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An experimental investigation of the shear plate connections Bienias, Grzegorz 1987

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EXPERIMENTAL INVESTIGATION OF THE SHEAR PLATE CONNECTIONS by GRZEGORZ BIENIAS B. A . S c . , S i l e s i a n P o l y t e c h n i c a l I n s t i t u t e , 1974 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in i i THE FACULTY OF GRADUATE STUDIES Department of C i v i l E n g i n e e r i n g We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA June,1987 © Grzegorz B i e n i a s , June,1987 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the re q u i r e m e n t s f o r an advanced degree a t the The U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s unde r s t o o d t h a t c o p y i n g or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department of C i v i l E n g i n e e r i n g The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date: June,1987 i i ABSTRACT In L i m i t S t a t e s Design f o r s t e e l s t r u c t u r e s , s i n g l e p l a t e c o n n e c t i o n s are designed t o t r a n s f e r beam shear t o s u p p o r t i n g member. These connections, w i t h the c o n n e c t i o n p l a t e shop-welded t o the s u p p o r t i n g member and f i e l d - b o l t e d t o the supported beam are becoming i n c r e a s i n g l y p o p u l a r due t o t h e i r economy and ease of f a b r i c a t i o n . S i n g l e p l a t e c o n n e c t i o n s are v e r y s u i t a b l e f o r cases where speed of e r e c t i o n i s a primary c o n s i d e r a t i o n . They are p a r t i c u l a r l y s u p e r i o r f o r skewed co n n e c t i o n s . T r a d i t i o n a l d e s i g n methods which d e a l w i t h c o n n e c t i o n problems g e n e r a l l y g i v e o v e r - c o n s e r v a t i v e s o l u t i o n s t o t h i s complex problem. Two s e r i e s o f experimental i n v e s t i g a t i o n s o f 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 beam-to-girder webs were conducted. A v a r i e t y of c o n n e c t i o n s were t e s t e d t o demonstrate t h e i r f e a s i b i l i t y and t o c o l l e c t data f o r a n a l y t i c a l c o r r e l a t i o n s t u d i e s . The u l t i m a t e g o a l of these t e s t s and s t u d i e s i s t o d e v i s e a r a t i o n a l b a s i s f o r the d e s i g n of these c o n n e c t i o n s . T h i s work i s p a r t of a comprehensive r e s e a r c h p r o j e c t and the r e a d e r i s r e f e r r e d t o ot h e r papers (References 1 and 2) f o r completeness. Based on experimental r e s u l t s and t h e o r e t i c a l c o r r e l a t i o n s t u d i e s , a m o d i f i e d d e s i g n formula i s proposed i n order t o p r e d i c t the u l t i m a t e c a p a c i t y of s i n g l e p l a t e c o n n e c t i o n s . The formula t r i e s t o i n c o r p o r a t e the i n f l u e n c e s o f a p p l i e d l o a d s (shear f o r c e , t o r s i o n a l moment, and bending moment), r e s i s t a n c e o f the s i n g l e p l a t e connection, skew angle of the c o n n e c t i o n p l a t e a n d t y p e o f h o l e s ( s l o t t e d a n d s t a n d a r d ) u s e d i n t h e c o n n e c t i o n . i v TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGEMENTS X GENERAL NOMENCLATURE x i 1. INTRODUCTION 1 1.1 INTRODUCTION 1 1.2 PRELIMINARY WORKS 5 1.3 OBJECTIVES OF THIS RESEARCH INVESTIGATION 12 2. TEST PROGRAM 14 2.1 TEST APPARATUS GEOMETRY 14 2.2 DESCRIPTION OF TEST SPECIMENS 27 2.3 DESCRIPTION OF LOAD BEAM 32 2.4 DATA ACQUISITION AND CONTROL SYSTEM 42 2.5 STRAIN GAUGES 4 5 2.6 LINEAR VARIABLE DIFFERENTIAL TRANSFORMERS 47 3. TEST RESULTS 49 3.1 TEST RESULTS, SLOTTED HOLES 49 3.2 TEST RESULTS, STANDARD HOLES 76 3.3 COUPON TESTS 102 4. ANALYSIS OF TEST RESULTS 106 4.1 SHEAR FORCE RESULTS 106 4.2 TORSIONAL MOMENT RESULTS 108 4.3 BENDING MOMENT RESULTS 110 4.4 RATIO INTERACTION RESULTS 113 5. CONCLUSIONS 121 V 6. RECOMMENDATIONS FOR FUTURE STUDIES 124 BIBLIOGRAPHY 125 v i LIST OF TABLES TABLE PAGE 2.2.1 Test Specimen Dimensions 27 2.2.2 Connection Plate Dimensions .28 2.2.3 Test Specimen Details 30 3.1.1 Test Results, Specimen # 1 52 3.1.2 Test Results, Specimen # 3 56 3.1.3 Test Results, Specimen # 5 59 3.2.1 Test Results, Specimen # 2 77 3.2.2 Test Results, Specimen # 4 81 3.2.3 Test Results, Specimen # 6 84 3.3.1 Coupon Test Results 103 4.1.1 Shear Results 107 4.2.1 Torsional Results 109 4.3.1 Bending Results 112 4.4.1 Ratio and Ratio Interaction Results 114 v i i LIST OF FIGURES FIGURE PAGE 1.1.1 Typical Single Plate Connections 3 1.1.2 Skewed Single Plate Connection 4 1.2.1 E c c e n t r i c a l l y Loaded Bolt Group 9 1.2.2 In-Plane Loaded Welded Group 10 1.2.3 E c c e n t r i c a l l y Loaded Weld Group 11 2.1.1 Test Apparatus Arrangement - Plan View 16 2.1.2 Test Apparatus Arrangement - Cross Section 17 2.1.3 Test Apparatus Arrangement - Front View 18 2.1.4 Test Apparatus Arrangement - Top View 19 2.1.5 Test Apparatus Arrangement - Side View 20 2.1.6 Test Apparatus Arrangement - Rear View 21 2.1.7 Test Apparatus Arrangement - Bracket 22 2.1.8 Test Apparatus Arrangement - Frame.. 2 3 2.1.9 Test Apparatus Arrangement - Pin 2 4 2.1.10 Test Apparatus Arrangement - Guides 25 2.1.11 Test Apparatus Arrangement - Load C e l l 26 2.2.1 Test Specimen - Shop Drawing 31 2.3.1 Load Beam - Shop Drawing 34 2.3.2 Load Beam - Details 3 5 2.3.3 Load Beam - Slotted Holes 36 2.3.4 Load Beam - Standard Holes 37 2.3.5 Load Beam - 0° Test 38 2.3.6 Load Beam - 30° Test 39 2.3.7 Load Beam - 45° Test 40 2.3.8 Load Beam - Shear Force D i s t r i b u t i o n 41 v i i i 2.4.1 Optilog System with IBM-PC 43 2.4.2 Back of Optilog Showing Channel Plug-ins 44 2.5.1 Location of Strain Gauges 46 2.6.1 Location of LVDT's 48 3.1.1 Specimen # 1 - Force vs. Displacement 62 3.1.2 Specimen # 3 - Force vs. Displacement 63 3.1.3 Specimen # 5 - Force vs. Displacement 64 3.1.4 Specimen # 1 - Force vs. Strain 65 3.1.5 Specimen # 3 - Force vs. Stra i n 66 3.1.6 Specimen # 5 - Force vs. Stra i n 67 3.1.7 Deformation Stages - Slotted Holes 68 3.1.8 Test # 5 - Top View of Fa i l e d Specimen 69 3.1.9 Test # 5 - Side View of Fa i l e d Specimen 70 3.1.10 Test # 5 - Side View of F a i l e d Specimen 71 3.1.11 Test # 5 - Rear View of Fa i l e d Specimen 72 3.1.12 Test # 5 - Front View of F a i l e d Specimen 73 3.1.13 Test # 5 - Side View of Fa i l e d Specimen 74 3.1.14 Test # 5 - Rear View of Fa i l e d Specimen 75 3.2.1 Specimen # 2 - Force vs. Displacement 87 3.2.2 Specimen # 4 - Force vs. Displacement 88 3.2.3 Specimen # 6 - Force vs. Displacement 89 3.2.4 Specimen # 2 - Force vs. Strain 90 3.2.5 Specimen # 4 - Force vs. Stra i n 91 3.2.6 Specimen # 6 - Force vs. Stra i n 92 3.2.7 Deformation Stages - Standard Holes 93 3.2.8 Test # 6 - Top View of Fa i l e d Specimen 94 3.2.9 Test # 6 - Front View of F a i l e d Specimen 95 ix 3.2.10 Test # 6 - Front View of F a i l e d Specimen 96 3.2.11 Test # 6 - Front View of Fa i l e d Specimen 97 3.2.12 Test # 6 - Rear View of Fa i l e d Specimen 98 3.2.13 Test # 6 - Rear View of F a i l e d Specimen 99 3.2.14 Test # 6 - Rear View of Fa i l e d Specimen 100 3.2.15 Test # 6 - Side View of Fa i l e d Specimen 101 3.3.1 Coupons 104 3.3.2 Coupon Test 105 4.4.1 Graph of Three-Ratio Interaction vs. Skew Angle 117 4.4.2 Graph of " F i t Functions" to Three-Ratio Interaction - Slotted Holes 118 4.4.3 Graph of " F i t Functions" to Three-Ratio Interaction - Standard Holes 119 4.4.4 Graph of Modified Three-Ratio-Interaction Formula vs. Skew Angle 12 0 X ACKNOWLEDGEMENTS I wish to acknowledge g r a t e f u l l y my indebtedness to many present members of the departmental s t a f f for suggestions and problems they have contributed. I e s p e c i a l l y appreciate the encouragement and p r o f e s s o r i a l counsel of Dr. S.F. Stiemer during the research and writing of the t h e s i s . The cooperation received from Mr. A. Ho and Mr. H. Ng was very b e n e f i c i a l i n t h i s investigation and i s sin c e r e l y appreciated. This thesis was made possible by the f i n a n c i a l assistance from the National Sciences and Engineering Research Council of Canada, Cooperative Research and Development Grant Program. The contributions received from B r i t t a i n Steel Ltd. and from Great West Steel Industries Ltd. are also g r a t e f u l l y appreciated. My spe c i a l thanks are also due to my fellow graduate students for many simulating and he l p f u l conversations. I would also l i k e to thank my friend, Mr. Z. Yao for h i s great help and assistance from the early stages of my studies to the very end. F i n a l l y , I must acknowledge the forbearance of my wife and daughter, and t h e i r partnership i n t h i s writing endeavour. x i GENERAL NOMENCLATURE a = t o r s i o n a l constant b^ = width of the girder flange BETA = skew angle of the connection d = s i z e of the f i l l e t weld d 1 = shear force r a t i o d 2 = t o r s i o n a l moment r a t i o d 3 = bending moment r a t i o dp = depth of the connection plate D = depth of the girder e, = eccentric distance between the centreline of the b specimen and the centreline of the bolt s e^ = eccentric distance between the edge of the connection plate and the centreline of the bolt s Ey = Young's modulus F = y i e l d strength F u = ultimate strength h = depth of the end shear plate h = depth of the girder web W I = moment of i n e r t i a of the girder I = moment of i n e r t i a of the weld group L = length of the girder M^ = applied bending moment M = p l a s t i c moment resistance P M^ . = applied t o r s i o n a l moment n^ ^ = shear force r a t i o and t o r s i o n a l moment r a t i o i n t e r a c t i o n x i i n 2 = shear force r a t i o and bending moment r a t i o i n t e r a c t i o n n 3 = t o r s i o n a l moment r a t i o and bending moment r a t i o i n t e r a c t i o n n. = "three r a t i o i n t e r a c t i o n " which combines shear 4 force r a t i o , t o r s i o n a l moment r a t i o , and bending moment r a t i o P = ultimate load max R = reduction i n maximum bending moment R b = t o r s i o n a l resistance constant of the girder R = t o r s i o n a l resistance constant of the connection P plate = factor which accounts for the type of holes = thickness of the girder flange = thickness of the connection plate t w = thickness of the girder web T avg = average shear stress T s = ultimate t o r s i o n a l moment resistance T u l t = ultimate shear stress V max = maximum shear force V u l t = ultimate shear resistance w p = width of the connection plate X u = ultimate strength of the weld Z x = p l a s t i c section modulus 1 Chapter 1 INTRODUCTION 1.1 INTRODUCTION For some b u i l d i n g a p p l i c a t i o n s , s i n g l e p l a t e c o n n e c t i o n s p r o v i d e good a l t e r n a t i v e s t o a l l common types o f beam shear c o n n e c t i o n s . They are becoming i n c r e a s i n g l y p o p u l a r i n the i n d u s t r y . The c o n n e c t i o n p l a t e i s shop-welded t o the s u p p o r t i n g g i r d e r and f i e l d - b o l t e d t o the supported beam as shown i n F i g u r e 1.1.1. T h e i r economy and ease o f f a b r i c a t i o n are the main f a c t o r s t h a t favour s i n g l e p l a t e c o n n e c t i o n s i n s t r u c t u r a l s t e e l c o n s t r u c t i o n . S i n g l e p l a t e c o n n e c t i o n s are p a r t i c u l a r l y s u i t a b l e f o r cases where speed of e r e c t i o n i s a primary c o n s i d e r a t i o n . In a d d i t i o n , s i n g l e p l a t e c o n n e c t i o n s are s u p e r i o r f o r