CONCRETE LIBRARY OF JSCE NO. 25, JUNE I995
ENERGY DISSIPATION IN PARTIALLY PRESTRESSED CONCRETE BEAMS
UNDER REVERSED CYCLIC LOADING AND DAMAGE EVALUATION
gggagslation fiom Journal of Materials, Concrete Structures and Pavements, No.496/V—24, August
;;§:1:§:;;ji:;l;§.,;;:§:I;§i.513:6:5;<§;I;-:i:I:a§:1:2-:1;;:2
:5;~:;;;$:;.;.;:;:§<:-.->1;1V;-:-1+:-1+:-:»:-:-:-:-:<»:-:-¢;
..-.,=...-...-..;.=.,=n=-..1,»ea>=->=,=a=-;-=.>¢-:..-.:;;;.;g.;;;:;;;;;.;.'.<:-.q:;.;.;:<$1,151-.;4.;:;:;:;:;;;:;:;:;:
;EE§3E;5§;E55;E_1;1E.<‘:--'1 1 ,
.;.,,,;,-,,,,-A..-V-
--=‘-1:;-;.;..I
-=, --
»';.1¢E=E;£$
,'1;£=E=.‘i'
-:5:-:;.§:;:g:;.;.'
;:
,§‘.;13:;;5=j:;=;=g.;;gi;E ; 1. ;~;'=‘F555;~.=;1E=i==i===%="'$====='====§=;gEgE5%=E¢E;‘;E==;£: -1'. ' 15.21315-5:515:-':i
51:=i§:=i=i=:=E==.=:'=i=I-< .;5:1E5;=i1E= ‘=95’
='¢==§?lE=5=Ei""'51r
I 11. '1=3=i>I=?=§1
.i1-ii5§1i55551i£=55il1=;'£‘ .
'5-‘i=?=5=E=E=i»'
-F
:2.2:5:.1:=:s=$:E-a=&:=:e-.
i:2:i;=3===;.2E
3:1rE1?=3rE1E€.E-Ei€1E:i' .r..Ez'£=E=E=E=E=E=;===E1E=I1E1E=IrE
r3T=E€1ir=1£‘:'r£$1T=E=;fi =.£‘<§=':' H“'¢*‘1‘1¢f?21s5i¢EE<;£=~1»< . ‘<{rE"5r?i"i1
E2515EEE?i:EE‘I53E§¥iEE§T. 2.15555;:ii€=3%1E¢E1%=E¢;=¢=:- *1:=:=E=E=Z1E1‘;= =*¢r='=‘11’==<¢=£=E1. I ériz’-€.'<5-5
. - .
’ - - »:-.-.-:<=.-:-:1:-:-:-1-;-1-:-:- =
.9
:-f.'=:;;:-:-::-:-:\:-:-:\r-' ""'
'-:-:-:-:-:-:-:-.as
;-.-;,>;~;.;v.<,-;-;.-.-;..g.,;;::;+._. 5. ;<‘ ;;--;=;->;=;‘- =s==>:===:$z=:=$.-.;=:-:i>=:1:=;1:'"=1:-:=»;I:2;;;:_
:=:-:~.=:=:'~-=:>.A‘mi-1:»-:-:~. '<:=§k=<L'<~:
:"$31:1:?:i:i:ri:I:i:i$:!:i:
~.';-:-1';-:-:1;-:-141.1
21:.;g=:~:;=;r‘:;;.;=:;1:1:=:1;
- --=======:=====;====='=.:=:aa=-=;r:=-:r:=:=
rE='=‘r;1E=‘1E1§=51E=:E1E:: 3<E=Eé<> \=ir51?$=
. ==£:E=£=3£=E=i:i=E='13:52:51E=5=5<L=5=5<E=£=5
335153£5152;E5135;;1IgE;igIgE;;gEgi;=g?;i3
_ <22;5:512"”
ai»
e
===“<E;£5E;E;E;5
3 532115115;T5351f;E=E_11§=E
‘*3?
$233I';5:3.3:5:‘I5'513;5:3.T;5;3.3;i;§3;-‘ ‘:11?-§3‘>E~$ii:' 4' '5.-:5:'
'.'!5¢:3:-.13117:‘:1:1:‘:1:1:1:1:1:‘r1:5
-=---I‘I-I-II=:=:=‘I:=-1~I:1s~I:=-2=:=:=;=-= -X:=+I-=-'»>r»r~.
. '-'-:l:-:-:l:-:-:l:-=. :5:-1‘:-:v:;->:-:-:-: .e.;;-:+: :+: :91’: :=’:~:
5:i:~:7;I.?:\:-:~:1:-.4I:-:-:IL-:-:I:-:5i1Z3‘?9:3":<Z?_Z3'1'-'*1IZ’:5:§¥FF:3:3:§:\:-> '1':§?:i:5:5:5:Ei:7:q7:3:i11:3:-13:21"
"H-1»'-'-"+1>1-1-1~r-1-1»:-:<»r-.‘r»r' —- '5-‘*;;$:?“>—-—='~-'+:‘A:;:;:;:,:;:;:;:;:-:-:-:->:-:1:-:
..->1 ..-.9
.. .. 1...
-. . .. .
4-2:~:2-2:‘:2-2i:=-;<:=-=:~r=-K.ears:
9:5:‘:¥2i:?:i:§::i:E:;%:%:5:52:25;
;;=:1:=:=:I:l;=:1:§:;:1j5;;1:;:;:§:1:'. ':-:;- -
”
I
=:=:=:=: -2:;-2:2:7-2-2-1:: z:r:z:z:;: zs:;:;:¢;z;:.:; :z-==;.z-an..
.-zfitiiiz$255221=E;i;ti;§?;i5?:i=’
'-1+'-=:=:1;=:=:€i:E;fi§;Z;E;E;§;E;E§Y:
e
r-:-9-¢:-at-=->=-:-=-r-1-;-.-.
, 1.1.,<.¢.;;:-:;;:-:,::¢:;:;:~
.<-';::¢;i;‘:7:5:§:§.<:§:_§§:5;5$j:}-,
..
-:-=--. .‘:=.~:“.=:-:=~.--.
*2-.<=r:1z>1 :1:.;-:=:=:1;=:=:=:1:=;=:=:=;=:=;=;=:=:=;-:-;-=7:
.~.;-:-:‘' -;:-;-:\_:--:- _ -».~:-1-:¢:< -;-;-:-:-:-:-:»:-:-:-:-:-:'
1;:;:;:;;;:;:;;;:;:;L;
.-;-!-1-2-7-l-'»:‘I-i-I-J-.>»_-<-.-
. .-:v.-:-:-:-- .
-’-
.';<-'2§:i'j:§:-.
;?§:§:§:§:§:§1§:{:§:5:5:51}:§:§:§:?:§:§:f:§:§:§:
.--.><-=:%'E=-':E>"=s2:<r:~:-.-.-.»... =~>':¢;¢'=:13*'/,> , .-;-13; -1:111::;=;==:4=<;r;==-:1;:==-=;=;1;=:r:¢:=;a-.-..-.
