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Single plate connections for steel beams Wyss, Urs 1967

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SINGLE PLATE CONNECTIONS FOR STEEL BEAMS by URS WYSS B.  Eng. Swiss F e d e r a l  I n s t i t u t e of T e c h n o l o g y ,  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED i n the  SCIENCE  Department of  Civil  We a c c e p t t h i s required  Engineering  t h e s i s as conforming to  standard  THE UNIVERSITY OF BRITISH COLUMBIA APRIL,  1967  the  1963  In presenting  t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements  for an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that die L i b r a r y s h a l l make i t f r e e l y available f o r reference and study.  I further agree that permission f o r extensive copying of t h i s  thesis f o r s c h o l a r l y purposes may be granted by the Head of my Department or by his representatives.  I t i s understood that copying  or p u b l i c a t i o n of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without, my written permission.  Department of  Civil  Engineering  The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8 Canada S  ABSTRACT S i n g l e p l a t e c o n n e c t i o n s f o r s t e e l beams, connected by h i g h s t r e n g t h b o l t s t o the beam web and welded t o the column, were i n v e s t i g a t e d t o determine T e s t s were performed i n the presence rigidity  their, b e h a v i o u r .  on the c o n n e c t i o n s i n the absence and  o f shear, and shear was found not t o a f f e c t the  of the c o n n e c t i o n s .  V a r y i n g the gauge d i s t a n c e , the weld s i z e ,  the p i t c h and  the number of b o l t s i n the t e s t specimens, showed t h a t o n l y the p i t c h and the number of b o l t s i n f l u e n c e d the r i g i d i t y of the c o n n e c t i o n s . b o l t s causes  An i n c r e a s e i n the p i t c h and the number of  an i n c r e a s e i n the r i g i d i t y  In a l l cases  of the c o n n e c t i o n s .  the major s l i p v a l u e was g r e a t e r than the  u s u a l l y assumed v a l u e . Under the a c t i o n of pure moment the c e n t r e of r o t a t i o n was  found  t o be s l i g h t l y above the c e n t r o i d of the c o n n e c t i o n ,  whereas under the a c t i o n of moment and shear the c e n t r e of r o t a t i o n was  s l i g h t l y below the c e n t r o i d of the c o n n e c t i o n . The maximum moment developed  45 k i p - i n c h e s f o r the two-bolt f o r the s i x - b o l t  connection.  by the connections v a r i e d  c o n n e c t i o n , to 355 k i p - i n c h e s  from  ii.  TABLE OF CONTENTS TITLE  PAGE  I - INTRODUCTION  1  Scope Advantages o f the New Type o f Connections Aim of the I n v e s t i g a t i o n E a r l y Work Method o f I n v e s t i g a t i o n  5  I I - DESCRIPTION OF TESTS 1.  Pure Moment Set-up Type of Connections  Investigated  D e s c r i p t i o n of Apparatus D e s c r i p t i o n of Tests Observations Moment-Rotation 2.  Curves  Moment Shear Set-up Type of Connections  Investigated  D e s c r i p t i o n of Apparatus D e s c r i p t i o n of T e s t s a) Without A p p l i e d b) With A p p l i e d  Rotation  Rotation  Observations Shear D e f l e c t i o n Curves Moment-Rotation  Curves  iii. TABLE OF CONTENTS  (Cont'd)  TITLE  PAGE  I I I - ANALYSIS AND RESULTS OF TESTS 1.  28  C a p a c i t y of the Connections Definitions Slip  2.  Values  R i g i d i t y of the Connections Definitions S e m i - R i g i d C o n n e c t i o n F a c t o r s from Moment and Moment Shear  3.  I n f l u e n c e of the D i f f e r e n t  Pure  Set-up  Variables  on the R i g i d i t y 4.  Centre of R o t a t i o n  IV - DERIVATION OF THEORETICAL CAPACITY AND  35  RIGIDITY OF THE CONNECTIONS 1.  Theoretical Capacity Derivation Comparison w i t h  2.  Experiments  D i s c u s s i o n of R i g i d i t y Approximation of R i g i d i t y Comparison w i t h  Experiments  V - CONCLUSIONS  40  BIBLIOGRAPHY  42  IV.  TABLE OF CONTENTS  (Cont'd)  TITLE  PAGE  APPENDIX "A"  44  Moment-Rotation Curves from Pure Moment Set-up APPENDIX "B"  50  S h e a r - D e f l e c t i o n Curves from Moment Shear Set-up without A p p l i e d  Rotation  APPENDIX "C"  56  Moment-Rotation and R e s u l t a n t Resultant  Bolt  Force-  Displacement Curves from Moment  Shear Set-up w i t h A p p l i e d  Rotation  LIST OF TABLES PAGE  TABLE I  Summary of Connections T e s t e d  II  Summary of F a i l u r e s  III  Maximum B o l t F o r c e s a t Major  IV  S e m i - R i g i d Connection F a c t o r s  33  V  Centres of R o t a t i o n  34  VI  T h e o r e t i c a l C a p a c i t y of Connections  35  VII  Comparison of S e m i - R i g i d Connection  38  Factors  4 22 Slip  31  vi.  LIST OF ILLUSTRATIONS AND PLATES FIGURE  PAGE  1.  S i n g l e P l a t e C o n n e c t i o n f o r S t e e l Beams  3  2.  T y p i c a l Moment R o t a t i o n Curve f o r S e m i - R i g i d  3  Connection 3.  T e s t Specimens  4  4.  Pure Moment Set-up  6  5.  T y p i c a l Moment R o t a t i o n Curves from Pure  12  Moment Set-up 6.  Moment R o t a t i o n Curves from Pure Moment Set-up  13  7.  Moment Shear Set-up  16  8..  T y p i c a l Shear D e f l e c t i o n Curves from Moment  25  Shear Set-up w i t h o u t A p p l i e d 9.  T y p i c a l Moment R o t a t i o n Curves from Moment Shear Set-up w i t h A p p l i e d  10.  Rotation  Centre of R o t a t i o n  27  Rotation 34  vii.  LIST OF ILLUSTRATIONS AND PLATES (Cont'd) PHOTO 1.  PAGE T e s t Specimen Mounted on the Beam i n the  8  Pure Moment Set-up 2.  Pure Moment Set-up i n the T i n i u s O l s e n Testing  3.  Machine  Pure Moment Set-up. Beam w i t h  Showing  the 21 WF 62  9  the Test Specimen and the  Distributing 4.  8  Beam.  T e s t Specimen Mounted i n the Moment Shear  18  Set-up 5.  End View of the Moment Shear Set-up Showing  18  End Frame w i t h Load C e l l s and H y d r a u l i c Jacks 6.  a t Top  T y p i c a l Test Specimen f o r the Moment Shear Set-up Showing Test  the Deformations a f t e r the  23  viii.  ACKNOWLEDGMENT The author wishes  t o acknowledge g r a t e f u l l y the v a l u a b l e  a i d and guidance a f f o r d e d by h i s a d v i s o r , P r o f e s s o r S.L. L i p s o n , throughout the e n t i r e work covered i n t h i s  thesis.  Acknowledgment and thanks a r e a l s o due t o a l l t h e C i v i l E n g i n e e r i n g ' Department T e c h n i c i a n s f o r t h e i r a s s i s t a n c e throughout the experiments.  To Messrs. P. Demco, F. Z u r k i r c h e n and J . Sharp  f o r t h e i r a s s i s t a n c e i n p e r f o r m i n g experiments; t o Mr. W.  Schmidt  f o r h i s a i d i n s e t t i n g up e l e c t r o n i c s equipment. S p e c i a l acknowledgment i s a l s o due t o M i s s L . Cowdell f o r h e r v a l u a b l e a i d i n the t y p i n g of d r a f t  copies.  T h i s p o s t - g r a d u a t e study was sponsored by the Canadian I n s t i t u t e of S t e e l C o n s t r u c t i o n .  