226 This paper i s t h £ r e s u l t of d e l i b e r a t i o n s o f t h e S o c i e t y ' s d i s c u s s i o n g r o u p o n , S E I S M I C D E S I G N OF D U C T I L E M O M E N T RESISTING REINFORCED CONCRETE F R A M E S SECTION J D E S I G N OF B E A M - C O L U M N JOINTS R. W . G. B l a k e l e y * JO.O NOTATION ]Z 2 = A jh gross area of section, m m effective total area of horizontal joint shear reinforcement, m m 2 effective total area of vertical shear reinforcement, mm A s A = area of bottom beam forcement' at column joint 2 horizontal design joint shear force to b e r e s i s t e d by h o r i z o n t a l j o i n t shear reinforcement, N = capacity lesser area of column flexural reinf o r c e m e n t in t e n s i l e o r c o m p r e s s i v e face at joint, m m force nominal horizontal shear stress effective joint area, MPa reinforcement 2 A shear vertical design joint shear force to b e resisted by v e r t i c a l joint shear reinforcement, N flexural reinface, m m = area of top b e a m flexural at column f a c e , m m S 'sh total horizontal joint in z d i r e c t i o n , N J1.0 reduction factor = in 0.85 SCOPE 2 A * SC greater area of column flexural reinf o r c e m e n t in t e n s i l e or c o m p r e s s i v e face at joint, mm overall width effective of column, joint width, overall width of beam, mm mm mm J1L V V. f + V = specified concrete, c compressive MPa strength of specified yield strength of nonprestressed flexural reinforcement, ^yh yv MPa = s p e c i f i e d y i e l d s t r e n g t h of h o r i z o n t a l joint shear reinforcement, MPa = specified yield strength of vertical joint shear reinforcement, MPa = overall depth = overall depth of h o r i z o n t a l of beam, mm of c o l u m n in the d i r e c t i o n shear to b e c o n s i d e r e d , m m = design axial compression column load, including vertical prestressing force where applicable, occurring simultaneously with V j ^ , N = *ch force after all losses in p r e s t r e s s i n g steel passing through a joint within the central third of the beam d e p t h , N horizontal joint shear force resisted by concrete shear resisting mechanism only, N vertical joint shear force resisted by concrete shear resisting mechanism only, N 3V - | X total horizontal shear force across a j o i n t , N (= V . or V. ) ' 3X jz' total vertical shear force across a joint, N total horizontal joint shear force in x d i r e c t i o n , N Design Engineer, Ministry Development, Wellington. of Works and P r o v i s i o n s are made for the d e s i g n of b e a m - c o l u m n joints s u b j e c t e d to the forces imposed when a frame sustains inelastic lateral displacements under earthquake loading. Both o n e - w a y and t w o way frames are considered. D e s i g n for h o r i z o n t a l a n d v e r t i c a l s h e a r f o r c e s is required for b o t h p o s s i b l e c a s e s of p l a s t i c hinges forming in the b e a m or the column. Special concessions are m a d e for significant c o l u m n a x i a l l o a d s , for i n c l u s i o n of p r e s t r e s s i n g s t e e l , and for w h e r e m e m b e r s are designed so that plastic h i n g e s w i l l not form next to the joint. The objective o f t h e d e s i g n r e q u i r e m e n t s is t o m a k e t h e joint stronger than the c o i n c i d e n t h i n g i n g m e m b e r s , and therefore to avoid s i g n i f i c a n t inelastic b e h a v i o u r w i t h i n the joint c o r e . J2.0 DESIGN FORCES J2.1 The design shear forces acting on a beam-column joint should be evaluated from the m a x i m u m forces in all m e m b e r s c o i n c i d e n t at the joint at flexural o v e r - s t r e n g t h of the hinging member or m e m b e r s . At columns of t w o - w a y f r a m e s , w h e r e b e a m s f r a m e into the joint from two directions", t h e s e forces need only be c o n s i d e r e d in each d i r e c t i o n independently. J2.2 The m a g n i t u d e s of the d e s i g n horizontal shear force, jh* a n d t h e d e s i g n v e r t i c a l s h e a r f o r c e , V j ^ , in t h e j o i n t s h o u l d b e evaluated from a rational analysis taking into a c c o u n t the effects of all forces acting on the joint. J3.0 GENERAL REQUIREMENTS J3.1 For shear design of the joint the c a p a c i t y r e d u c t i o n f a c t o r , <j>, s h o u l d b e 0.85. J3.2 The nominal horizontal shear stress in the joint in e i t h e r p r i n c i p a l d i r e c t i o n , s h o u l d n o t e x c e e d 1.5/fr j ' V jh where v (J-D jh <j> b . 3 v h J3.3 The effective joint w i d t h , bj , should B U L L E T I N O F T H E N E W Z E A L A N D N A T I O N A L S O C I E T Y F O R E A R T H Q U A K E E N G I N E E R I N G , V O L . 10, N O . 4, D E C E M B E R 1977 227 be taken as: (a) where b_ > b , c w either b. = b 3 c or b. = b + 0. 