偏心水平荷重を受ける鉄骨立体骨組の弾塑性性状(梗概)

(1)

Architectural Institute of Japan

ArchitecturalInstitute of Japan

[M

ve

at

N]

UDC:624.023I624.04

Journal

of

Stroctural

and

Construction

Engineering

{Transactiens

efAIJ)

No,357,

November,

1985

etsftee#ftasinthxdevLsctuthfi

n

357

e･

ewM

60

g11

fi

ELASTO-PLASTIC

BEHAVIOR

OF

STEEL

SPACE

FRAMES

UNDER

ECCENTRIC

HORIZONTAL

LOAD

by

SHOSUKE

MORINO*,

MINORU

WAKABAYASHI**

and

SHIRO

HOTAKA*",

Members

of

A:

I.J.

1. Introductien

When

a

building

frarne

is

subjected

to

earthquake excitation

in

an arbitrary

direction,

torsional

deformation

in

addition

to

_{2-directional}

horizontal

sway

take

_place

in

the

frame,

and effects of

biaxial

bending

appear

in

the

elasto-plastic

behavior

of

the

frame.

As

to

the

analysis of such a

frame,

some of

the

methods

developed

for

the

analysis of a single member under

3-dimensional

loading')

may not

be

directly

applicable

to

the

analysis ef a

_general

frame

of

high

redundanqy, since

they

require

_{prohibitively}

large

amount of compllting work.

Efforts

have

been

made

to

develop

simple methods of space

frame

analysis

based

on respective simplificationsMm]`),

In

addition,

the

strength

surface

for

a

_given

sturcture

and

loacling

condition,

and

the

eptimum

clesign

method

have

been

discussed

from

the

viewpoint of application

to

the

design

_{practice]5)"i').}

Experimental

work on

the

elasto-plastic

behavior

of

3-dimensional

stee]

fraines

has

been

reported

in

Refs.3)-5)

and

18)-22),

the

Jnost of

them

using small-scale rnodel

frames

subjected

to

the

constant vertical

load

and

the

monotonic or

the

cyclic

horizontal

load

with or without eccentricity.

Effects

of

the

following

_parameters

on

the

frame

behavior

are

investigatecl

:

eccentricity and

loading

angle

of

the

horizontal

load,

slenderness ratio of

the

column, vertical

load

ratio, stiffness ratio and

strength

ratio

in

two

directions

of

the

frame,

change

in

axial

force

in

columns

caused

by

bracing

ferce,

etc.

Recently

the

dynamic

response anatysis of space

frames

have

been

carriecl'O)Ni2)･k)･23)rr2Si, with

two

main

_purposes

:

to

clarify

the

difference

between

response

behavior

of space and

_plane

frames,

and

the

torsionat

response

behavior

of space

frames.

Although

the

number

is

limited,

shaking

table

tests

and

tests

by

computer-actuator system

have

been

carried

out

to

investigate

the'

space

frame

behavior

under

the

two-directional

_ground

motion2g)-3!),

The

behavior

of space

frames

are affected

by

many

_parameters

as

described

above,

hence

_quantitative

conclusion

cannot

be

derived

_yet

from

the

results

of

the

past

investigation,

In

addition,

it

seems

that

the

theoretical

investigation

is

far

ahead

and

the

verification

by

the

experirnental work,

_{particttlarly}

the

¢

yclic

loading

tests,

is

more

needed,

From

this

viewpeint,

simple

frame

models

consisting

of

four

columns

with

rigid

beam-and-roof

system were

tested

under

the

constant vertical

load

and

the

monotQnic or

the

cyclic

horizontal

load

with

fairly

large

eccentricity,

to

obtain

the

fundamental

knowledge

of

the

space

frame

behavior.

This

_paper

_presents

the

results of

tests

_together

with

the

results of

the

theoretical

analysis, and

discusses

the

restoring

force

characteristics of space

frames,

_putting

the

emphasis on

the

convergence-divergence

behavior.

2,

Experimentat

Work

2.1 Specimens

Shape

and

dimensions

of

test

specimens are shown

in

Fig.

_1.

Two

_plane

frames

are cut out and shaped

by

machine

from

a

SS

41

steel

sheet

:

they

are

connected

each

other

by

two

orthogonal

beams

by

welding, and a roof

plate

is

finally

welded

by

spot-welding.

Cross

sections

of

beams

and

columns

are

rectangular.

A

hole

of

diameter

40

mm

is

opened

at

the

center

of

the

reof

_plate,

through

which a round

bar

hangs

weights.

Another

hole

of

diameter

₁₀

mm

at

the

corner

of

the

roof

is

for

the

horizontal

loading.

Frame

specimens

and

coupon

test

_pieces

are all annealed

to

rernove residual stresses.

'

_Professe:,

_Dept.

_{Architecture,}

Mie

_University,

Ph.

D.

'i

Director,

General

Building

Research

Corporatien,

Piofessor

ErneTitus

of

Kyoto

University,

D,

Eng.

i"i

_Engineer,

_Nuclear

_Energy

Dept

,

Sato

Kogye

Co,

,

Ltd.

