一軸および二軸横力荷重を受ける鉄筋コンクリート柱の損傷挙動

【

報

　 制 　 　 　

．

UDC ：624

．

012

．

45　539

．

3　620

．

1

　　　日本 建 築 学 会構 造 系 論 文 艱 告 集

、

第

419

号

・

1991 _年

1

月 ∫ournat 　of　

Struct

．

　

C6nstr

．

　

Engng

，

　

AIJ

，

　

No

．

419

，

　

Jan

．

，

1991

DAMAGE

　

BE

耳

AvIoR

_．

oF

　

R

耳

INFoRCED

　

CoNcRETE

、

　　

　

・

．

COLUMNS

　

UNDER

　

UN

．

IAXIAL

　

AND

　

BIAXI

・

AL

・

　

　

　

，

．

，

　

_．

　　

．

．

LATERAL



_．

LOADING



_、

1

．



’

_．

　　　　　　　

r

_軸

お

よ び

二

_{軸横 力荷重}

を

受

け る

鉄 筋

コ ン

’

ク

リ

ー

ト

柱

の

損傷

挙

動

JunJ

’

i

　

O

（

｝

A

　

iVA

＊_，

　

Yoshihiro

　

ABE

＊ ＊_，

　

Michio

　

HOSHI

＊ ＊ ＊

、

　

and

　

Ma5ahiro

　

IKUTA

＊

嘗

＊ ＊

　　　　

、

「 ．．

． 一

、

．

小 川 淳

二

， 阿 部 良 ．

洋 ，

星

．

．

．

道 夫 ，生 ．

田 真 大

　　　　　　　．

　

　

　

　

　

　

　

　

　

　

　

　

　

　

　

　

　

　

　

　

　

　

幽

」

　

Ca

耳

tilever

−

．

！

ype

　rei ロ

forced

　

goncrete

　

qolumn

　speqin ｝eqF 　

are

　used 　

for

．

uniaxial 　and 　

biaxial

　static

lateral

　

loading

　

tests

．

　

Specimens

　are　approximately 　

full

　scale 　models 　considered 　

to

　

be

　representa

一

巨ve 　

_bf

　

_th6

　

fitst

　st6ry 　

interior

　columns 　

in

　

typicahhree

ゼ

o 　

five

　storied 　

buildings

　

in

　

Japan

_．

　　　　

_、

　

丁上

ebehavior

　of　crack 畫ng　and 　

spa

旦

ling

　of　

the

　re 量nforced

．

concrete 　co

．

lumns

　specimens 　

under

，

　

the

・

action 　of　

biax

置

al

．

　

loadi

ロ

g

　cDuld

、

　simulate 　somewhat 　

the

　earthquake 　

damage

　

features

　of　

frame．

type

RC

　

b

_“

ildings

_．

　

obS

，

erved

　

in

　

the

　

pas

し

strong

　earthquakes

．

　

The

　

biaxial

　

loading

　

gives

　

lnore

_『erious

d

・mage

−

t

・ し

b

・

b

・nc・et6

．

・ 。

1

伽 ・

th

・n出・uniaxi ・

1

・ne

・

　

．．

層 −

_{． ．}



．

　

．

Adcording

　

to

止 e　crack

−

spa 旺 oH 　

damage

　

index

，

　

discussed

　

in

．

　

this

　study ，

（1 ）

・

If．

the

　crack 　

length

　ratio

．

is

　around 　

10and

　

the

．

　spaU 　off　area 　ratio

．

is

　

Irom

　

10

　

to

　

30

％

，

　

the

　

・

　

maximum 　

ductility

　sho _“

ld

　

be

　around 　

3

．

　　

，

　　　　　

．

　　　　　　　

．

（

2

）

b

融

臨

黠 翻

二

1

詰

ln

、

認

讒

d

課

s

欄

e51a 「s

　

bec

？

m

，

el1°

啣

lbngi

 

nal

　

ba

「s

　

Keywonls

：

1

〜

C

　column

，

　uninXl

’

al　

loading

，

　

binxial

　

loading

，

　eaプ

tEquake

　

dOmage，

　crec 々

lengt

乃 ratio

，

、．

　　

．

　　　　

sPall　area 　ratio



．

_．．



_、



_，

t

踟

．

尸

　　　

圏

1．

　Infrl

）

duction　　　　　　

「

　　　　　　　

．

　　　　　　　

『

　The

　

earthquake

　

resistant

　

design

　

of

　

reinforced

．

concrete

　

buildings

　

is

　

based

　on 　

permitting

　certaindegree

・

fd

・

血

・

g

・

t

・ s

’

t

・ucty ・al・

el

_・

_m

_，

e

…

_，

wh ・・

th

・

y

・ ・

e

・

ubjec

・・

d

・・

_．



sev

・・

e



ea

・

thq

・

akr

．

・

xcit

・

ti

・

n

・

・

S

。



it

becomes

　

necessary

　

tolestimate

　

th

俘

degree

　

of

　

_structural

　

damage

　

in

　reinforced 　

concrete

　

structufes

_『

6

　

as

　

to

evaluate

　

their

　

_post

　earthquak

．

e

∵

serviceability

、

　

It

　

is

　

established

　

that

　

the

　

damage

　

features

　

of

　

columQs

under

　

the

　

uniaxial

　

loading

　are 　

different

　

from

　

thgse

　

under

　

the

　

biaxial

　

loading6

）

−

_{il ）}

．

　

