THE PERFORMANCE OF STEEL FRAMED STRUCTURES …fire-research.group.shef.ac.uk/Downloads/Mariati_Taib_thesis.pdf · THE PERFORMANCE OF STEEL FRAMED STRUCTURES WITH FIN-PLATE CONNECTIONS

THE PERFORMANCE OF STEEL FRAMED

STRUCTURES WITH FIN-PLATE CONNECTIONS IN

FIRE

By Mariati Taib

A thesis submitted to the Department of Civil and Structural Engineering in

partial fulfilment of the requirements for the degree of Doctor of Philosophy

July 2012

ABSTRACT

The behaviour of joint in global frames subjected to fire is greatly affected by

combination of forces and moments, originating from restraint to thermal expansion as

well as large vertical deflection of structural members. In order to facilitate the design

process of achieving robustness in simple beam-to-column connection, a component-

based model has been developed for fin-plate connections in this research. The new

model represents the realistic behaviour of such connections under the influence of

combined forces, together with the high rotations which can occur at the ends of beams,

during building fires. The key aspect of the component method is that it characterises the

force-displacement properties of each active component at any temperature, as a non-

linear “spring”. The temperature-dependent characteristics of each individual component

in each bolt row are defined, including the failure mechanism of the weakest component,

based on experimental and analytical findings. Primary failure modes adopted for fin

plate connections are bearing/block shear of the plates and bolt shear. A major additional

complication is force reversal in components, which may occur simply because of

temperature change, without any physical reversal of displacement. The Massing Rule

has been adopted to incorporate the effect of permanent deformations at any temperature

when force reversal occurs. To account for the bolt slip phases, force transitions between

tensile and compressive quadrants take place only when positive contact between a bolt

and the edge of its bolt hole is re-established.

The results of high-temperature tests on the fin-plate connections have been used to verify

the model for isolated joints at ambient and elevated temperatures. The developed

component model for the fin-plate connection has been extended for the application of

moment-resisting beam splice connection, also known as the “column-tree” system. The

component-based connection model has also been used to study joint behaviour in

structural sub-frame analyses. Incorporating it into non-linear finite element software will

enable engineers to generate the global structural interactions for steel and composite

structures in fire scenarios, up to and including connection failure. The new connection

element has been validated with reasonable agreement with the available experimental

data, showing its capability of capturing the key features of the overall connection

interaction in a realistic manner, based on the underlying mechanics, coupled with

evidence from experimental data.

i

ACKNOWLEDGEMENT

First and foremost, I wish to give all praise and thanks to Almighty God for taking me

through the most challenging episode of my life, bestowing wisdom and perseverance to

complete this research.

I would like to express my sincere gratitude to my supervisor Professor Ian Burgess, for

his continuous support and encouragement during the completion of this research. It

would have been more difficult without his inspiring advice, comments and devoted time.

His excellent guidance has served me well, and I will always remain grateful to him.

I would also like to acknowledge the financial support given by the Ministry of Higher

Education, Malaysia and Universiti Sains Malaysia during the course of this research.

Throughout this period, I am deeply indebted to my dear husband, Al-Zilal for his

patience and unconditional support. I also want to extend my appreciation and gratitude

to my family for their love, trust and endless encouragement to get through this time.

Last but not least, my heartfelt thanx to my past and present colleagues of Room D120

and friends who have shared the joy and hardship as postgraduate students. It has been a

great privilege to spend the years of great friendship during my time in Sheffield.

DECLARATION

Except where specific reference has been made to the work related to others, this thesis

represents the result of my own work. No part of it has been submitted to any University

for a degree, diploma or other qualification.

Mariati Taib

ii

TABLE OF CONTENTS

ABSTRACT ........................................................................................................ i

Acknowledgement ............................................................................................... i

Declaration........................................................................................................... i

Table of contents ................................................................................................ ii

List of figures .................................................................................................... vi

List of tables .................................................................................................... xiii

Notations .......................................................................................................... xiv

1. INTRODUCTION ....................................................................................... 1

1.1. Steel as a building material ............................................................................ 1

1.1.1. Design provision for fire in Europe ................................................... 2

1.1.2. Accidental fires in buildings .............................................................. 4

1.2. Fire design in steel structure ........................................................................... 6

1.2.1. Fire curves and growth ....................................................................... 6

1.2.2. Steel material properties at elevated temperature .............................. 8

1.2.3. Steel structures in fire ...................................................................... 13

1.3. Scope of research ......................................................................................... 17

1.4. Thesis layout ................................................................................................ 18

2. LITERATURE REVIEW OF MODELLING STEEL CONNECTIONS

IN FIRE ............................................................................................................ 20

2.1. Steel connections .......................................................................................... 20

2.1.1. Stiffness classification ..................................................................... 20

2.1.2. Fin-plate connection ......................................................................... 23

2.2. Background research on fin-plate connections ............................................ 27

iii

2.2.1. Review of experimental investigations on fin-plate

connection at ambient temperature. ................................................. 28

2.2.2. Review of research on fin-plate connection at elevated

temperature ...................................................................................... 33

2.3. Mechanical modelling .................................................................................. 39

2.3.1. Application of component method at elevated temperature ............ 40

2.4. Summary ...................................................................................................... 47

3. CHARACTERISATION OF FIN-PLATE CONNECTION

COMPONENTS ................................................................................................ 49

3.1. Design philosophy of fin-plate shear connections ....................................... 49

3.2. Failure modes of fin-plate shear connection ................................................ 52

3.2.1. Bearing of plates .............................................................................. 54

3.2.2. Bolt shearing .................................................................................... 66

3.2.3. Friction ............................................................................................. 72

3.3. Behaviour of equivalent bolt-row component .............................................. 80

3.4. Summary ...................................................................................................... 83

4. COMPONENT-BASED MODEL FOR FIN-PLATE CONNECTION .... 85

4.1. Arrangement of a single bolted joint component model .............................. 85

4.1.1. Equivalent component for single bolt-row ...................................... 86

4.2. Application of fin-plate connection in Vulcan ............................................. 89

4.3. Development of finite element software Vulcan .......................................... 91

4.3.1. General solution procedure in Vulcan ............................................. 91

4.3.2. Derivation of the component-based stiffness matrix model ............ 94

4.3.3. Validation of the stiffness matrix in Vulcan .................................... 99

4.4. Load reversal of component model ............................................................ 102

4.4.1. Masing rule approach .................................................................... 103

4.4.2. Modified Masing Rule at elevated temperatures ........................... 105

4.5. Influence of combined action on connection elements .............................. 107

iv

4.6. Summary .................................................................................................... 113

5. APPLICATION OF COMPONENT-BASED MODEL ......................... 114

5.1. Single-bolted connection behaviour ........................................................... 114

5.2. Multi-bolt-row fin-plate connection behaviour .......................................... 116

5.2.1. Fin-plate connection subjected to axial force................................. 116

5.2.2. Fin-plate connection subjected to inclined force ........................... 119

5.3. Application of component model at elevated temperature ......................... 124

5.4. Force and displacement of connections...................................................... 128

5.5. Parametric study ......................................................................................... 130

5.5.1. Influence of the bolt grade and sizes .............................................. 130

5.5.2. Influence of the connection position with respect to neutral

axis ................................................................................................. 134

5.5.3. Influence of loading angle ............................................................. 138

5.6. Application of the fin-plate connection element ........................................ 139

5.6.1. Influence of connection in isolated beam ...................................... 139

5.6.2. Influence of the applied load ratio ................................................. 142

5.7. Connection response on two-dimensional sub-frame. ............................... 144

5.8. Summary .................................................................................................... 151

6. COMPONENT-BASED MODEL FOR MOMENT-RESISTING

BEAM-SPLICE CONNECTION ................................................................... 153

6.1. Beam splice connection design philosophy................................................ 153

6.2. Mechanical model development ................................................................. 155

6.2.1. Proposed component-based model................................................. 156

6.3. Validation of lap-joint connection using preloaded bolts........................... 157

6.4. Beam-splice component model validation ................................................. 159

6.4.1. Material properties ......................................................................... 161

6.4.2. Temperature distribution ................................................................ 163

6.5. Implementation in Vulcan .......................................................................... 165

v

6.5.1. Individual component spring characteristic ................................... 168

6.6. Component model validation ..................................................................... 171

6.6.1. Deflection at mid-span ................................................................... 171

6.6.2. Moment distribution ...................................................................... 173

6.6.3. Change of connection bolt axial forces and displacements ........... 176

6.6.4. Component characteristic .............................................................. 179

6.6.5. End restraint of beams ................................................................... 181

6.6.6. Position of connection with respect to the beam ........................... 184

6.7. Summary .................................................................................................... 187

7. CONCLUSIONS AND RECOMMENDATIONS .................................. 189

7.1. Summary of the completed works ............................................................. 189

7.1.1. Characterisation of the component’s elements .............................. 189

7.1.2. Development of the fin-plate connection component

method ........................................................................................... 190

7.1.3. Application of the fin-plate component model .............................. 191

7.2. Recommendation for further work ............................................................. 192

7.2.1. Component detailing ...................................................................... 193

7.2.2. Overall connection response .......................................................... 193

7.3. Concluding remark ..................................................................................... 194

References ....................................................................................................... 195

Appendix ......................................................................................................... 206

vi

LIST OF FIGURES

Figure 1.1 Damage to the column-tree system (FEMA Report, 2002) .................... 5

Figure 1.2 Fire curves and development stages ........................................................ 7

Figure 1.3 (a) Specific heat and (b) Thermal conductivity of steel (CEN, 2005a) ... 9

Figure 1.4 Stress-strain relationship for carbon steel at elevated temperatures

(Franssen, et al., 2009). ......................................................................... 11

Figure 1.5 Reduction factor for structural members (CEN, 2005a). ...................... 12

Figure 1.6 Reduction factor for bolts and weld, EN 1993-1-2 (CEN, 2005a) ........ 12

Figure 1.7 Change of deflections, internal forces and moment in a) unrestrained

beam and b) axially restrained beam during fire ................................... 14

Figure 1.8 Axial force on beam-to-column connection (Burgess, 2008). .............. 16

Figure 1.9 Forces causing local buckling (Burgess, 2008). .................................... 17

Figure 2.1 Types of connection configuration in steel frames (CEN, 2005b). ....... 20

Figure 2.2 Common beam-to-column connections with stiffness classification

(Spyrou, 2007b). ................................................................................... 21

Figure 2.3 Stiffness classification for bolted joints, adapted from (Steurer,

1999) ..................................................................................................... 23

Figure 2.4 Typical fin-plate connection on (a) major axis (b) minor axis .............. 24

Figure 2.5 Fin-plate connection used in notched beams (a) single- (b) double- .... 24

Figure 2.6 Fin-plate connection for tubular column: (a) rectangular, (b) circular. . 25

Figure 2.7 Loading paths for fin-plate connections (Jaspart and Domenceau,

2008) ..................................................................................................... 26

Figure 2.8 Design resistances for individual components of fin-plate connection

(Jaspart and Demonceau, 2008) ............................................................ 27

Figure 2.9 Astaneh (1989a) test setup schematic diagram .................................... 30

Figure 2.10 Hierarchy of failure modes from yielding to fracture (Astaneh and

McMullin, 2002). .................................................................................. 31

Figure 2.11 Arrangement of structural members and connections in the tested

fire compartment (Wald, et al., 2006b). ................................................ 34

Figure 2.12 Cardington fin-plate connection failure during and after test ............... 34

Figure 2.13 Three-dimensional modelling of Sarraj (2007b) using Abaqus ............ 36

Figure 2.14 The test setup in University of Sheffield (Yu, et al., 2009). ................. 36

Figure 2.15 Buckling of the beam with fin-plate connection (Wang, et al., 2011). . 38

Figure 2.16 Tschemmernegg and Humer (1988) Spring model ............................... 40

vii

Figure 2.17 Yu et al. (2009) fin-plate connection component model ...................... 42

Figure 2.18 Hu (2009) component model for partial depth end-plate connection ... 43

Figure 2.19 Idealisation of component characteristics (Jaspart, 2002; Block,

2006) ..................................................................................................... 44

Figure 2.20 Ductility of end-plate connection (Simoes da Silva, et al., 2001; Del

Savio, et al., 2009). ............................................................................... 44

Figure 2.21 Cruciform beam-to-column connection (a) Geometry of joint (b)

Mechanical model (c) Basic non-linear model (d) Equivalent elastic

model (Simoes da Silva, et al., 2001). .................................................. 45

Figure 2.22 Definition of the reference point and permanent deformation (Block,

2006). .................................................................................................... 47

Figure 3.1 Beam-to-column rotation for simple connection (Astaneh, 1989a). ..... 49

Figure 3.2 Geometrical detail of a single-bolt lap-joint ......................................... 50

Figure 3.3 Load transfer mechanism in a bolted joint; (a) frictional force, (b)

bearing stress......................................................................................... 51

Figure 3.4 Typical deformation of lap joint with a single bolt subjected to single

shear (Sarraj, 2007b) ............................................................................. 52

Figure 3.5 Fin-plate connection failure mode; a) plate bearing and b) bolt

shearing ................................................................................................. 53

Figure 3.6 Other failure modes for single lap-joint; a) Net section failure, b)

Block shear failure and c) End-tearout failure (Ibrahim, 1995). ........... 54

Figure 3.7 Bearing stress area. ............................................................................... 55

Figure 3.8 Bearing stresses in bolted plates; a) Elastic, b) elastic-plastic and c)

Nominal. ............................................................................................... 55

Figure 3.9 Rex and Easterling (2003) Test setup. .................................................. 56

Figure 3.10 Rex and Easterling (2003) bearing stiffness model. ............................. 57

Figure 3.11 Rex and Easterling (2003) bending and shear stiffness model. ............ 59

Figure 3.12 Comparison of the plate bearing component up to yield. ..................... 64

Figure 3.13 Plate bearing characteristic for component model. ............................... 64

Figure 3.14 Temperature-dependent plate bearing characteristic for component

model; a) tensile and b) compressive. .................................................. 66

Figure 3.15 a) Single-shear failure and b) Double-shear failure. ............................. 67

Figure 3.16 Force-displacement graph for M20 bolt with thread or shank in shear

plane (Owens, 1992). ............................................................................ 68

viii

Figure 3.17 Sarraj (2007b) three-dimensional finite element model of single

bolted joint. ........................................................................................... 68

Figure 3.18 Residual area of bolt at post-yielding stage. ......................................... 71

Figure 3.19 Bolt shearing force-displacement graph in “tension” and

“compression”. ...................................................................................... 71

Figure 3.20 Temperature-dependent bolt shearing characteristics. .......................... 72

Figure 3.21 The friction resistance in double bolted joint ........................................ 72

Figure 3.22 Frank and Yura typical force-displacement curve for sandblasted

surface. .................................................................................................. 73

Figure 3.23 Rex and Easterling Bi-linear rational model ......................................... 74

Figure 3.24 Direction of bolt deformation for; a) oversized bolt hole and b)

slotted bolt hole ..................................................................................... 76

Figure 3.25 Sarraj’s frictional force-displacement relationship ............................... 78

Figure 3.26 Friction force-displacement curve at ambient temperature ................... 79

Figure 3.27 Temperature-dependent friction force-displacement curve .................. 80