Manuscript

received

January

7. 19S3

(2)

-8-NII-Electronic Library Service

4

specimens are

_prepared,

and

they

are

tested

under

the

constant vertical

load

and

the

monotonic or

the

alternately repeated

horizontal

load.

Tablel

indicates

the

name of

the

frame

specimen, vertical

load

6+

ratio

n!NllVY

(N=axial

force

in

a column

;

IVI=yield

axial

force

of a

,

column), width

-4nd

depth'6'f

column sectio", column

height

and cleal

span

length,

Mechanical

_properties

of

the

material are

shown

in

Table

2,

6+

where a.

denotes

the

_yield

stress; a.

the

ultimate strength,

E

Young's

modulus, and est

the

strain at

the

start of strain

hardening.

Coupon

tgst

piece

has

a

rectangular

cross

section

of

6

×

8

mm, which

is

iclentical

with

the

column section of

the

frame

spgcimens.

6+

2.2 Testing

Apparatus

Testing

apparatus

is

schematically

illustrated

in

Fig.2<a).

Test

specimen

(marked

as

'"a"

in

the

figure)

is

fixed

to

the

test

table

through

angles and

high

tehsile

bolts

<b).

The

vertical

load,

which

is

the

dead

weight

hung

by

a

steel

bat

(c),

is

applied

on

columns

through

loading

beams

(d.

e) and

pin-supports

(f).

The

steel

bar

(c)

penetrates

the

roof

plate

through

the

hele

opened

at

the

center.

Loading

devi6e

<g)

grips

the

specimen

by

a

_pin

(h)

inserted

to

the

corner

hole

of

the

roof

_plate

as shown

in

througha

hut

gauge

<i)

toa

channel

beam

Cj)

whose end

is

connected

to

a

loadin

and

the

horizontal

load

is

applied on

the

specimen

by

tightening

the

bolt,

horizontal

load

are shown

in

Fig.

3. The

loading

frame

(k)

whic

distance

about

2,

5

m apart

from

the

specimen,

Table1

Test

Conditien

and

Dimensions

of

Specimens

25 15ttto-IIl:,･II!l11

i

"::--;::::;:=:-===::".･"ii

O

IItl

e.x$"

$--li bl -1,t pi

ld

I:

tr;:--:--T---;-t:-L:---t:---=-t

_''

p

a

t

-e

s

oo

NO

8'

Fig.

g

frame

Direction

and

_p.oint

of application of

th

h

carries

the

reaction of

horizontal

load

stands at

the

in

order

to

minimize

the

effect

of

the

change

in

the

direction

of

the

'

$

(unit:rnm)

Fig.i

FrameSpecimen'

2(b).

This

device

is

connected

(k)

by

a

bolt

and a nllt

(1),

e

'CelumnSection

SpecimenHorizontal

_Loading

nWidth(crn)Depth(cm)ColumnHeight(cm)SpanLength(cm)

No.1No.2J---t---No.3No.4

Monotonic

r---t

Cyelie

O.3O.5---O.3Oi5

O.7974O.8013

---O.8010O.7991

O.5987O.6018---O.6020O.601S

9.9989.996

---9.98410.001･

19.1914.3919.1914.38

-.L---.--19.1914.3919.1914.38

Table2Mechanical

Properties

of

Steel

Material

O(tlcm2)

y

a(tlcm2)u

E(t/cm2)Est("x)Elong.(r.)

2.700

4.248 21652.49319.0

1 .d.e

.-11

1

o

fo

.J-1IH1->2g

ica.b

1tlJJ

r

@@

@

<<>.fr

i

-

1 LL.---u[-vfivr-rn-IL

1 -tNii

_SN1s

s vJ

tllJtt

-tt'a

.;th'.Lt

(a)

l//

t:

-o,

rl

/J

'Oil 1

h

g/

h.g

ill;l;l=

･/1

-.-Fig.2

Test

Apparattts[J5i

UJf

/-/ml

(b)

.7-j

(3)

Architectural Institute of Japan

zIJ2T5-.,,,"1Hl

DG.1":=--=:::--:

Ii2ii

e-<cr

F:.-:::;T.=..T:"'I

'coLlil!:tt

NEgga

Iiil3

_li41[･

aG2tt----+---J---JL:

DG3

D,G,4

Dl!h(%)

aj

5

4 Y

2 aj

1 de

:l

-4

-b

ybu.--1

'5

F]g.3

Displacement

Measuring

System

Fig.4

Loading

Prograrn

horizontal

load.

Another

set of

hut

gauge.

channel

beam

and

loading

frame

is

prepared

on

the

other side of

the

loading

device

_(g)

for

the

reversed

horizontal

loading.

The

movements of

the

roof

_plate

of

the

specimen are measured

by

4 dial

_gauges

as shown

in

Fig.3,

which are set along

the

beam

lines.

The

intensity

of

the

horizontal

load

is

computed

from

strains

measured

by

wire

strain

gauges

(m)

mounted on

the

flat

_plate

_portion

of

the

hut

_gauge

shown

in

Fig.2(b).