Features

　

of

・

bia

_冬

ial

loadin9

　were 　

ob

も

erved

　

in

　actual 　earthquake 　

damage

　

such

　

as

　

the

　

Hachinoh6

’

City

　

Libr

’

ary

　

and

　

the

　

Mutsu

Municipal

　

Hall

　

in

　

the

ユ

g68

　

Tokachi −Oki

　

earthquake

．

　

In

　

this

　

paper

，　

an

　

experimental

　

program

，　

including

・

he



uni ・

li

・

1

・ ・

d

・

h

・

bi

・xi ・

l



l

_煢

te

・

al

・

1

_・

_adi

_・

≧

ca

・

e

・

，

・・

inve

・・

ig

・

t

・ ・

h

・

d

・皿 ・

g

・

b

・

h

・

vig

・ ・

f

・

ei

・

f

・

_．

・

C

・

d

concrete 　

columns

　

upder

　

earthquake

　

loading

　

is

．

　

discussed

．

　

，

The

　

biaxia1

．

loading

　

ca

≦e

　conside エ

ed

　

i

_町

this

　

experimental

　

program

　

includ6s

　

simultaneous

　

application

。

f



lQ

・

d



i

・

．

N

＄

A

・

d



E

Ψ

di

・

g6ti

・

_．

n・

・9i

・

i

・

g．

・

i

・

．

e ・… eal



l

・

adi

・

g



P

・

th

・

・

uch

・・

ci

・

cul

_…

a

_与

w ・

ll

．

・・

alte

・

n

・

t

・

applicatiob

　

in

　

the

　

mutua

_，

11Y−

perpendicular

・

directiops

，

　

giving

　rise 　

to

　

alternately

　

cr6ss

　

loading

　

path．

H

・w・v・ ・

th

・

di

・

placement．

鋤

pllt

・

d

・ ・ a・

e

．

：

k

・

pt

_仁

h6：

．

s

、

aM

・

．

　

Th

・

uniaxi

・

l

　

and

　

th

・

biaxi

・

l

　

l

・

adirig

　

ca

・

9

・

di

・

9．

…

ed

　

i

・

thi

・

p

・

p

・・

a

・

e

　

p

・・

b

・

bly

　

_．

・

t

中

・

twg

・・

t

・

emiti

・・

with

　

the

　

act

・

al

　

ea

曲

q

・ ・

k

・

1

・

adi

・

g

　

P

・

tt

・

m

lyipg

　somdwhere 　

in

　

between ’

．

．

　　　　　　　　

_．

’

　　

「

　　　　　　　

．



・

　　

宰

Ass6c

：

Prof

，

，

Tohoku

　

Un

．

iv

．

，

Dr

．

’

Eng

．



ゴ

　

r

￥

Assoc

．



Prof

∴

Tohoku

・

1

丘st

．

　of　

Tech

．

，

Dr

、

　

E

皿

g

．



・

．

＊ ＊ ＊

Res

白arch　

Assdc

．

，

TohQku

　

Univ

．

榊 事 ＊

Hokka

_［

do

　

Rai

［wa

’

_y

．

CQ

．

，

Former

　

Grd

．

．

Student

　of　

Tohoku

　 　　

Univ

，

．

東北 大学 　 助 教授

・

工博 　 東北 工 業 大学

層

助 教 授

・

工 博 　 東北 大学 　 助 手

　

東北 大 学

　

大 学 院 生

．

（現

JR

北 海道

）

一

₈₇

一

Various

indices

for

evaluating

the

structural

damage

in

reinforced

concrete,

such as

damage

ratio'),

flexural

damage

ratio and

dissipated

energy2), slope

ratio3',

energy

dissipation

index"),

etc.

_,

have

been

proposed.

However,

all of

these

indices

require

the

use

of

hysteresis

loops

recorded

duting

earthquakes.

As

buildings

are

not

equipped

to

record

load

displacement

time

histories

during

earthquake

loading,

visual

inspection

may

be

the

only

practical

way

of

collecting

data

for

evaluation

of

the

structural

damage.

The-prirnary

data

from

visual

inspection

comprise

the

information

on

concretel

cracks

ancl

concrete

spalling5].

In

this

_paper,

relationships

between

the

displacement

ductility

and

the

information

on

crack

length

and

spall

off

area

are

exarnined

on

the

basis

of

test

results,

A.method

of estimating

the

maximum

displacement

experienced

by

reinforced

concrete

column

from

the

visual

damage

data,

based

on

the

_quantitative

relationship

between

them,

is

proposed,

2.

Test

Specimen

and

testing

_procedure

Separate

testing

_programs

for

the

uniaxial and

the

biaxial

lateral

loading

cases

have

been

undertaken.

Cantileyer-type

column specimens,

used

in

this

testing

_programs,

are

shown

in

Figs.

1

(LC-Type,

uniaxial) and

3

(BC-Type,

biaxial).

Specimens

are

appproximately

full

scale

models,

consiclered

to

be

representative

of

the

first

story

interior

columns

in

typical

three

to

five

storied

buildings

in

Japan.

Table

1

shows

the

loading

_paths,

the

loading

displacement

ductility

steps,

strengths

of

reinfoicement

and

concrete,

and

the

axial

load

for

each

test

specimen.

The

_general

setup

for

the

uniaxial

and

biaxial

loading

'tests

are

shown

in

Figs.

2

and

4,

respectively,

The

lateTal

load

is

appllecl

at

a

height

of

1

100

mm

from

the

upper

surface

of

the

footing

block

for

both

the

uniaxial

and

the

bihxial

loacling

cases.

