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Anchorage length in pretensioned concrete and the effect of some variables theron. Joa, Eric 1964

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ANCHORAGE LENGTH IN PRETENSIONED CONCRETE AND THE EFFECT OF SOME VARIABLES  THEREON  by ERIC JOA B.A.Sc. ( C i v i l  Engineering) U n i v e r s i t y  o f B r i t i s h Columbia, 1960  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  in  the Department of  Civil  We accept required  this  Engineering  t h e s i s as conforming  t o the  standard  THE UNIVERSITY OF BRITISH COLUMBIA May, 1964  In the  r e q u i r e m e n t s f o r an  British  mission  for reference  for extensive  p u r p o s e s may  be  cation.of  written  Department  of  and  by  Columbia,  fulfilment  University  shall  I further  Head o f my  permission*  1964.  the  this thesis  C i v i l Engineering  September 29„  Library  agree for  that  of  per-  scholarly-  Department  shall  of  make i t f r e e l y  or  t h a t , c o p y i n g or  f o r . f i n a n c i a l gain  The U n i v e r s i t y of B r i t i s h V a n c o u v e r 8i, Canada  ^  the  study,  the  in partial  degree at  I t i s understood  this thesis  w i t h o u t my  that  copying of  granted  representatives-  this thesis  advanced  Columbia, I agree  available  his  presenting  not  be  by publi-  allowed  ABSTRACT  The  e f f e c t o f a number o f v a r i a b l e s upon p r e s t r e s s  l e n g t h was  investigated.  The  end  zones o f p r e s t r e s s e d  anchorage pretensioned  c o n c r e t e members were s i m u l a t e d  by c a s t i n g a g a i n s t  3/8"  diameter w i r e s were used. . F i f t y  diameter strands  specimens were t e s t e d .  and The  .276"  v a r i a b l e s i n v e s t i g a t e d were; , s u r f a c e  condition of prestressing- steel, water/cement r a t i o o f c o n c r e t e , and  speed o f r e l e a s e o f age  of concrete,  prestress,  stress i n  concrete,  anchorage  length  vibration. •  . A r e l a t i o n s h i p between f r e e end was  s t e e l bulkheads.  found and  i s compared w i t h t h e  p u l l - i n and  r e s u l t s o f other i n v e s t i g a t o r s .  - Acknowledgement The a u t h o r wishes t o express h i s thanks t o h i s a d v i s o r , S.. L., L i p s o n f o r h i s i n t e r e s t , guidance and h e l p o n t h i s  Professor project.  The a u t h o r a l s o e x p r e s s e s h i s g r a t i t u d e t o t h e s t a f f o f t h e C i v i l Engineering  MAY  workshop f o r t h e i r  1962  Vancouver, B. C.  assistance.  TABLE OF C0NTENTS  Page CHAPTER I  Introduction D e f i n i t i o n o f t r a n s f e r "bond and anchorage l e n g t h D i s c u s s i o n . o f p r e v i o u s work  II  Description  o f t h e e x p e r i m e n t a l method  : T y p i c a l t e s t procedure Description.of III  1 2  test  series  7 9  E x p e r i m e n t a l r e s u l t s and c o n c l u s i o n s 13  Tables of r e s u l t s Discussion of test  series  29  Conclusions APPENDIX I  Graphs o f e x p e r i m e n t a l r e s u l t s  APPENDIX;II. S p e c i f i c a t i o n s BIBLIOGRAPHY  2U  and d e t a i l s o f m a t e r i a l s used  30 ^1 ^3  INTRODUCTION  D e f i n i t i o n of-" T r a n s f e r • Bond and. Anchorage Length  T h i s .'is t h e t h i r d : t h e s i s p r e p a r e d a t t h e U n i v e r s i t y of. B r i t i s h Columbia d e a l i n g with.the problem o f b o n d - i n p r e s t r e s s e d concrete.  . B a s i c a l l y , , i n . t h i s method, the  the c o n c r e t e the  s t e e l i s tensioned  i n the forms,  i s t h e n p l a c e d and when i t has reached s u f f i c i e n t  :  strength  s t e e l i s r e l e a s e d . - The - r e l e a s e d s t e e l r e t u r n s t o zero s t r e s s a t t h e  f r e e end and a t t a i n s a.constant s t r e s s a t some d i s t a n c e specimen. . T h i s d i s t a n c e value  l o s s which t h e o r e t i c a l l y .equals  where.Ec =  f s i . As AsEs AcEc  inside the  i s commonly c a l l e d " the anchorage, l e n g t h . .The  o f the r e t a i n e d . s t r e s s . i s equal t o the i n i t i a l  elastic  The  pretensioned  G  c  s t r e s s minus an  Ej  ( l ET AL)  bond by which t h e p r e s t r e s s f o r c e i s t r a n s f e r r e d from: the  steel into  the c o n c r e t e , i s c a l l e d ''prestress t r a n s f e r bond". .A . d i s t i n c t i o n s h o u l d be made between t h i s type o f bond and f l e x u r a l bond as produced: i n a l o a d e d beam. . T h i s t h e s i s w i l l d e a l w i t h p r e s t r e s s t r a n s f e r bond o n l y .  . D i s c u s s i o n o f ' P r e v i o u s Work  At .present  i t i s . g e n e r a l l y b e l i e v e d t h a t p r e s t r e s s t r a n s f e r bond i s  m a i n l y caused,by f r i c t i o n a l , f o r c e s .  .'This suggests t h a t t h e r a d i a l  e x i s t i n g , a t t h e i n t e r f a c e o f t h e s t e e l ' a n d concrete.has :  :  pressure  a n - i n f l u e n c e on  bond s t r e s s . . Thus, • t h e bond s t r e s s should be h i g h e r a t t h e f r e e end t h a n at  t h e t i g h t end'as suggested by Janney ( 2 ) . . A good d e f i n i t i o n o f p r e s t r e s s  t r a n s f e r bond i s g i v e n by P.. R .. T a y l o r ( 3 ) • . A.great  d e a l o f work-has been done r e c e n t l y i n c o n n e c t i o n w i t h bond  and anchorage. .Four b a s i c methods•of measuring bond and anchorage a r e p r e s e n t l y being-.used. , The f i r s t , concrete  and t h e most commonly.'used'method, i s one by which  s t r a i n s are.measured on the. s u r f a c e .  