Figure 3.28 Force-displacement characteristics for single-bolted joint

components. .......................................................................................... 81

Figure 3.29 Equivalent bolt-row component of a bolted lap joint ............................ 82

Figure 3.30 The non-linear response of a bolted lap joint ........................................ 83

Figure 4.1 Component-based model for a single-bolted lap-joint .......................... 86

Figure 4.2 Arrangement of component model in a bolted lap-joint ....................... 89

Figure 4.3 Beam-to-column arrangement of fin-plate connection in Vulcan ......... 90

Figure 4.4 Position of the centre of rotation of the connection .............................. 91

Figure 4.5 Newton-Raphson procedure .................................................................. 93

Figure 4.6 Simplified model of fin-plate connection component–based model ..... 95

Figure 4.7 Degrees-of-freedom of a two-noded spring element............................. 95

Figure 4.8 Two-noded spring element .................................................................. 100

Figure 4.9 Displacement and rotation of node j (Case 1) ..................................... 101

Figure 4.10 Displacement and rotation of node j (Case 2) ..................................... 101

Figure 4.11 Loading-initial-unloading sequence in typical force-displacement

graph (Azinamimi, et al., 1987) .......................................................... 103

Figure 4.12 Hysteresis behaviour using a modified Masing Rule. ......................... 104

Figure 4.13 The force-displacement relationship incorporating unloading phase

with temperature change. .................................................................... 106

Figure 4.14 Actual displacement pattern of bolt-rows ........................................... 108

ix

Figure 4.15 Kulak’s elliptical curve model ............................................................ 109

Figure 4.16 Component-model for combined forces in multiple bolt-rows ........... 109

Figure 4.17 Vertical and horizontal translations of the bolts. ................................ 110

Figure 4.18 Uniaxial component, Fu of the bolt ..................................................... 110

Figure 4.19 The failure envelopes for the actual and available, resistance

capacities of components .................................................................... 111

Figure 4.20 Implementation of Masing Rule in Vulcan ......................................... 112

Figure 5.1 Richard et al. (1980) single lap-joint specimen geometry and

dimensions. ......................................................................................... 114

Figure 5.2 Force-displacement comparison curves .............................................. 116

Figure 5.3 Hu (2011) test setup and specimen detail. .......................................... 117

Figure 5.4 (a) Tear-out failure in the beam web (b) Deformation in the bolts ..... 118

Figure 5.5 Force-displacement response for connection subjected to normal

tension (Ambient temperature) ........................................................... 118

Figure 5.6 Force-displacement response for connection subjected to normal

tension (elevated temperatures) .......................................................... 119

Figure 5.7 Yu et al. (2009) test setup ................................................................... 120

Figure 5.8 Geometry of the test specimen ............................................................ 121

Figure 5.9 Detailing of the tested fin-plate connection ........................................ 121

Figure 5.10 Force-rotation comparisons at loading angle 35° at ambient

temperature ......................................................................................... 122

Figure 5.11 Force-rotation comparisons at loading angle 55° at ambient

temperature ......................................................................................... 123

Figure 5.12 Comparisons of test results to the component model (load angle 35°)

at steady state temperature .................................................................. 125

Figure 5.13 Comparisons of test results to the component model (load angle 55°) at

steady state temperature ...................................................................... 126

Figure 5.14 Force-displacement curves of individual bolts, and the column

flange component. ............................................................................... 128

Figure 5.15 Partial unloading of bottom bolt (B3) ................................................. 129

Figure 5.16 Loading and unloading sequence ........................................................ 130

Figure 5.17 Force-displacement response for ambient temperature with load

angle 35° ............................................................................................. 132

Figure 5.18 Force-displacement response for T=550°C with load angle 35° ........ 132

x

Figure 5.19 Force-displacement response for ambient temperature with load

angle 35° ............................................................................................. 133

Figure 5.20 Force-displacement response for T=550°C with load angle 35°......... 134

Figure 5.21 Position of connection in respect to top beam flange .......................... 134

Figure 5.22 Force-rotation response for ambient temperature with varying

connection positions (shown in Figure 5.21) ...................................... 135

Figure 5.23 Force-rotation response for T=550°C with varying connection

positions (shown in Figure 5.21) ......................................................... 135

Figure 5.24 Comparison of maximum resistances for T=20°C and T=550°C ....... 136

Figure 5.25 Forces and displacements of bolts for T=20°C and T=550°C (refer

Figure 5.21) ......................................................................................... 136

Figure 5.26 Direction of horizontal forces on the bolt. .......................................... 137

Figure 5.27 Movements of bolt group for a) Model TP5 and b) Model TP8 ......... 138

Figure 5.28 Comparison force-rotation curve with loading angle 35°-55° ............ 138

Figure 5.29 The force-rotation response of combined forces at temperature

550°C .................................................................................................. 139

Figure 5.30 (a) Detailing of the connection element (b) The arrangement of the

isolated beam with connection elements. ............................................ 140

Figure 5.31 Midspan deflection of the beam .......................................................... 141

Figure 5.32 End moment in the connection for axially restrained. ........................ 141

Figure 5.33 Change of contraflexure point in beam during loading ....................... 142

Figure 5.34 Influence of load ratio on different connection temperatures. ............ 143

Figure 5.35 Top bolt forces of the connection (critical bolts). ............................... 143

Figure 5.36 Force-displacement graph of the bolt component for case (a) LR=

0.3; (b) LR= 0.7................................................................................... 143

Figure 5.37 Two-dimensional subframe model ...................................................... 145

Figure 5.38 Vertical displacement of the mid-span at the heating bay .................. 146

Figure 5.39 Vertical displacement at mid-span with two connection temperature

regimes ................................................................................................ 147

Figure 5.40 Rotation response of the connection element ...................................... 148

Figure 5.41 Component forces in the connection (Tc=0.8Tb). .............................. 148

Figure 5.42 Component displacements in the connection (Tc=0.8Tb). ................. 149

Figure 5.43 Force-displacement graphs of the components ................................... 150

Figure 5.44 Axial forces in the connection............................................................. 150

Figure 5.45 Change of bending moment during heating phase. ............................. 151

xi

Figure 6.1 Forces in splice connection ................................................................. 154

Figure 6.2 A bolted double-splice butt joint......................................................... 155

Figure 6.3 Component model of single bolted lap-joint. ..................................... 156

Figure 6.4 Component-based model of two-bolt row subjected to (a) tension;

(b) compression................................................................................... 156

Figure 6.5 Hirashima et al. (2007) lap-joint test specimen .................................. 158

Figure 6.6 Arrangement of the test specimen inside the electric furnace. ........... 158

Figure 6.7 Force- deflection response of double-bolted joint with M16 bolt. ..... 159

Figure 6.8 Force- deflection response of double-bolted joint with M20 bolt. ..... 159

Figure 6.9 The symmetric test setup .................................................................... 161

Figure 6.10 Connection details for (a) Test 2 (b) Tests 3 and 4 ............................. 161

Figure 6.11 Strength reduction factors for a) SN 400B steel b) F10T bolts. ......... 162

Figure 6.12 ISO 834 Temperature curve for Test 3 ............................................... 163

Figure 6.13 Fire protection scheme on mid-span section. ...................................... 164

Figure 6.14 Fire protection scheme on support section. ......................................... 164

Figure 6.15 Fire protection scheme at joint section. .............................................. 164

Figure 6.16 Fire protection scheme on section between joint and mid-span. ........ 165

Figure 6.17 Average temperatures at position (a) support (b) mid-span (c) joint .. 165

Figure 6.18 Simplified component model arrangement for double-splice butt-

joint ..................................................................................................... 166

Figure 6.19 Arrangement of one bolt row component model in beam splice

connection. .......................................................................................... 167

Figure 6.20 Component-based model arrangement in Vulcan. (Note that u1 is the

relative mean displacement across the whole connection). ................ 168

Figure 6.21 Tensile force-displacement characteristic for cover plate and beam

flange in bearing. ................................................................................ 169

Figure 6.22 Tensile force-displacement characteristic for cover plate and beam

web in bearing. .................................................................................... 169

Figure 6.23 Compressive force-displacement characteristic for cover plate and

beam flange in bearing. ....................................................................... 169

Figure 6.24 Compressive force-displacement characteristic for cover plate and

beam web in bearing. .......................................................................... 170

Figure 6.25 Tensile and compressive force-displacement characteristic bolt

shearing component. ........................................................................... 170

Figure 6.26 Mid-span deflection of Test 2 ............................................................. 172

xii



Figure 6.29 Positions at which moments are plotted in Figures 6.30-6.32 ............ 174

Figure 6.30 Moment distribution along the beam for Test 2 .................................. 175



Figure 6.33 Axial bolt-row forces on the beam splice connection ......................... 177

Figure 6.34 The friction and lap-joint forces on the flange splice. ......................... 177

Figure 6.35 Bolt displacements on the beam splice connections ........................... 178

Figure 6.36 Comparison of predicted upper beam flange forces for Tests 2 and 3.179

Figure 6.37 Bolt behaviour on upper flange splice. ............................................... 179

Figure 6.38 Friction component (a) Frict-A; (b) Frict-B and (c) Frict-C. .............. 180

Figure 6.39 Mid-span deflection comparison for Test 3. ....................................... 180

Figure 6.40 Comparison of the bolt forces on upper flange splice. ........................ 181

Figure 6.41 Partial-strength connection (Test 2) .................................................... 183

Figure 6.42 Full-strength connection (Test 3) ........................................................ 183

Figure 6.43 Full-strength connection (Test 4) ........................................................ 183

Figure 6.44 Axial forces for the case with end restraint. ........................................ 184

Figure 6.45 Positions of connection along the beam span ..................................... 185

Figure 6.46 Bending Moment in connection for various connection positions ...... 186

Figure 6.47 End moment at support for various connection positions ................... 186

Figure 6.48 Bending moment at mid-span for various connection positions ......... 186

xiii

LIST OF TABLES

Table 3.1 Plate bearing curve fit parameter Ω ...................................................... 59

Table 3.2 Tensile curve-fit values at different temperatures in the case of small

end distance (e2 ≤ 2.0db) ........................................................................ 63

Table 3.3 Compressive curve-fit values at different temperatures in the case of

large end distance (e2 ≥ 3.0db) ............................................................... 63

Table 3.4 Reduction factor for bolts in shear. ....................................................... 69

Table 3.5 Bolt shearing parameters at respective temperatures ............................ 69

Table 3.6 Values of ks ........................................................................................... 76

Table 3.7 Classification of surfaces assumed for the use of slip coefficient

values. ................................................................................................... 77

Table 4.1 Tensile equivalent bolt-row component of a single bolted joint ........... 87

Table 4.2 Compressive equivalent bolt-row component of a single bolted joint .. 88

Table 4.3 Deformation modes of the connection element .................................... 96

Table 5.1 Measured material properties at ambient temperature ........................ 116

Table 5.2 Comparison of the test and component model deformation response. 127

Table 6.1 Test detailing for different arrangement. ............................................ 160

Table 6.2 Section properties of structural members. .......................................... 162

Table 6.3 Material properties of steel grade SN 400B ........................................ 162

Table 6.4 Material properties of bolts (F10T)..................................................... 163

xiv

NOTATIONS

The following symbols are used in this thesis;

nominal area of bolt

tensile stress area of bolt

design bearing resistance of bolt

design shear resistance of bolt

applied force that correspond to yield

elastic stiffness of the component

post-limit stiffness of the component

diameter of bolt

end distance of plate

nominal ultimate stress of bolt

yield strength

reduction factor for the slope of linear elastic range

bolt shearing stiffness

reduction factor for effective yield strength

radius of bolt

radius of bolthole

shear modulus

number of bolt rows

thickness of plate

xv

Greek letters

temperatures

deformation that correspond to yield

deformation for basic joint components

poisson ratio

Chapter 1: Introduction

1

1. INTRODUCTION

1.1. Steel as a building material

Steel occupies a major position in human daily life, and is the material of choice in many

applications. Its popular reputation largely pertains to its versatility, durability and

recyclability. Steel is an iron alloyed primarily with carbon and with other metals, using

varying amounts of the alloying elements to control its required properties, such as

hardness, ductility and tensile strength. For the last three decades, steel as a building

material has become the naturally dominant material for construction of high-rise

buildings, bridges, towers and many others. The reputation of structural steel has been

indisputably proven, with evidences of productivity enhancement in the construction

industry due to its rapid design, fabrication and erection cycle. From the architectural

point of view, steel’s high strength-to-weight ratio allows slender and aesthetically

pleasing members to support large loads over long spans. This creates the opportunity for

architects and engineers to express their creativity in design, while efficiently addressing

the functional demands of the buildings.

Recently, the environmental impact of the construction industries has become high on the

public agenda. In this respect, steel’s inherent properties of being fully re-usable and

recyclable, make a significant contribution towards achieving sustainable development.

Every new steel product contains recycled steel, without loss of quality even after long

life-cycles. Thus, steel has become a favourite construction material which adequately

satisfies both design and building issues. With increasing demand, continuous

technological advances are continually devised by the steel industries to reduce CO2

emissions by improving recycling rates and enhancing energy efficiency in the

steelmaking process (Steenhuis, et al., 1997). Even after making these environmental

improvements, steel structural framing systems remain generally the economical cost

leader throughout the construction process, especially where labour costs are high.

Nonetheless, one of major weaknesses of steel is its susceptibility to fire, which induces

loss of strength and stiffness of the structural material. In comparison with other building

materials, the strength of steel structures decreases more rapidly when submitted to fire,

largely because structural steel tends to heat up more rapidly. The risk from this adverse

effect can be enormously destructive, both in terms of human life and property losses,

without appropriate design consideration. Although steel does not melt below 1500°C,

structural steel has lost one-third of its yield strength at an approximate temperature of


2

600°C, and this has further reduced to 11% at 800°C and 6% at 900°C (Burgess, 2002).

Because of this issue, a rational approach to fire safety assessment is required to permit

reliable prediction of structural performance, and thus to provide global stability of

designs. The application of Fire Safety Engineering generally relates to functional

requirements, in which the structural stability and control of fire spread are achieved by

applying active and/or passive systems to different degrees to steel members in different

locations. Alternatively, the performance of structural members can be enhanced by more

robust and ductile design through advanced structural fire engineering, to mitigate the risk

of progressive collapse and provide structural integrity in the event of fire. In this case,

the fire protection can be tailored specifically to the building’s needs, giving optimisation

either by reduction or elimination of fire protective materials, or by more efficient

structural fire engineering design.

1.1.1. Design provision for fire in Europe

In recognition of the more rational performance-based approach to fire-resistant design,

several national and international building codes and standards have been revised to

introduce performance-based methods into their design provisions. One such example is

the latest edition of the American Institute of Steel Construction design manual (AISC,

2011) . In the European Union, The European Commission and the Member States have

set standard provisions in the structural Eurocodes, providing common principles for

advanced design procedures (Franssen, et al., 2009). The guidelines include various

structural aspects in nine principal documents. In this thesis, frequent reference will be

made to the Eurocodes EN 1991 (Basis of Design) and EN 1993 (Design of Steel

Structures), particularly referring to parts EN 1991-1-2: General Actions-actions on

structures exposed to fire (CEN, 2002), EN 1993-1-2: General Rules-structural fire

design (CEN, 2005a) and EN 1993-1-8: Design of Joints (CEN, 2005b). The general

philosophy of fire design in the Eurocodes assumes that the actions due to fire exposure

of structures are treated as accidental actions, and therefore extreme physical loadings

have a lower probability of occurrence than in the ultimate limit state requirements.