skewed connections ( F i g u r e 1.1.2). The t o l e r a n c e s r e q u i r e d f o r f a b r i c a t i o n of s i n g l e p l a t e c o n n e c t i o n s p r e s e n t no problems when beams are c u t t o l e n g t h , and i t i s e a s i l y p o s s i b l e t o l o c a t e and support c o n n e c t i o n p l a t e s w i t h a h i g h degree of p r e c i s i o n d u r i n g f a b r i c a t i o n and welding. F i n a l l y , q u a l i t y c o n t r o l i s e f f o r t l e s s d u r i n g e r e c t i o n phase. E a r l i e r works on s i n g l e p l a t e connections were r e p o r t e d by F i s h e r [ 7 ] , Crawford and Kulak [8], B u t l e r and Kulak [9], B u t l e r , P a l , and Kulak [10], and Dawe and Kulak [11]. T h e i r i n v e s t i g a t i o n s have c o n c e n t r a t e d on p a r t i c u l a r components of the s i n g l e p l a t e c o n n e c t i o n such as welds and b o l t s . Others (Lips o n [ 3 ] , R i c h a r d e t a l . [ 5 ] , and Young and Disque [ 6 ] ) , 2 have examined the whole co n n e c t i o n c o m p r i s i n g o f b o l t s , welds, and c o n n e c t i o n p l a t e . T i d e [12] has reviewed the concepts t h a t form the b a s i s f o r the d e s i g n o f e c c e n t r i c a l l y loaded f i l l e t weld groups and h i s a t t e n t i o n has been d i r e c t e d t o b u c k l i n g o f the s u p p o r t i n g beam web i n the v i c i n i t y o f the conn e c t i o n . An i n v e s t i g a t i o n o f p e r p e n d i c u l a r and skewed s i n g l e p l a t e c o n n e c t i o n s ( F i g u r e s 1.1.la and 1.1.2) w i t h the c o n n e c t i o n p l a t e welded t o a f l e x i b l e element l i k e t he g i r d e r web was f i r s t r e p o r t e d by Stiemer, Wong, and Ho [ 2 ] . O v e r s t r e s s e d r e g i o n s were observed i n the s u p p o r t i n g g i r d e r due t o the combined e f f e c t s o f shear, t o r s i o n , and bending. An e m p i r i c a l d e s i g n formula was proposed: V max 2 + r M t i 2 + r M b i . V u l t . . T u l t . M r _ where: V „ = maximum shear f o r c e max V"u^ ^. = u l t i m a t e shear r e s i s t a n c e = a p p l i e d t o r s i o n a l moment = u l t i m a t e t o r s i o n a l moment r e s i s t a n c e = a p p l i e d bending moment M = bending moment r e s i s t a n c e 3 (a) Beam-to-Girder Web Connection (b) Beam-to-Column Web Connection (c) Beam-to-Column Flange Connection F i g u r e 1.1.1 T y p i c a l S i n g l e P l a t e Connections 4 F i g u r e 1.1.2 Skewed S i n g l e P l a t e Connection 5 1.2 PRELIMINARY WORKS U n t i l 1963 l i t t l e research had been conducted on the behaviour of e c c e n t r i c a l l y loaded fasteners with the load applied i n the plane of the fasteners. Designers and researchers were more interested i n the e f f e c t of loads on the o v e r a l l s t r u c t u r a l connection rather than on i n d i v i d u a l fastener. As a r e s u l t , the connection was designed with s u f f i c i e n t number of fasteners to ensure that any f a i l u r e w i l l occur at the members instead of occuring at an i n d i v i d u a l fastener i n the connection. In 1964, Higgins [22] reported on a series of tests on e c c e n t r i c a l l y loaded riveted connections. From the r e s u l t s of these t e s t s , formulas for evaluating an e f f e c t i v e e c c e n t r i c i t y evolved. The prediction of the ultimate load capacity of the connections was based on rotation of the connection about an instantaneous centre of rotation computed on the assumption that the r i v e t s remain e l a s t i c . The instantaneous centre i s defined as the point about which, at any instant, the fastener group s a t i s f i e s the three equilibrium equations for s t a t i c s : E F - 0; (1.2.2) x H F = 0; y (1.2.3) EM = 0; (1.2.4) In 1965, Fisher [7] developed mathematical expressions for the s t r e s s - s t r a i n r e l a t i o n s h i p of a plate with holes and for the shear-deformation rel a t i o n s h i p of bolts (both 6 applicable to the e l a s t i c and i n e l a s t i c regions). The load-deformation c h a r a c t e r i s t i c s of a single b o l t i n shear i s represented by a continuous function. This function i s : - M A X R = R u l t [ l - e j (1.2.1) where: R = b o l t force corresponding to a given deformation R u l t = ultimate shear strength of a b o l t e = base of natural logarithm /A.,X = regression c o e f f i c i e n t s A = deformation containing the components caused by shear, bending, and bearing of a b o l t as well as the shearing deformation of plates The shape of the function was governed by the ultimate shear strength and two empirical parameters. These parameters were found to vary for d i f f e r e n t bolts and d i f f e r e n t types of connected material. In 1971, Crawford and Kulak [8] developed a t h e o r e t i c a l formula to predict the behaviour of fasteners subjected to a combination of d i r e c t shear and moment (see Figure 1.2.1). Their evaluation of the ultimate connection strength i s based on three assumptions: 1. The fastener group, under an eccentric load, rotates about an instantaneous centre of ro t a t i o n . 2. The deformation of each fastener varies l i n e a r l y with the fastener's distance from the centre of rotation 7 and acts i n a d i r e c t i o n perpendicular to the radius of rotation of the fastener. 3. The ultimate strength of the group i s reached when the ultimate strength of the fastener farthest from the centre of rotation i s reached. From the known load-deformation r e l a t i o n s h i p of in d i v i d u a l fastener, the r e s i s t i n g force of each fastener can be calculated from Equation 1.2.1. Calcul a t i o n of the instantaneous centre i s described i n Reference 8. Since i t i s a t r i a l and error process, tables were introduced i n the CISC Handbook (1980 edition) which permit rapid evaluation of d i f f e r e n t common bolt groups subjected to various e c c e n t r i c i t i e s . However, using spreadsheets on a microcomputer, the instantaneous centre can be e a s i l y determined without the need for tables, which usually i n h e r i t a c e r t a i n ackwardness and p o s s i b i l i t y of errors i n use. In the work reported i n 1972, Butler, Pal, and Kulak [10] suggested a method of analysis based on the load-deformation c h a r a c t e r i s t i c s of the weld and the instantaneous centre of rotat i o n analogously s i m i l a r to the analysis of e c c e n t r i c a l l y loaded b o l t groups (see Figure 1.2.2.). Here, the weld group i s considered to be divided into a discrete number of f i n i t e weld elements. Equation 1.2.1 i s used to determine the magnitude of resistance of each weld element. The study was expanded i n 1974 by Dawe and Kulak [11] to consider e c c e n t r i c a l l y loaded f i l l e t weld group (see Figure 1.2.3). An analysis s i m i l a r to that for in-plane e c c e n t r i c i t y 8 was introduced. The ultimate loads of eccentric weld groups were predicted with bearing of the plate included i n the analysis. The magnitude and location of bearing forces were based on assumption of a triang u l a r stress block i n the compression zone. More recently (1980), Richard et a l . [5] conducted research on the behaviour of single plate framing connections. Tests and studies reported i n Reference 5 as well as Lipson [3] indicated that the single plate connections can develop a s i g n i f i c a n t end moment i n the beam and supporting member. However, the tested connections were attached to both sides of a supporting structure, which with r e s u l t i n g symmetry can be considered as a r i g i d support. Young and Disque [6] developed tabular design aids by applying the design procedure presented i n Reference 5. The design procedure considers both connection deformation and beam end rotation through the use of these design aids. 9 Figure 1.2.1 E c c e n t r i c a l l y Loaded Bolt Group 10 Figure 1.2.2 In-Plane Loaded Welded Group F i g u r e 1.2.3 E c c e n t r i c a l l y Loaded Weld Group 12 1.3 OBJECTIVES OF THIS INVESTIGATION Although the single plate connections has an apparent f a i l u r e - f r e e performance record, t h i s does not necessarily indicate that good design procedures have been used. The actual load and the design methods and s p e c i f i c a t i o n s should r e f l e c t the actual s t r u c t u r a l behaviour. Investigations into the s t r u c t u r a l action, strength, and d u c t i l i t y of the single plate connections have been lim i t e d and none have s a t i s f a c t o r y proved or disproved the v a l i d i t y of the standard design procedure (which assumes that each b o l t c a r r i e s an equal portion of the t o t a l shear load and, i n agreement with the simple support assumption, that r e l a t i v e l y free rotation occurs between the end of the beam and the supporting member). An investigation of single plate connections for beam-to-girder webs was i n i t i a t e d i n 1984 i n the C i v i l Engineering Department of the University of B r i t i s h Columbia. A v a r i e t y of connections were tested to demonstrate t h e i r f e a s i b i l i t y , with the ultimate aim of devising a r a t i o n a l basis for t h e i r design. For t h i s purpose the following items were of special i n t e r e s t : 1. F l e x i b i l i t y of the supporting element (girder) i n r e l a t i o n to the sub-element (connection plate.) 2. V a r i a t i o n of the connection plate dimensions. 3. Var i a t i o n of the connection plate l o c a t i o n with respect to the supporting element. 4. Slotted and standard holes. 5. Skewed connection angle (BETA=0 for a perpendicular 13 connection). 6. A n a l y t i c a l investigation consisting of f i n i t e element analysis. Tests c a r r i e d out by H.Wong [1] at UBC i n 1986 examined objectives 1, 2, and 5, using f u l l scale t e s t specimens. A preliminary design formula (Equation 1.1.1) was derived. The current investigation i s part of a more comprehensive research project and examines objectives 4 and 5. The preliminary design formula i s modified from experimental invest i g a t i o n to serve as the basis of a design procedure for single plate connections. Future a n a l y t i c a l studies w i l l be used to v e r i f y the proposed formula. 