Therefore,

the

shear span ratie of

this

column

specimen

is

2.2.

The

calculated

ultimate

flexural

and

shear

strengths

of

the

specimens ef

BC-3

series

are

about

40.6t

and

41.9t

respectively.

The

column

length

of

the

biaxial

loading

test

specimen

is

made

shorter

than

that

of

the

uniaxial

one,

because

the

specimen

for

biaxial

loading

needs

to

be

attached at

the

free

end of

the

column with a special

jig

(height

490

mm),

inducing

the

axial

and

lateral

loacls

at

the

column

top.

There

is

a

level

difference

of

140

mm

between

the

NS

ancl

EW

loading

axes,

because

the

NS

and

EW

loading

jacks

in

the

mutually

perpendicular

directions

haye

to

fit

in

the

same shaft

of

the

Load

inducing

jig,

Therefore,

the

loading

height

of

1100

mm

is

measured

from

the

top

of

the

'footing

block

to

the

center

of

the

two

mutually

perpendicular

]oading

axes.

The

footing

block

of

the

test

specimens

and

the

reaction steel

frames

are

firmly

bolted

and

tightened

to

the

extremely

rigid

testing

floor

(thickness

900

mm)

using

high

strength

sleel

rods,

screw

jacks

(capacity

25

t,

4jacks

for

the

uniaxial

loading

and

12jacks

for

the

biaxial

loading),

and

thick

steel

piate

shear

connectors

in

order

to

achieve

fixity

at

the

base,

The

lateral

loading

system

for

the

uniaxial

loading

test

is

made

up

of

two

hydraulic

oil

jacks

(capaciity

og-?>.,g?(S ooHo-oxgl::lillil1.1111 :ii'IIIili

s"il

.o.

.,,,,

g

:D:

ssosoesso

1600

Fig.1

Test

specimen

loading

test

4-sgg-L

Longitvdinal

Reinforcement

8-D19

(pt-O.34Z)

Transvers

Reinferaement

NS

Direction

3-Dlo

eloo

(Pw=O.43Z)

EW

Pireetton

2-DIO

@100

(pw=O.29Z)

for

uniaxial outem Lateral

Loeding

React

±en

Steel

Frame

Axial

Force

LoadingCirder

Oil

Jack

for

Lateral

Testing

Fig.2

Loading

Loadingt)IHe

±gh

-LoadCell

Prestressing

SteelLedef

32anDtaveter

ooenH

TestSpecirnenl

or

300o

set-up

for

uniaxial

]oading

test

Loading

-88-Table1

Loading

_program,

strbngth of reinforcement and concrete, and axial,]oad

for

each

test

specimen

" :

Displacement

tiuctility

Factor

LoadingProgram

'LongitudinalTransver$e

Concrete

Spec.PathSteps

{pt)Barsay!ov(kglcm2)Barsaylau(kglcm2)2eFe(kg/em2)testFe-{kglefu2)

AxialLoad<ton)CRatio)

LC-1

O.5-1-2-3-4-5-7-14

18475.9CO.13)

LC-2

O.5.1-2-3-5-7-IOx2

2137E.7(O.14)

LC-3

1-2x5=3x5-5xS--7x2

4000582e

NS4-DIOe16o

pw=o.3sg

EW3-DIOQ160

pw=O.271

402057EO22721575.9CO.l3)

LC-4

24974.9CO.13)

LC-S4ts'O.5-1-2r3-5-7--10-148-D19Pt=O.341 24'4130.2CO.23}

LC-10

'

1-2-]-5-7-IO-14

26S155.2(O.25)

L

¢

-ll

35465467

39235676246273155.8CO.25)

LC-12

O.S-l-2-3-S-7-10-14

NS3-DIOeloo

Pw=O.4,]t

EW2-DIOeloo

pw=o.2gg

2e'o'156.3(O.25)

LC-l3114

216145.7{O.'26}

LC-･14

36475621

3g92550722920976.0CO.l3)

BC-l1TTt"-''1-3-S-le

CN.S-E.W)

249lS4.2(O.25.)

BC-2

O.5-1-3.-5-7

37175331

_{3B45S662251-2eol57.0(O.2S}}

BC-3--tt'-iF'O.5-1-3--5-7

(N.S-E.W)

24S.!71.3(O.25)

BC-41v.-LLIO{N.S-E.W)

8-D19pt=o.34g

3-DIOeloo

pw=O.431

249'173.l{O.25}

'BC-5Nfvt'-xxsO.S-1-3-5

CNE.SW-NW.SE)

364755S2

34745150274254171.StO.25)

BC-6'O.S-1--3-5

232171.7(O.25)

50t

in

compression>.

One

of

them

is

used

for

the

positive

direction

loading

(towarcls

North)

and

the

other

for

the

negative

direction

loading

(towards

South).

The

test

specimen

is

subjected

to

one cycle

load

reversal along

the

NS

direction

at

each

target

displacement

ductility

step.

The

same

loading

procedure

is

repeated wjth

increasing

target

displacements

untii

the

test

_specimen

could

no

longer

support

the

axial

load.

The

lateral

loading

system

fer

the

bi'axial

loading

test

is

made

up

of

two

reversible

hydraulic

jacks

(cqpacity

50

t

in

both

compression

and

'tension).

Both

jacks

are attached

to

the

thick

shaft

of

the

load

inducing

_jig

with

vertical

and

horizontal

free

]oints

at

both

ends.

