水平荷重をうけた多層鉄筋コンクリートフレーム柱の鉛直耐力(第二報) : 各種水平加力プログラムが与える影響(梗概)

Architectural Institute of Japan

ArchitecturalInstitute of Japan

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'

THE

VERTICAL

LOAD

CARRYING

CAPACITY

OF

THE

COLUMNS

OF

MULTISTORY

REINFORCED

CONCRETE

FRAMES

WITH

THE

EXPERIENCE

OF

HORIZONTAL

LOADING

(PART

2)

-The

effect

of

various

horizontal

loading

by

TAKAYUKI

SHIMAZU'

and

MD.

ALI

AKBAR

MOLLICK"',

Members

of

A.

I.

J.

1.

Introduction

This

paper

is

the

second

presentation

of a

series

of studies

on

the

vertical

load

carrying

capacity

of

the

columns

in

mttltistory reinforced concrete

frames

with

the

experience

of

horizontal

ioading.

In

Ref.

(

1

)

a

theoretical

approach

and one experimental verification

of

it

were

presented.

In

that

approach

an

eiastic

stability

problem

of

a

cbntinuous

bar

built

'in

at

the

base

with multi-rotational springs over

the

height

was

dealt

with,

for

estimating

the

vertical

load

carrying capacity of

the

columns of amultistory weak

beam-strong

celumn

frame

already subjected

to

horizontal

load

up

to

_post

_yielding

range,

It

was assumed

by

consiclering

the

Testoring

force

characteristics of reinforced concpbte

members

to

be

basically

of

origin

oriented

type

with

degraded

stiffness

that

beam

ends act

as

rotationai springs

possessing

equivalent

elastic

stiffnesses

determined

from

the

maximum

rotations

ever

experienced

under

horizo"tal

loading,

while continubus columns

in

a rnultistery

frame

act as a continuous

bar

having

the

equivalent elastic

flexural

rigidity which

to

be

evaluated simultaneously

from

the

equation

derived

based

on energy rnethod

to

determine

the

value of

its

buckling

load.

Good

agreement was obtained

between

'calculated

resutts and

test

ones.

In

that

stucly,

however,

only one

horizontal

loading

_program

was adopted

to

verify

the

validity of

the

_proposed

theoretical

approach.

As

the

horizontal

loading

history

is

assumed

to

have

the

most

influence

on

the

vertical

load

carrying capacity of

the

columns owing

to

the

change of

the

horizontal

load

resisting characteristics of a

frame,

fot:us

is,

in

this

_paper,

_placed

on

the

effect of various

types

of

horizontal

loading

programs.

These

p[ogiams

were selected

to

observe

the

effect

of

the

magnitude of

the

maximum

total

deflection

angle,

the

number ef

loading

cycles and

the

history

of applied amplitudes.

Jn

this

study

the

better

correlation

between

the

model

test

structures and

_prototype

was also made

by

selecting

the

strength

distribution

of

the

beams

over

the

height

of

the

test

structures

and makiitg

the

additional arrangement of constant

_gravity

load

on each

floor

beam

than

in

the

study of

Part

_1.

'

'

It

has

been

taken

into

consideration

to

study

the

advantageous

_peints

of

the

limit

state

design

method oyer

the

currently used elastic

design

method, although

in

this

regard much more studies are reqttired

for

a

_genera!

cenclusion.

The

abstract

of

this

_paper

was

already

reported

in

Ref,2.

2.

Experimental

Program

2,

1

Test

Structures

:

A

single-bay

six-steried

reinforced

concrete

interior

frame

designed

following

the

AIJ

Building

Code

as shown

in

Fig.3

of

Part

1

was

also

used

as a

prototype

to

select

the

test

structures

of

this

study.

These

teststructures

were

_plane

frames

with

the

number ofstories reduced

to

four

for

the

simplicity of

the

app2ication of

loads

as

in

Part

1,

The

configuration of a

typical

model

test

structure with overall

dimension

and reinLforcement

details,

was

the

same as

_presented

in

Fig.s

of

Part1.

i

_Professor,

_University

_of

_Hiroshima,

_Dr.

of

Eng,

#

_G[aduate

_Student

_University

of

Hiroshima,

Mr.

of

Eng.

(Manuscript

received

Jan"ary

S,

1988)

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2-3.201.3.2fp'

Table1

,L

Mechanical,

Properties

t.

tt

of

MFterials

,

Test'StFuetures'Concrete

E.(xlOf)Fc'

/t'-//

'

'

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' uoit:

k.sl.cm

unit:

kg/c-tt/

'

Fig.1

LMIt:mm

CToss-section

Properties

of

Members

of

Test

Structures

BasedonLimitState

.DesigriMethod･Basecl'onCu[crentlyUsedElast

DestgrilrE2thod

±c

ttO,]4

tO.66

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Testtructarres Cl.vatlCl-UMI CITwn2Cltunt2 Cl-maC3-rm Cl-val4C]-LH4 lb-±zotalLoeding Prograns 2,oe'tl.OO o.so1 o.oo O.50 1.oe 2.oo a68 T

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ttt

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'

---

----.--

--

---

----

--

....-,--

---.-

--

---

![

...t

t/

tTotRi DcfLcctien'Aiigle{:')'

_.