2.3 TestResults

Figure

4

shows

loading

_programs

for

the

repeated

horizontal

load

applied

to

specimens

No.

3

and

No.

4,

in

which

D1

denotes

the

dispiacement

data

obtained

by

the

dial

_gauge

D.G.

₁

in

Fig.3,

andi

h

denotes

the

column

height

(=

10cm)

.

Direction

of

_positive

horizontal

load

is

indicated

by

a solid arrow

in

Fig.3.

Horizontal

load

displacement

curves,

displacement

_path

at

the

center of

the

roof

_plate,

and accumttiation of

the

column axial strains are shown

by

solid

tines

in

Figs.

6 through

12. In

the

figures,

H

denotes

the

horizontal

load,

and

u.,,

u.

and

di,

denote

the

horizontal

di$placements

at

the

center of

the

roof

_plate

in

_y

and

2 directions

and

the

rotation

angle

of

the

roof

_plate

about x axis, respectively.

The

values of

u.,,

u.,

and

ip,

are computed

in

the

foLlowing

manner

from

the

displacement

data

Dl

through

_D4

which are obtained

by

the

dial

_gauges

D.G.

1 through

D.G.4,

respectively,

In

view of

Fig.3,

we

have

Dl=upa-(a-un)ipo""'"-"-"-"'""'"""""'-"''"""'-'""''"""""'''"""''--･---･･-･-･･(O

D2=use+(a+un)dio-''-'--""'"'''-H''""-"''-''-'"----'''"'-'-'-"'"''''""""''""'-'-'"'(2)

D3=umo-(b+usu)

¢

o-･･･--･"''･--''''･･-'''''･･''''"'･''''･'''''-''''''"'':"''''''-'''''''''-'''"''''''''''''･-･'･･'･･･-･･<3)

D4=unt+{b-ust)

¢

o-･-･-･･･････････-･･-･･-･･-････-･･･-･･-･･･-･･･-･･･--･･･････-･･･-･･････-･･-･･･････--･･････-･･-･････････(4)

where "a"

denotes

half.

a

distance

between

D,G,1

and

D.G,2

(=

75

mrn), and "b"

_that

between

_D.G.3

and

D.G.4<=100

mm).

The

value of _¢_,

is

first

_given

by

an average of

two

values

:

the

one

is

obtained

from

Eqs.

(1)

and

(2

),

and

the

other

from

Eqs.(3)

and(4

).

Thus,

ipo=l(D2-Dl)la+(D4-D3)lbl!4-･-･-･-･-･-･--･-･-･-･-･---･･--･--･----(5)

The

values

of

use

and

u.

are

computed

by

solving

two

simultaneous equations, which are obtained

by.

tidcling

Eqs.(1)

to

(2

),

and

Eqs,(3)

to

(4

),

as

follows:

use=KDI+D2)-dio(D3+D4}ll(1+

¢

:)IZ････････････-･t･-･･･-･･･-･･･････-･･･--･･--･･･-･･････････-････-･･･････-･-････-･････(6>

un=KD3+D4)+

¢

o(D1+D2)ll(1+

¢

:)/2-'''''''''''''''-'''''''''''''''''''''''''''''''''''''''''''"'''-'''''''-'"''''<7)

In

the

equations above,

the

value of

the

clial

gauge

data

takes

positive

sign, when

the

rod of

the

dial

gauge

goes

out.

3. Theoretical

Analysis

Twe

methods

are

applied

te

analyse

the

elasto-plastic

behavior

of space

frames

tested.

The

first

is

the

_plastic

hinge

method2], and applied only

to

the

frames

subjected

to

the

monotonic

horizontal

load.

The

second method

divides

the

column

into

3 _portions

;

a

rigid

intermediate

_portion

and

elasto-plastically

deformable

end

_portionsiO].

Details

of

the

numerical computation

_procedure

are

_given

in

Refs.

2)

and

10).

3.1 Analytical

Model

and

Assumptions

Model

frame

analysed

is

the

one

used

in

the

test,

which

is

composed of4 columns of rectangttlar cross section,

(4)

-10-NII-Electronic Library Service

Assumptions

are as

follows

:

the

roof

is

completely rigid

in

its

_plane,

column

bases

are

fixed,

no

initial

imperfections

exist,

the

roof

_plate

does

not rotate about either

_y

or

z

axis

in

Fig.3,

and

the

intensity

of axial

force

is

identical

and eonstant

in

4

columns.

These

assumptions

imply

that

only

3

components

of

defermation

are

possible

to

take

_place

at

the

column

top;horizontal

translations

in

two

directions

and

torsional

apgle.

In

addition,

distributions

of

biaxial

bending

moments and

t6rsional

moment atong

the

longitudinal

axis

_pf

the

cloumn

become

antisymmetrical.

Other

assumptions related

to

the

evaluation of

the

column stiffness are

described

ip

the

following

section.