1. 1—INTRODUCTION  Scope.-  This t h e s i s covers the behaviour of s i n g l e p l a t e  connections f o r s t e e l beams, connected by high strength b o l t s to the beam web and welded to the column, (see F i g . 1) Advantages of t h i s Type of Connections.-  Compared w i t h the  r i v e t e d or bolted standard, double angle, connections as they are recommended i n the Manual of S t e e l Construction by the A.I.S.C. and C.I.S.C., the s i n g l e p l a t e connections with high strength b o l t s are more economical f o r the following reasons: 1.  I n the case of high strength b o l t s of the f r i c t i o n type, bearing s t r e s s i s not the governing f a c t o r f o r the number of b o l t s , and f o r the thickness of the connection plate> as i t i s f o r the double angle connections.  2.  Easy e r e c t i o n c o n d i t i o n s : the connection p l a t e w i l l be shop welded to the column and f i e l d b o l t e d to the beam web. Connecting the beam i n the f i e l d would be very simple. Aim of the I n v e s t i g a t i o n s . -  The behaviour and the features  of the s i n g l e p l a t e connections f o r s t e e l beams have been i n v e s t i g a t e d under d i f f e r e n t conditions and v a r i a b l e s . Qf s p e c i a l I n t e r e s t are the capacity and r i g i d i t y  of these  connections. Early Work.-  In the 1930's, C. Batho and H.C.  Rowan i n  1 2 Great B r i t a i n , and J.C. Rathbun i n the United States conducted t e s t s to f i n d a r e l a t i o n s h i p between the moment applied to a r i v e t e d connection and the corresponding r o t a t i o n .  2. A s e r i e s of t e s t s to compare the r i g i d i t y of welded r i v e t e d c o n n e c t i o n s were conducted i n 1934  3 i n Canada .  by C R .  J . L . Brandes and R.M.  and  Young and K.B.  Jackson  Mains r e p o r t e d t e s t s 4  of welded t o p - p l a t e and s e a t c o n n e c t i o n s i n 1944 r e p o r t , p u b l i s h e d i n 1947  .  A progress  by the American I n s t i t u t e of S t e e l  C o n s t r u c t i o n , recommended t h a t a dependable percentage  of r e s t r a i n t  of s e v e r a l types of s e m i - r i g i d c o n n e c t i o n s c o u l d be used i n design^. A l l t h i s e x p e r i m e n t a l r e s e a r c h has been undertaken the behaviour  of such c o n n e c t i o n s , and  to i n v e s t i g a t e  p o s s i b i l i t y of i n c l u d i n g t h e i r e l a s t i c r e s t r a i n t of s t r u c t u r a l framework.  The  t o study  the  i n the d e s i g n  f i n d i n g s of these r e s e a r c h groups  i n d i c a t e t h a t an approximate l i n e a r r e l a t i o n s h i p e x i s t s w i t h i n a s p e c i f i c r e g i o n between the a p p l i e d moment and  the  relative  r o t a t i o n of the beam and column, as shown i n F i g . 2. Method of I n v e s t i g a t i o n . - The s i n g l e p l a t e  connections  f o r s t e e l beams have been t e s t e d under t h r e e d i f f e r e n t c o n d i t i o n s , i n o r d e r to i n v e s t i g a t e , t h e i r behaviour 1.  In the "Pure Moment Set-up"  completely:  each c o n n e c t i o n was  to a pure bending moment i n the absence of  subjected  shear.  (see F i g . 4) 2.  In the "Moment Shear Set-up"  the same c o n n e c t i o n s were  t e s t e d under r e a l i s t i c beam end shears and  rotations,  (see F i g . 7) 3.  In the same "Moment Shear Set-up" t e s t e d a l s o i n the presence very small r o t a t i o n s only.  the c o n n e c t i o n s were  of beam end s h e a r s , but under  F i g . 2 - Typical Moment Rotation Curve for Semi-Rigid Connection.  4. >/  'X /  t  i  *  *  i  \  }  <\  7  /  0 /  f  /  jr j  1  / V  /  ?  A  i•  4'v  t  /  >  /\ \?  /\ \/  /\ \/  /\ \  /s  ?  /  \  *4  >  \?  /s \?  (\  /  \  \  s  /  F i g . 3 - Tes t A.  F o r Pure Moment Set-up  B.  F o r Moment Shear Set-up  Size of Weld in.  y  in.  in.  Pure Moment  2 1/2 1 3/4 1 3/4  3 3 2 1/4  1/4 1/4 1/4  Moment Shear no r o t a t i o n  2 1/2 1 3/4 4 2 1/2 1 3/4  3 3 3 2 1/4 2 1/4  1/4 1/4 1/4 1/4 1/4  Method Tested  1 2 3 4 5 6 7 8  r  Specimens  X  Series No.  9 10 11 12  /  ? \  \/  v  &  ?  /\  ?  /  Moment Shear 2 1/2 w i t h r o t a t i o n 1 3/4 2 1/2 2 1/2  3 3 3 3  1/4 1/4 3/16 1/4 one s i d e  TABLE I - SUMMARY OF CONNECTIONS TESTED  f  11—DESCRIPTION OF TESTS 1. Pure Moment  Set-up  Type o f Connections  Investigated.-  The type o f c o n n e c t i o n s  i n v e s t i g a t e d were s i n g l e p l a t e c o n n e c t i o n s f o r s t e e l beams aB shown i n F i g . 1.  The v a r i a b l e s were the number of b o l t s , the  gauge d i s t a n c e and the p i t c h ; they v a r i e d as shown i n T a b l e I . Each s e r i e s c o n s i s t e d of f i v e specimens w i t h d i f f e r e n t numbers of b o l t s , from two b o l t s t o s i x , i n c l u s i v e .  The t h i c k n e s s o f  the c o n n e c t i o n p l a t e s was 1/4 i n . f o r a l l specimens and the s i z e of the f i l l e t welds was 1/4 i n . f o r a l l cases except s e r i e s 11 The b o l t s employed i n a l l t e s t s were A.S.T.M. A-325 h i g h strength b o l t s .  Each b o l t was t i g h t e n e d t o a torque o f 356 f t . l b s  u s i n g a c a l i b r a t e d torque wrench. D e s c r i p t i o n of Apparatus.-  I n o r d e r t o o b t a i n the moment  r o t a t i o n c h a r a c t e r i s t i c s of the c o n n e c t i o n s under the a c t i o n of pure bending  and no shear, the t e s t specimens (see F i g . 3A and  Photo #1) were mounted i n the middle simple beam.  pf a s y m m e t r i c a l l y loaded  Two s h o r t wide f l a n g e s e c t i o n s (21 WF 62) were  b o l t e d t o each s i d e of the t e s t specimen, which c o n s i s t e d of two 1/4 i n . c o n n e c t i o n - p l a t e s , welded on e i t h e r s i d e t o a 1 i n . intervening  plate.  The beam was p l a c e d on the bed of the 200,000 l b . c a p a c i t y T i n i u s O l s e n t e s t i n g machine, and was supported on h i g h r o c k e r s at e i t h e r end.  The beam was then s y m m e t r i c a l l y loaded, l ' - 6 "  on e i t h e r s i d e o f the c o n n e c t i o n c e n t r e by means of a d i s t r i b u t i n g beam and r o c k e r s .  (see F i g . 4 and Photo #2,#3)  6.  P  fApp//ea /-OOc/ fnorn t//oper< L/eacJ )  Z)/sfa'buh!ng Beam  Beam  PL  MachmB  L - fosbo? Bed  S£C770N  J-A  F i g . 4 - Pure Moment Set-up.  \  7. In o r d e r to measure the r e l a t i v e r o t a t i o n of the p l a t e w i t h r e s p e c t t o the beam web, (4) were mounted on the web  connection  d i a l gauges ( 1 ) , ( 2 ) , (3)  of the beams.  and  These gauges were  b e a r i n g on s m a l l aluminum angles screwed to the c o n n e c t i o n - p l a t e , (see Photo  #1)  Description ofJTests.-  I n the f i r s t  s e t of specimens t e s t e d ,  s p e c i a l s l o p e - d e v i c e s were mounted on the top f l a n g e of the beam on e i t h e r s i d e of the c o n n e c t i o n , i n order to get the r o t a t i o n of the beam.  