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Analys is of lateral loadtransfer by internal s lab-c o l u m n j o i n t sDanie l N . Farhey , Dav id Z . Yanke levsky and Moshe A . Ad inFaculty of Civil Engineering and National Building Research Institute, Technion - IsraelInsti tute of Technology, H aifa - 32000, Israel(Received April 1991; revised version accepted December 1991)The resu l t s o f an ana ly t i ca l s tudy examin ing t he behav io r and loadt r a n s f e r m e c h a n i s m o f 1 6 i n t e ri o r f l a t s l a b - c o l u m n j o i n t m o d e ls ,t rans fe r r ing la te ra l l oad , a re p resen ted . P red ic t i ons o f t he connec t ionresponse were ca lcu la ted us ing a p ro fess iona l f i n i t e e lement com-pu te r p rogram, u t i l i z ing t h ree-d imens iona l , e las to -p las t i c , conc re tee l e m e n t s .Cu r r e n t l y , v a r i o u s a n a l y t i c a l m e t h o d s a r e s u g g e s t e d f o r c a l c u l a ti n gt h e l o a d t ra n s f e r . T h e y a s s u m e t h a t t h e s la b s e c t i o n s c a r r y t h e e x t e r -n a l u n b a l a n c e d m o m e n t b y d e v e l o p i n g a b e n d i n g m o m e n t o n t h e f r o n tand back f aces , and a t o rs iona l m om ent on the s ide faces . Severa ls tud ies have t ri ed t o de te rm ine t he re la t ive con t r ibu t ion o f t he b end ingand to rs iona l mom ents . S lo t s o r cu t t i ngs t h rou gh the s lab , made a longthe respec t i ve co lumn faces , were in t roduced in an a t t empt t o i so la tet h e c o m p o n e n t s t h a t r e s i s t t h e e x t e r n a l m o m e n t .A c c o r d i n g t o t h e p r e s e n t a n a l ys i s , t h e v a r i o u s ty p e s o f c o n n e c t i o n shave a m inor e f f ec t on t he response . They d isp lay ve ry s im i la r de fo r -mat ions and s t ress d i s t r i bu t ions in t he s lab , excep t f o r ve ry loca ls t r e s s c o n c e n t r a t i o n s , a l m o s t i g n o r i n g t h e s l o t s a n d c u t t i n g s . A s aresu l t o f t h i s ana lys i s , t he a t t empts t o i so la te appear t o be unsu i t ab les ince t he s lab 's bend ing and to rs iona l mechan isms a re h igh lyc o u p l e d .K e y w o r d s : b u i l d i n g s , s t r u c t u r a l a n a l y s i s ~ e a r t h q u a k e r e s i s t a n ts t r u c t u r e s , f l a t c o n c r e t e s l a b s , c o n n e c t i o n s

One of the significant steps taken towards the beginningof the twentieth century was the change from differentlysupported slabs to self-supported flat slabs. Today,towards the end of the century, one of the most widelyused construction methods for residential and otherbuildings is the structural system built of reinforced con-crete flat slabs. They are monolithically cast on columnheads, without beams on top of interior columns, butusually, according to codes, with edge beams on the cir-cumference.The architectural advantages and performance effi-ciency have accelerated the construction of flat slabssince the beginning of the century. However, we stillwitness structural failures. A structural frame, con-sisting of columns and fiat slabs, is prone to be injuredunder lateral and cyclic deformations, thus causing pro-gressive collapse. The presence of shear walls has notalways provided a guarantee against failure. Undersevere seismic excitation the flat slab-column frameshould carry the external unbalanced moment andtransfer the lateral force to the shear walls.Many studies on different flat slab -co lum n connec-tions have been carried out and, as a result, design codesof practice provide various simplified methods of12 C onca lcul at ion' . They omm ly supply empirical tools0141-0296 /92 /060379-16 1 9 9 2 B u t t e r w o r t h - H e in e r n an n L td

for the calculation of the ultimate load carrying capacityand represent the moment transfer mechanism of theconnection in completely different analytical models.The commonest methods are based on predeterminedyield line patterns 34, or equivalent beams framing thecolumn faces instead of the full slab -s or assumedlinear distribution of shear stresses on the slab aroundthe column 5. Nevertheless, significant uncertainties stillexist in the current methods of design simplification,which distract the designer from understanding the realbehaviour.Experimental studies were carried out 6 in an attemptto determine the resistance mechanism to an externalapplied moment, shared by: the bending moments in thefront and back faces of the column, and the torsionalmoments along the side faces. Furthermore, Kanoh andYoshizaki 7 performed tests on ' half' flat slab-c olu mnconnections, shown in F i g u r e 1 , claiming to transfer tor-sional moments only. In their tests, the external momentwas transferred to the slab exclusively through the sidefaces of the column. Their results, used by codes today,concluded that the torsional contribution is much largerthan it was believed to be. Nevertheless, crackingpatterns and the failure mode reported in their workclearly show that the slab also resisted in bending and

