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Investigation of continuity in joints between precast and "cast in place" reinforced concrete members Kratz, Rolf D. 1970

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INVESTIGATION  OF CONTINUITY  IN J O I N T S BETWEEN PRECAST AND "CAST IN  PLACE"  REINFORCED CONCRETE MEMBERS by ROLF D. KRATZ B. Sc. ( C i v i l Engineering) University of Capetown Rep. of South A f r i c a , 1965  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of CIVIL ENGINEERING  We accept this thesis as conforming to the required  standard  The University of B r i t i s h Columbia  In  presenting  this  thesis  an a d v a n c e d d e g r e e the I  Library  further  for  agree  scholarly  by h i s of  shall  this  written  at  the U n i v e r s i t y  make i t  freely  that permission  for  It  fulfilment  of  of  Columbia,  British  available  by  gain  shall  copying  that  not  copying  CIVIL  ENGINEERING  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  Date  SEPTEMBER  1970  Columbia  of  I agree and this  or  for that  study. thesis or  publication  be a l l o w e d w i t h o u t  R.D.KRATZ  of  requirements  reference  permission.  Department  the  t h e Head o f my D e p a r t m e n t  is understood  financial  for  for extensive  p u r p o s e s may be g r a n t e d  representatives. thesis  in p a r t i a l  my  i .  ABSTRACT  The transfer  investigation  capacity  of a j o i n t  column and a c a s t - i n - p l a c e concrete  cast,  mechanisms, a s e r i e s ratios  frames. A l l  electronically computer  in  beam.  loads  the  recording  reinforced  two c o l u m n s and two in a s p e c i a l of  c o n s i s t i n g of  of  concrete  Four  pattern  and a x i a l  shear  forces  test  failure  different were  d a t a was  form o f punched t a p e  to  imposed done  facilitate  analysis. The  values  of  a general  of moments, shears  on t h e s e  concrete  a s s e m b l e d and t e s t e d  f r a m e . To o b t a i n  the  between a p r e c a s t  f r a m e s , each c o n s i s t i n g o f  b e a m s , were loading  dealt mainly with  investigation  of shear  most a d v e r s e  transfer  load  showed c l e a r l y  that  can be r e a c h e d even  conditions.  high  under  the  T A B L E OF C O N T E N T S  ABSTRACT T A B L E OF C O N T E N T S L I S T OF T A B L E S L I S T OF F I G U R E S L I S T OF P L A T E S L I S T OF S Y M B O L S 1.0  INTRODUCTION  1.1  PURPOSE  1.2 S Y N O P S I S OF P R E C E D I N G I N V E S T I G A T I O N S 1.3 S C O P E OF T E S T S 1.4 D E S C R I P T I O N OF T E S T  FRAMES  1.5 S P E C I M E N P R O P E R T I E S 2.0 A P P A R A T U S 2.1  LOADING  FRAME  2.2 L O A D AND D E F O R M A T I O N  MEASUREMENT  3.0 A P P L I E D T H E O R Y 3 . 1 M A T H E M A T I C A L R E P R E S E N T A T I O N OF C O N C R E T E STRESS-STRAIN  CURVE  3.2 R E I N F O R C E D C O N C R E T E T H E O R Y 4.0 T E S T P R O C E D U R E AND E V A L U A T I O N 4.1  D E S C R I P T I O N OF T E S T S  4.2 C O R R E L A T I O N AND D I S C U S S I O N OF T E S T R E S U L T S 4.3 C O N C L U S I O N  L I S T OF  REFERENCES  A P P E N D I X : S T R E S S - S T R A I N C U R V E S OF S T E E L T E S T P L O T S O F T H E O R E T I C A L AND M E A S U R E D STRESS-STRAIN  CURVES  SPECIMENS CONCRETE  LIST OF TABLES  Table I.  Tabulation of shear strength theories  Table II. Shear capacity of j o i n t Table III.Joint forces and displacements at fai1ure Table IV. Joint forces and displacements at critical  shear  LIST OF FIGURES  Fi g . 1 .  Shear c a p a c i t y  F i g . 2.  Reinforced  F i g . 3.  Loading  Fi g. 4.  Rotation measuring  F i g . 5.  Stress  Crack  F i g . 7a.  Left  7b. F i g . 8.  Right  the  concrete  joint  frame  16  and s t r a i n  device  20  d i s t r i b u t i o n by  function pattern  crack  24  of  Frame 3  pattern  of  crack pattern  Theoretical rotation  11 13  frame  stress F i g . 6.  of  35  Frame 4  of  Frame 4  37 37  b e n d i n g moment and beam  curves curves  41  F i g . 9.  Loading  for  F i g . 10.  SLIP-SHEAR  F i g . 11.  SLIP-MOMENT  F i g . 12.  ROTATION-MOMENT p l o t  F i g . 13.  Loading  F i g . 14.  SLIP-SHEAR  F i g . 15.  SLIP-MOMENT  F i g . 16.  ROTATION-MOMENT p l o t  F i g . 17.  Loading  F i g . 18.  SLIP-SHEAR  F i g . 19.  SLIP-MOMENT  F i g . 20.  ROTATION-MOMENT p l o t  plot  for  plot  curves  Frame 1  for  for  plot  for  plot plot  for  46  Frame 1  for  48 49  Frame 2  50  for  51  Frame 2  Frame 3  for  44 45  Frame 2  for  43  Frame 1  Frame 2  for  plot  curves  Frame 1  Frame 3  52 53  Frame 3  54  for  55  Frame 3  vi. Fig.21.  Loading curves  Fig.22.  SLIP-SHEAR p l o t  Fig.23.  SLIP-MOMENT  Fig.24. Fig.25.  for  plot  Frame 4  for for  57  Frame 4  58  Frame 4  59  ROTATION-MOMENT p l o t  for  60  MOMENT-SHEAR f a i l u r e  interaction  Frame 4 plot  64  VI  L I S T OF  Plate  1. F r a m e s e t u p  P l a t e 2. F r a m e s e t u p Plate  PLATES  17 (closeup)  3. D e t a i l o f h o r i z o n t a l  P l a t e 4„ R o t a t i o n P l a t e 5. T y p i c a l  17 loading  setup  19  measuring device crack  pattern  o f beam-column  19 joint  35  1  L I S T OF SYMBOLS  shear arm, i . e . distance of v e r t i c a l load from column face (inches) area of steel  in tension zone (square  area of steel  in compression  total area of web  inches)  zone (square  inches)  reinforcement within a distance  "s" measured in a direction parallel to the longitudinal reinforcement (square  inches)  width of the beam (inches) column width compression  force in concrete (kips)  compression  force in steel (kips)  effective  depth of flexural sections measured from  the compression steel  face to the centroid of the  (inches)  distance from the centroid of the reinforcement to the compression  compression face (inches)  distance from centroid of tension steel  to the  tension face of a flexural member (inches) modulus of e l a s t i c i t y of concrete (Ksi) modulus of e l a s t i c i t y of steel  (29,000Ksi)  concrete stress (psi) hoop stress due to transverse reinforcement compressive  strength of concrete (psi)  stress in tension steel (psi) stress in compression  steel (psi)  i x.  f  = ultimate stress strength  r e a c h e d by c o n c r e t e  = yield  strength  f't  = modulus  h  = height  H  = axial  tension  HL  = equal  horizontal  of of  of  = ratio  of  k  u  = ratio  the  extreme ki  = ratio  of  concrete  load a p p l i e d  axis  to  axis  axis  to c e n t e r  to b o t h  o f beam  sides  of  (ft.)  the  the  compressive  section fibre  " d " of a f l e x u r a l  section  yields  extreme  its  fibre  " d " of a f l e x u r a l  steel  depth  reaches  compressive  extreme  depth  between  concrete  compressive  " d " of  fibre  a flexural  ultimate  strain  section  in  the  fibre distances stress  between  resultant  and t h e n e u t r a l  M  = b e n d i n g moment a t  between  over which  axis  column f a c e s  the  column f a c e  the  the  compressive to  kd  (inches)  beam r o t a t i o n  b e n d i n g moment a t  = b e n d i n g moment a t yields  the  to  = distance  ^  between  distance  1  = ultimate  (psi)  extreme  depth  when t e n s i o n  = Span l e n g t h  u  the  to  L  M  (psi)  frame  between  distance  and n e u t r a l when  of concrete  concrete  point of  steel  i n beam ( k i p s )  distance  and n e u t r a l at the  reinforcing  column from b o t t o m p i n  and n e u t r a l ky  of  rupture  reinforcing = ratio  cylinder  test  f  k  during  i s measured (kip-inches)  column f a c e  = axial  compression  n  = modular r a t i o  for  in  (kip-inches)  column f a c e when t e n s i o n  (kip-inches)  N  column  steel  (inches)  (kips)  and c o n c r e t e  E„/E s c  steel  concentrated point  l o a d on beam ( k i p s )  steel  ratio  A /bd  steel  ratio  A' /bd  s  s  web r e i n f o r c i n g horizontal  steel  ratio  sway f o r c e  (A /bd) v  (kips)  spacing  o f web r e i n f o r c e m e n t  overall  depth  shear s t r e s s  of  reinforced  V/bd  (psi)  concrete  shear s t r e s s  ultimate  shear s t r e s s  ultimate section shear  total /  V  u  D d  (inches) concrete  c a r r i e d by c o n c r e t e  shear s t r e s s (P )  of  a reinforced  (kips)  shear force  c a r r i e d by t h e  concrete  i.e.  shear at f i r s t  shear  force  c a r r i e d by the  total  shear  force  section  unit  concrete  c a r r i e d by  used i n s h e a r  (kips) concrete  cracking  at u l t i m a t e  a reinforced  in  strain  o f e l e m e n t dx  concrete in  outer  compression  