+Tensile Retnforcenent Ratio(m'

_.

Fig.3

Loading

Programs

Us.ed

in

Horl'zontal

_Loading

_Test

Fig.2

Modification

of

Bearn

Stre]gth

Ratios

frpm

Prototypes

to

Models

./

'

tt

t

tt

The

total

.pumber

of

test

structures

was-eight.

The

_{member cross s,ectional}

_properties

_{of all}

the

_eight

test

_structures

are

illust[ated

in

Fig.

11

The

moelificg.Fipn of

the

b,e4m

strength ratios

frorrl'piototype't.o

rpodel

is

illustrated

in

Fig,

2.

Four

_.test

st'fuctures in

Cl

series,

the

same as

the

test

structure

C63-41H

of

Part1,

were

designed

basicaily

according

to

the

liniit.state

desigp

methocl.

Th6

bther

four

test

structures

in

C3

series were

designea

basically

according

to

the

currently used elastic

design

method.

They

were simila[

to

the

test

structure

C63-42H

of

Part

1,

having

not sudden

but

gradual

clec'rease

of strength of

the

beams

from

top

to

bottom

ov'er'

the

height

of

the

frames.

The

summation'of

strength

of

the

beams

over

_t;

the

height

of

frames

of

6ach

series

was

the

same

to

bring

them

in

Teasonable

:aObMuPiaatr;301n

TTahbeleMie.ChrniCai

PIORertlf.S

Of

the

Matenal used

for

the

fonsEructio?.gf

ell

the

tr?t

structures afe

'

2,2

Horizontal

Loading

P'rograms

:

Four

horizontal

loading

_programs

charhcterized

by

the

magnitude of

deflection

amplitude, number'of cycles ancl

the

histery

of

tipplied

amplitude

_were

used

for

this

study as summarized

'

in

Fig.

3.

Two

test

structures, one

from

each series, were

tested

under

each

horizointal

loading

program.

In

these

programs,

an ultimate

total

interstory

deftect{on,angle

induced

by

severe earthquakes was assumed

to

be

2.

0

percent

'

-47-Architectural Institute of Japan

ArchitecturalInstitute of Japan

.

with

H3

_program

being

assumed

to

be

induced

by

extreme earthquakes.

Among

the

four

programs,

the

first

one

(H

O,

the

same

one as

that

used

in

Partl,

was considered

to

represent

one

response of

the

severe earthquakes

that

may

occur

one

time

in

the

life

time

of a

bttilding.

The

second one

(H2),

of

multi-cycles reversals at a constant amplitude, represents

one

respense of

the

moderate earthquakes

that

may

occur

several

times

in

the

life

time

ofa

buliding.

The

third

one

(H3),

also of multi-cyeles reversals at a constant amplitude,

represents

one

response of

the

extreme

earth-quakes

that

may occur

less

than

one

time

in

the

life

time

ofa

building.

The

last

one

<H

4),

the

reversed

type

of

the

first

one, aiso represents

one

response

of

the

severe

earthquakes

that

may occur as of

H1

and

is

similar

to

responses

mestly caused

by

actual

earthquakes

as characterized

by

higher

amplitudes

in

the

initial

stage and

lower

amplitudes

in

the

iater

stage

of

their

excitations.

2.

3

Testing

and

Measurernent

:

All

the

eight

test

strue-tures

were

tested

under

the

displacement

controlled

statical-ly

applied

reversed

horizontal

loading,

during

which a

pw A 1oo Cl-"lr 100

-]o

-2e

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1::･:1 ncL.C. D,T,Displaoenwittransducers w,s.g,wirestiraingage L,C.LnadCell

Fig.4Set

up

for

Loading

and

Measurement

-lo

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_eq("m)

C]･zaL]]co2oo LOO ) 'Fm) 1

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-r-HH."t'r zoo;:･l ]ooPtig)3co100 e]-"-100

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_' 1 ]N(ta"1

-r-"-+e

rm

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HorizentalLoading

-48-Table2

Experimental

Results

of aLl

the

Test

Structures

Vndertlori2ontalLuad

UnderYerticalLoad

Test

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ill3

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za

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{mmn)

1105110Stl

t

t

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cl.wn4

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Fig.6

Crack

Patterns

under

HorizontaL

Loading

-40 -co -20-ro

O 10ro so

co

(mm}

Fig.7

Deflected

Shape

under

Horizontal

Loading

constant vertical

load

of

wr12

FlbD=O.

2

{

;l4=5.

04

ton)

was under application on

the

tops

of columns with agravity

load

of

120

kg

on each

floor

beam

applied as

two

_points

loading

although

the

12e

kg

on each

floor

was a

little

lower

than

design

level,

At

the

end of

the

last

cycles of reversed

horizontal

loading,

the

vertical

loading

test

wa$

_performed

by

monotoneus

increment

of

the

vertical

load

on

the

columns up

to

the

occurrence of

frame

failure.

Ten

displacement

transducerS

were

installed

and wire strain

_gages

were attached on

twenty

strategic

_points

on

the

test

structures

for

the

measurement of various response of

the

test

s.tTuctu[es

during

the

test.

