Deterministic seismic design procedures tbr reintorced concrete buildings

8/18/2019 Deterministic seismic design procedures tbr reintorced concrete buildings

1/8

e t e r m i n i s ti c s e is m i c d e s ig n

p roced u res tb r re in torced

c o n c r e t e b u i l d i n g s

T h o m a s P a u l a y

D ep a r tm en t o f C ivi l E n g in eer in g, U n ivers i t y o f C a n terb ury , C h r i s t ch urch , N ew Z ea la n d

R ece iv ed Ju n e 1 9 8 2 )

A br ief review is g iven of a determ inis t ic des ign phi losophy w i t h respect to

earthqu ake resist ing d uct i le structures fo r reinforced concrete bui Idi ngs.

Th is was developed rece ntly m ainly in New Zealand. In this approach a

preferred hierarchy in the development of energy dissipat ing mechanisms

is postulated . Some app l icat ions of cap aci ty design proced ures relevant

to beams, columns and shear wal ls , are out l ined. The param ount impo r t -

ance of qu an ti f iable good de tai l ing is emphasized and the relevance of th is

w i th respect to shear effects in plastic hinges, the con finem ent of com-

pressed concrete , and bond be tween rein force me nt and concrete are

examined. These aspects of the speci fic seismic environ me nt are also

ut i l ized to show fundame ntal d if ferences in s t ruc tura l behav iour w hen

effects of g ravi ty loads or seismic displacements are compared.

Key words: re inforced concrete, bon d, bui ld ings, du ct i l i ty , dynamics,

frames, p last ic propert ies, shear strength, st i ffness, d eterm inist ic seismic

design

n t r o d u c t i o n

I t i s n o w g e n e ra l ly a c c e p te d th a t t h re e m a in c r i t e r i a n e e d to

b e s a t i s f ie d w h e n b u i ld in g s a re d e s ig n e d s o a s to r e s p o n d

s a t i s fa c to r i ly to e a r th q u a k e mo t io n s .

F i r s t ly , t h e d e s ig n e r mu s t e n s u re th a t n o d a ma g e o f a n y

k in d w o u ld o c c u r d u r in g a s ma l l e a r th q u a k e w h ic h w o u ld

h a v e a p ro b a b i l i t y o f o c c u r r in g in th e lo c a l i ty s a y o n c e

e v e ry 1 0 -1 5 y r . T h i s p r ima r i ly in v o lv e s th e p ro t e c t io n o f

re l a t iv e ly b r i t t l e n o n s t ru c tu ra l c o mp o n e n t s w h ic h h a v e

l imi t e d d e f o rm a b i l i t y . H e n c e e l a s t i c s t ru c tu ra l d i s p lac e -

me n t s , s u c h a s in t e r s to re y d r i f t , mu s t b e l im i t e d . T h e re fo re

th is is a s t i f fness c r i te r ion .

F o r l e s s f r e q u e n t mo d e ra t e e a r th q u a k e s w i th a r e tu rn

p e r i o d o f s a y 2 5 - 3 0 y r , s o m e n o n s t ru c t u r a l d a m a g e m i g h t

b e a c c e p ta b le . H o w e v e r , d a m a g e re s u lt in g f ro m s ig n if i c a n t

in e las t i c d e fo rma t io n s in c e r t a in lo c a l i t ie s o f t h e s t ru c tu re

i t s e l f s h o u ld b e a v o id e d b e c a u s e o f th e d i f f i c u l ty a n d c o s t

in v o lv e d in s t ru c tu ra l r e p a i r . H e n c e fo r t h i s k in d o f d y n a m ic

e x c i t a t io n , t h e o v e ra ll s t ru c tu ra l r e s p o n s e s s h o u ld b e e s s e n-

t ia l ly e las t ic . Th is can be ach ieved i f s t reng th c r i te r ia ,

usua l ly spec if ied by bu i ld ing codes , a re sa t is f ied .

T h i rd ly , t h e d e s ig n e r mu s t e n s u re th a t t h e b u i ld in g w i ll

n o t c o l l a p se d u r in g th e l a rg e st s e i smic e x c i t a t io n to b e

e x p e c te d o n c e d u r in g th e l i f e t ime o f th a t s t ru c tu re . C le a r ly

fo r th i s e a r th q u a k e to t a l e c o n o mic lo s s i s a c c e p ta b le . T o

e n a b le th e s t ru c tu re to s u rv iv e v e ry l a rg e mo t io n s , i t m u s t

p o s s es s c o n s id era b le in e l a s t ic d e fo rm a b i l i t y . H e n c e th e

th ird des ign c r i te r ion is duc t i l i ty .

T h e p r in c ip le s r e l e v a n t t o s t i f fn e s s a n d s t r e n g th a re w e l l

es tab l ished in genera l s t ruc tura l des ign . Aspec ts o f the

d e v e l o p m e n t o f d u c t i l i t y i n s t r u c tu r a l c o m p o n e n t s , o f t e n

s u b je c te d to c o m b in e d f l e x u re , s h e a r a n d a x ia l l o a d , o n ly

e me rg e d f ro m m o re r e c e n t r e s e a rch . A l s o it b e c a m e n e c e s-

s a ry to r e -e x a min e th e e s t a b l is h e d a n d c o d i f i e d p r in c ip le s

o f s t r e n g th in r e in fo rc e d c o n c re t e c o mp o n e n t s in th e l i g h t

o f t h e n a t u r e o f e a r t h q u a k e l o a d in g . I n s t e ad o f m o n o t o n i c

lo a d in g to f a i lu re , t r a d i t io n a l ly u s e d in th e v e r i f i c a t io n o f

s t r e n g th th e o r i e s , d u r in g e a r th q u a k e s r e v e r s ed c y c l i c

d y n a m ic d i s p la c e me n t s w e l l b e y o n d th e e l a s t i c l im i t a re

imp o s e d . T h e s e o f t e n a l t e r t h e b a s i c b e h a v io u r o f r e in -

fo rc e d c o n c re t e c o mp o n e n t s . In r e c o g n i t io n o f th e s e

c h a n g e s , a d d i t io n a l s e i s mic r e q u i re me n t s m u s t b e in t ro -

d u c e d in to th e d e s ig n p ro c e ss . T o e mp h a s iz e th e s e s o me -

w h a t l e ss k n o w n a s p e c t s o f d e s ig n , o n ly th e i s su e s o f

s t ruc tura l surv iva l , a s soc ia ted with la rge ine las t ic d isp lace -

me n t s d u r in g re v e r s e d c y c l i c lo a d in g , a re e x a min e d in th i s

s tu d y .

B e c a u se o f th e g ro s s a p p ro x im a t io n s in v o lv e d in th e

s p e c i f i c a tio n s o f b u i ld in g c o d e s w h e n u s in g e q u iv a le n t

la te ra l s ta t ic des ign loads , and the uncerta in t ie s assoc ia ted

w i th th e in e l as t i c d y n a mic r e s p o n s e o f b u i ld in g s to g ro u n d

mo t io n s , t h e c h a ra c te r i st i c s o f w h ic h a re a s y e t imp o s s ib l e

to p re d ic t , a h ig h d e g re e o f a c c u ra c y in th e e l a s t i c a n a ly s e s