unit  strain  in  tension  unit  strain  in  compression  unit  strain  in  tension  fibre  steel steel  steel  at i t s  yield  (kips)  concrete  expression  compression force  strain  concrete  concrete  (kips)  coefficient concrete  (psi)  S 1  a t column f a c e  shear,  beam ( i n c h e s )  (psi)  force  critical  X d/s  point  xi.  e  cy  = unit strain in concrete at y i e l d point of tension steel  E c .u, = ultimate strain for concrete e  = unit concrete strain corresponding to maximum  0  concrete stress e  s u  = strain in tension steel at ultimate strength of the concrete  6p  = p l a s t i c rotation of a concrete section  6  = ultimate rotation of a concrete section  U  <|>  = capacity reduction factor  4>p  = p l a s t i c curvature of a concrete section  <j)  = ultimate curvature of a concrete section  <j)  = y i e l d curvature of a concrete section  u  v  ACKNOWLEDGEMENTS  The author expresses  his grateful appreciation  to Professor S. Lipson of the C i v i l  Engineering  Department, University of B r i t i s h Columbia, for his constructive c r i t i c i s m during the investigation and writing of this thesis. The thesis is based on tests carried out in the structural laboratory of the C i v i l  Engineering  Department and was made possible by grants from the National Research Council. The co-operation and advice of the technical s t a f f of the C i v i l ing  Department is greatly appreciated.  September 1970 Vancouver, B.C.  Engineer-  1.  1.0 1.1  INTRODUCTION  Purpose The  object  transfer  of t h i s  capacity  cast-in-place of s h e a r ,  investigation  of a j o i n t  concrete  beam s u b j e c t e d  of preceding  Shear t r a n s f e r  technology.  capacity  shear  column and a  to v a r i o u s  combinations  tension.  has been one o f t h e most w i d e l y  Various  investi-  i n the f i e l d o f r e i n f o r c e d expressions  have been p r o p o s e d and t h e s e  parameters.  of  investigations  g a t e d and d i s c u s s e d t o p i c s crete  between a p r e c a s t  b e n d i n g moments, and a x i a l  1.2 S y n o p s i s  was t h e s t u d y  Some o f t h e s e e x p r e s s i o n s  con-  for calculating involve  shear  different  are d i s c u s s e d  below  and t a b u l a t e d on page 8 . Washa ( 1 ) tal  and Badoux and H u l s b o s  s h e a r between  This  precast  beams and c a s t - i n - p l a c e  i s of a s i m i l a r nature  column i n t e r f a c e ; these experimental Hulsbos  used f o r r o u g h ,  to v e r t i c a l  therefore, results  proposed f u r t h e r  (2) d e a l w i t h  slabs.  s h e a r a t a beam-  the e x p r e s s i o n s  were o f i n t e r e s t .  that  horizon-  a different  derived  from  Badoux and  c o e f f i c i e n t be  i n t e r m e d i a t e , and smooth i n t e r f a c e  of  joint. Kriz  and R a t h s  development corbels.  (3)  of design  describe criteria  a project  for reinforced  As t h e s e a r e e s s e n t i a l l y  o f a/d r a t i o s  up t o 1 . 5 , t h e y  directed  fall  short  concrete  cantilever  within  towards  beams  t h e range o f t h e  2. t e s t s made i n t h i s e f f e c t of d i r e c t strength resulting P.W.  as was  i n v e s t i g a t i o n . Of s p e c i a l i n t e r e s t i s the  t e n s i l e l o a d "H"  on t h e s h e a r t r a n s f e r  c l e a r l y s h o w n by t h e t e s t r e s u l t s , a n d  i n c l u s i o n o f "H" a n d H.W.  i n t o the u l t i m a t e shear  B i r k e l a n d (4) and  i n v e s t i g a t e d the s h e a r  friction  R.F.  Mast  compression  s e c t i o n . The  finish  s h o w n by t h e f o r m e r , w h i l e shear expressions  across  (rough  the  or smooth)  the l a t t e r f u r t h e r d e v e l o p e d  f i t t e d to experimental  K r e f e l d and T h u r s t o n of l o n g i t u d i n a l steel  (6,2)  the  expressions  data.  resistance of a simply  r e s i s t a n c e i s i n the form  d o w e l a c t i o n o f t h e s t e e l . D i s t i n c t i o n was stirrups.  I t was  found  of  made b e t w e e n  that in cases  cases without  s t i r r u p s the dowel a c t i o n r e s u l t e d i n t e n s i l e s p l i t t i n g t h e c o n c r e t e a l o n g t h e l o n g i t u d i n a l s t e e l . The stirrups  provides  forces which r e s t r i c t  p r o p a g a t i o n . The  f o r m e d and  thus  the r e l a t i v e  used  zone a f t e r  r e t a r d s the  f i t t e d to t h e i r r e s u l t s . Since  e x p r e s s i o n s were d e r i v e d f o r s i m p l y o f them w i l l  dis-  crack  d e r i v e d s h e a r e x p r e s s i o n s w e r e b a s e d on  above c o n c l u s i o n s and  supported  the  the  beams, p a r t s  not apply to a beam-column j o i n t which  in this i n v e s t i g a t i o n .  of  a d d i t i o n of  placement of the segments i n a d i a g o n a l l y c r a c k e d t h e i n c l i n e d c r a c k has  was  i n v e s t i g a t e d the c o n t r i b u t i o n  to the shear  beam. T h i s s h e a r  w i t h and w i t h o u t  (5)  to i n c l u d e j o i n t t e n s i o n . These  are s t r a i g h t l i n e s  supported  expression.  h y p o t h e s i s ; t h a t i s , the  increase of shear strength with influence of joint  the  was  3.  Hanson and Connor (8) performed c a s t frame which i n c l u d e d a j o i n t investigation. being repeated Special  t e s t s on a m o n o l i t h i c a l l y  similar to that i n this  The type o f l o a d i n g i s o f a n o t h e r loading to determine  seismic resistance.  a t t e n t i o n was g i v e n t o c o n f i n e m e n t  hoops o r s p i r a l s  determine was  o f c o n c r e t e by  and t o s p l i c e s a t the c r i t i c a l  shear and d e s i g n e x p r e s s i o n s were taken and E a r t h q u a k e  Manual.  Although  nature,  sections.  o u t o f t h e ACI code  an a t t e m p t  w a s n o t made t o  the q u a n t i t a t i v e e f f e c t o f j o i n t confinement, i t  established that the tests with confined joints  s t r o n g e r and more  to study shear  a n d M a t t o c k (9) p r e s e n t a t e s t s e r i e s  transfer in reinforced concrete.  The s t r e s s  s t a t e i n a l l t e s t s was c o n s t a n t ; t h a t i s , c o n s t a n t s t r e s s and near c o n s t a n t Although  Zia Envelope practical  shear s t r e s s across the j o i n t .  hypothesis  and very good agreement with t h e  t o Mohr C i r c l e s , no a t t e m p t  case with  was m a d e a t a m o r e  varying stresses across the joint.  f o l l o w i n g c o n c l u s i o n s were  reduce  axial  t h e i r t e s t r e s u l t s show c l o s e a g r e e m e n t w i t h t h e  friction  1)  proved  ductile.  Hofbeck, Ibrahim  shear  The  presented:  a p r e - e x i s t i n g crack along ultimate shear  The  the shear plane w i l l  t r a n s f e r and increase s l i p  both  at a l l  levels of loading. 2) S h e a r t r a n s f e r s t r e n g t h i s a f u n c t i o n o f " p f ". 3) plane  Dowel a c t i o n o f r e i n f o r c i n g b a r s a c r o s s t h e s h e a r  is insignificant  in initially  but i s s u b s t a n t i a l i n concrete with  uncracked  concrete,  a p r e - e x i s t i n g crack  along  4. the shear  plane.  4) S h e a r - f r i c t i o n t h e o r y g i v e s a r e a s o n a b l y estimate pf  y  of shear  conservative  t r a n s f e r i f t a n <f> = 1 . 4 , p r o v i d e d  < 15f' or < 600psi. c 5) T h e Z i a F a i l u r e E n v e l o p e  c l o s e l y agrees  with  observed  fai1ures. Smith  (10) presents  research centres. depending  a summary o f t e s t s made b y known  He d i v i d e s s h e a r  tension failure  Shear  compression  Shear  proper  failure  failure  For a/d>2.4, t h e P a d u a r t  curves  f o r 1.0<a/d<2.4  equation  corresponds  to Shear  Compression  The m a t t e r  i s a p p l i c a b l e ; while f o r  is applicable.  The Laupa and  to the transition  depending  from  Diagonal  failure.  