鉛直,水平両荷重作用下における鉄筋コンクリートフレームばりの挙動

[at

rt]

VDe:624.072.012

Journal

of

Structural

and

Constructlon

Engineering

(Transactions

of

AIJ)

No.

372,

Febiua[y,

1987

H"nR\amsvakitNWzaes

rg

372

e･waza

G2

fi2fi

THE

BEHAVIOUR

OF

BEAMS

IN

REINFORCED

CONCRETE

FRAMES

UNDER

THE

COMBINED

ACTION

OF

VERTICAL

AND

HORIZONTAL

LOADINGS

by

S.

M.

PARVEZ

MOHIT'

and

TAKAYUKI

SHIMAZU",

Members

of

A.

I.

J.

1.

Introduction

The

philosophy

of structu[al

design

of weak-beam, st[ong-column

type

of

frames

has

been

widely

adopted

for

aseismic

design

of reinforced concrete

buildings

during

the

latest

decade.

Little

informations

have,

howeveT,

been

obtained

on

the

combined effects

of

working vertical

load

and cyclic

horizontal

inertia

force

on such

type

of

frames,

though

some

investigations

without

the

definite

_philosophy

of such

type

of

ductile

frames,

have

been

reported'}h4],

Experimentai

study

is

being

continued

'in

our

laboratory

to

have

the

various

informations

concerning

the

behaviours

ef

such

type

of

frames

both

during

and afterearthquakes.

Two

of

the

study

tesults

have

been

_presented

in

Ref.

s

and

6

on

the

vertical

load

carrying capacity of

beams

in

reinforced concrete

frames

with

the

experience of reversed

horizontal

loading

and en

the

stability of

the

columns ofmulti-story

frames

with

the

experience of

horizental

loading

respectively.

When

a weak-bearn, strong-column

type

of reinforced concrete

frame

is

subjected

to

a series of reversed

horizontal

loading

cycles

along

with a

previously

applied

constant working veTtical

load

on

its

beams,

the

two

extreme ends of

the

beams

_gradually

lose

their

rotational stiffness.

The

beams

then

_graduaily

turn

to

behave

like

simply supported

ones,

by

decreasing

the

fixed

end moments and also

by

increasing

the

beam

center moment.

These

_phenomena

result

into

the

_gradual

increase

_of

the

_vertical

deflectign

_{along with}

the

beam

during

the

_reversed

horizental

loading.

Now

the

_practical

problems

that

may arise

due

to

this

increase

of vertical

deflection

along with

the

beam,

are

to

have

to

use

an

uneven

and

deflected

face

of

floors

and

roofs,

causing

_ponding

of

water

on

roofs which may result

in

acceleratecl

deterioration.

And

also

foi

instance,

the

door

and window

_panels

may not

be

closed or opened

_properly

during

emergency

etc.7).

The

possiblity

of

these

phenomena

may

be

overcome

by

providing

enough shear walls

for

the

buildings

to

reduce

_the

maximum

interstroy

deflection

during

reversed

horizontal

loading.

There

are some research examples of

behaviour

of

beams

in

frames

under combined action of yertical and

horizontal

loading.

Ernst'}

rep6rted

that

the

midspan

deflection

of

beams

we[e

increased

by

70

%

to

l40

%

after

the

first

_yield

of acritical section

in

reinforced concrete

_portal

frame

specirnens, subjected

to

working vertical as well as cycLic

lateral

loads.

Yamada

S)

found

also

the

_gradual

increase

of vertical

deflection

along steel-concrete composite

beams

subjected

to

alternately repeated cyclic

loading

with

incremental

deformation

amplitude uncler constant vertical

load.

Though

the

structures

tested

_by

him

were steel

_portal

frames,

the

slabs

which were

being

sustained

by

the

steel

beams,

were macle of reinforced concrete.

The

aspect of

this

_paper

is

to

observe

both

analytically and expeTimentally

the

behaviour

of

beams

in

reinforced concrete

frames

under

the

combined action of vertical and

horizontal

loadings.

In

_particular,

focus

is

_placed

on

the

continuous

_progress

of

the

vertical

deflection

along

the

length

of

the

beams

during

reversed

horizontal

loading

cycles, with working vertical

load

on

the

bearns

applied.

The

vertical

load

carrying capacity of

these

beams

with

the

experience

of

horizontal

loading

is

also

verified5).

The

abstract

of

this

_papeT

was already reported

in

Ref.

9

and

10.

First

a

symplified

analytical

model,

which

has

been

developed

te

explain

the

_phenomena

of

the

above mentioned continuous

_progress

of

the

vertical

deflection

of

the

beams,

is

_presented.

'

_Giaduate

_Student,

_University

_ef

_Hiroshima,

_Mr,

_of

_Eng,

i'

_Professor,

_University

_of

_Hiroshima,

_Dr.

_of

_Eng,

{Manuscript

recelved

May

15,19S6)

2.

Derivation

of

Analytjcat

Model

,

An

analytical

procedure

is

developed

to

suit

the

experimental

study

to

be

described

in

the

following

chapters,

which

deals

with a

series

of statically one

degree

indeterminate,

single-bay,

single-story

Teinforced

concrete

frames,

'

'

with

twe

mechanical,

hinges

at

the

bottoms

of

their

both

columns.

,

,

Based

on

the

following

assumptions,

the

vertical

deflection

of

beam

center under combined

horizontal

and vertical

loading

is

_going

to

be

calculated.

O

The

basic

assumptions

being

considered

are,

(a)

a'plane section of any member remains

_plane

at any stageof

loading,

_(b)

there

does

not

also

occur

any

shear

deformation

of

joints,

and

(c)

the

members

are axiaLly rigid.

2)

The

members of

the

frames

are

devided

transversely

into

desired

nurnbers,to

form

a

linear

mesh

of

finite

elements, which are connected

to

each other on

their

both

ends as shown

in

Fig.

