Developments in seismic structural analysis and design

Developments in seismic structural analysis and design The theory of performance-base seismic design (PBSD) was suggested firstly by the American scientists and engineers in the beginning of 1990s. The Japanese and European scholars in earthquake engineering field took great interest in it and devoted to it at all of the standpoints. In recent years, many researchers in China discussed the theory. Mr. Ya-yong wang suggested that the Chinese seismic design code would follow the trend of world and that the study of the theory would be integrated with the national condition of China. The background of the occurrence, the development, the basic idea, the main properties of the theory and the present research are summarized in this paper. Its importance to improve the seismic design theory is pointed out, too, finally.

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r ~ U T T E R W O R T H

I " I ~ E , N E M A N N

0141-0296(94)00006-9

Engineering Structures, Vol t7, No 3, pp 187-197, 1995

0141~0296/95 $10.00 + 0.00

Developments in seismic structural analysis and design

Egor P Popov, Carl E Grigorian and Tzong-Shuoh Yang

Department of Civil Engineering, University of California, Berkeley, CA 94720, USA (Received December 1993; revised version accepted March 1994)

After a brief overview of the world-wide state-of-practice in seismic design, nonlinear structural response spectra for strength, ductility and number of yield reversals as a function of building period and structure strength for several strong motion earthquakes are presented Illustrations of three-dimensional mesh surfaces for the absolute seismic energy input and the dissipated hysteresis energy for selected earthquakes are given These results are compared with conventionally evaluated elastic response spectra and code criteria The issues of overstrength factors in the Mexico City code are then examined The remainder of the paper is devoted to the description of a simple frictional energy dissipating connection Its behaviour in cyclic tests and in shake table tests of a three-storey braced steel structure is illustrated

K e y w o r d s : energy dissipation, friction, Mexico City seismic code, seismic design, over-strength factors

The world-wide state of seismic design practice based on

current codes and some developments in nonlinear seismic

spectra are highlighted first These include displacement

ductility and a number of yield reversals spectra for the

1986 San Salvador, the 1985 Chile and the 1985 Mexico

City earthquakes Three-dimensional mesh surfaces of

absolute input energy and hysteretic energy for the 1985

Mexico City earthquake are displayed These surfaces show

graphically the seismic energy demands on the structural

systems subjected to the Mexico City earthquake

The Mexico City code force spectra, supplemented with

spectra considering structural overstrengths above the code

minima, are then examined for the effect of overstrength

Spectra for the number of load reversals at different levels

of overstrength are also shown

The second part of the paper concerns itself with a

recently developed frictional energy dissipator This inex-

pensive and nonproprietary device dissipates energy

through friction during rectilinear tension and compression

cycles It can be conveniently used as a connection between

a brace and a gusset plate In addition to the gusset plate

having long slotted holes, the splice plates and two thin

brass shims make-up the assembly fastened together with

high-strength bolts tensioned to the required tension force

An extensive experimental programme was conducted on

the reliability of this connection The final verification of

these connections was obtained by doing a shake table test

on a three-storey model having 12 such connections and

the same number of chevron braces There are two pending

projects in California where it is intended that frictional

energy dissipating connections will be used

State-of-practice in design

The state-of-practice in design is based on response spectra determined by studying the behaviour of elastic systems For a fixed natural period of a system and damping coefficient, a step-by-step integration is performed for the duration of an eathquake determined from an accelerogram The largest value of the selected response, commonly acceleration, is the spectral value of the response of the system corresponding to the fixed period By repeating the process for numerous periods, a spectral curve is obtained This procedure was repeated for six different earthquakes to gen- erate the curves shown in Figure 1

ACCELERATION (g's)

11rTe M I Y A G ~ 1 ~ CHILE

,~ " C H - - - I m COMAP~'TA

e i 'r~"" LP" r,~

l " , t ~, 1"7-4

1 5 ~ I ,

o ,

0 0 o s 1.0 1 s 2.0 2.s 3.0

PERIOD ( s e e )

5% d a m p i n g f o r s e l e c t e d e a r t h q u a k e s ( c o m p i l e d b y E M i r a n d a )