-1
==I?5'E1'i‘*=>» '?=!13i;-“;5"’1? A‘ of:1:1r1:'<?:;E1:=:l>';§;':':1:I£:2=5:§:i:I:F:l:EI:7
--=:=E=E=2=EIi=:sE=:=5I:1;-:€¢:i=:=:=E=}=:=:=:=====-215:. ;=>.e=:;;:;> -=v.-:"<1:=-=:1.=--:.= I.>¢1:12er -'<‘-:=:=:=:=:=;=$:z?£=:€%=:=:$§Fii:1-'.':=-=:=-=:=-=:I
Susumu INOUE
Toyoaki MIYAGAWA
Manabu FUJII
We investigate the effects of mechanical degree of prestress, volumetric ratio of lateral confinement,
concrete compressive strength, steel index, and shear span effective depth ratio on the energy dissipation
properties of partially prestressed concrete beams under different loading histories. The relationships
between these test variables and non—dimensional dissipated energy are derived based on the test results.
Results indicate that seismic damage to partially prestressed concrete beams can be evaluated
quantitatively using a proposed damage index based on hysteretic dissipated energy.
Keywords:
partially prestressed concrete, non —dimensi0nal dissipated energy, loading history,
mechanical degree of prestress, volumetric ratio of lateral confinement, damage
evaluation
Susumu Inoue is Associate Professor of Civil Engineering at Osaka Institute of Technology, Osaka,
Japan. He received hisDoctor of Engineering Degree from Kyoto University in 1994. His research
interests include the ductility improvement of reinforced and prestressed concrete members and seismic
damage evaluation of concrete structures. He is a member of the JSCE, JCl, and JSMS.
Toyoaki Miyagawa is Associate Professor of Civil Engineering at Kyoto University, Kyoto, Japan. He
received his Doctor of Engineering Degree from Kyoto University in 1985. He is the author of a
number of papers dealing With the durability of reinforced concrete structures. He is a member of the
JSCE, ACI, JSMS, and a number of technical committees.
Manabu Pujii is Professor of Civil Engineering at Kyoto University, Kyoto, Japan. He received his
Doctor of Engineering Degree from Kyoto University in 1972. His current research activities are
focused on the optimal design of prestressed concrete cable—stayed bridges, structural safety
evaluations, and the durability of concrete structures. He has written some 50 papers on these subjects.
He is a member of the JSCE, ACI, JCI, JSMS, and a number of technical committees.
"~l51—
1.
INTRODUCTION
It is very importantto be able evaluate seismic damageto concretestructuresquantitativelyand
preciselyin order to judge the serviceabilityof suchstructuresafter an earthquake,and theneed for
repair and/orstrengthening. In general,seismicdamageisjudgedmainlyby a site inspectionof the
damagedstructures.Basedontheresultsof suchinspections,theresidualdeformabilityof the damaged
structuresis evaluated along with the maximumresponsedeformation[1]. The safety of concrete
structuresunderseismicloadingisusually estimatedfromthe deformationductility,so it is important
to relatethe degreeof damageto the residualdeformability.
It is alsowell known that the ductility of concretemembersunder reversedcyclic loadingsuch as
experiencedduhg anearthquakeissigniBcantlylowerthanthatundermonotonousloadhg. Thisimplies
thatseismicdamageto concretestructuresandmembersshouldbeevaluatedby takingintoconsideration
damageaccumulationdue to cyclic loadreversalsandrepetitions.
This situationhasledto certaindamageindexesthattakeintoaccountthedamageaccumulationduring
earthquakesbeingproposedbased on hystereticenergydissipationor low-cycle fatiguelaw [2, 3, 4].
However,these damageindexesarebased on test results forreinforcedconcrete(RC)membersand
they do not cover the case of partially prestressedconcrete(PPC) or prestressedconcrete (PC)
members. PPC structureshave attractedattentionrecentlyfor the high degreeof freedomtheygive
designersand they are often used for memberssubjectedto earthquakeloading as structuralbeams.
However,theenergydissipationpropertiesof PPCmembersare affectedby many factorsas compared
with RCmembers.Consequently,it is necessaryto quantitativelyclarifythe effectsof thesevarious
factorson energydissipationin orderto makepreciseevaluationof damageduring earthquakes.
In thispaper,the effectsof variousfactorson the accumulationof dissipatedenergyin PPC beamswhichulthately failin flexureunderreversedcyclicloading- arediscussedbased on resultsobtained
inexperimentsdoneby theauthors[5-10]. h addition,a newdamageindexbasedon the total energy
dissipatedup to theultimatestate is proposed.
2. EXPERIMENTAL PROCEDURE
2 .1
Test Variables
A largenumberof factorshave an inhence on the energydissipationproperties of PPC beams. In this
paper, however, the following five test variables, which are expected to have a relatively large
influence, are selected:
a) Volumetricratio of lateral confinement( p s)
The volumetricratio of lateral confinementp sis definedby the equation
P s=
volumeofone transeverse hop
X loo (%)
volume ofcoreconcreteconfinedby onehop
(1)
b) Mechanicaldegreeof prestress ( A)
Themechanicaldegreeof prestress A is definedas
a =__A
A, tv'AB fsy
(2)
Where,
gyp::
yalfeelad
OsftrpernegsttEeSsflpnrge
sSttreeesls
lngSteel
A s:area of non-tensioned deformed bar
fsy:yield strength of non-tensioned deformed bar
-152-
c) Concrete compressivestrength(fTc)
Table 1 Details of Test Variables
d) Steel index (q)
The steel index q is defined as Equation (3).
S e ri e s - A
S e r ie s - B
S e ri e s - C
S e ri e s - D
p s (% )
0 , 0 .6 , 1 .2 , 2 .4
0 .6 , 1 .2 , 2 .4
0 .6 , 1 .2 , 2 .4
0 , 0 .6 , 1 .2 , 2 .4
A
0 .4 , 0 .7 , i .0
0 ,4 , 0 .7 , 1 .0
0 .4 , 0 .7 , 1 .0
0 .4 , 0 .7 , 1 .0
4 0, 80
40
4O
4 0, 80
5 ,8 ,10, 12,2 3
5, 8, 12
5 ,8 , 12
5, 8 ,1 0, 12 ,2 3
flc
(M P a )
O I c,
q-qp.%=#.#
(M P a ) ∼
q
0 .2 , 0 .2 5 , 0 .3 ,
0 .2 5 , 0 .3
0 .2 5 , 0 .3
0 .2 , 0 .2 5 , 0 .3
a /d
2 .3 , 2 .9 , 3 .5
2 .3 , 2 .9 , 3 .5
3 .5
3 .5
nu m b er o f
63
l9
9
24
(3,
Where,
b: widthof cross section
s p e c im e n s
a cTcp:introduced prestress
dp.'s;effe?ctive
depth of prestressing
ds:effectivedepthof non-tensioned deformedbar
flc:compressivestrength of concrete
e) Shear span- effectivedepth ratio (a/d)
Detailsofthe adoptedvaluesof thesetestvariablesarelistedin Table 1 for each series of loadingtests.
In all test specimens,the tensile stress in the prestressingbars immediatelyafter prestressingwas
laSdjaustperdof3Beat7e?y%50iFae,h8t&n;=,e
aSnkdenlgFhAccfO.rrd
%g='.y
:.t?a.1ftar:ddulC.e.?
reefsf;cetcitvi:
ePlry:
SEetsEelncaCsOen
C.rfe;ec
=40MPa. On the other hand, the introduced prestressin specimens with fc=80MPa is 10MPa and
23MPa for A =0.4 and 1.0, respectively.
