Passive antiseismic protections of multistorey building by controlled buckling of a steel base-isolation system

MECHANICS RESEARCH COMMUNICATIONS 0093-6413/90 $3.00 + .00

Vol. 17 (3), 149-155, 1990 Copydght (c) 1990

Pdnted in the USA Pergamon Press plc

PASSIVE ANTISEISMIC PROTECTIONS OF MULTISTOREY BUILDING BY CONTROLLED BUCKLING OF A STEEL BASE-ISOLATION SYSTEM

A. C a r o t t i I a n d F.G. de M i r a n d a ' ' " Department of Structural Engineering, Politecntco di Mtlano, Milan, I t a l y o~ F. de Miranda & Associates Engineering Consultant, Milan, Italy

20133

(Received 3 October 1989; accepted for print 15 February 1990) Introduction

P r e l i m i n a r y p e r f o r m a n c e d a t a a r e g i v e n f o r a new t y p e o f a u x i l i a r y s y s t e m f o r the base isolation of buildings under seismic disturbance {Fig. 1}. The system's behaviour relies on second order geoaetric effects with a response always within the elastic range. A characteristic elastic horizontal force vs. displacement curve was obtained with progressive stepwise reduction in stiffness (FIE. 2). The advantage of the system compared with conventional reinforced rubber isolators is that high stiffness is aaintained in response to wind action and there is a limit to the total force transmitted to the building under severe seismic action. And because energy is always absorbed elastically, the number of seismic events the system may withstand is not predetermined. The base system seems to offer encouraging advantages both in terms of a progressive stepwise reduction of the overall stiffness under increasing horizontal loads, and of an indefinitely elastic behaviour.

Mechantca~ B e h a v i o u r

Each of the first schematically downward

as

floor support a

pendulum-type

force P and a horizontaI

columns

of

bearing. force

149

F.

the building Each

support,

Each column

may be vlsuallsed at

its

summit,

is connected

a

to an

150

A. CAROTTI and F.G. de MIRANDA

elastlc

structure

consisting

of 4 trusses

and 4 cantilevers

(Fig.

3)

whose

elements are sized to ensure the mechanical behavlour here described. For simplicity we consider that H I = H 2 = H 3 = H 4 = H and similarly that L LI =

L2 = L 4 =

L.

As

F

increases

from

zero

to

F3

with

P

constant,

= we

distinguish three phases:

1st P h a s e 0 ~_ F < E 1

Let

F 1 be

the

level

of

horizontal

reached as a result of wlnd action,

force

and 11, 12 , 13, 14

moments of inertia of the four cantilevers, In such a situation all force e q u a l

N~ 11

=

II

the

maximum

be the individual

so that Itot = 11 + 12 + 13 + 14 .

are

in play with a resultant

axial

(compressive element)

"

tot

13+14 =

the trusses

to

to

i(i) N~I)

corresponding

.

(tensile element)

.(I}

Itot

N~ I) =

12+13+14

• F

i(I) tot

N(1) 4

(compressive element)

(tensile element)

=

(1)

being

F=

P. ~

F+

H

u

(I)

~3 F = 3 E I (I) tot

1 • (I-P/P (1))

cr

The horizontal stiffness would be: 3 E I "I'(~

o

u(1)

H3~9~ • ( 1 - p - ' ~ ) cr

2 where p(1) _ cr is the Eurelian The f i r s t Eulerian

P

I(I)

E tot

critical

load of the system in this

p h a s e e n d s when t h e a x i a l load,

and whenever

force

in truss

phase. No.

1 reaches

its

critical

PASSIVEANTISEISMICPROTECTION

w

N1

2

151

E A1

= F 1. I ( I )

A!2

tot

2nd Phase E1 <_. F < E2 Let F2 be the second predetermined h o r i z o n t a l

force threshold

(normal s e i s m i c

design limit), here the axial force in truss No. I remains constant while the axial

displacement

of

the

end

connected

to

cantilever

No.

Displacement at the top of cantilever No. 4 remains constant and

3

increases. is equal

to

u I (see Flg. 4). The horizontal stiffness of the system under such conditions depends only on cantilevers I, 2 and 3, that is I (II) = I + 1 2 + 13 tot 1 The horizontal forces in the trusses are:

N~ II)

= N~I)cF1) + -~'--. i(II)

OF-F1)

(tensile element)

tot N3(II) = N~I)c~I) + I(II)I~+I3 . C~_~l)

(compressive element)

tot U( I I ) N4(II) = ~

heine

F = F + P

H

and the horizontal stiffness in thls phase is:

=

K1

F-F 1

=

3 E I (II)

P to% . ( 1 - p ( - - ~ )

H3

u-u I

CF

2 where p ( I I ) = cr

i(II) E tot 4 H2

The second phase ends when the axial force in truss No. 3 reaches the critical Eulerlan load, that is when: 2 N3 =

E A~ A32

I~ +I~+I 4 = Ii+12+13+I4

•

12+I 3 FI +

II+12+13 " (F2-FI)

At the end of this phase the displacement is equal to u 2.

152

A. CAROTTI and F.G. de MIRANDA

3r~ Phase F.,2~ E ~ E 3 We d e s i g n a t e quakes).

the third

Here

the

force

axial

threshold force

deformation;

the

equal

The d i s p l a c e m e n t

to

though, The

u 2.

displacements

and truss

stiffness

No.