14 Chapter 2 TEST PROGRAM 2.1 TEST APPARATUS GEOMETRY Single plate connections with the connection plate welded to the supporting girder and bolted to the supported beam were tested at the University of B r i t i s h Columbia's C i v i l Engineering Structures Laboratories. E x i s t i n g columns, load c e l l s , and load actuator were used for t e s t apparatus arrangement. The t e s t specimens were mounted between two W-shaped columns. The columns as well as the other equipments were arranged to coincide with anchoring holes i n the laboratory f l o o r . These holes are patterned as a 610 x 610 mm f l o o r g r i d . This arrangement allowed the bases to be t i e d down with anchor rods. A distance of 2438 mm between centres of columns was chosen to coincide with the previous i n v e s t i g a t i o n [1]. A bracket was attached to the bottom flange of the t e s t specimen to provide l a t e r a l r e s t r a i n t which simulates r e a l condition of a beam's compression flange restrained by either f l o o r or roof. The connection was loaded upward through a load beam by a 890 kN MTS System Corporations load actuator with a b u i l t - i n load c e l l . The end of the load beam farthest from the single plate connection was supported on a frame. Pins were added at the top of both frame columns which reduced the r i g i d i t y of the load beam-to-frame connection. The frame span of 3048 mm 15 was chosen to allow easy management of skewed connections. An MTS Systems Corporation 445 kN load c e l l was attached at t h i s end to record the reaction force. Also, guides were added at t h i s end to prevent any out-of-plane twisting of the load beam. Figures 2.1.1 to 2.1.11 show plan, cross section, and photographs of the t e s t apparatus arrangement. F i g u r e 2.1.1 T e s t Apparatus Arrangement - Plan View 17 GIRDER. . BRACKET COLUMNS LOAD BEAM \ \ LOAD CELL LOAD ACTUATOR FRAME fml 1219 457 1778 Figure 2.1.2 Test Apparatus Arrangement - Cross Section THE QUALITY OF THIS MICROFICHE IS HEAVILY DEPENDENT UPON THE QUALITY OF THE THESIS SUBMITTED FOR MICROFILMING. LA QUALITE DE CETTE MICROFICHE DEPEND GRANDEMENT DE LA QUALITE DE LA THESES SOUMISE AU MICROFILMAGE. UNFORTUNATELY THE COLOURED ILLUSTRATIONS OF THIS THESIS CAN ONLY YIELD DIFFERENT TONES OF GREY. MALHEUREUSEMENT, LES DIFFERENTES ILLUSTRATIONS EN COULEURS DE CETTE THESES NE PEUVENT DONNER QUE DES TEINTES DE GRIS. 18 Figure 2.1.3 Test Apparatus Arrangement - Front View 19 Figure 2.1.4 Test Apparatus Arrangement - Top View 20 Figure 2.1.5 Test Apparatus Arrangement - Side View 21 Figure 2.1.6 Test Apparatus Arrangement - Rear View 22 Figure 2.1.7 Test Apparatus Arrangement - Bracket 23 Figure 2.1.8 Test Apparatus Arrangement - Frame 24 Figure 2.1.9 Test Apparatus Arrangement - Pin 25 Figure 2.1.10 Test Apparatus Arrangement - Guides 26 Figure 2.1.11 Test Apparatus Arrangement - Load C e l l 27 2.2 DESCRIPTION OF TEST SPECIMENS The t e s t specimens were fabricated and supplied by a l o c a l s t e e l f a b r i c a t o r . A l l of the specimens conformed with the s p e c i f i c a t i o n s of CSA G40.21-M 300W f o r material properties, CSA G40.20-M for dimensional tolerances, and CAN3-S16.1-M78 f o r b o l t i n g and welding. The t e s t specimen represented the supporting girder of a one-sided single plate connection. Six t e s t specimens, each 2092 mm long, were fabricated from the same batch of W410 x 3 9 r o l l e d shape s i z e . This beam siz e was chosen because i t i s common i n l i g h t construction applications. End plates, each 10 mm thick, welded to both ends of the supporting girder were used to bo l t the t e s t specimen to the columns. Table 2.2.1 shows the dimensions of the t e s t specimen. Table 2.2.1 Test Specimen Dimensions girder depth flange width flange thickness web depth web thickness girder length D 399 mm b f 140 mm 9 mm h w 381 mm t w 6 mm L 2092 mm The sin g l e plate connection was located at the mid-span of the girder. The depth of the connection plate was chosen 28 as that of specimen number 5 from H.Wong [1]. This distance approximates a plate's depth for the supported beam t y p i c a l l y framing into the t e s t specimen and i s adjusted to account for l i m i t a t i o n s due to standard bolt spacing, end distance, and edge distance. Two 22 mm ASTM A490 b o l t s were used to transmit the load from the actuator to the tested connection. Table 2.2.2 shows the dimensions of the connection p l a t e . Table 2.2.2 Connection Plate Dimensions depth dp 203 mm width w 127 mm P thickness t 13 mm P The connection plate, welds, and b o l t s were sized to r e s i s t a l l resultant forces from ultimate load. This ultimate load was calculated as based upon t h e o r e t i c a l y i e l d i n g of the girder due to bending moment acting alone: Pmax = 4*Mp/L = 418.5 kN Mp = Zx*Fy/1000 = 218889.0 kN Zx = 729630.0 mmA3 Fy = 3 00.0 MPa L = 2092.0 mm 29 implied ultimate load p l a s t i c moment resistance of the gir d e r p l a s t i c section modulus assumed y i e l d strength of the girder length of the girder The connection plate thickness was designed for the bearing force, which i s equal to the shear resistance of the bol t s . The f i l l e t welds, which ran the depth of the connection plate on both sides, were designed to r e s i s t the resultant stresses due to shear and bending. Shop drawing of the t e s t specimens i s shown i n Figure 2.2.1. The parameter of the test specimens being varied was a skew connection angle BETA of 0, 30, and 45 degrees. This skew angle i s defined as the angle between the plane perpendicular to the girder and the plane of the load beam (see Figure 2.2.1). Test specimen number, t e s t designation number, and skew angle are tabulated i n Table 2.2.3. where: P max M P F y 30 Table 2.2.3 Test Specimen Details SPECIMEN NO. TEST NO. SKEW ANGLE 1 1 0 2 2 0 3 3 30 4 4 30 5 5 45 6 6 45 31 2092 1046 U3 V \ B A R 12x127x203 BAR 10229x229 W 410*39 F i g u r e 2.2.1 T e s t Specimen - Shop Drawing 32 2.3. DESCRIPTION OF LOAD BEAM The l o a d beam ( f a b r i c a t e d from W shape 310 x 52 o f 300W-steel) was used t o t r a n s m i t f o r c e s from the l o a d a c t u a t o r t o the s i n g l e p l a t e connections. Two s e r i e s o f t e s t s were c a r r i e d out. A s i n g l e l o a d beam w i t h each of the ends a p p r o p r i a t e t o accomplish one of the two s e r i e s o f t e s t s was c o n s t r u c t e d ( f o r the shop drawing of the l o a d beam see F i g u r e 2.3.1). Another l o c a l s t e e l f a b r i c a t o r p r o v i d e d the l o a d beam. In the f i r s t s e r i e s , a t the l o c a t i o n where the l o a d beam was b o l t e d t o the co n n e c t i o n p l a t e , s l o t t e d h o l e s were used t o achieve a pure shear f o r c e . D e t a i l s o f s l o t t e d h o l e s are shown i n F i g u r e 2.3.2. The l o a d beam a t the b o l t l i n e l o c a t i o n was assumed t o a c t l i k e a hinge; thus, the moment remains zero d u r i n g the t e s t . The specimens ## 1, 3, and 5 were t e s t e d i n t h i s s e r i e s (see F i g u r e 2.3.3). In the second s e r i e s the h o l e s of the l o a d beam as w e l l as o f the g i r d e r c o n n e c t i o n were o v e r s i z e d 2 mm. D e t a i l s o f these h o l e s ( l a t e r r e f f e r r e d as standard holes) are shown i n F i g u r e 2.3.2. The t h r e e remaining specimens ## 2, 4, and 6 were t e s t e d i n t h i s s e r i e s (see F i g u r e 2.3.4). I t i s noted t h a t both types of h o l e s are designed a c c o r d i n g t o s e c t i o n 22.3.2 of the CAN3-S16.1-M78 s t e e l code. Two p l a t e s (see F i g u r e 2.3.1), each 6 mm t h i c k , were added a t both ends of the l o a d beam web. T h i s r e i n f o r c e m e n t was necessary by a p l a t e f a i l u r e c r i t e r i o n due t o b e a r i n g . A l s o , t r a n s v e r s e web s t i f f e n e r s were added a t the l o c a t i o n s o f 33 the l o a d a c t u a t o r . The s t i f f e n e r s , i n t u r n , accounted f o r s t a b i l i t y o f the beam web. Due t o the dimensional s i z e o f the l o a d a c t u a t o r u n i t the c l o s e s t p o i n t o f l o a d i n g t o the t e s t specimen was 457 mm. With t h i s d i s t a n c e f i x e d , the l e n g t h of t h e l o a d beam was determined t o t r a n s m i t the maximum shear f o r c e V'1 (see F i g u r e 2.3.8) t o the t e s t specimen without the l o a d beam becoming too lo n g and unmanageable. At approximately 80% of t h e a c t u a t o r l o a d i n g a p p l i e d t o the t e s t specimen, t h i s l e n g t h was found t o be 2285 mm between supports. However, t h e l o a d beam was c o n s t r u c t e d l o n g e r i n order t o handle the skew c o n n e c t i o n cases of 30 and 45 degrees too (see F i g u r e s from 2.3.5 t o 2.3.7) . The two l o a d c e l l s p r o v i d e d i n f o r m a t i o n t o determine the f o r c e s a c t i n g on the t e s t specimen. Knowing the a p p l i e d l o a d and the l o a d a t the f a r end (away from the connection) of the l o a d beam, the shear f o r c e , bending moment, and t o r s i o n a l moment a t the b o l t l i n e c o u l d be e a s i l y c a l c u l a t e d (see F i g u r e 2.3.8) . 34 44 27 v 6 m m R. 330 ^190 + 44 127 in i cn' 167 W310x52 12mm (t Sec t ion A - A Figure 2.3.1 Load Beam - Shop Drawing 35 S T A N D A R D HOLES S L O T T E D H O L E S Figure 2.3.2 Load Beam - Details 36 Figure 2.3.3 Load Beam - Slotted Holes 37 Figure 2.3.4 Load Beam - Standard Holes 38 Figure 2.3.5 Load Beam - 0° Test 39 F i g u r e 2.3.6 Load Beam - 30°Test 40 Figure 2.3.7 Load Beam - 45°Test 41 Figure 2.3.8 Load Beam - Shear Force D i s t r i b u t i o n 42 2.4 DATA ACQUISITION AND CONTROL SYSTEM An Optim Electronics Corporation Optilog Data A c q u i s i t i o n and Control System was operated i n conjunction with an IBM-PC to acquire and reduce the experimental data (see Figures 2.4.1 to 2.4.2). The data was monitored on sixteen channels of the control system: eight for strai n s , s i x for de f l e c t i o n s , and two for loads. The te s t results of s t r a i n s , d e f l e c t i o n s , and loads were recorded at one minute i n t e r v a l s while the actuator load was applied at a rate of 20 kN per minute. A software program (Optim Opus 2 00) was run on the IBM-PC to operate the data a c q u i s i t i o n system. This program controls and interfaces to the Optilog system. The user i s prompted for information to: setup the experiment, run the experiment, and process and reduce the experimental r e s u l t s . C a l i b r a t i o n of instruments, operation of experiment, recording of data, and processing of data were a l l performed by the setup of Optilog, IBM-PC, and Opus. The following procedures are performed i n sequence during a t e s t . A f t e r the experimental setup, the specimen was preloaded to 100 kN and then unloaded. The preload and unload procedures were performed three consecutive times on the specimen before the ultimate f a i l u r e load was applied. Thus any slippage i n the bolted connection was eliminated as the bolts were brought into bearing against the connection plate. 43 Figure 2.4.1 Optilog System with IBM-PC 44 Figure 2.4.2 Back of Optilog Showing Channel Plug-ins 45 2.5 STRAIN GAUGES S t r a i n gauges were used t o measure the u n i - d i r e c t i o n a l s t r a i n s i n the l o n g i t u d i n a l d i r e c t i o n o f the s u p p o r t i n g g i r d e r . Two brands of s t r a i n gauges were used i n the experiment: Measurements Group Inc. type CEA-06-250UW-120 and Micro E n g i n e e r i n g I I type PA-06-125AA-12 0. Both brands of gauges are e q u a l l y a c c u r a t e i n measuring the estimated magnitude of s t r a i n s . These gauges were l o c a t e d on the g i r d e r i n a r e g i o n a d j a c e n t t o the co n n e c t i o n p l a t e (see F i g u r e 2.5.1). The gauges were p l a c e d t o c o i n c i d e w i t h the l o c a t i o n of p r e v i o u s r e s u l t s from H.Wong [ 1 ] ; thus, r e s u l t s from e x i s t i n g and p r e v i o u s i n v e s t i g a t i o n s can be e a s i l l y compared. 