2i23p9dfBSBS
b
Specimens used for the loading tests were
simplebeamsof partially prestressedconcrete,
includingalso fullyprestressedconcretebeams,
with a rectangularcross section ofb x h = 10 x
20cm (b:width,h:full depth of section) and a
totallengthof 160cm.As shown in Fig.1, they
were symmetrically reinforced with
prestressingbarsandnon-prestressingdefomed
bars. The effective depth of the lower
a
a
no n -te n sio n ed ba ( 2
v /
EL
Jl ..J
] 33
1
Jtl pre
i stre ssing ba r
a
I
v
tl
tT
b=400mm,
c=200mm
for a/d=2.3
b=400mm,
c=100mm
for a/d=2.9
a=600mm,
b=200mm,
c=100mm
for a/d=3.5
46
80
O1
n 3
I
O
OtL) a) O
O
CU
r
1DD
100
46
L
E
Ll
un it:m m
=400mm,
80
I
K
a=500mm,
100
T1
2
Ei
a a
LL>
0
1
46
80
0
Q
V)
I
p;iBecs:tu9;sefi3ftShfBlin'eg=dff'i1;ndlea5a:3nSi10,n
lt
were used to fabriaa)
-
case, the real value
rcoa7end.hbearsst
e(fesf-c4a9g5eT[TE?s
with the JSCE.s Standard Specification for
Design and Constructionof ReinforcedConcrete Structuresin orderto prevent premature
shear failure. As prestressing steel, round
prestressingbars (SBPR A-1, B-1 and C-1)
wereused in all specimens.Theseprestressing
-153-
Ago.
BO
a
a)
a
7
Q
JL>
0
O
0
a
∼
0
a
1
+13
1l
1050N/rnm2
I
fpy=1 1 20l l 70N/mm2
loo
Q
LO
a
r-
P1
0
a
•`
0
a
80
4I6
O
7
$13
I
0
Q i
LE> rQ
C)
CU
A3 %
DID
1=8:i?
J3
Q
OJ
1
A:B:
3S
+6
O
1 f" -
r--r
4I9. 2
PIS
fpy=
1270N/mm2
71
00
80
+6
.,
1
0
LI e %
0
a
-
0
m2
100
(fRV=495N/mm2)
were used. The spacing of the
Q
Q
CU
DID
i 93 i t
.fp3y3=.1; /0;
ioir.Chemeln3,5o"mm
hooks
rectangular
at the
closedcorners
hoops
- r-
ill
ll
0
A:S.: g?9
of A isslightlyshaller
!;0.f7:seisdee%6gih=
longitudinalreinforcingt2fafne
bars. As lateral confinementand shear rein-
reinforcementwas chosenin accordance
Sfhs;=af
C)
CO
fpy=
920 N/mm2
Fig.1 Dimensions of Specimens
1 :poy9- 0 N
/m m2
,agsuteTer;ithPOScte-ieennstionpeaSte
an.df los,-(x8y,
g
W/C=45 %.
OSItlvo(xby)
J
¥2
I
A
+
-1
cyc(a
i
2 i3W
3l
In this paper, the following four
loading histories are adopted in
order to investigatethe effectsof
loadinghistoryon energydissipation properties.
negatlve
pos(uve(xby)
P
5
4
>
i
9
2
I
J)
3
2
i
8
+
3
cycle
negative
(a) Series-A
cycle
3
TB
-l
<J
3i]
r)cgatfvo
(b) Series-B
posJtJvoxby)
(
(c) Series-C
10cycles
a) Series-A
cycle
Series-A consists of gradually
increasingreversedcyclicloading
with one load reversal at each
denectionamplitude.h this series,
negauve
(d) Series-D
Fig.2 Applied I,oading Histories
fsh
egraapdS
ill?yd
idnec?eeacst1?d?
e.agTf
lgTd(e(
eaarsr;f;ge.cg;piac6ify(
if it dyiecledddte.n8e.CZ?.ni
,th2e6&,a3x
i6myL
A.lu.PaLo(
t6h
:).diflh
: C;1i:1nd
ad=RleiE;idoei
wherethe load E
&omthe measuredload-deflectioncurve and is somewhatlarger thanthe calculated
v6afuies
,oBt?i_?,ed?
using thebaaC,tsu
actual
yieldssttrreesnseihg
strength obfa,tsh
of theeh::1ffa?,recamdgy
reinforcing byTerlSdaenddafrei
bars-andpre_stressingbars.
tdhearti;zqhb,ye
iunSf1.nrgcltnhge
:Ldyiside
iahliuseiiglXICea;)
U
b)Series-B
Series-Bconsistsofgraduallydecreasingreversedcyclicloadingwithone loadreversalat eachdeflection
amphtude,inwhichthe apphed deflectionamplitudeis gradually decreasedfrom 6 uto 6 y.The sum
of the applieddeflectionamplitudesis adjusted to equal that of Series-A.
c) Series-C
Series-Cconsistsof mixedSeries-A andSeries-Bloading'in which the applied deflectionamplitude
isbst graduallyincreasedup to 6 uandthen graduallydecreased.The sum of the applied deflection
amplitudesin Series-C is also equalto that of Series-A.
d)Series-D
Series-D is graduallyincreasingreversed cyclicloadingwith ten load reversalsat each deflection
amplitude.
Theseloadinghistoriesare shownschematicallyin Fig.2.Specimenswere tested under symmetrical
two-pointloadingwith various shearspan lengthsandflexural spanlengthscorrespondingto the a/d
ratio.Aner the prescribedloadingsequences,all specimensweresubjectedto additional loadingcycles
untiltheir load carrying capacity fell to approximately509To
of the maximum.
3iBBSiiW
3-iBBBAhiQABiBs*
It isnecessaryto dehe theultimatestateof membersif seismicdamageto concretestructuresis to be
evaluated.In this paper,the ultimatestateis definedas thepointat whichthe load carryingcapacity
has fallento 80% of the maximumload.All testedspecimensreachedtheir ultimatestate as a result
of crushhgandspaningof concretewithinthenexuralspanas morecycleswere appliedafteryielding
of the tensilereinforcement.
-154-
a;30
B20
i
0
A
H15
D
V
J=0%
p._-0.67%
p '=1.93%
p._-2.68%
•`Q
Ql
0:.LEO.94
0
J=
I)
gpo
Jb
0:
^=0.50
^=o.70
^=0.89
%25
I
SSb5
Q
Z=
B 15
2
3
4
5
6
7
8
9
defleetlon,
101112
i
A I-0.94
: f''--8QNP&,
s:y5
EsR5
5
yO
A_-o.43
A _-o.60
^=o.89
: 1''=80NP&,
S510
a)
q
S
1''=40NF'&,
A : (''=40NF'&,
+
•`i520
•`E I
b i1 10
a
1
525
A:
0:
V:
l•` L
q3
J= J=Ql20
S5
vO
5 30
0 : ^=o.43
p
1
2
3
4
6/6yo'l
5
6
7
8
deflectlon,
9
1011
12
-0
1
2
3
4
6/6yo'I
5
6
7
dof/ect]on,
8
9
101112
6/6yc'(
Fig3 Effects of ps on EdTValue Fig.4 Effects of A onEdTValue Fig.5 Effects of fTcon EdTValue
(Series-A,
A =0.70)
(Series-A,
p s%2.50%)
(Series-A,
p s%1.25%)
On the other hand, the dissipated energy at each deflection amplitude Pd) is equal to the area
surroundedby each loop in the load-deflection hysteresis.Dissipatedenergy itself,however,varies
greatlyunderdifferentloadingconditionsforthe samesection.Therefore,non-dimensional dissipated
energyat each deflectionamplitude(Ed')is definedin this paper as follows,
Ei-
B:a
(4)
P ycd 6 ,cd
are the calculatedyieldloadand yield deflectionof each beam, respectively.This
tahnedef6flgt
zh&rien,aEgg
of differencesin maximum load carrying capacityamongthe beams.
