鉄筋コンクリート造実大7層建物の振動特性および動的応答解析 : 日米共同耐震実験研究

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:

DYNAMIC

PROPERTIES

AND

RESPONSE

ANALYSIS

OF

A

FULL-SCALE

REINFORCED

CONCRETE

SEVEN-STORY

STRUCTURE

-Part

of

the

U.

S.

-JAPAN

Cooperative

Research

by

YOSHIKAZU

KITAGAWA'

and

MITSUMASA

MIDORIKAWA",

Members

of

A.

I.

J,

1.

Introduction

As

part

of

the

United

States-Japan

Coeperative

Research

Pregram

Utiiizing

Large-Scale

Testing

Facilitiesi),

full-scare

seismic

tests

on a seven-story reinforced concrete

(RIC)

structure were recommended

in

order

to

make

comparisons among actual

full-scale

structural

behavior,

small-scale model

behavior

and analytical

studies,

and

in

order

to

assess

the

damage

and safety

levels

of structures

designed

by

current

design

practices.

Consequently,

pseudo-dynamic

seismic

tests

were

peJformed

in

order

to

investigate

stiffness, strength and

inelastic

behavior

of an

RIC

test

structure subjected

to

simulated earthquakes of

different

intensities.

Also,

vibration

tests

were carried out

to

examine

the

dynamic

properties

of

both

elastic

and

damaged

test

structures.

This

paper

presents

the

results

of

vibration

_tests

and

inelastic

dynamic

response analyses on

the

full-scale

seven-story

RIC

structure,

In

vibration

tests,

the

structural

dynamic

_properties,

such as natural

_periods

of

vibration, mode shapes and critical

damping

ratios, were obtained at

the

beginning

and

the

end of

_{pseudo-dynamic}

seismic

tests.

Vibration

tests

were carried out

five

times

throughout

all

test

_programs.

Finally,

a change of

dynamic

properties

of

the

test

structure

is

discussed

and

interpreted.

In

addition

to

vibration

tests,

inelastic

dynamic

response

analyses were

done

which considered

the

dynamic

effects of strain rate and

stress

relaxation

during

_the

pseudo-dynamic

tests.

The

analytical results were compared with

the

_{pseudo-dynamic}

test

results, and

the

dynamic

effects on

inelastic

behavior

of

the

test

structure were examined.

Pseudo-dynamic

tests

were comprised of

two

_phases.

In

the

first

_phase,

the

structure without nonstructural

elements

was

tested

under various

earthquake

motions6]･')･S}･ii}･i4)･iS)･i8).

After

the

first

_phase,

the

installation

of

various nonstructural

elements

followed

the

repair of

the

damaged

structure.

In

the

subsequent $econd

_phase,

the

effectiveness ef repair and

interaction

between

the

structural

and nonstructuTal elements was exarninedi2).

In

this

paper,

the

test

results

in

the

firSt

_phase

are

discussed.

The

test

results

in

the

second

_phase,

however,

are

listed

and

shown

in

the

tables

and

figures

for

reference.

2.

Test

Program

and

Procedure

of

Vibration

Tests

2.1

Test

Building

Figure

1

illustrates

the

test

structure.

In

_{pseudo-dynamic}

tests,

the

load

was applied

in

the

X-clirection,

i.

e, _,

the

longitudinal

<NS)

direction.

The

cross section of columns and

_girders

was

₅₀₀

×

500

mm and

₅₀₀

×

300

mm,

respectively.

The

structure

had

a

shearwall

of

200

mm

in

thickness

in

the

middle

line

(B

Line)

_parallel

to

the

NS

direction.

Shear

walls of

150

mm

in

thickness,

isolated

from

the

columns, were also arranged

in

the

exterior

frames,

1

and

4

Lines,

_parallel

to

the

Y-direction,

i.

e, _,

the

transverse

(EW)

direction,

Cross

sections

of

members are

listed

in

Table

1'S).

2.2

Test

P:ogram

Table

2

indicates

the

test

_program

and sequence.

Pseudo-dynarnic

tests

were

comprised

of

two

phases

as

mentioned above.

Each

_phase

censisted of

four

subprograms.

They

are

described

in

detail

in

Refs.3

and

9.

The

structure

was

subjected

to

an earthquake

before

starting

the

first

vibration

test(VTI).

'

Head,

Civil

_Engrg.

Div,,

Building

Research

_Institute,

_Ministry

_of

_{Construction,}

_Dr.Eng[g.

#

_Chief

_Res.

_Struct.

_Eng[.,

_Struct.

_Dynamics

_Diy.,

_Building

_Reseaich

_Institute,

_Ministry

_of

_{Const[uctlon,}

_D[.

_Engrg.

{Manuscript

received

July

8,

19S6)

2.3

Procedure

of

Vibration

Tests

Viisration

tests

(VT)

were carried out2]･')･SL9)'i3)

five

times,

labelled

VTI

through

VT5.

The

state of

the

structure or

the

degree

of

damage

at

each

stage

of

the

vibration

tests

are

described

in

detail

in

Refs,

3,61

11

and

12,

and

briefly

reviewed

as

follows

:

i

)Test

VTI

;

the

structure was

in

the

elastic range,

iOTest

VT2

;

the

maximum angle of

rotation

of

the

structure

had

reached

_ll64

at

the

roof

level

in

the

_previous

test

SPD43L`)･"),

Figure

2

showF,

the

side

view of

the

cracking

_pattern

in

B

Line,

iii

)Test

VT3

;

the

damaged

structure

had

been

repaired

by

means of

the

epoxy

injection

technique]2),

iv)Test

VT4;

various noristructural

elements

such as spandrel

beams

and

_partition

walls

had

been

installed

in

the

repaired structure'2].

The

reinforced concrete spandrel

beams

were set

ih

one of

three

s'pans of

Li4es

A

and

C,

that

is,

between

Lines

3

and

4,

frorri

the

2nd

fioor

to

the

7th

floor

level.

