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The shear capacity of reinforced concrete beam - column connections Peter, Bruce Gregor William 1971

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THE SHEAR CAPACITY OP REINFORCED CONCRETE BEAM - COLUMN CONNECTIONS by BRUCE GREGOR WILLIAM PETER D i p l . E n g . , S t . M a r y ' s U n i v e r s i t y , H a l i f a x , N.S., 1958 B. E n g . ( H o n o u r s ) , Nova S c o t i a T e c h n i c a l C o l l e g e , H a l i f a x , I960 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n t h e D e p a r t m e n t o f C I V I L ENGINEERING We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J a n u a r y 1971 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the Univer-s i t y of B r i t i s h Columbia, I agree t h a t the l i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r -ther agree that p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s under-stood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n -c i a l g ain s h a l l not be allowed without my w r i t t e n permis-s i o n . B. Peter Department of C i v i l E n g i n e e r i n g The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada January 1 9 7 1 ABSTRACT T h i s t h e s i s i s t o d e t e r m i n e t h e s h e a r c a p a c i t y o f a r e i n f o r c e d c o n c r e t e beam column c o n n e c t i o n a t z e r o moment. The j o i n t u n d e r s t u d y i s f o r m e d by c a s t i n g t h e beam a g a i n s t a smooth c o l u m n f a c e w i t h t h e t o p and b o t t o m r e i n f o r c i n g b a r s p r o j e c t i n g t h r o u g h t h e j o i n t and no k e y o r s u r f a c e r o u g h e n i n g p r o v i d e d . The v a r i a b l e s c o n s i d e r e d a r e the s i z e o f r e i n f o r c i n g b a r s and t h e d i s t a n c e to t h e f i r s t beam s t i r r u p . The s t r e n g t h o f t h e j o i n t i s b r o k e n down i n t o components o f a) top dowels b) b o t t o m d o w e l s and c) i n t e r -f a c e bond and f r i c t i o n . The components and the e n t i r e j o i n t s t r e n g t h a r e i n v e s t i g a t e d t h e o r e t i c a l l y and e x p e r i -m e n t a l l y . C o m p a r i s o n s o f b o t h t h e o r e t i c a l and e x p e r i m e n t a l r e s u l t s a r e compared and show t h a t t h e s t r e n g t h o f t h e j o i n t c a n be p r e d i c t e d f r o m t h e sum o f the t o p and b o t t o m dowel s t r e n g t h s . The s t r e n g t h o f t h i s beam column c o n n e c t i o n i s shown t o p r o v i d e a d e q u a t e s t r e n g t h and a method i s s u g g e s t e d f o r c a l c u l a t i n g t h e s h e a r c a p a c i t y o f the j o i n t . TABLE OP CONTENTS Page ABSTRACT TABLE OP CONTENTS LIST OF FIGURES LIST OF TABLES LIST OP GRAPHS CHAPTER 1 1 . 1 INTRODUCTION 1 1 . 2 DESCRIPTION OP JOINT 2 CHAPTER 2 2 . 1 FORCES ACROSS JOINT 3 2 . 2 BOTTOM DOWELS k a) E l a s t i c Analysis i+ b) P l a s t i c Analysis 8 c) Shear F r i c t i o n and Bond Stresses 9 2 . 3 TOP DOWELS 11 a) E l a s t i c Analysis -Crack Loads 11 b) P l a s t i c Analysis -Hinge Mechanism 1 2 CHAPTER 3 TESTING PROGRAMME lb, CHAPTER I4. I4..I BOTTOM DOWEL TESTS 1 5 i i . 2 TEST RESULTS 20 I4..3 DISCUSSION OF RESULTS 20 CHAPTER 5 5 . 1 TOP DOWEL TESTS 23 5 . 2 TEST RESULTS 2 9 5 . 3 DISCUSSION OF TEST RESULTS 2 9 TABLE OP CONTENTS - Cont'd Page CHAPTER 6 6.1 FRAME TESTS 32 6.2 TEST RESULTS 36 6.3 DISCUSSION OF TEST RESULTS 111 CHAPTER 7 JOINT DESIGN (A METHOD FOR CALCULATION) U-5 CHAPTER 8 CONCLUSION I4.8 REFERENCES l\S GRAPHS L I S T OP FIGURES F i g u r e No. Page 1 Beam Column J o i n t 2 2 F o r c e s A c r o s s J o i n t 3 3 U l t i m a t e Dowel L o a d 7 k F r e e Body D i a g r a m o f Bottom Dowel a t U l t i m a t e L o a d 8 5 Normal F o r c e s A c r o s s J o i n t 9 6 Top Dowel Beam on E l a s t i c F o u n d a t i o n T h e o r y 11 7 P l a s t i c H i n g e Mechanism f o r Top Dowels 13 8 B o t t o m Dowel S p e c i m e n 16 9 Bottom Dowel T e s t S p e c i m e n 17 9a B o t t o m Dowel L o a d i n g T e s t 17 10 Bottom Dowel T e s t s 19 11 Top Dowel T e s t s 21L 12 Top Dowel T e s t Beam 27 13 Top Dowel T e s t Beam End S u p p o r t s 27 II4. T y p i c a l C r a c k P a t t e r n f o r Top Dowel T e s t 28 15 D e v e l o p m e n t o f S e c o n d a r y C r a c k i n Top Dowel 28 16 Frame T e s t s S p e c i m e n 31 17 Frame T e s t 3k 17a T e s t Frame f o r C o m p l e t e J o i n t 35 18 Frame T e s t I n s t r u m e n t a t i o n 35 19 T y p i c a l C r a c k P a t t e r n f o r Frame T e s t o f J o i n t 38 20 S e c o n d a r y C r a c k D e v e l o p m e n t i n Complete J o i n t 39 LIST OP TABLES TABLE 1 Summary of Bottom Dowel Tests TABLE 2 Summary of Top Dowel Tests TABLE 3 Summary of Joint Tests TABLE I4. Comparison of Frame Tests to Calculated Data and Dowel Tests Page 21 26 37 kk L I S T OF GRAPHS G r a p h No. Page 1 D a t a f r o m H. M a r c u s 50 2 #3 B o t t o m Dowel 51 3 #5 Bottom Dowel 52 #6 B o t t o m Dowel 53 5 B o t t o m Dowel A v e r a g e s 5U-6 E x p e r i m e n t a l and T h e o r e t i c a l D a t a 55 7 #5 Top Dowel 3" S p a c i n g 56 8 #5 Top Dowel 2" S p a c i n g 57 9 #5 Top Dowel 1" S p a c i n g 58 10 #5 Top Dowel A v e r a g e s 59 11 C o m p a r i s o n o f T e s t s t o C a l c u l a t e d D a t a 60 12 Frame T e s t s 1" S p a c i n g 61 13 Frame T e s t s 2" S p a c i n g 62 II4, Frame T e s t s 3" S p a c i n g 63 15 Frame T e s t s 1" and 3" S p a c i n g 6Lj. 16 Frame T e s t s 65 17 C o m p a r i s o n o f Frame T e s t s t o Top and Bottom Dowels 66 18 C o m p a r i s o n o f Frame T e s t s t o Top and Bottom Dowels 67 19 C o m p a r i s o n o f Frame T e s t s t o Top and B o t t o m Dowels 68 20 Top Dowels - P l a s t i c Mechanism S t r e n g t h 69 21 Top Dowels C r a c k L o a d 70 ACKNOWLEDGMENTS I w i s h t o e x p r e s s my s i n c e r e a p p r e c i a t i o n t o P r o f e s s o r S. L i p s o n f o r h i s g u i d a n c e and c o n s t r u c t i v e h e l p t h r o u g h o u t t h i s t h e s i s . A l s o , I w i s h t o t h a n k M e s s r s . R. P o s t g a t e and W. S c h m i t t f o r t h e i r v a l u a b l e a s s i s t a n c e i n m a k i n g t h e t e s t e q u i p m e n t and c a r r y i n g o u t t h e t e s t s . F i n a l l y , I w i s h t o ack n o w l e d g e f i n a n c i a l a s s i s t a n c e f r o m t h e N a t i o n a l R e s e a r c h C o u n c i l o f Canada and t h e C o m p u t i n g S c i e n c e C e n t r e o f t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . 