DUCTILITY OF THIN EXTENDED ENDPLATE CONNECTIONS

Transcription

1 DUCTILITY OF THIN EXTENDED ENDPLATE CONNECTIONS Israel Oludotun Adegoke A thesis subitted to the Faculty of Engineering and the Built Environent, University of the Witwatersrand, Johannesburg, in fulfilent of the requireents for the degree of Doctor of Philosophy.

2 DECLARATION I declare that this thesis is y own unaided work. It is being subitted for the Degree of Doctor of Philosophy to the University of the Witwatersrand, Johannesburg. It has not been subitted before for any degree or exaination to any other University. (Signature of Candidate) day of year i

3 Abstract A odel of the extended endplate behaviour has been developed in this thesis, which allows the prediction of the endplate contribution to the connection rotation in ters of the connection strength (oent capacity) and ductility (rotation capacity). The extended endplate strength odel developed in this thesis is unique in that it addresses the possibility of strain hardening and ebrane action in the endplate. These phenoena are shown to be critical for the ductility and strength of thin endplates, but they have not previously been odelled by other researchers. Because the leading odels of the day have not catered for these effects, they seriously underestiate the strength of thin extended endplates. The odel is bi-linear, with the strength and ductility evaluated at two points the swivel and axiu strain points. The flush region strength behaviour is based on a yield-line analysis of the endplate flush region at the swivel point, and an analysis for a plate supported on three sides and with a central point load, at the axiu strain point. The deforation of the flush region is based on the plate odel. The strength and deforation of the extended region is based on uni-axial double-curvature bending of the portion between the bolt line and the weld line, for both the swivel and axiu strain points. Strain hardening and ebrane action are catered for in the odel by adjusting the aterial properties fro elastic values to strain-hardening values, and by applying solutions for the deforation that takes account of large deflections and thick eber theory. This akes the odel developed here unique. This thesis odel is also unique in that the ductility of the endplate is easured directly by the odel in a echanical analogy. There are existing FEA and atheatical odels of the oent-rotation curve, but these tend to be ostly epirical and copletely opaque to the user. Coparisons with connection tests and published test results show that the ductility odel developed here provides an excellent assessent of the ultiate rotations of a thin extended endplate connection. ii

4 DEDICATION Thine, Oh Lord, is the greatness & power. Thine is the glory. Thank you Lord God Alighty! My deep gratitude and heartfelt thanks to y wife, Ros and to our children, Ife, Buki & Sheba. Thank you for being so supportive, patient and caring. Thank you also Ojo. You ve each sown into this thesis iii

5 Acknowledgeents My supervisor Professor AR Kep, for all his assistance over the years, and for his invaluable guidance and direction. Muy and Daddy and y brother and sisters for constantly supporting and encouraging e. All y brethren in SA, Nigeria, Canada and US who have prayed for e, encouraged, cajoled, nagged or bullied e to coplete this thesis. Thanks and God bless you all. My thanks to all the individuals who assisted e with this research at soe point or contributed in soe fashion. My forer colleagues at the then Technikon Witwatersrand, especially Des Lange, Junior Butler, Fred Otieno, Thoas Auf der Heyde and the late Geoff Hartzenberg. In the Wits labs: Andy Hofeyr, Gideon Ntoagae & the late John Dyer. The late Geoff Scott, and the late Duccio Milo y equipent suppliers. My forer students Vitor Albuquerque and Sethu. Cheryl Lobard at the National Research Foundation. Forer fellow postgrads who lent a helping hand: Sola Ileobade and Paolo Trinchero Professor Taigbenu, and all the others who encouraged e along the way. Roy Mackenzie, forerly at the Steel Institute, for his support. I gratefully acknowledge that the research in this thesis was supported financially by the following organisations at different ties: The Southern African Institute for Steel Construction. The National Research Foundation. Technikon Witwatersrand Research Fund. Fluor Daniel South Africa (Pty) Ltd. iv

6 Contents DECLARATION ABSTRACT ACKNOWLEDGEMENTS LIST OF FIGURES LIST OF TABLES I II IV IX XIII 1. INTRODUCTION BACKGROUND TO THE PROBLEM 1 1. PROBLEM STATEMENT COMPONENTS OF EXTENDED ENDPLATE CONNECTIONS DEFINITION OF KEY TERMS THE CLASSIFICATION OF CONNECTIONS THE LIMITATIONS OF THE STUDY 9. LITERATURE REVIEW 10.1 EARLY EXTENDED ENDPLATE MODELS Sherbourne s Model Surtees & Mann 13. TEE-STUB PRYING FORCE MODELS Douty & McGuire 16.. Nair, Birkeoe & Munse Agerskov (1976) Understanding the Early Research 1.3 COLUMN FLANGE STUDIES.3.1 Zoeteeijer s Work at Delft.3. Packer & Morris (1977) Tarpy & Cardinal Discussion of the Colun Flange Studies 8.4 EXTENDED ENDPLATE STUDIES IN THE EIGHTIES Krishnaurthy s Finite Eleent Studies 9.4. Kennedy s Split Tee Analogy 33 v

7 .4.3 Murray s Research at Virginia Polytechnic Soe Other Relevant Models 37.5 THE SHIFT TO MODELLING BY COMPONENTS By Coponents - Yee & Melchers Moent-Rotation Model Studies by Zandonini and Co-investigators 44.6 EUROCODE 3 ENDPLATE MODELS Extended Endplate Model of Eurocode 3 Annex J The Revised Annex J Model The SCI Moent Connections Manual The Model of BS EN SOUTH AFRICAN EXTENDED ENDPLATE STUDIES EXPERIMENTAL WORK SETUP OF CONNECTION TESTS THE TEST SPECIMENS Bea and Colun Material Properties Bolt Material Properties THE TEST INSTRUMENTATION THE TEST PROCEDURE CONNECTION TEST RESULTS OBSERVATIONS IN CONNECTION TESTS Test 1 Observations Test Observations Test 3 Observations Discussion of Test Observations and Endplate Failure Modes BEAM ROTATION DATA FROM THE CONNECTION TESTS Moent-Rotation Curves for Connection Test Moent-Rotation Curves for Connection Test Moent-Rotation Curves for Connection Test Discussion of Test Rotation Data BOLT STRAIN GAUGE DATA Bolt Strains and Bolt Forces Measured in the Connection Tests Bolt Strains in Connection Test Bolt Strains in Connection Test Bolt Strains in Connection Test Bolt Forces in the Connection Tests Discussion of Bolt Forces ENDPLATE STRAIN GAUGE DATA Endplate Strain Gauge Data Discussion of Endplate Strains 140 vi

8 4.5 STRAIN DATA ON THE BEAM WEBS AND FLANGES Description of Bea Web and Flange Strain Gauge Data Discussion of Bea Web and Flange Strain Gauge Data SUMMARY OF DEDUCTIONS FROM THE CONNECTION TESTS FE ANALYSES OF CONNECTION TEST ENDPLATES FINITE ELEMENT MODELLING APPROACH Modelling the Endplate Geoetry The FEA Material Models RESULTS FROM THE FEA MODELS The FEA Model Moent-Rotation Curves Stresses and Deforations in the 10 Endplate FEA Model Stresses and Deforations in the 1 Endplate FEA Model Stresses and Deforations in the 14 Endplate FEA Model DISCUSSION OF FEA MODELS A MODEL OF ENDPLATE DUCTILITY INTRODUCTION THE ENDPLATE MATERIAL MODEL The Endplate Stress-Strain Curve in Uniaxial Tension The Endplate Moent-Curvature Relation DEVELOPING THE DUCTILITY MODEL EQUATIONS The Endplate Flush Region at the Swivel Point The Endplate Flush Region at the Maxiu Point The Endplate Extended Region Flange Force AN ENDPLATE DUCTILITY MODEL The Stress-block Approach A Suary of the Ductility Model DISCUSSION OF DUCTILITY MODEL JUSTIFICATION OF ASPECTS OF THE DUCTILITY MODEL Introduction The Endplate Yield-line Pattern The Deflection of the Flush Region The Bea End and Bolt Contributions to Connection Rotation PARAMETERS INFLUENCING ENDPLATE BEHAVIOUR DUCTILITY MODEL COMPARISON WITH THE THESIS EXPERIMENTS MODEL COMPARISON WITH PUBLISHED TEST RESULTS Coparison with Test Results fro Bernuzzi et al (1991) 35 vii

9 7.4.. Coparison of Ductility Model with Eurocode 3 Model Predictions Coparison with Test Results fro Jenkins et al (1986) CONCLUSION SUMMARY AREAS FOR FURTHER STUDY 45 REFERENCES 47 ANNEXURE A 53 A.1 MATERIAL TEST DATA 53 viii

10 List of Figures Chapter 1 Figure 1.1 Types of endplate bea-to-colun connections 4 Figure 1. Coponents of a typical extended endplate bea-to-colun connection 5 Figure 1.3 The distinction between the connection and the joint 6 Figure 1.4 The classification of joints in Eurocode 3 7 Chapter Figure.1 Sherbourne s fixed-ended bea odel 10 Figure. Yield-line echanis adopted in Surtees & Mann (1970) 13 Figure.3 The tee-stub analogy for extended endplates 15 Figure.4 Conceptualising a tee stub as a siply supported bea 16 Figure.5 Tee-stub failure odes in Douty & McGuire (1965) 18 Figure.6 Zoeteeijer s paraeters 4 Figure.7 Zoeteeijer (1974) s colun flange collapse echaniss 5 Figure.8 Endplate geoetry in Krishnaurthy (1978) 3 Figure.9 Physical Paraeters in Yee & Melchers (1986) 4 Figure.10 Paraeters Characterizing Moent-Rotation Curves (Zandonini & Zanon, 1988) 44 Figure.11 Moent-Rotation Paraeters in Tri-linear Representation (Bernuzzi et al, 1991) 46 Figure.1 Peranent Deforation Pattern in Thin Endplates (Bernuzzi et al, 1991) 48 Figure.13 Mechanis A in Bernuzzi et al (1991) 48 Figure.14 Noenclature used in Eurocode 3 (199) Annex J 53 Figure.15 Forces acting on tee-stub stiffness odel in Revised Annex J 59 Figure.16 Yield-line Pattern of Truby (1995), fro Bernuzzi et al (1991) 65 Chapter 3 Figure 3.1 Setup for the Connection Tests 69 Figure 3. Lateral restraint of the colun 70 Figure 3.3 Supports at Test Bea ends 7 Figure 3.4 Typical Stress-Strain Curve fro an Endplate Coupon 75 Figure 3.5 Layout of Bolt Yoke 77 Figure 3.6 Bolt Material Test in progress 78 ix

11 Figure 3.7 Strain gauging the bolt 78 Figure 3.8 Bolt Stress-Strain Curves 79 Figure 3.9 Test Instruentation 81 Figure 3.10 Strain Gauges on the Endplate and Bea End 83 Chapter 4 Figure 4.1 Pilot Test A in progress 87 Figure 4. Fractured endplate fro Test 1 88 Figure 4.3 Beas 10A and 10B after the test 89 Figure 4.4 Cracking in Bea 1A endplate 90 Figure 4.5 Endplate for Bea A fro 1 Endplate Test 91 Figure endplate Test 3 in progress 93 Figure 4.7 Endplate 14B fro Test 3 94 Figure 4.8 Extent of yielding observed in Test 96 Figure 4.9 Cracks on far-side of 10 endplate in Pilot test A 97 Figure 4.10 Yield-line Pattern proposed in this thesis 98 Figure 4.11 Fractured Extended Region Bolt fro Pilot Test A 100 Figure 4.1 Moent Rotation Curves for Bea 10A, Test 1 10 Figure 4.13 Moent Rotation Curves for Bea 10B, Test Figure 4.14 Raw Moent Rotation Curve for Bea 1A at joint, Test 104 Figure 4.15 Moent Rotation Curves for Bea 1A, Test 104 Figure 4.16 Raw Moent Rotation Curve for Bea 1B at joint, Test 105 Figure 4.17 Moent Rotation Curves for Bea 1B, Test 105 Figure 4.18 Moent Rotation Curves for Bea 14A, Test Figure 4.19 Moent Rotation Curves for Bea 14B, Test Figure 4.0 Coparison of Moent Rotation Curves - Beas 10A and 10B 108 Figure 4.1 Coparison of Moent Rotation Curves - Beas 1A and 1B 109 Figure 4. Coparison of Moent Rotation Curves - Beas 14A and 14B 110 Figure 4.3 Moent Rotation Curves for Tests 1 3 at the Joint 113 Figure Section through instruented bolt, with strain gauge positions 114 Figure 4.5 Orientation of Bolt Strain Gauges on Endplate 115 Figure 4.6 Calculating the bolt down strain 116 Figure 4.7 Bolt Strains in Connection Test Figure 4.8 Bolt Strains in Connection Test 11 Figure 4.9 Bolt Strains in Connection Test 3 13 x

12 Figure 4.30 Bolt Forces for Connection Test 1 15 Figure 4.31 Bolt Forces for Connection Test 17 Figure 4.3 Bolt Forces for Connection Test 3 18 Figure 4.33 Locations of Strain Gauges in the Endplate Extended Region 133 Figure 4.34 Locations of Strain Gauges in the Endplate Flush Region 133 Figure 4.35 Endplate Strains in Connection Test 1 Bea 10A 134 Figure 4.36 Endplate Strains in Connection Test 1 Bea 10B 135 Figure 4.37 Endplate Strains in Connection Test Bea 1A 138 Figure 4.38 Endplate Strains in Connection Test Bea 1B 139 Figure 4.39 Endplate Strains in Connection Test 3 Bea 14A 141 Figure 4.40 Endplate Strains in Connection Test 3 Bea 14B 14 Figure 4.41 Locations of Strain Gauges on the Bea Web and Flanges 144 Figure 4.4 Strains in the Bea Webs and Flanges fro Connection Test Figure 4.43 Strains in the Bea Webs and Flanges fro Connection Test 148 Figure 4.44 Strains in the Bea Webs and Flanges fro Connection Test Figure 4.45 Strain Distribution across Bea Profile in Tests 1 and 155 Chapter 5 Figure 5.1 FEA Model of Endplate Geoetry 160 Figure 5. Moent-Rotation Curve for 10 Endplate FEA Model 164 Figure 5.3 Moent-Rotation Curve for 1 Endplate FEA Model 165 Figure 5.4 Moent-Rotation Curve for 14 Endplate FEA Model 166 Figure 5.5 FEA Model Stresses in 10 Endplate at Maxiu Moent 167 Figure 5.6 Yield-lines inferred fro FEA Stresses in 10 Endplate 168 Figure 5.7 FEA Model Deforations in 10 Endplate at Max Moent 169 Figure 5.8 FEA Model Stresses in 1 Endplate at Maxiu Moent 171 Figure 5.9 FEA Model Stresses in 1 Endplate at Swivel Moent 17 Figure 5.10 FEA Model Deforations in 1 Endplate at Max Moent 173 Figure 5.11 FEA Model Stresses in 14 Endplate at Maxiu Moent 174 Figure 5.1 FEA Model Deforations in 14 Endplate at Max Moent 175 Chapter 6 Figure 6.1 Typical Bilinear Model of a Moent-Rotation Curve 180 Figure 6. Idealized Material Stress-Strain Curve 18 xi

13 Figure 6.3 Changes in Stress Distribution on Meber Section under Increasing Bending Moent 184 Figure 6.4 Proposed Bi-linear Moent-Curvature Relation for the Endplate Material187 Figure 6.5 Idealized Yield-line Pattern Adopted for Flush Region at Swivel 188 Figure 6.6 Detail of Assued Yield-line Pattern 189 Figure 6.7 Longitudinal Section through Flush Region at Swivel 191 Figure 6.8 Transverse Section through Flush Region (Sect. X-X in Fig 6.7) 19 Figure 6.9 Square plate odel for flush region deflection 195 Figure 6.10 Bending Moent Distribution across extended region 01 Figure 6.11 Location of yield-lines in Extended Region 03 Figure 6.1 Longitudinal Section through Endplate at Swivel 03 Figure 6.13 Conceptual Model of Extended Region 05 Figure 6.14 Longitudinal Section through Endplate at Swivel 07 Figure 6.15 Forces and Stresses across the endplate in the Stress-block approach 09 Figure 6.16 Noenclature for endplate geoetry in ductility odel 10 Chapter 7 Figure 7.1 The Governing Yield-line Pattern for the Endplate 15 Figure 7. Square plate odel for flush region deflection 17 Figure 7.3 Deflections for 10 rectangular and square plate odels 0 Figure 7.4 Deflections for 1 rectangular and square plate odels 1 Figure 7.5 Deflections for 14 rectangular and square plate odels Figure 7.6 Noenclature for endplate geoetry in ductility odel 31 Figure 7.7 Ductility Model Results for Connection Test 1 33 Figure 7.8 Ductility Model Results for Connection Test 34 Figure 7.9 Ductility Model Results for Connection Test 3 34 Figure 7.10 Endplate Geoetry in Bernuzzi et al (1991) 35 Figure 7.11 Coparison of Ductility Model with Test EP 1-1 of Bernuzzi et al, Figure 7.1 Coparison of Ductility Model with Test EP 1- of Bernuzzi et al, Figure 7.13 Endplate Geoetry in Jenkins et al (1986) 39 Figure 7.14 Coparison of Ductility Model with Tests 4 & 15 of Jenkins et al, Figure 7.15 Coparison of Ductility Model with Test 9 of Jenkins et al, xii

14 List of Tables Chapter 3 Table 3.1 Noinal Diensions for Test Section Sizes 73 Table 3. Material Properties for Connection Tests 74 Table 3.3 Actual Section Properties for Test Speciens 76 Table 3.4 Measured Material Properties for Bolts 80 Chapter 4 Table 4.1 Moents and rotations in connection tests Table 4. Specien Material Properties Relevant to Endplate & Bea Strains 13 Chapter 5 Table 5.1 Material Properties for FEA Models of Endplate Behaviour 16 Table 5. Coparison between FEA Results and Experiental Values 177 Chapter 6 Table 6.1 Material Properties in Connection Tests as Diensionless Paraeters 183 Chapter 7 Table 7.1 Material Properties for FEA Deflection Models 19 Table 7. Deflections Measured for Rectangular and Square Plate FEA Models 3 Table 7.3 Relative Contributions of Connection Coponents to Maxiu Rotation, in Bernuzzi et al (1991) 4 Table 7.4 Connection Test Endplate Geoetry for the Ductility Model 30 Table 7.5 Results of the Ductility Model for the Connection Tests 31 Table 7.6 Coparison between Ductility Model and Connection Test Results 3 Table 7.7 Coparison between Ductility Model and Eurocode 3 Model Predictions 38 Table 7.8 Coparison between Ductility Model and Jenkins et al Test Results 4 Annexure A Table A.1 Test Specien Material Properties fro Tensile Tests 54 xiii

15 1. INTRODUCTION 1.1 BACKGROUND TO THE PROBLEM Fro the thirties, structural engineers have been aware that the behaviour of steelfraed structures is greatly influenced by the connections (Steel Structures Research Coittee, 1936). In everyday design practice however, structures are analysed either as though the connections are unable to resist any bending oent at all, (noinally pinned connections) or as though they will carry the full oent at the end of the bea without any rotation (noinally fixed connections). More appropriate ters for these idealisations as used in the SCI Moent Connections Manual (SCI, 1995) are siple fraes where the connections are conceptualised as pinned, and continuous fraes where the connections are considered fixed. However, any practical connections can not be considered copletely pinned or fully fixed, and the SCI Manual refers therefore to sei-continuous fraes as well. If a frae is being analysed elastically, the key property of the connection is its stiffness. For a sei-continuous frae this stiffness is finite i.e. neither zero stiffness (pinned) nor infinite stiffness (rigid), and such connections are then described as sei-rigid. If a frae is being analysed plastically however, the connection strength is the key property, and the sei-continuous connection is then neither zero strength (pinned) nor full strength (fixed). The connection strength of a sei-continuous connection in a plastic analysis ust be less than that of all connected ebers, so that the connection fails first. Such a connection is said to be partial-strength. A partial-strength connection could also be seirigid in ters of its stiffness, but this is not an essential requireent. In an elasticplastic analysis, the connections will either be sei-rigid or partial-strength, or both, for the frae to be considered sei-continuous. 1

16 The use of partial-strength connections in a plastic analysis is an attractive design option. The bea-end hinges are induced to for in the connection, which can lead to reduced bea sizes by coparison with fixed-end beas. Moreover, joint resistance is possibly independent of colun size, reducing the design effort, as failure is easily guaranteed to be by a bea echanis. Furtherore, fabricating a connection to be full strength and rigid is labour-intensive and so costly. The details could potentially be sipler and cheaper however, if the designer is able to accoodate flexibility in the connection and if the connection is partial-strength. Partial-strength connections can lead to cost savings over pinned beas as well, as the available oent at the connection reduces the id-span oents and so leads to a reduced bea depth. Steenhuis (199) reported a 9% cost savings fro shallower beas, due to the use of partial-strength rather than pinned connections, in a braced frae study. The extended endplate connection is a widely used oent-resisting connection in South Africa and worldwide. It is usually assued to be full-strength and fixed, but given the right configuration of endplate details, bolt size and bea/colun sizes, this connection can behave in a sei-rigid or/and partial-strength anner. Designing the connection as sei-rigid or partial-strength could allow the use of lower bea ass or/and depth. The South African Code of Practice for steel structures, SANS 1016 (005), provides for design based on sei-rigid or partial-strength construction, but requires the designer to show that the connection oent-rotation properties are suitable by experients or fro published experiental results. Thus, there are no established design odels in the South African context. Global (frae) elastic analysis with sei-rigid connections requires accurate knowledge of the connection stiffness as well as its oent capacity. A lot of international research effort has gone therefore into predicting sei-rigid connection stiffness and strength. Plastic frae analysis with partial-strength connections however, rather requires a knowledge of the oent capacity and the

17 connection ductility or rotation capacity. This latter aspect of ductility has not been researched to the sae degree as strength and stiffness. Because of the popularity of the connection type, extended endplates have been extensively studied in the last thirty-five years or so. However, as shown in the next chapter, ost such studies have been fro a full-strength sei-rigid paradig rather than a partial-strength paradig. For the plastic failure of a connection to be safe, it ust fail by gradual deforation (excessive rotation), rather than by brittle fracture. Ideally, therefore, failure should not be initiated in the bolts or welds, since bolt and weld fractures ay be brittle and sudden, and are often catastrophic. It is preferable also to achieve the expected deforation in the endplate rather than the colun flange, since it ay be difficult to predict the effects that colun flange deforation could have upon the carrying capacity of the colun especially in ters of buckling instability. Thus, the reaining option is to force ductile deforation of the endplate itself. The objective here therefore, is to study the ductility of a partial-strength extended endplate connection where failure initiates in the endplate. 1. PROBLEM STATEMENT The proble is to develop a odel of the partial-strength extended endplate beato-colun connection that enables prediction of the ductility or rotation capacity of the connection, when the connection failure is initiated by inelastic deforation of the endplate. 3

18 1.3 COMPONENTS OF EXTENDED ENDPLATE CONNECTIONS Extended region Colun Bea Flush region Endplate (a) Extended Endplate (b) Flush Endplate (c) Partial-depth Figure 1.1 Types of endplate bea-to-colun connections Endplate bea-to-colun connections consist of a plate (the endplate) that is welded to the end of the bea profile. The endplate is then bolted on site to the colun flange or web, using pre-drilled holes. In an extended endplate connection, the endplate is welded to both bea flanges as well as the web, and the endplate extends beyond one or both flanges so that soe bolts lie outside the bea profile. This is illustrated in Figure 1.1(a). If the endplate covers the entire bea depth but does not extend beyond the bea, it is known as a flush endplate connection. If it does not extend beyond the full depth of the bea, it is known as a partial-depth endplate connection. In the flush and partial-depth endplates, all bolts lie generally within the bea section profile. This study considers only extended endplate connections. The bolts lying within the bea profile are said to be in the flush region while the bolts in the endplate extension are in the extended region. The extended endplate of Figure 1.1 (a) is extended on one side only, and this would then be on the bea tension flange side. Where an extended endplate connection could be subjected to oents in both directions, it could be extended on both sides. Bernuzzi et al (1991) carried out tests of extended endplate connections extended on one side and noinally 4

19 identical connections extended on both sides. Their results show that for connections with identical geoetry, the oent-rotation curves of the singly extended and doubly extended endplates are very siilar. It has been decided here to consider only the case where the endplate is extended on one side. Endplate or Applied Shear Force Tension bolts Tension Flange Panel shear zone Shear bolts Copression Flange Colun flange or Web weld Flange weld Applied Moent Figure 1. Coponents of a typical extended endplate bea-to-colun connection The coponents of a typical extended endplate are shown in Figure 1.. This thesis is liited to extended endplates extended on one side only, with four tension bolts disposed ore or less syetrically about the bea tension flange. The bolt rows adjacent to the bea tension flange on either side are loaded in tension, while the lowerost (copression area) bolt row resists the shear forces. It is soeties necessary to have an additional row for shear. There could also be ore than one tension bolt row in the flush region. These other configurations are not coon in SA practice and so are not considered here. It is typical to have two bolts per row (on either side of the bea web), though four bolts ay soeties be used for larger bea sizes. This study considers only the case of 5

20 two bolts per row, as this is again ore coon. As shown in Figure 1., the bea flange-to-endplate welds could be butt or fillet welds depending on oent requireents. 1.4 DEFINITION OF KEY TERMS Connection Joint Figure 1.3 The distinction between the connection and the joint Connection vs. Joint: The ter connection properly refers to the interface between connected ebers. In an extended endplate bea-to-colun connection, that would refer to the endplate, the colun flange, the welds and the bolts. The ter joint refers to the connection as well as those parts of the connected ebers that are adjacent to the connection and which affect the connection. See for exaple, clause 1.4 of Part 1-8 of Eurocode 3 (Eurocode 3, 005). The distinction between the two ters is illustrated in Figure 1.3. In this thesis, the joint is taken to include the portion of bea iediately adjacent to the connection up to a distance of about a bea depth fro the connection. The joint is also taken to include that length of colun about a bea depth and centred on the bea centreline. The ters joint and connection are however used interchangeably here, as this is in line with everyday usage. Ductility: In a uniaxial tension test, ductility is used to refer to the deforability or extensibility of a etal. By analogy, it ay be used in the case of a connection 6

21 Moent Moent to refer to its rotation capacity. The two ters are used interchangeably in this study. The rotation capacity of a connection is not liited to inelastic strains only, as in the uniaxial test, but all deforations of the connection coponents will contribute. Endplate thickness: In this study an endplate is said to be thick or thin depending on whether or not the endplate undergoes elastic or plastic deforations prior to failure of the connection. In this usage, which is based on Grundy et al (1980) and Packer & Morris (1977), a connection with a thick endplate fails fro fracture of soe other coponent (bolts or welds), before the endplate has yielded. In a connection with a thin endplate, the endplate yields extensively prior to fracture of any connection coponent. An endplate ay also be interediate in behaviour between the two, with soe liited yielding before a bolt or weld fractures. 1.5 THE CLASSIFICATION OF CONNECTIONS Fullstrength Bea or Colun M p Rigid Partialstrength Seirigid 0.5 M p Pinned S j,ini 5EI b /L b or 8EI b /L b Pinned Rotation S j,ini 0.5EI b /L b Rotation (a) Strength classification Figure 1.4 The classification of joints in Eurocode 3 (b) Stiffness classification 7

22 In Eurocode 3 (Eurocode 3, 005), joints are classified in ters of stiffness or strength. The joint stiffness criterion pinned, rigid or sei-rigid - is applicable to elastic frae analyses, while the strength criterion pinned, full-strength or partial-strength - is applicable to a rigid plastic frae analysis. If the frae analysis is elastic-plastic, a cobination of both stiffness and strength is required for joint classification. Strength: Connections ay be full-strength, partial-strength or noinally pinned. A full strength bea-to-colun connection is able to transfer either 100% of the full bea design oent to the colun or 100% of the colun design oent to the bea, while a noinally pinned connection transfers less than 5% of the bea or colun design oent. Thus, a joint is fullstrength if the joint design oent resistance M j,rd the lesser of the bea plastic resistance oent capacity and the colun plastic resistance oent capacity. Where the colun continues to the floor above the joint, the colun oent is doubled to cater for the contribution of the upper colun. Likewise, a joint is defined as pinned if it transits 5% or less of the fullstrength criterion, and in addition has sufficient rotation capacity. The partialstrength connection lies between those two liits i.e. it transits between 100-5% of the full-strength criterion. This is illustrated in Figure 1.4 (a). Stiffness or rigidity: A connection is classified as rigid, sei-rigid or noinally pinned depending on the initial rotational stiffness S j,ini. S j,ini is the slope of the initial portion of the oent-rotation curve where the connection still behaves elastically. For a braced non-sway frae, a joint is considered rigid if S j,ini 8EI b /L b. The corresponding liit for an unbraced frae or a sway frae is 5EI b /L b. I b and L b refer to the bea second oent of area and span, and non-sway braced fraes are those where the bracing reduces the horizontal displaceent by ore than 80%. In relation to stiffness, a joint is considered pinned if the initial stiffness S j,ini 0.5EI b /L b. This applies to both sway and non-sway fraes. Sei-rigid joints are defined as all joints falling between the liits for rigid and pinned joints (Figure 1.4b). 8

23 Ductility or rotation capacity: Eurocode 3 (005) does not classify joints in ters of rotation capacity. The rotation capacity of the joint is not calculated directly for extended endplates, but instead rules-of-thub are given for situations where the rotation capacity ay be assued satisfactory. Following Surtees & Mann (1970) and Bose & Hughes (1995), this thesis assues that any connection achieving a rotation of 30 x 10-3 radians is sufficiently ductile for global plastic analysis. This fors therefore, a liit state threshold for ductility. Connections achieving lower rotations than this will be regarded as non-ductile. In current practice, global plastic analysis is only peritted if the frae ebers are Class 1 and Class sections, and the ebers in which the plastic hinges for (except the last hinge) should be Class 1. This definition of a ductile connection iplies that the need for a Class 1 section can be relaxed if the connection is ductile (achieves a rotation of 30 x 10-3 radians), as long as the plastic hinges for in the connection. 1.6 THE LIMITATIONS OF THE STUDY This study is liited to extended endplate connections with the extension only on the side of the bea tension flange. It is also liited to the case where there are two shear bolts and four tension bolts two in the flush region and two in the extended region as shown in Figure 1.. These are all assued to be Grade 8.8 high-strength bolts. This study would therefore not apply to those large section size beas, for which four tension bolts and two shear bolts would not be adequate to transfer the load. This study is liited to connections under static or quasi-static loads, excluding dynaic, cyclic and seisic loads. 9

24 . LITERATURE REVIEW Previous investigations of extended endplate behaviour are reviewed in this chapter. For consistency and ease of reference, a unifor notation is used throughout the thesis rather than the original sybols used by the respective authors. This unifor notation is based on Part 1-8 of Eurocode 3 (Eurocode 3, 005) and on SCI (1995). Each sybol is defined at the first point of usage..1 EARLY EXTENDED ENDPLATE MODELS.1.1 Sherbourne s Model Sherbourne (1961) proposed an early odel of the extended endplate connection. His investigation was in the context of the global plastic analysis of a frae, and he assued that optiu econoy would be obtained by allowing the connection to fail plastically at the sae tie as the bea. Thus, his objective was for the connection to develop exactly the full plastic oent M P of the bea, with sufficient rotation capacity for other required plastic hinges to develop elsewhere. In other words, he wanted a odel to design full-strength and ductile extended endplate connections. Extended bolt line Weld line p 1 Tension flange force Flush bolt line Conceptualised as a fixed-ended bea Figure.1 Sherbourne s fixed-ended bea odel 10

25 Sherbourne tested five extended endplate connections with varying thickness fro approxiately 19 (¾") to 3 (1¼"). Stiffener and bolt sizes were also varied. Based on his observations, Sherbourne proposed a design odel for the endplate, in which the endplate was assued to behave as a fixed ended bea spanning fro the flush region tension bolt line to the extended region bolt line, with a line load at the centre applied by the bea tension flange. The odel assues a plastic collapse for this fixed-ended bea, with plastic hinges foring at the extended and flush bolt lines, and at the endplate-to-bea flange weld line. A plastic odulus is used for the internal oent of resistance but odified for shear using a Von Mises criterion. Thus, the endplate paraeters taken into account are the bolt pitch p 1, the endplate width b p, and the endplate thickness t p. b and t f are the breadth and thickness respectively of the bea flange, and f y is the aterial yield stress for both the bea flange and endplate. The resulting equation (Sherbourne, 1961) is: f y bt f p b pt p 3f y 1 bt f f y Eqn b pt p 8 in which f y bt f on the left hand side represents the force required to cause yielding of the bea tension flange. Thus, the left hand side is the theoretical collapse load (plastic bea theory) for a fixed-ended bea with span p 1 and a central point load. The right hand side of the equation represents the oent to cause plastic collapse across the breadth of the endplate, odified for shear. The bea flange yield stress (f y on the left) is taken equal to the endplate yield stress (f y on the right), so that the equation can be siplified to: bt f b pt p p t 1 p Eqn. The bolts on either side of the tension flange are assued to restrain the endplate copletely, and the bolts are sized by assuing the all to be equally stressed 11

26 and to be fully loaded (proof or yield load) at the sae tie as the bea tension flange. Hence the bolt thread area A s is given by: A s bt 4 f f. f y yb where f yb is the proof stress for the bolts. Thus, the bolts yield as the plate plastic hinge is fored. It sees then that Sherbourne s odel is essentially a one-diensional plastic bea odel assuing double curvature in both the extended and flush regions. This is illustrated by the longitudinal profile of the endplate in Figure.1. Since the flush and extended regions are assued to behave identically, the stiffening effect of the bea web is ignored and the endplate tension area is effectively considered a tee-stub (though Sherbourne did not use that ter). The use of a siple plastic hinge iplies a rigid-perfectly plastic aterial odel, so that strainhardening effects are excluded. Sherbourne noted in his experients with thin endplates that the tension bolts in the flush region ay attract ore load than the bolts in the extended region. However, he ade no attept to account for this in the odel forulated. Neither did he ake any ention of prying forces in the bolts. A criticis of Sherbourne s odel is that it can seriously underestiate the flange tension force at the plastic oent M p of the bea, since it is quite evident that the axiu tension force at M p ay greatly exceed the force f y.bt f to cause yield in the tension flange. Besides the fact that the contribution of the web is ignored, the bea flange ay sustain loads well beyond the first yielding condition, until the bea fors a plastic hinge adjacent to the connection or the copression flange fails in local buckling. Despite stating the need for the connection to be full-strength, Sherbourne recognised the value of designing the connection to fail inelastically rather than the bea end, so that he was really catering for a partial-strength connection. As 1

27 such, he correctly stressed the need for the connection to develop adequate ductility, but did not attept to odel or predict the rotation capacity..1. Surtees & Mann Surtees and Mann (1970) described a detailed investigation of extended endplate connections at the University of Leeds. They tested six single-sided extended endplate connections of varied endplate thickness, including one pilot test and an exploratory test on a deeper bea section. In one of their tests they varied the bolt pretension and so deonstrated that the initial connection stiffness was sensitive to the applied pretension. b p p Extended region p 1 / p 1 Flush region d f 0.5d f Hogging lines Sagging lines Thickness t p t f b Figure. Yield-line echanis adopted in Surtees & Mann (1970) The yield-line pattern adopted by Surtees and Mann is shown in Figure.. The yielding takes place in two regions the extended region and the flush region. The pattern for the extended region is the sae as that assued by Sherbourne, but the flush region is ore coplex, taking into consideration the bending across the 13