The

_partition

walls

were arranged

on

the

3rd

and

5th

floor,

The

types

of

the

_partition

walls were as'

follows

;.(

1

)metal

stud and

_gypsum

board,

(

2

)wooden

stud,

_gypsum

lath

and

_plaster

finishing,

(

3

)metal

stud, metal

lath

and cement mprtar

finishing,

O

o

e

@.

Tablel

Ligt

of

Mernber

Cross

Section

@i'==:r=+i==rT--ill--:,--'

-'

_･

V

1/

ld ±1 bl

Ll

Lx

e

..S..-"

:

"..jil... e 11 _{IP /b 11 ll}

p

I:

ll

ll

!!

!l

8

11 11 11 11 14 e 11 _{tl 11 11} /i ut H LI /1 11 at

@

===IL==="

==Lta=ti===!'=== 1 db ll d8

im

cu

6ooo sooo 6eoo 17ooO

-1 Cross ties ere DIO elOO ineoundery Colufim et 1.st a"d 2-nd stories.

Table

2

Test

Sequence

secutn

ev

Fig.1

Plan

and

Elevation

of.the

Test

Building

'

eeemooeneaeoegnggeanoeeMoRee

COLUHH ENDCEHIER VALL

Longi'

tt

_Beem :"._{ttS:DSOOI500bxO3oessoeThticknesszoo}

U-uo

MainBarse-o!zTop1-Dlg!-DlgLenthsooo HeopD]oelooaottom2-D193-D19Reinf.vsH2-Dloe2oo CrossTiesDlopsee+1stirrupDIOelooDloe2ooCelumsooxsee E"OCENTER OVTSIDE[EHTERINStDE[Unit.nen, Trens,HedmuauoSubaeamuououo b:D300x450bxD 2SOx450 TopS-DISz-DISTep2-D19z-D193-D19 Bottom2-D193-D19Bottom2-D192-Dlg2'e19 StirrupDloelooOIOe2ooStirrup D]Oe!oo TESTMe. r.ONTENTS n-1FreeEfer[edvibratientests-r

_{-tttt.-tt-m-tt!1020ko't.m}

FtL]Eachfleorlevelloedringtest SL]Staticloadingtest underinvertedtriangular]eaddistribution SPD1Pse"do-dynemictest(Gmax

±

±dnm, i'lodifiedHITAGIKENOKITOHOKUUNI.NSRmaxtlt70nO)Gmas=23,5eeT' SPD2Pseude-dymemictest[Emex= ±5S"En, MedfffiedMITAGIKEHOKTTOHeKUUNI.NSPanax=lf400)rgTax=105gn] SPD1Pseudo-dynamictest(Emex= ±ISIffun, riodifiedTAFTEW1052dnax=3ZOoral-knei!3t4eD) SPD4Pseudo-dynemictest{6max= ±290mm, TOxu,CHIOKIHACHINOHEE!"Giext350oel'Rmax=li7S} FLL2Eethflearlevelloadingtest VT2Free&forcedvibratientestswr!sle?o)tkg-m REpairs byepoxy injectien

VT 1FLL

3Free

e forced vibretien tests wr

=

5, 20 kg-m Each floorlevel loedingtest

Arrangement ofnenstructurel elements

Elg.2

o

Crack

@

@'

o

FRAHE-B

ing

Pattgrn

in

Line

B

after

Test

SPD4

VT4Free&forcedvibretiontestswr=ZOkg-m FLL4Enchfleor]evelIDadfingtest SL?Staticleading underinvertedtesttriengularleaddistribution SPD5-]Pseudo-dynemibyuseofthe

(kffex=lt]oooctestssameinput

-3t400)matienfromSPD1teSPD4

_'

SL3Staticloadi

_{(knax=1/50)ngtestunderuniform･}

'

loaddistributian. VT5Free&farcedvribretiontestswr

±

5,10,?Otq･m'

SmaxRmsx

HGma.

wr

:

Target

maximum

dispEacement

at the roof

leve[

:

Taiget

maximum angle et rotatien

ema.fH

:Total

heihgt

of

the

test

building

:Maxirnurn

acceleration of an

input

ground motion

:Unbalanced

moment adopted

in

transtatienal

nance tests

(4

)autoclaved

lightweight

concrete, and(5

)concrete

block,

v)Test

VT5;at

the

final

stage of

the

static

loading

test

SL3,

shear

failure

hpd

occurred

in

the

shear

wall

at

the

first

story.

The

maximum rotation angle

of

the

structure

had

_gome

up

to

1167

at

the

roof

level.

In

the

VT

test,

four

types

of

clynamic

tests

were carried out

_;

a)

Observation

of natural earthquake response

(EQ),

b)

Observation

of microtremor excitecl vibration

<VT-M-1-5),

c)

Free

vibration

tests

(VT-F-1-5),

d)

Forced

vibration

tests

(VT-G-1-5).

There

was repetition

of

sudden

release

seven

times

with applied

tension

between

_O,

₅

'

and

3,5

tons

in

each

free

vibration

test.

The

forced

vibration

tests

were carried out

by

employing

two

rotating eccentric weight

exciters

on

the

rooL

At

one

time,

the

structure was excited

translationally

in

the

NS

or

EW

direction,

while at

the

other

time

the

torsional

vibration was

_generated,

In

torsional

vibration

tests,

the

sweep'up

technique

around

the

torsional

natural

frequency

was adopted

because

of very

low

level

excitations.

3.

Measurements

and

Data

Reduction

3.1

Instrumentation

and

Measurements

The

free

vibration

tests

(VT-F)

were made

by

the

"pull-back

and

quick

release" method.

The

forced

vibration

tests

(VT-G)

were

_performed

by

two

exciters as shown

in

Fig.

3,

whose

characteristics

and

the

adopted

values

of

unbalanced moment are

listed

in

Table

3.

The

instrumentation

system consisted of structural response

transdttcers,

amplifiers associated with

integral

circuits, a magnetig-tape recorder and oscillographs.

The

transducer

was a velocity and electromagnetic

_pickup,

with a natural

frequency

and critical

damping

ratio of

1

Hz

and

O.67,

respectively.