0141-0296/83]01079-08/ 3.00

© 1983 B utterworth & Co. (Publishers) Ltd

Eng. Struct., 1983, Vo l. 5, Jan uary 79


2/8

De term in is t ic se ismic des ign p roced ures fo r RC bu i ld ings : 7 . Pau lav

o f t h e s t r u c t u r e i s n o t w a r r a n t e d . S p e c i f i e d s t a ti c l a t e ra l

l o a d s o r e l a s t i c m o d a l a n a l y s i s t e c h n i q u e s s h o u l d b e c o n -

s i d e r e d o n l y a s m e a n s t o e n s u r e a r a t i o n a l d i s t r i b u t i o n o f

p o t e n t i a l s t r e n g t h t h r o u g h o u t t h e s t r u c t u r e . T h e f a c t t l r a t

t \~r mo s t bu i ld ings these loa ds resu l t in mentbe r s t r eng th s

c o n s i d e r a b l y l e s s ( t y p i c a l l y 2 5 % ) t h a n w h a t w o u l d b e

r e q u i r e d i f b u i ld i n g s w e r e t o r e s p o n d e l a s ti c a l ly t o t h e

d e s ig n e a r t h q u a k e , a l s o s ug g e s t s t h a t a c c u r a c y i n e l a s ti c

ana lys i s i s o f r e la t ive ly l i t t l e impor tance . There l \~re in the

d e s ig n o f d u c t i l e s t r u c t u r e s f o r b u i l d i n g s , a n y a n a l y s i s

t e c l m i q u e t h a t p r e s e r v e s c o n s i s t e n c y i n t i r e t r e a t m e t r t o f

m e m b e r s o f st a t i c a ll y i n d e t e r m i n a t e s y s t e m s , s h o u l d b e

c o n s i d e r e d s a t i s f a c t o r y . T h e s e i n c l u d e a p p r o x i n r a t e m a n u a l

a n a l y s is p r o c e d u r e s . ~

Ut i l i z ing t ir e r esu l t s o f an e las t i c ana lys i s fo r com bin ed

g r a v i t y a n d s p e c i f i e d l at e r al l o a d i n g , a n a c c e p t a b l e e n e r g y

d i s s ip a t i n g m e c h a n i s m n m s t b e f o r n m l a t e d . M o r e o v e r , a

d e s i r ab l e h i e r a r c h y i n t h e d e v e l o p n r e n t o f r e g i o n s w h e r e

p l a s t i c d e f o r n r a t i o n s m u s t o c c u r ( p l a s t i c b i n g e s ) s h o u l d

a l s o b e e , ( a b l i s h e d . O n c e t h e c h o i c e i s m a d e , e a c h m e m b e r

c a n b e g i v e n t h e a p p r o p r i a t e s t r e n g t h t o e n s u r e t h a t , i f

n e c e s s a r y , o n l y t h e c h o s e n p l a s t i c m e c h a n i s l n c a n d e v e l o p

in the bu i ld ing .

T o b e a d o p t e d a n d u s e d b y a w i d e s e c t i o n o f t h e e n -

g i n e e r i n g p r o f e s s io n s u c h a p r o c e d u r e m u s t b e s i m p l e . T h e

s iu rp l ic i ty o f th i s des ign ph i lo sop hy a r i ses f ron t it s in ten t to

c o m m a n d t h e s t r u c t u r e w h a t i t n m s t d o in t h e e v e n t e r a

v e r y la r g e e a r t h q u a k e , r a t h e r t h a n t o a s k , b y w a y o f a n a ly s i s ,

w h a t i t m i g h t d o ? I t is a l s o p o s t u l a t e d t h a t t h e p r o t n i s e o f

s u r v iv i n g c a t a s t r o p h i c g r o u n d s h a k i n g i s p r i m a r i l y d e r i v ed

f r o m t i m g o o d q u a l i t y o f t h e d e t a i l i n g o f r e i n f o r c e d c o n -

c r e t e c o m p o n e n t s i n r e g i o n s o f in e l a st i c d e f o r m a t i o n s . O n e

o f t h e a i m s o f r e c e n t r e s e a rc h e f l \+ r ts h a s b e e n t o q u a n t i f y

t h i s g o o d n e s s . 2

h o i c e o f e n er g y d i s s i p a ti n g m e c h a n i s m s

I n m u l t i s t o r e y f r a m e s t h e w e a k b e a m - s t r o n g c o l u m n

s y s t e m h a s g a i n e d g e n e r a l a c c e p t a n c e . T h e r e b y p l a s t i c

h i n g e s a re m a d e t o d e v e l o p i n a ll b e a m s w h e n , i f n e c e s s a r y ,

a c o m p l e t e f r a m e m e c h a n i s m , a s s h o w n i n Figure la, is to

b e u t i l iz e d . I n s e is m i c d e s i g n , th e f o r m a t i o n o f p l a s t ic

o a d

igure I

f

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_ 7

~ 7 7

b

w a y m e c h a n is m s i n l a t e r a l l y l o a d e d m u l t i s t o r e y f r a m e s

h i n g e s a t t h e b a s e o f t h e c o l u m n s i s g e n e r a l l y u n a v o i d -

a b l e . T h e e x c e s s i v e d u c t i l i t y d e m a n d i m p o s e d o n c o l u m n s

o f s o - c a l le d ' s o f t s t o r e y s ' , i s ev i d e n t f r o m Figure lb. F o r

f r a m e s t a l l e r t h a n t h r e e t o f o u r s t o r e y s , t h i s n r e c h a n i s n r

s h o u l d b e a v o i d e d . T h e r e t \ ) r e c o h n n n s t n u s t b e m a d e

s t ronger than beams and th i s i s e tnphas ized in t i r e se i smic

p r o v i s i o n s o f m o s t b u i l d i n g c o d e s . H o w e v e r , c o d e s d o n o t

s p e c i f y ]r o w n m c h s t r o n g e r c o l u m n s s h o u l d b e .

I f s u f f i c i e n t r e s er v e s t r e n g t h i s p r o v i d e d i n c o l u n m s w i t h

r e s p e c t t o t i r e s t r e n g t h t h a t c a n b e d e v e l o p e d i n a d j a c e n t

b e a m s , t h e n , n o m a t t e r w h a t k i n d o f g r o u n d t n o t i o n o c c u rs ,

o n l y t h e p r e f e r r e d n m c h a n i s n r o f

Figure la can

d e v e l o p .

T h e c h o i c e

o f a

u n i q u e m o d e o f e n e r g y d i s s i p a ti o n i n a

s t r u c t u r e , s u c h a s t h e f r a m e s o f b t~trc 1, d u r i n g u n p r e d i c t -

a b l e s e v e r e g r o u n d m o t i o n s , f o r m s t h e c o r e o f t h e d e t e r -

m i n i s t i c d e s i g n p h i l o s o p h y p o s t u l a t e d . B e c a u s e t h e s t r e n g t h

t h a t m i g h t b e d e v e l o p e d i n t h e m e m b e r d e l i b e r a t e l y m a d e

w e a k e r , i s r e l a t e d t o t h e r e q u i r e d c a p a c i t y o f t h e s t r o n g e r

c o m p o n e n t , t h e p r o c e d u r e t h a t f o l l o w s is r e f e r r e d t o a s

' c a p a c i t y d e s i g n ' .

h r t n o s t t n u l t i s t o r e y f r a m e s t h e t n a j o r p a r t , i t n o t t h e

en t i re r es i s tance o f l a te ra l R ) ,ces , is a ss igned to s t ruc tu ra l

( shear ) w a l l s . Poss ib le fa i lu re m ode s in can i il eve r wa l l s a re

s h o w n i n Figure 2 . T h e d e t e r m i n i s t i c s e i sm i c d e s ig n a p p r o a c h ,

o u t l i n e d a b o v e , d i s t a t e s t h a t f l e x u r a l y i e l d i n g i n t h e c l e a r l y

d e f i n e d p l a s t i c b i n g e z o n e s h o u k l c o n t r o l t h e d e s ig n . A s a

c o r o l l a r y t o t h e s e r e q u i r e m e n t s , f a i l u r e d u e h ) d i a g o n a l

t e n s i o n , s l i d in g a l o n g h o r i z o n t a l c o n s t r u c t i o n j o i n t s , a s s e e n

in l:~¢urc 2, i n a d e q u a t e a n c h o r a g e o r s p l i c in g o f t im r e i n -

f o r c e u r e n t, i n s t a b il i ty o f c o n c r e t e c o m p o n e n t s o r c o m p r e s -

s ion ba rs n rus t be avo ided , whi le l a rge ine las t i c se i smic

d i s p l a c e m e n t s a r e s u s t a i n e d b y t h e s t r u c t u r e . C o n s e q u e n t l y ,

t h e c a p a c i t y o f t h e m e c h a l l i s m s l is t e d a b o v e m u s t b e i n

e x c e s s o f t h e a c t i o n s t h a i r e s u lt w h e n i n t h e p r e s e n c e o f

g r a v i t y l o a d s e n e r g y d i s s ip a t i o n d u e t o f l e x u r al y i e l d i n g

deve lo ps a t the base o f a can t i l eve r w a l l .