3.2 Column

Stiffness

The

column stiffness

is

obtained,

in

_general;

by

solving a set of coupled

differential

equations which

govern

the

equilibrium of elasto-plastically'deformed column memb6r undeT combined

Loading.

However,

closed-form solution cannot

be

obtained,

hence

the

column stiffness

is

evaluated

in

approximate manner

in

the

_present

analysis

6f

two

kinds

by

assuming

that

the

differential

equations are not coupled,

The

first

analysis employs

the

generalized

plastic

hinge

method,

in

whjch

the

column stiffness

in

the

elastic Tange

is

assumed

to

be

_given

by

the

stability

functions

for

a member of

doubly

symrnetrical cross section2), and

the

stiffness of a

hinged

member

is

6btained

from'

the

_yield

function

and

the

_plastic

fiow

rule, as

described

in

Ref.

32).

As

to

the

_yield

function

Y,

'

the

following

spheTical

function

is

employed

:

Y=(NINo)t+(Mle11lfro)!+(My/Mge)l+(MxlMav)!=1･O'-'''''''''''''''-'''-''''''''''''''''''''-''''''''''-'''''''-'''(8)

where

N,

M.,

M.

and

M.

= axial

force,

torsional

moment, and

bending

moments abottt

_y

and z axes,

respectiv.ely, and

the

subscript

o

designates

the

full

_plastic

value.

The

celumn

stiffness

in

the

second method of

Analysis

is

_gbtained

based

en

two

assumptionsiO)

:

_i

₎

elasto-plastic

flexural

defo[mation

takes

place

only

in

the

end

_portions

of

the

column whose

length

is

116

of

the

column

height,

and

other

_portion

is

completely rigid;ii) as

to

the

torsion,

the

column

behaves

in

the

_perfectly

elastic

manner.

3.3 Numerical

Computation

Input

data

for

the

analysis

of

the

frames

tested

are

those

listed

in

Tables1

and

2. Hysteretic

stress･strain

retation used

in

the

analysis

by

the

method assuming

the

deformable

_portions

at column ends

is

a

bilinear

_type

as shown

in

Fig.5.

The

value of

_u

is

taken

equal

to

8

×

10-3

for

frames

subjected

to

the

repeated

horizontal

load,

which

approximates

the

stress-strain

curves obtained

by

coupon

tests,

while

it

is

taken

equal

to

_10m4

for

frames

under

the

monotonic

loading,

since

the

effect of strain

hardening

hardly

appears

in

the

tests

of

those

fTames.

In

the

_analysis

by

the

_plastic

hinge

_method,

the

_end

force

vector _{at a}

_plastic

hinge

is

_assymed

to

_remain _on

the･

tangent

_plane

to

the

_yield

surface,

hence

the

end

ferce

vector extends

beyond

the

initial

yietd

surface,

Y=1.0,

RefeJence

32)

shows

a

technique

to

reduce

the

force

vector at

the

_pastic

hinge

without

disturbing

the

ovetall equilibrillm condition.

In

the

_present

analysis,

the

column

stiffness

of

the

hinged

column

is

modified moie

simply

by

ihtroducing

anew

tangent

_plane

whenever

the

force

vector at

the

_plastic

hinge

reaches anew

_yield

surface,

which

is

_predefined

as

Y=

'

1. 0,

1. 05,

1. 10"'

with

an

interval

ofO.

05. This

treatmenthas

been

shown

in

Ref.

33).

Nume'rical

results of

the

values of

Y

of

the

first

hinge

at

the

time

of

the

last

hinge

forming

are

'as

follows:Y=1.051

in

spe6imen

No.1,

and =1.075

in

No.2.

Ih

the

analysis

by

the

method assuming

the

deformable

_portions

at

'

colurnn ends,

iterative

_procedure

is

required, of which

details

are

described

in

'4.

Discussion

and

Conclusions

4,1

Discussionon

Test

Results

of

Mbnotonic

Loading

71rsts

Test

results

of

specimens

No.1

_(N=O.

3 IVI)

and

No.

Z

(N=O.

5 N.),

are shown

by

solid

lines

in

intensity

of

the

vertical

load

appear

clearly

on

the

reduction of

the

6 6yJEE

pEtt

.6y

Fig5

the

column stiffness

depends

on

the

deformation

as usual

in

a

general

nonlinear

_problem,

Ref,

10),

E

Idealized

Stress-Strain

Relation

and

thus

an

subjected

to

the

monot,onic

h6rizontal

load,

Figs.6

and

7,

respectiv6Iy.

Effects

of

the

maximum

load

carrying capacity

and

the

(5)

Architectural Institute of Japan

ArchitecturalInstitute ofJapan

H(kg)

80

60

40

20 "

tj7

tlt

"t

ft t .' t NM -tl t

Ii

itl .7,vv

''-t'-H(kg)

80･kt

601l

40!

120 o

2

4

6 -2

Uzo(rn

rn)

Uyo

(mm)

(b)

Fig.6

Results

of

Test

and

Anatysis

:

H(kg)

80

60

40

20 (a)

-'1s-NX

v, NX

"

Ns

sc

N ".