In the second and  absolute  t h i r d s e t s these  devices  were not used, but d i a l gauges were i n s t a l l e d as shown i n F i g . 4. Finally  the same type of specimens as i n the f i r s t  s e t were t e s t e d ,  u s i n g the d i a l gauges i n s t e a d of the s l o p e - d e v i c e s , and  these  r e s u l t s r e p l a c e d the s l o p e d e v i c e r e a d i n g s from the f i r s t The  same beams were used f o r a l l specimens.  c o n n e c t i o n w i t h a p i t c h of 2 1/4 wide-flange  i n . the two  For  set.  the  other ends of  the  beams were used to a t t a c h to the specimen, so t h a t  the c o n d i t i o n of the f a y i n g s u r f a c e s f o r the 3 s e t s of specimens were somewhat d i f f e r e n t .  The beam ends to which the specimens  w i t h a 3 i n . - p i t c h were a t t a c h e d , had been used i n e a r l i e r and  t h e r e f o r e the f a y i n g s u r f a c e had become p o l i s h e d .  each new two  specimen was  i n , were o r i g i n a l l y p a i n t e d .  removed w i t h a s p e c i a l l i q u i d and  brushed.  The b r u s h i n g was  The  connections The p a i n t  the s u r f a c e was  repeated b e f o r e each  Before  w i r e brushed.  other ends of the beams, which were used f o r the  w i t h a p i t c h of 2 1/4 was  mounted, the s u r f a c e was  tests,  test.  wire  Photo #1 - Test Specimen Mounted on the Beam i n the Pure Moment Set-up.  Photo #2 - Pure Moment Set-up i n t h e T i n i u s T e s t i n g Machine.  Olsen  Photo #3 - Pure Moment Set-up.  Showing the  21 WF 62 Beam w i t h the T e s t and the D i s t r i b u t i n g  Beam.  Specimen  The l o a d was a p p l i e d i n i n c r e m e n t s .  As soon as the r e l a t i o n  between a p p l i e d l o a d and r o t a t i o n was no more l i n e a r , s m a l l e r increments were chosen.  A f t e r each increment  the machine was  stopped and the d i a l gauges were observed and noted. was i n c r e a s e d u n t i l  The l o a d  c l e a r a n c e s or l a r g e deformations made any  f u r t h e r r o t a t i o n i m p o s s i b l e , then the c o n n e c t i o n s were unloaded i n two or t h r e e increments and r e a d i n g s were a g a i n taken. Observations.-  When t h e c o n n e c t i o n s were b e i n g b o l t e d  t o g e t h e r i t was noted t h a t the beams tended t o m i s a l i g n .  This  was due t o the f a c t t h a t the c o n n e c t i o n p l a t e s were not welded e x a c t l y i n a r i g h t angle t o the i n t e r v e n i n g p l a t e .  Because  of the v e r y s m a l l e x c e n t r i c i t y i t was n o t found t o be n e c e s s a r y to p r e v e n t o r measure any l a t e r a l movements. N o t i c e a b l e c o n n e c t i o n s l i p s were u s u a l l y observed on;the machine l o a d d i a l :  w h i l e the l o a d i n g r a t e was m a i n t a i n e d the  l o a d dropped o f f or c o u l d not be i n c r e a s e d .  I n most cases the  l o a d drop o f f was accompanied w i t h a c r a c k i n g n o i s e .  This  observed v a l u e i s shown on the v a r i o u s c u r v e s . In many cases the l o a d i n g was c o n t i n u e d to g i v e a l a r g e deflection.  I n these cases the d e f o r m a t i o n i n the c o n n e c t i o n  p l a t e s was marked, e s p e c i a l l y a t the h o l e s where b o l t s were bearing.  The deformations were b i g g e r on the t e n s i o n s i d e of  the c o n n e c t i o n and the magnitude i n c r e a s e d w i t h the number of bolts.  11.  Moment-Rotation Curves.-  I n order t o determine  of these c o n n e c t i o n s i t was of f i r s t are developed  the behaviour  i n t e r e s t t o know what moments  d u r i n g an a p p l i e d beam r o t a t i o n .  The developed  moments were c a l c u l a t e d from the a p p l i e d l o a d f o r each and  increment,  the c o r r e s p o n d i n g beam r o t a t i o n s were o b t a i n e d from the d i a l  gauge r e a d i n g s .  Moments were p l o t t e d v e r s u s r o t a t i o n s f o r a l l  t e s t s made, and the complete s e t of these graphs i s r e c o r d e d i n Appendix A. Only  the v a r i a t i o n of the p i t c h produced  d i f f e r e n c e i n the developed  a considerable  end moment.  The moment r o t a t i o n curves f o r the same p i t c h  (3 i n . ) but  d i f f e r e n t gauge d i s t a n c e s (2 1/2 i n . and 1 3/4 i n . ) agree each other q u i t e w e l l .  E x c l u d i n g the two b o l t  connections, i t  can be s t a t e d t h a t f o r any one r o t a t i o n the developed d i f f e r by maximum  moments  15% o f the h i g h e r v a l u e , but no c o n s i s t e n c y  can be noted i n the magnitude o r s i g n of t h i s d i f f e r e n c e . statement  i s v a l i d up to the t e s t e d d e s i g n r o t a t i o n .  f o r t h i s range:  with  This'  (Limits  see page 2Q)  The moment r o t a t i o n curves f o r the same gauge d i s t a n c e (1 3/4 i n . ) but d i f f e r e n t p i t c h e s (3 i n . and 2 1/4:'in.) show f o r the same r o t a t i o n a d i f f e r e n c e i n moments between 20% and 50% of the h i g h e r v a l u e .  The s i g n o f t h i s d i f f e r e n c e i s i n a l l  cases the same; the moment f o r the c o n n e c t i o n w i t h the 2 1/4: i n . p i t c h i s always s m a l l e r .  The v a l i d i t y of t h i s o b s e r v a t i o n goes  a l s o as f a r as the maximum d e s i g n r o t a t i o n .  13.  O  0.00/  OOOS. 0.003 S?OrAT/OA/ {RAZD/ANS )  o.oov  F i g . 6 - Moment R o t a t i o n Curves from Pure Moment Set-up.  14. The diagrams seem t o be curved r i g h t away from the o r i g i n , but the f i r s t p a r t o f the curves can be approximated line.  by a s t r a i g h t  The s l o p e o f t h i s l i n e which g i v e s an i n d i c a t i o n f o r the  rigidity  of the c o n n e c t i o n , seems t o v a r y w i t h the p i t c h and the  number o f b o l t s o n l y .  With a decrease  i n the p i t c h or number of  b o l t s , the s l o p e and t h e r e f o r e the r i g i d i t y decreases a l s o .  The  steep range of the moment-rotation curves i s f o l l o w e d by a s h a l l o w e r p a r t , i n d i c a t i n g the major s l i p  of the c o n n e c t i o n .  A further  i n c r e a s e i n r o t a t i o n b r i n g s the b o l t s i n t o b e a r i n g which shows i n the moment-rotation curves as an i n c r e a s i n g s l o p e .  15. 2.  Moment-Shear Set-up Type of Connections  Investigated.-  was t e s t e d i n t h i s s e t - u p .  The same type of connections  The s i z e of the weld was i n t r o d u c e d as  a new v a r i a b l e . D e s c r i p t i o n o f Apparatus.were t e s t e d i n the presence  I n t h i s arrangement the c o n n e c t i o n s  of shear as w e l l as moment, i n order  to s i m u l a t e the c o n d i t i o n s o c c u r i n g i n a c t u a l p r a c t i c e .  