Figure

₃

shows

the

typical

measurement

locations.

A

strong-motion accelerograph,

SMAC-M

type,

was set up on

the

roof

to

obtain

the

natural earthquake responses.

3.2

Data

Reduction

In

VT-F

tests.

the

fundamental

natural

frequency

and

the

damping

ratio were obtained

from

the

ayerage of

the

stable and

first

five

waves of

the

record.

In

VT-G

tests

by

Exciter

1,

accurate values of

the

translational

natural

frequency

and

associated

damping

ratio could

be

obtained

from

the

resonance curves.

The

damping

ratio was obtained

by

use ef

the

half-power

(bandwidth)

method.

The

records

of

torsional

vibrations

by

Exciter

2

were

Tabie

3

Vibration

Exciter

Characteristics

SedhrWesternlbataki Ref,Eartmpake

Jamary 2B 19M di100

g

s

N

t

8 dlO

1100

vo

i

e

e

SIO% s te ls 10 Tin,eCsecl moesuredReefAcce[eration

Fig.4

Accelerograms

on

the

Roof

Obtained

by

S,MAC-M

1.

Exciter2

Excherl

oe@@

a

,9

bl li O 11 L

SL-7N

a

LaadingDirectien

O

@

a

@

-e.horizontalcemponent

eyertlcatEonyponent

O.

ao

2.o

4.o

6.o

s.o

_f(Ht

Fig.3

Location

of

Piekups

and

Vibration

Exciters

in

Longitu-

Frequeney

dinal

(NS)

Direction

Fig.5

Fourier

Spectrat

Ratio

ef an

Earthquake

Record

-34-CharacteristicExciter1Exciter2

(BRI-Btype){EX-4DCtype)

Dlrection TwohoritentnlOnehorilental

e"evertical

Hiximumgenerated force,intonf lo O.1 Frequen[yrange,inHertlo.Z-IS 2-25 Unbelancedmement.

inkiloeram-meters

'

75 o.e4 Adopteaunbalan[edmoment,s,10,20 o.e4 inkilepram-",eters o _{EW-Ccapctxtrt} Mlai.s3.Sgal o% 5 10 IS 20T'inetseel 1t"edliLJLSouth-Weste;nlbaraki-Pref.

Eerthquake

1981.1.2e

1111tltpl1lldi

NSEW---

-Jdl4,pbl"i11JLPbr+-t.t

-SMAC-M

I1"lllL/lLlii:d1,

N-S

:LJ-"-1ldtl"'iv-tXxNtS

-.t

Table4

Natural

Periods

and

Damping

Ratios

Obtained

by

Vibration

Tests

vrl vlz VTI VT4 YT5 beforeP.D.TestafterP,D.TestdftetRepairefterN,E.afteFFeiluee Her.6-919SlJulys-lolgslAug.1-419SlSept.9-1219SlNev.S-719Sl PenodDamp.PeriodOnmp.PeriedOnmp.PerjedDftmp.PeriodDamp. Micro-trerror

tl

NSlstO.42sec.O.TSsec.O.S5s!c.OA3see.O.SOSDC.

(VT-M)2nde.11seE.O.15sec.O.13set.O.12sec.O.21Ee[.

ENlsto.zyse{.O.35sec.D,3Gsec,O.3Esec.o,qssec, 2nd O.11sec.D,11sec.O.11sec.O.14sec. FreeVibration

'

NSlsto.4Ssec.O.021O.8Dsec.O.02nO.57seE.M.O19O.45sec.O.02So.s6seE.O,O19 11dl/ 1/ 1

CVT-F)

O.81se[.O.031o,6esec,o.olsO,4Tsec.O,035ostsec,o,o3r

+]

FercedVibratiDn+z NS}str O,83sec,O.O09o.sosec.o.mlx O.S6sec.O.O15 x O.S5sec.O.Ollx I O.91sec.O.O13

{VT.G]

O.41seE.O.O19O.91sec.O.O19O.63sec.O.O13O.52sec.O.o?qO.96sec.O.Olg NSZndx O.11sec.O.O14O,i4sec.O,OIZr O,2fisec.O.DIO x O.]8se[.O.O12x x o.zlse[.O.O19 O.11se[.O.Ol?O.20sec.O.O19o.ISsecO.OISO.14sec.O.OISe.ztsec.o.e14 EvelstO.10sec.o."stc.o.oleO.44se[.o.024e.44sec.O.o20O.S]sec.O.e!3 2ndO,OE9sec.O,14sec,O,O13O.14sec.O,14sec,O.O13O,]]sec,O,O19 TorsfionO,23sec.O.00eO.30sec.-O.2gsec.O,2Ssec,O.31sec. FreeVibretion

fP,D,Test}O.q3sec.{1.trtrm)O･74s{c.{o.im]_{1,scsec.(15im)I} D.STIec,{1.0mo)x

Notel

_h)

_(-)

Data

were not obtained.

'3)

Three

_{values ineach colurnn}

20

kg-m,

Table

'2)

_(X)

_Vibtation

_{testwasnot carrledout.}

correspond tounbalanced rnernent5, 10 and

5

Cemparison

among

Natu'ral

P

Raties

in

Longitudinal

(NS)eriods

and

Damping

Difection

ModeNumberE]rthq.RecordFreevib.TegtForcedVfib.Iest

'StaticTettFrameAnalysis

NeturelPerfiod(sec,)lstZndO.410O.107O.43t4o.e3o.11o.a4sO.125rmoftS6s'nsos(O,4sa)tFO.133O,l2th DampingR-tiolst2ndO.02E-]D.021O.O19+iO.Ol?.l

tt+!-7+-Yeung's modulus is210 tlorm'.

Tovng'srrodulus is!44tXan2.

Dampjng rntio isobtained by the hnlf-power method. Data -ere not obteined.