3
i2BfkGtS_Qf3ksi*
a) Effectsof volumetricratio of lateral confinement( p s)
Figure 3 showsthe effectsof volumetricratio of transversehoops ( p s)on the energydissipationof
Series-A beams; the horizontal axis represents non-dimensional applied deflection amplitude
and the vertical axis is the non-dimensional dissipatedenergy PdT)at each deflection
Esp/
lfticda2.
As Fig3, the Eatvalueincreasesalmostlinearlywith increasingdeflectionamplitudewithin the range
ofrelativelysmall applieddeformationandthe rate of increaseis almostconstantirrespectiveof p s
vha.1xeevgelrV,esnt
ihpast
lTcer:2siLgeStr
vb=3:Sets.wdee
S?eeassaema?.sTmha?lE,d
IdVeai::t19.fnaab=;HtuwdiiE.
aTShTsailsl
ebre
cPasu;ealtuhee,
beamswith a smaller p svalueexhibitsigniBcantstrengthdegradationat smallerdeflectionamplitudes,
resultingin reduced energy dissipationlater.In other words,the point afterwhich the qTvalue does
not increase linearlycan be correlatedwith a point of significantstrengthreduction - that is, the
ultimatestateof the beam.
b) Effectsof mechanicaldegreeof prestress( A)
Figure4 showsthe effectsof mechanicaldegreeof prestress( A) on Ed'Valuesfor beamswith p sof
approximately 2.59To.
As seen in this figure, for the particular deflectionamplitude, the Ed' Value
EEcaol=fswslThanhe:r:its?n%cr^e?smg
"hs isbecause
theareaenclosed
byeachhysteresisloopbecomes
c) Effects of concretecompressivestrength (fc)
Figure5 showsthe EdTvaluesof the beamsmadewith concreteof different compressivestrengths.The
Ed Value of the flc=40MPabeam is somewhatlarger than that of the flc=80MPabeam at the same
-155-
a;30
B30
525
: q=o.257
+ : q--0,434
0
%25
ko
•`igpo
gy5
a/a_-2.33
a/d=2.91
/
/
,U
a/d=3.49
-I.-A
gy5
S510
S._q10
gas
vO
0
A
0
EB5
1
2
3
4
5
6
7
deflectlon,
8
9
101112
,0
1
2
6/6yc'I
3
4
5
6
7
deflect(on,
8
9
1011
6/
12
6yc.'l
Fig.7 Effects of a/d on Ed' Value
Fig.6 Effects of q on Ed' Value
(Series-A, A %0.45, ps%2.50%)
(Series-A,
A =0.46,
p s=2.43%)
d
enectionamplitude.However,the A value of the former is 0.43 (0.89) and somewhatsmallerthan
thatof the latter,whichis 0.50(0.94).Therefore,consideringthe differencein A value betweenthese
two beams, the effect of concrete compressive strength can be seen to be smaller than that of
volumetricratio of lateralconfinementand mechanicaldegree of prestress.
d) Effects of steelindex (q)
Figure 6 showsan exampleof Ed'Valuesof beams with differentsteel indexes; that is, q=0.257and
0.434. The Bgureindicatesthat the Eatvaluesof these two beams at the same deflectionamplitudeare
almost equal.Therefore,the effects of steel index on the non-dimensional dissipatedenergy can be
consideredto be negligibleif the othertest variables are the same.
e) Effects of shear span-effective depth ratio(a/d)
In Fig.7,Eatvaluesof beams loaded under differenta/d ratios are shown. The Eu'value at a particular
non-dimensionaldeflection amplitudeis almost the same irrespectiveof the a/d ratio. With different
a/d ratios,the acting shear force differseven if the applied deflectionamplitudeis the same. In these
tests, however, each specimen was reinforced accordingto the maximum shear force, so energy
dissipationpropertieswere almost identicalsince flexure is more predominantthan shear. This result
impliesthat the effectsof a/d ratioon non-dimensionaldissipatedenergyare smallif a beamis designed
to fail in flexureeven when loaded under a smallera/d ratiowithin the range of 2.33-3.77 adopted
in thesetests.
3i3W
Fromtheresultsof the Series-A tests,it is clear that the effectsof concretecompressivestrength,steel
index,andshearspan-effectivedepthratioon the accumulationof non-dimensional dissipatedenergy
are relativelysmall as comparedwith volumetricratioof lateralconfinementand mechanicaldegree
of prestress. Here, then, the process of non-dimensional dissipatedenergy accumulationup to the
ultimate state under different loading histories is discussedmainly in the light of the effects of
mechanicaldegreeof prestress andvolumetricratioof lateralconfhement.
a) Series-A
b
etweennon-dimensionaldissipated energy(Eat)and normalized
LeHdtBo(ns7p6S
TppFiea8daeraeScht?.wnnEep
ycal)for the Series-A beams. The Ed'Value of each Series-A beam
i
ncreases almost linearlywith incJr-6-asing
applied deflectionamplitudeup to the ultimate state.As
previously shown in Fig3, the volumetric ratio of lateral confinementaffects only the deflection
amplitudeat the point where the EdTvalue stopsincreasinglinearly,that is, at ultimatedeflection.On
the other hand, the gradient of the initial linear section is affected by the mechanical
prestress,made clearby Fig.4. Consideringthese results,the relationshipbetweenEdTand 6 /dBgyrc?1
eCaOnf
be expressedin linear form as follows.
-156-
1
LLl
I
i;3
LLJ
t
Jt
--- : t71eaSured
: c&fculated
+
5
ig:
f
0
g!1
/
5
/
7Q
i.,_EL
5B
5
C b
+ : measured
A
•`/+-
H
75
.''
I
.+
5B
,+I
I:i
¥f
7
(a) A =0.46
2
+
-.--
: m8&Sured
: c&Icu[&1ed
6
4
/,..''
,i.,J''
T 8 9101112
deffectlon,
6/ 6yc'I
e
%gg
5
J= 't}
,f
1 23456
,+.
/
Z=S
S5i
10
H
:i
---- : eelctlla(ed
gb
1Q
qb •`
.8'
A
C
3 4 5 6
deflectlon,
b
(.-,t'-
'
2
7 8 9
6/ 61C'I
3
'
4
deflect/on,
(b) A =0.71
5
6
6/ 61C-I
(c) A =0.87
Fig.8 Examples of Relationships between EdTand 6 / 6 ,cat(Series-A, p s-2.43%)
t3
A
A
-
-
C
Q
•`
i o
5i
a2
•`
Q
Q
0
1
•`
•`t>
S-1
.•`.......I.@..g.
8
Q
t>
-2
1
.;i-..,.......8s....--.-a.i'
OOO
-3
0
e)
-4
0.3
0.4
0.5
0.6
0.T
0.8
0.9
1.0
meobanfcatdegree of prestress, 1
(a) coefficient a
0 .3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
mechanlc&(
degree of prestress, 1
(b) coefficient B
Fig.9 Relationships betweenCoefficients a , B , and A
Ei-a73=.B
(5)
(626ycd,
Where, a and B are functions of the mechamicaldegreeofprestress A.
and (b), respectively.