5 h ~j w c whichever , . smaller. J is the or (b) where < b c w either b. = b 3 w or b b. = b 3 + 0.5h whichever c smaller. c J4.0 REINFORCEMENT J4.1 General is (c) When frame design precludes the formation of any beam plastic h i n g e s at the j o i n t , or w h e n all b e a m s at the joint are detailed so that the c r i t i c a l s e c t i o n o f t h e p l a s t i c h i n g e is l o c a t e d a t a d i s t a n c e of not less than the d e p t h of the m e m b e r or 500mm, w h i c h e v e r is g r e a t e r , away from the c o l u m n f a c e , or for e x t e r n a l joints w h e r e flexural s t e e l is a n c h o r e d o u t s i d e the column core in a s t u b in accordance with E4.4.4 c. N V (-J-5) (i + 0.6JLA rr) 2 ch K the e x c e p t that, w h e r e the axial c o l u m n load r e s u l t s in t e n s i l e s t r e s s e s o v e r t h e g r o s s concrete area, the value of V h should be linearly interpolated between the value g i v e n b y E q . (J-5) w i t h N taken as z e r o , and zero at an axial tensile stress of 0 . 2 f^. Thereafter the entire horizontal joint shear should be resisted by reinforcement . c u J4.1.1 A rational system should be provided to r e s i s t the h o r i z o n t a l and v e r t i c a l s h e a r forces induced in the joint. J4.1.2 The provisions of J4.2 and J4.3 apply to joints in w h i c h the shear r e i n f o r c e ment comprises horizontal and vertical stirrups or b a r s . T h e required horizontal and vertical joint shear reinforcement should be placed w i t h i n the effective- j o i n t w i d t h , d e f i n e d in J 3 . 3 , r e l e v a n t to e a c h d i r e c t i o n o f loading. J4.1.3 Special joint reinforcement details, such as d i a g o n a l b a r s b e n t across the j o i n t in one or b o t h d i r e c t i o n s , or o t h e r s p e c i a l d e v i c e s , m a y b e u s e d if it is s h o w n b y analysis and/or tests that the shear forces that may be induced during large inelastic deformations of the coincident beams are adequately transferred by an acceptable m e c h a n i s m and that anchorage of the flexural r e i n f o r c e m e n t a c r o s s t h e j o i n t is a s s u r e d . J4.2 Horizontal Joint Shear J4.2.1 The horizontal design shear force to b e resisted by the h o r i z o n t a l joint shear reinforcement should be V. V V (J-2) sh ch u where Vu is t h e a l l o w a b l e h o r i z o n t a l s h e a r carried by the concrete shear resisting mechanism. c J4 .2.2 The value to b e z e r o e x c e p t of V ^ in the should be following c assumed cases: (a) When the minimum average compressive stress on the gross area of the column above the joint, including prestress where a p p l i c a b l e , e x c e e d s 0.1 f^/Cj J4.2.3 The horizontal shear reinforcement s h o u l d b e c a p a b l e of c a r r y i n g t h e d e s i g n shear force to b e carried by the r e i n f o r c e ment, , across a corner-to-corner diagonal tension crack plane. The effective t o t a l area of h o r i z o n t a l r e i n f o r c e m e n t that c r o s s e s the c r i t i c a l f a i l u r e p l a n e , determined according to the o r i e n t a t i o n of the individual tie legs w i t h respect to t h i s failure p l a n e , and t h a t is w i t h i n the effective joint w i d t h , bj , should not be less than sh V L A n y tie leg b e t w e e n b e n d s a r o u n d c o l u m n bars that does not cross the p o t e n t i a l f a i l u r e p l a n e , or is s h o r t e r t h a n o n e third of the d i m e n s i o n of the c o l u m n in the appropriate plane of b e n d i n g , should be neglected. The required number of h o r i z o n t a l sets of stirrup ties or b a r s should b e placed between the outermost layers of the top and b o t t o m b e a m r e i n f o r c e m e n t , and s h o u l d b e d i s t r i b u t e d as u n i f o r m l y as is practicable. J4.3 Vertical ch = °- (b) When joint *ch + 2 5 0.7 beams £c> 25 are ^ j u C N A g __ c f 1 (bj c through the and J4.3.2 from The value sc A' sc (J-4) s The values of V E q . (J-4) m a y be c obtained added when n force shear to (J-7) (J-3) where P is the force after all losses in the p r e s t r e s s i n g s t e e l t h a t is l o c a t e d within the central third of the beam depth. c shear joint v A P. Shear where V is t h e a l l o w a b l e v e r t i c a l s h e a r carried by the concrete shear r e s i s t i n g mechanism. h ) 0 prestressed Joint J4.3.1 The vertical design be resisted by the vertical reinforcement should be V. V - V sv c V (J-6) yh f r o m E q . (J-3) applicable. of V c should v be determined V. j v 2 (1 + j 0.6 (J-8) C A f' g except (a) Where the axial column load results in t e n s i l e s t r e s s e s o v e r t h e g r o s s c o n c r e t e a r e a , the value of V should be linearly c v 228 interpolated between the value given by E q . (J-8) w i t h N taken as z e r o , and zero a t a n a x i a l t e n s i l e s t r e s s o f 0.2 f £ . Thereafter the entire vertical joint shear should b e resisted by reinforcement. C' ° = c o m p r e s s i o n force in the concrete in the flexural c o m p r e s s i o n zone of a b e a m C' = c o m p r e s s i o n f o r c e in t h e reinforcement of a b e a m and f* u s = overstrength of longitudinal f o r c e m e n t , g e n e r a l l y 1.25 f Y (b) W h e r e plastic hinges are expected to form in t h e c o l u m n a b o v e or b e l o w the j o i n t , as p a r t of the p r i m a r y seismic e n e r g y dissipating mechanism, V should be assumed to b e zero for any axial load. Grade 1 1 J4.3.3 The vertical joint shear reinforcement should consist of intermediate column b a r s , p l a c e d in the plane of b e n d i n g b e t w e e n c o r n e r bars, or vertical stirrup ties, or special v e r t i c a l b a r s p l a c e d in t h e c o l u m n a n d a d e q u a t e l y a n c h o r e d to t r a n s m i t the r e q u i r e d tensile forces within the joint. 