Nuh[eele.---,2<EeEdeUea･-o!gdi :vE=E:.(6aj

Fig.7

4 2

oO.5

o･.--ocrE]=vetrco

so

60

40

2

RFIIFNS-Direction

Micre-tremor111,34Hz(O]5sec)

i

i

6.66HztO.ISsec)

024GSf(Hi}

Frequency

Fig.6Fourier

_Speetra

Test

VT-M-2

in

ReoftstTTinsiatLonalMode i NS7Directon11.1OHI[a.slsec] /enbalthcedrtnment2ekpmJ"-10kpm1ii72HoiH(SteaSfiS3ecse][)E.,tt.i Sbgrn:tlL:IL/-s/,/1Jny'e't

F.,..z==T=ttttttYl'･ly.L.ijh..'

Resonance

1.0 IS Freqveney

Curyes

in

NS

ef

_Microtremers

_;

NS

Dfrection

lt(

_] ra

r'cEL

't

E

u

Frequenty

Direction

;

Test

VT-G-2

analyzed

by

means of

the

fast

Fourier

transform

(FFT),

which was also applied

to

the

spectral analysis of

the

records

of

an earthquake response and microtremor excited vibrations.

4,

Vibration

Test

Results

The

structure was subjected

to

an earthquake with amagnitude of

5.

0

on

January

28

of

1981.

Figure

4

shows

the

accelerograms whose

FQurier

spectra are shown

in

Fig.

_s.

The

_predorninant

_periods

of vibrations of

the

structure

in

the

NS

and

EW

directions

were

_O.4Z

sec. and

_O.29

sec.,

respectively.

The

natural

_periods

and

damping

ratios

in

the

NS,

EW

and

tersional

directions

_procured

from

the

micr'otremo[ measurement

(VT-M)

and

the

free

and

forced

vibration

tests

_(VT-F

and

VT-G)

are summarized

in

Table

4.

Typical

examples of

the

results of

the

spectraL analysis and resonance curves are

depicted

in

Figs,

6

and

7,

which correspond

to

test

VT-M-2

and

VT=G-2,

respectiveiy.

5.

Discvssion

of

Test

Results

Vibration

test

results

in

the

longitudinal

_(NS)

direction,

in

which

the

loading

of

_{pseudo-dynamic}

seismic

tests

was carried out, are

_principally

discussed

.in

this

section.

5.

1

Comparison

Among

Natural

Periods

in

Initial

Elastic

Range

The

trans.lational

natural

periods

and

damping

ratios

in

the

initial

elastic range were obtai.ned

from

four

dynamic

tests,

each

floor

levei

loadipg

test

(FLLI),

and

the

frame

analysis3Lii}.

These

results

in

the

NS

direction

are

summarized

in

Table

5.

The

correlation

between

the

_dynamic

tests

_(VT-M-1,

VT-F-1

and

VT-G-1)

and

the

earthqua'ke record

(EQ)

was excellent with respect

to

the

natural

periods.

The

funclamental

natural

period

turned

out

to

be

4

ancl

₁₇

_percent

longer'in

_the

FLLI

test

and

the

frame

analysis respectively

than

in

the'VT-G-1

test.

If

the

-35-"6.'b'

:'i'woE;.shloilgg

Te6.eSD4010m1,eQe as 1ttcasinajij'ReefTrensLaliefialNS-1stModeUabtlthttdMomlntnbm :ittOM'h:fQgl:/l::!Lselt:r/(oss-tj /t:L･1,'1/:,tmvatsrilaptc

,1ils!nd1

:'i'/i':':i'.,stI.Xttt

ttttttt'.tt:t.vt

1.o t5

Fig.8(a)

"l"-g･

X.tec

1LvgB{i\: ILO!1010.0aoao40zoo.o

Resonance

Test

'A'uot!.E'95so4e102D1.ea 2D 2,5 3,O

FREaUENCY

9urves

VT-G-1-5

Fig.8{b)

4,e so

ae

T.e so s,o

[H:)

in

NS

Direction

,

FREQUENCY

tH,)

Resonance

Curves

in

_EW

_Direction;

Test

VT-G-1-5

UtuutzHoo-rhi-J<crDP<z os:a9ewts?z

1.1

1.0

o.e

O.6

o.4

e.2

o.o before Pnl

cvT-eo

Fig.9

Change

Fig

₁₀

FORCEDVIBRATrONa:DisplaeementAmp[ftude

attheRootCmm) o.ess on"

'sasgett

EW-lstttt.ttttttttttttttttaao..J-ii' a=1.09L

'.iiJl.X--

Torsion---N-2ndttttttttttttttt-..-

---J---E-W:in-d`t:tttttttt;1--ttt--.."--t4121.0asq6QLaz atter after

PDT.

Flepalr

rvT-G-3}

rvFG-2)of

NaturalPeriods

atter atter N.E. Faiture

(VT-G-4)

rvILG-5)

l

VT-G-1-s

hSDIre[tton

'

!lOAeeeeforePsedobywTiEfesmo.

-'sP

'i

-"-AtberOAomNletOAoOAtler

t-r.tt1tttttt..ttt--O-tt''aAcaAstetAMimo-nemor(VT-M)

-oneevlbt=tionTestCvFn

RaT.(VT.1)(VT-1} RepabttT-3)NE.rvT-4)FaihiecvFs)PblesPD)

-oReeMbeaimby OFbrcedMha1thTesttvT-G)

Relationship

Amplitude

_;

abl Qe5al DtSPLACEMENT of

Test

as l s lo so loo soo AMPuTvDE AT

THERcoF

6Cmm}

Natural

Period

VS.

Displacement

VT-1-5

rnodulus of elasticity

derived

from

the

concrete cylinder

tests

was used

in

the

analysis,

however,

the

difference

was reduced

to

₉

_percent.

5.2

Change

of

Natural

Periods

Throughout

Forced

Vibration

Tests

The

comparison

among

resonance

curves

in

the

NS

and

EW

direction$

procured

from

each

forced

vibration

test

(VT-G-1-5)

are

shown

in

Fig.8.

Figure

9

represents

the

change of naturai

_periods

throughout

alt

VT-G

tests.

