/~-_' __ ~~~
o
. ~ . .', .~." ~
, .-. ~ . - -107 -
4.3 COMP ARISON WITH . PREVIOUS WORK
• # • 3. 1 Recommenda
Paulay (..3) have presented desi~n recommendations
for rèinforced concrete coupled slabs ba~ed on ,a stu~y do ne , by
Taylor (11) ..
The . design of the 3 specimens in this study i8 based on
Taylor's Unit design. 4 The force-displacement rèlatlonship for
~s Unit 1 is shown in Fig. 4.2(a). Shear failure occurreçl in the . specimen at a displacement ductility of '1 at the edge of the central
double stirrup portion of the stiFr~ cage - the fa il uree line runnlng
parallel to, and 150 mm from, the shearwall cen treline. The specimen
continued to carry load in subsequent cycles.
)
A comparison of observations fr=om this study with observations
made by Paulay and Taylor (3) ~~ardlng the behaviour of Xay~or's
Unit 2 (Fig. 4.2(b~), which ls a1so typ~a1 of the' resP9nse'~f Taylor's
) Uni t 1, ls presented:.
o a) Ac~ord1ng to Paulay and Taylor (3),. "the ultimate' load ..
attained was slgnlflcantly higher than the value l>ased on full1""width
yleld lioes and the measured s~rength of the longi tudlnal bars" • , ~ \
This dO,es not corr~spond to the. obse~vatlon 'made l.n
Section 4.1(e) that the ultlmate load predlction using the,yleld 1ine
theory, an~.assumlng the participation or the full slab widthj was,l~
close agreemen~ wl th the experlmental reaul ta •
;
1 -1
•
1
• !JI
, .~
:.' . ,
59
, . ,
(b)
,
, .
10S' -
,
ï .,.. ,
~~~~--~~~~~~~~~~~~~P-~œ---~~~'~-oo~
~ èS ..
''II g ..
~
"fi'
15 20 _ 25
, 1 PEA~ DISPLACEMENJ crêtEs 1 , ;
FIGURE 1& ~ 2 (a) TAYLOR' S UNIT 1 FORCE-DISPLACÈMENT . CHARACTERISTICS (Ret'. 11).
'cl,) TAYLOR'S UNIT 2 FORCE-DISPtACEMENTCWCTF.;RISTICS (~et". 3)
1
)
"
.,
.:0--,1,
Q,
o
, .
-,
"
'b) Paulay and Taylor (3'- observed that:
"The reduction of stiffness of the alab dur1ng reversJed cyc110 loading with increasing' displacement duétility. demand was round to be very sign1tlcant. Thè obseJ'ved stiffness at t'he final stases of the test loading was less, than 10 percent of 'the stlffness ~ncountered' at first loading.. The stiffness observed during the first two" cycles .of loadi!'g when extensl ve cracking developed w.1 thout the yield strain being exceeded IR the slab re1nforcement was signifioantly less than that predicted bY, p~eviously published e1astio theories".
This agrees with the observations 'in Section 3.2(c) based on •
Table 3.2, and in Section 11. 1( f) • , At the end of 'testing for Unit 1,
the stiff'ness was ?nly 6%. of the stif'fness in cyCl~ 1. However, . the
1argest single decrease occurred at the ftrst lo'ad stage (to cycîe 9) .• ,
Thus, Taylor's coment that 'the beneficial c014pling effect 'of the siab . ,
will be slOal1" , e'specially after the first large load cY91e' ls
aocurate. ,../
A typical stif'f'ness value of 37.77 kN/~ based on the è1as~lc "
i"
, tAleory ia obta~ned using the recommenda tions of 9adee"r and Sta't'ford
1 Smith (S). lt ovèrestimates by about a factor df 3 the stÜfn-ess in , ~
tlle' firs-t load' cycle before extensive cracking ,is developed. 'Hencé, . '\.'
stiffnesses for .. the elastid· .theory la very limited \ ln predic~ing
" \
•
specimens subjected to' re~erse'd cycUc loading.
..
. . , .
c), According to Paulay an(i Tayldfo (3): , .