A si m i la r s t r e n g t h h i e r a l c h y m u s t b e e st a b l i sh e d b e t w e e n

t h e s u p e r s t r u c t u r e a n d i ts f o u n d a t i o n s . F o r o b v i o u s r e a s o n s

d a m a g e in th e c o m p o n e n t s e r a r e i nf o r c e d c o n c r e te f o u n d a -

l i o n s t r u c t u r e s h o u l d b e a v o i d e d . A l s o c o m p o n e n t s o f

t h e

t \mnda t ions a re as a genera l ru le l e ss su i t ab le fo r energy

d iss ipa t ion because in deep n renrbers i t i s more d i f f i cu l t to

ach ieve s ign i f i can t duc t i l i ty d ue to f l exu ra l y ie ld ing . I l ence ,

in such s i tua t ions i t i s necessa ry to ensure tha t t i r e founda-

t i o n s t r u c t u r e , w h i l e h i g h l y s t r es s e d , r e m a i n s e l a s t ic w h e n

t h e c o m p l e t e e n e r g y d i s si p a t i n g m e c h a n i s m e l t i m s u p e r -

s t r u c t u r e , s u c h a s s h o w n i n

Figure la,

is mobil ized. At t l r is

s t a g e s t r u c t u r a l a c t i o n s a p p l i e d t o t i r e f o u n d a t i o n s t r u c t u r e

have l i t t l e r e la t ion to the l a te ra l and g rav i ty loads used in

the in i t i a l e la s t i c ana lys i s . Ra th e r i t i s the ac t io ns tha t have

b e e n s q u e e z e d ' o u t o f t h e i n e la s t i c s u p e r s t r u c l u r e d u r i n g a

v e r y la r g e d i s p l a c e u r e n t p u l s e , t h a i s h o u l d c o n t r o l t h e

d e s ig n o f t h e f o u n d a t i o n s y s t e m .

A s a m a t t e r o f r o u t i n e , a d e s i g n e r w il l e n s u r e t h a t t h e

s p e c i f ie d l o a d s a r e sa f e l y t r a n s l n i t t e d t h r o u g h t h e f o u n d a -

t i o n s t r u c t u r e i n t o t h e s u p p o r t i n g s o i l . [ l o w e v e r , n r u c h

l a r ge r f o r c e s n e e d t o b e t r a n s m i t t e d w h e n t h e c h o s e n

e n e r g y d is s i p a t in g m e c h a n i s m s o f t h e s u p e r s t r u c t u r e a r e

b e i n g f u l l y d e v e l o p e d . T h e s e a c t i o n s c a n n o t b e b a s e d o n

' c h a r a c t e r i s t i c ' o r ' r e l i a b l e ' s t r e n g t h p r o p e r t i e s . T h e y m u s t

b e e v a l u a t e d f r o m p r o p e r t i e s t h a t a r e ' r e c o g n i z e d b y e a r t h -

q u a k e s ' . T h i s n e c e s s i ta t e s t h e e v a l u a t i o n o f a p r o b a b l e

u p p e r b o u n d v a lu e o f t h e s t r e n g t h o f t h e s u p e r s t ru c t u r e .

Many shear co res o f h igh- r i se bu i ld ings in se i smic a reas ,

a s s u m e d t o b e h a v e a s d u c t i le c a n t i l e v e r w a ll s , su c h a s t h o s e

8 0 E n g . S t r u c t. 1 9 8 3 V o l . 5 J a n u a r y


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Figu re 2 Fai luremodes in cantilever shear walls

D e t e r m i n i s t i c s e i s m i c d e s ig n p r o c e d u r e s f o r R C b u i l d i n g s : 7 -. P a u l a y

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V f J N f

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Figure 2b,

h a v e b e e n b u i l t a n d p r o v i d e d w i t h

fo u n d a t io n s t h a t w o u ld n o t b e cap ab le o f re s i s ti n g ac t io n s

d ev e lo p ed in t h e fu l ly p l a s t ic sh ea r c o re a s d e t a i l ed . A s a

c o n s e q u e n c e , r o c k i n g o f th e e n t i re c o r e m i g h t o c c u r a n d

t h e i n t e n d e d e n e r g y d i s si p a ti o n i n t h e s u p e r s t r u c t u r e m a y

n o t t ak e p l ace a t a l l 3

T h e p h i l o s o p h y o f c a p a c i t y d e si g n

In th e ca p ac i ty d es ig n o f ea r th q u ak e - re s i s t i n g s t ru c tu res ,

e l e m e n t s o f p r i m a r y l a t e r a l l o a d r e si s ti n g s y s t e m s a r e

ch o sen an d su i t ab ly d es ig n ed an d d e t a i l ed fo r en e rg y d is si -

p a t io n u n d e r sev e re i n e l a s t i c d e fo rm a t io n s . A l l o th e r

s t ru c tu ra l e l em en t s a r e p ro v id ed w i th su f f i c i en t s t r en g th so

t h a t t h e c h o s e n m e a n s o f e n e r g y d i s s ip a t i o n c a n b e m a i n -

t a i n e d . 2 4 F o r e x a m p l e i n b e a m s o f m u l t i s t o r e y f r a m e s ,

p l a s ti c h i n g e s a t p o i n t s o f m a x i m u m m o m e n t s

Figure la)

a r e c h o s e n a n d a p p r o p r i a t e l y p r o p o r t i o n e d . F l e x u r a l r ei n -

f o r c e m e n t i s t h e n p r o v i d e d a t a l l o t h e r s e c t io n s o f t h e s p a n

in su ch a w ay th a t y i e ld in g can n o t o ccu r w h en th e fu l l

s t en g th o f t h e tw o p l a s t i c h in g es d u e to an ea r th q u a k e i s

d ev e lo p ed .

I n o r d e r t o e va l u a t e t h e p r o b a b l e m a x i m u m m o m e n t ;

t h a t i s t h e f l ex u ra l o v e r s t r en g th ; w h ich can ev e r b e

g en e ra t ed d u r in g a la rg e se ism ic p u lse , a l l o w an ce m u s t b e

m a d e f o r b o t h t h e m e a n y i e l d s t re n g t h a n d t h e s t r a i n

h a rd en in g o f t h e s t ee l u sed. T h e re fo re i n se i sm ic d es ig n i t is

n ecessa ry to a sce r t a in t h a t s t ee l w i th y i e ld s t r en g th s i n

ex cess o f t h a t sp ec i f i ed i s n o t u sed in t h e co n s t ru c t io n .

W h en th e f l ex u ra l o v e r s t r en g th o f a b ea m i s e s t ab l i sh ed , t h e

asso c i a t ed sh ea r fo rces , i n c lu d in g th o se d u e to g rav i ty lo ad

o n th e sp an , a r e r ead i ly d e t e rm in ed . W h en a b eam i s

d es ig n ed to r e s i st t h i s sh ea r d em an d , an u n d e s i r ab l e sh ea r

f a i l u re , w h ich i s u n su i t ab l e fo r p u rp o ses o f en e rg y d i s s ip a-

t i o n , can n o t o ccu r . T h i s i s t h e s im p les t ex am p le o f t h e

ap p l i ca t io n o f ca p ac i ty d es ig n . In a s im i l a r f a sh io n co lu m n s

m u s t b e d es ig n ed to b e s t ro n g e r t h an b eam s an d th i s i s

ex am in ed in a su b seq u en t sec t io n .

W i th a c lea r d e f in i t i o n o f t h e e x t en t o f t h e p l a s t i c h in g e

an d th e e l a s t i c r eg io n s o f a ll s t ru c tu ra l m e m b e rs , t h e

a p p r o p r i a t e d e t a i li n g o f t h e r e i n f o r c e m e n t c a n b e e s t a b -

l i sh ed . A s y i e ld in g can n ev e r o ccu r i n t h e e l a s t i c r eg io n s o f

m e m b e rs b ecau se p l a s t i c h in g es p ro t ec t t h ese r eg io n s ag a in s t

o v e r lo ad in g d u r in g l a rg e in e l a s ti c l a t e r a l d i sp l acem en t s ,

s t an d a rd d e t a i l in g u sed fo r g rav i ty l o ad ca r ry in g s t ru c tu res

w i ll su f f i ce i n t h ese a r eas . H o w ev e r , i n r eg io n s o f en e rg y

d i s s ip a t io n , p a r t i cu l a r ly w h en y i e ld in g in b o th t en s io n an d

co m p ress io n can o ccu r a s a r e su l t o f r ev e r sed cy c l ic l o ad in g ,

special deta i l ing is requ ired and th is requ ires considerab le

a t t e n t i o n .

eismic detail ing requirements

O n e o f t h e p r in c ip a l a im s o f t h e d es ig n fo r se ism ic r e s is t an ce

i s t o en su re t h a t , w h en r eq u i r ed d u r in g in e l a s t i c d y n am ic

resp o n se , t h e c h o sen m ech an i sm s w i l l d i s s ipa t e s ig n i f ican t

am o u n t s o f en e rg y in a s t ab l e m an n er . S t ab i l i t y i n t h i s

c o n t e x t m e a n s t h e m a i n t e n a n c e o f r e a so n a b l y c o n s t a n t a n d

h ig h l ev e l s o f l o ad r e s i s t an ce d u r in g sev e ra l la rg e r ev e r sed

cy c le s o f i n e l a s t i c d i sp l acem en t s , w i th a s l i tt l e l o s s o f s t i f f -

n ess a s p o ss ib l e a f t e r ev e ry su ch cy c l e .