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s h e a r , s o t h a t t h e c o n t r i b u t i o n o f t h i s r e s is t a n c e c o m p o -n e n t s h o u l d n o t b e d i s r e g a r d e d . T h e r e i s a n e e d t oi n v e s t i g a t e t h e m e c h a n i s m o f l o a d t r a n s f e r b e t w e e n t h ec o l u m n a n d t h e s l a b , a n d t o s t u d y t h e p o s s i b i l i t y o f' i s o la t ing ' t he re s i s t ance comp onen t s an d ju s t i fy in g c l ea rd i s t i n c t i o n b e t w e e n t h e m b y m e a n s o f s l o t s a r o u n dt h e c o l u m n o r c u t t i n g s a l o n g t h e s l a b sN o t a t i o nDMAXMXVINC

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m a x i m u m d i s p l a c e m e n t i n l a t e r a l l o a d d i r e c -t i o n x, a t l o w e r e d g e o f c o l u m n ( l o a d i n g p o i n t )m a x i m u m v a l u e o n s t r e s s d i s t r i b u t i o n d i a g r a mv a l u e o f i n c r e m e n t b e t w e e n c o n s t a n t s t r e s sc o n t o u r l i n e sn o r m a l s t r e s s e s a l o n g l o a d d i r e c t i o n xn o r m a l s t r e s s e s i n t r a n s v e r s e d i r e c t i o n ys h e a r s t r e s s e s p e r p e n d i c u l a r t o p l a n e x y

O b j e c t i v e s a n d s c o p eT h e o b j e c t i v e o f t h i s i n v e s t i g a t i o n w a s t o a n a l y s e t h eb e h a v i o u r a n d l o a d t r a n s f e r m e c h a n i s m o f i n t e r i o r f i a ts l a b - c o l u m n c o n n e c t io n s , r e p r e se n t at i v e o f th o s e u se di n t y p ic a l fr e q u e n t s l a b - c o l u m n f r a m e d s t r u c tu r e s . T h es pec i f i c ob jec t ive s o f the inves t iga t ion we re : f i r s t ly tos t u d y t h e e f f e c t o f c o l u m n f a c e s l o t s o n t h e g e n e r a lr e s p o n s e o f t h e c o n n e c t i o n ; s e c o n d l y t o s t u d y t h e l o g i c

b e h i n d t h e b e a m a n a l o g y c o n c e p t a n d t h e e q u i v a l e n tw i d t h r e c o m m e n d a t i o n s ; a n d f i n a l l y t o s t u d y t h ei n f l u e n c e o f t h e c o n n e c t i o n t y p e b e t w e e n t h e c o l u m n a n dthe s l ab on the to t a l behav iou r .S i x te e n i n te r i o r f la t s l a b - c o l u m n j o i n t s y s te m s w e r em o d e l l e d u s i n g t h r e e - d i m e n s i o n a l c o n c r e t e f i n i t ee l e m e n t s . T h e m o d e l s w e r e s u b j e c t e d t o a s ta t ict r a n s v e r s e l o a d i n g o f u n i t y m a g n i t u d e . T h e m a i ni n v e s t i g a t io n v a r i a b l e s c o n s i d e r e d i n t h i s s t u d y w e r e t h el o c a t i o n , s i z e a n d o r i e n t a t i o n o f s l o t s c u t t h r o u g h t h es l a b , m a d e a l o n g r e s p e c t i v e c o l u m n f a c e s , th e w i d t h s o fe q u i v a l e n t b e a m s , a n d t o t al ' i s o l a t i o n ' c u t t i n g s a lo n g t h es l ab .