The

load

inducing

jig

is

fastened

to

the

free

encl

of

the

_,column

with

high

strength

bolts,

The

test

specirne.n

is

subjected

to

one

cycle

load

reversal along

the

NS

and

EW

directions,

alternately

or simultaneously, at each

target

displacement

step.

The

_pump

lor

the

lateral

loading

is

controlled

manually

in

both

loading

cases.

The

applied

load

is-adjusted

to

follow

aPproximately

the

_prescribed

displacement

_paths.

The

target

displacement

ductilities

are.

O.5,

1,

3,

etc.,

as

shown

in

Table1.

The

displacement

ductility

is

calculated-by

dividing

the

displacement

by

the

_yieLding

displacement.

So

the

displacement

ductilit'y

at

the

_yielding

dispiacement

becomes

equai

to

1.

The

yielding

displacement

is

defined

as

the

displacement,

at which

the

strai'n

of

the

longitudinal

reinferce･mept

in

the

tensile

zone reaches or exceeds

the

target

strain value

_gf

O.2

%.

The

yielcl

strain

of

the

longitudi'nal

reinforcernent

is

O,

20-O,

21

･%

as

obtained

from

standard

tensile

tests.

The

_yielding

displacement

occurs at

the

top

displacement

to

column

length

ratiQ

of

about

11200,

in

both

the

uniaxial

and

biaxial

ioading

tests,

,

,

The

axial

load

values are

13

or

25

%

of

the

axial

ultimate

strength.

This

ultimate

strength

is

obtained

by

the

_product

of

the

28-day

concrete

strength

and

_.the

_gross

sectionat

area

of

the

column.

The

axial

load

is

applied

to

the

'free

end of

the

column

through

an

universal

joint

attached

to

a

loading

_girder.

The

hydraulic

center

hole

jacks

(celpacity

100

t

in

compression)

are

driven

by

the

automatically

controlled

hydraulic

_pump

_(pressure

720

kglcm2,

capacity

O.

5

llmin.

).

The

capacity

of

the

_pump

is

not

enough

to

89--

cape:IlgSL:::lai[ES:;iilt-:ptT

:8coiiiii:,lii1･l･11tltt/IEpb

ses8e

"･D""

an40DBOO4001600

ess

4-sQg-L

Longttudtnal Re±nforcement 8-D19

(ptdO.34Z)

Tramsverse RAtn[eTeement 3-Dlo

eleo

(pw!e.43z)

Hg.3

Test

specimen

for

biaxial

loading

test

pt8q AxialFerce Loa"ng:o

girderH

ots

_{LoadingHeight}

''''

'

'

e)"- Prestressir/gee-SteelLedof2eJ

32rnmDiameter-Test o

Specimen

oco 1500

1500

1000TestingFloer

follow

the

sudden

change

in

the

axial

load.

As

a

result,

the

values

of

the

axial

load

are

seen

somewhat

scattered.

For

the

sake

of

safety

and

stability

of

the

axial

load

induc-ing

system,

the

contact

_points

of

the

_girder

ends

and

the

axial

load

inducing

tension

rods

are

made

to

be

lower

than

the

free

end

of

the

column

like

a

balancing

toy.

Then,

the

axial

load

inducing

girder

is

fabricated

in

C-shape

for

the

unia-xial

loading

test

and crossed

C-shape

for

the

biaxial

loading

test,

foroedSng

Fig4

Loading

set-up

for

biaxial

loading

test

3.

Instrumentation

and

ment

The

displacement

at

the

top

of

the

column

is

measured

at

two

_points,

near

the

corners

of

a

face,

so

as

to

take

into

account

the

effect

of

possible

horizontal

rotation.

The

displacement

measurement

is

made

in

the

direction

of

the

lateral

loading

(NS)

in

case of

the

uniaxial

loading

test,

and

in

the

mutually

perpendicular

directions

(NS

and

EW)

in

case

of

the

biaxial

loading

test.

Differential

transformer

tyPe

transducers

are

used

for

the

displacement

measurement at

the

column

top.

Both

lateral

and axial

loads

are

measured

by

strain

_gage

type

load

transducers,

which

are

connectecl

to

the

loading

_jacks.

The

vertical

deformation

and rotation are measured

in

100

or

200

mm

_gage

length

using strain

_gage

_type

U-shaped

deformation

transducers.

These

transducers

are

fixed

to

the

bolts

specially

anchored,

using

thrust

bearings

in

order

to

form

rotation

free

joints.

In

the

uniaxial

loading

test,

the

vertical

deformation

and

rotation

are

measured along one colu'mn

face,

_parallel

to

the

loading

direction.

In

the

biaxial

loading

test,

they

are

measured

along

the

two

adjacent

faces

of

the

column.

Strains

in

the

longitudi]nal

and

the

transverse

reinforcement are measured

by

using

electrical

resistance

strain

foil

_gages,

with

2

rnm

gage

length.

Strain

gages

of

5

mm

_gage

length

are used

for

measurement

of

large

strains

of

up

to

10

%

.

The

axial

loads,

lateral

loads,

deflections,

rotatio.ns and strains

are

converted

into

electrical

signals

by

transducers.

During

each

cycle,

the

loading

is

temporarily

stopped

while

the

output

signals

are

automatically

scanned

and

stored

in

a

computer

floppy

disk.

In

addition,

signals

from

the

displacement

and

load

transducers

are

displayed

by

cligital

volt

meters,

and

recorded

in

analog

form

in

a

X-Y

-90-recorder,

The

lo'ading

program

is

contlolied

manually

by

monitoring

the

digital

volt

Meter

readings and

'

the

X-Y

recorder

diagrams

of

the

'displacernents

trajectory.

