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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 Federal I n s t i t u t e of Technology, 1963 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of C i v i l Engineering We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA APRIL, 1967 In presenting this thesis in part i a l fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that die Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without, my written permission. Department of C i v i l Engineering The University of B r i t i s h Columbia Vancouver 8 S Canada ABSTRACT Single plate connections for s t e e l beams, connected by high strength bol t s to the beam web and welded to the column, were investigated to determine their, behaviour. Tests were performed on the connections i n the absence and i n the presence of shear, and shear was found not to a f f e c t the r i g i d i t y of the connections. Varying the gauge distance, the weld s i z e , the pi t c h and the number of bolts i n the test specimens, showed that only the p i t c h and the number of bolts influenced the r i g i d i t y of the connections. An increase i n the p i t c h and the number of bolts causes an increase i n the r i g i d i t y of the connections. In a l l cases the major s l i p value was greater than the usually assumed value. Under the action of pure moment the centre of r o t a t i o n was found to be s l i g h t l y above the centroid of the connection, whereas under the action of moment and shear the centre of r o t a t i o n was s l i g h t l y below the centroid of the connection. The maximum moment developed by the connections varied from 45 kip-inches for the two-bolt connection, to 355 kip-inches for the s i x - b o l t connection. i i . TABLE OF CONTENTS  TITLE PAGE  I - INTRODUCTION 1 Scope Advantages of the New Type of Connections Aim of the Investigation Early Work Method of Investigation II - DESCRIPTION OF TESTS 5 1. Pure Moment Set-up Type of Connections Investigated Description of Apparatus Description of Tests Observations Moment-Rotation Curves 2. Moment Shear Set-up Type of Connections Investigated Description of Apparatus Description of Tests a) Without Applied Rotation b) With Applied Rotation Observations Shear D e f l e c t i o n Curves Moment-Rotation Curves i i i . TABLE OF CONTENTS (Cont'd) TITLE PAGE  III - ANALYSIS AND RESULTS OF TESTS 28 1. Capacity of the Connections D e f i n i t i o n s S l i p Values 2. R i g i d i t y of the Connections D e f i n i t i o n s Semi-Rigid Connection Factors from Pure Moment and Moment Shear Set-up 3. Influence of the Di f f e r e n t Variables on the R i g i d i t y 4. Centre of Rotation IV - DERIVATION OF THEORETICAL CAPACITY AND 35 RIGIDITY OF THE CONNECTIONS 1. Theoretical Capacity Derivation Comparison with Experiments 2. Discussion of R i g i d i t y Approximation of R i g i d i t y Comparison with Experiments V - CONCLUSIONS 40 BIBLIOGRAPHY 42 I V . TABLE OF CONTENTS (Cont'd) TITLE PAGE  APPENDIX "A" 44 Moment-Rotation Curves from Pure Moment Set-up APPENDIX "B" 50 Shear-Deflection Curves from Moment Shear Set-up without Applied Rotation APPENDIX "C" 56 Moment-Rotation and Resultant Bolt Force-Resultant Displacement Curves from Moment Shear Set-up with Applied Rotation LIST OF TABLES TABLE PAGE I Summary of Connections Tested 4 II Summary of F a i l u r e s 22 I I I Maximum Bolt Forces at Major S l i p 31 IV Semi-Rigid Connection Factors 33 V Centres of Rotation 34 VI The o r e t i c a l Capacity of Connections 35 VII Comparison of Semi-Rigid Connection Factors 38 v i . LIST OF ILLUSTRATIONS AND PLATES FIGURE PAGE 1. Single Plate Connection f o r Steel Beams 3 2. T y p i c a l Moment Rotation Curve f o r Semi-Rigid 3 Connection 3. Test Specimens 4 4. Pure Moment Set-up 6 5. T y p i c a l Moment Rotation Curves from Pure 12 Moment Set-up 6. Moment Rotation 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 without Applied Rotation 9. Typical Moment Rotation Curves from Moment 27 Shear Set-up with Applied Rotation 10. Centre of Rotation 34 v i i . LIST OF ILLUSTRATIONS AND PLATES (Cont'd) PHOTO PAGE 1. Test Specimen Mounted on the Beam i n the 8 Pure Moment Set-up 2. Pure Moment Set-up i n the Tinius Olsen 8 Testing Machine 3. Pure Moment Set-up. Showing the 21 WF 62 9 Beam with the Test Specimen and the D i s t r i b u t i n g Beam. 4. Test Specimen Mounted i n the Moment Shear 18 Set-up 5. End View of the Moment Shear Set-up Showing 18 End Frame with Load C e l l s and Hydraulic Jacks at Top 6. T y p i c a l Test Specimen f o r the Moment Shear 23 Set-up Showing the Deformations a f t e r the Test v i i i . ACKNOWLEDGMENT The author wishes to acknowledge g r a t e f u l l y the valuable aid and guidance afforded by his advisor, Professor S.L. Lipson, throughout the e n t i r e work covered i n t h i s t h e s i s . Acknowledgment and thanks are also due to a l l the C i v i l Engineering' Department Technicians for t h e i r assistance throughout the experiments. To Messrs. P. Demco, F. Zurkirchen and J . Sharp for t h e i r assistance i n performing experiments; to Mr. W. Schmidt for h i s aid i n set t i n g up e l e c t r o n i c s equipment. Special acknowledgment i s also due to Miss L. Cowdell for her valuable aid i n the typing of dr a f t copies. This post-graduate study was sponsored by the Canadian I n s t i t u t e of Steel Construction. 1. 1 — I N T R O D U C T I O N Scope.- This thesis covers the behaviour of single plate connections for s t e e l beams, connected by high strength bolts to the beam web and welded to the column, (see F i g . 1) Advantages of t h i s Type of Connections.