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J. Con struct. Steel Resea rch 15 (1990) 191-213

Internat ional A ssessm ent of Des ign G uidance forCom pos ite Co lum ns

A . S . E l n a s h a i , A . Y . E 1 - G h a z o u l i & P . J . D o w l i n gDepartment of Civil Engineering, Imperial College of Science and Technology,London SW7 2BU, UK

(Rec eived 5 Septem ber 1989; revised version received and accepted2 Novem ber 1989)

A B S T R A C TThis paper reviews the current s ta te o f des ign code provis ions forcom pos i te stee l~concre te co lumns f ro m W es t Europe , Nor th A me r ica ,Japan and the Peop le ' s Repub l ic o f Ch ina , in add it ion to dra f t p roposa lsf r o m Ea s t Eu r o p e a n d Au s t ra l ia . A g en er a l co mp a r i s on o f co d e r ecom-m end atio ns in term s o f design basis, slendern ess considerations, ma terialproper t ies and d imens iona l l imi ta tions i s p resen ted . Th is is fo l low ed by aquantitative assessment of capacity calculation for a specific cross-sectionunde r ax ia l load ing and com bined ax ia l load ing and f l exure . A range o fs lenderness ( in terms o f equiva lent length d ivide d by relevant sect iondim ension) fr om zero to 30 is covered. I t is con clude d that largediscrepancies exist betw een codes, e ven those using essentially the sam edes ign method o logy , and somet imes the sam e exper imen ta l da ta base . Th isemp has i zes the case fo r harm oniza t ion to arrive a t a h igher degree o fun i form i ty o f code des ign procedures and m ore ra tiona l sa fe ty marg ins .

N O T A T I O NA CA gA rA sbb c

A r e a o f c o n c r e t eG r o s s c r o s s - s e c t i o n a l a r e aA r e a o f l o n g i t u d i n a l r e i n f o r c in g b a r sA r e a o f st e e l s e c t io nB r e a d t h o f s te e l s e c t io nB r e a d t h o f c o n c r e te s e c t io n191

J. Construct. Stee l Research 0143-974X/90/$3-50 (~ 1990 Elsevier Science Publishers LtdEngland. Printed in Great Britain


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Design guidance for composite columns 193t u r e s u s e s s t e e l s e c t io n s i n c o n j u n c t i o n w i t h c o n c r e t e . S u c h s y s t e m s i d e a l l yc o m b i n e t h e a d v a n t a g e s o f b o t h c o m p o n e n t s . I n th is c o n t e x t , c o m p o s i t ec o l u m n s o f f e r a n a t t ra c t i v e s o l u t i o n t o p r o b l e m s s u c h a s lo c a l a n d o v e r a l lb u c k l i n g f o r s t e e l c o l u m n s , a n d s h e a r f a i l u r e a n d d e t e r i o r a t i o n f o rc o n c r e t e c o l u m n s . M o r e o v e r , t h i s f o r m o f s t r u c t u r a l m e m b e r e x h i b i t se x c e l l e n t e a r t h q u a k e - r e s i s t a n t p r o p e r t i e s , n a m e l y h ig h st if fn e s s, s t r e n g t h ,d u c t i l i t y a n d e n e r g y a b s o r p t i o n c a p a c i t y .C o m p o s i t e c o l u m n s c a n b e b r o a d l y c l a s s i f i e d a s e i t h e r h o l l o w s e c t i o n sf il le d w i t h c o n c r e t e o r s t e e l s e c ti o n s e n c a s e d i n c o n c r e t e . I n c o n c r e t e - f il l e dc o l u m n s , t h e r e is a m u t u a l e n h a n c e m e n t o f d u c ti li ty , as th e t u b e p r o v i d e sc o n f i n e m e n t f o r t h e c o n c r e t e w h i c h in t u r n p r e v e n t s t h e i n w a r d b u c k l i n g o ft h e t u b e . O n t h e o t h e r h a n d , e n c a s e d c o l u m n s o f f e r h i g h s t r e n g t h a n dd u c t i l it y , w h i l e p r o v i d i n g t h e s t e e l s e c ti o n w i t h f i re p r o t e c t i o n . P a r t i a ll ye n c a s e d c o l u m n s o f f e r a d d i t i o n a l a d v a n t a g e s s u c h a s h i g h i m p a c t r e s i s t -a n c e , s i m p li fi ed b e a m - t o - c o l u m n c o n n e c t i o n s a n d r e d u c e d o r o m i t t e ds h u t t e r i n g .D i f f e r e n t m e t h o d s f o r t h e d e s i g n o f c o m p o s i t e c o l u m n s e x i st in c o d e s o fp r a c t i c e . l - 6 A c o m p o s i t e c o l u m n m a y b e t r e a t e d i n s o m e m e t h o d s a s as t e e l c o l u m n s t r e n g t h e n e d b y c o n c r e t e , w h e r e a s o t h e r m e t h o d s m a yc o n s i d e r i t as a r e i n f o r c e d c o n c r e t e c o l u m n w i t h s p e c ia l r e i n f o r c e m e n t .F u r t h e r m o r e , t h e s tr e n g th o f a c o l u m n m a y b e e v a l u a t e d a s t h e s u m o fs t re n g t h s o f b o t h c o m p o n e n t s .E x i s t i n g c o d e d i f f e r e n c e s c a n b e a t t r i b u t e d t o t w o m a i n r e a s o n s :d i f f e re n c e i n d e si g n p h i l o s o p h y , a n d n u m e r i c a l q u a n t i fi c a ti o n . W h e r e a st h e f o r m e r c o v e r s t h e f u n d a m e n t a l c o n s i d e r a t i o n s , s u c h a s st ra i n d i s tr ib u -t i o n a n d c o m p a t i b i l i ty , t h e l a t t e r is a c o n s e q u e n c e o f t h e u s e o f a sp e c if ice x p e r i m e n t a l d a t a b a s e t o a r r i v e at a c tu a l d e s ig n e x p r es s io n s . E v e n w h e nt w o c o d e s u s e t h e s a m e p h i l o s o p h y a n d t h e s a m e e x p e r i m e n t a l r e s u l t s ,s o m e d i s c r e p a n c i e s a r e t o b e e x p e c t e d i n e s t i m a t i n g t h e f i n a l s e c t i o np r o p e r t i e s f o r a g i v e n lo a d , o r t h e c a p a c i t y o f a p r e - d e f i n e d s e c t i o n . T h i sm a y b e d u e t o t h e d i f f e r e n c e s i n s a f e t y f a c t o r s , a l l o w a b l e m a t e r i a lp r o p e r t i e s , l i m i t i n g d i m e n s i o n s , c o n s i d e r a t i o n o f l o n g - t e r m l o a d i n g , e t c. I tis t h e r e f o r e n o t s u r p r i s i n g t h a t v a r i o u s c o d e s w o u l d y i e l d a w i d e r a n g e o fd e s i g n s f o r t h e s a m e c o n d i t i o n s .