.

'

Test

specimens, are whitewashed

to

make

it

easy

to

detect

cracks en

the

concrete surface.

Cracks

developed

during

loading

are marked with a

_pencil,

so

that

crack

_patterns

can

be

follQwed

easily.

At

the

loading

stage when

the

residual

displacement

becomes

zero, ciack

_patterns

ancl outlines of

.concrete

spall･

off

area

are

traced

with

_q

fiber

tip

_pen

on

a

transparent

thin

plastics

sheet

of

_,500

mm width.

The

width

of

the

'sheet

is

made equal

to

that

of

the

column,

so

as

to

make

it

easy

to

reset

the

_sheet

as

required, when

tracing.

Crack

patterns

and

outlines of

the

concrete spall eff

area

are

divided

into

small

linear

siegments

at

adequate

intervals

by

manual

operation,

Vector

data

of

these

linear

segments

'are

obtained

by

a

tablet

digitizer

and stored

in

a computer

floppy

clisk,

The

cracks

at

the

corner

between

the

column

face

and

the

top

of

the

feoting

block

are

not

traced,

The

color

infoimation

of

a

_pixel

of

a computer color

display

is

indicated

by

green,

red

and

blue'

bits.

Those

c61or

bits

data

can

be

read

into

array

clata

of a

Basic

program.

After

setting

a

computer

display

(640

×

475,

pixels)

to

500

pixels

representing

the

column

width of

500

mm

(1

mlnlpixel), crac,k

patterns

are

drawn

with'

'blue

lines

on

the

computer

display,

using vecCor

data

of cra6k

_patterns.

The

linear

segments of

crack

_patterns

are

_gr6uPed

into

three

cornpOrients,

horizontal',

diagonal

and

vertical,

The

last

pixel'ofeach

segment

is

coleredgreen,

in

order

to

avoid counting

the

last

pixel

three

times,

as

the

equivalent

erack,16ngth

is

calcul.ated

by

each

component

_grdup.

If

cpncrete

spalling

data

exist,

outlines

of

the

spall

off area are

drawn

with'Ied

lines

on

the

same

display,

The

inside

of

the

figure

is

_painted

recl,

in

otder

to

delete

cr'ack

patte'rns

included

in

the

figure.

The

equivalent

crack

length

is

obtainecl

by

counting up

the

number

of

the

blue

pixels

indicating

the

trajectory.

The

totar

equi,yalent crack

length

is

calculated

by

adding

the

equivalent

crack

length

for

the

three

components.

This

_pixel

counting method

can

_give

103.0%

(the

average value

of

39cases

without

spalling,

maximurp

_111.9%,

minimum

97,

3

%

)

ef

the

acctirate

crack

length

c'alculated

frorn

crack

vector

data

by

the

Py.thagorean

theorem.

The

total

spall

off

area

is

obtained

by

counting

up

the

number

of

the

red

pixels

indicating

the

spall

off

'

areas

on

'the

disPlay,･'

'

',

4.

Test

results

Loading

_path

'

.

:

Fig,

5

shows

measured

ioading

_paths

on

the

NS-EW

displacement

plane

for

the

biaxial

loading

tests,

which

are

obtained

as

the

trajectory

of

the

column

top

displacernents

along

the

two

_principal

axes

during

the'biaxial

loading.

It

is

seen

that

the

manual

control

of

loadings

has

been

_good

in

achieving

the

prescribed

displacement

paths,

which are shown

in

the

second

column

ef

Table

1.

,Damage

In

the

uniaxial

loading

test,

there

is

a

significant

difference

in

the

qamage

behavior

between

loading

surfaces,

_{perpendicular}

to

the

lateral

load

direction

and

indicated

by

S

'and

N

surfaces

in

Fig.

6,

and

non-loading

surface,

_parallel

to

the

load

and

in-dicated

by

E

surface

in

Fig.6.

0n

loading

surfaces,

horizontal

flexural

cracks

are

domi-nant,

And

on

non-loading

surface,

diagonal

cracks

h're

dominant.

Ih

the

biaxiar

loading･test,

horizontal

flexural

crlacks

are

observed

on

all

surfaces up

to

the

_yielding

displacement

load

cycles, as shown

in

Fig.

7.

In

thg

uniaxial.

Ioad-ing

test,

spalling occurs mainly

in

full

column

width-

of

the

loading

surfa'ces

and

in

beth

the

corner

_parts

of

the

non-loading

surface.

In

the

biaxial･loading

test,,spalling

occurs

in

al'most

N w;E

40

_Bc

_-1

S

20

40

20

20

40

A

E

2o

v

tP'

Lo

4o

40:BC-4

v20no20

204e

Defleetton

40

3

5

o 40B9-3 20

o20

204

'403eBe-s

o20 a2040

Fig.5

Measured

loading

_path

of

biaxial

loading

test

sSurfaee(Leading

A

-ESurfaee

1Xl

s

/Z

NSurfadeCLoadtng)

-v-i

Jt-.

s

J--'

p=l

N

.

E

p-3

s

-f'tt''t-'

N

-t,

.-.tit.-eet

y

-.

d N w t s -t E

il)sN

pm5

N

}.k-E

k

xN

L N

-'it'

_as

pt =

10

and spall off area of specimen

.i:..xj

L

.l,-pt

E

1s･.-･E,-ii

steps

pe7Fig.6

Crack

_pattern

LC-12

at

end ofloading

ESurfaeeNSurface

_--IT---"..