N.

1

N

s,,

L1':'1 UIO(MM)

:

X

5

s.L -'hN ,,11

4

"X

3 X2

N

Xx

1 H(kg)

H(kg)

pt.

,Rl

60f'x..

t'

l60

I N 1 JSS I

40:

Nx.Sslk.

/L4o

x

F

N.

i

20

XN

_l

tt

O,2

4-2

O

Uzo(mm)

Uyo(mm)

(a>

(b}

Fig.

7 Results

of

Test

and

Analysis

deformation

capacity.

The

negative slope of

the

load-dis

becomes

steeper

as

the

vertical

load

becomes

larger.

It

is

in

Figs.6(d}

and

7(d)

that

the

value of u.

keeps

'

displacement

range.

The

value of

u.,

which corresponds

the

vatue of

u.

at a certain

level

of

the

horizontal

load

_H

:

z

axis, and

the

value of

un

further

increases.

The

mark

_v

in

Fig,

6 indicates

the

_point

at which

the

does

net

appear

in

the

results

ef

specimen

No.2

shown'

Fig,7.

In

the

case

of

frarnes

with

slender

columns

andlor

subjected

to

the

large

vertical

load,

the

failure

due

to

the

instability

effect

takes

place

befo!e

the

strain

reaches

into

the

strain

hardening

range.

Figure

8

shows

the

centroidal strains

thi

and Eosat

the

bases

of colttmns

1

and

3

shown

in

Fig.

3,

which aTe

the

closest and

the

farthest

to

the

hoTizolltal

lead

_point,

respectively.

Although

the

extreme

fiber

strains

become

yeTy

large,

the

centroidal strains remain rather small, especially

in

the

case of Eos.

Results

of

(

lyclic

Loading

7lasts

Test

results of specimens

No.

3 {N=O.

3 IVL,)

ancl

No.

4 (N=O.

5 IVI)

which are subjected

to

the

repeated

horizontal

load

are shown

by

solid

lines

in

Figs.

g

and

10,

respectively.

The

load-displacement

relations

placement

observed

lncreaslng

to

the

weak

th

largest

ln

O

O.04 -3

-2

-i

Uyo(rnm)

%

Crad.)

{c)

{d)

Specimen

No.

1 _(n=O,

_3}

Uzo<mm>

H(kg)

pt60

'k,

i40

X

x

20 X

t

'

O

O04

tg

(rad.)

Uyo

<Mm)

(c)

{d}

Specirnen

No,

Z

(n=O.

5)

curve after

the

maximum capacity

is

attained

in

the

diagrams

ef

displacement

_path

shown

'

while usc shows slow

progress

in

the

large

axis

bending

of

the

column,

is

largeT

than

is

situatien causes

larger

_PA

moment

about

_y

than

strain exceeds

the

value of E.,

in

Table

2. This

H(kg)

80

60

40

20 ls

_NNxNxN

4 qtt13tsls"2,"s1

-2-1

No.

1 N

Neo3

N. N

Eel

k

H(kg)

60 tx40

X

N

20 X

eo3

o

E]oi(Fig.8

No

N

.2

eol

o

O.1xl

o'i

)

Centroidal

Strain

O.05Eoi(x1o'i)

(6)

NII-Electronic Library Service

of

specimen

No.

3

shown

in

Figs.

9(a),

(b)

and

<c)

indicate

the

following

characteristics

:

hysteresis

loop

enlarges

as

the

number of

loading

cycles

increases;the

shape of

loops

is

a stable spindle

type

and

symmetrical

about

the

origin.

On

the

other

hand,

in

the

case of specimen

No.4

subjected

to

the

larger

vertical

load,

the

loop

drifts

away

to

the

negative

loading

side

from

the

origin,

as

observed

in

Figs.

10(a),

(b)

and

(c),

although

the

values of

D1

used as

a

monitor

for

the

loadipg

are controlled

to

･the

prescribed

values at

the

turning

points,

as

shown

in

Fig.

10(d).

In

the

case of

the

frame

with slender columns under

the

relatively

large

vertical

load,

it

may

be

said

thai

the

displacements

'

accumulate

in

one

direction

although

displacement

at a specific

_point

is

controlled according

to

the.

_prescribed.

program,

which makes

the

frame

_gradually

unstable and

leads

it

to

the

faiiure

state,

Test

of

specimen

No.

4

was

lini$hed

before

the

_planned

number of

loading

cycles were applied.

Figures9(d)

and

10(e)

show

the

relations

between

u.

and

u..

In

the'

case of specimen

No.3,

the

displacement

_path

stays on a nearly

identical

line,

while

the

drift

of

loops

is

observed

in

the

displacement

_path

of

specimen

No.4.

Strains

at

the

centroid of column

1,

E,,, are

_plotted

in

Figs.9(e)

and

10(f).

It

is

clearly seen

that

e,,

of

specimen

No.4

accumulates with

increasing

cycles,

but

the

value of e,,stays about

o,

s

%

in

the

case of specimen

No.