'"Although, wi th progressi v~ cyolic loading" yiel.ding w~s observed ln a11 longi tlldlna1 bars, the ef'f'ecti veness of b~rs placed near the -free edges ,of- < the ,siab reduced r8.p1diy. Ever l.noreâs1ng inela~tic dêformatiôns are" re~t11~ed to mobil1ze th~ strength of bars whloh are situated at. a large distance f,rom the; coupled, wa'.Lls. 'lt, is _ 8uggested, there.fore, that only minimum long1tudiruf1 re1nt'orcement consistent wi th bull"ding code' requlremènts' be .. piaced Quts1de !;.~ central s.trip acro~s the 'doorway.' _ ·Bars enclosed by'
"-~stirrup ties withil'l,.a strip w1dt,h approxi,mately equal to the width -of the' door opening were t'ound :to be ~ore effective in
ft "
o
" -
l,
• , ,
, ,
. ' 110 -
. developing fiexural strength requ!red for- coupling two shearwalls" • It was aiso noted that Rat an' 1.mposed disPlacement'Luctilfty ra'tio of 3, aIl but the outermost longi tudinal bars at each free edge have yielded". . '~
The findings are in complete agreement with the general
observations in this investigatiol1. Referring to Figures 3.29 to 3.31
and Fig. ·3.?6; the - longitudinal ba!'s at the slab edges ,were not as
effective as the' reinforcement closest to the shearwell centreline.
,However, there is disagreemept . with._ Paulay's finding that the
longitudinal reinforcemènt at the slab edges had not yielded at a
<i:'Lsplacement ductility of 3, and wi th Taylor' s .( 11) obsElrva,tion "that
" through?ut this test nO longi tudinal bars ouside of the stirrup cage . 1
than gave measured strains greater 1 • .8 tim~s. Yield". It cao be noted . -~ .tJ
fr;om Flog. 3.'30 that all 'oC--the reinforcement strains are cle,ar1y ab9ve -the yield values, and From Fig. 3.31 th~t reinforcement strains outside
-
,
the stirrup_cage were àbove 10,000 M1oroatrain (wh~re yield ,strain. ia-
1030 microatrain).' One reason for' t'hese discrepancies, i t l,a
s,uggest-ed, Is that the, ~lectrical strain gaugès used 'in Taylor'-~ te:;lt .. ~ J
slmply 'did not pick up any higher strains (.~ee discus'slon ln Section ,. ,
3.4) because 'the gauges are very sensitive ta the aize-and locations of 1 • ....
, craclç:f. Demee gauge:} responded more .aacurate in' this investigation.
, . '
d) Accor~1ng to Taylor (11):'
"Stirrup ti~s, enclo#ng the, longitudinal top and bOttom, flexural reinforcament in the oentral strip, were foun4 ~~
'.enh~nce'duotility by confining excess~y cracked concrete and-. by preventing prelllatüre buokl1ng'ofl flexural ~ars" (3t-, Taylor addèd tha t "stirrups are prov1ded malnly for oonfinement "of the flexural steel across ·the corr190r ~idth. When these slab stirups', ar,e continued ,behind the wall tQe, they-provide punching shear, control byacting. 1Q sbear friction. However,. •• oonsiderable de formations mus~ ... ooocur, at the- wall toe before" a' suffiolent nUmbèr ofst1rr~ps are' mobllised"( 11).
. " , ft ".:n.,~
- ,
............ -.J
"
• 1
'~ i
• 1 ~ ~ .. ". ~
,"
' .... '"
r J'
lo': .-, 111
This ls in agreement with observation$ in SectIon 4.1(j)~~The ~ , ,
con~ining ~ffect of the stirrups was aomparatively more .effective in
• enhancing the shear resistance of the slab than Wàs the aption of the
vertical stirrup legs.
No premature buckll(lg of flexural bars was obs-erved 1n any of
the specimens, thus' the need,' flor stirrups to' prev'ent such action was 1"
nQt apparent. However, 'enhancement in ductility due ~.
to the .
stirrup
confining effect .wàs observed (compare Units 1 and 2 in Figures '3.20 ~ c
. Uni t 1 'rias not ,a .trua '2/3 scale model o~ Taylor' s Urli t 1. The
formér unit's concrete strength was increased disproportiona~ely by ,
140~. (Tab,le 2~ 5) to s~udy tJle effect of such an l,ncrease on the slab' s
shear èapàçity and overall behavlour. The following oQservatlons are
made:
, l,
~) The' 1Daxlmum ~et force (V) resist~d I)y Unit at cycle '5.
was_42.5'kN. The corresponding maximum horizontal force in Taylor's .