---H--+-t

''

NeA

"=o.s

"-1

"

±

3

"=S

Fig.7

Crack

_pattern

and spall

off

area

of

specimen

BC-6

at end of

loading

steps

full

colurnn

width

in

all

surfaces.

Spalling

of

concrete

cover

starts

from

a

displacement

ductility

of

3

in

biaxial

loading,

compared

to

that

of

5

in

uniaxial

loading,

In

case

of

the

biaxial

loading,

horizontal

cracks

at

the

bottom

parts

become

visible

in

all

sufaces

at

displacement

ductility

of

O.

5.

_.As

the

ductility

increases

to

1,

mainly

horizontal

cracks

continue

to

develop

together

with

a

few

diagonal

cracks.

At

this

ductility,

the

cracks

are

seen

to

develop

up

to

a

height

of

legs

than

one column width.

The

authors

also

noticed a

few

vertical cracks near

the

free

end of

column

specimens.

It

seems

that

insufficient

anchorage

of

longitudinal

reinforcement at

the

to])

of

the

colurnn

is

the

cause ef

these

cracks,

The

cracks

at

the

bottom

_parts

continue

to

increase

and expand as

the

displacement

of

the

column

increases

up

to

a

ductility

of

3.

Beyond

a

ductility

of

3,

the

rate

of

development

of new

cracks

slows

down,

the

existing cracks

are

seen

te

widen

further,

and

shallow

concrete spalling

begins

in

all

surfaces.

At

a

ductility

of

5,

concrete

cover spalling

occurs

oyer wide

area

on all surfaces,

and

the

reinforcement

is

uncovered.

Sorne

of

the

longitudinal

reinforcement

buck].e

slightsy

between

transverse

reinforcements.

At

a

ductility

ef

7,

the

core

concrete,

confined

with

crossties

and

transveTse

reinforcement,

disintegrates

seriously.

This

!eads

to

epening of end

hooks

(lc:s

or

180

deg.

)

of

ctossties

and

transverse

reinforcernent,

so

that

the

concrete

core

is

no

longer

confined.

The

column

length

becomes

rapidly shorter

under

the

action of axial

IQad

with

the

con$eque/nt

lafge

scale

buckling

of

longitudinal

reinforcement.

Hysteresis

loops

Load-displacernent

hysteresis

loops

of

the

specimen

LC-12

are

_given

in

Fig.8,

as

a

typical

representative

of

specirnens

under

the

uniaxial

loadings.

The

load-displacement

relationship

of

the

specimen

LC-13

is

also

drawn

by

a

broken

line

in

Fig.

8.

The

specimen

LC-13

was subjected

to

the

one

way

monotonic

lateral

loading

along

one

of

the

_principal

axes.

These

cyclic

hysteresis

loops

are yery

stable

up

to

very

high

displacement

ductility

of

the

order

of

10.

The

specimen

LC-12

reaches

the

-92-ultimate

strength

at

around

displacement

ductility

of

3.

After

the

ultimate

strength,

the

spe.cirT}en

shows

very slight strength

d,egradation

up

to

very

high

displacement

ductility,

The

envelope

curve

of

the

specimen

LC-12

almost

coincid6s

with

the

load-displacement

relationship

of

the

･specimen

LC-13.

It

'seems

that

there

is

almost

no

effect

of

the

cyclic

loading

on

res.toring

force

characteristics

when

there

is

only one cycle

in

each

loading

step.

Load-displacement

hysteresis

loops

of

the

specimens

BC-3

and

BC-6

are

_giyen

in

Figs.

9

and

_lo,

respectively, as

typical

representatives of

specimens

under

the

biaxial

loadings.

The

specimen

BC-3

is

subjected

to

the

cross

altemate

,loading

paths

along

the

NS

and

EW

axes.

The

load-displacement

hysteresis

loops

of

the

specimen

BC-3

are

drawn

independently

on

the

NS

and

EW

_planes.

The

specimen'

BC-6

is

subjected

to

the

circular

load-ing

_paths,,

so

the

load-displa'cement

hysteresis

loopg

are

independently

drawn

as

_projected

charts

on

the

NS

nad

EW

_planes.

The

load-displacernent

relationship of

the

specimen

BC-4

is

drawn

by

a

broken

line

in

Figs.

9

ancl

10.

The

specimen

BC-4

is

subjected

to

very

large

bia-xial

one

cycle

loadings

with

a

displacement

duc-tility

of10,

The

load

was applied

firstly

along

the

NS

axis,

and

then

along

the

EW

axis,

The

specimen

collapsed

half

way

through

the

EW･

loading.

Both

envelope

curves

of

the

specimens

BC-3

and

BC'6

reach

the

ultimate

strength

at

around

displacement

ductility

of

2.

After

the

ultimate

strength,

hysteresis

loops

show

rapid

strength,degradation.

The

specimen

BC-6

shows

more

serious･

strength

degradation

than

the

specimen

BCJ3.

It･can

be

said

that

the

bia-xial

loading

_path

_gives

mucfi

severer

damage

on

the

column

than

the

uniaxial

loading.

And

with-in

the

biaxial

loading,

the

areal

loading

_paths,,

like

circular

loading

_paths,

give

severer

damage

than

the

linear

loading

_paths,

like

alternative

cross

loading

_paths.