However,

all

the

test

results are not

_presented

in

this

paper.

Fig.4

illustrates

the

testing

arTangement.

The

vertical

loading

apparatus was

designed

in

such a way

that

the

top

of

the

tesit

structures could move

freely

in

its

vertical

_plane.

3.

Test

Results

D

The

Behavior

under

Horizontal

Loading

All

the

eight

test

structures show

the

failure

mechanism

by

_yielding

under

bending

at

the

column

bottorn

of

the

first

stery and

beam

ends of

the

second

to

fifth

stories under

the

reversed cyclic

horizontal

loading

to

demonstrate

the

hy'steretic

response characteristics of

ductile

type.'

･

The

relations

between

story

force

and

top

displacement

during,the

reversed

horizontal

loading

for

all

the

test

structures are shown

in

Fig.5.

The

maximurn response values

for

horizontal

load

with respective

horizontal

displacement

and residual

h'orizontal

displacement

are

tabulated

in'

the

left

_part

of

Table

2.

The

hysteretic

response characteristics of reversed

horizontal

loading

test

of

the

structures under

the

four

different

loading

_programs

are naturally

different

but

the

response characteristics of

two

test

structures under

･the

same

loading

_prograrns

are almost

the

same,

However,

the

rate of

degradation

of stiffness

during

the

same

horizontal

loading

history

is

a

little

largeT

in

the

test

structures

in

C

3

series

than

in

the

C

1

series.

The

horizontal

strength of

the

test

strdctures

C

1-WH

1

of

this

study and

the

same

one,

C

63-41

H

of

Part

1

also

showed

nearly

_the

same

values,

indicating

_that

a

constant

gravity

load

on each

floor

has

little

influence

on

the

final

collapse mechanism against

horizontal

loading.

-49-Architectural Institute of Japan

ArchitecturalInstitute of Japan H"1 }Ltl"lit2 -1

'

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;

th/

-se

-no

Fig.9-30

-20

-10

Deflected

Maximum

-o

lo 2o ]e (ntql

Shape

at

the

Vertical

Load

Fig.8

Crack

Patterns

under

Vertical

Loading

W(tan)

W(ton)

3e

20Cl-rm

10

W(ton)

30

2eCl-WH2

la

3o

W(tan)

20Cl-wrl3

10

30

20Cl-;H4

10

W(ton)

-so-6o-4o-2oo2o4o6oso-4o-2oo2o4e6e-6o-4o

UlaL.aclvn

30

W(ton)

20C3-Lut1

10

tnt;W{ton)

30

'Heli,L't

20c3-vel2

10

-20O2040-80-60-40-20O2040GH<im)

30

30

20

20

c3-wn3C3-wn4

10

10

.

W(ten)

-60-40-20O20"80-6o-4o-2oo2o4oso-60-40-20O204060-60-40-20O2040'

6H

<nrn)

Fig.10

Load-Deflection

Curves

under

Vertical

Loading

The

cragk'

patterns

of

three

from

eight

test

structures observed

under

horizontal

loading

are

illustrated

in

Fig,

6,

Fig.7

illustrates

the

deflected

shape of

these

test

structures

at

the

peak

and at

the

end of

different

cyc],es under reversed

horizontal

loading,

It

should

be

neted

_that

_there

is

little

evidence

of residual

deflection

caused

by

horizontal

loading

in

case of

H4

_program

though

remarkable

deflections

are

found

to

remain

in

ca$e of

H1

and

H3

programs

having

the

same value of

_given

maxlmum amplitude

{2

×

10J'

rad,

)

with

that

in

H4,

The

H4

_program

was

selected

to

be

the

typical

one of actual responses

to

earthquake rnotions,

ii)

The

Behavior

undet

Vertical･

Loading

Fig.

8

shows

the

crack

_patterns

of all

the

test

structures

developed

under

vertical

loading

applied after

horizontal

loading

test,

Among

eighttest structures,

four

(of

H

1,

H4)

failed

at

the

third

floor

bearn-column

_joints,

two

(of

H

2)

failed

at

the

second

floor

beam-column

joints

and

the

rest

two

(of

H3)

showed overall

buckling

failure.

This

difference

of

failure

_patterns

can

be

diTectly

related with

the

_given

horjzontal

loading

_pTogTams.

Fig.

9

_s/hows

the

-50-'

Tabte3

CorfelationofExperlmentedandCalculated

VaLues

of

Ultimate

Horizontal

Load

and

the

CalculatedValuesofCoefficients

Hax.Ilori2ontalLoafl

Test'StructuresallpExp･<kg)Cal.<kg>ExprCal(ratio)

Cl-VHIO.33i,oo'315,2289,ql.09

Ci-Wll2o.srJO.TB27?.5'291.qo.grJ

Cl-WT13O,33'[.oe281.3289.0O.9T

cl-wllqO.33t.eo294,O290.21.01

C3-VlltO.35･O.98300.0285,O1.05

C3-Vl)2O.64O,69262,5282.4O.93

C3-Vlt3O,35O.9B26B.7285.q'o.gq

C3-Vll4O.3TO.962B8.5286,e1.01

Table4

Distribution'of

_fu.

in

Interster{es

ef

a

Typical

Test

Structure

Frame

TestStru

¢

tufe:Cl-WHI-s

R(xiOcad.)