2 D E S I G N C O D E S , A B R I E F D E S C R I P T I O N2.1 AIJ s tandard s (Architectural Inst i tute of Japan)C o m p o s i t e c o n s t r u c t i o n , t e r m e d s t ee l r e i n f o r c e d c o n c r e t e (S R C ) i n J a p a ni s i n c o m m o n u s e . T h i s i s a t t r i b u t e d t o i t s s u p e r i o r e a r t h q u a k e - r e s i s t a n t


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194 A. S . E lnasha i, A . Y . E I -G hazo u l i , P . J . D ow l ing

b e h a v i o u r c o m p a r e d w i t h r e i n f o r c e d c o n c r e te s t ru c t ur e s . H e n c e , e x t e n si v er e s e a r c h o n t h is s u b j e c t h a s b e e n u n d e r t a k e n b y J a p a n e s e r e s e a r c h e r sd u r i n g t h is c e n t u r y . C o n c r e t e - e n c a s e d s t ee l c o l u m n s a r e f r e q u e n t l y u s e df o r m e d i u m - t o h i g h - r i se b u i l d i n g s . C o n c r e t e - f i l le d s te e l tu b e s a r e u s e d f o rc o l u m n s o f s u b w a y s t a ti o n s a n d a ls o in b u i l d in g s .

T h e d e s i g n i s b a s e d o n t h e a l l o w a b l e s t r e s s m e t h o d . H o w e v e r , t h eu l t im a t e s t r e n g t h o f t h e m e m b e r h a s to b e e v a l u a t e d f o r e a r t h q u a k er e s is t a n ce . T h e c r o s s -s e c t io n a l s t r e n g t h is c a l c u l a te d b y s u p e r i m p o s i n g t h es t r e n g t h o f b o t h t h e s te e l a n d 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 . F u l l p l as ti cd i s t r i b u t i o n i s u s e d w i t h a r e d u c t i o n f a c t o r i n t h e c o n c r e t e s t r e n g t h t oa c c o u n t f o r t h e s t r a i n l i m i t i n c o n c r e t e . T h i s f a c t o r is a s s i g n e d a d i f f e r e n tv a l u e f o r fi ll ed s e c t i o n s , w h e r e t h e c o n c r e t e s t r e n g t h is e n h a n c e d b yt r i a x i a l c o n f i n e m e n t . T h e m e t h o d i s a p p l i c a b l e t o a s y m m e t r i c a l s e c t i o n sa n d c o l u m n s u n d e r b ia x ia l b e n d i n g .

A s f r a m e d c o l u m n s a r e u s u a l ly s to c k y , b e c a u s e o f t h e d e s ig n f o r la r g el a te r a l f o rc e s u n d e r e a r t h q u a k e l o a d i n g , le ss a t t e n t i o n h a s b e e n g i v e n t os l e n d e r c o l u m n s . B e a m - c o l u m n s a r e s i m il ar ly d e s i g n e d b y th e s u p e r i m -p o s i t i o n o f s te e l a n d r e i n f o r c e d c o n c r e te b e a m - c o l u m n s . T h e E u l e rb u c k l i n g l o a d i s u s e d w i t h a r e d u c e d c o n c r e t e s t i ff n e s s a n d f a c t o r s o f s a f e t yf o r b o t h m a t e r i a l s . M o m e n t m a g n i f ie r s a r e u s e d f o r s l e n d e r n e s s c o n s i d e r a -t io n i n th e r e i n f o r c e d c o n c r e t e p o r t i o n . T h e c o d e a l so sp e c if ie s m i n i m u ma x i a l l o a d e c c e n t r i c i t i e s .

T o a c h i e v e s u f f i c i e n t d u c t i l i t y , f l e x u r a l f a i l u r e s h o u l d p r e c e d e s h e a rf a il u re in a m e m b e r . M o r e o v e r , t h e ax ia l c o m p r e s s i o n f o rc e a n d t h ew i d t h / t h i c k n e s s r a t io s o f s t e e l s e c t i o n s a r e l i m i t e d to s p e c i f i e d v a l u e s . O nt h e o t h e r h a n d , l o a d s a re t r a n s f e r r e d b e t w e e n s t e el a n d c o n c r e t e b y b o n d .I f t h e b o n d s t r e n g t h is i n s u f f i c ie n t , d i r e c t b e a r i n g is u s e d .2 . 2 B S 5 4 0 0 P a r t 5 ( B r it is h S t a n d a r d s I n s t it u t io n )E a r l y t es ts o n e n c a s e d c o l u m n s in th e U K l e d t o th e c a s e d - s t r ut m e t h o d o fd e s i g n a d o p t e d i n th e B r i ti s h S t a n d a r d s ( B S 4 4 9 P a r t 2 a n d B S 5 9 5 0 D r a f t ) .T h i s e m p i ri c a l m e t h o d w a s d e v e l o p e d f r o m e a r li e r d e si g n p r o c e d u r e s f o rs te e l c o l u m n s , a n d w a s n o t b a s e d o n f u n d a m e n t a l r e se a r c h o n c o m p o s i t ec o l u m n s . C o n c r e t e - f i l l e d t u b e s a r e n o t a p p l ic a b l e t o th is m e t h o d , n o rm e m b e r s w h e r e t h e c o n c r e t e s e c t io n i s h e a v i ly r e i n f o r c e d o r is si g n if ic a n tl yl a r g e r t h a n t h e s t e e l s e c t io n . R e s e a r c h o n i m p r o v e d m e t h o d s h a s s in c et h e n b e e n c a r r i e d o u t m a i n l y at I m p e r i a l C o l l e g e . 7"s T h i s w o r k f o r m e d t h eb a s is o f t h e c u r r e n t b r i d g e c o d e ( B S 5 4 0 0 P a r t 5 ).

C o d e p r o v i s i o n s in B S 5 4 0 0 a r e b a s e d o n l i m i t s t a t e d e s i g n w i t h l o a d i n gf a c t o r s a n d p a r t i a l s a f e t y f a c t o r s f o r m a t e r i a l s . T h e u l t i m a t e m o m e n t i s


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Design guidance for compo site columns 195calculated from plastic stress distribution over the cross-section, and anapproxi mation for the interaction curve for axial load and m om en t is used.Red uced concrete properties are used to account for the effects of creepand the use of the uncracked concrete section in stiffness calculation.Minim um eccentricities due to construction tolerances are considered. Inthe case of filled columns, an e nhanced concrete strength due to triaxialconfinement may be taken into account.

Slenderness effects are accoun ted for by the use of a non-dimensionalslenderness parameter and the European buckling curves used for thedesign of steel columns. The choice of the appropria te curve de pends onthe geometry of the cross-section. The different curves reflect the effect ofresidual stresses and initial imperfections in the me mbe r. The uncr ackedconcrete section is used in stiffness calculation. The use of the slendernesspar ame ter is consistent with tl~e design of steel columns as the me tho dreduces to the bare steel column design when the concrete portion isremoved. Consequently, the method is applicable to symmetric sectionsonly, and is restricted to the range of sections cate red for in the Europeanbuckling curves. For uniaxial bending, distinction is made for the presenceor lack of restraint in the direction orthogonal to the bending axis.Expressions are given for biaxial bend ing for filled circular hollow sectionsas well as encase d sections.2 . 3 A C I - 3 1 8 - 8 3 ( A m e r i c a n C o n c r e t e I n s ti tu t e )The building code of the Amer ica n Concrete Institute uses the limit statedesign format with loading factors and capacity reduction factors. Thestrength of a composite column is computed as for reinforced concretemembers. Failure is defined in terms of a 0.3% strain limit for any concretefibre. This failure strain is used with a set of neutral axis locations to arriveat an interaction curve for thrust and moment. Slenderness effects areanalysed in terms of mome nt magnifiers using a reduced Euler load. Theexpression for equivalent stiffness includes a creep fac tor, and a crackedconcrete stiffness is considered. Minimum eccentricities are specified tocover construction tolerances.2 . 4 A I S C - L R F D - 1 9 8 6 ( A m e r i c a n I n s t it u t e o f S t e e l C o n s t r u c t io n )The load and resistance factor design uses the limit state design withloading factors and capacity reduction factors. The design of compositecolumns is based on the design equations for steel columns. However, theslenderness and area parameters are modified for the presence of