Equivalent

crack

length

ratio and spall off area

ratlo

'

･

The

total

equivalent crack

length

is

calculated

on

the

square area

(500

×

500

mm2)

of

one

col-umn width sides at

the

bottom

of

the

Column

bY

the

_pixel

･counting

method

mentioned

above.

The

equivalent

crack

length

ratio

is

defined

as

the

ratio of

the

total

equivalent

crack

length

to

the

column

width,

Fig.11

shows

the

rela--tionship

between

the

equivalent

crack

length

ratio

and

the

clisplacement

ductility

foT

both

the

uniaxial

and

the

biaxial

loading

cases,

For

the

uniaxial

case,

the

equivalent

crack

length

ratio

is

seen

to

increase

with

displace-rnent

ductility

up

to

a

value of

5.

After

that;

the

s soAg"vao213ttS7t-T---t.---pt=leL--t--L

:30e-20

-30-2e

203040 beflectton{mn)

-2e-30

LC-12LC-i3---"--40-so

Fig.8Load-displacement

LC'l2

and

LC-13loops

ofspecimens

?so

N

e

l

U4o

t rd V---+--E'-03ols.3s

/.-.--.--."s.-pt=

it"3'--"

')

t

t

' 'rS

..J/'/-rt---.t''

-30

_'

_..V-10

.'!77i,y

t/i'y/gtf

,ttt

,f"'

tt

tytt

.tt'

tt.

t

'i's

/' ''.t."

/

'''"t"

tt

,:

･fi!

t

ttt.

'7･fi'lo.."x3o

,,'tf..""Deflecti'en(m])

tttttt

t

.

y'x""""'''x'1'

(

v'.l,･･r

BC-3NS

r1

EW----'

-h"H'J""r---!,!=:rr:tV.ii.',･z':E'Y･''-4D

BC-4NS----50

Fig.9Load-displaeement

BC-3

and

BC-4loops

ofspeelmens

Fig.1O

p

L'oad-di$placemenr

BC-6

and

BC-4

lb

loops

ofspeclmens N

-93-etrlvtuk=pv･H3gE=-eo=vtn:odMoatgvp=o"tu>.H=orut

20

IS

10

s

B=SOOh=O-SOO

E

:

E

SuTface

EN

:

A.V

of

E

G

N

Surface

SN

:

A.V

of

S

_G

N

Surface

Ol23

S7

10

14

#

Fig.11

Equivalent

crack

Iength

column width ratio

and

ductility

n-wo-vutkcovked"igod-ptAtn

100

7S

so

2S

O123

S7

10

14

#

Fig.

12

Spall

off area ratio and

ductility

equivalent

crack

length

ratio

for

the

loading

surface

decreases

due

to

the

effect

of

concrete

spalling,

but

it

still

continues

to

increase

for

the

non-loading surface.

At

a

displacement

dllctility

of

1,

the

equivalent

crack

length

ratio

is

about

2.

5

in

beth

the

loading

and

the

non-loading

surfaces.

At

a

duc/-tility

of

3,

the

ratio

becomes

about

6.

At

a

ductility

of

7,

the

ratio

is

about

5

in

the

loading

surface, and about

10in

the

non-loading

surface.

For

the

biaxial

case,

the

crack

length

ratio

is

_seen

_to

in-crease

with

displacement

ductility

up

to

a

value

of

3,

After

that,

the

crack

length

ratio

decreases

rapidly

due

to

the.

effect

of

concrete

spalling.

At

a

displacement

ductility

of

1,

the

crack

length

ratio

is

about

5.

At

a

ductility

of

3,

the

ratio

becomes

about

10.

The

total

spall

off

area

is

also

calculated

on

the

square area

(500

×

500

mrn2) of one colurnn width

sides

at

the

bottom

of

the

column

by

the

_pixel

counting method mentioned above.

The

spall off area ratio

is

defined

a$

a

_percentage

ratio

of

the

total

spall

off

area

to

the

whole

targeted

square

area.

Fig.

₁₂

shows

the

relationships

between

spall

off

area

ratios

and

displacement

ductilities

of

both

the

uniaxial

and

the

biaxial

cases.

The

spall

off

area

ratio

increases

rapidly

with

the

increment

in

the

displacement

ductility.

It

is

to

be

noted

that

the

equivalent

crack

length

ratio

and

the

spall

off

area ratio used

in'

_this

study

are

the

relative values

for

expressing

the

level

of

earthquake

damage.

The

equivalent

crack

length

ratio

and

the

spall

off

area

ratio

for

the

biaxial

loading

case

shoulcl

be

used

for

evaluating

the

earthquake

damage

of

reinforced

concrete

buildings

which

have

alrnost

same

deformation

characteristics

in

both

the

longitudinal

and

transverse

directions.

The

information

on

the

crack

width

is

not

considered

here,

5.

Conclusions

The

experimental

_program

is

conducted

to

study

the

damage

behavior

of

reinforced

concrete calumns,

subjected

to

the

uniaxial

a4d

the

equal

amplitude

biaxial

lateral

loadings,

in

the

nonlinear

_plastj,c

range.

A

methed

of

evaluating

the

damage

level

of

reinforced

concrete

columns,

based

onL

visual

information

such

as

cracks

and

spall

off

area,

is

_presented,

Further

research

is

needed

_to

investigate

_tkte

effects

of

various

_parameters

such

as

the

different'

amplitude

biaxial

loading

_paths,

the

variation of

the

-94-axial

load,

the

repetition

of

loading

cycles

at

each

step,

the

velocity

of

the

deformation,

and so on.