46 Figure 2.5.1 Location of Strain Gauges 47 2.6 LINEAR VARIABLE DIFFERENTIAL TRANSFORMERS Six l i n e a r variable d i f f e r e n t i a l transformers (LVDT's) were placed at the mid-span of the girder to measure the girder's deflections at various points of the midspan cross-section (see Figure 2.6.1). LVDT's ## from 1 to 4 were oriented to measure horizontal displacements and LVDT # 5 was oriented to measure v e r t i c a l displacement of the girder. LVDT # 6 was l a t e r added to measure the v e r t i c a l displacement of the compression flange's back edge. LVDT's manufactured by Hewlett-Packard were used i n the experiment. These LVDT's were ca l i b r a t e d to measure displacement i n the ranges of +/-25.4 mm and +/- 12.7 mm. 48 Figure 2.6.1 Location of LVDT's 49 Chapter 3 TEST RESULTS 3.1 TEST RESULTS. SLOTTED HOLES Specimens ## 1, 3, and 5 were tested to determine ultimate f a i l u r e loads of single plate connections with s l o t t e d holes. The skew angle for each specimen were respectively 0, 30, and 45 degrees. The connection plate depth to girder depth r a t i o d p / D w a s maintained at 0.5. Failure of the tests was defined as the f i r s t appearance of any v i s i b l e f a i l u r e i n the specimen such as p l a s t i c hinge, buckling, and crack. Strains, displacements, and loads were recorded as described i n e a r l i e r sections (2.4.2, 2.4.3, 2.4.4). The si z e , shape and span of a l l three specimens were kept constant throughout the te s t s . Connection plates and bolts used i n the tests also have the same properties. A l l specimens were loaded to f a i l u r e ; thus the connections' maximum resistance have a l l been exceeded. The only varying parameter i n the tests were the skew angles. The recorded data for each te s t are l i s t e d i n Tables from 3.1.1 to 3.1.3. In tests ## 1 and 3, f i v e l i n e a r v a r i a b l e d i f f e r e n t i a l transformers (LVDT's) were used to measure the displacements while i n t e s t # 5 six LVDT's were used. A s i x LVDT was added l a t e r to measure the v e r t i c a l displacement of the girder's compression flange where l o c a l buckling was previously observed. Force vs. displacement curves for LVDT # 1 are shown for a l l three tests i n Figures from 3.1.1 to 3.1.3. 50 These curves are representative of curves recorded i n other locations. LVDT # 1 was used to represent the displacements because extensive deformation occured near t h i s LVDT's locatio n . Test # 1 used eight s t r a i n gauges (SG's) to measure strai n s at various locations. For tests ## 3 and 5, only SG's ## from 5 to 8 were used because the skew angle created d i f f i c u l t y i n placing the s t r a i n gauges. Typical force vs. s t r a i n curves are shown in Figures from 3.1.4 to 3.1.6 for a l l three t e s t s using the recorded curves at SG # 8. The location of SG # 8, which was immediately below the connection plate, was e s p e c i a l l y i n t e r e s t i n g because i t was found to be the overstressed region. The maximum loads for the three t e s t s were respectively recorded to be 24 6 kN, 238 kN, and 270 kN. The three t e s t specimens a l l deformed i n s i m i l a r manners. Yi e l d i n g i n the material and deformation of the geometry of the supporting girder were observed during the t e s t s . At f a i l u r e , both top and bottom flanges of the girder (near the connection plate) twisted due to the e f f e c t s of applied t o r s i o n . The girder web buckled i n the region below and above the connection plate, but the web remained straight i n the v i c i n i t y of the weld. The back edge of the girder's compression flange buckled l o c a l l y at the mid-span due to combined t o r s i o n and flexure. Figure 3.1.7 shows approximate e l a s t i c and p l a s t i c deformation stages for a l l three specimens. Photographs of experimental f a i l u r e s for specimen # 5 are shown in Figures from 3.1.8 to 51 3.1.14; these photographs are representative of a l l s l o t t e d connection f a i l u r e s (specimens ## 1, 3, and 5). 52 Table 3.1.1 T e s t R e s u l t s , Specimen # 1 NO. MTS#1 MTS#2 CONN.PL. CONN.PL. kN kN kN % 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 0.000 4.136 8.767 13.353 18.451 22.641 17.819 13.059 8.304 3 . 687 8.313 13.011 17.739 22.588 17.899 12.953 8.371 3.589 8.696 12.988 17.686 22.187 27.436 31.755 36.453 41.169 45.291 50.158 54.606 58.342 63.565 0, 20, 42, 64 , 89, 108, 86, 64, 42. 20. 42 . 64. 86. 109. 87. 62 . 42 . 19, 44. 64. 86. 107. 131. 152. 175. 197. 219. 242 . 260. 286. 309. 000 137 201 681 121 928 567 503 053 195 142 383 718 257 518 191 436 541 037 414 567 504 289 582 864 634 906 236 029 309 351 0. 16, 33, 51, 70, 86, 68, 51, 33 , 16. 33. 51, 68, 86. 69. 49. 34. 15. 35. 51. 68. 85. 103 . 120. 139. 156. 174 . 192 . 205. 227. 245. 000 001 432 328 668 286 747 443 748 507 828 372 978 669 619 237 064 951 341 425 881 316 852 827 412 465 614 078 423 967 786 0. 00 79.46 79.22 79.36 79.30 79.21 79.42 79.75 80.25 81.74 80.27 79.79 79.54 79. 33 79.55 79.17 80.27 81.63 80.25 79.84 79.57 79.36 79.10 79. 19 79.27 79.17 79.40 79.29 79. 00 79.62 79.45 53 Table 3.1.1 (cont.) T e s t R e s u l t s , Specimen # 1 NO. SG#1 SG#2 SG#3 SG#4 m/m m/m m/m m/m +VE=COMPRESSIVE STRAIN -VE=TENSILE STRAIN 1 0. 000000 0. 000000 0. 000000 0. 000000 2 0. 000029 0. 000030 0. 000030 0. 000029 3 0. 000029 0. 000030 0. 000030 0. 000058 4 0. 000087 0. 000059 0. 000088 0. 000146 5 0. 000117 0. 000030 0. 000088 0. 000205 6 0. 000146 0. 000030 0. 000147 0. 000263 7 0. 000146 0. 000059 0. 000118 0. 000234 8 0. 000117 0. 000030 0. 000118 0. 000205 9 0. 000087 0. 000030 0. 000088 0. 000175 10 0. 000087 0. 000030 0. 000088 0. 000117 11 0. 000087 0. 000059 0. 000088 0. 000175 12 0. 000087 0. 000030 0. 000118 0. 000205 13 0. 000117 0. 000030 0. 000147 0. 000263 14 0. 000146 0. 000030 0. 000147 0. 000293 15 0. 000146 0. 000059 0. 000118 0. 000234 16 0. 000117 0. 000059 0. 000118 0. 000205 17 0. 000087 0. 000059 0. 000088 0. 000175 18 0. 000087 0. 000030 0. 000088 0. 000117 19 0. 000087 0. 000030 0. 000118 0. 000175 20 0. 000117 0. 000059 0. 000118 0. 000205 21 0. 000117 0. 000059 0. 000147 0. 000234 22 0. 000146 0. 000059 0. 000147 0. 000293 23 0. 000175 0. 000030 0. 000176 0. 000351 24 0. 000234 0. 000030 0. 000235 0. 000527 25 0. 000322 0. 000030 0. 000323 0. 000674 26 0. 000410 0. 000030 0. 000411 0. 000908 27 0. 000498 0. 000059 0. 000587 0. 001231 28 0. 000498 0. 000118 0. 000733 0. 001671 29 0. 000498 0. 000176 0. 001115 0. 002316 30 0. 000410 0. 000352 0. 001525 0. 003312 31 0. 000234 0. 000587 0. 002053 0. 004749 54 Table 3.1.1 fcont.^ T e s t R e s u l t s , Specimen # 1 NO. SG#5 SG#6 SG#7 SG#8 m/m m/m m/m m/m +VE=COMPRESSIVE STRAIN -VE=TENSILE STRAIN 1 0. 000000 0. 000000 0. 000000 0. 000000 2 0. 000030 0. 000030 0. 000029 0. 000059 3 0. 000030 0. 000030 0. 000058 0. 000088 4 0. 000118 0. 000030 0. 000088 0. 000176 5 0. 000176 0. 000059 0. 000117 0. 000235 6 0. 000206 0. 000059 0. 000146 0. 000264 7 0. 000206 0. 000030 0. 000146 0. 000235 8 0. 000147 0. 000030 0. 000146 0. 000235 9 0. 000147 0. 000000 0. 000117 0. 000176 10 0. 000118 0. 000000 0. 000088 0. 000176 11 0. 000147 0. 000030 0. 000117 0. 000176 12 0. 000147 0. 000030 0. 000146 0. 000235 13 0. 000176 0. 000059 0. 000146 0. 000235 14 0. 000235 0. 000059 0. 000175 0. 000264 15 0. 000176 0. 000059 0. 000146 0. 000264 16 0. 000147 0. 000030 0. 000146 0. 000235 17 0. 000147 0. 000030 0. 000117 0. 000205 18 0. 000088 0. 000000 0. 000088 0. 000147 19 0. 000147 0. 000030 0. 000146 0. 000205 20 0. 000176 0. 000030 0. 000146 0. 000235 21 0. 000206 0. 000088 0. 000146 0. 000264 22 0. 000235 0. 000059 0. 000175 0. 000293 23 0. 000264 0. 000088 0. 000205 0. 000352 24 0. 000323 0. 000059 0. 000322 0. 000528 25 0. 000440 0. 000088 0. 000263 0. 000674 26 0. 000499 0. 000088 0. 000322 0. 000850 27 0. 000587 0. 000088 0. 000527 0. 001173 28 0. 000587 0. 000088 0. 000703 0. 001525 29 0. 000645 0. 000059 0. 000996 0. 002082 30 0. 000645 0. 000088 0. 001290 0. 002902 31 0. 000528 -0. 000058 0. 001759 0. 004427 55 Table 3.1.1 fcont.) T e s t R e s u l t s , Specimen # 1 NO. LVDT#1 LVDT#2 LVDT#3 LVDT#4 LVDT#5 mm mm mm mm mm +VE=SHORTENING -VE=EXTENDING 1 0.000 0 . 000 0 .000 0 .000 0. 000 2 0.127 0 .076 0 .203 0 . 152 -0.127 3 0.127 0 .076 0 . 305 0 .254 -0.254 4 -1.092 -1 .626 2 .032 2 .362 -0.356 5 -1.524 -2 . 159 2 .515 2 .972 -0.508 6 -1.880 -2 . 616 2 .819 3 . 378 -0.635 7 -1.829 -2 .565 2 .819 3 . 378 -0.483 8 -1.778 -2 .489 2 .769 3 .327 -0.356 9 -1.727 -2 .413 2 .718 3 .251 -0.229 10 -1.651 -2 .311 2 .565 3 . 124 -0.076 11 -1.651 -2 . 337 2 .642 3 . 150 -0.229 12 -1.676 -2 . 388 2 .692 3 .226 -0.356 13 -1.727 -2 .464 2 .769 3 .277 -0.483 14 -1.905 -2 . 667 2 .921 3 .454 -0.635 15 -1.880 -2 . 642 2 .921 3 .454 -0.508 16 -1.803 -2 .540 2 .845 3 .404 -0.330 17 -1.778 -2 .489 2 .794 3 .353 -0.229 18 -1.651 -2 .311 2 .565 3 .099 -0.076 19 -1.651 -2 .311 2 .616 3 .124 -0.229 20 -1.676 -2 .362 2 .692 3 . 175 -0.356 21 -1.753 -2 .464 2 .794 3 .277 -0.508 22 -1.956 -2 .743 2 .972 3 .505 -0.635 23 -2.667 -3 . 581 3 .454 4 .242 -0.787 24 -4.191 -5 . 359 4 .394 5 . 639 -1.016 25 -5.182 -6 .528 5 .791 7 .214 -1.194 26 -7.087 -8 .407 6 .299 8 .230 -1.499 27 -10.541 -10 .795 5 .994 9 . 042 -1.930 28 -12.344 -10 .795 5 .588 9 . 601 -2.464 29 -12.395 -10 .846 4 .724 10 .592 -3.353 30 -12.573 -11 . 151 2 .438 11 .430 -4.978 31 -12.827 -11 .506 -3 .124 13 . 106 -12.319 56 Table 3.1.2 T e s t R e s u l t s , Specimen # 3 NO. MTS#1 MTS#2 CONN.PL. CONN.PL. kN kN kN % 1 0. 000 0.000 0.000 0.00 2 3.781 20.640 16.859 81.68 3 7.962 44.705 36.742 82.19 4 11.076 62.320 51.243 82.23 5 15.791 88.609 72.817 82.18 6 20.150 111.917 91.767 82 . 00 7 23.620 130.956 107.336 81.96 8 19.706 110.271 90.566 82.13 9 15.791 89.231 73.440 82.30 10 10.987 63.298 52.311 82.64 11 7.206 43.014 35.808 83.25 12 3.425 20.818 17.393 83 . 55 13 7.651 45.016 37.365 83 . 00 14 11.210 64.944 53.734 82.74 15 15.035 86.029 70.994 82.52 16 18.816 106.935 88.119 82 .40 17 23.753 133.802 110.049 82.25 18 18.727 105.957 87.230 82 . 33 19 14.902 84.917 70.015 82.45 20 11.387 65.700 54.313 82 . 67 21 7.562 44.215 36.653 82.90 22 3.114 18.638 15.524 83.29 23 7.651 44.883 37.232 82.95 24 11.032 63.699 52.667 82 . 68 25 14.501 83.048 68.547 82.54 26 19.706 111.695 91.989 82 . 36 27 23.398 131.934 108.537 82.27 28 27.268 151.907 124.639 82 . 05 29 31.894 176.772 144.879 81.96 30 35.942 200.481 164.540 82.07 31 39.856 222.856 183.000 82 .12 32 43.726 245.141 201.415 82.16 33 47.018 264.847 217.829 82.25 57 Table 3.1.2 (cont.) T e s t R e s u l t s , Specimen # 3 NO. SG#5 SG#6 SG#7 SG#8 m/m m/m m/m m/m +VE=COMPRESSIVE STRAIN -VE=TENSILE STRAIN 1 0. 000000 0. 000000 0. 000000 0. 000000 2 0. 000049 0. 000030 -0. 000018 -0. 000057 3 0. 000095 0. 000052 0. 000004 -0. 000108 4 0. 000126 0. 000068 0. 000585 -0. 000145 5 0. 000173 0. 000089 0. 001118 -0. 000201 6 0. 000210 0. 000087 0. 001193 -0. 000254 7 0. 000260 0. 000091 0. 001615 -0. 000361 8 0. 000227 0. 000068 0. 001556 -0. 000324 9 0. 000194 0. 000044 0. 001534 -0. 000281 10 0. 000149 0. 000023 0. 001517 -0. 000232 11 0. 000112 0. 000005 0. 001506 -0. 000191 12 0. 000074 -0. 000001 0. 001473 -0. 000143 13 0. 000121 0. 000023 0. 001436 -0. 000197 14 0. 000160 0. 000045 0. 001436 -0. 000236 15 0. 000199 0. 000066 0. 001436 -0. 000280 16 0. 000238 0. 000089 0. 001825 -0. 000324 17 0. 000285 0. 000110 0. 002553 -0. 000387 18 0. 000236 0. 000080 0. 002468 -0. 000329 19 0. 000197 0. 000057 0. 002428 -0. 000286 20 0. 000160 0. 000034 0. 002410 -0. 000245 21 0. 000119 0. 000011 0. 002383 -0. 000202 22 0. 000072 -0. 000004 0. 002251 -0. 000149 23 0. 000122 0. 000021 0. 002182 -0. 000205 24 0. 000157 0. 000041 0. 002159 -0. 000241 25 0. 000194 0. 000063 0. 002155 -0. 000281 26 0. 000247 0. 000093 0. 002171 -0. 000340 27 0. 000284 0. 000110 0. 002514 -0. 000389 28 0. 000315 0. 000107 0. 003979 -0. 000506 29 0. 000365 0. 000089 0. 004306 -0. 000781 30 0. 000469 0. 000040 0. 011173 -0. 001217 31 0. 000607 -0. 000019 0. 013250 -0. 001790 32 0. 000579 -0. 000083 0. 013673 -0. 002440 33 0. 000527 -0. 000160 -0. 039884 -0. 