3. 4,2

Comparison

between

Results

of

Tests

and

Analysis

Results

of

analysis

by

the

_plastic

hinge

method are shown

by

dashed

lines

with circles, and

those

by

the

method which assumes

the

deformable

_portions

at column ends are shewn

by'dashed

lines

in

some of

Figs.

6 through

_10.

Circles

in

the

former

indicate

the

formation

of

the

_plastic

higes,

which

form

in

the

order of cloumns

1,

_,4,

2

and

3 in

both

specimens under

the

monotonic

horizontal

loading.

Comparisons

between

the

results of

test

and analysis

for

specimens subjected

to

the

repeat.ed

horizontal

loading

are made

for

several selected

loops

as shown

in

Figs,11

and

12,

in

order

to

avoid

the

confusion.

'

The

analysis

by

the

_plastic

hinge

method well

_grasps

the

overali

behavior

of

the

space

fra'mes

subjected

to

the

Htk

x,

"

ll

MM'

li,

Li-lsil-l!YSIIg

'

RIA,,

it,

ll dL"r 11 [ (.UV.e}

'

[gt

kisxN

/

/tt

-4L

･::,

(a)

(b)

(c)

{d)

Ce)

'

Fig.9

ResuLts

ef

Test

and

Analysis

:

Specimen

No.

3 (n=O.3)

'

Htkq)

HC"g) H{kg)

'

HcLg)

Un{mm.)

I

i

_i

･,

I

i･

z

'

,,

+f

Yr,

'

:,

s,

,,.

(a)

(b)

(c)

(d)

(e>

(f)

Fig

10 Results

of

Test

a.nd

Analysis

:

SpecimeR

No.

4 (n=O.

5)

H(kg}20[rtt80lLO

.aL/$(raa.

ve'

`-1ro

'

(7)

-13-Architectural Institute of Japan

,

"tk9)

_Htltg)

1Jt1''rd

H(kg)ltan;

X.tt:i

80r

".t d//'1 1 _It1

il

lt

1/:':1 Hfkg)'

O,02

I

i

'%

i

,rtsost.ssssr'-lelitd+NtMs' dl d 1 , ,

:

" 1

ifr,1i2:rld3um{mm

t+d g:i-co: NJd

v""l4J,

-so1'

H[kg}

-TtoL

(a)

{b)

(c)

Fig.11

Comparison

of

Hysteresis

Loop$

1 Specirnen

No.3

(n=O.3),

5th

and

9th

Cycles

(a)Fig.12

80

11 ti

t 1 , IL ll 11

11-L1

11 lb

i

II-cai

:

L:.soli

" 1:1:,

401;

, 'l uyo

ICmm)

;

t J t ttr'rt

{b)

Hkg)eof,;1fi,co:l/11di1ddt-1Il:'ooz1o.pa

::$::Crad,)

r1,,to,1,'''1d,1-so

Comparison

ef

Hysteresis

Loops

:

No,4

_(n=O.

_5),

_3rd

and

6th

Cycles

(c)Speclmen

monotonic

horizontal

load,

except

that

it

_gives

felatively

higher

maximum

load

carrying capacity

than

that

obtained

in

the

test.

This

is

simply

because

the

assumed

yield

condition,

Eq,(8),

is

an appioximation

to

the

true

_yield

surface

from

the

outside, and

it

overestimates

the

stress

state

at

yielding.

In

the

analysis

by

the

method assuming

the

deformable

_portions

at column ends,

the

approximate

solution

for

th

column

top

displacement,

based

on

the

length

of

the

defoTmable

_portion

equal

to

_hl6,

becomes

larger

than

the

exact solution, once

the

_yielding

starts

in

the

column.

This

resu}ts

in

the

larger

PA

moment and consequently

in

the

low

estimate

of

the

maximum

load

carrying

capacity.

However,

the

analysis

by

this

method wetl

_grasps

the

following

characteristics

observed

in

_the

tests

_:

_i)

ceasing

of

increase

in

u.

in

the

large

deformation

range

in

specimens subjected

to

the

monotonic

horizontal

load

(Figs.6(cl)

and

7(d));

ii)

small values of E,, and eo!

(Fig.8);iiO

gradual

enlargement

of

hysteresis

Ioops

(Figs.

11(a),

(b)

and

(c))

and

linear

relation

between

u.

and u. of specimen

No.3

(Fig.9(d))

_;and

iv)

drifts

of

hysteresis

loops

(Figs.12{a),

(b)

and

(c))

and accumulation of

the

strain E,,of specimen

No.4

(Fig.

10(f)).

Phenomena,

similar

to

those

obseJved

in

the

present

test,

e.g.,

the

enlarging

loops

and

the

axial strains which may or may not converge

depending

on

the

intensity

of

the

axial

force,

have

been

observed

in

the

in-plane

behavior

of members and

framesM)･35).

The

divergent

behavier

ef specimen

No.4

may

be

due

to

the

non-symmetrical

deflection

of

beam-colttmns

which

has

been

investigated

in

Ref.

_36).