1 8 7

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1 8 8 Seismic structural analysis and design: E P Popov e t al After numerous studies of spectra, idealized elastic ulti-

mate state spectra were adopted by different authorities

Two such idealized curves proposed by the Applied Tech-

nology CounciP are shown in Figure 1 One of these curves

is for Soil 1, corresponding to stiff soil conditions; the

other, for Soil 3 is for soft clays and sand Similar curves

in the form of an equation are promulgated by the UBC

(Uniform Building Code) z , giving the total design base

shear, Vs, for the allowable stress design

V8 = n - W w h e r e C - T2,3 <- 2.75 (1)

1 %

and Z = seismic zone factor, I = importance factor,

Rw = structural system coefficient, S = site coefficient for

soil, T = fundamental period of vibrations of the structure,

and W = total seismic load

Assuming the largest seismic zone factor Z = 0.40, I = 1,

S = 1.2 for stiff soil, Rw = 1, and a period T near zero, the

ratio of the design shear of the total seismic reactive dead

load W, is 1.10, as shown in Figure 2 The remainder of

the curve for the various periods T follows from equation

(1) Since Rw is assumed to be unity, such a curve rep-

resents the elastic ultimate limit state For allowable stress

design the values so established are divided by R, For

major construction either in concrete or steel, Rw is either

8 or 12, dramatically reducing the design values of the ratio

V J W from the elastic ultimate limit state spectrum For

example, V J W = 1.10 for R w = 8 becomes 0.1375 For

R, = 12 such a value is even smaller

Equation (1) is formulated on linearly elastic concepts

and is modified for ductile behaviour by Rw Brittle mem-

bers are generally excluded from seismic resistant construc-

tion The behaviour of structures constructed from ductile

members can generally be idealized as shown in Figure

3, where:

Ce, = mathematically plausible elastic ultimate limit state

corresponding to a fixed period T

Cy seismic coefficient for idealized plastic capacity of

the system

v ,wJ

1.10 1988 UBC (Rw = I, S = 1.2)

ELASTIC ULTIMATE

PERIOD, T (SEC)

Figure2 Empirical seismic force spectra

VB/W

,,v~ELASTIC ULTIMATE

/ ( P E R I O D DEPENDENT )

/

C,=C.o/R,

C= = Ceu/R I - - - Y - FIRST PLASTIC HINGE (NEHRP) Cw= Ce u/Rw I~LALLOW STRESS DESIGN ( UBC / SEAOC )

VI I

STORY DRIFT, ZI

Figure 3 Structural system response 3,5

Cs = seismic coefficient for formation of the first plastic hinge, or first significant yield

Cw = seismic coefficient for reaching the allowable work- ing stress

Ry, R, Rw = reduction factors for determining C~., Cs, and

Cw, respectively, from C~, The diagram in Figure 3 represents the behaviour of steel frames as well as those of ductile reinforced concrete Note that on forming the first plastic hinge, provided the consecutively forming hinges retain strength and capacity for deformation, the ultimate capacity of the structure is reached at mmax 3'4 On forming the first plastic hinge, in general, the capacity of a structure is not exhausted The useful capacity of a structure can be approximated by

Cy = Ce,/Ry It is higher than the capacity Cs = Ce,/R occur- ring at the first plastic hinge The ratio of R over Ry, is the overstrength factor YL i.e

Cs Ry

For some steel frames Uang and Bertero 5 and Whittaker

et al 6 estimated this factor to be of the order of 2 The overstrength is due to the inadvertent statical indetermin- ancy of a system, selection of oversize members to control drift, stronger material than the specified minima etc For optimized systems, such as perimeter frames, EBFs etc., the overstrength factor may be small

Comparison of lateral load provisions in various countries

A comparison of current code provisions in several countries is given in Table 1 In the US there are two different approaches: the Allowable Stress Design (ASD) approach exemplified by UBC z and the Ultimate Stress Design (USD) procedure advocated by N E H R P 6'7 In the table, the main features of the Japan Building Standard Law (BSL) s,

as well as the National Building Code of Canada 9 and the Eurocode l° are summarized 4

Except for differences in notation, the second column is very similar for all co_des The Canadian code has a special feature of dividing R by U, a calibration factor set at a constant value of 0.6 Hence the Canadians for the present assume that 1 ) - - 1 / U = 1/0.6 = 1.67 In the New Zealand

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S e i s m i c s t r u c t u r a l a n a l y s i s a n d d e s i g n : E P Popov et al