- Compared with the riveted or bolted standard, double angle, connections as they are recommended i n the Manual of Steel Construction by the A.I.S.C. and C.I.S.C., the single plate connections with high strength bolts are more economical for the following reasons: 1. In the case of high strength bolts of the f r i c t i o n type, bearing stress i s not the governing factor for the number of b o l t s , and for the thickness of the connection plate> as i t i s for the double angle connections. 2. Easy erection conditions: the connection plate w i l l be shop welded to the column and f i e l d bolted to the beam web. Connecting the beam i n the f i e l d would be very simple. Aim of the Investigations.- The behaviour and the features of the single plate connections for s t e e l beams have been investigated under different conditions and variables. Qf special Interest 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 tests to f i n d a relationship between the moment applied to a riveted connection and the corresponding rotation. 2. A ser i e s of tests to compare the r i g i d i t y of welded and r i v e t e d connections were conducted by CR. Young and K.B. Jackson 3 i n 1934 i n Canada . J.L. Brandes and R.M. Mains reported tests 4 of welded top-plate and seat connections i n 1944 . A progress report, published i n 1947 by the American I n s t i t u t e of Steel Construction, recommended that a dependable percentage of r e s t r a i n t of several types of semi-rigid connections could be used i n design^. A l l t h i s experimental research has been undertaken to study the behaviour of such connections, and to investigate the p o s s i b i l i t y of including t h e i r e l a s t i c r e s t r a i n t i n the design of s t r u c t u r a l framework. The findings of these research groups in d i c a t e that 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 within a s p e c i f i c region between the applied moment and the r e l a t i v e r o t a t i o n of the beam and column, as shown i n F i g . 2. Method of Investigation.- The s i n g l e plate connections for s t e e l beams have been tested under three d i f f e r e n t conditions, i n order to investigate, t h e i r behaviour completely: 1. In the "Pure Moment Set-up" each connection was subjected to a pure bending moment i n the absence of shear. (see F i g . 4) 2. In the "Moment Shear Set-up" the same connections were tested under r e a l i s t i c beam end shears and rotati o n s , (see F i g . 7) 3. In the same "Moment Shear Set-up" the connections were tested also i n the presence of beam end shears, but under very small rotations only. Fig. 2 - Typical Moment Rotation Curve for Semi-Rigid Connection. 4. >/ ' X t / * * 0 / f jr • 4 t 'v i i 7 i j / & / / 1 / \ / V / <\ } A / ? \ ? / / ? \ / > \ ? \ \ / ? \ \ / / \ > \ / / s \ / ? \ \ / ? s v \ ( / \ \ / ? s r f \ \ / F i g . 3 - Tes t Specimens *4 A. For Pure Moment Set-up B. For Moment Shear Set-up Series Method X y Size No. Tested i n . i n . of Weld i n . 1 Pure Moment 2 1/2 3 1/4 2 1 3/4 3 1/4 3 1 3/4 2 1/4 1/4 4 Moment Shear 2 1/2 3 1/4 5 no r o t a t i o n 1 3/4 3 1/4 6 4 3 1/4 7 2 1/2 2 1/4 1/4 8 1 3/4 2 1/4 1/4 9 Moment Shear 2 1/2 3 1/4 10 with r o t a t i o n 1 3/4 3 1/4 11 2 1/2 3 3/16 12 2 1/2 3 1/4 one side TABLE I - SUMMARY OF CONNECTIONS TESTED 11—DESCRIPTION OF TESTS  1. Pure Moment Set-up Type of Connections Investigated.- The type of connections investigated were s i n g l e plate connections for s t e e l beams aB shown i n F i g . 1. The variables were the number of b o l t s , the gauge distance and the p i t c h ; they varied as shown i n Table I. Each seri e s consisted of f i v e specimens with d i f f e r e n t numbers of b o l t s , from two bolts to s i x , i n c l u s i v e . The thickness of the connection plates 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 . for a l l cases except s e r i e s 11 The b o l t s employed i n a l l tests were A.S.T.M. A-325 high strength b o l t s . Each b o l t was tightened to a torque of 356 f t . lbs using a c a l i b r a t e d torque wrench. Description of Apparatus.- In order to obtain the moment ro t a t i o n c h a r a c t e r i s t i c s of the connections under the action of pure bending and no shear, the test specimens (see F i g . 3A and Photo #1) were mounted i n the middle pf a symmetrically loaded simple beam. Two short wide flange sections (21 WF 62) were bolted to each side of the test specimen, which consisted of two 1/4 i n . connection-plates, welded on eit h e r side to a 1 i n . intervening p l a t e . The beam was placed on the bed of the 200,000 l b . capacity Tinius Olsen t e s t i n g machine, and was supported on high rockers at e i t h e r end. The beam was then symmetrically loaded, l ' - 6 " on e i t h e r side of the connection centre by means of a d i s t r i b u t i n g beam and rockers. (see F i g . 4 and Photo #2,#3) 6. P fApp//ea t//oper< /-OOc/ fnorn L/eacJ ) Z)/sfa'buh!ng Beam P L L - fosbo? MachmB Bed Beam S£C770N J-A Fig. 4 - Pure Moment Set-up. \ 7. In order to measure the r e l a t i v e r o t a t i o n of the connection plate with respect to the beam web, d i a l gauges (1), (2), (3) and (4) were mounted on the web of the beams. These gauges were bearing on small aluminum angles screwed to the connection-plate, (see Photo #1) Description ofJTests.