Unit 1, obtained ~rom Fig. 4.2, ,is approxlmately 58.0 kN.' Using the
approPr:'1ate convers,ion, ehe equivalent vertical force, is 103.5 kN.
Incorporating the ooncentrated load scale factor fif 3.8 round in
~a:ble 2.5, -the pred1cted maximum venticsl net ~oroe for-thls study "
ls ,>
-103.5 ,kN/3.8 = 27.2 kN. Th~s, the lhcrease ln the Vnl~ 1 experimental
âhèar capaci ty i~ « 42.5 - 21.2,)/27.2) x 100. = 56. 3~. 1
1
The ,theoretical shear,' capaci ty of a cQllcrete' member shoul:d ~
vary as . the square root of the concr~te strength'. . Therefore, the
. ,theoretical increase should' have - been ~
',55.8 ,,; which 1s very close to 56:;3"-.
: .... ~ I ... ~ ~~ ( (V 36 • 4 ,- -~ 15.0) I-V • 5 ~ 0 ) x 100 =
. ,.
l'
, "
\
"
, .
, .
o
l'
, ,
• '.
'"
1 l'
, ,
"
/'
- 112 -
l:P Thls increased slTear capacl~y was ,sUCcessful ln delaylng
,the pun~hlng shear failure in Unit 1 untll a di.splacem~nt ductllity of
p = 13. Unl1ke Taylor' s Unit 1 whi~h fa~led in shear at a dlsplacement
ductility of 1, flexure was the prlmary failure mode in Unit 1 and
occurred at a' displacemet duct~lity .. = 9 with the onset of concrete
, crushing.
The r'esul.ts of this research pro gram are in in agreement with r, Taylor's overall con6,lusion t~t "floor slab coupling will make a
negligible contributiQn to the overall response. Control of the damage
'ta the slab should be the designer' s lIIain objective" (11). \ ,
, .
4.3.2:, Recommendations Of Schwaighofer and ColLins , 1
Schwaighof'er 'and" Collins (1) have presented some design
,recommendations for reinforced concrete coupl1ng slabs based on a study - . ,
'dane by.Szalwinsk'i (10)." The study reports the ,'results of a 1/4-scale
reinforced concrete model 1 (shown in Fig., 4.3) loaded monotonically
(Fig. '4.4) into its ioelastic range. At load stage D, a punchlng
fal1ure of the sla1>. 1n the vicinity, of the c~uPle'd1 edge of Wall W2 was
encountered. The dis placement of the test unit was then lnc~easEtd
until pun'ch:lng fallure OCcurred at the exterior walls. h .,
It ls noted that no special flexural Or' shear relnforcement
was placè<1' acro~s the door openlngs.
Accordlng to Stlhwalghofer ~d Collins (1) 1 it was found that: t
1
a) "The peak 'value of the steel 'stiraln (along iine K-K in . . ',1 . '
" Il
,
\
o
, , -' , " ,
,;- 113
, , , '
/
, '1
Fig. 4.3) Qccurs at the raoe of the wall" tse~ Fig. '4.5). 1
Tm.à is in complete agreement with ,the res~lts ,or this study
where primary , yield lJ.qes, 'll(hich mark. ~he locations of, peak .
',-longitudinal reinforcement strains ,1 commencéd at the shearwall to~s, and
_ .. • ,.:I •• t.
propo,ga t.ed along the wall face' centrel1ne to ~he s,l~ edges. }
b) "The' ste..,el strain become:s 1 n~gl1gibly small about one
corridor width 'back from the face of' the wall".
This is a1so in close agreement with the observation tha,t
approximately a s1ab # width equal ~o one and one quàrter corridor
openings was a re~sonable eut-off point for the concen t ra ted
longi tudinal seism,ie reinforc~ment. The latter resul t is based on
longitudinal displacemen,t proriles while the 'former is obtained from
strain values in the top steel.
c) Figure 4.6 illustrates "the strains' in the bars parallel
'to the wall diminish(ing) with distance t'rom the wall ... and that the
magnitude of the steel strain ls very small one corridor width a~ay
from the centreline of the shearwall".