28 endplate due to the presence of the web. In their odel, they assued the flush yield-lines to extend a distance of 0.5d f, where d f is as shown in Figure.. This would iply that the neutral axis for bending of the endplate is at that depth. They recorded carbon-backed iprints of the endplate-colun contact surface during tests, which showed indeed that the copression zone was triangular with a base along the bea copression flange and an apex along the lower web. However, in the photograph provided in their paper, the apex only extended to the level of the shear bolts. Surtees and Mann proposed equations for obtaining the endplate thickness and the bolt sizes. Sherbourne s odel served as their point of departure, but they oitted the shear odification in the expression for M p in Sherbourne s equation for endplate thickness. They also calculated the axiu tension force as the ratio M p /d f rather than equating it to the bea flange tension capacity at yield. d f is the depth between centres of the bea flanges i.e. the bea total depth D inus the bea tension flange thickness t f. The ost radical difference however was that Surtees and Mann based the internal oent of resistance on a plate yield-line echanis rather than on Sherbourne s bea analysis, though they still assued the extended bolts to restrain the endplate copletely. Thus, they effectively treated the extended region as half of a fixed-ended bea. Their resulting equation (Surtees & Mann, 1970) for endplate thickness t p was: M p t p Eqn.3 b p d f 16d f p1 p where d f is the depth between centres of the bea flanges and p is the bolt gauge distance. They explained that this equation leads to generally thinner endplates than Sherbourne s. A second radical change in Surtees & Mann fro Sherbourne s proposals was that they considered the possibility of prying action, catering for this with an epirical 30% increase in the bolt load. Thus, the bolts are to be sized for a force P, where: 14

29 M p M p P 1.3 Eqn.4 4d f 3d f However, they also recoended that this bolt load be equated to the ultiate tensile capacity of the bolt rather than the proof load as suggested by Sherbourne. This would ean an effective increase of about % in bolt size as copared to Sherbourne s odel. The adoption of an ultiate criterion was considered better as it leads to an earlier redistribution of forces between the tension bolt rows. Surtees & Mann (1970) deonstrated that a connection rotation of 30 x 10-3 radians is a reasonable value for the required connection rotation for plastic analysis of a structure failing in a bea echanis. That value is therefore adopted in this thesis as the liit value for the ductile non-ductile distinction.. TEE-STUB PRYING FORCE MODELS Working at about the sae tie as Surtees & Mann, other investigators were researching the assessent of prying forces. Most of this research was based on an analogy between the extended region of the endplate and tee-stubs, since it is easier to conceptualise and estiate prying action with tee-stubs. Tee-stub e x Q P x Bea Flange F Fillet or butt weld Tension bolts Q (a) Idealisation of tension region as (b) Enlarged view of tee-stub, in flexure a tee-stub. under load. Flange force is F, prying force is Q, and bolt force is P. Figure.3 The tee-stub analogy for extended endplates 15

30 The extended region of the endplate, or/and the colun flange in the tension region, is considered to behave like a tee profile with four bolts placed syetrically around the ste. This is illustrated in Figure Douty & McGuire In the United States, Douty & McGuire s investigation at Cornell University (Douty & McGuire, 1965) was initially into tee-stub connections. However, they recognised the close reseblance between the tee-stub and the tension part of the extended endplate, and drew an analogy between both connections. Their tee-stub odel led to the coputation of the prying force in the extended bolt either at working load or at ultiate load. Their prying force derivation is involved, based on the initial elastic deforation of the endplate around the bolts due to the bolt pretension, and also including the initial bolt elongations. This analytical odel was derived fro an assuption of the tee flange behaving as a siply supported elastic bea, spanning across the flange ends, with the equations derived fro copatibility of deforation principles, but odified for design based on their observations. This is shown in Figure.4. Bolt force Tension force Tee-stub Support Siply supported bea Figure.4 Conceptualising a tee stub as a siply supported bea The sei-epirical prying force Q at ultiate load was given by Douty & McGuire (1965) as: 16

31 Q 1 b t 30e 4 p p A x x s F 4 u k Fu Eqn.5 e x e x b pt p 1 x 3 x 6e x x A s in which Q is the prying force, and b p and t p are the width and thickness respectively of the endplate. The end distance e x for the extended bolt row, and the effective distance x between the extended bolts and the weld line, are as shown in Figure.3. A s is the bolt effective area and F u is the ultiate force in the bea flange. Once the prying forces were obtained, the total bolt forces could be checked to ensure that bolt fracture does not govern failure. The endplate (or tee-stub flange) thickness was then checked to ensure that the axiu bending stress does not exceed the plastic value of 4M p /t p, in which the bending oent M is taken at the bolt line or the weld line, whichever is higher. The bolt and weld line oents are calculated by taking oents for the prying force Q about the bolt line and for Q and the total bolt force about the weld line. Thus, their inelastic endplate odel was derived fro the assuption of a siply supported bea, but with a axiu plate oent of M p either at the bolt line or the weld line, or at both. Like Sherbourne in England, Douty & McGuire (1965) were essentially applying a one-diensional yield echanis odel, assuing double-curvature bending in the inelastic phase - though Douty & McGuire did not include Sherbourne s odification of the plastic oent for shear. Their external applied oent however is based on the calculated prying force and the corresponding restraining couple, rather than on an assuption of full fixity at the bolt lines. As in Sherbourne, the axiu connection load would occur when the bolt-line and weld line oents are both at M p so that a echanis fors. Douty & McGuire pointed out that uch higher endplate (or flange) oents than M p were observed in practice, and this was thought to be due to strain hardening. However, their odel ignores this strain hardening effect. The prying force value was also rather sensitive to the assued location of the prying forces, which location was 17

32 found to be rather uncertain. Douty & McGuire clearly differentiated between two failure odes in the tee-stub flange one in which the two tee-stubs separated before yielding of the flange set in, and a second where yielding took place before the stubs separated, so that a echanis fored. These are shown in Figure.5. They considered the first a condition to be avoided as it led to thick endplates, and their ai was for the connection to fail in the second ode as a thin endplate. (a) Tee-stubs separate first (b) Tee-stubs yield first Figure.5 Tee-stub failure odes in Douty & McGuire (1965).. Nair, Birkeoe & Munse Nair et al (1974) investigated the sensitivity of prying action in tee-stubs to changes in the bolt pitch and the end distance, and also considered the effect of cyclic fatigue loads. They found that the prying forces in the bolts increased with the bolt pitch, particularly at interediate values of end distance. The prying was also ore pronounced for A490 bolts than for A35 bolts (higher strength steel). They went on to carry out a -diensional FEA study of the connection to further study the paraeters. Based on the FEA results, a sei-epirical odel was derived for the prying force. By idealizing the connection as a siply supported bea with the prying forces as reactions at the edges of the tee-stub flange, and the web load and bolt forces as applied loads, a odel was derived. The odel assued that bolt failure would be critical at a bolt load including prying, such that the prying force Q (Nair et al,1974) would be obtained fro: 18

33 p b t 1 p p β Q d Prying ratio Eqn.6 P b pt p e x β d In this equation, ß is an epirically-derived constant for a given endplate yield stress and bolt type, b p and t p are the width and thickness respectively of the plate, and d is the bolt diaeter. P is the bolt force fro the flange loading only, and e x is the end distance fro the bolt line to the edge of the tee flange, easured perpendicular to the web. Q, P and e x are as illustrated in Figure.3. The distance p 1 is the span fro the bolt line on one side to the bolt line on the other i.e. the bolt pitch. Once the prying ratio is obtained, the ultiate load P u per bolt is calculated as: P F Q 1 P ub u Eqn.7 u where F ub is the ultiate capacity of each bolt in tension. An obvious drawback of this odel is that it is based on bolt failure as the critical failure ode, and this brittle failure ode is of course not desirable. It sees therefore that these researchers took for granted that the resulting connection fro their odel would only be applied as a full-strength connection. The research of Nair, Birkeoe & Munse was incorporated in the design odel of the seventh edition of the Aerican AISC Manual...3 Agerskov (1976) In Europe, Agerskov (1976) reported on an investigation of tee-stubs and beato-bea endplate connections, in which the theory presented by Douty & McGuire (1965) was used as a point of departure. By easuring the bolt forces in his experients, Agerskov deterined the oents on the bolt line and on the weld line. He cae to the conclusion that after an initial yielding of the endplate on the weld line, the oent increases there due to strain hardening, but the bolt 19

34 line oent does not increase due to a drop in prying force - the prying force dropping as a result of reduced stiffness fro the endplate yielding. He therefore rejected the echanis odel that had been advocated by earlier authors, rather conceptualising failure as first yield on the weld line. To develop a odel, Agerskov also treated the tee-stub as a siply supported bea spanning across the flange ends, but with a hinge developing only at the center (weld line). The unknown bolt and prying forces were obtained fro equilibriu conditions, and by considering copatibility of deforation at the bolt locations in a siilar anner to Douty & McGuire. For the deforation equation, Agerskov went to considerable effort to include the deforations of the washer, nut and bolt shank, equating these to the elastic deforation of the endplate at that location, using elastic bending theory for a siply supported bea. In deriving the yield oent at the weld line, Agerskov referred back to Sherbourne and included a reduction for shear, also using the Von Mises criterion. In essence, Agerskov was really considering a third failure ode, different fro and interediate between the two considered by Douty & McGuire (1965). Such an interediate ode would apply if the bolt sizes were not large enough to restrain the endplate sufficiently for a hinge to for at the bolt line, but yet the bolts were too strong for the tee-stubs to separate before the weld line and bolt line yielded. It sees very unlikely though that the elastic bea deforation equations assued by Agerskov would be applicable over such sall spans, particularly after the weld line oent approaches or exceeds the yield oent M y. This is probably why Agerskov defined failure as the onset of yielding on the weld line. Nevertheless his odel is conceived as an elastic one rather than a plastic one (in ters of the connection coponents) and so there is a large reserve of strength due to the observed strain hardening, which is ignored. 0

35 ..4 Understanding the Early Research By now two distinct streas of enquiry or research were eerging. On the one hand there were researchers such as Sherbourne and Surtees and Mann, who tried to odel endplate connections directly, and who conceptualised the extended region of the endplate as half of a fixed ended bea terinating at the bolt line. On the other hand, there were researchers such as Nair et al and Agerskov, who concentrated ore on tee-stubs and the tee-stub analogy, and who tended to conceptualise this as a siply supported bea extending to the edge of the plate. The forer group of researchers tended to ignore prying forces or to assess the using siple rules of thub, while the latter group went to considerable trouble to calculate the prying forces exactly on tee-stubs. The prying action assuptions for tee-stubs were then extrapolated to extended endplates. A fundaental difference between Sherbourne, Surtees and Mann on the one hand, and the other researchers developing prying force odels on the other, was the objective in design. Sherbourne and Surtees and Mann started fro an ultiate strength paradig in which plastic collapse of the endplate was the goal. The prying force researchers were ore in a working load paradig, though trying to account for ultiate load conditions. Douty & McGuire derived their prying force equation using an elastic forulation, but then applied these elastic prying forces to the inelastic endplate odel. As shown by Agerskov, prying forces are significant in the elastic phase but not after the endplate has yielded. For Sherbourne and his colleagues, a plastic echanis in the endplate was the fundaental starting point - and if one assues that there is a plastic hinge along the bolt line as assued by both Sherbourne and Surtees & Mann, there would be no need to easure the prying force to calculate the bolt line oent. There is therefore also no need to investigate beyond the area bounded by the weld line and the bolt line in the extended region. 1

36 Of course, Sherbourne s approach is only valid if the endplate is thin enough to allow the endplate to yield sufficiently on the bolt line (see the two failure odes identified by Douty & McGuire). Moreover, the assuption of a plastic hinge at the bolt line is only feasible at ultiate load. If the behaviour at working loads is considered iportant (in order to assess initial stiffness and liit deflections, or to allow a sei-continuous analysis of the frae) then a odel that includes the prying force ay be ore appropriate. In the prying force literature, all these researchers showed experientally that the oent on the bolt lines ay not reach M p under certain conditions, which would invalidate the assuptions of Sherbourne and Surtees and Mann. This iplies that there is ore than one failure echanis. It would see that the failure echanis is linked to how thin the endplate is and how strong the bolts are. Thus, the iportant questions at this stage were to deterine the conditions under which the bolt line oent will attain M p, and the conditions under which the weld line oent reains at M p or increases through strain hardening. A third question of interest propted by Surtees & Mann s yield-line pattern is whether or not a tee-stub adequately represents the flush region behaviour in the endplate..3 COLUMN FLANGE STUDIES Parallel to the developents in understanding the contribution of the endplate, other researchers were ephasising the effects of colun deforation in their investigations. The next three papers reviewed ade ajor contributions in assessing the colun flange deforation..3.1 Zoeteeijer s Work at Delft Zoeteeijer (1974) reported on a detailed investigation of tee-stub connections in which the connections are initially syetrical about the contact surface of each individual tee-stub. His odel of the tee-stub flange was a one-diensional collapse analysis, idealized as a siply supported bea with a plastic hinge of agnitude M p at the weld line, and with a second plastic hinge possibly

37 developing at the bolt line. He considered two possible patterns of failure collapse Mechanis A in which the bolt line plastic hinge does not develop (although the weld line one does) and failure is by fracture of the bolts, and Mechanis B in which both plastic hinges develop and failure is by excessive deforation of the tee-stub flange. Thus, Mechanis A is siilar to Agerskov s (1976) failure ode. Douty & McGuire s (1965) first ode is subsued in Mechanis A as a third possibility, in which the endplate is so thick that the teestub flanges separate before any flange yielding, and the assebly fails by bolt fracture. Fro a consideration of static equilibriu of the forces on the tee-stub, Zoeteeijer found that at one extree when the prying force is zero (collapse Mechanis A Douty & McGuire, 1965), then: T u T u M p t Eqn.8 bf y where = p 1 / (half the bolt pitch) and b is the width of the tee-stub. T u is the ultiate tension load on half of the tee-stub and t is the tee-stub thickness. At the other extree, when the prying force is at a axiu (collapse Mechanis B), then: T u T u M p M p t 1.41 Eqn.9 bf y The first equation corresponds to the iniu plate thickness for the sallest bolt size at a given connection load (no prying), while the second equation corresponds to the axiu plate thickness to ensure plate failure for the sae connection load, but using the largest bolt diaeter. (M p and M p ' are plastic oents at the weld and bolt lines respectively). In the first case bolt diaeter is obtained fro ΣF ub T, but in the latter fro ΣF ub T + M p /e - where F ub is the ultiate capacity of a bolt and e is the edge distance to the edge about which prying is taking place. Thus, Zoeteeijer deonstrated that the designer can control the failure ode quite easily by varying the plate thickness and bolt size for a given plate and bea geoetry. He also deonstrated that larger (stronger) 3

38 bolts cobined with thin plates are required to develop M p in the plate for double curvature plate collapse, but thicker plates will eliinate prying and cause failure by bolt fracture. For cases where the prying force is between these extrees, the two conditions to be satisfied (Zoeteeijer, 1974) are: T u Fub Te M p where F ub T 0 else T Fub if bolt fracture is the deterining factor, and T u M M if excessive plate deforation is the deterining factor. p p When a tee-stub is connected to a colun flange however, the connection is not syetrical about the connected faces, for though the portion of the colun in contact ay be idealized as a second tee-stub, this second tee-stub is rotated at 90 degrees to the first. Thus, the above equations that were developed for the syetrical case cannot be applied without careful consideration. Colun flange e' e e p 1 Tee-stub (a) Paraeters for tee-stub (b) Colun flange paraeters Figure.6 Zoeteeijer s paraeters Nevertheless, Zoeteeijer showed that these equations could be applied to the colun flange and the tee-stub independently, to obtain separate values for the liiting value of T u for a echanis to for. The echanis would for first in 4

39 whichever coponent has the ore flexible flange the colun or the tee-stub. Thus, the flange with the lower value of T u would be the critical one for failure. The colun flange is always wider than the tee-stub flange, and this raised a question about what would be an acceptable value for e (now the edge distance fro the bolt holes on the colun flange) to use in the above equation. The assuption that prying would take place at the edge of the tee-stub parallel to the colun flange edge dictated that that distance be used to ark e. Zoeteeijer suggested that e should not be taken as greater than 1.5. To distinguish e in the equations fro the actual edge distance, the edge distance was denoted e' (see Figure.6). Also, because the colun flange has a fillet of radius r at the flangeweb junction, was taken as being fro the face of the web but inus 0.8r. To apply his two equations above to colun flanges, Zoeteeijer needed to calculate M p for the colun flange. This required a decision as to what length of the colun was actually yielding. He used the concept of a participating or effective length of colun flange, which was decided by energy considerations fro studying the yield-line echaniss for collapse of the colun flange. Negative yield-line Negative yield-line Positive yield-line Positive yield-line (a) Mechanis I (b) Mechanis II Figure.7 Zoeteeijer (1974) s colun flange collapse echaniss Two collapse echaniss were considered for the colun flange (see Figure.7), which he tagged Mechanis I and II. Mechanis I was analogous to Mechanis 5

40 A in the tee-stub and resulted in bolt fracture. Mechanis II was analogous to Mechanis B in the tee-stub and resulted in excessive deforation of the colun flange. The resulting participating colun length he proposed was a value of: Participating length = p e' where p 1 is the bolt pitch. This participating length is then ultiplied by the plastic oent per unit length to obtain M p. Zoeteeijer then investigated the effect of stiffening the colun flanges with backing plates to reduce colun flange deforations. He showed that the two possible collapse echaniss in the colun flange would not be altered by the presence of backing plates, though the plastic oent per unit length would change on soe of the yield-lines. He did not attept to justify this approach analytically, but argued that the predictions of this equation were in accordance with experients conducted..3. Packer & Morris (1977) Packer & Morris (1977) took a siilar approach to Zoeteeijer (1974) and concentrated on the colun flange deforation, also assuing that shear deforations were negligible. They separated Zoeteeijer s tee-stub Mechanis A into two failure odes. Thus, their own Mechanis A was for really thick teestubs where there is no tee-stub yielding at all, and the bolts fail in fracture. Their Mechanis B was then the case where the tee-stub flange yields along the weld line but not the bolt line, and then the bolts fracture. Finally, the case where both weld line and bolt line yield, and the tee-stub collapses, was referred to as Mechanis C. The equation for Mechanis A was that: Bolt ultiate capacity = the total tension force divided by 4 i.e. F ub = T/ = F/4. For Mechaniss B and C they retained the tee-stub equations proposed by Zoeteeijer. In applying the equations for Mechaniss B and C to colun flanges (referred to as Mechaniss I and II respectively by Zoeteeijer), Packer & Morris adopted circular yield-lines in the corners of the patterns, rather than the straight lines 6

41 investigated by Zoeteeijer. The basis for this was that their experiental observations showed a circular rather than a straight pattern. For Mechanis B they obtained the equation: p / e F e / ( e F T t f Eqn.10 fc yc 1 where p 1 is the vertical bolt pitch, and t fc and f yc are the thickness and yield strength respectively for the colun flange. They suggested F ub could be ultiplied by 0.8 to provide a safety factor against undesirable bolt fracture. ub In the case of Mechanis C in the colun flange, Packer & Morris considered several yield-line patterns. In a further refineent to Zoeteeijer s proposals, Packer & Morris also investigated yield patterns for a colun flange with transverse stiffeners, where the stiffeners are idway between the tension bolts. In all their equations they neglected strain hardening and ebrane action..3.3 Tarpy & Cardinal Tarpy and Cardinal (1981) also considered the deforation of the colun flange, liiting their studies to unstiffened flanges and using finite eleent analyses rather than yield-lines. They odelled 97 connections using standard sections, and then derived prediction equations for the colun flange displaceent and web stress, using ultiple linear regression. The displaceent was given in inches (Tarpy & Cardinal, 1981) as: b p M Eqn.11 p fc t fc t p D where D = bea depth t fc = colun flange thickness p = gage b fc = colun flange width p 1 = pitch M = applied bea end oent t p = endplate thickness In the equation for the doinant paraeters are the bolt gage, and the endplate and colun thicknesses. By assuing the centre of rotation to act at the botto 7

42 flange of the bea, they could then derive an equation for the applied bea oent in ters of the bea end rotation. Tarpy and Cardinal found in coparative studies that with what they considered to be thin endplates (t p = 1.5t fc ), the colun flange was the stronger bending eleent, while with thick endplates (t p = 4t fc ), the endplate was stronger..3.4 Discussion of the Colun Flange Studies Zoeteeijer s paper provides a eans of differentiating between three failure odes in tee-stubs (and by inference, in endplates), and he also shows how these tee-stub failure odes can interact with the colun flange thickness. He introduced the very iportant concept of a participating length for the colun flange yield lines, and illustrated how this could be used in practical design. He also showed that the tee-stub/endplate and the colun flange could in fact be analysed separately, though using the sae principles. Zoeteeijer showed a relationship between thin and thick endplate behaviour, and the bolt size/ strength. In order for the connection to fail by excessive endplate yielding and deforation, and so be thin, larger and stronger bolts are required. Packer & Morris extended this by analysing several yield-line patterns for colun flanges and defining participating lengths for these. Interestingly though, in their extended endplate connection tests, Packer & Morris found that those tests that failed by endplate Mechanis C (double curvature collapse) behaved differently fro the tee-stub tests that failed by the sae echanis. Their use of Zoeteeijer s equations led to a consistent overestiate of connection strength for the extended endplate, but to a consistent underestiate for the tee-stubs. Thus, they concluded that thin endplate behaviour is not quite analogous to tee-stub behaviour, though Zoeteeijer s equation led to better predictions than any of the other odels available to the such as Surtees and Mann s. Their easureents of bolt forces indicated that the value of M' p /3d f suggested by Surtees and Mann, 8

43 and which includes a 30% estiate of prying, was a good approxiation to the bolt force. A second ajor contribution by Zoeteeijer is that he showed the iportance of the interaction between the endplate and the colun flange, by deonstrating that the location and agnitude of the prying forces depends on the relative thickness of the endplate copared to the colun flange. Tarpy and Cardinal confired this interaction using a different approach. The colun flange behaviour is affected by the presence of stiffeners as shown by Packer & Morris. At this stage in the review, it is clear fro Packer & Morris that there are three failure odes in endplates one of which is the thin endplate behaviour. The other two odes (interediate bolt fracture after endplate yielding, and thick bolt fracture prior to endplate yielding) are undesirable fro the viewpoint of ductility since they involve the brittle failure of bolts. It is also clear that an endplate is thin in relation not only to its own thickness, but also in relation to the bolt size/strength and the colun flange thickness. Clearly also, the tee-stub analogy is not really applicable to thin endplates in which the flush region exhibits coplex bending behaviour. The presence of strain-hardening in thin endplates has been acknowledged by several researchers (leading to different plastic oents on the weld and bolt lines), but has not been accounted for. The colun flange and endplate can be uncoupled fro each other and analysed separately at the ultiate liit state. The elastic behaviour of the endplate and the colun flange are linked together via prying forces, but this is de-ephasised once either coponent has fored a yield echanis..4 EXTENDED ENDPLATE STUDIES IN THE EIGHTIES.4.1 Krishnaurthy s Finite Eleent Studies Krishnaurthy (1978) carried out an extensive FEA study of extended endplate connections, and cae up with a odel of behaviour for these connections. He 9

44 suggested that the actual behaviour of the end plate in the extended region differed fro Sherbourne s odel in that the force transferred to the extended region is not necessarily half of the bea tension flange force, but depends on the relative stiffness of the extended region and the flush region (between the flanges). His analyses showed that the extended region typically accounted for between 30 50% of the bea flange force. He hypothesized that the bea web transfers soe of the force that goes into the flush region, so that the tension force in the bea is not liited to the tension flange. Sherbourne had assued that the tension bolts in the extended region would restrain the plate copletely and so odelled it as a fixed-ended bea. That eant that at collapse the point of inflexion in the endplate oent diagra would be halfway between the weld and bolt lines if the axiu oent is M p at both lines. Krishnaurthy pointed out that the bolts do not restrain the plate copletely and will also bend and stretch under load. All this leads to less stiffness at the bolt line so that the point of inflexion shifts towards the bolt line. His analyses showed that the inflexion point could be anywhere fro halfway between the weld and bolt lines, right up to the bolt line itself. (He also showed that the weld line position is approxiately at the toe of the bea tension flange to endplate fillet weld, rather than at the face of the flange). Thus, by allowing the inflexion point to shift, he was catering for the possibility of a different failure echanis such as Packer & Morris Mechanis B, in which the weld line oent is M p but the bolt line oent < M p. Thirdly, Krishnaurthy pointed out that the prying forces and the bolt forces on the extended region are not concentrated forces as coonly assued, but for curved pressure bulbs. On the basis of these observations, he proposed that the oent for which the endplate is sized, i.e. the design oent M d, could be considered a odification of the theoretical oent M t for a fixed-ended bea with concentrated loads resisting half the flange force, as follows: M d M t C C 1 C 3 M t 30

45 where the C coefficients each cater for one of the three effects described above (ratio of the flange force resisted, shift in inflexion point and non-concentrated loads), and are all suarized in the α coefficient. Krishnaurthy was unable to suggest a physical approach for odeling these coefficients directly, and resorted to a regression analysis of the FEA generated results. Based on the statistical analysis, Krishnaurthy (1978) cae up with the following forula for the plate design oent (the oent at the weld line): M d f 1.9 f C a M t y bu 0.4 C a f 1.9 f f f y bu bt p A f C b A w f f bt p b b 0.3 p ; C A A p e d b f w M b b p p e d t M t Eqn.1 In this equation, f p and f y are the working and ultiate stresses in the endplate, while f bt and f bu are the corresponding working and ultiate values for the bolt. b and b p are the bea flange and plate widths respectively, and A f and A w are the areas of the bea flange and bea web. The noinal bolt diaeter is d and x is the effective span (between the bolt and weld lines), taken as p e = p f 0.5d s wf. p f is the distance fro the bolt centre-line to the face of the flange, and s wf is the throat size of the fillet weld. These paraeters are shown in Figure.8. According to Krishnaurthy, the design oent obtained by the above equation could be used as a basis for obtaining the endplate thickness (Krishnaurthy equated the design oent to the endplate yield oent of resistance rather than the plastic oent of resistance), while the bolts were sized on the basis of working load by dividing the total flange force by the total nuber of tension bolts. The effective plate width was restricted to the axiu value obtained by assuing a 45-degree dispersion fro the flange-to-plate weld toe. Thus, b p could not be taken as greater than b + (p f - s wf ). 31

46 While Krishnaurthy s odel adds valuable inforation to the body of work on extended endplates, it is an epirical odel and thus the key paraeters have no physical eaning such as would aid conceptual understanding of the connection behaviour. The use of a yield criterion for failure (in deriving endplate thickness) eant that the odel still led to fairly thick endplates, and since the odel does not explicitly recognise the different failure odes, it does not provide guidance for a designer on when the connection will fail in one ode or the other. b p p e x p e s wf p 1 Thickness t p t f b Figure.8 Endplate geoetry in Krishnaurthy (1978) His odel allows indirectly for the possibility that a yield line does not for at the bolt line but there is no guidance as to when this happens. His work also shows that the tee-stub analogy ay be really weak in soe cases and his odel accounts for the increased load in the flush region. However there is no attept to cater for the strain hardening of the weld line since he was using a yield failure criterion. Since his equations are based on regression analyses, the units becoe quite iportant. Nevertheless, Krishnaurthy is iportant in deonstrating that the restraint effect of the bea web cannot be ignored as it increases the flush bolt forces over the extended region significantly. Moreover, his insight into the shift 3

47 in the inflexion point provides a reasonable explanation for Zoeteeijer s observation that the oents can differ on the bolt and weld lines. In Krishnaurthy & Oswalt (1981), the earlier work by Krishnaurthy was extended to include the effect of the bolt heads and the fillet welds in the extended region of the connection. These had not been odelled previously in the FEA analyses of the earlier work and there was a consistent underestiate of the connection stiffness easured in tests, when copared to predictions by the previous odel. Krishnaurthy concluded that this underestiate was because the bolt head and weld detail had been oitted. Besides the design oent equation described in the previous publication, Krishnaurthy & Oswalt referred to an equation for the connection rotation, which had been derived as part of the sae work. That equation was: p f Eqn.13 t r r.048 f b p a b where f b is the extree fibre stress in the bea, t p is the endplate thickness, and a b is the net area of the bolt shank. Krishnaurthy & Oswalt found that the inclusion of the bolt head and weld did give ore accurate results. The proble was then how to account for these details in the previous equations for M d and θ. This was solved by changing the equation for the effective bolt (vertical) pitch, p e, so that: p er = p f 0.15d 0.5 s wf, and Eqn.14 p e = p f 0.5d 0.707s wf where the subscripts r and denote different values for the rotation and oent equations, and s wf is the weld size. They suggested that it would be easier to use a single value for p e and that p e would then be ore appropriate..4. Kennedy s Split Tee Analogy Kennedy et al (1981) presented an iportant study of endplate connections, in which they concentrated on the analogy between the extended region of the 33

48 endplate and the tee-stub the so-called split-tee analogy. Kennedy and his coinvestigators follow Packer and Morris (1977) in considering three failure echaniss in the tee-stub the thick endplate which fails by bolt fracture and no endplate yielding; the thin endplate that fails by yielding at the weld and bolt lines; and the interediate case that fails by bolt fracture but only after yielding of the weld line. Unlike Packer and Morris however, Kennedy et al conceived of these three endplate types, not siply as fixed failure echaniss, but also as odes of behaviour such that an endplate could ove fro one behaviour ode to another, at different levels of loading. Kennedy et al s conceptualisation of the endplate load level is that initially the loads are low and so every endplate is effectively behaving as though it is thick i.e. no yielding and very low prying forces assued zero. As the load increases, if the bolts are large enough so that bolt fracture is precluded, the thick behaviour ceases when the weld line yields. At that point the plate would be behaving as though in the interediate range. If the load increases further and a second hinge fors at the bolt line, then the plate would be behaving as though thin. Thus, the challenge for the was to ensure that the load, at which the transition fro one ode to the other takes place, could be correctly predicted. In their words for ideal design the end plate should be thick under service loads, interediate under factored loads and function as a thin plate at ultiate load. In the odel presented by these authors, the transition fro one behaviour ode to the other was dictated by the endplate thickness for a given geoetry. Thus, for a thick plate, the endplate thickness t p is set at t 1 the thick behaviour cut-off point, where t 1 is given by: t 1 bt f f yf pf b f yf.11 pf t f Eqn.15 b p f y bt f b p f y 3 f yf b pt1 In this equation: 34

49 b, t f and f yf are the width, thickness and yield stress respectively, of the bea flange; p f is the distance fro the bolt line to the face of the bea flange; b p is the endplate width, and f y is the endplate yield stress. The first exact equation for t 1 has to be solved iteratively but the second provides a quick approxiation. The bea flange force is set at its elastic liit F ax (Kennedy et al, 1981), where F ax bt f f When the endplate thickness t p exceeds t 1, the endplate cannot yield before the bea flange force exceeds F ax, so the endplate fails in the thick ode and the prying force Q is zero. yf Kennedy et al also defined a thin behaviour cut-off when the endplate thickness is t 11, such that: t 11 b p f y bt f 3 b pt bt 11 f f f yf yf p f d 16 b p Eqn.16 3 bt f f yf pf d bf yb b p 0.80b p f y where d b is the bolt diaeter and b p ' is the endplate width inus the bolthole diaeters. 3 b f f y yb bt f 3 b p t 11 f yf Again the exact for is iterative and the approxiate solution ay be used to obtain a first approxiation. This equation is derived by taking oents with the axiu bolt line and weld line oents at M p, but with the bolt line oent (width) reduced for the bolt holes. Thus, while the endplate width at the weld line is b p, the width at the boltholes is taken as b p '. In their forulation of M p, a shear 35

50 correction is included as in Sherbourne (1961). The equilibriu equation includes the resisting oent of the bolt M b, where M b 3 d bf yb. 3 When the endplate thickness t p is less than t 11, the endplate is thin at ultiate load and the prying force is at its axiu value, Q ax. The value of Q ax is given by: Q ax b p t p F f y 3 4e Eqn.17 x b p t p in which e x is the edge distance fro the bolt line to the endplate edge, and F is the flange force which has its axiu at the elastic liit as F ax. The authors placed a liit on e x, such that d b e x 3d b. For interediate plates, t 1 t p t 11, the axiu value of the reduced prying force Q' ax is taken to occur when F = F ax, and is then given by: 3 b pt p F ax d b Fax pf Qax f y 3 f yb Eqn.18 4e x b pt p 3e x e x The bolt is sized to be stronger than (F+Q') ax to achieve ductile failure. The approach of Kennedy et al (1981) is very siilar to Zoeteeijer (1974), but is ore sophisticated in that the three endplate odes are explicitly recognised and are treated as behaviour odes in the endplate load level rather than siply failure odes. Moreover, Kennedy et al include the bolt resisting oent M b and a shear adjustent for M p. The work by Kennedy et al highlights the fact that the endplate behaviour is in relation to the applied load on the connection, but fails to ephasise the possibility that under certain conditions an endplate cannot go beyond the thick liit or thin liit because another coponent (such as the bolt) has failed. 36

51 The ain criticiss of Kennedy et al (1981) are that at both the endplate thick and thin liits, F ax is taken to be the elastic liit of the flange force. A thin endplate is inelastic, and there is no justification then for liiting the bea tension flange force to an inelastic criterion. As is shown later also, the inclusion of a prying force in analysing a thin endplate is unnecessary. Secondly, the splittee analogy ignores the fact that the flush region ay not really behave in the sae anner as the extended region. Finally the strain hardening of the weld line and bolt line is ignored..4.3 Murray s Research at Virginia Polytechnic Murray and his co-investigators at Virginia Polytechnic have adapted the work of Kennedy et al into a design odel (Abel & Murray, 199). They use the yield-line echanis of Surtees & Mann (1970), but with the location of the centre of rotation as a variable. The endplate thickness is based on solving the resulting work equation, with the centre of rotation located so as to iniise the internal work. The bolt forces however are deterined fro the Kennedy et al (1981) equations, with the prying force assued to be located at a distance a fro the bolt centreline, where a is given as: 3 t p a d Eqn.19 b This equation, which was epirically obtained, relates the distance 'a' to the endplate thickness and the bolt diaeter. All diensions are in inches. Murray has also investigated the extension of this design approach to extended endplates with ore than two tension bolt rows or with ore than two bolts in each row, as in for exaple, Murray and Borgsiller (1996)..4.4 Soe Other Relevant Models In Australia, Grundy et al (1980) proposed a detailed design procedure, also based on Sherbourne s odel, suitable for different variations of the extended endplate 37