003049 58 Table 3.1.2 (cont.) T e s t R e s u l t s , Specimen # 3 NO. LVDT#1 LVDT#2 LVDT#3 LVDT#4 LVDT#5 mm mm mm mm mm +VE=SHORTENING -VE=EXTENDING 1 0.000 2 0.076 3 0.229 4 0.279 5 0.076 6 -0.838 7 -1.880 8 -1.676 9 -1.499 10 -1.321 11 -1.194 12 -1.092 13 -0.940 14 -0.914 15 -1.041 16 -1.245 17 -1.778 18 -1.600 19 -1.448 20 -1.346 21 -1.295 22 -1.194 23 -1.016 24 -1.016 25 -1.118 26 -1.372 27 -1.651 28 -2.870 29 -5.639 30 -9.576 31 -14.122 32 -19.787 33 -25.425 0.000 0.000 0.000 0.229 0.127 0.559 0.127 0.762 -0.102 1.016 -1.118 1.803 -2.108 2.210 -1.905 2.286 -1.753 2.311 -1.575 2.261 -1.397 2.159 -1.194 1.499 -1.092 1.803 -1.118 1.930 -1.270 2.007 -1.473 2.108 -2.007 2.235 -1.829 2.261 -1.676 2.261 -1.575 2.210 -1.499 2.083 -1.295 1.549 -1.194 1.880 -1.219 2.007 -1.346 2.057 -1.600 2.134 -1.880 2.184 -2.972 2.311 -5.410 2.159 -8.661 2.134 -12.268 1.905 -16.789 1.549 -20.091 0.584 0.000 0.000 0.203 -0.127 0.483 -0.330 0.660 -0.483 0.965 -0.686 2.032 -0.889 2.743 -1.143 2.743 -0.991 2.743 -0.813 2.692 -0.635 2.540 -0.457 1.854 -0.279 2.083 -0.457 2.184 -0.635 2.286 -0.813 2.413 -0.965 2.667 -1.194 2.667 -0.991 2.642 -0.813 2.616 -0.660 2.489 -0.483 1.930 -0.279 2.184 -0.483 2.286 -0.610 2.337 -0.787 2.464 -0.991 2.565 -1.168 3.073 -1.422 3.683 -1.854 4.750 -2.565 5.842 -3.581 7.188 -5.182 8.204 -7.290 59 Table 3.1.3 Te s t R e s u l t s , Specimen # 5 NO. MTS#1 MTS#2 CONN.PL. CONN.PL. kN kN kN % 1 0. 000 0.000 0. 000 0. 00 2 3.323 22 .775 19.452 85.41 3 6.641 45.345 38.704 85.35 4 9.857 67.115 57.257 85. 31 5 13.411 90.481 77.070 85.18 6 16.316 109.373 93.057 85. 08 7 19.679 134.256 114.577 85.34 8 16.436 111.628 95.192 85.28 9 13.500 90.277 76.776 85. 05 10 10.315 67.204 56.888 84.65 11 6. 628 39.500 32.872 83.22 12 4.386 21.854 17.468 79.93 13 7.388 44.157 36.769 83.27 14 10.240 65.718 55.478 84.42 15 13.287 88.524 75.237 84.99 16 16.280 110.503 94.222 85.27 17 19.497 134.020 114.524 85.45 18 16.436 111.419 94.983 85.25 19 14.061 93.715 79.654 85. 00 20 10.338 66.906 56.568 84.55 21 7.460 45.047 37.587 83.44 22 4.390 21.854 17.464 79.91 23 7.486 43.744 36.257 82 .89 24 10.551 65.602 55.051 83.92 25 12.726 82.087 69.361 84.50 26 16.712 112.073 95.361 85. 09 27 19.959 136.600 116.641 85. 39 28 22.228 152.049 129.821 85. 38 29 25.399 175.567 150.167 85.53 30 28.709 198.969 170.260 85.57 31 32.494 225.925 193.431 85.62 32 35.052 244.701 209.649 85.68 33 38.028 265.995 227.967 85.70 34 41.404 290.491 249.087 85.75 35 44.487 314.218 269.731 85.84 60 Table 3.1.3 fcont.) T e s t R e s u l t s , Specimen # 5 NO. SG#5 SG#6 SG#7 SG#8 m/m m/m m/m m/m +VE=COMPRESSIVE STRAIN -VE=TENSILE STRAIN 1 0. 000000 0. 000000 0. 000000 0. 000000 2 0. 000027 0. 000009 -0. 000029 -0. 000047 3 0. 000050 0. 000011 -0. 000063 -0. 000096 4 0. 000074 0. 000008 -0. 000093 -0. 000141 5 0. 000111 0. 000021 -0. 000102 -0. 000190 6 0. 000138 0. 000019 -0. 000120 -0. 000260 7 0. 000149 0. 000011 -0. 000152 -0. 000376 8 0. 000119 -0. 000006 -0. 000136 -0. 000338 9 0. 000091 -0. 000016 -0. 000114 -0. 000298 10 0. 000061 -0. 000021 -0. 000088 -0. 000252 11 0. 000030 -0. 000027 -0. 000057 -0. 000200 12 0. 000015 -0. 000019 -0. 000039 -0. 000170 13 0. 000043 -0. 000008 -0. 000064 -0. 000214 14 0. 000071 0. 000000 -0. 000089 -0. 000257 15 0. 000098 0. 000007 -0. 000117 -0. 000304 16 0. 000125 0. 000013 -0. 000144 -0. 000345 17 0. 000152 0. 000007 -0. 000164 -0. 000391 18 0. 000121 -0. 000005 -0. 000139 -0. 000349 19 0. 000096 -0. 000014 -0. 000120 -0. 000314 20 0. 000061 -0. 000023 -0. 000093 -0. 000261 21 0. 000044 -0. 000019 -0. 000070 -0. 000222 22 0. 000015 -0. 000018 -0. 000044 -0. 000180 23 0. 000046 -0. 000002 -0. 000067 -0. 000224 24 0. 000074 0. 000007 -0. 000095 -0. 000269 25 0. 000093 0. 000008 -0. 000118 -0. 000302 26 0. 000129 0. 000014 -0. 000149 -0. 000359 27 0. 000157 0. 000009 -0. 000171 -0. 000404 28 0. 000187 -0. 000031 -0. 000270 -0. 000606 29 0. 000226 -0. 000033 -0. 000343 -0. 000740 30 0. 000222 -0. 000082 -0. 000467 -0. 001012 31 0. 000212 -0. 000146 -0. 000612 -0. 001249 32 0. 000170 -0. 000245 -0. 000771 -0. 001579 33 0. 000075 -0. 000383 -0. 000933 -0. 001847 34 -0. 000057 -0. 000534 -0. 001070 -0. 002050 35 -0. 000260 -0. 000723 -0. 001162 -0. 002249 61 Table 3.1.3 (cont.) T e s t R e s u l t s , Specimen # 5 NO. LVDT#1 LVDT#2 LVDT#3 LVDT#4 LVDT#5 LVDT#6 mm mm mm mm mm mm +VE=SHORTENING -VE=EXTENDING 1 0 .000 0. 000 0.000 0 . 000 0. 000 0. 000 2 0 . 000 -0. 036 0.152 0 . 175 -0.076 -0.124 3 -0 .003 -0. 099 0. 394 0 .429 -0.165 -0.251 4 -0 .081 -0. 267 0.813 0 .810 -0.259 -0.361 5 -0 .594 -0. 869 1.488 1 .816 -0.381 -0.467 6 -1 .483 -1. 552 2.045 2 .781 -0.505 -0.602 7 -3 .307 -1. 681 2.604 4 . 323 -0.673 -0.869 8 -3 .203 -1. 684 2.596 4 . 338 -0.579 -0.719 9 -3 .096 -1. 684 2.537 4 . 300 -0.500 -0.584 10 -2 .957 -1. 689 2.388 4 . 186 -0.401 -0.427 11 -2 .832 -1. 689 2.108 3 .983 -0.315 -0.264 12 -2 .692 -1. 689 1.742 3 . 698 -0.241 -0.157 13 -2 .761 -1. 689 1.821 3 . 746 -0.292 -0.284 14 -2 .837 -1. 689 1.928 3 .828 -0.376 -0.414 15 -2 .941 -1. 689 2.121 3 .970 -0.485 -0.566 16 -3 .076 -1. 689 2.299 4 . 107 -0.584 -0.709 17 -3 .429 -1. 689 2 .741 4 .493 -0.701 -0.876 18 -3 .330 -1. 689 2.667 4 .455 -0.589 -0.724 19 -3 .256 -1. 689 2.611 4 .417 -0.523 -0.612 20 -3 . 114 -1. 689 2.461 4 .308 -0.419 -0.437 21 -2 .941 -1. 689 2 .108 4 .044 -0.292 -0.284 22 -2 .827 -1. 692 1.773 3 .795 -0.244 -0.157 23 -2 .888 -1. 689 1.791 3 .792 -0.282 -0.279 24 -2 .967 -1. 689 1.908 3 .879 -0.376 -0.417 25 -3 .066 -1. 692 2.060 3 .998 -0.470 -0.531 26 -3 .218 -1. 692 2.327 4 . 199 -0.592 -0.721 27 -3 .449 -1. 692 2.733 4 .491 -0.699 -0.876 28 -3 .595 -1. 692 3.627 5 . 682 -0.953 -1.120 29 -4 .672 -1. 692 3.546 5 .718 -1.118 -1.354 30 -7 .275 3 .114 6 . 238 -1.387 -1.816 31 -10 .742 2.492 6 .886 -1.760 -2.553 32 -14 .834 1.910 7 .899 -2.289 -3.965 33 -19 .363 0.737 8 .936 -3.089 -3.978 34 -19 .470 -0.787 9 .804 -4.196 -3.985 35 -19 .528 -1.275 10 .978 -6.096 -3.990 62 SPECIMEN # 1 FORCE/DISPLACEMENT 0 2 4 6 8 10 12 Displacement Imm] Figure 3.1.1 Specimen # 1 - Force vs. Displacement 63 SPECIMEN # 3 FORCE/DISPLACEMENT 0 4 8 12 16 20 24 Displacement [mm] Figure 3.1.2 Specimen # 3 - Force vs. Displacement 64 SPECIMEN tt 5 FORCE/DISPLACEMENT 280 -| 0 2 4 6 8 10 12 14 Displacement Imml Figure 3.1.3 Specimen # 5 - Force vs. Displacement 65 SPECIMEN tt 1 FORCE/STRAIN 0 0.002 0.004 0.006 Strain [m/m] Figure 3.1.4 Specimen # 1 - Force vs. Strain 66 SPECIMEN # 3 FORCE/STRAIN 0.0032 Strain [m/m] Figure 3.1.5 Specimen # 3 - Force vs. Strain 67 SPECIMEN # 5 FORCE/STRAIN 0 0.0004 0.0008 0.0012 0.0016 0.002 0.0024 Strain [m/m] Figure 3.1.6 Specimen # 5 - Force vs. Strain 68 W410 x 39 P-104.0 kN 4 . 2 — J P: 246.0 kN 111 z u 3 0 UJ o_ Straight w«b Local budding of '. compraaalon flcng* Torilonol *««tct 11.3 P= 108.0 kN Z UJ 3 u UJ a. cn P ; 217.0 kN 8.2' Straight Local buckling of compression flonga Torsional "tfftci 20.1 P: 118.0 kN z u 2 O UJ a. in P : 270.0 kN 11.0 — | Locat buckling of compratston flonga Torsional "affed ELASTIC DEFORMATION PLASTIC DEFORMATION Figure 3.1.7 Deformation Stages - Slotted holes 69 Figure 3.1.8 Test # 5 - Top View of F a i l e d Specimen 70 Figure 3.1.9 Test # 5 - Side View of F a i l e d Specimen 71 Figure 3.1.10 Test # 5 - Side View of F a i l e d Specimen 72 F i g u r e 3.1.11 T e s t # 5 - Rear View of F a i l e d T e s t Specimen 73 Figure 3.1.12 Test # 5 - Front View of F a i l e d Specimen 74 Figure 3.1.13 Test # 5 - Side View of F a i l e d Specimen 75 Figure 3.1.14 Test # 5 - Rear View of F a i l e d Specimen 76 3.2 TEST RESULTS. STANDARD HOLES Single plate connections with standard holes were investigated i n te s t s ## 2, 4, and 6. The skew angles of the tes t s were equal to 0, 30, and 45 degrees. The experimental setup was i d e n t i c a l to that for the s l o t t e d holes t e s t s . F a i l u r e c r i t e r i o n was also i d e n t i c a l to that defined for previous t e s t s . The maximum loads recorded for these three t e s t s were equal to 336 kN, 378 kN, and 382 kN. Similar to s l o t t e d holes connections, the standard holes connections also f a i l e d i n twisting, web buckling, and flange buckling. In Tables from 3.2.1 to 3.2.3 there are l i s t e d recorded data of forces, displacements, and stra i n s for the three t e s t s with standard holes. Typical curves of force vs. displacement (at location of LVDT # 1) and force vs. s t r a i n (at loc a t i o n of SG # 8) are displayed i n Figures from 3.2.1 to 3.2.6. Drawings of e l a s t i c and p l a s t i c deformation stages for a l l three t e s t s are given i n Figure 3.2.7. Photographs of experimental f a i l u r e s for specimen # 6 are shown i n Figures from 3.2.8 to 3.2.15. Failures of other specimens tested i n t h i s series were s i m i l a r to the above example. 77 Table 3.2.1 T e s t R e s u l t s , Specimen # 2 NO. MTS#1 MTS#2 CONN.PL. CONN.PL. kN kN kN % 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 0. 4, 000 315 8.541 12.677 17.126 20.907 16.770 11.921 7.651 3.247 7.740 11.877 16.192 20.462 16.280 12.188 7.473 3.114 7.340 11.565 16.592 20.373 24.955 29.269 33.984 38.566 43.504 47.863 52.711 56.848 62.275 66.747 71.709 76.493 81.421 0, 22, 44, 66, 89, 110, 89, 66, 44, 22, 46, 67, 89, 111. 89, 67, 43. 22, 44, 65. 91. 110, 134, 155. 178, 200. 224, 244. 266, 286. 311, 333. 357, 378. 401. 000 641 705 367 632 939 943 056 616 908 128 213 454 117 365 657 948 241 171 700 678 716 025 821 463 392 146 830 760 777 687 750 237 232 007 0. 18. 36, 53. 72, 90, 73, 54, 36, 19, 38, 55, 73, 90. 73. 55. 36. 19, 36, 54, 75, 90, 109. 126. 144. 161. 180. 196, 214, 229, 249. 267. 285. 301. 319. 000 327 164 690 506 032 173 135 965 661 388 336 262 655 084 469 475 127 831 135 086 343 070 552 478 826 642 967 048 928 412 003 527 739 586 0. 00 80.94 80. 90 80.90 80.89 81.15 81.36 81.95 82.85 85.83 83.22 82 .33 81.90 81.59 81. 78 81. 99 83 . 00 86.00 83.38 82.40 81.90 81. 60 81.38 81.22 80.96 80.75 80.59 80.45 80.24 80.18 80.02 80.00 79.93 79.78 79.70 78 Table 3.2.1 (cont.) T e s t R e s u l t s , Specimen # 2 NO. SG#1 SG#2 SG#3 SG#4 m/m m/m m/m m/m +VE=COMPRESSIVE STRAIN -VE=TENSILE STRAIN 1 0. 000000 0. 000000 0. 000000 0. 000000 2 0. 000031 0. 000006 0. 000021 0. 000031 3 0. 000061 0. 000012 0. 000041 0. 000063 4 0. 000087 0. 000021 0. 000053 0. 000101 5 0. 000122 0. 000027 0. 000076 0. 000142 6 0. 000160 0. 000024 0. 000106 0. 000174 7 0. 000145 0. 000024 0. 000085 0. 000145 8 0. 000116 0. 000012 0. 000065 0. 000107 9 0. 000090 0. 000000 0. 000047 0. 000089 10 0. 000061 -0. 000008 0. 000041 0. 000043 11 0. 000096 0. 000000 0. 000056 0. 000098 12 0. 000110 0. 000012 0. 000065 0. 000113 13 0. 000137 0. 000021 0. 000079 0. 000148 14 0. 000160 0. 000024 0. 000103 0. 000186 15 0. 000145 0. 000018 0. 000079 0. 000148 16 0. 000113 0. 000012 0. 000065 0. 000119 17 0. 000090 -0. 000000 0. 000047 0. 000089 18 0. 000061 -0. 000005 0. 000041 0. 000043 19 0. 000090 -0. 000000 0. 000047 0. 000089 20 0. 000116 0. 000012 0. 000082 0. 000107 21 0. 000145 0. 000024 0. 000079 0. 000154 22 0. 000163 0. 000024 0. 000103 0. 000183 23 0. 000195 0. 000038 0. 000126 0. 000218 24 0. 000224 0. 000044 0. 000138 0. 000262 25 0. 000271 0. 000056 0. 000135 0. 000329 26 0. 000309 0. 000076 0. 000153 0. 000373 27 0. 000353 0. 000097 0. 000173 0. 000437 28 0. 000391 0. 000109 0. 000191 0. 000528 29 0. 000470 0. 000123 0. 000223 0. 000616 30 0. 000502 0. 000132 0. 000261 0. 000680 31 0. 000540 0. 000141 0. 000310 0. 000838 32 0. 000570 0. 000144 0. 000387 0. 001025 33 0. 000587 0. 000147 0. 000433 0. 001154 34 0. 000625 0. 000144 0. 000556 0. 001601 35 0. 000666 0. 000141 0. 000664 0. 002359 79 Tabl e 3.2.1 (cont.) T e s t R e s u l t s , Specimen # 2 NO. SG#5 SG#6 SG#7 SG#8 m/m m/m m/m m/m +VE=COMPRESSIVE STRAIN -VE=TENSILE STRAIN 1 0. 000000 0. 000000 0. 000000 0. 000000 2 0. 