1

for

the

model specimen, which was

divided

at an

interval

of

1

cm,

The

bending

moment, curvature,

deformatio,n

etc.

along

the

entire

length

of an element will

take

the

correspqnding yalues obtained

forits

center.

The

loads

may only

be

applied

･at

the

centers of

the

'

elementsii)

,

,

t

.

t

'

3)

The

tri-linear

rnoment-curvature

(M-di)

relations

for

the

segtions of

the

elements of

the

members

for

various

axial

force

levels,

N

may

be

obtained

by

the

rnethod as explained

in

Ref.

5.

To

suit

the

experimental

study,

for

the

beams,

the

_portion

between

the

crack and

the

_yield

moments of

these

curves,may

be

taken

to,be

represented

by

,the

straight

line

joining

the

cracking

_point,

corresponding

to

the

axial

for

¢e Tesulting

from

the

effect of

the

working vertieal

load,

and

the

_yield

_point

corresponding

to

the

maximum axial

force

developed

in

the

beam

when

it

yields

under

the

combihed

loadifigsi.

On

the

otheT

tiand,

for

the

columns,

it

may

be

done

by

joining

the

cracking and

_yield

points

cor[esponding

to

the

minimum and

the

maximum axial

force

which occur

in

the

columns under

the

combined

loadings,

The

effect of

the

slipping-out

of

the

tensile

reinforcernent may

be

considered

by

increasing

the

_yield

values of cuTvature, whiCh

is

calculated

from

that

_given

in

the

R.C.

Code

of

AIJ

for

the

corre.sponding values

of

rotations.

Fig

2

shows

the

way

how

to

determine

these

yield

curyatures

from

the

corresponding

yield

rotations.

The

value o.f a.

in

Fig.2

(c)

takes

the

form,

R.IR.=a.=CO.043+1.64np,+O.043alD+O.33

thXd/D)!'Z).

In

this

study,

this

effect

has

been･considered

for

the

beams

only.

For

the

relatively.strong columns, which are

being

used

in

the

experimental

study,

it

has

been

checked

analytically

that

there

are

almost no

effects

on

the

responses, +p p

whether

the

slipping-out effects of

the'

tensile

reinforcement of columns are considered or not.

Thus

the

calcu-lated

moment-curvature relations

for

k"-

･,

different

members are shown

in

.

i

Fig.3,

for

the

specimens of

F'ig

g.

Fig.1

Discretization

of

Frame

Structufe

4)

Fig.4

shows

the

degrading

stiffness

_properties,

considered

to

trace

the

_paths

in

the

_M-ip

cllagram

for

the

cyclic

loadings.

To

trace

the

6urves

for

the

Ioading

_portions,

it

is

assumed

that

either

it

aims

towards

the

experienced maximum moment-cttrvature

_point,

or

just

traces

on

the

envelope curve.

For'

the

unloading

portions,

when

the

experienced

max-imum

moment

lies

between

the

crack

and

the

_yield

moments,

it

traces

such

that

the

residual, curvature would

be

about

the

one-third of

the

difference

b'G

also6o7esowtz

g,

wtz1S 1802Dl P

-.tT

40io20le'1 1 Hinge 1

'

Ulng. 1020oql

fy

-

(a)

--tw---

---

Ry

)Wig

M

1by

Nt '''i' ''J'

'

'

'

'

'--tt

t

tt

tt

tt

_.a'

.･･K

tZ/'

..t

.t..;tl

i

..:

1

tt

1･

l

_/

i

1..

I

ltt 1 li.'

]

lt'i"

:

lt

l

d 1 1

1

/ / 1

./

d t / d

%

(b)

F.'ig.2

Dete[minatien

ef

Yleld

Cutvature,

Censidering

Slipping-out

of

Tensile

Reiriforcement

.R

{e)t,he

Effects

Ry

due

to the

-73-between

the

cracking

curvature

and

the

ever experienced maximum curvature7).

Thus

obtaining

the

curvatures at

the

centers

of

the

elements

along

the

length

of

the

members,

the

rnember

deflections

can

be

calculated.

5)

Under

reversed

horizontal

load,

for'

higher

ampli-tudes,

_the

bending

moments

at

different

critical

sectiens

of

the

beam

reach

their

_yielding

yalues,

resulting

in

the

fermation

ef

yield

hinges.

These

yield

hinges

are

formed

alternately

at

tlte

both

end

sections

of

the

beam.

It

may

be

considered

that

there

occurs a

flow

of curvatures

in

these

regions over a certain

length

along

the

beam

axis,

For

simplicity of calculation,

for

th{s

study,

_this

length

of

the

yield

hinges

was considered

to

be

{d.l2+db)

which

is

a

Iittle

medified

form

of

that

reported

in

Ref.

5.

Table

1

shows

the

values

of

the

_yield

hinge

length,

_proposed

by

different

authors,

calculated

for

the

model specimens

being

used

in

the

experimental

studyi3).

After

yielding

of

these

sections,

the

_plastic

curvatufes

e.,

constant over

these

lengths,

are

added

to

the

curvature

distributions

of

the

elements

in

these

regions,

at

the

starting

of

yielding

of

those

critical

sections

foT

any

instants

of

loadings.

Then

the

added

_plastic

curvatures

remain

active as

long

as

the

bending

moments of

the

respective

elements

do

not

change

their

signs.

6)

For

the

statically

indeterminate

structures,

the

values of

bending

moment

for

the

elements

along

_the

members may

be

calculated

by

considering

the

_geometrical

compatibilities of

the

frames.

In

this

study

the

only one

_geometrical

compatibility

is

to

be

considered

for

the

one

degree

indeterminate

structures, which was

done

in

such a way

that

the

vertical

deflection

of

the

beam-column

_joint

of

the

right

column

becomes

zero.