In t h e an a ly t i ca l a s ses sm en t o f t h e i n e l a s t i c d y n am ic

r e s p o n se o f f r a m e s , m e m b e r b e h a v i o u r i s o f te n m o d e l l e d a s

sh o w n b y cu rv e 1 i n Figure 3. S u ch a p e r f ec t ly e l a s t i c -

p l a s t i c l o ad -d i sp l acem en t r e l a t i o n sh ip i s u n a t t a in ab le i n

p l a s t i c h in g es o f r e in fo rced co n c re t e m em b ers . In s t ee l

b e a m s a n o n l i n e a r m o m e n t - r o t a t i o n r e l a t io n s h i p , c h a ra c t e r -

i zed b y th e B au sch in g e r e f f ec t , su ch a s t h a t sh o w n b y

/ / ~ C

/ f

o / C L 3

Displacement

Figu re 3 Idealized (1), optimal (2) and degrading 3 , 4) displace-

men t response of a mem ber during an inelastic pulse

E ng . S t r uc t . , 1983 , V o l . 5 , Janu a r y 81


4/8

Deterministic seismic design procedures fo r RC buildings

T. Paulov

curve 2 in

Figure 3,

i s u s u a l l y o b s e r v e d . W h e n i n t e r n a l

f o r c e s , s u c h a s t e n s i o n , c o m p r e s s i o n a n d s h e a r , i n th e p l a s t i c

h i n g e o f a b e a m o r a sh e a r w a l l ar e t r a n s f e r r e d p r e d o m i -

n a n t l y b y r e i n f o r c i n g s t e e l , a r e s p o n s e s i m i l a r t o t h a t o f

a s{eel beam, i .e . curve 2 in Figure 3 , w i l l b e a p p r o a c h e d .

S u c h a r e s p o n s e r e p r e s e n t s o p t i m u m r e a li s ti c e n e r g y d i s s ip a -

t i o n i n r e i n f o r c e d c o n c r e t e m e m b e r s , a s m e a s u r e d b y t i r e

a r e a u n d e r t h e l o a d - d i s p l a c e m e n t c u r v e , a t t a i n a b l e d u r i n g

i n e l a s t i c d i s p l a c e m e n t e x c u r s i o n s .

When dur ing l a rge d i sp lacement reversa l s , s ign i f i can t

f r a c t i o n s o f t h e i n t e r n a l n r e m b e r f o r c e s a r e t o b e tr a n s f e r r e d

b y c o n c r e t e , b o t h s t r e n g t h a n d s t i f fn e s s d e g r a d a t i o n m a y

o c c u r . F o r r e a s o n s d i s cu s s e d l a t er , o n e q u a d r a n t o f a

c o m p l e t e t y p i c a l h y s t e r e s i s l o o p m a y t a k e t i r e f o r m o f

curve 3 in Figure 3. C l e a r ly t h e e n e r g y d i s s i p a t io n a n d

h e n c e h y s t e r e t i c d a m p i n g , e x p r e s s e d b y t h e s h a d e d a r e a

in Figure

3 , i s d i s t inc t ly l e ss than in the p rev ious cases .

A p las t i c h inge tha t fo l lows in a pa r t i cu la r cyc le the load-

d i s p l a c e m e n t p a t h a l o n g c u r v e 3 , is l i k e l y t o f o l l o w c u r v e 4

i n t h e f o l l o w i n g d i s p l a c e m e n t c y c l e . T h e r e f o r e , t h e r e s i s t -

a n c e a n d e n e r g y d i s s i p a t i o n d u r i n g t h e s a m e t o t a l d i s p l a c e -

m e n t w i l l n o w b e l e s s t h a n i n t h e p r e v i o u s c y c l e . T h e

s t ra igh t l ines rad ia t ing f rom the o r ig in in Figure 3 m a y b e

t a k e n a s t y p i c a l m e a s u r e s o f t h e s t i f f n e s s a s s o c i a t e d w i t h

e a c h t o a d p a t h . T h e a i m o f d e t a i l in g n r u s t t h u s b e t o e n a b l e

i n e l a s t i c r e s p o n s e r e a s o n a b l y c l o s e t o t h a t s h o w n b y c u r v e 2

t o b e a t t a i n e d .

Shear defi)rmations in plastic hinges

M o d e l s t o s i m u l a t e t h e b e h a v i o u r o f c r a c k e d r e i n f o r c e d

c o n c r e t e m e m b e r s s u b j e c t e d t o s h e a r a n d f l e x u r e , a n d t o

e n a b l e t h e i r d e s i g n t o b e d o n e i n a s i m p l e m a n n e r , h a v e

b e e n p o s t u l a t e d s i n c e t h e t u r n o f th i s c e n t u r y . T h e t r u s s

a n a l o g y a n d t h e m o r e r e c e n t d i a g o n a l c o m p r e s s i o n f i e ld

t h e o r y , a r e o n l y t w o o f t h e a p p r o a c h e s t h a t h a v e b e e n

e x t e n s i v e l y u s e d . T h e p r i m a r y c o n s i d e r a t i o n i n s h e a r r e s i s t -

a n c e h a s b e e n t o e n a b l e a v i a b l e m e c h a n i s m t o b e m o b i l i z e d

w h i c h c a n t r a n s m i t s h e a r i n g f o r c e s a f t e r t h e f o r m a t i o n o f

d i a g o n a l c r a c k s . A r e l a t i v e l y r a r e b u t e q u a l l y i m p o r t a n t

c o n s i d e r a ti o n w a s t h e p r e v e n t i o n o f p r e m a t u r e c r u s hi n g o f

t h e c o n c r e t e , p a r t i c u l a r l y i n t h i n w e b s , d u e t o d i a g o n a l

c o m p r e s s i o n . I n s e i s m i c s i t u a t i o n s t h i s l a t t e r a s p e c t b e c o m e s

m o r e s i g n i f i c a n t b e c a u s e t h e c o n c r e t e i n t h e w e b p o r t i o n o f

p l as t ic h i n g e s m a y b e c o m p l e t e l y b r o k e n u p b y i n t e r s e ct i n g

d i a g o n al c r a c ks . S o m e o f t h e s e c r a c k s m a y b e v e r y w i d e

b e c a u se t h e y m a y b e t h e c o n t i n u a t i o n o f f l e x ur a l c r a ck s .

U p o n l o a d r e v e r s al s a c o m p l e t e c l o s u r e o f t h e i r r e g u la r

s u r f a c e s o f d i a g o n a l c r a c k s m a y n o t t a k e p l a c e . H e n c e t r a n s -

m i s s io n o f d i a g o n a l c o m p r e s si o n w i t h u n i f o r m c o n c r e t e

s t r e s s e s a c r o s s p r e v i o u s l y f o r m e d d i a g o n a l c r a c k s m a y n o t

b e p o s s i b l e . T h i s m a y l e a d t o p r e m a t u r e d i s i n t e g r a t i o n o f

t h e c o n c r e t e i n w e b s . I f c o m p u t e d s h e a r s t r e ss e s , d e v e l o p e d

w i t h t t re f l e x u r a l o v e r s t r e n g t h o f t h e m e m b e r , a r e k e p t w e l l

b e l o w t h e m a x i m a s u g g es t ed f o r m o n o t o n i c a l l y l o a d e d

m e m b e r s , f a i l u r e d u e t o d i a g o n a l c o m p r e s s i o n w i l l n o t

oc cu r

The more c r i t i ca l e f fec t o f shea r in p las t i c h inges a r i ses

f r o m t h e n e c e s s i t y o f h a v i n g t o t r a n s f e r s h e a r f o r c e s a c r o s s

i n t e r c o n n e c t e d f l e x u r a l c r a c k s w h i c h f o r m p o t e n t i a l f a i l u r e

p l a n e s a t a p p r o x i m a t e l y r i g h t a n g le s t o t h e a x i s o f t h e

m e m b e r . A f t e r s e v e ra l l o a d r e v e r s al s , i n v o l v i n g a l t e r n a t i n g