AtthePeakofCycleNo.

StoryLevet

1(O.'25X)T(2.0X)

4

2.74(1.14)22.84(I.11)

3

3.08(1.28)24.55(1.19)

2

2.35(O.98)23.16(I.12)

1

1.q8(O.61>11.90(O.58)

Average2.4t(1.00)20.61(1.00)

deflected

shape at maximum vertical

load.

'

'

The

maximum response values

for

vertical

load

with respective

horizontal

diEplacement

and

residual

displachinent

are

tabulated

in

the

right

_part

of

Table

_2.

Vertical

load

versus

horizontal

displacement

for

all

the

test

structures

are shown

in

Fig.

10.

The

highest

or

lowest

vertical

load

carrying capacity was observed

in

case of

the

test

structure

experienced

i'n

the

horizonial

loading

of

H

2

or

H

3

_program

respectively,

The

vertical

load

carryi'ng

capacity

and

the

buckl'ipg

mode _of

the

'test'stru'ctures

with

the

_{expelien'ce of'Hl}

_program

were _nearly

the

_{same as}

those

_of'the

test

Structures

of

H4

program.'

This

shows

that

the

'vertical

load

carrying capacity

is

determined

only

by

the

eve'r

experienced

maximum

amplitude

regardless

of

the

loading

history,

indicating

the

va[idity

of

the

equiv'alent

elast-ic

stability

theory

method

_proposed

in

Part

1.

With

the

expetience of

the

stime

horizontal-lotiding

_program,

the

ultimate

'

'vertical

lpad

carrying

capacity

of

the

test

structures

in

C

1

series'is

always

a

little

higher

than

in'the

C

3

serie's.

The

vertidal

load

carrying capacity of

the

test

structure

C

_1-WHI

of

this

study'was ne'arly

the

same as

that

of

C

_63-41

H

of

part

1

which

_was'the

identical

sPecimen.

This

may

be

clue

to

the

developmentbf

the

same rotational stiffness under

the

action of

horizontal

loadihg.'

On

the

other

hand,

the

vertical'

lead

carrying capacity of

the

test

structure

C

3-WH

1

of

this

study shows much

_greater

value

than

C63-42

H.of

Part

1.

This

may

be

da'e

to

the

_gradtial

arrangement ef

'

'

stfe'ngth

distributibn

of

the

beams

over

the

height

of

framek

of

this

study.'

'

_'

_'

4.

Discu$sions

i)

Maximurn

Strength

unqer

Horizontal

Loading

Table

3

shows

the

comparison

between

test

results and calculated values

for

the

maximum strength of eight

test

'

structures under

horizontal

loading.

Thes'e

calculated values were obtained

by

assuming simple equilibrium conditien on a

frame

as

defined

by

Eq.

(17)

in

Part

1,

Table

3

also showg

the

results of' a. and

_l9

defined

in

Part

1

for

the

test

structuTes of

this

study.

These

values

indic.ate

that

all

the

test

structures except

H2

loading

_program

ones

'

'

'

t

t

tt

Table5

Correlationef

Experimented

and

Calcutated

Ultimate

Vertical

Load

Car[ylng

Capacity

and the

Values

of

-

'

the

Coefficients

and t'he

Shape

Function

'

Max,YertiealLead

TestStructuresT

avmExp.(Lon)Cal.(ton)ExpXCal<ratLo)

C]-VHIo.snO.T3I.6520.10]9.2q].06

Cl-VH2O.B6O,481.E527,9328.02O.99

Cl-V"3'O.56O.841.6514,4115,qlD.93

[1-VIMO.89o.6eL.6520.9119.T4L.06

C3-WHIO.T9'O.802[251?.80IT.69].o]

C3-Vtt2O,82O.522,SO24.522q.r2le.99

C3-VH3O.35O.93zieLl.41n.6]lo.gs

C3-VH4O,82O,742.30i9.20I7.5511.09

t/

littt...i---t.'Atl'

'''''ltA

'''

/

'tttttltt'

//

.t-.J.'-'

/6thi PointA!Highestj

'HorizontalIoad

PeintA=ItwestHoi ±zcrntallaad T=Pg-C!gNeEQChighest)

'

Fig.

1'1

Deterrnination

of

'the

VaLue'

of

_r

-51-Architectural Institute of Japan

ArchitecturalInstitute of Japan

T1.0

O.7

o,s

o.

Werwcu1

lt3

O

O･Ol

O･02

O･03

O･04

eav.(rad)

1/3

1av

Fig.12

The

Decrease

of

Strength

under

fforizontal

Fig.

13

Determination

ef

the

Calculated

Values

of

Wcr

Loading

with

the

Increase

of

NumbeT

of

Cycles

reach

the

horizontal

strength

of

collapse mechanism

(fi

==0.

It

can

be

seen

from

the

table

that

the

measured values

of

maximum strength under

horizontal

loadings

have

_good

agreement with calculated values,

It

ean

be

also observed

that

both

the

experirnental and calculated values of

the

maximum strength under

horizontal

loading

for

the

test

strllctures

in

C1

series are

a

little

_greater

than

for

their

counterparts

in

the

C3

series.