;Bee
rceiaeff7:fehiss
baeTnedenF;ncgeq%c;ean,tS
aas
;uBm,eTtdo
^b
ealrien
S2roTn1:;i
:igss;9f-ia,)
although some scatter
is observed.ney can be expressed as in Eq.(6) and Eq.(7) from a regression analysisTofthe test data.
oc--2.43
A.3.25
a-4.17^-4.15
(0.43 S^So.94)
(0.43 S^S
(6)
o.94)
(7)
Figure 8 also shows calculatedE; values derived&omthe regressionanalysis mentionedabove.As
indicatedin Fig.8,the calculatedvaluesderived from Eq.(5)-Eq.(7) coincidewell with the measured
values.In somebeamswith larger A values,however,the differencebetweenmeasured and calculated
EdT
valuestendsto be greaterinthe largerdeflectionamplituderangenear the ultimatestate dueto the
instabilityof the dissipatedenergy.
b)Series-B
Figure10showssomeexamplesof the relationshipsbetweenEd'and 6 / 6 ycdfor the Series-B beams.
-157-
a2
L= 30
+ : me&9ured
h
J{
-M_ : C&lculafed
•`ii22:
: me&9ured
_", : c&lcul&(ed
5
gg!7
¥i
!g':i
!g
'A
: measured
!f:8
^'
A
/
!f2
5
7
2
6/ 6yQ'I
9
4
5
6
de(Iect/on,
(a) A =o.46
I:I
C b
,.4.,''
89701112
deflectlon,
+
_-.. : ealeulaled
/
0
J= I
34567
A
+
tiE7
A
g!15
iE 70
A
T
8
9
2
6/61O'E
A
9
4
dQ(Ieetlon,
5
6
6/61C'I
(c) A =0.87
(b) A =0.71
Fig.10 Examples of Relationships between Ed. and 6/ 6 ycal(Series-B, p s-2.43%)
In Series-B, the Eat Value is found to decrease
tt
0.6
S,0.5
aaLm,ohSLdqeu
;sd;taidCua!lnyy%e,neEe:
dafrpolie
d6due.nTehCit!Oi:
•`
becauseno new cracks occurfor deflectionamplia o.4
fudessmaller than 6 uwhen deflection amplitude
0 : ^=o.46
q
th
lS gradually decreased, so there is less dissipated
energy than in corresponding Series-A beams at
the same deflection amplitude. Therefore, the
relationship between EdTand 6/6ycal can be
written as Eq.(8).
q)
8
0.3
a
0.2
(626ycal,
•`
%1&
3
4
5
6
T
8
9 107112
6 H&X/
Fig.ll
J
^=o.87
A
'S'
The value of the coefficient 7, is affected by the
A value and the maximumdenection amplitude
^=0.71
D:
0.1
1 2
Ei-y(i)2
A:
6 yc.I
RelationshipbetweenCoefficient r
and
6max/6ycal
A
edTceatfirdS
LcZlsef1(g6urmg:
't.hFei
g7ur:
all:eShd:Trsei!eesraellslfsTsihnifnbveeTee;;ocpo.edfftci
etn.t
arm:7d?
,?alTaxiE
faaf
tees
beamstested,the equationsbelow are obtainedfromregressionanalysisof the experimentaldata.
v
=1.494
y
=1.488
v
=0.879
(i=)
(i=)
+0.088
(^=0.46)
(9)
+0.088
(^=0.71)
(10)
(^=0.87)
(ll)
(k)
+0.036
Figure10 alsoshowscalculafedEd'Valuesat each deflection amplitude derived from Eq.(8)-Eq.(ll).
Lh.e;slrcEtaatAds
Ewditvhal^u
e-s.?80TiCsi
dne.twaesl
lg:Atdh
:5eth=teafS:re^m=e.T.s;
aalihdO.u.g,h1.
tThhei:qsreL?ienT;
bbeeTaeues:
fE:
relativereductioninEatvalue&omthe hst cycleto the secondtends to becomelarger withincreasing
A value,while a quadraticreductionrate is assumedin the calculationirrespectiveof A values.
-158-
a20
i= 30
4L
...__ : caleul&(ed
I
h! 5522o5
A
+
i ;U: 1I/
+ : 1*e&Sured
.-_. : calculated
+
: :measured
____
c&Ieul&ted
!E16
/+I
g!15
iE 10
L
+ : me&sqred
ige
:8
gin
.I.'>/
7;g5
A,
/
C b
4
S%
.i.:.i}'
SB2
a b
¥L../
2
1 234567
89701112
deflect/ot7,
6/ 6yQ'l
3
4
5
6
7 I78
de(Iect]oT7,
(a) A =0.46
1
9
2
3
4
dQflectlon,
6/6ycJl
(c) A =0.87
(b) A =0.71
Fig.12 Examples of Relationships between Ed' and 6 / 6 ycal(series-C,
1 72
112
a 8
a 8
L4
A.4
5
6
5/5yc'I
p s-2.43%)
J=
C
Q
Q
•`
4L
b
Tb
;o
;a
•`
•`
-4
-4
-8
-8
0
_40
_30
_20
_1Q
0
10
20
30
40
50
0
_40
_30
-20_70
0
10
20
90
40
50
DeFlectlon, 6 (mm)
Deflectlon,
6 (mm)
(a) A=o.70
(b) A =0.89
Fig.13 Examples of Load-Deflection Hysteresis Loops (Sereis-D, P s%2.50%)
c) Series-C
Esiq?hraet
ls:esnhoinws
e?idi6A/
eeyaahrse
'aast
itohneShd1&Sefcot;otnh3
sslenrireesa-sSd?
e8T;LeT5?hbe:hhaaVnidO,r
tlhSeatThOaS:
it.h,eassatEee
dedection is reduced resembles that of Series-B beams. Therefore, the Eatvalue of Series-C beams
;:mad?aetiecXfPurneg;ie.dn
aosf
a6lin6e;cral
fuWTtchtiinoThOefde6fl/eStylCGln31:chrienasfnegd,eeflg;.cii.on
hcreasingregionand by a
d) Series-D
In Fig.13areshownsomeexamplesof load-deflectionhysteresisloopsfor the Series-D beams.Figure
14 gives an exampleof the ratio of non-dimensional dissipatedenergyat the n-th cycle(EdT(D(n)))
for each deflectionamplitude to that at the first cycle pat(D(1))). Figure 15 shows the ratio of
non-dimensionaldissipatedenergyat the flrStCyclefor each deflectionamplitudeof Series-D beams
(Edy(D(1)))
to that of the correspondingSeries-A beams at the same deflectionamplitude(Ea(A)).
Figure14showsthat the Ed'Valueat a particulardeflectionamplitudedecreaseswith increasingcycles
z5ea8d.;Pep.eft
ittioaT.atAtthtehfeirds?
flc;cctlie?
nAaRmef
lti;und
;.oafd
1,e6pyg
t;Fie.nEsd,I
tVhaeluEe;
a:atlhuee
siesC.0.nic6y.C3oe.hfa;hfaatl
laetntLoe
first cycle. Almost the same t-endencyis observed aAf
the deflecfionuampliludeof 2 6 eltPso;g6h
cvIJi
;lnV.aLfTeli^
7euLT=adu
urAg^pVe
;TfAiAounV;A7;
sAB&ve&L
;t"s&Lal7A{r.
W&LvevJfvLAe
ujAeAaAeA;Iiw.vn
vaAm•`p
fityldue";sv
T 3uD8Ath.er
•`A6yr
;lelduL
more,on the otherhand,the reductioninEdTvalue is somewhatdifferent;the fall in the Eatvalue fryom
the bst cycletothe secondis very small,and the total reductionratio afterten cycles is at most 10%.