y i e l d i n g i n t e n s i o n o f ti re f l e x u r a l r e i n f o r c e m e n t a t b o t h

e x t r e m i t i e s o f a b e a m s e c t i o n , s h e a r t r a n s f e r b y i n t e r-

l o c k i n g a g g r e g a t e p a r t i c l e s b r e a k s d o w n a n d i n s t e a d t h e

d o w e l l i n g a c t i o n o f t h e f l e x u r a l b a r s i s m o b i l i z e d . T h i s

m e c h a n i s m , h o w e v e r , a l l o w s r e l a ti v e l y l a r ge s l i d in g s h e a r

d i s p l a c e m e n t t o o c c u r , w h i c h i n t u r n n r a y r es u ll i n d r a m a t i c

l o ss o f s t i ff n e s s , p a r t i c u l a r l y a t l o w l o a d s i n n n e d i a t e l y a f t e r

d i sp lacement reversa l s . A typ ica l r e sponse s t rong ly in -

f luenced by s l id ing shear ac ross a p las t i c h inge i s shown by

curves 3 and 4 in Figure 3 . A v e r y e f f e c t i v e m e t h o d i n

i m p r o v i n g t ir e e n e r g y d i s s i p a t in g p r o p e r t i e s o f s u c h p l a s ti c

h i n g e s is th e u s e o f s o m e d i a g o n a l r e i n f o r c e n r e n t , a c t i n g i n

b o t h t e n s io n a n d c o m p r e s s io n , s R e c o m m e n d a t i o n s h a v e

b e e n f o r m u l a t e d f o r th e d e s i g n o f s u c h s h e a r r e i n f o r c e m e n t

w h e n b o t h t h e s h e a r s tr e s s a n d t h e a m p l i t u d e o f s h ea r

r e v e rs a ls a r e l a r g e . 4 T h e p h e n o m e n o n d o e s n o t a r is e i n

e l a s ti c s t r u c t u r e s o r i n t h o s e s u b j e c t e d t o g r a v i t y l o a d in g

a l o n e .

Cotl.[ illeDlelll o.f com pre ssed con cre te

I t i s n o w w e l l e s ta b l i s h e d z t h a t b y s u i t a b le c o n f i n e m e n t

o f c o n r p r e s s e d c o n c r e t e , t h e l i m i t i n g s t r a i n a t w h i c h s i gn i fi -

c a n t r e d u c t i o n i n t h e l o a d c a r r y i n g c a p a c i t y i n c o m p r e s s i o n

c o m m e n c e s , c a n b e g r e a t l y i n c r e a s e d . S t r a i n s w e l l in e x c e s s

o f 3 h a v e b e e n a t t a i n e d i n c o n f i n e d a x ia l l y l o a d e d s p e c i-

m e n s . T h e r e b y l a r g e c u r v a t u r e d u c t i l i t i e s c a n a l s o b e

d e v e l o p e d i n c o m p r e s s i o n d o m i n a t e d c o l u n m s u n d e r b o t h

e a r t h q u a k e s i n m l a t i n g s t a t i c a n d d y n a m i c l o a d i n g . 6 L a r g e

c u r v a t u r e s a r e n e c e s s a r y a t t h e b a s e o f c o l m n n s o f m u l t i -

s t o r e y d u c t i l e f r a m e s , w h e r e t h e f o r m a t i o n o f p la s t i c h i n g e s

w i t h s i g n i f i c a n t d u c t i l i t y d e m a n d s c a n n o t n o r m a l l y b e

aw) ided .

A n o t h e r b e n e f i t t h a t m a y b e d e r i v e d f r o m t h e c o n f i n e -

m e n t o f c o n c r e t e , i s a s ig n i f i c an t i n c r e a s e o f i t s s t r e n g t h i n

t h e c o n f i n e d c o r e . W h e n c o n f i n e m e n t b e c o m e s e f f e c t iv e t h e

u n c o n f i n e d c o v e r c o n c r e t e s p a l ls o f f. T h e i n c r e a s e d s t r e n g t h

i n t h e c o r e o f t e n m o r e t h a n o f f s e t s t h e l o s s t h a t r e s u l t s

f r o m t h e c o n t r i b u t i o n o f t h e s pa l le d c o v e r c o n c r e t e .

T h e n r e c h a n i s m o f c o n f i n e m e n t b y r e c t a n g u l a r t i e s ,

t r a d i t i o n a l l y u s e d i n r e c t a n g u l a r c o l u m n s , i s o f t e n a s s u m e d

t o b e a n a l o g o u s t o t h a t o f c i r c u l a r t ie s o r s p ir a ls . C o d e

r e c o m m e n d a t i o n s i n t h e U n i t e d S t a t e s a r e b a s e d o n t h e

a s s u m p t i o n t h a t t i e s s u s t a i n l a t e r a l p r e s s u r e , s h o w n i n

Figure 4a, a s s m a l l b e a m s s p a n n i n g b e t w e e n s u p p o r t s , w i t h

a n e f f i c i e n c y o f 5 0 o f t h a t o f i d e n t i c a l l y s p a c e d c ir c u l a r

t i e s f T h e c o r e c o n c r e t e i s t h e n a s s u m e d t o a r c h v e r t i c a l l y

be tw een such se t s o f t i e s spaced ve r t i ca l ly a t a su f f i c ien t ly

c lose d i s tance as seen in Figure 4a. I t m u s t b e a p p r e c i a t e d

t h a t t i e s , n o r m a l l y c o n s i s t i n g o f s m a l l , t y p i c a l l y 1 0 - 1 2 m m

b a r s , a r e v e r y f l e x i b l e i n b e n d i n g . C o n s e q u e n t l y t h e y a r e

i n e f f i c ie n t i n c o n f i n e m e n t w h i l e a c t i n g a s b e an r s .

I t i s s u g g e s t e d t h a t a m o r e e f f e c t i v e c o n f i n e m e n t o f t h e

c o r e c o n c r e t e i n c o l u n m s c a n b e a c h i e v e d b y u t i l i z i n g t h e

m a i n v e r t i c a l c o l u n m b a r s w h i c h n o r m a l l y h a v e a l a r g e r

d ianre te r . These ba rs can ac t a s r e la t ive ly s t i f f beams i f they

a r e s u p p o r t e d a g a i n s t l a t e r a l m o v e m e n t b y t i e s . T h i s m e c h a -

n i sm i s shown in Figure 4b. This necess i t a tes a r e la t ive ly

c l o s e s p a c i n g b e t w e e n v e r t i c a l b a r s a r o u n d t h e p e r i m e t e r o f

t h e s e c t i o n . 4 T h e v e r t i c al s p a c i n g b e t w e e n t i c s is d i c t a t e d b y

i n s t a b i l i t y c r i t e r i a f o r t h e v e r t i c a l b a r s w i t h d i a m e t e r d,,. In

t h i s c a s e th e s p a l l in g o f t h e c o v e r c o n c r e t e , t h e r e d u c t i o n o f

t h e m o d u l u s o f e l a s t ic i t y o f t h e s te e l d u e t o t h e B a u s c h i n g e r

e f f e c t a n d t h e l a t e r a l p r e s s u r e d u e t o t h e e x p a n d i n g

c o n c r e t e i n t h e c o r e m u s t b e c o n s i d e r e d . A s p a c i n g s n o t

le ss than

6d/,

has been fou nd to m ee t these c r i t e r i a . 4 '~ '

otld

arid anchorage

T h e e f f i c i e n t i n t e r a c t i o n o f t h e t w o m a t e r i a l s i n r e in -

f o r ce d c o n c r e t e c o m p o s i t e s t r u c t u ra l m e m b e r s d e p e n d s o n

82 En g. St ruct. 1983 Vol . 5 January


5/8

Deterministic seismic design procedures for RC buildings: T Paulay

o o Z 2

a )

/ / C o n c r e t e a r c h

b )

V ~ Z J x ~ ~Y C A

Figure 4 Con t r ibu t ion o f ove r lapp ing t ies to the con f inem ent o f

compressed concrete in co lumns

t h e b o n d b e tw een th e su r f ace o f t h e r e in fo rc in g b a r s an d

th e su r ro u n d in g co n c re t e . T h i s b o n d m u s t b e su f f i c i en t t o

e n a b l e th e f u ll s t r e n gt h o f t h e m e m b e r t o b e d e v e l o p e d ,

w h i l e u n d e r s e rv i ce l o ad co n d i t i o n s d e fo rm a t io n s a s so c i a t ed

w i th b o n d m u s t n o t r e su l t i n u n accep tab l e c r ack w id th s .