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196 A.S. E l n a s ha i , A . Y . E l - G h a z o u l i , P . J . D o M i n g

c o n c r e t e . T h e c o d e r e c o g n i z e s t h e c o n f i n e m e n t ef f e ct in fi ll ed c o l u m n s a n du s e s a s i m p l e i n t e r a c t i o n f o r m u l a f o r u n i a x i a l a n d b i a x i a l b e n d i n g .M o m e n t m a g n i f ie r s a re s p e c i fi e d t o a c c o u n t f o r s l e n d e r n e s s e f fe c t s e x c e p tf o r t h e c a s e o f u n i a x ia l b e n d i n g o n l y w h e n a s te e l b u c k l i n g c u r v e i s u s e d a sn o m i n i m u m e c c e n t r i c it ie s a re s p e c if ie d . L o a d t r a n s f e r s h o u l d b e p r o v i d e db y d i re c t b e a r i n g a t t h e c o n n e c t i o n s .2 .5 Eurocod e 4 and DIN 18806E u r o c o d e 4 w a s d r a f t e d t o c o v e r th e d e s i g n o f c o m p o s i t e s t ee l a n dc o n c r e t e s t r u c t u r e s . L i m i t s t a t e d e s i g n is a p p l i e d w i t h p a r t ia l s a f e t y f a c t o r sf o r m a t e r ia l s . T h r e e m e t h o d s o f d e s i g n ar e a v a il a b le i n t h e E C 4 d r a f t . T h efir st t w o m e t h o d s a r e d e r i v e d f ro m t h e W e s t G e r m a n p r a ct ic e ( D I N1 88 06 ) w h e r e s l e n d e r n e s s e f f e c t s a r e a n a l y s e d in t e r m s o f b e n d i n gm o m e n t s as in r e in f o r c e d c o n c r e t e d e si g n. H o w e v e r , a s o p p o s e d t om o m e n t m a g n i f i c a t i o n , a n e q u i v a l e n t s t r e n g t h r e d u c t i o n i s d e r i v e d u s i n gt h e E u r o p e a n S t e e l B u c k l i n g C u r v e s in c o n j u n c t i o n w i th t h e c r os s -s e c t i o n a l i n t e r a c t i o n c u r v e . F u l l p l a s t i c d i s t r i b u t i o n i s u s e d t o o b t a i n t h ea x ia l to f le x u r a l s t r e n g t h i n t e r a c t i o n c u r v e , w h e r e a s a s i m p l i f ie d p o l y g o n -a l a p p r o x i m a t i o n is i n t r o d u c e d in t h e s e c o n d m e t h o d . T h e t h ir d m e t h o d isb a s e d o n t h e c a s e d s t r u t d e s i g n u s e d i n t h e e a r l y B r i t i s h S t a n d a r d B S 4 4 9P a r t 2 , w h e r e s t e e l c o l u m n d e s i g n is u s e d w i t h a n i n c r e a s e i n t h e r a d i u s o fg y r a t i o n t o a c c o u n t fo r t h e p r e s e n c e o f c o n c r e t e .2 .6 M in istry o f W ater Conservancy and Electr ic Pow er , Peop le ' s Rep ubl ico f C h i n aT h e c o d e i n c l u d e s s p e c i f i c a t i o n s f o r fi ll e d t u b e s o n l y . D e s i g n is b a s e d o nu l t i m a t e l im i t s ta t e , a n d s l e n d e r n e s s i s c o n s i d e r e d u s i n g d i f f e r e n t c u r v e sf o r s t r e n g t h r e d u c t i o n d e p e n d i n g o n m a t e r i a l, s t e el ra t io a n d s l e n d e r n e s sr a t io a s s u m i n g a n i ni ti a l im p e r f e c t i o n o f L e n g t h / 8 0 0 .2 .7 Aus tra l ian and East Europ ean S tandards (unpubl i shed)T h e A u s t r a l i a n c o d e p r o v i s io n s d o n o t i n c lu d e d e s ig n o f c o m p o s i t ec o l u m n s . H o w e v e r , p r o p o s a l s fo r dr a f t c o d e p r o v i si o n s h a v e b e e nd i s c u s s e d , ~'1 w h e r e a l im i t s ta t e p h i l o s o p h y is a d o p t e d . T w o m e t h o d s a r ep r o p o s e d ; o n e r e la t es t o r e i n f o r c e d c o n c r e t e c o l u m n d e si g n , a n d t h e o t h e ris a k i n t o st e e l c o d e s , n a m e l y m o m e n t m a g n i f ie r a n d s t r e n g t h r e d u c t i o n .S p e c i f ic a t io n s i n E a s t E u r o p e a r e c u r r e n t l y u n d e r c o n s i d e r a t i o n , w h e r ep l a st ic d e s i g n a p p r o a c h is a l lo w e d .


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Design guidance for composite columns 197

3 C O D E D I F F E R E N C E S3 . 1 D e s i g n b a s i s3.1.1 Origin of methodT h i s i s b y a n d l a r g e d i c t a t e d b y w h e t h e r s te e l d e s i g n e r s w e r e c o n s i d e r i n gc o m p o s i t e c o n s t r u c t i o n a s a n i m p r o v e m e n t o v e r b a r e s t e e l d e s i g n , o rc o n c r e t e d e s i g n e r s w e r e a t t e m p t i n g t o a c h i e v e h i g h e r s t r e n g t h s . I n t h ef o r m e r c a s e , s t e e l b u c k l i n g c u rv e s w e r e u s e d , a n d i n th e l a t t e r r e i n f o r c e dc o n c r e t e d e s ig n m e t h o d s w e r e a d o p t e d .T h e m o d i f i e d s t ee l d e s ig n m e t h o d s a r e u s e d in A I S C - L R F D a n d B S5 4 00 , b o t h e x p li c it ly re d u c i n g to t h e b a r e s t e e l s e c t io n . T h e A m e r i c a nC o n c r e t e I n s t i t u t e m a k e s u s e o f r e i n f o r c e d c o n c r e t e c o l u m n d e s i g n ,w h e r e a s E C 4 a n d D I N u s e a c o m b i n a t i o n of b o t h a p p r o a c h e s . D i s t in c t ly ,t h e J a p a n e s e C o d e ( A I J ) u s e s a s u p e r i m p o s i t i o n o f t h e i n d iv i d u a l l yc a l c u l a t e d c a p a c i ti e s .3.1.2 Loading and resistanceV a r i o u s c o d e s u s e s i g n i fi c an t ly d i f f e r e n t l o a d i n g fa c t o r s a n d c o m b i n a t i o n s .O n t h e o t h e r h a n d , c a p a c it y re d u c t i o n is a c h ie v e d th r o u g h o n e o f t w oa p p r o a ch e s . W h e r e a s t h e N o r t h A m e r i c a n c o d e s ( A C I a n d A I S C ) u s ec a p a c i t y r e d u c t i o n f a c t o r s 4 ' ( o f 0 . 7 a n d 0 . 85 r e s p e c t i v e l y ) , t h e E u r o p e a np r a c t i c e i s t o u s e p a r t i a l s a f e t y f a c t o r s o n m a t e r i a l s . D i f f e r e n t v a l u e s f o rt h e s e a r e g i v e n f o r c o n c r e t e , s t e e l a n d r e i n f o r c i n g b a r s ( t y p i c a ll y 1 -5 ,1 . 0 - 1 - 1 a n d 1 . 1 5 r e s p e c t i v e l y ) .I n c o n t r a s t t o t h e a b o v e l i m i t s t a t e - b a s e d c o d e s , t h e J a p a n e s e c o d e( A I J ) u s es t h e a l l o w a b l e s tr es s a p p r o a c h . H o w e v e r , o w i n g t o t h e s e v e r ee a r t h q u a k e p r o b l e m i n J a p a n , t h e u l ti m a t e s t r e n g t h h a s to b e v e r i fi e d .