This

might

be

due

to

the

variation

of

the

strength

_properties

of

concrete,

relating

to

flexural

strength

at

the

bottom

of

columns.

ii)

Maximum

Strength

under

Vertical

Loading

The

analytical approach made

in

Part

1

was rnodified especially on

the

equivqlent

rotational stiffness of

beam

enCEs

by

introducing

the

rotational stiffness recluction ratio

₇

during

horizontal

loading.

This

modification was made

due

to

the

employment of various

horizontal

loading

_programs

in

this

study

_partieularly

by

taking

into

account

the

effect of

H

3

horizontal

loading

_program.

Thus,

equivalent rotational stiffness

becomes

_7.M.,1enma.,

The

value of

_r

has

been

defined

as

the

ratio

of

the

lowest

to

the

highest

loads

at

the

ever

experienced

maximum

arnptitude

in

horizonthl

Ioading

history

as shown

in

Fig.

11,

Table

4

lists

the

distributions

ef

a.,.

over

the

height

of a

frame

for

a

typical

test

structure at

the

_peak

of

the

lst

and

the

7th

cycles of

the

horizontal

loading

_program.

Except

the

lst

story

level

one,

the

values of

e,...

do

not vary with

their

average value

da..

significantLy allowing

to

use

the

average value

_tza.,

for

a representative

index.

Fig.12

shows

the

correlation

between

the

values of

_r

and

the

yalues of

da..

whilch we/re

obtained

from

deflected

shape of

Fig.7.

This

figure

indicates

how

the

values of

₇

decrease

with

the

successive

loading

cycles without

increasing

the

average

beam

end rotation

th...

Also

in

this

figure

two

lines

are

_plotted

with

the

data

available

in

case of all

the

test

structures,

indicating

the

decrease

of

₇

with

the

increase

of

da..

in

the

second and

in

the

tenth

cycles.

Fig,

13

shows

the

deterrnination

of

the

calculated values of

VVI,.

from

the

intersection

between

the

curve

by

Eq.

(12)

in

Part1

and

_WL.IWL.-a.

curve

for

eight

test

structures of

this

study.

The

comparison

between

measured and calculated values

for

the

vertical

load

carrying

capacity

of columns

is

listed

in

Table

5.

This

table

also shows

the

values of

flexural

rigidity reduction ratio of columns

during

vertica],

loading

(a.),

constant used

for

the

shape

function

of columns

(m)

as well as rotational stiffness reduction ratio of

beam

ends

during

horizontal

loading

_<7),

It

is

seen

that

there

is

_good

agreement

between

the

calculated and experimented values

,of maximurn strength under vertical

loacling.

All

the

test

structures under

limit

state

design

method show

the

values of

Vli}.

a

little

higher

than

those

under currently used elastic

design

method.

Figure

9

in

the

above section

shows

the

comparison

between

the

measured

and

calculated

deflected

shapes at maximum vertical

load

in

case

of all

the

test

structures,

which show

_the

idientical

eonfiguration

each

other.

Fig.

14

shows

the

experimented and calculated vertical

load

earrying capacities of columns as

the

strength ratio

-52-wdr2FEit5i5D

1.

L

o.s

es(Exp.)h

es(Cal.)

es(Exp.)

es(Cal.)

(Exp.)

(Cal.)

s---

---L

.--.-.

---

t

h'=--==e

oo

1

2

3

Fig.

₁₄

Cornparison

of

Experimented

and

Calculated

Vertical

Loa

Including

those

in

Part]

4･

5

'

6max

(xioe

)

Y･H

d

Carrying

Capacity

ofall

the

Test

Structures

acrlE =

VliLrf2

Er

bD

_versus

amaxlr'H

_where

a.a.IH

is

the

_{ever experiencecl maximum}

deflection

_{angle of a}

frame.

It

is

fovnd

t.hat

a..IF:,

decreases

into

the

one' narrow strip as

Oma.lr.H

increases,

regardless

of

strength

distribution

of

beams

over

the

height,'

number of stories and

_program

of

horizontal

loading.

The

trend

of

this

figure

shows

the

necessity of

imposing

sorne

reistrictions on

the

_probable

values of maximum

deformation

angle

induced

by

'

_earthquakes

_or

_the

_design

_level

_of

_long-term

_axial

_force

_for

_columns

_in

_aseismic

_design

_of

_btrildirigs,

_It

_has

_been

generally

recognized

that

the

higher

seisrnic strength a

building

has,

the

sinaller

the

maximum

deformation

angle

induced

by

earthquake

becomes.,

If

sufficient

seismic

strength

is

_provided

with

hffective

seismic elements;

_such

as shear walls

for

a

building,

the

maxirnum

deformation

angle will

be

small, may

be

within

1.

0

×

10'Z

rad. even

during

extreme earthquakes.

In

this

case

there

occur no

seFious

problems

on

the

vertical

load

carrying capacity of columns after earthquakes

judging

from

the

figu;e

14.