According to Nwosu and Kodur (1997), the limit states are associated with structural

collapse, or other forms of structural failure. Current fire design strategies incorporate a

combination of passive and active fire protection schemes, which are measured in terms

of a fire resistance rating, specified on the type of building occupancy and fire safety

objectives. According to the Eurocodes, fire resistance is expressed in terms of three

criteria: R (stability, ability to maintain load-bearing capacity), E (integrity, ability to


3

maintain compartment integrity against penetration of hot gases) and I (insulation, ability

to limit temperature rise across separating elements) (Petterson, 1988; Kruppa, et al.,

2005).

a) Structural fire engineering approach

Analysing and designing structures for fire loading can undoubtedly be a very

challenging problem for structural engineers. General design procedures at ambient

temperature involve non-varying combinations of the loadings, and therefore the design

requirements allow simplifying assumptions to be made. In most structures, these

simplifications result in extremely small deflections to satisfy design serviceability

requirements. In contrast to this scenario, there are inevitable complications involved in

the design process at high temperatures, particularly in dealing with material and

geometric non-linearity, as well as large deflections. These are increased by the effects of

restraint to thermal expansion of heated elements by cooler structure. Further complexity

involves non-uniform stresses induced by the heating-cooling cycle, when temperatures

differ between structural members in different parts of a structure at any point during the

growth and cooling of a fire.

b) Performance-based structural fire approach

Traditional prescriptive fire protection simply aims to provide a thickness of protection

material which limits the temperature of any element to a pre-determined value (typically

550°C for steel) within the statutory fire resistance period of the building, if it were

subjected to the ISO 834 Standard Fire (ISO834, 1975). Prescriptive protection has

proven satisfactory for many buildings in the real accidental fires which have occurred.

However, the use of new materials and the development of new construction technologies

are restricted by the prescriptive method. The advantage of this method is that it is very

straightforward in design of buildings, but it does not represent the most accurate

assessment of fire safety in the modern built environment (Parkinson & Kodur, 2007).

This drawback has led to an increasing transition all around the globe to a more

intelligent philosophy, known as the performance-based approach, of which a simple

version is the basis of the Eurocodes EN 1991-1-2 (CEN, 2002) and EN 1993-1-2 (CEN,

2005a; CEN, 2005b). This method provides more flexibility in design, whilst achieving

the quantified safety criteria, in cases where the conditions of a single-span furnace test

are a reasonable representation.


4

Structural fire engineering follows the performance-based philosophy, in attempting to

agree clear objectives for the building performance in the context of its functional

requirements and using appropriate models for the fire and for the affected region of the

building. This design method has evolved rapidly in recent years to deal with innovations

in building design, including advanced building systems and materials. Although the

understanding of basic fire engineering has improved substantially over the last few

decades, it is doubtful whether the implemented solutions have completely succeeded in

meeting their objectives. Advances in research have consistently been outpaced by the

emergence of new problems, which can make fire potentially even more harmful to both

human life and property. Through an improved understanding of the fire phenomena and

a more precise analysis of structures in fire, a safety level at least equal to, or higher than,

that given by prescriptive fire protection can be obtained with greater flexibility in

methods. Both deterministic and probabilistic design criteria can be incorporated to

achieve not just practical but cost-effective design, according to the building’s geometric

features and building occupancy (Parkinson and Kodur, 2007).

1.1.2. Accidental fires in buildings

A review of the performance of a real steel-framed structure subjected to a major

accidental fire is given in this section. The catastrophic event of which this forms a part

has led to a great deal of reflection on the effectiveness of design and the regulatory

process for building construction.

a) World Trade Center, Building 5

One of the most catastrophic events in the history of steel-framed buildings was the

disaster of the World Trade Center on 11th September 2001. The World Trade Center

complex was composed of seven buildings including the “Twin Towers” (WTC 1 and

WTC 2), each of 110 stories high. WTC 3 was a 22-storey hotel building, and WTC 4, 5,

6 and 7 were office buildings. Buildings 1 to 6 were built in close proximity to one

another within a 5-acre plaza. The two towers were first struck by hijacked aircraft,

causing massive local damage and multi-storey fires ignited by fuel droplets. The multi-

storey simultaneous fires eventually caused the collapse of WTC 2 within one hour,

followed by that of WTC 1 approximately 1.5 hours after the impact. It is believed that

flying débris dislodged fireproofing material from nearly all the steel members in the

impact zone, and the simultaneous heating of these now-unprotected members eventually

led to progressive collapse of the towers. Unlike the aircraft impacts on the towers, WTC


5

7 suffered a fire-induced global collapse several hours after the Twin Towers; fires were

initiated by the flying débris of WTC 1, some of which was burning, impacting on its

south face. Fires burning at various levels of the building are believed (NIST, 2008) to

have heated long-span composite beams to 500-600°C, and their thermal expansion

eventually caused non-composite supporting beams to be pushed off their column

connections, initiating the progressive collapse.

Most of WTC 4 collapsed when heavily impacted by exterior column debris from WTC

2, and its remaining section suffered complete burnout. Large sections of the roofs of

WTC 5 and WTC 6 collapsed locally because of column débris from WTC 1.

Subsequently, fire spread throughout these buildings led to extensive local collapse.

The nine-storey WTC 5 building had a specified fire resistance rating of; 3 hours on its

columns and 2 hours on its floor assemblies. Fire protection to this office building

included an automatic sprinkler system, together with passive protection using sprayed

mineral fibre on its structural steel members. The framing system utilised column-trees

(Gerber beam design) at its interior columns between the 5th and 8

th floors, as shown in

Figure 1.1.

Figure 1.1 Damage to the column-tree system (FEMA Report, 2002)

The symmetrical nature of the collapse strongly suggests that the uncontrolled fire caused

local fractures at the beam-to-beam connections, and this is strongly supported by the

straightness of the free-standing remaining columns. The structural collapse appeared to

be due to the combination of excessive shear forces on the fin-plate connections, together


6

with large tensile axial forces which developed as a result of catenary action; see the inset

photo of a failed plate in Figure 1.1. Failure of these connections was clearly a major

factor in the subsequent slab collapse. The fire-induced collapse due to connection failure

was unexpected, as the steel beams were predicted to deflect significantly without failure

of the connection (NIST, 2005). The 9th floor and roof experienced similar fire exposure

but did not collapse and remained stable due to the conventional bay system in which

connections were made at columns. The performance of the building frame as a whole

appears to have been limited by the specification and detailing of its connections. This

suggests that the behaviour of connections in fire conditions needs to be taken into

account if the behaviour of whole buildings needs to be modelled so that the probability

of progressive failure can be avoided.

1.2. Fire design in steel structure

Accurate prediction of structural fire resistance depends on the prescribed temperature

curve in a given fire exposure scenario. The specification of appropriate fire scenarios

greatly influences the modelling done for fire safety design. The specification of

appropriate fire curves varies for different levels of calculation method. The range of fire

models used is governed by the usage of the building and the level of comprehensiveness

required for structural safety across the possible fire scenarios.

1.2.1. Fire curves and growth

There are three distinct combustion regimes which apply to compartment fires in the

evaluation of any adopted fire models; pre-flashover, post-flashover and decay (Figure

1.2). The occurrence of flashover signifies the transition point in fire development, which

can be described as a perilous stage in the course of a fire. After flashover, the exposed

surfaces of effectively all of the combustibles within the compartment are fully ignited

(Bwalya, et al., 2004). The first stage of fire growth is the pre-flashover stage, which is

initiated by fire ignition and burning. At this stage the combustion is restricted to local

areas near the ignition source, and therefore the average rate of rise of temperature is

small and localised within the compartment. Thus, the application of any active measures

such as fire extinguishers or sprinklers may effectively prevent further fire development

at this stage.

Flashover tends to occur when flames from the fire source carry unburnt fuel with them

along the compartment ceiling, so that ignition spreads across the roof of the

compartment. In the post-flashover phase, the increase of temperature is caused by


7

radiation from all compartment surfaces, leading to an increased rate of release of volatile

gases which in turn contribute to an uncontrolled growth in the fire temperature. This

process rapidly ignites all the available combustible material in the compartment. The

intense amount of heat release results in very hot gas temperatures which can possibly

reach over 1000ºC (Lie, 1988). The fire enters a peak stage during which its temperature

becomes practically uniform. The rate of heat release throughout is governed by the

compartment ventilation, the geometry and heat absorption of the compartment, and the

amount of available (or unburnt) fuel. The strength and stability of structural assemblies

are expected to be jeopardised mainly during this critical stage of the fire. Towards the

end of post-flashover stage, if the fire is left to burn, then it will continue into its decay

period as the available fuel decreases, and will eventually cease (Purkiss, 2009).

Figure 1.2 Fire curves and development stages

a) Standard/nominal fire model

The nominal time-temperature curve does not represent a real fire, but serves as a

representation of average post-flashover compartment gas temperature, which is used to

evaluate the fire resistance of structural members. This standard time-temperature curve

allows common rules to be used for testing purposes, which gives a consistent basis of

comparison between different structural members’ performance in fire. The use of this

Tem

per

atu

re

Time

Pre-

flashover

Post-

flashover Decay

1000°C -1200°C

Natural Fire

curve

ISO834

Standard fire curve

Ignition – smouldering Heating Cooling

Nothing occurred Constantly heated up

Natural

Fire

Standard

Fire


8

fire curve controls the prescriptive design principles of the International Standard ISO

834 (ISO834, 1975) and EN 1991-1-2 (CEN, 2002). As a time-temperature curve in

which temperature never decays, the only way of specifying the fire resistance of a

structure subjected to this curve is to impose criteria which may not be violated within

specified time periods. Hence the concept of the appropriate fire resistance period for a

building of a certain usage arises from the form of the standard fire curve.

Structural fire engineering design based on the standard fire generally only accounts for

material weakening in predicting critical temperatures, because members are tested in

isolation in a standard fire regime. This simplistic assessment may not provide an

accurate representation of the member’s behaviour under the effects of continuity,

including the structural effects which ensue when a real compartment fire enters its

cooling stage.

b) Natural/Parametric fire model

The parametric fire model provides, within limits, a realistic approach to real fire

temperature development, using compartment characteristics and fire load to model a

single-zone post-flashover compartment fire, including the decay phase. This predicts the

actual time-temperature relationship for a compartment of known dimensions, ventilation

and thermal properties of its bounding walls. The severity of the fire also depends on the

fire load, which is ignored in the standard fire, with the assumption that it never decays

even when all the combustible materials have been exhausted (Kirby, 1986).

1.2.2. Steel material properties at elevated temperature

The temperature rise of a steel member is a function of its exposure and its thermal

material properties. The heat flux transferred into the surfaces of steel members generally

derives from convection and radiation from the fire atmosphere, as well as on conduction

through the insulating material if the steel is protected. Evidently, an unprotected steel

member heats more quickly than a protected one, which usually causes larger

deformation, progressing to structural failure. Therefore, optimum design solutions for

steel structures subjected to high temperature can either provide better fire protection to

reduce structure temperatures, or can make the unprotected structural system capable of

surviving the fire event. In either case the inherent material properties of the steel

structure at elevated temperatures must be understood.


9

a) Thermal properties of carbon steel

The standard value of steel density given in EC3-1-2 (CEN, 2005a) is 7850kg/m3, and

this value is assumed to be independent of temperature increase. In EC3-1-2, the specific

heat of steel as a function of temperature is given in the fashion illustrated in Figure

1.3(a). The large spike results from a metallurgical change which applies to low-carbon

steel, which absorbs considerable energy (heat). The atomic structure changes from a

face-centred to a body-centred cubic structure, starting at about 730°C (Kodur, et al.,

2010).

The thermal conductivity defines the amount of heat flux per unit area transferred by

conduction through the material, for a unit temperature gradient. It can be observed in

Figure 1.3(b) that the thermal conductivity of steel reduces almost linearly from 54

W/mK at 20°C to 27.3 W/mK at 800°C (Buchanan, 2002; CEN, 2005a).

Figure 1.3 (a) Specific heat and (b) Thermal conductivity of steel (CEN, 2005a)

The coefficient of thermal expansion measures the material’s ability to expand or contract

in response to temperature change. This thermal strain is defined as the expansion of a

unit length of material when it is raised by 1°C (Lie, 1988), and is measured on unloaded

specimens in a transient test. The type of steel and its strength characteristics have little

influence on the thermal strain (Anderberg, 1988). EC3-1-2 recommends the following

equations to determine the thermal elongation for structural and reinforcing steels;

For

(1.1)

Specific heat

[j/kg K]

0

10

20

30

40

50

60

0 200 400 600 800 1000 1200

0

1000

2000

3000

4000

5000

0 200 400 600 800 1000 1200

Thermal Conductivity

[W/mK]

Temperature [°C] Temperature [°C]


10

For

For

In a simple calculation model, EC4-1-2 (CEN, 2005c) suggests a linear function of

temperature T (°C) to calculate the thermal elongation (Buchanan, 2002; Purkiss, 2009);

The thermal elongation, according to EC3-1-2, increases linearly up to 700°C, and is

followed by some shrinkage, which is assumed as a pause in thermal expansion (Equation

(1.2) for design purposes. This is caused by the steel transformation phase from pearlite

to austenite between about 730°C and 860°C, which includes rearrangement of the crystal

structure (Cooke, 1988; Tide, 1998).

b) Mechanical properties of carbon steel

The mechanical properties of carbon steel at elevated temperature are described in a

stress-strain relationship, of which the model according to EC3-1-2 is shown in Figure

1.4. The definitions of the effective yield strength fy,θ, the proportional limit fp,θ and the

slope of the linearly elastic range Eα,θ are associated with this relationship. In contrast to

the ambient-temperature case, the mechanical behaviour develops its plasticity gradually

beyond the proportional limit. A linear relationship is initially adopted in the stress-strain

curve, followed by an elliptical curve until the yield stress is achieved at 2% strain; there

is no strain hardening beyond this point for temperatures above 400°C. The stress-strain

curves are truncated at a relatively high strain level, defining a yield plateau as most of

the elevated-temperature relationship. This is because there is no explicit strain-hardening

beyond this strain in the elevated-temperature case (Kirby and Preston, 1988; Cooke,

1988). At temperatures above 450°C, steel displays a creep phenomenon, in which the

deformation of a steel member increases with time, even if the temperature and stresses

remain unchanged. In this presentation of the strength and deformation properties, the

effect of creep is implicitly included and represented by a set of temperature-dependent

stress-strain relationships (Twilt, 1988).The creep effect is taken into account by basing

the stress-strain curves on transient tests in which the force on a specimen is kept constant

while the temperature is slowly raised.

(1.2)

(1.3)

(1.4)


11

Figure 1.4 Stress-strain relationship for carbon steel at elevated temperatures (Franssen, et

al., 2009).