- In the f i r s t set of specimens tested, s p e c i a l slope-devices were mounted on the top flange of the beam on e i t h e r side of the connection, i n order to get the absolute r o t a t i o n of the beam. In the second and t h i r d sets 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. F i n a l l y the same type of specimens as i n the f i r s t set were tested, using the d i a l gauges instead of the slope-devices, and these r e s u l t s replaced the slope device readings from the f i r s t set. The same beams were used for a l l specimens. For the connection with a p i t c h of 2 1/4 i n . the two other ends of the wide-flange beams were used to attach to the specimen, so that the condition of the faying surfaces for the 3 sets of specimens were somewhat d i f f e r e n t . The beam ends to which the specimens with a 3 i n . - p i t c h were attached, had been used i n e a r l i e r t e s t s , and therefore the faying surface had become polished. Before each new specimen was mounted, the surface was wire brushed. The two other ends of the beams, which were used for the connections with a p i t c h of 2 1/4 i n , were o r i g i n a l l y painted. The paint was removed with a s p e c i a l l i q u i d and the surface was wire brushed. The brushing was repeated before each t e s t . Photo #1 - Test Specimen Mounted on the Beam in the Pure Moment Set-up. Photo #2 - Pure Moment Set-up i n the Tinius Olsen Testing Machine. Photo #3 - Pure Moment Set-up. Showing the 21 WF 62 Beam with the Test Specimen and the D i s t r i b u t i n g Beam. The load was applied i n increments. As soon as the r e l a t i o n between applied load and r o t a t i o n was no more l i n e a r , smaller increments were chosen. Af t e r each increment the machine was stopped and the d i a l gauges were observed and noted. The load was increased u n t i l clearances or large deformations made any further r o t a t i o n impossible, then the connections were unloaded i n two or three increments and readings were again taken. Observations.- When the connections were being bolted together i t was noted that the beams tended to misalign. This was due to the fact that the connection plates were not welded exactly i n a ri g h t angle to the intervening p l a t e . Because of the very small e x c e n t r i c i t y i t was not found to be necessary to prevent or measure any l a t e r a l movements. Noticeable connection s l i p s were usually observed on;the machine load d i a l : while the loading rate was maintained the load dropped off or could not be increased. In most cases the load drop o ff was accompanied with a cracking noise. This observed value i s shown on the various curves. In many cases the loading was continued to give a large d e f l e c t i o n . In these cases the deformation i n the connection plates was marked, e s p e c i a l l y at the holes where bolts were bearing. The deformations were bigger on the tension side of the connection and the magnitude increased with the number of b o l t s . 11. Moment-Rotation Curves.- In order to determine the behaviour of these connections i t was of f i r s t i n t e r e s t to know what moments are developed during an applied beam r o t a t i o n . The developed moments were calculated from the applied load f o r each increment, and the corresponding beam rotations were obtained from the d i a l gauge readings. Moments were pl o t t e d versus rotations for a l l tests made, and the complete set of these graphs i s recorded i n Appendix A. Only the v a r i a t i o n of the p i t c h produced a considerable diffe r e n c e i n the developed end moment. The moment r o t a t i o n curves f o r the same p i t c h (3 in.) but d i f f e r e n t gauge distances (2 1/2 i n . and 1 3/4 in.) agree with each other quite w e l l . Excluding the two bolt connections, i t can be stated that f o r any one r o t a t i o n the developed moments d i f f e r by maximum 15% of the higher value, but no consistency can be noted i n the magnitude or sign of t h i s d i f f e r e n c e . This' statement i s v a l i d up to the tested design r o t a t i o n . (Limits for t h i s range: see page 2Q) The moment r o t a t i o n curves for the same gauge distance (1 3/4 in.) but d i f f e r e n t pitches (3 i n . and 2 1/4:'in.) show for the same r o t a t i o n a difference i n moments between 20% and 50% of the higher value. The sign of t h i s difference i s i n a l l cases the same; the moment for the connection with the 2 1/4: i n . -p i t c h i s always smaller. The v a l i d i t y of t h i s observation goes also as far as the maximum design r o t a t i o n . 13. O 0.00/ OOOS. 0.003 o.oov S?OrAT/OA/ {RAZD/ANS ) F i g . 6 - Moment Rotation Curves from Pure Moment Set-up. 14. The diagrams seem to be curved r i g h t away from the o r i g i n , but the f i r s t part of the curves can be approximated by a str a i g h t l i n e . The slope of t h i s l i n e which gives an i n d i c a t i o n for the r i g i d i t y of the connection, seems to vary with the p i t c h and the number of b o l t s only. With a decrease i n the p i t c h or number of b o l t s , the slope and therefore the r i g i d i t y decreases also. The steep range of the moment-rotation curves i s followed by a shallower part, i n d i c a t i n g the major s l i p of the connection. A further increase i n r o t a t i o n brings the b o l t s into bearing which shows i n the moment-rotation curves as an increasing slope. 15. 2. Moment-Shear Set-up Type of Connections Investigated.- The same type of connections was tested i n th i s set-up. The s i z e of the weld was introduced as a new v a r i a b l e . Description of Apparatus.- In t h i s arrangement the connections were tested i n the presence of shear as w e l l as moment, i n order to simulate the conditions occuring i n actual p r a c t i c e . It was decided to use the same set-up as had been used before, by R.C. Starr, who tested the sing l e angle beam web connections, (see F i g . 