000000 0. 000006 0. 000041 0. 000039 3 0. 000000 0. 000015 0. 000088 0. 000080 4 0. 000062 0. 000015 0. 000117 0. 000124 5 0. 000088 0. 000009 0. 000153 0. 000170 6 0. 000088 0. 000015 0. 000185 0. 000214 7 0. 000088 0. 000006 0. 000176 0. 000176 8 0. 000068 0. 000006 0. 000129 0. 000132 9 0. 000056 -0. 000006 0. 000106 0. 000100 10 0. 000024 -0. 000000 0. 000074 0. 000056 11 0. 000056 -0. 000006 0. 000103 0. 000100 12 0. 000068 -0. 000000 0. 000129 0. 000132 13 0. 000088 0. 000006 0. 000176 0. 000176 14 0. 000088 0. 000009 0. 000191 0. 000214 15 0. 000088 0. 000000 0. 000161 0. 000176 16 0. 000088 -0. 000006 0. 000135 0. 000138 17 0. 000062 -0. 000006 0. 000097 0. 000094 18 0. 000044 -0. 000000 0. 000074 0. 000051 19 0. 000068 -0. 000006 0. 000097 0. 000094 20 0. 000082 0. 000006 0. 000129 0. 000132 21 0. 000088 0. 000006 0. 000176 0. 000176 22 0. 000088 0. 000009 0. 000185 0. 000214 23 0. 000088 0. 000026 0. 000223 0. 000270 24 0. 000214 0. 000038 0. 000243 0. 000320 25 0. 000258 0. 000044 0. 000272 0. 000390 26 0. 000275 0. 000062 0. 000308 0. 000445 27 0. 000328 0. 000067 0. 000334 0. 000524 28 0. 000351 0. 000079 0. 000372 0. 000586 29 0. 000395 0. 000091 0. 000427 0. 000679 30 0. 000421 0. 000105 0. 000477 0. 000782 31 0. 000471 0. 000094 0. 000571 0. 000925 32 0. 000480 0. 000067 0. 000697 0. 001095 33 0. 000483 0. 000056 0. 000787 0. 001200 34 0. 000483 -0. 000017 0. 001042 0. 001422 35 0. 000439 -0. 000172 0. 001393 0. 001671 80 Table 3.2.1 (cont.) T e s t R e s u l t s , Specimen # 2 NO. LVDT#1 LVDT#2 LVDT#3 LVDT#4 LVDT#5 mm mm mm mm mm +VE=SHORTENING -VE=EXTENDING 1 0. 000 2 0.102 3 0.330 4 0.356 5 0.381 6 0.635 7 0.635 8 0.559 9 0.483 10 0.330 11 0.483 12 0.584 13 0.635 14 0. 660 15 0.660 16 0. 610 17 0.508 18 0.381 19 0.508 20 0.610 21 0.660 22 0.686 23 0.584 24 0.356 25 0.864 26 0.787 27 0.508 28 0.279 29 -0.254 30 -0.533 31 -1.245 32 -2.413 33 -3.353 34 -5.817 35 -9.144 0.000 0.000 -0.254 0.584 -0.025 1.118 -0.102 1.600 -0.178 2.032 0.051 2.667 0.076 2.642 0.025 2.515 -0.051 2.362 -0.229 2.108 -0.025 2.337 0.051 2.515 0.102 2.642 0.076 2.769 0.102 2.718 0.076 2.591 -0.000 2.413 -0.178 2.184 -0.000 2.388 0.076 2.540 0.127 2.718 0.102 2.794 -0.102 2.921 -0.483 2.997 0.000 -43.840 -0.178 -43.840 -0.686 -43.815 -1.041 -43.815 -1.753 -43.815 -2.083 -43.815 -2.896 -43.815 -4.166 -43.815 -5.131 -43.815 -7.671 -43.815 -10.897 -43.815 0.000 0.000 0.254 -0.178 0.508 -0.330 0.737 -0.483 0.838 -0.660 1.118 -0.813 1.168 -0.686 1.194 -0.533 1.194 -0.381 1.194 -0.229 1.194 -0.356 1.194 -0.508 1.194 -0.660 1.194 -0.813 1.194 -0.686 1.194 -0.533 1.194 -0.381 1.194 -0.229 1.194 -0.330 1.194 -0.508 1.194 -0.686 1.194 -0.813 1.219 -0.965 1.219 -1.143 -15.392 -1.295 -15.392 -1.448 -15.392 -1.651 -15.392 -1.829 -15.392 -2.083 -15.392 -2.261 -15.392 -2.515 -15.367 -2.769 -15.392 -2.997 -15.392 -3.404 -15.367 -4.013 81 Table 3.2.2 Te s t R e s u l t s , Specimen # 4 NO. MTS#1 MTS#2 CONN.PL. CONN.PL. kN kN kN % 1 0.000 0.000 0.000 0. 00 2 3.003 20.760 17.757 85.54 3 6.223 43.299 37.076 85.63 4 9.252 64.148 54.895 85.58 5 13.007 89.770 76.763 85.51 6 15.533 107.567 92.034 85.56 7 19.755 135.711 115.956 85.44 8 16.098 111.094 94.996 85.51 9 11.472 81.558 70.086 85.93 10 8.999 63.703 54.704 85.87 11 6.219 44.931 38.713 86.16 12 3.149 22.984 19.835 86. 30 13 6.316 45.937 39.620 86. 25 14 9.332 66.817 57.484 86. 03 15 12.540 88.555 76.016 85.84 16 15.533 108.901 93.368 85.74 17 19.114 133.069 113.954 85.64 18 15.533 108.634 93.101 85.70 19 12.139 85.028 72.889 85.72 20 9.457 66.697 57.240 85.82 21 6.023 42.409 36.386 85.80 22 2.954 21.085 18.131 85.99 23 6.130 44.665 38.535 86.28 24 9.368 67.141 57.773 86.05 25 12.468 88.377 75.909 85.89 26 15.484 108.692 93.208 85.75 27 18.838 131.174 112.335 85.64 28 22.250 153.624 131.374 85.52 29 25.849 178.089 152.240 85.49 30 29.069 200.183 171.114 85.48 31 32.730 224.769 192.039 85.44 32 35.608 243.749 208.141 85.39 33 38.775 264.629 225.854 85.35 34 42.485 288.534 246.049 85.28 35 46.368 314.689 268.321 85.27 36 49.491 335.093 285.602 85.23 37 52.413 353.869 301.456 85.19 38 56.056 377.947 321.891 85.17 39 59.246 398.592 339.346 85.14 40 62.796 421.429 358.633 85.10 41 66.314 444.680 378.366 85.09 82 Ta b l e 3.2.2 (cont.) T e s t R e s u l t s , Specimen # 4 NO. SG#5 SG#6 SG#7 SG#8 m/m m/m m/m m/m +VE=COMPRESSIVE STRAIN -VE=TENSILE STRAIN 1 0. 000000 0. 000000 0. 000000 0. 000000 2 0. 000011 0. 000000 -0. 000013 -0. 000026 3 0. 000028 -0. 000001 -0. 000038 -0. 000061 4 0. 000050 0. 000006 -0. 000067 -0. 000104 5 0. 000075 0. 000010 -0. 000099 -0. 000159 6 0. 000086 0. 000001 -0. 000119 -0. 000205 7 0. 000119 0. 000001 -0. 000140 -0. 000268 8 0. 000082 -0. 000019 -0. 000131 -0. 000230 9 0. 000046 -0. 000037 -0. 000121 -0. 000188 10 0. 000022 -0. 000050 -0. 000107 -0. 000156 11 -0. 000002 -0. 000061 -0. 000095 -0. 000125 12 -0. 000020 -0. 000064 -0. 000086 -0. 000094 13 -0. 000002 -0. 000063 -0. 000104 -0. 000131 14 0. 000017 -0. 000054 -0. 000125 -0. 000172 15 0. 000049 -0. 000039 -0. 000134 -0. 000203 16 0. 000075 -0. 000026 -0. 000143 -0. 000236 17 0. 000107 -0. 000010 -0. 000159 -0. 000281 18 0. 000073 -0. 000030 -0. 000148 -0. 000241 19 0. 000043 -0. 000045 -0. 000135 -0. 000203 20 0. 000018 -0. 000057 -0. 000125 -0. 000173 21 -0. 000009 -0. 000068 -0. 000103 -0. 000133 22 -0. 000028 -0. 000073 -0. 000089 -0. 000102 23 -0. 000010 -0. 000072 -0. 000110 -0. 000140 24 0. 000016 -0. 000061 -0. 000132 -0. 000176 25 0. 000044 -0. 000045 -0. 000141 -0. 000212 26 0. 000069 -0. 000034 -0. 000153 -0. 000247 27 0. 000100 -0. 000018 -0. 000166 -0. 000287 28 0. 000122 -0. 000023 -0. 000179 -0. 000338 29 0. 000158 -0. 000037 -0. 000204 -0. 000472 30 0. 000193 -0. 000044 -0. 000243 -0. 000591 31 0. 000217 -0. 000049 -0. 000292 -0. 000702 32 0. 000232 -0. 000063 -0. 000347 -0. 000807 33 0. 000239 -0. 000089 -0. 000431 -0. 000947 34 0. 000242 -0. 000116 -0. 000532 -0. 001101 35 0. 000248 -0. 000141 -0. 000637 -0. 001261 36 0. 000240 -0. 000181 -0. 000745 -0. 001370 37 0. 000205 -0. 000255 -0. 000893 -0. 001525 38 0. 000199 -0. 000294 -0. 000989 -0. 001650 39 0. 000156 -0. 000380 -0. 001129 -0. 001951 40 0. 000082 -0. 000519 -0. 001343 -0. 002295 41 -0. 000035 -0. 000716 -0. 001595 -0. 003020 83 Table 3.2.2 (cont.) T e s t R e s u l t s , Specimen # 4 NO. LVDT#1 LVDT#2 LVDT#3 LVDT#4 LVDT#5 mm mm mm mm mm +VE=SHORTENING -VE=EXTENDING 1 0. 000 2 0.213 3 0.544 4 0.841 5 1. 049 6 0.874 7 0.564 8 0.541 9 0.511 10 0.363 11 0.175 12 -0.185 13 0.244 14 0.467 15 0.574 16 0.620 17 0. 635 18 0.594 19 0.500 20 0.386 21 0.114 22 -0.224 23 0.178 24 0.478 25 0.569 26 0.615 27 0.632 28 0.178 29 -1.173 30 -2.177 31 -2.898 32 -3.741 33 -4.813 34 -5.903 35 -7.048 36 -8.176 37 -10.145 38 -11.410 39 -13.848 40 -17.521 41 -24.102 0.000 0.000 0.157 0.249 0.419 0.630 0.655 0.996 0.813 1.392 0.564 1.951 0.132 2.576 0.122 2.461 0.112 2.332 -0.005 2.098 -0.163 1.849 -0.480 1.443 -0.104 1.908 0.079 2.202 0.152 2.380 0.183 2.510 0.180 2.634 0.157 2.504 0.091 2.327 0.005 2.141 -0.208 1.786 -0.503 1.400 -0.165 1.852 0.084 2.217 0.142 2.393 0.173 2.512 0.175 2.609 -0.333 3.150 -1.740 4.293 -2.692 4.821 -3.376 4.851 -4.176 4.841 -5.136 4.740 -6.104 4.475 -7.117 4.176 -8.120 3.764 -9.858 3.231 -10.996 2.837 -13.094 2.146 -16.363 1.115 -22.184 -0.693 0.000 0.000 0.188 -0.071 0.480 -0.165 0.759 -0.241 1.082 -0.343 1.714 -0.406 2.446 -0.500 2.367 -0.422 2.276 -0.335 2.106 -0.262 1.908 -0.185 1.628 -0.104 1.966 -0.191 2.172 -0.272 2.299 -0.343 2.388 -0.419 2.479 -0.503 2.393 -0.419 2.263 -0.340 2.129 -0.274 1.862 -0.188 1.587 -0.107 1.923 -0.188 2.184 -0.277 2.316 -0.353 2.395 -0.422 2.466 -0.490 3.137 -0.571 4.651 -0.686 5.398 -0.805 5.593 -0.922 5.786 -1.054 5.969 -1.219 5.979 -1.412 6.012 -1.603 5.961 -1.829 6.093 -2.141 6.185 -2.398 6.469 -2.835 7.069 -3.559 8.382 -5.116 84 Table 3.2.3 Test R e s u l t s , Specimen # 6 NO. MTS#1 MTS#2 CONN.PL. CONN.PL. kN kN kN % 1 0. 000 0.000 0.000 0.00 2 3.407 22.837 19.430 85. 08 3 5.698 38.406 32.708 85.16 4 9.742 66.968 57.226 85.45 5 13.100 90.931 77.831 85.59 6 15.386 107.300 91.914 85.66 7 19.158 135.622 116.463 85.87 8 15.809 111.717 95.908 85.85 9 12.304 86.865 74.561 85.84 10 9.235 66.047 56.813 86.02 11 6.881 50.149 43.268 86.28 12 2.455 19.305 16.850 87.28 13 7.268 53.058 45.790 86.30 14 8.825 63.378 54.553 86.08 15 12.308 87.577 75.268 85.95 16 16.472 116.521 100.049 85.86 17 18.758 132.330 113.572 85.82 18 14.799 105.045 90.245 85. 91 19 12.566 89.863 77.297 86.02 20 8.692 64.682 55.990 86.56 21 5.987 45.612 39.625 86.87 22 2.260 19.928 17.668 88.66 23 5.631 43.419 37.788 87.03 24 8.558 63.583 55.024 86.54 25 12.121 88.377 76.256 z>\\ 86.28 26 15.733 113.763 98.030 86.17 27 18.892 134.910 116.018 86.00 28 21.690 154.691 133.002 85.98 29 24.861 178.743 153.882 86.09 30 27.677 200.690 173.014 86.21 31 30.466 221.508 191.042 86.25 32 33.553 243.487 209.934 86.22 33 37.774 272.787 235.013 86.15 34 40.301 290.642 250.341 86.13 35 43.192 310.779 267.587 86.10 36 46.097 331.005 284.908 86. 07 37 50.029 358.584 308.555 86. 05 38 52.787 377.801 325.014 86. 03 39 56.301 402.359 346.058 86.01 40 59.281 422.794 363.513 85.98 85 Table 3.2.3 (cont.) T e s t R e s u l t s , Specimen # 6 NO. SG#5 SG#6 SG#7 SG#8 m/m m/m m/m m/m +VE=COMPRESSIVE STRAIN -VE=TENSILE STRAIN 1 0. 000000 0. 000000 0. 000000 0. 000000 2 0. 000038 0. 000021 -0. 000035 -0. 000057 3 0. 000055 0. 000025 -0. 000055 -0. 000092 4 0. 000081 0. 000034 -0. 000081 -0. 000150 5 0. 000103 0. 000038 -0. 000107 -0. 000201 6 0. 000108 0. 000025 -0. 000130 -0. 000251 7 0. 000118 0. 000003 -0. 000174 -0. 000341 8 0. 000082 -0. 000020 -0. 000159 -0. 000306 9 0. 000046 -0. 000039 -0. 000142 -0. 000267 10 0. 000013 -0. 000057 -0. 000134 -0. 000236 11 -0. 000010 -0. 000072 -0. 000127 -0. 000214 12 -0. 000054 -0. 000096 -0. 000107 -0. 000165 13 -0. 000011 -0. 000074 -0. 000139 -0. 000230 14 -0. 000000 -0. 000068 -0. 000151 -0. 000249 15 0. 000030 -0. 000054 -0. 000172 -0. 000295 16 0. 000064 -0. 000037 -0. 000200 -0. 000350 17 0. 000081 -0. 000029 -0. 000218 -0. 000385 18 0. 000019 -0. 000096 -0. 000210 -0. 000369 19 0. 000002 -0. 000103 -0. 000203 -0. 000346 20 -0. 000029 -0. 000117 -0. 000190 -0. 000311 21 -0. 000057 -0. 000132 -0. 000177 -0. 000280 22 -0. 000090 -0. 000148 -0. 000161 -0. 000236 23 -0. 000058 -0. 000132 -0. 000183 -0. 000283 24 -0. 000033 -0. 000120 -0. 000201 -0. 000321 25 -0. 000001 -0. 000103 -0. 000222 -0. 000365 26 0. 000031 -0. 000085 -0. 000245 -0. 000411 27 0. 000041 -0. 000088 -0. 000276 -0. 000466 28 0. 000081 -0. 000058 -0. 000281 -0. 000492 29 0. 000089 -0. 000099 -0. 000320 -0. 000582 30 0. 000115 -0. 000157 -0. 000410 -0. 000765 31 0. 000139 -0. 000201 -0. 000509 -0. 000972 32 0. 000143 -0. 000229 -0. 000593 -0. 001152 33 0. 000125 -0. 000302 -0. 000774 -0. 001540 34 0. 000128 -0. 000313 -0. 000833 -0. 001696 35 0. 000107 -0. 000372 -0. 000973 -0. 001952 36 0. 000081 -0. 000424 -0. 001111 -0. 002170 37 0. 000037 -0. 000513 -0. 001306 -0. 002460 38 -0. 000036 -0. 000629 -0. 001508 -0. 002862 39 -0. 000130 -0. 000768 -0. 001691 -0. 003360 40 -0. 000232 -0. 000889 -0. 001848 -0. 004172 86 Table 3.2.3 (cont.) T e s t R e s u l t s , Specimen # 6 NO. LVDT#1 mm +VE=SHORTENING -VE=EXTENDING LVDT#2 mm LVDT#3 mm LVDT#4 mm LVDT#5 mm LVDT#6 mm 1 0. 000 0.000 0. 000 0.000 0. 000 0.000 2 -0.074 -0.066 0.114 0.152 -0.058 -0.084 3 0.246 -0.109 0.218 0.292 -0.117 -0.147 4 0.234 -0.147 0.503 0.594 -0.201 -0.246 5 0.221 -0.203 0.787 0.902 -0.279 0. 005 6 0.124 -0.353 1.156 1. 349 -0.351 -0.064 7 -0.297 -0.828 1.847 2.189 -0.437 -0.175 8 -0.323 -0.815 1.717 2.060 -0.373 -0.081 9 -0.330 -0.800 1.567 1.913 -0.300 0. 