of confinement  of concrete  in the joint  zone  i n f l u e n c e t h e f a i l u r e m e c h a n i s m c o n s i d e r a b l y as  demonstrated  b y N e w m a r k ( 1 1 ) . He s t a t e s :  " I t i s seen the c o n c r e t e For a l a t e r a l  t h a t both  19,000psi  the s t r e n g t h and d u c t i l i t y o f  i n c r e a s e s as t h e l a t e r a l pressure  at a strain  i s increased. (unconfined  a t t a i n s a maximum s t r e s s o f  o f 0.05, the l a t t e r value being  t i m e s w h a t w o u l d be e x p e c t e d  maximum s t r e s s . "  pressure  o f 4,090psi , the concrete  c y l i n d e r s t r e n g t h 3,660psi)  25  f o r a/d>2.4  intersect in a series of points  on " p " , w h i c h  can  groups  f o r a/d<1.0  a/d<2.4, t h e Laupa e q u a t i o n  Shear  into three  on a / d r a t i o a s f o l l o w s :  Diagonal  Paduart  failure  f o r unconfined  about  concrete at  5. For the c o n f i n e d concrete t h e f o l l o w i n g e x p r e s s i o n was . = 0.85f' +  a a  4  core o f a r e c t a n g u l a r column derived:  *  v y  1 A  f  s(d-d')  c  Newmark a l s o d e v e l o p e d  an e x p r e s s i o n  f o r shear  strength  of a r e i n f o r c e d concrete s e c t i o n s u b j e c t e d to a t e n s i l e force  "H". The  in shear T.C. analysis  ACI (318-63) s t a n d a r d s  Zsutty (13) a p p l i e d the techniques and s t a t i s t i c a l  By  he s h o w s t h a t t h e v a l u e o f  i s t h e t r a n s i t i o n b e t w e e n beam a c t i o n a n d a r c h The s m a l l p e r c e n t a g e  c r a c k i n g and u l t i m a t e Burton,  e r r o r shows t h e good f i t o f were d e r i v e d both f o r  load.  C o r l e y and Hognestad  to evaluate the shrinkage  (14) developed  forces developed  of a m u l t i - s t o r y r e i n f o r c e d concrete showed the i n c r e a s e o f s h r i n k a g e  frame.  Combined with Mattock's  expressions members  The t e s t s by  partially  interval.  r e p o r t (15) regarding the  i n f l u e n c e o f s h a p e f a c t o r on t h e s h r i n k a g e from  i n beam  forces developed  f u l l y - r e s t r a i n e d beams o v e r a t i m e  recorded  of dimensional  at major research centres.  the r e s u l t i n g e x p r e s s i o n s which  and  used  r e g r e s s i o n a n a l y s i s t o data of  the method o f l e a s t squares  action.  t o be  transfer calculations(12).  beam-shear t e s t s performed  a/d=2.5  show e x p r e s s i o n s  a n d c r e e p as  r e i n f o r c e d c o n c r e t e t e s t beams, t h e above  6. i n f o r m a t i o n p r o v i d e d a means t o d e t e r m i n e which  the t e n s i l e  force  was a p p l i e d t o t h e t e s t b e a m s i n t h i s i n v e s t i g a t i o n . Cohen (16) d e v e l o p e d  a series of rotation expressions  f o r r e i n f o r c e d c o n c r e t e members i n t h e p l a s t i c r a n g e .  Some  of these e x p r e s s i o n s were a p p l i e d i n the e v a l u a t i o n o f limiting  conditions. 6  These are given  = plastic rotation = P  p  0 o  below:  <j> dx P  *p * u • *y d>u = e c u /k u d d*>y = e c y /k u d =  Where:  Y  For c o n s t a n t s t r e s s c o n d i t i o n s over the p l a s t i c e„u = $u 1 = ec_u„ l / k u d  ... 1.2-1  T  y V cy y "1" i s the d i s t a n c e over which e  Where: The Curves  =  =  "Ultimate  e  1 / k  zone:  d  ...1.2-2 r o t a t i o n i s measured.  F l e x u r a l A n a l y s i s Based  o f C y l i n d e r s " by Y o u n g a n d S m i t h  On S t r e s s - S t r a i n  (17) proved  useful  in the t h e o r e t i c a l c o r r e l a t i o n and e v a l u a t i o n o f concrete strength tests performed o f t h e same b a t c h  on a n u m b e r o f c o n c r e t e c y l i n d e r s  as t h e t e s t beams.  T a b l e I shows a summary o f t h e s h e a r t r a n s f e r e x p r e s s i o n s as d e r i v e d b y t h e a b o v e m e n t i o n e d Table  authors.  II shows t h e s e e x p r e s s i o n s  as a p p l i e d t o t h e j o i n t  t e s t e d i n t h i s i n v e s t i g a t i o n . F i g u r e 1 shows a p l o t o f t h e s e expressions.  The widest  v a r i a t i o n was f o u n d  f o r low a/d r a t i o s ,  7.  while towards the generally accepted transition point of a/d=2.5 the agreement was better.  8.  INVESTIGATOR' ULTIMATE SHEAR EXPRESSION SAEMANN and WASH A  v  c u  33-a/d  = 2700+30,000p  (a/d)  a/d+5 3500  BADOUX and HULSBOS y  c u  =  2  0  0  rough  c u  (1000p)^ 1 0  '  1 / 3 + Q  4 H  d / a  )  *  /V)!i  ^s<.013, bd  .8H/V  u  bd  v =[ pTd.a+d/d'j + is.ooop] c  fiTd  +  P (M/Vd)  v =v + i i l r f u  cu  2  6  V  l i m i t e d by:  V cu u cu v  cu  A ^0.5A<  v  d' /d  v =1.8fF;  0  =v  for  Q  v =v  u cu  x  for  y  f  +  o  r  v  c u  = <j)[1.9ff ^ + ** 2500pVd ww Q f T  V  V  M-N(4t-d)/8 v  u cu =v  +  M/Vd<l,  <*>y  Table  I  TABULATION OF SHEAR STRENGTH THEORIES  y  f  <  3  °  y  30<rf <90 y  + rf y 90<rf„  1  rf  r  l-5rf -44  tr ACI(318-1963) HANSON and CONNOR  finish  tan $=0.7 to 1 . 4 according to j o i n t roughness  =  y  finish  r e s t r i c t i o n s on reinforcement:  c u ( A f - H ) t a n 4> s  =3000psi  intermediate  20,000p  +  0  f'  +6a/d+5  + 20,000p  v =.85[6.5fFjl-0.5  v  for  <j)=l  INVESTIGATOR  ULTIMATE SHEAR E X P R E S S I O N  SMITH  v = 1 . 9 f F ^ ( l + 750p)  REMARKS for  x  c u  a/d>2.4  [0.186+.00157(9-a/d) ] 2  v = 1 . 9 Vf  1  cu  NEWMARK  T  c u  v  u  c  = v  c r  cu  +  =59(f  c  v =63.4(f c u  c  , c  J  y  r f  l<a/d<2.4  ( Y'lOOp-iypJd/a  v =(l-H/8A \/f ~ )1.9Vf v  ZSUTTY  c  pd/a) c  1 / 3  pd/a)  1 / 3  Table I (continued)  10,  INVESTIGATOR  M=112.5K i n a/d=0.5  M=225K i n a/d=l  SAEMANN a n d WAS HA BADOUX a n d HULSBOS  M=450 a/d=2 17+27=44  14+12=26  13+12=25  12+12=24  8+12=20  7.5+12=19.5  7+12=19  4.4+3.1=7.5  3.1+2.2=5.3  2.2+1.6=3.8  4.5+3.2=7.7  4 . 5 + 1 . 6 = 6. 1  4.5+0.8=5.3  7.7+33=40.7  6.1+33=39.1  5.3+33=38.3  4.8+2.9=7.7  4.8+1.4=6.2  4.8+0.7=5.5  7.7+33=40.7  6.2+33=39.2  5.5+33=38.5  SMITH  9.0  4.5  2.25  NEWMARK  2.9  2.9  2.9  2.9+33=35.9  2.9+33=35.9  2.9+33=35.9  11.5  9.1  7.2  12.4  9.8  7.8  KRIZ and RATHS BIRKELAND BIRKELAN D a n d MAST KREFELD and THURSTON  ACI(318-1963) HANSON a n d CONNOR  ZSUTTY  Table II S H E A R C A P A C I T Y OF J O I N T  c u  c u  c u c u  c r c u  0.5  1.0  1.5  a/d r a t i o  .1 S h e a r c a p a c i t y o f the  joint  2.0  12. 1 . 3 Scope o f The of  tests  investigation  three-pinned  c o n s i s t e d of failure axial  reinforced  The o n l y  arrangement  having  difference  of  the second h a v i n g  l e n g t h s were a d e q u a t e The  tests  were  a p p l i e d to 1)  2)  joint  in  symmetrical  to  tension  Figure concrete The interface  and  two  groups the  reinforcement,  and  reinforcement  at  anchorage  failure. the  following  in  restrict  test  the  failure  limita-  to  the shear  joint.  i n d u c e d was t o s i m u l a t e  shrinkage  r e s t r a i n e d members.  the o t h e r w i s e  1.4 D e s c r i p t i o n  loads  t o be s m a l l e r t h a n  sway was a p p l i e d to p r o d u c e  conditions  to  loading:  developed  3)  loaded  -  c a s e s l a p and  performed w i t h i n  a t the b e a m - c o l u m n the  the  groups  group  reinforcement  to p r e v e n t bond  u l t i m a t e moment i n o r d e r  forces  both  t h e maximum moments were  failures  between  longitudinal  In  two  f r a m e s . Each  lapped l o n g i t u d i n a l  the beam-column j o i n t .  of  l o a d s , sway  longitudinal  continuous  testing  f r a m e s w h i c h were  by a c o m b i n a t i o n o f p o i n t  was t h e  tions  the  concrete  two i d e n t i c a l  loads.  first  involved  different  identical  failure  two j o i n t s  of  the  frames. of  test  2 shows  frames  one h a l f  section  of the  reinforced  frame. columns were against  was c a s t s i x  weeks  cast f i r s t  steel later  with  the s i d e  of  joint-  f o r m s . The w e a k e r beam c o n c r e t e against  t h e smooth column  surface  13.  f  2 -6  4# 10 threaded bar 2 # | 0 threaded bar 2#5  Pi 2*3  #3 ties at 2 ^  lap  b  T %  bars in frames 3^4 only  #3 ties at 4 ' %  -4#8  f  ~ 4 # l " threded  bar  "T CD  Fig.2 R e i n f o r c e d  concrete  6  frame  to  represent  columns  actual  and c a s t - i n - p l a c e  longitudinal Figure  construction  steel  2 . The  18 i n .  lap  for  was  beams.  lengths  Three of  were the  concrete,  and 12 i n .  frame s i x  were  and t h e o t h e r The  the  frame t e s t  measurements were developed  stress-strain steel  curves  readings  loaded to  taken are  in  the  were  code  direct  shown  of the crushed  failure  in the  as t h e  Stress  and  Appendix.  the  The  strain  the  theory  represented  Several  tension.  as  on the same day as  to a i d w i t h  A.  test  column  same b a t c h  the #5 and #3 s t e e l  in  were:  compression.  same b a t c h  the A p p e n d i x  failure  in  diameter concrete  3 . 1 and 3 . 2 . These a r e in  lines  the  #3 b a r s  was p e r f o r m e d .  t a k e n up t o  specimens of both  beams were  of  cylinders  in sections  precast  two f r a m e s  dotted  t o ACI  four-inch  t h r e e were  beam c o n c r e t e .  