The change i n s t r a i n between  s e c t i o n s can t h e n be r e l a t e d , t o bond s t r e s s . .The d i s t a n c e from t h e end o f t h e specimen.to a . p o i n t  where t h e s t r a i n reaches a c o n s t a n t  c a l l e d t h e anchorage ..length. ..Strains a r e measured e i t h e r w i t h 1  attached t o the concrete  s u r f a c e , o r by t h e movement o f p l u g s  v a l u e .is strain-gauges which have  been, i n s e r t e d , i n t o t h e specimen. . Kaar ( l ) used t h i s method. .. A number- o f o b j e c t i o n s t o t h i s method exist'. .The anchorage l e n g t h as e s t a b l i s h e d by. t h i s method w i l l . b e . l o n g e r than.the t r u e anchorage l e n g t h o f t h e strand, s i n c e t h e p r e s t r e s s f o r c e . i s d i s s i p a t e d - i n a manner s i m i l a r t o a  concentrated;force  a c t i n g , o n t h e end-of a beam. ..'Thus,, t h e s t r e s s e s - a s measured on t h e s u r f a c e of the'concrete  w i l l be s m a l l e r t h a n . t h e s t r e s s e s which e x i s t a t t h e  i n t e r f a c e . o f - t h e s t e e l and c o n c r e t e ,  a t t h e same s e c t i o n . . Therefore,. t h e  anchorage l e n g t h measured depends on.the t h i c k n e s s o f c o n c r e t e . Since.the  cover.  bond s t r e s s e s a r e c a l c u l a t e d by. d i f f e r e n t i a t i o n o f the' s t r a i n s  t h e y w i l l be low- a n d w i l l not n e c e s s a r i l y convey a t r u e . p i c t u r e o f bond 1  s t r e s s d i s t r i b u t i o n at. t h e i n t e r f a c e . -Furthermore, d i f f e r e n t i a t i o n . o f an .  3-  experimental  curve i s . s u b j e c t t o l a r g e e r r o r s .  • In another-method,. markers are embedded a t i n t e r v a l s i n t o the prestre.ssing- s t e e l . . Upon r e l e a s e o f the p r e s t r e s s the-markers are sheared off] by The  s l i p . ..The, s l i p can t h e n be measured on. x-ray.- photographs.  argument, a g a i n s t t h i s method: is,.-as ' f o l l o w s .  Bond-is e s s e n t i a l l y a  s u r f a c e phenomenon. . By. i n s e r t i n g t h e s e markers one disturbance  o f the  i s t a k e n . . By attached  t o the  Evans (U)  s u r f a c e c o n d i t i o n a t the p o i n t where the measurement  s i m i l a r ^ r e a s o n i n g the s u r f a c e o f w i r e s may  t h i r d method i s one  i s used. . The  r e s u l t s obtained  w i t h s t r a i n gauges  be  - Janney (2)  questionable.  and  concrete  i n which the t h e o r y o f - p h o t o e l a s t i e i t y  i s replaced-by  poured, i n t o f o r m s ' c o n t a i n i n g . t h e the p r e s t r e s s an.isochromatic  by a p l a s t i c .  a bi-refringent.plastic  p r e s t r e s s i n g strands.  f r i n g e -pattern i s o b t a i n e d  t r a j e c t o r i e s can be drawn. .The  It  a  used t h i s method.  . The  concrete  introduces  which.is  Upon.release o f and  stress  problem here i s the replacement o f t h e  Concrete i s by no means a homogeneous m a t e r i a l .  i s composed o f - a number o f m a t e r i a l s o f . d i f f e r e n t h a r d n e s s e s . - The,  modulus o f e l a s t i c i t y as measured by a standard •represent  c y l i n d e r t e s t would seem.to  o n l y an average o f t h e s e m o d u l i . . E s p e c i a l l y when.one.is  concerned w i t h  s u r f a c e c o n d i t i o n s i t appears d o u b t f u l whether such  a.replace-  ment i s j u s t i f i a b l e . The  f o u r t h method has been used f o r the experiments conducted i n  t h i s t h e s i s . . A - c o n c r e t e specimen.is c a s t a g a i n s t a s t e e l b u l k h e a d . . Upon r e l e a s e of" the p r e s t r e s s the p l a t e . . Thus,. t h e • member,. the frame.  specimen b e g i n s t o bear on.the  specimen r e p r e s e n t s . t h e  zone o f constant  anchorage zone o f a p r e s t r e s s e d  s t r a i n b e i n g r e p l a c e d by a . r i g i d  Upon s l i p the l o a d a n c h o r e d - i s  steel  measured and  steel  the l e n g t h o f  the  specimen equals t h e anchorage l e n g t h . (3).  same method was  used by Dinsmore ( 5 ) .  A s i m i l a r method was  e s t a b l i s h '!the s l i p l i m i t  The  used by  Dinsmore attempted t o  envelope". , That i s , he attempted t o f i n d  l e n g t h r e q u i r e d which would permit  anchoring  s t r e s s i n the  s t e e l to  i t s u l t i m a t e v a l u e . . H i s r e s u l t s i n d i c a t e d t h a t t h i s l e n g t h was  first  diameter 7 wire  the  of the-prestress force plus  a subsequent a p p l i c a t i o n o f l o a d i n c r e a s i n g t h e  f o u r f e e t , f o r 7/l6"  Taylor  less than  s t r a n d . - I n o t h e r words, Dinsmore  r e l e a s e d the p r e s t r e s s and t h e n performed a p u l l - o u t t e s t on h i s  specimens. . T h i s method a l s o has  s e v e r a l disadvantages.  a r e measured o n l y at t h e ends o f the have t o be  specimen.  .-Firstly,  slips  A number o f specimens  c a s t t o produce a f o r c e anchored v s . l e n g t h graph. . The  d e f l e c t i o n o f the s t e e l bulkhead: produced a r e d u c t i o n i n l o a d i n t h e ;  "constant  s t r a i n zone" which does not  e x a c t l y equal the e l a s t i c l o s s i n  a normal p r e s t r e s s e d specimen, t h u s p r o d u c i n g b e a r i n g end  o f the t e s t  bond s t r e s s e s at  the  specimen.  A number o f r e l a t i o n s h i p s between anchorage l e n g t h , end  slip,  and  s t e e l s t r e s s have been suggested. .For ease o f comparison o f r e s u l t s  the  f o l l o w i n g nomenclature i s i n t r o d u c e d : 0  =  Ps  =  force i n steel:  fs  =  stress i n steel  Es, Ec  o  moduli o f e l a s t i c i t y o f s t e e l and  =  s t r a i n i n s t e e l and  =  d i s t a n c e from f r e e end o f specimen  •  =  anchorage l e n g t h  •Vs j-Vc  =  P o i s s o n r a t i o s of s t e e l and  £ j.