015 10 -0.325 -0.772 1.455 1.781 -0.236 0.099 11 -0.312 -0.744 1.361 1.671 -0.178 0.170 12 -0.272 -0.691 1.212 1.488 -0.104 0. 282 13 -0.300 -0.732 1.374 1.666 -0.191 0.150 14 -0.325 -0.762 1.412 1.717 -0.226 0.112 15 -0.305 -0.777 1.567 1.877 -0.307 0.018 16 -0.353 -0.841 1.712 2.050 -0.394 -0.097 17 -0.394 -0.894 1.783 2.141 -0.460 -0.175 18 -0.960 -1.463 2.197 2.738 -0.401 -0.046 19 -0.914 -1.405 2.141 2.654 -0.345 0. 020 20 -0.795 -1.285 2.078 2.530 -0.272 0.119 21 -0.810 -1.275 1.969 2.416 -0.203 0.198 22 -0.726 -1.191 1.880 2.286 -0.132 0.305 23 -0.762 -1.234 1.969 2.393 -0.198 0.211 24 -0.798 -1.275 2.055 2.487 -0.259 0.130 25 -0.790 -1.300 2.197 2.642 -0.348 0. 028 26 -0.841 -1.367 2.289 2.738 -0.417 -0.074 27 -1.001 -1.527 2.304 2.835 -0.488 -0.175 28 -1.052 -1.590 2.362 2.911 -0.561 -0.262 29 -2.062 -2.746 3.020 3.886 -0.671 -0.373 30 -4.552 -5.573 4.031 5.613 -0.831 -0.541 31 -6.444 -7.595 4.364 6.485 -1.011 -0.754 32 -7.648 -8.839 4.127 6.662 -1.148 -0.955 33 -9.736 -10.899 3.518 6.800 -1.410 -1.354 34 -10.310 -11.433 3.246 6.767 -1.509 -1.537 35 -11.770 -12.852 2.680 6.795 -1.720 -1.930 36 -13.256 -14.188 2.101 6.820 -1.928 -2.332 37 -15.524 -16.388 1.189 6.972 -2.278 -3.040 38 -18.311 -19.055 0.163 7.308 -2.654 -3.990 39 -22.555 -23.604 -1.163 7.940 -3.353 -29.403 40 -28.872 -25.227 -1.166 8.694 -4.582 -37.663 87 SPECIMEN tt 2 FORCE/DISPLACEMENT Displacement [mm] F i g u r e 3.2.1 Specimen # 2 - Force vs. Displacement 88 SPECIMEN tt 4 FORCE/DISPLACEMEN 400 - r Displacement [mm] F i g u r e 3.2.2 Specimen # 4 - Force vs. Displacement 89 F i g u r e 3.2.3 Specimen # 6 - Force vs. Displacement 90 SPECIMEN # 2 FORCE/STRAIN 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 Strain [m/m] F i g u r e 3.2.4 Specimen # 2 - Force v s. S t r a i n 91 SPECIMEN # 4 FORCE/STRAIN 400 n 0 0.0004 0.0008 0.0012 0.0016 0.002 0.0024 0.0028 0.0032 Strain [m/m] Figure 3.2.5 Specimen # 4 - Force vs. Stra i n 92 SPECIMEN # 6 FORCE/STRAIN 400 - i Strain [m/m] F i g u r e 3.2.6 Specimen # 6 - Force v s . S t r a i n 93 P= 109.0 kN % Z Ul 2 o u o. W410 x 39 P: 319.8 kN P = 112.3 kN Z3 *-j 2 UJ O Ul to z Ul 3 o u a. tn ELASTIC DEFORMATION 19.0 Straight wsb Local buckling of ', comprsnton (long* Tonlonal "•ffsct 10.9 P = 378.4 kN Straight Local buckling of ™ comprsnton flangs Tonlonal •ffsct •22.2 P = 363.5 kN 8.7-Straight wsb Local buckling of comprM«[on flangs PLASTIC DCFORUAT10N Torilonol " inset j-»25.2 Figure 3.2.7 Deformation Stages - Standard Holes 94 Figure 3.2.8 Test # 6 - Top View of F a i l e d Specimen 95 Figure 3.2.9 Test # 6 - Front View of F a i l e d Specimen 96 Figure 3.2.10 Test # 6 - Front View of F a i l e d Specimen 97 Figure 3.2.11 Test # 6 - Front View of F a i l e d Specimen 98 Figure 3.2.12 Test # 6 - Rear View of F a i l e d Specimen 99 Figure 3.2.13 Test # 6 - Rear View of F a i l e d Specimen 100 Figure 3.2.14 Test # 6 - Rear View of F a i l e d Specimen 101 Figure 3.2.15 Test # 6 - Side View of F a i l e d Specimen 102 3.3 COUPON TESTS Tension t e s t s were conducted for each specimen to determine material properties of y i e l d strength F at 0.2% of f s e t , ultimate t e n s i l e strength F , and Young's modulus E . Three t e s t coupons were cut from the web of each of the t e s t specimens. The coupons were machined and tested according to ASTM Standards. The setup of Optilog , Opus, and IBM-PC was again used to acquire t e s t r e s u l t s . Figures 3.3.1 and 3.3.2 show photographs of the coupons and setup of the coupon t e s t . S t r a i n gauges were placed on both faces of the coupons to obtain force vs. s t r a i n curves. Also, LVDT's were used to v e r i f y the measured s t r a i n s . Material properties for each coupon were determined from the force vs. s t r a i n curves. Results from each specimen's three coupon tests were then averaged to provide average values of material properties for each specimen. The average material properties were then applied to determine the true resistances of the tested specimens. Table 3.3.1 l i s t s the average material properties for each specimen. 103 Tabl e 3.3.1 Coupon T e s t R e s u l t s F F E y u y [MPa] [MPa] [MPa] SPECIMEN # 1 345 523 202382 SPECIMEN # 2 356 547 197741 SPECIMEN # 3 344 514 188610 SPECIMEN # 4 340 519 190785 SPECIMEN # 5 342 522 187249 SPECIMEN # 6 343 522 194295 104 Figure 3.3.1 Coupons Figure 3.3.2 Coupon Test 106 Chapter 4 ANALYSIS OF TEST RESULTS 4.1 SHEAR FORCE RESULTS The ultimate f a i l u r e load for each t e s t (defined as the maximum load recorded) i s used for the analysis of the connection. The maximum shear force for each t e s t i s equal to one-half of the recorded ultimate f a i l u r e load. The average shear stress i s then determined from the maximum shear force. Now, analogous to the Canadian code for e l a s t i c analysis, t h i s i nvestigation applies the average shear stress to the analysis of the connection. However, the r a t i o of maximum shear force to ultimate shear resistance V /V ,. which i s equal to the max u l t r a t i o of average shear stress to ultimate shear stress T a v g / / T u l t "*'s included. The following equations are used to calculate the stresses and resistance: V =0.5*P (4.1.1) max max k ' T u l t=F y/SQRT(3) (4.1.2) V =T * t *D (A 1 3} U l t U l t W U (4.J..JJ T =V / ( t *D) (4.1.4) avg max7 v w ' K ' where: V = maximum shear force max Vu^^. = maximum shear resistance T = average shear stress avg T u ^ = ultimate shear stress 107 P = maximum load applied to the t e s t specimen max D = depth of the girder t = thickness of the girder web w F = y i e l d strength of the girder The V /V ,. r a t i o ranges from 0.24 to 0.38. This shows max u l t 3 that f a i l u r e of single plate connections must be governed by more than shear alone. Table 4.1.1 contains shear r e s u l t s . Table 4.1.1 Shear Results TEST 1 TEST 2 TEST 3 TEST 4 TEST 5 TEST 6 V max [kN] 123 168 119 189 135 191 V u l t [kN] 501 501 501 501 501 501 T u l t [MPa] 196 196 196 196 196 196 T avg [MPa] 48 66 47 74 52 75 V /V max' u l t 0. 25 0.34 0.24 0.38 0.27 0.38 108 4.2 TORSIONAL MOMENT RESULTS The t o r s i o n a l moment Mt, applied to the centerline of the supporting girder web, stems from the t o r s i o n a l component of the moment r e s u l t i n g from eccentric loading. The ultimate t o r s i o n a l moment resistance T g of the single plate connection i s calculated from summation of the contributions of the beam and of the plate. The following equations are used to calcul a t e the t o r s i o n a l moment and resistance: M t = P m a x * e b * C O S ( B E T A ) (4.2.1) T =R *F /SQRT(3)+R *300/SQRT(3) (4.2.2) R b=(2*b*t f 2+(D-2*t f)*t w 2)/3 (4.2.3) R p=a*d p*e t 2 (4.2.4) e t=(e b-t w/2)*cos(BETA) (4.2.5) where: M t = t o r s i o n a l moment P_ = maximum load applied to the t e s t specimen max T = ultimate t o r s i o n a l resistance s R. = t o r s i o n a l resistance constant of the tes t D girder R = t o r s i o n a l resistance constant of the connection P plate D = depth of the girder t = thickness of the girder web w e^ . = eccentric distance between the edge of the connection plate and the centreline of the bolts 109 a = t o r s i o n a l constant which depends on the dp to e^ . r a t i o dp = depth of the connection plate e. = eccentric distance between the centreline of b specimen and the centreline of the bolt s b = width of the girder t ^ = thickness of the girder flange BETA = skew angle The r a t i o of applied t o r s i o n a l moment to the ultimate t o r s i o n a l moment resistance M^/T varies between 0.4 and 0.79. This reinforces that f a i l u r e of the single plate connections i s not caused by t o r s i o n a l moment alone. The t o r s i o n a l r e s u l t s are given i n Table 4.2.1. Table 4.2.1 Torsional Results TEST 1 TEST 2 TEST 3 TEST 4 TEST 5 TEST 6 M t [kNm] 16.4 22.4 13.8 21.9 12.7 18.0 T g [kNm] 41.1 41.1 41.1 41.1 41.1 41.1 M./T 0.40 0.55 0.43 0.68 0.56 0.79 110 4.3 BENDING MOMENT RESULTS The bending moment M^ , applied at the mid-span of the te s t specimen, i s calculated from the maximum applied load and from the bending component of the moment due to load e c c e n t r i c i t y . The p l a s t i c bending moment resistance of the te s t specimen M i s provided by the girder only. Any bending P moment resistance of the connection plate i s considered to be i n s i g n i f i c a n t . The end plate connection i s usually assumed to perform as a shear connection. However, research conducted to date indicates that t h i s type of connection r e s i s t s some bending moment. The portion of applied bending moment taken up by the connection was found to depend on the f l e x i b i l i t y and strength of the end plate connection and the supporting girder. In our investigation, an assumption of 10% reduction i n maximum bending moment i s introduced. This 10% value i s determine from the following c a l c u l a t i o n : R = 0.5*Xu*Iw/(Fu*Ig)*100 = 9.4 % Fu = 450.0 Mpa Xu = 480.0 MPa Ig = 127000000.0 mmA4 Iw = (2*d+tw)*hA3/12 = 22299516.7 mmA4 d = 8.0 mm tw = 6 . 4 mm h = 228.6 mm I l l where: R = reduction i n maximum bending moment F u = assumed ultimate t e n s i l e strength of the girder X u = ultimate strength of the f i l l e t weld (as rated by the Electrode C l a s s i f i c a t i o n number) I = moment of i n e r t i a of the girder g I = moment of i n e r t i a of the weld group d = s i z e of the f i l l e t weld t = thickness of the girder web w h = depth of the end shear plate The 10% reduction i s then introduced into the bending moment equation as a modification factor of 0.9 times the th e o r e t i c a l maximum bending moment. The following equations are used to calculate bending moments and resistance: M, =0. 9*P *L/4 + 0. 5*P *e,*sin (BETA) (4.3.1) b max ' max b x ' x ' M p=Z x*F y (4.3.2) where: M. k = maximum bending moment applied to the girder Mp = p l a s t i c moment of resistance of the girder F = minimum y i e l d stress of the girder P = maximum load applied to the t e s t specimen max e^ = eccentric distance between the centreline of specimen and centreline of the bolt s BETA = skew angle 112 L = length of the t e s t specimen = 2092 mm Z x = p l a s t i c section modulus of the t e s t girder The r a t i o of the applied bending moment to the bending moment resistance M j j / M p ranges from 0.47 to 0.76. These values are much less than 1.0, thus i n d i c a t i n g that the f a i l u r e of the single plate connection i s not caused by the bending moment acting alone. The r e s u l t s are shown i n Table 4.3.1. Table 4.3.1 Bending Results TEST 1 TEST 2 TEST 3 TEST 4 TEST 5 TEST 6 Mb [kNm] 116 158 116 184 133 189 Mp [kNm] 248 248 248 248 248 248 M./M 0.47 0.64 0.47 0.74 0.54 0.76 113 4.4 RATIO RESULTS Various interactions among the r a t i o s of maximum shear force to ultimate shear resistance (V /V , . ) , applied v max' u l t ' ' ^ to r s i o n a l moment to ultimate t o r s i o n a l moment resistance (M t/T g), and applied bending moment to ultimate bending moment resistance (Mb/Mp) are investigated f o r each of the t e s t specimens. The "square root of the sum of the squares method" i s used to calcu l a t e i n t e r a c t i o n r a t i o s of shear, tor s i o n , and bending. The r a t i o s and inte r a c t i o n r a t i o s are given i n Table 4.4.1. The r a t i o s and inte r a c t i o n r a t i o s that are examined include: d l V m a x / V u l t (4.4.1) d 2=M t/T s (4.4.2) d3=Mb/Mr (4.4.3) n 1=SQRT(d 1 2+d 2 2) (4.4.4) n 2=SQRT(d 1 2+d 3 2) (4.4.5) n 3=SQRT(d 2 2+d 3 2) (4.4.6) n 4=SQRT(d 1 2+d 2 2+d 3 2) (4.4.7) where: V = maximum applied shear force max V u ^ t = ultimate shear force resistance of the t e s t specimen Mfc = applied t o r s i o n a l moment T g = ultimate t o r s i o n a l moment resistance of the te s t specimen 114 Mb = applied bending moment Mp = p l a s t i c bending moment resistance of the t e s t specimen d 1 = shear force r a t i o d 2 = to r s i o n a l moment r a t i o d_ = bending moment r a t i o = shear force r a t i o and t o r s i o n a l moment r a t i o i n t e r a c t i o n n 2 = shear force r a t i o and bending moment r a t i o i n t e r a c t i o n n 3 = t o r s i o n a l moment r a t i o and bending moment r a t i o i n t e r a c t i o n n. = "three r a t i o i n t e r a c t i o n " which combines shear 4 force r a t i o , t o r s i o n a l moment r a t i o , and bending moment r a t i o Table 4.4.1 Ratio and Ratio Interaction Results TEST 1 TEST 2 TEST 3 TEST 4 TEST 5 TEST 6 d l 0.25 0.34 0.24 0.38 0.27 0.38 d2 0.40 0.55 0.43 0.68 0.56 0.79 d3 0.47 0.64 0.47 0.74 0.54 0.76 n i 0.47 0.64 0.49 0.78 0.62 0.88 n2 0.53 0.72 0.52 0.83 0. 