last in  for  between  Properties  l o a d e d to f a i l u r e  cylinders  respective  the  according  1 . 5 Measurement o f S p e c i m e n  cylinders  In  l a p p e d as shown  #5 b a r s  For e a c h t e s t  conditions  as  reinforcing  used i n  the  stress-strain  2.0 APPARATUS 2.1  Loading  frame  Figure  3, plate  1 and p l a t e  Three h y d r a u l i c load connections  2 show t h e  load c y l i n d e r s  between  the  loading  provided  loading  the  frame.  required  frame and t h e  test  frame. The  two h o r i z o n t a l  frame i n nected  l i n e with  t o t h e ends  and b a l l load,  the  joints,  as shown The  of the  to  side  after  shutting  test  insure  on p l a t e  off in  the  The  side  "loading  pressure.  all  jointed  stages  is  which of  connected  connection  on top o f  the  test  bolts  connecting  joint  to  the  plates.  of  the  a neg-  with  a constant  frame w h i l e  is it  on  valve,  increased  for  situated in  "loading  The  the j a c k the  the  The  the  frame,  force  can  force  on  side-sway. inside  a vertical  the  position  vertical  load  beam" by two  pin-  " l o a d i n g beam" i s  frame on two a d j u s t a b l e  load  resting points.  measurement l o a d s were  the h o r i z o n t a l  loading  position  rods  movement o f  Thus  the  keeps  to the  two h o r i z o n t a l  loading  connecting  f r o n t of  frame s i d e - s w a y .  2.2 Load and d e f o r m a t i o n The  of  load c y l i n d e r  triangle"  cylinder  in  supply  can be f u r t h e r  vertical  the  3.  be m a i n t a i n e d a t one s i d e  during  frame by  the h o r i z o n t a l  south  jack  to  o f t h e beams and c o n -  f a c i l i t a t e d a horizontal  change  the o t h e r  bolted  centre-line  accumulator connected  south  ligible  j a c k s were  frame.  m e a s u r e d by  load jacks  "Strainsert"  through  a ball  J""— horizontal load jack  F i g.3 L o a d i n g  frame  Plate 1 . Frame setup  Plate 2 . Frame setup (closeup)  18. T h e c e n t r a l l o a d was m e a s u r e d b y a l o a d c e l l  placed in  series with the central load c y l i n d e r . All  deformations  were m e a s u r e d by d i r e c t c u r r e n t  placement transducers  ( D C D T ' s ) . The v e r t i c a l  beam  dis-  slip  r e l a t i v e t o t h e c o l u m n was m e a s u r e d b y a 7 D C D T - 5 0 0 w i t h a displacement  range of  +  . 5 i n . The t r a n s d u c e r s were  attached  to t h e c o l u m n , one above a n d one b e l o w t h e beam. The extensions  core  r e s t e d on a h o r i z o n t a l p ; l a t e g l u e d on t h e b e a m ,  t h e b o t t o m one b e i n g h e l d i n p l a c e by a r u b b e r s l i n g . and column r o t a t i o n s were m e a s u r e d by a s e t u p F i g u r e 4 a n d P l a t e 4. T h e t r a n s d u c e r s with  a displacement  Beam  as shown i n  used were  7DCDT-100  of *. l i n .  The r o t a t i o n s were measured as f o l l o w s : S i n c e t h e pendulum always assumes  the vertical  p o s i t i o n due t o g r a v i t y , any r o t a t i o n o f t h e frame  will  move t h e t r a n s d u c e r c o r e , w h i c h i s c o n n e c t e d t o t h e p e n dulum through a b e a r i n g ( F i g . 4 ) . F o r small horizontal rotation.  core movement i s p r o p o r t i o n a l t o the pendulum In o r d e r t o o v e r c o m e  of the core s l i d i n g a buzzer  rotations the  the f r i c t i o n a l  resistance  i n the t r a n s d u c e r and i n t h e b e a r i n g s ,  oscillating  a t a h i g h f r e q u e n c y , was a t t a c h e d t o  t h e t r a n s d u c e r b r a c k e t . An a d j u s t m e n t d e v i c e was between  the mounting p l a t e and the c o n c r e t e  d o t t e d l i n e s ) . Thus t h e t r a n s d u c e r readings c a l i b r a t e d a g a i n s t a known a n g l e  attached  (Fig. 4 in c o u l d be  change.  F i g u r e 3 shows t h e p o s i t i o n s o f t h e l o a d and d e f o r mation measurement  d e v i c e s . A l l measurements  were  recorded  P l a t e 4.  Rotation measuring  device  bearing (center of rotation of pendulum ) •mounting plate  tension spri ng (between arm and plate ) screw stop (on plate )  rotation adjustment arm (fixed t o the concrete) adjustment  screw  - m a i n fastening screw (joining arm to Concrete) •connecting pin (arm to plate )  rr-><=s,  buzzer  • transducer(dcdt) •transducer bracket -transducer core attached to pendulum by bearing  pi njoi nt (transducer core extension to pendulum)  pendulum  Fig.4 Rotation measuring  device  in  the  form of v o l t a g e s  punched out puter the  by a V i d a r  on p a p e r t a p e . T h i s  digital  voltmeter  s e r v e d as i n p u t  for  and com-  programs which p e r f o r m e d the n u m e r i c a l a n a l y s i s  test  data.  of  3.0 3.1  Mathematical  A P P L I E D THEORY  r e p r e s e n t a t i o n of concrete s t r e s s - s t r a i n curve  In o r d e r t o d e t e r m i n e  the moment o f r e s i s t a n c e o f a  r e i n f o r c e d c o n c r e t e beam s e c t i o n a t a s t r e s s s t a t e b e l o w u l t i m a t e where n e i t h e r the l i n e a r c o n c r e t e s t r e s s v a r i a t i o n (modular  r a t i o ) method nor the r e c t a n g u l a r (Whitneys)  b l o c k a p p l i e s , i t was stress distribution evaluating  to r e p r e s e n t the a c t u a l  by a m a t h e m a t i c a l  s t r a i n s and  by Y o u n g a n d S m i t h f c = f 'c G e Where G = e / e  ( 1  c  "  The  c  =  load  the b e s t  data.  fitting  1  1  i /n e  0  f i r s t e x p r e s s i o n was  author: 1_G  taken  from  Saenz  + ( R R " 2 ) G - ( 2 R - 1 ) G + RG ] +  c  2  E  f  derived  used with the f o l l o w i n g c o r r e c t i v e  Cos(tf^/8000) (l-G)G]e^ ^  1  Where R = R ( R - 1 ) / ( R - 1 ) £  The  0  fc^ " " *  E  to f i n d  and  ...3.1-1  n e x t e x p r e s s i o n was f  a correlation is  G )  t e r m a s d e r i v e d by t h e =  expressions  (17):  s a m e e x p r e s s i o n was  c  the  r e p r e s e n t a t i o n of the s t r e s s - s t r a i n curves  obtained experimentally.  f  1.2,  displacement  Four e x p r e s s i o n s were used theoretical  specific  values to the  in Chapter  p o s s i b l e between the r e c o r d e d  to  By  the r e s p e c t i v e p o s i t i o n of  a x i s , and a p p l y i n g t h e s e  as g i v e n by C o h e n ( 1 6 )  The  expression.  r e s i s t i n g moments c o r r e s p o n d i n g  concrete or s t e e l neutral  attempted  stress  g  2  -  1/R  e  3  (18):  ...3.1-2  R  = E /E e cu o R. = f ' / f „ . ,  Ec = S e c a n t  Modulus =  E..- = I n i t i a l  Tangent  F  The  f'/e C o Modulus = E  fourth expression based  r e l a t i o n s h i p was f. = c  SE .e  on p a r a b o l i c s t r e s s - s t r a i n  d e r i v e d by t h e  author:  2f'G(l-G/2) c  In t h e A p p e n d i x experimental  ...3.1-4 these e x p r e s s i o n s were superimposed  s t r e s s - s t r a i n data found  p l o t s were done, each  by t h e t e s t s .  c o n t a i n i n g the i n f o r m a t i o n  from the s i x t e s t c y l i n d e r s b e l o n g i n g From the c o m p a r i s o n  t o one  on  Two  obtained  batch.  of a l l these p l o t s the f o l l o w i n g  c a n be s a i d : i) expression experimental high  3.1-1  v a l u e s , but  shows c l o s e a g r e e m e n t w i t h i s s o m e t i m e s s l i g h t l y on  the the  side. i i ) e x p r e s s i o n 3.1-4  experimental Both  v a l u e s and  a l s o shows c l o s e a g r e e m e n t w i t h i s more c o n s e r v a t i v e i n most  of these e x p r e s s i o n s were a p p l i e d to  reinforced concrete  theory  in section  3.2.  the  the  cases.  24.  BEAM  STRAIN DIAGRAM  STRESS DIAGRAM  F i g . 5 S t r e s s and s t r a i n d i s t r i b u t i o n by s t r e s s function  3.2 R e i n f o r c e d C o n c r e t e The  Theory  f o l l o w i n g a n a l y s i s i s s i m i l a r t o t h e one (17).  by Y o u n g a n d S m i t h  From t h e g e o m e t r y o f t h e s t r a i n k ci s _ 1  presented  diagram  we  have:  k  k-d'/d e  = e  1  s  . . .3.2-2 1-k  s  (a) e x p o n e n t i a l  . fee"" '  f H  13  C  c  C  = f b dx c  Where G =  c /e c  Therefore and  s t r e s s - s t r a i n r e l a t i o n s h i p g i v e n by 3 . 1 - 1 :  C  =  c  0  Pkd  f b dx J o e  e  = e .x/kd c ct Hence by e v a l u a t i n g t h e i n t e g r a l s pkd c Jo 'c  Pkd  1  and  k!kd = —  (f  c J  b dx) x  0  c  the e x p r e s s i o n s leverarm C and  f o r the concrete  k.  Where J  f o r c e and i t s  c o e f f i c i e n t are obtained: = k b d f c' [ l - ( J + l ) e " ] e / J  ...3.2-3  2-[J+2(1+J)]e" = — J[l-(J+l)e- ]  ...3.2-4  J  r  compression  J  =  e c t  /  £ 0  J  26.  