In

the

NS

direction,

the

fundamental

natural

_period

derived

from

the

test

VT-G-2

increased

by

2.

1

times

from

that

of

the

test

VT-G-1.

The

change of

the

second natural

_period

showed

a

similar

tendency.

The

ratio of

the

fundamental

to

second

natural

_period

was

O.256

in

test

VT-G-1

and

decreased

to

_O,

₂₂₀

in

test

VT-G-2.

5.3

Relationship

of

NaturaL

Period

VS,

Displacement

Amplitude

The

relationship

between

the

fundamental

natural

period

and

the

displacement

amplitude of vibration at

the

roof

level

in

the

NS

direction

is

shown

in

Fig.10.

This

figure

includes

the

results

of

the

free

vibration

by

the

pseudo-dynamic

tests

(SPD)

which are continuously

_performed

just

after each

SPD

seismic

test.

An

increase

in

the

fundamental

natural

_period

was associated

_gradually

with

the

increase

of

the

response

displacement

except

for

the

first

vibration

test

VTI.

In

the

test

VTI,

the

natural

_period

was almost constant within

the

range

ef

displacement

amp]itude of

1

millimeter:

In

the

test

VT2,

the

fundamental

natural

_periods

derived

from

the

ffee

and

forced

vibration

tests

(VT-F

and

VT-G)

were

longer

by

7

to

16

percent

and

by

11

to

₂₁

_percent

respectively,

than

those

obtained

from

the

micretremor measurements

(VT-M),

5.4

Change

of

Mode

Shapes

The

translational

mode shapes

in

the

NS

and

EW

directions

are summarized

in

Fig,

11.

In

the

first

mede of

the

NS

direction,

the

ratio

df

the

displacement

amplitude at

the

2nd

th[ough

7th

flooi

level

to

that

at

the

roof

level

increased

in

the

test

VT-G-2,

in

comparison

to

the

Tatio

in

the

test

VT-G-1.

These

_phenQmena

may

be

caused

by

the

damage

of

the

structure

at

the

lower

stories.

In

the

EW

direction,

the

first

and second mode shapes

did

not change as much as

-36-'

RF7F6F5F`31

N5-lst

MOOE

Fig.11(a)

Change

of

Direction;

'RF765`3

2F

EW-lst

MODE

Fig.11(b}

Change

ef

Direction;

uPs+ Do Betore.PDT,

--

paFG-1) AtterRD,T.

""'

_Att"rRe

_℃

_/P-2)

1:

A"t',t.",',"ierl&1 3j rvFG-5] NS-2nd

MODE

Translational

Mode

Shapes

Test

VT-G-lh5'

EW-2nd

MODE

Translational,

Mode

firest

VT-G-1-s

in

NS

Shapes

in

EW

O.04

9

Qe3kcre o.o2zttE( QOIa NSDtrectlon DDD'x oBeimeRD.T.rvT-F-1) eAtterRD.T,CVT-F2) aNterRepair(VT-F-3) oAfteroPfF:4) xAtterFailure oooXtsAea A

(vv")

aosO.1

DISPLACEMENT

Fig.13

Retationship

of

Amplitude;

Test

1

$

va

100

l

;

2

so

ts

za

v

t

5

BetoreNtcr･ Atter Atter Afler PD.T, MT, Repair ME. FaiLure

rvT-el}rvT-G-VNFV3)Cvr-ouorTe5)

Fig,14

Equivalent

Stiffness

of a

SDOF

o.s

1.e

Ee

'lo.o

(mm)

AMPLITUDE

AT

THE

ROOF1

Darnping

Ratio

VS.

DisplacemFnt

VT-F-1-5

''''''''''

Systern

-eelertPD.T.

----A"-rRDJ.

L

:'

2::

reef'r

-･･-

MterFeilure(vT-G-1)rvT-evCVT-G-3)CVFG.4)(yT.G-5)

tp

VERJICAL DISPLACEMENJ txlOmm)

di

6

de

VERTICALb[SPLACEMEHT(NIO'tpmmnJ w 123a VT-GTIo,roo12SO'-1,!co-asfio vT.G-2-eosoOSIO-aseo-aeLo VT-G-3-O,IW1.Sco-lkaoo,oce VT.G-L-aoeoafi4o-e,76o-aonD vT-G-S-2.4ooltSM-etoo-aloo A c LelL57telzsusua O,7TO.90O,S3a,10Zll

Fig.12Vertical

Mode

Shapes

of

the

Resenance

;

Test

VT-G-]-5Roof

at

Translational

7F6f5F.4F3F2FIF

ii\Ii4.:tv,

･m

L: :.,ti

_'g.

}

,

x]

O-eBetorePD.T.(VT-G-1) ---eAtter

PbT.CVILG-2)

Ar'"Atter

_{RepeirCVILG-])}

-･OAfter

_N.E.

{VT-G-4)

.--xAfter

FailureCVT-G-,

k

''\kx･

'ts

Fig.15

soo

iooe i5oo 2Pt92.)

EQUIVALENT

SroRY

STIFFNESS

Equivalent

Story

Stiffness

Obtained

from

VT-G

Test

those

in

the

NS

direction

did.

Figure

12

shows

the

_comparison

among

the

_{vertical mode}

sh,apes

at

the

roof

level

resonating

at

the

fundamental

natural

frequency

in'

the

NS

and

EW

directions,

In

the

NS

direction,

the

vertical

motion

of

the

roof was

significantly

dominated

by

the

rotational component of

displacements

associated with

flexural

deformation

of

the

shear wall

throughout

all

forced

vibration

tests.

s.s

Relationship

of

Damping

Ratlo

VS.

Displacement

Amplitude

t

t

The

relationship

between

the

damping

ratio and maxirnum

displacement

amplitude of vibration at

the

roof

level

in

'

'the

NS

direction,

obtainedi

from

free

vibration

tests

VT-F-1

through

VT-F-5,

is

shown

in

Fig.

13.