1 ' n 1 c T Confinement The horizontal transverse confinement r e i n f o r c e m e n t in b e a m - c o l u m n joints should n o t be less than that required by H 6 . 1 , except for j o i n t s c o n n e c t i n g b e a m s a t all four c o l u m n faces that are n o t expected to form plastic h i n g e s or a r e d e s i g n e d a c c o r d i n g to J 4 . 2 . 2 ( b ) or ( c ) , in w h i c h case the t r a n s v e r s e joint r e i n f o r c e m e n t may be reduced to one half of t h a t r e q u i r e d in H 6 . 1 , b u t in no case s h o u l d t h e s t i r r u p t i e s p a c i n g in t h e j o i n t core exceed ten times t h e d i a m e t e r of the c o l u m n b a r or 150mm, w h i c h e v e r is l e s s . ECCENTRIC BEAM-COLUMN JOINTS J5.1 The eccentricity of any beam relative to the column into w h i c h it frames should not exceed t h a t p e r m i t t e d in E 4 . 1 , e x c e p t as allowed in J 5 . 2 ( b ) . J5.2 All joint design provisions section apply except that of this (a) In a d d i t i o n t o t h e e f f e c t i v e j o i n t width limits of J 3 . 3 , the following should apply; b ^ b w + b c + 0.25h - e (b) Where the eccentricity exceeds that p e r m i t t e d in E 4 . 1 , all of the required flexural steel in the column should be placed within the effective joint area, b j h . Additional longitudinal column reinforcement should b e placed outside of the effective joint area in accordance w i t h H 5 . 2 . c COMMENTARY CJO.O NOTATION = area of leg of tie set centre-to-centre = length of clear span of b e a m , measured face-to-face of supports = tension ,T P c yv J4 .3.5 T h e s p a c i n g of c o l u m n b a r s in e a c h plane of any beams framing into a joint should n o t exceed 200 m m , and in no case should there b e less than one intermediate bar in e a c h side of the c o l u m n in that p l a n e . - centre-to-centre 1 f p V J J5.0 n steel reinfor. M* Mi = flexural over-capacity of beam section at faces of a column shear joint V -^ J4.4 2 275 span of b e a m between of supports , 1 ' = height of column, ° of floors or roof T J4.3.4 T h e a r e a of v e r t i c a l j o i n t reinforcement within the effective w i d t h , bj , should not be less than = 1 l compression o 1 CJ1.0 force in t e n s i o n reinforcement = prestressing force at faces of c o l u m n a t f l e x u r a l c a p a c i t y of section = horizontal column shear force across a a SCOPE Severe c o n d i t i o n s o f shear and of a n c h o r a g e of f l e x u r a l r e i n f o r c e m e n t c a n a r i s e in joints. Inelastic b e h a v i o u r in the form of yield of shear r e i n f o r c e m e n t o r loss of bond to f l e x u r a l r e i n f o r c e m e n t c a n lead to rapid loss of strength under seismic conditions and i s , t h e r e f o r e , to b e a v o i d e d . CJ2.0 DESIGN FORCES C J 2 .1 In o r d e r t o p r o v i d e a d e q u a t e r e s e r v e s t r e n g t h w i t h i n a j o i n t , t h e f o r c e s in t h e coincident beams and columns m u s t be evaluated at flexural o v e r s t r e n g t h of the hinging members. Generally the hinging m e m b e r s w i l l be the b e a m s , e x c e p t in o n e or two-storey frames or at the top of c o l u m n s in m u l t i - s t o r e y f r a m e s w h e r e columns may b e designed to h i n g e . Where b e a m flexural r e i n f o r c e m e n t is detailed to force the p l a s t i c h i n g e to form away from the c o l u m n f a c e , the f o r c e s in the beam at the column face should b e determined for flexural o v e r s t r e n g t h at the critical section of the plastic h i n g e . A l l o w a n c e for o v e r s t r e n g t h of flexural r e i n f o r c e m e n t should b e as r e c o m m e n d e d in E4 . 4.5. P r o v i s i o n s for the c o n t r i b u t i o n of the slab r e i n f o r c e m e n t , w h e r e a p p l i c a b l e , should be not less than those recommended in E 4 . 4 . 2 . - B e c a u s e that c l a u s e r e p r e s e n t s a lower b o u n d of e f f e c t i v e s l a b steel for flexural design purposes, a greater contribution from the slab should be assumed appropriate to the u p p e r bound required for joint shear d e s i g n . The basis for d e s i g n of b e a m - c o l u m n joints in two-way f r a m e s , by c o n s i d e r a t i o n of forces acting in each principal direction i n d e p e n d e n t l y , is r e c e n t (1977) t e s t i n g at University of Canterbury. A joint designed on this b a s i s and e x t e n s i v e l y t e s t e d , including several major cycles of concurrent h i n g i n g of b e a m s in b o t h p r i n c i p a l d i r e c t i o n s , performed satisfactorily. W h i l e it m a y b e undesirable to b a s e d e s i g n p r o v i s i o n s on only one test, the complexity of such tests means that there is unlikely to be further t e s t i n f o r m a t i o n a v a i l a b l e in the foreseeable future. 