T h i s c a n a l s o be w r i t t e n C  =  c  kbdf  a  Whe r e : f  = average  a  concrete stress  = f[l-(J+1)e~ ]e/J c  ...3.2-5  J  This i s used  i n the h o r i z o n t a l e q u i l i b r i u m equation:  H = T - C  c  - C  s  I n t h e f o l l o w i n g a n a l y s i s e i t h e r "e  " i s known; t h a t i s ,  ct s t r e n g t h , o r "c " i s known; i . e . ct cu s e s =e s y a t o n s e t o f y i e l d i n g o f t e n s i o n s t e e l . Thus e i t h e r  e  =e  at ultimate flexural J  the s t e e l  3  s t r a i n s a r e g i v e n i n terms  or the concrete s t r a i n g i v e n i n terms  of the concrete  and compression  of the tension steel  steel  strain  strain,  strain are  to e v a l u a t e the  moment o f r e s i s t a n c e o f t h e s e c t i o n . F o r  e  c t  =  e  cu  :  H = A f - k bdf - A'E (l-k,,d'/d) e s y u a s s u ' ' cu T h i s produces a q u a d r a t i c e x p r e s s i o n i n " k " which i s solved to produce: C  v  u  k u = [\/(A v s fy +s A s' Ec e u L  v  c  +H)  2  + 4 b d f aA's Es ec u d ' / d  (-A f +A'E e + H ) ] / 2 b d f s y s s cu a  ...3.2-6  Hen c e : M  = A f (t/2-d ) s y 1  u  + k b d % [.5t/d-k (1-k.)] u a u  A'f (t/2-d') s s Where f = E ( 1 - k d'/d)e < f s s u cu y ,  1  1  + ...3.2-7  For  e  =  e  s  sy  (k -d'/d) - kbdf - A'f — y a s y _ y v  H = A f y  s  but f  1  1  k  =C[l-(F+l)e' ]e/F r  a  where F =^ e (l-k ) s y  y  0  y  T h i s c a n be s o l v e d f o r " k ^ " b y a p p r o x i m a t e m e t h o d s , b u t i t i s t o o cumbersome f o r p r a c t i c a l  calculations.  "k " i s f o u n d b y t h e p a r a b o l i c s t r e s s - s t r a i n y as s h o w n i n s e c t i o n ( b ) . (b) P a r a b o l i c s t r e s s - s t r a i n  Therefore, distribution  r e l a t i o n s h i p g i v e n by 3.1-4:  f  = 2f'(l-G/2)G c c W h e r e G = E„/e c o Using  t h e same a p p r o a c h C  or  a s a b o v e we g e t :  = kbdf'(l-J/3)J c  c  Cc = kbdfa  Where f  = f(l-J/3)J c  a  Also k  =  i  2-3J/4  ct  /e„  Equations f  .. . 3 . 2 - 9  3-J  Where J = £  where e  ...3.2-8  = e  0  3.2-6 a n d 3 . 2 - 7 , as d e r i v e d b e f o r e i n t h e c a s e , still  apply i f the above e x p r e s s i o n s f o r  " f " and "k," are used.  For e s =  se y„ : p  Substituting  into the horizontal  equilibrium  equation  we g e t  k -d'/d H = A f - k b d f - A' s y y a s  f y  1 - k  Where: f  = f'F[l-F/3] c  a  a  Substituting  and r e a r r a n g i n g  terms produces the  following  eq u a t i on i n " k ^ " : k b d f e (1+e /3) + k * ( A + A ' - b d f e - H / f ) y r r r y s s r r y 3  v  k [2A +A'(l+d'/d)-2H/f  y  s  ] + A  s  + A'd'/d  y  s  -  - H/f  s  =0  y ...3.2-10  Where: f e  This  r r  =f ' / f c y = e  sy  /e  o  c a n be s o l v e d  by t h e a p p r o x i m a t i o n  technique:  (k ) = (k ) - f ( k ) / f ' ( k ) y n+l y'n y n y n v  The  moment e q u a t i o n i s : t t M = A f ( — -d') + k bd f [ 2  y  s  y  y 2  a  2 d  k (1-k,)]  +  y  t Whe r e :  A'f ( s s £ k -d'/d  d')  ...3.2-11  In  order  developed  in  to v e r i f y this  corresponding stress  block  expressions  this  k  u  M  u  M (iii)  u  = 165.OK  u  M  stress  u  For  theory  a c o m p a r i s o n was done w i t h as d e r i v e d  stress  from the  state,  the  rectangular  a p p l i e d to  the  i n beam as 5 K i p s ,  stress it  block:  was f o u n d  that:  inches  moment f r o m e x p o n e n t i a l  tension  stress  distribution  = 5Kips  = .212 = 166.2K  axial  (iv)  tension  Ultimate  k  the  = .220  axial u  of  moment from r e c t a n g u l a r  Ultimate  k  validity  investigation.  Ultimate  Assuming a x i a l  (ii)  chapter,  at u l t i m a t e  beam used i n (i)  the  inches  moment f r o m p a r a b o l i c  tension  stress  distribution:  = 5Kips  = .218 = 166.8K  inches  the same a x i a l  distribution,  it  tension,  u s i n g the  was f o u n d t h a t  parabolic  at y i e l d i n g  of  the  t e n s i on s t e e l : k  y  M (v)  y  = .378 = 138.OK  To show  moment as f o u n d zero a x i a l k  u  M  u  inches  the e f f e c t from the  tension  rectangular  is:  = .248 = 180.5K  of a x i a l  inches  tension,  the  stress  block  ultimate for  The (iii)  u l t i m a t e moments found  show c l o s e a g r e e m e n t .  i n s e c t i o n s ( i ) , ( i i ) and  Therefore, the expressions  3 . 2 - 6 , 3 . 2 - 7 , 3.2-10 a n d 3.2-11 w e r e u s e d  in the f o l l o w i n g  chapter  corresponding  to determine  the bending  to any s p e c i f i c s t r e s s l e v e l steel.  moments  i n the concrete or r e i n f o r c i n g  4.0 T E S T P R O C E D U R E AND  4.1  Description  of tests  For a l l t e s t frames, except c y c l e s were p e r f o r m e d . s e q u e n c e : The f i r s t  zero  the l a s t , three  They consisted  corresponding performed with  shear.  the vertical  to failure  stress  The t h i r d  the f i r s t  load p o s i t i o n at 5 inches  displacements  The loading  axial  The in  became s e v e r e  vertical  joint.  the  to the point  sway and v e r t i c a l  where  they  first,  f o r c e on t h i s  vertical  and sway  l o a d i n g were i n c r e a s e d  s u c h a way t h a t t h e m o m e n t a t t h e s o u t h  by  registered  T h e n t h e v a l v e was c l o s e d on t h e s o u t h  the subsequent a l t e r n a t e  was  to the equipment.  until  constant  from  when t h e l o a d  was a p p l i e d t o t h e b e a m s  t o p r o d u c e an a p p r o x i m a t e l y during  was  the  o r d r o p p e d o f f , o r when  t h e two h o r i z o n t a l j a c k s  about 5Kips.  cycle  cycle with  c o u l d c a u s e damage  tension  level  from the beam-column  and c r a c k i n g  loading  joint.  The l a s t frame  F a i l u r e was a s s u m e d t o h a v e o c c u r r e d became e r r a t i c ,  vertical  load p o s i t i o n at 5 inches  up t o f a i l u r e .  during  the  from the beam-column  to cracking  beam-column j o i n t  continued  joint,  T h e s e c o n d c y c l e was p e r f o r m e d w i t h  Working s t r e s s here r e f e r s to a shear  increase  vertical  l o a d up t o w o r k i n g s t r e s s r a n g e a n d b a c k t o  load.  loaded  the  from the beam-column  l o a d p o s i t i o n a t 22 i n c h e s  the  loading  of the following  c y c l e was p e r f o r m e d w i t h  load p o s i t i o n at 5 inches from zero  EVALUATION  jack side  loading.  alternately  joint  remained  low w h i l e  t h e moment a t t h e n o r t h j o i n t k e p t i n c r e a s i n g .  T h u s t w o d i f f e r e n t s t r e s s s t a t e s w e r e c r e a t e d i n t h e two joints. lower  The s o u t h j o i n t  than  a shear stress  c o n s i d e r a b l y lower  a t t h e same a x i a l  than  at the north  joint,  tension force.  s l i p was r e c o r d e d o n l y b y t h e b o t t o m  the wedge o f c o n c r e t e u n d e r n e a t h relative  slightly  t h e n o r t h j o i n t , w h i l e t h e m o m e n t on t h e s o u t h  j o i n t was k e p t  The  reached  to the column.  DCDT's s i n c e  t h e t o p DCDT's d i d n o t move  A l l r o t a t i o n s recorded below are  t h e r o t a t i o n o f a s e c t i o n on t h e b e a m 2.5 i n c h e s a w a y the column, w i t h paragraphs on e a c h in  respect to the column.  the magnitudes of v e r t i c a l  from  In t h e f o l l o w i n g  l o a d s a r e as  recorded  s i d e o f t h e h o r i z o n t a l frame member, o r h a l f t h e f o r c e  the jack.  Behavior  o f the frames  during the loading to  f a i l u r e was as f o l l o w s : Frame Number 1 : The  f r a m e was l o a d e d h o r i z o n t a l l y a t b o t h e n d s u n t i l a  l o a d o f 5.5K was r e a c h e d . The of this bottom  sway-load  No v i s u a l o b s e r v a t i o n s w e r e  was t h e n  a p p l i e d up t o 2 . 7 5 K .  loading stage, tensile o f t h e beam u n d e r  made.  At the end  c r a c k s became v i s i b l e a t t h e  the south  vertical  load point.  T h i s s i g n i f i e s t h e low moment c a p a c i t y o f t h e beams t o p o s i t i v e moment due t o t h e w e a k e r l o n g i t u d i n a l r e i n f o r c e m e n t on t h e b o t t o m  o f t h e beam.  Vertical  l o a d was t h e n  The  c r a c k i n g d i d n o t i n c r e a s e as moments i n both  increased in the negative were  a p p l i e d up t o 5.5K on e a c h  made.  sense  and no o t h e r  beam.  joints  observations  As the  vertical  l o a d was i n c r e a s e d t o 6K a c r a c k  be seen on t h e b o t t o m s o u t h beam. The height,  crack  then  increased  ran  had y e t  vertical  With  ing.  loading cracks  further  1/2" s l i p .  