An

increase

in

the

damping

ratio was associatecl

gradually

with

the

increase

of

the

displacement

amplitucle except

fo[

the

first

test

VT-F-1.

This

increase

may result mainly

from

the

increase

of

hysteretic

dam'ping.

5.6

Equivalent

Stiffness

'

'

'

Any

structure

of

arbitrary

form

is

able

to

be

treated

as a

single-degree-of-freedom

(SDOF)

system

if

it

is

assumed

that

its

disp!acements

are restricted

to

a single mode shape3]･6)･iO),

The

equivalent stiffness

of

an equivalent

SDOF

system

is,

therefore,

derived

from

the

fundamental

translational

natural

frequency

and

first

mode shapeS)･').

The

-37-equivalent

stiffness

in

the

NS

direction,

derived

from

forced

vibration

tests

VT-G-1

through

VT-G-5,

is

shown

in

Fig.

14.

The

change of equiyalent stiffness, as a matter of course, corresponds well

to

that

of

fundamental

natural

periods.

The

equivalent story stiffness

in

NS

direetion5)

is

shown

in

Fig,15.

This

stiffness was

derived

from

the

fundamental

natural

f[equency

and

first

mode shape which were obtained

from

all

VT-G

tests.

The

distribution

of

story stiffness along

the

height

of

the

structure was

a

triangular

shape

in

the

test

VT-G-1,

while

that

of

the

damaged

structure was changed

te

a nearly uniform shape

in

the

test

VT-G-2.

6.

Inelastic

Dynamic

Response

Analysis

6.1

Analytical

Procedure

Inelastic

dynamic

response analyses were

_performed

with use of a

lumped

mass model considering

the

dynamic

effects of strain rate and stress relaxationi6)

during

the

_phase

I

_{pseudo-dynamic}

test

SPD32)･3]･6)･iS).

This

analytical method

is

described

in

detail

in

Ref.

17.

Now

it

will

be

convenient

to

assume

that

the

loading

velocity remains constant

during

each

loading

step under

_{pseudo-dynamic}

testing

conditions.

Evaluating

the

basic

equation of

the

Maxweli

visco-elastic model

leads

to

the

following

equation

for

the

restoring

foTce

at

the

end of

the

i-th

loading

step

:

Q,=e+'X`=ISA"dt

･Q,-,+

v}-,.n

(1-e"""li'!"d'

)･･-･-･--･･----･-･-･-･･-･--･"",,,""""----",-...,.(

O

where

Q,,

Q,-,:applied

loads

at

the

end of

the

i-th

and

(i-1)-th

ioading

step, respectively,

in

ton

K,T,:tangept

stiffness at

the

end of

the

(i-1)-th

loading

step

in

tonlcm

v:coefficient

of vi$cosity

in

ton･seclcm

VIL,

:

loading

velocity

during

the

(i-1)-th

loading

step

in

cmlsec

At,:time

taken

for

the

i-

th

loading

step

in

sec

Letus

consider

that

the

displacement

is

kept

constant.

The

loading

velocity

becomes

zero and

the

viscous coefficient

n

can

be

obtained

directly

from

Eq.1

by

use of

the

_{pseudo-dynamic}

test

results:

K,T,･At,

n==daQ,.,-zaQ,'''''''''''''''''''''''''"''''''''''''''H''H'''''''''''''''''''H''''''''''''''''''''H''''''''''H'''''''･･-･･(2)

In

the

dynamic

analysis and

the

pseudo-dynamic

test,

the

seven-story

RIC

test

structure was Teduced

to

the

equivalent

luniped

SDOF

system.

The

restoring

force

characteristics

of

the

SDOF

system

was

assurned

to

be

the

modified

D-Tri-linear

model,

The

hysteresis

rules are shown

in

Fig,

_16,

where

K,

and

_6b

are

the

unloading

stiffness

and

the

maximum

displacement

in

the

hysteresis

loop,

respectiyely.

This

model

follows

the

rule

that

the

force-displacement

relation always unloacls

in

the

direction

of

the

origin unless

the

maximum

displacement

exceeds

the

yield

point.

If

the

maximum

displacement

is

in

excess of

the

yield

_point,

the

unloadi'ng stiffness

is

decreased

as

1<..

The

stiffness and strength of

the

system were

determined

from

the

_{pseudo-dynamic}

test

SPD3

results,

The

characteristics of

the

_piece-wise

linear

_primary

(backbone)

curve are

listed

in

Table

6.

The

input

excitation was

the

modified

(filtered)

Taft

1952

EW

component record which was adopted

in

the

test

SPD3.

_,The

first

10

seconds of

this

record, with a

_peak

aeceleration of

₃₂₀

_gal,

were used.

For

the

computer

_program,

the

integration

method

based

on

a

constant

acceleration

within

the

time

interval,

the

central

difference

method, was adopted.

All

of

the

analyses were

performed

with

a

e.Ol

seconcl

time

interval

assuming

that

tlje

critical

damping

ratio was zero.

Table

6

PrimaTy

CuTve

CharacteTistics

of

the

Equivalent

SDOF

System

-Note

:

(

)

indicetes thecherecteristic ve]ues of the

equivalent SDOF system.

Gts

qtttr,s,z-z-'

l

e1zS'1I' s,tt attt/zslIle

''

'1/

':

/

ro

''

//t

'

5t

gst'

':

:

/iSE'CSvos17S6sJ : /''''

'

''

/pt...`'a[

''

i'tttt'...:'t/ttttop

Kp:[otluptCl-a)}.KT 3 12 xt.=Sp-Sv e{asl

Fig.16

Hysteresis

Rules

of

Modified

D-Trilinear

Model

-38--20Esd'te

-20

reST-3 2 tualsue2tfo""RFimptacrmertma:tianabb EythE ipEt: 2eto SDD4DO3oe2eD100

Fig.17

4 6 e n fime

Cset

)

Displacement

and

Time

Test

SPD3

-leo-2ao-300--oo-500

-30

-20

-]Oo

TotalHistorySheaf

VS.