To represent the main aspects of material weakening in fire, the reduction factors for

effective yield strength, proportional limit and elastic modulus are presented in Figure 1.5

according to EN 1993-1-2. The rate of degradation of these properties varies significantly

between structural steels, depending on their chemical and crystalline structures (in some

cases associated with their grades) and manufacturing process in forming structural

sections (for example, hot rolling or cold forming). Loss of strength and stiffness can be

evident at temperatures above 300°C, with further reduction at a steady rate until around

800°C.The appropriate strength reduction factors can be determined following two

methods; isothermal (/steady-state) tests or anisothermal (/transient) tests. The former

method subjects a test specimen to constant temperature and further strain is applied at a

steady rate, whilst the other method applies a constant load to a specimen which is then

subjected to a pre-determined rate of heating (Petterson, 1988).

Stress σ

Strain

: Effective yield stress

: Proportional limit

: Slope of linear elastic range

: Strain at the proportional limit

: Yield Strain

: Limiting strain for yield strength

: Ultimate strain


12

Figure 1.5 Reduction factor for structural members (CEN, 2005a).

An early study on the evaluation of bolt strength characteristics in fire was performed by

(Kirby, 1995) using M20 bolts and Grade 8.8 nuts; the findings were verified more

recently (Hu, 2009). The properties of the bolts are a product of their hot-forging

manufacturing process, in which the final quench and temper heat treatment provides the

required strength and ductility. It is observed that, at high temperatures, softening of the

bolts occurs, giving a very rapid loss of strength between approximately 300°C and

700°C, under either pure tension or double shear loading conditions. In general, the

ultimate capacity of bolts can be defined by applying the bolt strength reduction factor to

the ambient-temperature design resistance. The reduction factors given by Eurocode 3-1-

2 (Figure 1.6) represent the residual strength of bolts at elevated temperature, showing

that these have less strength than the parent structural steels from which they are

manufactured.

Figure 1.6 Reduction factor for bolts and weld, EN 1993-1-2 (CEN, 2005a)

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200

Temperature, θa

Reduction

factor

Weld kw,, θ

Bolt kb, θ

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200

Reduction

factor

Steel

Temperature, θa

Elastic Modulus Ea, θ

Proportional

Limit fp, θ

Yield Strength fy, θ


13

1.2.3. Steel structures in fire

The structural response of steel framing systems in fire conditions has been intensively

researched for the past 30 years. These activities have largely been motivated by

accumulated evidence of disastrous structural failures which have caused casualties and

economic losses. Due to the complexity of the behaviour of structural frames in fire, a

detailed understanding is inevitably required to resolve uncertainties about the structural

mechanisms at work. Large deformations are expected under fire exposure, and these can

lead to local collapse of supported beams and floor systems. The fire resistance of a

building component concerns its ability to withstand exposure to fire without loss of its

load-bearing function, or (in appropriate cases) its ability to act as a barrier against fire

spread, or both. Owing to the inherently high thermal conductivity of steel, the

temperature of a steel member varies according to the amount of fire protection applied,

the severity of the fire and the time of exposure (Buchanan, 2002). When a steel member

is exposed to fire, its load-bearing properties change dramatically due to its declining

strength and stiffness with increased temperature. However, this loss of load capacity can

be compensated for by a logical assessment of the interactions between different

structural members due to the continuity of the whole structure in the real situation.

a) Restrained and Unrestrained beams

The response of structural members at high temperature is largely a product of the

thermal strains induced in the members through heating. If a beam is longitudinally

unrestrained, the strains which are free to develop as a result of thermal gradients through

the section depth induce curvature, leading to bowing of a member which results in large

displacement, even at low temperatures (Usmani, et al., 2001). On the contrary, for

restrained heated beams, which apply to many cases in construction, large axial

compressive stresses are developed in the initial stage of heating. This is due to the axial

restraint from cool structure surrounding the fire compartment, preventing the thermal

expansion from displacing the ends of the beam. The sequence of beam deformation and

moment development as temperatures change is illustrated in Figure 1.7.


14

Figure 1.7 Change of deflections, internal forces and moment in a) unrestrained beam and

b) axially restrained beam during fire

From relatively low temperatures, an axially and rotationally unrestrained beam starts

bowing towards the fire, largely due to the temperature gradient across its depth; at this

stage the increase of the beam’s mechanical deflection (caused by its declining stiffness

in bending) is relatively small. Beyond this temperature deflection increases due to an

increasing loss of stiffness due to the high steel temperatures in the cross-section. For

beams with rotationally restrained ends, there is no purely thermal deflection, because the

uniform hogging bending moment distribution along the beam is counterbalanced by the

end moments at the supports (Newman, et al., 2000). As the beam gets hotter, the

temperature gradient stabilises, and vertical deflection increases largely due to reduced

beam stiffness at high temperature. Subsequently, local buckling can be generated near

the beam’s ends, in particular the lower beam flange zone (indicated as Stage 1 in Figure

1.7). The local buckling of this flange changes the distribution of the moments, and the

compressive axial force starts to be relieved gradually, accompanied by an increased

vertical deformation. When the beam deflection becomes sufficiently large, the effective

Δv Δv

M M

Δv Δv

θ

θ

θ

θ

θ

θ

F F

M M

1 2 3

Tensile

Compressive

F F F F

a) Unrestrained beam b) Restrained beam


15

shortening of its length causes the beam to pull in, and tensile force develops after Stage

2. Wang (2002) explained that at this stage the beam is under catenary action, and the

catenary tension force will therefore govern its ultimate collapse. Due to the reduction of

elastic modulus and strength the bending stiffness and the bending moment capacity of

the beam are negligible. At Stage 3, the force in the hanging beam is resisted mainly by

its reduced tensile capacity, with a deflection appropriate to its strength and the tension

caused. However, if further large rotation of the connections is needed, failure of the

beam may be governed by fracture of its connections to the adjacent structure.

In addition, large tensile forces may also lead to connection fracture as the beam starts to

cool and contracts. This effect was observed during the full-scale fire tests on a steel-

framed building at Cardington, which will be discussed further in the next chapter. The

large tensile forces generated in beams due to cooling from high temperatures sheared

bolts in the fin-plate connection at their ends (Wald, et al., 2006b). This behaviour is quite

different compared to the common furnace test scenario of individual members in

isolation, because of the structural continuity with adjacent structure. In addition to their

high rotations, the frame connections were also subjected to high variation of axial force

due to restraint acting against the thermal expansion and then the contraction of the

connected beams. It is evident that the degree of axial restraint in structural members

considerably influences their deflection and internal forces during both the early stage of

heating, and the subsequent catenary action. The utilisation of catenary action can

explicitly provide a longer survival time (Yin and Wang, 2005), provided that the

adjacent structure and the connections have sufficient strength.

b) Steel connection response at elevated temperature

In current design practice, joints are required to be protected to the same level as the more

protected of the connected members. This is intended to ensure that the joints are not the

critical parts of the structural assembly. Under equivalent protection schemes, the

temperatures in connections develop more slowly than those in the connected members,

due to the relatively low exposed surface area and the additional mass of material to be

heated at a joint. In consequence, connections have been treated as of less concern than

the members they connect. Nonetheless, a major redistribution of internal forces in joints

is liable to happen, making them more vulnerable during the sequence of heating and

cooling (Burgess, 2008).


16

The first reported tests on beam-to-column connections at high temperatures were

performed by Kruppa (1976), focusing on establishing the performance of high strength

bolts on a range of joint types from “flexible” to “rigid”. However, the onset of

significant developments in steel joint research at elevated temperature was initiated by

(Lawson, 1990), who performed the first furnace tests to investigate the global rotational

behaviour of a range of connections, using a cruciform test arrangement.

The behaviour of connections is usually defined in terms of their moment-rotation

characteristics at ambient temperature, including their rotational stiffness, moment

capacity and ductility. At high temperature, it is desirable for joints to be designed to

provide robustness, retaining their structural integrity despite large rotations and tying

deformations. During the heating stage, the axial compressive stresses caused by

restrained thermal expansion of a beam, causes buckling in its lower flange and web near

to its connections. Subsequently, as temperature is further increased, the compressive

force is reduced rapidly as the steel loses its strength, and eventually a tensile force which

is high compared with the elevated-temperature strength of the material, is exerted on the

connection at very high temperatures (Figure 1.8). If cooling occurs from this state, then

the tensile force increases rapidly as thermal contraction takes place, and this force may

outstrip the recovery of strength with cooling. The whole process of heating and cooling

are equally important, in the sense that, even if no fracture of the connection occurs

during the heating phase, the connection may still be subject to fracture during cooling,

which may endanger fire service personnel or lead to progressive collapse.

Figure 1.8 Axial force on beam-to-column connection (Burgess, 2008).

400

200

0

- 200

- 400

- 600

0 200 400 600 800 1000 1200

Temperature (°C)

Ax

ial

Fo

rce

(kN

)

TENSION

COMPRESSION

Cooling Joint

strength

Heating

- 800


17

At very high rotation, local buckling of the lower beam flange adjacent to the joint may

potentially induce shear buckling and diagonal tension field action (Figure 1.9), which

may combine with the tying force on the joint to initiate an “unzipping” effect, in which

the bolt rows fracture in sequence from the top to the bottom. This may cause a total

connection failure (Burgess, 2008) well before an evenly distributed net tying force on

the connection would have reached its capacity. In current performance-based fire

engineering design, joints are implicitly assumed to retain their structural integrity.

However, evidence of joint failure in WTC building 7, leading to progressive collapse,

has emphasised the importance to designers of including the behaviour up to fracture of

the connections in their whole-structure modelling. Observations on structural behaviour

in a natural fire (Wald, et al., 2006a) and furnace testing (Yu, et al., 2009; Santiago, et al.,

2008a) have shown failure of the joint components due to the high forces induced by the

thermal expansion/contraction and the high deformations of the connected members.

Figure 1.9 Forces causing local buckling (Burgess, 2008).

1.3. Scope of research

In the software Vulcan, connections are currently modelled as either rotationally pinned

or fully rigid whereas, even in rotational stiffness terms, the real joint behaviour lies

between these two extreme cases. In order to account for the semi-rigidity of connections,

a simple two-noded rotational spring element, which employs temperature-dependent

moment-rotation curves, is also implemented in the existing program.

In this research, the behaviour of connections subjected to fire is investigated particularly

for fin-plate connections. The research develops a connection finite element assembly in

the framework of the component-based method, which has been implemented into the

connection modelling module in Vulcan, and therefore allows the complex combinations

of forces and movements within the connection to be treated appropriately. As part of the

Column

Shear buckling

Tension field

Vertical

Shear

Catenary

Tension

Hogging

Moment


18

global structural assembly of beam-column, slab and connection elements, the non-linear

solution process for equilibrium guarantees that the connection deformations are

accounted for within the equilibrium of the whole structural assembly.

It is evident from previous part of this chapter that connections in fire can be subjected to

combinations of moments and normal forces which may be either tensile or compressive.

Modelling of the connections using component-based models may provide a progressive

picture of their internal forces and prediction of their local and overall behaviour during a

particular fire event. Thus the research can be beneficial not only in design but also in

assisting in interpretation of the experimental and analytical responses of connections

within structures at elevated temperature. Further consideration of the nature of moment-

axial force combinations, and component loading and unloading, is included.

The objectives of this research are;

1. To classify the individual components which can be assembled to create a fin-

plate connection model, and modelling their behaviour at ambient and elevated

temperatures, including during reversed deformation.

2. To create a component-based connection finite element from these components,

which is valid for connections with different detailing.

3. To incorporate the component-based model of fin-plate connections into the

connection module in Vulcan.

4. To investigate and validate the behaviour of fin-plate connections within

structural frames at ambient and elevated temperatures using the component

model.

1.4. Thesis layout

The thesis comprises of eight chapters.

Chapter 2 gives an introduction to the design procedure for connections in steel frames at

ambient and elevated temperatures. State-of-the-art research on steel joints, particularly

fin-plate connections, is then discussed in detail.

Chapter 3 focuses on the simplified modelling and numerical investigation of fin-plate

connections, through their breakdown into components and the characterization of the

behaviour of these components. The force-displacement behaviour associated with the


19

main failure modes is discussed in detail, generating the primary component

characteristics for fin-plate connections.

Chapter 4 concerns the assembly of components into a component-based connection

element for fin-plate connections. This is then implemented in Vulcan. Subsequently,

further studies on the unloading of the connection elements are discussed in detail.

Chapter 5 present validation studies of the fin-plate component model against available

experimental results. Parametric studies based on the connection characteristics are also

conducted using the developed model. It is also used to predict the behaviour of fin-plate

connections in a structural sub-frame.

Chapter 6 extends the applicability of the developed component model to a different,

moment-resisting, type of connection which is subjected to elevated temperatures.

Chapter 7 concludes the present work and gives recommendation for future work.

Chapter 2:Literature review of modelling steel connection in fire

20

2. LITERATURE REVIEW OF MODELLING STEEL

CONNECTIONS IN FIRE

2.1. Steel connections

Steel connections essentially link together members in order to transfer loads within a

structural assembly. The terms ‘connection’ and ‘joint’ are explained in the European

Standard (CEN, 2005b) using a beam-to-column configuration. A location where two or

more structural components are mechanically fastened is referred to as a ‘connection’,

whilst the zone within which the interconnected members act together is referred to as a

‘joint’. Common types and layouts of major-axis joint configurations are exemplified in

Figure 2.1.

Figure 2.1 Types of connection configuration in steel frames (CEN, 2005b).

2.1.1. Stiffness classification

Traditionally, steel joints are considered to exhibit rotational behaviour ranging from very

rigid to extremely flexible. The latter significantly simplifies the analysis and design

procedures when such joints are considered as “simple” or “pinned”. However, neither

notion of simple or rigid joints represents the exact joint behaviour. Most connections

which are regarded as simple (or pinned) possess some rotational stiffness, while

connections which are regarded as rigid always display some flexibility (Astaneh, 1989a).

In this section, the discussion on the rigidity of steel connections classifies them into three

main categories; pinned connections (non-moment-resistant), semi-rigid connections

(partially moment-resistant) and moment connections (fully moment-resistant). The

1 Single-sided beam-

to-column joint

configuration;

2 Double-sided

beam-to-column

joint configuration;

3 Beam splice;

4 Column splice;

5 Column base.

1 3 3

1 2

2

4

5


21

rigidity regions of the connections are illustrated in Figure 2.2, according to their types. A

compilation of the common connection types is then summarised relative to their moment

resistance, Mpl and stiffness in Figure 2.3.

Figure 2.2 Common beam-to-column connections with stiffness classification (Spyrou,

2007b).

a) Moment connections

This type of connection is designed ideally to transfer moments without any relative

rotation between the connected members. This connection can be classified by its

moment resistance (it may be either full-strength or partial-strength) and its rotation

capacity. Moment connections are inevitably more expensive to fabricate than simple

connections, and require extra detailing and good workmanship. Hence, this connection is

not preferred, other than in seismic zones, despite being more advantageous in permitting

longer spans, shallower beams and elevations without bracing. Common types of moment

connection used in construction are extended end-plate and flush end-plate connections.

b) Semi-rigid connections

Extensive research has evolved recently to characterise the behaviour of semi-rigid, and

partial-strength connections. This is partly due to their perceived complexity and the lack

of effective tools for designers, despite the fact that the utilisation of these connections

has been recognised to have advantages over idealised pinned or rigid connections. This

type of connection possesses a finite moment resistance which is less than the full beam

moment capacity, and a rotational stiffness which permits some relative rotation (Cabrero

Rotation

ϕ

RIGID

SEMI-RIGID

PINNED

Moment

ϕ

Extended End-plate with

column stiffener

Extended End-plate

Flush End-plate

Top and seat angle with

double web-angle

connection Flexible end-plate

Double angle web-cleat

Fin-plate


22

and Bayo, 2005). Compared to rigid connections, it still allows sway frames to be

designed despite its reduced stiffness. Semi-rigid connection can create lighter frames

appropriate to the defined connection geometry, by reducing the need for bracing.