0n

the

other

hand

if

a

building

consists

of only

frame

systems which are

expected

to

have

much capability of

deformation

with relatively

low

strength,

the

maximum

deformatio4

angle may reach

2

×

10'!rad.

or more

during

major or extreme

earthquakes,

In

this

case

strong restrictions are need

for

the

'

design

level

of

long-term

axial

force

for

columns at

the

stage of aseismic

design

of

builclings,

for

instance,

about

_115th

'

to

116th

of

LbD

to

secure

the

safety

factor

of

3

on

the

premise

of

the

eontinued serviceability of

buildings

after major or extreme earthquakes.

Based

on

the

findings

at

this

stage

the

following

approach may

be

suggested.

The

maximum

deformation

angles

induced

by

earthquakes

may

be

estimated

by

the

_proposed

methods, one of which was reported

in

Ref.

3,

derived

from

the

dynamic

analysis results

on

single

degree

of

freeclom

systems.

Using

these

methods and

taking

into

account

the

tre'nd

of

Fig.

12,

the

way of

determining

the

design

level

o

£

long

term

axial

load

of columns

from

the

trend

of

Fig.

14

will

be

established although-more experimental results should

be

added

for

making

the

final

'

'

conclusions.

'

'

5.

Conclusions

The

following

statembnts can

be

made

from

_the

study.

1)

Experimental

works were conducted on eight

IAoth

scaled

_plane

frame

strudtures

of

single-bay, multistdry reinforced concrete weak

beath-strong

column

type

to

study

the

effect

of

the

different

_patterns

of reversgd

horizontal

loading

on

the

vertical

load

carrying capacity

of

col,ulnns.

Four

different

patterns

of

horizontal'loading

program,

characterized

by

maximum

deflection

angle, number of

loading

cycles

and

the

history

of applied amptitude were employed.

'

2)

For

the

response･analysis

under

vertical

loading,

the

characteristics of

the

degradation

of stiffness of

frames

'

obtained

under

horizontal

loadipg

_were

applied

into

the

theoretical

appraach.presented

in

Part

1.

It

was

found

that

-53-Architectural Institute of Japan

Arohiteotural エnstitute 　of 　Japan

this

　

modified

　method 　

_gives

　

_good

　

_predictions

　

of

　

the

　ve 【

tical

　

load

　carryi11g 　capacity 　of　

the

　columns 　of　multistory 　

_plane

frame

　structures 　

Qf

　weak 　

beam

・

strong 　column 　

type

　even 　wlth 　

the

　experience 　of　

different

　

types

　of　

horizontal

　

loading

，

　 3

）

　

It

　was 　

found

　

from

　

all

　

the

　

test

　results 　of　

frames

　

including

　

those

　of　

Part

　

l

　

that

　

the

　reduced 　values 　of　

the

　vertical

load

　

carrying

　

capacity

　

can

　

be

　

closely

　related 　

with

　

the

　

ever

　

experienced

　maximum 　

deflection

　angle 　

divided

　

by

　

the

stiffness

　

degradation

　

ratio

　under 　

horizontal

　

loading

，

　regardless 　of　sttength 　

dist

τ

ibution

　of　

beams

　over 　

the

　

heigh

電

，

number 　of　stories 　and 　

_program

　of　

hoizontal

　

loading

．

【

t

　was 　

also

　

found

　

that

　

the

　

proposed

　

limit

　

state

　

design

　

method

gives

　

higher

　values 　

of

　

safety

　

factor

　against 　

gravity

　

load

　

for

　multistory 　

frames

　with 　

the

　experience 　of　

h

（〕rizontal

loading

　

than

　

the

　

currently

　used 　elastic 　

design

　method

．

　 4

）

　

Further

　

studies

　

a

【

e

　required 　

to

　

get

　

general

　

conclusions

　about 　

the

　

stability

　of　continuous 　coLumlls 　of　weak

beam−

strong 　colu 皿n　

type

　of　

frames

　regarding 　

the

　aseismic 　

design

　of　

buildings

．

　

6．

Acknowledgements

　

T

揃sstudy 　

has

　

been

　conducted 　at　

the

　

Structural

　

Engineering

　

Depart

皿ent 　of　

the

　

University

　of　

HiroshiIna

．

　

The

authors 　would 　

like

　

to

　

thank

　

H ，

　

Araki，

　research 　associate 　of　

the

　

Earthquake

　

Engineering

　

Laboratory

．

　

The

　authors acknowledge 　

the

　cooperation 　

of

　

H ．

　

Ohtani

　and 　

Y ．

　

Kakita

，　

graduates

．

Reterences

D

　

Shimazu

，

　

T ．

　and 　

Mohit

，

　

S．

　

M ．

P．

：

“

The

　

Vertical

　

Load

　

Carryng

　

Capacity

　ef　

the

　

Colu

皿ns　of　

Multistory

　

Reinforced

　

Concrete

　

Frames

　wi 山 出e　

Experience

　of 　

Horizontal

　

Load

五ng

”

，

　

Jo

腫mal 　of 　

Structural

　a皿

d

　

Construction

　

Engineering

_（

Transaction

　of　

AIJ

_）

　

No

．

360

，

　

February

，

1986

，

　

pp

．

119

−

131

．

2

_）

MoHick

_，

　