Also

the

magnitude of

the

_plastic

curvatures

along

the

_yield

hinge

length

may

be

calculated

in

the

same

way

to

fulfill

the

_geemetrical

compatibility,

providiing

that

the

bending

moment at

that

critical section

takes

its

_yield

value.

7)

The

qualitative

deflected

shapes of

the

model

speci-men at

the

_peak

and at

the

end of

the

_positive

horizontal

loading

cycle are

_giyen

in

Fig.

s

(a)

and

s

(b)

respectively.

From

the

_georuetry

of

these

fignres

the

following

equations can

be

reduced

for

both

the

cases, with

the

sign of

_e

taken

clockwise.

of,-:ie'･-IL-･-･･･--･--･--･･-･--･･-･････-･･-･--･a)

a,,=(-e

±

e'-e")･

!･･･-･･-･･･-･-･--･･-･･･-･･-････(2)

e,,=={R-e)･{L･-･･･-･･-･･･-･･--･･-･･･-･･-･･････-･･{3)

6t,=(R-e")･e-･･-･--･･-･-･---･-･･･-･･-･･････<4)

(t

o

Fig.3

1h-¢

Calculated

2

3

(xlO'"an-i)

Moment-Curvature

4

Relations

..T

F.-!eL..

:

n-"-'---i::::

thet"

1.

'

ll

¢e'o"- ¢)

Fig.4

Table1

Degracling

Stiffness

Properties

of

Moment-Curvature

Relatiofis

for

Analvtieal

Modet

The

CornpaTison

of

Equivalent

Yield

Hinge

Length

Proposed

by

Different

Aulhorsi3)

PreposerEquivalentVield

ttiiigeLenath,LpCalculatedLd,([m)HotielSpeeimensforthe

Baker2{O,8klk,(zld)c}

2],O

Hattock2<O,5d+O.05z)

LV,fi Sa-yer2<O.25d+O,075a) 15,q Authorsdc{igeb(,,Se:f･l l8,225,G

5,

_la

_wo

P-b

Mi

N-"--di-.--'

''t'.x,let',Rt't

-."tHt./-th'--.-.-.--.-,-sL"ss-sh'v

･-･"-ajel''-''it'''

.-t-.-t-.i'-t'-'ii'l't'll.J..iRiJtt'

pa

[a)M im Peak of tnrinonta! Icai Srbug

ttrS

WVd

---v

fiv

6i[d

L4

i･: ii;''i

iR:

Fig.5

e

.-t-.

(b)At theEhi

The

Geometry

Specimens

for

g

_y l"

'ie

i

fR

r

ef fbrizenta1 ZDal ing

ef

Defleeted

Shape

ef

the

+P-v

x

'

' 1

Atth"peak ef laadirg avcles

-"--

Atti}emi ef laHdlrgcycles Hy wi2Wt2

r･･.,,'iH"

'

_.s

_'''

'

st.---Frt''

Moment Dl2gram MyMe'-C2Vtllfrl ',1''xLt---'''-.] ' ' Hement Dtagram''lg:

Curveture Dtagian

,

Cvrv,aLureD±agram

t

t

(a)ForPositivenorizmita!LmadtrE (b)For Neeattve HDrtzonter lnHdirg

tt

Fig.6

_Qualitative

Bencling

Moment

and

Curvature

Distributions

Along

tfie

Frame

Members

Calculated

by

the

Analylical

Methoa

'

Table2

Deslgn

of

Model

Sbecimens

with

the

Results

Obtained

1

_frorn

the

PrototypesPROTOTYPE

MODEL RthFloorBeamtttt"hFloerBe"mttt.tlttltFloorBeam(es-qH)4thFloorBeam(BL-61H) EndCenterEnd[enterEndCentetEndCemter Lon#itudinalUprierOADO.4cle.84O.40+o.s7O.37o,HqO.B4 Reinfercement itatioC:)Le"erO.4ptO,S2O.40tO.54O.3TO.37O,S4O.84 VebReintorcement

RatioC:) O'.2o O.20 o.qo o,qo

WorkinsVerticalLoad(Wo>(ke)20,OOOsotilt22.50090es

600 1,D70

+ Mipimumreimfo#tement Fatie requiretaents of R.C.

Cede

vas applted correspendin:1v "Load reductien facter+s112Sferone-Nfth scate model

'

where,

e,

e',

e"

and

R

are

the

deflection

angles as shown

in

the

figures,

and

ofL,

afiR,

6t:L,

and

Dcn

are

the

member

deflections

of

the

left

half.-length

beam,

right

half-length

beam,

left

colum,n and right

column

respectively.

By

using

the

Eq.s

_(1)-:(4>

the

interstory

deflection

angle

R

and

the

y.ertical

deflection

of

the

beam

center

S.

b

ecome

.

t

'

1

R=(-of,-S.,+2S,,+2tib,).T･････････････-･--･･(5)

1

a.=(i,,-

a,,-2

o,,+2

at,)･2･･･-･･-･･----･････(

6

)

Trie

_qualitative

bending

m,oment and curvature

diagrams

of

the

frame

under

different

stages of

loadings

calculated

by

the

above analytical method are shown

in

Fig.6

(a)

and

6

(b>.

From

these

figures,,

it

can

be

ebserved

that,the

residual

moment and

curvature

diagrams

at

the

end of

_positive

and

'

negative

loading

cyeles

are

not

the

same.

3.

Preparation

for

Experimintal

Study

An

interior

frame

of

a six-,story,

single-bay

reinforced concrete

building

was selected

to

be

the

_prototype

for

the

specimens

tested

for

tfiis

study.

Fig,7shows

the

_ptan

and

the

elevatio'n of

the

frame,

_which

was

designed

according

to

the

R,

C,

Code

of

AIJ.