As a consequence of the recognition of its advantages in building design, the use of semi-

rigid joints has been introduced into the design standard, Eurocode 3-1-8 (CEN, 2005b).

Contrary to the traditional design basis, semi-rigid designs classify their joint behaviour

by modelling their real behaviour, allowing a more subtle and sophisticated approach to

connection behaviour in whole structures. Thus, the application of the connection semi-

rigidity seems logical and practical for the designer to gain benefit, but the main difficulty

revolves around how to bring it to everyday practice. Following this advance in the

connection design, the so-called component-based method has been developed to

facilitate the application of the proposed semi-rigid design method. The implementation

of semi-rigid design can also be beneficial at high temperature, particularly when

redistribution of forces from beams to other structural members is critical, thus

influencing the survival time of the whole framing system.

c) Simple (pinned) connections

Pinned joints should possess large rotation capacity, but are incapable of transmitting

significant moments between connected members of the structure. Most simple

connections are assumed only to transfer the design shear reaction between members,

idealising their behaviour as pins or rollers for design. Therefore, simple connections are

also referred as shear connections, and are invariably cheaper to fabricate than moment-

resisting connections as they have simpler details and can be constructed to standard

dimensions. Their cost advantage largely influences the popular utilisation of simple

connections in building construction. In many countries labour costs increase

substantially each year, while material costs remain more or less constant, especially in

the context of steel construction industries (Steenhuis, et al., 1997). The simplification

process for most labour-intensive parts is of more practical benefit than minimising the

use of materials. Three main connections which are outlined, with detailed design

procedures, in the “Green book” (BCSA, 1991) are double-angle web cleats, flexible end-

plates and fin-plates. In this study, the investigation of simple connections, both

numerically and analytically, is performed using a component-based model, concentrating

on fin-plate connections in particular.


23

Figure 2.3 Stiffness classification for bolted joints, adapted from (Steurer, 1999)

2.1.2. Fin-plate connection

Until the present day, the majority of structural steel frame connections are shear

connections. Even most moment connections include shear connection to transmit the

shear component of the beam reaction. The worldwide utilisation of this type of shear

connection means that it is given different names, according to the national design

provision. In the USA and Canada, it is known as the shear tab or single-plate connection

in the AISC Steel Construction Manual (AISC, 1999). In Australia and New Zealand, it is

widely known as the web-side plate (Hogan, 1992) based on a design guide by the

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Stiffness of the connection

Mpl / Mpl, Beam

1 Fin-plate

2 Double angle web-cleat

4 Top-and seat-angle with

double web-angle connection

5

Flush end-plate

6

Extended end-plate

7 Extended end-

plate with column

stiffener

Flexible end-plate

3


24

Australian Institute of Steel Construction (1992). In the UK, it is usually known as the

fin-plate connection, and is one of the types of connection recommended by the Steel

Construction Institute and the British Constructional Steelwork Association (BCSA,

1991). For standardisation in this thesis, it is referred to fin-plate connection throughout.

The fin-plate connection consists of a single plate welded to its supporting column along

at one edge and bolted to a beam web near its opposite edge (Figure 2.4). The supported

member can frame into either the major or minor axis of a column, or into a beam web.

The end of the connected beam to the supporting member may be un-notched, single-

notched or double-notched (Figure 2.5). The design specifies an arrangement of bolts

grouped in either single or double vertical rows, providing connection shear capacity

ranging between 25% to 50% of the beam’s capacity for single, and 75% for double rows

(BCSA, 1991). With these simple fabrication details, this connection usually expedites

on-site steel erection and provides a simple field connection, as well as being simple to

fabricate off-site.

Figure 2.4 Typical fin-plate connection on (a) major axis (b) minor axis

Figure 2.5 Fin-plate connection used in notched beams (a) single- (b) double-

The use of fin-plate connections to structural tubular columns is also gaining popularity

due to the cost-efficiency of the combination. Structural hollow sections are practically

lighter in terms of material mass, but are more expensive on a per-tonne basis; however

Beam Beam

Fin-plate

(a) (b)

Beam

Single-vertical

bolt row

Beam

Column

Double-vertical

bolt row

Fin-plate (a) (b)

Weld


25

the overall weight saving gained can deliver much more cost-effective construction

(Kurobane, et al., 2004). The hollow sections, commonly produced in circular, square or

rectangular shapes (Figure 2.6), are more efficient as compression members compared to

other steel sections because their geometric shape does not require one axis to have much

weaker properties. Fin-plate connections compensate for any excess cost, offering an

economic joint system, particularly for multi-storey construction (Hicks and Newman,

2002).

Figure 2.6 Fin-plate connection for tubular column: (a) rectangular, (b) circular.

a) Ductility and rotation requirements of fin-plate connections

In an ideally pinned connection, the joint is assumed to be subjected only to shear force,

but in reality both moment and shear force act simultaneously on the joint. Despite having

little or no rotational resistance, experiments have shown that shear connections possesses

finite rotational restraint. For design purposes, ignoring this resistance produces

conservative results. Jaspart and Demonceau (2008) have represented these requirements

in the form of simple criteria, based on the mechanical and geometrical characteristics of

the individual components forming the connections. The general principles are explained

in terms of:

1. Geometrical limitations which control the rotation capacity without developing

significant bending moment in the members of the structure.

Fin-plate

Beam

Column

Beam

Column

(a) (b)

Weld


26

2. A ductility limitation, which avoids the occurrence of any brittle failure,

particularly in bolts and welds, which are defined as the more adverse failure

modes.

The evaluation of design resistance can be illustrated by combining the effects of applied

shear force and applied bending moment, representing the fin-plate connection’s real

behaviour (Figure 2.7). The actual and idealised loading paths are defined corresponding

to the general assumptions of the forces acting on the connection. Two loaded cross-

sections inside the joint have to be considered separately due to their dissimilar actual

loading condition. For instance, if a ‘hinged’ model is considered, the external face of the

column is assumed to transfer only shear force (Med = 0), whilst the bolt group section

transfers the same shear force Ved and and ‘eccentricity’ moment Med, eccentricity z. The

length z indicates the distance between the external face of the supporting element and the

bolt group centre.

Figure 2.7 Loading paths for fin-plate connections (Jaspart and Domenceau, 2008)

In the late 1980s, Astaneh (1989b) established the dominant failure modes for shear

connections. This development was later included in the AISC 2nd

Edition Manual for

Load and Resistance Factor Design (AISC, 1993)for single-plate shear connections. The

order of the following failure modes reflects that of the most ‘desirable’ failure to the

most brittle failure:

1. Yielding of the plate in shear – (Most ductile)

2. Yielding of the bolt holes in bearing

Moment Med

a Design loading path for

external face of the supporting

member

b Design loading path for the

section of the bolt group centre

c Actual loading path for the

external face of the supporting

member

d Actual loading path for the

section of the bolt group centre

d c

b

a

z

1

Design loading path Vfd


27

3. Fracture of the edge distance of the plate

4. Fracture of the net section of the plate

5. Fracture of the bolts

6. Fracture of the weld lines – (Most brittle).

Jaspart and Demonceau (2008) identified partly similar failure modes, according to EN

1993-1-8 (CEN, 2005b). The design resistances of individual components in a fin-plate

connection are represented with a vertical line or curve, depending on the influence of the

applied moment (Figure 2.8). Relative positions of the individual resistances are given

with the respective mechanical characteristics of the joint components. Using a similar

approach, the actual and design shear resistances can be obtained at the intersections

between the loading paths and the design resistance curves (or lines for the weakest

component). Detailed investigation of the mechanical characteristics of each individual

component will be given in Chapter 3.

Figure 2.8 Design resistances for individual components of fin-plate connection (Jaspart

and Demonceau, 2008)

2.2. Background research on fin-plate connections

When carrying out analysis on steel structural frames, the rotational stiffnesses of the

joints generally dominate the performance of joints in global analysis, according to their

stiffness classification highlighted in Figure 2.2. The rotational flexibility of a joint

depends on the rigidity of the plate and the support, as the orientation of this connection

lies in the plane of the web of the supported member. If the support is flexible, then the

Moment

Fin-plate in bearing

Fin-plate in shear

Bolt in shear

Design loading path

Vra Vrd

Ved

Med

z


28

rotation is accommodated by deformation of the supporting member. However, if the

support is rigid, the rotations are primarily resisted within the plate connection (Ferrell,

2003; BCSA, 1991). Thus, for the past few decades, considerable effort has been

concentrated on predicting or controlling this behaviour, primarily focusing on

establishing the moment-rotation relationships of the joints. Nethercot and Zandonini

(1989) listed several widely-adopted models to ascertain the derivation of this moment-

rotation relationship.

1. Experimental tests

2. Mechanical models

3. Empirical model

4. Simplified Analytical model

5. Finite element (Numerical) model

6. Informational models (Databases)

It is evident that the prediction of joint behaviour in global structure by means of any of

the methods above has to be accompanied by a mathematical representation of the

moment-rotation curve. In the following section, only the first two will be reviewed in

detail. The other modelling techniques are applied indirectly to derive the connections

connection characterisations.

2.2.1. Review of experimental investigations on fin-plate connection at

ambient temperature.

Early experimental investigation of shear connections can be traced back about 30 years.

Initially, it was widely performed in the USA and Australia, and later gained popularity in

the UK (Moore and Owens, 1992). The execution of the experimental tests is a

fundamental step, giving evidence to support state-of-the-art development in analytical

and simplified modelling of connections. A brief overview of the experimental tests

which have made an impact on the development of fin-plate connection design is given in

this section.

Early work by Lipson (1968) examined the rotational capacity of three types of shear

connection, including fin-plate connections. Three failure modes were identified, namely

tensile yielding of the plate, weld rupture and vertical tearout of the bottom bolt. The

amount of end moment transferred to the supporting member was found to be dependent

on the following factors:


29

a) The number, size and configuration of the bolts

b) Thickness of the plate and/or beam web

c) The beam span-to-depth ratio

d) Beam loading pattern

e) Relative stiffness of supporting member.

The work by Lipson was later simulated using finite element analysis by Caccavale

(1975). The models generated were consistent with the experimental results, recognising

similar observations on ductility provided by significant deformation of bolt holes. In

1980, an initial study by Richard et al. at the University of Arizona involved the

development of the connection design using beam-line theory, generating the moment-

rotation relationship from double lap-joint tests. The beam line utilised the relationship

between linear beam action and nonlinear connection behaviour to determine the

moment-rotation capacity. A total of 126 fully-tightened bolts with strengths A325 and

A490 were tested, for a range of commonly-used diameters of bolts. Based on the results

obtained, an equation for predicting the moment in the connections was developed with a

finite element program called Inelas.

The proposed design procedure recommended by (Richard et al., 1980) on standard bolt

holes controlled the ductility of the connection by limiting the plate thickness, with

reference to the bolt diameter and minimum edge distances of the plates. The bolts were

designed with eccentricity to ensure that plate yielding precedes any brittle limit state of

the bolts. However, despite providing more understanding of the connections behaviour,

the ultimate strength could not be investigated due to the use of non-destructive

experiments.

One major development of fin-plate connection design is based on research by Astaneh

(1989a) at the University of California, through examining the demand and supply of

ductility in steel shear connections. Astaneh’s early work was based on a modified beam

line model, with the elastic and inelastic regions being the typical portions of an elastic-

perfectly-plastic curve. Contrary to Richard’s beam line model, the consideration of the

inelastic stage for both the beam and connection allowed the model to be used with the

ultimate strength and factored load design methods. The proposed concept was validated

with 19 experiments for three types of shear connection including fin-plate and flexible

end-plate connections. The tests were arranged to represent realistic combinations of

shear, moment and rotation in real structures. Three actuators R, A and S were installed in

order to control the beam end rotation, axial force and shear force respectively, as shown


30

in Figure 2.9. A cantilevered beam-to-column setup was connected with one-sided fin-

plate connections whose geometry was varied accordingly. The investigation indicated

that the effect of shear on connection moment is rather crucial, particularly when

approaching the shear capacity. It was observed that, in the early stages of loading, the

moment increases almost in proportion to the shear. However, as yielding starts, the

connection moment remains almost constant until strain hardening causes another

increase of moment.

Figure 2.9 Astaneh (1989a) test setup schematic diagram

In successive experimental tests, Astaneh et al. (2002) concentrated on fin-plate

connections under two loading regimes. This research sought to determine the connection

rotation capacity, and limit states, and to investigate the influence of geometric and

material parameters. In total twenty-five tests were carried out; fifteen full-scale tests for

monotonic gravity loading and ten tests for combinations with cyclic lateral drifts. By

utilising the previous test setup, the fin-plate connections were investigated as both beam-

to-beam and beam-to-column connections, for both circular and slotted bolt holes. In

order to establish design recommendations and a rational procedure for safe and

economical connection, the limit states were identified.

The failure modes adopted by Astaneh were listed in the previous Section 2.1.2, and are

simplified schematically in hierarchical order in Figure 2.10. Two primary factors

influencing the connection behaviour were identified as the number of bolts and the type

of support (rigid or pinned). Astaneh subsequently developed a strength-based design

procedure, allowing the beam to reach its full moment capacity, taking account of the

required shear capacity and connection rotation. This procedure was evaluated using a

Beam

Column

Fin-plate

Actuator ‘R’ Actuator ‘S’

Actuator ‘A’


31

finite element model by Ashakul (2004). This researcher also proposed a different

method to calculate shear yielding of the plate, based on investigation of the connection’s

geometric parameters (plate material, plate thickness, distance between bolt line and weld

line). Extensions of the model also included the response of double–vertical-column fin-

plate connections.

Figure 2.10 Hierarchy of failure modes from yielding to fracture (Astaneh and McMullin,

2002).

Creech (2005) conducted experimental tests to create a baseline for comparison to the

existing design procedure, particularly of Astaneh’s work. The focus of this research was

to identify means for improving the adopted fin-plate connection design method in the

AISC LRFD 3rd

Edition Manual (1992). In addition, an extensive database of design

methodologies and findings by previous researchers were gathered for analytical

comparison. Ten full-scale tests incorporated both rigid and flexible support conditions,

using either standard or short-slotted holes in the connection. In the case of flexible

support, simulated slab restraints were considered, in an attempt to generate the effects of

concrete slab superstructure. In contrast to Astaneh’s experimental setup, this research

was loaded by two actuators at positions at the one-third and two-third lengths of the

beam. The test beam was supported with either a column or a beam, whilst the free end of

the beam was supported by a roller. From the test results, the majority of the test

specimens failed by shear rupture of the bolts. A similar observation was recorded with

Astanehs’s test results varying the bolt hole type. Larger connection rotation was

observed for short-slotted holes as compared to general circular bolt holes, but the

ultimate strength was approximately equal for both types.