I t was  d e c i d e d t o use the same set-up as had been used b e f o r e , by R.C. S t a r r , who t e s t e d the s i n g l e angle beam web (see F i g . 7)  connections,  The c o n n e c t i o n assembly was b o l t e d t o a v e r y  column, t o develop  a maximum end moment.  rigid  In the v i c i n i t y o f the  beam c o n n e c t i o n s , the column had web s t i f f e n e r s between i t s 1 i n . t h i c k f l a n g e s i n o r d e r t o prevent any l o c a l f l a n g e d e f o r m a t i o n s . For the column and f o r the beam the deformations without  i n f l u e n c e , s i n c e o n l y the r e l a t i v e r o t a t i o n o f one w i t h  r e s p e c t t o the other was d e s i r e d . pitches  were s m a l l and  Because of the two d i f f e r e n t  (3 i n . and 2 1/4 i n . ) , two d i f f e r e n t beams were employed,  both were 21 WF 62 s e c t i o n s of the same l e n g t h .  The f i r s t s e t  w i t h a 3 i n . - p i t c h was t e s t e d , having a s u r f a c e smoothed down by earlier test. beam used  A f t e r t h i s s e t the beam was sand b l a s t e d .  t o t e s t the c o n n e c t i o n s w i t h a 2 1/4 i n . - p i t c h was  sand b l a s t e d t o s t a r t w i t h . wire  The  A f t e r each t e s t the s u r f a c e was  brushed. The  column frame was p l a c e d on the bed of the 200,000 l b .  T i n i u s O l s e n t e s t i n g machine.  The beam was then r a i s e d above  S'-  SB  7&f  r - Frxjme  J? fApp//ed fcy//'*- Upper -—  -foac/Ce/Zs  load)  /Jeoc/  T5  Pocfrer  63"  /2W=/06 O 2/  4  //////  Z2.  B e a m  fV=VO  r 'TV / V, k  I  Bed af 7esf/s?g Mach/ne  Co/umn Frame  —  17. t h i s frame and b o l t e d t o the column f a c e u s i n g the t e s t  specimen.  T h i s specimen c o n s i s t e d of the c o n n e c t i o n p l a t e welded t o a 1 in.-plate.  (see F i g . 3B)  The 1 i n . - p l a t e was b o l t e d t o the  column u s i n g twice as many b o l t s as f o r the c o n n e c t i o n i t s e l f , and therefore very l i t t l e expected.  displacement  r e l a t i v e t o the column was  D i a l gauge No. 4 (see F i g . 7) i n d i c a t e s d i r e c t l y  this  d e f l e c t i o n of the c o n n e c t i o n r e l a t i v e t o the column and the maximum observed  v a l u e s a r e 0.002 i n . a t working l o a d and 0.048 i n .  at maximum l o a d . In the case where no r o t a t i o n was a p p l i e d t o the c o n n e c t i o n , the o t h e r end of the beam was supported arrangement a t i t s top f l a n g e .  on a double  screw  For the other case, where r o t a t i o n  was a p p l i e d , the screws were r e p l a c e d by a p a i r o f h y d r a u l i c jacks.  Each screw or j a c k was connected  the whole arrangement was supported bed of the machine. D i a l gauges  t o a l o a d c e l l , and  on a frame connected  t o the  (see Photo #5)  (1) and (2) were a t t a c h e d t o the web of the  beam and were b e a r i n g on s m a l l aluminum  angles screwed t o the  c o n n e c t i o n p l a t e , i n o r d e r t o measure the r o t a t i o n of the beam web r e l a t i v e t o the c o n n e c t i o n p l a t e .  A d d i t i o n a l gauges  (3) and  (4) were r e q u i r e d t o measure the v e r t i c a l d e f l e c t i o n o f the beam r e l a t i v e t o the c o n n e c t i o n , and of the specimen r e l a t i v e t o the column.  A s l o p e - d e v i c e was mounted a t the end of the beam as  an a i d i n a p p l y i n g l o a d and r o t a t i o n a t the same time. Photo #4)  (see  Photo #4 - T e s t Specimen Mounted i n the Moment Shear S e t - u p .  Photo #5 - End View of the Moment Shear Set-up Showing End Frame w i t h Load C e l l s and H y d r a u l i c Jacks at T o p .  19. D e s c r i p t i o n of T e s t s . -  a) Without A p p l i e d R o t a t i o n  B e f o r e any l o a d was a p p l i e d the screw arrangement was s e t  so t h a t  h a l f of the weight of the beam was c a r r i e d by each s u p p o r t , order to impose no i n i t i a l moment on the c o n n e c t i o n .  in  The l o a d  was a p p l i e d i n i n c r e m e n t s , w h i l e m a i n t a i n i n g the same screw setting  throughout the whole t e s t .  At each l o a d increment  r e a d i n g s were r e c o r d e d i n the f o l l o w i n g manner: amount of l o a d was a p p l i e d ,  all  When the d e s i r e d  the machine was stopped and the l o a d  c e l l v a l u e s were immediatly r e a d , u s i n g a two-way s w i t c h and the Budd d a t r a n d i g i t a l s t r a i n i n d i c a t o r .  These r e a d i n g s were taken  w i t h i n the space of seconds i n o r d e r to a v o i d any drop o f f by c r e e p .  A f t e r w a r d s a l l the d i a l gauge r e a d i n g s were  caused  recorded.  N o t i c e a b l e c o n n e c t i o n s l i p s were u s u a l l y c h a r a c t e r i z e d by a sudden l o a d drop o f f on the machine l o a d d i a l , with a cracking n o i s e .  accompanied  T h i s i s an i n d i c a t i o n of a sudden or  i n c r e a s e d r a t e of v e r t i c a l movement.  The l o a d i n g was c o n t i n u e d  u n t i l a l a r g e d e f o r m a t i o n of the c o n n e c t i o n - p l a t e was r e a c h e d ,  at  t h i s stage the r e l a t i v e v e r t i c a l d e f l e c t i o n s of the beam w i t h r e s p e c t to the 1 i n . t h i c k p l a t e 1/5  to 1/2  connected to the column were  in. b) With A p p l i e d R o t a t i o n  B e f o r e the b o l t s were t i g h t e n e d , screws were set horizontally.  at  the j a c k s which r e p l a c e d  the  t h e i r maximum t r a v e l and the beam was a d j u s t e d  Then a f t e r the b o l t s were t i g h t e n e d , a s m a l l  adjustment had to be made by means of the screw c o n n e c t i n g  the  20. l o a d c e l l t o the w i r e s t r a n d , to get h a l f of the weight of the beam on each s u p p o r t . As the l o a d was  a p p l i e d , the v a l v e of the j a c k s was  opened  to a l l o w the beam r o t a t i o n t o be a p p l i e d s i m u l t a n e o u s l y w i t h the i n c r e a s e of l o a d .  I t was  attempted  to m a i n t a i n a f i x e d  r a t i o of beam r o t a t i o n to end shear throughout the two  i n c h maximum t r a v e l of the j a c k s was  time the l o a d only was a p p l i e d i n increments. was  kept  constant.  increased. The  the t e s t ,  until  reached, a t which  Load and r o t a t i o n were  l o a d i n g or s t r a i n r a t e of the machine  The machine was  stopped  a t each  increment,  w h i l e a l l r e a d i n g s were r e c o r d e d . A r e l a t i o n s h i p between l o a d and end r o t a t i o n had determined,  i n order to apply r o t a t i o n s t o the t e s t beam.  c a l c u l a t i o n was connections^. boltforce  t o be  done a l r e a d y t o t e s t the s i n g l e web  This  angle  Based on these r e s u l t s and on the a l l o w a b l e  (6.6 k i p s ) i t was  d e c i d e d t o apply the r o t a t i o n as  follows: No. of b o l t s i n connection  r o t a t i o n i n r a d . per k i p end s h e a r :  2 or 3  0.00057  4  0.00048  5  0.00032  6  0.00040  As b e f o r e n o t i c e a b l e c o n n e c t i o n s l i p s were noted a l s o as a sudden l o a d drop  o f f on the machine l o a d d i a l ,  accompanied  w i t h c r a c k i n g n o i s e s , but t h i s time i t i s an i n d i c a t i o n of a sudden or i n c r e a s e d r a t e of r o t a t i o n .  