Table 1 C o m p a r i s o n o f seismic codes

189

NEHRP (USD)

UBC (ASD)

BSL ( J a p a n )

NBCC (Canada)

EUROCODE

Ce = CsR

Ce° = C~qw

C~ = Csq = AR( T) w h e r e q = R and 12 = Ceu/e I =# const

C = Ceu/R (Rw= 1.51~

Cs = (0.25 - 0.38)ZRt

c~= D (ZR,)

Typ U = 0.6

code D is set at 1.511 Both values of D appear to be con-

servatively set, as they should be, compared with the value

of 2 determined by Uang and Whittaker noted above

The Japanese code (BSL) requires consideration of two

design phases: serviceability, implying elastic behaviour,

for moderate earthquakes, and determination of the ultimate

limit state for a major seismic event For short and regularly

shaped buildings there are two escape routes requiring only

the use of ASD Thus for a steel building of no more that

13 m (43 ft) in height, nor more than three storeys, equa-

tions on line (1) of Table 1 with a coefficient of 0.18 for

Cw which has been adjusted to account for the difference

of the allowable stress increase (1/3 in UBC and 1/2 in

BSL) for earthquake load combinations, is used to deter-

mine serviceability For checking the ultimate state the

coefficient Cw is increased to 0.27 It can be shown that

this coefficient extrapolates into 0.38 for Cs, corresponding

to a conservative value of 2.6 for NEHRP-type R factor 4

For symmetric buildings not exceeding 31 m (102 ft) in

height, again using the equations on line (1), the coefficient

for Cw can vary from 0.18 to 0.27 depending on the ratio

of lateral shear resisted by braces to total shear; the larger

the shear resisted by the braces, the larger is Cw The

smaller values of Cw are used in predominantly moment

resisting dual systems These values of Cw extrapolate into

0.25 and 0.38 for Cs, corresponding to an R factor of 4

(versus 8 in NEHRP) for ductile moment frames, and to

2.6 for braced frames The conservative nature of BSL can

be readily judged from the values of these coefficients

The basic features of the two-phase BSL design pro-

cedure can be seen more clearly from the equations on line

(2) These provisions apply to complex buildings as well

as those exceeding 31 m (102 ft) in height Here the ser-

viceability requirements are checked using the values of Cw

that are shown A mandatory explicit check for the build-

ing's ultimate strength, requiring nonlinear analyses, is also

required using Cy The values of Ds, a reciprocal of Rs

in other codes, are 0.25 for ductile frames, and 0.55 for

nonductile structures

In Japan the design of buildings over 60 m (approx

200 ft) in height requires the creation of a government com-

mittee, and approval of the Minister of Construction

The Eurocode ~° is similar to others In the last line of

Table 1, A is ground acceleration, and R(T) simply indi-

cates that the normalized elastic design spectrum R is a

function of the building period T In application it is neces-

sary to determine the actual overstrength factor D requiring

nonlinear iterative solutions Such an approach, without an

appropriate software, may be difficult to implement How-

ever, default values are given, avoiding complex calcu-

lations for a large range of situations In this respect the

Eurocode resembles the approach adopted by the Japanese

BSL for lower rise buildings

Displacement ductility and number of yield reversals spectra

The constant ductility force spectra for the 1986 San Sal- vador, the 1985 Chile, and the 1985 Mexico City earthquakes are shown in Figures 4(a), (b) and (c), respectively These spectra are determined using nonlinear differential equations and applying numerical methods of analysis ~2 Note that unlike the seismic code coefficients Cw or Cs

which vary linearly with the displacement ductility /x, the variation of the Cy from the nonlinear analysis is shown to decrease exponentially with/x In other words, a change in ductility, as from ~ = 1 (elastic state) to 2, or from /z = 2

to 4, causes a much more rapid decrease in Cy than, for example from/x = 6 to 8

The shapes of the displacement ductilty spectra for the San Salvador and the Chile earthquakes are rather typical, whereas for the Mexico City earthquake the spectra has a unique shape with the maximum at a period T of about 2 s

In all three cases for large values of/x the spectra are less jagged than those for small values of/x