At t h i s  was assumed t o  Vertical  vertical diagonal  joint,  column  2/3 o f  and  the beam  load p o i n t . crack to  although  At  lengthened it.  No c r a c k s  it  recorded a  vertical  loading,  t h e same p a t t e r n rapidly  stage  the  and f u r t h e r  have  taken  of  north  of shear  and b o t h rate  the  sides  showed  increase  l o a d i n g was  crack-  of  slip  terminated.  place.  2; j a c k s were  l o a d was a p p l i e d  l o a d e d to  4K.  up to 5 K . No v i s u a l  observations  made. S w a y - l o a d was  as i n  the  first  Vertical started  faulty  recording  applied  Tensile  l o a d was i n c r e a s e d a g a i n and t h e in  the  t h e same way  last  recording. terminated)  five  the n o r t h  joint  as t h e  observation  At a v e r t i c a l the  moved as damage from t h e stage  up t o 2 . 2 5 K .  cracks  opened  frame.  cracking  Unfortunately to  of  developed  Both h o r i z o n t a l  were  the  this  showing  was c o n s i d e r e d e x t e n s i v e  Frame Number  up t o a b o u t  appeared p a r a l l e l  increase  also started  Failure  between  moment.  These c r a c k s  about  toward  a p p e a r e d on the n o r t h  much h i g h e r  joint  vertically  2 inches  and more d i a g o n a l  interface  could  had a l s o  previous cycles  joint  frame.  were  lost  l o a d o f 23K (2K  bottom-slip slipping  south  transformers  after were  beam was e x p e c t e d .  cracked extensively  due  At  and  rethis slip  occurred. At a v e r t i c a l load increase run was in  the  load of  became e r r a t i c  remarkably first  2 4 . 5 K l o a d i n g was t e r m i n a t e d as and t h e s l i p  severe.  s i m i l a r to c r a c k i n g and s l i p  This  the  test  behaviour  frame.  Frame Number 3 : This having  frame and }  the n e x t , d i f f e r e d  lapped i n s t e a d of continuous  ment t h r o u g h  the  first  longitudinal  two  by  reinforce-  joint.  Both h o r i z o n t a l Vertical  from the  jacks  were  l o a d was a p p l i e d  l o a d e d to  5.2K.  up t o 5 K . No v i s u a l  observations  were made.  the  S w a y - l o a d was a p p l i e d up to  2.75K.  tensile  under  load  c r a c k s was o b s e r v e d  A slight the  south  opening  of  vertical  point. The  vertical  l o a d was a g a i n i n c r e a s e d ,  c r a c k i n g was o b s e r v e d Figure load  6 shows  at  10K on the s o u t h  the e x t e n t  of  these  and s l i g h t  shear  joint.  cracks  at the  following  stages: (1)  At a v e r t i c a l  load of  (2)  At a v e r t i c a l  l o a d o f 17K  (3)  At a v e r t i c a l  l o a d o f 21K  At  the  vertical  considerably  and v i s u a l  column was n o t i c e d . slight The  shear south  load of  21K t h e  slip  of  the  first  c r a c k s had opened up  south  beam r e l a t i v e  north  joint  also started  cracking similar  to #1  above.  joint  The  1 1 . 3K  t h e n showed t h e  following  to  to  its  show  increased  cracks  35.  Fig.6 South crack pattern of Frame 3 Scale: 1/4 inch = 1 foot  (4) A t a v e r t i c a l  l o a d o f 22K  (5) At a v e r t i c a l  l o a d o f 23K  The  north  s i d e a l s o s h o w e d some v i s u a l  had  s t a r t e d to drop a t this The  vertical  which stage  stage  a n d was  l o a d was i n c r e a s e d  The sway  down  load  t o 2K.  f u r t h e r u n t i l 29.5K a t  an a p p a r e n t m a x i m u m h a d b e e n r e a c h e d  f a i l u r e was a s s u m e d t o h a v e t a k e n Frame Number  slip.  and  place.  4:  Both h o r i z o n t a l S w a y - l o a d was  jacks were loaded  increased  t o 5.5K.  up t o 1.5K.  No  observations  were made. Vertical shear  cracks  the j o i n t .  l o a d was  increased  a p p e a r e d on t h e s o u t h This  increased  vertical The  cracking  This  at the bottom o f the south observed  l o a d was i n c r e a s e d  displacement  increased  in  jack  the right  side along  t o 4.75K.  l o a d p o i n t , t h a t was vertical  t o an e x t e n t  (producing  c o u l d n o t be r e c o v e r e d  A t 8K t h e  first  the bottom of  i n a s i m i l a r way a s f o r F r a m e  S w a y - l o a d was i n c r e a s e d tensile  up t o 15K.  produced the beam  under the  in previous again.  3.  The  frames. sway  where the o i l pressure  sway-load) dropped o f f and  as i t d r a i n e d  the h y d r a u l i c  hand  pump. At a v e r t i c a l south  l o a d o f 16.5K t h e s h e a r  j o i n t became c l e a r l y As t h e v e r t i c a l  load dropped to zero,  cracks  on t h e  defined.  l o a d was i n c r e a s e d the south  side  t o 21K a n d t h e sway-  cracked  extensively  and  37.  Fig.7a South Crack Pattern S c a l e : 1/4 i n c h = 1 f o o t  Fig.7b North Crack Pattern S c a l e : 1/4 i n c h = 1 f o o t  Crack Patterns  For  Frame 4  visual  slip  took p l a c e w h i l e  the n o r t h  side also  started  cracki ng. At 2 2 . 5 K t h e and the  top s l i p  A t 24K t h e force)  rotational  transformers  c r a c k i n g of  had d e v e l o p e d  plate  started  deformations  the n o r t h  t o come o f f  load  severe  removed t o p r e v e n t damage.  side  to a s t a g e where  (under negative  sway  the beam pendulum  due to c r a c k s e x t e n d i n g  Other c r a c k s appeared at at the  were  had become  the b o t t o m o f  under  the n o r t h  it.  beam  point.  A p p a r e n t maximum l o a d s were  reached at 29.7K  l o a d i n g was t e r m i n a t e d . At  this  r e a c h e d the s t a g e shown  Figure  in  stage  and  further  t h e c r a c k i n g had  7a & b f o r  the s o u t h  and  north. Generally showed l a r g e r was s l i g h t l y less  than  continuous slip  slips less  Table  III  the n o r t h  s i d e . The  longitudinal  at a lower  bigger,  than  the  reinforcement,  shows  side,  first  last  and t h e  although  each frame a t  loads  failure.  the  shear  considerably the  showed c r a c k i n g and  two f r a m e s w i t h final  slip  recorded at s m a l l e r u l t i m a t e the  l o a d and  two f r a m e s w i t h  reinforcement  l o a d than  and were  cracked at a lower  and t h e b e n d i n g moment was  the n o r t h  longitudinal  for  the south j o i n t  and d i s p l a c e m e n t s as  lapped  values  were  loads. recorded  Table III JOINT FORCES AND DISPLACEMENTS AT FAILURE  4.2 C o r r e l a t i o n The of the  plotted four  to e x p l a i n plots  test  frames are the  joint To  investigate  tension yield  Fig.  steel  were  in  for  evaluated rotation The ditions  chapter  displacement data,  3 . 0 was  were  order  the  applied.  plotted  against  the  displacement observations,  the  beam r o t a t i o n  at which  rotation The  the  between  was m e a s u r e d ,  theoretical  beam r o t a t i o n  complete  rotation  calculations  o v e r the 2 . 5 i n c h e s This  is  ultimate  were  theoretical  also moment  but  side,  can n o t  since  t h e moment v a r i a t i o n curvature  Therefore  only  loads  over which  the  plot  of  is  too  inside  theoretical  and c o r r e s p o n d i n g as  l o a d on each beam  the  for  the south  large,  were  the  side  sometimes  the 2.5 inch side  con-  rotations  comparison  the n o r t h  and j o i n t b e n d i n g moment a r e P = vertical  for  be a p p l i e d t o  reversal  the  comparison with  a r e b a s e d on c o n s t a n t  c l o s e enough  north  The  the  In  curve.  measured.  in  in  failure  of  corresponding to  section.  w&ich t h e y i e l d i n g  each f r a m e .  in order  to  8.  moment and c o r r e s p o n d i n g  evaluated  cycle  and o b s e r v e d  expressions  has on the  moment and t h e  ing  observed  the e f f e c t  column f a c e and p o i n t  loading  theoretical  as d e v e l o p e d  in  results  compared i n t h i s  theoretical  tension  the  irregularities  theory  relevant  of t e s t  data for  and to c o r r e l a t e  concrete The  and d i s c u s s i o n  test  resultlength.  can s e r v e  as a  results. joint  tension,  follows:  joint  shear  41 .  0  20  40  GO  80  100  120  UO  160  180  200  BENDIN6 MOMENT (KIP IN.) o  V RATIO F 0 R D E P T H OF N E U T R A L A X I S ROTATION OF B E A M ( D E G R E E S ) 2  2  F i g . 