1. THE SHEAR CAPACITY OP REINFORCED CONCRETE BEAM - COLUMN CONNECTIONS CHAPTER 1 1.1 INTRODUCTION I n r e i n f o r c e d c o n c r e t e c o n s t r u c t i o n i t i s some-t i m e s d e s i r a b l e t o h a v e a c o n s t r u c t i o n j o i n t between a beam and a c o l u m n . C o r b e l s a r e o f t e n u s e d a t t h e j o i n t t o t r a n s -f e r t h e s h e a r f o r c e . The u s e o f c o r b e l s c a n be c o s t l y and i m p r a c t i c a l , p a r t i c u l a r l y when d e a l i n g w i t h p r e c a s t c o n c r e t e members. W i t h o u t c o r b e l s t h e s h e a r t r a n s f e r w o u l d be a c -c o m p l i s h e d s o l e l y by t h e r e i n f o r c i n g b a r s t h r o u g h t h e j o i n t a c t i n g as d o w e l s , p l u s any bond and f r i c t i o n a l f o r c e s be-tween t h e c o n c r e t e s u r f a c e s . P r e v i o u s i n v e s t i g a t i o n s o f t h e s e beam-column j o i n t s by K r a t z ^ D i n d i c a t e d t h a t t h e s h e a r c a p a c i t y o f t h e j o i n t was i n v e r s e l y p r o p o r t i o n a l t o t h e moment a c r o s s t h e j o i n t . The p u r p o s e o f t h i s t h e s i s i s t o d e t e r m i n e t h e s h e a r s t r e n g t h o f r e i n f o r c e d c o n c r e t e beam-column j o i n t s a t z e r o moment f o r v a r i a t i o n s i n s t i r r u p s p a c i n g s . 2. 1.2 DESCRIPTION OP JOINT COLUMN BEAM — TOP BAR STIRRUP BOTTOM BAR L - S = DISTANCE TO 1 s t STIRRUP F i g u r e 1 BEAM-COLUMN JOINT The t y p i c a l beam-column j o i n t i n v e s t i g a t e d i s as shown i n f i g u r e 1. The j o i n t i s formed by p o u r i n g the column f i r s t , a l l o w i n g i t to cure, and then p o u r i n g the beam a g a i n s t the column. The top and bottom r e i n f o r c i n g bars protrude through the j o i n t and no key or surface roughening i s p r o v i d e d . The l o a d i s pure shear across the j o i n t . There i s no bending moment, t o r s i o n a l or a x i a l f o r c e s across the j o i n t . The t e s t v a r i a b l e s are bar s i z e and s p a c i n g to the f i r s t s t i r r u p . 3. CHAPTER 2 2 . 1 FORCES ACROSS JOINT The f o r c e s t h a t a c t t h r o u g h t h e j o i n t a r e shown i n f i g u r e 2. The t o p and b o t t o m d o w e l s c o n t r i b u t e a x i a l , moment and s h e a r f o r c e s . The c o n c r e t e s u r f a c e may c o n t r i -b u t e a x i a l , b o n d and f r i c t i o n f o r c e s . The t o t a l s h e a r a c r o s s t h e j o i n t i s t h e sum o f t h e dowel s h e a r s p l u s c o n c r e t e s u r f a c e f o r c e s . t F i g u r e 2 FORCES ACROSS JOINT v = v T D + v B D + v B + V P where: V, TD = s h e a r i n t o p dowels Vgp = s h e a r i n b o t t o m d o w e l s Vg = s h e a r f o r c e due t o bond V F = s h e a r f o r c e due t o f r i c t i o n V = t o t a l s h e a r a c r o s s j o i n t 2.2 BOTTOM DOWELS a) E l a s t i c A n a l y s i s The b o t t o m dowel i n the beam and column i s an-a l a g o u s t o a beam on an e l a s t i c f o u n d a t i o n . S o l u t i o n s t o beams on e l a s t i c f o u n d a t i o n s have b e e n d e v e l o p e d by S. IP) T i m o s h e n k o v '. The s o l u t i o n f o r a s e m i - i n f i n i t e beam on an e l a s t i c f o u n d a t i o n i s : y = ~ ¥ j Pe(/3X)'^Mo e ( ^ x ) " ^ x ) } where y = d e f l e c t i o n a t x 41 0 \ 4 E I P = v e r t , f o r c e on dowel K = F o u n d a t i o n Modulus 6 = e~^ xcos /3x f = e~^xsin jsx M 0 = Moment on dowel x = d i s t a n c e f r o m end beam Some e a r l y work on dowel s t r e n g t h was done by F r i b e r g ^ ) u s i n g T i m o s h e n k o 1 s beam on e l a s t i c f o u n d a t i o n e q u a t i o n s . The f o u n d a t i o n m odulus K i s d i f f i c u l t t o e s -t a b l i s h f o r a dowel i n c o n c r e t e . F u r t h e r m o r e , b e c a u s e o f c o n s i d e r a b l e y i e l d i n g i n t h e s t e e l and c r u s h i n g o f t h e c o n c r e t e , t h i s e l a s t i c method i s u n s u i t a b l e f o r p r e d i c t i n g t h e u l t i m a t e l o a d . # F o r m u l a e numbered i n r i g h t m a r g i n s . The foundation modulus i s the load per unit length to produce a unit d e f l e c t i o n . Grinter, i n discus-sion of Priberg's paper, suggests values i n the range of 300 to 1 5 0 0 k s i . A c a l c u l a t i o n f o r the foundation modu-lus can be made from the following: assume that the stress i s di s t r i b u t e d at 1+5 degrees under the dowel, then the stress a at a distance a below the dowel i s : f j 0 = a ~ "a+t P = bearing load on dowel per unit length a = distance below dowel t' = diameter of dowel The d e f l e c t i o n A of the dowel i s then: .d n I b 'O d = depth of beam r d _q_ / da E / a+ t For the foundation modulus, A =1 and Q = K , therefore: {= K = [ l o g e ( d + t ) - l o g e t ] To calculate the crushing load: The bearing stress <rQ under the dowel i s ffo = K y t y = d e f l e c t i o n from equation 1 . 6. The c r u s h i n g l o a d (P ) c a n be d e t e r m i n e d f r o m e q u a t i o n s 1 , 2 and 3 i f t h e c r u s h i n g s t r e s s i s known. The c r u s h i n g s t r e s s u n d e r the dowel i s g r e a t e r t h a n the c r u s h i n g s t r e n g t h o f the c o n c r e t e c y l i n d e r t e s t s . Marcus'^'^ d e t e r m i n e d t h a t t h e c r u s h i n g s t r e s s u n d e r the d o w e l s i n c r e a s e d f r o m 1 . 8 f ^ f o r 2 i n c h dowels t o 2 . 6 f ' f o r 3A i n c h dowels ( G r a p h 1 ) . The c r u s h i n g l o a d c a l c u l a t e d f r o m e q u a t i o n s 1 and 3 i s n o t v e r y s e n s i t i v e t o t h e K v a l u e . F o r example, t h e c r u s h i n g l o a d f o r No. 3 dowel was I . 8 3 k i p s f o r K = 3 5 0 k s i and I . 3 8 k i p s f o r K = IOI4O k s i . A l s o , f o r No. 6 dowel the c r u s h i n g l o a d was 6 . 3 5 k i p s f o r K = 3 5 0 k s i and I4..6 k i p s f o r K = 1 3 0 0 k s i . INITIAL POSITION DEFORMED POSITION PLASTIC BEARING STRESS SHEARING FORCE BENDING MOMENT FIG 3 ULTIMATE DOWEL LOADS 8. b) P l a s t i c A n a l y s i s A t t h e u l t i m a t e l o a d t h e a s s u m p t i o n i s made t h a t t h e c o n c r e t e u n d e r t h e dowel h a s c r u s h e d . T h i s a l o n e w i l l n o t be f a i l u r e ; t h e l o a d c a n s t i l l be t r a n s f e r r e d a c r o s s by t h e dowel i n b e n d i n g ( f i g u r e 3)» E v e n t u a l l y , s u f f i c i e n t c u r v a t u r e w i l l o c c u r i n the dowel s t o a r r i v e a t t h e u l t i -mate b e n d i n g c a p a c i t y o f t h e d o w e l s . Two p l a s t i c h i n g e s w i l l o c c u r i n t h e dowel s f o r m i n g a c o l l a p s e mechanism. The f o r c e s a c r o s s t h e j o i n t a r e shown i n f i g u r e II, V SYMMETRICAL ABOUT JOINT w l_i M p . F i g u r e 1+ FREE BODY DIAGRAM OF BOTTOM DOWEL AT ULTIMATE LOAD From e q u i l i b r i u m .. _ ... wL Mp = VL 2 ~ V = wL V = ^ 2 w M p ' (1+) F o r r o u n d d o w e l s Mp=1.7f y S = 0.167fvcT (5) The c r u s h i n g s t r e n g t h u n d e r t h e d o w e l s , b a s e d on M a r c u s ' work, i s : w = f^d c TC = C f c d = c o n s t a n t f o r e a c h dowel s i z e ( G r a p h 1) (6) 9. Prom equations I4., 5 and 6 V = 0-575 d 2 V c f c f y ' (7) The value C varies from about 2 to 3 f o r the common ranges of r e i n f o r c i n g bars. Hence, i f a value of 2.5 i s assumed f o r C » the maximum error i s about t 10 percent. C = 2.5 V = 1.16AsVfc fy ' (8) As = Area of dowel I t i s therefore apparent that f o r the dowel the shear force at which the p l a s t i c hinge forms i s i n l i n e a r pro-portion to the area. c) Shear F r i c t i o n and Bond Stresses A X TOOTH ACTION CURVATURE OF DOWEL Figure 5 NORMAL FORCES ACROSS JOINT In addition to dowel forces across a j