60 0.85 n3 0.61 0.84 0.64 1.01 0.77 1.10 n4 0.66 0.90 0. 68 1.08 0.82 1.16 115 Results from the Table 4.4.1 show that perpendicular connections give lower r a t i o s than skewed connections (eg. Test 1 vs. Test 5). Lower r a t i o s are also shown when s l o t t e d holes are used i n the experiments (eg. Test 1 vs. Test 2). Of the three i n d i v i d u a l r a t i o s d , d^, and d 3 and the four i n t e r a c t i o n r a t i o s n 1, n 2, n 3, and n 4, the three components in t e r a c t i o n r a t i o n 4 gives the highest r e s u l t s (nearly 100% fo r standard holes) and therefore provides the best p r e d i c t i o n of the ultimate f a i l u r e load for single plate connection. The graph i n Figure 4.4.1 shows the n 4 i n t e r a c t i o n r a t i o for both s l o t t e d and standard holes. Various functions and factors were evaluated to achieve a suitable f i t to each of the two n. i n t e r a c t i o n r a t i o s (see 4 v Figures 4.4.2 and 4.4.3). With the aim of devising a solution which could be equally shared by s l o t t e d and standard holes, even though i t i s not the best possible f i t , the "s^* (l+BETA/PI) 1 1 function was chosen. Thus, the f a i l u r e c r i t e r i a for a single plate connection of a beam to a girder web proposed by previous research i s modified to: s k*(l+BETA/PI) (4.4.8) 116 where: sk=0.63 for sl o t t e d holes sk=0.91 for standard holes The graph i n Figure 4.4.4 confirms that the above formula w i l l provide a safe connection. 117 TEST RESULTS THREE - RATIO INTERACTION 0.9 0.8 H 0.7 0.6 0.5 0.4 H 0.3 0.2 H 0. ' Slotted Holes l i i i I I I M M i i i i i i i i 10 20 30 40 SKEW ANGLE Figure 4.4.1 Graph of Three-Ratio Interaction vs. Skew Angle 118 Figure 4.4.2 Graph of Interaction " F i t Functions" to Three-Ratio - Slotted Holes 119 CURVE FITTING THREE - RATIO INTERACTION 1.2 n 0 10 20 30 40 SKEW ANGLE Figure 4.4.3 Graph of " F i t Functions" to Three-Ratio Interaction - Standard Holes 120 TEST RESULTS THREE - RATIO INTERACTION 1.2 Standard Holes. 0 0 0 0 0 0 0 C ^ J J M H T J M I 0.7 H 0.6 0.5 -0.4 -0.3 -0.2 -0.1 "i r~ 10 20 30 i r~ 40 SKEW ANGLE Figure 4.4.4 Graph of Formula vs. Modified Three-Ratio-Interaction Skew Angle 121 Chapter 5 CONCLUSIONS Ultimate capacity of single sided sing l e plate connections for s t e e l beams attached to the web of I-shaped girders was experimentally investigated. The following conclusions can be drawn from the investigation: 1. The supporting girder behaves f l e x i b l y when ultimate capacity of the single plate connection i s reached. Various regions of the supporting girder display f l e x i b l e behaviour and are overstressed when the connection i s loaded near i t s ultimate f a i l u r e load; 2. The increase i n skew angle augments ultimate capacity of the single plate connection; 3. The magnitude of ultimate capacity of the single plate connection i s affected s u b s t a n t i a l l y by the type of holes (slotted or standard) used; 4. A modified three-ratio i n t e r a c t i o n i s proposed to form the basis of a design formula for single plate connections. Single plate connections with a r a t i o of connection plate depth to supporting girder depth d /D of 0.5 tested i n t h i s P research behaved f l e x i b l y as t h e i r ultimate capacity was approached. This confirms previous observations for single plate connections with d /D r a t i o less than 0.6. P Three d i f f e r e n t skew angles (0, 30, and 45 degrees) between the connection plate and the girder were tested. The 122 re s u l t s showed an increase of r a t i o s of V /V ,., M./T , Mb/Mp, and a l l i n t e r a c t i o n r a t i o s with the skew angle. This tendency was s i m i l a r for both types of the te s t s i . e . with s l o t t e d and oversized holes. From the previous i n v e s t i g a t i o n [1] r e s u l t s from tests numbered 2A, 4A, and 5A with the skew angle of 0, 30, and 45 degrees respectively were selected for c o r r e l a t i o n studies with the present study. Even though, values of r e s u l t s of the t e s t 4A are exceptionally high, the same tendency as described above can be observed. However, the extent of the r a t i o and i n t e r a c t i o n r a t i o r e s u l t s varies because of d i f f e r e n t a n a l y t i c a l approaches. Previously [1], a length L=2438.4 mm of the t e s t specimen was taken as a distance between centres of the supporting columns i n order to calcu l a t e the applied bending moment; i n t h i s work, the length was taken as that of the supporting girder L=2092 mm. In addition to the length reduction the 10% reduction i n the applied bending moment also s u b s t a n t i a l l y decreased the M,/M P r a t i o . The r a t i o and r a t i o i n t e r a c t i o n r e s u l t s for the tests with standard holes are approximately 0.45 higher than t h e i r corresponding r e s u l t s for s l o t t e d holes. This finding favours standard holes i n construction applications. A close examination of the t e s t r e s u l t s leads to a design formula that may be used for single plate connections j o i n i n g beams to girder webs. The previously proposed formula [1] has been modified to: 123 <_ < x sk*(1+BETA/PI) (4.4.8) The skew angle has been incorporated into the formula. An important aspect of the modified design formula i s the "s^" factor which accounts for the types of holes. A design procedure can be developed from the above equation, depending on the amount of shear force, t o r s i o n a l moment, and bending moment applied and the available resistance of the single plate connection. The r a t i o of maximum shear force to ultimate shear resistance V /V must be less than 0.26 for max' u l t sl o t t e d holes and 0.37 for standard holes of the supporting girder. 124 Chapter 6 RECOMMENDATIONS FOR FUTURE STUDIES A comprehensive project was undertaken to devise a ra t i o n a l method for the design of the single plate connections. Based upon experimental studies, a modified design formula has been proposed for the design of the single plate connections. Further research to complete t h i s comprehensive research project includes: 1. Conduct an a n a l y t i c a l f i n i t e element invest i g a t i o n and correlate with the experimental r e s u l t s ; 2. Include v a r i a t i o n of the connection plate l o c a t i o n with respect to the supporting member; 3. Extend the number of experimental t e s t s to v e r i f y the design formula; 125 BIBLIOGRAPHY 1. Wong, H.H.J. "An Experimental Investigation of the Ultimate Capacity of Single Plate Connections", Master  Thesis. The University of B r i t i s h Columbia, Vancouver, B r i t i s h Columbia, Canada, A p r i l 1986 2. Stiemer, S.F., Wong, H.H.J., and Ho, A. "Ultimate Capacity of Single Plate Connectors", Proceedings. P a c i f i c  Structural Steel Conference. Vol.2, Auckland, New Zealand, Aug. 1986, pp.117-132. 3. Lipson, S.L. "Single-Angle and Single-Plate Beam Framing Connections", Proceedings of the Canadian Structural  Engineering Conference". Toronto, Ontario, Canada, Feb. 1968, pp.139-162. 4. Lipson, S.L. and Antonio, M.L. "Single-Angle Welded-Bolted Beam Connections", Journal of the Structural  D i v i s i o n . ASCE. Vol.103, NO.ST3, Proceeding Paper 12813, March 1977, pp.559-570. 5. Richard, R.M., G i l l e t t , P.E., Kriegh, J.D., and Lewis, B.A. "The Analysis and Design of Single Plate Framing Connections", AISC Engineering Journal. Vol.17, No.2, Second Quarter, 1980, pp.38-52 6. Young, N.W. and Disque, R.O. "Design Aids for Single Plate Framing Connections", AISC Engineering Journal, Vol.18, No.4, Fourth Quarter, 1981, pp.129-148 7. Fisher, J.W. "Behaviour of Fasteners and Plates with Holes", Journal of the Structural D i v i s i o n . ASCE. Vol.91, N 0 . S T 6 , Dec. 1965, pp.265-286. 8. Crawford, S.F. and Kulak,G.L. " E c c e n t r i c a l l y Loaded Bolted Connections", Journal of the Structural D i v i s i o n .  ASCE. Vol.97, NO.ST3, March 1971, pp.765-783. 9. Butler, L.J. and Kulak, G.L. "Strength of F i l l e t Welds as a Function of Direction of Load", Welding Journal. Welding  Research Council. Vol.50, No.5, May 1971, pp.231s-234s. 126 10. Butler, L.J., Pal, S., and Kulak, G.L. " E c c e n t r i c a l l y Loaded Welded Connections", Journal of the Structural  D i v i s i o n . ASCE. Vol.98, NO.ST5, May 1972, pp.989-1005. 11. Dawe, J.L. and Kulak, G.L. "Welded Connections Under Combined Shear and Moment", Journal of the Structural  D i v i s i o n . ASCE. Vol.100, NO.ST4, A p r i l 1974, pp.727-741. 12. Tide, R.H.R. "Design Limitations of Weld Strength for E c c e n t r i c a l l y Loaded F i l l e t Weld Groups", Proceedings of  the Canadian Society for C i v i l Engineering Conference. May 26-27, 1981, Fredericton, New Brunswick, Canada, pp.59-80. 13. Archer, F.E., Fisher, H.K., and Kitchen, E.M. " F i l l e t Welds Subjected to Bending and Shear", C i v i l Engineering  and Public Works Review. Vol.54, No.634, A p r i l 1959, pp.455-458. 14. Canadian I n s t i t u t e of Steel Construction, Handbook of  Steel Construction. Third E d i t i o n , Willowdale, Ontario, 1980. 15. American I n s t i t u t e of Steel Construction, Inc., Manual of  Steel Construction. Eigth Edition, Chicago, I l l i n o i s , 1980. 16. Brandt, G.D. "Rapid Determination of Ultimate Strength of E c c e n t r i c a l l y Loaded Bolt Groups", AISC Engineering Journal, Vol.19, No.2, Second Quarter, 1982, pp.94-100. 17. Swannell, P. "Weld Group Behaviour", Journal of the  Structural D i v i s i o n . ASCE. Vol.107, No.ST5, May 1981, pp. 803-815. 18. Neis, V.V. "Factored Resistance of Welded Connections Subject to Shear and Moment", Canadian Journal of C i v i l  Engineering. Vol.7, No.l, March 1980, pp.84-92. 19. Brandt, G.D. "A General Solution for Eccentric Loads on Weld Groups", AISC Engineering Journal. Vol.19, No.3, Third Quarter, 1982, pp.150-159. 20. Neis, V.V. "An Ultimate Strength Test Program for E c c e n t r i c a l l y Loaded Welded Connections", Proceedings of 127 the Canadian Society for C i v i l Engineering Conference. May 26-27, 1981, Fredericton, New Brunswick, Canada, pp.81-95. 21. Beaulieu, D. and Picard, A. "A Contribution to the Study of E c c e n t r i c a l l y Loaded Fillet-Welded Connections", Proceedings of the Canadian Society f o r C i v i l Engineering Conference. May 23-25, 1984, Halifax, Nova Scotia, Canada, pp.237-252. 22. Higgins, T.R. "New Formulas f o r Fasteners Loaded Off Center", Engineering News-Record. May 21, 1964. 

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