The spectra for the number of yield reversals (NYRs) for the 1986 San Salvador, the 1985 Chile, and the 1985 Mexico City earthquakes are shown in Figures 5(a), (b)

and (c), respectively The curves for NYR = 1 are the same

as those for/x = 1 in Figure 4 and correspond to a purely elastic response The small discrepancy between the two sets of curves is attributable to the numerical procedure used It is significant that the curves for the San Salvador and the Chile earthquakes are very similar Therefore, seismic design based on ductility requirements, such as alone, would be essentially the same because the duration

of an earthquake and the consequent NYRs is not considered in such analyses

By comparing the NYR curves given in Figures 5(a)

and (b) it is clearly seen that the Chile earthquake lasting

116 s was much more damaging than the 9 s San Salvador earthquake Including NYRs in design would provide a clearer picture as to what is required of members and connections The procedure for determining the NYR spectra

is now available

Seismic energy input and dissipated hysteresis energy

It is instructive to display the seismic energy input for a given earthquake Confining the calculations to a selected

T-Cy region, the calculated contours for the seismic energy

of the Mexico City earthquake are shown in Figure 6(a)

The corresponding three-dimensional mesh surface is shown in Figure 6(b) This surface clearly shows that structures with a period T less than one should experience very little damage: whereas for those that would display larger

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1 5 ,

I.O

0 8

C~ 0.8

0.4

O 2

0.0

a

~ I , ~ D U C T I I J T Y ( ~ 4 N B & L V A D O R I ~ N 5 )

Period (8)

1.2

1.0

0.8

C; 0.8

0.4

0 2

0.(

0

b

D u c ' m 4 w (csn.le ~eee)

~,-e

\

Period 1=1

1.2

1.0

0.8

C~ 0.8

0.4

0 2

0.0

0

C

~ - 1

J e

P ~ ' t o d (=)

/~ varying from 1 to 8 for: (a) 1986 San Salvador earthquake; (b)

periods, substantial d a m a g e can be expected These con-

c l u s i o n s are in c o m p l e t e a g r e e m e n t with other studies

a n d o b s e r v a t i o n s ~3

P r o c e e d i n g similarly, the hysteresis e n e r g y that is dissi-

pated d u e to this earthquake c a n be calculated T h e contours

for this e n e r g y for the s a m e T-C,, region are s h o w n in Fig-

ure 7(a) T h e c o r r e s p o n d i n g t h r e e - d i m e n s i o n a l m e s h sur-

face is s h o w n in Figure 7(b) T h e hysteresis energy

Cy 0.8

0.4

OJ~

0.0

0

a

k'U~B]~ OF y l m n ~ ( S ~ l SALVADOR 1986

1.2

i / k ' " " " : '- "

O.B

" ~ ~

i | .

l ~ a o d 1.1

NUlemCR OP "n]~J) ~ (cem~ ~e8,~)

NYR,, !

0.4 \ ,

F'f "~ X _ " V""-~

% " % -

PERIOD (s)

b

- - - NYR-IO

0.8

C T 0.6 0.4

* * ° - o o - o

C

e x p e n d e d o n inelastically d e f o r m i n g a structure can be, in the a b s e n c e o f n o n d e s t r u c t i v e m e a n s o f energy dissipation,

c o n s i d e r e d as the seismic d a m a g e energy T h u s with e v e n greater clarity than s h o w n by the surface for the seismic

e n e r g y input, Figure 6(b), the regions v u l n e r a b l e to seismic

d a m a g e c a n be seen from Figure 7(b) There is also a large region where the dissipated hysteretic energy is very small where repetition o f the 1985 earthquake w o u l d cause little

or no damage

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1 2

0 h

0.1~

O.l 0

0 h

t.O

0.8

C 3, O.e

0.4

o 2

0.0

0

a

nmv'r nmzRC:y Ou:xro cn'y soe6)

' " " " "i ' ; l t j ', " ; " "~

• I |

-~:.~., , ~ - 0 ® :

• ~ i4-~J ' 1 ¢ - 0 2: t [,11 I , - - ,8 8.:

lip | :t'" ~ • )i

i I t ! ! • | : , s e I

i!,V .,: I

I t

Period 1=1

b

Seismic structural analysis and design: E P Popov e t a l

2

Figure 6

191

I N P U T ENERGY (MEXICO C I T Y 1985) ( m g e s 2)

o ~ , e r i o d (')