7) The connection assembly was bolted to a very r i g i d column, to develop a maximum end moment. In the v i c i n i t y of the beam connections, the column had web s t i f f e n e r s between i t s 1 i n . thick flanges i n order to prevent any l o c a l flange deformations. For the column and for the beam the deformations were small and without influence, since only the r e l a t i v e r o t a t i o n of one with respect to the other was desired. Because of the two d i f f e r e n t pitches (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 sections of the same length. The f i r s t set with a 3 i n . - p i t c h was tested, having a surface smoothed down by e a r l i e r t e s t . A f t e r t h i s set the beam was sand blasted. The beam used to test the connections with a 2 1/4 i n . - p i t c h was sand blasted to s t a r t with. After each test the surface was wire brushed. The column frame was placed on the bed of the 200,000 l b . Tinius Olsen t e s t i n g machine. The beam was then raised above S'- 7&f /2W=/06 4 J? fApp//ed load) fcy//'*- Upper /Jeoc/ -— Pocfrer ////// O 2 / B e a m Z2. fV=VO r S B T5 - Frxjme — -foac/Ce/Zs 63" I k r 'TV / V, Bed af 7esf/s?g Mach/ne Co/umn Frame 17. th i s frame and bolted to the column face using the test specimen. This specimen consisted of the connection plate welded to a 1 i n . - p l a t e . (see F i g . 3B) The 1 i n . - p l a t e was bolted to the column using twice as many bolts as for the connection i t s e l f , and therefore very l i t t l e displacement r e l a t i v e to the column was expected. D i a l gauge No. 4 (see F i g . 7) indicates d i r e c t l y t h i s d e f l e c t i o n of the connection r e l a t i v e to the column and the maximum observed values are 0.002 i n . at working load and 0.048 i n . at maximum load. In the case where no r o t a t i o n was applied to the connection, the other end of the beam was supported on a double screw arrangement at i t s top flange. For the other case, where ro t a t i o n was applied, the screws were replaced by a p a i r of hydraulic jacks. Each screw or jack was connected to a load c e l l , and the whole arrangement was supported on a frame connected to the bed of the machine. (see Photo #5) D i a l gauges (1) and (2) were attached to the web of the beam and were bearing on small aluminum angles screwed to the connection p l a t e , i n order to measure the r o t a t i o n of the beam web r e l a t i v e to the connection p l a t e . A d d i t i o n a l gauges (3) and (4) were required to measure the v e r t i c a l d e f l e c t i o n of the beam r e l a t i v e to the connection, and of the specimen r e l a t i v e to the column. A slope-device was mounted at the end of the beam as an aid i n applying load and r o t a t i o n at the same time. (see Photo #4) Photo #4 - Test Specimen Mounted i n the Moment Shear Set -up. Photo #5 - End View of the Moment Shear Set-up Showing End Frame with Load C e l l s and H y d r a u l i c Jacks at Top. 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 Rotat ion Before any load was a p p l i e d the screw arrangement was set so that h a l f of the weight of the beam was c a r r i e d by each support , i n order to impose no i n i t i a l moment on the connect ion. The load was a p p l i e d i n increments, while mainta ining the same screw s e t t i n g throughout the whole t e s t . At each load increment a l l readings were recorded i n the f o l l o w i n g manner: When the desi red amount of load was a p p l i e d , the machine was stopped and the load c e l l values were immediatly read, using a two-way switch and the Budd datran d i g i t a l s t r a i n i n d i c a t o r . These readings were taken w i t h i n the space of seconds i n order to avoid any drop of f caused by creep. Afterwards a l l the d i a l gauge readings were recorded. Not iceable connection s l i p s were u s u a l l y charac ter ized by a sudden load drop o f f on the machine load d i a l , accompanied with a cracking n o i s e . This i s an i n d i c a t i o n of a sudden or increased rate of v e r t i c a l movement. The loading was continued u n t i l a large deformation of the connect ion-pla te was reached, 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 with respect to the 1 i n . t h i c k p l a t e connected to the column were 1/5 to 1/2 i n . b) With A p p l i e d Rotat ion Before the b o l t s were t i g h t e n e d , the jacks which replaced the screws were set at t h e i r maximum t r a v e l and the beam was adjusted h o r i z o n t a l l y . Then a f t e r the b o l t s were t i g h t e n e d , a smal l adjustment had to be made by means of the screw connecting the 20. load c e l l to the wire strand, to get h a l f of the weight of the beam on each support. As the load was applied, the valve of the jacks was opened to allow the beam r o t a t i o n to be applied simultaneously with the increase of load. I t was attempted to maintain a f i x e d r a t i o of beam ro t a t i o n to end shear throughout the t e s t , u n t i l the two inch maximum t r a v e l of the jacks was reached, at which time the load only was increased. Load and r o t a t i o n were applied i n increments. The loading or s t r a i n rate of the machine was kept constant. The machine was stopped at each increment, while a l l readings were recorded. A r e l a t i o n s h i p between load and end r o t a t i o n had to be determined, i n order to apply rotations to the t e s t beam. This c a l c u l a t i o n was done already to test the si n g l e web angle connections^. Based on these r e s u l t s and on the allowable b o l t f o r c e (6.6 kips) i t was decided to apply the r o t a t i o n as follows: No. of b o l t s r o t a t i o n i n rad. per i n connection kip end shear: 2 or 3 0.00057 4 0.00048 5 0.00032 6 0.00040 As before noticeable connection s l i p s were noted also as a sudden load drop off on the machine load d i a l , accompanied with cracking noises, 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 increased rate of r o t a t i o n . 