€ S  e  x  r  • =  • c o e f f i c i e n t o f f r i c t i o n between s t e e l and  radius of  wire  concrete  concrete r e s p e c t i v e l y  concrete  concrete  5-  n  -  modular r a t i o  A_*  =  shortening o f s t e e l at d i s t a n c e x  _\ £ =  shortening of s t e e l at distance  3  l^  as  w  )  (l)  s u b s c r i p t s . = i n i t i a l and f i n a l v a l u e s r e s p e c t i v e l y  Guyon (7)  suggested two  equations  =  2~~7—A__assuming  bond o f uniform i n t e n s i t y a l o n g the anchorage l e n g t h and  a  friction  -c =  3  . assuming an e l a s t i c bond s t r e s s , , i . e . the i n t e n s i t y o f the bond , s t r e s s i s p r o p o r t i o n a l t o the r e l a t i v e displacement . s t e e l . . Thorsen  (8)  produced  o f concrete  an e x p e r i m e n t a l curve, u s i n g  .276"  diameter w i r e , which agrees w i t h Guyon's second e q u a t i o n . .The appears (-2)  t o have been.drawn from one  Janney (2)  developed  Psi -  an  Ps*  and  curve  test.  equation  2-t?s  __  * Ee  on the b a s i s o f t h i c k - w a l l e d c y l i n d e r t h e o r y , and  assuming,the  bond s t r e s s b e i n g p r o p o r t i o n a l t o the r a d i a l p r e s s u r e e x i s t i n g at the i n t e r f a c e . . T a y l o r ( l ) has m o d i f i e d : t h i s e x p r e s s i o n t o r e a d • (3)  Psi ~  Psx  _____ _  */s K  Evans (k) suggests.a r e l a t i o n s h i p between end p u l l i n and anchorage /j  length  JL  3.C  =  A s-e.  7:—; e s c  — —  Evans does not s t a t e how  the e q u a t i o n i s e x p e r i m e n t a l  and  C c f  many specimens were t e s t e d . i n o r d e r t o  a r r i v e at t h e above e q u a t i o n . Now,  a t t e m p t i n g t o develop a r e l a t i o n s h i p between p u l l - i n  o f the wire and anchorage l e n g t h f o r Janney's e q u a t i o n .  2<*  Let  P« =  Then  *s  p  sl  (1 - ' e  K K  )  Guyon's second e q u a t i o n . i s based on an e x p r e s s i o n o f s i m i l a r T h e r e f o r e we  form.  can expect the same r e l a t i o n s h i p between anchorage l e n g t h and  pull-in.  . Now, - n e g l e c t i n g the l o s s i n s t e e l o f the c o n c r e t e AsEs A  sa.  =  f  Psu£~  Guyon suggests t h a t anchorage  s t r e s s due t o e l a s t i c  Ps^ C '~ 6*  i s completed when  OP  —  A  s  • 3  ~TT  4  =  A  S  ~  However,  ^  K  —•  flsEs  ) ^* •  Psx  which r e q u i r e s the exponent t o be - 3 . . T h e r e f o r e  shortening  it  -  *sl I  ^  f"  Kx  1  fl  0  isi  " f . N C «  (\ -  e"  )  olx "•  ^  i  K -  seems t h a t t h i s r e s u l t  one c o u l d set  s  i s o n l y a matter o f d e f i n i t i o n s i n c e  the c r i t e r i o n . for anchorage  l e n g t h t h a t Psx =  .98:P§tr  which t h e n r e q u i r e s the exponent t o be -k, as T h o r s e n m e n t i o n s . will,  by s i m i l a r r e a s o n i n g , produce the r e l a t i o n s h i p : . . £ ' =  4  TT  This A. SJ2. »  Tit  -These expressions  suggest  of force being t r a n s f e r r e d .  It  t h a t anchorage  would seem, t h e r e f o r e ,  v a l u e s which have been assumed constant transferred_.  t h a t some o f the  depend on the f o r c e b e i n g  - F o r example, • the r e l a t i o n s h i p between 0' a n d - r a d i a l p r e s s u r e  i s not n e c e s s a r i l y a . s t r a i g h t  line,  s t r e s s e s i n the p l a s t i c range are . Kaar ( l ) strand t r a n s f e r  especially, since.  according to  Janney,  encountered.  has i n v e s t i g a t e d the i n f l u e n c e o f c o n c r e t e s t r e n g t h on l e n g t h . . . He a c h i e v e d a v a r i a t i o n i n c o n c r e t e  by t r a n s f e r r i n g - t h e of transfer  l e n g t h i s independent  p r e s t r e s s at  strength  d i f f e r e n t a g e s . ..He suggests t h a t  o f p r e s t r e s s has no a p p r e c i a b l e e f f e c t  on anchorage  time  length.  T h i s agrees w i t h the f i n d i n g s o f P e a t t i e and Pope ( 9 ) who found t h a t ."growth o f bond r e s i s t a n c e  i s much more r a p i d - t h a n t h a t o f c o n c r e t e  s t r e n g t h a n d ; . i t seems• d o u b t f u l i f i t bond s t r e s s e s i n t e r m s . o f  i s d e s i r a b l e t o quote a l l o w a b l e  compressive, s t r e n g t h o f c o n c r e t e " .  Peattie  • had-.performed p u l l - o u t t e s t s on u n t e n s i o n e d rods . specimens end: t o end around the released)the  s t r a n d . ., He  then ends o f  the  r e f e r s t o t h e s e ends a s " c u t " ends, and :to the ends away :  from t h e s e as ""dead" ends. " c u t " " end was  anchorage  cast, d u p l i c a t e  p r e s t r e s s by flame c u t t i n g between.the a d j a c e n t  specimens. ..He  "dead" end.  same t e n s i o n e d  Kaar  He  found t h a t the anchorage , l e n g t h at  the  always somewhat l o n g e r t h a n the anchorage l e n g t h at  the  ..That i s , an i n c r e a s e i n . speed o f r e l e a s e  increases  length.  •Experimental Method. A s k e t c h o f the t e s t i n g apparatus i s shown.in F i g u r e 1. Taylor  (3)  used:the same apparatus except f o r t h e • h y d r a u l i c  which had b e e n . i n s t a l l e d p r e v i o u s seen.from the  s k e t c h the  to t h i s series of t e s t s .  s t e e l was  pretensioned  As can  i n the frame b y  end the  concrete  b e a r s a g a i n s t the b u l k h e a d . . T h i s e n d . i s  r e f e r r e d t o as the  w h i l e the o t h e r  end".  The  end  i s termed the  "free  t e s t i n g sequence f o r s t r a n d s was  To o b t a i n uniform as noted,, was  u s u a l l y as  use  the  "tight  Twelve hours l a t e r the l o a d was  tensioned  t h a t a f t e r t h i s • t i m e l o s s o f l o a d due in.the strand was.negligible. then-weighed and p l a c e d  t o a l o a d o f 15  reduced t o l i l k i p s .  .The  except a  kips.  . I t had been. found  t o s l i p p i n g o f the  g r i p s or creep  aggregates, cement, and-water, were  i n : a Liner-Cumflow. 2 c u . ..ft.. mixer. :  m a t e r i a l s - w e r e mixed- f o r one minute. mixer and'the forms.were t w o - t h i r d s  end"  follows.  c l e a n e d w i t h a power-driven w i r e b r u s h u n t i l i t had s t e e l was  be  specimen  surface conditions a l l prestressing- s t e e l ,  p o l i s h e d appearance. .The  R.  system  o f the h y d r a u l i c jacks.... Concrete specimens were c a s t a g a i n s t b u l k h e a d . . Upon r e l e a s e o f p r e s t r e s s at one  P.  The  concrete  filled.  . The  was  mix  The  t a k e n from the  was  vibrated.for  8.  1G seconds w i t h a l a b o r a t o r y v i b r a t o r a t t a c h e d , t o t h e forms. .The forms were: t h e n f i l l e d • • t o t h e t o p and v i b r a t e d , f o r a n o t h e r 10 seconds.  The  specimens were t h e n c o v e r e d w i t h m o i s t b u r l a p bags o v e r l a i n by 6  mi I  polyethylene sheets.  The b u r l a p bags remained m o i s t f o r t h e c u r i n g p e r i o d .  C u r i n g t e m p e r a t u r e was a p p r o x i m a t e l y 7 2 ° F.  Two i d e n t i c a l  specimens  were c a s t f o r each t e s t , and two c o n t r o l c y l i n d e r s were poured a t t h e same time.  The same v i b r a t i o n and c u r i n g methods were used f o r t h e c y l i n d e r s • At 2 h o u r s  a f t e r c a s t i n g , t h e b u r l a p bags and forms were  removed. . A t 30 hours t h e i n s t r u m e n t e d specimen was s l o w l y r e l e a s e d i n i n c r e m e n t s o f 1 . 2 5 k i p s . .. A t each increment t h e r e l e a s i n g was stopped by closing the valves.  Readings o n b o t h l o a d c e l l s and a l l d i a l gauges were  taken. . The d i f f e r e n c e : i n r e a d i n g s o f t h e d i a l gauges minus t h e e l a s t i c s h o r t e n i n g o f t h e s t e e l due t o t h e l o s s o f l o a d , a s r e a d on t h e corresponding l o a d c e l l s , equals the shortening o f t h e s t e e l w i t h i n t h e c o n c r e t e . As-6 as shown. i n F i g u r e 6 c o r r e s p o n d s t o t h i s s h o r t e n i n g . k . The l o a d c e l l s were r e a d ' t o .01 , and a l l d i a l gauges were r e a d to  .001" a t each i n c r e m e n t .  S l i p i s d e f i n e d a s a r e l a t i v e movement o f  t h e s t e e l and c o n c r e t e a t t h e t i g h t end w h i c h , i n t h e case o f s t r a n d s , c o i n c i d e s w i t h b e g i n n i n g o f r o t a t i o n a l movement a t t h a t end. A t t h e same t i m e a,drop i n l o a d anchored was o b s e r v e d . equals the d i f f e r e n c e in. readings o f t h e load  The " l o a d  cells.  anchored"  . DESCRIPTION OF TEST: SERIES Series I The purpose of t h i s series was to e s t a b l i s h a t e s t procedure and a curing c y c l e . . Six t e s t s were made using 18" long specimens, varying the surface condition o f the s t e e l , and curing time o f the concrete. . The r e s u l t s are not p a r t i c u l a r l y noteworthy except f o r t e s t number k which was accidentally quickly released. - Specimens of series I t o VI i n c l u s i v e were 3" x 3* i n cross section while the others were k  n  x V.  Series I I The purpose of these t e s t s was t o e s t a b l i s h (a) the v a r i a t i o n of force anchored with the length o f the specimen, (b) the e f f e c t o f v i b r a t i o n , (c) the e f f e c t of stress concentrations  caused by bearing  at the t i g h t end. . The force anchored: i s defined as the maximum force which was anchored i n the specimens just before s l i p occurred;  where  s l i p has been defined previously. . Thus, only those specimens which slipped were plotted;to prevent confusion. . A t o t a l of Ik t e s t s were made varying the length of specimens from 5" t o 13", curing time and conditions were i d e n t i c a l f o r a l l specimens. -The  other variables such as, concrete  strength, age o f concrete  at release, surface condition, and speed o f release were kept as constant  as possible. . The concrete used f o r t h i s series was; Mix I  with a water/cement r a t i o o f -396 and a cement/aggregate r a t i o o f .290. . D e t a i l s of the mix are given.in.Appendix I I and.the stress s t r a i n curve i n •• F i g . 9 • .The  e f f e c t of v i b r a t i o n was tested i n Tests 3 and k, .Both  specimens were poured at the same time. . The concrete  f o r Specimen  3 was placed very c a r e f u l l y with a trowel, compacted by about 1G blows with i t s edge, and received: two seconds v i b r a t i o n . .Specimen k was placed i n the usual manner but the normal time o f v i b r a t i o n was doubled. The outward: appearance of the specimens was i d e n t i c a l . .To e s t a b l i s h the e f f e c t , i f any, o f stress concentrations due to end-bearing, a \  w  two specimens 18" long were cast. .. At the bearing end  copper tube 6" long had been.slipped over the 3/8" strand. . The  ends o f the tube were f i l l e d with putty t o prevent any concrete from entering. .The e f f e c t of t h i s was t o e s t a b l i s h a 6" de-bonded length at the bearing end. Series:III : The purpose o f t h i s series was t o f i n d the v a r i a t i o n o f the force anchored with the length o f the specimen.for were made using specimen lengths ranging-from Mix:  a d i f f e r e n t mix. ..Ten t e s t s 5" t o 2 0 " .  I I was used for t h i s series with a water/cement r a t i o o f  .500 and a cement/aggregate r a t i o of .290. . This mix was i d e n t i c a l with Mix I except that enough water was added.to bring the water/cement r a t i o to the above value.  The stress s t r a i n curve i s given i n F i g . 