1 9 8 5 M e x i c o C i t y e a r t h q u a k e (a) c o n t o u r s o f s e i s m i c e n e r g y i n p u t ; ( b ) 3 D m e s h s u r f a c e o f a b s o l u t e s e i s m i c e n e r g y i n p u t

12

t.O

O.8

~ , o e

0.4

0 2

0.0

0

a

Figure 7

m , s ' r m m ~ ~ , t O a m c o crry s ~ )

r.~=0.028

r~-0.042

~-O.OM

mils z )

- - - | * i • • | * * * *

HYSTERESIS ENERGY (MEXICO CITY 1 9 8 5 ) ( m E z,,2)

0 h

0.~

1 ,

c ) .~ ,t (s)

1 9 8 5 M e x i c o C i t y e a r t h q u a k e (a) c o n t o u r s o f h y s t e r e s i s e n e r g y ; ( b ) 3 D m e s h s u r f a c e o f s e i s m i c h y s t e r e s i s e n e r g y

By integrating the volume under the mesh surfaces and

assuming uniform strength building population, it is poss-

ible to obtain meaningful indices of earthquake strength and

damage potential 14 The volume under the mesh surface for

the absolute seismic energy input can be related to the

strength of the earthquake; the volume under the mesh sur-

face for the hysteretic energy can be considered to be the

potential damage that would be caused by an earthquake

On this basis both indices rate the Mexico City earthquake

as the most damaging, and the San Salvador the least dam-

aging of the three earthquakes considered On a relative

basis, if the Mexico City earthquake has a damage potential

of 1, the Chile earthquake is 0.42, and the San Salvador

earthquake is 0.13

O v e r s t r e n g t h f a c t o r s in t h e M e x i c o C i t y c o d e

It was pointed out earlier that in well designed structures

for resisting seismic forces overstrength factors, as defined

by equation (2), are inadvertently present The Canadian

code 9 and the Eurocode j° recognize this possibility and

reduce the ductility requirement somewhat Therefore it is

of interest to examine the effect of the overstrength on the

designs based on the Mexico City code

The code force spectra for Zone III of the lake-bed area

of Mexico City for selected overstrength factors ~ are shown in Figure 8 The one for fully ductile systems of Group B buildings, qualifying for seismic behaviour factor

Q = 4 (formerly called the ductility factor), is shown with

C O D E F O R C E S P E C T R A

o 4 ~ , ' " " ' " u ~ I c ~

= • B = 1 0 ~

flA 1.00 t'ls= 1.5~

DA: 1.33 fib 2.0

0.3 ~ J - ~ " - ' - ~ - ~

I

t r

I l ,'/

% 0 2 : I / ' -

" 1 /

1 , / ,

/ / , ' ,

1 / / ,"

I I •

0 1 • t p ¢ • o O / J ° *

• t oO,O

o O * °

0 0 ' ' ' J ' ' '

P E R I O D (s)

Figure 8 S e i s m i c force spectra f o r first y i e l d for Z o n e III and

Q = 4 at D,A = 1, D, e = 1 a n d for o v e r s t r e n g t h d e s i g n up to -QA = 2

a n d D, a = 3

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1 9 2 Seismic structural analysis and design: E P Popov e t a l