At a deflection amplitude near the ultimate state, such as 6 6y, the Eat value begins to decrease
remarkablywith repeated cycles.
-159-
•`
lT
•`
i
ab
•`
LLJ
1
•`
tt
7 .1
I_
•`
0.9
uJb 1.1
tth
C
a
0.6
•`
b
0.5
i
L
LLJ
0 : ^=o.43,
A
U
V
0
l1
0.8
0.7
L
i 1.2
1.Ol
0.4
0 .3
0 : ^=0.43,
A : A_-0.70,
1'c=40NP&
f'c=40NP&
U : A_-0,89,
V:
^=0.50,
f'c=40NP&
f'c=80NP&
0:
('c=80NP&
^=o.94,
1.0
.b
0.9
Lq
S
0.8
0 .7
58y
48y
38y
28y
8y
68y
(I.=40AIF'&
l'c=40NP&
Ire_-40NP&
f'e=80NF'&
f'c=80NF'&
A_-0.70,
^=o.89,
^=0.50,
^=o.94,
tb
0.2
0.7
a
:
:
:
:
GA9o
Ag
Ao
Vv
5
0
0.6
10
1
1
10
10
7
1
10
10
1
2
10
n (cycle)
5
6
deFlect]oT1,
7
8
6/6ye'I
Fig.14 Changes of EdT(D(n))md'(D(1))with
Fig.15 Relationship between EdT(D(1))md'(A)
Repeated Cycles (Series-D, p s% 2.509To)
and 6 / 6 ,cal
fgedreonneectciyocnl
eaTfP
lbteundeest?.fnqso
rreeihuac:
d2t6o
y,u.p-ts.tp7oe
oufl
ttihmatat.ef
Set.ate;stphznEdLvgalsuee,iOefs
_SAribeeSa-mDsbaetatTes
same deflection amplitude, as seen in Fig.15. This implies that the energy dissipated at a certain
deflection amplitude is influencedby the preceding number of load cycles at smaller deflection
amplitudes.
Theseresultsallowthe Eatvaluesof beamssubjectedtoreversedcyclicloadingwith 10 loadrepetitions
at each deflectionamplitudeto be estimated,as describedbelow.
Asmentionedpreviously,Ed'Valuesat a particulardeflectionamplitudedecreasewith increasingload
cycles, and the amount of the its reduction is affectedby the applied deflection amplitudeand the
numberof cycles.It can be assumedthatthe reductionfromthe first cycleto the secondis the greatest,
thenbecominga smaller constantvalue fromthe secondcycleto the tenth. It is also assumedthat the
Edlvalues of Series-D beams at the first cycle at each deflection amplitude is lower than that of
correspondingSeries-Abeamswith only one loadrepetitionat that amplitude.These reductionratios
are taken fromthe experimentaldatafor Series-D beams.
OInthecaseof
6=6
(12)
Ei p(1))-Ei (A)
Eip(n))-o.7Ed'P(I))-%(n-2)
@Inthecaseof
(22; n2;10)
(13)
6-26,
(14)
Ei p(I))-0.88Ei (A)
Ed/P(A))-0.8Eip(I))-%(n-2)
(22; n2;10)
-160-
(15)
@Inthecaseof
6 2;36
Ei p(I))-0.88Ei (A)
Ed'P(n))-0.95Eio'(1))-9f(n-2)
Where,
(16)
(17)
(22; nao)
non-dimensionaldissipatedenergyat the first cycleat each
deflectionamplitude
Ed[(D(n)) : non-dimensionaldissipatedenergyat the n-th cycleat each
deflectionamplitude
Eat(A) :
nonJimensional dissipated energy of corresponding Series-A beam
calculatedfrom Eq.(5)at the same deflectionamplitude
n:
number of cycles
E at(D(1)):
Figure 16 shows a comparison of calculated EdT
values and measurements. As this shows, the
a 8.0
C
a 7.0
0
¥.-...
coo o
CO
: measured
: celcuI8tOd
;cS?yunlttaaetl:rSe;u:'ltVusan;:'trShe1'sn:iin1hCaeitd:ea:7gee:lea::5ht?t.h6neya
tudes of more than
>
b
This is mainly because
the EdTvalues at the 4fiesyt.
cycle at each deflection
amplitudecalculatedhm Eq.(14) or Eq.(16) tend
to be underestimated at larger deflection amplitudes.However,the differencebetween measured
and calculatedEdT
valuesis relativelysmall and EdT
values of Series-D beams can be well estimated
by this method.
6.0
J..--I.--
0
LJJ 5.0
.=.?I?54
4 .0
O
.=.'qxmqi
3.0
0
2.0
.:.'bn333
1.0
6y
10
7
3Q
Say
=: 26y
1
70
46y
70
7
56y
7
70
70
n (cycle)
untiltheUltimateState
Fig.16 Example of Changes in Measured and
Even if the total energy dissipatedover a given
Calculated Ed'Value
loadinghistory can be calculatedas described,it
(A =o.70, ps=2.66%)
isdifficultto evaluatethe degreeof damageunless
the totalenergywhich a membercan dissipateup
to the ultimate state is known. Therefore, the effects of volumetric ratio of lateral confinement,
=etchheE%Lda?egr(ef
Bfd.:;Sahreess,isacnudslsoeaddFegreTstory
onthenon-dimensional
totaldissipatedenergyup
Figure 17 shows the effect of loading history on the accumulationof non-dimensional dissipated
eEneErd!u:.
Tsniii,trh.exuA1;Te;:elS5tZ7st5Fedr'
uLt2a
eTrhg:addeuPa;.nyddSeOcrne:eag^
c-yVcAlcu.ei
aYihneg:eas^s=e?i.e4s6l
Lhteesvtas!utehaOnf
thatundergraduallyincreasingloadingas in Series-A. In Series-B tests, a relativelylarge deflection
cTcplehidne
iseaaEpsliewdi
tag?E2lSet,1oparde5fecs:,clsei
cChOnaSseq^u
e=n61.y.,61.wTghe
edsieagcor;catscrraecEsalanrgS
e.,deunri:5
etnheufF.si
unloading,
hysteresis loop and reduced energy dissipation. On the
otherhand,rasublebissinw;thp
lLnighh1?rg^O
fvtahleu
eps-(
6^=0.71 and 0.87), no significant difference according to
loading history can be observed. In these cases, diagonal cracking is insignificant even at large
deflectionamplitudesandthe crackrestorationperformanceis gooddue to the effectivenessof higher
Enter?gdyu?zd,parr?1?i;;3s;rFersot=stsheesecroenscu,list,eteee
aemffse
cits
Osfhl.o3dnT.g
bheisct.o=ye
osnmta7?e;
c3TtTZiactrieoans10nfgdi^s
slfaaltueed.
-161-
-I
L4J
N
40
i----.
H
100
L-.-.--.1-..-.-l.
-J-_-
I-
Lb 70
I
tt) 50
120
LN
Lu
H
i
l--.lL---
I-I
-.__-
e
A---i-1:-i.