In t h e i n e l a s t i c r eg io n s o f ea r th q u ak e r e s i s t i n g co m p o n en t s

t h e d e s ig n e r is p r im a r i l y c o n c e r n e d w i t h t h e r e p e a t e d

d ev e lo p m en t o f t h e fu l l s t r en g th u n d e r r ev e r sed cy c l i c

lo ad in g . B o n d - s l ip , w h en ex cess iv e , can a f f e c t t h e h y s t e r e t i c

r e sp o n se an d m ay cau se l o s s o f en e rg y d i s s ip a t i o n a s sh o w n

b y cu rv es 3 an d 4 i n Figure 3

B o n d i s t h e m o s t c r i t ica l a sp ec t o f t h e d es ig n o f

i n t e ri o r b e a m - c o l u m n j o i n t s i n m u l t i s t o r e y f r a m e s . C o m -

m o n l y p l a s t ic h i n g e s in b e a m s m u s t b e e x p e c t e d a t a l l fa c e s

o f i n t e r i or c o l u m n s . Y i e ld i ng o f t h e b e a m r e i n f o r c e m e n t

t h a t p a s s e s c o n t in u o u s l y t h r o u g h s u c h j o i n t s, c a n n o t b e

res t r i c t ed t o t h e h in g e l en g th o n ly a lo n g th e b eam . In ev i t -

ab ly y i e ld s t r a in s w il l p ro p ag a t e a lo n g b eam b a r s a l so i n to

th e j o in t co re , p a r t i cu l a r ly w h en d u e t o l a rge cu rv a tu re

d u c t i l it y d e m a n d s s t r a in h a r d e n i n g c o m m e n c e s a t t h e

c r i t i ca l b eam sec t i o n a t t h e f ace o f t h e co lu m n . W h en

d efo rm ed b a r s y i e ld , t h e su r ro u n d in g co n c re t e i s s e r io u s ly

a f f ec t ed . A s a co n seq u en ce b o n d t r an s fe r i s d r am a t i ca l l y

r ed u ced . W i th e v e ry l o ad r ev e r sa l , cau s in g y i e ld in g i n

t en s io n an d co m p ress io n , y i e ld s t r a in s p ro p ag a t e fu r th e r

t o w a r d s t h e c e n t r e o f t h e c o l u m n c o r e . I n m a n y t e s t s t h e

co m p le t e s li p o f b eam b a r s h as b een o b se rv ed , v

T h e p a r t i cu l a r ly sev e re co n d i t i o n s fo r b o n d a ro u n d

b eam b a r s ac ro s s in t e r io r j o in t s a r i s e s f ro m th e f ac t t h a t

d u r in g l a rg e i n e la s t i c d i sp l acem en t p u l ses a b a r i s p u l l ed

a t o n e s id e w h i l e i t i s p u sh ed a t t h e o th e r s i d e o f t h e

c o l u m n . T h e r e b y a b a r m a y h a v e t o t r a n s m i t t w i c e t h e

y i e ld fo rce w i th in t h e d ep th o f t h e co lu m n an d su b se -

q u e n t l y w i t h i n a r e d u c e d e f f e c t i v e e m b e d m e n t l e n g t h i n t h e

j o i n t c o r e . C o m m o n l y t h e s i t u a ti o n i s fu r t h e r a g g r a v a t ed b y

ex t r e m e ly la rg e co n cu r r en t sh ea r ing s t r e s ses w h ich cau se

ex t en s iv e d i ag o n a l c r ack in g in t h e co re co n c re t e i n b o th

d i r e ct i o ns . T h i s m e a n s t h a t b e a m b a r s a re n o t e m b e d d e d

i n th e s a m e q u a l i t y o f c o n c r e t e t h a t t h e y w o u l d b e h a d

o n ly g rav i ty l o ad in g b een a p p l i ed . B o n d f a i lu r e u n d e r su ch

co n d i t i o n s i s d i f f i cu l t t o av o id . H w o ev er , w i th t h e se l ec t i o n

o f su f f i c i en t ly sm a l l d i am e te r b eam b a r s , 4 a b o n d s l ip can

b e d e l ay ed su f f i c i en t ly so a s n o t t o i n t e r f e r e w i th e f f i c i en t

en e rg y d i s s ip a t io n .

A t e x t e r i o r b e a m - c o l u m n j o i n ts , c o n d i t i o n s a re m u c h

m o r e f a v o u r a b l e b e c a u s e b e a m b a r s c a n b e b e n t i n t o t h e

jo in t a t t h e f a r f ace o f a co lu m n . In d e t e rm in in g th e n eces -

sa ry d ev e lo p m en t l en g th , i n c lu d in g a s t an d a rd h o o k , a

l en g th ( t y p i ca l l y 1 0d t~ o v e r w h ich b o n d i s g o in g to b e

l a rg e ly l o s t d u e t o r ev e r sed y ie ld in g i n t h e b e am h in g e ,

sh o u ld b e d i sco u n ted .

W h en p l a s t i c h in g es a r e d e l i b e ra t e ly r e lo ca t ed aw ay

f ro m co lu m n f aces , so t h a t y i e ld in g a t t h e co lu m n f aces

c a n n e v e r o c c u r , b o n d c o n d i t io n s i m p r o v e d r a m a t i c a l l y.

L ap p ed sp l ices p resen t p o t en t i a l w eak n esses i n t h e

c r i t ica l r eg io n s o f ea r th q u a k e r e s i s t i n g m em b er s . I n

g en e ra l cu r r en t sp ec i f i ca t i o n s a r e i n ad eq u a t e t o en su re

th a t l ap p ed sp l ices w o u ld su s t a in sev e ra l cy c l e s o f r ev e r sed

cycl ic load ing up to and includ ing y ield s t ress . The s i tua-

t i o n i s p a r t i cu l a r ly c r i t i ca l in b eam s o r co lu m n s w h ere

sev e ra l an d so m et im e s a ll t h e b a r s a r e l ap p ed in t h e sam e

area. Increased sp l ice leng ths wi l l on ly delay a fa i lu re .

g en e ra l l y d u e t o p ro g res s iv e sp li t t in g o f t h e co n c re t e

b e tw een sp l i ced b a r s , b ecau se w i th l a rg e r ev e r sed s t r e s ses

l ap p ed sp l i ces t en d to u n z ip . H o w ev er , u s in g t h e co n cep t s

o f t h e sh ea r f r i c t i o n m ech an i sm , su f f i c i en t t r an sv e r se

c l am p in g fo rces ac ro ss p o t en t i a l s l id in g p l an es c an b e

g en e ra t ed w h e n t r an sv e r se b a r s c ro s s in g t h i s p l an e a r e

s t r e s sed . S u ch b a r s o f t i e s o r s t i r ru p s m u s t n o t b e a l l o w ed

to y i e ld . T h e sp ac in g o f t ie l egs m u s t b e su f f i c i en t ly sm a l l

t o en su re a r easo n ab ly u n i fo rm d i s t r i b u t io n o f t r an sv e r se

c l am p in g fo rces a lo n g th e l en g th o f t h e sp l i ce . S o m ew h a t

c lo se r sp ac in g o f t r an sv e r se b a r s a t t h e en d s o f t h e l a p p ed

b ar s , w h ere sp l i t t in g c r ack s co m m en c e , i s b en e f i c i a l . T h e

d es ig n o f t h e r eq u i r ed am o u n t o f t r an sv e r se b a r s m ay b e

b ased o n an eq u iv a l en t f r i c t i o n co e f f i c i en t o f u n i ty ac ro ss

a sp l it t i n g c r ack , p ro v id ed th a t t h e s t ee l s tr e s ses d u rin g

so m e 3 0 cy c l e s o f r ev e r sed cy c l ic l o ad in g d o n o t ex c eed

8 5 o f t h e y ie ld s t r en g th . S

T ran sv e r se r e in fo rcem en t i n t h e en d r eg io n s o f t h e

co lu m n s co u ld b e p ro v id ed in su f f i c i en t q u an t i t y t o en su re

th a t t h e fo rce s ac ro ss sp l i ces w o u ld b e t r a s f e r r e d w h i l e a

p l a s t i c h in g e d ev e lo p s . H o w ev e r , it h as b ee n fo u n d s t h a t

w h en b o n d t r an s fe r fu n c t io n s e f f i c i en t ly , t h e y i e ld in g

in su ch co lu m n b a r s i s r e s t r ic t ed t o a m u c h sm a l l e r l en g th

th an in p l a s ti c h in g es w i th o u t l ap p ed sp li ces . T h i s m e an s

th a t t h e e f f ec t i v e p l a s ti c h in g e l en g th i s v e ry sh o r t . A s a

co n seq u en ce ex t r em e ly l a rg e t en s i l e s t r a in s m ay b e g en e ra t ed

in b a r s w h en th e t o t a l an g u la r p l a s t i c ro t a t i o n s , a s so c i a t ed

w i th l a rg e b u t a ccep t ab l e d i sp l acem en t d u c t i l i t i e s , a r e b e in g

d ev e lo p ed d u r in g a s e i sm ic p u l se , T h i s i s h ig h ly u n d es i r ab l e .