These observations correspond to the strains obtalned in this
study in the first 10ad cycles to 20 kN (Fig. 3.29), but do nO,t apply
artel' a slab has been subj ected to load reversals (Figures 3.30 and
j ,
.. d) The observations by Schwaighofer and Collins (1) in (0)
above were combined with experimental stiftness values CÙnes L , 1 ,
L2 and' L3) trom Fig. 4.4 to ob tain the tollowing oonc~usions:.-
1 ...... '"
. . ,i
0
• "
. ,
(a)
\
..
\ 3· 6'·0
ro 07 .... lU",
tB
114 ".
12'· 9 1 3 ..... 1
W· 6'·0 1 3' 1 Il,,, - OCl7Sm ,. B
FIGURE 4.3 (a) PLAN OF SZALWINSKI-HODEL (Ref. 1) (b) ELEVATION OF SZALWINSKI HODEL (Ref.. 1.)
= .
, "
. '
!f. ~. • .. ,.
"
, -- 115
r
o ...
•
, '
K,ps kN .. r l~ 10 / , ,
60 " / - ® .J:l 1 / ft!
J üi 8 y ,-
2 N
~ ~
~ 6
0 è
>- 20 al
:i 4 _L a. .11. D- r 1
c( ~ ,1
D U 2 )w ... 0
1&.
G , ~ 10 20 z , mm
0 ., , 0,2 04 ~ () 8 ln
, Verlteal D,splacement of Wall' W~ -' "
;~
1 , ,
. 'FIGURE Q.4· LOAD DISPLACEHENT DIAGRA'M (Rer. 1) . . .. -
" .
.>
...
- 116 -
-0 hee of Wail W2 , Corridor Width Ir C Face of Wall W 2
.... ~ ,
5 . , • . \ Corridor Opeoing 1 . , . \ Loading , '"
" 1 CD . ~. \. Stage 1 . . - '* ®
C"')
3 •
~r 1
Cy r
~ ca· o. --(1)
'; ---- = (1)
"
J 'l-~
fi>
. FIGURE 4.5 STR~INS IN TOP STEEL. ALONG LINE K-K (Ref. l) ,
• 1
, -'.
1 • :.
f
Face of 6 Wall W2
\
\ Loading. \
'0 \ \
~ SIege \ \
® - ,
tV'-' -M .. $?
~ 2 c:
~ï; ... 'cii
.. -,
, ,
1 •
. , , -
OntCorridorWidth . .... ,il . . ,
1 J ~ ,
f'IGURE 4.6 STRAINS IN TOP ~TEEL ALONG LINE'L-L (Ref. 1) ., "
" i ' ! .
__ h, .~"": . ..: / l , ..,J
o
• \
," "
- '111 -
. 1) "The ini Ual st1ffness of the uncr'a,.cked ~oupl1ng slab can be
predlcted using the gross section of the slab ,and an effective width of
one-half of the corridor .~hing,:, and ,
11) "l'he cracked st1ffness of the coupllng slab can be predicted by
assum1ng an et:'fective wldth of one-half of the ooprldor- opening 'and .
u:;Slng the moment of inertla ot" the cracked section". 1
The cracked ---stlft'ress or the- coupling slab study,
~ assuming beff = 1/2 corl'"idor opening = 193 9.90 kN/mm
(= VI d ). Usi,ng equatlon 5, the equivalent ,effec~ c :..:~dor width
e~press .. d a8 a function of. the uncra~ked .lab <~ne;;'" . i) 75.8 mm
(19 % of the ·stirrup cage width).. This 1s clearJy an ·Le~::t1mate of ,
the coupling stiffness for displacement ductlli.ties above 1. It 19
lSJuggestetl that th1s recommendation be us'ed only 'ta estimate initial·
slab' stiffness.
. . ., ~ ~),. ~The flexural strength' of the' coupl1ng . slab can,' be
predlcted by using 'a slab width equal to the. corridor'· opening plus the t.
wall thickness" •
. Th~s recommandation would lead to a very conservative ~st1mat.e
of the flexural capacity. th!} above recommendation does no~ corr:,espond t •
t;o. obs~rvatlops mad.e .in.' Section 4-.1.(f) where the "full slab wldth was .
used to predict the slab 1 s ul timate lOéld rés1stanèe.