l ~ e = 1 Multiplying the ordinates for this case by 1.5

results in a curve having two meanings, corresponding to

the case of an overstrength factor of 12, = 1.5 for Group B

buildings, or of fie = 1 for 'essential' facilities referred to

as Group A buildings Meanings can be attached to the lines

identified by l~u = 2 corresponding to either an overstrength

factor of 2 for Group B buildings, or of an I)A = 4/3 for

Group A buildings The lines associated with ~ = 3 are

for Group B buildings with overstrength of 3, or of an

~ a = 2 for Group A buildings Other building groups in

other zones, and of further types, are not considered here

Performing nonlinear analyses, the ductility demand IX

corresponding to the five cases of f~s given in Figure 8 are

shown in Figure 9 From these results it appears that the

Mexico City code has a flaw, in c o m m o n with other seismic

codes, by underestimating the seismic forces in the low per-

iod range below about 0.6 s A less pronounced inadequacy

is also found in the current US codes 2'7 Outside of this

range the seismic provisions appear to be particularly well

chosen for Group A buildings up to the period of about

1.6 s Thereafter a line gradually sloping downward to the

right could be chosen to retain the ductility Ix at 4 Allowing

a higher ductility factor Ix seems inappropriate, because, as

shown in Figure 4, little is gained by specifying higher

ductilities The most beneficial contribution to structural

behaviour occurs at the smaller ductilities, such as 2 or 4

The situation is quite different for Group B buildings

For building periods in the range up to 1.4 s the ductilities

Ix over 8 may be required Therefore for this group of build-

ings considerable reliance must be placed on the over-

strength factor Thus if f ~ = 1.5, a seismic performance

equivalent to I'~A = 1.0 can be expected

The conservatism of the seismic provisions for Group A

buildings in Mexico City can be further justified by examin-

matic decrease in the number of yield reversals occurs with

an increase in the strength of a structure The large NYRs

for Group B buildings when ~ = 1.0 may initiate fatigue

failures For both groups of buildings overstrength of

I I a = 4/3 or ~ , = 2.0 and higher are unnecessary, but would

not be disadvantageous In reality, well designed and con-

structed buildings are likely to develop some overstrength

lO_q ~,,'~ " ' " " ' ' "IUlEXICO"

f l e = l ~

f~A 1 3 3 f l o = 2 0 "

}~i

$~)}; f / - 1.67 tqs'= 2.5"

fl~=2.oo na=3.o"

l O ~ ,,,-

i!

.t t ,,

~b,,

,b~ "

/~ h',,, ,,

;~.,, .,

~ t t t %

1 0 | ; , ~ ' , , , , , , " - ' - ,

, t | ~ ~ " • % o ° - - - * ' - %

i • i ~ l - ~ - ( ~ %

/ "X ,-.-.- • "'-" ~ " ' ~ ¢ - - -

10 0 ~- :~.,-.~ ~. -:.-" = - -

P E R I O D (s)

Figure9 Reduction in ductility demand /x with increase in

available overstrength factor f~ for 1985 Mexico City earthquake

N U M B E R O F YIELD R E V E R S A L S (MEXICO CITY 1 9 8 5 )

! I • • • " • !

4 0 r / ~ f i e = 1.0]

F ~ ~ n ' : l lOG n = 1"5 3

J " : " O A 1 3 3 O s = 2 0 4 [~ • " " ~ = 1 6 7 f l a = 2 S q

Fi /v" n ; = z o o n = 3 o 1

• , ,, - - , "- ,~

- , , , ' , , :

PERIOD (s)

in a v a i l a b l e o v e r s t r e n g t h f a c t o r ~Q f o r 1985 M e x i c o C i t y e a r t h -

q u a k e

A s i m p l e e n e r g y d i s s i p a t o r

To survive an earthquake enough means of energy dissipation must be supplied by the structure In conventional construction this is provided by hysteresis energy dissipated

in the members and connections Hysteretic energy is developed by inelastic action and causes damage This can

be avoided by providing nondestructive means of energy dissipation such as frictional energy dissipators The trend

to using such devices is increasing Damage to a structure can be greatly reduced by using dissipators Currently there

is a surge in their development ]5']6 Here the discussion is limited to the Slotted Bolted Connection (SBC) as tested

at the University of California, Berkeley wJ~

The SBCs are designed to dissipate energy through friction during rectilinear tension and compression cycles Typical details of an SBC are shown in Figure 11 The design with brass shims was arrived at after much exper- imentation Connections with steel on steel friction surfaces were erratic and were abandoned In the adopted design the friction occurs between clean mill-scale A36 steel and half- hard cartridge brass USN-260 surfaces The assembled connections (Figure 12) with different numbers of 1/2 in high- strength A325 bolts were placed into an MTS loading frame, and subjected to the displacement-time history shown in Figure 13 Representative generated hysteresis loops for a two-bolted SBC test specimen are shown in

~-" I / 2 " D4~ 4~25 BOLT, 3 - I / 2 " LONC

I

J

i COMPR~ON W ~ E R

t NUT

c q ~ c v TE~ON iNDiCATOR (O~) ~ UNDER

T y p i c a l d e t a i l o f S B C

UCE PLATES

i

L o / | e ~ - 1 1 2 - LONe ,SLOT

Trang 7

Seismic structural analysis and design: E P Popov et al 193

:"::::: l / B " BRASS SHIMS

'~,

WELD::::::

1

o °°% I

i

5 / B " A36 PLATES::

;I oooooo j

BOLT HOLES FOR ATrACHMENT TO J

SPECIAL MTS CLEVICES

Figure 12 Assembly of two-bolted SBC specimen for test in

MTS testing machine

STEEL ON BRASS IMPOSED DISPLACEMENTS

1.5 r !