These

characteristics

must

be

the

column

slenderness,

the

vertical

load

ratio and

the

displacement

amplitllde,

but

the

derivation

of

the

_quantitative

relation

is

left

to

the

future

theoretical

investigation.

4.3 Conclusions

1. The

frame

specimen

tested

has

the

strong and weak axes as

to

the

resistance against

the

horizontal

load,

and

they

are

pararell

to

those

of

individual

column.

In

such a

frame,

it

has

been

already

ebserved elsewheTe5)

that

the

displacement

corresponding

to

bending

about

the

strong

(2)

axis,

u.,

cea$es

to

_progress

in

the

large

displacement

range,

if

the

monotonic

horizontal

load

passing

throuth

the

centroid with an

inclined

angle

to

the

principal

axis of

the

frame

is

applied,

but

not

in

the

case

of

the

cyclic

loading.

The

_present

test

shows

that

such

a

_phenomenon

also occurs

in

the

case of

the

horizontal

loading

with a

large

eccentricity, regardless of

the

loading

type;monotonic

or cyclic,

The

reason

is

clearly explained

:

the

increment

of

u.

is

accelerated

due

to

the

PA

moment which

becomes

largei

about

_y

than

z

axis,

2. The

specimen subjected

to

the

cyclic

horizontal

load

with

the

vertical

load

ratio equal

to

_O,

₃

show

spindle

shaped

load-displacernent

hysteresis

loops

which are stable, symmetrical about

the

origin, and enlarge with

the

increase

in

the

loading

cycle, eyen

though

the

horizontal

load

eccentricity

is

faifly

large.

On

the

other

hand,

in

the

case of

the

specimen

with

the

vertical

load

[atio equal

to

O. 5,

even

though

the

loading

is

controlled so

that

(8)

NII-Electronic Library Service

the

values of a specific

displacement

at

turning

points

become

prescribed

values,

hysteresis

loops

for

other

general

displacements

drift

away

from

the

origin, which results

in

the

instability

failure

with excessive

displacements'.

3. It

is

observed

in

the

tests

that

the

centroidal stiains at column

bases

remain rather smatl

in

the

frames

subjected

to

_monotonig

hgrizontal

loading.

As

to

the

frgmes

_subjected

to

the

cyclic

Ioading,

the

centroidal strain

in

the

column closest

to

the

load

_point

converges

to

a certain value

in

specimen

No,

3

with

the

vert'ical

load

ratio equal

to

O.3,

while

_plastic

compressive

strain accumulates with'the

increase

in

the

loading

cycle

in

specimen

No.4

with

the

verticat

load

ratio

equal

to

_O.

_5.

4. The

_present

tests

confirm

the

convergence and

divergence

_phenomena

stated ab6ve

to

occur

in

the

space

frame

behavior,

which

have

been

obseryed

in

the

tests

of

_plane

frames

and

members34)n36).

The

clear-cut

boundary

between

the

convergence and

the

divergence

may exist, and.may

be

several

_principal

parameters

such as column slenderness, vertical

load

ratio and

displacement

amplitude,

Derivation

of

quantitative

relations

is

left

to

the

future

work.

.

'

s.

Two

methods of analysis emloyed

in

the

_present

work are

both

simple, easy

to

apply,

and

satisfactory

to

gra$p

the

overall restoring

force

characteristics of space

frames,

although

they

have

a

little

deficiency

such as

in

'

evaluating

the

load

carrying

capacity.

'

Acknozvledgments

The

authors wish

to

express

their

appreciation

to

Mrs.

Fumiko

Saito,

formerly

a

_gradu.ate

student of

Kyoto

University,

for

her

assistance

in

carrying

the

experiments and

_processing

the

data.

The

authors

are also

_gTateful

to

Di.

Yasuhiro

Uchida,

an assistant of

Mie

University,

for

his

help

in

the

numerical

computatlon.

Reterences

.

'

1)

Chen,

W.

F.

and

Atsuta,

T. :

Theery

_of

Beam-Columns,

Vol.2

:

Space

Behavior

_and

Design,

McG{aw

HiLI

{]977)'.

2)

Merino.

S.

and

Lu,

L.W.

:

Fritz

EngineeTing

LaberatoTy

Report

Ne.331.1,

Lehigh

Univ.

(197o.IQ)'.

3)

Wakabayashi,

M.,

Morino,

S.,

Nishimura,

F.,

and

Hetaka,

S. :

Abstracts,

Annual

Meeting'of

AIJ,

_p.]osg

(1973.10).

4)

Wakabayashi,

M.,

Nakamura,

T.

and

Inoue,

A. :

Annuals,

DisasterPrevention

Research

Institute,

Kyoto

Univ.,

p.105

(1976.4}.

s)

Fujimoto,

M.

and

Okada,

H. :Trans.

AIJ,

No.244,

p.41

(1976,6),

No.245,

p.75

(1976.7),

No,246,

_p,

43 (1976.8}.

6}

IgarashL,

S.,

Tsujioka,

S.,

Uno,

N,,

et al.