It

was considered

that

the

columns of ev ev em

Fig.7

+P.

'

Wa(a) Plan

Plan

and . .9

//t/

Eleyation

evrn

'

Em

-

,

'

'

'

tt

R

6

5 4

3

2 G

'

of

thePretotype(bl

Elevation

Frame

Fig.8

(a)T=1,OO

(BL-61H)

o

'

t.+..

99

o

@T:'

'

'3-6tp2 Z

6

/

'2-"3

i8

i,-,-14r,1-(b)

T

-

O.66

a

@tt.t/

rt

a(vp.tllx･/

3-6"1

r

'

iipa@

.F1-603

L-v4-FoTmatlon

Loading,

(a)

T

-

O.13

of

Yield

Ainges

under

for

D{fferent

₇

Values

1-6

¢

1 3-6¢

ti

L/4-Combined

-75-this

frame

would

carry

the

one-third

of

the

horizontal

inertia

force

_produced

in

its

span

during

earthquake,

while

the

rest

two-third

would

be

taken

up

by

the

end walls

_provided

in

that

building,

The

section

_properties

of

the

Rth

_(roof)

and

the

4

th

floor

beams,

according

to

the

results of

the

above

design,

are

_giyen

in

Table

2.

Table

2

also

shows

the

amount of working vertical

load

to

be

carTied

by

the

beams

of

the

respective

floois.

The

beams

of

the

model specimens were

provided

with

the

calculated

amount

of

reinforcernent ratios as well as

the

working

veritcal

load

as shown

in

Table

2.

The

tensile

reinforcement ratio$

throughout

the

length

of

the

beams

for

both

the

upper

and

lower

_positions

in

the

cross

section

were selected

to

be

the

same as

those

which

had

¢ome out

from

the

design

for

the

upper

_position

at

the

end

section

of

the

respective

beams

of

the

_prototype

frame.

Thus

the

resulting ratio,

_r

of compressive reinforcement

to

the

tensile

reinforcement along

the

beams

of

the

models

became

unity.

This

was

done

for

the

simplicity

of

the

construction of

the

reinforcement skeleton, which

is

nowadays

being

used

in

commercial

cases.

The

hysteresis

loops,

calculated

by

the

above

mentioned

analytical method are shown

in

Fig,

8,

in

terms

of

the

horizontal

load,

P

versus

the

interstory

deflection

angle,

R

for

a

typical

4th

flooi

model specimen

wlth

three

different

values of

_7,

(1,O,

O.

66

and

O.

33>

for

its

beam.

It

can

be

seen

by

comparing

these

three

figures

that

the

tensile

reinforcement at

the

both

end sections of all

the

three

beams

_yields

at

abottt

o.

O05

radian of

interstory

deflections,

but

foT

the

cases with

the

values

of

_r

other

than

unity,

there

appears one

more

_yield

_point

which corresponds

to

the

_yielding

of

the

tensile

reinforcement at

_the

lower

layer

of

the

sections

at

a

distance

of

one-foruth

span

length

from

the

both

ends of

the

beams,

where

the

reinforcement ratio

is

changed

for

its

bending

up

from

the

lower

layer

to

the

upper.

Table3

shows

the

_progress

of

the

vertical

deflection

of

beam

center

for

the

above

three

cases with respect

to

the

interstory

deflection

angle.

In

this

Table

it

can

be

seen clearly

that

the

beam

center

deflection

increases

continuously with

the

_progress

of

the

deflection

for

all

the

three

cases, showing almost no

reasonable

effects

of

the

variation of

the

value of

_7.

For

the

aboye calculations,

the

material

_properties,

the

horizontal

loading

_program

and

the

working verti ¢al

load

(33

%}

on

these

beams

were considered

to

be

the

same

for

all

the

three

cases.

4.

Experimental

Study

4,1

Test

Specimens

Two

typical

one-fifth scaled model specimens

BS-41

H

and

BL-61

H

were supposed

to

represent

the

Rth

and

₄

th

fleor

beams

of

the

aboye

mentioned

_prototype

frame

without

the

floor

slabs.

As

the

tensile

reinforcement ratios

at

the

center

of

the

beams

in

the

case

of

models, compared

to

those

of

the

protetype,

were rounded

down

from

_O.

₅₂

%

to

O.

37

%

and rounded up

from

_O.

₅₄

%

to

_O.

₈₄

_%

in

the

cases

of

Rth

and

4

th

floor

beams

respectively,

the

amounts of

the

working vertical

load

were also changed almost

in

the

same ratio$ as

shown

in

Table

4.

Thus

the

leyel

of

the

vertical

loads

happenecl

to

be.about

₃₀

_%

of

the

calculated

ultimate

capacity

for

vertical

loads

of

the

beams

without

the

expeTience of

horizontal

loading.

Fer

the

reason of

this

increased

level

of working vertical

load,

the

web reinforcement ratios were also made

double

to

the

designed

ones

to

ensuTe sufficient

ductility.

The

both

_types

of

reinforcement ratios

in

the

columns of

these

specimens were

_provided

sufficiently

to

ensure

the

weak-beam, strong-column mechanism.

Table3

TheValuesofBearnCenterDefiection,

cr.