0

- 0 5

Figure 13 Typical imposed displacements by MTS to speci-

men such as shown in Figure 12

Figure 14 The remarkable stability and uniformity o f the

hysteresis loops, particularly in the relevant range o f +1 in,

can be observed from this diagram

After repeated verification o f SBCs with brass shims as

to their repeatability and reliability under prescribed dis-

placements (Figure 13), a similar connection with a slip

STEEL ON BRASS HYSTERESIS DIAGRAM

4 0

2 0

r,~

m 0

-20

.-40

DISPLACEMENT (INCHES)

Figure 14 Hysteresis loops for two-bolted SBC test specimen

with friction between mill-scale steel and brass surfaces

Figure 15 Two general views of test structure on shake table

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1 9 4 Seismic structural analysis and design: E P Popov e t al

0

w

°

V

LU

,

0

O

DISPLACEMENT(INCHES)

force of 60 kips was subjected to simulated earthquake

responses in the MTS machine The earthquake record

chosen first was the Pacoima earthquake, followed with

simulation tests for five times the Taft, twice the E1 Centro,

and 40 times the Whittier Narrows earthquakes Results

from the experiment correlated very well with the analyti-

cal predictions 19

The final verification of the SBCs was on a shake table

in the braced structure shown in Figure 15 This structure

represents the two end walls of a building There were six

braces in each of the two end frames The SBCs were

placed at the top of each brace Wire potentiometers were

used to measure the essentially rectilinear motion of each

dissipator The 0.5 in bolts were used at the connections in

the bottom braces, and one active 0.5 in bolt was provided

at the top connections for each of the braces at the upper

floors Strain gauges continuously monitored data for

determining the axial forces in the braces The model was

loaded with dead weight of approximately 30 kips per floor

Accelerometers provided information for verifying the

magnitude of horizontal lateral forces

The model was subjected to over 40 inputs of table

motion for different earthquakes and several severe sinusoidal motions Examples of recorded hysteresis loops for axial brace forces versus dissipator slip for one of the test frames are shown in Figures 16 and 17 Those in Figure 16

are for the table motion simulating the 1985 Chile Llolleo earthquake amplified to the peak table acceleration (PTA) =0.88g Those in Figure 17 are for a sinusoidal motion on the shake table amplified to PTA = 1.25g, corresponding to the maximum acceleration that the table could deliver Several interesting observations can be made regarding these hysteresis loops

The largest brace forces were developed in the first storey reaching approximately _+15 kips This is the result of using two 0.5 in bolts in the SBCs The second floor SBCs, having just single 0.5 in bolts per connection, with the capacity of _+7.5 kips, experienced the largest displacements; the third floor SBCs, also with single 0.5 in bolts, displaced the least amount In all cases the displacements were remarkably small

It is to be noted that although in fabricating these frames great care was taken to achieve symmetry, precise antisym- metry of the resulting hysteresis loops is not evident

Trang 9

Seismic structural analysis and design: E P P o p o v et al 195

o

O

- 0

0

o

0

4 ) 4

li

DISPLACEMENT(INCHES)

Figure 18

ABSOLUTE INPUT ENERGY TOTAL DISSIPATED BY 8BC

~ I r - ' -

~ r Z , - " _ _ ~ - -

'rlUS (SECOk~)S)

Energy histogram for 1985 Chile Llolleo earthquake amplified to PTA = 0.88g

DISSIPATED "VISCOUSLY"

AT LEVEL $ BY $BCs

AT LEVEL 2 BY SBCs

AT LEVEL 1 BY $BCs

|

30

Two examples of reduced data showing the comparison

between the input energy by the table and the sum of the

energy dissipated by the SBCs at the top of the braces are

shown in Figures 18 and 19 It is clear from these diagrams

that SBCs are very effective in dissipating most of the input energy These experiments also showed that the residual deflections are very tolerable Such behaviour speaks well for energy dissipators in general for seismic applications