o i n t , there also may be f r i c t i o n a l forces. B i r k e l a n d ^ has proposed a shear f r i c t i o n hypothesis to explain the strength of pre-cast j o i n t s . This hypothesis maintains that the two surfaces 10 move away f r o m e a c h o t h e r b e c a u s e o f s u r f a c e i r r e g u l a r i t i e s . The r e i n f o r c i n g a c r o s s t h e j o i n t i s t h e n s t r e s s e d t o y i e l -d i n g . The n o r m a l f o r c e a c r o s s t h e j o i n t ( A s f y ) m u l t i p l i e d by a c o e f f i c i e n t o f f r i c t i o n d e t e r m i n e s t h e s h e a r s t r e n g t h . No a l l o w a n c e i s made f o r t h e bond s t r e n g t h o r dowel s h e a r . W h i l e B i r k e l a n d o n l y t a k e s i n t o c o n s i d e r a t i o n the s t e e l y i e l d i n g due t o t o o t h a c t i o n , a x i a l s t r e s s e s w i l l a l s o be c a u s e d b y t h e s h o r t e n i n g o f t h e dowel due t o c u r v a t u r e . T h i s c u r v a t u r e e f f e c t w o u l d be more s i g n i f i c a n t f o r smooth c o n c r e t e s u r f a c e s and l a r g e d i s p l a c e m e n t s . C o m p a r i s o n o f j o i n t t e s t s c o n d u c t e d on p u s h - o f f s p e c i m e n s by H a n s o n ^ 1 2 ^ , A n d e r s o n ^ ) and M a s t ^ 1 1 ^ shows t h a t t h e s h e a r f r i c t i o n h y p o t h e s i s p r o v i d e s a l o w e r bound f o r a c o e f f i c i e n t o f f r i c t i o n M o f 1.1). f o r o r d i n a r y c o n -s t r u c t i o n j o i n t s ( n o t r o u g h e n e d o r c a s t m o n o l i t h i c a l l y ) . B i r k e l a n d recommends a v a l u e o f 0.8 t o 1.0 f o r M . Some t e s t s f o r c o e f f i c i e n t o f f r i c t i o n o f c o n -( 7 ) ( fi } c r e t e h a v e b e e n c o n d u c t e d b y Jones ' and G a s t o n v '. F o r smooth p r e c a s t members w i t h m o r t a r e d j o i n t s , Jones i n d i -c a t e s v a l u e s o f M = 0.7 • G a s t o n a l s o s u g g e s t s a v a l u e o f 0.7 f o r n b u t i n a d d i t i o n u s e s a b o n d i n g s t r e s s o f 0.110 k s i . H o f b e c k ^ ^ c o n d u c t e d t e s t s on p u s h - o f f s p e c i m e n s s i m i l a r t o A n d e r s o n . H o f b e c k ' s f i g u r e s 5 and 6 show t h a t f o r c r a c k e d s p e c i m e n s t h e s h e a r s t r e n g t h i n c r e a s e s by 0.85 A g f y . T h e r e i s a l s o an a p p a r e n t b o n d i n g s t r e s s o f 0.300 k s i . 1 1 . B i r k e l a n d : G a s t o n : H o f b e c k : SUMMARY V = 1.4f y A s ( M o n o l i t h i c ) V = O.HOA+0.7A s fy(Mortared P r e c a s t ) V = 0.300A + 0 ,85A q f v ( c r a c k e d s V M o n o l i t h i c ) A = c o n c r e t e a r e a i n s q u a r e i n c h e s i s i n u n i t s o f k i p s , fy i n k s i , and As i n s q u a r e i n c h e s . 2.3 TOP DOWELS a) E l a s t i c A n a l y s i s - C r a c k Loads The t o p do w e l s a r e d i f f e r e n t f r o m t h e b o t t o m dowels i n t h a t t h e s h e a r t r a n s f e r a c r o s s t h e dowel p r o d u c e s t e n s i l e s t r e s s e s a c r o s s t h e f a c e o f the beam w h i c h may l e a d t o c r a c k i n g a c r o s s t h e beam. A method o f a n a l y s i s f o r t h e s e t e n s i l e s t r e s s e s i s t o c o n s i d e r t h e t o p dowel and c o n c r e t e above t h e dowel as a beam on e l a s t i c f o u n d a t i o n , s u b j e c t t o a s h e a r f o r c e a t one e n d , and a d i s t r i b u t e d t e n s i l e f o u n d a t i o n r e a c t i o n ( f i g u r e 6 ) . — nA s — 1 TRANSFORMED SECTION F i g u r e 6 TOP DOWEL BEAM ON ELASTIC FOUNDATION THEORY 12. T h i s beam o n e l a s t i c f o u n d a t i o n a n a l o g y h a s b e e n p r e s e n t e d by K r e f e l d ^ ^ i n a s t u d y o f s h e a r f o r c e s i n beams. The moment o f i n e r t i a o f t h i s beam c a n be d e t e r m i n e d b y u s i n g t h e t r a n s f o r m e d s e c t i o n . The d e t e r m i n a t i o n o f t h e f o u n d a t i o n m odulus c a n be b a s e d on t h e u n i t d e f l e c t i o n o f a column t h e h e i g h t o f w h i c h i s t h e beam d e p t h . The s t r e s s c o n d i t i o n s a r e known o n l y a t the t o p and b o t t o m o f t h e c o l -umn, and a l i n e a r v a r i a t i o n b etween t h e s e two b o u n d a r y c o n -d i t i o n s i s assumed. T h i s a s s u m p t i o n seems j u s t i f i e d o n t h e grounds t h a t t h e beam on e l a s t i c f o u n d a t i o n e q u a t i o n s a r e n o t v e r y s e n s i t i v e t o s l i g h t v a r i a t i o n s o f f o u n d a t i o n modu-i f 1 P = K 2bE d W i t h t h i s v a l u e o f f o u n d a t i o n modulus t h e c r a c k i n g s h e a r f o r c e may be o b t a i n e d f r o m e q u a t i o n 1. b) P l a s t i c A n a l y s i s - H i n g e Mechanism A f t e r a c r a c k h a s d e v e l o p e d i n t h e top o f t h e beam t h e s h e a r l o a d c o u l d s t i l l be c a r r i e d by t h e dowel s p a n n i n g t o t h e f i r s t s t i r r u p . l u s . A = F o r A = K = 13. PLASTIC HINGES i n n 1 V 2M, F i g u r e 7 PLASTIC HINGE MECHANISM FOR TOP DOWELS A p l a s t i c h i n g e w o u l d d e v e l o p a t t h e f a c e o f t h e col u m n and a t t h e f i r s t s t i r r u p . The s h e a r l o a d c a r r i e d by t h e top dowel i s t w i c e t h e p l a s t i c moment d i v i d e d by t h e s t i r -r u p s p a c i n g . CHAPTER 3 TESTING PROGRAMME The s t r e n g t h o f t h e j o i n t depends b o t h on dowel a c t i o n and o n bond o r f r i c t i o n a l f o r c e s . The t e s t i n g p r o -gramme was l a i d o u t t o d e t e r m i n e t h e dowel f o r c e s s e p a r a t e -l y , t h e n t o d e t e r m i n e t h e t o t a l s t r e n g t h o f t h e j o i n t w i t h b ond and f r i c t i o n a l f o r c e s . The t e s t i n g programme was t o : a) D e t e r m i n e t h e s h e a r s t r e n g t h o f t h e b o t t o m d o w e l s w i t h o u t f r i c t i o n a l o r b o n d f o r c e s . b) D e t e r m i n e t h e s h e a r s t r e n g t h o f t h e t o p d o w e l s w i t h o u t any f r i c t i o n a l o r bond f o r c e s . c) D e t e r m i n e t h e s h e a r s t r e n g t h o f t h e c o m p l e t e d j o i n t where bond and f r i c t i o n a l f o r c e s a r e p r e s e n t . The m a j o r v a r i a b l e s were s t i r r u p s p a c i n g and b a r s i z e s . The method o f i n v e s t i g a t i o n was t h u s t o b r e a k down t h e j o i n t i n t o i t s components and t e s t t h e s e s e p a r a t e l y ; t h e n f i n a l l y , t o t e s t t h e t o t a l u n i t w i t h a l l components. 