M

．

A

．

A

．

，

Shimazu

，　

T

．

　and　

Mohit

，

　

S

．

　

M

．

　

P

．

：　

“

_The



_Vertieal



_Lead



_Carrying



_Capacity

_of

_the



_Colurnns

_of

_Multistory

　

Fra

皿es　with 　

theExperience

　of　

Horizon

ヒal 　

Loading

．

　

Part

　

3

−

The

　

Exper

血ental 　

Study

　of 　

Single

・

Bay

，

　

Multistory

　

Frairtes

_（

叮

）

脚

9

，

　

Summaries

　of 　

Technical

　

Papers

　of　

Annuai

　

Meeting

　of　

Architectilral

　

lnstitute

_of

Japan，

1986

，



Struct

_{皿τe 皿}

，



_pp

．

373

−

374

．

3

）

　

U

皿em 訂 a

，

　

H

．

：

“

Seismic

　

Design

　of　

Structures

−

From

　

Timber

　

Structures

　

to

　

High

−

Rise

　

Bundings

”

，

　

Revised

　

Editien

，

　

Koz

．

ai

　

C

且ub

，



1976

，



_pp

．

42

−

56

．

幟

　 　

文

】

UDC ：624

．

012

．

45

：

624

．

072

．

31 ：539

．

3

日本 建 築 学 会 構造系詭 夊 報 告 集 第 392 号

・

昭和

63

年 10 月

水

平

荷

重 を う

け た

多

層

鉄筋

コ

ン

ク リ

ー

ト

フ

レ ー ム

柱

の

鉛

直

耐 力 （

第

二

_{報 ）}

一

_各種

_水

_平

_{加 力 プ}

_ロ

_グ

_{ラ ム}

_が

_与

_{え る}

_{影 響}

一



_（

_梗

_概

_）

正

会

員 正 会 員

嶋

　 　

津

　 　孝 　 　

之

＊

Md

．

　

Ali

　

Akbar

　

Mollick

＊ ＊

　

第

一

報

におい て

，

水

平

荷

重

載

荷 経

験 を もつ はり

降 伏 型

多 層

フ レ

ー

ム の

_{連 層}

_柱

につ いて， そ れの鉛

直

耐 力

を

求

め る た

め

の

理 論 を展 開

し， かつ この

理 論

の

有 効

性

を

確

か め る た めに

実 施

し た

実

験 的研

究

の

_報

告 を

行

っ た。

　

こ の

理 論

は

_多層

フ レ

ー

ム に おいて，

各

層

は り の

端 部 回

転 剛 性 を 等 価 線 形

バ

ネ

（

Ke

）

と し， かつ

連 層 柱

も

等

価

線 形 断 面 剛 性

［

（

EI

）

。q

］

を

有

す る

弾 性

体

に

仮 定

し

，

そ ’ _広

島

大

学 　教授

・

工

博

＊ “ 広 島 大 学 　 大 学 院生

・

工 修 　 〔昭 和 63 年 1 月

8

日原 稿 受 理 ） れの

座 屈 耐 力

を

求

め る

も

の であ る。 こ こ に

Ke

は

水

平

荷

重 載 荷

で

経 験

した はり

端 部

の

_{回 転}

量

最 大 値

に よっ て

定

め

，一

方

（

EI

）

ee は 理

論

方 程 式 を解

くこ

と

に よっ て，

座

屈

耐力

と

同

時

に

_得

ら れ る もの で あ る

。

第

一

報

で この理

論

の

_{有 効 性}

を み る た めの

_{実 験}

を

行

い， こ の理

論

で

耐 力 実 験

値

を

予

測で き るこ と を 示 し た

。

実験

と し て は

4

層 お よ

び

2

層

の フ レ

ー

ム

試験体

を

用

い

，

与

え た

水平荷重 載荷

の

履

歴

はフ レ

ー

ム の

平 均 層 間 変 形 角

が

2．0

×

10−

2rad にな る

ま

での

振 幅 段 階 的 増 加 型 正 負 繰 返

し

加 力

の

1

タ

イ

プ

の み で あっ た

。

一

₅₄

一

　

本 報

告

は

同 様

の

4

_{層 試 験 体}

を

用

い た

実 験 的 研 究

に

_関

す る も のであ る が

，

次

に

示

す

各種

の

水

平

荷

重

載 荷

履

歴 の

影

響

を

調

べ _てい るQ

　

イ

）

水 平 荷 重 載 荷

によっ

1

（

r

与

え

る

べ _き

_{平 均 最 大 層 間変}

形 角 を 第

一

報

の

半

分の

1

×

10

” 　rad に し た 場

合

の

連

層

柱

の鉛

直 耐 力

はど う か

。

建 物

の

耐

用

年

限 中 数 回 は

襲

っ て く る と

_考

え られ る

強 震

程度

の

地 震 を

対象

に し た もの

で

_，

_水

平 加 力 実 験

で は

一

定 振 幅

で

20

回

の

正 負 繰 返

し

を 与

える

（

H2

加 力 プ

ロ グラ ム

）

。

　

ロ

）

’

与

えるべ き

最 大 変 形 角

を

2

×

10

”