52 connection. The bolts were sized as in Surtees & Mann (1970) but with a twenty percent addition rather than thirty percent. The endplate thickness was decided as in Sherbourne (1961) but without the shear correction, and the internal oent of resistance was for an elastic rather than a plastic failure criterion. Grundy et al went on to suggest a detailed odel for the colun flange behaviour. For unstiffened flanges they used a participating length concept as introduced by Zoeteeijer, and for transversely stiffened flanges they suggested a plastic interaction forula. Unfortunately, they only reported two connection experients, and these experients did not test their hypotheses about the colun flange behaviour. Interestingly, in one of their tests, they reported the developent of a crack in the endplate-to-bea-web weld in the tension zone. They pointed out quite correctly that this showed a failure in Sherbourne s odel to consider copatibility of deforation between the bea flange and web. Bahia et al (1981) tested 4 tee-stubs and 1 extended endplate connections. In their tee-stub tests, they found that the easured bolt forces did not end up in equilibriu with the assued pattern of oents if the weld line oent was assued to be M p. Thus, they corroborated the findings of Agerskov, also on teestubs. Bahia et al hypothesized that the out-of-balance oent could be explained either by a oent on the bolt line (possibly due to prying of the head), or due to a reduction in the diension x (the distance between bolt line and weld line), or by increasing the resistance of the plastic hinge at the weld line. They rejected the first hypothesis on the basis that the bolts failed at the full tensile strength so that the bolt oents did not appear to be significant. They also rejected the second hypothesis on the basis that their observations of the defored endplate shape did not support a reduction in x. They therefore decided that the explanation had to be an increase in the hinge oent due to strain hardening. In order to investigate the strain hardening further, Bahia et al carried out bending tests on siply supported strips of the endplate aterial (yield stress of 9 MPa), applying a central point load and easuring the load deflexion curve. The span of 38

53 the steel strip was conceptualised as being the sae as the span fro the bolt line on one side of the tee-stub flange to the bolt line on the other side. They found that for the saller span to strip thickness ratios, there was evidence of strain hardening with the plastic hinge foring at oents uch higher than theoretically predicted. For a typical value of a plate thickness of 15,9, the hinge fored at.m p the difference was considered to be due to strain hardening. Bahia et al (1981) suggested therefore that the load-deflection curve could be represented as a bi-linear curve with the strain-hardening oent of resistance ph at the discontinuity being epirically deterined to be: ph l l p ; 6 t Eqn.0 t In this forula, p is the unit width theoretical plastic oent of resistance, l is half the span of the siply supported strip and t is the thickness of the strip. Bahia et al suggested a forula for the bolt prying force in tee stubs fro siilar considerations as Douty & McGuire (1965). Based on the prying force forula and the above expression for strain hardening oent, and defining failure of a coponent as the point at which its load-deforation curve ceases to be linear, they established equations for the axiu oent at the weld line in the endplate and for the equivalent oent in the colun flange. For the colun flange they used an effective width derived fro Tioshenko (1959) to allow the to apply the prying force forula, based on the understanding that the colun flange behavior would reain elastic up to the discontinuity. The tensile bolts were all assued to be equally loaded and to have equal prying forces. These prying forces had been noticed to be twice as large at separation as at ultiate loads. It was then possible to establish the bea oent as at ultiate load (when the weld line or the colun flange is at the point where the loaddeforation becoes non-linear). Bahia et al s study is particularly interesting as it includes an attept to explicitly cater for the strain hardening effect at the weld line. It uses Douty & McGuire s 39

54 (1965) prying force forula as the departure point but adopts the oent of resistance ph for the weld line, rather than p. This odel is uch ore sophisticated however, in that the deforation of the colun flange is considered, as in Zoeteeijer (1974) for exaple. But there are questions as to the liits of applicability of Douty & McGuire s forula, which is based on the initial elastic deforation of the endplate around the bolts due to the bolt pretension, and which also includes the initial bolt elongations. Moreover, Douty & McGuire s forula is sei-epirical. A further criticis is that the forula for ph is epirical and does not consider the aterial strength; oreover the siple-support span tests used to deterine ph were inconsistent with the assuptions ade by Douty & McGuire regarding spanning across the tee-stub flange edges. Their value for x does not take the effect of the weld into account as Krishnaurthy does. In accordance with classical echanics, their siply-supported strip plate tests (equation.0) showed a relationship between the level of strain hardening on the one hand, and the plate thickness relative to the bending span on the other hand. The possibility of strain hardening on the bolt line was not considered. Nevertheless, the findings of Bahia et al about the bolt forces not balancing the weld oent are consistent with the findings of Agerskov, who had concluded that the bolt line does not really yield but the weld line strain-hardens. They are also consistent with the findings of Krishnaurthy in the sense that he also accepted that the bolt line would not yield due to what he referred to as a shift in the inflexion point. Krishnaurthy did not consider strain hardening as a critical contributor. However, any strain hardening effects would be asked and included in his regression-analysis-derived coefficients. Krishnaurthy, Agerskov and Bahia et al were all iplicitly considering a echanis in which the bolts fractured after yielding of the weld line but before yielding of the bolt line. This differs fro the thin endplate behaviour revealed by Zoeteeijer (1974). Bahia et al focused on tee-stubs, and ignored the weld effect on the effective span between weld and bolt lines, but they clearly deonstrated that strain hardening does play an iportant role under certain circustances. 40

55 .5 THE SHIFT TO MODELLING BY COMPONENTS.5.1 By Coponents - Yee & Melchers Moent-Rotation Model Soe early researchers had been working on including the connection nonlinearity into non-linear frae analyses. For such researchers, the ephasis was not on the connection proportions but on correctly odelling the connection oent-rotation characteristic, and preferably in a anner aenable to easy inclusion in a frae analysis. Thus, soe of the initial research developed atheatical expressions for the oent-rotation curves of specific connections, by fitting polynoials (Frye & Morris, 1975) or power functions (Krishnaurthy et al, 1979 for exaple), to experiental data. The probles with such attepts are that there is often a wide variation in test connections, the paraeters in fitted polynoials typically have no physical eaning, and the oent-rotation curves therefore cannot be adjusted for changes in connection geoetry and layout. Yee and Melchers (1986) proposed a atheatical odel for extended endplate oent-rotation curves, in which the oent M and the rotation θ at a point in the curve are related by the expression: K i K p Cθ θ M M p 1 exp K pθ Eqn.1 M p where M p is the axiu oent transferred by the connection before strainhardening sets in, K i is the tangential initial stiffness of the oent-rotation curve, and K p is the tangential strain hardening stiffness. The paraeter C was introduced to control the rate of decay of the slope. The physical paraeters are illustrated in Figure.9. In order to deterine the oent M p, Yee and Melchers suggested that six failure odes be investigated to establish the lowest load at which one of these would occur and the connection would begin to behave non-linearly. The failure odes were: 41

56 Moent M Bolt failure in tension Foration of an endplate plastic echanis Foration of the colun flange plastic echanis Shear yielding of the colun web Web buckling, and Web crippling M p K p K i Rotation θ Figure.9 Physical Paraeters in Yee & Melchers (1986) Their odel for deterining the endplate failure load was derived fro Whittaker and Walpole (198), an adaptation of Surtees and Mann (1970). Their colun flange load was based on Packer and Morris (1977). To evaluate K i and K p, Yee and Melchers suggested a by coponents approach, in which the connection rotation was expressed in ters of the deflection at the level of the tension flange, and the connection deflection was deterined by suing up the deflections of the coponent parts endplate and colun flange flexure, bolt extension, colun web panel shear, and colun web copression. Thus, Yee and Melchers had to derive expressions for the coponent deflections. They applied siple bea bending theory and drew on the work of Agerskov (1976) for the endplate and colun flange contributions, and for bolt elongation. The bea tension force was assued to be concentrated in the tension flange, and 4

57 the copression force in the copression flange. The rotation was assued to be around the copression flange centroid. The work of Yee and Melchers was significant in that ost of the paraeters in their odel were physical ones. Moreover, their suggested odels such as Packer and Morris or Agerskov, for establishing M and θ, were directly based on the geoetry of the connection. A really interesting aspect was the use of the coponents approach, in which they deonstrated the usefulness of suing up deflections to obtain the connection stiffness. Unfortunately however, their odel still included the non-physical paraeter, C, and the siple bending theory they utilised ay not really be applicable for soe of the sall connection coponents. Jenkins et al (1986) also produced a design odel that was based on oentrotation characteristics. Their odel was for flush endplates (endplates having no extension beyond the bea tension flange see Section 1.3), rather than extended endplates, but it is entioned here because of certain siilarities to Yee and Melchers proposals. Jenkins et al suggested a bi-linear oent-rotation curve defined by three points the origin, the point at the end of the linear elastic section, and the ultiate point at the onset of strain hardening. They also applied a by coponents approach, considering endplate flexure, colun flange flexure and bolt extension. However, rather than evaluate deflections to obtain rotations as in Yee and Melchers, they evaluated the stiffness of each coponent and calculated the connection stiffness by suing the inverse of coponent stiffnesses. Moreover, instead of deterining the oent and stiffness of each coponent fro behavioural odels as in Yee and Melchers, they drew up design charts for various bea and colun sections and for different endplate thicknesses. These charts were based on Finite Eleent analyses of various configurations, calibrated with experiental results. Rather intriguingly, they reported that they could not get the FE analyses results to atch the experiental ones until they allowed for an enhanced aterial yield stress in the heat affected zone area adjacent to the endplate welds. 43

58 Moent M.5. Studies by Zandonini and Co-investigators Zandonini and Zanon (1988) reported on a study at the University of Trento, in which they tested 10 extended endplate connections five were extended on one side only and the other five on both sides. The Trento researchers approached the proble of characterizing the oent-rotation curve fro the sae preise as Yee and Melchers (1986), assuing that the joint rotation could be broken down into the coponent parts. In this particular study however, they focused only on the contribution of the connection endplate and bolts - and the bea end. Bolting the endplate to a very rigid counter-bea eliinated the colun flange contribution. Zandonini and Zanon took easureents of deflections at three points: Deflections of the endplate at the levels of the bea flanges. Deflections of the tension bolt heads away fro the counter-bea, and Deflections of bea flanges at a point 300 fro the endplate surface. They also easured the tension bolt axial forces by easuring the extensions of the bolts. M p K i K i,red K st M e Figure.10 Paraeters Characterizing Moent-Rotation Curves (Zandonini & Zanon, 1988) Rotation φ The connections tested by Zandonini and Zanon were identical except for the endplate thickness, which ranged fro 1 to 5. As would be expected, 44

59 the connections with thinner endplates had uch higher rotations but lower ultiate strengths nevertheless they were all able to resist the full bea oent so that the bea end buckled locally in each test. In the 1 endplate connections, endplate deforation accounted for as uch as 90% of the total rotation. In no case however was the bolt contribution negligible. The contribution of the bea was high in the thick endplates but very sall in the thin endplates. Each connection was tested to failure in ultiple load cycles. Based on their very careful observations, Zandonini and Zanon arrived at several iportant conclusions about the behaviour of the connection as follows: The initial pretension force in the bolts (snug-tight set at 40% of the bolt s noinal yield strength) tended to disappear after a few loading cycles. This was thought to be due to the fact that the washers defored plastically. (It could also be due to burrs or high spots on the bolt head or nuts leading to lack of fit. This possibility was apparently not considered by Zandonini and Zanon.) The consequence of this was that the initial stiffness of the elastic part of the oent-rotation curve was consistently uch higher in the first loading cycle than in subsequent cycles. This is illustrated in Figure.10, in which the M-φ curve for subsequent loading cycles is shown superiposed on the M-φ curve for the first load cycle. The elastic stiffness of the first cycle is K i, while that for subsequent cycles is K i,red. The stiffness of the strain-hardening part of the curve is shown as K st. Secondly, Zandonini and Zanon found that there was consistently a difference between the axial bolt forces in the flush region and those in the extended region, and concluded that the effect of the bea web in restraining the flush region cannot be ignored. This was especially true for the thinner endplates. They found oreover that the bolts in the thinner endplates were subject to appreciable bending oents as well as the axial forces, and this was ore pronounced for the extended region than the flush region. Because of the bea web effect, Zandonini and Zanon rejected the tee-stub analogy and suggested that the extended region could rather be odelled as a cantilever and the flush region as a plate with a point load. 45

60 Moent M Zandonini and his associates concluded that a first step towards describing the oent-rotation curve would be to establish the five paraeters k i, k i,red, k st, M e and M p shown in Figure.10. Thus, they would have a benchark against which to copare the predictions of any analytical odel of the connection oentrotation curve. M e is the connection oent at the liit of elastic behaviour on the first loading cycle, and M p is the connection oent when the connection is fully plastic. In order to deterine M p on their experientally-obtained curves (to facilitate coparison with later-to-be-developed analytical curves), they initially suggested that M p be defined as the average point between the intersection of the k st and k i lines and the intersection of the k st and k i,red lines (see Figure.10). Zandonini and Zanon (1988) suggested further research to establish echanical odels for deterining these five paraeters analytically. M u M p K p K e,r K e,r M e K i,r Φ e Φ p Φ u Rotation Φ Figure.11 Moent-Rotation Paraeters in Tri-linear Representation (Bernuzzi et al, 1991) In Bernuzzi et al (1991), Zandonini and his colleagues continued to exaine the sae data fro their experients. However, they changed their approach to the evaluation of oent-rotation paraeters fro experiental data. They now suggested a tri-linear representation as shown in Figure.11, with an initial elastic 46

61 portion, then a second phase with a reduced but still elastic stiffness, and finally a third plastic portion. The slope for unloading was taken as being the sae as for the second phase, as shown in the Figure. With this new representation, the characterisation of the oent-rotation curve fro experiental data now becae dependent on the deterination of the strength paraeters M e, M p and M u, and the stiffness paraeters K e,i, K e,r and K p. Bernuzzi et al deterined these paraeters fro their test results, using linear regression to establish the locations of the three lines in the tri-linear representation. The slopes of the lines were then obtained fro the regression analyses, and the values of M e and M p were obtained fro the intersections of the lines; M u was easured directly in each test. The developent of the analytical odels for estiating these paraeters was based on yield-line analyses of the endplate. In order to better understand the endplate behaviour, Bernuzzi et al described a photograetric study of the peranent deforations in the endplate surface, drawing contour lines and establishing the positions of axiu gradient. Based on this study, they concluded that there were three possible failure echaniss in the endplate. Like other researchers before the they noted that the extended region of the thin endplates failed in double curvature by the developent of two parallel transverse yield-lines - across the bolt-line and adjacent to the weld-line. The flush region however was clearly ore coplex, and resebled a partially circular pattern as shown in Figure.1 Bernuzzi et al chose to represent the pattern in the flush region by one very siilar to that used in Surtees & Mann (1970). However, the centre of rotation for the endplate (transition fro copression to tension), was taken as either being at the level of the copression bolts (Mechanis A) or as being at the inside edge of the copression flange (Mechanis B). In Surtees & Mann (1970) the centre of rotation was assued to be at a point halfway along the depth of the bea. Bernuzzi et al s Mechanis A is shown in Figure.13. A second difference was that Bernuzzi et al took the extended region bolt yield-line as eccentric to the bolthole axis by a quarter of the bolt diaeter. 47

62 Negative Yielding Positive Yielding Figure.1 Peranent Deforation Pattern in Thin Endplates (Bernuzzi et al, 1991) They also considered a third echanis for thick plates (Mechanis C), in which the only yield-line was in the extended region along the weld. Hogging lines Sagging lines Figure.13 Mechanis A in Bernuzzi et al (1991) In order to validate the echaniss assued, Bernuzzi et al calculated the M p strength paraeter for each of the tested connections using the three different echaniss. They found that for the 1 endplate the M p calculated for 48

63 Mechanis A had a good agreeent with the experiental value, while the Mechanis C values showed good agreeent with experiental values for the other connections with thicker endplates. However, Bernuzzi et al did not include the details of the yield-line equations, nor did they attept to analytically derive the other strength or stiffness paraeters. Finally, in Bernuzzi and Zandonini (1990), the Trento researchers reported on four additional connection tests carried out to extend the data to include partial strength connections. These connection details were identical to those fro the first series of tests, except that the bea aterial was chosen to be uch stronger so that the connections were partial strength, and secondly, in these tests the bolt oents were easured. The results fro Bernuzzi and Zandonini (1990) confired their earlier results. As expected, the connection strength was reduced since the bea aterial was weaker. The thicker plates also exhibited a changed stiffness in the plastic region. They found oreover that the bolt oents were significant in the thin endplates. The work by Zandonini and his associates is valuable because of the detailed and eticulous nature of their experiental observations, which give insight into the behaviour of the connection in its coponent parts. The tri-linear approxiation used to evaluate paraeters of the oent-rotation curve is useful and relatively straightforward in application. It is clear though that initial stiffness is a variable phenoenon, being affected by bolt pre-tension and the connection lack of fit. There is also a question as to whether or not the iddle portion of the tri-linear curve is actually a reduced elastic stiffness region as they ter it. There is already yielding taking place on soe yield-lines at that point, so the slope of that line is not siply an elastic portion inus the effects of pre-tension and lack of fit. That would be true for the unloading portion of the curve, but not for the iddle line in the tri-linear loading curve. In the test instruentation used by Zandonini and his associates, the connection rotations were easured at the bea flanges so that the rotations easured for the 49

64 thin endplates (where the rotation axis would have been between the flanges), possibly underestiate the connection coponent and correspondingly overestiate the bea coponent. This would not however affect the qualitative validity of the ajority of their conclusions. It is probleatic though that their analytical calculations of M p were reportedly based on the assuption that the rotation axis was at the copression flange, as this is at variance with the yieldline position in Mechanis A..6 EUROCODE 3 ENDPLATE MODELS Part 1 of Eurocode 3 was initially released in 199 as DD ENV , which was a draft for developent with voluntary usage in EU eber states (Eurocode 3, 199). In this docuent, bea-to-colun connections were covered in Annex J, which was revised in That revision is referred to here as Revised Annex J of DD ENV : 199 (Revised Annex J, 1994). In the final version of Eurocode 3 which is a andatory standard, joints are treated as a separate sub-part 1.8 rather than as an annex to sub-part 1.1. This was published in Britain in 005 as BS EN : 005 (Eurocode 3, 005). Thus, there have been three odels for extended endplate connections in Eurocode 3 to date. These are discussed below..6.1 Extended Endplate Model of Eurocode 3 Annex J The by coponents approach was refined and codified in Eurocode 3 (199). In DD ENV199 the connection was introduced into the global analysis of the frae as pinned, rigid or sei-rigid based on stiffness; and as pinned, full strength or partial strength based on strength. The connection was considered conceptually as a rotational spring with a known secant stiffness S j acting to soe oent resistance M Rd. Thus, the ephasis was on predicting the oent resistance and the stiffness. 50

65 Connection Strength The tension bolt forces were deterined first - either as a plastic distribution (all bolts at yield) or as a linear triangular distribution (furtherost bolt fro copression flange at yield and others resisting forces proportional to ratio of the distances fro the copression flange). These bolt forces could then be adjusted to a value copatible with the forces transitted by each coponent, checking each bolt row individually and as part of the group of bolts. The chosen distribution was aintained plastic or triangular. The connection oent was then derived fro the bolt forces in each coponent, taking the lever ar at the centroid of the bea copression zone. For a triangular bolt distribution the extended and flush tension bolt forces would first be assued at particular levels, and then adjusted to be copatible with the coponent failure forces. The difference in the plastic ethod was that the bolt forces corresponding to failure of the endplate and colun flange were deterined first, and then checked against yielding of the bolts. The bolt forces had to be copatible with the strength of five coponents the endplate strength in bending, the colun flange strength in bending, the colun web in tension, the colun web in copression, and the colun web in shear. The bolt itself was the sixth coponent under consideration. The bending strength of the endplate was deterined based on a yield-line odel using the tee-stub analogy. Following Zoeteeijer (1974), an effective tee-stub length concept was used as a eans to relate the possible yield-line patterns in the endplate (and the colun flange), to that of a tee-stub. The flush and extended regions were considered separately, with the bea flange taken as the tee-stub web for the extended region (half of a tee-stub really), and with the bea web taken as the tee-stub web for the flush region. The effective or participating length of the analogous tee-stub would depend on the yield-line pattern being considered. Though the yield-line patterns were not described in Eurocode 3 (199), the participating length values were given in 51

66 clauses J and J of the code, for colun flanges and endplates respectively. The yield-line patterns assued could then be easily deduced. The participating lengths in the code and the yield-line patterns iplied by these are given below for the extended endplate with four tension bolts. The participating length considered for each region was the least of: l eff in extended region Yield pattern iplied b p Two straight lines at weld and bolt lines.. 0.5w + x e x Half-circular pattern around both bolt-holes as a group, interrupted at free edge x + 1.5e x, Half-circular pattern around each bolt-hole, interrupted at free edge. 4. π x Circular pattern with bolt-hole as centre. l eff in flush region 1. α Half-circular pattern, interrupted at free edge, but constrained by the bea tension flange.. π Circular pattern with bolt-hole as centre. In these expressions (see Figure.14), x is the distance between the extended bolt centreline and the nearest face of the bea flange, less 0.8 ties the leg length of the bea flange endplate weld. e x is the distance fro the extended region bolt centreline to the end of the endplate, easured perpendicular to the bea tension flange. e is the distance fro the bolt centreline to the nearest edge of the endplate, easured parallel to the bea tension flange. w is the bolt pitch. b p is the endplate width. α is deterined using a graph, and is a function of two ratios: λ 1 and λ 1 1 ; e 1 e 1 5

67 1 or is the distance between the flush tension bolt centreline and the nearest face of the bea web, less 0.8 ties s ww (the leg length of the bea web endplate weld). is the distance between the flush bolt centreline and the nearest face of the bea flange, less 0.8 ties s wf (the leg length of the bea flange endplate weld). e b p W 0.8a x e x 0.8a e 0.8a (a) Extended region (b) Flush region Figure.14 Noenclature used in Eurocode 3 (199) Annex J In Eurocode 3 the strength of these analogous tee-stubs is based on three tee-stub failure odes, siilar to Kennedy et al (1981). Thus, ode 1 failure assues two parallel yield-lines on either side of the web of an equivalent tee-stub one yieldline at the bolt line and the other at the weld line - with coplete yielding of the flange on the four yield-lines. Mode is bolt failure cobined with yielding of the flange on the weld lines, while ode 3 is bolt failure only with no endplate yielding. The Eurocode 3 (199) equations for the design tension force F t.rd in the tee-stub web are: 4Mpl,Rd Mode1: Ft,Rd Eqn. Mode : F t,rd M pl,rd n Bt,Rd Eqn.3 n Mode 3: F t B Eqn.4,Rd t, Rd 53

68 n is the saller of the edge distances for the endplate and the colun flange but n 1.5. B t,rd is the design tension resistance for a bolt. M pl,rd is the plastic oent of resistance per each yield line, which is given by: M pl,rd l 0.5 eff t f MO y This is the failiar expression for plastic oent per unit length of aterial, ultiplied by the participating length of the yield-line and divided by a aterial partial safety factor. Endplate Stiffness The secant stiffness S j of the connection at a given oent M, was to be calculated as: Eh1 t wc S j Eqn.5 i Fi k i Fi.Rd where M < M Rd and M Rd is the connection design resistance oent. h 1 is the distance fro the flush tension bolt row to the centre of resistance of the copression zone. μ 1 and k i are the odification and stiffness factors respectively for coponent i. F i and F i.rd are the applied force and the design resistance respectively for coponent i. t wc is the colun web thickness. The subscript i referred to the six coponents that had to be considered, nubered as follows: 1. Colun web shear zone. Colun web tension zone 3. Colun web copression zone 4. Colun flange tension zone 5. Bolts tension zone 54

69 6. Endplate tension zone The endplate stiffness was based on the forula: k 6 t 1 in which 3 p t wc but t k 6 4 as before e 3 p The factor μ 1 was taken as 1 for the first three coponents and = others. t wc h1f M 1.Rd Rd for the Since Sj could be calculated at any value of M, it eant that a designer could deterine a point on the oent-rotation curve corresponding to M. In effect therefore, Annex J was providing a eans to predict the oent-rotation characteristic for the connection. The designer could however choose to apply a bi-linear or ulti-linear siplification instead. Rotation Capacity The ductility or rotation capacity of the connection was to be assessed via rules of thub. Thus, a connection was considered to have adequate ductility for plastic analysis purposes, either if the oent resistance was governed by colun panel shear or by bending of the endplate or colun flange. The latter was subject to the condition that either the colun flange or the endplate was governed by a ode 1 failure in bending. The failure ode could be confired by the check 1 for ode 1, where β is the ratio of 4M pl.rd / to the su of bolt forces, calculated for both the colun flange and endplate at each bolt row. λ = n/ If the endplate and colun flange were governed by ode failures however, the rotation capacity θ Cd was to be calculated as: 1 10,6 4 cr Cd Eqn.6 1,3h 1 55

70 The subscript cr on β indicates the lower of the two values calculated for the endplate and the colun flange. The extended region was to be excluded in calculating β cr. The rotation capacity θ Cd refers to the rotation of the entire connection, and includes both elastic and plastic contributions. Criticiss of DD ENV : 199 Annex J The Eurocode 3 (199) approach to connection resistance effectively extended Kennedy s split-tee analogy and Zoeteeijer s participating (effective) length concept, by applying the split-tee to the flush region as well. As entioned earlier, the yield-line pattern in the flush region is actually quite coplex and bears no reseblance to a tee-stub. There is no allowance for strain-hardening in this strength odel, even though the code explicitly allows for ductile partial-strength joints. The allowed option of adopting a triangular linear bolt distribution is difficult to justify since that iplies a thick (and inefficient) elastic endplate, leading to bolt failure. The stiffness odel of Eurocode 3 (199) was particularly criticised in the literature. In SCI (1995) for exaple, it was reported that the stiffness odel of Eurocode 3 Annex J does not give accurate predictions, and designers are warned against reliance on it in critical cases. In their paper on the need for the Annex J revision, Weynand et al (1996) ention that the odel led to contradictory results an unstiffened endplate was predicted to be stiffer than a stiffened endplate. There is no ductility (rotation capacity) odel in Eurocode 3 (199) for ode 1 failures. Moreover, the liits for checking ode 1 failure are again based on the tee-stub analogy, and bear little reseblance to actual behaviour in the flush region. The forula for θ Cd in ode failure sees to have a sei-epirical basis, and no ductility liit is given to provide a basis for accepting or rejecting the calculated θ Cd. The inclusion of elastic coponents in θ Cd is probleatic given the criticiss of the initial stiffness odel, and given that initial stiffness has been known to vary for noinally identical connections (see Chapter four). 56

71 .6. The Revised Annex J Model In the Revised Annex J (1994), the strength odel was unaltered in its philosophy except that the (elastic) triangular bolt force distribution was taken out. Soe other changes were as follows: An alternative expression was included for calculating the tee-stub design tension force in Mode 1 failure, as follows (Revised Annex J, 1994): Mode1: F T,Rd (8n e w )M pl1,rd Eqn.7 n e ( n) w where e w is d w /4 and d w is the diaeter of the bolt head (or nut) across points. This alternative equation was derived by assuing that the forces at the bolt line are not concentrated at the centreline but are uniforly distributed under the bolt head or nut. It leads to a higher bolt force for ode 1. There was an attept to deterine the liits of odes 1 and failure in ters of the endplate geoetry in Eurocode 3 (199), but this was taken out of the Revised Annex J. The chart used to deterine α (for the yield-line case of sei-circular yielding in the flush region next to the stiffener) was also extended to include ore values of α. The nuber of yield-line patterns checked for a 4-bolt extended endplate increased for the extended region, so that the prticipating lengths were now: l eff in extended region Yield pattern iplied 1. 4 x + 1.5e x, Half-circular pattern around each bolt-hole, interrupted at free edge on end of plate.. e + x e x Corner patterns around each bolt-hole, in a quarter-circle shape b p Two straight lines at weld and bolt lines w + x e x Half-circular pattern around both bolt-holes as a group, interrupted at free edge on end of plate. 57

72 5. π x Circular pattern with bolt-hole as centre. 6. π x + w Circular patterns around both bolt-holes but with portion between holes also yielded. 7. π x + e Half-circular pattern around each bolt-hole, interrupted at free edge on edge of plate. l eff in flush region 1. α Half-circular pattern, interrupted at free edge, but constrained by the bea tension flange.. π Circular pattern with bolt-hole as centre. In these participating lengths the sallest value was adopted for each region, and the sybols ean the sae as before. The stiffness odel was where ost of the changes to Annex J took place. The basic forula for the stiffness S j at a oent M j.sd less than the design oent resistance M j.rd, was now given (Revised Annex J, 1994) as: S j Ez 1 k i i Eqn.8 with k i = stiffness coefficient for coponent i z = lever ar µ = a stiffness ratio S j.ini /S j, and S j.ini = the initial tangential value of the stiffness S j 1.5M µ was to be deterined fro M For a bolted endplate, ψ =.7. j.rd j.sd but 1 Eqn.9 Thus, the definition of µ iplies a constant ratio between the initial tangential stiffness on the oent-rotation curve, and the secant stiffness of the curve at failure. This ratio was defined as equal to 3 for an endplate connection. Weynand et al (1996) explained that the µ values were sei-epirical, based on tests and 58

73 paraeter studies. Fro coparing the equations for µ and S j, it is evident that the iplicit forula for S j.ini would then be (Revised Annex J, 1994): Ez S j.ini Eqn.30 1 k i i For an extended endplate, the coponents whose stiffness coefficients k i were to be considered included the colun flange in bending, the endplate in bending, and the tension bolts. The endplate stiffness for each tension bolt row was given as: k leff t p Eqn.31 3 where l eff is the participating (effective) length for an equivalent tee-stub as deterined for the strength odel. 3 leff,ini t p In Weynand et al (1996), the sae forula is given as k5 where l 3 eff,ini is the value of participating length required to establish the initial stiffness fro a tee-stub odel. Thus, l eff,ini = 0.85 l eff. The participating length l eff of course relates to the strength odel. Their odel for k 5 is shown in Figure.15. F 0.63F 0.63F F 0.13F Figure.15 Forces acting on tee-stub stiffness odel in Revised Annex J (based on Weynand et al, 1996) Secondly, when the first plastic hinge fored on the tee-stub flange, this was assued to for at the weld line, and to have a value of 0.3F.. (When this 59

74 value is scrutinized however, it iplies a 8.5% prying force rather than 6%). By equating this oent to the plastic oent of resistance for a flange width of l eff,ini, Weynand et al (1996) calculated the bolt force F el corresponding to this oent of 0.3F. as F el l t eff,ini f y Eqn They then obtained the bolt force at the (ultiate) design value by ultiplying F el by 3/. Clearly, there are inconsistencies in this stiffness odel, with the use of a 8.5% prying force in one area and a prying force of 6% in another area. In the aterial odel used in Revised Annex J strain-hardening is oitted, so that there cannot be prying forces on the tee-stub at ultiate collapse fro the odel, or the plate oent of resistance on the bolt line would exceed the plastic oent. It sees questionable to siply scale up bolt forces derived on the assuption of axiu prying, so as to obtain ultiate bolt forces that occur when prying forces are very low (and are here iplicitly assued to be zero). But this is what happens when F el is ultiplied by 3/ above. In the ductility or rotation capacity odel of Revised Annex J (1994), a bolted connection was again considered to have adequate rotation capacity for plastic analysis purposes if the oent resistance was governed by a ode 1 failure in bending of either the endplate or the colun flange. In addition however, the endplate thickness t p was liited to a value: t p = 0.36d f ub f Eqn.33 y where d is the noinal bolt diaeter, f ub is the bolt ultiate tensile strength, and f y is the endplate yield strength. This appears to be a sei-epirical rule. The calculation for rotation capacity θ Cd in ode failure was now oitted. 60

75 .6.3 The SCI Moent Connections Manual In 1995, the British Steel Construction Institute published a design guide on oent connections (SCI, 1995). This guide and Revised Annex J were in preparation at the sae tie period, and it was based partly on Eurocode 3 (199) and partly on BS 5950: Part 1 (1990). The resistance oent or strength odel was again based on the use of effective tee-stubs with all the yield line patterns of Revised Annex J being allowed for to deterine the partipating length l eff. Unlike Eurocode 3 (199), but siilar to the revised Annex J, the SCI anual considered only the possibility of a plastic distribution of bolt forces, oitting the triangular bolt distribution. SCI (1995) however included a triangular distribution upper liit on the bolt forces, where the endplate ay be too thick to defor sufficiently to allow the full plastic distribution. SCI (1995) did not include the Annex J stiffness odels neither the original nor the revised version. Instead, the rule was adopted that full-strength connections used in braced or single-storey portal fraes and designed according to the guide could be considered rigid. For ulti-storey unbraced fraes, the designer was encouraged to adopt thick, full-strength and rigid endplates. These endplates would fail in ode 3, but as full-strength connections, the bea would fail first. In order to deterine if the endplate was thin enough for a full plastic distribution (ode 1 failure), SCI introduced a siilar rule of thub to that in Revised Annex J: d t fub fy 0.53d fub fy Eqn Thus, the acceptable endplate thickness for ode 1 was 46% ore than the corresponding liit in Revised Annex J. The two liits apply to different aspects of the odel however, with the Revised Annex J liit referring to the tee-stub 61

76 odel for a single bolt-row, and the SCI liit applying to the behaviour of ultiple rows in the actual connection. There was however a section of the guide dealing with wind-oent connections for unbraced fraes. These are connections that are assued to be pinned when designing for gravity loads, but assued to be rigid under wind loads. This philosophy leads to partial-strength connections which ust be sufficiently ductile. SCI (1995) suggested as a rule of thub that these connections be proportioned so that the endplate thickness is about 60% of the bolt diaeter, to establish the right balance of strength, stiffness and ductility. The strength odel to be used in design would be the sae as for the full strength connections, but with the designer liited to connections that fail in ode 1. SCI (1995) presented standard connections for which the ductility had been confired by testing. Thus, we find that the philosophy of SCI (1995) was siilar to Eurocode 3 (199) Annex J but with additional checks taken fro BS As in Eurocode 3 (199), there was only liited guidance in the area of ductility, however standard details were presented which had been verified by tests..6.4 The Model of BS EN BS EN (Eurocode 3, 005) was published in 005 and replaces Annex J. The design philosophy for extended endplate connections is unchanged, with the strength and stiffness being calculated by coponents, using the analogy with teestubs. The possibility of a triangular bolt distribution (which was criticised in SCI, 1995) is retained. However, it is reserved now for slip-resistant connections and connections subject to ipact, vibration and load reversal (except due to wind). The strength odel of Revised Annex J has been retained, with the three failure odes and the tee-stub participating lengths. As in Revised Annex J, an alternative equation is given for Mode 1, which takes the width of the bolt head into consideration. The equations for Modes 1 and are unchanged fro Revised 6

77 Annex J. A variation fro Revised Annex J however, is that the possibility is now considered of an endplate failing in a cobination of Modes 1 and without prying forces. The criterion for this fourth no-prying ode to apply is that: 8.8 A L Eqn.35 3 s b 3 leff,1t f where, as before, is the distance fro the bolt centreline to the nearest face of the teestub web, less 0.8 ties the leg length of the weld, A s is the tensile stress area of the bolt, L b is the bolt elongation length (grip length + ½ bolt head height + ½ nut height), l eff,1 refers to the effective tee-stub length l eff for ode 1, and t f is the thickness of the tee-stub flange. The participating lengths (and so the yield-line patterns) considered for endplates and colun flanges in bending, are the sae as those considered in Revised Annex J (1994) seven for the extended region, and two for the flush region when there is only one row of flush tension bolts. The stiffness odel of Eurocode 3 (005) is again the sae as for Revised Annex J. However, the factor of 0.85 in the value of l eff,ini has been altered to 0.9, so that l eff,ini = 0.9 l eff. That effectively resolves the inconsistency in Revised Annex J where a prying force of 5% is iplied in one equation and a value of 8.5% is iplied in another equation. The prying force applied in both cases is now 6%. Eurocode 3 (005) also gives a siplified ethod for the stiffness of extended endplates with only two tension bolt-rows. Rather than calculate k eff,r and k eq for each bolt-row fro k eff,r i 1 1 k i, r, and k k h eff,r r r eq ; z eq Instead, k eff,r is calculated for the extended bolt-row, and k eq is then calculated using twice that value for each bolt-row, and taking z eq as the average value of h r 63