8 T h e o r e t i c a l b e n d i n g moment and beam r o t a t i o n c u r v e s  5  42. HL = h o r i z o n t a l l o a d a p p l i e d a t e a c h e n d o f t h e f r a m e S  = horizontal sway-load applied at the north the  frame  only  H  = j o i n t t e n s i o n = HL + S/2 - P x ( a + c / 2 ) / h  V  = j o i n t s h e a r = P - S x h / l  f o r south  side  = j o i n t shear  f o r north  side  M  side of  = P + S x h/1  = j o i n t bending  moment P x a - S ( 1 - c ) h / ( 2 x 1 )  f o r south  side  = j o i n t bending  moment P x a + S ( 1 - c ) h / ( 2 x l )  f o r north  side  F r a m e N u m b e r 1: Fig.9 against  shows t h e a p p l i e d l o a d i n g c u r v e  the observation  Fig.10, slip and  the  numbers.  t h e SLIP-SHEAR p l o t , shows a r a p i d i n c r e a s e i n  after reaching  a shear  a similar increase  18 K i p s  f o r the north  o f 13 K i p s  in slip side.  f o r the south  after reaching  The curves  r e g i o n where most o f t h e s l i p  almost  as p l o t t e d  side  a shear o f  are p a r a l l e l over  takes  place, ending  with  t h e same f a i l u r e s h e a r . Fig.11,  t h e SLIP-MOMENT p l o t , shows t h e r a p i d  of s l i p  f o r the south  bending  moment i s q u i t e s m a l l  the n o r t h  side occurs  (My = 1 3 8 K i n c h e s  at a p o i n t where the  ( 3 5 t o 50 K i p i n c h e s ) .  side the rapid increase  moment a t w h i c h t h e t e n s i o n  of slip  at a j o i n t tension  shows t h e ROTATION-MOMENT  s h o w s an e r r a t i c r e s p o n s e  On  coincides with the  steel starts to yield o f 5.5K) and  r a p i d l y e v e n a f t e r t h e moment has f a l l e n Fig.12  increase  progresses  off slightly.  plot.  The south  side  due t o > t h e moment r e v e r s a l a n d  43.  F i g . 9 L o a d i n g c u r v e s f o r Frame 1  44.  •slip  1  •slip  sign convention  30  20  T  1  VERTICAL SLIP (INCHES) Fig.10 S L I P - S H E A R p l o t  f o r Frame 1  •SLIP  sign convention  300  250  +SLIP  A  CL *-?  200  LU  north 150  CD  LJ CD  0.1  0.2  VERTICAL Fig.11  0.3  0.4  SLIP (INCHES)  SLIP-MOMENT p l o t f o r Frame 1  +M ^ROTATION  Fig.12 ROTATION-MOMENT p l o t f o r Frame 1  +M +ROTATION  the summing above.  o f p o s i t i v e and negative  curvature  The n o r t h s i d e shows a somewhat f l a t t e r  the recorded  data than expected  from  mentioned curve f o r  the theoretical plot.  Frame Number 2: F i g . 1 3 shows t h e a p p l i e d l o a d i n g c u r v e as p l o t t e d against the observation Fig.14,  numbers.  the SLIP-SHEAR p l o t , and Fig.15, t h e SLIP-  MOMENT p l o t , s h o w a r a p i d i n c r e a s e i n s l i p  f o rthe south  s i d e a f t e r r e a c h i n g a s h e a r o f 18 K i p s a n d a m o m e n t o f 50 K i p i n c h e s .  The n o r t h s i d e shows a r a p i d i n c r e a s e i n  slip  o n l y a f t e r r e a c h i n g a s h e a r =25 K i p s a n d a m o m e n t o f  over  180 K i p i n c h e s .  lost  due t o f a u l t y e q u i p m e n t s o t h a t t h e data  to t h e o b s e r v e d  The l a s t  part o f the records  were  corresponding  visual cracking o f the north side could not  be p l o t t e d . The to  MOMENT-ROTATION  the curves  Frame Number Fig.17  observed  curves, Fig.16, are very s i m i l a r from  F r a m e 1.  3: shows t h e a p p l i e d l o a d i n g c u r v e  against the observation  as p l o t t e d  numbers.  Fig.18, t h e SLIP-SHEAR p l o t , and Fig.19, t h e SLIPMOMENT p l o t , s h o w a r a p i d i n c r e a s e i n s l i p  f o r the south  s i d e a f t e r r e a c h i n g a s h e a r o f 13 K i p s a n d a m o m e n t o f 25Ki p inches.  T h e n o r t h s i d e shows a r a p i d i n c r e a s e i n s l i p  only a f t e r reaching a shear inches.  The tension steel  o f 24 K i p s a n d a moment o f 1 6 3 K i p s t a r t s t o y i e l d a t a moment o f  48.  Fig.13 Loading  c u r v e s f o r Frame 2  .  i*  +  slip  * + slip  sign  convention  "XT  north  south  l |— 0.0  f = _ 0.1  , t  ,  ,  0.2  VERTICAL F i g . 1 4 SLIP-SHEAR p l o t  =4  .  0.3  SLIP  . 0.4  (INCHES)  f o r Frame 2  50.  +M  ••SLIP  +SLIP  sign convention 300  250  -cr  -  F i g . 1 5 SLIP-MOMENT p l o t f o r Frame 2  +M +ROTATION  sign  convention  300  250 +  ROTATION  (DEGREES)  16 R O T A T I O N - M O M E N T p l o t f o r F r a m e 2  +M +ROTATION  52.  Fig.17 Loading_ curves  f o r Frame 3  53.  +v  +V  HCZtfZ t  t  •slip  +slip  sign convention  cn  on <  LU CO  X  0.0  0.1  0.2  VERTICAL  0.3  S L I P (INCHES)  F i g . 1 8 SLIP-SHEAR p l o t f o r Frame 3  0.4  0.5  F i g . 1 9 SLIP-MOMENT p l o t f o r Frame 3  +M +ROTATION  +M +ROTATION  sign convention  300  +  250  |  i—t  Fig.20 ROTATION-MOMENT,plot f o r Frame 3  143K i n c h e s  f o r a j o i n t t e n s i o n o f 2.4K.  c a r r i e d by t h e two j o i n t s  i s again almost  The f i n a l t h e same.  shows t h a t t h e ROTATION-MOMENT p l o t i s a g a i n a l m o s t with the response Frame Number Fig.21  o b t a i n e d from  the f i r s t  shear  two  Fig.20 identical  frames.  4: shows t h e a p p l i e d l o a d i n g c u r v e .  During  the l a s t  s t a g e o f l o a d i n g t h e s w a y - l o a d was r e v e r s e d a n d t h e j o i n t tension  i n c r e a s e d up t o 10K.  displacement  response  This resulted in a d i f f e r e n t  in the final  load  stage.  Fig.22, the SLIP-SHEAR p l o t , and Fig.23, the SLIPMOMENT p l o t , a g a i n s h o w a r a p i d i n c r e a s e i n s l i p south  f o r the  s i d e a f t e r r e a c h i n g a s h e a r o f 14K a n d a m o m e n t o f 40K  inches.  The n o r t h s i d e shows a r a p i d i n c r e a s e i n s l i p  a f t e r r e a c h i n g a s h e a r o f 2 0 K a n d a m o m e n t o f 170K The  only  inches.  t e n s i o n s t e e l y i e l d m o m e n t i s 136K i n c h e s f o r a j o i n t  t e n s i o n o f 6K. F i g . 2 4 , t h e ROTATION-MOMENT p l o t , shows a r e s p o n s e before  f o r t h e n o r t h s i d e up t o t h e p o i n t w h e r e t h e s w a y -  l o a d was r e v e r s e d .  The r e v e r s a l o f s w a y - l o a d ( a n d thus  moment) r e s u l t e d i n a d e c r e a s e and  as  o f r o t a t i o n on t h e n o r t h  swayside  an i n c r e a s e o f r o t a t i o n on t h e s o u t h s i d e d u r i n g t h e  final  stages  of loading.  the s l i p r e s p o n s e , almost  The moment r e v e r s a l d i d n o t a f f e c t  as t h e f i n a l  t h e same f o r b o t h j o i n t s .  and s l i p  results of this  slip  and s h e a r  i s again  Since the f a i l u r e  f r a m e , u n d e r a much  larger joint  t e n s i o n , w e r e o f t h e same m a g n i t u d e as f o r t h e f i r s t f r a m e s , i t m u s t be c o n c l u d e d  shear  three  t h a t t h e j o i n t t e n s i o n has no  + H L  +p  +p  j  L  sign convention 30  i  25  A  20  i  (Si CL *—  15  4  •z. %—i  O  10  < O 5  4  OBSERVATION Fig.21 Loading  NUMBERS  c u r v e s f o r Frame 4  58.  30  +  25  20 4  south 15 4  10  5  4  0.0  0.1  0.2  VERTICAL  0.3  SLIP  0.4  (INCHES)  Fig.22 SLIP-SHEAR p l o t f o r Frame 4  0.5  F i g . 2 3 SLIP-MOMENT p l o t f o r Frame 4  +M  +ROTATION  ROTATION ( D E G R E E S ) F i g . 2 4 ROTATION-MOMENT p l o t f o r Frame 4  +M +ROTAT ION  major e f f e c t joint  on the  tension  stress  of  beam.  Since  of  shrinkage To  which  of  of  12000psi  rupture  is  about 200psi  an upper  be e x c e e d e d  Table  shows  as o b s e r v e d  at c r i t i c a l  explain  two a p p a r e n t  components w h i c h  under normal  test  for  the  joint  action  was a t t e m p t e d ,  Critical  loads  for  shear the  shear  initiates  the  shear  transfer  respect  shear d i f f e r e n c e s  failures.  IV  the  l i m i t of  made w i t h  plot  as t h e s h e a r w h i c h  the j o i n t .  in  of  variation.  critical  moment-shear  A  concrete  stress  an i n t e r a c t i o n  shows  capacity.  t o an a v e r a g e  the main o b s e r v a t i o n s  clearly  the  transfer  constitutes  and t e m p e r a t u r e  was d e f i n e d of  10 K i p s  shear,  and h i g h  a steel  s h o u l d not  relate  critical  or  the modulus  which  shear  10K c o r r e s p o n d s  185psi  beam c o n c r e t e , tension  ultimate  slip  and  25, low  in t h i s  case  cracking  displacements In  order  modes, the  s h e a r have  Fig.  between  and  each f r a m e .  failure  to  to be  to  physical  investigated  i n more d e t a i 1 . The  shear  following  is  three  transferred structural  1)  beam t e n s i on  2)  beam c o m p r e s s i o n  3) beam Without shear  results  by  the  steel steel  can be a l l o c a t e d to t h e s e  (bottom)  joint  components:  more d e t a i l e d e x p e r i m e n t a l  different  the  concrete  mechanism o f t h e is  across  dowel  from the  steel,  action dowel  no m a g n i t u d e s  components.  