’_rad とし て_， こ の

振 幅

で

，

か な りの

多 数 回

の

正 負 繰 返

し

水 平 荷 重 を加

え た

場 合

はど うか

。一

般

に

，

大 振 幅

で

，

多 数 回

の

繰 返

し

を

加

え ると_，

水 平 耐 力

が

著

しく

低 下

する ことが予

想

され る

。

その

結 果

，

連 層 柱

の

鉛 直耐 力

は

ど

う な る か

。

こ の

加 力 プ

ロ グ ラム は か な りの

高

レベル の

地 震 動

を

考

え てい るこ と に な る

（

H3

加 力 プ

ログ ラム

_）

。

　

ハ

）

_第

一

_報

で

行

っ た よ

う

に

段 階 的

に

水 平 変 位 振 幅

を

増

やし て ゆ くの で は な く

，

逆 に

，

は じ め に

大 振 幅

を

与

え_， そ れ か ら

徐

々 に

_{振 幅}

を

減

ら して

ゆ

く

場 合

の

連 層柱

の

鉛 直

耐 力

は ど う か

。

現

実

の 地

震 動

は は じ めに

主 要 動

が

存 在

す る場 合 が 多い ことが観 測 され て いる が

，

こ の加 力

プ

ロ グ ラ ム は こ の よ う なこと

を

考

慮

し た もの であ る

（

H4

加力

プ

ロ グ ラム

）

。

　

以 上

の

3

種 加 力

プ

ロ グ ラム に

第

一

報

の もの

_（

H1

加 力

プ

ロ グラ ム

） を 加

え_，

計

4

種

の

水

平

加 力 プ

ロ

グ ラ

ム につ いて

，

新

たに

_，

4

層 骨 組

8

試 験 体 を

作

成

し

実

験 を

行

っ た

。

今 回

は

，

高

さ

方 向

の は りの

強 度

分

布

の

与

え

方

につ い ても

若

干

の

_変更

を

行

い_， さ らに

_各

_層

は りに は

_{常 時 荷 重}

を

考

え た

鉛 直 荷 重 （

鍾

り

） を付 加

した

。

　 実験

の

_結

_果

_，

_第

一

_報

で

誘 導

し た

連 層 柱

の

鉛

直

耐 力

を

求

め る

理 論

は

，

このた

び

の

_{各種 水}

_平

_加

力 プ

ロ

グ

ラムに

対

し て も

基

本的

に

_有

効

な もの であ ること が

明

ら か と なっ た。 す な わ ち

水平荷

重

載荷

で

経験

し た

最

大変

形

角

お よ

び

その

振 幅

で の

耐 力 低 下 率

の

値

に よっ て，

連

層

柱

の

鉛 直 耐 力

が

求

めら れ る

。

な お_，

H4

加 力

プロ グラ ムを う けた フ レ

ー

ム の

連 層 柱

は

，

水 平 荷 重 載 荷 後

において，

水 平 残 留 変 形

は ほ と ん ど

生

じて お

ら ず

，

鉛 直 耐 力

は

Hl

加 力 プ

ロ グ ラ ム の もの と

同

じ で あっ た。 こ の ことは，

地 震 後

，

建 物

被 害

が

外 観

には

表

れて お

らず

と

も

，

連 層 柱

の

鉛

直

耐 力

が

大

き く

低 下

して いる

可 能 性

が

あ

ること

を示

して い る

。

　

図

一

14

に_，

第

一

報

の

結 果 も含

め，

連 層 柱

の

鉛 直 耐 力

を

ま と めて

示 す

。

水 平 荷 重 載

荷

経 験 変 位 最 大 値 と

その と ・・

耐 力 低 下 率

（

δ  γ

H

）

・ よ

・ て

・ 理

・

う

・ ・ と

を 表

・ て い る

。

　

こ の

図

の

傾 向

か ら，

建 物

の

耐 震 設 計 を行 う 際

に，

地 震

後 も建 物

を

使 用

す ること を

前 提

に して

，

地 震

に よっ て

生

じる

最

大

変

形 角 ある い は

，

柱

の長

期 軸

力 レ ベ ル につ い て

制

限

を

与

え ね

ば

な ら ない こ と が

分

か る。

地 震 時

に

建 物

に

生

じ る

最 大

変

形

角

を

推

定

す る

方

法

は

文

献

3

等

に

提

案

さ れ て い る が

，

基 本 的

に は

，

建

物の強

度

レ ベ ル

（

保 有 耐 力 ）

と

考 慮

すべ _き

_{地 震 動}

レベ ルお よ び

建

物 総 高

によっ て

定

ま る よ う で あ る。 し た がっ て こ の

よ う

に して

求

め た

最 大

変

形 角 と

，

大

変

形

角

であれ ば

，

図

一

12

の

耐 力 低

下

率

を 考

慮

して_， 図

一

14

の

傾 向

に

従

い

，

設 計 時

の

長 期 軸 力

レベ ル

を

制 限

す ることに

な

る。

し

か しこ の

制 限 値

につ いて は

，

今後

，

現

在

実

施 中

の

分 布 加 力実 験

の デ

ー

タ

等

も

加

え

，

提

案

を 行っ てゆ きた いと

考

え て い る

。

一

₅₅

一