78 for both bolt-rows. This siplification is said to lead to a lower value for the rotational stiffness S j. As in Revised Annex J, there is no odel given for rotation capacity of extended endplates, but the sae rule of thub is provided. Thus, the rotation capacity is assued satisfactory when the design resistance is governed by (ode 1) bending of the endplate or bending of the colun flange, as long as either the colun flange or the endplate has a thickness t such that t < 0.36d f ub f, where d is the noinal bolt diaeter, f ub is the bolt ultiate tensile strength, and f y is the endplate or colun flange yield strength. y Discussion of Eurocode 3 odels Eurocode 3 (005) is open to the sae criticiss as Revised Annex J (1994) and DD ENV (Eurocode 3, 199) before it. The yield-line pattern in the flush region is actually quite coplex and bears no reseblance to a tee-stub, so that the use of an equivalent length is questionable. As reported later, experients suggest that the yield-line pattern distribution ay change as the flush region becoes inelastic, so that a participating length that is suitable at the early onset of inelastic behaviour ay not be suitable for the entire range of behaviour. Eurocode 3 allows certain joints to be designed as ductile, but the underlying aterial odel excludes strain-hardening. This is contradictory as ductile inelastic strains iply that there ust be strain-hardening. The tee-stub odel for stiffness is based on an assued geoetry that is not explicitly stated in the code itself (edge distance e = 1.5 see Figure.15 in Section.6.), and the odel iplicitly assues large prying forces at collapse a further contradiction. Fro the perspective of this work, the ost iportant criticis however, is the lack of a suitable odel for estiating rotation capacity, which would be required for serviceability calculations on partial strength connections for exaple. In Eurocode 3 (199) the possibility of a ode endplate failure being sufficiently ductile for plastic analysis was accepted. However, this was reoved in the 64

79 subsequent revisions. In effect therefore, the ductility criterion becae ore stringent in Revised Annex J by coparison with Eurocode 3 (199), and ode has now been excluded fro plastic analyses. For the connection tests reported later in this thesis (chapter four), with an M0 Grade 8.8 bolt (average f ub = 788 MPa) and Grade 300WA endplate (average f y = 309 MPa), the Revised Annex J and Eurocode 3 (1995) rule-of-thub would lead to a axiu endplate thickness of This liit is rather conservative as shown later. For the sae connection tests (M0 bolt, average f ub = 788 MPa, average f y = 309 MPa), the SCI rule-of-thub would lead to a axiu endplate thickness of This is uch less conservative than the Eurocode 3 (005) requireent. For use in partial-strength (wind oent) connections however, SCI (1995) liits the endplate thickness to 60% of d b. For an M0 bolt that would ean a axiu endplate thickness of 1..7 SOUTH AFRICAN EXTENDED ENDPLATE STUDIES Truby ade position of this yield-line a variable Hogging lines Sagging lines Figure.16 Yield-line Pattern of Truby (1995), fro Bernuzzi et al (1991) Dekker (1986) carried out an investigation of extended endplates at the University of Pretoria. Dekker applied siple bea theory to the endplate tension region, and used a nuerical ethod (finite differences) to obtain a solution for the flush region as a plate. The endplate geoetry was taken into account using a flexibility 65

80 approach. Dekker s odel was then copared with test results. Dekker s work was liited to the elastic range however, and neither his odel nor his tests considered inelastic behaviour. Thus, his odel is not really applicable to the ephasis in this thesis. Truby (1995) proposed a odel of extended endplate connections to establish the connection ultiate oent and the corresponding rotation, for a thin extended endplate connection. Truby carried out a yield-line analysis of the Mechanis A yield-line pattern of Bernuzzi et al (1991) to obtain the endplate tension bolt forces. This pattern was illustrated in Figure.13 and is reproduced here again for convenience as Figure.16. Truby however ade the location of the lowest hogging line a variable in his odel, so that the odel could only be solved iteratively using a purpose-written coputer prograe. In Truby s prograe the effect of tension bolt elongations was included as an option. The possibility of assessing bolt forces in the extended region as a fixed proportion of forces in the flush region was also included as an option. To establish the corresponding rotation at the endplate yielded oent, Truby considered the deflection of only the extended region of the endplate fro the assuption that this portion of the endplate yields first. His deflection is obtained by assuing that the portion fro the bolt line to the weld line is in double curvature bending, with equal oents at the bolt line and weld line. He then assued a oent-curvature relationship across a section of the endplate fro the bolt line to the weld line, and deterined the deflection fro the oent of the areas of the curvature diagra. There are two key criticiss of Truby s work. The yield-line forulation is coplex and could only be solved iteratively with a coputer odel. This would not be suitable for everyday applications. The output fro his coputer siulations are useful however as they show that the inclusion of the bolt elongations does not significantly affect the yield-line analyses. The second criticis is fundaental and relates to the calculation of rotations. He assues 66

81 that the endplate deflection is governed by the deforation of the extended region. Observation would suggest however, that the endplate rotation is governed by the deforation of the flush region. This is further discussed in Chapter five. Truby did attept to cater for strain hardening in the aterial odel assued in his coputer prograe, but he conceded that large strains would be incopatible with the yield-line analysis. Truby also did not attept to deterine the connection rotation capacity, but only the rotation at the fully yielded point taken as the ultiate oent in his forulation. 67

82 3. EXPERIMENTAL WORK In order to have a better understanding of the ductility behaviour of relatively thin extended endplates, five connection tests were carried out as part of this study. The first test with 1 endplates and a second with 10 endplates were pilot tests carried out to verify the test setup and to rectify probles with the instruentation. Three other tests were then carried out with two connections per test, involving the testing to failure of 10, 1 and 14 endplates. The intention in these tests was to gain insights into thin extended endplates and increase the available data to include endplates as thin as 10. Thus, there were five connection tests in total as follows: Pilot Test A 10 endplates Pilot Test B 1 endplates Test 1 10 endplates Test 1 endplates Test 3 14 endplates 3.1 SETUP OF CONNECTION TESTS A crucifor arrangeent was adopted in the tests, with two beas connected into each flange of the colun at the sae level. Thus, two bea-to-colun connections were tested siultaneously. Figure 3.1 shows the crucifor arrangeent used. The test specien beas were supported at their far ends on beas running perpendicularly on trestles. The load was then applied to the top of the colun stub using a hydraulic jack. In this way, the lower bea flanges were in tension while the upper flanges were in copression. The load was applied to the colun top with a square load button screwed onto the ra of the jack, with the button bearing on a recess in a load plate welded to the colun. Thus, the load point was restrained against lateral and longitudinal displaceent. 68

83 Figure 3.1 Setup for the Connection Tests The colun web was also laterally restrained against out-of-plane rotation just above the bea tension flanges, using struts of adjustable length, with rollers at their far ends that fitted into guides fixed to the load frae. These restraints were necessary to prevent out-of-plane rotation of the colun (leading to unwanted secondary effects), and to prevent instability under load. The colun had two pairs of 10 web stiffeners at locations opposite the bea flanges at the joint. There was also a 16 plate welded to the top of the colun where the load would be applied, to distribute the load evenly through the cross-section and prevent bearing failure. It was our ai to test the endplate in isolation while iniizing the interaction with the colun flange. In order to replicate a practical connection we chose not to use an unrealistically stiff colun, but rather to provide stiffeners at the flange levels and accept inor colun deforations. 69

84 During the pilot test the colun was instruented with an inclinoeter to easure any in-plane colun rotations. In the latter tests this easureent was discarded and the botto part of the colun was instead restrained with snug fitting vertical guides to prevent any in-plane rotation. The colun restraints are shown in Figure 3.. At the bea-to-colun connection end, each bea was welded to its endplate with E70XX 10 fillet welds (flanges - both sides) and 6 fillet welds (web - both sides). These welds were chosen to exclude the possibility of the connections failing by weld fracture. Recessed load button Lateral restraint: Colun out-of-plane rotation Figure 3. Lateral restraint of the colun Lateral restraint: Colun in-plane rotation 70

85 At the siply supported end, each bea was supported on back-to-back double channel cross-beas, which were supported in turn on laced and battened towers secured to the ground. Above the support, each bea had its (upper) copression flange restrained against lateral oveent but not against rotation. This was done by providing a pair of ribbed bar guides fitting snugly on either side of the bea flange. Thus, the beas were laterally restrained but allowed to ove longitudinally and to rotate. This was to prevent the developent of extraneous axial forces and end oents due to rotational restraint, during tests. Rotational and longitudinal freedo was ensured using a rocker consisting of a half-round bar supported on needle roller bearings, with a load cell between the half-round and the rollers. The rollers allowed the bea to ove longitudinally. The bea end had a recess welded on with the sae shape as the rocker, to reduce the likelihood of the rocker shifting fro beneath the bea during testing. Essentially therefore, the bea end was on a line support. In the first pilot test we supported the half-round on the button of a load cell so as to have a point support at each bea. This proved to be unsuitable as the arrangeent becae unstable at large deflections. This realisation was brought hoe in draatic fashion as during the test a load cell at one end suddenly shot out fro its position. We therefore changed to the line support described above. The two support arrangeents are shown in Figure 3.3. The choice of endplate geoetry was ade to reflect typical South African practice and also to facilitate coparison with the predictions and tests of other researchers. The endplate diensions and geoetrical details are given in Figure 3.1. The plate was 430 x 180 wide, with diaeter bolt holes for M0 Grade 8.8 HSFG bolts. The bolt holes were located at a gauge of 100 syetrically about the plate centreline, with an edge distance of 40 on each side. The extended region row of bolts was 50 fro the plate end as can be calculated fro the diensions in Figure 3.1. The distance fro the tension bolts centre to the bea flange surface was ade as sall as feasible for tightening of 71

86 bolts (58). Thus, the tension bolt pitch is not a round figure but rather 16., which is (noinal flange thickness). (a) Initial unstable point support (b) Stable line support Figure 3.3 Supports at Test Bea ends 3. THE TEST SPECIMENS My choice of section sizes for the tests was based on the following considerations: The use of average -sized sections/details that would be applicable in a wide variety of situations. Section sizes and details that are relatively coonly used in South Africa, and which are typically used together. The need for failure of the test speciens to be initiated by the endplate rather than by failure of the bea flanges or colun flange. Based on these considerations, I elected to use a 305 x 165 x 41 I section (305 UB 41) as the bea in all the tests, with a 03 x 03 x 60 H colun (03 UC 60) both in Grade 300WA. The use of a 305 series bea facilitates coparison with several well-docuented published test results using siilar sized beas (Bernuzzi et al (1991), Zandonini & Zanon (1988) and Jenkins et al (1986). It was 7

87 considered that the 305 UB 41 and 03 UC 60 sections could typically go together, and would be suited to a ediu load in a coercial or industrial structure. These parallel-flange section sizes are in coon usage in South Africa. The intention in the tests is to liit bending of the colun flange so the colun flange contribution to connection deforation is sall or negligible. The 03 UC 60 has a 14 flange, and web stiffeners are introduce at the bea copression and tension flange levels, to achieve this. Both sections are Class 1 plastic design sections (both flange and web) under the provisions of SANS 1016 (005). The bea web is Class 1 in bending but not in axial copression. Fro the South African Institute of Steel Construction s Handbook (SAISC, 1997), these section sizes have the following noinal diensions: Table 3.1 Noinal Diensions for Test Section Sizes Designation D b t w t f r 1 h w A x x kg/ kg/ x165x41 I x03x60 H In Table 3.1, D is the overall depth of the section, b is the breadth, t w is the web thickness and t f is the flange thickness. The diension r 1 is the root radius at the web-flange joint, and h w is the clear distance fro the top of the root radius above the botto flange to the botto of the root radius below the top flange. The bea ass is denoted as in kg/ and the cross-sectional area as A. Three endplate thicknesses were used in the tests 10, 1 and 14. These were all in Grade 300WA steel. A 14 endplate was taken as the upper liit, since this was the axiu value at which I expected to find the endplate behaving as thin, based on the literature reviewed. 10 was selected as a lower liit as there are few tests reported in the literature with thinner endplates than 1. 73

88 Thus, the 10 endplate test would help extend the range of available endplate test results. I did not extend the lower liit to 8 as an 8 endplate would be considered unreasonably thin, relative to the bea size, in current practice. Typical South African practice is to standardize connection bolts on M0 and M4 sizes for Grade 8.8 HSFG. I therefore used M0 Grade 8.8 HSFG bolts in all the tests Bea and Colun Material Properties Table 3. Material Properties for Connection Tests Young s Yield Yield Hard g Hard g Ultiate Modulus stress strain strain Modulus Stress GPa MPa GPa MPa Col flange Col web B flange (1) B web (1) B flange () B web () plate (pilot) plate (pilot) plate (Test 1) plate (Test ) plate (Test 3)

89 Stress MPa The bea and colun aterial was donated by fabricator eber copanies of the Southern African Institute for Steel Construction, and fabricated by the in their shops to typical tolerances and standards. The beas and coluns were taken fro one length each, and the endplates fro one plate each for a given thickness. Off cuts were obtained and used to deterine the aterial properties, in tensile tests. Two coupons were taken per bea or colun flange (for each flange), and two coupons per bea web. Also a iniu of four coupons were taken per plate two in the longitudinal direction and two fro the transverse direction. The aterial test data is included in Appendix A, and the averages of the properties deterined are suarized in Table 3.: The aterial properties easured in the tensile tests were essentially tri-linear with a linear elastic portion, then a flat yielding plateau with zero slope, and finally a strain-hardening region with a reduced but non-zero slope. Thus the aterial behaviour has been suarized by the oduli of the elastic and strainhardening regions, and the stresses at which yielding coenced and at which strain-hardening coenced. We were unable to easure the strain-weakening behaviour because of the likelihood of causing daage to the extensoeter, however we did deterine the fracture load and so the ultiate stress in each test. A typical stress-strain curve derived in one of the aterial tests is shown in Figure 3.4 to illustrate the tri-linear nature Strain Microstrain Figure 3.4 Typical Stress-Strain Curve fro an Endplate Coupon 75

90 As can be seen in Table 3., the aterial for the beas cae fro two sources. The ones arked () were used in the 10 endplate tests, while the ones arked (1) were used in all other tests, including the 10 pilot tests. The actual diensions of the beas, coluns and plates were easured, and these and the aterial properties above have been used to copute the actual bea and colun section properties, which are reported in Table 3.3. The yield oent M y for the colun and beas has been derived fro the following equation: M y I xx.f y Eqn 3.1 y where the suation is for the flanges and web; I xx is the second oent of area, f y is the yield stress and y is half the section depth. M y and M p both refer to bending of the bea (and colun) about the strong axis. The values given for the plates are calculated per eter length. Table 3.3 Actual Section Properties for Test Speciens Flange Web Elastic Plastic Yield Plastic thickness thickness Modulus Modulus Moent Moent x 10 3 x M y M p kn- kn- 03UC60 Col UB41 B (1) UB41 B () plate/ / 1 plate/ / 14 plate/ / 76

91 3.. Bolt Material Properties All the bolts used in the aterial and connection tests were M0 Grade 8.8 HSFG bolts taken fro a single production batch. In order to deterine the aterial properties for the bolts, saples were tested to failure in pure tension, while recording the applied load and corresponding strains. Strain is easured as a surrogate for the bolt extension. The literature suggested that bolt strains would be related to the bolt grip length i.e. the total thickness of plies (colun flange, endplate and washer) gripped between the bolt head and the nut. Thus, I needed to deterine stress-strain characteristics for the different grip lengths to be used in the actual connection tests. These corresponded to the 10, 1 and 14 endplate thicknesses. Figure 3.5 Layout of Bolt Yoke We designed a yoke that could be gripped in the Asler tensile testing achine, and which would allow the bolt and nut assebly to be pulled apart in pure tension. The layout of one of the syetrical halves of the yoke is shown in Figure 3.5, and a picture of the test is shown in Figure 3.6. The yoke consists of 77

92 two syetrical halves with each half having a base and an upper part attached to a rod. The base has a recessed hole in which the tested bolt with its washer and nut is fitted, and the rods for both halves are then claped into the tensile testing achine so the bolt can be pulled apart. Three yokes with different recess depths were used to siulate three different grip lengths. Figure 3.6 Bolt Material Test in progress Hole for gauge wires Figure 3.7 Strain gauging the bolt Gauge position 78

93 Bolt Axial Stress (MPa) The bolt strains were easured by putting strain gauges onto the bolt shank, just adjacent to the threaded region. The gauges were placed to easure longitudinal strains along the length of the bolt. In order to ensure that bending effects could be eliinated, three gauges were used on each bolt, with the gauges at 10 degrees around the bolt circuference. It was necessary to achine the bolt surface flat at the position of each gauge, to prepare a flat surface for the gauge and to prevent the gauge fro daage during tests. The achined region was 6 wide and 10 long, so that the noinal bolt diaeter was reduced locally by 0.46 and the area reduced by The actual shank diaeter and actual achined area was easured for each bolt, and the actual areas were calculated and used to convert forces to stress. Holes were drilled into the bolt head to pass the gauge wires through without daaging the, and the installed wires and gauges were all coated with non-conducting lacquer. The drilled holes had to continue as a groove into the shank for a short length so the gauge wires did not pinch with bolt tightening. The bolt odification for strain gauges can be seen in Figure plate 6-1 plate 8-14 plate Bolt Gauge Strain x 10^-3 Figure 3.8 Bolt Stress-Strain Curves Two bolts were tested for each of the three required grip lengths. Each test was carried out to failure. The stress rate was kept at about 3 MPa/sec, and the strain was kept to about 0.005/s fro the yield point to fracture. In all tests, the bolts failed in tension by fracturing across the threads. The exact yield point was 79

94 deterined graphically. The stress-strain curves for the bolts are essentially bilinear with no interediate plateau. These are shown in Figure 3.8. The curves can therefore each be represented in ters of the initial elastic odulus and the strain-hardening odulus, together with the yield point and the ultiate fracture point. The easured bolt properties are suarized in Table 3.4 for each of the tested grip lengths. These bolt properties provide a eans of converting bolt strains easured in the connection tests, into actual bolt forces. The average yield stress easured was MPa, versus the noinal yield value of 640 MPa. The average ultiate stress easured was 788. MPa versus the noinal value of 800 MPa (but there would be stress concentrations at the threads). The ratio of yield to ultiate stress is 9% rather than the noinal 80%. Thus, a bolt failure would be ore brittle and unexpected and possibly ore catastrophic. The change in grip length fro one test to another did not appear to have a consistent effect. Therefore, although the easured values for each endplate thickness are used wherever appropriate, grip length was not considered as a variable after these tests. Table 3.4 Measured Material Properties for Bolts Grip Length (Excluding washer thickness) Young s Modulus (GPa) Yield Stress (MPa) Yield Strain (10-3 ) Harden Modulus (GPa) Ultiate Stress (MPa) Ultiate Capacity (kn) 4 (10 plate grip) (1 plate grip) (14 plate grip)

95 3.3 THE TEST INSTRUMENTATION In order to understand the behaviour of the connections tested, we needed to deterine the following paraeters for each test bea connection to the colun. 1. The connection oent and the corresponding rotation.. The tension bolt forces in the extended and flush regions. 3. The stress distribution patterns along and across the endplate, and in the bea adjacent to the connection. The connection oent could be deterined fro the load applied to the connection. The load transferred into each of the two connections was easured fro a load cell at each far end bea support, with the jack load being onitored as a check on the load cell easureents. 90 Load fro Jack Support on Load Cell 300 Tension Bolts Support on Load Cell - LVDT Not to scale - Inclinoeter Figure 3.9 Test Instruentation The rotation easureents were ade with linear voltage-displaceent transducers (LVDTs) and with inclinoeters (see Figure 3.9). LVDTs actually 81

96 easure displaceent but this is easily converted to rotation once the exact distance fro the colun axis is known. Inclinoeters easure angles directly. The positions of soe LVDTs and inclinoeters were changed after the first test, and Figure 3.9 shows positions that were constant for all the connection tests. Each bea had an inclinoeter at the bea support and another at 300 fro the endplate face. A fifth (dual-axis) inclinoeter on the colun web was used to onitor in plane and out of plane colun rotations. Siilarly, each bea had an LVDT on the bea colun flange adjacent to the colun face (90 fro the colun face the closest distance practicable), a second on the copression flange at 300 fro the colun face, and a third at the bea support. There was also an LVDT on the tension flange at 300 fro the colun face, as a check on the copression flange LVDT. The easureent at 300 approxiates a distance equal to the bea depth away fro the colun face. This is coonly taken as the extent of the joint region. These LVDTs at the colun face and at the joint liit were ounted off the colun face, so that they easured bea displaceent parallel to the colun axis, while the bea support LVDT was ounted off the support steelwork and easured displaceent of the bea support under load. The displaceent transducers were intended as a check on the inclinoeter readings. However, probles with faulty inclinoeters led to us discarding the inclinoeter readings and using the LVDT data only. The colun inclinoeter readings becae redundant after the pilot test and were discontinued, as lateral restraints were introduced to prevent in-plane and out-of-plane rotation of the colun. Guides were introduced at the level of the bea copression flanges to prevent out-of-lane rotation. Other supports were fixed in place at the base of the test rig to guide the lower part of the colun and prevent in-plane rotation. In order to deterine tension bolt axial forces, bolt strains were easured with three strain gauges at 10 per bolt, as in the bolt aterial tests. Two of the four tension bolts were instruented per connection one in the tension flush region 8

97 (iediately above the bea tension flange in Figure 3.9) and the second in the extended region of the connection aking four instruented bolts in each test. These easured bolt strains could then be converted to stresses and axial force, using the stress-strain curves obtained in the bolt aterial property tests for the given grip length, and the easured bolt diaeter, to effect the conversion. In the two pilot tests and in the Test (1 endplate test), I attepted to easure the deflection of the endplate away fro the colun at the level of the bea tension flange. In order to do this, a hole was drilled through the colun flange and horizontal slots were cut into the colun web, to allow an LVDT to bear on the endplate surface. Cover plates were therefore welded across the colun fro flange toe to flange toe, to counteract any weakening effect due to the cuts. This easureent was discontinued after the first test because it was difficult to anoeuvre the LVDT into position. Thus, the colun web cut-outs and cover plates were not used in the 10 and 14 tests. Figure 3.10 Strain Gauges on the Endplate and Bea End Strain gauges were placed on the endplate and bea ends as shown in Figure There were 13 gauges on each endplate including three rosettes, and 10 gauges on each bea including two rosettes. The bea gauges were placed 83

98 with their axes along the bea length, at 5 fro the end of the bea-endplate weld. When the strain gauges on the bolts are included, a total of 58 strain gauges were onitored during each test, for both beas, with ten of these being rosettes. For convenience of referral, the endplate gauges are labelled using a grid syste as shown in Figure Thus, for exaple the upperost gauge on the left in the figure is referred to as gauge A1. Gauges A1-3, B1, B, and C1-3 are in the extended region of the endplate; gauges A6, A8, B6-7 are in the tension part of the flush region, while gauges B4-5, B1-13, C4, C8-11, and C13 are on the bea end web and flanges. By coparison with Figure 3.1 which gives the endplate diensions, Figure 3.10 has been rotated to have the bea tension flange above the copression flange, as this is the ore typical presentation in literature. The strain gauges used on the bolts, endplates and bea ends were ostly Kyowa single gauges KFG--10-C1-11 bonded with CC-13A glue a rooteperature-setting cyanoacrylate. These are self-teperature-copensating (SELCOM) gauges designed to operate around abient teperature on steel speciens with a linear expansion coefficient of 11 x 10-6 /degree Centigrade. All the tests were carried out in an indoors laboratory environent with no exposure to direct sunlight. Abient teperatures indoors during tests varied by only a few degrees Centigrade, with 0 degrees Centigrade as an average value, and there were no teperature gradients across the speciens. SELCOM gauges are copletely self-copensating under those conditions, fro about roo teperature up to about 60 degrees Centigrade. Thus, teperature copensation easures were not required in the tests. The three gauges arked as rosettes in Figure 3.10 were KFG--10-D These are rosettes with the three resistive eleents being siilar to the eleent in the KFG--10-C1-11. Thus, the behaviour is siilar. 84

99 Strain easureent was carried out for each gauge, using a 1-gauge Wheatstone bridge i.e. a bridge with the active gauge on one gauge ar and three precision resistors (10 Ω) on the other three ars. Little portable bridges were anufactured for this purpose, each with its potentioeter. To reduce errors fro noise in long lead wires (3 length) the Wheatstone bridge output was aplified before being fed into the recording ultiplexer. Calibration of the strains was based on the specified gauge factors, which ranged fro.05 to.15 for different batches. For the KFG--10-C1-11 the use of a specified gauge factor rather than a calibrated gauge factor leads to an estiated 5% error for plastic strains i.e. above to µstrains. This was considered an acceptable error range. The resistive eleent in the KFG--10-C1-11 is long, which eans the easured strains are really averaged over a length. This was also considered a reasonable level of accuracy. 3.4 THE TEST PROCEDURE Each test was carried out in three steps as follows: 1. The bolts were initially ade finger-tight, then load was applied slowly via the jack to approxiately 30 kn at the jack (15 kn- per connection), and then unloaded, to allow the endplates to bed in and seat properly.. The bolts were then ade snug tight and bolt strain readings were taken. Clause 1.1. of the South African structural steel design code SANS :005 requires bolts in a slip-critical connection (which would be a typical application for an extended endplate), to be pretensioned. The pretension for an M0 Grade 8.8 HSFG bolt should be at least 14 kn (Table 7). The code provides for the pretension to be easured by the turn of the nut (Table 8) or with the use of a direct indicator. This approach is endorsed in Clause of SANS 001-CS1:005. We have chosen to use the turn of the nut ethod as this is ore typical in everyday South African practice, and we consider this to be better than the other ethods. Thus, the bolt pretension was applied by 85

100 applying a third turn to each bolt. The bolt strains were again recorded after the pretension was applied. 3. The load was applied until a connection failed. In the loading we initially controlled the test based on the load applied (a constant rate of load application), but then oved to displaceent-based control once it was clear that the connection had begun to yield and/or defor. In test (which was the first test chronologically), the load application was actually carried out in four load cycles of load and unload an elastic cycle first, then three plastic ones with the last cycle continued to failure. In these tests, failure was defined as either the connection becoing incapable of sustaining a load any longer, or as fracture of a connection coponent. 86

101 4. CONNECTION TEST RESULTS The results for Tests 1 3 are given below in the rest of this chapter. The Pilot Test results are only included in the qualitative descriptions of section 4.1 as the instruent readings for the pilot tests are not available. The data fro each test can be distinguished into four categories the observations and failure odes, the connection rotation data, the bolt strain gauge data, and the endplate and bea strain gauge data. I have distinguished between the data for both beas in each test, differentiating the as a Bea A and a Bea B. Thus, in Test for exaple, Bea 1A refers to the A bea in the 1 endplate test. 4.1 OBSERVATIONS IN CONNECTION TESTS Test 1 Observations Figure 4.1 Pilot Test A in progress 87

102 Figure 4.1 shows the specien in Pilot Test A during the conduct of the test. In both Pilot Test A (the pilot 10 test) and Test 1 (the actual 10 test), the bending of the endplate was about two axes. There was considerable bending along the length of the endplate, especially about the bea tension flange. There was also clearly transverse bending across the width of the endplate, with this being particularly evident in the flush tension region. (a) Endplate fracture & deforation (b) Buckle in copression flange Figure 4. Fractured endplate fro Test 1 The endplate yielding started around the extended and flush region tension bolts and initially appeared to be rotationally syetrical around each bolt-head, thus suggesting a circular yield-line pattern. As the test progressed however, the yielding, the progression of which could be distinguished by the flaking off of ill scale, becae siilar to that described for thin endplates in Surtees & Mann (1970) and Mechanis A of Bernuzzi et al (1991). As the test progressed further, 88

103 the yielding progressed into straight lines rather than the initial circular pattern, until the endplate fractured in the flush tension region with straight longitudinal cracks running parallel to and adjacent to the bea web welds. There were also transverse cracks in the endplate extended region, parallel to and adjacent to the bea tension flange weld. The longitudinal cracks are apparent in Figure 4. (a). In Figure 4. (a) it is also possible to see a kink in the bea profile where it is welded to the endplate, at the shear bolt level. Thus, the bea profile is in copression to the shear bolt level. In Test 1 the test was stopped only when the crack next to the bea tension flange weld developed into a coplete transverse fracture across the endplate width on one connection, so that the endplate tore into two pieces. Figure 4.3 Beas 10A and 10B after the test The fracture of the endplate in Test 1 was alost laellar in nature, tearing at a shallow angle through the endplate, rather than in a clean break see Figure 4. (a). (In Pilot Test A, which was on a noinally identical saple, the test was stopped when a bolt in the extended region fractured on one connection). The arrows on Figure 4. (a) show the transverse fracture and the longitudinal crack 89

104 on the endplate. Prior to the endplate fracture, the bea copression flange had developed a local buckle. This is shown in Figure 4. (b). By coparison with bea 10B that failed, the local buckling in bea 10A was less noticeable. Figure 4.3 shows both beas 10A and 10B after testing. The ore pronounced local buckle in 10B is evident, as also the greater peranent deforation. In Figure 4.3, we notice that each endplate is peranently defored such that there is a bulge away fro the colun flange, between the level of the flush tension bolts and the shear bolts Test Observations Figure 4.4 Cracking in Bea 1A endplate In Test with the 1 thick endplates, there was noticeable flaking of the endplate as early as the first plastic cycle starting first on the transverse line adjacent to the weld in the extended region, then in a transverse line around the bolts. The bending of the endplates was initially quite slight, and only becae 90

105 pronounced in the second plastic cycle. There was ore noticeable buckling of the bea copression flanges towards the end of the test. There were loud cracking noises at 300 kn (approxiately 150 kn- per connection) and 308 kn, and the actuator load began to drop shortly afterwards, going fro a recorded axiu of 311 kn to about 305 kn at failure. Test was terinated when the endplate on bea 1A sheared - fracturing into two pieces - on the weld line in the extended region. On exaination, endplate 1B was seen to have also cracked on the weld line. In addition, both endplates had fine cracks at the root of the bea web weld, on both sides. These longitudinal cracks extended fro the tension flange to about half the bea depth. Figure 4.5 Endplate for Bea A fro 1 Endplate Test 91

106 The transverse fracture is clearly visible in Figure 4.4 and the longitudinal crack can just be seen in that figure. There were also fine cracks in the bea flange weld on the flush side, also visible in Figure 4.4. The failure ode was identical to that observed in pilot test B. As with the 10 endplates in Test 1, the deforation pattern during the tests was siilar to that described by Bernuzzi et al (1991) for thin endplates (Mechanis A). Again, the bea that failed (1A) appeared to have ore pronounced local buckling in the copression flange than bea 1B. By coparison with the 10 endplates, the 1 endplates defored less both longitudinally at the bea tension flange, and transversely across the endplate width, about the bea web. The cracks along the bea web were finer but the buckling of the bea copression flange was ore pronounced and there was a slight but noticeable curvature of the tension flange adjacent to the endplate as well. The flush side cracks in the bea flange weld which were reported for the 1 endplates, were not visible in the 10 endplates. The local buckle in the bea copression flange can be seen in Figure 4.5 for bea 1A. The sae bulge is observable in the endplate, between the flush tension bolts and the shear bolts. 9

107 4.1.3 Test 3 Observations Figure endplate Test 3 in progress Figure 4.6 shows the deforation of the endplate during the course of the 14 endplate test - Test 3. In Test 3 the endplate deforation differed fro that in tests 1 and. There was very little of the transverse bending about the bea web that was evident in the other tests, and the partial circular pattern in the flush region about the tension bolts, was not discernible. Nevertheless, there was significant bending in the endplate longitudinal direction, about the tension flange. 93

108 Location of fractured bolt Figure 4.7 Endplate 14B fro Test 3 There were fine longitudinal cracks along the bea web but there was no sign of cracking adjacent to the bea tension flange. The buckling of the bea copression flange was pronounced (see Figure 4.7), but there was no discernible curvature in the tension flange adjacent to the endplate. The test was stopped when a bolt fractured suddenly in the tension flush region of Bea 14B. The endplate with a issing flush region bolt can be seen in Figure 4.7. By coparison with tests 1 and, the 14 test endplates did not defor as readily, and as entioned above there was little cracking and little apparent transverse bending. The bulge in the endplate between the flush tension bolts and the shear bolts was also observed here but was less pronounced than in the other two tests. 94

109 It can be seen in Figure 4.6 that the colun flange has defored noticeably at the flush bolt level. In Figure 4.7 taken after copletion of the test, the residual plastic deforation of the colun flange is uch less. It is evident therefore that ost of the colun flange deforation in Figure 4.6 was elastic. By coparison with Test 1 and Test (Figures 4. a and 4.5), there was only a very slight plastic deforation of the colun flange at the flush bolt level in Test 1. In Test there was no deforation of the colun flange probably because of the additional stiffener. 95

110 4.1.4 Discussion of Test Observations and Endplate Failure Modes On the near-side face of the endplate (the face visible on the connection), the 10 and 1 endplates fractured in the sae locations adjacent and parallel to the bea web, and at the bea tension flange on the extended side. The location of the cracks in the flush region see to suggest that the initial seicircular pattern grows in size as the yielded area spreads, until it is restrained by the web and the bea flange, and then becoes ore or less straight lines. The initial circular yield area and the subsequent restraint by the bea web/flange can be seen in the photograph of Figure 4.8 for bea 1A. Yielding evident in a circle around bolt head Figure 4.8 Extent of yielding observed in Test Yielding evident in transverse band across the bolt line 96

111 Figure 4.9 Cracks on far-side of 10 endplate in Pilot test A When the 10 and 1 connections were unbolted after the tests, cracks were observed on the far-side of the connections around the tension bolt holes, in a radial pattern. This is shown in Figure 4.9 for bea 10A fro Pilot test A. These cracks suggest that negative yield lines are developing radially fro the bolt holes. They support the observation that the pattern was initially circular and centred around the bolt holes. The 14 endplates did not behave in the classical thin anner. There was yielding on the weld line of the extended region, and that region behaved like the tee-stub Mode of Eurocode 3. The bolt failure was in the flush region rather than the extended region. The flush region had signs of the sae circular yielding 97

112 around the tension bolt-heads as in the other tests, but these did not develop into the sei-circular pattern. Thus, instead of considering it a Mode tee-stub, the behaviour of the flush region is probably better regarded as siilar to the thin plates, but with the bolt being too weak to develop the full yield pattern. Far-side cracks on plate Near-side cracks on plate (a) Initial yielding in experients (b) Negative Yielding Positive Yielding Final yield pattern in experients Figure 4.10 Yield-line Pattern proposed in this thesis (c) Yield line proposed (after Bernuzzi et al, 1991) Does not yield here We conclude that the yielding in the flush region is initially in a sei-circular pattern, but this develops into straight lines along the web and flange as the test continues. For reasons that becoe clear later out ephasis is the final pattern rather than the initial. It eans then that the yield line pattern of Bernuzzi et al (1991) for thin endplates (1 and 15), which they referred to as Mechanis A, is relevant here. On close exaination however, it is evident that the positive yield line shown at the level of the shear bolts in Figure 4.10b cannot develop. There is no evidence of yielding or cracking at that level in any of the tests, and deforation of the endplate in that region cannot be large enough for the yield line to develop. Thus, in this thesis, the proposal of Bernuzzi et al (1991) has been odified as shown in Figure 4.10c. We note that the largest cracks on the far side of the endplate around the bolt holes (Figure 4.9) coincide with the positions 98