Increasing

Along

with

the

Interstory

Deflection

Angre,

R,

for

DifferentValues

ef

r

r

Sv(mm) r=1.00r=O.66r=O.33

O.O025 1.q5(1.49) 1.51{1.54) 1.55(1.58) O.O050 1.Be"a.aL) ].8af(1.8E) 1.81t(t.S5) R(rad.)O.OIOO

3.D5(3.29} 3.19<3,40) 3,Ltti(3,5T)

O,0200

5.50(5.34)

6,offtde(G.53)

5,B5(G,93)

(

)

Values

Cerresponding

te

Residval

interstuty

Def)eetien

+

Upper

Reinforcetuent

Yield

lt Le"er Reinfercement YieLd

Table4

The

Variation

of

Different

Specimens

LongitudinalReinforteptent

Ratie"(;) Worki"aVertlc:1Load Beam SpeciurenEndCenteFCotutu" Vo(kg)WelW"(x> eS-41H 600 2T BS-41Ve,3TO.3T

-

-RL-OIH 2,49 1,070

33

BS-61He.sqO.84

1.a-o 45

BS-6LV

L

-Stirrups&Hoepspw

±

-O.4DX

3.2

¢

-50mnt@pw=e,42X

4.oe-soptm@

tThe _{saate values for both tensile aTtd couLtressiv" reiiiforcement}

'

-76-'

1600

su

oo-otetH

+

-

-co-16eO/3'

i6oo/3

i6ooi34-l2glg"

8-DIO4opSOd-108

+g8!-o

t

! !

se'

+ +ri

RM

s

'

･6-4"er3.2dee50d=128

'

suafta

o

o-oe-Table5

/1,jMechanical

Prgperties.of

Materials

_t./

(a)

Coneret.e

testSpecimenCOM[b.Str,engthYeung'sModulus

BS-41HO.282･3xloZ Bs-qlvO.352.2klei

BL-61HO,282･2xl02

BS-61HO.2B2.3xl02

Bs-61vlo.2B,.,2･4xlo2

unit: ton/cm2

(b)

Reinforeement

.

Bar,YieldStrengthVltimateStrepgthVOungisMedulus

.3.2di.q.s66.721.9x･los

4.0th4.675.991,9xlo9

6.0¢

･3.104.201.9xioe

ole¢ 4.035.T52.lxloS '

,

unlt: rm

.

FigLg

The

Specimen

vvith

Reinforcement

.-

_.

_{unit: ton/cmi}

'

'

In

this

study

the

number

of

two

different

types

of specirnens

totaled

five,

TwQ

of which were

_the

R'th

_story

flgor

bleam

frames

and

the

rest

three

were

the

4th

story

floo;

beam

frames..

Fig.9

shows

the

overalt

dimension

and

the

reinforcement of all

the

specimens.

For

simplicity of construction,

in

the

case of

the

_4th

floor,

the

_portions

of

the

c61uinns

developed

above

the

beam

level

were not

included.

To

observe

the

effects

of

higher

level

of working

vertical

load,

the

specimen

BS-61

H'

was

tested

under an

incieased

level

of

45

%

of

its

ultimate vertical capacity without

the

experience of

horizontal

,loading.

,

,

.

'

The

mechanical

_properties,

of

the

mateiials used

for

the

cofistruction of

the

_.models

are shown'

in

Table

5

(a)

and

5

i

(b).

,

･

.

,

4.2

LQading

,and

Measurement

Three

specimens

.with

their

numbers ending with

the

alphabet

`H'

(eg.

BS-41

H),were

tested

under

displacement

controlleq reversed

h6r.izontal

load,

during

which

there

was a

_previously

applied constant･

two

_points

working

vertical

load

(

wr)

on

the

beam

as

explaiped

above,

At

the

end

of

the

last

cycles

of

horizotal

loading,

_thevertical

load

on

the

beam

was

increased

up

to

the

failure

ef

the

beam

in

terms

of

three

_gradually

increasing

repeated vertical

toading

cycles

in

the

case of

EBS'

series only,

On

the

other

hand

the

same

type

of specimens

in

'BL] series are

being

used

in

the

long

term

(creep)

test

under

the

same wprking vertical

load,

to

_get

the

time-dependept

informations

of

these

beams

of

the

frames

･with

the

experience of

_{eversed

horizontal

loading.

However

the

time-dependent

informations

are not

included

in

the

scope

of

this

_paper,

ln

this

study,

the

working

_4xial

force

in

the

columns

is

not

Interstory

deflection aqgle, R

_[X]

2.oo

-.---.-.-..TT-.-7..8

1.oo

---...5..6

o.so

-.".-3"4

o.2s

1.t2

g::3

1!i:.:.2:T

...

cyeies

-3

-4

.

I.oe

---J-"'""':s"-6

2.00

---..."....".--...

"

-7 -8

2I:I

2g.:s:ig:rtge,tTraiiSdiie"rS

'

Fig.11

Horizontal

Loading

Progiam

W.S.G. Wire StrairiGages

C.G. C[mtact Gages-

.

Fig.10

Setup

for

Loading

and

Measurqments

-77-included,

as

it

has

very negligible effects on

these

types

of strong columns.

The

other

two

specimens with

the

alphabet

`V'

in

their

numbers were

tested

only under

three

_gradually

increasing

repeated

two

_point$

vertical

loading

cycles,

Fig.

10

shows

the

setup

for

the

test

as well as

the

loading

and

the

rneasuring apparatus.

Both

_the

_positive

and

the

negative

horizontal

loadings

were applied on

the

outer surface of

the

columns at

the

beam

axis

leyel,

while

the

two

_points

vertical

load

was applied at

the

one-third

points

on

the

beams.

The

vertical

loading

apparatus was

designed

in

such a way

that

the

top

of

the

specimens

could

rnove

freely

in

its

_plane,

Oil

jacks

were used

to

apply

both

the

types

of

loadings,

Seven

Displacement

Transducers

(D.

T.

)

were used along

the

length

of

the

beam

to

measure

the

vertical

deflection

of

the

beam

while six mQre were used

to

read

the

two

lateral

(horizontal

and

transverse)

directional

deflectiens

of

both

the

columns.

Twenty

Wire

Strain

Gages

(W.

S.

G.

)

were used on concrete

to

rneasure

_the

either

side surface strains at

ten

different

_points

on

the

beam

and columns.