229 W h e n s t i f f s t r u c t u r a l s y s t e m s , such as shear w a l l s , p r e v e n t yielding in beams or columns in one or both principal directions of the building, a rational analysis should b e u s e d to d e t e r m i n e t h e f o r c e s in t h e frame members at the maximum anticipated seismic loading. CJ2.2 The internal forces imposed on the j o i n t by f l e x u r e of m e m b e r s in o n e v e r t i c a l plane only at the connection are shown in Fig. C J 1 , for b o t h internal and e x t e r n a l beam-column joints. The concentrated t e n s i o n and c o m p r e s s i o n forces in b o t h beam a n d column, minus the much smaller v a l u e s of c o l u m n and b e a m s h e a r s , induce r e s u l t a n t s h e a r s t r e s s e s in the p a n e l z o n e . The horizontal shear force V j ^ across a g e n e r a l i n t e r n a l joint is V.. jh = T + C' + C + T c s p T (CJ-1) f p col For conventionally reinforced members without prestressing, to: concrete this simplifies internal s v f s y s • j o i n t s V., = A ' f * 3h s y col joints V . external K = A'f* + A -)h J col (CJ-2a) (CJ-2b) The value of the column shear, V o l , will depend on the column m o m e n t gradients above and b e l o w the joint. However, from Fig. CJ2 its v a l u e m a y b e estimated using a m e a n moment gradient, thus M* V (CJ-3) ^ M g ) / ( l 2 U col c ln 2n C c + 1 ) L A l t e r n a t i v e l y , the maximum horizontal joint shear m a y b e derived from the g r a d i e n t of the column m o m e n t diagram through the joint. W h e n necessary the value of the v e r t i c a l joint shear force, V j , may be derived from similar considerations to the above for horizontal joint shear force. Alternatively, the vertical joint shear force may be a p p r o x i m a t e d as follows: s h e a r in j o i n t s o f o n e - w a y f r a m e s b i s e c t s the joint along a diagonal from one beamcolumn edge to a n o t h e r ( 1 , 2 , 3 , 4 ) . Under cyclic loading, the diagonal tension cracks o p e n and close in e a c h d i r e c t i o n as the d i r e c t i o n of load a l t e r n a t e s . If t h e j o i n t r e i n f o r c e m e n t y i e l d s so t h a t the cracks become w i d e , relative shear displacements along the crack can lead to u n e v e n bearing followed by grinding o f the c o n c r e t e and g e n e r a l d e t e r i o r a t i o n of the joint. G e n e r a l l y t h i s w i l l n o t o c c u r if any y i e l d i n g is l i m i t e d to i s o l a t e d t i e legs. Shear transfer across the panel zone m a y b e i d e a l i s e d as d u e , in v a r y i n g p r o p o r tions , to four m e c h a n i s m s : diagonal strut action, truss action, aggregate interlock and d o w e l a c t i o n . Concrete compression forces tend to b e transferred d i r e c t l y by diagonal strut action. Although, theoretically, diagonal strut action requires no shear reinforcement, the diagonal compression force creates a splitting force perpendicular to it and r e i n f o r c i n g s t e e l is r e q u i r e d to c o n t r o l the w i d t h of the c r a c k s . Those forces induced in the p a n e l zone t h r o u g h bond to the reinforcing bars tend to b e transferred by a truss mechanism comprising a number of diagonal compression struts in the c o n c r e t e , p a r a l l e l to the p o t e n t i a l failure p l a n e , and t e n s i o n ties in the h o r i z o n t a l and v e r t i c a l s t e e l , as shown in F i g . C J 1 . Usually horizontal stirrup ties are provided to resist the h o r i z o n t a l forces but the vertical strut components m u s t be resisted by intermediate column bars, vertical stirrup ties or special vertical bars. Aggregate interlock may only be relied on where the cracks are n a r r o w and the b e a r i n g surfaces n o t w o r n . Dowel action of the ties across the diagonal tension cracks will only be s i g n i f i c a n t w h e r e the cracks are w i d e and t h e j o i n t is l i k e l y t o h a v e a l r e a d y deteriorated. v K V. * V., CJ3.0 ~ (CJ-4) GENERAL REQUIREMENTS CJ3.2 A n u p p e r limit for joint s h e a r s t r e s s is s p e c i f i e d to safeguard the core c o n c r e t e against excessive diagonal compressive stresses. The horizontal nominal stress corresponding to the c r i t i c a l h o r i z o n t a l shear f o r c e , V j ^ , is b a s e d o n t h e n o m i n a l g r o s s h o r i z o n t a l area of the joint bj h as d e f i n e d in J 3 . 3 . c CJ3.3 A l i m i t a t i o n is p l a c e d on the a r e a of a joint core which may be considered to b e e f f e c t i v e in r e s i s t i n g j o i n t s h e a r w h e n the beam or beams framing into a connection are considerably narrower than the column. The e f f e c t i v e joint w i d t h , b j , w h e r e b j is less than b i s i l l u s t r a t e d in F i g . C J 3 . W h e r e the b e a m is w i d e r than the c o l u m n , the effective joint width is assumed to spread b e y o n d the b o u n d s of the c o l u m n in a similar manner• c CJ4.0 CJ4.1.1 REINFORCEMENT The observed failure plane due to CJ4.1.3 Innovative details which encourage a m o r e direct transfer of forces across the panel zone, such as main b e a m or column steel bent diagonally across the joint or e n c o u r a g e m e n t of a r c h a c t i o n by use of m e c h a n i c a l anchors o n flexural steel at the extremities of the j o i n t ( 5 ) , appear attractive. Any arrangement which represents a major departure from previously used details should be tested before adoption. CJ4.2 Horizontal Joint Shear CJ4.2.1 The horizontal joint shear force is assumed t o b e t r a n s f e r r e d b e t w e e n the levels of the top and b o t t o m b e a m f l e x u r a l r e i n f o r c e m e n t by s t r u t a c t i o n in the concrete c o r e , V ^ , and by a truss mechanism, V h. The dependable shear capacity, u s i n g <j> = 0 . 