21.  Observations.-  During  l o a d c e l l r e a d i n g s was c o n n e c t i o n p l a t e and  the t e s t s a d i f f e r e n c e i n the  noted, which was  due  two  to the f a c t t h a t the  t h e r e f o r e a l s o the beam web  was  not e x a c t l y  vertical. From the moment where the c o n n e c t i o n s t a r t e d to s l i p  to the  end of the t e s t , c r a c k i n g n o i s e s were observed w h i l e l o a d i n g f o r most c o n n e c t i o n s . how  These n o i s e s were very much dependent  the j a c k s were r e l e a s e d . In the case without  a p p l i e d r o t a t i o n very large  of the c o n n e c t i o n p l a t e were o b t a i n e d . u n t i l the end shear reached  The  l o a d was  The  i s g i v e n i n the standard s p e c i f i c a t i o n s as 6.6 f o l l o w i n g modes of f a i l u r e have been  F a i l u r e type A: immediatly F a i l u r e type B:  Crack  times one  connection  kips. observed:  i n the t e n s i o n edge of the p l a t e ,  a d j o i n i n g the toe of the weld. Crack  at a d i s t a n c e 3/4 F a i l u r e type C:  increased  d e s i g n v a l u e of  i n . A-325 h i g h s t r e n g t h b o l t i n a f r i c t i o n type  The  deformations  a magnitude of about t h r e e  the d e s i g n v a l u e of the c o n n e c t i o n . 3/4  on  i n the t e n s i o n edge of the p l a t e , i n . away from the 1 i n . - p l a t e .  V e r t i c a l c r a c k a t the lower edge of  the  c o n n e c t i o n p l a t e , d i r e c t l y under the b o l t h o l e . F a i l u r e type D: the  plate.  Crack  i n the weld at the t e n s i o n edge of  22.  Series No.  5  rot.  no  f o r c e per b o l t at f a i l u r e kips  A  24.3  3.7  C  24.9  3.8  5  C  24.1  3.7  6  A  25.7  3.9  B  18.5  2.8  B  18.9  2.9  B  18.4  2.8  C + A  21.2  3.2  C  21.0  3.2  C  20.0  3.0  3  1/4 i n . both s i d e s  4  7  no  s i z e of fillet weld  1/4 i n .  4  both s i d e s  5 6 8  no  3  1/4 i n . both s i d e s  4 6 12  y es  factor of safety  Failure Type  No. of bolts  2  1/4 i n .  D  17.5  2.6  3  one s i d e  D  17.3  2.6  4  D  16.6  2.5  5  D  21.0  3.2  6  D  20.4  3.1  TABLE I I - SUMMARY OF  FAILURES  The " f o r c e per b o l t " i s o b t a i n e d from the t o t a l end shear a t f a i l u r e d i v i d e d by the number of b o l t s .  D i v i d i n g the " f o r c e  per b o l t " by the d e s i g n v a l u e  leads  (6.6 k i p s )  to the " f a c t o r of  safety". For each t e s t a new  s e t of h i g h  strength  None of the b o l t s f a i l e d , o n l y v e r y s m a l l due to b e a r i n g  have been observed.  b o l t s has been used.  local  deformations  Photo #6 - T y p i c a l Test Specimen f o r the Moment Shear Set-up. the  Test.  Showing the Deformations  after  24. Shear D e f l e c t i o n Curves.-  The shear d e f l e c t i o n curves a r e  o b t a i n e d from the t e s t s i n which no r o t a t i o n was a p p l i e d t o the connections.  These curves have the same g e n e r a l shape as the  moment r o t a t i o n c u r v e s .  The shear f o r c e a c t i n g on the c o n n e c t i o n  was c a l c u l a t e d as the d i f f e r e n c e between the a p p l i e d load and the r e a c t i o n i n the l o a d , c e l l s , and was p l o t t e d a g a i n s t the r e l a t i v e d e f l e c t i o n between the beam and the column, o b t a i n e d from gauge r e a d i n g s .  dial  These graphs a r e r e c o r d e d i n Appendix B.  As was expected, the experiments  show t h a t f o r the same  shear f o r c e the d e f l e c t i o n i n c r e a s e s as the gauge d i s t a n c e increases.  T h i s f a c t was observed o n l y b e f o r e the s l i p was  reached. A l i n e a r r e l a t i o n s h i p between shear and d e f l e c t i o n seems t o occur as f a r as about  50% o f the maximum observed shear.  s l o p e of t h i s l i n e v a r i e s due t o the above mentioned to the number of b o l t s .  The  f a c t and due  F o r the same gauge d i s t a n c e but i n c r e a s i n g  number o f b o l t s the s l o p e i n c r e a s e s a l s o . The two p i t c h d i s t a n c e s used d i d not produce  a consistently  d i f f e r e n t b e h a v i o u r f o r the d i f f e r e n t numbers o f b o l t s . A f t e r the s l i p o f t h e c o n n e c t i o n the shear d e f l e c t i o n reaches a maximum and then the shear decreases w i t h  curve  increasing  d e f l e c t i o n u n t i l the b o l t s a r e i n b e a r i n g , from then on the shear i n c r e a s e d a g a i n w i t h i n c r e a s i n g Moment R o t a t i o n Curves.a p p l i e d l o a d , the weight  deflections.  The moment  c a l c u l a t e d from the  of the beam and the l o a d c e l l  reactions  was p l o t t e d a g a i n s t the r e l a t i v e r o t a t i o n between the beam and  25.  F i g . 8 - T y p i c a l Shear D e f l e c t i o n Curves from Moment Shear Set-up Without A p p l i e d  Rotation.  26. the c o n n e c t i o n , which was a p p l i e d by means of the h y d r a u l i c j a c k s . These diagrams a r e r e c o r d e d i n Appendix C. Not much c o n s i s t e n c y can be noted i n t h i s s e t o f c u r v e s . The i r r e g u l a r i t i e s a t the h i g h e r v a l u e s a r e p r o b a b l y due t o the way  the r o t a t i o n was a p p l i e d .  d i d n o t permit a continuous have been n e c e s s a r y increasing  load.  The v a l v e o f the h y d r a u l i c pump  r e l e a s e of the j a c k s , which would  t o a p p l y the r o t a t i o n s i m u l t a n e o u s l y w i t h  The v a l v e had t o be opened i n i n t e r v a l s .  A n e a r l y l i n e a r r e l a t i o n s h i p between moment and r o t a t i o n occurs w i t h i n about 50% of the maximum moment.  27.  O  O.OOV  0.008  O.O/2.  ROTAT/OM  f  0.0/6  O.OSO  RADiAMS)  F i g . 9 - T y p i c a l Moment R o t a t i o n Curves from Moment Shear Set-up w i t h A p p l i e d  Rotation.  0.02V  28. Ill—ANALYSIS  AND RESULTS OF TESTS  1. C a p a c i t y o f t h e Connections Definitions.-  Slip:  S l i p i n the c o n n e c t i o n takes p l a c e  as soon as the r e l a t i o n between l o a d and d e f o r m a t i o n  i s no l o n g e r  l i n e a r o r i n other words as soon as the s l o p e of the l o a d deformation changes.  curve  (moment-rotation o r s h e a r - d e f l e c t i o n curve)  T h i s i s v a l i d o n l y as long as the c o n n e c t i o n p l a t e  i s stressed w i t h i n the e l a s t i c  range.  