F la t s l a b - c o l u m n m o d e lsGeometric idealizationT h e c h o s e n p r o t o t y p e i s a p o p u l a r r e s i d e n c e b u i l d i n gwi th f i a t s l abs o f 15 cm (6 in ) th i cknes s , 4 m (157 . 5 in )s p a n i n e a c h d i r e c t i o n a n d 3 m ( 1 1 8 i n ) h i g h c o l u m n o f20 x 20 cm (8 x 8 in ) s qu a re s ec t ion , a s s ho wn inFigure 2.A q u a r t e r o f t h i s p r o t o t y p e s e r v e d a s a s p e c i m e n f o rt h e i n v e s ti g a t i o n . T h e f o l l o w i n g b o u n d a r y c o n d i t i o n sw e r e a s s i g n e d : s y m m e t r y c o n d i t i o n s a l o n g t h e lo n g i -t u d i n a l l o a d i n g a x i s a n d a n t i s y m m e t r y c o n d i t i o n s a l o n gt h e t r a n s v e r s e a x i s . T h e m o d e l s w e r e s u b j e c t e d t o as t at i c t r a n s v e r s e l o a d i n g o f u n i t y m a g n i t u d e , a c t i n gh o r i z o n t a l l y a t t h e l o w e r e n d o f t h e c o l u m n , r e p r e s e n t i n ga n o r m a l i z e d e q u i v a l e n t e a r t h q u a k e l o a d i n g .Material propertiesT h e c o n c r e t e t y p e w a s t h e c o m m o n B - 2 0 , w i t h a c u b es t r e n g th o f 2 0 M P a ( 2 8 4 4 . 7 p s i ) , a m o d u l u s o f e la s t i c it yo f 2 5 0 0 0 M P a ( 3 . 5 5 6 E 6 p s i ) a n d a P o i s s o n r a t i o o f1 /6 . T h e s t r e s s - s t r a i n d i a g r a m o f t h e c o n c r et e m a t e ri a lw a s i d e a l i z e d b y a m u l t i l i n e a r e la s t o - p la s t ic c u r v e , h a v -i n g a c r a c k i n g s t r e n g t h o f 1 . 7 M P a ( 2 4 1 . 8 p s i ) , a y i e l ds t r e n g t h o f 1 7 M P a ( 2 4 1 8 p s i ) a n d a n u l t i m a t e c r u s h i n gs t r e n g t h o f 2 0 M P a ( 2 8 4 4 . 7 p s i ), a s s h o w n i n Figure 3.Finite element modellingT h e m e s h l a y o u t u s e d i n t h i s s t u d y i s s h o w n i n Figure4 . T h e s m a l l e s t s l a b e l e m e n t s w e r e l o c a t e d a d j a c e n t t othe co lumn and were a 5 x 5 x 15 cm (2 x 2 x 6 in )c u b e . T h e s m a l l e s t c o l u m n e l e m e n t s w e r e l o c a t e d a d j a -cen t to the s lab and wer e a 5 x 5 x 10 cm (2 x 2 x 4 in)c u b e .T h e p r i m e f i n i t e e l e m e n t p r o g r a m c h o s e n f o r t h i ss t u dy w a s th e ' A N S Y S ' , v e r s i o n 4 . 2 B , w i t h S T I F - 6 5 ,t h r e e - d i m e n s i o n a l , s o l i d f i n it e e l e m e n t s h a v i n g c o n c r e t ec h a r a c t e r i s t i c s . T h e e l e m e n t i s d e f i n e d b y e i g h t n o d a lp o i n t s h a v i n g t h r e e d e g r e e s o f f r e e d o m a t e a c h n o d e w i t ht rans la t ions in the noda l x , y and z d i rec t ions . T he e l e -m e n t h a s 2 x 2 x 2 i n t e g r a t i o n p o i n t s . T h i s s t u d y d o e sn o t i n c l u d e t h e r e b a r c a p a b i l i ty f o r m o d e l l i n g r e i n f o r c e -m e n t b e h a v i o u r .R e s e a r c h m e t h o dT o a c h i e v e t h e a b o v e o b j e c t i v e s , t h r e e s e r i e s o f m o d e l s( I , I I , I I I ) we re de s igned fo r ana lys i s .