.tL
,,>
•`tJL
8D
i
i
30
A : Serle9.8
I :/ Serlee-0
60
i •`
,t<ittI
40
Ji
+
: Ser/oe-A
A : Ser/e9-a
I : 9erIQe-C
6
+ : Serlec-A
A : SerlqQ-a
J : Serlee-a
/J
20
,I
1
/tt
t1
4
tl
I
J(
10
20
1
2 3
4
5
6 7
e
defJectlot7,
9 7017
12
A
1
2
9
4
5
8
7
deflect[on,
6/6yc'I
(a) A =0.46
e
9
0
70
7
2
3
deflectlot7,
6/6yc'I
4
5
6/6ycal
(c) A =0.87
(b) A =0.71
Fig.17 Effects of Loading Histories on EEdT(p s=2.43%)
120
110
Lq 100
BJ 90
80
70
60
50
40
30
2 a
10
•`
l-
L
a
b
120
110
LJJ 100
H
90
80
70
60
50
40
30
20
10
-
•`
a
A
0 : ^=o.43,
@:
^=0.50,
i:
A_-0.71,
I : ^=o.89
0
th
+ : ^=o.46
A:
0:
V:
•`
^=0.70
^=o.87
^=0.94
/-/
.,-.-----.A.,I/-i
A -----1/
1
2
3
yotume(rtc ratlo of hoops, p. (%)
Fig.18
0 : p.=o%
A : p-=0.67%
0 : p.=1.22%
V:
pJ=2.43%
.3
0.4
0.5
0.6
0J
0.8
0.9
1.0
meohanlcat degree of pros(ress,
A
Fig.19 Effects of A on EEdlult. Value
(S Cries-A)
Effects of ps on EEdTult.Value
(Series-A)
fT;rdPFgfsa7e8e=sd-S]h;:e3rageo;Las?i.;:he;bdee:be
hand, the value of EEd'ult.decreases with increasing A value within the range 0.43S A 5;0.94 and
can be assumedto be almost inverselyproportionalto A when ps is constant. Further,the
effectiveness
oflateralconhement onimprovementto theenergydissipationpropertiesis dependent
of A. From these results, the =EdTult.Value can be expressed as in Eq.(18).
(18)
EELt.=a
ps2.b(i).c(#).d
The values of the coefficients, a, b, c, and d should be estimatedseparately for Series-A beams and
Series-D beams, since =EdTult.
Values of Series-D beams are substantially higher than those of
Series-Abeamsas a resultoften load repetitions at each denection amplitude.On the other hand, the
values of these coefficientsestimated for Series-A beams should be applicable to Series-B and
tsheerite&-e?
sbeerTs:
saTZe.uthgehttO1:1
dEis#u:tevdaleuneesrg.yf
SSrTenstilihbeeuakiLartee
ssiaieeShna?tsVmearYledri.fferent
among
-162-
•`
I
4
12J 0
i
I:
b
h
0 : ^=o.43
a
+..
^=0.44
A:
^=0.46
i..
^=0.50
D:
I:
^=o.51
A_-o.70
b
10.
0
LIJ
H
e.0
E
L_
Lb
•`
A
n
A
+
0
A
A:
^=0.50
I
D:
V:
A_-o.70
^=0.89
C):
^=o.94
HLu240
200
A .
4Jd
v
160
120
A %v,I
40
I
D
+
2'0
-t
a
A
E]
20
40
0 : ^=0.43
t> 280
J1
60
320
V:
A_-o.77
Y:
^=0.86
O:
+..
^=o.87
^=o.89
a
60
80
80
40
: ^=0.94
100
120
40
80
120 160 200240280320
E Ed'u(1<c&l)
I Ed'ut(.(c'L)
(a) Series-A
Fig.20
(b) Series-D
Comparison
between E EdTulI.(mea)
Values and E EdTulI.(cd)
Values
The coefficients a, b, c, and a obtained for Series-A beams by regression analysis of the test results
are as follows:
a=-5.52,
b=32.48,
c=7.44,
d=-35.20
(standard
deviation
of =Ed'ul.. is 13.52)
On the otherhand, the values of these coefficientsfor Series-D beamsare the following:
a=-2939,
b=45.69,
c=30.28,
d=-46.44
(standard
deviation
of i:EdTul..is 24.01)
Eachcalculatedvalueofthe non-dimensionaltotaldissipatedenergyuntilthe ultimatestate obtained
from Eq.(18) (=Ed
andP) forSeries-A khcaldei?eSn-djcbaeta!?
geest,hee:tTvi!f;hTehTseeasfZgr:rae;
aslhu.ei
fhEtd
'yEeda)u)lt.inva7igess.
2c2n(bae)
33@
re:tll;Ti:teeldy
tlOa,ag
eCeLtai:rfeesg-rae
,baelatEos?
gasfhned
idclistcerdePbayntChye
bs;a%ezTdmdeeavSi:trieodna.nfd
lC3a.l5C2u.I
aiE?sfsE&'adi.nl1;
becauseonlytheeffectsof volumetricratio of lateralconfinementandmechanicaldegreeof prestress
areconsideredin the calculationprocess
If the degreeof seismicdamageto concretestructuresor membersunder earthquakeloadingcouldbe
expressednumerically, it would be a criterion by which to carry out repairs or strengthening to
damagedstructures.Herewe discussthe possibilityof evaluatingseismicdamage based on hysteretic
dissipatedenergy.
A damageindex (DI) as Eq.(19) in this study is defhed.
EEd'
DI-ii=
'19'
Where,
i: Ed'ul..:
the non-dimensional total energywhich can be dissipated by a member until
EEd.:
fE::tttiu=lataecStuaieufoafeadgni.v:n_iiAdelins5ohni:foernyergy
dissipated
duringl.ading
-163-
•`
Q
•`
•`
I)------_-_
Q
1.0
•`
o,6
qb
A : SIrfI&.a
D : SrTIIJIC
v : Strl*a-D
)ii:tt
I
g' o.4
5
Q
..-.-
Att I . E3
o.6
5 o.6
•`
:tit
q>
a o.4
6Tim
o : SrrtJJI-A
A : SrrlIJ-a
D : S*TIJaJ
v : SJrlt&-D
:::iB
--.I.ll
a..
Ji--4_.
A : SJTl*8-a
J=tqo.2
b
Eq".2
b
1.0
a 0.e
tL
B' o.4
•`
•`
YL
a Q.e
o : S*rltJ-A
•`
S
•`
a 0.8
5
•`
-t 7a7.=iL,
1.0
E:•`o.2
b
D : SIr'l*JJ
v : SITl*J-D
7
1 2 3 4 5 6 7 8 9 101112
2
3
4
5
6
7
B
9
10
.---
1
2
3
4
5
6
deflect[on, 6/6ycat
deflectlon, 6/6yc'I
deflectlon, 6/6ycBI
(a) A %o.46
(b)
(c) A %o.87
Fig.21
A i;0.71
Examples of Changes in DI (p s%2.50%)
DI=Orepresents the no damage situa
tion and DI=1.0 means that a member
has reachedits ultimatestate; that is, in
this study,when the load carrying capacity at a given deflection amplitude
falls to 80% of the maximumultimate
load.
As mentionedpreviously, the value of
differswith the number of rep=e
aEg'at.
cyclesat a particulardeflection
amplitude.This impliesthat the effect
of dissipatedenergy after the second
cycle on the degreeof damage is different from that of the first loading at
thesamedeflectionamplitude.In consideration of practical application,
therefore, it is desirableto modify the
I Eatvalue where several loadrepetitions take place at the same deflection
a
20
3l,
Q
18
C
Q
JL
ql
tL
Q
76
5 14
4
Z=
a 12
10
lJ
O.L e}
B.1 P.50J
B7 I.& 1} 1J
IJ
1} 1} 1J
1.5 1.f 17 1.8 1J
2JI ZJ I.1L,,
I.I
Z.S1,f
damage
)I
2.8&3
9A
ft7dex, DI
Fig.22 Statisticsof DI inthe Ultimate State
ST,pelEtluddaembaygue?
iEhgea
draeAuacgt!ocnaEa;Loernwbe
i:5acl::tSidde;Ssitnhge
tehfefeAtoodfif%SdS
i%ated?