For the c o n n e c t i o n t e s t e d , d i s t i n c t i o n has t o be made between the g r a d u a l and n o t v e r y s u b s t a n t i a l s l i p , which seems t o occur more or l e s s from the b e g i n n i n g  of the t e s t , and the major  slip  which i s c h a r a c t e r i z e d by a sudden appearance and by very considerable displacements.  I d e a l l y the major s l i p would appear  as an i n c r e a s i n g d e f l e c t i o n under constant  l o a d , r e p r e s e n t e d by  a h o r i z o n t a l l i n e i n the moment-rotation o r s h e a r - d e f l e c t i o n c u r v e s , u n t i l the b o l t s go i n t o b e a r i n g . The  f i r s t s l i p p i n g has been observed  groups"^, and i n comparison w i t h substantial.  the major s l i p , was not v e r y  The c o n d i t i o n t h a t the c o n n e c t i o n p l a t e has t o be  s t r e s s e d i n the e l a s t i c range t o observe fulfilled  the f i r s t s l i p p i n g , i s  i n a l l t e s t s performed. Maximum B o l t f o r c e :  determined  by other r e s e a r c h  The maximum b o l t f o r c e i s  i n t h r e e d i f f e r e n t ways c o r r e s p o n d i n g  t o the three  methods of i n v e s t i g a t i o n . a)  F o r the Pure Moment Set-up the maximum b o l t f o r c e s have been c a l c u l a t e d under the f o l l o w i n g assumptions:  magnitude of b o l t  f o r c e s p r o p o r t i o n a l t o t h e i r d i s t a n c e from the c e n t r e of  29;.  r o t a t i o n , which i s assumed t o be i n the c e n t r e of the connection. The c e n t r e o f r o t a t i o n o b t a i n e d from d i a l gauge r e a d i n g s i s i n a l l cases s l i g h t l y above the c e n t r e o f the c o n n e c t i o n , but w i t h i n reasonable each o t h e r .  l i m i t s t o say t h a t they agree w i t h  (see Table V)  Based on the assumption t h a t the b o l t f o r c e s are p r o p o r t i o n a l t o t h e i r d i s t a n c e from the c e n t r o i d o f the c o n n e c t i o n , a r e l a t i o n s h i p i n which the moment i s expressed as a f u n c t i o n of the number o f connectors n, the p i t c h p and the maximum c o n n e c t i o n f o r c e R has been  M = S^S±a R b  developed:  (I)  The maximum b o l t f o r c e was o b t a i n e d a p p l y i n g t h i s  formula.  For the Moment Shear Set-up where r o t a t i o n was a p p l i e d t o the beam, the maximum b o l t f o r c e was c a l c u l a t e d as the r e s u l t a n t o f the f o l l o w i n g two components:  the v e r t i c a l  component was o b t a i n e d , d i v i d i n g the end shear i n the c o n n e c t i o n by the number of b o l t s , whereas the h o r i z o n t a l component was c a l c u l a t e d from the developed formula  end moment u s i n g  ( I ) , although the c e n t r e o f r o t a t i o n i s i n a l l cases  s l i g h t l y below the c e n t r o i d of the c o n n e c t i o n . In the case of the Moment Shear Set-up where no r o t a t i o n was a p p l i e d t o the beam, the h o r i z o n t a l component c o u l d be n e g l e c t e d s i n c e t h e developed moment was s m a l l and the c e n t r e of r o t a t i o n was mostly  f a r o f f the c e n t r o i d of the c o n n e c t i o n .  30. Capacity: i s reached  The  c a p a c i t y of the  as soon as the major s l i p  occurs.  connection  The maximum b o l t  f o r c e s c a l c u l a t e d from the v a l u e s of moments and shears a t major s l i p g i v e the c a p a c i t y of a s i n g l e S l i p Values.-  bolt.  Attempts have been made to determine  the  maximum b o l t f o r c e a t the major s l i p i n 3 d i f f e r e n t ways: 1.  I n t e r s e c t i o n of the two  2.  For an a r b i t r a r i l y  tangents  chosen,  as shown i n F i g . 2.  small r e s i d u a l deformation  p a r a l l e l l i n e t o the i n i t i a l . t a n g e n t was s e c t e d w i t h the l o a d - d e f o r m a t i o n 3.  The  inter-  curve.  The r e a d i n g on the machine l o a d d i a l was at which t h e r e was  drawn and  a  taken f o r the l o a d  no l o a d i n c r e a s e or even a l o a d drop o f f .  s l i p v a l u e s determined  by the f i r s t method are l i s t e d i n  Table I I I . None of the methods d e s c r i b e d gave any  consistent results  f o r the f o l l o w i n g r e a s o n s : Inaccuracy  of t e s t  results.  No d e f i n i t e h o r i z o n t a l or n e a r l y h o r i z o n t a l tangent  to the  l o a d - d e f o r m a t i o n c u r v e s , which would i n d i c a t e c l e a r l y major  the  slip.  The  s l i p v a l u e i s a f u n c t i o n of the c o e f f i c i e n t  of  friction,  and  the main reason f o r the i n c o n s i s t e n c y of the s l i p  values  can be found i n the v a r i a t i o n of these c o e f f i c i e n t s f o r the same type of s u r f a c e . shown t h i s f a c t ^ .  A g r e a t number of experiments  For a m i l l s c a l e s u r f a c e the  of f r i c t i o n v a r i e d from 0.16  to  0.46.  have  coefficient  31.  TestMethod  X  y in.  in.  2 1/2 3 PureMoment  Max. B o l t Force at Major S l i p kips No. o f b o l t s 2 5 6 3 4  Weld in.  s i d e s 14.7 11.8 15.2 16.0 17.0  X=14.48 k i p s  1 3/4 3  10.8 13.8 14.2 17.0 15.9  s= 2.15 k i p s  1 3/4 2 1/4  10.0 13.5 14.7 17.5 15.1  v=14.8%  2 1/2 MomentShear 1 3/4 no 4 applied r o t a t i o n 2 1/2  1/4 bot h  Remarks  3  1/4 bot h  s i d e s 12.4 13.7 10.8 11.4 12.4  3  15.2 13.6 13.6 13.8 17.2  X=13.23 k i p s  3  12.3 14.1 14.3 15.2 15.4  s= 1.50 k i p s  2 1/4  11.7 12.1 12.5 12.4 13.0  v-11.3%  1 3/4 2 1/4  13.6 11.1 14.6 12.9 11.4  Moment- 2 1/2 3 Shear 1 3/4 3 with applied 2 1/2 3 rotation 2 1/2 3  sides  15.9 15.6 16.7 16.6  X=15.15 k i p s  1/4 both s i d e s  12.8 12.7 14.7 11.2  s= 2.09 k i p s  15,2 15.1 15.5 17.5  v=13.7%  1/4 both  3/16 both  sides  1/4 one s i d e  11.0 16.7 17.3 17.9  TABLE I I I - MAX. BOLT FORCES AT MAJOR SLIP  where X = mean v a l u e s = standard  deviation  v = c o e f f i c i e n t of v a r i a t i o n i n c l u d i n g a l l values i n Table I I I : X = 14.11 k i p s s =  2.07 k i p s  v = 14.7%  32. Using the method o f l e a s t squares a smooth curve was c a l c u l a t e d through the p o i n t s r e s u l t i n g produce  from the t e s t , but h i s d i d n o t  any g r e a t e r c o n s i s t e n c y .  2. R i g i d i t y of the Connections Definitions.-  Rigidity:  be d e f i n e d as i t s a b i l i t y for  this r i g i d i t y  moment-rotation  The r i g i d i t y  o f a c o n n e c t i o n can,  t o develop a bending moment.  A measure  i s g i v e n by t h e s l o p e of the tangent t o the  curve a t the o r i g i n  ( i n i t i a l tangent).  Semi-rigid connection f a c t o r :  The i n v e r s e of  the s l o p e of the assumed s t r a i g h t - l i n e p o r t i o n of the momentr o t a t i o n curve ( i n i t i a l connection f a c t o r ^ .  