Twenty

more

embedded

W.S,G.

were used on

the

longitudinal

reinfercement of

the

beams

of

4

th

story

floor

beam

specimens only.

In

addition

_to

_these,

Contact

Gages

(C.

G.

)

were

used

at

six

places

on

the

beam

and

beam-column

joints

to

measure

the

ciack width at

the

different

levels

of

horizental

and

vertical

loading.

However,

all

the

experimented

results

has

not

been

included

in

this

_paper.

Fig.11

shows

the

_program

for

the

reversed

horizontal

loading

which

is

the

same

as

that

used

in

Ref,5

and

6.

5.

Experimented

and

Calculated

Resutts

and

Discussions

Frorn

the

test

results of all

the

five

specimens,

it

was

observed

that

the

specimens

of

both

the

Rth

floor

and

the

4

th

floor

beams

show almost similar

behaviour

undei

different

loadings.

Here,

in

this

_paper,

focus

is

_going

to

be

_placed

on

the

4

th

floor

bream

specimens,

because

the

_qualitative

test

results

of

the

Rth

floor

beam

specimens are more er

less

similar

to

their

corresponding

ones

of

4th

floor

beam

specimens.

5.1

The

Crack

Progress

Observed

on

Beams

During

Horizontal

Loading

The

crack

_pattefns

of

BL-61H

under working vertical

load

and

at

the

end

of

the

2nd,

4th,

6th

and

8th

(last)

cycles of

horizontal

loading

are

_given

in

Fig.

12

(a).

It

was observed

in

the

cases

of

all

the

specimens

that

the

working vertical

loading

cau$ed a

few

hair

cracks on

beam

just

under

the

two

_points

of yertical

load

and or at

the

two

extreme ends.

With

the

application of reversed

horizontal

loading,

the

flexural

cracks

began

to

appear at

the

interval

of

_7-10

cm, starting

from

the

bottom

surface

in

the

middle-third

_portion

of

the

beam.

As

the

interstory

deflection

angle was

increased,

these

cracks

began

to

extend

deeper

and wider

inside

the

beam

as new cracks appearecl and spread on

both

sides

along

the

length

of

the

beam.

On

the

other

hand,

on

the

top

surface

there

appeared almost no new cracks except

those

at and very near

the

two

extreme ends of

the

beam.

If

the

figures

of cracks of

both

BL-61H

and

BS-61H

at

the

end of

the

_8th

cycle of

horizontal

loading

in

Fig.

12

(a)

and

12

{b)

are compared,

it

will

be

found

that

there

are almost no significant effects

ef

the

increased

level

of working

.

,

thrierVft)rkingVerticailnad

,

･'

Attheedof2rtiCv ¢le

･

,

: Atmberrtof4thqycle 4...

-+

"

[trrlerWOrkSngVerticalrnal{BS-SliI)

+

,'

At tiietu of 8th

CyclefBS-6N)

,

₊

1/･t.ttr)r".rst/1 AtUltirmteVerticalInaltES-6ma) +,...

,

,

ttt

l･'l,1･

Atdeeniof6thClycle

,

･

'//.

1/lt1/(･l

Attheendof8thCycle f---

g.--+

+

fiAtU!timteVertdcalLoaatBS-Srv)

Ca)

aLr6M

LtrtlerVario,s ZDaairbg Stages

Cb)

BS-61H

ana BS-6]r Ltr[ierVatious Zneding

Stages

Fig.

12

Crack

PatteTns

of

Specimens

Under

Varions

Loadings

78

-.---P

200

'

Cal.P(tg)

'

1iooo-:'tt

'

tt

'

8-6-4:

tt.tttt.,CF2''468

'i't''r-

tt/tttt.i:t7..,..ttt.t.t.

.6H(mTn)

/'

.v

tt

(a)

BS-41H

-Fig.13Experimented

and

(b)CalculatedBS-61H

HysteresisLoops

underHorizentalLoading '

lsoe

ltsl･

(ng

1

iooo

500

o

Fig.14

1

Progress

2

of

Vertical

3

4

S

"

6y

(mm)'

Deflection

at

Bearn

Center

during

6

Horizontal

7

Loading

8

(BS-61H)

/

yertical

load

on

the

crack

_patterns.

5.2

The

Hysteresis

Loops

of

Horizontal

Load

Versus

Interstory

Deflection

Angle,

The

experimented

and

calculated

load-deflection

(P-ai,)

curves

for

reversed

horizontal

loading

test

of

two

different

specimens

BS-41H

and

BS-61H

are

given

in

Fig.

13

(a)

and

13

(b),

and

those'for

BL-61H

was already

_given

in

Fig.8

(a).

Up

to

the

interstory

deflection

angle,of

O.

5

_percent,

the

hysteresis

loops

were spindle shaped

for

all

the

specimens

tested

under

horizontal

loadingl

Then

as

the

loading

was

increased

beyond

the

deflection

angle

of

O,

5

percent,

the

shape of

the

loops

appeared

to

be

of

inverted

`S'

type

one.

It

was observed

by

comparing

the

hysteresis

loops

of

BL-61H

and

BS-61H

that

there

weie almost no remarkable effects of

the

increased

level

of working vertical

-79-load

on

the

pattern

of

the

loops

but

the

required

level

of

horizontal

load

for

determined

interstory

deflection

was

decreased

in

the

case

of

BS-61H,

It

can

be

seen

from

the

comparison

of

these

figures

that

the

calculated curves resemble well enough

the

experimented ones.

Thus

the

analytical method seems

to

be

_quite

reliable

for

the

_prediciton

of

the

hysteresis

loops

under

the

combined

loadings.

5,3

The

Increase

of

Vertical

Deflection

of

Beam

Dttring

Horizontal

Loading

Fig.

14

shows

the

vertical

deflection

progress

at

the

center of

the

beam

(

_0b}

during

reversed

horizontal

loading

test

(BS-61H),

As

it

is

seen

in

Fig.