8 5 , i s t h e n e q u a t e d t o t h e overstrength shear demand, Vjh. s CJ4.2.2 When plastic hinges form under reversed load in r e i n f o r c e d c o n c r e t e b e a m s immediately a d j a c e n t to the joint c o r e , wide cracks develop at the column face and m o m e n t tends to b e t r a n s f e r r e d by a steel couple. The major part or all of the internal c o m p r e s s i o n f o r c e in t h e b e a m s is then t r a n s f e r r e d to the j o i n t by the flexural reinforcement. Consequently it m u s t be assumed for this c o n d i t i o n , and 230 when column axial loads are low, that all the beam forces are transmitted by a truss m e c h a n i s m and = 0. Recent recommendations (°' a l l o w i n g t h e c o n c r e t e t o c a r r y s o m e s h e a r are n o t c o n s i d e r e d j u s t i f i e d in t h a t c a s e . V h is a s s u m e d to b e e f f e c t i v e following circumstances: c in the beams w h e r e w i d e cracking at the column face is a v o i d e d . Case studies of the c o n t r i b u t i o n of the c o n c r e t e s t r u t to shear transfer have been made based on a m o d e l s h e w n in F i g . C J 4 . The shear forces from the b e a m s and columns may be assumed as b e i n g t r a n s f e r r e d in the c o r r e s p o n d i n g compression zones only. V and V are the h o r i z o n t a l and vertical components of the d i a g o n a l thrust D that w i l l pass through the centre of the joint c o r e . The case studies have shown that approximately one half of the horizontal joint shear, Vjh, can b e t r a n s f e r r e d by t h e d i a g o n a l c o n c r e t e s t r u t w h e n t h e r e is zero a x i a l c o m p r e s s i o n on the c o l u m n and w h e r e there is e q u a l top and b o t t o m b e a m s t e e l . The proportion of joint shear resisted by the diagonal strut i n c r e a s e s w i t h i n c r e a s i n g axial load and d e c r e a s e s as t h e r a t i o of a r e a s of top and bottom beam steel increases. These trends a r e r e p r e s e n t e d i n E q . (J-5) a n d i l l u s t r a t e d in F i g . C J 5 . T h e i n t e n t i o n of E q . (J-5) is t h a t A is e q u a l to or g r e a t e r than A , which normally will mean that A is the area of top b e a m s t e e l and A the area of bottom beam steel. When columns are s u b j e c t e d to a x i a l t e n s i o n it is a s s u m e d that the shear resistance from diagonal strut action diminishes. When the axial tensile stress on the gross column section exceeds 0.2fc f u l l j o i n t s h e a r r e i n f o r c e m e n t is required. In e x t e r n a l b e a m - c o l u m n j o i n t s f a v o u r a b l e d i a g o n a l s t r u t a c t i o n is developed provided anchorage of flexural b a r s is a s s u r e d , p a r t i c u l a r l y w i t h u s e o f external stubs. Testing of such joints i n d i c a t e s t h a t E q . (J-5) r e p r e s e n t s s a t i s factorily the contribution of the concrete strut. c (a) With increasing axial loads on columns the internal column concrete c o m p r e s s i v e forces tend to increase, w i t h c o n s e q u e n t i n c r e a s e in the w i d t h of the d i a g o n a l compression strut. When axial compression e x c e e d s 0.1 f^ , s u f f i c i e n t b o n d t r a n s f e r from t h e f l e x u r a l r e i n f o r c e m e n t is a s s u m e d to occur within the strut region, even considering y i e l d p e n e t r a t i o n i n t o the j o i n t , to allow some of the beam bar forces to be transferred by this strut. E q . (J-3) i s s i m i l a r t o E q . (F.l) f o r members subject to flexure and axial load. On the basis of analyses and limited test d a t a ( 7 ) , t h i s e q u a t i o n is c o n s i d e r e d to underestimate the advantages of column axial load on joint shear s t r e n g t h and w i l l be reviewed w h e n further e v i d e n c e is a v a i l a b l e . T h e f a c t o r C j is i n t r o d u c e d t o a l l o c a t e the e f f e c t of axial c o m p r e s s i o n to the two p r i n c i p a l directions x and z of the e a r t h quake loading when joint shears V j and Vj are concurrently developed. The e f f e c t of t h i s p r o v i s i o n is t o p r e v e n t t h e a d v a n t a g e s of full a x i a l load b e i n g u t i l i s e d in each p r i n c i p a l d i r e c t i o n for the i n d e p e n d e n t shear design provisions of J 2 . 