21. Observations.- During the tests a d i f f e r e n c e i n the two load c e l l readings was noted, which was due to the fa c t that the connection plate and therefore also the beam web was not exactly v e r t i c a l . From the moment where the connection started to s l i p to the end of the t e s t , cracking noises were observed while loading for most connections. These noises were very much dependent on how the jacks were released. In the case without applied r o t a t i o n very large deformations of the connection plate were obtained. The load was increased u n t i l the end shear reached a magnitude of about three times the design value of the connection. The design value of one 3/4 i n . A-325 high strength bo l t i n a f r i c t i o n type connection i s given i n the standard s p e c i f i c a t i o n s as 6.6 k i p s . The following modes of f a i l u r e have been observed: F a i l u r e type A: Crack i n the tension edge of the p l a t e , immediatly adjoining the toe of the weld. F a i l u r e type B: Crack i n the tension edge of the p l a t e , at a distance 3/4 i n . away from the 1 i n . - p l a t e . F a i l u r e type C: V e r t i c a l crack at the lower edge of the connection p l a t e , d i r e c t l y under the b o l t hole. F a i l u r e type D: Crack i n the weld at the tension edge of the p l a t e . 22. Series r o t . No. of si z e of F a i l u r e force per factor No. bolts f i l l e t Type bolt at of weld f a i l u r e kips safety 5 n o 3 1/4 i n . A 24.3 3.7 4 both sides C 24.9 3.8 5 C 24.1 3.7 6 A 25.7 3.9 7 n o 4 1/4 i n . B 18.5 2.8 5 both sides B 18.9 2.9 6 B 18.4 2.8 8 n o 3 1/4 i n . C + A 21.2 3.2 4 both sides C 21.0 3.2 6 C 20.0 3.0 12 y es 2 1/4 i n . D 17.5 2.6 3 one side D 17.3 2.6 4 D 16.6 2.5 5 D 21.0 3.2 6 D 20.4 3.1 TABLE II - SUMMARY OF FAILURES The "force per b o l t " i s obtained from the t o t a l end shear at f a i l u r e divided by the number of b o l t s . Dividing the "force per b o l t " by the design value (6.6 kips) leads to the "factor of safety". For each test a new set of high strength b o l t s has been used. None of the bolt s f a i l e d , only very small l o c a l deformations due to bearing have been observed. Photo #6 - T y p i c a l Test Specimen for the Moment Shear Set-up. Showing the Deformations a f t e r the Test. 24. Shear De f l e c t i o n Curves.- The shear d e f l e c t i o n curves are obtained from the tests i n which no r o t a t i o n was applied to the connections. These curves have the same general shape as the moment r o t a t i o n curves. The shear force acting on the connection was calculated as the difference between the applied load and the reaction i n the l o a d , c e l l s , and was plotted against 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, obtained from d i a l gauge readings. These graphs are recorded i n Appendix B. As was expected, the experiments show that f o r the same shear force the d e f l e c t i o n increases as the gauge distance increases. This fa c t was observed only before 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 to occur as f a r as about 50% of the maximum observed shear. The slope of t h i s l i n e varies due to the above mentioned fact and due to the number of b o l t s . For the same gauge distance but increasing number of bolts the slope increases also. The two p i t c h distances used did not produce a consistently d i f f e r e n t behaviour for the d i f f e r e n t numbers of b o l t s . A f t e r the s l i p of the connection the shear d e f l e c t i o n curve reaches a maximum and then the shear decreases with increasing d e f l e c t i o n u n t i l the bolts are i n bearing, from then on the shear increased again with increasing d e f l e c t i o n s . Moment Rotation Curves.- The moment calculated from the applied load, the weight of the beam and the load c e l l reactions was plotted against 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 De f l e c t i o n Curves from Moment Shear Set-up Without Applied Rotation. 26. the connection, which was applied by means of the hydraulic jacks. These diagrams are recorded i n Appendix C. Not much consistency can be noted i n t h i s set of curves. The i r r e g u l a r i t i e s at the higher values are probably due to the way the r o t a t i o n was applied. The valve of the hydraulic pump did not permit a continuous release of the jacks, which would have been necessary to apply the r o t a t i o n simultaneously with increasing load. The valve had to be opened i n i n t e r v a l s . A nearly 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 within about 50% of the maximum moment. 27. O O.OOV 0.008 O.O/2. 0.0/6 O.OSO 0.02V ROTAT/OM f RADiAMS) F i g . 9 - Ty p i c a l Moment Rotation Curves from Moment Shear Set-up with Applied Rotation. 