IAbstracts,,Annual

Meeting

of

AIJ,

_p.1137

(1976.10),

_p,l139

(1976.10),

p.1377

(1977.]O),

p.1395

{1978.9).

7)

Kojima,

H.,

Hirao,

K,

and

Yano,

T.:Proc.

･JSCE,

No.240,

p.ll

(1977.'8).

s)

Okamote,

H..

:

Abstracts,

Annual

Meeting

of

AIJ,

p.

I419

(1978.

9)1

g)

Igarashi,

S.,

Tsujioka,

S.

and

Ikoma.

Y. :

Abstracts.

Annual

Meeting

ofAIJ,

_p.114t

(1978.9},

_p.815

(1979.9},

_p.995

(1980.9),

'

lo)

Matsui,

C.,

Morino,

S.

and

Uchida,

Y. :

Abstracts,

Annual

Meeting

of

AIJ,

_p.1179

(l980,9).

Trans.

AIJ,

No.319,

p.l

{l982.9),

'

11)

Kadokawa,

N.

and

Nishikawa,

H. :

Abstracts,

Annual

Meeting

of

AIJ,

p.

759 _{1981.9),

12)

Suzuki,

T.

and

Takeda,

T. :

Abstracts,

Anntial

Meeting

of

AIJ,

_p.761

(1981.9),

_p.763

(1981.9}.

'

13}

Shugyq

M. :

Abstracts,

Annual

_Meetlng

of

AIJ,

p.

19]9

(1981.9).

14)

Yamazaki,

Y.:Trans.

AIJ.'No.310,

_p.61

(1981J12}.

'

ls)

Ishikawa,

N.,

Ohno,

T.

and

Okamoto,

K.:Proc.

JSCE,

No.279,

p.45

(1978.11).

16)

Zlmmerli,

B.

and

Thurlimann,

B.:Proc,

ASCE,

J,

Str,

Div.,Vol.105,

No.ST3,

p.481

(1979.3)'.

17)

Kimuia,

M.

and

Nanba,

H,

:

AbstTacts,

Annual

Meeting

of

AIJ,

_p.

1349

(1980.9),

_p,

l9Z3

(1981.9),

_p.

1925

(1981,

9).

"ls)

Fujimoto,

M.

and

Matsumoto,

Y. :

Trans.

AIJ,

No.186,

p.27

(1971.8),

No.187,

p.51

(1971.9).

Ig)

Wakabayashi,

M.,

Okamoto,

H.

and

Ura,

H. :Abstracts,

Annual

Meeting

of

AIJ,

p.1361

(1972.10).

2o)

Suzuki,

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'･

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)

(10)

-16-NII-Electronic Library Service

【

研

究論文】

UDC ；624

．

023 ：624

．

04 日本建築学会構造系論文報告集第 357 号

・

昭和

60

年

11

月

偏

心

水

平

荷

重

を

受

け

る

鉄骨立

体

骨組

の

_{弾塑性}

_性

_状

_（

_梗

_概

_）

† 正会員正会

員

正会員

野

林

高

森

若

穂

捷

志

輔

＊

實

＊＊

郎

＊＊＊

　

1 ．

序

　柱

およびはりの

3 次元的

な

集合体

である

骨組構造物

に

地震

などに

よ

る

水平荷重

が

任意方向

から

作用

すると

，

骨

組

には

並進

とと

も

にねじれが

生

ず

る

。

骨

組全体

の

3 次

元

的

な

弾塑性性状や強度を解析す

るには

，

従来単

一

材

の

_解

析

に

用

いら

れ

た

精密

な

方法

1）

_{を直接適用す}

_{ると}

_{計算量}

_が

膨大

となるため

，

軸力

・

ねじり

・

2 軸

曲

げを

受

ける

材

の

剛性行列を導

いてこれ

を

一

要素

として

取扱う方法

など

，

それぞれの

仮定

に

基

づく

簡便

な

方法

が

提

案

されz）

−

17 〕

_，

実験的検証

も

行

われてきている3 ｝

−

S｝

・

i8｝

−

Z！〕

。一

方

，

立体骨組

の

_動

的

応

答

_{解析}

が

行

われるとともに1°）

一

］2）

・

14〕

・

13｝

−

28），

数

は

．

少

い

が振動台を用

いた

実

験

や，

電

算機

一

試験機

オンラ

イ

ンシステムによる

実

験

も

報告

されているz9）

−

31）

_。

　

立体骨組

の

挙動

の

解明

については，

影響を与

え

る因子

の

数

が

多

いため

，

定量的結論

は

ま

だ

導

かれてい

ず

，

また理

論的

研

究

が

先

行

して

_実

験

による

検証

がたちおくれているのが

現

状

である

。

本論文

は_，かなり

大

きな

偏心を持

った

水平力が作用

する

立体骨組

の

，

収束あ

るいは

発散的挙

動

に

_関

する

基

礎

的

知見

を

得

る目

的

で

_行

った_，

4 本柱

より

成

る

鉄

骨

立

体

骨

組

に

一

定鉛直荷重

と，

単調

ないし

繰

り

返

し