, . f) A, conservat1.ve estimatt? ,;of the coupled slab'a !hear
.capa,.oity 1s given by. (Fig. 4.7):
. where
V = v (3)(d)(t .' d) n
vn =:-33Fc, . { , , , .~
"
. ,
o
,,'
.....
1 •
-cs + -
.. ,
- 118 -
/,I----Shear
t-HI
Wall
Critical ,Section
, .
v = , n v
3d (t +d)
FIGURE 4.7 CRI:rICAL SECTION FOR SHEAR STRENGTH (Rer. 1)
J, .,'
" . ":. • ............ , .~;;.~ ~, .J' ._ ,_",;1, __ •
, .' '.' /, ,. .,.· ... 1,. -.
/
f
o
, ,
1ïr..L .. ~ ... ~_, 1' .. ' '
- 119 -
For Uni t 2 (no stirrups), the shear tailure would be predioted -as V = 39.3 kN. Compar1ng this Rredict10n wi th the • speoimen st.rength
l, values ln Table 3.1, the estimate is conservative for loading cyole 5,
but in ~ubsequent, oycles it overestimates the specimen load oarrying
C'ilp~1ty by a considerable margine
g) The final recommendàtion to concerttrate the longitudinal
reinforcement as shown in Fig. 4.8 was followed closely in this study'
and observed to be effective in resisting the applied loads.
4.3.3 Recommendations of Qadeere and Staf'ford Smith
The graphs used' to obtàin. values of Ye (the effective slab
widt~) and k (nondimensional" slab stifness .Y'ai-ameter) are shown in
Fig. 1.2. . The patamettrs for thi~ case are Y = 2065.0 mm, C = 0.0,
L = 386.0 lDDl ~d X = 3050.0, mm. The nondimensional parameters are:
C/X = 0.0, YIX = .68, L/X = .13., Using Fig. 1.2(b), Ye'Y - .14 is
obtdned. Thus Ye = .14(2065) '= 289 mm wh10h 1. 72~ or t:~ stirrup
cage width. This value does not agree wi th the findings pre'ented in
Table '4.1. This me~hod, based orr an elastic an~lysls, greatly
overestima-tf~s the stiff'ness of a coupled shearwall-slab structure
subject to "oycl1c loadlng.
" ..
\'
•
'. ",
-: 120 - . .
.'
o , ,
7'
c
c
c
§I- Shear Wall - "'\4'"1-
FIGURE 4.8 FLE~URAL REINFORCING IN COUPLING SLAB ,1 TO RESIST LATERAL LOADING (Rer. 1)
et
, " •
~{' >t: ï __ ',' ... ' _ ...... _' . ______ -..:..' ,'.::.--' _",~:.~-'~. ~_-C-"':"~_:"" ._r~ ., 'M •• ,,,,--"--
\
\
J
\ i
, " l'_
._.; .... '"
o
>,
o
/-
f' ...... ·_~ . .-------------_i-,II!I; .... <
121 -
c'
• l. CHAP'TER 5
RECO~DATIONS AN~\CONCLUSIONS
•
. 5.1 DESIGN RECOMMENDATIONS
The fol,lowing recommendations are based on. the results of the 1 ,
tests ~onducted on the three slab coupled shearwalls subjected to •
re~ersed cyclic loading, and on the results of previous studies ih ·this y U
a,rea. These recommendations apply to interior-bay, flat, coupllng
'slabs.
1
L 1) Based on the transverse displacement profiles and the
longitudinal relnforcement strain profiles, the longitudinal selsmic.
reinforcement should be placed as follows:
a) Wlthin a strip up to one corridor openlng, wide, centred upon.