Trang 10

1 9 6

Figure 19

Seismic structural analysis and design: E P Popov et al

;

i

TiME (aC-CONOS)

Energy histogram for sinusoidal motion input of PTA = 125g

OISSIPATED "VISCOUSLY"

AT LEVEL $ BY SBCs

AT LEVEL 2 BY SBCs

AT LEVEL t BY 8BGs

Conclusions

The large increase in the number of strong motion records

world-wide, together with careful studies of structural dam-

age caused by the earthquakes, is helping to advance the

art and science of earthquake engineering Our ability to

carry out complex calculations with the aid of computers

is also playing a valuable role in enhancing knowledge

Based on the issues discussed in this paper the following

conclusions can be drawn:

The nonlinear response spectra for ductility force

decreases in an exponential manner with /x A change in

ductility, as f r o m / x = 1 to 2, or f r o m / x = 2 to 4, causes a

much more rapid decrease in Cy than from /z = 6 to 8

Codes do not recognize this variation

Nonlinear response spectra for the number of yield rever-

sals are of great value in assessing building response Such

spectra are very sensitive to the duration of earthquakes,

and indirectly provide a measure of input energy

The overstrength factors already appearing in several

codes warrant further study Their implications for the

Mexico City code have been briefly considered The inad-

equacy of code specified spectra in the low period ranges is

to be noted Further study on this question is recommended

Displays of three-dimensional mesh surfaces for seismic

energy input and for hysteretic energy provide guidance for

establishing seismic zones Such diagrams are particularly

appropriate for Mexico City with its unique ductility force

response spectrum

The great advantages of passive energy dissipators have

been demonstrated Rapid development and extensive use

of passive energy dissipators in seismic design is envisaged

Acknowledgments

Partial support of the research by the National Science

Foundation (Grant BCS-9016781) and the American Iron

and Steel Institute is greatly appreciated The continued

encouragement of NSF Project Director Dr S C Liu is

particularly valued Useful discussion with Professor V V

Bertero of the University of California, Berkeley, and Mr

Enrique Martinez-Romero of Mexico City were essential

in clarifying the Mexico City new code Any opinions, fin-

dings, and conclusions are those of the authors, and, in

particular, do not necessarily reflect the views of the spon- sors

This paper was first presented at the III International Symposium and VI National Symposium on Steel Struc- tures at Oaxaca, Mexico, in November 1993, and is repro- duced with their permission

References

1 Applied Technology council 'Tentative provisions for the development of seismic regulations for buildings', ATC 3-06, Redwood City,

CA, 1978

2 International Conference of Building Officials (ICBO) Uniform

3 Newmark, N M and Hall, W J Earthquake spectra and design,

EERI monograph, 1982

4 Uang, C-M 'Structural overstrength and limit state philosophy in seismic design provisions', Report CE-91-01, Department of Civil Engineering, Northeastern University, Boston, MA, 1991

5 Uang, C-M and Bertero, V V 'Implications of recorded earthquake ground motions on seismic design of building structures', Report

versity of California, Berkeley, CA, 1988

6 Whittaker, A., Uang, C.-M and Bertero, V V 'Earthquake simulation tests and associated studies of a 0.3-scale model of a six-story eccentrically braced steel structure', Report UCB/EERC-87/02, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1987

7 National Earthquake Hazards Reduction Program (NEHRP) Rec- ommended provisions f o r the development of seismic regulations f o r

1991

8 International Association for Earthquake Engineering (IAEE) Earth-

9 National Building Code of Canada (NBCC) National Research Coun- cil of Canada, Ottawa, Ontario, 1990

10 European Convention for Constructional Steel (Eurocode) European

cal Committee, Brussels, Belgium, 1988

11 Clifton, C 1993 (private communication)

12 Yang, T.-S Structural seismic design for frictional energy dissipators, Report CE299 Department of Civil Engineering, University of Cali- fornia, Berkeley, CA 1993

13 Bertero, V V (Ed.) Lessons learned from the 1985 Mexico Earth-

14 Popov, E P., Yang, T.-S and Grigorian, C E 'New directions in

structural seismic design', Earthquake Spectra, (in press)

15 ATC 17-1 Seminar on seismic isolation, passive energy dissipation,

sco, March 1993, pp 447-698

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