S u ch l ap p ed co lu m n b a r s h av e b een o b se rv ed to f r ac tu re i n

t e s t s . 8 T h e re fo re l ap p ed sp l ices , h o w ev er w e l l d es ig n ed ,

sh o u ld n ev e r b e l o ca t ed i n p o t en t i a l p l a s t i c h in g e zo n es .

sp e c t s o f c o lu m n d e s ign

I t w a s p o s t u la t e d t h a t t h e f o r m a t i o n o f s o f t s t o r e y s , w h e re -

b y p l a s t i c h in g es can d ev e lo p s im u l t an eo u s ly a t t h e t o p an d

b o t t o m e n d o f c o l u m n s i n a s t o r e y , i s u n a c c e p t a b l e i n

m u l t i s t o r e y f r a m e d b u i ld i n gs . T h e r e f o r e c o l u m n s o f u p p e r

s t o r e y s m u s t b e s t r o n g e r t h a n t h e b e a m s t h a t f r a m e i n t o

E n g . S t r u c t . , 1 9 8 3 , V o l . 5 , J a n u a r y 8 3


6/8

Determ inistic seismic design procedu res fo r R C buildings: 7 . Paulay

t h e m . I n m o s t s i t u a t i o n s i t is a d v a n t a g e o u s t o a v o i d p l a s t i c

t r in g e s i n c o l u m n s a l t o g e t h e r . I f t h i s c a n b e a c h i e v e d :

( i ) G r e a t e r r e l i a n c e c a n b e p l a c e d o n s h e a r r e s is t a n c e o f

e n d r e g i o n s o f c o l u m n s a n d h e n c e l e s s s h e a r r e i n f o r c e m e n t

i s r e q u i r e d t h e r e .

( i i ) N o d u c t i l i t y d e m a n d s o f s i g n i fi c a n c e w i ll a r i s e a n d

h e n c e t i l e t ra n s v e r s e r e i n f o r c e m e n t F o r c o n f i n i n g t h e c o r e

c o n c r e t e i n t h e e n d r e g i o n s c a n b e d r a s t i c a l l y r e d u c e d .

( i i i) I n s t e a d o f t h e n l i d h e i g h t o f c o l u m n s , l a p p e d s p l i c e s

c a n b e p l a c e d a t t h e e t a d r e g i o n i m m e d i a t e l y a b o v e f l o o r s ,

w h e r e t h e y c a n b e m o r e e a s i l y c o n s t r u c t e d .

T o a c h i e v e t h e n e c e s s a r y r e s e r v e f l e x u r a l s t r e n g t h o f

c o l u m n s , f ir st th e m a x i m u m m o m e n t i n p u t F r om a n a d j a c e n t

b e a m o r f r o m b e a m s m u s t b e e v a l u a t e d . T h i s is t i l e f l e x u r a l

o v e r s t re n g t b o f t h e b e a m , t i l e m e a n i n g o f w h i c h w a s d e f i n e d

e a r l i er . I n o u r a t t e m p t t o e s t i m a t e t h i s u p p e r b o u n d o f t i le

b e a m s t r e n g t h a t p l a s t i c b in g e s , a l l o w a n c e m u s t b e m a d e f o r

t i le m e a n y i e l d

strength

o f t i l e s te e l w h i c h i s a l w a y s i n

e x c e s s o f t h e g u a r a n t e e d s t r e n g t h , i n c r e a s e d r e s i s t a n c e d u e

t o s t r ai n h a r d e n i n g w h i c h w i l l o c c u r w h e n d u c t i l i t y d e m a n d s

a r e la r g e , a n d f i n a l l y f o r a l l b a r s t h a t c o u l d c o n t r i b u t e t o

m o m e n t r e s is t a nc e in t h e b e a m a s c o n s t r u c t e d . T h e r e f o r e

s o u l e o f t h e s l a b r e i n f o r c e m e n t , p l a c e d p a r a l l e l t o a n d c l o s e

t o t h e b e a m , l n u s t a l s o b e i n c l u d e d . 4 T h e i n c r e a s e i n f l e x u r a l

r e s i s t an c e m a y b e c o n v e n i e n t l y e x p r e s s e d b y t t l e f a c t o r ~ 50

w h i c h i s t i l e ra t i o o f t i l e F l e x u ra l o v e r s t r e n g t h t o t h e

m o m e n t r e s u l t i n g f ro m a n e l a s t i c a n a l y s i s fo r t h e c o d e

s p e c i f i e d s e is m i c l o a d i n g , M c o de . B o t h q u a n t i t i e s s h o u l d b e

t a k e n a t t h e t h e o r e t i c a l e n d s o f b e a n r s p a n s , i .e . a t c o l u m n

c e n t r e l i n e s .

T i l e m o m e n t p a t t e r n s o v e r t h e e n t i r e h e i g h t o f a c o l u m n ,

g e n e r a t e d a t v a r i o u s i n s t a n t s o f a n e a r t h q u a k e , c a n b e v e r y

d i f f e r e n t f r o m t h e p a t t e r n t h a t r e s u l t e d F r o m t i m e la s t i c

a n a l y s i s o f t h e f r a m e f o r t h e s p e c i f i e d l a t e r a l s t a t i c l o a d i n g .

T h i s i s i l l u s t r a t e d i n

Figure 5.

I t is s e e n t h a i t h e p o i n t

o f

ze ro n roment , t yp i c a l l y s i tua t ed near t he m i dhe i gh o f

u p p e r s t o r e y c o l u m n s , c a n h a v e w i d e l y v a r y i n g p o s i t i o n s .

T h i s m e a n s t h a t , i f p la s t i c b in g e d e v e l o p m e n t a t t h e l o p o r

o r t i re b o t t o m e n d o f a c o h n n n i n a s t o r e y i s t o b e a w ) i d e d ,

a l l o w a n c e m u s t b e i n a d e F o r t h e p o s s i b l y v e r y u n e v e n d i s t r i-

b u t i o n o f b e a m m o m e n t i n p u t s a t a F l oo r b e t w e e n t h e

c o l u m n a b o v e a n d b e l o w t h a t f l o o r . B e c a u s e t if fs l a r ge

w t r i at i o n o f m o m e n t s r e s u lt s p r i m a r i l y f ro m l h e p a r t i c i p a -

t i o n o f t h e f r a m e i n t h e h i g h e r m o d e s o f v i b r a t i o n , a ll o w -

a n c e c a n b e m a d e w i t h t i le i n t r o d u c t i o n o f a d y n a m i c

m a g n i f i c a t i o n f a c t o r c o. T h e f l e x u r a l s t r e n g t h o l l h e

c o h l n r n Mc i s h o u l d t b e r e l o r e b e b a s e d on :

Mco - - Co~oMcodc

i f h i n g i n g is to b e a v o i d e d . T h e i n t e r p r e t a t i o n o f t h i s t w o -

s t e p m a g n i f i c a t io n o f c o l u m n m o m e n t s i s s e en i n Figure 6.