the shéarwall centreline (as recommended by SChwaighofer and
b)
Collins (1), see Figv 4.8), when stirrups are not used in the
slab;
Within a st~ip up to two corridor openings wid~, centred
the shearwall centreline, when stirrups are placed in the slab. 4
2) The theoretical ultimate sheàr capacity of'the coupling elab
(V) can be predicted using the simple U-shaped critical eeotion
presented by Schwaighofer and Collins (1) (s~e Fig. 4.7) with the
followlng modifications:
a) For coupling slabs w!th stirrups placed across ~he ~orrldor
o
'."-0· , '
, "
: " 122 • J
.-
opening at a 'spacing not exceedlng d/2,
V :::: .9vn(3d) (t+d) (n'
,
'where vn ::: .33(ri; . t ::: thickness of the wall
d ::: eff'ective depth of tQe slab
b) 'For coupllng slabs coupling slabs without stirrups or with
stlrrup ~paoings greater than d/2,
(8)
3) 'Effectilv~ width recommendations are based on the progressive
deterioratlon of the specimen 'stiffnesses observed du ring the testing., -, a) in i~c.atio~~ where ori1~ minor earth~uakes are predicted, that
'" " , ls, wher.e no signif'icant y~elding of the.f'l~xura~ "reinforcement
and rela't1vely minor cracking - would be expeçted, tÇ) occur,. an,
b)
effective slab wi'dth équivale~t to 50% of the, corridor openins.
mày be ~sèd.
~
For ~~derate earth9uak~ zones, where' yielding'of the flexur~l.. " . ,
reinf'orcement ' in the sJ.ab is anticip'ated" effective slab, widths
between 10% and 25% of the corridor opening ~ay be ~~ed. " , "
c) 'For severe e~rthquake zones, the atiffness of the slab may be 1
19nored.
. ,
4)"' The full sla,b wldtb should be used in predicting the slab' s
ultimate .flexural capacity based on the yield line theory. -
--, . , --,
l'
'" " _.~. ' , ' \
, .
.,--"
-. ' , :
ï
.'
o .. '
"
0, • 1
: , ,
.. 123
. ' • 9
5.2 COKCLUSIONS l ,
The main objective of th'ls investigation was to study the
respcmse of slab ooupled ~hearwall modela sUbJected to ~9férsed oyclic
loading. The primary uoncern was to determlne the effectivenes~ of
stirrups with1n the slabs, tô evaluate the yield linè theory s~rength , '
predic.tion~, ,and to evaluate the effective slab widths. The, thr.ee
,1/3-scale models, which were modelled following the design of 1/2-scale
modela teated by Ta~lor (11) in 1977, were aubjected to a series of
impoaed vertical deform,ations progressively increasin~
\
'diaplacément ductili~ies until failure. The on1y notable.difference
b~tween the three modela was the spacing of ,the stirrups in the central
cor~idbr region of the slabs,' and the prlmary differences betwee~ these. , .J '
Jo •
'modela and' thl)se of Taylor was the disprQportionatElly hlgher, çonc~ète',
atrength in the for~~r specimens and the stlrrup spacings. 1
The exper.imental program ylelded .the force-displacement
characteri$tica of eaé!'t' apec~nÏen (Seètion' 3.1) a:! w~ll as~' thelr;
reinforcementoand concrete strains,' ând 'dlsplacement profiles. Good , ,
l 'slm1l1tùde was. éstàblish~d betweeri thls, study ,nct Taylor's (11) ~ ~
experimental prografu. ,
While the specimen contalning ~tirrup~ space~ ~t d/2 fal1ed in
flexure " and _exhib14ed an overall' dùctile response, the othéi- two
specimens, ohe containing 'no stirrups and' the other w1th stirrups ,,' • 1
spaced at d, faHed ln fi. vertl.9al sliding shear mode, at the toes of ,the
shearwalls. Th~ latter two specimens"hQweve~; continaed ·to carry Ibad
although the reaponses were not as ductile as the fOrmer spècimen.
AlI three specimens exhib1ted· rapid and severe stiffnes8 " '
degredaiion. ,.
"
. , '. ) . , . ,,' ....
(
;<
.. - \~
-,
. '
"',
. , '. O·
124 -
The~e results,- summarized in Section 4.1, ~nd co~pared with
the st~dies repdrted by Paulay and Taylor (3), Schwaighéfer'and Collins .. . '" ..