T A B L E 1S p e c i f ic a t io n s f o r C o n c r e t e C o m p r e s s i v e S t r e n g t hCode Encased Filled

A I J ( a l l o w a b l e s t r e n g t h ) F c yl ( 1 -1 5 s P c) F cy l( u l t i m a t e s t r e n g t h ) F c yl ( 0 -8 5 -2 - 5 8p c ) 0 " 8 5 F c y lB S 5 4 0 0 ( a x i a l c o m p r e s s i o n ) 0 "6 7 5 Fc u 0 " 67 5 F cu ( /~ )( b e n d i n g ) 0 .6 F c u 0 .6 F u ( ~ )E C 4 0-85Fcyl 0-85Fcyl (13)D I N 1 8 8 0 6 0 -6 0 F c u 0 .7 0 F c u ( ~ )A C I 318-83 0 -85Fcyl 0 -85Fcy l


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198 A.S. Elnashai, A . Y. EI-Ghazouli, P. J. Dowling3 . 2 C o n c r e t e s t r e n g t hT a b l e 1 g iv e s a b r i e f c o m p a r i s o n o f r e c o m m e n d e d v a l u e s fo r c o n c r e t ec o m p r e s s i v e s t re n g th .

I t is n o t e w o r t h y t h a t s o m e c o d e s u s e c u b e w h e r e a s o t h e r s u s e c y l i n d e rs t re n g t h . F u r t h e r m o r e , t h e r e is s o m e c o n t r o v e r s y o n th e e f fe c t o fc o n f i n e m e n t o n t h e c r u s h i n g s t r en g t h . F o r an a s s u m e d r a t io o f Fcu/Fcy~ o f1 .2 , th e r a n g e o f c o m p r e s s i v e s t r e n g t h ( n o r m a l i z e d b y F cy 0 is b e t w e e n 0 . 7a n d 1 .0 , f o r u n c o n f i n e d c o n c r e t e .3 . 3 I n t e r a c t i o n c u r v e sD i s c r e p a n c i e s o b s e r v e d f o r m i n o r a n d m a j o r a x is b e n d i n g i n t er a c t i o nc u r v e s a r e d i s c u s s e d i n d e t a i l in S e c t i o n 4 . 3 , a n d s h o w n in F ig s 3 -1 2 . T a b l e2 g i v e s a g e n e r a l c o m p a r i s o n .

TABLE 2Basis of Interaction DiagramsCode Specifications

A IJ Plastic distribution (PD )BS 5400 PD for MuirEC4, DIN Full PDACI 318-83AI SC - L R FD

Equilibrium andcompatibility of strainsPD for Mult

Reduced FcylApproximate surfaceRedu ced moment capacitySimplified surface in me thod B0.3% Concrete strain limitApproximate surface

A s d i s c u s s e d b e l o w , t h e r e a r e l a r g e v a r i a t i o n s i n c a p a c i t y u n d e rc o m b i n e d a x ia l l o a d in g a n d b e n d i n g , d e p e n d i n g o n th e c o d e u s e d . T h ec o m p a r i s o n g i v en h e r e i n d o e s n o t c o n s i d e r b ia x ia l b e n d i n g c a se s .3 . 4 E q u i v a l e n t s t if f n e s sF o r s l e n d e r n e s s c o n s i d e r a t i o n s a n d d e f l e c t io n c a l c u l a t i o n s , t h e e q u i v a l e n t( E / ) is r e q u i r e d . V a r i o u s c o d e s u s e d i f f e r e n t a p p r o a c h e s t o ar r iv e a t av a l u e o f E ,. w h i c h t a k e s a c c o u n t , d i r e c t l y o r in d i r e c tl y , o f c r a c k e d s t if f n e s sa n d c r e e p . T h e r e c o m m e n d e d E c v a l u e s f o r t h e c o d e s c o n s i d e r e d h e r e i na r e p r e s e n t e d in T a b l e 3 .


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Des i gn gu i dance f o r com pos i t e co l umnsT A B L E 3

E q u i v a l e n t S t i ff n e ss

199

C o d e E c C o m m e n t sB S 5 4 0 0E C 4A C IA I S C

450Fcu600Fcyl

5 7 0 0 0 (F c y l ) 1/2 ( p s i )wl"S Fcyl)1/2

L o w , t o a c c o u n t f o r u s e o f u n c r a c k e d s e c t i o na n d c r e e pS a m e a s a b o v e , b u t c r e e p a c c o u n t e d f o r i ne x p r e s s i o nH i g h e r , a s a c r a c k e d s e c t i o n i s u s e d , w i t h ac r e e p f a c t o rH i g h , a s a c r a c k e d s e c t i o n i s u s e d( w = u n i t w e i g h t o f c o n c r e t e i n l b / ft 3 a n d F cyi n k s i )

T A B L E 4S l e n d e r n e s s C o n s i d e r a t i o n s

Code Speci f icat ionsS t r e n g t h r e d u c t i o nI J

B S 5 40 0 , D I N , E C 4A C 1 3 1 8 - 8 3A I S C - L R F D

S t r e n g t h r e d u c t i o nM o m e n t m a g n i fi c a t io nM i n i m u m e c c e n t ri c it yM o m e n t m a g n i fi c at io nf o r c o m p r e s s i o n a n d b e n d i n gC r i t i c a l l o a d f o r a x i a lc o m p r e s s i o n

R = (1 - vP/PE)w h e r e v = f a c t o r o f s a f e t yE u r o p e a n s te e l b u c k l i n g c u r v e st5 = Cm /(1 - P/CkPE)

= C m / ( 1 - P / P E )r c o m p o s i t e = r s t e e 1( n o t l e s s t h a n 0 . 3 d e p t h )

T h e e x p r e s s i o n f o r ( E / ) eq u i v a le n t m a y o r m a y n o t u s e a c r e e p c o e f f i c ie n t ,d e p e n d i n g o n t h e c o d e .3 . 5 S l e n d e r n e s s c o n s i d e r a t i o n s

T h e e f f e c t o f s le n d e r n e s s is a c c o u n t e d f o r in o n e o f t w o w a y s , s t r e n g t hr e d u c t i o n o r m o m e n t m a g n i f ic a t i on . E u r o p e a n c o d e s (B S 5 40 0, D I N a n dE C 4 ) u s e a s t r e n g t h re d u c t i o n , so d o e s t h e A I J c o d e . A l t e r n a t i v e l y , A C Iu s e s a m o m e n t m a g n i f ic a t i o n f a c to r a s w e l l a s th e d e f i n i ti o n o f a m i n i m u me c c e n t ri c i t y a s d i sc u ss e d be l ow . T h e A I S C r e c o m m e n d a t i o n s u s e am o m e n t m a g n i f i e r f o r b e n d i n g w i t h ax i al l o a d , a n d a c ri ti c a l l o a d f o r p u r ec o m p r e s s i o n , w i t h n o m i n i m u m e c c e n t r i c i ty . T a b l e 4 g iv e s a c o m p a r i s o n o ft h e s p e c i f i c a t i o n s .