Major

conclusions

include

the

following,

_.

1)

The

damage

features

of

columns

under

the

biaxial

loading

are

differenE

from

those

of

the

uniaxial

ioading.

The

biaxial

loading

cases are seen

to

simulate

somewhat

the

actual

earthquake

damage

on

columns

of

reinforeed

concrete

buildings,

for

whieh

the

deformation

characteristics

in

longitudinal

and

transverse

directions

are

same.

Sb

the

crack-spatl

damage

indices

from

the

biaxial

loadings

ban

be

applied

for

_evaluating

the

_{state of}

damage

in

_such

buildings

in

the

_{event of}

_qctual

earthquakes.

The

equivale'nt

crack

length

ratio

should

be

used

in

evaluating

the

degree

of

damage

for

a

displacement

ductility

of

up

.to

3.

The

spall

off

area

ratio

should

be

used

beyond

a

ductility

of

3.

'

'

According

to

the

crac.k-spall

darnage

indices,

the

fpllowing

observations

can

be

made

with

regard

to

the

gener,al

trend

of

clamage

to

biaxially

loaded

column

in

this

experimental

study

:

a

)

If

the

equival'ent

crack

length

ratio

is

around

s

and

the

highest

crack

height

is

less

than

one

column

width,

the

maximum

displacement

ductility

experienced

is

less

than

1.

b)

If

the

equivalent

crack

length

ratio

is

around

10

and

the

spall

off

area

ratio

is

from

10

to

30

%,

the

maximum

ductility

is

around

3,

c

)

If

the

spall

off

area ratio

is

from

30

te

85

%

and reinforcirig

bars

are uncovered

due

to

the

spalling

of

concrete

cover,

the

maximum

ductility

is

_around

_5.

d')

If

the

spall

off

area ratio

is

more

than

50,%

and

transverse

bars

become

loose

and

longitudinal

bars

buckle,

the

maximum

auctility

is

over

5.

'

2)

The

biaxial

loading

_gives

rnore

serious

damage

to

the

concrete

columns

than

the

uniaxial

roading.

In

the

biaxial

loading,

the

･areal

loading

_path,

in

which

the

displacement

trajectory

of

the

column'forms

areal

figures

like

the

circular

loading

_path,

_gives

rise

to

more

serious

strength

degradation

of

the

concrete'columns

than

the

linear

_path

such

as

the

alternate

cross

loading

_path.

Therefore,

the

biaxial

loading

effects should

be

taken

into'account

for

the

modeling of restoring

force

characteristics

for

the

type

o'f

buildings

mentioned above,

'

'

6,

Acknowledgement

_,

.

The

authors

wish

to

express

their

appreciation

to

the

Science

Research

Foundati.on

of

the

Ministry

of

Education,

Goyernment

of

Japan

for

a

_grant

(No.

O1601008)

in

_parti,al

support

of

this

expe'rimental

research

_program.

They

'also

wish

to

thank

Prbfessor

Akenori

Shibata

for

his

valuable

advice

and

suggestions,

and

the

students

and

graduate

students

of

the

Sttuctural

Laboratory

of

the

Department

_pf

Architecture,

Faculty

of

Engineenng,

Tohoku

University

for

their

assistance while conducting

_the

expenrnents.

Reterences'

'

1)

Shibata,

A.

, and

Sozen,

M.

A.

:

Substitute-Structure

Method

for

Seismic

Design

in

RIC,

JouTnal

of the

Structural

Division,

ASCE,

VoLI02,

No,ST.1,

pp.1-18,

1976.1,

2)

Banon,

H.

,

Biggs,

J.M.,

and

Max

lrvine,

H.

:

Seismic

Damage

in

Reinforced

Concrete

Frames,

Journat

of

the

Structural

.Diyision,

ASCE,

Vol,I07,

Ng.ST9,

pp.1713-I730,,

]981.9.

,

3)

Toussi,

'S.

,

Yao,

J.

Y.

P.

, and

Chen,.

W.

F.

:

APamage

Indicator

for

Reinforcecl

Concrete

FTarnes,

Jguinal

of

ACI,,

Vol,,81,

No.3,

pp.260-267,

1984,3..

4)

Darwin,

D.,

and

Nmai,

e,K.

:

Energy

Dissipation

in

RC

Beams

under

Cyclic

Lead,

Journal

of

the

Structurat

Division,

ASCE,

Vol.112;

No.8,

pp.]829-1846,

1986.8,

.

5)

Project

Reports

on "Develbpement of

Post-Earthquake

Measures

for

Buildingg

and

Structures

Damaged

by

Ear'thquake".

On

'

Japapese)

Building

Research

Institute,

Ministry

of

Construction.,

Japan,

]981-1985.

'

6)

List

of

Experimental

Results

on "Dynamlc

Properties

of

Relnfofceti

Concrete

Columns

Under

Inelastic

Load

Reversals",

(in

Japanese)

Building

Research

Institute,

Ministry

of

Construction,

Japan,

]975-1977.

7)

Maruyama,

K.

_,

Ramirez,

H.

, and

Ji.rsa,

J.

O.

:

Short

RC

Celumns

under

Bilateral

Load

Histories,

Journat

of

the

Structural

'

Dvision,

ASCE,

VoLllO.

No:1,

pp.120-137,

1984.1.

'

'

8)

Umehara,

H.

, and

Jirsa,

J,O.

:

Short

Rectangular

RC

Celun]ns

under

Bidirectional

Loadings,

Joulnat

of

the

Structuial

'