15. CHAPTER I4. I4..I BOTTOM DOWEL TESTS For the bottom dowel tests the variables i n v e s t i -gated were (a) v a r i a t i o n i n bar size and (b) e f f e c t of a 1.0 k s i compressive ax i a l load on the column. The a x i a l load on the column was considered because i t might reduce the strength of the dowel since a crushing f a i l u r e under the dowel was anticipated. The test specimens were 11" x 6" x 16" concrete prisms. A dowel extended from the face of each prism (figure 8). Four specimens f o r each of dowel sizes No. 3» No. 5 and No. 6 were made f o r a t o t a l of twelve dowel tests. The concrete was supplied from a l o c a l "ready-mix" plant, and a l l specimens were cast at the same time. The cast concrete was wrapped i n wet burlap bags and covered with p l a s t i c sheets. The specimens were maintained at room temperature to cure for seven days, afte r which they were stripped and allowed to dry. The specimens were tested i n p a i r s . Each speci-men was bolted through the bottom to steel support columns. One of each pair of prisms was loaded v e r t i c a l l y by four tensioning rods through a cap plate. The stress i n each tensioning rod was read on a "Strainsert" b o l t . Two h a l f sections of bronze tube were placed around the dowel and clasped with steel plates (figures 9 and 9a), which were bolted to a loading beam. PLAN 16. CO £ rt 11 r t I ELEVATION 3 STIRRUP 6 VERT. 5 6 or 7 TEST DOWEL 3^ THREADED ANCHOR ROD CONCRETE f c = 4 300 psi % n MAX AGG. 2" SLUMP FAILURE TYPES CRUSHING + DOWEL SHEAR CRUSHING + VERTICAL CRACK CRUSHING -h DIAGONAL CRACK FIG 8 BOTTOM DOWEL SPECIMEN F i g u r e 9 BOTTOM DOWEL TEST COLUMN F i g u r e 9 a BOTTOM DOWEL LOADING TEST 18 . The l o a d was a p p l i e d by an Amsler h y d r a u l i c jack p l a c e d at the c e n t r e of the l o a d i n g beam ( f i g u r e 1 0 ) . Deformation of the dowel was measured wi t h L i n e a r V a r i a b l e D i f f e r e n t i a l Transformers (L.V.D.T.) attached to the prism and b e a r i n g on the clamping p l a t e s . During the t e s t s the transformers and s t r a i n b o l t s were monitored at constant l o a d i n t e r v a l s and recorded on punched paper tape. M a t e r i a l p r o p e r t i e s shown i n Table 1 are averages of concrete c y l i n d e r and s t e e l t e n s i l e t e s t s . S i x concrete c y l i n d e r s x 8" ) were taken from the same batch as the prisms and cured together. Three c y l i n d e r s were broken at the s t a r t of the dowel t e s t s , and the o t h e r three at the completion of the t e s t s . The average of a l l s i x c y l i n d e r s was used. The s t e e l s t r e n g t h s were determined from three samples, two f e e t l o n g , of each dowel s i z e . The rods were loaded to t h e i r y i e l d p o i n t and then to t h e i r u l t i m a t e l o a d i n a u n i v e r s a l t e s t i n g machine. TEST SPECIMEN CLAMPING PLATES T I F LOAD TEST SPECIMEN UNDER AXIAL LOAD TENSION RODS m I mi LOADING BEAM t> \1 J 5 L JJ FIG 1 0 BOTTOM DOWEL TESTS 20. It. 2 TEST RESULTS F a i l u r e i n t h e b o t t o m dowel t e s t s o c c u r r e d by-c r u s h i n g o f t h e c o n c r e t e u n d e r t h e d o w e l . T h i s c o n c r e t e c r u s h i n g o c c u r r e d a t 0.025 t o 0.050 i n c h d e f o r m a t i o n s . The l o a d d e f o r m a t i o n c u r v e s f r o m t h e t e s t s a r e p r e s e n t e d i n g r a p h s 2 t o 5« I n c r e a s e d l o a d i n g r e s u l t e d i n f u r t h e r c r u s h i n g u n d e r t h e dowel u n t i l e i t h e r t h e b a r f a i l e d i n s h e a r (No. 3 b a r s o n l y ) o r s p l i t t i n g o c c u r r e d i n t h e c o n -c r e t e f r o m a w e d g i n g a c t i o n o f t h e dowel ( f i g u r e 8). The l o a d o n a l l dowels k e p t i n c r e a s i n g t o d e f o r m a t i o n s o f a b o u t 0.3 i n c h e s when s p l i t t i n g o f t h e c o n c r e t e o c c u r r e d . A summary o f t h e t e s t r e s u l t s i s p r e s e n t e d i n T a b l e 1. 14.. 3 DISCUSSION OF RESULTS The f a i l u r e l o a d was n o t c l e a r l y e v i d e n t f r o m t h e t e s t s , and h e n c e a f a i l u r e c r i t e r i o n h a d t o be e s t a b -l i s h e d . C o l l a p s e o f t h e j o i n t o c c u r r e d w i t h d e f o r m a t i o n b e y o n d 0.3 i n c h e s . S u c h d e f o r m a t i o n s a r e t o o l a r g e t o be t o l e r a t e d i n n o r m a l s t r u c t u r e s , and so a f a i l u r e l o a d a t a l o w e r d e f o r m a t i o n was s e l e c t e d . The l o a d - d e f o r m a t i o n c u r v e s were somewhat b i l i n e a r , w i t h t h e change o f s l o p e o c c u r r i n g a t a b o u t 0.025 t o 0.05 i n c h d e f o r m a t i o n s . The f a i l u r e l o a d was t h e r e f o r e s e l e c t e d as t h e l o a d a t w h i c h a d e f o r m a t i o n o f 0.05 i n c h e s o c c u r r e d . 21. Table 1 SUMMARY OF BOTTOM DOWEL TESTS TEST NO. BAR SIZE COL. STRESS LOAD @ .05" DEF. CALCULATED FAILURE V CALC. V. TEST 1 C 3 U #3 0.0 k s i 1.8 2.0 1.10 1C3S #3 1.0 k s i 2.5 2.0 0.80 2 C 3 U #3 0.0 k s i 2.7 2.0 o.lk 2 C 3 S #3 1.0 k s i 3.0 2.0 0.66 1 C 5 U #5 0.0 k s i 7.0 5.2 0.75 less #5 1.0 k s i 6.14- 5.2 0.82 2 G 5 U #5 0.0 k s i 7.2 5.2 0.72 2 G 5 S #5 1.0 k s i 6.8 5.2 0.76 1C6U #6 0.0 k s i 8.0 7.9 0.99 1C6S #6 1.0 k s i 9.3 7.9 0.85 2C6U #6 0.0 k s i 9.6 7.9 0.82 2C6S #6 1.0 k s i 10.1 7.9 0.78 F a i l u r e loads are fo r one dowel. CONCRETE f £ = a,.350 k s i STEEL #3 f y #5 •fy #6 f y = 53.5 ksi = 1+7.2 k s i = 53.7 k s i f u = f u = f u = 79.5 k s i 77.7 k s i 81.2 k s i Calculated f a i l u r e loads V = l . l 6 A _ J f t f «* ~ c 7 22. The t e s t r e s u l t s were compared t o (1) p l a s t i c a n a l y s i s and (2) beam on e l a s t i c f o u n d a t i o n . From t h e s e c o m p a r i s o n s ( g r a p h 6) i t i s a p p a r e n t t h a t : a) The p l a s t i c a n a l y s i s method g i v e s c l o s e r e s u l t s when compared t o t e s t d a t a (0.395 v e r s u s 0 • i+3) • The v a l u e s a r e on t h e s a f e s i d e and t h e d i f f e r e n c e c o u l d e a s i l y be e x p l a i n e d by a s l i g h t v a r i a t i o n i n c r u s h i n g s t r e n g t h o f t h e s e s p e c i m e n s t o t h o s e u s e d by M a r c u s . b) The beam on e l a s t i c f o u n d a t i o n a n a l o g y gave v a l u e s t h a t a r e b e l o w t h e f a i l u r e l o a d s . T h i s i s e x p e c t e d as t h i s a n a l o g y g i v e s t h e l o a d a t w h i c h c r u s h i n g s t a r t s . 23. CHAPTER 5 5.1 TOP DOWEL TESTS The t o p dowel t e s t s were c a r r i e d o u t t o i n v e s t i -g a t e t h e i n f l u e n c e o f s t i r r u p s p a c i n g . T e s t samples were a l l o f No. 5 d o w e l s , w i t h t h e d i s t a n c e t o t h e f i r s t s t i r -r u p v a r i e d f r o m 1 t o 3 i n c h e s . T e s t s were c a r r i e d o u t o n 10" x 12" x V - 5 " beams f r o m w h i c h two No. 5 d o w e l s p r o t r u d e d a t e a c h end ( f i g u r e 11). A f t e r p l a c i n g , t h e c o n c r e t e was c u r e d f o r a s e v e n day p e r i o d b y c o v e r i n g t h e s p e c i m e n s w i t h wet b u r l a p b a g s and w r a p p i n g them i n p l a s t i c . 