tangent) i s d e f i n e d as the s e m i - r i g i d  F o r p r a c t i c a l purposes, <P=Mv\  was  c o n s i d e r e d as an a c c e p t a b l e r e l a t i o n s h i p i n the. d e s i g n of frames g with s e m i - r i g i d connections . are  F o r a l l t e s t s these f a c t o r s  ^  l i s t e d below. The A's were o b t a i n e d by d i v i d i n g the r o t a t i o n i n r a d i a n s  through the moment i n i n c h - k i p s , both c a l c u l a t e d from the r e a d i n g s at  the f i r s t  load  increment.  S e m i - R i g i d C o n n e c t i o n F a c t o r s from Pure Moment and Moment Shear Set-up.-  A l l these f a c t o r s a r e l i s t e d  i n T a b l e IV.  33.  X  in.  Weld in.  y in.  Semi-Rigid Connection F a c t o r No. of b o l t s i n c o n n e c t i o n 2  •io"  3 5  •io-  5  4 5  •IO"  5  •IO"  Set-up  6 5  •io'  5  2 1/2  3  1/4  7.13  2.67 . 1.43  0.88  0.35  Pure-Moment  2 1/2  3  1/4  9.65  3.21  1.51  0.36  0.28  Moment-Shear  1 3/4  3  1/4  7.20  3.20  1.56  0.81  0.37  Pure-Moment  1 3/4  3  1/4  6.12  1.79  1.33  1.22  0.47  Moment-Shear  1/4  11.73  6.40  2.20  1.62  0.64  Pure-Moment  1 3/4  2 1/4  2 1/2  3  3/16  10.87  6.44  1.67  0.61  0.64  Moment-Shear  2 1/2  3  *  5.97  4.63  1.31  0.38  0.43  Moment-Shear  * 1/4 weld on one s i d e o n l y .  TABLE IV - SEMI-RIGID CONNECTION FACTORS  3. I n f l u e n c e o f the D i f f e r e n t V a r i a b l e s on the R i g i d i t y I n t e r p r e t i n g Table  IV and the graphs i n Appendix A and C  l e a d s to the f o l l o w i n g c o n c l u s i o n s : Presence o f shear,  gauge-distance and w e l d - s i z e  i n f l u e n c e the r i g i d i t y  of the c o n n e c t i o n s ,  do not seem t o  whereas f o r the  v a r i a t i o n o f the p i t c h and the number of b o l t s the f o l l o w i n g statements can be made: I n c r e a s i n g the p i t c h and the number of b o l t s causes an i n c r e a s e i n the r i g i d i t y  of the c o n n e c t i o n s .  34.  4. C e n t r e of R o t a t i o n The c e n t r e s o f r o t a t i o n f o r the Pure Moment Set-up and f o r the Moment-Shear Set-up w i t h a p p l i e d from the d i a l gauge r e a d i n g s .  No. of Bolts  r o t a t i o n were determined  The r e s u l t s a r e shown i n Table. V.  Pure Moment Set-up  series 1 k  l  series 2 k  l  k  2  MomentShear Set-up series 9  series 3 k  l  k  2  k  l  k  2  2  -0.033 +0.233 +0.025 +0.142 +0.267 +0.358  3  +0.017 +0.233 -0.008 +0.158 +0.025 +0.167 -0.017 -0.100  4  +0.017 +0.167 +0.017 +0.167 +0.025 +0.225  5  +0.017 +0.150 +0.025 +0.167 +0.075 +0.175 -0.092 -0.142  6  +0.008 +0.092 +0.017 +0.092 +0.083 +0.175 -0.025 -0.117  0  -0.092  TABLE V - CENTRES OF ROTATION  of rote?A/or? 1_ CGr77ho/c/ of oo/7/7ec/~/or7  F i g . 10 - Centre of R o t a t i o n .  ii  35.  IV—DERIVATION OF THEORETICAL CAPACITY AND APPROXIMATION OF THE RIGIDITY OF THE CONNECTIONS 1. T h e o r e t i c a l  Capacity  Derivation.-  The c a p a c i t y  of a s i n g l e h i g h s t r e n g t h  bolt  i n a f r i c t i o n type c o n n e c t i o n i s o b t a i n e d by m u l t i p l y i n g the c o e f f i c i e n t o f f r i c t i o n by the t e n s i o n  f o r c e a c t i n g i n the a x i s  of the b o l t . The  average c o e f f i c i e n t of f r i c t i o n  i s taken from the  S t e e l Manual (A.I.S.C.):JUL = 0.35, and the r e q u i r e d for  an A.S.T.M. A-325 h i g h s t r e n g t h  Resulting  bolt  b o l t i s T = 28.5 k i p s .  from these v a l u e s the c a p a c i t y  o f one b o l t i s 10 k i p s .  C o n s i d e r i n g t h i s as the maximum b o l t f o r c e , the c a p a c i t y c o n n e c t i o n can then be c a l c u l a t e d  M  =  °P(;+1> D  of the  as shown i n chapter I I I :  R  Shear S = n-R S  Moment  No. of b o l t s  tension  in-kips P = 2 1/4 i n .  kips.  n  p = 3 in.  2  .30  22.5  20  3  60  45  30  4  100  75  40  5  150  112.5  50  6  210  162  60  TABLE VI - THEORETICAL CAPACITY OF CONNECTIONS.  36.  Comparison w i t h Experiments.The  a)  Pure Moment  set-up  above v a l u e s f o r the moments a r e i n d i c a t e d on the moment-  r o t a t i o n curves.  I n the case of the 2 b o l t - c o n n e c t i o n w i t h  1 3/4 i n . - p i t c h and 2 1/4 in.-gauge d i s t a n c e , the t h e o r e t i c a l capacity  agrees w i t h the major s l i p , i n a l l other cases the  t h e o r e t i c a l v a l u e i s below the major s l i p v a l u e , b) without  applied  rotation.  Moment Shear set-up  The comparison of the shear d e f l e c t i o n  curves w i t h the v a l u e s o b t a i n e d by m u l t i p l y i n g capacity  (see Appendix A,)  the t h e o r e t i c a l  of one b o l t by the number of b o l t s shows t h a t a l l these  t h e o r e t i c a l v a l u e s a r e below the major s l i p v a l u e , c) with applied  rotation.  (see Appendix B)  Moment Shear  The maximum b o l t f o r c e was  set-up  calculated  as d e s c r i b e d on pg. 28 and 29 and was p l o t t e d v e r s u s the r e s u l t a n t d e f l e c t i o n , which was c a l c u l a t e d displacement  a t the top b o l t .  from  the v e r t i c a l and h o r i z o n t a l  The h o r i z o n t a l d e f l e c t i o n was  o b t a i n e d from the r o t a t i o n , assuming the c e n t r e of r o t a t i o n a t the centroid  of the c o n n e c t i o n .  t h e o r e t i c a l capacity  Comparing these graphs w i t h t h e  of a s i n g l e b o l t shows a g a i n t h a t  t h e o r e t i c a l v a l u e s a r e below the r e g i o n of the major (see Appendix C)  these  slip,  37. 2. D i s c u s s i o n o f R i g i d i t y Rough Approximation of R i g i d i t y . factor  The s e m i - r i g i d  connection  "^ was c a l c u l a t e d on the b a s i s of the f o l l o w i n g i d e a l i z e d 0  conditions: 1.  The c o n n e c t i o n p l a t e i s t r e a t e d as a c a n t i l e v e r beam. 2  2.  The e n t i r e p l a t e i s e l a s t i c w i t h E = 29,000 k i p s . / i n . .  3.  The p l a t e i s s u b j e c t t o pure moment.  Thus the approximated s e m i - r i g i d *°  E-I  where  I = x + 1.25 0.25f(n-1)-y+2.501 12  3  c o n n e c t i o n f a c t o r becomes  Comparison w i t h  X  Experiments.-  n  y  X = 2 1/2  y = 3  X = 1 3/4  y = 3  X = 1 3/4  y = 2 1/4,  2  3.74-10'  1.9  2.6  3  1.01  2.7  3.2  4  0.41  3.5  3.7  5  0.20  4.4  1. 5  6  0.12  2.9  2. 3  2  2.99-10  2.4  2. 0  3  0.81  3.5  2.2  4  0.33  4.9  3.9  5  0.16  5.0  6.4  6  0.09  4.1  5.2  2  4.63'10~  3  1.45  4.4  4  0.63  3.5  5  0.33  4.9  6  0.19  3.4  5  -5  5  2.5  TABLE V I I - COMPARISON OF SEMI-RIGID CONNECTION FACTORS  where /\ = a p p r o x i m a t i o n f o r s e m i - r i g i d  connection f a c t o r  7\, = s e m i - r i g i d  connection f a c t o r  from pure moment set-up  ^=  c o n n e c t i o n f a c t o r from moment shear set-up  0  semi-rigid  39.  No consistency can be noted i n Table VII.  Generally the tests  show that the connections are from 1.5 to 6.4 times less r i g i d than the rough approximations indicate. It i s believed that this i s due to a combination of the following:  some small amount of s l i p from the beginning;  p l a s t i c deformation around the holes; throughout the plate.  