14,

it

was not

possible

to

keep

the

working vertical

load

on

the

beam

at

its

constant

level

during

the

horizontal

loading

tests.

The

vertical

toad,

which was

decreasing

with

the

increase

of

the

vertical

deflection

of

the

beams,

was

being

readjusted

at

the

end

of

every

horizontal

loading

cycle.

Fig.

15

(a)

and

15

(b)

{a)

At

the

Peak of Horizontal

LDaling

Cycles

Fig.15

Deflected

Shapes

of

Beams

s

_sss ' /tt

s-L

_.v

₁

_tt1

M-L

"J=1'ni'

x+

--

txl

ssN.x.N+SXKNL--2-1--'i':-tZtzt'llll NNN+s

rv-1'

NNst---4.--'''' N _x' +Ns '

Ns

''--..-7

6(rmO

(b}

At the

_bl

of

}lorizontal

[Daiing

¢

_yeles

under

Cornbined

Loadings

(BL-61H)

o

o

o

e+g(rad.)o

o

o

o

O.O05

O.OIO

O.020

O.O05

O.OIO

O.O15

"

R

(rad.)

.

Fig.

16

Experimented

and

Calculated

Values

ofInterstery

Deflection

Angle,

R

Vefsus

the

Beam

Half-length

Deforrnation

Angle

e+

0',

at the

Peak

and at

the

End

of

Horizontal

Loading

Cycles

-

80

--.Ol .--"iixP-

AtthePeakofCycles

."oCal'

.oo

'-.n---e-.---.o

9-'-''

-.h'

BS-41H

"n' .oo

rad.).oo

---.-L'---...

.

-...'"--'b--J-"-..J.4

.nt'

BL-61H

.ooo

.---'.'''-'''''''

.O05

i--'.'-F

h

..h'''-.n'

BS-6!H

.ooo

AttheIindofCycles

?F%--'-e.-F.Jtrv"'d'''''"'

o--..Jv]-..---'FFDtcr'''U pt n''''''irp-e-gib''-.]fh'' /

'

shows

the

deflected

shapes of

the

beain

of

BL-61H

at

the

_peak

and at

the

end of reversed

horizontal

loading

cycles

iespectively.

At

it

is

seen

from

these

three

figures,

it

was observed

that

the

vertical

deflectionsi

along

the

length

of

the

beams

were

increasing

continuously

during

the

reversed

horizontal

loading

tests

in

the

cases of all

the

three

specimens.

Moreover,

'it

can

be

se'en

by

the

comparison

between

Fig.

₁₅

(a)

and

15

(b)

that

_the

vertical

deflections

along

the

beams

were not

decreasitig

when

the

horizontal

loading

was withdrawn at

the

end of every

_positive

and negative

loading

cycles.

This

increase

of

the

vertical

deflection

ol

beams

was

more

for

the

higher

level

of

applied working vertical

load

during

the

initial

stages

of

horizontal

loading.

The

experimented

as well

as

the

calculated values of

the

interstory

deflection

angle,

R

versus

the

beam

half-length

deformation

angie,

e+

e'

at

the

_peak

and at

the

end

of

every

cycle

of

_positive

and negative

horizontal

loading

of all

the

three

specimens are

_given

in'Fig,

_16.

In

this

figure,

the

way

of

the

progress

of

verticai

deflection

of

beam

centers

during

horizontal

loading

can

be

observed

clearly.

It

is

also

seen

that

the

cqlculated

valJes

obtained

by

the

analytical method

described

above.

Iies

between

₈₀

%-95'%

of

the

experimented values

for

both

at

the

_peaks

and at

the

ends

of

'

the

horizontal

loading

cycles.

Thus

the

method seems

t6

be

_quite

able

to

_predict

the

_progress

of

the

vertical

defLection

of

beam

center under

the

combihed

loadings.

5.4

The

Vertical

Load

Carrying

Capacity

of

Bearns

Experimented

and calculated

load-deflection

(

W-tt.)

curves under vertical

loading

of all

the

specimens are

_given

in

'Fig,

17,

in

which

the

vertical

load

carrying

capacity

of

'the

specimens

with or without

the

experience

of

horizontal

loading

can

be

cbmpared.

The

straight

line

_portions

of

the

curves extended

horizontally

are

the

effects of

the

increased

vertical

deflection

during

horizontai

loading,

The

aetual

beh'aviour

of

this

_portion

for

BS-61H

ivas

alrea'dy

given

in

Fig,

14,

Though

the

specimen

BS-61H

was carrying

the

working vertieal

load

ef

45

%

of

its

ulitmate

capacity,

the

ultimate vgrtical

load

earrying capacity of

this

specimen with

the

experience of

horizontal

loading

was about

95

%

of

that

of

BS-61V,

which was

tested

without

the

experience of any

horizontal

loading.

On

the

other

hand,

at

the

end of

horizontal

loading,

the

stiffness against vertical

loading

of

BS-61H

compared

to

BS-61V

was

decreased

to

a conSiderable extent.

This

_phenomenon

was alsd observed

between

BS-41H

and

BS-41V,

'

The

crack

patterns

of

BS-61H

and

BS-61V

for

ultimate

vertical

load

are.given

in

the

last

two

figures

in

Fig.

12

'

<bL

'

'

'

Table

6

shows

the

comparison

between

experimented

and

calculated

ultirnate vertical

load

carrying

capacities

of

'

the

four

specimens of `BS'

series.

The

calculated ultimate vertical

load

carrying capacity of

th'ese

specimens were obtained

by

considering

the

collapse rpechanism of

the

bearns

by

forming

simultaneous

_yield

hinges

at

their

both

ends ancl also under

the

vertical

loading

_points.

From

the

experimented results

it

is

seen

that

the

specimens with

the

3000

2ooe

w

(tg?