2 1 4 - . rS-DISTANCE TO 1 s t STIRRUP VARIED FROM 1-3 IN. 2 *5 6 -0 " LONG 1 <— 3 8 14 *3 STIRRUPS AT 4 IN. 4 ^ TOP DOWEL TEST BEAM -CM - * • -SEC. A NOTES COVER TO*5 BARS 1.5 IN MAX. AGG- SIZE % IN. TYPE 3 CEMENT 2 IN. SLUMP CONCRETE BEAM B 1 STEEL CLAMP PLATE BRONZE SHIM REINFORCING BAR SEC. B CLAMP SUPPORT FOR DOWEL FIG 11 TOP DOWEL TESTS 25. The dowels p r o t r u d i n g from the t e s t beam were c l a s p e d between p l a t e s , u s i n g s p l i t bronze t u b i n g to a c t as a s e a t i n g m a t e r i a l . A con c e n t r a t e d l o a d was a p p l i e d at the centre of the beam with an Amsler h y d r a u l i c jack. V e r t i c a l displacements were measured by L.V.D.T. Recor-d i n g i n s t r u m e n t a t i o n was a m u l t i - c h a n n e l V i d a r Recorder, with punched tape output ( f i g u r e s 12 and 13). L.V.D.T.'s were l o c a t e d on (a) each s i d e of the beam - to e l i m i n a t e r o t a t i o n e f f e c t s and (b) the top and bottom of the beam -to determine both v e r t i c a l displacement and crack widths. Loading was a p p l i e d to the beams c o n t i n u o u s l y and the deformations were recorded at constant i n t e r v a l s u n t i l f a i l u r e . Concrete s t r e n g t h s were determined from e i g h t c y l i n d e r s (Lj." x 8"). Three samples were broken at the s t a r t of the t e s t s and three at completion. In a d d i t i o n , The B r a z i l i a n S p l i t C y l i n d e r Test was performed on two c y l i n -ders f o r d e t e r m i n a t i o n of t e n s i l e s t r e n g t h s . S t e e l s t r e n g t h s were determined from three specimens, 2 f e e t l o n g , taken from the same l e n g t h of r e i n f o r c i n g bar from which the top dowels were made. 26. Table 2 SUMMARY OF TOP DOWEL TESTS BEAM NO. DISTANCE TO FIRST STIRRUP TEST FAILURE 1 LOAD (KIPS) PLASTIC FAILURE MECH. (K) CRACK FAILURE F CALC. F TEST IA S O.8I44. 8 . 9 9 . 2 0 1 4 . . 9 2 I.OI4. IA N O.8I4J4. 1 0 . 0 9 . 2 0 1 4 - 9 2 . 9 2 IB S 0 . 9 3 9.I+ 8 . 3 5 l V . 9 2 . 9 0 IB N 1 . 1 2 1 0 . 0 6 . 9 3 14-.92 . 6 9 2 A S 1 . 8 7 6.3 U-.15 U-.92 . 7 7 2 A N 1 . 8 7 6.3 J+.15 ^ . 9 2 . 7 7 2 B S 2 . 0 0 6 . 5 3 . 8 8 I+.92 . 7 6 2 B N 1 . 8 7 6 . 2 I4--15 i^ . 9 2 .82 3 A S 2 . 8 7 1+.8 2 . 7 0 U--92 1 . 0 2 3 A N 2 . 8 1 2 . 7 6 14-.92 3 B S 2 . 8 14-.7 2 . 7 6 U..92 1 . 0 5 3 B N 2 . 8 U-.7 2 . 7 6 I+.92 1 . 0 5 MATERIAL PROPERTIES (AVERAGE VALUES) pONCRETE f ^ = 5 . 3 0 0 k s i f£ = 0 . 1 * 5 0 k s i STEEL f = I4.7.6 k s i f = 8l.O ksi J '"'*, F a i l u r e load at 0 . 0 5 " displacement + 0 . 3 1 2 ^ Additional load i s for the s e l f weight of the test beam 27. F i g u r e lU, TYPICAL CRACK PATTERN FOR TOP DOWEL T EST Fi g u r e 1 5 DEVELOPMENT OF SECONDARY CRACK IN TOP DOWEL TESTS 29. 5.2 TEST RESULTS F a i l u r e o f t h e beams o c c u r r e d b y c r a c k i n g o f t h e c o n c r e t e t h r o u g h t h e beam a t dowel h e i g h t ( f i g u r e II4.). P l a s t i c h i n g e s t h e n d e v e l o p e d i n t h e r e i n f o r c i n g b a r s a t the f a c e o f t h e s t i r r u p and a t t h e s u p p o r t . F u r t h e r l o a d i n g c a u s e d a s e c o n d a r y c r a c k b e l o w t h e i n i t i a l c r a c k ( f i g u r e 15). These s e c o n d a r y c r a c k s a p p e a r e d t o be c a u s e d by t h e y i e l d i n g o f t h e f i r s t s t i r r u p i n t e n s i o n . The s e c o n d a r y c r a c k o n l y d e v e l o p e d a f t e r t h e j o i n t h a d d e f o r m e d a b o u t 1/2 i n c h . L o a d d e f o r m a t i o n c u r v e s f o r t h e t o p dowels a r e p r e s e n t e d i n g r a p h s 7 t o 10. When the t e n s i o n c r a c k de-v e l o p e d t h e r e was no s u d d en d e c r e a s e i n t h e l o a d . F o r t h e 1 and 2 i n c h s t i r r u p s p a c i n g t h e c r a c k s d e v e l o p e d v e r y s l o w l y , w i t h no d e c r e a s e i n l o a d . F o r the 3 i n c h s p a c i n g t h e r e was a s m a l l d e c r e a s e i n l o a d ( g r a p h 7)• The j o i n t s i n g e n e r a l were v e r y s o f t and w o u l d a l l o w o v e r 1/2 i n c h o f t r a v e l b e f o r e c o l l a p s e . U l t i m a t e f a i l u r e o c c u r r e d b y t e n s i o n f a i l u r e o f t h e f i r s t s t i r r u p . By the t i m e t h i s f a i l u r e o c c u r r e d t h e r e h a d b een c o n s i d e r a b l e geometry change i n t h e t o p d o w e l , c a u s i n g a s i g n i f i c a n t v e r t i c a l component o f f o r c e . 5.3 DISCUSSION OF TEST RESULTS The t e s t r e s u l t s i n d i c a t e t h a t t h e s h e a r s t r e n g t h o f t h e dowels i s s i g n i f i c a n t l y i n f l u e n c e d by t h e d i s t a n c e t o the f i r s t s t i r r u p . G r a p h 11 shows the e f f e c t o f s t i r r u p 3 0 . s p a c i n g t o s t r e n g t h . F o r a s m a l l s t i r r u p d i s t a n c e - a b o u t 1 i n c h - t h e r e i s good agreement between t e s t d a t a and t h e p l a s t i c h i n g e mechanism. F o r l a r g e s t i r r u p s p a c i n g s t h e c r a c k l o a d g o v e r n s o v e r the p l a s t i c h i n g e mechanism and t h e r e i s good agreement between c a l c u l a t e d d a t a and t e s t s . F o r i n t e r m e d i a t e s t i r r u p s p a c i n g s - i . e . 2 i n c h e s - t h e r e i s a 30 p e r c e n t d i f f e r e n c e between c a l c u l a t e d and t e s t d a t a . On t h e b a s i s o f t h e s e t e s t s , t h e f o l l o w i n g c o n -c l u s i o n s c a n be made: 1) S h e a r s t r e n g t h o f t h e t o p dowe l s i s i n v e r s e l y p r o -p o r t i o n a l t o s t i r r u p s p a c i n g . 2) F o r s m a l l s t i r r u p s p a c i n g t h e s h e a r s t r e n g t h c a n be d e t e r m i n e d a c c u r a t e l y b y t h e p l a s t i c h i n g e mechanism. 3 ) F o r l a r g e s t i r r u p s p a c i n g t h e f a i l u r e l o a d i s gov-e r n e d by t h e c r a c k l o a d . The c r a c k l o a d c a n be c a l c u -l a t e d f r o m t h e beam on e l a s t i c f o u n d a t i o n t h e o r y . ii) A d e q u a t e t i e - d o w n f o r c e f o r t h e dowel must be p r o -v i d e d by t h e f i r s t s t i r r u p o r t h e s t i r r u p w i l l f a i l i n t e n s i o n . 31 2-0 ' 7 ^ " 3'-6" " O _ I PLAN 2*6 4 1 * 8 2 # 5 ^2*3 L 3 9 , 1 4 S T I R . AT 3"O.C. 2 # 6 COL. TIES 3 AT 4* 1 THREADED COUPLING ELEVATION FIG 16 FRAME TESTS SPECIMEN 3 2 . CHAPTER 6 6 . 1 FRAME TESTS Frame t e s t s were c a r r i e d o u t t o d e t e r m i n e t h e c o n t r i b u t i o n o f bond and f r i c t i o n a l f o r c e s t o t h e j o i n t s t r e n g t h . The s u r f a c e o f t h e j o i n t h a d t o be smooth c o n -c r e t e t o s i m u l a t e t h e w o r s t c o n d i t i o n s t h a t would be a c h -i e v e d by s t e e l o r f i b r e g l a s s f o r m s . F o r the p u r p o s e o f t h i s i n v e s t i g a t i o n t h e n a t u r e o f t h e j o i n t i n t e r f a c e was t h u s m a i n t a i n e d r e a s o n a b l y c o n s t a n t . The v a r i a b l e s i n t h e f r a m e t e s t s were (a) t h e d i s t a n c e t o t h e f i r s t s t i r r u p and (b) t h e s i z e o f the t o p dowel.. An A t t e m p t was made t o l o a d t h e j o i n t i n p u r e s h e a r w i t h no moment, a x i a l o r t w i s t i n g f o r c e s . The frame u s e d f o r t e s t i n g t h e c o m p l e t e d j o i n t i s shown i n f i g u r e 1 6 . The column was 1 2 " x 2 1 + " x h , ' - 8 " and was c a s t w i t h the t o p and b o t t o m d o w e l s e x t e n d i n g f r o m the f a c e . The column f a c e a t the j o i n t was c a s t a g a i n s t a " c e l l o - f i n i s h e d " p o l y e s t e r - c o a t e d p l y w o o d f o r m . When wet the c o n c r