In 2006, Metzger performed eight full-scale experimental tests to examine the

performance of connection design, according to the published AISC 13th Edition Steel

Loading

starts

Plate

Yielding

Bearing

Yielding

Edge Distance

Fracture

Net Section

Fracture

Bolt Fracture

Weld Fracture

YIELDING MODES FRACTURE MODES


32

Construction Manual (AISC, 2005). Two types of connections were tested; conventional

and extended fin-plate connections. Various parameters including the number of bolts,

and the support condition were varied to evaluate the connections on the basis of their

ultimate strength and rotational ductility. It was concluded from the tests that fin-plate

connection design using the AISC 13th Edition procedure conservatively predicts the

ultimate strengths as compared to the previous AISC method. However, it also provides a

more accurate design procedure for fin-plate connections.

Most researchers reviewed in this section were concerned with the moment-rotation or

shear-rotation interaction of fin-plate connections. Theoretically, the fin-plate connection

can accommodate the requisite beam end rotation through a combination of different

mechanisms. The ductility requirement for a target end-rotation of 0.03 radian by Astaneh

et al (1989a) has become a de facto standard for most researchers as the established

rotational requirement (Muir and Thornton, 2011). The ductility requirement was

proposed to achieve the requisite beam end rotation without rupture of any elements in

the connection. The 0.03 radian value, however, was considered to be a conservative

upper bound for the end rotation based on Sarkar and Wallace’s (1992) experimental

results.

Identified dominant failure modes for fin-plate connections were observed to be plate

end-distance yielding, bolt hole bearing failure and weld yielding (Lipson, 1968; Richard,

et al., 1980). Richard prescribed the horizontal edge distance requirement to be twice the

bolt diameter, which was later adopted in the AISC book Engineering for Steel

Construction (AISC, 1984). A similar approach is applied to the Green Book (BCSA,

1991) on this end distance requirement. In contrast, Astaneh’s (1989a) procedure

recommended a total edge distance of 1.5 times the bolt diameter, on the basis that bolt

tear-out never occurred in his testing, and no observation indicated that failure was

imminent.

The “brittle” failure mode of bolt shearing fracture was observed in most of Astaneh’s

research. Another common failure mode observed was weld failure in (Lipson, 1968;

Astaneh, 1989a; Moore and Owens, 1992), and when 8mm welds were used, weld failure

was rare (Aggarwal and Coates, 1988). The bolt group effect effectively assumes an

eccentric offset from the face of the support. Of the methods examined, Creech (2005)

and Baldwin (2006) concluded that the eccentricity can be neglected if the calculated

resistance to vertical shear is reduced by 20%. The strength reduction factor is referred to


33

as the bolt group action factor, and is adopted in AISC specification with the basis of the

research on shear splice plate connections.

2.2.2. Review of research on fin-plate connection at elevated temperature

Until recently, joint behaviour in fire has not been studied extensively, and this applies to

fin-plate connections. Investigation of the structural behaviour through experimental tests

undeniably allows realistic global investigation, on all levels, of structural members.

Therefore, full-scale building fire tests are inevitably required to provide the most

accurate picture of connection response. However, this option is unlikely to be an

economically appealing solution for researchers. Many researchers’ have alternatively

turned to testing on isolated joints, due to the inadequacy of the dataset on full-scale

structural fire tests. These are useful, but the actual behaviour of joints in buildings is not

truly reflected, due to the absence of structural continuity.

The unique first full-scale test on fin-plate connection at elevated temperature was carried

out in a test facility in Cardington. The collaborative project was coordinated jointly by

the Building Research Establishment (BRE) and British Steel (known as Tata now). The

details of the tests were documented by Wang (2002), combining a broad range of

research studies for the interested reader. The tests were conducted on an eight-storey

steel-framed test building which was subjected to seven fire tests, providing a wealth of

experimental evidences on structural frame response in fire. In this research, only the

structural integrity test (No.7) will be reviewed, which was carried out in a centrally-

located edge compartment of the building (Wald, et al., 2006b). The structure was laid

out in five 9m bays along its elevation, and three bays spaced at 6m, 9m and 6m across

the width. Overall, the setup provided a total floor area in plan of 45m x 21m, with an

overall height of 33m (Figure 2.11). The main frames were connected using flexible end-

plates for beam-to-column connections and fin-plates for beam-to-beam connections.


34

Figure 2.11 Arrangement of structural members and connections in the tested fire

compartment (Wald, et al., 2006b).

Figure 2.11 shows fin-plate connection after the test. Local buckling of the lower beam

flange is shown in Figure 2.12a, this was caused by the high compressive forces

generated in the lower flanges adjacent to the beams after closing the lower gap at large

rotation. While the fin-plate remained intact, bolt-hole elongations were observed in the

beam web, which was 4mm less in thickness than the fin-plate. The yielding of the bolt-

holes provides ductility, allowing larger deformations without connection fracture. The

maximum temperature of the fin-plate connections was 908.3°C, reached at 63 minutes,

when the secondary beam peak temperature was 1088°C (57 minutes) on its lower flange.

In several cases, the bolts were observed to be sheared at the interface of the fin-plate and

beam web (Figure 2.12b). Thermal contraction in the cooling phase generated a high

tensile force on the connection. Fin-plates exhibit low ductility; the rotational stiffness

increased when the lower beam flange made contact with the face of the supporting

member (Newman, et al., 2000).

Figure 2.12 Cardington fin-plate connection failure during and after test

(a) (b)

Fin-plate connection

P10-260×100

D E

2

1

Secondary beam

305×165×40UB

Primary beam

356×171×51UB

End-plate connection

P10-260×100

4M20

40 50

27

60

60

60

40


35

In 2005, Ticha and Wald conducted (Sarraj, 2007b) a fire test in Veselí nad Lužnicí, in

the Czech Republic, on a beam with fin-plate connections following the Cardington

laboratory test. A 3m long simply supported beam with three bolted fin-plate connections,

was loaded with two hydraulic jacks (60kN each) at 250mm from each of the beam ends.

Both the beam and fin-plates were grade S235, with the bolts being fully-threaded Grade

8.8 high-strength bolts of 12mm diameter. The geometry of the fin-plate was

125mm×60mm, with 6mm thickness. Lateral restraint was applied by regularly spaced

thin steel strips welded to the beam top flange, connecting it to the test rig. The main

objective was to study the temperature profile of the connection through simulating the

gas temperatures of Cardington fire test No. 7. After the test, the fin-plate showed no sign

of fracture, despite the bolts being sheared completely due to the high tying forces applied

to them during cooling. It was also observed that the beam web suffered diagonal local

buckling in the region between the stiffener and the beam end.

Following this development, Sarraj et al.(2007a, 2007b) studied the behaviour of fin-plate

connections with a highly detailed three-dimensional finite element model. An

investigation was carried out with Abaqus software, using eight-node continuum

hexahedral brick elements for the main parts of the connection. The model was analysed

through the elastic and plastic ranges, up to failure. It was firstly developed on the basis

of a single plate with a bolt bearing against the hole, which was subsequently assembled

into a series of lap-joint as shown in Figure 2.13. The finite element models simulated the

bolt shearing and bearing behaviour in a simple shear connection. It was later verified in

the tests at Veselí nad Lužnicí for both the heating and cooling stages, with reasonable

agreement. Slight discrepancies in the runaway stage were caused by the complexity of

the test arrangement, which applied specific lateral restraint, and this effect was simulated

by simply restraining several nodes on the top flange.

Further investigation on fin-plate connection behaviour was performed in the framework

of a component-based model. An extensive parametric study varying the connection

geometry in the Abaqus modelling provided the optimum load-deflection behaviour,

allowing the mechanical model to be constructed. The generation of this model was

simply derived based on a series of single-bolt lap-joints under tensile force. Three main

components defining the lap-joint characteristic were identified; the plate in bearing, bolt

shear and friction. The evaluation of the proposed component model was carried out

using Abaqus, and compared against the experimental test by Ticha and Wald (Wald et

al., 2006a), with reasonable accuracy.


36

Figure 2.13 Three-dimensional modelling of Sarraj (2007b) using Abaqus

In 2005-2008, a collaborative project between the Universities of Sheffield and

Manchester was carried out to investigate the robustness of common types of steel

connection at elevated temperature. The connections were subjected to combinations of

moment, shear and tying force using the test setup shown in Figure 2.14, specimens were

loaded to large deformation and fracture. Yu et al. (2009) performed experiments for

flush endplates, flexible endplates, web cleats and fin-plates, using an electric furnace

with an internal volume of 1.0m3. A detailed description of these experiments will be

given in Chapter 5, in the context of the component model for fin-plate connections

developed in this research.

Figure 2.14 The test setup in University of Sheffield (Yu, et al., 2009).

The test setup for the fin-plates used 200mm deep × 8mm thick plates with three bolt

rows, designed in accordance with the UK design recommendations (BCSA, 1991). Three

Furnace

Reaction Frame

Load Jack


37

steady-state elevated-temperatures of 450°C, 550°C and 650°C were used, representing

the temperature range giving rapid degradation of the material properties of both steel and

bolts. The connections were designed to be tested under a combination of shear and tying

forces, corresponding to initial angles of 35º and 55º between the resultant force and the

beam axis. This was possible with an experimental setup that was tilted in the furnace.

Two bolt sizes, of M20 and M24, with grades 8.8 and 10.9, were tested.

It was observed that the failures of the fin-plate connections with Grade 8.8 M20 bolts

were controlled by bolt shear, with visible bearing deformation on the bolt holes, for both

ambient and elevated temperatures. Similar fracture patterns were exhibited by all the test

specimens. The top two bolts were completely sheared before the third bolt was subjected

to significant shear deformation. Based on comparison of the maximum connection

resistances, it was reported that the design resistance recommended by EN 1993-1-8

(2005b) and BCSA (1991) are conservative. Both design guides imply that the failure

mode should be dominated by bearing on the plates, however, this is contradicted by the

test observations.

The studies by Sarraj (2007b) and Yu et al. (2009) have built the fundamentals of this

research through their findings on fin-plate connection behaviour. Using their findings as

a point of reference, a more refined mechanical model has been established here to model

more realistic connection behaviour in fire. The essential behaviour of any connection in

fire involves redistribution of the forces from the connected member, during load

reversals and in both heating and cooling. However, the component models by Sarraj and

Yu both did not considered this effect, and proposed more simplified models. In this

research, force reversal has been dealt appropriately by introducing the unloading of

components and considering the ambiguous effect the of combined forces generated at

the bolt rows. Utilising a bolted shear connection, the slip characteristic of a bolt is

generally simulated by shifting the overall connection bearing behaviour, over a range of

a clearance between the bolt hole and bolt position.

Based on the Cardington database, Selamat and Garlock (2010a, 2010b) investigated a

simple and cost-effective modification of the fin-plate intended to improve connection

performance during a real fire scenario. A finite element model was developed using

Abaqus, applying appropriate boundary conditions simulating the restraint to connections

and structural members. An uncoupled thermo-mechanical analysis was applied in two

phases to the beam-to-beam subassembly. The connection weld was assumed not to fail

in the model, in accordance with Eurocode design. It was discovered that significant


38

improvements on the connection behaviour could be achieved by modifying their

geometric detailing, namely by using double plates to the beam web, matching the

thickness of the fin-plate to the beam web thickness, increasing the distances of the bolts

relative to beam end and the gap distance between bottom beam flange and column face.

Three failure modes were examined, for the fire case; bearing by significant deformation

of bolt hole, bolt shear and block-shear tearout. The first two limit states correspond to

the observations and results by Sarraj (2007b) and Yu et al. (2009); block shear tearout

failure was not reported by them.

Jones and Wang (2011) and Wang et al. (2011) conducted ten fire tests on a ‘rugby

goalpost’ subframe to investigate two column sizes and five types of joint, namely: fin-

plate, web cleat, flush endplate, flexible endplate and extended endplate. For each

representative medium-scale restrained subframe, the connections were examined through

equivalent beam-to-column joints. Whilst all the steelwork was left unprotected, the top

flange of beam was wrapped with a layer of 15mm ceramic blanket to generate the effect

shielding of concrete slabs in realistic construction. Two sizes of column were tested,

with connection dimensions of H=150, D=130mm and t=10mm. Both cases generally

exhibited similar beam deflection patterns with buckling of the beam web, resulting in

out-of-plane deformation and twisting of the lower beam flange. The combination of

bending moment and shear force caused fracture of the connection weld between the fin-

plate and column. Smaller column size (UC 152×152×23) generated much smaller force,

with less deformation in the bolt holes as compared to the larger column size (UC

254×254×73). Much larger rotation was also observed with the smaller column, resulting

in substantial bearing of the lower beam flange which caused the column to deform as

shown in Figure 2.15.

Figure 2.15 Buckling of the beam with fin-plate connection (Wang, et al., 2011).

Yang and Tan (2012) presented numerical results for six beam-to-column connection

tests using six different types of connections; web cleat, fin-plate, top and seat with


39

angles, flush end-plate and extended end-plate. The objectives of this study were to

improve the understanding of bolted joints under catenary action, and subsequently to

produce better joint design to mitigate progressive collapse. The experimental research

project was conducted at Nanyang Technological University, Singapore. Static and

dynamic finite element models were employed to overcome the common computational

problems of convergence, contact, large deformation and fracture simulation. The fin-

plate connection was observed to fail by shear fracture for both static and dynamic

solution process.

2.3. Mechanical modelling

In searching for alternative methods to compensate for the impracticality of conducting

sufficient high-temperature tests over a wide range of joint types and assemblies, it is

most beneficial to study complex joints using the component-based method. It can be

argued that all connections are semi-rigid, as no practical connection is ideally ‘pinned

‘or ‘rigid’. Thus, applying the philosophy of the component method to sensibly

characterise the behaviour of connections seems the most reasonable and practical

method. In contrast to the detailed finite element analysis, the behaviour of a connection

is subdivided into that of simpler zones with distinct structural functions, represented by

non-linear translational springs, either in parallel or series where appropriate. These

arrangements directly lead to a so-called ‘component-based model’. Ongoing research on

connection design is largely influenced by the philosophy of this approach; which allows

of individual component’s contributions to the deformation behaviour to be evaluated

independently.

The implementation of the component-based model in EN1993-1-8, Annex J (CEN,

2005b) comes about as a result of progressive research reported by the European

workgroup COST C1 during 1990s. The original principles of the component method

were based on experimental and analytical work by Zoetemeijer (1983). The application

of this approach was also detailed by Tschemmernegg and Humer (1988) at the

University of Innsbruck, Austria, focusing on the elastic-plastic behaviour of connection

design for semi-rigid construction. Continuous research throughout the 1980s followed as

a series of projects by Tschemmernegg et al. (1987, 1988, and 1989), performing

extensive test series on welded and bolted joints, and subsequently developing panel zone

models for the joints. Basic relationships were derived on the flexibility between the

panel zone and the connections, describing the overall behaviour of the joint as a

moment-rotation relationship. A general spring model was introduced with reference to


40

the test loading arrangement which consisted of three major springs, namely: the load

introduction spring, the shear spring and the connection spring (Figure 2.16). The sum of

the rotations for the joint is based on the activated springs assembled in series, for either

symmetrical or unsymmetrical loading condition. Prompted by the developed component

model, new calculation procedures were also introduced based on the findings.