T h e v a l u e o f do i s p e r i o d d e p e n d e n t . F r o m a l a rg e n u n l b e r

o f t i m e h i s t o r y s t u d i e s o f t h e i n e l a s t i c d y n a m i c r e s p o n s e t o

v a r i o u s g r o u n d e x c i t a t i o n s o f f r a m e s s t) d e s i g n e d , i t w a s

f o u n d

that

1.3 < co < 1.8. 4

S i m i l a r c o n s i d e r a t i o n s a l l o w an u p p e r b o u n d e s t i m a t e I t)

b e m a d e f o r e a r t h q u a k e i n d u c e d a x i a l a n d s h e a r l o a d

delllands o cohnnns

hear w a l l s

T h e u s e f u l n e s s o f s t r u c t u r a l w a l l s in t i r e l a t e ra l l o a d r e s i st -

a n c e o f t a l l b u i l d i n g s h a s l o n g b e e n r e c o g n i z e d . B e c a u s e

b u i l d i n g s w i t h s i g n i f i c a n t s h e a r w a l l s a r e m u c h s t i f f e r t h a n

t h o s e r e l y i n g o n f r a m e s , t h e f i r st c r i t e r i o n o f s e i s m i c d e s i g n

o u t l i n e d i n t h e i n t r o d u c t i o n , i . e . p r o t e c t i o n a g a i n s t a l l

k i n d s o f d a m a g e , i s e m i n e n t l y f u l f i l l e d . S u s p i c i o n s t il l

p r e v a i l s , h o w e v e r , w i t h r e s p e c t t o t h e a b i l i t y o f s h e a r w a l l s

I

P l a s t i c

be u

h i n g e s

M o m e n t s f r o m 2 .7 0 s 3 . 09 s 3 . 7 0 s 7. 8 0 s 8 0 0 s

s t a t i c a n a l y s t s

Figure

A c o m p a r i s o n o f b e n d i n g m o m e n t p a t t e r n s e n c o u n t e r e d d u r i n g i n s t a n ts o f l ar g e e a r t h q u a k e m o t i o n s w i t h t h o s e d e r iv e d f r o m

c ode s p ec i f i ed la t e ra l s t a t i c l oad i ng

84 En g. St ruct. 1 983 Vol . 5 January


7/8

F -J

-•'-- •

[ ~ \ \ . y /

g r a d i e n t / ~ / ~

/ / /

i i i /

~

- -

Mcode

I

Cr i t i c o l

m o m e n t

Figu re Magnification of design moments for columns

k l ~ r , t ~ i r ~ l r ~ i n i r r a ~

m

M

m

r e

Figu re 7

walls

L 3 . , . A , . ~ ~ I I I k J I I I K ~ I I L . k . A L I , , .A K ~ k . A I ~ t . I ~ - I / ~ t , I I

Design bending mom ent envelope for cantile ver shear

to respond in a ductile manner to the same extent as rein-

forced concrete ductile frames are expected to. For this

reason many building codes require shear walls to be

designed for significantly larger earthquake forces.

The previous review of seismic aspects emphasized that

proper understanding of structural behaviour, quantified

good detailing of critical regions and the suppression of

undesirable failure modes will ensure that ductile structures

can be constructed. This applies equally to shear walls.

Recent studies have greatly added to our understanding of

the inelastic response of shear wall structures.

D et e rm i n i s t ic se ism i c desi gn p rocedu res f o r R C bu i ld i ngs : T Pau lay

To illustrate the simple concepts of capaci ty design

in relation to shear walls, the behaviour of a cantilever

wall is briefly examined. The failure modes that can be

encountered are shown in Figure 2. For the necessary

/ energy dissipation to occur when required, inelastic flexural

response

Figure 2b)

must be encouraged and failure due to

other causes as shown in Figure 2 and reviewed in an

earlier section of this paper, must be suppressed. In shear

walls with small gravity load, or when shear walls are squat,

significant sliding in the plastic hinge region

Figure 2e)

may lead to loss of energy dissipation (see curves 3 and 4 in

Figure 3)

and this may have to be controlled by providing

some diagonal reinforcement to cross the potentia l sliding

plane.

The necessary curvature ductility in shear wall sections is

usually achieved with ease. However, when axial compres-

sion is insignificant or when articulated sections with non-

symmetrical flanges are used, the flexural compression

strains may become excessive while the necessary rotational

ductility in the plastic hinge, usually at the base of the wall,

is being developed. In such situations at least the outer ha lf

of the theoretical flexural compression zone should be pro-

vided with transverse confining reinforcement. 4 The confine-

ment should extend over the length of the potential plastic

hinge, which may be assumed to be of the order of the

length of the wall lw (see Figur e 7).

It will be appreciated that moment patterns over the

height of a cantilever wall, derived f rom elastic analyses for

lateral static load, are poorly representing moment demands

that will arise during the inelastic dynamic response of the

structure. Numerous case studies indicate, however, that

for uniform cantilever shear walls of regular buildings, a

linear moment variation gives a good envelope for dynamic

moment demands. Therefore it has been suggested 4 that the

vertical wall flexural reinforcement be curtailed in accord-

ance with the moment envelope shown in

Figure 7.

With

this procedure we can ensure that for cantilever shear walls

of regular multis torey buildings, flexural ductility demands

are restricted to the potential plastic hinge zone at the base.

Consequently in the upper storeys the special seismic detail-

ing requirements , applicable to inelastic regions of the

structure, need not be applied. This normally results in a

considerable saving in the amount o f labour intensive trans-

verse reinforcement needed.

To ensure that the shear strength of cantilever shear walls

always be slightly in excess of the shear demands during a

large earthquake, ductile structural walls should be designed

to resist:

V w a l l = o J v O 0 g c o d e

where Vcode s the shear force derived with an elastic

analysis for the specified load, ¢0 account s for the flexural

overstrength of the wall section as detailed at the base, and

cov is a dynamic shear magnification factor. The latter

allows for higher mode dynamic effects and consequently

its value depends on the fundamental period of the struc-

ture. Typica lly 1.0 < coy < 1.8 for walls from one storey to

over 15 storeys high. This is yet another example of the

application o f capac ity design principles.

Conclusions

The basic concepts of a simple deterministic design philo-

sophy, relevant to buildings that are situated in areas of

high seismic risk, has been outlined. This approach aims to

Eng. St ruc t . , 1983, Vo l . 5 , January 85


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Determ inistic se ismic design procedure s for RC buildings: T Paulay

ensure that, when required, plastic hinges will develop in

ductile reinforced concrete struc tures only in desirable

localities which have been carefully selected by the designer.

Tire application of these conc epts with respect to upper

storey colu nms of ductile frames and to cantilever shear

walls were briefly outlin ed. Some aspects of structur al

behaviour during seismic excitations, that are distinctly

different from well defined behaviour encountere d in

reinforced concrete structures that are subjected to gravity

and wind loadings only, have been specifically reviewed. To

ensure that the selected level of resistance of the structure

for the building can be ma intaine d with only negligible

decay, while large ductility demands are imposed, potential

plastic hinge regions must be detailed most carefully. A few

recently identified areas, where the quality of detailing is

of paramo unt importance , have also been discussed briefly.

cknowledgements

The cont ribut ion of the colleagues of the auth or at the

University of Ca nterbury , Christchurch, New Zealand, and

within the New Zealand National Society for Ear thquake

Engineer ing to the deve lopme nt of a seismic design philo-

sophy briefly outline d here, is gratefully acknowledged.

This presentation to honour Professor B. Thm-limann is

mainly intended for designers who are trot regulaily

inw)lved with earthquake problems.

References

I Mute, K. Design analysis of buildings', Maruzen, lo ky o, 1974,

361 pp.

2 Park, R. and Paulay, T. 'Reinforced concrete smlctures', John

Wiley, New York, 1975

3 Binney, J. and Paulay, T. 'Foundations for shear wall structures'.

Bull. :~k,w Zeala nd Nat. Soc. Ear thqu ake Eng.

1980 , 13 (2), 171

4 Standards Association of New Zealand, 'Code of practice for the

design of concrete structures', Draft New Zealand Standard

NZS3101, Parts 1 and 2, 1982

5 Paulay, T. and Bull, I. N. 'Shear effects on plastic hinges of

earthquake resisting reinforced concrete frames', Comitd Euro-

International du B~ton, Bulletin d'Information No. 132, April

1979, pp. 165-172

6 Scolt, B. D., Park, R. and Priestlcy, M..1. N. 'Stress-strain

behaviour of concrete confined by overlapping hoops at low

and high strain rates',.l. ,4incr. Concre te Ins t., lb oe. 1982,

79 (1), 13

7 Paulay, T., Park, R. and Priestley, M. J. N. 'Reinforced con-

crete beam-column o ints under seismic actions' . I..truer. Con-

crete Inst., Prec. 1978, 75 tl 1), 585

8 Paulay, T. 'Lapped splices in earthquake-resisting columns' ,

J. Amer. Concrete b~st.. Prec. (in press)

8 6 E n g . S t r u c t . 1 9 8 3 V o l . 5 J a n u ar y

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