e t e s u r f a c e f e l t l i k e p o l i s h e d m a r b l e . The columns were c o v e r e d w i t h wet b u r l a p t h e n wrapped w i t h p l a s t i c . They were c u r e d a t room t e m p e r a t u r e f o r a s e v e n day p e r i o d . When t h e columns were c u r e d t h e i r f a c e s were k e p t wet f o r t w e n t y - f o u r h o u r s and beams c a s t a g a i n s t t h e col u m n s . The beams were 1 0 " x 2 0 " x 3 ' - 6 " . Beam r e i n f o r c i n g was e i t h e r two No. 5 o r No. 6 t o p b a r s w i t h 1 t o 3 i n c h s p a c i n g t o the f i r s t s t i r r u p . A l l j o i n t s h a d two No. 3 b o t t o m d o w e l s . Columns were c a s t i n two g r o u p s (Frame 1 and 2 ) . A l l e i g h t 33. beams, however, were c a s t a t t h e same t i m e f r o m t h e same c o n c r e t e b a t c h . The f r a m e was a n c h o r e d t o t h e t e s t s l a b by a 1 i n c h d i a m e t e r t h r e a d e d r o d i n t h e column. L o a d s were a p p l i e d by two A m s l e r h y d r a u l i c j a c k s p u s h i n g i n o p -p o s i t e d i r e c t i o n s ( f i g u r e s 17 and 17a). One j a c k h a d h a l f the c a p a c i t y o f t h e o t h e r and was l o c a t e d t w i c e t h e d i s -t a n c e f r o m t h e column f a c e . The r e s u l t o f t h i s j a c k l o -c a t i o n was t o p r o d u c e z e r o moment a t the column f a c e . The j a c k s a r e s p h e r i c a l l y s e a t e d a t b o t h e n d s , h e n c e a l l a x i a l f o r c e s were e l i m i n a t e d i n t h e beam. To e l i m i n a t e t o r s i o n the j a c k s were c a r e f u l l y c e n t r e d on the beam. The ends o f t h e beams were b r a c e d to p r e v e n t e x c e s s i v e t w i s t i n g t h a t c o u l d l e a d t o t o r s i o n a l f o r c e s and a l s o t o a c t as s a f e t y b r a c i n g f o r c o l l a p s e . D e f o r m a t i o n s were m e a s u r e d a t t h e t o p , m i d d l e and b o t t o m o f t h e beam ( f i g u r e 1 8 ) . L.V.D.T.'s were u s e d f o r d e f o r m a t i o n m e a s u r e m e n t s . S i g n a l s were r e c o r d e d on punched t a p e by a m u l t i - c h a n n e l V i d a r R e c o r d e r . L o a d i n g t o e a c h f r a m e was a p p l i e d c o n t i n u o u s l y w i t h d e f o r m a t i o n r e a d i n g s t a k e n a t c o n s t a n t l o a d i n t e r v a l s . D e f o r m a t i o n r e a d i n g s were a l s o t a k e n a t any i n s t a n c e s o f l o a d f a l l - o f f c a u s e d by c r a c k i n g o r s l i p p a g e . A l l t r a n s -f o r m e r s were removed as a p r e c a u t i o n a r y measure p r i o r t o a t t a i n i n g c o l l a p s e l o a d . 3U,. JACK NO. 1 2 P TEST FRAME JACK NO. 2 ANCHOR ROD FIG 17 FRAME TEST 35. F i g u r e 18 FRAME TEST INSTRUMENTATION .36. 6.2 TEST RESULTS Loading o f the frames r e s u l t e d i n no j o i n t move-ment u n t i l a bond f o r c e between column and beam was over-come. When t h i s bond was broken the l o a d u s u a l l y f e l l o f f . Crack p a t t e r n s developed at the top of the beam which were s i m i l a r to those observed on the top dowel t e s t s . These cracks o c c u r r e d at the centre o f the top dowels, s t a r t i n g at the column f a c e and working up to the top of the beam ( f i g u r e 1 9 ) . F u r t h e r l o a d i n g produced secondary cracks below the i n i t i a l crack; these secondary cracks were l i k e l y due to s t i r r u p s t r e s s e s ( f i g u r e 2 0 ) . The top t r i a n g u l a r prism of concrete remained bonded to the column. F u r t h e r l o a d i n g produced deformations exceeding l / 2 i n c h which was beyond the range of the L.V.D.T. The u l t i m a t e f a i l u r e of the j o i n t o c c u r r e d by one of the bottom No. 3 dowels b r e a k i n g . Ultimate loads were about two to three times the f a i l u r e loads a t 0.05 i n s l i p . D uring the t e s t s there was no i n d i c a t i o n t h a t moments were developed across the j o i n t . The j o i n t remained c l o s e d both at the top and the bottom of the beam. Load-displacement curves f o r the t e s t s are p r e -sented i n graphs 12 to 16. A l s o , Table 3 p r o v i d e s a summary of the j o i n t t e s t s and m a t e r i a l p r o p e r t i e s . Examination of the bottom dowels, a f t e r the t e s t , showed t h a t c r u s h i n g of the concre t e under the dowels had occ u r r e d , r e s u l t i n g i n c o n s i d e r a b l e bending and the eventual f a i l u r e of the bottom dowels. 37. T a b l e 3 SUMMARY OP JOINT TESTS TEST FRAME NO. TOP BARS BOT. BARS DIST. TO 1 s t S T I R. (INCHES) S L I P LOAD 0.001 I N . (KIPS) FAILURE LOAD 0.05 IN. (KIPS) ULTIMATE LOAD (KIPS) IP-1 - 5 2#5 2#3 1.2 20.0 U2.1 1F-2-5 2#5 2#3 2.2 UO.O - % 63.0 * IF - 3 - 5 2#5 2#3 3-0 10.0 12.5 1*0.2 1F-1-6 2#6 2#3 1.2 25.0 21^ .0 50.0 2F-1-5 2#5 2#3 1.2 17.2 22.6 51.2 2F-2-5 2#5 2#3 2.1 13.0 114-.5 39. k 2P - 3 - 5 2#5 2#3 3.0 11.0 13.3 1*0.7 2F-3-6 2#6 2#3 3.1 10.0 16.0 36.8 MATERIAL PROPERTIES. CONCRETE: Column F I Column F2 Beams f • = 14-390 p s i f ^ = U060 p s i *l = 5250 p s i S T E E L : #3 f y - 55.2 k s i f u = 80.1*. k s i #U- f y = 50.7 k s i f = u 714.-5 #5 f y " U.6.9 k s i f u = 78.7 k s i #6 f = y 53.i k s i f = u 73.3 k s i * Frame 1P - 2 - 5 f a i l e d by s h e a r i n beam. J o i n t d i d n o t f a i l , D i s t a n c e t o 1 s t s t i r r u p i s m e a s u r e d f r o m f a c e o f column t o f a c e o f f i r s t s t i r r u p . 38. F i g u r e 19 TYPICAL CRACK PATTERN FOR FRAME TEST OF JOINT 39. F i g u r e 20 SECONDARY CRACK DEVELOPMENT IN COMPLETE JOINT l+O. One o f the f rames (1F-2-5) d i d no t f a i l a t the j o i n t b u t by s hea r f a i l u r e i n the beam a t 63 k i p s . A d u p l i -c a t e frame (2P-2-5) f a i l e d a t the j o i n t a t Ik'k k i p s . E x -a m i n a t i o n o f the beam (1F-2-5) showed t h a t the bond was no t b r oken between column and beam. The beam was f i n a l l y b r o ken by l o a d i n g w i t h one j a c k o n l y . The bond between the c o n -c r e t e pours was s u f f i c i e n t l y s t r o n g t h a t s l i p o c c u r r e d about 0.1 i n c h e s i n s i d e the co lumn and no t a t the j o i n t l i n e . There i s no appa ren t r e a s o n why t h i s one beam s h o u l d d e v e l o p such e x c e l l e n t bond as a l l f rames were made and t r e a t e d e q u a l l y . F i g u r e 21 SMEAR FAILURE IN BEAM OF FRAME 1F-2-5 1*1. 6 . 3 DISCUSSION OP TEST RESULTS It i s apparent that there i s a s i g n i f i c a n t i n i -t i a l bond between column and beam. The load at which the i n i t i a l s l i p of the j o i n t occurs i s s i g n i f i c a n t l y i n f l u -enced both by the bond foce and the dowel strength. I t can be seen from Table 3 that the s l i p load decreases as the s t i r r u p space increases. Dowel forces thus contribute to j o i n t strength even before the j o i n t has slipped. This increased bond force cannot be explained by the area of steel across the j o i n t . The shear across the j o i n t at s l i p varied f o r the tests from 0 . 0 0 0 to 0 . 1 2 5 k s i . Since some of the load i s transferred by dowel action, the shear force due to bond would be less than 0 . 