Figure 2.16 Tschemmernegg and Humer (1988) Spring model

2.3.1. Application of component method at elevated temperature

Over the past decade, the component model has been further developed for different types

of connection, with further scientific refinements to take account of axial force, bending

and shear interaction, for most common types of connections. Successful evaluation of

the component model at ambient temperature was achieved, with a wide range of

experimental data available for validation. Following the continuous development and

improvement of the mechanical model for steel joints at ambient temperature, limited yet

successful research has been carried out on the component method at elevated

temperatures, particularly for the flexible/pinned connection type. The implementation of

this approach has been complemented by finite element computer programs, developed in

research centres and universities. Over the years, significant research has been carried out

MA ΔM=MA MA

MA

LOAD

INTRODUCTION

SPRING

SHEAR SPRING CONNECTION

SPRING

OVERALL

SPRING

+ + =

MP

MeO

θEI θEI θC

MeA

MeE

θ


41

at the University of Sheffield Structural Fire Engineering Research Group. Early research

was performed on connection moment-rotation behaviour in two phases, collaborating

with the Building Research Establishment and the Steel Construction Institute (Leston-

Jones, 1997; Al-Jabri, et al., 1997).

At the University of Liége, Jaspart (1997) combined the available component data to

develop a practical design concept for joints at ambient temperature. According to Jaspart

(2000, 2002), in order to integrate the actual joint response in a more consistent approach,

the joint representation can be carried out in four successive steps; joint characterisation,

classification, modelling and idealisation. The application of the component method at the

initial stage of joint characterisation requires the following steps, which will be

introduced mainly in the context of application to fin-plate connections.

a) Identification of the active components

The active components of a joint consist of the elements that directly contribute to the

deformation or limit its strength (Block, 2006). In Annex J of Eurocode 3 (CEN, 2005b)

design rules are given for a number of components of different types of joints. The

resistance and stiffness of the provided components mainly focuses on major-axis joints

using European hot-rolled sections. The assessment of these component properties have

been validated through comparison with experimental results.

Evaluation of the key components can be made by describing their idealised load-transfer

mechanisms. Failure of fin-plate connections at high temperatures involves their response

to a combination of beam end-shear and normal forces, and large rotations. Preliminary

investigation of a fin-plate connection can be carried out by representing the shear

connection as a lap-joint, which transfers the force across the connection via sheared

bolts. Rex and Easterling (2002) modelled the behaviour of single-bolt lap-joints as a

combination of three fundamental behaviours; plate friction, plate bearing and bolt shear.

Similar primary components were adopted by Sarraj (2007b) to accompany the 3D finite

element modelling mentioned in Section 2.2.2. Yu et al. (2009) subsequently applied a

more refined component-based model for fin-plate connections (Figure 2.17), with

reference to the isolated tests she performed at the University of Sheffield. Additional

components are introduced at large rotations at high temperature, which are positioned at

the lower beam flange. Another modification effectively assesses the influence of larger

bolt holes. Movement of the bolt, generating positive contact to the bolt holes, is


42

considered by shifting the shear curves accordingly. The development of this model will

be further described in Chapters 3 and 5.

Figure 2.17 Yu et al. (2009) fin-plate connection component model

On a different application of a component-based method, Hu (2009) proposed a newly

developed component model for the flexible end-plate connection, based on Al-Jabri’s,

under various loading conditions. The model included the basic component zones, of

tension and compression, as well as shear, in the fire condition (Figure 2.18). For the

tension zone components, the contributions of the column flange and column web were

ignored, given that flexible end-plate connections are designed as simple joints with

limited stiffness. However, a weld component was introduced, based on Spyrou’s

experimental observation of the possible plastic failure modes. An additional shear

component characteristic was defined, based on the investigation by Sarraj (2007b). This

consideration was adopted on the basis of the active components in shear connections, but

without a friction component. The model was subsequently verified against experimental

data by Yu et al. (2009) to determine the resistance and rotation capacity of the

connection.

Fin plate in

bearing Bolt in shear Beam web in

bearing

Friction

Beam lower flange in contact with column


43

Figure 2.18 Hu (2009) component model for partial depth end-plate connection

b) Specification of component characteristics

Comprehensive understanding of the overall behaviour of steel structures is crucial to

guaranteeing their fire-resistance, and so the alternative of using analytical tools may

further improve design efficiency by providing a rational representation of the behaviour.

According to Simões da Silva et al. (2001) any attempt to predict the behaviour of steel

connections in fire loading is further complicated by several phenomena:

1. Variation of the material properties of steel with temperature,

2. Accurate prediction of time-temperature variation within the various joint

components,

3. Differential elongations of the various components because of increasing

temperature,

4. Proper definition of fire development models within a building envelope, and the

subsequent time-temperature profiles of the joint components.

Thus, the accuracy of prediction of overall connection behaviour largely depends on the

interpretation of individual component characteristics. The characterisation of these

components can be represented through their force-displacement curves. The effect of

weakening of steel at elevated temperature can be applied at this stage, using high-

temperature material properties, as was done by Leston-Jones (1997) and Al-Jabri (1999),

or by developing an elevated-temperature model predicting the capacities of the

components (Spyrou, 2002). There are several different options to model the real

component behaviour, elastic-plastic, multi-linear and non-linear, as shown in Figure 2.19

(Block, 2006). The stiffness and resistance of individual constitutive relationships govern

the manner in which the connections will behave. The application of the adopted model


44

may depend on the required level of analytical accuracy. Simplified characterisations of

the components are possible whenever only the resistance, or the initial stiffnesses, of the

joints are required, without significant loss of accuracy.

a) Elastic-plastic b) Muli-linear c) Non-linear

Figure 2.19 Idealisation of component characteristics (Jaspart, 2002; Block, 2006)

Connection design should satisfy the dual criteria of not just providing sufficient strength,

but also ductility. Simões da Silva et al. (2001) proposed a component model for typical

bolted end-plate joints. The components are classified according to their ductility in three

main groups; high-ductility, limited-ductility and brittle-failure (Figure 2.20). The

evaluation of the joint ductility constitutes an essential characteristic to ensure sufficient

rotation or deformation capacity for the connection.

d) High ductility e) Limited ductility f) Brittle failure

Figure 2.20 Ductility of end-plate connection (Simoes da Silva, et al., 2001; Del Savio, et

al., 2009).

In this fin-plate component characterisation, Yu et al. (2009) assumed that a bolt’

resistance decreased to zero gradually. This enabled the component model to simulate the

progressive shear of bolts observed in the tests. This contradicts Sarraj’s (2007b)

assumption, that immediate fracture occurred after the maximum shear resistance of a

bolt was exceeded. The post-yielding of the component characteristic is able to predict

more accurately the connection behaviour, provided that the definition of the

characteristics can be closely generated.

Δ

F

FRd

Ke

Kp

Δe

F

FRd

Ke

Kp

Δe

Δ

F

Δe

FRd

Ke Δ

δ

F

δ

F

δ

F


45

c) Assembly of the components

Assembly of connection components is based on the distribution of the internal forces

within the joint. The overall applied forces are distributed at each loading step between

the individual components according to the instantaneous stiffness and resistance of each

component (Jaspart, 2000). The component-based model assembly comprises zero-length

extensional springs representing components, and rigid links. In instances where the

initial model is rather complicated, simplification of the component model by reducing

the number of components that may present is required, in order to obtain analytical

solutions for the proposed assembly. A simplification process for connection elements

can be exemplified using an equivalent elastic model developed by Simões da Silva

(2001), which was able to yield a closed-form analytical expression to overcome

numerical complexities. The elastic model showed identical results to the original elastic-

plastic model, shown in Figure 2.21.

Figure 2.21 Cruciform beam-to-column connection (a) Geometry of joint (b) Mechanical

model (c) Basic non-linear model (d) Equivalent elastic model (Simoes da Silva, et al.,

2001).

In general, for all types of connection, analytical prediction of the response of steel joints

requires a continuous change of the mechanical properties with temperature. According to

Simões da Silva (2001), for a given temperature θ, and for component i, the properties

can be described as;

M

M

k2

ϕ

k3,1

k4,1 k5,1 k6,1 k7,1 k8,1

k3,2

k4,2 k5,2 k6,2 k7,2 k8,2

M

Kc

ϕ Kt

M

Lc

ϕ ket

Lc kec

kpc, Pc

kpt, Pt

Lt Lt

(a) (b)

(c) (d)


46

(2.1)

(2.2)

(2.3)

The isothermal response of a steel joint loaded by a moment is summarised using a non-

linear numerical procedure by Silva. For a given level of applied component force

, the equivalent deformation given by;

(2.4)

Similarly for

,

(2.5)

Considering equilibrium, the moment at a given level of joint deformation is,

(2.6)

Thus, referring to Figure 2.21c, the stiffness and rotation of the joint, at temperature θ,

can be derived accordingly. At , stiffness . Implementation of this

solution requires an incremental procedure, which results in the derivation of a moment-

rotation curve for a given connection at temperature θ.

(2.7)

So the rotation,

(2.8)

In a framed structure during fire, a beam-to-column connection experiences changing

combinations of axial forces and bending moments. In order to respond correctly to such

load reversals, a load-reversal approach needs to be defined for each connection element

at elevated temperature. This is partly due to the likely occurrence of large displacements,

but is also due to the thermal effects and their transient character.

Block (2006) has adopted the Masing rule (Masing, 1923) to include the hysteresis

behaviour of the tension and compression zones. The concept of a “reference point” and

“permanent displacement” has been used to predict the unloading curves at changing


47

temperature (Figure 2.22). Santiago et al. (2008a) applied the same theory, based on the

assumption that the tensile and compressive curves do not share the same line of action.

Ramli-Sulong et al. (2007) also developed a tri-linear monotonic force-deformation

characteristic, and subsequently extended it to account for cyclic loading using the

research code Adaptic, The simulations of the component model gave reasonable

agreement to the experimental results from Al-Jabri (1999) and Spyrou (2002), but were

sensitive to the modelling idealisations and the simplified temperature-dependent material

representations.

The possibility of highly realistic simulation of structural interaction provides an

alternative to compensate for the impracticality of conducting sufficient high-temperature

tests over a wide range of members in isolation and in assemblies. Many computer

programs have now been developed by research groups, and these are becoming

increasingly popular for engineers as specialist design tools to facilitate appropriate

strategies in fire resistance design.

Figure 2.22 Definition of the reference point and permanent deformation (Block, 2006).

2.4. Summary

In this chapter, modelling of steel connections is firstly introduced in the context of their

design stiffness classification, which is a key component to the behaviour of connection

in structural frames. This review on available research results from studies of connection

Loading curves

Intersection

point

Unloading curves

Displacement

Fo

rce

T1< T2

F1> F2 F1

F2

δ2 δ1

δpl, 1

Reference Point

δpl, 2

T1

T2


48

behaviour in the framework of the component-based method indicates that it has proven

successful for most majority types of connections. It seems that application of the

component-based model may contribute to the development of enhanced analysis of

connections in fire. This is paralleled by advances in computer modelling for structural

analysis, which has grown in complexity to cater for more advanced structural

assessment; for instance, the consideration of beam catenary action and membrane action

in slabs at elevated temperatures. However, none of these studies haveresearched on the

fin plate connection subjected to combined shear, moment and axial tensile load during

the force reversal at high temperatures. The review on the experimental tests for fin-plate

connections also indicates that limited number of investigation is available; particularly

dealing with these combination forces. In this circumstance, with the popular usage of

fin-plate in building construction, this research is necessary to understand the real

performance of simple connections in fire.

Chapter 3: Characterisation of fin-plate connection components

49

3. CHARACTERISATION OF FIN-PLATE CONNECTION

COMPONENTS

The general requirement for design of any type of connection involves providing

sufficient ductility and rotation capacity to ensure the safety and performance of the

connection. Ductility is defined as the connection’s capability to undergo large inelastic

deformations without losing all its strength. For the case of a simple shear connection,

normal design concerns only the strength and ductility needed to transfer the beam end

reaction to its support and to rotate with the beam end without failing, as shown in Figure

3.1 (Astaneh, 1989a). In most cases, an explicit approach to connection design is

necessary, as the inherent steel ductility can not provide the desired overall ductile

performance. Therefore, appropriate design strategies must be adopted, recognising and

avoiding any conditions that may lead to brittle failures in the shear connections.

Figure 3.1 Beam-to-column rotation for simple connection (Astaneh, 1989a).

3.1. Design philosophy of fin-plate shear connections

One of the fundamental components of a fin-plate connection is the high-strength bolt in

single shear. The simplest example which uses this is a single-bolt lap-joint connection.

This joint is formed by attaching two plates with a single bolt fastening them through

oversized holes. The geometrical detail of a single-bolted lap-joint is illustrated in Figure

3.2.

θ


50

Figure 3.2 Geometrical detail of a single-bolt lap-joint

In any connection, evaluation of the key aspects requires an appreciation of the idealised

load transfer mechanisms. For a fin-plate shear connection, the line of action of the net

shear force is assumed to pass through the centroid of the bolt group, thus, loading the

connection in shear via the sheared bolts. The force transfer mechanism adopted in this

research is ideally defined as a combination of friction, acting alone in the initial stage,

and subsequent bearing once the major components in the connection are in bearing

contact. Lap-joint connections can be subjected to either single- or double-shear,

according to the number of shearing planes adopted. The use of double plates reduces the

number of bolts by utilising their capacity to shear across multiple planes (BCSA, 1991),

and also makes the load path through the connection symmetric.

The behaviour of a lap joint connection can be described throughout the progress of its

loading stages. The corresponding forces and stresses in the connected materials can be

detailed using the free-body diagrams for the interfaces between the plates and the bolt

shown in Figure 3.3. During the initial loading phase, it is assumed that the bolts are

installed centrally, and so do not carry any bearing or shear force. When a high-strength

bolt is fully tightened, a clamping force T, which prevents any relative movements of the

connected plates, is produced (Figure 3.3a). This force utilises the plate’s frictional

resistance in order to transfer the load solely by the friction between the plates. The

frictional resistance is a function of contact area of the plate surfaces and the level of

tightening of the bolt. A slip-resistant joint is one which is designed, using bolts with a

specified tension force, to avoid slip at any time during the life of the structure, and so the

design of this kind of joint is to be carried out at working load (Kulak et al., 1987). When

the load exceeds the frictional resistance, unlimited relative displacement occurs, until the

bolt comes into simultaneous contact with the opposite bolt hole edges. This displacement

End distance

Edge

distance

I

I


51

is a finite slip, ranging from zero up to two hole clearances. In general, the positions of

the bolts in their respective holes during the assembly process define the slip ranges.

The bolt shank subsequently bears onto the circumferences of the bolt holes. At this

stage, after slip has occurred, the load is transmitted largely through shear of the bolts

(Figure 3.3b), which is equilibrated by the bearing stresses between the bolt and the edges

of the holes in the plates. The connection behaves elastically with increasing load until

the appropriate stress in either the bolt or the plates reaches the yield strength of the

material. This establishes the lower bound limit to the connection strength of the bolted

lap-joint.

Figure 3.3 Load transfer mechanism in a bolted joint; (a) frictional force, (b) bearing

stress.