1 . For a s y m m e t r i c a l t w o - w a y frame Cj = 0.5; for a one-way frame Cj = 1.0. x z n c v s s s s (b) Prestressing within the central area of the b e a m h a s the e f f e c t of e n c o u r a g i n g joint concrete strut action and of restraining diagonal tension c r a c k i n g ( 2 , 3 ) However, prestressing steel near the extreme fibres of the section sustains p e r m a n e n t sets and loss of p r e s t r e s s after i n e l a s t i c b e a m h i n g e rotations . Thus, only the prestressing steel at the central third of the beam depth may b e c o n s i d e r e d for shear r e s i s t a n c e in the joint. It should b e r e c o g n i s e d t h a t where prestressed concrete beams support cast insitu floor slabs, the effective p r e s t r e s s is likely to b e d i s t r i b u t e d into the slab. The full p r o v i s i o n s should n o t be applied unless the p r e s t r e s s can be relied o n , for example w h e r e the floor s y s t e m is n o t r e s t r a i n e d to the b e a m . Where t h e f l o o r s l a b is m o n o l i t h i c w i t h t h e b e a m and t h e p r e s t r e s s is i n d e t e r m i n a t e , b o n d e d cables w i l l still serve a function of restraining diagonal tension joint cracks a n d h a l f t h e a l l o w a n c e o f E q . (J-4) m a y b e assumed. CJ4.2.3 Research on planar beam-column assemblies has shown that the c o r n e r - t o corner crack across the joint represents the critical failure p l a n e . Strain gauge r e a d i n g s o n t i e s in j o i n t c o r e s ( 1 , 2 , 3 , 4 ) have shown considerable scatter of strains w i t h i n any tie set and m o d e r a t e v a r i a t i o n of e f f e c t i v e n e s s o f d i f f e r e n t tie s e t s . In p a r t i c u l a r , t i e s e t s i n t h e c e n t r a l region of t h e core tend to be m o r e e f f e c t i v e than those near the top and bottom of the core. It has been shown(3) that yield of isolated tie legs need n o t lead to joint d i s i n t e g r a t i o n , and it is felt t h a t t h e n o r m a l c a p a c i t y r e d u c t i o n f a c t o r o f 0.85 allows s u f f i c i e n t account to b e taken of the variation of effectiveness of d i f f e r e n t tie sets. Because the contributions to shear s t r e n g t h of the joint f r o m c o l u m n a x i a l load and from b e a m prestress involve d i f f e r e n t mechanisms, the contributions toward V may be added. Stirrup ties should be placed adjacent to t h e t o p a n d b o t t o m b e a m f l e x u r a l r e i n forcement as in this position they are e f f e c t i v e in bond transfer from the flexural bars. U n i f o r m spacing of tie sets is consistent w i t h the desired uniform diagonal crack spacing. m c n (c) The advantages for shear d e s i g n w h e r e b e a m s a r e d e t a i l e d so t h a t p l a s t i c h i n g e s are forced to form away from the column face include the prevention of beam bar yield penetration with consequent loss of bond in the joint region, the increased c o n t r i b u t i o n of the c o n c r e t e strut to shear transfer, and the confinement effects of the In t h e c a s e of s t i r r u p t i e s o f d i a g o n a l shape in p l a n , the appropriate component of each tie leg c r o s s i n g the f a i l u r e p l a n e in the d i r e c t i o n of the joint s h e a r f o r c e should be considered. CJ4.3 Vertical Joint Shear CJ4.3.1 Vertical joint shear reinforcement is r e q u i r e d t o c o m p l e t e a t r u s s m e c h a n i s m capable of resisting diagonal compressive forces. The d e s i g n of such r e i n f o r c e m e n t may b e made u s i n g the same a p p r o a c h as that for t h e h o r i z o n t a l j o i n t s h e a r r e i n f o r c e m e n t . The vertical joint shear force may be approximated as suggested in Eq. (CJ-4}. CJ4.3.2 Generally columns will not yield when the flexural overstrength of the b e a m s , adjacent to the joint, is d e v e l o p e d . Therefore , the concentrated compression forces in t h e c o l u m n s m a y b e e x p e c t e d t o b e t r a n s ferred by direct concrete strut action. These forces also provide partial vertical restraint to the joint truss mechanism, thereby reducing the vertical joint steel requirements. Case studies indicate that V increases sharply with increasing axial load. c v Where V may be determined according t o E q . (J-5) a n d V may be determined a c c o r d i n g t o E q . { J - 8 ) , t h e n in c o m p u t i n g vertical steel c h c V V ( C J " ECCENTRIC BEAM-COLUMN JOINTS 231 When the axes of beams and columns are eccentric at a connection, secondary actions such as torsion w i l l b e generated. The behaviour of joints under the combined shear and torsion is m o r e c o m p l e x than t h o s e u n d e r s h e a r a l o n e and is a s y e t unresearched. Evidence from earthquakes shows that such joints are to b e avoided. Torsion introduced through such details caused heavy d a m a g e in b u i l d i n g s d u r i n g the Tokachioki e a r t h q u a k e . C J 5 . 2 ia) T h e e f f e c t o f t h i s e x t r a l i m i t on effective joint w i d t h , b j , is to follow the same assumption m a d e for e c c e n t r i c joints as shown in Fig. C J 3 , b u t to cover t h e c a s e of an e c c e n t r i c j o i n t w h e r e t h e face of the c o l u m n is c l o s e r t h a n 0 . 2 5 h to the side of the beam for b o t h poss ibilities of the beam b e i n g narrower or w i d e r than the column. c v c v = ch ITc CJ5.0 5 ) W h e r e f r a m e d e s i g n is o n the b a s i s of c o l u m n p l a s t i c h i n g i n g , for e x a m p l e in the c o l u m n s o f o n e of two-storey frames or in the top storey of a multi-storey b u i l d i n g , these provisions require that the vertical joint shear r e i n f o r c e m e n t be d e s i g n e d on the same b a s i s as t h e h o r i z o n t a l j o i n t shear r e i n f o r c e m e n t for h i n g i n g b e a m s . (b) In c i r c u m s t a n c e s w h e r e e c c e n t r i c i t i e s exceeding the limit of E 4 . 