Roof'

;

Pseudo-Dynamic

le o2Psp [cM?O

6,2

Response

of,

the

Test

Structure

Subjected

to

a

Filtered

The

dynamic

response

analysis

was

carried

out

w'ithout

the

effects

of strain rate

and

18

show

the

results, sllch as

the

total

shear

force

vs. roof

displacement

accompanied with

th'e

time

history

of

displacement,

obtained

from

the

_{pseudo-dynamic}

_test

_SPD3

The

clynamic

analysis was

done

with

the

effects of strain rate and stress

telaxation.

obtained

from

the

results

in

the

test

SPD3

with use

6f

Eq.

ge;2g8EbllksiU

too so o

oo

o

£

-o

oExperlrr)enteL

Date

Notme1Distribetien 02468 VISCOUS

COEFF]CIENT

Cumulative

Frequency

Viscous

Coefficient

10 12

14

xl

1(t･sectcm)

Distribution

of a

,

i::;

2 , s e

VD

T[ME ISEC]

Fig18

Total

Shear

VS..Reof

Displacement

and

Time

History;

Analysis

of

Test

S?D3

without

Dynamic

Effects

Motion

and stress ielaxation.

Figures

17

roof

and

the

analysis, respectively,

The

viscous

coefficient

o

wqs

2.

The

data

were

coliected

from

two

successive

loading

'

tt

'

l

:

[

g

ElEnr:b-10e m-10-10

-/-l-]-I.s

Fig,19

:t:!#

:

sol:moi SeoM 300 100

o-/DD

-200-aDo.4DD-seo

?o!ILDT

L],

4'

L

!t-la-tea;pIG3OISPCCH/

Fmb--pmwhVAMAeeof

Fig.20(b)

!E:i !EEtii-2010 D-IS-20

-Total

Shear

VS.

Roof

History

;

Analysis

with

o=2000e

ton･seclcrn

[.oe400:oo200100-100-200-300T4ao-soo

-30

10

T]"E [SECI

Disp!acement

and

Dynamic

Effects

-20

-LO

O

A

lo 20 la DISPfCHI

sl･

Tirne

.,ll

.ol

Fig.20(a)Total

_Shear

VS.

Reof

History

;

Analysis

with

n=10000

ton･seclcm

Tln[ tSE[/

Displacement

and

Time

Dynamlc

Effects

Fig.20(c)'

2

'

Total.Sheai

VS.

Roof

History

_;

Analysis

with

v=40000

ton･seclcm

6V "a ₁₀

J[ME

JsEET

Displacement

and

Dynamic

EffectsTime

-39--

sea

:

loo

C

_?eo

:

iSD

-1[D

I;:

Il:

i:iol

3o

-?a

-]oDla

2o so DISP[tli] i

A

i

2 6 D

-10

-20

1 1[HE ISE[]

Fig,20<d)

Total

Shear

VS.

Roof

Displacement

and

Time

History

;

Analysls

with

Dynamic

Effects

v==50000

toa ･ seclcrn

steps

where

the

response

displacement

was

identical.

initialelasticstiffness.

in

Fig.

19.

Therefore,

this

coefficient

took

the

assumed

in

the

analysis as

follows:in

the

pseudo-10

seconds

with

the

loading

velocity

of

O.

2

cmlsec,

seconds at each

loading

step.

This

assumption was

Figures

20

(a)-(e)

history

of

roof

displacement.

The

additional

proportional

damping

and

the

viscous coe Ware

shown

in

Figs.

21

(a)

and

(b).

6.3

Discussion

of

Analytical

Results

A

surnmary of

the

results

is

shown

below,

1)

The

analytical results are very much

in

2)

Figure

22

shows

the

re

viscous coefficient

_n.

These

results are expressed

analysis without

dynamic

effects

{

_o=::

oo

).

while

the

maximum

displacement

increased

with

it.

result of Toughly estimating

the

frequency

-

so

g

4o

:

so

fi

2e

i

.10

tto

-20

-:o

-40

-so

-so

-2o

-lo

e lo 2o 3o

OISP[[fi) i 20 y

za

le

E

o 2 6 e lO

I):+

_{TItiE ISEC]}

Fig.21(a)

Total

SheaT

VS

_Reef

Displacement

and

Time

History;

Analysis

with

Dynamic

Effects

and

Damping

o=50eOO

ton

･

sec/cm

h=::2%

-

40

l

io : ! io

e

o -e

-2a

Fig.20(e)

seg･: -a;t ]aum 10 ]a

-!o'-pe-le

-o.sO '

/

e 10

In

this

_procedure,

The

obtained viscous coefficients

_generally

varied

from

20000

to

₈₀₀₀₀

ton

values Qf

10000,

dynamic

tests

the

actuators moved

by

command

displacernents

and

successively

they

helcl

the

displacemellts

as

th

introduced

show

the

analytical

results

which

are

the

total

shear

force

vs.

analyses

fficient

o

of

₅₀₀₀₀

here

the

damping

ratio

of

2%

was

the

value

obtained

from

the

forced

TIHE tSEM

Total

Sheai

VS.

Reof

Displacement

and

Time

History

;

Analysis

with

Dynamic

Effects

e=60000

ton･seclcm

the

stiffness was

assumed

to

remain

as

the

. seclcm as shown

20000,

40000,

50000

and

60000

in

the

analysis,

It

was

in

ey were

for

50

on

the

basis

of

_{pseudo-dynamic}

test

conditions.

roof

displacement

and

the

time

were

performed

which

assumed

the

tangent

stiffness

.

The

introduced

critical

damping

ratio was

_2%

and

5%,

vibration

tests

(VT-G).

The

analytical results

agreement with

the

experiment

as

shown

in

Figs.

17

and

18.

Iationship

of

the

_yield

strength

_Q.

andlor

the

maximum roof

displacement

ab

versus

the

in

values relative

to

the

standard which was obtained

from

the

The

yield

strength

decreased

with

the

increase

of

the

visceus coefficient

The

viscous coefficient was expected

to

be

about

50000

as a

distribution

as shown

in

Fig.