of  the  action  no g e n e r a l i z a t i o n  show t h a t  tests  tension  of the is  the s h e a r t r a n s f e r  Since (top)  of  the steel  compression  possible. capacity  The of the  test joints  is higher i n the presence for a small bending induced  of a large bending  moment.  S i n c e an a x i a l  i n t h e beam, enough c o m p r e s s i o n  moment  than  t e n s i o n was  was n o t d e v e l o p e d  in the c o n c r e t e t o t r a n s f e r a s i g n i f i c a n t amount o f shear (shear friction couple  hypothesis  of a large bending  ( 4 ) , (5) ).  B u t under the  moment, t h e c o m p r e s s i o n  block  i n t h e beam c o n c r e t e , e n h a n c e d due t o t h e c o n f i n i n g f o r c e s of top and bottom  steel  and s t i r r u p s  capacity i n the presence  of lateral  (axial  compression (11)  confinement  ),  c o u l d t r a n s f e r a s i g n i f i c a n t l y h i g h e r amount o f shear t o the column. especially  This tendency  was o b s e r v e d  during the i n i t i a l  stages  in a l l four  of joint  frames,  cracking.  Once t h e j o i n t c o n c r e t e has c r a c k e d t o a h i g h e r  degree,  as shown i n t h e p r e v i o u s  action  of the steel  remained  c h a p t e r , o n l y t h e dowel  and i n a l l cases  at ultimate approached i r r e s p e c t i v e o f moment.  the shear t r a n s f e r r e d  t h e same v a l u e o f a b o u t  30 K i p s  1  SLIP  ROTATION DEGREES  SHEAR KIPS  MOMENT KIP INCHES  1-South  ,3.0  35.0  .0 30  .06  1-North  18.0  140.0  .028  -.20  2-South  18.0  50.0  .014  -.12  2-North  ±25.0  ±180.0  .016  -.20  3-South  13.0  25.0  .0 40  + .20  3-North  24.0  163.0  .024  -.28  4-South-  .14.0  40.0  .010  + .12  4-North  20.0  1 70.0  .010  -.24  FRAME NUMBER  INCHES  T a b l e IV JOINT  FOR CES AND D I S P L A C E M E N T S AT C R I T I C A L  SHEAR  |  64.  theoretical ultimate  shear  100  M  c r  150  200  (KIPSlN)  Fig.25 Moment-shear f a i l u r e  interaction  plot  4.3  Conclusion The  obtain  j o i n t i n t e r f a c e was p u r p o s e l y made s m o o t h t o uniform  t e s t c o n d i t i o n s and t o produce  shear-transfer condition with This joint s t i l l c a p a c i t y , even  under  adverse  j o i n t , taking into account  loading combinations.  this  investigation.  t r a n s f e r c a p a c i t y o f such  a  the l i m i t e d r e s u l t s obtained  I t i s f e l t , however, that the  major observations described i n the previous clearly  To  a l l the f a c t o r s c o n t r i b u t i n g  i t , i s n o t p o s s i b l e from  from  regard to the concrete.  showed a c o n s i d e r a b l e s h e a r - t r a n s f e r  calculate the ultimate shear  to  the worst  chapters  indicate the following:  1) T h e t y p e o f j o i n t i n v e s t i g a t e d c a n t r a n s f e r t h e full  beam s h e a r t o an a d j a c e n t 2) S h e a r  column.  f a i l u r e i n the form  tension  c r a c k i n g and v e r t i c a l  levels  of shear-moment a c t i o n .  joint slip  which  developes  under  s t e e l , and a c o n s i d e r a b l e shear  3) L a p p i n g  low s h e a r  slip which  under the force.  approximately  The moment,  the y i e l d i n g of the tension force.  The u l t i m a t e  shear,  t h e same v a l u e i n b o t h  cases.  o f t h e l o n g i t u d i n a l r e i n f o r c e m e n t has no  d e t r i m e n t a l e f f e c t on t h e j o i n t c a p a c i t y . observed  a t two  t h e a c t i o n o f a much h i g h e r  apparently coincides with  however, reaches  diagonal  occurs  One d e v e l o p e s  a c t i o n o f a low moment a n d f a i r l y second  o f combined  that the f i r s t  two f r a m e s  d e f l e c t i o n s at lower were r e i n f o r c e d with  showed s l i g h t l y  loads than lapped  I t was  t h e l a s t two  even higher frames  longitudinal reinforcement.  4)  The  appreciably  shear transfer affected  More d e t a i l e d e n v e l o p e u n d e r the applied required and  the  capacity  by t h e tests  required  of the  in this investigation. to f i n d the  contribution  c o n c r e t e to the  joint is  presence of a j o i n t  are  action  of the  tension.  to produce a f a i l u r e  type of loading More t e s t s of the  shear capacity  not  are  which also  reinforcing  of the  was  joint.  steel  67. References  1. S A E M A N N , J . C . a n d WASHA, G.W. " H o r i z o n t a l S h e a r C o n n e c t i o n s B e t w e e n P r e c a s t Beams and C a s t - I n - P l a c e S l a b s " , ACI , November 1964. 2. B A D O U X , J . C . a n d H U L S B O S , C . L . " H o r i z o n t a l Shear Connection i n Composite Concrete Beams U n d e r R e p e a t e d L o a d s " , A C I , D e c e m b e r 1 9 6 7 . 3. K R I Z , L . B . a n d R A T H S , C.H. "Connections i n Precast Concrete Structures-Strength of C o r b e l s " , P C I , February 1965. 4. B I R K E LAN D , P.W. a n d B I R K E L A N D , H.W. "Connections i n Precast Concrete Construction", ACI , M a r c h 1 9 6 6 . 5. M A S T , R . F . "Auxiliary Reinforcing in Concrete ASCE, June 1968.  Connections",  6. K R E F E L D a n d T H U R S T O N . " C o n t r i b u t i o n of L o n g i t u d i n a l Steel t o Shear R e s i s t a n c e o f R e i n f o r c e d C o n c r e t e Beams", ACI, March 1966. 7. K R E F E L D a n d T H U R S T O N . "Shear and Diagonal T e n s i o n S t r e n g t h o f Simply S u p p o r t e d R e i n f o r c e d C o n c r e t e Beams", A C I , March 1966. 8. H A N S O N , N.W. a n d CONNOR, H.W. "Seismic Resistance of Reinforced Concrete Column J o i n t s " , ASCE, O c t o b e r 1967.  Beam-  9. H O F B E C K , J . A . , I B R A H I M , 1 . 0 . a n d M A T T O C K , A . H . "Shear T r a n s f e r i n Reinforced Concrete", ACI, February 1969. 10. SMITH, R.B.C. " I n t e r a c t i o n o f M o m e n t a n d S h e a r on t h e F a i l u r e o f R e i n f o r c e d C o n c r e t e B e a m s W i t h o u t Web R e i n f o r c e m e n t " , C I V I L E N G I N E E R I N G & P U B L I C WORKS R E V I E W ( L O N D O N ) , June, J u l y and August, 1966. 1 1 . P O R T L A N D CEMENT A S S O C I A T I O N . D E S I G N OF M U L T I - S T O R Y R E I N F O R C E D C O N C R E T E B U I L D I N G S FOR E A R T H Q U A K E M O T I O N S , 1 9 6 1 .  68.  12.  AMERICAN CONCRETE I N S T I T U T E . BUILDING CODE REQUIREMENTS FOR REINFORCED ACI ( 31 8 - 1 9 6 3 )  CONCRETE,  13.  ZSUTTY, T . C . "Beam S h e a r S t r e n g t h E x i s t i n g Data", ACI,  14.  BURTON, CORLEY and HOGNESTAD. "Connections in Precast Concrete S t r u c t u r e s E f f e c t s o f R e s t r a i n e d Creep and S h r i n k a g e " , P C I , A p r i l 1967.  15.  MATTOCK, A . H . " C r e e p and S h r i n k a g e S t u d i e s " , PCA RESEARCH & DEVELOPEMENT LABORATORY, May 1 9 6 1 .  16.  COHEN, M . Z . " R o t a t i o n C o m p a t i b i l i t y i n the L i m i t Design Reinforced Concrete Continuous Beams", REINFORCED CONCRETE SYMPOSIUM.  P r e d i c t i o n s by A n a l y s i s November 1 9 6 8 .  of  of  17.  YOUNG, L . E . and S M I T H , G . M . " U l t i m a t e F l e x u r a l A n a l y s i s B a s e d on S t r e s s - S t r a i n C u r v e s o f C y l i n d e r s " , A C I , December 1 9 5 6 .  18.  SAENZ, L . P . D i s c u s s i o n of " E q u a t i o n f o r the S t r e s s - S t r a i n C u r v e o f C o n c r e t e by P . D e s a y i and K r i s h n a n " , A C I , September 1964.  APPENDIX:  STRESS-STRAIN  CURVES  OF T E S T  SPECIMENS  100  utt. 73.6ksi (turned down to 0=.29in)  0 +• 0  2  4  6  8  10  12  STRAIN (%IN/IN ) Stress-strain  diagram  f o r 3/8 i n c h d i a m e t e r r e i n f o r c i n g  steel  100  ult. 87.2ksi (0 = 5/8in.nominal)  ult.78.5ksi (turned down to 0=.423in.)  80  ult.72.4ksi(turned down to 0=.42in) ult.73.gksi(tured down to 0=.447in)  CO  60 ult.72. 8 ksi (turned down to 0 = . 4 2 i n . )  cn cn  LU  CC hcn  40  20  0  1 2  4  6  8  10  12  14  STRAIN ( % IN/IN ) Stress-strain  diagram  f o r 5/8  inch diameter r e i n f o r c i n g  steel  16  5000  4000  t  4  0.0  0.1  0.2  0.3  S T R A I N <% I N / I N )  S t r e s s - s t r a i n p l o t o f 6 t e s t c y l i n d e r s t a k e n f r o m beamc o n c r e t e and s u p e r i m p o s e d t h e o r e t i c a l c u r v e s  0.4  6000  STRAIN (%IN/IN)  S t r e s s - s t r a i n p l o t of 6 t e s t c y l i n d e r s taken from columnc o n c r e t e and s u p e r i m p o s e d t h e o r e t i c a l c u r v e s  

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