9•  A l l other conditions were the same as i n Series •II". Series IV Six t e s t s were made i n t h i s series varying the length o f specimens from 5" t o l W  I t was attempted to f i n d the behaviour o f  the specimens before, during and a f t e r s l i p . . For t h i s purpose each load cell,was hooked: into an automatic  s t r a i n recorder. .Thus.it was  possible t o obtain continuous readings o f the load:at each end o f the specimen during release.  Noteworthy i s the fact that each  specimen showed: a drop i n load anchored at s l i p . with the force anchored at s l i p .  This drop increased  One of these continuous records i s  shown i n Figure 2. Before s l i p , as the load i s released, the load c e l l at the bearing end remains at almost i t s : i n i t i a l value, the drop i n load being due to•the e l a s t i c deformation of the frame and bulkhead.. As the s t e e l begins to s l i p through the specimen, the load at the bearing end drops, while the load at the releasing end remains r e l a t i v e l y stable.  The tension i s being released at the same time.  This, of course, means that the strand i s s l i p p i n g through the specimen while the force anchored remains r e l a t i v e l y constant.  This  behaviour was found to be quite t y p i c a l and'was v e r i f i e d by t e s t s without the automatic equipment. .. At the same time t h i s series of t e s t s attempted:to f i n d the relationship between force anchored and length o f specimen f o r Mix I I I . Mix I I I i s i d e n t i c a l with Mix I except that the coarse aggregate was omitted.  i  Itss. stress^ s t r a i n curve i s shown i n F i g . 9-  -Again, a l l other variables were held as constant as possible.  Series V Two t e s t s were made i n which the strand was covered with a t h i n f i l m of form o i l .  No other variables were:introduced. .The  concrete mix for these specimens was i d e n t i c a l to the mix for series I and I I . Series VI For  t h i s series .276" diameter wire was used.  The purpose  of t h i s series was t o f i n d the mode of anchorage o f wires, and t o  find the difference, i f any, i n the manner of anchorage of wires and of strands.  Four tests were made using specimen lengths of l6" and 2k . n  No other variables were introduced. Series VII Two tests were made to find whether anchorage length i s affected by concrete stress.  This was done by increasing the cross-  section of the specimens from 3" x 3" to V x k", thus decreasing the concrete stress by hk$. As in series VI, .276" diameter wirei was used. Series VIII Four pull-out tests with untensioned wires were made. No other variables were introduced. Series IX Two tests were made to find the effect of time of transfer upon anchorage length.  For this purpose the normal curing time of 30  hours was increased;to kQ hours. A l l other conditions, except for specimen cross-section which was now k" x h , was as in series III. n  No.  Length  P  Shortening of Steel i n x 10"3  Slip  c K/in f  05  Remarks  inches  • anch. kips  1  18  13-15  kS  No  6-93  Rusty strand, U8 hrs.  2  18  13-35  57  No  6-93  Rusty strand, U8 hrs.  3  18  13-16  k9  No  5.28  Clean strand, 30 hrs.  k  18  13.2k  66  No  5-28  Clean strand, 30 hrs.  5  18  13-22  k3  .No  6  18  13-29  kl  a> H*  2  No  •M.96  to w M  Fast releasing.  Clean strand, 30 hrs.  k.96  1  1  CO  i  Concrete  I ;  1 CO  3/8" Strand;  Purpose:  To e s t a b l i s h curing cycle; and method of testing.  Note:  Test No.V  P u l l i n at free end on f a s t release i s much l a r g e r than others.  No.  Length  Shortening of Steel i n . x 10"  Slip  f*  Remarks  inches  *anch. kips  1  10  7-26  21  Yes  5.52  2  10  10-90  29  Yes  5.52  3  12  13-26  45  No  5-50  No v i b r a t i o n .  4  12  13.26  hi  No  5.5O  20 • 20 seconds  3  p K/in^. c  5  18 - 6  •=11.55  57  Yes  5.31  20 • 20  6  18 - 6  13.85  48  No  5.31  20 • 20  46  No  5.61  No  5-61  7  13  13.68  8  13  13.30  9  5  4.11  6  Yes  5.47  10  5  5-26  9  Yes  5.47  11  8  7-96  22  Yes  5.27  12  8  9.95  20  Yes  5.27  13  10  12.88  44  Yes  5-»*5  14  10  11.51  32  Yes  Concrete I Purpose:  ;  3/8" Strand,  (a)  To e s t a b l i s h v a r i a t i o n of force anchored with length of specimen.  (b)  E f f e c t of v i b r a t i o n (Test No.3 and  (c)  E f f e c t of t i g h t end bearing.  No.4)  No.  Length inches  p anch. kips  Shortening of Steel i n . x 10~3  Slip  f£  Remarks  K/in . 2  7-33  26  Yes  2.8U  13  7.U0  26  Yes  2.8U  3  16  9-75  50  Yes  2-53  k  16  9.80  kk  Yes  2.53  5  20  13.38  65  No  2.67  6  20  13.20  66  No  2.67  7  9  U.29  13  Yes  2.5^  8  9  5-92  16  Yes  2.5^  9  5  2.7U  5  Yes  2.91  10  5  2.50  k  Yes  2.91  1  13  2  Concrete I I Purpose,  ;  3/8"  a> H*  (D cn M M M  Strand,.clean, ;  (a)  To e s t a b l i s h v a r i a t i o n of force anchored with length of specimen.  (b)  To establish v a r i a t i o n of required anchorage length with concrete strength.  H  Shortening of Steel i n . x 10"J  . Length inches  ^anch. kips  1  10  8-55  25  Yes  5-22  2  10  9-35  27  Yes  5-22  •3  14  13-8  48  No  5-02  4  i4  13-8  ^5  No  5.02  5  5  4.00  6  Yes  4.86  6  5  4.50  6  Yes  4.86  No.  Concrete I I I , 3/8"  -  Slip  f' K/in p  Remarks  c  05  Strand, clean,  Automatic Equipment. Purpose:  (a)  To f i n d v a r i a t i o n of required anchorage length with s t r e s s - s t r a i n curve of concrete.  (b) .To v e r i f y method of taking measurements. (c)  To f i n d difference of before and a f t e r s l i p behaviour.  H ON  No.  Length inches  P  anch. kips  Shortening Of Steel 3 * ^ i n  Slip  x  f K/in . 2  1  10  .58  1  Yes  5.U9  2  10  .52  1  Yes  5.62  Concrete I  ;  3/8" Strand;  Oiled.  Remarks  c  Series VI.  % & &, 3  ft  w .01  as  to o>  u  K -  •H H  I  A. u •si' .a _»  fi\  &\  _*  v© • •I  N  H  CM  M  e  1  No.  Length, inches  1  16  2  16  5-50  Concrete I ; Purpose:  'anch.  .276"  H  H*  Shortening of Steel i n . x 10" 3  Slip  32.5  Yes  , 2^.5  Yes  wire, clean, J*" x h  Remarks K/in . 2  m  specimens.  To f i n d e f f e c t of stress i n concrete.  k.Qk  cn  <  M M  •No.  Length inches  P  an h.  Shortening . of.Steel i n . x 10"J  C  '  1  16  3.3O  16.5  2  16  3-15  15.5  3  32  N.D  N.D  k  32  3.20  Concrete Purpose:  I ;  .276"  -Slip  U5.O  ,  clean  T o f i n d mode o f  wire, untensioned. ;  anchorage of. untensioned  wires.  No.  Length inches  P^h.  . Shortening of Steel in..x"10~J  S  l  i  p  f  /  ^-,-^2 in  1  10  3.96  6.5  Yes  3.28  2  10  3.95  10.5  Yes  3.28  Concrete I I ; Purpose:  3/8"  Remarks  S t r a n d , 48 h r s . c u r i n g .  To f i n d the e f f e c t o f time o f t r a n s f e r on anchorage  length.  Reading No.  Load  '-#1  . Kips  #  D i a l Gauges  Panch.  Cells ...  2  Kips  Kips :  ,; S h o r t e n i n g of. S t e e l i n . x 10~3  •Rotational Gauge' . in... x 10"3  Cl c  i n ,. x l O  =4  1  3  4  - 1  2  5-5  .2.56  '9  2  7  ..15  1 .1  5  7-6  3-75  ,14  2  12  31  2; 2  8  8.3  . 14  11.1  21  13.2  27  1^-3  ,3V  15.5  42  16.7  13-90  l.4o  3  11.25  13.81  4  10.0  13-75  • 03  13-70  4,95  21  •3  18  •56  •2  6  7-5Q  13.67  6.17  29  3  26  78  •3  7  6.25  13.60  33  108..  3  3  8  5-0G  13-54  8.54  46  41  145  4  3  9  3-75  13 - 50  9-75  56. . 6  50  -  10  4.80  12.20  7.40  66  18"  48  2.98  10.25  7.27  103  39  64  -  -  1.80  9-30  7-50  120  50  70  -  -  •'7.-35. .  37  9:45 A.M. 3 in. x 3in.  ;  k  5  '  4  • DATE TESTED:  2 . •  :  2  :  k ••.  SERIES  8.J5  .  -  -  5  SPECIMEN CROSS-SECTION:  in.  -  • 13.-98'  JULY 23  i n . x 10"3.  0  12.50  DATE. .CAST:  3  0  2  12  -  0  13-95  . l l •  calc .  :  2  0  1  ;  #2 #1 x.10-3 in.. :  H H M  • t)  >  slip  -cn t?d cn 1-3  -  JULY 24  SPECIMEN LENGTH:  3:1.5 P.M.  16 x n .  LOAD CELL #1 I S AT TIGHT END LOAD CELL #2 I S AT FREE END DIAL GAUGE #1 REPRESENTS READING.-AT FREE END (AVERAGE' 0F TWO GAUGES), DIAL GAUGE:#2 REPRESENTS.READING.AT TIGHT END (AVERAGE OF TWO GAUGES)  ro ro  C-i  For  Ci  - Correction  CU see F i g . 1  = ( d " P) (  P. - P —jr—^ CL "s s  f a c t o r a t f r e e end _  p  t  ct « 7/8"  x . 0 8 G x 28,00C) =  - )  ?  8  P:  C2  = Correction  f a c t o r a t t i g h t end = As  p  x  -  P  -393 ( 1 0 ) "  3  .  Es (<£ta*)  Where £, _ Specimen l e n g t h  For  Po  = Initial  force  P  _ Force i n l o a d  (  .02  - (13.98 - 13.50)  (.  A  = • Shortening o f S t e e l  $ A  c e l l at reading  reading..#9 $ I - 16"  - (13--95 - 3-75)  Ci  i n . l o a d . c e l l a t end c o n s i d e r e d  8  x .080 x 2 8 . 0 ) = (  o 8  o  6  x  8  2 lo)  From e x p e r i m e n t a l r e l a t i o n s h i p  £  C ) = 50 - (k  - 3-75)  h)  2  As Es 1-73 Panch  - 1.73 x .080 x 2 8 . 0 x h2 9-75  Compare: length  -95  d 3 - 9 8 " 13.50)  8  - (___  1 3  o f specimen = 16"  _ 3.  8  8  (-.393)  (7.5^.)  = k2 x-.10"3 i n .  ^S-€  x  »  h2 9-75  = 16.7"  . DISCUSSION OF TEST RESULTS  (a)  R e l a t i o n s h i p b e t w e e n , S h o r t e n i n g o f S t e e l and. Anchorage•Length ;  . I n . F i g u r e 6 t e s t r e s u l t s o f 25 specimens w h i c h , s l i p p e d upon i n i t i a l r e l e a s e were p l o t t e d .  The e x p r e s s i o n . d e v e l o p e d . f r o m t h i s i s  —IT* _P___ ^ where P^ i s t h e f o r c e anchored a t s l i p . . S i n c e t h i s expression.reduces t o  /.?3  ^  p.  , .  ^- 3" * St  ^  T h i s does not agree w i t h t h e r e s u l t s o f o t h e r i n v e s t i g a t o r s . . F o r t e s t s e r i e s I t o V I I I . i n c l u s i v e . t h e d i a l gauges.used. for. s l i p measurement had ;  been a t t a c h e d t o t h e s t e e l frame. frame i s i n compression.  Before the release o f p r e s t r e s s the  I t a l s o c a r r i e s some bending moments. , As t h e  p r e s t r e s s i s r e l e a s e d . t h e compression i n p a r t o f t h e . f r a m e . i s reduced. The  s i g n and magnitude  o f t h e bending.moments i s a l s o changed. . T h e r e f o r e  t h e p o s i t i o n of. the d i a l gauges w i t h r e s p e c t t o each o t h e r may change somewhat d u r i n g t h e . t e s t . . T h i s may- i n t r o d u c e e r r o r s o f some s i g n i f i c a n c e . i n t o t h e slip•measurements. . In. s e r i e s . I X t h e d i a l gauges were suspended  from an aluminum frame, thus b e i n g u n i n f l u e n c e d by. d e f o r m a t i o n s  and r o t a t i o n s o f t h e s t e e l frame. , However, t h e aluminum.frame was found t o be t o o f l e x i b l e , t h e r e f o r e ,  t h e r e s u l t s were i n c o n c l u s i v e .  , I t appears t h a t t h e r e l a t i o n s h i p between s t e e l s h o r t e n i n g and anchorage - l e n g t h i s t h e same•for w i r e s as f o r s t r a n d s ( F i g . . 6 ) ,  .Assuming  t h a t t h e above shown e q u a t i o n . i s c o r r e c t , t h e a n c h o r a g e • l e n g t h can now be c a l c u l a t e d f o r each increment o f p r e s t r e s s r e l e a s e .  I n o t h e r words,  u n t i l t h i s e x p r e s s i o n had been developed, each t e s t s p e c i m e n . f u r n i s h e d o n l y one p o i n t on.the graph o f . f o r c e anchored a g a i n s t l e n g t h o f specimen ( F i g . T ) • T h i s p o i n t was found by measuring.the  f o r c e anchored a t s l i p .  25-  . Measuring t h e . f o r c e anchored, and t h e s h o r t e n i n g o f the increment  o f p r e s t r e s s r e l e a s e o f one  s t e e l at each  specimen, and c a l c u l a t i n g the  anchorage length,, should'now produce a s i m i l a r .graph as shown i n F i g . 7 f o r a c o r r e s p o n d i n g . s e r i e s o f specimens.  T h i s has been done i n . F i g .  .. Sample c a l c u l a t i o n s f o r s e r i e s . I l l t e s t #3 r e s u l t s . .At  a r e . i n c l u d e d . i n the. t e s t  s l i p t h e c a l c u l a t e d . a n c h o r a g e l e n g t h was :  l e n g t h o f . t h e specimen w a s l 6 " .  l6.7" while: t h e  But an e r r o r o f k x 10~3.in. i n t h e  measured s h o r t e n i n g o f the s t e e l w i l l i n t r o d u c e a 10$  e r r o r i n t o the  c a l c u l a t e d anchorage l e n g t h . . T h e r e f o r e utmost a c c u r a c y gauge r e a d i n g s i s d e s i r a b l e .  8.  i n the  dial  There appears t o be some agreement  between c a l c u l a t e d r e s u l t s and:the curve o b t a i n e d from a s e r i e s o f specimens.  By v i s u a l i n s p e c t i o n the r e s u l t s o f KAAR ( l ) show a  o f l o a d p i c k - u p which, i s s i m i l a r t o - t h e curves  (b)  manner  shown on.. F i g . 7.  ;  Vibration. . T e s t s no.- 3 and no..k  its.manner  o f a p p l i c a t i o n , may  of series I I indicate that v i b r a t i o n ,  or  not be a c r i t i c a l . f a c t o r i n t r a n s f e r  l e n g t h . . I t i s e s s e n t i a l , however, t h a t t h e c o n c r e t e be w e l l compacted. . There was  no  s i g n i f i c a n t d i f f e r e n c e i n the b e h a v i o u r  o f the  two  specimens.  •(c)  Surface C o n d i t i o n . Oilingthe  (d)  strand reduced-the•force  anchored-by  95$-  Stress in.Concrete. . The  f o r c e anchored . i n a . l 6 i n c h l o n g c o n c r e t e specimen u s i n g :  . e i t h e r 3•inch x 3 i n c h or k i n c h x h i n c h b l o c k s i s approximately. for-Mix-. I and <^  .276"  specimens i s I.78,  5^  smooth w i r e . . S i n c e the • r a t i o o f t h e areas o f t h e s e one would expect  a s u b s t a n t i a l d i f f e r e n c e i n the  26.  f o r c e anchored, i f t h e s t r e s s . l e v e l i n . t h e c o n c r e t e Suryaprakasam (10) length of  10"  s u b s t a n t i a t e s . t h i s t o some extent  required-to; anchor a- f o r c e o f :  :  specimens•prestressed  (e)  were  10  K  in  an.important.factor.  s i n c e he shows a  2"  x  2" and-A" x U "  with.3/8" strand.  • '  Age of. C o n c r e t e . '.For  ,  .  s e r i e s IX two specimens were cast-.  The c o n c r e t e  used-,was t h e  same as i n s e r i e s . I I I . - C u r i n g time i n . S e r i e s I I I was 3© hours, and k2 : hours i n s e r i e s IX. -A 10" l o n g specimen cured 30 hours was expected.to  K  anchor about 5 • - The" two specimens o f s e r i e s IX anchored. 3 - 9 6 It  i s f e l t t h e r e f o r e t h a t time o f c u r i n g has l i t t l e  length of prestress. and  (f)  K  K and 3-95 •  i n f l u e n c e on t r a n s f e r  T h i s agrees w i t h t h e f i n d i n g s o f Kaar ( l ) and; P e a t t i e  (9)•  Pope  Repetitive Tests. . Some specimens w h i c h d i d ' n o t  retensioned  t o the i n i t i a l value  was t h e n r e p e a t e d .  of prestress.  l e n g t h but remains somewhat  remains.in  The r e l e a s e o f p r e s t r e s s  . A t y p i c a l r e s u l t o f t h i s o p e r a t i o n i s shown . i n . F i g u r e  k. . Note t h a t • u p o n retensioning-.the  that f r i c t i o n  s l i p u p o n . i n i t i a l slow, r e l e a s e were  s t e e l does not r e t u r n t o i t s o r i g i n a l  s h o r t e r . . T h i s i s e a s i l y e x p l a i n e d ' by t h e f a c t  i s not r e v e r s i b l e , thus upon r e t e n s i o n i n g -some compression  the c e n t r a l area o f the concrete  diagrams below.  specimen.as e x p l a i n e d . i n t h e  27CONDITION.AFTER FIRST RELEASE  r  •x. p Bond on.Wire  so  Psi  Force-in.Wire CONDITION. AFTEFJ RETENSIONING  Psi  Psi  Shortening i s t o the Area  F o r c e : i n Wire  T h i s b e h a v i o u r t h e n s u b s t a n t i a t e s the f r i c t i o n bond. "be r e v e r s i b l e . o f the  g e n e r a l agreement  on  Were p r e s t r e s s . t r a n s f e r bond e l a s t i c e v e r y e f f e c t . I t was  a l s o noted t h a t upon each r e l e a s e the  s t e e l became g r e a t e r ,  should  shortening  i . e . the anchorage l e n g t h i n c r e a s e d .  .The  i n c r e a s e per r e l e a s e became p r o g r e s s i v e l y s m a l l e r as the number o f retensionings  increased.  This effect  can b e s t be e x p l a i n e d by  suggesting  t h a t e v e r y r e l a t i v e movement between s t e e l and.concrete causes a smoothing o f t h e ; i n t e r f a c e and. t h u s reduces the c o e f f i c i e n t o f  (g)-  friction.  Concrete M i x e s . . As m e n t i o n e d . p r e v i o u s l y t h r e e d i f f e r e n t  concrete  mixes were used  due  i n . t h e s e . t e s t s . . F i g . 7 shows t h a t t h e specimens c a s t w i t h c o n c r e t e  I  and. concrete I I I appear t o • have s i m i l a r anchorage p r o p e r t i e s . ..The, :  water/cement r a t i o s of.. these.:mixes. are t h e same, w h i l e t h e cement/, aggregate, r a t i o s . a r e .290 and .522 r e s p e c t i v e l y . . Furthermore:mix I I I does not c o n t a i n any aggregate l a r g e r • t h a n 3/8"• • Mix I I p o s s e s s e s . t h e same cement/aggregate r a t i o as mix.I w h i l e h a v i n g , a s u b s t a n t i a l l y :  h i g h e r water/cement r a t i o . • . Specimens.poured w i t h mix I I r e q u i r e a l o n g e r anchorage l e n g t h , a l l o t h e r c o n d i t i o n s b e i n g - t h e same. 9'the.stress-strain-curves  f o r the various concretes  On.Fig.  a t the.time o f  ' < K t r a n s f e r a r e shown. .A p r e s t r e s s o f 1 4 w i l l s t r e s s . a . 3 " x 3"  concrete  specimen, t o approximately. 1.57; k s i . , At time of. t r a n s f e r mix-.II has an ultimate  s t r e n g t h o f approximately. 