(1), and Qadeer and ~tafford Smith (5), lead. to design recommendations ,_ , , .
for the design of the reinforcement (Section 5.1). The results can be
summarized and conclus~qns drawn as follows:
1) The increas'e in the-shear resistance of the slabs, due to the .'
of' stirrups àt ,
lnclusion within the -slab. corridor width is best
marginal. However, th~ increase \
in duct~lity i3 substantiaL Thus, T
tbe stirrups controlled the se'verity 'of the damage to the slab at h~gh
dis placement duct;lities ahd reducéd the ~hances of - brittle failuré or )
'oomplete collapse. r - .....
2) The stiffness degredation aCter tne first'load cycle into the. , -
inelastic response' range ~as rapid and seyere. Thus, effeotive widths
'are only a small fraction of the -overall slap w1dth, (Section' 4.2).
TypicalIy, as ~ecommended 'for made~~te earthq~ake ~ones, the effectrve
wldth ls only', 10% to 25% of the corri.dor, o~enirig. ,In ~evereJ e~rthquake
zone.s, the contribution of, ~l,ab ",co?pling ta the· 9verall structural
response ià negligible. , l
3). . As' observed. by , the' other investigat.o'rs· (1, t· 5)'':' the , ,
participation of the seismio longitudinal reinfo~oement conoentrated in
the corridor opening was relatlvely higher than the Ion.gitudi-nal
reinforcement ~loser to, the bay oen~reline. Howèver, at high o
dlsplacement ductiiit~es the' participation of the l~bter re1nforqe~ent
was substantial.
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5.3 SUGGESTIONS FOR FUTURE RESEARCS
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The observed resp~ns~s of the test specimens to reversed· ,
cydUc loadlngs' ~ve r.aised manr ques tiorts whi'Ch should be' gi ven , .
'further consideration .in any further, research in this area • .- '. Wlth objectivè of estabIlshing use fuI design
r~comm~nd~tions for the.englnè~rl~g profes~lon, efforts shoù1d be made
to' identlfy effeotive ~ethods of enhanoing the shear reslstance of slab • 1
coupled shearwall structures which are also simple and not ·time
consumlng to implement with eX1stlng construction- techniques. For
instance, there is' the recent use of_ post-tensioned tendons ln slabs tc?
enbance thelr flexural cap~c~ty,and' reduce the ~ept9 of the slab. It " ,
ls'not known to what degree the compressive forces created' by the ,
post-tenslonlng would \
enhance ... , the shear resistance ,of' the'
'slab-shea.rwall unit under Ôycllc loading. '
~A ~ore.common feature ln North American struct~res, is the use
of drop'panels.to incrèase th~ depth of a slab around a cOlUmn, therepy . .
In~r~aslng its punching· ~esistance. The potential of Its appIlcàtion
ln slab-sh~arwall structures Is great (a possible use' i9 shown in
Fig. 5.1). Apart from decreas1ng th~,vertical ~eight restrictions 'for
the vèrtlcal stirrup' legs; ··thereby increaslng their efrectlveness ln 1 " ., •
.reslstlng shearing forces, it ls not clear as' to what
set-up---wotlld produce' 'if no stlrrups were pr~sent •
effect such,a:
. In thé same' vane, furtper testing' of a coupllng beam cast'
mono~i thl,ca:llY wÙh the sl~b, :as Introduced by' Taylor , requlred. Partlcular'attentlon sho~ld be càst upon thè'dètal11~g 'of ~hè.
" ,
~hear relnfo~cement wlt~in the beam to pr~vent prematu~e horl~ontal
slld~ng shear fallures.
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WALL
• • • • • • • • •••• • ,... , SLAB • •• • • - r, • • • .' • .• ,1
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\" . FIGURE 5.1 CROSS-SECTIO" ALONG THE WALL FACE CENTRELINE OF A
" . SLAS COUPLED SHEARWALL SPECIMEN WITH A DROP PANEL , .
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Repair _ techniques of damaged slab-sheal"wall structures which .
have been:subjected to mild to moderate earthquake forces (where , .
cracking and some yierding has occurred· Dut the structure retains its
overall integrity) have yet to be studied. It may be feasible, and ln
fact ecohomically desirable, than' , , to repalr damaged > area;3 > ra t her
rebuilding thé entire structure. ,
The response of these -rèpaired
slab-shearwall structures to subsequent moderate earthquakes ls
relatively unknown and needs to be lnv~tigated. : 1
Finally, the effect of wall spacings on stiffness degredation -. and the slab eff.ective width in cyclically loade~' models needn - to be
, stuc1ied.