28. Ill—ANALYSIS AND RESULTS OF TESTS  1. Capacity of the Connections D e f i n i t i o n s . - S l i p : S l i p i n the connection takes place as soon as the r e l a t i o n between load and deformation i s no longer l i n e a r or i n other words as soon as the slope of the load-deformation curve (moment-rotation or shear-deflection curve) changes. This i s v a l i d only as long as the connection plate i s stressed within the e l a s t i c range. For the connection tested, d i s t i n c t i o n has to be made between the gradual and not very s u b s t a n t i a l s l i p , which seems to occur more or less from the beginning of the t e s t , and the major s l i p which i s characterized by a sudden appearance and by very considerable displacements. Ideal l y the major s l i p would appear as an increasing d e f l e c t i o n under constant load, represented by a h o r i z o n t a l l i n e i n the moment-rotation or shear-deflection curves, u n t i l the bolts go in t o bearing. The f i r s t s l i p p i n g has been observed by other research groups"^, and i n comparison with the major s l i p , was not very s u b s t a n t i a l . The condition that the connection plate has to be stressed i n the e l a s t i c range to observe the f i r s t s l i p p i n g , i s f u l f i l l e d i n a l l tests performed. Maximum Bo l t f o r c e : The maximum b o l t f o r c e i s determined i n three d i f f e r e n t ways corresponding to the three methods of i n v e s t i g a t i o n . a) For the Pure Moment Set-up the maximum b o l t forces have been calculated under the following assumptions: magnitude of bolt forces proportional to t h e i r distance from the centre of 29;. r o t a t i o n , which i s assumed to be i n the centre of the connection. The centre of r o t a t i o n obtained from d i a l gauge readings i s i n a l l cases s l i g h t l y above the centre of the connection, but within reasonable l i m i t s to say that they agree with each other. (see Table V) Based on the assumption that the bolt forces are proportional to t h e i r distance from the centroid of the connection, a r e l a t i o n s h i p i n which the moment i s expressed as a function of the number of connectors n, the p i t c h p and the maximum connection force R has been developed: M = S ^ S ± a R (I) b The maximum bo l t f o r c e was obtained applying this formula. For the Moment Shear Set-up where r o t a t i o n was applied to the beam, the maximum b o l t force was calculated as the resultant of the following two components: the v e r t i c a l component was obtained, d i v i d i n g the end shear i n the connection by the number of b o l t s , whereas the h o r i z o n t a l component was calculated from the developed end moment using formula ( I ) , although the centre of 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 centroid of the connection. In the case of the Moment Shear Set-up where no rot a t i o n was applied to the beam, the h o r i z o n t a l component could be neglected since the developed moment was small and the centre of r o t a t i o n was mostly f a r off the centroid of the connection. 30. Capacity: The capacity of the connection i s reached as soon as the major s l i p occurs. The maximum bolt forces calculated from the values of moments and shears at major s l i p give the capacity of a s i n g l e b o l t . S l i p Values.- Attempts have been made to determine the maximum bolt force at the major s l i p i n 3 d i f f e r e n t ways: 1. Intersection of the two tangents as shown i n F i g . 2. 2. For an a r b i t r a r i l y chosen, small r e s i d u a l deformation a p a r a l l e l l i n e to the i n i t i a l . t a n g e n t was drawn and i n t e r -sected with the load-deformation curve. 3. The reading on the machine load d i a l was taken for the load at which there was no load increase or even a load drop o f f . The s l i p values 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 described gave any consistent r e s u l t s for the following reasons: Inaccuracy of test r e s u l t s . No d e f i n i t e h o r i z o n t a l or nearly h o r i z o n t a l tangent to the load-deformation curves, which would indi c a t e c l e a r l y the major s l i p . The s l i p value i s a function of the c o e f f i c i e n t of f r i c t i o n , and the main reason for the inconsistency 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 for the same type of surface. A great number of experiments have shown t h i s f a c t ^ . For a m i l l scale surface the c o e f f i c i e n t of f r i c t i o n varied from 0.16 to 0.46. 31. Max. Bolt Force at Test-X i n . Weld i n . Major S l i p kips Remarks Method y i n . No. of b o l t s 2 3 4 5 6 2 1/2 3 1/4 bot h sides 14.7 11.8 15.2 16.0 17.0 X=14.48 kips Pure-Moment 1 3/4 3 10.8 13.8 14.2 17.0 15.9 s= 2.15 kips 1 3/4 2 1/4 10.0 13.5 14.7 17.5 15.1 v=14.8% Moment- 2 1/2 3 1/4 bot h sides 12.4 13.7 10.8 11.4 12.4 Shear 1 3/4 3 15.2 13.6 13.6 13.8 17.2 X=13.23 kips no applied r o t a t i o n 4 3 12.3 14.1 14.3 15.2 15.4 s= 1.50 kips 2 1/2 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 1/4 both sides 15.9 15.6 16.7 16.6 X=15.15 kips Shear with 1 3/4 3 1/4 both sides 12.8 12.7 14.7 11.2 s= 2.09 kips applied 2 1/2 3 3/16 both sides 15,2 15.1 15.5 17.5 v=13.7% r o t a t i o n 2 1/2 3 1/4 one side 11.0 16.7 17.3 17.9 TABLE I I I - MAX. BOLT FORCES AT MAJOR SLIP where X = mean value 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 including a l l values i n Table I I I : X = 14.11 kips s = 2.07 kips v = 14.7% 32. Using the method of least squares a smooth curve was calculated through the points r e s u l t i n g from the t e s t , but h i s did not produce any greater consistency. 2. R i g i d i t y of the Connections D e f i n i t i o n s . - R i g i d i t y : The r i g i d i t y of a connection can, be defined as i t s a b i l i t y to develop a bending moment. A measure for t h i s r i g i d i t y i s given by the slope of the tangent to the moment-rotation curve at 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 inverse of the slope of the assumed s t r a i g h t - l i n e portion of the moment-ro t a t i o n curve ( i n i t i a l tangent) i s defined as the semi-rigid connection f a c t o r ^ . For p r a c t i c a l purposes, <P=Mv\ was considered as an acceptable r e l a t i o n s h i p i n the. design of frames g with semi-rigid connections . For a l l tests these factors ^ are l i s t e d below. The A's were obtained by d i v i d i n g the r o t a t i o n i n radians through the moment i n inch-kips, both calculated from the readings at the f i r s t load increment. Semi-Rigid Connection Factors from Pure Moment and Moment  Shear Set-up.