0 5 0 k s i . These bond shears are lower than the 0 . 1 1 0 k s i suggested by Gaston. The f a i l u r e load of the j o i n t should be considered at some deformation af t e r the s l i p has occurred. A f a i l u r e c r i t -erion of 0 . 0 5 inches deformation was selected. This c r i t -erion was also i n keeping with the dowel tests. Prom the f a i l u r e load i n Table 3 i t may be seen that the strength of the j o i n t i s dependent on the s t i r r u p spacing. This, therefore, rules out the shear f r i c t i o n hypothesis as a complete explanation of joint strength. The j o i n t strength i s dependent on s t i r r u p spacing, hence the load must be transferred i n part by dowel action. The comparison between the sum of the dowel tests and the frame tests i s shown on graphs 1 7 to 1 9 . The dowel test curves are arrived at by adding the loads from the top dowel t e s t s t o t h e l o a d s f r o m t h e b o t t o m t e s t s a t e q u a l d e f o r m a t i o n s . The c o m p a r i s o n shows t h a t t h e i n i t i a l s t r e n g t h o f t h e f r a m e t e s t s i s above t h e sum o f the dowel t e s t s . However, a t a b o u t 0.3 i n c h d e f o r m a t i o n t h e c u r v e s a r e e q u a l . These c u r v e s c a n be e x p l a i n e d as f o l l o w s : -i n i t i a l l y , t h e bond s t r e s s adds t o t h e s t r e n g t h o f t h e j o i n t . The bond i s e v e n t u a l l y b r o k e n . The s h e a r c a n n o t be c a r r i e d b y bond a f t e r s l i p h a s o c c u r r e d , b u t t h e l o a d does n o t f a l l t o t h e dowel c u r v e . F r i c t i o n a l f o r c e s must be p r e s e n t and h e l p c a r r y t h e l o a d . These f r i c t i o n a l f o r c e s a r e p r o d u c e d by t h e b o t t o m d o w e l s o n l y s i n c e t h e b e n d i n g o f t h e t o p d o w e l s o c c u r s o v e r t o o g r e a t a l e n g t h t o c a u s e a x i a l y i e l d i n g o f the b a r s . The b o t t o m dowels c o n t i n u e t o bend and f i n a l l y f o r m a p l a s t i c h i n g e . When t h e b e n d i n g e x t e n d s t h r o u g h t h e f u l l d e p t h o f t h e b a r , d e v e l o p i n g t h e maximum moment c a p a -c i t y o f t h e b a r , t h e t e n s i o n and c o m p r e s s i o n s t r e s s a r e e q u a l - h e n c e , the a x i a l f o r c e must be z e r o . T h u s , as the d e f o r m a t i o n i n c r e a s e s t h e p l a s t i c h i n g e s become f u l l y d e-v e l o p e d i n b e n d i n g , l e a v i n g no a x i a l f o r c e , and h e n c e , no f r i c t i o n . The l o a d i n t h e beam i s t r a n s f e r r e d by dowel a c t i o n a l o n e and t h e dowel and f r a m e c u r v e s meet. A t c e r t a i n d e f o r m a t i o n s the b o t t o m dowels c o n t r i -b u t e t o t h e s h e a r s t r e n g t h b o t h by b e n d i n g and by a x i a l f o r c e . B o t h f o r c e s a r e p r o p o r t i o n a l t o t h e a r e a o f t h e b a r - O.I4. A g f y f o r b e n d i n g and 0.7 t o 1.0 A g f y f o r a x i a l . T e s t s c o n d u c t e d b y B i r k e l a n d and J o n e s i n d i c a t e v a l u e s f o r 14-3. bottom dowels across smooth concrete f a c e s of 0 . 7 to 1 . 0 Agfy* F a i l u r e f o r the frames was e s t a b l i s h e d at 0.05 i n c h deformation. At t h i s deformation the bottom dowels are i n both t e n s i o n and bending. Thus they should c o n t r i -bute to the shear s t r e n g t h somewhere i n the range of 0 . I 4 . to 1 . 0 A s f v . T h e r e f o r e , 0 . 7 A f would be a reasonable J s y value to assume. A comparison between c a l c u l a t e d f a i l u r e loads and the frame t e s t s i s shown i n Table I4.. The bottom dowel s t r e n g t h was c a l c u l a t e d u s i n g 0 . 7 A f . The top dowel S j s t r e n g t h was c a l c u l a t e d as the l a r g e r of (a) the c r a c k l o a d (beam on e l a s t i c foundation) or (b) the p l a s t i c hinge theory. Y i e l d or c r u s h i n g s t r e s s e s were those o b t a i n e d from t e s t s o f the a c t u a l s t e e l and c o n c r e t e . The r a t i o Of sum of the dowel t e s t s to the frame t e s t s v a r i e s from O . 6 I 4 . to 0.81+, i n d i c a t i n g the e f f e c t of n e g l e c t i n g f r i c t i o n . The r a t i o o f the c a l c u l a t e d data to frame t e s t ranges from 0 . 7 0 to 1 . 0 3 . I f frame 2F-1-5 i 3 d e l e t e d the r a t i o v a r i e s from 0 . 8 9 to 1 . 0 6 . The c a l c u l a t e d data, t h e r e f o r e , agrees w e l l w i t h t e s t d ata. 1*4. Table 1+ COMPARISON OP FRAME TESTS TO CALCULATED DATA AND DOWEL TESTS TEST FRAME NO. CALCULATED (1) CALC. FAILURE (KIPS) (2) TOP PLUS BOT. DOWEL TESTS (3) FRAME TESTS (KIPS) (1) (2) T3T TOP DOWEL BOT. DOWEL PLASTIC HINGE MECH. CRACK ELAST. FDN. (3) 1P-1-5 7.3 k-9 8.5 15.8 111-. 5 17.4 0.91 0.8I4. lP - 2 - 5 I4-.O 1+.9 8.5 13.14- 11.0 1F-3-5 2.9 U-.9 •8.5 13.14- 9.2 12.5 1.06 0.74 1F-1-6 II4..8 k.7 8.5 23.3 2li.O 0.97 2F-1-5 7.3 U,.9 8.5 15.8 114-.5 22.6 0.70 0.61+ 2F-2-5 14..2 14-.9 8.5 13-lj. 11.0 ilv-5 0.93 0.76 2F-3-5 2.9 4.9 8.5 13.4 9.2 13.3 1.01 0.69 2P-3.-6 5.7 14..7 8.5 11+.. 2 16.0 0.89 F a i l u r e loads taken at 0.05 i n c h deformation. C a l c u l a t e d data based on t e s t e d m a t e r i a l s (see Table 3). PLASTIC HINGE MECHANISM V = 3.14-Z Z = S e c t i o n modulus of bar S S = Distance to s t i r r u p CRACK-BEAM ON ELASTIC FOUNDATION K = 8200 K/IN. Formula (1) E = 1+.2 x 103 k s i I = 10.28 IN.4 b = 10 IN. = .1+50 k s i BOTTOM DOWEL V = 0.70 A g f y US-CHAPTER 7 JOINT DESIGN (A METHOD FOR CALCULATION) Joint design can be broken into components of top and bottom dowel strength. The bottom dowel strength can be calculated by the expression: BOTTOM DOWEL SHEAR = V B D =0.70 A g f y The top dowel shear i s the larger load of (a) the crack load or (b) the p l a s t i c mechinism load. The p l a s t i c hinge mechanism i s r e l a t i v e l y e a s i l y calculated: PLASTIC HINGE V T D = 3.1*. Z f y s Z = section modulus of dowels f = y i e l d stress of steel v s = distance to f i r s t s t i r r u p The curves f o r a v a r i a t i o n of bar sizes and a steel strength of 1*0 k s i have been plotted i n graph 20. These curves could be used as a design aid. The top dowel crack load i s a more cumbersome cal c u l a t i o n and design aids Would be h e l p f u l . The beam on e l a s t i c foundation equations are functions of: 1) Moment of i n e r t i a of the cracked section, there-fore, beam width, concrete cover and bar s i z e . 