1

iooo

y,2

..yi.-.t.P-S-Jy,2

,x'tif

7-yk?97!

y･

t"

i

/i

f

tl

t

-1

i

--"-.

_･i･

,J-.

t'y'

/

.il /' ,-

.t.//

"'--

&-r

-'h

-.-..''ny'-"'-',h

y

{

al cl1 y ''

y,1

Z,1

'"/ 71l

ry,i7if

.,7,'

t

Wf2

sc'

_BS-41H

-･---BS-41V

-･-･-･-

BL-61H

---･･

_BS-61H

...-.:x-

BS-61V

H

Ca!.

y

;!

yield

c = _erack

Y2

o

u

y,4

10

IS

20

"

6,

(mm)

as well'as

the

Progress

of

Vertical

25

30

/

5

Fig17

Load-Deflection

Curves

under

Vertical

Loading

Horizontal

LoadLng

Deflectien

at

Beam

Center

during

-81-Table6

Cemparison

between

Experimented

and

Calculated

Ultirnate

Vertical

Loads

ULtimateVerticalLeads

SpecimenExp.(kg)Cal,(kg)E,xp,ICal.(ratie)

BS-qlH2,0902,0301,03

BS-41V2,19e2,03D1,08

BS-61H2,9TO3,L20O.95

BS-61V3,2003,L20L.03

Table7

Calculated

Values

of

Shear

Capacity

ef

Members

and

Boundary

Sections5)

Beam

CoLumnBo"mdarySection

FloorFrameAtCracking AtUltimateAtCrackingAtUItimatell･As,"y Rth1,480L,OIO1,5902,1503,S20 4th1,5301,S301,5502,1506,100 unit: kg

experience

of

horlzontal

loading

also show nearly

the

same ultimate vertical

load

carrying capacity as

that

for

their

similar specimens without

the

experience

of

horizontal

loading.

This

means

that

the

reversed

horizontal

loadings

have

iittle

effects

on

the

ultimate

vertical

load

carrying capacity of

the

beams

in

seismic-resistant

ductile

reinforced concrete

frames

even

if

the

maximum

interstory

defleciton

angte caused

by

horizontal

loading

reaches

the

_great

value of about

2,O

_percent.

From

Table

6

and

Fig.

17,

it

is

seen

that

the

analytical method

can

fairly

_predict

the

ultimate vertical

toad

carrying capacity and also

the

beam

center

deflections

under vertical

loading

for

beams

in

frames

with or without

the

experience of reversed

horizontal

loading.

Table

7

shows

the

calculated values of shear capacities

of

the

frame

members and

the

column

faces

at

beam

ends.

The

values were obtainedi

from

the

shear strength equations as

described

in

Ref.

5,

It

can

be

seen

from

Table

7

that

shear

is

not acritical

factor.

except

that

shear cracks may occur

in

the

beams,

The

calculated

shear

in

the

columns

for

the

ultimate vertical

load

is

only about

1.0ton,

which

is

not

a critical

factor

also,

6.

Conclusions

Based

on

the

study

reported

herein,

the

following

conclusions may

be

made.

O

An

analytical rnethod

has

been

developed

to

_predict

the

behaviour

of single-bay, single-$tory

reinforced

concrete

frames

under

the

combined effects of vertical

and

horizontal

loading.

This

method

includes

the

assumptions of

finite

element

theory,

the

equivalent

_yield

curvature,

the

_plastic

curvature

of

any section and also

the

hysteretic

properties

in

the

moment-curvature relation.

2)

The

11sth

scaled single-bay,

five

reinfoTced concrete

frame

specimens

haye

been

tested

to

study

the

behavieur

of

the

beams

of

frames

undei combined aciton of vertical and

horizontal

loadings.

Two

of

the

specimens were

considered

to

represent

the

roof

floor

beam,

while

the

rest

three

were

to

the4

th

floor

bearn

ofa

single-bay,

six-story

building,

designed

according

to

the

R.

C.

Code

of

AIJ.

With

these

specimens,

the

effects

of

the

cornbined

vertical and

horizontal

loads

on

the

behaviour

of

the

frames

have

been

observed,

And

also

the

effects

of

the

increased

level

of

the

working veTitcal

load

during

the

combined

loading

have

alse

been

investigated.

3)

It

has

been

found

from

the

experimental resu]ts

that

the

reversed

horizontal

loading

_producesa

considerable continuous

_progress

of

the

vertical

deflection

along

the

length

of

beams,

under working vertical

loacl

on

the

beam.

It

was also observed

that

the

_deflections

_become

even

_greater

at

the

ends of

the

horizontal

loading

cycles

than

those

at

the

_peaks

'of

them,

4)

The

experimented results

have

been

compared

with

_those

found

from

the

calculations, using

the

above mentioned analytical method.

It

has

been

found

that

this

method

is

_quite

reliable

foi

the

_prediction

of

the

hystere$is

loops

and

also

the

_gradual

increase

of vertical

defrection

at

the

center of

the

beams

during

the

horizontal

loading

cycles,

while

there

is

a

previously

applied constant working verticat

load

on

the

beams.

5)

Even

when

the

beams

a;e

carrying a considerable amount of working vertical

load,

the

reversed

horizontal

loading

does

not significantly affect

the

ultimate vertical

load

carrying capacity of

the

beams

of seismic resistant

ductile

frarnes

as

long

as

the

previously

applied maximum

interstory

deflection

angle caused

by

reve:sed

horizontal

loading

is

less

than

2,O

percent,

6)

Further

study

is

needed

to

_get

the

_general

conclu$ions

by

conducting experimental

studies

on

beams

of

fiame

with various

horizontal

loading

_programs

as well as with

the

different

_patterns

of

improved

reinforcement against

the

increase

of vertical

cleflection

of

the

beams.