- A l l these factors are l i s t e d i n Table IV. 33. X i n . y i n . Weld i n . Semi-Rigid Connection Factor No. of b o l t s i n connection Set-up 2 3 4 5 6 • i o " 5 • i o - 5 •IO" 5 •IO" 5 • i o ' 5 2 1/2 2 1/2 3 3 1/4 1/4 7.13 9.65 2.67 3.21 . 1.43 1.51 0.88 0.36 0.35 0.28 Pure-Moment Moment-Shear 1 3/4 1 3/4 3 3 1/4 1/4 7.20 6.12 3.20 1.79 1.56 1.33 0.81 1.22 0.37 0.47 Pure-Moment Moment-Shear 1 3/4 2 1/4 1/4 11.73 6.40 2.20 1.62 0.64 Pure-Moment 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 side only. TABLE IV - SEMI-RIGID CONNECTION FACTORS 3. Influence of the D i f f e r e n t Variables on the R i g i d i t y Interpreting Table IV and the graphs i n Appendix A and C leads to the following conclusions: Presence of shear, gauge-distance and weld-size do not seem to influence the r i g i d i t y of the connections, whereas for the v a r i a t i o n of the p i t c h and the number of b o l t s the following statements can be made: Increasing the p i t c h and the number of b o l t s causes an increase i n the r i g i d i t y of the connections. 34. 4. Centre of Rotation The centres of r o t a t i o n f o r the Pure Moment Set-up and for the Moment-Shear Set-up with applied r o t a t i o n were determined from the d i a l gauge readings. The r e s u l t s are shown i n Table. V. No. of Bolts Pure Moment Set-up Moment-Shear Set-up serie s 1 series 2 series 3 series 9 k l k l k2 k l k2 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 0 -0.092 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 TABLE V - CENTRES OF ROTATION of rote?A/or? 1_ CGr77ho/c/ of oo/7/7ec/~/or7 ii F i g . 10 - Centre of Rotation. 35. IV—DERIVATION OF THEORETICAL CAPACITY  AND APPROXIMATION OF THE RIGIDITY OF THE CONNECTIONS 1. Theoretical Capacity Derivation.- The capacity of a sing l e high strength b o l t i n a f r i c t i o n type connection i s obtained by multip l y i n g the c o e f f i c i e n t of f r i c t i o n by the tension force acting i n the axis 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 Ste e l Manual (A.I.S.C.):JUL = 0.35, and the required b o l t tension for an A.S.T.M. A-325 high strength b o l t i s T = 28.5 kip s . Resulting from these values the capacity of one b o l t i s 10 kip s . Considering t h i s as the maximum b o l t f o r c e , the capacity of the connection can then be calculated as shown i n chapter I I I : M = °P(;+1> R D Shear S = n-R No. of bolts n Moment in-kips S kips. p = 3 i n . P = 2 1/4 i n . 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 with Experiments.- a) Pure Moment set-up The above values f o r the moments are indicated on the moment-ro t a t i o n curves. In the case of the 2 bolt-connection with 1 3/4 i n . - p i t c h and 2 1/4 in.-gauge distance, the t h e o r e t i c a l capacity agrees with 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 value i s below the major s l i p value, (see Appendix A,) b) Moment Shear set-up  without applied r o t a t i o n . The comparison of the shear d e f l e c t i o n curves with the values obtained by mul t i p l y i n g the t h e o r e t i c a l capacity of one b o l t by the number of bolts shows that a l l these t h e o r e t i c a l values are below the major s l i p value, (see Appendix B) c) Moment Shear set-up  with applied r o t a t i o n . The maximum b o l t force was calculated as described on pg. 28 and 29 and was plo t t e d versus the resultant d e f l e c t i o n , which was calculated from the v e r t i c a l and h o r i z o n t a l displacement at the top b o l t . The h o r i z o n t a l d e f l e c t i o n was obtained from the r o t a t i o n , assuming the centre of r o t a t i o n at the centroid of the connection. Comparing these graphs with the t h e o r e t i c a l capacity of a sing l e b o l t shows again that these t h e o r e t i c a l values are below the region of the major s l i p , (see Appendix C) 37. 2. Discussion of R i g i d i t y Rough Approximation of R i g i d i t y . - The semi-rigid connection factor "^0was calculated on the basis of the following i d e a l i z e d conditions: 1. The connection plate i s treated as a can t i l e v e r beam. 2 2. The en t i r e plate i s e l a s t i c with E = 29,000 k i p s . / i n . . 3. The plate i s subject to pure moment. Thus the approximated semi-rigid connection factor becomes * ° E-I where I = x + 1.25 0.25f(n-1)-y+2.501 3 12 Comparison with Experiments.-X y n 2 3.74-10'5 1.9 2.6 X = 2 1/2 3 1.01 2.7 3.2 y = 3 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 - 5 2.4 2. 0 X = 1 3/4 3 0.81 3.5 2.2 y = 3 4 5 6 0.33 0.16 0.09 4.9 5.0 4.1 3.9 6.4 5.2 2 4.63'10~5 2.5 X = 1 3/4 3 1.45 4.4 y = 2 1/4, 4 5 6 0.63 0.33 0.19 3.5 4.9 3.4 TABLE VII - COMPARISON OF SEMI-RIGID CONNECTION FACTORS where /\0 = approximation f o r semi-rigid connection factor 7\, = semi-rigid connection factor from pure moment set-up ^ = semi-rigid connection f a c t o r from moment shear set-up 3 9 . No consistency can be noted in Table VII. Generally the tests show that the connections are from 1.5 to 6.4 times less rigid than the rough approximations indicate. It is believed that this i s due to a combination of the following: some small amount of sli p from the beginning; some plastic deformation around the holes; and effect of shear strains throughout the plate. 