some  and effect of shear strains  40.  V—CONCLUSIONS 1.  The  feasibility  has been In  of s i n g l e p l a t e c o n n e c t i o n s f o r s t e e l beams  proven. a l l cases the major s l i p v a l u e f o r the 3/4 i n .  diameter b o l t s was of 2.  10 k i p s per  g r e a t e r than the u s u a l l y assumed v a l u e  bolt.  A l l c o n n e c t i o n s were t e s t e d over 2 times t h e i r p e r m i s s i b l e design value.  The  amount of d i s t o r t i o n at t h i s stage  was  undesirable. A l l c o n n e c t i o n s w i t h the weld on one The  f a i l u r e s occured  permissible value.  i n the weld at 2.5  s i d e only  to 3.2  times  failed. the  In the other c o n n e c t i o n s where f a i l u r e s  were noted, they o c c u r r e d i n : t h e p l a t e a t 2.8  to 3.9  times  the p e r m i s s i b l e v a l u e . 3.  The maximum b o l t f o r c e s at s l i p v a r i e d from 10.0 17.9  4.  k i p s , and  The presence  the mean v a l u e from a l l t e s t s i s 14.1  of the  The  rough approximations  of the  t o 7.6  times s m a l l e r .  causes  connections.  f o r the s e m i - r i g i d  connection  f a c t o r s are compared w i t h the ones o b t a i n e d by 1.8  size  connections.  An i n c r e a s e i n the p i t c h and the number of b o l t s an i n c r e a s e i n the, r i g i d i t y  6.  kips.  of shear, the gauge d i s t a n c e and the weld  do not seem t o i n f l u e n c e the r i g i d i t y 5.  k i p s to  experiments  41.  7.  Maximum moment developed by the c o n n e c t i o n s v a r i e d  from  45 k i p - i n c h e s f o r the two-bolt c o n n e c t i o n t o 355 k i p - i n c h e s f o r the s i x - b o l t c o n n e c t i o n . 8.  The c e n t r e of r o t a t i o n v a r i e s w i t h i n the f o l l o w i n g f o r the Pure Moment Set-up: f o r the Moment Shear Set-up:  range:  from -0.033'h t o +0.358'h from -0.117«h  where h i s the d i s t a n c e between the extreme  bolts.  t o 0.0-h  42.  BIBLIOGRAPHY 1.  Batho, C. and Rowan, H.C.  —  "The A n a l y s i s of the Moments  i n the Members of a Frame Having R i g i d or S e m i - R i g i d C o n n e c t i o n s , under V e r t i c a l Loads".  Second  Report, S t e e l  S t r u c t u r e s Research Committee, London, England, 2.  Rathburn, J.C. —  " E l a s t i c P r o p e r t i e s of R i v e t e d C o n n e c t i o n " .  T r a n s . A.S.C.E. V o l . 101, 3.  Young, C R .  1934.  1936.  and J a c k s o n , K.B.  —  Welded and R i v e t e d C o n n e c t i o n s " .  "The R e l a t i v e R i g i d i t y of Canadian J o u r n a l of Research,  N a t i o n a l Research C o u n c i l of Canada, Ottawa, Canada. V o l . 11 and 12, 4.  1934.  Brandes, J . L . and Mains, R.M.  —  "Report of T e s t s of Welded  T o p - P l a t e and Seat B u i l d i n g C o n n e c t i o n s " . American Welding S o c i e t y ; New 5.  Hechtman, R.A.  York, V o l . 23, No.  and J o h n s t o n , B.G.  York, 6.  3,  1944.  P r o g r e s s Report  I n s t i t u t e of S t e e l C o n s t r u c t i o n ,  New  1947.  S t a r r , R.C.  —  "One  S i d e d S t e e l Beam C o n n e c t i o n s " .  T h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Canada, 7.  Journal,  :— " R i v e t e d and Semi-Rigid  Beam to Column B u i l d i n g C o n n e c t i o n s " . Number I , American  Welding  V a s a r h e l y i , P.P.  and Co. —  F a b r i c a t i o n Techniques". P a r t I I , 1961.  Masters  1965.  " R i v e t s and B o l t s , E f f e c t s of T r a n s . A.S.C.E., V o l . 126,  43.  8.  Monforton, G.R. and Wu, T.S. — Rigidly Connected Frames".  "Matrix Analysis of Semi-  Journal of the Structural  D i v i s i o n , A.S.C.E., V o l . 89, Dec. 1963. 9.  Gaylord and Gaylord —  "Design of Steel Structures", McGraw  H i l l Book Company, 1957. 10.  Cullimore, M.S.G. —  " F r i c t i o n Grip Bolt J o i n t s " , C i v i l  Engineering and Public Works Review, A p r i l 1963.  APPENDIX A MOMENT -  ROTATION CURVES FROM  PURE MOMENT SET-UP  45.  so  ^0  I*?  / / / / // // f  i  II 1  /  ll  *  /  r  -  1 i  /o  j  i  1  A  fheort tlca/  capac/fy  i  1  // o  0  0.009  O.OOS  2-Bolt Connections from Pure Moment Set-up.  O.OZZ  0,0/4  1  / // // // //  -e  rr /  /  a  /  t  /  Afheare h'ca/ capoc/'/y Os/p on machine, /oadcf/b,  f o  o.oo<*  QOO8  0.0/2.  tforzr/o/V f/z4o//tA/s) 3-Bolt  Connections  f r o m P u r e Moment  Set-up.  ao/y  4-Bolt Connections from Pure Moment Set-up.  (7 / 1 /  *  /  $L  -©---  // i  / /  A theorei •/co/ capac/'/y  1  //  O s//por,mocfr/nefooda*/  1  It  f  O  Q0O4  0.008  0.0/2.  tfOTZr/O/V ('/Z40/AwsJ 5-Bolt Connections from Pure Moment Set-up.  0,0/*/  800,  6W  O  O.OOf  O.OO&  6-Bolt Connections from Pure Moment Set-up.  0.0/2.  ao/*/  APPENDIX B SHEAR - DEFLECTION CURVES FROM MOMENT SHEAR SET-UP WITHOUT APPLIED ROTATION  51.  £>£7p-L£Cr/OA/  f/M  )  2-Bolt Connections from Moment Shear Set-up without Applied Rotation.  53.  54.  100,  so  5-Bolt  Connections from Moment Shear Set-up without A p p l i e d  Rotation.  55.  A P P E N D I X  MOMENT  -  C  ROTATION  CURVES,  AND  RESULTANT  FROM  BOLT  FORCE  -  RESULTANT  MOMENT  SHEAR  S E T - U P  WITH  D I S P L A C E M E N T  A P P L I E D  CURVES  ROTATION  57.  /  4*  / _  / /  /  /  I  /  1 /  / 1 '  //\ /  1  £  // // /  c—f—  /  // X  -J—f  // V O  •  fh Z'h" x-  X' I'M" —a— 0.002  /?07xr/o/v  Z'/a."  y = 3" web ft" ^ 3 " we/d y=3" ve/d :*//*" y-3"  O.OO*/ f/^n/AA/s-  J  »e&  ones/cfe.  0.006  2-Bolt Connections from Moment Shear Set-up w i t h A p p l i e d R o t a t i o n .  58.  /OO  SO  1  /  /  / /  \  60  [ *•  S A*  /  /  /  /  y  1/ /  I  / /  f />  90  1  / 20  O  f  /  /  »  /  //  *  /  A fheore x-2'A'  y=3" r/e/d:'/>," y-3' we/d :W y=3" we/d :'/v"o> one 7  5/'de  O.OOZ  O.0O<? /9Q7XT/OA/  0.006  ftt4D//l/VS)  3-Bolt Connections from Moment Shear Set-up with Applied Rotation.  59.  2O0  T  4-Bolt Connections from Moment Shear Set-up with Applied Rotation.  60.  fOO  r  320  O  0.002  O.OOV /por/\r/o/v  (mo/AMs)  0.006  5-Bolt Connections from Moment Shear Set-up w i t h A p p l i e d R o t a t i o n .  6-Bolt Connections from Moment Shear Set-up with Applied Rotation.  20  /6  /2.  // /  /  X X /  ^ ^ ^ ^ ^ ^  B^j  .  J*  //  7 / / i •  f  theone. -/co/'capoc/Ay ' y 3 » we/d'/v' He/e/:fr* /= /fy\ ' y = 3" ' y= 3" we/d: fa" X*l'A y=3 we/d:'h" on or?<£ s/di 3 <  A  u  0 o  O.O/  o.oz  0.03  3-Bolt Connections from Moment Shear Set-up with Applied Rotation.  63.  10  /6  /  12  X  7  '  J  .  f/co/capoc/fy X«2'/z" y~3" we/d7 X-/*/<,»  —  w ¥  6  \i  f  Jl 1  1  _._ X-2'A" •  1  0.0/  /?£S//l77iA/r  H/e/d.'W'  or? one  s/'de  X-2fi?  O.OZ £>/5P/.4C£/l>f£Nr  f//V.)  0.O3  4-Bolt Connections from Moment Shear Set-up with Applied Rotation.  64.  2D  ,  X  O  0.0/  _,  f?£St/Lr/INr  ,—:  0.02. 0.03 DISPLACEMENT  1  f//V. )  1  0.04  5-Bolt Connections from Moment Shear Set-up with Applied Rotation.  6 - B e l t Connections from Moment Shear Set-up w i t h A p p l i e d  Rotation.  

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