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200 A . S . E l n a s h a i , A . Y . E l - G h a z o u l i , P . J . D o w l i n g

T A B L E 5M i n i m u m E c c e n t r i c i t i e s

C o d e M i n i m u m e c c en t ri c it yA I J 5 % HB S 5 4 00 3 % B

E C 4 N o n eD I N 1 88 06 N o n eA C 1 3 1 8 - 8 3 ( 0 .6 + 0 . 0 3 H )

i n c h e sA I S C - L R F D N o ne

( f o r t h e c o n c r e t e p o r t i o n d e s i g n )( i n b r i d g e s , w o u l d b e 4 % i n b u il d i n g s )( a x i al lo a d l i m i te d to 8 5 % o f th e s h o r t c o l u m n m i n o ra x i s c a p a c i t y )( in m e t h o d s A a n d B , 4 % in m e t h o d C )( a x i a l l o a d l i m i t e d to 8 5 % o f t h e p l a s t i c c a p a c i t y )

3 . 6 M i n i m u m e c c e n tr i ci ti e sRecommended values of minimum eccentricity are given hereafter inTable 5.

It is not ewor thy that limiting the axial capacity to a pe rcen tage of theflexural plastic capacity imposes a further limitation on the minimumeccentricity, hence values quot ed above ma y not be strictly comparab le insome cases.3 . 7 S h e a r t r a n s f e rAll codes assume full interaction, but some impose restrictions on theshear stress at the steel/concrete interface. It is customary to use directbearing, or provide shear connectors, if and where the specified limitingshear stress is exceeded. Table 6 lists the various approaches and valuesadopted by design codes.

Fur the rmore , design of shear connectors , if requi red, is given in detail inmost codes.3 . 8 M a t e r i a l p r o p e r t i e sLimits on the e xtr eme values of conc rete crushing and steel yield strengthare given in most codes, as shown in Table 7. The upper limits for steelyield stress are considered to ensure that concrete remains stable untilsteel reaches yield.


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Design guidance fo r com posite co lumns 201T A B L E 6

Sp e c i f i c at i o n s f o r Sh e a r T r a n s f e rCode Specifications

A I JB S 5 4 0 0 , E C 4

D I N 1 8 8 0 6

A C I 3 1 8 - 8 3A I S C - L R F D

D e t a i l e d d e s i g n f o r E N CD i r e c t b e a t i n g f o r F I L i f b o n d is in s u f fi c i en tC o n n e c t o r s p r o v i d e d i fT > 0 -6 N / m m 2 f o r E N Co r 0 -4 N / m m 2 f o r F I LC o n n e c t o r s p r o v i d e d i fr > 0 . 5 5 -0 . 8 0 N / m m 2 f o r E N Cr e d u c e d b y 3 0 % f o r F I L( f o r Fcu = 2 5 - 5 5 N / m m 2 )D i r e c t b e a t i n g a t c o n n e c t i o n sC o n c r e t e s t r e n g t h f o r b e a t i n g = 1 . 7 ( 0 .7 a ) ( Fc y0D i r e c t b e a r i n g a t c o n n e c t i o n sC o n c r e t e s tr e n g t h f o r b e a t i n g = l '7 ( 0 " 6 a )( Fc y l )

a C a p a c i t y r e d u c t i o n f a c t o r ( r e s i s t a n c e f a c t o r ) f o r b e a t i n g .

T A B L E 7Sp e c i f ic a t io n s f o r M a t e r i a l P r o p e r t i e s

Cod e Con crete strength Steel yield( N / m m 2) (N/mm 2)A IJ Fcy -> 15 Fy - 360 (fo r tp l < 40 m m )

Fcyl --> 18 (w ith re- ba rs) Fy -< 340 (fo r tpl > 40 m m )BS 5400 Fcu -> 20 ( fo r enca sed )

Fcu -> 25 (fo r filled)E C 4 F~y l - 20 Fy -< 450 (350 in m e th od C)D IN 18806 F~u -> 25A C I 3 18 -8 3 Fc y I - -> 17 Fy -< 330A I S C - L R F D 2 0 ~ < F c y I ~ < 5 0 Fy --< 36 5

3 . 9 D i m e n s i o n a l l i m i t a ti o n s3.9.1 Steel wall thicknessE x p r e s s i o n s g i v e n f o r s t e e l w a l l t h i c k n e s s r e d u c e t o t h e s a m e v a l u e s i nN o r t h A m e r i c a n a n d W e s te r n E u r o p e a n c o d e s . H o w e v e r , o n l y E C 4 a n dD I N i n c l u d e v a lu e s f o r p a r ti al ly e n c a s e d s e c t i on s . O n t h e o t h e r h a n d , A I Ji s t h e o n l y c o d e t h a t c o n s i d e r s l im i t s f o r fu l l y e n c a s e d s e c t i o n s d u e t o t h ed e s i g n f o r e a r t h q u a k e l o a d s.


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2 0 2 A . S . E l n a s h a i , A . Y . E l - G h a z o u l i , P . J . D o w l i n g

3 . 9 . 2 S t e e l a n d c o n c r e t e c o n t r i b u t i o n sL i m i t s o n c o n c r e t e c o n t r i b u t i o n t o t h e p l a s t i c a x i a l l o a d a r e i n c l u d e d i nW e s t er n E u r o p e a n c o d e s . N o r t h A m e r i c a n a n d J a p a n e se c o d e s d e f in ed i r e c t l i m i t a t i o n s o n t h e s t e e l o r c o n c r e t e a r e a . T h e s e d i f f e r e n c e s a r es u m m a r i z e d i n T a b l e 8 .

T A B L E 8S t e e l a n d C o n c r e t e C o n t r i b u t i o n s

C o d e S p e c i f i c a t i o n sA I J A~/Ag >- 0 - 8 %B S 5 4 0 0 0 . 1 5 < a c < 0 - 8 0 ( f o r e n c a s e d )

0 . 1 0 < c~ < 0 . 8 0 ( f o r f i l l e d )D I N 1 8 8 06 0 . 2 0 < ~ < 0 . 9 0

At~A,. >- 3 %A C I A , / A , , < 0 . 0 8 ( f o r f i l l e d )

0411 < A r / A g ~ 0 " 0 8 ( f o r e n c a s e d )A I S C - L R F D A~/Ag > 0 - 0 4

(c~,, = NI~ /Nr, )( ~ = N p / N p )( ~ = l - a ~ , i fr e i n f o r c e m e n t i sd i s r e g a r d e d )

3.9.3 Slenderness and section dimensionsL i m i t s o n s l en d e r n e s s a re i n c lu d e d in s o m e c o d e s w h i c h c o r r e s p o n d t o th er a n g e o f a v a i la b l e e x p e r i m e n t a l d a t a a s s h o w n i n T a b l e 9 .