113 where negative yield lines are located in the proposed yield line pattern of Figure 4.10c. This further confirs the appropriateness of the chosen yield line pattern. It should be noted that the yield line pattern proposed here is also very siilar to the earlier proposal by Surtees & Mann (1970), but with the yielding extending to the shear bolt level. Thus, the validity and relevance of this pattern is wellestablished. Soe observations that were coon to all three tests are as follows: In all cases, yielding (as inferred fro the flaking of ill scale) started on the bolt line in the extended region. Subsequently, there was yielding on the weld line in the extended region as well as around the flush bolt. The greatest endplate deforation was around the bea tension flange. The curvature was higher in the extended region adjacent to the bea flange than on the flush side, and no doubt this is why those endplates that fractured did so in the extended region. Cracks in the endplate consistently developed in the stiffer flush region first, around the bolt-holes and adjacent to the bea web. There appears to be a relationship between larger local buckling curvatures in the bea copression flange, and the failure of the connection. Under oent, the bea profile initially rotates about a point in the copression flange depth. At large oents approaching the connection oent capacity however, soe of the bea web sees to coe into copression also to about the shear bolt level. This can be seen clearly in Figures 4. and 4.7. The endplate reains flat against the colun flange between the bea copression flange and the shear bolt level. There was a slight peranent curvature (bulge) of the endplate between the level of the flush tension bolts and the shear bolts. 99

114 Figure 4.11 Fractured Extended Region Bolt fro Pilot Test A An interesting issue for consideration is the difference in failure odes between pilot test A and test 1. The test endplates and bolts were noinally identical, nevertheless pilot test A failed by fracture of the extended bolt while bea 10B in test 1 failed by endplate fracture. The fractured bolt fro pilot test A is shown in Figure We notice that it was the instruented bolt that failed. As a atter of interest, the flush region bolt that fractured in test 3 was not an instruented bolt. 4. BEAM ROTATION DATA FROM THE CONNECTION TESTS In the connection tests, bea rotations were easured using LVDTs and inclinoeters. Each bea had three LVDTs that easured bea rotation directly - iediately adjacent to the colun (90 fro the endplate face), at 300 fro the endplate face, and at the bea support 1000 fro the endplate face. The value of 300 is approxiately the bea depth, and it represents the point coonly accepted as the liit of the bea to colun joint. The easureent at 300 was carried out to allow coparison of the results with other published work. Previous investigators have defined the boundary of the joint at a bea depth away fro the colun face, and any have taken their rotation easureents at that distance fro the endplate face, in order to establish the total joint rotation. However, since bea end rotations could be quite large in soe cases, it was considered desirable to also easure the rotations adjacent to 100

115 the endplate hence the LVDT at 90 fro the face. The 90 value reflects the practical difficulty of ounting the LVDT agnetic clap on the colun face while resting the needle-point off the bea flange iediately adjacent to the endplate. The LVDTs at the bea supports were ounted off the supporting steelwork while the others were ounted off the colun face. Besides the LVDTs, inclinoeters were ounted on each bea at the sae positions as the LVDTs (300 fro the face and at the bea support). There was also a dualaxis inclinoeter on the colun stub itself to easure in-plane and out-of-plane rotations of the colun stub. However, the inclinoeter readings at the bea support and at 90 fro the colun face tended to be erratic in Test 3 (14 test). The LVDT readings were generally less erratic than the inclinoeter readings. I have therefore focused ore on LVDT easureents of joint rotations at a bea depth fro the colun face, and these are used for coparison purposes. The bea rotation data is reported as oent-rotation curves in subsequent sections. The raw oent rotation curves for test have been cleaned-up into loading envelope versions. This was necessary as the load in test was applied though four load and unload cycles. The load envelope versions have been obtained by reoving the unloading readings for each cycle, thus obtaining an envelope of readings Moent-Rotation Curves for Connection Test 1 The oent-rotation curves for test 1 are shown in Figures 4.1 and 4.13 below. In the Bea 10A curve, as one would expect, the rotations at the joint are uch higher than those for the colun face (90), and those for the bea support are again higher than those for the joint. The sae situation occurs in the Bea 10B graph, however the difference between the joint and the colun face readings is now less, while the difference between the joint and bea support readings is higher. 101

116 Connection Moent (kn-) Using joint values, the highest oent recorded for Bea 10A was kn- or 75.6% of the bea M p (09 kn-), at a rotation of 87. illi-radians. The corresponding value for Bea 10B was kn- at illi-radians. The swivel point is the oent at which the transition knee between the initial linear elastic region and the next linear inelastic region occurs. For bea 10A the swivel was at 81.1 kn-, and for 10B it was at 79.5 kn-. In this test, it was bea 10B that failed by fracture of the endplate, so that the test had to be terinated. It sees likely therefore that the connection on bea 10A could have supported a higher rotation Rotation (Radians x 10^-3) Col Face Joint B Sppt Figure 4.1 Moent Rotation Curves for Bea 10A, Test 1 The dip in connection oent, at about 70 kn- on bea 10A, is thought to be due to slip at the bolts. The M0 bolts with a noinal diaeter of 0 were in holes. Thus, a axiu slip could occur of the endplate when the endplate friction is overcoe. The later dip, at about 140 kn- in the sae bea, could be due to cracks developing in the endplate. The difference in rotations at siilar load levels, between both beas, is possibly due to differences in bolt pretension forces or slight colun rotations. 10

117 Connection Moent (kn-) Rotation (Radians x 10^-3) Col Face Joint B Sppt Figure 4.13 Moent Rotation Curves for Bea 10B, Test Moent-Rotation Curves for Connection Test In Test, the load was applied in four load cycles. Hence, the experiental curves include unloading and re-loading portions. These had to be cleaned-up for readability and ease of coparison with the other tests. To illustrate, the raw results are given below for the joint readings in Figures 4.14 and 4.16, along with the clean versions for the colun face, joint and bea support in Figures 4.15 and The first reading in each test was a non-zero oent. This was retained as is without adjustent, but a zero reading is included in the clean graphs. In this test also, unlike in the other tests, the colun was reinforced with plates welded across the flange tips in the tension area. It sees clear fro the literature that the bulk of the inelastic rotations are contributed by the endplate (e.g. see Bernuzzi et al, 1991). Therefore the effect of this reinforceent on oentrotation is considered negligible. 103

118 Connection Moent (kn-) Connection Moent (kn-) Rotation (Radians x 10^-3) Figure 4.14 Raw Moent Rotation Curve for Bea 1A at joint, Test Rotation (Radians x 10^-3) Col Face Joint B Sppt Figure 4.15 Moent Rotation Curves for Bea 1A, Test The swivel oent for beas 1A and 1B respectively was 95.4 kn- and 97.1 kn-. The highest connection oent easured for 1A was kn-, at a rotation of 67.3 illi-radians (joint values). The corresponding value for bea 1B was kn- at 47.3 illi-radians. However, at the final rotation of 77.5 illi-radians the load was still increasing. The plastic oent M p calculated for the bea in this test was kn-. Thus, the highest connection oents of 104

119 Connection Moent (kn-) Connection Moent (kn-) kn- on bea A, and kn- on bea B, are respectively 0.76 and 0.74 of M p. Bea 1A sustained this oent for a short while before fracture Rotation (Radians x 10^-3) Figure 4.16 Raw Moent Rotation Curve for Bea 1B at joint, Test Rotation (Radians x 10^-3) Col Face Joint B Sppt Figure 4.17 Moent Rotation Curves for Bea 1B, Test When the fracture crack coences in bea 1A, the oent-rotation curve goes through a little loop (see Figure 4.15). This appears to be a easureent error fro the shock. The quasi-static cycling of the loads in Test does not 105

120 Connection Moent (kn-) appear to have had any significant effect on either the outcoe of the tests or the behaviour of the connections. This aspect is not studied further in this thesis Moent-Rotation Curves for Connection Test Rotation (Radians x 10^-3) Col face Joint B Sppt Figure 4.18 Moent Rotation Curves for Bea 14A, Test 3 Soe probles were experienced in Test 3 with voltage fluctuations on the inclinoeters, leading to variations in the colun face and bea support readings. The test ended when a flush region bolt fractured on bea 14B. At that point the oent on bea 14A was kn- at a rotation of 64.7 illi-radians, while the oent on bea 14B was kn- at 80. illi-radians. The swivel oents are 14.6 kn- on 14a and 10.4 kn- on 14B. The oent-rotation results are given in Figures 4.18 and

121 Connection Moent (kn-) Rotation (Radians x 10^-3) Col face Joint B Sppt Figure 4.19 Moent Rotation Curves for Bea 14B, Test Discussion of Test Rotation Data The oent-rotation curves easured at the joint are all presented in Figures 4.0, 4.1 and 4. with both connections in a test per each figure. The Eurocode 3 classification criteria (see Section 1.6) have been superiposed on all three figures, in order to classify the test connections. To apply the Eurocode 3 stiffness criteria, a bea span is required. For ost practical applications bea spans are between 15D to 5D, where D is the bea overall depth. Thus, for the 305 UB 41 I sections tested in this thesis, 6 ( 0D) would be a practical bea span. The average value of E (Young s odulus) for the bea flanges in the connection tests is 08.4 GPa. Siilarly, an average value for I (second oent of area), based on easured diensions for the beas, is 84.5 x Therefore: 5EI b /L b = kn- (Rigid for sway frae) 8EI b /L b = 3408 kn- (Rigid for non-sway frae) 0.5EI b /L b = 1463 kn- (Pinned) 107

122 Connection Moent (kn-) It can be seen therefore that in relation to strength all these connections are partial strength as the strength exceeds the 0.5M p criterion for the to be pinned. In relation to stiffness, none of the tested connections would qualify as rigid in an unbraced frae and so would be considered sei-rigid, but in a braced, non-sway frae the 10B, 1B and 14B connections would all just qualify as rigid. All the connections would qualify as ductile also, as the axiu oent rotations are uch larger than 30 illirads (see Surtees & Mann, 1970). An observable feature in these figures is that there are differences in the oentrotation curves for noinally identical connections. In test 1 and test 3 (Figures 4.0 and 4.1 respectively), the connections that failed 10B and 14B exhibited larger rotations than their counterparts that did not fail. Nevertheless, the connection oents were very siilar in 10A and 10B when test 1 was terinated. Likewise, 14A and 14B had siilar oents when test 3 was terinated EI b /L b 8EI b /L b EI b /L b 0.5M p 10 A B Rotation (Radians x 10^-3) Figure 4.0 Coparison of Moent Rotation Curves - Beas 10A and 10B On exaination, it can be seen that connections 10B and 14B both had higher initial slopes (stiffness) than connections 10A and 14A respectively. A likely explanation is that connections 10B and 14B had higher bolt pre-tension forces, or a slightly larger bolt diaeter. (The turn of the nut ethod we adopted in this 108

123 Connection Moent (kn-) thesis is known to produce variable results, but it is the ethod of preference in everyday South African structural steel practice). Other possible reasons include the possibility of slight deviations in weld size fro the noinal value, or differences in specien syetry between the A and b speciens. The possibility of colun rotation was obviated with lateral restraint of the colun below the connection level; however, there ight be inor differences in the noinally identical speciens. Nevertheless, since the speciens A and B were taken fro the sae bea length and the endplates were cut fro the sae plate, any differences in the speciens would be inor. Yet another explanation would be the incidence of higher residual stresses in the stiffer speciens, possibly related to a greater spread of the heat-affected zone adjacent to the welds. It sees then that a higher pre-tension force or a slightly larger bolt diaeter in noinally identical connections, as well as differences in the weld-related residual stresses, ay lead to a higher initial stiffness, and also see to lead to greater rotation capacity. This last is a surprising observation as it is counter-intuitive. One would suppose the initially stiffer connection would rotate less EI b /L b 8EI b /L b EI b /L b 0.5M p 1 A 0. 1 B Rotation (Radians x 10^-3) Figure 4.1 Coparison of Moent Rotation Curves - Beas 1A and 1B 109

124 Connection Moent (kn-) EI b /L b 8EI b /L b EI b /L b 0.5M p 14 A B Rotation (Radians x 10^-3) Figure 4. Coparison of Moent Rotation Curves - Beas 14A and 14B When the individual test readings for tests 1 and 3 are considered however, one observes that at each point in the test prior to failure, the oent applied to each of the A and B connections reains approxiately equal. Thus, the difference in initial stiffness does not have an ipact on the oent-resisting capacity of the connection, and the difference in rotation behaviour cannot be attributed to differences in applied oents. Again, the onset of yielding sets in at approxiately the sae level of applied oent for each of the A and B connections in both tests. The superior rotation perforance of 10B and 14B copared to their counterparts only starts when the connections have started to yield. A plausible explanation is that the a slightly larger bolt allows the flush or extended tension bolts to restrain the endplate ore effectively, so that yielding progresses faster and further in the connections that fail. Thus, the yield line pattern described in the previous section is better developed in the specien that fails. The reduction in the odulus of elasticity due to widespread yielding is then what leads to the observed iproveent in rotation capacity. In Figure 4.1, beas 1A and 1B do not appear to have confored to the preceding observations as 1B has a greater initial stiffness than 1A that failed. However, there was an intervening factor in the developent of the 1B oentrotation curve, just after it got to the highest oent attained of 0.74M p or

125 kn-. This was the point at which the first loud cracking noises were heard during the test when both connections were resisting about 150kN-. The second cracking noise was when Bea 1A was resisting 154 kn-. On exaination afterwards, it was noticed that both endplates had cracked, and the test terinated when bea 1A fractured. It sees likely then that the crack in bea 1B was severe enough to affect its oent resistance capacity and this explains why connection 1A attained the failure oent first. The curve for 1B does appear to be flattening out just before the crack, and one can speculate that it would have crossed the 1A curve and exhibited greater ductility if the crack had not occurred. We find then that where the connection initial stiffness was sufficiently high enough that the connections behaved in a rigid fashion rather than sei-rigid (at least for a braced frae), the connections exhibited iproved rotation capacity. The presence of large residual stresses in the area adjacent to the bea flange weld (heat-affected zone) would explain why this area is susceptible to cracks at large strains. In Figure 4.3 all six experiental curves are presented together for ease of coparison. The oents resisted by each connection are also given in Table 4.1, together with the corresponding rotations, to facilitate the coparison. The swivel points in Table 4.1 refer to the point in the oent-rotation curve where the change in slope fro the initial stiffness to the second stiffness (leading to the axiu oent) is coplete. We notice that the ratio of this swivel oent to the axiu connection oent changes with endplate thickness. The ratio varies fro 0.50 for 10B to 0.69 for 14A. The plastic coponent of the rotation is also deterined for each curve in Table 4.1. The plastic oent of resistance of the endplate aterial is directly proportional to the square of its thickness. Thus, one would expect bea 1A and 1B to fail at higher oents than beas 10A and 10B, given the difference between the 14 connections and the 1 connections. It is surprising to note that both of the 10 endplate connections (10A and 10B) exhibit ultiate oent capacities that are higher than the 1 endplate connections even for 1A where the failure ode is identical to 10B. It appears likely then that 1A cracked preaturely due to a loss 111

126 in ductility in the heat affected zone of the bea flange weld. Connection 10B failed in the sae location, but noinally identical welds ay involve varying aounts of heat input, depending on the skill of the welders. The shaded rows in Table 4.1 are suary values of oent and rotation for the three tested endplate thicknesses. The swivel values are obtained by averaging the A and B connections, while the axiu values are based only on the failed connection. Table 4.1 Moents and rotations in connection tests 1-3 Swivel point Maxiu point Connection Rotn. Moent Rotn. Moent Failure Mode -rads kn- % of M p -rads kn- % of M p Bea 10A Did not fail but endplate cracked Bea 10B Endplate fracture 10 e/plate Bea 1A Endplate fracture Bea 1B Did not fail but endplate cracked 1 e/plate Bea 14A Did not fail Bea 14B Flush bolt fracture 14 e/plate In Figure 4.3 we see that the noinally identical test 1 connections (bea 10A and 10B) have quite different initial stiffnesses. Thus, there is a concern about the predictability of the initial stiffness. 1 The corresponding rotation to the axiu oent is reported here on the preise that the connection has failed once it begins to shed its oent. However, this definition is not entirely applicable for bea 1B as it sustained oent after the axiu point. 11

127 Connection Moent (kn-) Rotation (Radians x 10^-3) 10 A 10 B 1 A 1 B 14 A 14 B Figure 4.3 Moent Rotation Curves for Tests 1 3 at the Joint 113

128 4.3 BOLT STRAIN GAUGE DATA Bolt Strains and Bolt Forces Measured in the Connection Tests In each connection test, the A and B beas each had two bolts instruented with strain gauges one bolt in the extended part of the endplate below the tension flange, and the other in the flush region iediately above the tension flange. There were three gauges on each instruented bolt, aligned at 10 degrees around the bolt shank as shown in Figure 4.4, so that a horizontal line through gauges A and B was parallel to the bea tension flange. Gauge C Bolt shank Gauge A Gauge B Figure Section through instruented bolt, with strain gauge positions Studying the strains recorded for each extended bolt and each flush bolt enables a further understanding of the endplate bending and yielding. In both the extended and flush regions, the endplate deforation tended to bend the bolts both longitudinally and transversely, and the relative proportions of these are evident in the different strains easured. In soe instances, the foil gauges peeled fro the specien at high strains before the test was over. Thus, the strain gauge data is incoplete in those areas where gauges failed early. Nevertheless, those gauges that continued to function do allow useful insights. Gauges A, B and C of Figure 4.4 are referred to in the text as follows: gauge B is the gauge closer to the bea web and is referred to as the web-side gauge, and gauge A is referred to as the edge-side gauge. Gauge C is referred to as the down gauge, where up and down are based on an orientation of the endplate in which the extended region is above the flush. This is illustrated in Figure

129 Y X X Y Figure 4.5 Orientation of Bolt Strain Gauges on Endplate It is evident that the difference between the web-side and edge-side bolt strains gives an indication of the extent to which the bolt is bending about the axis through the bolt centre, parallel to the bea s inor (Y-Y) axis. I have referred to this as transverse bending of the bolt. In order to obtain a siilar indication of the bending of the bolt about an axis through the bolt centre parallel to the bea s ajor (X-X) axis, I have calculated the strain at the position on the bolt surface opposite the down gauge. The bending of the bolt about this latter axis I refer to as longitudinal bending. Thus, the transverse bending of the bolt is related to deforations of the endplate across its width, while the longitudinal bending of the bolts is related to deforations of the endplate along its longitudinal axis. The calculated strain is referred to as the derived down strain. In test however, up and down were reversed so that the down strain was easured and the up strain was derived. The derived strain is calculated fro the understanding that the strain on the bolt shank at any point has two coponents an axial strain due to the axial force, and an elongation or copression due to bending. By considering the bending to be 115

130 further decoposable into two oents in orthogonal directions along the bea X-X and along the bea Y-Y directions it is possible to calculate the strain at desired positions fro the easured strains. This is illustrated in Figure 4.6. The easureent ε web is the su of three coponents the axial strain, the X-X bending strain and the Y-Y bending strain. If easureents ε web and ε edge are averaged, the Y-Y strain would cancel out. Thus the average X-X bending strain in Figure 4.1 is found by averaging ε web and ε edge and subtracting the axial strain. Figure 4.6 Calculating the bolt down strain The total bolt down strain ε down is therefore equal to the average X-X bending strain at the height of the edge and web gauges, ultiplied by the bolt radius R / RCos60, plus the axial strain. The axial strain is siply the average of the three gauge readings gauges A, B and C (up, edge and web). Thus: down R RCos60 web edge 6 web edge up web web edge 3 edge 3 up up 1 3 web web edge 3 edge up up 116

131 1 down web edge up Eqn The bolt strains and bolt forces for the three connection tests are presented in the following sections. In the graphs, the legends show how the bolt strains are referred to. Thus, the curve 10 A Flush Edge refers to the strains easured by the edge-side gauge for the flush tension region of bea 10A. The point at which the bolt first begins to yield is also indicated where applicable. This point is deterined by observing where any strain easureent exceeds the yield strain value easured in the bolt aterial tests. These values which were previously reported in Table 3.4 are: 10 plate: Bolt ε y = 3174 µstrains 1 plate: Bolt ε y = 366 µstrains 14 plate: Bolt ε y = 3358 µstrains Each strain curve has been terinated at the point where it becoes clear that the gauge is no longer functioning correctly. Thus, the terination of a curve ay not ean the strains did not exceed the values shown, but that the gauge had ceased to function. In soe instances also, the strains recorded exceed the range chosen for display on the graphs. In several of the bolt strains reported here, there was soe initial bending of the bolts, as shown by the fact that the web and edge values differed (transverse bending) at the start of the test, or the up and down strains differed (longitudinal bending) at the start of the test. This is thought to be due to iperfections such as inor welding distortions of the endplate, plate surface roughness, irregular bolt head or nut surfaces, or/and unequal bolt pre-tension Bolt Strains in Connection Test 1 On the Bea 10A extended strain curves (Figure 4.7a), the down and up strain initially start at about the sae positive value (indicating a strain due to 117

132 iperfections and bolt pretension) and then increase at about the sae rate, but with the down gauge increasing in tension and the up gauge increasing in copression. Thus, up to about an applied oent of 11 kn-, the predoinant effect in the longitudinal direction is bending i.e. bending about the bea ajor (X-X) axis. Beyond this point however, the tensile down strains increase rapidly, indicating yielding of the bolt shank in that region. The up strains begin to yield a little later, and the strain curve does not flatten out to the sae extent. Thus, there is a tensile axial coponent in the easured strains at this point. The edge and web-side strains are quite flat by coparison; they reain fairly parallel indicating little or no transverse bending of the bolt. At about the tie the up side of the bolt yields however, the edge and web strains becoe tensile and increase rapidly, indicating that the entire cross-section is now yielding in tension. The up and down strains for the extended bolt of Bea 10B exhibit a siilar pattern to those for 10A (Figure 4.7b), though the initial yielding takes place at a higher connection oent. The edge and web strains are also siilar, and fairly flat, but have alost exactly the sae value until the up part of the shank yields. In suary then, the extended bolts were in cobined axial elongation and X-X axis bending, with X-X bending doinating. Each bolt was fully yielded at about a connection oent of kn-. The strain gauges on the flush region bolt of Bea 10B failed preaturely, so that the only data retrieved was for the web-side gauge. The up and web gauges of bea 10A s flush bolt also failed rather early, but the patterns are fortunately still discernible (Figure 4.7c). The up and down strains coincide in the early part of the load cycle and are both tensile throughout. This iplies that there is little or no bending about the bea X-X axis (bending in the bea longitudinal plane), and the key effect is axial elongation. 118

133 1st Bolt Yield Connection Moent in kn- Connection Moent in kn- 1st Bolt Yield Connection Moent in kn- 1st Bolt Yield 1st Bolt Yield Connection Moent in kn- 1st Bolt Yield Conn. axiu oent 160 Conn. axiu oent Conn. 'swivel' oent 10 A Ext Edge 10 A Ext Web 10 A Ext Down 10 A Ext Up Derived Gauge Strain in Microstrains Conn. 'swivel' oent 10 B Ext Edge 10 B Ext Web 10 B Ext Down 10 B Ext Up Derived Gauge Strain in Microstrains (a) Bea 10A - Extended Bolt Strains (b) Bea 10B Extended Bolt Strains Conn. axiu oent 160 Conn. axiu oent Conn. 'swivel' oent 10 A Flush Edge 10 A Flush Web 10 A Flush Down 10 A Flush Up Derived Gauge Strain in Microstrains Conn. 'swivel' oent 10 B Flush Web Gauge Strain in Microstrains (c) Bea 10A - Flush Bolt Strains (d) Bea 10B Flush Bolt Strains Figure 4.7 Bolt Strains in Connection Test 1 119

134 There is however transverse bending about the bea Y-Y axis (bending in the bea transverse plane), as shown by the edge and web-side strains. Yielding initiates on the edge side of the bolt as would be expected, and this takes place at only about 90 kn- - uch earlier than in the corresponding extended bolt (11 kn-). The bolt is fully yielded at about 11 kn-, and all the strains becoe tensile, although the edge and web-side strains still differ widely so that there is still transverse bending Bolt Strains in Connection Test The bolt strains fro connection test are given in Figure 4.8. For the extended bolt of bea 1A the down and up strains diverge rapidly (Figure 4.8a), showing that there is considerable bending about the bea ajor (X-X) axis direction. Longitudinal yielding is initiated at about 10 kn- on both the down and up sides. In bea 1B the down and up strains also diverge quickly though not to the sae degree as in 1A. Yielding is again initiated at about 10 kn-. The edge and web-side strains for the extended bolts are clearly quite different fro those for beas 10A and 10B for both 1A and 1B the edge and web-side strains diverge considerably, showing that transverse bending is quite significant here. Bea 1B in fact sees to indicate ore transverse bending than longitudinal bending. Thus, the extended bolts in the 1 tests were bent considerably about both axes. The flush strains for Bea 1A differ even ore fro those for 10A. Unlike in Bea 10A where there was no longitudinal bending, the flush strains for 1A indicate a significant degree of longitudinal bending besides the transverse bending. The down strain only becoes copressive slowly so there is still an axial effect; but the up and down strains are clearly diverging. Yielding initiates at about 110 kn-. 10

135 Connection Moent in kn- 1st Bolt Yield Connection Moent in kn- 1st Bolt Yield Connection Moent in kn- 1st Bolt Yield Connection Moent in kn- 1st Bolt Yield 1st Bolt Yield Conn. axiu oent 160 Conn. axiu oent 10 Conn. 'swivel' oent 10 Conn. 'swivel' oent A Ext Edge 1 A Ext Web 1 A Ext Up Derived 1 A Ext Down B Ext Edge 1 B Ext Web 1 B Ext Up Derived 1 B Ext Down Gauge Strain in Microstrains Gauge Strain in Microstrains (a) Bea 1A - Extended Bolt Strains (b) Bea 1B Extended Bolt Strains Conn. axiu oent 160 Conn. axiu oent 10 Conn. 'swivel' oent 10 Conn. 'swivel' oent A Flush Edge 1 A Flush Web 1 A Flush Up 1 A Flush Down Derived B Flush Web 1 B Flush Up Gauge Strain in Microstrains Gauge Strain in Microstrains (c) Bea 1A - Flush Bolt Strains (d) Bea 1B Flush Bolt Strains Figure 4.8 Bolt Strains in Connection Test 11

136 4.3.4 Bolt Strains in Connection Test 3 The easured bolt strains fro connection test 3 are plotted in Figure 4.9. Only a few gauges were recorded for the extended bolts, and none for the extended bolt of bea 14B. Thus, Figure 4.9b shows the flush bolt strains of bea 14A, 4.9c is the flush strains in bea 14B, and Figure 4.9d is a close-up of part of the latter curve. The 14 test strains are all rather sall by coparison with the other tests. This reflects the fact that there was considerably less deforation of the endplate (and therefore of the bolts) during the test. The inforation fro the extended bolts is liited but the edge strain for bea 14A is constant for ost of the test, and then yields at a connection oent of about 160 kn-. This clearly indicates that there is no transverse bending since the edge strain would have to becoe copressive for transverse bending. There is also no transverse bending in the flush bolt. In Figure 4.9d the edge and webside strain readings coincide so exactly that they can hardly be distinguished fro each other. Thus, the sole effect there is axial tension. There is soe bending longitudinally as shown by the up and down strain curves, but this is liited and sall in coparison with bending in the 10 and 1 tests. In fact, in Figure 4.9 (c) all four strain coponents coincide exactly till about a connection oent of 80 kn-. So there is neither longitudinal nor transverse bending till that point in the test. The bolt force curve in Figure 4.3 shows that the bolt force does reain constant at a pre-tension of about 6 kn until a connection oent of 80 kn-. The bolt does not yield but the curve does begin to bend away fro the vertical indicating an increase in axial force along with connection oent. 1

137 Connection Moent in kn- 1st Bolt Yield Connection Moent in kn- Connection Moent in kn- 1st Bolt Yield Connection Moent in kn- 1st Bolt Yield 00 Conn. axiu oent 00 Conn. axiu oent Conn. 'swivel' oent 10 Conn. 'swivel' oent A Ext Edge 14 A Ext Down A Flush Web Gauge Strain in Microstrains Gauge Strain in Microstrains (a) Bea 14A - Extended Bolt Strains (b) Bea 14A Flush Bolt Strains Conn. axiu oent 00 Conn. axiu oent 10 Conn. 'swivel' oent B Flush Edge 14 B Flush Web 14 B Flush Down 14 B Flush Up Derived 10 Conn. 'swivel' oent 14 B Flush Edge 14 B Flush Web 14 B Flush Down 14 B Flush Up Derived Gauge Strain in Microstrains (c) Bea 14B - Flush Bolt Strains (d) Bea 14B Flush Bolt Strains (Expanded) Figure 4.9 Bolt Strains in Connection Test Gauge Strain in Microstrains 13

138 4.3.5 Bolt Forces in the Connection Tests The average force in each bolt can be calculated fro the axial bolt strain. Once the axial strain exceeds the yield strain, the corresponding bolt stress and force ust be adjusted to reflect the change fro the initial to the strain-hardening slope. Thus, for axial strain ε axial : If ε axial ε y : axial stress f axial = E. ε axial If ε axial > ε y : axial stress f axial = E. ε y + E sh. (ε axial - ε y ) Eqn 4. where E is the Young s odulus and E sh is the strain-hardening odulus easured in the bolt aterial tests. Bolt Force = f axial.a Eqn 4.3 where A is the easured bolt cross-sectional area. Bolt forces can only be calculated where all the bolt strains were recorded i.e. where the strain gauges all functioned well. Thus, the flush bolt force for bea 10B could not be calculated for exaple, since only one gauge functioned. The extended and flush bolt forces for bea 10A and the extended bolt force for 10B are shown in Figure There are four distinct regions in the extended bolt force curves of Figure The first is an approxiately linear segent where the bolt force increases only very slowly for large increases in the connection oent. There is soe initial bedding-in, and then this first segent has a steep slope and is alost vertical. This region sees to indicate the range of connection oent in which the bolt forces are only a little greater than the initial bolt pre-tension force. In a second region of the extended bolt force curve, the curve flattens out slowly in a knee. This second region is ore apparent in the 10B ext bolt force curve. It can be seen that a straight line through this region would pass ore or less through the graph origin. Thus, this second region sees to indicate the range of 14

139 Connection Moent in kn- 1st Yield Trans. 1st Yield Long. 1st Yield Long. Full Yield Full Yield connection oent for which the bolt pre-tension has been overcoe, so that the bolt force is increasing linearly with connection oent A Conn. axiu oent A Conn. 'swivel' oent Strain hardens A Flush 10 A Ext 10 B Ext Pre-tension Bolt Axial Force in kn Figure 4.30 Bolt Forces for Connection Test 1 In a third region of the extended bolt force curve, the curve becoes alost horizontal, and the bolt forces increase considerably with little increase in connection oent. This region sees to be initiated by yielding of the bolts in bending. (The onset of yielding is identified when one of the easured strains first exceeds the yield value full yielding is where the average axial strain exceeds the yield value). By coparison with Figures 4.7 (a) and (b), we see that the extended bolts are yielding in bending in a longitudinal plane i.e. in a plane parallel to the bea web. Thus, in this third region the bolt is bending to confor to the endplate bending, due to the plate prying against the bolt head. Finally in a fourth region, the slope becoes steeper again. This fourth region clearly corresponds to the attainent of axial yielding, when the entire crosssection appears to be yielding in tension. This region appears in the 10A Ext bolt force curve, but not in the 10A. We assue that the latter strain gauges failed prior to full yield of the bolt. 15

140 When the flush and extended bolt forces of Bea 10A are copared, it can be seen that the flush bolt attracts a lot ore force than the extended bolt right up to the point where the flush bolt gauges stop recording. When the flush bolt begins to yield at a connection oent of about 90 kn-, the flush bolt force is 105 kn as copared to 40 kn for the extended bolt. Secondly, whereas the extended bolt force initially reains alost constant at the pre-tension force of approxiately kn, the flush bolt force increases right fro the onset. So initially, the flush region is uch stiffer, attracting ore force, and the extended region is relatively flexible. Of the four regions identified for the extended bolts, only regions two and three can be seen clearly for the 10A flush bolt. The first region where the curve is vertical is issing, and the bolt force increases fro the pre-tension fro the start of the test. The fourth region is also not evident, but this is probably due to the strain gauges failing before the end of the test. Fro Figure 4.7 we notice that the flush bolt bending is principally in the transverse plane rather than the longitudinal. We also notice that unlike the extended bolts which continue to bend longitudinally till the gauges stop functioning, the transverse bending of the flush bolt gives way to superiposed axial tension. The bolt forces for test are plotted in Figure The extended bolt forces for bea 1A and 1B both exhibit the four regions described above for the bolt forces in connection test 1. An alost vertical pre-tension region is evident, with a pre-tension of approxiately 60 kn for 1A and a pre-tension of approxiately 90 kn for 1B. The third region after yielding coences is also evident in both extended bolts, with the bolt force increasing rapidly with little increase in connection oent. However, the transition knee (second region) is now quite long. As in Figure 4.30 before, the extended bolt forces stop increasing rapidly once the bolt is fully yielded, and the slope of the curve becoes steep. The flush bolt curve for bea 1A could only be plotted as far as a connection oent of 110 kn-. In that range however, if one allows for the fact that it 16

141 Connection Moent in kn- 1st Yield Long. 1st Yield Long. 1st Yield Long 1st Yield Trans. Full Yield Full Yield starts at a lower pre-tension copared to the extended region bolt, the two bolt forces run ore or less parallel all the way with the flush force being higher by about kn A Conn. axiu oent 10 1A Conn. 'swivel' oent B Ext 1 A Flush 1 A Ext Bolt Axial Force in kn Figure 4.31 Bolt Forces for Connection Test The flush bolt curve is practically a straight line and is just showing signs of yielding when the gauge readings terinate. When the flush bolt begins to yield at a connection oent of about 100 kn-, the flush bolt force is 1 kn as copared to 106 kn for the extended bolt. This is a ratio of extended to flush bolt force of 0.87, copared to 40:105 or 0.38 for bea 10A. Of the four regions identified the 1A flush bolt shows only the second region. The strain gauges have evidently ceased functioning before the third and fourth regions coence. The flush bolt force in bea 14B is uch saller by coparison with the flush bolt force in beas 1A and 10A. For exaple, at a connection oent of 100 kn-, the flush bolt forces for 10A, 1A and 14B are 14, 1 and 34.5 kn respectively. Thus, the flush bolt force at a given connection oent appears to decrease with increasing endplate thickness. By coparison the extended region 17

142 Connection Moent in kn- bolt force went up fro 43 kn and 70 kn for 10A and 10B, to 105 and 114 kn for 1A and B, at the sae connection oent B Conn. axiu oent B Conn. 'swivel' oent B Flush Bolt Axial Force in kn Figure 4.3 Bolt Forces for Connection Test 3 By coparison with the 10A and 1A flush bolts, the 14B flush bolt force exhibits different behaviour. The first two regions of the extended bolt curve are evident here, rather than the second and third only as before. It sees then that the flush bolt force in the 14 endplate does not increase as fast as in the thinner endplates, so that the pre-tension is not exceeded until id-way through the test. Fro Figure 4.9 we also notice that the 14B flush bolt bends in the longitudinal plane like the extended bolts, rather than the transverse plane as for the 10 and 1 cases Discussion of Bolt Forces In all the tests, the easured bolt pre-tension was lower than the 14 kn required by SANS While applying the turn-of-the-nut ethod, we observed that there is a degree of subjectivity in deterining the snug-tight condition. There was also the added coplication that we soeties could not really ipart the full third of a turn required by the code, because of the craped spaces we had to 18