1 c a n n o t be a v o i d e d , all of the required c o l u m n flexural s t e e l as w e l l as all of t h e r e q u i r e d joint s h e a r s t e e l is to b e i n c l u d e d w i t h i n the ' effective joint area, b j h . Outside of this area additional column longitudinal reinforcement and transverse reinforcement for c o n f i n e m e n t w i l l b e r e q u i r e d . c REFERENCES CJ4.3.3 The simplest solution to p r o v i s i o n o f v e r t i c a l s h e a r r e i n f o r c e m e n t i s to u s e the existing column bars w i t h i n the joint core. The intermediate bars are not expected to be fully stressed by column flexure alone. If e x t r a b a r s a r e p l a c e d they need not extend over the full height of the column, but they need to be adequately a n c h o r e d in the c o l u m n above and b e l o w the joint. - CJ4.3.4 W h e n only four corner b a r s are required for the column flexural reinforcement, at least one intermediate vertical b a r m u s t b e p l a c e d in e a c h f a c e in e a c h plane of bending. For larger columns two or more intermediate vertical column bars, situated between corner bars, should pass through the joint with spacing not exceeding 200 m m . T h i s r e q u i r e m e n t is to allow t r u s s action consistent with uniformly spaced diagonal tension cracks. CJ4.4 1. 2. 3. 4. Confinement The diagonal compression stresses induced within the joint core may be very l a r g e and h e n c e e f f e c t i v e c o n f i n e m e n t is necessary. When plastic hinges could form in the b e a m s a d j a c e n t to the c o l u m n f a c e s , the m i n i m u m transverse reinforcement r e q u i r e d in t h e j o i n t is the same as the c o n f i n e m e n t r e i n f o r c e m e n t r e c o m m e n d e d for the c o l u m n ends immediately above or below the joint. However, in two-way frames when the b e a m p l a s t i c h i n g e s are forced to form away from the column faces, or where the column will hinge rather than the beams at a joint, the beam region adjacent to the c o l u m n is a s s u m e d to p r o v i d e a d e q u a t e transverse confinement. Consequently the c o n f i n i n g steel may b e reduced to one h a l f of that otherwise required. To safeguard column bars against buckling, particularly those at the corners of rectangular column sections which may be outside the joint c o r e , t h e tie spacing is l i m i t e d . 5. P a r k , R. a n d P a u l a y , T . , " B e h a v i o u r o f R e i n f o r c e d C o n c r e t e E x t e r n a l Beam--Column J o i n t s u n d e r C y c l i c L o a d i n g " , V o l . 1, Paper 88, Proceedings 5th W o r l d Conference on Earthquake Engineering, R o m e , 1973, pp 772-781. P a r k , R. a n d T h o m p s o n , K . J., "Progress Report on Cyclic Load Tests on Prestressed, Partially Prestressed and Reinforced Concrete Interior Beam-Column Assemblies", Bulletin of the N . Z . National Society f o r E a r t h q u a k e E n g i n e e r i n g , V o l . 8, N o . 1, M a r c h , 1 9 7 5 , p p 1 2 - 3 7 . B l a k e l e y , R . W . G . , E d m o n d s , F. D . , M e g g e t , L. M . , a n d P r i e s t l e y , M . J. N . , " P e r f o r m ance of Large Reinforced Concrete BeamColumn Joint Units Under Cyclic Loading", Proceedings 6th World Conference on Earthquake Engineering, New Delhi, January 1977, 6 pp. B l a k e l e y , R. W . G . , M e g g e t , L . M . a n d Priestley, M. J « N . , "Seismic Performance of Two Full Size R e i n f o r c e d C o n c r e t e Beam-Column Joint U n i t s " , Bulletin of the N . Z . National Society for Earthquake E n g i n e e r i n g , V o l . 8, N o . 1 , M a r c h , 1 9 7 5 , pp 38-69. F e n w i c k , R. C . and I r v i n e , H. M. , "Reinforced Concrete Beam-Column Joints for Seismic L o a d i n g " , B u l l e t i n of the N J . N a t i o n a l Society for E a r t h q u a k e Engineering, Vol. 10, No. 4, December 1977. 6. 7. ACI-ASCE Committee 352, "Recommendations for Design of B e a m - C o l u m n J o i n t s in Monolithic Reinforced Concrete Structures", A C I J o u r n a l , P r o c e e d i n g s V 6 9 , N o . 7, July 1976, pp 375-393. H a n s o n , N. W . , "Seismic R e s i s t a n c e of C o n c r e t e F r a m e s w i t h G r a d e 60 R e i n f o r c e m e n t , Journal of the Structural Division, A S C E , V o l . 97, S T 6, J u n e 1 9 7 1 , p p 1685-1700. Paper received 25 N o v e m b e r , 1977. 232 I I T" c c V" C's 7 7 7 " T \ V fv / - / f t V * r, V'" fc? cm T »' V'" T i t FORCES ON INTERNAL JOINT FORCES ON EXTERNAL JOINT Transfer of concrete compression forces STRUT ACTION Transfer of steel bond f o r c e s TRUSS F I G U R E C J 1 : B E A M - C O L U M N J O I N T FORCES A N D I D E A L I Z E D M E C H A N I S M S OF RESISTANCE. ACTION whichever is smaller C J 3 : EFFECTIVE JOINT A R E A FIGURE FIGURE C J 2 : F R A M E D I M E N S I O N S AT INTERNAL BEAM-COLUMN JOINT FIGURE 1 -0 reinforcement A 0-75 ' •. ' , " I s(o •. CO I |-. . 2 ('Cj Shear +0-25 CD V jh |v] Mi fa •.' ..X|.'-. 0-5CL Vjh (v) 0-50 • • • . • ' • • • • • • • • • • • • ^ 0-2E *S1 < f f V c n = D C O S oc V r v - D sin oc S2 < s 3 f Y f Y «f 0-75 X\X^^ Concrete strut NN^v ^^^^^^^^^^^^ Y Vch-tfco!