Veanleureg
yaOnnd
tthhee
a=mg?.nd:.
value for a basic loading history which is already known, for example, Series-A. In this paper,
however,DI valuesof Series-D beamsare calculated from the = Eatvalues without modificationand
coefficientsfor Series-D beams. As for the
the I Ed'ult.Values are calculated from Eq.(18) us
Series-B and Series-C beams, on the other hand, in#i5:lt.
valuesare calculated using the coefficients
for Series-A beams.
Figure21 showssome examplesof the changesin DI during loadingtests. In Series-A, the degree of
damageis smallat an earlystageof loadingandthe ratio of accumulateddamage riseswith increasing
applieddeflectionamplitude.In Series-B, on the otherhand, the DI value afterthe first cycle reaches
0.3•`0.4. This implies that the beams are significantly damagedif subjectedto a deflectionclose to
the ultimate value at the first cycle of loading. Subsequently,however,the increasein accumulated
damagebecomessmaller.h Series-D beams,damageis accumulatedas ten load repetitionstake place
at each deflectionamplitude, and the ultimatestate is reached at a smaller deflection amplitudeas
comparedwith the correspondingSeries-A beam. In case of the beams with A=0.87, the DI value
ecause the relative difference between
doesnot reach 1.0 even at the end of loading. This is mai
ngEbd
'u1..
Value itself is smaller than that of a
gaelac=lai;tdh
aEl:tug.raxdvtah.euea?tual
valueislargesincethe
h Fig.22,a histogramof DI correspondingto the ultimate state calculated for each beam is shown.A
high degree of scatter (C.0.V.=0.454) in the DI value at the ultimate state is observed, although the
averagevalue of DI is almost 1.0. The relative difference tends to be particularly large in the case of
-164-
b
eamswith higher A value andlower p svalue. Thisis mainly dueto thegreater uncertaintyin the
defhition of theultimatestate underreversedcyclicloadingand in the effectsof test variables.
As previouslymentioned,non-dimensionaltotaldissipatedenergyup untiltheultimatestate is affected
by notonlythetestvariablesadoptedin this studybut alsoby certainother factors.Therefore,further
investigationsof energydissipationpropertiesarenecessaryin orderto establishanevaluationmethod
for seismicdamageto concretestructuresbasedon hystereticdissipatedenergy.
4ii2QW
In this paper, the effects of varioustest variableson the energydissipationpropertiesof partially
prestressedconcretebeamsareinvestigated.h addition,a damageindexbasedon hystereticdissipated
energyis proposedbasedon the experimentalresults. The mainconclusionsreachedin thisworkare
as follows.
(1) The energydissipationpropertiesof partiallyprestressedconcretebeams are affectedmainlyby
volumetricratio of lateral confinementand mechanicaldegreeof prestress.The effects of concrete
?ompressivestrength,longitudinalsteelindex,andshearspan-effectivedepthratio are relativelysmall
ln comparison.
(2)Thenon-dimensionaldissipatedenergy,which is the dissipatedenergynormalizedby the product
of calculatedyieldloadandyielddeflection,of partiallyprestressedconcretebeams is also influenced
by the loadinghistory.The value of non-dimensionaldissipatedenergyat eachdeflectionamplitude
can be expressedas a linear functionof the applieddeflectionamplitudeas the deflectionincreases,
andas a quadraticas the denectiondecreases.Thevalues of the coefficientsin these functions depend
mainlyon the level of mechanicaldegreeof prestress.
(3) The non-dimensional dissipated energy at a particular deflection amplitude decreases with
increashgcycles.Therate of decreaseis affectedby the applieddeflectionamplitudeand the number
of cycles.Thenon-dimensionaldissipatedenergyat the first of ten loadrepetitionsis less thanwhere
onlyone repetitiontakes place at eachdeflectionamplitude.
(4)Thenon-dimensional total dissipatedenergyup untilthe ultimatestateincreaseswith increasing
volumetric ratio of lateral confinement,while it decreaseswith increasing mechanical degree of
prestress. It can be estimatedto a certain extent by a functionof these two variables.The value of
non-dimensional total dissipatedenergy until the ultimate state is almost constant if the sum of
applied deflection amplitudes is the same, although it tends to be somewhat smaller with less
mechanicaldegreeof prestresswhere the deflectionis graduallydecreased, as in Series-B.
(5)The degreeof damageto partiallyprestressedconcretebeams under reversedcyclicloadingcan be
expressedquaJltitatively
by a damageindexbasedonthe hystereticdissipatedenergy. However,further
investigations on the process of dissipatedenergy accumulationare necessaryfor a more accurate
evaluationof seismicdamageto concretestructures.
References
1
2
3
P ublic Works Research Center: Manual for Restorationof CivilEngineering Structures Damaged
during Earthquakes, Ministry of Construction, 1986
Park, Y. J. and Ang, A. H-S.: Mechanistic Seismic Damage Model for Reinforced Concrete,
Joumal of Structural Engineering, ASCE, Vol.111, No.4, pp.722-739, 1985
Uomoto, T., Yajima, T., and Hongo, K.: Damage Evaluation of Reinforced Concrete Beams
Subjected to Cyclic Bending Moment Using Dissipated Energy, Proc. of JSCE, No.460N-18,
pp.85-92,
[4]
1993
Stephens, J. E. and Yao, J. T. P.: Damage Assessment Using Response Measurements, Journal
of Structural Engineering, ASCE, Vol.113, No.4, pp.787-801, 1987
-165-
[5]
Kobayashi, K., houe, S., and Matsumoto, T.: helastic Behavior of Partially Prestressed Concrete
underReversedCyclicLoading,Proc.of the 5thCanadianConferenceon EarthquakeEngineering,
Ottawa, pp.841-848,
1987
[6] houe, S., Kobayashi,K., and Katsuno,Y.: helastic Defomation Propertiesof PartiallyPrestressed
Concrete Beams under Reversed Cyclic Loading, Proc. of the 42nd Amual Conference of the
JSCE, Vol.5, pp.232-233,
7
8
9
1987
Igo, Y. et a1.: Load Carrying Capacityof PartiallyPrestressedConcreteMembers under Reversed
Cyclic Loading, Proc. of the 43rd Amual Conference of the JSCE, Vol.5, pp.610-611, 1988
Inoue, S. et al.: Application of Rectangular Hoop as Lateral Confhement for Concrete Beam
Members, CAJ Proceedings of Cement & Concrete, No.43, pp.340-345, 1989
Inoue, S. et al.: Effect of Loading Histories on the Energy Dissipation of Partially Prestressed
Concrete Beams and Their Damage Evaluation, Proc. of the JCI, Vol.15, No.2, pp.401-406,
1993
[10] Fukushima,Y. et al.: Effectsof Various Factorson the DissipatedEnergy of Partially Prestressed
ConcreteBeams,Proc. ofAmual Meetingof the JSCE Kansai Branch, pp.V-5-1-V-5-2, 1993
-166-