143 work in, and because of the risk of daaging bolt gauge wiring. However, this was not considered as having a ajor effect on the test results. In section 4..4 it was suggested that the differences in the initial stiffness of the noinally identical A and B beas in a test could be partially explained by a difference in the bolt pre-tension. This hypothesis is supported by Figure 4.30 which shows that the 10B extended bolt had a higher pre-tension than the extended bolt of 10A 58 kn vs 35 kn. Figure 4.31 also shows that the extended bolt in bea 1B had a higher pre-tension (90 kn) than the corresponding bolt in 1A (60 kn). In all three connection tests, we notice the presence of a second region in the bolt force curves, where the bolt force increases rapidly with only a little increase in the applied connection oent. It sees then that the echanis of load transfer/ resistance in the connection changes during the test, fro one where the bolts are not required to resist large forces to one where they are required to carry large forces. As described in the previous section, the extended bolt force curves exhibit four regions as follows: 1. An alost vertical region where the bolt pre-tension exceeds the force applied to the bolt by the connection.. A ildly sloping transition region, in which the slope is such that the curve could be extrapolated to pass through the origin. The bolt force is increasing elastically and linearly with connection oent in this region. 3. A third region where the bolt force curve is alost horizontal with a very shallow slope. This region is where the bolt is yielding in bending in the longitudinal (bea web) plane. 4. A fourth region where the bolt section is fully yielded in axial tension, so that the slope is once ore gentle, though slightly steeper than region. 19

144 The curves for the flush bolt forces fro Tests 1 and are siilar to the extended bolt curves, except that the first region is not clearly defined. This would result fro the greater stiffness of the flush region in the initial stages of loading, so that the flush bolt forces increase very quickly at first. The other difference is that the flush bolts in these tests bend ore in the transverse plane (a plane parallel to the bea flanges), rather than the longitudinal. The flush bolt force curve for the thicker 14 endplates of test 3 differed however. These flush bolts bent ore in the longitudinal plane and behaved ore like the extended bolts at least until the strain gauges ceased to function. In all three tests, the yielding of the flush bolt in bending was alost coincident with the swivel point in the connection oent-rotation curve. Thus, the endplate was priarily restrained by the end oent due to prying of the bolt head prior to that point, but after that it is restrained ore by an axial bolt force than by the bolt oent. One can deduce that the increased bolt force is necessary for the endplate flush region yield-lines to develop properly and hence for the connection rotation to swivel. The bending of the flush and extended bolts is due to prying of the endplate against the bolt head. This prying oent will lead to an increase in the axial bolt force, over and above the value due to an average axial strain as given in this section. As the endplate gets thicker, the ratio of the bolt forces in the extended region to that of the flush region, changes. The change in the ratio of extended bolt force to flush bolt force eans the bea tension force is being transferred differently. In the thinner endplates a larger proportion of the bea tension force is transferred via the flush bolts than in the thicker endplates. It sees then that the extended part of the endplate acts as a cantilever to soe extent, and when the endplate is thin, the cantilever is not stiff enough to attract as uch force as the flush region. 130

145 In Figures 4.30, 4.31 and 4.3, we notice that none of the bolt force curves continue to the connection axiu oent. This is because the curves are all terinated preaturely by failure of one or ore of the bolt strain gauges. Thus, these are not the axiu bolt forces attained, but the axiu bolt forces easured. In Figure 4.30 for exaple, we notice that the 10A extended bolt force was easured to 37 kn at about 90 % of the axiu connection oent. 4.4 ENDPLATE STRAIN GAUGE DATA The strain gauges on the bea and endplate can be divided into four groups: 1. Strain gauges on the extended portion of the endplate, which were intended to allow the estiation of stress gradients along and across the extended region for varying load values.. Gauges on the flush tension region of the endplate were included to help to understand the yield and deforation patterns better in that region. 3. The gauges on the bea flanges were intended to allow an estiation of the flange forces. 4. The gauges on the bea web were intended to allow an understanding of the (non-linear) strain distribution across the bea web and to estiate the location of the strain neutral axis. The data fro these four groups are reviewed below. The endplate aterial properties were previously given in Tables 3. and 3.3. For ease of reference however the key properties are re-tabulated in Table 4.. In the graphs for the gauge strains on the endplates and bea ends, the strain e y at which the bea/plate begins to yield is shown where relevant. 131

146 Table 4. Specien Material Properties Relevant to Endplate & Bea Strains Young s ε y - Yield Strain ε sh - Strain Modulus Hardening Onset GPa B flange (1) B web (1) B flange () N/A B web () plate plate plate Note: Bea () was used only for test Endplate Strain Gauge Data Figure 4.33 shows the strain gauge positions in the extended region while Figure 4.34 shows gauge positions in the flush region. The gauges in the extended region are along three vertical (longitudinal) and three horizontal (transverse) gridlines, and each gauge is referred to by these grids. Grid 1 is along the bolt line while grid 3 is along the weld line. Also grid A is along the plate edge while grid C is along the plate centreline. Thus, gauge A1 is on the bolt line by the plate edge. Gridline 3 is at 1 fro the bea tension flange, which is actually 4 fro the assued position of the weld line at 8 fro the bea flange surface. This is necessary because of the practical difficulty of fitting in the gauges into the space next to the bea flange weld. Siilarly, gridline 1 is offset 10 fro the 13

147 bolt centreline towards the bea flange to allow soe clearance for the gauge fro the bolt head. Gridline is exactly halfway between gridlines 1 and 3. Figure 4.33 Locations of Strain Gauges in the Endplate Extended Region Figure 4.34 Locations of Strain Gauges in the Endplate Flush Region The gauges in the flush region are along the sae three longitudinal gridlines, and three transverse gridlines as shown. Grid 6 is on the flush region weld line while grid 8 is on the flush region bolt line. Gauge B7 is a rosette with a longitudinal (vertical) and a transverse (horizontal) easureent. The third gauge in the rosette is either tangential or radial to a circle with bolt hole as centre. In Figures 4.35 to 4.40 the strain gauge easureents on the endplate are presented for each of the three tests. 133

148 Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Conn. axiu oent Bolt full yield Bolt 1st yield Conn. axiu oent Bolt full yield Bolt 1st yield Conn. swivel oent B 10A A1 - Bolt line B 10A A B 10A A3 - Weld line Conn. swivel oent B 10A C1 - Bolt line B 10A C B 10A C3 - Weld line ε sh ε y 0 ε y ε sh ε sh ε 0 y ε y ε sh Gauge Strain (Microstrains) Gauge Strain (Microstrains) (a) Ext Region Grid A Strains (b) Ext Region Grid C Strains Conn. axiu oent Conn. swivel oent Bolt 1st yield 40 B 10A A6 - Flush Weld B 10A A8 - Flush bolt 40 ε sh ε y 0 ε y ε sh εsh εy 0 Gauge Strain (Microstrains) (c) Flush Region Grid A Strains (d) Flush Region Grid B Strains Figure 4.35 Endplate Strains in Connection Test 1 Bea 10A Conn. axiu oent Conn. swivel oent Bolt 1st yield B 10A B6 - Weld line B 10A B7 - Vertical B 10A B7 - Tangential B 10A B7 - Horizontal εy εsh Gauge Strain (Microstrains) 134

149 Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Conn. axiu oent Bolt full yield Bolt 1st yield Conn. axiu oent Bolt full yield Bolt 1st yield Conn. swivel oent B 10B A1 - Bolt line B 10B A B 10B A3 - Weld line Conn. swivel oent B 10B C1 - Bolt line B 10B C B 10B C3 - Weld line ε sh ε y 0 ε y ε sh ε sh ε 0 y ε y ε sh Gauge Strain (Microstrains) Gauge Strain (Microstrains) (a) Ext Region Grid A Strains (b) Ext Region Grid C Strains Conn. axiu oent 160 Conn. axiu oent Conn. swivel oent B 10B A6 - Weld line B 10B A8 - Flush Bolt Conn. swivel oent ε sh ε y 0 ε y ε sh ε sh ε 0 y ε y ε sh Gauge Strain (Microstrains) Gauge Strain (Microstrains) B 10B B6 - Weld line B 10B B7 - Vertical B 10B B7 - Tangential B 10B B7 - Horizontal (c) Flush Region Grid A Strains (d) Flush Region Grid B Strains Figure 4.36 Endplate Strains in Connection Test 1 Bea 10B 135

150 The easured strains on the endplate would be ipacted by the occurrence of residual stresses in the heat-affected zonefro the welding of the bea flanges to the plate, and fro possible distortions of the endplate during welding. These residual stresses and distortions were iniized by requiring the use of fillet welds rather than a full-penetration groove weld. The effect of residual stresses would oreover cease to have significant influence once the plate yields. These effects are therefore not considered further in this discussion. In the extended regions of beas 10A and 10B (Figures 4.35 and 4.36) we see that endplate 10A begins to yield first on the weld line at 41 kn- and only begins to yield on the bolt line at 71 kn-. The position of yielding is shown approxiately by the vertical chain-dotted lines at a strain of ± ε y, which is the yield strain for the endplate aterial. However, the actual strain at which yielding is coplete ay be slightly offset fro ε y due to the occurrence of residual stresses fro welding, and is better estiated by the change in slope in the strain curve. Bea 10B yields first on the weld line at 46 kn-, and then on the bolt line at 69 kn-. By coparison, yielding in the flush region of bea 10A initiates on the flush weld line at 4 kn (gauge A6), and on the flush bolt line at 53 kn- (gauge A8). Siilarly, yielding in the flush region of bea 10B initiates on the flush weld line at 46 kn (gauge A6), and on the flush bolt line at 65 kn- (gauge A8). Thus yielding in the flush region lags behind that in the extended region. In beas 10A and 10B, the strains on gridline start out being tensile and increasing linearly at a slow rate. This shows that gridline is not at the point of inflexion for the longitudinal strain distribution along the extended region. The tensile stresses on gridline are in approxiate agreeent with where the point of inflexion would be if the bolt line runs through the bolt centreline. At a connection oent of 110 kn-, the strain on gauge A of bea 10A begins to increase in tension at a higher rate, until it yields in tension at about

151 kn-. The gauges C of bea 10A and A of bea 10B exhibit a siilar pattern, however gauge C of bea 10B inexplicably goes into copression instead. A likely explanation for this is that the fracture in bea 10B began to develop as a crack at that point, in the centre of the weld line. The effect is to reduce the weld line oent, shifting the inflexion point towards the weld line, on gridline C. In Figures 4.35d and 4.36d, the rosette at gauge position B7 initially easures alost zero vertical strain and zero horizontal strain. In both cases, at about the connection swivel oent, both the vertical and horizontal coponents yield in tension and begin to increase rapidly. The siilarity between the vertical and horizontal coponents shows the principal strain is approxiately radial to the flush bolt hole centre. The tangential coponents yielded at 56 kn- for 10A and 74 kn- for 10B. In the extended regions of beas 1A and 1B (Figures 4.37 and 4.38) endplate 1A begins to yield first on the weld line at 43 kn- and begins to yield on the bolt line at 80 kn- (gridline C). Bea 1B yields on the weld line at 83 kn (gridline A), and on the bolt line at 83 kn- (gridline C). By coparison, yielding in the flush region of bea 1A initiates on the flush weld line at 61 kn (gauge A6), and on the flush bolt line at 66 kn- (gauge A8). Siilarly, yielding in the flush region of bea 1B initiates on the flush weld line at 73 kn (gauge A6), and on the flush bolt line at 83 kn- (gauge A8). In general, as one would expect, yielding in the 1 endplate speciens takes place at higher connection oents than in the 10 speciens. In beas 1A and 1B, the strains on gridline also start out being tensile and increasing linearly at a slow rate (Figures 4.37 and 4.38). Unlike the gridline easureents of test 1 however, these strains don t increase quickly. In bea 1A that fractured, gridline never really yielded, and both the gauges A and C went into copression before the connection axiu oent. This probably reflects cracking of the endplate on the weld line. 137

152 Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Conn. axiu oent Conn. swivel oent Bolt full yield Bolt 1st yield Conn. axiu oent Conn. swivel oent Bolt full yield Bolt 1st yield B 1A A1 - Bolt line B 1A A B 1A A3 - Weld line B 1A C1 - Bolt line B 1A C B 1A C3 - Weld line ε 0 sh ε y ε y ε sh ε 0 sh ε y ε y ε sh Gauge Strain (Microstrains) Gauge Strain (Microstrains) (a) Ext Region Grid A Strains (b) Ext Region Grid C Strains Conn. axiu oent Conn. swivel oent Bolt 1st yield B 1A B6 - Weld line B 1A A6 Weld line B 1A B7 - Radial B 1A A8 - Flush bolt B 1A B7 - Tangential 40 ε sh ε y 0 B 1A B7 - Horizontal ε y ε sh ε 0 Gauge Strain (Microstrains) sh ε y ε y ε sh Gauge Strain (Microstrains) (c) Flush Region Grid A Strains (d) Flush Region Grid B Strains Figure 4.37 Endplate Strains in Connection Test Bea 1A Conn. axiu oent Conn. swivel oent Bolt 1st yield 138

153 Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Conn. axiu oent Conn. swivel oent Bolt full yield Bolt 1st yield B 1B A1 - Bolt line B 1B A B 1B A3 - Weld line Conn. axiu oent Conn. swivel oent B 1B C1 - Bolt line B 1B C B 1B C3 - Weld line ε sh ε y 0 ε y ε sh ε sh ε y 0 ε y ε sh Gauge Strain (Microstrains) Gauge Strain (Microstrains) Bolt full yield Bolt 1st yield (a) Ext Region Grid A Strains (b) Ext Region Grid C Strains Conn. axiu oent 160 Conn. axiu oent 160 Conn. swivel oent Bolt 1st yield B 1B A6 - Weld line B 1B A8 - Flush Bolt Conn. swivel oent Bolt 1st yield B 1B B6 - Weld line B 1B B7 - Radial B 1B B7 - Horizontal ε sh ε y 0 ε y ε sh εsh εy 0 εy εsh Gauge Strain (Microstrains) Gauge Strain (Microstrains) (c) Flush Region Grid A Strains (d) Flush Region Grid B Strains Figure 4.38 Endplate Strains in Connection Test Bea 1B 139

154 In bea 1B, both A and C reained tensile till the connection axiu oent, but then becae copressive thereafter as the weld line cracked on that bea as well. In connection test, the radial and horizontal coponents were easured at flush gauge B7 rather than the longitudinal coponent (Figures 4.37d and 4.38d). The radial and tangential coponents both yielded at about 80 kn- for bea 1A, and the radial at about 93 kn- for 1B. As with connection test 1 the flush region lags behind the extended region in yielding. The endplate strains for connection test 3 are given in Figures 4.39 and 4.40 A. In the extended region of endplate 14A the weld line yielded as early as 30 kn-, however, the endplate only began to yield on the bolt line at 96 kn-. Bea 14B yielded first on the weld line at 30 kn-, and then on the bolt line at 110 kn-. Yielding in the flush region initiated at 40kN- on the weld line of bea 14A, but only at 8 on 14B. The strains on gridline are once ore tensile, reflecting the offset between gridline and the point of inflexion. Unlike in tests 1 and though, there is no evidence of yielding on gridline. The only exception to this is at gauge C of 14B (Figure 4.40b). In bea 14A, rosette B7 has a larger horizontal coponent than the radial, showing that the strain is ostly horizontal. This is corroborated by the fact that the vertical strain is copressive. Thus, the bending in that area is ostly transverse, rather than circular as in tests 1 and Discussion of Endplate Strains We notice that for both 10A and 10B, the top of the yield knee on the extended region bolt line strains (gauges A1 and C1), coincides ore or less with the connection swivel oent. This sees to be consistently true for tests and 3 as well (Figures 4.37 to 4.40). Thus, we infer that the connection swivel starts with yielding on the extended region weld line and ends with full yielding of the extended region bolt line. Between these two is yielding of the flush region. 140

155 Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Conn. axiu oent 00 Bolt full yield 00 Conn. axiu oent Bolt full yield Conn. swivel oent B 14A A1 - Bolt line B 14A A B 14A A3 - Weld line Conn. swivel oent B 14A C1 - Bolt line B 14A C B 14A C3 - Weld line 0 ε sh ε y ε y ε sh ε 0 y ε y ε sh Gauge Strain (Microstrains) Gauge Strain (Microstrains) (a) Ext Region Grid A Strains (b) Ext Region Grid C Strains Conn. axiu oent 00 Conn. axiu oent 00 Conn. swivel oent Bolt full yield Conn. swivel oent Bolt full yield B 14A B6 - Weld line B 14A B7 - Radial B 14A B7 - Vertical B 14A A6 Weld line B 14A B7 - Horizontal B 14A A8 - Flush bolt ε 0 ε sh ε y 0 sh ε y ε y ε sh ε y ε sh Gauge Strain (Microstrains) Gauge Strain (Microstrains) 0000 (c) Flush Region Grid A Strains (d) Flush Region Grid B Strains Figure 4.39 Endplate Strains in Connection Test 3 Bea 14A 141

156 Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Conn. axiu oent 00 Conn. axiu oent Conn. swivel oent 10 Conn. swivel oent B 14B A1 - Bolt line B 14B A B 14B A3 - Weld line B 14B C1 - Bolt line B 14B C B 14B C3 - Weld line ε sh ε y 0 ε y ε sh ε sh ε 0 y ε y ε sh Gauge Strain (Microstrains) Gauge Strain (Microstrains) (a) Ext Region Grid A Strains (b) Ext Region Grid C Strains Conn. axiu oent 00 Conn. axiu oent Conn. swivel oent 10 Conn. swivel oent B 14B A6 - Weld line B 14B A8 - Flush Bolt 40 B 14B B6 - Weld line B 14B B7 - Horizontal ε sh ε y 0 ε y ε sh ε sh ε y 0 ε y ε sh Gauge Strain (Microstrains) Gauge Strain (Microstrains) (c) Flush Region Grid A Strains (d) Flush Region Grid B Strains Figure 4.40 Endplate Strains in Connection Test 3 Bea 14B 14

157 The yielding along gridline in tension in tests 1 and shows that the weld line is really a whole band of yielding extending at least halfway of the distance to the bolt line. Thus, a true plastic hinge develops at the weld line, with substantial strain-hardening adjacent to the bean flange, and with extensive yielding along the endplate to a considerable distance fro the bea flange. This continues until cracks develop on the weld line. The point of inflexion sees to shift closer to the bolt centreline as the yielding develops, possibly either because of a shift in the bolt line away fro the flange (due to bolt yielding in bending, with a reduction in prying of the bolt head by the plate), or because of the growth in extent of the plastic oent at the weld line fro a local hinge to becoe a band of plasticity spreading towards the bolt line. In tests 1 and, the yielding of the vertical and horizontal coponents of the rosette easureents at B7 in the flush region sees to be siilar to the behaviour on gridline. We surise that the B7 coponents yield in tension as a plastic hinge develops on the weld line and on a bea web line adjacent to the bea web. The strains here are clearly radial, with the bolt hole as centre, and hence the tangential coponent is in copression. In test 3, the fact that this tension yielding on gridline does appear though on only one gauge (C of bea 14B), suggests that the sae kind of yielding pattern is developing in the extended region of test 3 as the previous tests. It is clear though that there is a difference in test 3 nevertheless, as the bending at the B7 position of the flush region is transverse rather than radial. It sees then that the 14 endplates would have the sae deforation pattern as the other two tests, but this deforation does not develop before the bolt fractures. We surise therefore that the bolt is not strong enough to restrain the endplate in either the extended or the flush region, and this is why the deforation pattern does not develop in either region. This should be considered in relation to the observation in section that the ratio of extended bolt force to flush bolt force increases with endplate thickness. 143

158 4.5 STRAIN DATA ON THE BEAM WEBS AND FLANGES Figure 4.41 Locations of Strain Gauges on the Bea Web and Flanges Figure 4.41 shows the strain gauge positions on the bea web and flanges. These gauges are all positioned to easure strains along the bea length. There are three gauges on each flange, with one pair opposite each other on the flange. The tension flange has gauges B4 and B5 opposite each other, and then C4 on the bea longitudinal centreline. The copression flange has gauges B1 and B13 on gridline B, and C13 on the centreline. There are four gauges on the bea web B8 is at the height of the flush tension bolts, B9 is alost exactly on the bea transverse centreline, B10 is 5 above the centre of the shear bolts, and B11 is approxiately halfway fro the centroid of the bea copression flange to the level of the shear bolts. All these gauges are positioned 5 fro the edge of the flange or web welds. The test bea web and flange strains are presented in Figures 4.4 to

159 4.5.1 Description of Bea Web and Flange Strain Gauge Data Test 1 In connection test 1 the flange strains for beas 10A and 10B are virtually identical (Figures 4.4a and 4.4b). The strains easured by gauges B4 and B5 on the tension flange are sall and are linear until fairly high connection oents. Even though both gauge easureents are linear, B4 is in tension and B5 is in copression, and B4 has larger strain agnitudes than B5. At about 135 kn-, the tensile strain on B4 begins to increase rapidly reaining linear but at a new slope. In Figures 4.4a and 4.4b, the copression flange gauges B1 and B13 are in linear copression with virtually the sae agnitude up to the connection swivel oent. The initial slope for both gauges is negative i.e. sloping so that the strains becoe copressive. Just after the connection swivel oent at about 80 kn-, the slopes change and the strains begin to increase rapidly. B1 reverses direction and becoes tensile, while B13 increases faster in the copression direction. We notice also that the strain agnitudes are uch higher in the copression flange (B1 and B13) than the tension flange (B4 and B5). So yielding of the copression flange initiates at about 80 kn- or 38% of M p (09 kn-) There is a kink in the B1 strain curve for bea 10B which is not evident in curve B1 for bea 10A. Fro a connection oent of 113 kn- to 139 kn-, the B1 strain curve changes direction, with the strains reducing in agnitude. At about 139 kn- it changes direction again and the tensile strains begin to increase once ore. In Figures 4.4c and 4.4d showing the web strains, the curves C4 and C13 are very siilar to B4 and B13 respectively for both beas, as would be expected. At a given connection oent however, the C gridline strains are larger than the B gridline strains. 145

160 Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Conn. axiu oent 160 Conn. axiu oent Bolt 1st yield 10 Conn. swivel oent B 10A B4 B 10A B5 B 10A B1 B 10A B13 Conn. swivel oent B 10B B4 B 10B B5 B 10B B1 B 10B B13 ε y 0 ε y Gauge Strain (Microstrains) ε 0 y ε y Gauge Strain (Microstrains) (a) Bea 10A Bea Flange Strains (b) Bea 10B Bea Flange Strains Conn. axiu oent 160 Conn. axiu oent 160 Conn. swivel oent Bolt 1st yield 10 B 10B C4 10 B 10A C4 B 10B C8 Conn. swivel oent B 10A C8 80 B 10B C9 80 B 10A C9 B 10B C10 B 10A C10 B 10B C B 10A C11 B 10B C13 B 10A C ε y 0 ε y ε y ε y Gauge Strain (Microstrains) Gauge Strain (Microstrains) (c) Bea 10A Bea Web Strains (d) Bea 10B Bea Web Strains Figure 4.4 Strains in the Bea Webs and Flanges fro Connection Test 1 146

161 On the bea web, all four easured strains start out as tensile. Initially, strains C9, C10 and C11 are ore or less equal in agnitude while strain C8 is larger than the others. In Figure 4.4c, C9 and C10 are identical right through the test and cannot be distinguished fro one another. However, at a point in the test, strain C8 begins to increase faster in tension and C11 begins to increase faster in the opposite direction, becoing copressive. Thus, initially only the bea copression flange is in bearing against the colun flange, but the copression zone later extends into the web to C11. For bea 10A this change in slope occurs at about 91 kn- for both strain easureents. For bea 10B the slope change in C8 occurs at about 119 kn- and the slope change in C11 at about 89 kn-. C9 and C10 reain linear to the end of the test for both beas. Test In connection test the flange strains for beas 1A and 1B are shown in Figures 4.43a and 4.43b. For both 1A and 1B, strains B4 and B5 on the tension flange are sall in agnitude and linear. Only B4 in test 1B shows a definite slope change at a connection oent of about 134 kn-. In test 1A, both B4 and B5 begin to reduce in agnitude at about 147 kn-, becoing zero at the connection axiu oent. The reduction in strain at the tension flange is thought to be due to the initiation of cracks in the endplate and the bea flange weld. For both beas, fro the start of the test, copression flange gauge B1 is in tension and gauge B13 is in tension. Initially both gauges easure linear strains with steep negative slopes and only slight increents in strain. At about 90 kn- and 11 kn- respectively for beas 1A and 1B (0.44M p and 0.55M p ), the strain on gauge B13 begins to increase faster in the copressive direction with a change in slope. Gauge B1 siilarly increases faster in the tensile direction at about 86 kn- and 134 kn- for 1A and 1B respectively. As with bea 10B, the B1 curve for bea 1A has a change in direction kink between 119 kn- and 145 kn-. 147

162 Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Conn. axiu oent 160 Conn. axiu oent 160 Conn. swivel oent 10 Bolt 1st yield Conn. swivel oent 10 Bolt 1st yield B 1A B4 B 1A B5 B 1A B1 B 1A B B 1B B4 B 1B B5 B 1B B1 B 1B B13 ε y 0 ε y 0 ε y ε 0 y Gauge Strain (Microstrains) Gauge Strain (Microstrains) (a) Bea 1A Bea Flange Strains (b) Bea 1B Bea Flange Strains Conn. axiu oent 160 Conn. axiu oent 160 Conn. swivel oent Bolt 1st yield B 1A C4 B 1A C8 B 1A C9 B 1A C10 B 1A C11 B 1A C13 Conn. swivel oent 0 0 ε ε y ε y ε y y Gauge Strain (Microstrains) Gauge Strain (Microstrains) Bolt 1st yield B 1B C4 B 1B C8 B 1B C9 B 1B C10 B 1B C11 B 1B C13 (c) Bea 1A Bea Web Strains (d) Bea 1B Bea Web Strains Figure 4.43 Strains in the Bea Webs and Flanges fro Connection Test 148

163 Figures 4.43c and 4.43d show the web strains in test. Strains C4 and C13 are again siilar to B4 and B13 but with higher agnitude for a given connection oent. In the bea webs, at low connection oents (up to 76 kn- for 1A and 73 kn- for 1), strains C9, C10 and C11 are about the sae agnitude and are increasing linearly in the tension direction with a steep slope. In bea 1B the strains are actually copressive, but this sees to be due to an initial copressive residual stress at the beginning of the test. On the bea web, all four easured strains start out as tensile. Initially, strains C9, C10 and C11 are ore or less equal in agnitude while strain C8 is larger than the others. In Figure 4.4c, C9 and C10 are identical right through the test and cannot be distinguished fro one another. However, at a point in the test, strain C8 begins to increase faster in tension and C11 begins to increase faster in the opposite direction, becoing copressive. For bea 1A this change in slope occurs at about 91 kn- for both strain easureents. For bea 1B the slope change in C8 occurs at about 119 kn- and the slope change in C11 at about 89 kn-. C9 and C10 reain linear to the end of the test for both beas. In test 1, of the four web strains, only C11 changes slope and becoes copressive. In test 1A, both C10 and C11 exhibit this pattern. However, C10 changes slope later in the test than C11. The slope change in C11 is at about 80 kn- and the slope change in C10 is at about 110 kn-. In bea 1B, C11 exhibits a slope change at about 73 kn-. There is however no discernible slope change in C10. In bea 1B, even after the slope change in C11, the rate of strain increase is arkedly less than for C11 in bea 1A. Test 3 The bea web and flange strains fro connection test 3 are given in Figure The flange strains easured by gauges B4 and B5 on the tension flange for beas 149

164 14A and 14B are siilar to tests 1 and. The strains are linear and are sall until fairly high connection oents. Strain B5 in particular is virtually constant until a connection oent of 143 kn- and 138 kn- for 1A and 1B respectively, after which it undergoes a slope change and increases in copression. The corresponding slope changes in B4 are initiated at about 149 kn- for bea 1A and 116 kn- for 1B. The copression flange strains B1 and B13 are virtually parallel in the initial part of the test. Gauge B1 is initially tensile while B13 is copressive, but both gauges show a slight slope towards the copression direction. For bea 14A, B1 becoes copressive within that initial linear portion. The sae change in direction kink that was observed for gauge 1B in beas 10B and 1A, is observable here again for 14B and to a lesser extent for 14A. The change in direction for 14A is fro about 15 kn- to 139 kn-, and in 14B fro about 15 kn- to about 154 kn- The bea web strains are shown in Figures 4.44c and 4.44d. Gauge C8 is initially linear and tensile with a large slope. In bea 14B, at about 154 kn-, the strains easured by C8 begin to increase rapidly in tension. This change in slope is not shown on C8 of bea 14A as that gauge failed preaturely before the end of the test. The strains on gauges C9, C10 and C11 are initially linear with very steep slopes in the early part of the test. At about 135 kn- in bea 14A, C9 strains show a gentle slope change, with the strains increasing in copression. C10 strains also show a slight slope change at about 97 kn- but increasing in tension, while C11 strains begin to increase in copression at about 10 kn-. The corresponding oents for bea 14B are 106, 9 and 9 kn-, for C9, C10 and C11 respectively. In both 14A and 14B, the strain C10 shows a change in direction kink at about 143 kn- and 138 kn- respectively. At that point the tensile strain begins to decrease with increasing strain, but then resues increasing again at about 149 kn- for both beas.. 150

165 Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Connection Moent (kn-) Conn. axiu oent 00 Conn. axiu oent 00 Conn. swivel oent Bolt full yield Conn. swivel oent B 14A B4 B 14A B5 B 14A B1 B 14A B B 14B B4 B 14B B5 B 14B B1 B 14B B13 ε y 0 ε y 0 ε y ε y Gauge Strain (Microstrains) Gauge Strain (Microstrains) (a) Bea 14A Bea Flange Strains (b) Bea 14B Bea Flange Strains Conn. axiu oent 00 Conn. axiu oent 00 Conn. swivel oent Bolt full yield B 14A C4 B 14A C8 B 14A C9 B 14A C10 B 14A C11 B 14A C13 Conn. swivel oent B 14B C4 B 14B C8 B 14B C9 B 14B C10 B 14B C11 B 14B C13 ε y 0 ε y 0 ε y ε y Gauge Strain (Microstrains) Gauge Strain (Microstrains) (c) Bea 14A Bea Web Strains (d) Bea 14B Bea Web Strains Figure 4.44 Strains in the Bea Webs and Flanges fro Connection Test 3 151

166 4.5. Discussion of Bea Web and Flange Strain Gauge Data The differences between the tension flange strains on B4 and B5 suggest that the tension flange is in cobined bending and axial (tensile) strain fro the onset of testing. In connection test 1, in the initial part of the test, the relative agnitude of strains is such that B4 tensile strains are higher than the B5 copressive strains fro.5 to 4 ties higher. Thus, there are bending effects superiposed on the doinant axial strains. When the slope of B4 changes and the strains begin to increase faster, this is due to yielding of the flange outerost fibres on the external surface in cobined bending and tension. By coparison, in test 1, bending effects cannot be distinguished in the copression flange strains B1 and B13. Rather, the strains are strongly copressive fro the onset of the test. Yielding of the copression flange at approxiately 80 kn- sees to be linked to the connection swivel oent. The change in direction kink that is a feature of strain easureent B1 in all three tests is an interesting observation. We notice that the sae change in direction does not occur on other gauges, so that this is unique to the gauge B1 position. We also notice that except in the case of test 3, this change in direction appears only on the bea that failed in that test i.e. bea 10B in test 1 and 1A in test. Even in test 3 where it appears on both beas, it is ore pronounced on 14B, the bea that failed. We conclude therefore that this change in direction kink is the strain gauge picking up the local buckling of the bea flange. It was entioned already in Section that physical observation showed that the bea that failed in each test appeared to be the one with the larger local buckle in the copression flange. The change in direction kink of strain gauge B1 confirs this visual assessent. There is a regular pattern in the occurrence of the kink it was at approxiately 113 kn- for bea 10B, 119 kn- for 1A, and 15 kn- for 14B. This ay not be the oent at which local buckling coences. It is rather the oent at which the local buckle extends to a gauge 15

167 position. There was local buckling observed on the beas that did not fail 10A, 1B and 14A even if it was less extensive. In all three tests, we notice that the web strain C8 is relatively large and tensile. This gauge is opposite the flush tension bolts. We conclude therefore that a significant portion of the tension force transfer fro the bea profile to the endplate takes place at that level rather than all the forces being transferred via the bea tension flange as is coonly assued. The point at which the flanges begin to yield is shown by the slope changes in B4, C4, B13 and C13. In all cases, the copression flange yields first, and the copression flange strains are uch higher than the tension flange strains at each load level. C8 in the web yields before C4 in the flange. Also C4 and C8 are very siilar in agnitude until C8 yields, except for beas 14A and 14B. This substantiates the above supposition that tension force is being transferred via the tension part of the bea web as well. This haronizes with the cracks observed adjacent to the bea web in the flush tension region in the 10 and 1 endplates, and with the observed endplate bending patterns. In all three tests, the C11 strains generally start out as weak tensile strains, but soon change direction and becoe copressive, yielding in copression soon after C13. Thus, it sees clear that the neutral axis dearcating tensile strains fro copressive strains, initially lies in the copression flange, but then oves into the bea web. The latter part of the curves for C13 and C11 are generally of the sae shape and approxiately parallel, but with C13 deforing ore than C11 (see for exaple Figures 4.4c, 4.43c and 4.44d). It sees then that the copressive strain is loosely linearly distributed across the bea copression flange and the portion of web up to the level of the shear bolts even after the flange and that portion of web becoe inelastic. The difference in strain agnitudes actually suggests that the curve is possibly parabolic rather than linear, but it can be approxiated as linear here. 153

168 In beas 10A, 10B and 1B, the C9 and C10 strains are sall in agnitude and are tensile, increasing only slightly as the tests progress, except that in bea 1B the gauge C10 actually yields just before the test ends and begins to increase rapidly. Interestingly, the C10 strain increent is actually a little larger than that of C9 in each of these beas, with oent increase. It sees therefore that the tensile force transfer just above the shear bolt level (C10) ay be facilitated by the claping effect of the shear bolts. This effect is not there at the bea centre (C9), so the C10 strains are higher. This suggestion haronizes with the observed bulge in the endplate peranent deforation (see section 4.1), between the level of the flush tension bolts and the shear bolts. The web strain for bea 1A differs fro the others, as C10 in 1A is copressive, and yields in copression. In bea 1A, C10 follows the curve of C11 and ends up foring a pattern of copressive strains with C11 and C13. Thus, the neutral axis in bea 1A appears to ove higher than the level of the C10 gauge (slightly above the shear bolts), and the copressive strain distribution is still linear fro the neutral axis to the outerost fibre of the bea copression flange. Clearly, this is not the case in bea 1B discussed in the last paragraph, where the C10 curve reained tensile and yielded in tension. In 1B, the neutral axis reains under the level of the C10 gauge. It is now possible to infer the strain distribution across the bea profile in tests 1 and, and this is sketched in Figure 4.45b. The tensile strains are approxiately unifor across the bea tension flange and flush tension region, with a sharp transition or jup fro the flange into the web. The copressive strains are approxiately linear fro the copression flange to a point in the bea web the neutral axis. The location of this neutral axis is dictated by the endplate thickness for a given endplate geoetry. Figure 4.45b shows this assued strain distribution in an idealised fashion. Gauge C10 starts out as slightly copressive in bea 14A, while C10 and C11 are both slightly copressive in bea 14B. For both beas, the C9 strains 154