T A B L E 9S l e n d e r n e s s R a n g e s

C o d e S p e c i f i c a t i o n sB S 5 4 0 0 L c / B


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Design guidance fo r com posite co lumnsTABLE 10Specifications for ReinforcementDetailing

203

Code SpecificationsBS 5400AC1318-83

AISC-LRFD

Stirrups spacing -< 200 mm, with 4 corner longitudinalbarsCover to surface of steel shape -> 50 mmStirrups spacing


14/23

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

I n F i g s 1 - 1 2 t h e r e s i s ta n c e s g i v e n b y t h e d if f e r e n t m e t h o d s a r e s h o w nw i t h t h e v a l u e s o f N p a n d M p c a l c u l a te d a c c o r d i n g t o E C 4 . C o m p a r i s o n o fr e s is t an c e s u n d e r c o m b i n e d f le x u r e a n d c o m p r e s s i o n w a s m a d e a s s u m i n gc o n s t a n t e c c e n t r ic i ti e s m e a s u r e d f r o m t h e o r i g in o f th e i n t e r c e p ts o f th e


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c u r v e s . T h e l o a d i n g f a c to r s w e r e n o t in c l u d e d i n t h e c o m p a r i s o n b e c a u s eo f t h e d i f fe r e n t l o a d c o m b i n a t i o n s g i v e n i n e a c h c o d e , a n d o n l y t h e fa c t o rso n t h e r e s i s t a n c e s i d e w e r e c o n s i d e r e d .

I n t h e f o l l o w i n g q u a n t i t a ti v e c o m p a r i s o n , t h e c o d e i s i n t e r p r e t e d f r o mt h e l a t e s t a v a i la b l e v e r s i o n , a s w o u l d b e t h e c a s e i n d e s i g n o f f i c e p r a c ti c e .T h e p o s s i b i l i t y o f i n a d v e r t e n t l y m i s i n t e r p r e t i n g c e r t a i n c l a u s e s e x i s t s .


16/23

206 A . S . E l n a s h a i , A . Y . E l - G h a z o u l i , P . J . D o w l i n gi

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H o w e v e r , t h is m a y h i g h li gh t a n i n h e r e n t a m b i g u i t y in th e c o d e p r e s e n t a -t i o n . F i n a l l y , n u m b e r s a p p e a r i n g i n s q u a r e b r a c k e t s i n d i c a t e t h e c l a u s en u m b e r i n t h e c o d e u n d e r c o n s i d e r a t i o n .4 . 2 C o m p a r i s o n o f a x i al c a p a c i t ie s4.2.1 Un factored ax ial capacityT h e u n f a c t o r e d a x i a l c a p a c i t i e s o f t h e f o u r m e t h o d s a r e s h o w n i n F i g . 1n o r m a l iz e d t o t h at o f E C 4 . S l e n d e r n e s s is r e p r e s e n t e d in t e r m s o f t h e r a t io


17/23

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M/MpF i g . 8 . M a j o r a x i s b e n d i n g ; Ley/h = 2 0 .

o f th e p i n - e n d e d c o l u m n l e n g t h t o th e c r o s s- se c ti o n a l d i m e n s i o n i n t h ed i r e c ti o n o f m i n o r a x is b e n d i n g .F o r v e r y l o w s l e n d e r n e s s r a t io s , B S 5 4 0 0 g i v e s t h e l o w e s t c a p a c it y : 1 9 %l es s th a n E C 4 a n d a b o u t 4 % l e ss t h a n A C I a n d A I S C . T h i s is a t tr i b u te d t o( 1 ) t h e r e d u c e d c o n c r e t e s t r e n g t h o f 0 -6 F cu ( 0 . 4 5 f a c t o r e d ) [ 1 1 . 1 . 4 ] t o t a k ea c c o u n t o f c r e e p w h i c h i s n o t i n c l u d e d i n t h e e q u i v a l e n t s t i f f n e s s , a n d ( 2 )t h e m i n i m u m e c c e n tr i c it y r e q u i r e m e n t f o r s h o rt c o l u m n s c a l c u la t e d f r o mt h e l i m i t a t i o n o n a x i al c a p a c it y ( 0 . 8 5 o f t h e m i n o r a x i s a x i al c a p a c i ty )[ 1 1 . 3 . 2 .1 ] . T h e A C I c o d e g i v e s v a l u e s w h i c h a re 1 5 % l e s s t h a n E C 4 a s a


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2(J8 A . S . E l n a s h a i , A . Y . E l - G h a z o u l i , P . J . D o w l i n g0 . 4 80 . 4 4

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r e s u lt o f l i m i t a t io n o f 0 - 8 5 o f t h e a x i a l p l a s ti c c a p a c i t y , i n a c c o r d a n c e w i t ht h e m i n i m u m e c c en t r ic i ty r e q u i r e m e n t [ 1 0 . 3 . 5 . 1 ] . F o r A I S C , t h e v a l u e sa r e 1 6 % l e s s t h a n E C 4 b e c a u s e o f th e r e d u c e d c o n c r e t e s t r e n g t h o f 0 -6 F cy 1i n e n c a s e d c o l u m n s [ I2 . 2 ] .

F o r h i g h e r s l e n d e r n e s s r a t io s , th e d i f f e r e n c e b e t w e e n E C 4 a n d B S 5 4 0 0is r e d u c e d b e c a u s e t h e v a l u e o f e q u i v a l e n t s t i f f n e s s is l o w e r a s i t t a k e sa c c o u n t o f c r e e p [ 4 . 8 . 6 ] . H o w e v e r , t h e m i n i m u m e c c e n t r i c i t y r e q u i r e m e n to f 0 -0 4 i n B S 5 4 0 0 c a u s e s a r e d u c t i o n i n c a p a c i ty i n th e r a n g e o f s l e n d e r n e s s


19/23

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u s e d i n p r a c t ic e . T h e c a p a c i t i e s o f A C I a r e i n a g r e e m e n t w i t h o t h e r c o d e s ,b u t d e c r e a s e a t h i g h s l e n d e r n e s s d u e t o t h e f o l l o w i n g : ( 1 ) u s e o f t h ec r a c k e d s e c t i o n o f c o n c r e t e , ( 2 ) t h e c r e e p f ac t o r i n c l u d e d i n t h e e x p r e s s i o nf o r e q u i v a l e n t s t i f fn e s s [ 1 0 .1 4 ] a n d ( 3 ) t h e m i n i m u m e c c e n t r i c i t y r e q u i r e -m e n t a c c o m p a n i e d b y a m o m e n t m a g n i f i c a t i o n f a c t o r [ 1 0 . 1 1 . 1 5 ] .A l t h o u g h t h e A I S C c o d e u s e s th e r a d iu s o f g y r at io n o f t h e s te e l s e c t io no n l y , t h is is li m i t e d t o 0 . 3 o f th e o v e r a l l s e c t i o n d i m e n s i o n [ 12 .2 ] w h i c h i st h e g o v e r n i n g c a s e f o r t h e m i n o r a x i s f o r t h e c u r r e n t e x a m p l e . A t a