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- 128 ..
LIST OF REFERENCES
1. SChwa1ghofer, Joseph, amd Co1l1n's, Michaél P", "An Experimental ~
Study of the Behaviout of Rélnforced Concreté Coupllng Slabs," ACI
Journal, Proceedings V. 7~, No. 3, Mar. 1977, pp. 123-127.
, . 2. Park, Robert, and Paulay, 'Thomas; Relnforced Concrete Structures,
John Wlley and Sons, New York', 1975, '769 pp. , ,
Paula~, ~ T., and :t'allor, ~R. G.,. "Slab 'Coupllng of Earthquake-'
R!Sist.i:ng' Shearwal~s, " ACI 'Journaf' Proceedings V. 7,8, No. 2, Mar. -Apr.
't981" pp:. '130-140. , l '
4. ' Barnard, Pet~r R., and Schwaighofer, 'Jo~eph,,' ":t'he . Int~ract10n of
Shear' Walls çonnected SolelY Throùgh Slabs," PrQceedlngs, Symposium on
Tall Buildings (University t)f Southampton, April' 1966), .Persamon Press,
'Oxford; 1966, pp. 157-113.
s'., Qadeer;~·A.siam, and Smith', Bryan Staffor.d, "The Bending Stiffness of , ' L-""
.. sl~6s;'co!lnect1n~' ~hè~ ~alls," ,~c:i' Journal, Proceediqgs V. 66, No. 6;.'
, " .
June 1969; pp. 464-473. '"
• 'J ~' . ... -~ ,~
'. ',) , , Chang, Y. Ch., "Slabs 1n Shea~ W~ld, Buildings," M.Sc.' Thesls,
, , ~ - , ' .. ,,- 'Jl .... ,_ ~... r •
. 6.
Department of 'Civil Engineering, Unlvèr~ity of~Topqnt9;·SePt. 1969. • ~ ., • "'1., -
-, ~- '"-
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7. Hirza, M. S., and Jaeger, L. G., "A Study of the Beha~our of
Coupled Shear Wall Structures," Proceedings, First Canadian Conference <
on Earthquake Engineering (University of British Columbia, May 1971),
Vancouver, 1972.
8. Coull, A., and El Hag, A. A., "Effective Coupling of Shearwall
Floor Slabs," AC! Journal,-Proceedlngs V. 72, No. 8, Aug. 1~15,
429-431.
9. Black, D. C., Pulmano, V. A., Kaballa, A. P.,
Supported on Walls," Memoires, International Association for Bridges
and Structural Engineering, Swtss Federal .Instit.ut.e of Technology,
Zurich, Jol 36-1, 1976, p: 79.
10. Szalwinskl, C. H., "Inter-Connecting -.$labs ln Sheaf Wall
Structures," M.Sc. Thesis, Department of CiVil Engineering, University'
of Toronto, Oct. 1976.
fi .' Taylor,· Roy G • ., "The Nonlinear Sesmic Response of' Tall Shearwalr ,
Structures," Research . Report No. 17/12,' D~partment ' .ot qlvll J , , , '.
-Engine~rlng". Uni,versl~y of Cantel"bur'y, Chl"btchürch,. 1911~ 2,34 ,pp.
l '
, --" 12. Canadian Stan,dards Association. Code for the Design of Conc~te
,St~uctur~s f?t" Buildings i CSA St~dard 'CAN~-A23. 3 .. ~77 •
1~. ,National Building Code of Canada, 1980, Issued by -the Associate , "
ComJi11ttee on thé National Bllilbl'ng 'Code , National·Research Couneil or
. Canada, Ottawa, ~RCC No. 17303. -
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130
14. Hirza, H. S., "Rel1abil1ty of Structural Hodela'," Proceedings of
the Joint Institution of Structural Engineers/ Building Research
Establishment - Seminar on Reinforced and Prestresaed Hicroconcréte
.j Models, Garston, England, Hay 1978.
"
15. Sabnis, H. G., Harris, H. a.,\ White, N. R. and Hirza, H. S.,
Structural Hodeling and Experimental Technique, Prentice-Hall, Edgewood
Cliffs, New Jersy, 1983, pp. 585.
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