169 increase faster in the copressive direction later in the test, but not as fast as C11. However, the C10 strains becoe tensile. It appears contradictory to have tensile strains at C10 just above the shear bolts but copressive strains at C9 and C11 on either side. The other contradictory observation about C10 in test 3 is that it has a change in direction kink for both beas 14A and 14B. Thus, the C10 gauges are likely quite close to the neutral axis position, so that inor differences between the speciens are sufficient to odify the neutral axis level sufficiently that it is above the gauge position in one case, though below the gauge in other cases. Tensile strains N.A. Copressive strains (a) Endplate and bea profile (b) Observed strain distribution (c) Idealised strain distribution Figure 4.45 Strain Distribution across Bea Profile in Tests 1 and 4.6 SUMMARY OF DEDUCTIONS FROM THE CONNECTION TESTS Based on the experiental observations and discussions above, the following deductions ay be ade concerning the behaviour of practical, well-proportioned, thin, partial-strength extended endplates: 1. The deforation of the flush region is initially in a circular pattern, with radial strains around the bolt hole as centre. The circle enlarges until it is constrained 155

170 by the bea web and flange, and the pattern then becoes siilar to the yield line pattern adopted in this thesis.. In the extended region, the region between the bea flange and the bolt line is in double curvature with a point of inflexion between the flange and bolt line. This inflexion point oves towards the bolt line as the applied oent increases. 3. In thinner endplates the flush region deforation pattern is stiffer than the extended region cantilever deforation, and thus the flush bolt forces are initially uch higher. Deforation and yielding of the endplate, as well as yielding of the bolts in bending, later leads to a redistribution of forces away fro the flush towards the extended region. 4. The weld line extended region of the endplate starts yielding ahead of the flush region, which is probably because of the larger curvatures required for copatibility on the weld line. 5. By the tie the stiffer flush region is yielding extensively, the extended region with larger curvatures is already strain hardening. Thus, the swivel point rotation in the oent-rotation curve of the connection is dictated by yielding of the stiffer flush region rather than by the extended region. Nevertheless, the swivel knee is only coplete when the extended region bolt line has also yielded. 6. At load levels beyond the swivel point, portions of the flush region also begin to strain harden. When the deforations increase further, both regions also exhibit ebrane action, associated with large displaceents of the endplate. 7. Cracks in the thin endplate usually develop in the stiffer flush region first, around the bolt-holes and adjacent to the bea web. In deciding on a axiu strain criterion to deterine the axiu perissible rotation therefore, it is reasonable to base this on behaviour in the flush region. However, the connection is still able to resist load after these initial cracks, and endplate fracture only occurs when the extended region weld line also cracks and then fractures. Endplate fracture would depend on the endplate strains approaching the ultiate strains in the tensile test, but preature 156

171 fracture ight occur fro the loss of ductility in the heat-affected zone associated with the bea flange weld. 8. At high connection load levels approaching the bea plastic capacity, the bea copression flange undergoes inelastic local buckling accopanied with yielding. This yielding initiates in the bea flange and then spreads to the adjacent area of web. 9. Tension force transfers fro the extended bolts via the endplate to the bea section around the level of the bea tension flange, and tension force transfers fro the flush bolts via the endplate to the bea section in the upper (tension region) part of the bea web. The tensile strains are highest in the part of the web opposite the flush region tension bolts. 10. Copression force transfer fro the bea profile to the endplate takes place across the bea copression flange and the region of web iediately adjacent to the copression flange, with the web contribution coencing at higher load levels. 11. The fulcru or centre of rotation about which the bea profile rotates is initially at the external edge of the bea copression flange, but at higher connection oents, the centre of rotation shifts into the web and is eventually at about the level of the shear bolts. 1. In the endplate the extent of the copression area is dictated by the presence of shear bolt pre-tension forces that extend the copression area to the level of the shear bolts. The shear bolt pre-tension provides a claping force that claps the endplate to the colun face between the shear bolts and the bea copression flange. This claping force is not unifor across the endplate width however, as the portion of the web adjacent to the bea copression flange will exert an outward force to reduce the claping effect. Thus, bearing of the endplate in copression against the colun flange also extends to about the shear bolt level. 13. The shear bolt level ay therefore be considered a plastic neutral axis for the change fro tension to copression in the endplate, as well as a centre of rotation for the bea profile, at high load levels. 157

172 14. Pre-tensioning of the bolts has a beneficial effect on the initial stiffness of the connection as one would expect. Surprisingly however, it also sees to increase the connection rotation capacity. This effect is difficult to take into account however, as current practice leads to variable pre-tension forces. 15. The flush and extended bolts bend significantly during at ediu to high levels, and yield in bending prior to yielding axially. Bending of the extended bolts is priarily longitudinal while bending of the flush bolts is priarily transverse. In the 14 tests however, bending of the flush bolts was also longitudinal. 16. The swivel point in the connection oent-rotation curve appears linked to the yielding of the flush bolts in bending and the developent of a yield pattern in the flush region. 158

173 5. FE ANALYSES OF CONNECTION TEST ENDPLATES In this chapter, a finite eleent analysis is presented for each of the three endplate geoetries tested in the experiental prograe of Chapter Four. The intention is to isolate and study the fundaental behaviour of the endplate itself, while eliinating aterial and experiental iperfections such as welding and lack-offit residual stresses as well as test specien dissyetry. 5.1 FINITE ELEMENT MODELLING APPROACH The endplates have been odelled with 3-diensional brick eleents using the ANSYS ED software version 9.0. The chosen eleent was the SOLID 186 a 3- diensional 0-node structural solid eleent, suppleented with the SOLID 187 eleent, a 10-node tetrahedral. Contact was odelled with CONTA 174 and TARGE 170 contact eleent pairs. In order to siplify the analysis, only the endplate itself and the flush and extended region bolts were odelled. The effects of bolt pre-tension, as well as colun flange deforation and bea bending, were not odelled Modelling the Endplate Geoetry Since the endplate geoetry is syetrical about the centreline through the bea web, only half of the width was odelled. Thus, each endplate FEA odel coprised half of the endplate on one side of the line of syetry. This is illustrated in Figure 5.1. The effect of syetry was odelled by applying a frictionless boundary condition to the surface on the line of syetry, so that perpendicular displaceents and rotations on that face are constrained to zero, but 159

174 tangential displaceents and rotations are peritted. Figure 5.1 shows the coordinate syste used. The colun flange was idealised in the FEA odels as an unyielding surface. In order to odel the endplate interaction with the colun flange therefore, a copression-only support boundary condition was applied to the far-side surface of the endplate, which would be in contact with the colun flange. As the nae iplies, a copression-only support prevents displaceent of the surface in the direction iplying copression (negative Z direction in this case), but does not resist deforation in the opposite (positive Z) direction. Thus, the copression-only support allows separation of the supported surface fro the support when tensile stresses develop. (a) Perpendicular view on endplate. The reote load point can be seen acting at the bea centroid, but it is1000 above the surface. (b) Side view on endplate. The frictionless support (line of syetry) can be seen as well as the bolts extending past the endplate. Figure 5.1 FEA Model of Endplate Geoetry Three surfaces were dearcated to ark the positions where the endplate interacts with bolt-heads. These were each circular annuli, centred around the bolt-holes. The diaeter of these contact surfaces was taken as the average of the M0 160

175 Grade 8.8 HSFG bolt-head width, taken across corners and across flats. The flush and extended region bolts were odelled, with the bolt head exerting pressure on the contact surfaces. The bolt length was taken as grip length, and the width as the thread area diaeter. The far end of both bolts away fro the endplate had a fixed support condition applied to it i.e. zero displaceents in the x, y and z directions, as well as zero rotations about the three axes. The shear bolt in the copression area was odelled with a radially-fixed (but axially and tangentially free) support on the inside surface of the bolt hole, and a 14 kn force (the noinal pre-tension for an M0 Grade 8.8S bolt) claping the endplate to the colun flange copression-only support. The contact between the flush and extended bolt shanks and the endplate holes inner surfaces was not odelled. Thus, in the FEA odels, the shear coponent of the applied load was resisted only by the radial fixity at the shear bolt-hole. The load was applied to the endplate near face by dearcating a surface to atch the bea web and flanges (again considering syetry about the frictionless surface). The load was then applied to a reote point with coordinates atching the actual point of load application i.e. at 1000 fro the endplate surface. The load was then transferred to the dearcated surface by linking the surface to the reote point with rigid links. In this way, the correct ratio of shear force to applied oent was aintained during the load application. Meshing of the FEA odels was carried out using the progra s built-in autoated eshers The FEA Material Models In the FEA odels, the endplate aterial was odelled using tri-linear stressstrain relationships derived fro the experiental endplate saples for each endplate thickness. The flush and extended region bolts were siilarly odelled using the bi-linear stress-strain relationships deterined experientally for the bolts under a given grip length (endplate thickness and 14 colun flange). 161

176 However, the FEA odels require the use of true stress-strain relations rather than the noinal stress and strain values easured experientally. Thus, the experiental values were adjusted using the following equations: True stress = f y (1 + ε y ) Eqn 5.1 Log strain = ln (1 + ε y ) where fy is here used as the yield or ultiate stress, and ε y is used to refer to the yield or ultiate strain. The bolt tensile test readings were taken on the shank, however, the thread diaeter was used to odel bolts in the FEA odels. Thus, the bolt stress-strain values were further adjusted to account for the difference between the thread diaeter and the shank diaeter, so as to obtain the sae bolt forces at the swivel and bolt fracture points in the bolt bi-linear stress-strain curve. A noinal thread diaeter of 16.9 was used in all the FEA odels as this was the average easured thread diaeter for the bolts in the tests. Table 5.1 Material Properties for FEA Models of Endplate Behaviour Young s Modulus True Yield Stress True Yield Strain True Hard g Strain True Ultiate Stress True Ultiate Strain GPa MPa MPa plate (Test 1) 1 plate (Test ) 14 plate (Test 3) Bolt for 10 plate (4 grip length) Bolt for 1 plate (6 grip length) Bolt for 14 plate (8 grip length)

177 The true stress-strain values are tabulated in Table 5.1, with the adjusted bolt stresses. The tri-linear aterial odels are based on a secant approxiation in the strain hardening region i.e. the ultiate point coincides with the experientally observed point in ters of ultiate stress and ultiate strain, but the iplied value for the Strain hardening Modulus with thus differ fro the experiental value, since the strain hardening region is odelled as a linear region. 163

178 Connection Moent (kn.) 5. RESULTS FROM THE FEA MODELS The FEA Model Moent-Rotation Curves The oent-rotation curves derived fro the 10, 1 and 14 endplate FEA odels are shown in Figures 5. to 5.4, superiposed on the respective test experiental oent-rotation curves. The oent-rotation curves were plotted by applying the reote displaceent in increental steps during the siulation, while calculating the endplate rotation fro the geoetry of the reote end relative to the endplate. The applied oent was calculated by the software at each load increent plate FEA Test 1, 10A Test 1, 10B Rotation (Radians x 10^-3) Figure 5. Moent-Rotation Curve for 10 Endplate FEA Model It can be seen that there is reasonably good agreeent between the 10 FEA oent-rotation curve and the Test 1 experiental curves in Figure 5.. However, the FEA connection is clearly stiffer, getting to the swivel point at 5.1 illi-rads copared with 9.8 and 6. illi-rads for the experiental curves 10A and 10B. Siilarly, the FEA axiu oent of 184 kn- occurs at 80 illirads, copared to the Test 1 axiu of kn- at 101 illi-rads. 164

179 Connection Moent (kn.) plate FEA 40 Test, 1A Test, 1B Rotation (Radians x 10^-3) Figure 5.3 Moent-Rotation Curve for 1 Endplate FEA Model In the sae way, in Figure 5.3 the oent-rotation curve for the 1 FEA odel shows a good agreeent in its shape with the experiental curves, but is stiffer and fails at a higher connection oent. The FEA odel swivel takes place at 10 illi-rads copared to 8. illi-rads and 6.8 illi-rads for the 1A and 1B test speciens. The axiu oent for the FEA odel is 187 kn- at 60 illi-rads, copared with 154 kn- at 67 illi-rads in the experients. The oent-rotation curve for the 14 FEA odel is given in Figure 5.4. This curve does not atch the experiental curves as well as the other two. Swivel takes place at 5 illi-rads copared with the experiental values of 10.6 and 11.9 illi-rads, while the axiu oent is kn- at 35 ili-rads copared to kn- at 80 illi-rads in Test 3. The greater stiffness of the FEA odels as copared to the experients is largely explained by the oission of the bea fro the FEA odels. The bea contributes to the rotation in two ways first by bending of the bea end between 165

180 Connection Moent (kn.) the endplate face, and the joint where the experiental rotation easureents were ade. Secondly, the bea contributes to the connection rotation through inelastic deforation of the bea region adjacent to the endplate. This includes inelastic buckling of the copression flange as observed in the experients. The contribution of bea bending to the total connection rotation increases with endplate thickness, which is why the discrepancy between the FEA odel oent-rotations and the experiental oent-rotation curves, also increases with endplate thickness plate FEA 40 Test 3, 14A Test 3, 14B Rotation (Radians x 10^-3) Figure 5.4 Moent-Rotation Curve for 14 Endplate FEA Model 5... Stresses and Deforations in the 10 Endplate FEA Model Figure 5.5 shows the stress pattern in the 10 endplate FEA odel at axiu oent. This is the equivalent Von Mises stress plotted in contour bands. Figure 5.5 (a) shows the stresses on the top surface next to the bea, while 5.5 (b) shows the stresses on the botto surface next to the colun flange. The true yield stress in the odel (as distinct fro the noinal yield stress) is 331 MPa, so that any areas in the figure with stresses above 331 MPa have yielded. The true ultiate stress is MPa. It can be seen that the axiu stress has just been attained 166

181 on the botto surface, and the contours in the axiu stress band on both surfaces reveal locations susceptible to stress cracks. These locations agree exactly with the experiental observations. (a) Stresses on top surface (looking fro the (b) Stresses on botto surface (looking fro bea side towards the colun flange) the bea side towards the colun flange) Figure 5.5 FEA Model Stresses in 10 Endplate at Maxiu Moent In the extended region there are two horizontal bands of yielding one across a horizontal line through the bolt hole on the botto surface, and the other on the top surface, parallel and adjacent to the bea tension flange position. These indicate yielding on the bolt line and the weld line respectively the classical double-curvature of the extended region. 167

182 In the flush region of the endplate, the positive yield-lines on the top surface are two essentially straight lines. The first is adjacent and parallel to the bea tension flange position while the second is adjacent and parallel to the bea web position. Three negative yield lines can be discerned on the botto side. The first is horizontal through the bolt line, but only on the plate edge side. The second is along the bea web, and the third is radial fro the bolt hole upwards. Figure 5.6 is a close-up view of the 10 endplate FEA stresses, with the yield-lines superiposed. (a) Stresses on top surface with inferred yieldlines (b) Stresses on botto surface with inferred superiposed yield-lines superiposed Figure 5.6 Yield-lines inferred fro FEA Stresses in 10 Endplate It appears then that there are essentially two yield-lines in the extended region both horizontal, with one at the bolt line and the other at the weld line. And there are four distinct yield-lines in the flush region a vertical one by the bea web, a horizontal one by the bea flange, a second horizontal one through the bolt line 168

183 but only on the outer edge of the plate, and a fourth one which is diagonal fro the bolt hole to the corner between the bea web and bea flange. At those yield-lines where the yielding is on both surfaces and the plate curvatures are large, the plate is predoinantly subject to bending stresses. However, at the bolt line in the extended region and the partial bolt line in the flush region, as well as the horizontal weld line in the flush region below the bea flange, the yielding is extensive on one surface but insignificant on the other. It would see therefore that ebrane stresses are superiposed on the bending stresses in those regions. (a) Side view on endplate (b) Front view on endplate Figure 5.7 FEA Model Deforations in 10 Endplate at Max Moent 169

184 Figure 5.7 shows the deforations of the 10 endplate FEA odel at axiu connection oent. The contours are directional i.e. are based on deforation coponents in the Z direction along the bea axis. A side elevation is shown in Figure 5.7 (a) where it can be seen that the bea profile rotates as a single piece. This is linked to the finite eleent forulation as the bea end is odelled with non-deforable rigid links. In Figure 5.5 (b), even though it is partly obscured by the ruler, it is possible to see that there is a region of high stress on the botto surface of the endplate, opposite where the copression flange bears against the top endplate surface. This does not iply however that the copression of the endplate against the colun flange is confined to the region opposite the bea copression flange. A second region of high copressive stresses is visible in Figure 5.5 (b), around the shear bolt. This is due to the claping effect of the pre-tension in the shear bolt. By virtue of the plate geoetry, the shear bolt could resist high shear forces, but would only resist low to oderate axial forces when the connection is subjected to bending oent. Thus, the claping force is not overcoe under load. In Figure 5.7 (b) it can be seen that the part of the endplate below the level of the shear bolt does not defor away fro the colun flange, and reains ore or less in contact with the colun flange. This also applies to a narrow strip along the free edge of the endplate. Thus, in ters of the prying of the endplate flush region against the colun flange, a neutral axis can be discerned, approxiately at the level of the shear bolts. This refers to where the endplate, bea and bolt interaction with the colun flange changes fro a force on the endplate towards the colun flange surface, to a net force on the endplate to pull away fro the colun flange surface. In Figure 5.5 it can be seen that above the shear bolt level, the bea web acts on the endplate to exert a force away fro the colun flange. 170

185 5..3. Stresses and Deforations in the 1 Endplate FEA Model The stress pattern in the 1 endplate FEA odel is very siilar to that in the 10 endplate FEA odel at the axiu oent. The true yield stress used in the tri-linear aterial odel for the siulation is 306 MPa, and the true ultiate stress is MPa. (a) Stresses on top surface (looking fro the (b) Stresses on botto surface (looking fro bea side towards the colun flange) the bea side towards the colun flange) Figure 5.8 FEA Model Stresses in 1 Endplate at Maxiu Moent In Figure 5.8, the sae double curvature patterns on the bolt line and weld line can be seen in the extended region. Siilarly, in the flush region, the sae yieldline bands are discernible, though not as pronounced on the top surface. 171

186 Figure 5.9 shows the FEA stress pattern in the 1 endplate at the swivel oent. Most of the yield-lines that appear at the axiu oent can be seen to be eerging already at swivel, though the stresses are still below yield value. (a) Stresses on top surface (looking fro the (b) Stresses on botto surface (looking fro bea side towards the colun flange) the bea side towards the colun flange) with an inferred yield-line superiposed Figure 5.9 FEA Model Stresses in 1 Endplate at Swivel Moent However, a difference between the yield and swivel patterns can be seen in the flush region, halfway between the flush and shear bolt positions. There is an additional inclined yield-line apparent in this region, running fro the web side at flush bolt level towards the plate edge at shear bolt level. This is arked up on the botto surface in Figure 5.9. It can also be noticed that the incipient yielding in 17

187 the flush region at the bea web bea flange junction is ore widespread than at the axiu oent. These differences in the swivel fro the axiu stress pattern are in harony with the experiental observations where the yield pattern at swivel was seen to be different fro that at axiu oent. (a) Side view on endplate (b) Front view on endplate Figure 5.10 FEA Model Deforations in 1 Endplate at Max Moent The deforation of the 1 endplate FEA odel at axiu oent is shown in Figure It can be seen that the deforation pattern and contours are identical to those for the 10 endplate FEA odel in Figure 5.7. However, the absolute values differ. Thus, the axiu deforation in the z axis direction for the 10 odel was 4., while the sae value for the 1 endplate odel is This is again in harony with the experiental observations. 173

188 5..4. Stresses and Deforations in the 14 Endplate FEA Model (a) Stresses on top surface (looking fro the bea side towards the colun flange) (b) Stresses on botto surface (looking fro the bea side towards the colun flange) Figure 5.11 FEA Model Stresses in 14 Endplate at Maxiu Moent 174

189 The stress patterns of the 14 endplate FEA odel are shown in Figure In Figure 5.11 the failiar double-curvature yield-lines can be seen in the extended region. However, in the flush region, only one of the four yield-lines observed for the 10 and 1 odels is fully developed. This is the horizontal yield-line on the bolt line fro the bolt hole to the edge of the plate. There is yielding apparent parallel to and adjacent to the bea web, but only over a short length. Again, there is yielding parallel to and adjacent to the bea flange, but only for a short length also. (a) Side view on endplate (b) Front view on endplate Figure 5.1 FEA Model Deforations in 14 Endplate at Max Moent The axiu stress of 431 MPa in the 14 endplate at axiu connection oent, is uch less than the value of 504 MPa for the ultiate stress of the aterial. This is different fro the 10 and 1 odels where the axiu 175

190 connection oent corresponded to the ultiate stress, but it is in accordance with the experiental observations. In the experients, the 10 and 1 endplates were susceptible to fracture, while the 14 endplate did not fail by plate fracture but by bolt fracture. The deforation pattern for the 14 endplate odel in Figure 5.1 is siilar to that for the 10 endplate and 1 endplate odels. 5.3 DISCUSSION OF FEA MODELS The FEA odels allow us to confir the fundaental behaviour of the endplates apart fro possible influences of residual stresses fro welding or lack of fit. As observed in the experients, it can be seen that the deforation of the flush region is initially in a circular pattern, and then becoes siilar to the yield line pattern suggested in this thesis. The circular pattern would be applicable at the beginning of the swivel knee in the oent-rotation curve, just before the flush region deforation becoes significant. Our interest however, is at the top of the swivel knee when the yield-line pattern has changed to that suggested in this thesis.. The FEA odels accurately predict the locations susceptible to high stresses and cracks at ultiate connection oents. The odels confir that the endplate reains in bearing against the colun flange to the level of the shear bolts, so that the endplate neutral axis is at the shear bolt level. The bending behaviour of the bolts is confired qualitatively, as the longitudinal and transverse bending of the extended and flush bolts respectively is siilar to the experiental observations. As could be seen fro the experiental strains, the high stresses in the FEA odels reveal the occurrence of strain hardening on the extended region weld line close to the plate edge; and ore widespread strain hardening on the extended 176

191 region bolt line right across the plate. The odels also show strain hardening taking place in the flush region on the yield line adjacent and parallel to the bea web, and on the flush bolt line, especially fro the plate edge to the bolt hole. The FEA odels for the 10 and 1 endplate show in addition that ebrane stresses occur in the extended region on the bolt line, and in the flush region on the partial bolt and the weld line. A coparison is ade in Table 5. between the experiental results and the FEA odel values, for the connection oent-rotation curve. We notice that the FEA odels consistently overestiate the connection ultiate oent and consistently underestiate the connection rotation. In the FEA odels the bea end is odelled with non-deforable rigid links. This has the effect of increasing the initial stiffness, and increases the apparent stiffness of the flush region of the endplate, thus leading to higher ultiate oent resistance. Table 5. shows that the FEA overestiate is consistently about 5% at swivel, but varies fro 1% to 3% at the axiu oent. Table 5. Coparison between FEA Results and Experiental Values Moent values (kn-) Rotation values (rads x 10-3 ) Expt FEA FEA/Expt Expt FEA FEA/Expt 10 endplate 1 endplate 14 endplate Swivel Maxiu Swivel Maxiu Swivel Maxiu The underestiate of connection rotation is due to the oission of the bea end contribution to rotation in the FEA odels. In the tests of Bernuzzi et al (1991), the IPE 300 bea end contributed over 50% of the total rotation at the axiu point in a test on a 15 endplate connection, while the contribution was about 177

192 0% for a 1 endplate connection. Thus, the FEA/Experiental ratios of 0.80 and 0.44 respectively, for the axiu point rotation of the 10 and 14 endplates, show excellent agreeent with the observations of Bernuzzi et al. The value of 0.80 iplies a 0% contribution by the bea end for the 10 endplate, while a value of 0.44 iplies a 56% contribution by the bea end for the 14 endplate. We suggested in the previous chapter that the 1 experiental endplate probably fractured preaturely, possibly due to loss of ductility in the heataffected zone. This supposition is supported by the FEA/Experient ratios at axiu point, as the 1 experiental axiu oent and rotation do not fit the patterns suggested by the 10 and 14 endplate values. Lower values for the axiu oent and rotation FEA/Experiental ratios (iplying larger axiu oent and rotation in the experients), would be ore consistent with the 10 and 14 endplate ratios. 178

193 6. A MODEL OF ENDPLATE DUCTILITY 6.1. INTRODUCTION In this chapter a odel is presented for predicting the ductility of a partial-strength extended endplate connection with four tension bolts syetrically disposed about the bea tension flange. The interactions between three key areas are considered the flush region of the endplate between the flanges, the extended region of the endplate beyond the tension flange, and the portion of the bea iediately adjacent to the connection, which properly fors part of the joint. Bending of the colun flange and shear panel deforation are not included in this odel. The oent-rotation behaviour of the connection can be idealized as a bi-linear curve. Thus, the ductility odel proposed here is based on identifying the connection oents and rotations at two points in the oent-rotation curve. These two points are referred to as the swivel point where the two lines of the bi-linear odel intersect, and the axiu point where the axiu oent is predicted to occur. This is illustrated in Figure 6.1. In the odel to be developed, the swivel point is taken as the point at which the yield lines in the flush region are fully developed, so that the flush region is about to start strain-hardening. The axiu point is taken as the point at which the strains in the flush region reach a axiu perissible strain level, or as the point at which the force in either the flush or extended tension bolts attains to the ultiate bolt capacity in tension, F ub. 179

194 Moent Maxiu Point Swivel Point Actual Moent-Rotation Curve Bi-linear Model Rotation Figure 6.1 Typical Bilinear Model of a Moent-Rotation Curve In order to deterine the oents at the swivel and axiu points, the tension bolt forces in the extended and flush regions ust be calculated. The tension bolt force in the flush region at swivel is based on a yield-line analysis of the flush region, using a well-established yield-line odel. The rotation of the connection at both the swivel and axiu points is based on the deforation of the stiffer flush region. The flush region deforation is assessed using a echanical odel of a siply supported square plate with a central point load. The odel provides a relationship between the applied force and the plate deflection, including ebrane action, and also a relationship between the plate deflection and the axiu strain in the plate. Strain hardening is catered for at the axiu point by adjusting the plate bending stiffness fro a function of E to a function of E sh, for the force increent fro the swivel point to the axiu point. The square plate odel is used to obtain the flush region deforation at the swivel point, with the point load taken as the previously calculated flush tension 180

195 bolt force at swivel. The sae square plate odel is used to obtain the flush region deflection at the axiu point, by setting the axiu strain in the plate at the axiu perissible strain level. The flush tension bolt force at axiu point can then be calculated fro the flush region deforation at axiu point. The extended region deflections at swivel and axiu points are obtained fro the corresponding flush region deflections at those points, by considering copatibility of deforation. A conceptual odel of the extended region as a siply-supported bea is then used to provide a relationship between the extended region bolt force and the extended region deflection. Strain hardening and ebrane action are included in this odel. Thus, the extended bolt tension forces can be calculated fro the extended region deflections, at both the swivel and axiu points. Once the extended and flush tension bolt forces are all known, the connection oents and rotations can be calculated using a stress-block approach. It is necessary however, to first establish a aterial behaviour odel for the endplate in ters of its oent-curvature relationship. This fors the basis for the aterial assuptions in the developent of the odel. Thus, before considering the odel developent further, the next section deals with the endplate aterial odel to be adopted. 181

196 Stress 6.. THE ENDPLATE MATERIAL MODEL The Endplate Stress-Strain Curve in Uniaxial Tension The easured aterial properties for the connection test ebers were reported earlier in Table 3.. In Table 6.1 these sae aterial properties are presented again but as diensionless ratios. The ultiate strain in this latter table has been calculated fro the ultiate stress and the strain-hardening odulus. f u Maxiu Yield E sh = E/50 f y Strain hardening Slope = E Strain as a Multiple of e y Figure 6. Idealized Material Stress-Strain Curve The ratios in Table 6.1 lead to average values for the E/E sh ratio of 50.43, for ε sh / ε y of 9.83, and for ε ult / ε y of in the endplates. These values agree closely with typical averages of 50 and 10 for E/E sh and ε sh / ε y, reported for steels produced in South Africa and North Aerica (Kep, 1988 and Galabos & Ravindra, 1978). Thus, it is reasonable to idealize the aterial uniaxial stressstrain curve as a tri-linear curve with a linear elastic region, a perfectly plastic region to a strain of 10ε y, and then with a strain-hardening region at a slope of E/50. This siplified representation is shown in Figure 6.. For the endplates only, a reasonable assuption of the ultiate strain would be 38ε y. 18

197 Table 6.1 Material Properties in Connection Tests as Diensionless Paraeters Young s Yield Yield Harden g Harden g Ultiate Ultiate Modulus stress Strain Strain Modulus Stress Strain GPa MPa GPa MPa 10-3 E/E sh ε sh / ε y ε ult / ε y (E) (f y ) (ε y ) (ε sh ) (E sh ) (f ult ) (ε ult ) Col flange Col web B flange (1) B web (1) B flange () N/A N/A N/A N/A N/A N/A B web () plate (pilot) plate (pilot) plate plate plate Averages

198 6... The Endplate Moent-Curvature Relation Given the rectangular section shown in Figure 6. with breadth b and depth d, and subjected to a bending oent M, then the theoretical plastic oent of resistance M pth for the section is bd f y where f y is the yield stress. If the tri-linear stress-strain curve of Figure 6. is assued, then the stress distribution across the section changes with increasing load, fro a linear elastic stress distribution to an inelastic stress distribution, and finally to an inelastic stress distribution with strain-hardening. The section would eventually fracture with cracks developing at the outerost fibres. These three stages are shown in Figure 6.3. Even when a large portion of the section is inelastic and already strain-hardening, there will still be a sall central core of linear elastic strains less than ε y. The next region bounding the elastic core on either side is inelastic but without strainhardening. The outerost fibres are however strain-hardening in tension and copression. d b N.A. ε ax f ax < f y f ax = f y f ax = f u y < y = y e y e y = y e d f y Section Strain Elastic Inelastic Inelastic Stress Stress Stress with Strain-hardening Figure 6.3 Changes in Stress Distribution on Meber Section under Increasing Bending Moent If curvature is denoted as k, the strain in the outerost fibre is denoted as ε ax, and the subscripts y, sh and ult (or u ) are used to denote values at yield, strainhardening and ultiate strains respectively, the oent-curvature relations are deterined as follows: 184

199 When the axiu stress f ax < f y, the strain ε ax < ε y (section entirely elastic). The bea curvature k = ε ax /d, and when the outerost fibre yields, k = k y = ε y /d (d = y e ). Calculating the oent of the forces: M bd 3 bd.e 3 f 3 3 y bd.ek bd. 3 3 k M 3 k. k M 3.f pth pth.k ax ax y y when ε = ε y, then k = k y and M = M y = M pth /3 Eqn 6.1 For the range f y f ax f sh, then ε y ε ax ε sh. The inner elastic core is still obeying elastic relations, but there is an additional oent of resistance due to the plastic regions on either side. The curvature is of course the sae for the elastic and inelastic zones, but the elastic relations for curvature are only true in the elastic zone. The oent of resistance is: M k y by 3 y e 3 e.ek bf y e y f y Ek d y d y f y e Eky e e M by 3 3 e e.ek by Ek d y e f y bf y y bf y yd 1 M bf y d M pth M pth M pth 1 Eqn 6. 3E k 3k 3 3k When ε = ε sh, then k = k sh and ε sh = 10ε y, then M = M sh = 99M pth /300 = 0.997M pth For ε sh ε ε ult M bf f u E y sh d Ek 10 f d 10y ult M bf f y 3E k y M 4 5 y d bf y d b y f y 3E k bf y d 10y. f f d 10y bf Ekd 75f 50 y 3 y e u Ekd 75f y 3 19f y 3E k e y f d 5 y 4 5 0f y 3E k M 3 pth bf y e Ekd 75f 10y y 3 e 19f y 3E k 185

200 E d 19f y d 19 4 M pth bf 4 y M pth bf yd 5 75f y 3E 5 75 y 3 y 4 k 19 M M pth Eqn k For the endplates, ε ult = 38ε y fro Table 6.1, therefore M u = 1.311M pth In ters of the diensionless constant M' = M/M pth these equations would becoe: y sh y sh ult k 1 1 k 10 M k 3 1 M 1 3k 4 k k 10 k 38 M Eqn 6.4 Following Kep et al (00), a siple bi-linear approxiation to the oentcurvature curve ay be adopted, with the slope of the elastic portion as EI x and the slope of the inelastic portion as E sh I x. By plotting the line of best fit for the inelastic and strain-hardening region, the inelastic region is found to have a slope of E/e, where e ranges fro a lower liit of 75 to an upper liit of 60, and has a ean value of 65. The line of best fit intersects the linear elastic line at 0.9M pth. For siplicity, this intersect is taken here as 0.9M pth. The upper liit of e = 60 is adopted here. The resulting bi-linear approxiation is shown in Figure 6.4 along with the full theoretical oent-curvature curve. The curvature k p at the swivel point is taken as 0.9M pth /EI, so that k p = 1.35k y, where k y is the curvature at first yield, as in the equations above. The axiu oent ratio in the bi-linear approxiation is at a axiu strain of 8.15k p (38k y ). The slope of the strain-hardening segent is taken as E sh I x but with E sh now set at a liiting value of E/60 rather than the tri-linear average value of E/50. The equation for the bi-linear curve in Figure 6.4 ay then be written as follows: 186

201 when when M M pth M M pth M M pth M M pth k k y k 1.35k y Eqn Slope = E sh I x M' = M/M p Slope = EI x Full Curve 0.9 at E/ k p = 0.9M p /EI x 38k = 1.35k y k' = k/k y = 8.15k p p Figure 6.4 Proposed Bi-linear Moent-Curvature Relation for the Endplate Material 187

202 6.3. DEVELOPING THE DUCTILITY MODEL EQUATIONS The Endplate Flush Region at the Swivel Point Following the evidence of the experiental observations in this study and recoendations in Zandonini and Zanon (1988), the flush region is conceptualized as a plate supported on three sides resisting a point (bolt) force. The connection swivel point occurs when a yield-line collapse echanis is fully developed in the flush region. Based on experiental observations, the yielding pattern is initially circular around the bolt-head; however, as the yielding develops, it changes into the pattern shown in Figure 6.5. This is essentially the thin-plate pattern proposed in Bernuzzi et al (1991). Extended region e x x p 1 Segent 1 Flush region Segent Segent 3 3 h f Centre of Rotation Negative yield-line Positive yield-line e 1 Does not yield here p Figure 6.5 Idealized Yield-line Pattern Adopted for Flush Region at Swivel Adapted fro Bernuzzi et al,

203 Bea web centreline A key difference here though is that the line at the base of segent 3 in Figure 6.5 is not considered to be a proper yield-line. The reasoning behind that change is as follows: The connection forces are applied via the bea web and tension flange. However, segent 3 is claped against the colun flange by the tension and shear bolt pre-tension forces, and is continuous with the portion of endplate adjacent to the bea copression flange. Y Bea flange centreline y 1 Segent 1 y 4 ψ 1 y r Segent y 3 3 Segent 3 y 5 ψ Key +ve yieldline -ve yieldline e 1 Y Figure 6.6 Detail of Assued Yield-line Pattern The deforation of segents 1 and away fro the colun flange is sufficient to allow the bea profile to rotate ore or less as a straight line fro the tension flange to the copression flange level, but is not sufficient to allow a fully 189