*' v cv =D'sin«' C J 4 : M E C H A N I S M OF S H E A R T R A N S F E R BY A DIAGONAL S T R U T IN " E L A S T I C " BEAM-COLUMN J O I N T S "0-2 -0-1 Tension 0-1 0-2 0-3 CK Compression 0-5 0-6 ,1-00-7 C A t N g fc u FIGURE C J 5 : NOMINATED CONTRIBUTION OF DIAGONAL S T R U T ACTION TO V E R T I C A L AND HORIZONTAL J O I N T SHEAR R E S I S T A N C E £ go 234 ADDENDUM:WORKED EXAMPLES The following worked examples illustrate application of the provisons of this section to d e s i g n of b e a m - c o l u m n j o i n t s . The examples chosen are a conventional beamcolumn joint, designed to form plastic h i n g e s in t h e b e a m s a d j a c e n t to t h e j o i n t , w i t h a n d w i t h o u t c o l u m n a x i a l l o a d , a n d an "elastic" joint with beam plastic hinges designed to form the required distance away from the column face. D e t a i l s of all c o n c e n t r a t e d forces in the m e m b e r s h a v e b e e n s h o w n for i l l u s t r a t i o n . Only the c o n c e n t r a t e d b e a m forces and column shear need be calculated during routine design. In d e r i v a t i o n o f t h e d i a g o n a l s t r u t f o r c e , D, t h e a s s u m p t i o n h a s b e e n m a d e i n E x a m p l e s 1 and 2 t h a t t h e r e is a l i n e a r r a t e of c h a n g e o f s t r e s s in t h e f l e x u r a l r e i n f o r c e m e n t b e t w e e n the m a x i m u m tension and compression values at opposite column faces. Experimental e v i d e n c e s u p p o r t s this assumption at the stage of c y c l i c loading i l l u s t r a t e d in the example, before wide full-depth cracks have formed in the beams and there has b e e n yield penetration along the flexural reinforcement into the joint. The bond forces from the flexural reinforcement within the assumed bounds of the principal diagonal compression strut have b e e n taken as contributing to the p r i n c i p a l d i a g o n a l s t r u t f o r c e , D. In Example 3 the simplifying assumption has b e e n m a d e that the f l e x u r a l steel c o m p r e s s i v e f o r c e o n l y is a n c h o r e d w i t h i n t h e b o u n d s of the d i a g o n a l strut and contributes to that force. In all c a s e s it h a s b e e n assumed that beam and column shear forces are t r a n s f e r r e d in the r e s p e c t i v e m e m b e r compression zones only. T h e p r o c e d u r e i l l u s t r a t e d in E x a m p l e s 1 and 2 for t h e c a l c u l a t i o n of t h e m e a n e f f e c t i v e area of the tie sets w a s as f o l l o w s . L i n e s c o r r e s p o n d i n g to the i n t e r s e c t i o n of the plane of the corner-to-corner diagonal crack and the planes of each tie set w e r e projected on to the plan view of the column. T h e sum of the components of area of the tie l e g s , A ^ , c r o s s i n g the c r a c k in the d i r e c t i o n of the joint shear force has b e e n shown for each tie set. A mean effective area of all tie sets has then been calculated. A simpler but more conservative procedure would h a v e b e e n to n e g l e c t the legs of the rectangular tie not extending full depth in each s e t , and d i r e c t l y d e r i v e the m e a n e f f e c t i v e a r e a a s (4 + /2) A £ = 5.4 A £ . This p r o c e d u r e w a s f o l l o w e d i n E x a m p l e 3. 235 M :995kNm <^ CT°825kN 4 9 2 6 mm C 2 0.013 275, f* 30, 3 4 0 MPa f <* 4 5 MPa (^=1370 C<~ 3 8 0 8-D28 3 | F O 1256 M*=898kNn M* =1232kNm cr V =331kN b T=1256 Cs=^00 6-D28 o a -450mm BEAM o ' < CM t o CD %mK jjjh16-HD32 mi5 + ^ ^ + t; + ^ + S2 !£ <S i£j 4- It C o e (a) H o r i z o n t a l J o i n t Shear V.. = 1 2 5 6 + 1 6 7 4 825 2105 kN Jh 450 + 350 = 800 }> 700 mm J 2105/(0.85 x 700 x 700) = 5.05 MPa < 1.5/30 = 8.2 MPa V = 2105/0.85 - V s h Try 5 tie sets, A J h c h = 2476 kN ( V = 0 ) ch h _ 2476kN =-V ^H = |476kN s = 275MPa 9 0 Q ^ 4 " 9004. lt Jl 5 7 ^ 6 ' Use 5 sets R20 ( A = 3 1 4 m m ) h A = = 2 7 y m m 2 2 £ (b) Vertical v jv J o i n t Shear 2105x900/700 = 2706 kN Vjh b/ c s c J v (1 x A h h Cf 0.6A f< ) V u + g V 12868 mm ! 2 Pt 0.026 380 MPa 30 MPa = 1 x 2706/2 (1 + 0 ) = 1353 kN = 2706/0.85 - 1353 = 1830 kN AjV -700mm COLUMN THROUGH V /fy s v V 1830/380 = 4 8 1 6 m m 6 ^ HD32 (4825 m m ) O.K. 2 JOINT E X A M P L E 1: C O L U M N W I T H O U T AXIAL LOAD 2 236 M = 9 9 5 k N m ^j^'l Nu=U10kN (0-3fc Ag) A' s V |=825kN 4926 mnr = C 0 340 MPa 275, f* 30, f'^ c = 45 MPa Cc=137i C = 380 T = 494 s Mi=898kNm V = 331kN b T=1256 = 0.25 (1 +^)v'(0.3~0. 1 )30 (700x700) (J-3) = 660 kM u 2 5 1816 kN 1816 kN = 6604 m m Vj ^V v J h x h /h b c = 2105x900/700 = 2706 kN : 2029 kN 2029 = 1155 kN Ajv = V COLUMN THROUGH JOINT \ s v 6^HD /f y v =• 11.55/380 = 3039 m m 32 (4825 m m ) O.K. E X A M P L E 2 : C O L U M N W I T H A X I A L LOAD 2 2 2 237 Cj N C c =390 u =0 2510 m m s M=249kNm 2 0.0167 500 275 MPa f 30 MPa f c Cc = 4 7 6 C =2U -D20 S 500mm 8 ~D20 r> f =275MPa s when 350mm- at plastic d hinge BEAM f =340MPa s Horizontal J o i n t Shear 476 + 214 + 690 - 178 = 1202 kN 1202/(0.85x400x600) = 5.9 MPa 'jh < 1 .5 / f = 8.2 MPa c f\ A' ch c V.. 2 C.N 0.6 A f M s gc 1202 1 x - ^ r - (1 + 0) = 601 kN = 1202/0.85 - 6 0 1 = 813 kN sh sh |13kN 4 tie sets, Ajh 275MPa . yh 2956 185 m m 4x4 .-. Use 4 sets R16 ( A = 2 0 1 m m ) w = = 2 9 5 6 m m 2 f 2 2 £ Vertical J o i n t Shear V. = 390+110+500-89 = 911 kN (V..x b=1002) jv jh — . . . C.N c V = s c liv (1 + - L " ) A e sc 911 1 x V V= 8 9 k N s v A = 911/0.85 - 455 = 617 kN ., sv'V V s v (1 + 0) = 455 kN 617/380 1623 m m Use 6 * HD 20 (1884 m m ) 2 H = 178kN 6400 EXAMPLE 3: " E L A S T I C " BEAM-COLUMN JOINT 2