40. V—CONCLUSIONS 1. The f e a s i b i l i t y of s i n g l e plate connections for s t e e l beams has been proven. In a l l cases the major s l i p value for the 3/4 i n . diameter bol t s was greater than the usually assumed value of 10 kips per b o l t . 2. A l l connections were tested over 2 times t h e i r permissible 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 connections with the weld on one side only f a i l e d . The f a i l u r e s occured i n the weld at 2.5 to 3.2 times the permissible value. In the other connections where f a i l u r e s were noted, they occurred in:the plate at 2.8 to 3.9 times the permissible value. 3. The maximum b o l t forces at s l i p varied from 10.0 kips to 17.9 kips, and the mean value from a l l tests i s 14.1 k i p s . 4. The presence of shear, the gauge distance and the weld s i z e do not seem to influence the r i g i d i t y of the connections. 5. An increase i n the p i t c h and the number of b o l t s causes an increase i n the, r i g i d i t y of the connections. 6. The rough approximations f o r the semi-rigid connection factors are compared with the ones obtained by experiments 1.8 to 7.6 times smaller. 41. 7. Maximum moment developed by the connections va r i e d from 45 kip-inches f o r the two-bolt connection to 355 kip-inches for the s i x - b o l t connection. 8. The centre of r o t a t i o n varies within the following range: for the Pure Moment Set-up: from -0.033'h to +0.358'h for the Moment Shear Set-up: from -0.117«h to 0.0-h where h i s the distance between the extreme b o l t s . 42. BIBLIOGRAPHY 1. Batho, C. and Rowan, H.C. — "The Analysis of the Moments i n the Members of a Frame Having Rigid or Semi-Rigid Connections, under V e r t i c a l Loads". Second Report, Steel Structures Research Committee, London, England, 1934. 2. Rathburn, J.C. — " E l a s t i c Properties of Riveted Connection". Trans. A.S.C.E. Vol. 101, 1936. 3. Young, CR. and Jackson, K.B. — "The Relative R i g i d i t y of Welded and Riveted Connections". Canadian Journal of Research, National Research Council of Canada, Ottawa, Canada. Vol. 11 and 12, 1934. 4. Brandes, J.L. and Mains, R.M. — "Report of Tests of Welded Top-Plate and Seat Building Connections". Welding Journal, American Welding Society; New York, Vol. 23, No. 3, 1944. 5. Hechtman, R.A. and Johnston, B.G. :— "Riveted and Semi-Rigid Beam to Column Building Connections". Progress Report Number I, American I n s t i t u t e of Steel Construction, New York, 1947. 6. Starr, R.C. — "One Sided Steel Beam Connections". Masters Thesis, University of B r i t i s h Columbia, Canada, 1965. 7. Vasarhelyi, P.P. and Co. — "Rivets and B o l t s , E f f e c t s of Fabr i c a t i o n Techniques". Trans. A.S.C.E., Vol. 126, Part I I , 1961. 43. 8. Monforton, G.R. and Wu, T.S. — "Matrix Analysis of Semi-Rigidly Connected Frames". Journal of the Structural Division, A.S.C.E., Vol. 89, Dec. 1963. 9. Gaylord and Gaylord — "Design of Steel Structures", McGraw H i l l Book Company, 1957. 10. Cullimore, M.S.G. — "Friction Grip Bolt Joints", C i v i l Engineering and Public Works Review, April 1963. APPENDIX A MOMENT - ROTATION CURVES FROM PURE MOMENT SET-UP so 45. 0^ I*? i /o o / / / / / / // f II 1 ll * / / r 1 i 1 -i j i 1 // A fheort tlca/ capac/fy 0 0.009 O.OOS O.OZZ 0,0/4 2-Bolt Connections from Pure Moment Set-up. 1 / // // // / / -e rr / / / a t / f Afheare Os/p on h'ca/ capoc/'/y machine, /oadcf/b, o o.oo<* QOO8 0.0/2. ao/y tforzr/o/V f/z4o//tA/s) 3 - B o l t C o n n e c t i o n s f r o m P u r e Moment S e t - u p . 4-Bolt Connections from Pure Moment Set-up. / / (7 / 1 i * $L -©---// / / 1 1 // It f A theorei O s//por, •/co/ capac/'/y mocfr/ne food a*/ O Q0O4 0.008 0.0/2. 0,0/*/ tfOTZr/O/V ('/Z40/AwsJ 5-Bolt Connections from Pure Moment Set-up. 800, 6W O O.OOf O.OO& 0.0/2. ao/*/ 6-Bolt Connections from Pure Moment Set-up. 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 Applied Rotation. 55. A P P E N D I X C  MOMENT - R O T A T I O N C U R V E S ,  A N D R E S U L T A N T B O L T F O R C E - R E S U L T A N T D I S P L A C E M E N T C U R V E S F R O M MOMENT S H E A R S E T - U P W I T H A P P L I E D R O T A T I O N 57. / / / 4* / _ / I / / 1 / £ //\ / / 1 // // / ' 1 // c—f— / X -J—f // V • fh x-X' — a — Z'h" y = 3" web ^ 3 " we/d I'M" y=3" ve/d Z'/a." y-3" »e& ft" :*//*" ones/cfe. O 0.002 O.OO*/ 0.006 /?07xr/o/v f/^n/AA/s- J 2-Bolt Connections from Moment Shear Set-up with Applied Rotation. 58. /OO SO \ I 60 90 1 y / / / / / / / / [ S 1 / / / f / > 1 / / *• A* / » / // / * / f A fheore x-2'A' y=3" r/e/d:'/>," y-3' we/d :W y=3" we/d :'/v"o> 5/'de 7 one 20 O O.OOZ O.0O<? /9Q7XT/OA/ ftt4D//l/VS) 0.006 3-Bolt Connections from Moment Shear Set-up with Applied Rotation. 59. 2O0T 4-Bolt Connections from Moment Shear Set-up with Applied Rotation. 60. fOOr 320 O 0.002 O.OOV 0.006 /por/\r/o/v (mo/AMs) 5-Bolt Connections from Moment Shear Set-up with Applied Rotation. 6-Bolt Connections from Moment Shear Set-up with Applied Rotation. 20 /6 /2. / // / // X X . J* / ^ ^ ^ ^ ^ ^ B^j 7 / / i f • theone. /= /fy\ X*l'AA <-/co/'capoc/Ay ' y 3 » we/d'/v' ' y = 3" He/e/:fr* ' y= 3" we/d: fa" y = 3 u we/d:'h" s/di on or?<£ 3 0 o O.O/ o.oz 0.03 3-Bolt Connections from Moment Shear Set-up with Applied Rotation. 63 . 10 /6 12 X 6 / 7 ' J w ¥ \ i — f Jl 1 1 1 X«2'/z" . X-/*/<,» _._ X-2'A" • X-2fi? f/co/capoc/fy y~3" we/d7 H/e/d.'W' s/'de or? one 0.0/ O.OZ 0.O3 /?£S//l77iA/r £>/5P/.4C£/l>f£Nr f//V.) 4-Bolt Connections from Moment Shear Set-up with Applied Rotation. 64. 2DX , _, , — : 1 1 O 0.0/ 0.02. 0.03 0.04 f?£St/Lr/INr DISPLACEMENT f//V. ) 5-Bolt Connections from Moment Shear Set-up with Applied Rotation. 6 -Belt Connections from Moment Shear Set-up with Applied Rotation. 

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