204 developed yield-line at the base of segent 3. Thus, segent 3 only defors a little, and yielding at the base of segent 3 is assued negligible. In fact, if the shear bolt pre-tension has not been exceeded, the plate reains claped against the colun flange at the shear bolt level. Bolt force In order to deterine the tension bolt forces at the swivel point, a yield-line analysis is carried out using the well-established yield-line pattern of Figure 6.5b. Figure 6.5a shows the observed positions of yield-lines in the experients, while 6.5b shows the idealized positions used in the analysis. The endplate geoetry is described using the diensions shown in Figure 6.5b, following the notation of SCI (1995) and Eurocode 3 (005). Thus, 1 and are the distances fro the bolt-hole centre to the face of the web and flange respectively, less 0.8 ties the respective fillet weld leg length. The edge distance is e, and the bolt-hole radius is r. 4 is easured to the face of the bea copression flange less 0.8 ties the fillet weld leg length. The tension bolts are at a pitch of p 1 and a gauge of p, and the flush tension bolts are at a height of h f above the base of the copression flange. Other sybols used in the odel are E for Young s odulus, b p and t p for the endplate width and thickness respectively; f y for the endplate yield strength, and pth for the theoretical plastic oent per unit length of plate. The yield-line pattern is shown in close-up for one side of the endplate in Figure 6.6. The lengths of the yield-lines in Figure 6.6 are: y y y 1 3 e e r 1 3 y y r r Eqn

205 θ 1 = δ fs / Bea profile X h f 3 δ fs P fs Segent 1 Segent 3 θ = δ fs / 3 X D - t f Col flange surface No yieldline here Center of rotation Figure 6.7 Longitudinal Section through Flush Region at Swivel (Sect. Y-Y in Fig 6.6) It is assued that the flush tension bolts will bend/defor sufficiently so that the plate is not closely claped against the flange, which is why a circular yield-line is not included iediately around the bolt head. This is consistent with the experiental observations and the literature. It was observed that there was initially widespread yielding around the bolt-head, but at higher rotations the prying of the bolt-head led to inelastic deforation of the bolt in bending so that the claping effect was reduced. In Figure 6.7 showing a longitudinal section through the endplate, segents 1 and 3 on the plate, which would have been in line with the bea profile, can be seen to rotate through θ 1 and θ respectively, away fro the bea profile. Deflection δ fs is the oveent of the endplate away fro the bolt-head on the colun flange, easured in a direction perpendicular to the endplate. The last subscript s denotes that this is at the swivel point. As explained previously, the bea profile is assued to rotate about the copression flange at swivel. 191

206 The internal work done by unit resistance oents p1 and p (kn-/ width) on yield-lines y 1 and y respectively, will be: y 1 : fs fs 1 p1 y1 p1 e 1 p1fs Eqn 6.7 e y : p y fs 3 fs p p e r fs fs 3 e r 3 3 fs Eqn 6.8 There is no yield-line at the botto end of segent 3 as indicated in the figure. In the figure, P fs is the coponent of the bolt force that is perpendicular to the bea profile and so parallel to the bea tension flange at the joint. The external work done by the bolt in causing the plate rotation is therefore: External Work P Eqn 6.9 fs fs Figure 6.8 is a transverse section through the endplate, but taken at an angle so that the section shown is perpendicular to the bea profile (X-X in Figure 6.7). θ 3 = δ fs / 1 δ fs Partial section thru web e 1 Colun flange surface Segent 1 P fs Segent Figure 6.8 Transverse Section through Flush Region (Sect. X-X in Fig 6.7) In Figure 6.8, we see that yield-line y 3 has rotated through the angle θ 3. The internal work done on yield-line y 3 by unit oent of resistance p3 is: 19

207 fs p3 1 fs 3 p3 1 fs 3 p3 3 y : y Eqn 6.10 The rotation θ 4 on yield-line y 4 is the su of the coponents of the slopes (relative to the bea profile) for segents 1 and i.e. θ 1.Cos ψ 1 + θ 3.Sin ψ 1 (see Figure 6.6 for definitions of ψ 1 and ψ ). Siilarly, the rotation θ 5 on yield-line y 5 is the su of the coponents of the slopes for segents and 3 i.e. θ 3.Cos ψ + θ.sin ψ. The internal work done on yield-lines y 4 and y 5 by the oents of resistance p4 and p5 respectively is: 1 1 fs 1 fs 1 1 p4 1 1 fs 1 fs 4 p4 4 Sin Cos r Sin Cos y : y Eqn fs 1 fs p5 3 fs 1 fs 5 p5 5 Sin Cos r Sin Cos y : y Eqn 6.1 Fro Figure 6.6, x Sin ; Cos Sin ; Cos Therefore the work equations for y 4 and y 5 ay be written as: 1 fs p4 1 1 fs p4 4 r r : y Eqn fs p fs p5 5 r r : y Eqn 6.14 Thus, the virtual work equation is:

208 fs p5 1 fs p4 1 3 fs p3 3 3 fs p 1 fs p1 fs fs r r r e e P 3 1 p5 1 p4 1 3 p3 3 3 p 1 p1 fs r r r e e P At the swivel point, the unit oents of resistance p1 p5 in the flush region are equal to 0.9 pth (see Section 6.1.). Therefore, the virtual work equation can be written as: pth fs r r 4 r e e 0.9 P Eqn 6.15 The diensions 1 and are usually in the range of 40 60, and so are typically uch larger than the bolt-hole radius r, which is 11 or 13 for M0 or M4 bolts respectively. The diension 3 is of course even larger than. Thus, the last two ters in the virtual work equation above will be of the order of 10%, so that for siplicity it was decided to eliinate these ters. Therefore the equation for P fs can be siplified to obtain: 4 r e e 0.9 P pth fs Eqn 6.16 Flush region deflection To obtain the flush region deflection, each half of the flush region of the endplate ay be conceptualised as a rectangular plate with a concentrated load due to the bolt force, and with fixed supports on the adjacent edges where it is bordered by the bea web and flange. The third edge is at a line through the shear bolts, and

209 that edge is siply-supported since the restraining oent there is very sall. The fourth edge is free. This is illustrated in Figure 6.9a. An exact solution for the deflection of a rectangular plate with this particular cobination of loading and supports has not been identified. However, an approxiate solution ay be obtained by considering the case of a siply-supported square plate under a concentrated load, as shown in Figure 6.9b. 3 a/ a/ Key Siple edge Fixed edge Free edge Applied load position e 1 a/ a/ (a) Conceptual odel of flush endplate region (b) Approxiate odel for deflection solution Figure 6.9 Square plate odel for flush region deflection In Figure 6.9 a siple support eans the plate is restrained fro in-plane and out of plane translation, while a fixed support is additionally also rotationally restrained. A free edge is not supported at all. When the plate is not subject to an initial deflection due to its own self-weight, Roark (1965: 47) gives a solution for the siply-supported square plate of Figure 6.9b, described in equations 6.17 and 6.18 as follows: 1Pa 1 3 Et 1 t t Eqn

210 This first equation is a relationship between the applied force and the plate deflection, and it includes an allowance for ebrane action, which is catered for by the ter including φ on the right-hand side. P is the applied concentrated force, δ is the deflection at the point of load application, and t is the thickness of the plate. The plate width/breadth is a, and E and ν are Young s odulus and Poisson s ratio respectively. The coefficients φ 1 and φ are 87 and 8 for a plate that is siply-supported on all four sides, and are 19 and 36 respectively for a plate with fixed edges. At the swivel point, there is already yielding along the two fixed edges in the idealized odel of Figure 6.9a, and so a siply-supported solution odel is considered ore appropriate. The plate is considered to have an initial deflection δ i due to pre-applied loads, so that the total deflection δ t = δ + δ i. Secondly t i f center E Eqn 6.18 a This second equation is a relationship between the axiu ebrane stress f center at the centre of the plate, and the deflection δ. Coefficient α is 1.6 for siply-supported edges and.9 for fixed edges. In order to apply these equations to the endplate deflection at the swivel point, we consider that there is no strain-hardening or ebrane action yet in the flush region at the swivel point, and there is no initial self-weight deflection δ i. Thus, using the notation adopted in this thesis, equation 6.17 siplifies to: 1Pfs a Et 1 1P a 1 3 p 87 fs fs fs 87Et 3 p P fs a 8Et 3 p where a = 1 and Poisson s ratio is taken as

211 The square plate approxiation to the actual flush region geoetry has been investigated using an FEA odel in Chapter 7. The FEA odel results show that a reasonable agreeent is obtained between the deflection of the original geoetry and the square plate deflection, if the square plate width a is taken as a = 1 (the lesser diension of 1 and ), and the square plate deflection at swivel is ultiplied by a factor of 3. Therefore: a fs Pfs 3Pfs 1.5Pfs Eqn Et Et Et 3 p 1 3 p 1 3 p Therefore the connection rotation θ cps due to endplate deforation at the swivel point, is given by: cps h fs f 1.5P fs Et 1 3 ph f which assues the bea profile to rotate about the centroid of the bea copression flange at the swivel point. Ignoring the contributions of the bea end and the bolt extensions, then the total connection rotation θ cs = θ cps, and θ cs is given by: fs 1 cs 1.5Pfs Eqn h f Et ph f The Endplate Flush Region at the Maxiu Point The axiu point is dictated by the occurrence of either of two events the tension force in either the flush or extended region bolts attains a liiting value, or the occurrence of a liiting strain in the endplate flush region. The liiting bolt force is chosen here as the bolt ultiate strength F ub, though a safety factor would doubtless be included in practical design. Siilarly, the liiting endplate strain is chosen to liit the likelihood of endplate cracks to acceptable values. For the endplates tested in this study, a suitable liit would be 38ε y (see section 6..1). The first endplate cracks appear around the bolt-hole. 197

212 At the axiu point, the flush region of the endplate is undergoing both strainhardening and ebrane effects. The solution odel of Roark (1965) ay still be used as an approxiate basis for a solution; however, the elastic odulus E is now relaxed to the value for strain-hardening, E sh in equations 6.17 and This is justified fro the understanding that at the axiu point, yielding would be widespread over ost of the flush region, and the plate bending stiffness would have deteriorated. At a liiting endplate strain of 38ε y the liiting endplate stress is given approxiately by f u, where f u E sh E y ult 10 y fy 3810 fy 1.47f y Therefore f u = 1.47f y. 60 At the axiu point, we are effectively considering the endplate deflection as consisting of two steps an initial elastic deflection given by δ fs and the plastic or inelastic increent in deflection. Thus, δ i = δ fs and the total stress at the plate centre will increase fro a axiu of f y at swivel, to a axiu of 1.47f y at the axiu point an increent of 0.47f y. Equation 6.18 gives the ebrane plate stress at the plate centre. At the axiu point therefore, the ebrane plate stress will equal the increent of 0.47f y as we have assued the ebrane stress to be zero at swivel in the flush region. Hence, f center E sh fs a fs 0.47f y fs 0.47a f E sh where α is 1.6 (siply-supported), and δ fs refers to the flush region deflection at the axiu point as calculated by the liiting strain criterion. y fs The elastic deflection δ fs is sall, so that the square ay be neglected. Thus, the equation siplifies to: fs 0.47a 1.6E f sh y a f y 3.4E sh 198

213 However, our axiu stress does not occur at the plate centre but, allowing for stress concentrations, on the bolt-hole radius r. This ay be accounted for with a linear approxiation so that f y r 60f y r f y fs a 1 a 1 4.a r Eqn E a 3.4E a E sh Equation 6.17 can be re-written for the axiu point to obtain: 1Pf a E sh 1 3 t p fs fs 87 8 t fs p where ΔP f refers to the increent in the flush region tension bolt force fro the swivel point to the axiu point. This ay be siplified to: 655.P f a 3 Et p fs fs 87 8 t fs p Again neglecting δ fs for siplicity, Et pfs 8 Et pfs Et pfs Et pfs Pf Eqn a 655. a 7.53a 3.4a and P f = ΔP f + P fs Eqn 6.3 However, the liiting bolt force criterion is that neither the flush region nor extended region tension bolt forces ay exceed the bolt ultiate capacity in tension. Thus, P f F ub Eqn 6.4 If P f as calculated with equations 6. and 6.3 is greater than F ub, then ake P f = F ub, and δ fb, the flush region deflection at the axiu point using the bolt 199

214 force criterion, ust be calculated. This is obtained by substituting δ fb for δ fs and F ub for P f in equations 6. and 6.3. This leads to a cubic equation in δ fb which can be solved by trial and error. In a design situation however, where the designer wishes to avoid failure of the connection fro bolt fracture, a governing liiting bolt force criterion would indicate the need to change to a larger bolt or a thinner endplate. In a siilar anner to equation 6.0, the connection rotation θ cp due to endplate deforation at the axiu point, is given by: cp f 3 which assues the bea profile to rotate about the level of the shear bolts at the axiu point. At axiu point the contributions of the bea end and the bolt extensions are significant, therefore the endplate contribution is increased by a factor of 1.33 to account for these. This epirical factor is based on test results published in Bernuzzi et al (1991) as explained in chapter seven. Thus, the total connection rotation at the axiu point θ c is taken as: 4 f c Eqn

215 Bolt line Weld line The Endplate Extended Region Flange Force P x x (a) Endplate geoetry P x Inflexion point (b) Deflected shape l w δ w θ xw (c) Siplified deforation θ xb (d) Bending oents Figure 6.10 Bending Moent Distribution across extended region For a thin endplate with reasonable diensions and typical proportions, experiental observations show that the extended region of the endplate, fro the bea tension flange to the bolts, is in double-curvature. Maxiu oents occur adjacent to the bea tension flange weld (referred to here as the weld line), and close to the centreline of the two bolts in the extended region (referred to as the bolt line). This is shown in Figure 6.10 (d). There is an inflexion point between 01

216 the bolt line and the weld line, and because the weld line oent exceeds the bolt line oent, this inflexion point is closer to the bolt line. Figure 6.10 depicts a cross-section through the extended region of a thin endplate, with the geoetry and deflected shape shown in parts (a) and (b). Part (c) shows a siplified, linearized version of the deflected shape, while (d) shows the bending oent distribution across the cross-section. Bending and ebrane action in the extended region of the endplate is due to an applied force P x at the bea tension flange as shown in Figure This force excludes any flange forces resisted by the flush region, and also excludes the self-equilibrating prying action forces in the endplate. Fro equilibriu P x is also the bolt force at the bolt line, inus prying action. In SCI (1995) and EN (Eurocode 3, 005) the weld line is offset fro the bea flange face by 80% of the flange weld leg length s wf, as in the flush region. This is due to the uch greater stiffness of the portion of endplate underlying the weld. Following the notation in Eurocode 3, the diensions x and e x shown in Figure 6.11 are taken as: e x = distance fro bolthole centre to plate edge x = distance fro bolthole centre to face of tension flange 0.8s wf. At the swivel point in the connection oent-rotation curve, it is assued here that yield-lines are just fully developed at the bolt line and the weld line. Yieldline y 6 in Figure 6.11 is the negative yield-line on the weld line while y 7 is positive and is on the bolt line. At the axiu strain point in the oentrotation behaviour, these yield-lines have grown to becoe bands of plastic aterial with an elastic zone between. 0

217 e x y 7 x y 6 b p / 0.8s wf Negative Yield-line Positive Yield-line Figure 6.11 Location of yield-lines in Extended Region x l w θ 1 = δ fs / Bea profile θ xw h f δ w 3 δ fs Extended bolt force θ xb Inflexion point Col flange D - t f / θ = δ fs / 3 Figure 6.1 Longitudinal Section through Endplate at Swivel Bolt force P xs at Swivel In order to establish the extended bolt force at swivel, consider Figure 6.1 which is a longitudinal section through the endplate at swivel. The flush region is shown as well to clarify how the bea profile rotation affects the rotation of the extended region about the weld line. The plate deflected shape is clearly non-linear between the bolt and weld lines, since the bending oents are non-linear and there is also plastification around the yield-lines. However, a linear siplification ay be usefully adopted to establish approxiately the point of inflexion. The rotation on the bolt line is defined as θ xb and the rotation on the weld line is θ xw. It can be seen that the weld line rotation ust exceed the bolt line rotation, so 03

218 that the weld line oent ust exceed the bolt line oent. For the siplified linear deforation shown, θ xw = θ xb + θ cp where θ cp is the rotation of the bea profile due to plate deforation (θ cps or θ cp as the case ay be). Then fro siilar triangles, θ xb is given at swivel by xb cps D t f x cps D x Thus, xw xb cps cps D 1 Eqn 6.6 x Thus, l w in Figures 6.10 and 6.1 is given as l w xw x D x x Eqn 6.7a D xw xb x If we consider the length l w fro the inflexion point to the weld line as half of a siply-supported bea with the support at the point of inflexion, the central deflection of this bea equals the deviation δ w of the weld line fro the point of inflexion, which is given for the siplified deforation as: cps x D xw w xw l w x Eqn 6.7b D xw xb x Since θ cps has previously been obtained at the swivel point fro equation 6.0, equation 6.7b allows us to calculate δ w at the swivel point. This conceptual odel is illustrated in Figure The siply-supported bea is restrained axially at the ends so that axial ebrane forces develop as would actually occur in the endplate due to the restraint at the bolt line and weld line. The force P acting at the bea centre to produce the sae deflection δ w as in the 04

219 Inflexion point Weld line extended region of the endplate will be twice the force P x acting on the endplate. This odel is statically equivalent to the endplate extension fro the weld line to the inflexion point, regardless of whether or not yielding is occurring, as long as the second oent of inertia and the aterial odel are the sae as for the extended region. P = P x δ w l w l w Figure 6.13 Conceptual Model of Extended Region Sherbourne and Lu (1993) present a solution for establishing the central point load P acting on an axially restrained, siply supported bea which undergoes large deflections, siilar in agnitude to its own depth or greater, and where the central force is sufficient to cause inelastic strains in the bea fibre so that the bea yields and strain hardens significantly at the centre. This atches the behaviour of the conceptual odel above. In their solution, Sherbourne and Lu assue a rigid linear strain hardening aterial odel, so that elastic strains are neglected. For our endplate extended region, the elastic strains are negligible by coparison with the inelastic strains so that this is acceptable. In non-diensional for, the solution of Sherbourne and Lu is given below as Equation 6.8. p h 6w w w 1 w Eqn 6.8 where w is the ratio of central deflection to the endplate thickness = δ w / t p h is the ratio of thickness to half the span length = t p / l w 05

220 λ is the hardening factor - a easure of the aterial strain-hardening behaviour and E 3f sh for our aterial odel. y E 180f y p = P/ P 0 and is the ratio of P to the theoretical plastic collapse load P 0 For a siply-supported bea with span L, P 0 4M L p M l w p where M p is the bea fully plastic oent. In the aterial odel adopted in this thesis, the plastic oent is taken as 0.9 of the theoretical value (oentcurvature relation of Section 6.), so that P 0 0.9M pth 0.9 pthb Eqn 6.9 l l where M pth is the theoretical plastic oent for bending across the entire endplate width, pth is the theoretical plastic oent per unit width, and b is the endplate width. Only half the endplate is considered here (for one extended region bolt), hence a factor of 0.9 has been used in equation 6.9 rather than 1.8. w w In Equation 6.8, the second ter represents an aplification of the collapse load due to axial ebrane effects, while the third ter represents aplification due to strain hardening. For the connections tested in this thesis the effect of strain hardening was to increase the effect of collapse load plus ebrane by a factor that was consistently about 5%. Thus, for siplicity, the strain hardening ter ay be replaced with a ultiplier k es where k es = 1.5, and the equation becoes: p kes 1 4w = P/ P 0 = P x / P 0 k k b es P xs P0 Eqn 6.30 kes 4w es pth 4 w 1 4w P t p.l w t p Equation 6.30 gives the agnitude of the swivel bolt force P xs in our extended region of the endplate. 06

221 In order to apply equation 6.30 it is necessary to know δ w. However, we have found an approxiate solution for δ w in equation 6.7b. Thus, equations 6.7 and 6.30 together provide a solution for the flange force due to bending and ebrane action in the endplate extended region, which is to the swivel point. Note that P xs cannot exceed the bolt ultiate capacity F ub since the bolt would fracture first. x l w θ 1 = δ f / Bea profile δ w θ xw 3 h f δ f Extended bolt force θ xb Inflexion point Col flange D - h f t f / θ = δ fs / 3 Center of rotation Figure 6.14 Longitudinal Section through Endplate at Swivel Bolt force P x at Maxiu Point The above analysis for the extended bolt force at swivel applies also to the axiu point, except that the bea flange now rotates about the shear bolt level rather than the copression flange centroid. This is shown in Figure The previous equations already defined will still apply, except that the lever ar for bea rotation is no longer D but D' where D' = D h f + 3 t f / Then l w x D x Eqn 6.7c D x and cp x D w Eqn 6.7d D x 07

222 Since θ cp has previously been obtained at the axiu point, equation 6.7d allows us to calculate δ w at the axiu point. The rest of the analysis is identical to that for the swivel point, and thus k es pthb 4w P x 1 Eqn 6.30a.l w t p When this equation was applied to the connection tests in this thesis, the ebrane ter returned reasonable values, however the strain-hardening ter (represented by k es ) fluctuated for inor differences in endplate thickness, at the 10 endplate values. Thus, the k es ter appears less well-conditioned at large deflections. The average value for k es at the axiu point was about However, due to the large fluctuations and for siplicity, it has conservatively been retained at the swivel value of 1.5. In setting a practical liit for P x, cognisance should be taken of the occurence of prying forces as well, since these are not included in the odel. 08

223 6.4. AN ENDPLATE DUCTILITY MODEL The Stress-block Approach Extended region P x a) Thin extended endplate in steel bea Flush region Neutral axis P f Copression Section Strain & Extension Stress & Force b) Thick extended endplate in steel bea Extended region Flush region Neutral axis P x P f Copression Section Strain & Extension Stress & Force Figure 6.15 Forces and Stresses across the endplate in the Stress-block approach, based on Brown & Anderson (001) The approach taken here to estiating the connection oents at the swivel and axiu points is siilar to the stress-block/spring approach of Brown and Anderson (001) for coposite beas, but includes strain-hardening of the endplate and ebrane action in the endplate, rather than strain-hardening of the steel section and yielding of the reinforceent as proposed by Brown and Anderson. In our odel the plastic neutral axis reflects the level of zero copression strain in the stress blocks of the steel bea adjacent to the connection. In the steel bea and extended endplate assebly, the force coponents are the tension forces P f and P x developed by the tension bolts in deforing the endplate, and the balancing copression forces in the botto flange and the adjacent web of the steel section. Figure 6.15 illustrates how saller copression forces are required 09

224 for thin extended endplates, and how these copression forces increase as there is an increase in stiffness/thickness of the extended endplate. Along with the progression in increased copression forces, the neutral axis position oves higher. For the thin endplates considered here, the plastic neutral axis in the bea profile is assued to be within the copression flange centroid at the swivel point, and at the level of the shear bolts at the axiu point. Thus, the centroid of the area in copression is at the centroid of the bea copression flange at the swivel point, but is halfway between the level of the shear bolts and the external face of the copression flange at the axiu point. The connection oent is deterined fro the forces acting on the endplate due to the flush tension and extended region bolts. The effective line of action of force P x is therefore taken to act at the level of the extended region bolts, while the force P f is taken to act at the level of the flush tension bolts. Bolt-hole radius is r t f t w e x x p 1 D 3 h f t f e 1 p Figure 6.16 Noenclature for endplate geoetry in ductility odel 10

225 Thus, once P f and P x are deterined, the connection oent M can be calculated as: M cs fs f xs f 1 P h P h p at the swivel point Eqn 6.31 M c t f t P f f hf 3 Px hf 3 p1 f x 1 P h P h p at the axiu point Eqn 6.3 where h f, 3, p 1, and t f are diensions in the endplate geoetry as shown in Figure 6.16, and h = ½(h f t f / ). The subscripts s and refer to the swivel and axiu values respectively. The swivel point in a oent-rotation bi-linear odel is where the two lines of the bi-linear approxiation intersect, as the connection stiffness reduces fro one approxiately constant level to a second approxiately constant level, in a anner reiniscent of Young s odulus and the strain-hardening odulus in ild steel. The axiu oent will be deterined by iposing a axiu acceptable strain level on the endplate beyond which it is considered that fracture is likely to occur, AND by iposing a axiu bolt force beyond which bolt failure is likely to occur A Suary of the Ductility Model The odel is then as follows: 1. At swivel, the flush region swivel bolt force P fs and the swivel connection rotation θ cs are deterined fro endplate geoetry using equations derived in section 6.3 as: e Pfs 0.9 pth e r 4 and Eqn

226 cs 1.5Pfs Eqn 6.0 Et 1 3 phf E refers to Young s odulus, t p is the endplate thickness and pth is the theoretical plastic oent for the endplate, per unit length of plate. The other variables describe the endplate geoetry.. The endplate deflection δ f at the flush bolt position at axiu point, is: f y f 4.a r Eqn 6.1 E 3. The corresponding flush region bolt force P f and connection rotation θ c at axiu strain are given by: P f 3 3 Et pf Et pf Pfs (but P f F ub ) Eqn a 3.4a where F ub is the bolt ultiate capacity in tension. And 4 f c Eqn Note that if P f > F ub then we need to increase the bolt capacity (bolt size or grade) or reduce the endplate thickness, to avoid the bolt fracture failure ode. Alternatively, if bolt fracture is considered acceptable, then P f is taken as equal to F ub, and deflection δ f is obtained by substituting P f in equation 6. and solving by trial and error. 4. At the swivel point, the extended region variables for estiating the region deflection at the bea flange-to-endplate weld are: cs x D w and D x l w x D x Eqn 6.7a,b D where D is the bea depth and θ cs is the connection rotation at swivel (θ cps = θ cs ). The extended region bolt force acting at the weld line is then calculated for the swivel point fro: x 1

227 k es pthb 4w P xs 1 Eqn 6.30.l w t p where b p is the endplate width, k es is the strain-hardening ultiplier, and k es = At the axiu point, the extended region variables for estiating the region deflection at the bea flange-to-endplate weld are: x 0.75 c x D w and l D w x D x Eqn 6.7c,d D where D' = D h f + 3 t f / and θ c is the connection rotation at the axiu point (θ cp = 0.75θ c ). The extended region bolt force acting at the weld line is then calculated for the axiu point fro: k es pthb 4w P x 1 (but P x F ub ) Eqn 6.30a.lw t p with k es = 1.5 as before. x Note that where P x > F ub, then we ake P x = F ub, which iplies extended region bolt fracture as the failure ode. As for the flush bolt; we can increase the bolt size (or reduce the endplate thickness) to avoid this failure ode. 6. The connection oents are then calculated at the swivel and axiu points fro equations 6.31 and 6.3: M M cs c fs f xs f 1 P h P h p at swivel, and f x P h P h p at axiu strain. and h = ½(h f t f / ). 1 13

228 7. DISCUSSION OF DUCTILITY MODEL 7.1. JUSTIFICATION OF ASPECTS OF THE DUCTILITY MODEL Introduction In the experients on extended endplate connections carried out as part of this research and reported here, it was found that relatively thin endplates defor considerably under conditions where bolt and weld failure is precluded, leading to high connection rotations. The ductility odel developed in Chapter five provides a eans of assessing the deforation of thin and interediate endplates, and uses that assessent of deforation to estiate the connection rotation under load. The odel is based on two preises: The first is that even for a thin endplate, the scale of endplate thickness to endplate planar diensions/geoetry is such that thick plate effects such as strain hardening cannot be overlooked in endplate deforation. For the connection to be ductile, the endplate deforations ust be large and inelastic, and large inelastic rotations require strain hardening of the endplate aterial. A second preise is that the agnitude of deforation is such that the applied forces will develop significant coponents in the plane of the endplate, so that the endplate resistance includes ebrane action. The underlying philosophy applied is that the connection swivel point is the point at which the flush region yield-lines are fully defined but are just beginning to strainharden, and the connection axiu point is the point at which the endplate has reached soe liiting strain or a bolt has fractured The Endplate Yield-line Pattern The forces acting on the endplate are transferred via the bolts, and in order to understand the endplate deforation we need to calculate the bolt forces. In the 14

229 flush region the tension bolt force is calculated using a yield-line approach. The yield-line pattern for the flush region shown in Figure 7.1 is well-established, having been used by Surtees & Mann (1970), Zandonini & Zanon (1988), Bernuzzi & Zandonini (1990), Bernuzzi et al (1991), and Abel & Murray (199) but with slight differences between these various researchers. y 1 P x p 1 D t f x y 5 y y 4 3 y 6 y 3 h f Negative yield-line Positive yield-line p Figure 7.1 The Governing Yield-line Pattern for the Endplate In Surtees & Mann s original yield-line pattern, the line arked y 6 in Figure 7.1 was not included as a yield line, and the diension arked x was taken at half the bea depth so that x = 0.5(D t f ). When Zandonini and his colleagues at Trento first applied this yield-line echanis in Zandonini & Zanon (1988), they introduced an additional yield-line at y 6 and changed the position so that diension x = 0.6(D t f ). In their later publication Bernuzzi & Zandonini (1990) they kept the yield-line but oved the position to the inside face of the copression flange so that diension x = D 1.5t f, where t f is the flange thickness. In Bernuzzi et al (1991), they again revised the position of y 6, placing it on the centreline of the shear bolts and aking the diension x = 3. 15

230 Abel & Murray (199) kept the additional yield-line at y 6 but based the position on a iniu energy calculation. Their equation would result in an expression for x such that x = 0.5p (b.p ) 0.5. For the speciens tested in this thesis, with D t f = 93.6, b = 180, and p 1 and p = 16 and 100 respectively, the Abel & Murray expression would give x = 130 i.e. 40 above the level of the shear bolts or x = 0.443(D t f ). We see then that the location of the diension x and the presence of a yield-line at y 6, or not, has been considered differently by previous researchers. In this thesis the position of diension x was established at 3 fro both the experiental observations and FEA odels. I have however gone back to the thinking of Surtees & Mann in excluding a yield-line at position y 6. This is based on the arguent that the endplate segent above y 6 is claped against the colun flange by the tension and shear bolt pre-tension forces, and so is continuous with the portion of endplate between y 6 and the bea copression flange. Thus, the endplate cannot yield at y 6. Surtees & Mann correctly ade the assuption in their paper that the line y 6 would coincide with the neutral axis in the bea profile. They assessed the neutral axis position by easuring the strain distribution across the bea end. However, their endplates were relatively thick, ranging fro ¾" to 1.15" (19 to 8.6). Thus, the neutral axis would be higher up in the bea profile than for the thin endplates considered in this thesis. (It should also be borne in ind that yielding in the endplate along its edges ay extend further down than the observed neutral axis position, as the neutral axis was estiated based on strain easureents at the bea web only). In this thesis therefore, I have set the diension x at x = 3, which value is based on y experiental observations for thin endplates. This agrees with the value for x in the last publication of Zandonini and his colleagues (Bernuzzi et al, 1991) on the subject, for endplates of siilar thickness. 16

231 The Abel and Murray approach is probably a good way of deterining the value of x ore accurately. However, their forula would need to be corrected to exclude the yield-line they assued at y 6. For the thin range of endplates, our approach here was considered sufficiently accurate The Deflection of the Flush Region In order to deterine the flush region deforation at the bolt position, we used square plate deflection forulae taken fro Roark (1965). Roark attributed the forulae to Stur & Moore (1937). 3 a/ a/ Key Siple edge Fixed edge Free edge Applied load position e 1 a/ a/ (a) Conceptual odel of flush endplate region (b) Approxiate odel for deflection solution Figure 7. Square plate odel for flush region deflection Each half of the flush region of the endplate is conceptualised as a rectangular plate with a concentrated load due to the bolt force, and with fixed supports on the adjacent edges where it is bordered by the bea web and flange. The third edge is at a line through the shear bolts, and that edge is siply-supported since the oent there is negligible. The fourth edge is free. To apply Roark s forula we 17

232 approxiate the flush region into a square plate with all four sides siplysupported and with sides a = 1. The assuption of siple supports where the flush region is actually fixed is copensated for in part by the use of a siple support where the flush region edge is really free. It is further justified by the fact that our definitions of the connection swivel and axiu points require the fixed supports to be fully yielded anyway, so that they are no longer fixed. The approxiation is illustrated in Figure 6.9 reproduced here as Figure 7.. To ensure that the square plate approxiation of Figure 7. (b) leads to siilar deforations as the actual rectangular flush plate behaviour of Figure 7. (a), the square plate has been epirically calibrated using FE analysis. FEA calibration procedure In the FEA calibration of the square plate, FEA odels of Figure 7. (a) and Figure 7. (b) were prepared for the endplate geoetry tested in this thesis, for the 10, 1 and 14 endplate tests. Loads were then applied to each odel as a pressure over the bolt-hole area, to siulate the flush bolt force at swivel and axiu strain points. In the developent of the ductility odel, in order to apply Roark s square plate forulae at the axiu point, we treated the deforation of the flush region as consisting of two consecutive steps a first step up to the swivel point in which the deforations are ostly elastic within the flush region but becoe inelastic on the boundaries. Then a second step in which the yielding has spread over wide bands with attendant strain hardening, so that ost of the endplate is now resisting loads inelastically. This iplies a bi-linear odel of the endplate stress-strain relationship with a slope of E up to yield, and a slope of E sh after yield. In the FEA calibration odels therefore, the square plate is tested in two load steps as per the derived equations with a different aterial odel for each step. In the first step up to swivel, the aterial odel is linear elastic with a stress-strain slope of E (elastic Young s Modulus). In the second step fro swivel to the axiu point, the aterial odel is again linear elastic but with a stress-strain slope of E sh 18

233 (Strain-hardening Modulus assued to be E sh = E/60). Thus, the deflection observed in the second FEA step is taken as the increent in deflection fro swivel to the axiu strain point. This agrees exactly with our approach to deriving Equations 6.1 and 6. in Section By contrast, the FEA rectangular plate deflection odels are based on a full bilinear endplate aterial odel, with the sae aterial odel used at both swivel and axiu load points. The slope of the strain-hardening portion will not achieve the sae ultiate strain at the axiu stress as would be achieved with the experiental tri-linear aterial odels of Chapter Three. However it should lead to a better estiate of the deflection. In Table 7.1, these bi-linear aterial odels are presented along with the linear elastic odels used for the square plate FEA odels. Table 7.1 Material Properties for FEA Deflection Models Young s Modulus Bi-linear Model for Rectangular Plates True Yield Strain Strain Hard g Modulus Linear elastic odels for Square Plates Young s Strain Hard g Modulus Modulus (deflection at (Swivel to Max Swivel) increent) GPa 10-3 GPa GPa GPa 10 plate (Test 1) plate (Test ) plate (Test 3) In the FEA odels the swivel bolt force was based on the easured values in the test data, while the axiu strain bolt force was taken as the ultiate bolt force F ub. The deflection on the bolt load annulus was then easured at each of the two bolt force levels, for both the rectangular and the square plates. In order to confir the swivel bolt force, the load was applied in unifor steps fro zero to 19

234 F ub and a graph of load versus deflection was plotted. Thus, we could confir the swivel point for the flush region deflection. (a) 10 rectangular plate deflection at swivel (b) 10 square plate deflection at swivel (c) 10 rectangular plate deflection at axiu point (d) 10 square plate deflection at axiu point Figure 7.3 Deflections for 10 rectangular and square plate odels 0

235 (a) 1 rectangular plate deflection at swivel (b) 1 square plate deflection at swivel (c) 1 rectangular plate deflection at axiu point (d) 1 square plate deflection at axiu point Figure 7.4 Deflections for 1 rectangular and square plate odels 1