2) Foundation modulus, therefore, beam depth, E<j. 3) Tensile strength of concrete. U.6. The two most i m p o r t a n t v a r i a b l e s a r e the moment o f i n e r t i a o f t h e c r a c k e d s e c t i o n and the t e n s i l e s t r e s s o f c o n c r e t e . The c o n c r e t e c o v e r i s u s u a l l y one o f ab o u t t h r e e v a l u e s . T h i s l e a v e s the v a r i a b l e s o f b a r s i z e and s p a c i n g t o e s t a b l i s h t h e moment o f i n e r t i a . The t e n s i l e s t r e n g t h c o u l d be t a k e n f o r d e s i g n p u r p o s e s as 6vf^. G r a p h 21 shows c r a c k s t r e n g t h as a f u n c t i o n o f b a r s p a c i n g and s i z e . T h i s c u r v e i s f o r a 20 i n c h beam d e p t h . S i m i l a r c u r v e s c o u l d be d e v e l o p e d f o r o t h e r beam d e p t h s . A d j u s t m e n t t o t h e c r a c k l o a d f o r d i f f e r e n t t e n s i l e s t r e n g t h s i s d i r e c t l y p r o p o r t i o n -a l t o t h e r a t i o o f t h e t e n s i l e s t r e n g t h s . I n o r d e r t o i l l u s t r a t e t h e u s e o f t h e s e d e s i g n c u r v e s and t h e f e a s i b i l i t y o f t h i s t y p e o f j o i n t , c o n s i d e r a s i m i l a r beam t o t h e t e s t beam: b = 10" d = 18" f y = 1+0 k s i f t = 0.1*50 The a r e a o f s t e e l t o d e v e l o p t h e maximum moment c a p a c i t y o f t h i s beam i s 0.75 P D = 0.0370 ( A . C . I . D e s i g n H a n d b o o k ) . Assume t h a t o n l y one t h i r d o f t h i s s t e e l i s c a r r i e d t h r o u g h t h e b o t t o m o f the j o i n t and t h e same amount i s c a r r i e d t h r o u g h t h e t o p . F u r t h e r assume s t i r r u p s a t d /2. T h i s w o u l d g i v e 1+-1/2 i n c h e s t o t h e f i r s t s t i r r u p . J o i n t s t r e n g t h : BOTTOM DOWELS A 0 = 1/3 x 0.0370 x 180 = 2.2 s q . i n c h e s V R n = 0.70 x l|D x 2.2 = 61 k i p s TOP DOWELS (three No. 8) Crack l o a d V T D = 1.1+ x 3 = I+.2K P l a s t i c hinge V T D = 3.0 x 3 = 9.0 K (The p l a s t i c hinge governs) . * . V = V T D + V B D = 61 + 9 = 7 0 K = 70 = 0.390 k s i 180 This c o n n e c t i o n would g e n e r a l l y provide adequate shear f o r t h i s beam. I t should be noted, however, that the top bars c o n t r i b u t e o n l y t h i r t e e n percent of the j o i n t s t r e n g t h even though t h e i r area i s equal to the bottom s t e e l . 14.8. CHAPTER 8 CONCLUSIONS A l t h o u g h t h e number o f s p e c i m e n s 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 was l i m i t e d , t h e f o l l o w i n g c o n c l u s i o n s a r e i n d i c a t e d : 1) Beam column c o n n e c t i o n s , w i t h o u t c o r b e l s and smooth j o i n t s u r f a c e s , c a n p r o v i d e a d e q u a t e s h e a r s t r e n g t h . 2) The s h e a r s t r e n g t h o f t h e c o n n e c t i o n i s t h e sum o f t h e f o r c e s f r o m t h e top and b o t t o m d o w e l s . 3) The s t r e n g t h o f t h e t o p d o w e l s c a n be c a l c u l a t e d f r o m a beam on e l a s t i c f o u n d a t i o n a n a l o g y o r a p l a s t i c h i n g e mechanism. I4.) The b o t t o m d o w e l s c o n t r i b u t e t o s h e a r s t r e n g t h by b o t h b e n d i n g i n t h e dowel and f r i c t i o n a l f o r c e s a c r o s s t h e j o i n t . 5) The s h e a r f r i c t i o n h y p o t h e s i s i s n o t v a l i d f o r t o p d o w e l s . However, s h e a r f r i c t i o n c o n t r i b u t e s i n p a r t t o t h e s t r e n g t h p r o v i d e d b y t h e b o t t o m d o w e l s . 6) Bond f o r c e s a r e p r e s e n t f o r v e r y s m a l l d i s p l a c e -ments . 7) B o t t o m d o w e l s a r e f a r more e f f i c i e n t i n t r a n s f e r -r i n g s h e a r a c r o s s t h e j o i n t t h a n t h e top d o w e l s . 1+9. REFERENCES 1. Kratz, R. M.A.Sc. Thesis. Vancouver, Canada. Uni-v e r s i t y of B r i t i s h Columbia, 1970. 2. Timoshenko, S. Strength of Materials, Part I I . Prince-ton, N.J. D. Van Nostrand Co. Inc., 191+1. 3. Friberg, B.F. Design of Dowels i n Transverse Joints of Concrete Pavements. American Society of C i v i l Engineers, Proceeding November, 1938. Pp. 1076 - 1100. j+. Marcus, H. Load Carrying Capacity of Dowels at Trans-verse Pavement Joints. Journal of the American Con-crete I n s t i t u t e , October, 1951. Pp. 169 - I83. 5. Birkeland, P.W., and Birkeland, H.W. Connections i n Precast Concrete Construction. A.C.I. Journal, March, 196T: Pp. 345 - 367. 6. Anderson, A.R. Composite Design i n Precast and Cast-in-Place Concrete. Progressive Architecture, Septem-ber, I960. P. 17)+. 7. Jones, L.L. Shear Tests on Joints Between Precast and Post Tensioned Units. Magazine of Concrete Research, No. 31, March, 1959. Pp. 25 - 30. 8. Gaston, J.R., and K r i z , L.B. Appendix to Connections i n Precast Concrete Structures - Scarf Joints. P.C.I. Journal, June, 1961+. Pp. 51+ - 59. 9. Hofbeck, J.A., Ibrahim, 1.0. and Mattock, Alan H. Shear Transfer i n Reinforced Concrete. A.C.I. Journal, Feb-ruary, 1969. Pp. 119 - 128. 10. Krefeld, W.J. and Thurston, CW. Contribution of Longi-tudinal Steel to Shear Resistance of Reinforced Con-crete Beams. A.C.I. Journal, March, 1966. Pp. 325 -• 314-3. 11. Mast, R.F. A u x i l i a r y Reinforcement i n Concrete Connec-tions. A.C.I. Journal, June, 1966. Pp. II4.85 - 1503. 12. Hanson, N.W. Precast-Prestressed Concrete Bridges, 2-Horizontal Shear Connections. Journal P.C.A. Re-search and Development Laboratories, Vol. 2, No. 2, May, I960. P.C.A. Development B u l l e t i n D35. 50 • M l - O CC p < BAR SIZE * 3 4 5 6 7 8 9 10 2.98 2.84 2.72 2.62 2.46 2.34 2.20 2.08 1.95 - 11 > 0 1 1 2 : J BAR DIAMETER (in.) G R A P H 1 D A T A F R O M H . M A R C U S Si* LOADS ARE FOR 1 DOWEL S= STRESSED COL. U = UNSTRESSED COL. 52. 14 12 10 ~ 8 (/> CL SHEAR (Kl SHEAR (Kl SHEAR (Kl UJ O Q 2 • n 0 .05 DISPLACEMENT (IN.) .10 GRAPH 3 *5 BOTTOM DOWEL 53. 14 0 0.05 0.10 DISPLACEMENT IN. GRAPH 4 * 6 BOTTOM DOWEL Sk-LOADS ARE FOR ONE DOWEL 14 12 0 .02 .04 .06 -08 .10 DISPLACEMENT IN. GRAPH 5 BOTTOM DOWEL AVERAGES BOTTOM DOWELS 20 As IN-GRAPH 6 EXPERIMENTAL & THEORETICAL DATA 56. LOADS ARE FOR ONE DOWEL 7 6 5 4 Q < O < DISPLACEMENT IN. GRAPH 7 * 5 TOP DOWEL 3 " SPACING 58. GRAPH 9 *5 TOP DOWEL l" SPACING 5 9 . LOADS ARE FOR 1 DOWEL 7 6 GRAPH 1 0 *5 TOP DOWELS AVERAGES 6 0 . TOP DOWEL TESTS LOADS ARE FOR 1 **5 DOWEL 9 I— : . - i 1 DISTANCE TO 1st STIRRUP IN. COMPARISON OF TESTS TO CALCULATED DATA GRAPH 11 61. LOAD ARE FOR 2*5 TOP + 2 *3 BOT. 30 25 20 CL * 15 cc < UJ CO 10 2F- 1-5 •1-b .05 .10 DISPLACEMENT IN. GRAPH 12 FRAME TESTS l" SPACING 6 2 . 3 0 2 5 2 0 c/> C L CC < HI X CO 15 2F-2 -5 10 .05 .10 D I S P L A C E M E N T IN. GRAPH 13 FRAME TESTS 2" SPACING 63 . 3 0 2 5 2 0 CL 15 2F-•3-5 •3-5 .— • 1 F-cc < Ui CO 10 •05 .10 D I S P L A C E M E N T IN . GRAPH 14 FRAME TESTS 3 SPACING LOADS ARE FOR 2 *6 TOP + 2 *3 BOT. 61t. 30 20 CL 15 cc < H I co 10 .05 .10 DISPLACEMENT IN. GRAPH 15 FRAME TESTS 1"& 3" SPACING SHEAR KIPS •59 30 OJ 1 L - 1 1 0 0.1 0.2 0.3 0.4 DISPLACEMENT IN. GRAPH 17 COMPARISON OF FRAME TESTS TO TOP& BOTTOM DOWELS 30 20 co 0. cc < UJ X CO 10 / / 2 5 TOP BARS 2 * 3 BOT BARS 2" TO 1st STIRRUP 0.1 0.2 DISPLACEMENT IN. 0.3 0.4 GRAPH 18 COMPARISON OF FRAME TESTS TO TOP & BOTTOM DOWELS 30 20 (ft O. CC < UJ X CO 10 ^ ^ F l r-vow / / 1 1 1 2 * 5 TOP BARS 2 * 3 BOT BARS 3" TO 1 s t STIRRUP 0.1 0.2 DISPLACEMENT IN. 0.3 0.4 GRAPH 19 COMPARISON OF FRAME TESTS TO TOP. & BOTTOM DOWELS 69. 6 2 4 6 8 10 12 DISTANCE TO 1 s t STIRRUP TOP DOWELS GRAPH 20 PLASTIC MECHANISM STRENGTH 70 CRACK LOAD FOR VARIABLE BAR SIZE & SPACING CO CL < O o < o 14 12 10 8 K = 8200 K/IN E = 4200 K I f^= .450 K I d =20 IN. 4 6 8 10 BAR SPACING B (IN.) 12 ' 6 ^11 14 GRAPH 21 TOP DOWELS CRACK LOAD 

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