38 0 E ng. S t r uc t . 19 92 , V o l . 14 , N o 6

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Ana lys is o f la te ra l load t ransfe r : D. N. Farhey e t a l .2.Ore

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Figure 2 Fullspecimen or analysisSeries IThe f i r s t se r i e s was de s igned t o s t udy t he a t t empt s t oisola te the resistance cont r ibutors and the i r inf luence onthe overa l l respon se of the slab, by means of di f ferentco lumn face s lo t s .The ser ies (see Figure 5) inc luded f ive pr inc ipalmod e l s (A, B , C , D , E ) and fo ur add i ti ona l mo de l s (B 1 ,B2 , C1 , C2) wi th va r i a t i ons , i n t roduc ing s lo t s t h roughthe s l ab , hav ing d i f f e ren t d imens ions and made a longappropr i a t e co lumn faces .Mode l A i s a r egu l a r s l ab wi th symmet r i ca l bounda rycond i t i ons i n t he d i r ec t i on o f t he l oad ing ax i s , a l ong t hesec t ion t h roug h the co lumn, and an t i symmet r i ca l boun-da ry cond i t i ons i n t he pe rpend icu l a r d i r ec t ion , a long t hesec t i on t h rough the co lumn.Mode l B i s s im i l a r t o mode l A bu t i nc ludes a s l o t , o fze ro wid th , be tween the s l ab and t he co lumn face ,pe rpend icu l a r t o t he l oad ing d i r ec t i on . Mode l B1 i ssimi lar to model B but the slot i s 5 cm (2 in) wide . In

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StrainFigure 3 Stress-straindiagram o r concrete material

model B2 the slot i s 5 cm (2 in) wide as in model B1 buti t s length i s longer - - 40 cm (16 in) long, w hich i sdoub le t he co lumn d imens ion .Mode l s C , C1 and C2 a re s imi l a r t o B mode l s ,how eve r , t he s l o ts a re pa ra l l e l t o t he l oad ing ax is . Mo de lD has ze ro wid th s lo t s a long a l l t he co lumn faces and t heco lumn the re fo re r ema ins connec t ed a t t he four co rne r son ly t h rough the t h i ckness o f t he s lab . M ode l E i ss imi l a r t o mode l A, bu t i s d i sconnec t ed a t t he four co r -ners a long 5 cm (2 in) to each side . I t i s thereforeoppos i t e ly connec t ed fo r mode l D.Series HThe second se r i e s was de s igned t o s t udy t he behav iouro f d i f f e ren t equ iva l en t beam s com pared t o t he behav iouro f t he who le s l ab . The se r i e s ( see Figure 6) inc luded 3m o d e l s ( Q 1 , Q 2 , Y D ) .The f i r s t mode l (Q1) used 1 m (39 in ) wide equ iva l en tbeams , t he second mode l (Q2) had 40 cm (16 i n ) wideequivalent beams. The last model in th is ser ies , YD, i ssimi lar to QI , but wi th a t r iangular ly widening comerwhich b lun t s t he r i gh t ang l e and t he re fo re enab l e s asmooth t r ans fe r o f s t r e sse s .Series IIIThe th i rd se r i e s was de s ign ed t o s t udy t he poss ib i l i ty o fisola t ing the torsional resis tance or the bendingre s i s tance by co nnec t ing on ly o ne s ide f ace o f t he co l -umn to the slab. The ser ies (see Figure 7) inc luded 4m o d e l s ( Y 1 , Y 1 S , Y 2 , Y 3 ) .The f i rs t model (Y1) i s a ha l f -slab wi th a f ree edgea long the l oad ing ax i s . Mode l Y1S i s s im i l a r t o mode lY 1 bu t wi th s ymm et r i ca l bound a ry con d i t i ons a long t hecu t edge . Mode l Y2 i s s im i l a r t o mode l Y1 , bu t wi th5 x 5 x 5 cm (2 x 2 x 2 i n ) cube g rooves fo r fu r the risola t ion of the torsional s ide face . Mo del Y 3 is s imi larto model Y 1S, tho ugh rota ted by 90 for the respect iveconnec t ed f ace o f t he co lumn, t ry ing t o i so l a te t hebend ing re s i s t ance .

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Figure 4 V i e w a n d p l a n o f f i n i t e e l e m e n t m e s h l a y o u t o f s p e c i m e n q u a d r a n t

D e s c r i p t i o n o f r e s u l t sGen e r a lTh e predicted stress distribution diagrams on the botto mface of the slab were ox (normal stresses in lateral loaddirection x), o~ (normal str esses in transverse dire ction

y) , Z~,. (shear str esses perpendicular to plane xy ) . Th eydescribe the general behaviour and representqualitatively and quantitatively the bending in the tw oorthogonal d irections and the tors ion with shear, respec-tively In addition , the maximum value of each s tressdistribution diagram is also calculated and printed to itsright, denoted by MX. Th e va lu e o f th e in cremen t

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