2.95 k s i . .At t h e w o r k i n g , s t r e s s  of  1.57 k s i . . t h e d i f f e r e n c e . i n . s t r e s s s t r a i n - c h a r a c t e r i s t i c s of. mix I I at 42 hours and mix I I I at,3© h o u r s . i s not n o t i c e a b l e . . The.anchorage requirements, however, vary w i d e l y  s i n c e a.10" long.specimen of. mix I I  anchored.3-95 k i p s a t 42 hours, and 10" l o n g specimen o f mix.I o r I I I w i l l anchor between 7 and 10 k i p s a t 30 hours. , I t appears, t h e r e f o r e , t h a t near u l t i m a t e c o n d i t i o n s e x i s t a t the i n t e r f a c e .  .  CONCLUSIONS  Anchorage l e n g t h .required, does not depend on, time • of-..prestress :  .transfer. The most important f a c t o r a f f e c t i n g , t h e bond s t r e n g t h o f c o n c r e t and:.thus t h e p r e s t r e s s anchorage• l e n g t h required,.is t h e water/ cement r a t i o o f t h e c o n c r e t e  mix.  A q u i c k l y , r e l e a s e d specimen w i l l require, a l o n g e r length.than  a•slowly released  anchorage  one.  The manner o f anchorage o f w i r e s and s t r a n d s . i s s i m i l a r . {  •  •  Length o f anchorage i s . n o t g r e a t l y i n f l u e n c e d by s t r e s s i n . t h e concrete. Bond: i s m a i n l y a f r i c t i o n a l phenomenon. V i b r a t i o n as such i s not a c r i t i c a l . f a c t o r  i n bond s t r e n g t h o f  concrete. Ultimate  c o n d i t i o n s e x i s t at t h e i n t e r f a c e o f s t e e l and.concrete  4  a:  K  o  0\ V  K k  Ac  0  -1 o U) IS  la 1 V o /  i  I  -i *  Z 3  «0  v»  1 Ul  »o z  32.  SHOFSTgWNg  -  S H O R T E N IN 6  20 OP  OF  STRft Ub  30  5T«ftWD  V.S.  40  IN  IHCHSS  LO*b  #HCHOKeb  SO X >o  _  60 3  OJ  lofiD  ANCHOR  IM  *  "\  KIPS  N  o  i/» (/>  WW  o  W  »  ^  0  LENGTH  SPECIMEN  LEW6TH IN  OF  SPECIMEN  V.S.  INCHES FIG.  7  FORCE  ANCHORED  37  TrHCftL  LOftb-  STKBtU PfT  CONCRETES  2.0  I.O STRftm  IN  3.0 in/ir>  x io  OF  CUftVgS TIME  4.o  O f  5:0  39-  APPENDIX I I S p e c i f i c a t i o n o f M a t e r i a l s Used. STRAND The strand used was a 7 wire nominal 3/8" diameter o f Japanese manufacture.  Its. s p e c i f i c a t i o n s . a s supplied by. the manufacturer were as N  follows.  Prestressed concrete-wire,.uncoated 7 wire stress r e l i e v e d strand, 3/8" diameter.  S p e c i f i q a t i o n A.S.T.M.. A 4l6-57T.  3/8" •  Nominal Diameter  Construction (Centre and Outer Wire)  1*6  Strand Diameter and Tolerance  3/8  l/64  ^ .080 i n .  Nominal S t e e l Area  4.50— 6.0 i n .  P i t c h (12 ~ l 6 D )  20,000 l b .  • Breaking Strength,> Min. Y i e l d Strength at 1$ Extension, Min.  17,000 l b .  Elongation i n 24 i n . , Min.  3.5  Nominal Wt: per 1,000 < f t .  . 274 l b .  Difference in-Wire Size (Center-Outer)  .002 i n .  The strand was t e s t e d by Suryaprakasam  #  (lO) and found t o s a t i s f y  , specifications.  ,  WIRE The wire used was s p e c i f i e d as .276 i n . diameter and conforming t o •A.S.T.M..specifications; Breaking Load  . '.  A 421-59T Type W.A. 14. 5 - 14.6 Kips.  T e n s i l e Strength  244 - 246 K s i .  Yield  215  Elongation i n 10"  5-5 #  Ksi.  The wire was tested by P. Taylor (3) and found to s a t i s f y specifications. The i n i t i a l tangent modulus was found to he between 27,700 as measured with an extensometer and29^000 K s i . measured with a s t r a i n gauge. CONCRETE , Type I I I "ELK" Portland cement was used f o r a l l mixes. the various mixes are as shown below.  D e t a i l s of  Percentages given are by wei  Mix I. •1". Aggregate  =  * 34.2#  3/8" Aggregate^  l4.6#  Water/Cement  Ratio - .396  Sand  = .  28.8$  Cement  «=  22.  Cement/Aggregate  3^.2*  Water/Cement  Ratio a .290  Mix I I . 1"  Aggregate =  3/8" Aggregate •« Sand Cement  Ratio = .500  lk.6<f>  .«  28.8  *  22. k  Cement/Aggregate  Ratio = .290  Mix I I I . 1"  Aggregate =  3/8" Aggregate =  0  Water/Cement  Ratio = .396  22.2  Sand  =  43,5  Cement  ,=  34-3  Cement/Aggregate  Ratio  . 522  Load - Strain r e l a t i o n s h i p s f o r the various concretes at the time of prestres transfer  are as shown i n Figure 9  Mix I i s shown i n Figure  11.  . The strength-time r e l a t i o n s h i p f o r  Load - S t r a i n relationships f o r the same  concrete at various ages are shown i n Figure  10.  BIBLIOGRAPHY  KAAR,.LaFRAUGH & MASS • "Influence o f Concrete Strength on Strand Transfer Length" P.C.I. Journal October 1963. ' , J.. R. JANNEY "Nature o f Bond in.Prestressed: Concrete"  A . c i l . . Journal May 1954.Vol. 25,. No. 9.  P. R. TAYLOR "Investigation of Transfer Bond in.. Pretensioned.Prestressed Concrete Members" M.A.Sc.. Thesis,U.B.C. .June 1962. EVANS & ROBERTSON •"Bond, Stress in.Prestressed Concrete from X-ray Photographs" Proc.. Inst. of C i v i l Engineers, Pt. 1, V o l . k, No. 2 March 1955. LINGER & BHONSLE "An:Investigation of Transfer Length i n Pretensioned Concrete using;Photoelasticity" P.C.I. Journal August 1963. DINSMORE, DEUTSH, & MONTEMAYOR "Anchorage and Bond; i n Pretensioned.Prestressed: Concrete Members" Prestressed Concrete Bridge Members Progress Report#19 Lehigh University, I n s t i t u t e of Research December 1958GUYON : "Prestressed Concrete". N. THORSEN "Use o f Large Tendons in.Prestressed. Concrete" A.C.I., Journal V o l . 27,. 52 ..kl. PEATTIE & POPE "Effect o f Age of Concrete on Bond. Resistance" A.C.I. Journal V o l . 27, 52 .42.  BIBLIOGRAPHY  (10)  (continued)  K.. SURYAFRAKASAM "Investigation o f Bond; i n 3/8 inch Diameter Strands f o r Pretensioned Concrete Members". M.A.Sc. Thesis U.B.p. 1963.  LE3 BT  1964 A7  J 6  •• Joa, E r i c , 1936Anchorage length i n pretensioned concrete and the e f f e c t of some variables theron. [Vancouver] The U n i v e r s i t y of B r i t i s h Columbia^  1964.  hh 1. diagrs. 28 cm. Thesis(M.A.Sc. i n C i v i l Engineering) - The University of, B r i t i s h Columbia, 1964. Bibliography: leaves k-3-kk. 1. Prestressed  concrete. 2. Strains I. T i t l e .  

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