19.

Therefore,

the

_yield

strength and

the

-

soo

g

Aoo

2'

3oo

i

200 th 10D

-IOO

-!oo

-300

-ioo

-soo

-:o

-20

-]O

O tO ?O !O DISP[CH]

g.

2o

±

10

e _o

-:0

-20

Fig.

₂₁

_(b)

2

Total

Shear

VS.

History;

Analysis

Damping

o=50000

s e tg Tl"E [SEC]

Roof

Displacement

and

Time

with

Dynamic

Effects

and

-maximum

roof

displacement

of

the

test

structure

sub-jectecl

to

an actual eaithquake motion may

be

estimated

to

become

l.

20

and

O.

87

times

respectively, as much as

the

resp6fise

in

the

test

_SPD3.

Furtherfriore,

the

maximum rooi

displacement

decreased

with

the

increase

of

the

damping

ratio while

the

_yield

strength

did

not change as shown

in

Figs.

21

(a)

and

(b).

The

_yield

strength and

the

maximum roof

dispLacement

may

be

estimated

t6

reach

1.2o

and

o.

67

times

respectively, as much as

the

response

in

the

test

SPD3,

if

_an actyal

earthquake

hits

this

structuie whose

damping

is

5%.

3)

It

is

pointed

out

from

the

analytical reFults

that

the

dynaTTiic

effect$, such as stTain

_;ate

and stress relaxation, should

be

evaluated

_properly

in

discussing

the

earthquake

_performance

of an

RIC

building

on

the

'

basis

of

_{pseudo-dynamic}

test

reSults.

7.

Conclusions

Vibration

tests

were carried out

to

acquire a change

builcling

progressed

due

to

_{pseudo-dynamic}

seismic

direction

In

addition

to

vibration

tests

t

)

effects of strain rate and stress relaxation

during

the

The

major results obtained

from

the

vi

summarized as

follows

:

1)

Before

the

phaseI

pseudo-dynamic

tests,

that

is

microtremor measurement,

the

free

and

forced

vi

to

the

translational

natural

_periods

in

the

NS

2)

Ac

¢ording

to

the

free

and

forced

vibration

tests,

in

the

NS

direction

as

the

damage

of

the

buildin

the

NS

direction,

the

fundamental

natural

_perio

phase

I

tests,

the

natural

_period

changed

to

O,

80-O.

91

initial

elastic range,

3)

_.In

the

fundarpental

natural

_period

in

the

NS

vibrational

displacement

except

for

the

initial

elastic

periods

were alrnost constant within

the

range of

the

4)that

at

the

roof

increased

at

the

iower

floors

as

the

5)

The

damping

ratio

in

the

NS

direction

increased

initial

elastic range..

,

6>

The

distribution

initial

elastic range, while

that

of

the

damaged

7)

It

was shown

from

the

results of

the

that

the

_yield

strength

decreased

with

the

increase

of

increased

with

it.

Consequently,

it

is

important

that

accurately

in

discussing

_earthquake

_performance,

_{of an}

desirable

to

continue

further

study on

this

subject.

'

Acknowledgements

'

The

authors wish

to

express

their

_gratitude

to

(Co-chairman

;

Profs.

H.

Umemura

and.J.

Penzien),

Fig.

22

or<cruutzoiuthlor

5.0

1.0

O.5

O.1

Yieldvs.

1

5

xlO` n{ton･sestm)

VISCOUS

coEFFSCIENT

Strength

and

Maximum

Displacemgnt

Viscous

_Coefficient

'

of

dynamic

_properties

of

the

structure as

the

damage

of

the

tests

in

which

loading

was applied

in

the

･longitudinal

(NS)

inelastic

dynamic

response analyses were

done

by

consideTing

the

dynamic

.pseudo-dynamic

test

SPD3.

'

bration

test$

especially

in

the

NS

direction

and

the

dynamic

analyses are

,

in

the

initial

elastic

range,

the

corre.lation

among

the

bration

tests,

and

the

earthquake record was excellent with respect

direction.

'

the

fundamental

natural

_period

of

the

structure varied

greatly

g

progressed,

whereas

it

did

not very much

in

the

EW

direction.

In

ds

was

O.

43

sec.

before

the

phase

I

pseudo-dynamic

tests.

After

the

sec.

which was an

increase

oi

li9-2.1

times

that

in

the

direction,

an

increase

occurred

_gradually

with

the

increase

of

range.

In

the

inital

elastic range,

the

fundamental

natural

displacement

amplitude o{

I

ipillimeter at

the

Toof

leve!.

In

the

translationql

_{mode shapes of}

the

NS

direction,

the

ratio of

the

displacemgnt

amplitude at each

floor

to

damage

of

the

structure

developed.

'

with

the

increase

of

response

displacement

except

for

the

of equivalent story stiffness along

the

height

of

the

structure was a

triangular

shape

in

the

structure was changed

to

a nearly uniform shape.

'

dynamic

response analyses with and without censidering

dynamic

effects

the

viscous coefficient while

the

maximum

displacement

the

dynamic

restoring

force

characteristics are evaluated

R/C

building

from

a

dynamic

response analysis.

It

is

members of

the

Joint

Technical

Coordinating

Committee

who encouraged

the

authors and cordially

_gave

advice, and

-41-members

of

Building

Research

Institute.

The

authors sincerely

thank

the

following

members

of

the

BRI

staff

for

their

participation

in

the

vibration

test

_program:

Drs

Y.

Yamazaki

and

I,

Nishiyama,

and

Messers

T.

Kashima

and

T.

Hamamatsu.

The

authors are a!so

thankful

to

Messers

H.

Yokoyama,

Y.

Tamamura

andR.

Nitta,

who were visiting researchers

from

the

Building

Contractors

Society,

for

their

assistance and

contribution

to

the

success

of

this

test

program,

We

gratefully

appreciate

Misses

H.

Ichishima

and

T,

Takahashi's

help

in

drawing

the

graphs

and careful

typing

of

the

manuscript.

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