1:

the

I (Ill)= tot

Let

p(III)cr =

with F

the safety

The h o r i z o n t a l

the

top

1

is

constant,

o£ c a n t i l e v e r s o£ c a n t i l e v e r

maintaining

the axial

earthis

the

2 and 3 are

both

No.

force

as

1 does

constant

phase depends solely

increase (Fig.

5).

on c a n t i l e v e r

I

s 2 E 11 4 H2 > P'Fs

o£ t h e s y s t e m i n t h i s

3 E I(IIl)tot

phase is

P

H3

(1- p(iii------~) cr when t h e f i r s t

phase terminates

as a result

No.

tops

severe

factor.

K2 - U-U2 = The t h i r d

at

(exceptionally

truss

the

sytem in this

I

stiffness

F-F2

in at

No. 3 d e f o r a s o£

as F

of the displacement

occur i n t h e s y s t e m

plasticisations

u 3.

Conclusions The p r o p o s e d shows

a

system

two-phase

substituted L-frames.

may be

arrangement

by pretensioned The

implemented

maximum

where

cables,

linear

in various the

For example

horizontal

and the

elastic

ways.

vertical

lateral

trusses cantilever

displacement

difficulty,

r e a c h t h e 8 0 - 1 0 0 =at p e a k e x p e c t e d

under strong

It

that

to assess

is clear

further

proposed system and its initial

results

developments

are

in the

research

dynamic response

encouraging direction

with small

elasto-plasttc

anti-seismic

protection

is required

and

to the seismic

lead

o£ c o m b i n i n g

dissipators o£ l a r g e c i v i l

will

to

the

offer

engineering

have

been

realized may,

6

by

without

earthquake.

the feasibility input. the

o£ t h e

However,

expectation

In parallel

Fig.

that

these

further

isolation

improved performance

system in the

structures.

Re~erences 1.

P r o c . I n t . Conf. Vlbr. Isolation.

Natural Rubber for Earthquake Protection K u a l a L a ~ p u r , H a l a y s l a , (1982)

o£ B u i l d .

and

PASSIVE ANTISEISMIC PROTECTION

2.

3.

4.

A.G. Tamics, J.H. K e l l y , D. Way and R. Holland. Q u a l i t y assurance and c o n t r o l o f f a b r i c a t i o n f o r a h l g h - d a m p l n g r u b b e r b a s e I s o l a t l o n system. Seminar on Base Isolation and Passive Energy Dissipating devices. Francisco. California. (1986} A.G. Tarlcs. A new strategy for Earthquake protection of Buildings. Seminar on Base Isolation and Passive Energy Dissipating devices. Francisco. California. (1986) A. Carottl and F.M. de Miranda. Contribution to the application base-lsolatlon

5. 6. 7.

8.

9.

153

technique

to the antlselsmlc

design of r.c.

San

San of

multlstorey

b u i l d i n g s , I n g e g n e r l a S l s m l c a , 3 (1986) ( I n I t a l i a n ) G.C. G l u l l a n l . A New t e c h n o l o g y : a n t l s e l s m l c b a s e - l s o l a t l o n of large buildings. AICAP Conf. "Large C o n s t r u c t i o n in s e i s m i c a r e a s " , Stresa ( I t a l y ) (1987) ( I n I t a l i a n ) A. P a r d u c c i . S p e c i a l d i s s i p a t i n g d e v i c e s t o r e d u c e t h e s e i s m i c r e s p o n s e . CTE Conf. " S p e c i a l p r o b l e m s o f i n d u s t r i a l b u i l d i n g s In s e i s m i c a r e a s " P e r u g i a ( I t a l y ) (1985) ( i n I t a l i a n ) A. Carotti and F.G. de Miranda, "Active Nails" for the antlselsmlc protection of multlstorey r.c. bulldlng. Design criteria and feasibility analysis. Froc. 7th Syrup. on Dyn. and Control of Large Srtuctures, Virginia Polytechnlc Inst. & St. Univ., Blacksburg, USA, (1980} A. Carottl, F. de Mlranda and E. Turcl. An active protection system for wind induced vibrations of plpellne suspension bridges. Proc. 2rid Int. Symp. Structural Control, Waterloo, Ontario, Canada (1985), )4m-tlnus NIJhoff, Amsterdam 76-104 (1987). A. Carottl, Active Control of stress In torsional dynamics of structures under seismic disturbance, Proc. 2nd Int. Conf. Fatigue & Stress, Imperial College, London, UI((1988)

154

A. CAROTTI and F.G.de MIRANDA

-] I I

I

FIG.

i

I I I --_J

/,///////////////////////////////J"

/\ F3 F2, -

FIG. W 1"

/

~rc

I

u

J

elas~c

~ <

2

U

elas1:@-plas~c

P 4

,k 3

#

2 1

FIG. 2

O

I///////~

% L~

$

1

//S

,/

"4 "s "2 %

rf,," .

"I

I

.L n

3

PASSIVEANTISEISMICPROTECTION

155

P

(,'~<'<',~

4

FIG.

/, L=

%~P

u2

"2 (c,'---t)

u2 (ccemt) 4

\ ',r \

. . . .

--a

. . . .

? i'I~,,==,

\

FIG. 5

1Jllt

L

I

F][G. 8

m

=

~