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210 A. S. E lnashai, A. Y. EI-Ghazou li, P. J. D owlings l e n d e r n e s s o f 30 , th e A C I c o d e g i ve s a c a p a c i ty 4 8 % le ss t h a n A I S C a n da b o u t 4 1 % le ss t h a n E C 4 a n d B S 5 40 0.4 . 2 . 2 F a c t o r e d a x i a l c a p a c i tvF i g u r e 2 s h o w s t h e a x i a l c a p a c i t i e s g i v e n b y t h e d i f f e r e n t c o d e s , i n c l u d i n gt h e c a p a c i t y fa c t o r s in A C I a n d A I S C a n d t h e p a r ti a l sa f e ty f a c to r s in E C 4a n d B S 5 4 00 . T h e v a l u e s ar e n o r m a l i z e d b y t h a t o f t h e f a c t o r e d c a p a c i t y o fE C 4 . T h e s a m e g e n e r a l o b s e r v a t i o n s a re m a d e a s f o r t h e c a se o f f a c t o r e da x ia l c a p a c i t y , f o r a ll c o d e s b u t A C I . T h i s is a c o n s e q u e n c e o f t h ee q u i v a l e n c e o f t h e p a r t i a l s a f e ty f a c to r s u s e d b y E C 4 a n d t h e r e s i s t a n c ered u c t i o n f ac t o r u s ed i n AISC . In co n t r a s t , AC I cu rv e d ro p s s u b s t an t i a l l y ,a s a c o n s e q u e n c e o f t h e i n c lu s i o n o f a r e d u c t i o n f a c t o r o f 0 . 7 ( a s o p p o s e d t o0 . 8 5 f o r A I S C ) . T h i s s i t u a t i o n i s a g g r a v a t e d f o r h i g h e r s l e n d e r n e s s ,a d m i t t e d l y a b o v e t h e p r ac t ic a l l im i ts , w h e r e t h e d i s c r e p a n c y b e t w e e n A C 1a n d a ll t h e o t h e r c o d e s i s in t h e r a n g e o f 6 5 % .4 . 3 C o m b i n e d f l e x u re a n d a x ia l c o m p r e s s i o n4 .3 . l U n f a c t o r e d c a p a c i tyF i g u r e s 3 a n d 5 s h o w t h e u n f a c t o r e d m a j o r a n d m i n o r i n t e r a c t i o n c u r v e sf o r s h o r t c o l u m n s . Np a n d M p a r e t h e p l a s t i c c a p a c i t i e s c a l c u l a t e da c c o r d i n g t o E C 4 .

A C I c o n s i d e r s a f u l l i n t e r a c t i o n c u r v e c a l c u l a t e d f r o m c o n d i t i o n s o fe q u i l i b r i u m a n d c o m p a t i b i l i t y o f s t ra i n s w i t h a st r a in l i m i t i n c o n c r e t e o f0 - 3 % . O n t h e o t h e r h a n d , i n E C 4 t h e r e si s ta n c e m a y b e c a l c u l a t e d f r o mf ir st p r i n c i p l e s u s in g a p p r o p r i a t e s t r e s s - s t r a i n c u r v e s . A l t e r n a t i v e l y , t h eE u r o c o d e c o n s i d e r s a f u l l i n t e r a c t i o n c u r v e b u t w i t h f u l l p l a s t i c d i s t r i b u -t io n u s i n g r e c t a n g u l a r s t re s s b l o c k s , w h i c h le a d s t o a n o v e r e s t i m a t e o f th eu l t im a t e r e s is ta n c e . H o w e v e r , t h e m o m e n t c a p a c it y in E C 4 is a c c o m p a -n i e d b y a r e d u c t i o n o f 9 0 % o n t h e m o m e n t c a p a c it y [4 .8 .8 ] to a c c o u n t f o rt w o a s s u m p t i o n s : ( 1 ) u s e o f u n c r a c k e d s t if fn e s s f o r c o n c r e t e a n d ( 2) u s e o fr e c t a n g u l a r s t r e s s b l o c k s w i t h o u t d u e c o n s i d e r a t i o n t o c o n c r e t e s t r a i nr e s t r i c t i o n s .

F o r m a j o r a x is b e n d i n g a t z e ro a x i al f o r c e , E C 4 c o n v e r g e s to 0 . 9 in s t e a do f u n it y , b e c a u s e o f t h e a b o v e - m e n t i o n e d r e d u c t io n i n m o m e n t c a p ac i ty( w h i c h o v e r c o m p e n s a t e s f o r t h e p l a st ic d i s t r ib u t i o n i n th i s ca s e ). T h ec a p a c i t ie s o f B S 5 4 00 , A I S C a r e a l m o s t t h e s a m e ( a b o u t 9 8 % o f th e p l a s ti cc a p a c i t y o f E C 4 ) b e c a u s e b o t h c o d e s u s e p l a st ic d i s t ri b u t i o n f or d e t e r m i n -i n g th e p u r e b e n d i n g c a p a c i t y . I n th i s c a s e , t h e c a p a c i t i es o f B S 5 4 0 0 a n dA I S C a r e s i m i l a r t o t h a t g i v e n b y A C I b e c a u s e i n t h e m a j o r d i r e c t i o n a tt h is p o s i t i o n o f th e n e u t r a l a x is , m o s t o f t h e s t ee l w o u l d h a v e y i e l d e d , a n dh e n c e , t h e p l a s ti c d i s t ri b u t i o n d o e s n o t s ig n if ic a n tl y o v e r e s t i m a t e t h e


21/23

Design guidance for compo site columns 211s t r e n g t h . I t is a ls o o b v i o u s t h a t t h e d i f f e r e n c e i n c o n c r e t e s t r e n g t h is n o ts i g n i f i c a n t i n p u r e b e n d i n g i n t h e m a j o r a x i s d i r e c t i o n b e c a u s e t h e m a i nc o n t r i b u t i o n t o t h e s t r e n g t h is d u e t o t h e s t e e l s e c ti o n .

S i m i l a r ly , f o r m i n o r a x is b e n d i n g a t z e r o a x ia l f o r c e , E C 4 g i ve s a v a l u e o f0 -9 , a s a r e s u l t o f t h e r e d u c t i o n f a c t o r . H o w e v e r , o t h e r c o d e s s h o w s l ig h t lyl a r g e r d i f fe r e n c e s t h a n i n t h e m a j o r a x is c a se , a s th e c o n c r e t e s t r e n g t h a n dt h e u s e o f p l a s ti c d is t r ib u t i o n a s s u m e a m o r e p r o m i n e n t r o l e , b e c a u s e o ft h e g e o m e t r y o f th e c r o s s - s e c ti o n .

W i t h r e g a r d t o t h e s h a p e o f th e i n t e r a c t io n c u r v e , E C 4 is c o m p a r a b l e t oA C I b y v i r t u e o f t h e 9 0 % r e d u c t i o n , w h i c h c o m p e n s a t e s f o r t h eo v e r e s t i m a t i o n o f th e s t r e n g th . B S 54 00 a n d A I S C u s e a p p r o x i m a t ei n t e r a c t i o n c u r v e s w h i c h a r e v e r y s i m p l e t o c o n s t r u c t b u t w i t h s o m es a c r i f i c e o f s t r e n g t h . I n B S 5 4 0 0 n o a c c o u n t i s t a k e n o f t h e i n c r e a s i n gm o m e n t c a p a c i t y a t l o w a x ia l l o a d s b e c a u s e i ts a v a il a b il it y d e p e n d s o n t h el o a d i n g h i s t o r y o f t h e c o l u m n . O w i n g t o t h e u s e o f si m p l if ie d i n t e r a c t i o nc u r v e s , B S 5 4 0 0 g i ve s r e s i s ta n c e s 1 4 a n d 1 1 % l es s t h a n E C 4 f o r m a j o r a n dm i n o r a x is b e n d i n g , r e s p e c t i v e l y , F o r A I S C , t h is d r o p i n s tr e n g t h i s a s h i g h a s3 2 a n d 3 6 % , r e s p e c t i v e l y .4 .3 .2 Fa c to red ca p a c i t yT h e f a c t o r e d r e s is t an c e s f o r m a j o r a n d m i n o r a xis b e n d i n g w e r e c a l c u l a te df o r c o l u m n s o f s l e n d e r n e s s z e r o , 1 2, 20 a n d 3 0 . F i g u r e s 4 , 7 , 8 a n d 9 s h o wt h e i n t e r a c t i o n c u r v e s f o r m a j o r a x is b e n d i n g a t a s l e n d e r n e s s o f z e r o , 1 2,2 0 a n d 3 0 re s p e c t i v e l y , a n d F i g s 6 , 1 0, 1 1 a n d 1 2 s h o w t h e c o r r e s p o n d i n gc o m p a r i s o n s f o r m i n o r a x is b e n d in g . T h e m o m e n t m a g n i f ic a t io n u s e d i nA C I a n d A I S C w a s c o n s i d e r e d b y a n e q u i v a l e n t s t r e n g th r e d u c t i o n .

A t l o w l e v e l s o f c o m p r e s s i o n , t h e r e s i s t a n c e f a c to r s p e ci f ie d b y A C I m a yb e i n c r e a s e d l i n e a r ly t o r e a c h 0 - 9 a t z e r o a x i a l f o r c e [ 9 .3 .2 . 2] . F o r A I S C ,w h e n t h e a x ia l fo r c e is le s s t h a n 0 .3 o f t h e f a c t o r e d n o m i n a l a x i a l c a p a c i ty ,t h e n o m i n a l f l e x u r a l s t r e n g t h i s d e t e r m i n e d b y a s t r a i g h t - l i n e t r a n s i t i o nb e t w e e n t h e n o m i n a l f l e x u r a l s t r e n g t h d e t e r m i n e d f r o m t h e p l a s t i cd i s t r i b u t io n o n t h e c o m p o s i t e c r o s s - s ec t io n a t 0 . 3 , a n d t h e f l e x u ra l s t re n g t ha t z e r o a x i a l l o a d [ 14 ]. T h i s e x p l a i n s t h e t w o r e s i s t a n c e s t h a t a p p e a r i n t h ef i g u r e s a t l o w v a l u e s o f a x i a l f o r c e f o r A C I a n d A I S C . C o m p a r i s o nb e t w e e n t h e u n f a c t o r e d a n d f a c t o r e d r e s is t an c e s fo r m a j o r a n d m i n o r a x isa t z e r o s l e n d e r n e s s s h o w s t h a t t h e c a p a c i t y f ac t o r s a r e , i n g e n e r a l , m o r ec o n s e r v a t i v e ( e s p e c i a l l y t h e 0 - 7 f a c t o r g i v e n b y A C I , a s i t i s b a s e d o nr e i n f o r c e d c o n c r e t e d e s ig n ) .

F o r m a j o r a x is b e n d i n g , a t a s le n d e r n e s s o f z e r o , E C 4 a n d B S 5 40 0 a r eg e n e r a l l y in g o o d a g r e e m e n t , w h e r e a s B S 5 40 0 g iv e s v a l u e s w i th i n 5 %d i f fe r e n c e . A C I a n d A I S C g iv e v a l u es u p t o 2 0 a n d 3 2 % , r e s p e ct i ve l y , le sst h a n E C 4 , e x c e p t a t l o w v a l u e s o f a x ia l l oa d s a n d a t h i g h ax i al lo a d s w h e r e


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21 2 A. S. Elnashai, A. Y. El-Ghazouli, P. J. Dowling

the minimum eccentricities affect the resistance. At slendernesses of I2and 20 the methods of ACI and BS show a much bett er ag reemen t but areabout 25% less than EC4, whereas AI SC generally gives resistances up to36% less than EC4, except at very low and very high levels of compression .As the s lende rness increases to 30, the resistances given by EC4 and BS aresimilar within a discrepancy of 10%, whereas ACI and AISC are about33% less than EC4, except at extreme values of axial compression.

For mino r axis bending at zero slenderness, BS, ACI and AISC are up to9, 18 and 33% less than EC4 except at extreme values of axial force. Atslenderness of 12, ACI , BS and AISC show very good agr eem ent except atextreme values of normal force, but are up to 24% less than EC4. Atslenderness of 20 and 30 the agreement between AISC and BS is stillobserved and the discrepancy with EC4 decreases to a maximum of about12%. Also, ACI shows very low resistances of up to 40% less than EC4 atslenderness of 30 except at extreme values of axial forces, where thediscrepancy increases because of the minimum eccentricity require ment.This low resistance is due to the low value of stiffness, which is less thanhalf that given by ot her codes.

5 CONCLUSIONSLarge discrepancies between various design codes exist in terms ofphilosophy and geometric and strength parameters, even when the samedesign philosophy is adopted. The comparat ive study present ed in Section4 highlights the impact of code differences on safety of column design. Asshown in the figures, a design which conforms to one code may be morethan 60% unconservative according to a different code, notwithstandingthat both adopt the same general principles. This is particularly true forslenderness ratios other than the middle range. Based on the observationsabove, the case for rationalization of code provisions for compositecolumns cannot be overemphasized, so that a higher degree of uniformityin design for a given load, or capacity assessment for an existing design,may be achieved.

REFERENCES1. Building Code Requirements for Reinforced Concrete (ACI 318-83).

American Concrete Institute, Detroit, MI, 1983.2. BS 5400, Steel, Concrete and Composite Bridges, Part 5, Code of Practice forDesign of Composite Bridges. British Standards Institution, London, 1979.3. Eurocode 4, Composite Steel and Concrete Structures, First Draft, 1984.


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Design guidance fo r composite columns 2134. Roik, K. & Bergmann, R., DIN 18806 Part 1. In Introductory Document,Stability o f Metal Structures, A World View , Chapter 12, Compositemembers, Structural Stability Research Council, Bethleham, Pennsylvannia,

USA, 1989, pp. 12/38-12/44.5. Wakabayashi, M., AIJ Standards for Steel-Reinforced Concrete Structures.In Introductory Do cum ent, S tability o f Metal Structures, A World View ,Chapter 12, Composite members, Structural Stability Research Council,Bethleham, Pennsylvannia, USA, 1989, pp. 12/15-12/26.6. LRFD Specifications for the Design, Fabrication and Erection of StructuralSteel for Buildings. American Institute of Steel Construction, Chicago, IL,1986.7. Basu, A. K. & Sommerville, W., Derivation of formulae for the design ofrectangular composite columns. ICE Pro c ., 4 0 (1969) 37-60.8. Virdi, K. S. & Dowling, P. J., Derivation of design formulae for compositecolumns. CESLIC Rep. CC10, Imperial College, 1975.9. Bridge, R. Q., Ansourian, P., Rotter, J. M., Patrik, M. & Pham, L.,Australian Standards for Composite Construction, Engineering FoundationConference on Composite Construction in Steel and Concrete. Henniker,NH, 1987, pp. 71-83.10. Lapos, J. & Streleckij, N., East European Draft Recommendations. InIntroductory D ocum ent, Stability of M etal Structures, A World V iew, Chapter12, Composite Members, Structural Stability Research Council, Bethleham,Pennsylvannia, USA, 1989, pp. 12/9-12/13.11. Smith, D. G. E. & Johnson, R. P., Commentary on the 1985 Draft ofEurocode 4, Composite Steel and Concrete Structures. BRE Rep., 1986, pp.91-108.

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