Typical deformation of a single-shear bolted connection can be explained with reference

to Figure 3.4. As the plates are loaded in tension (pulling apart in opposite directions), the

eccentricity between the lines of action of the loads pulling on the connected members

causes plastic secondary bending of each of the plates, which reduces this eccentricity.

Provided that the initial eccentricity is kept small, the development of secondary bending

stresses may be disregarded. In instances where secondary bending develops, uneven

bearing of the plates and bending of the bolt results. In such cases the effective shear

strength of the bolt is reduced to approximately about 60% of its tensile strength (Owens

and Cheal, 1989). This effect is more pronounced in thin plates; as the loads tend to align

axially the bolt rotates so that it is partly in tension and partly in shear. However, if the

specimen is symmetric, with double-shear action on the bolt, there is no bending of the

net sections.

Bearing

stresses

F

F

F

F

T

T

T

T

Frictional

force

(a) (b)

Shearing

forces


52

Figure 3.4 Typical deformation of lap joint with a single bolt subjected to single shear

(Sarraj, 2007b)

Eurocode 3-1-8 (CEN, 2005b) does not provide a detailed analysis of bolted shear

connections, but recommendations are given for the evaluation of stiffness and resistance

properties for several individual primary components. In this chapter, the derivation of

the fin-plate connection’s rotational capacity is carried out by considering the effective

stresses and forces exerted during the whole loading-unloading cycle. These affect the

connection mainly through hole distortions in the plates and shear deformations of the

bolts. Subsequently, the characterisation of the behaviour of the components that

contribute to the deformation of the fin-plate connection will be discussed in detail.

3.2. Failure modes of fin-plate shear connection

Connections in general should possess the characteristics of both strength and ductility,

which in the context of shear connection refers to their ability to articulate plastically at

some stage of the loading cycle without failure; this is governed by the ductilities of their

elementary parts. The ductility of a joint reflects the length of the post-yield

characteristic in its moment-rotation response, which for the case of fin-plate connection

is provided mainly by its capacity for plate yielding and bearing deformation at its bolt

holes as a means of accommodating the beam-end rotation. This is supported by early

research by Lipson (1968), who concluded that the ductility of fin-plate connections is

derived from the bolt deformation, plate and/or beam web hole distortion, and by out-of

plane bending of the plate and/or beam web.

Failure of a structural connection occurs when the forces transferred exceed the load-

carrying capacity of the connection. In essence, the overall capacity of a connection is

based on the strengths of its components. The limit states identified for a bolted lap-joint

shear connection are bearing failure, bolt-shear failure, shear-out (“block-shear”) failure

and net section tensile failure (Kulak et al., 1987; Sarraj, 2007b). However, not every

limit state is of interest, as the design guides (CEN, 2005b; BCSA, 1991) permit

conservative design, with implicit consideration of the non-dominant limit states.

Rotation of bolt, shearing

and tension

Secondary bending

F F


53

Therefore, only critical limit states that contribute to the effectiveness of the connection

design, mainly involving plate bearing and bolt shearing components (Figure 3.5), are

investigated further. Brief overviews of other types of failure mode are also given below,

to describe the possible occurrence of other localised failures in shear connections.

Figure 3.5 Fin-plate connection failure mode; a) plate bearing and b) bolt shearing

The existence of holes in a plate causes discontinuities in its geometry, thus causing

disruption of the stress trajectories, and subsequently causes high stress concentrations in

the region of the holes. Net section failure is characterised by uniform cross-section

distortion (necking) at the maximum stress concentration, which then propagates

transversely and causes fracture of the plate across the net section (Salih, et al., 2010).

Block shear failure is defined as the tear-out failure of a portion of the connection, which

occurs due to combination of fracture at the net section and yielding in shear at the gross

section of the perpendicular plane (Ibrahim, 1995). It is not considered to be the

governing limit state by the design provisions of AISC-LRFD (AISC, 1999) or EC3-1-8

(CEN, 2005b), as their practical recommendation provides a dimensional limitation on

the horizontal end distance to be equal to or greater than twice the diameter of the bolt db,

for both the plate and the beam web. This failure mode is precluded by setting this limit

for sufficient end-distance in design.

End-tearout is caused by the bolts in a connection tearing out the end of a plate before the

net cross-section capacity or the bearing stress capacity can be reached. This failure

occurs in the principal force direction, when the end distance is insufficiently long,

because of yielding along the plate-shearing path (Sarraj, 2007b). The weld thickness and

length requires that the plate yield prior to weld rupture. Thus, the design requirement for

the fin-plate connection has usually discounted weld failure as one of the dominant

Bolt

shearing

Plate

yielding

(a) (b)


54

factors. In addition, avoidance of buckling in the plate can also be ensured with the

requirement of the distance from the weld to the bolt column (Muir and Thornton, 2011).

Figure 3.6 Other failure modes for single lap-joint; a) Net section failure, b) Block shear

failure and c) End-tearout failure (Ibrahim, 1995).

In this research, the dominant failure criteria are introduced for each individual

component to facilitate the simulation of its behaviour at different temperatures, and

including its final fracture. The design procedure classifies the failure modes into

‘ductile’ and ‘brittle’, and attempts to ensure that ductile failure modes precede the brittle

ones. Beyond this stage, the maximum resistance of the aggregate bolt-row characteristic

is controlled by that of its weakest component. Thus, the post-yield failure characteristic

for a bolt-row follows the dominant component. It should be noted that the initial

frictional resistance between plates diminishes somewhat when slip occurs in a bolt row.

3.2.1. Bearing of plates

Bearing failure of the plates involves yielding of the plate material close to the contact

region at the hole edge. The bearing strength is highly affected by the lateral confinement

of the material surrounding the hole. The contact area between the bolt and connected

plates is referred to as the bearing area (Figure 3.7). The stress concentration near the

bearing area at a hole develops when a bolt bears on the edge of the bolt hole. This causes

localised yielding or fracture around the hole, changing the overall configuration of the

connection. The limiting condition of the yielding at this stage can significantly affects

the strength, or facilitates ductile failure of the connection. The presence of threads in the

bearing zone increases the flexibility of bearing behaviour, without reducing its strength.

An increase of bearing strength is developed once the threads have dug into the plate,

caused by the additional through-thickness restraint (Owens and Cheal, 1989)

Tensile

area

(a) (b) (c)

Shear

area


55

Figure 3.7 Bearing stress area.

The development of the bearing stresses in the material adjacent to the hole and the bolt

can be explained in stages, illustrated Figure 3.8. At the early stage, the bearing stress is

concentrated at the point where positive contact is made, indicated as the elastic bearing

stress region (Figure 3.8a). Subsequently, increased loading causes yielding and bolt

embedment on a larger contact area, which results in the more uniform stress distribution

depicted in Figure 3.8b during the elastic-plastic stage. Although the actual bearing stress

remains ill-defined at this stage, it can be assumed that a uniform stress distribution

(Figure 3.8c) exists, expressed as a function of the plate thickness and nominal bolt

diameter (Kulak, et al., 1987). According to Owens (1989), the actual bearing strength is

approximately a linear function of the geometrical parameters, particularly the end

distance. Bearing of the plate will only become critical provided that the specimen is

sufficiently wide for the net section not to yield in tension previously. Design provisions

(BCSA, 1991; AISC, 1999) recommend that the failure of shear connections should be

dominated by bearing of plates, so that the definitions of these limiting parameters are

crucial.

Figure 3.8 Bearing stresses in bolted plates; a) Elastic, b) elastic-plastic and c) Nominal.

a) Initial stiffness Ki of the plate-in-bearing component

In 2003, Rex and Easterling conducted experimental research at Virginia Polytechnic

Institute, USA to provide data on the strength and load-deformation behaviour of a single

plate bearing on a single bolt. Several parameters were systematically studied; these

included the end distance (le), the plate thickness (tp), bolt diameter (db), edge condition

(sheared or saw) and plate width. The test setup (Figure 3.9) shows the test specimen,

d

P

P P P

P P

P/2 P/2

P

db

t

Bearing

Area


56

positioned between the top and bottom of the test rig in the testing machine. During the

test, the specimens were loaded until either the limit load was reached or the specimen

failed. The primary interest in the tests was the characterisation of the initial stiffness.

Nevertheless, measuring this value from experiments was rather complicated. Hence, a

combination with finite element data was used to develop and evaluate the initial stiffness

values based on predictive models.

Figure 3.9 Rex and Easterling (2003) Test setup.

The proposed prediction model identified three primary factors influencing the derivation

of the initial stiffness; namely bearing, bending and shearing. The bearing stiffness (Kbr)

was referred to the bolt bearing at the hole, whilst the bending stiffness (Kb) and the

shearing stiffness (Kv) were calculated from the material between the bolt and the ends of

the plates. The accuracy of this model was assessed using best-fit data with reference to

the upper-and lower-bound stiffnesses, considering the precision of the deformation- and

load-measuring devices. Thus, the final stiffness accounts for the model with an

arrangement in series, and is given by;

(3.1)

Alternatively, the current Eurocode 3-1-8, Annex J (CEN, 2005b) provides an equation

for prediction of the initial stiffness of the bearing component, which is given for the case

when the bolts are not fully tightened.

(3.2)

Where; (3.3)

(3.4)

A325 Bolt

Tested plate

51mm Bolts

Top of test rig Bottom of test rig

Spacing plates


57

b) Bearing stiffness, Kbr

According to Rex and Easterling, the bearing of a bolt on the bolt hole requires

simplifications to relate the bearing stiffness model to the plate geometry and material

characteristics. The bearing stiffness model was assumed as two-dimensional, and contact

was established at the yield stress. With this simplification, the geometrical model can be

exemplified as in Figure 3.10, where r1 and r2 represent the radii of the bolt and bolt hole

respectively. From the model illustrated, the Δbr indicates the local bearing deformation,

for which the initial value is assumed to be 0.102 mm based on comparison of values of

Kbr and finite element models. The area of bearing deformation Ap is given by Equation

(3.5), and the arc angle α1 between the bolt and plate is defined by Equation (3.6).

Figure 3.10 Rex and Easterling (2003) bearing stiffness model.

(3.5)

(3.6)

The nonlinear relationship between the bolt diameter and the stiffness given in the

following equation is derived based on the relationship

:

(3.7)

Sarraj (2007b) adopted a similar equation describing the plate bearing component, but

with a few modifications based on a finite element parametric study. A three-dimensional

model was simulated in Abaqus based on the Rex and Easterling experimental setup, but

with the assumption that the bolt was fully tightened, in contrast to the original setup. The

parameters attributable to the bearing deformation were investigated in detail; for instance

Δbr y

x

α1

α2

r1

r2

Bearing

deformation


58

end distance e2, plate thickness tp, the angle of bearing, plate temperature and bolt

diameter db.

In the parametric study, the end distance of the plate was varied from 2db to 7.5db, with

constant plate thickness of 10mm and bolt type M20 high-strength Grade 8.8, installed in

a 22mm bolt hole. From the FE model, the ultimate bearing strength was observed to

improve gradually as the end distance increased from 2.0db to 3.0db. However, beyond

this range no distinctive influence was established. Sarraj later distinguished the

component behaviour in two cases of bearing on the basis of a small end distance (e2 ≤

2.0db) for tension and a large end distance (e2 ≥ 3.0db) for compression, as detailed in

Table 3.1.

In order to identify the influence of bolt size on the bearing component, three bolt sizes

(M16, M20 and M22) at Grade 8.8 were considered. Constant plate strength of S275 and

thickness of 6mm were defined for the models. The plate end distances of 2.0db and

3.0db were varied for all bolt sizes. For both cases, a proportional increase of the bearing

strength was observed with bolt diameter. Thus, it was proposed that for large end

distance, two separate cases should be distinguished, for M24 bolts and upward, and M20

bolts and downward. For small end distance, the same expression applied to all bolt sizes.

Sarraj initiated an attempt to model the behaviour of fin-plate connections at elevated

temperature, and successfully substantiated an FE model against available experimental

results. Based on the results generated, a general expression to describe the force-

displacement behaviour was developed using curve-fitting to several non-linear

equations. The bearing stiffness equation (3.8) was proposed by Sarraj using the curve

fitting value Ω, with reference to the Rex and Easterling Equation.

(3.8)

In the plate bearing component model, the temperature effect was considered by applying

the strength reduction factors of Eurocode 3-1-2 (CEN, 2005a) to the yield stress fy as

indicated in the second column of Table 3.1.


59

Table 3.1 Plate bearing curve fit parameter Ω

c) Bending and shearing stiffness (Kb and Kv)

For connections with large end distance, the bolt bearing stiffness governs the initial

stiffness. However, as the end distance decreases, the final stiffness Ki is primarily

influenced by the bolt bending and shearing stiffnesses (Oltman, 2004). Rex and

Easterling addressed the shear and bending stiffness using simplified assumptions about

the geometrical attributes of the plate and bolt. The steel in between the hole and the end

of the plate is considered as an elastic fixed-ended beam with height h and length l, as

shown in Figure 3.11.

Figure 3.11 Rex and Easterling (2003) bending and shear stiffness model.

The derivation of the bending and shearing stiffnesses can be expressed by considering

the theoretical load distribution of the short deep-beam model, in addition to its

slenderness ratio (l/h). The equations (3.9)-(3.10) are derived on the assumption of a

Temperature

T (°C)

Reduced

yield stress,

fy,θ

Tension, small end

distance, (e2 ≤ 2.0db)

Compression, Large end

distance(e2 ≥ 3.0db)

All sizes of bolt For M24 bolts

and larger

For bolts up

to M20

20 1.0 × fy 145 250 250

100 1.0× fy 180 250 220

200 1.0× fy 180 250 220

300 1.0× fy 180 250 220

400 1.0× fy 170 200 200

500 0.78× fy 130 170 170

600 0.47× fy 80 110 110

700 0.23× fy 45 40 40

800 0.11× fy 20 20 20

db

e2

Height = e2-db /2 Fixed end

beam


60

uniform load distribution, generating best-fit values when compared to the finite element

models.

Bending Stiffness;

(3.9)

Shearing Stiffness;

(3.10)

The expression for the final stiffness Ki derived by Rex and Easterling produced an

average difference of +12% from the actual experimental stiffness, with a coefficient of

variation (COV) of 23%. The comparison of the experimental results with Eurocode 3-1-

8 (CEN, 2005b) gave an average of 15% with COV of 24%. Therefore, the proposed

bearing model is shown to have the best correlation with the experimental results.

d) Plate strength

The nominal plate bearing strength is given with different expressions by existing design

codes (AISC, 1993; AISC, 1999; CEN, 2005b), which will be reviewed in this section.

The bearing and tear-out strengths are calculated identically in all design provisions, as a

limitation in the direction of the force applied to the bolt hole.

The bearing strength recommended by AISC-LRFD 3rd

(AISC, 1993) is given in

Equation (3.11) The plate strength is defined by considering the shear yielding, shear

rupture, block shear rupture and bearing capacity of the plate. This design equation is

defined for a standard bolt hole, as well as for oversized, short-slotted and long-slotted

bolt holes, when deformation of the bolt hole at service load is a design consideration.

(3.11)

Where e2 is given as the end distance, t as thickness of plate, db is the bolt diameter and fu

as the yield strength of the plate.

The AISC-LRFD 13th Edition manual (AISC, 1999) extended the procedure for the

flexibility requirement as given in Equation (3.12). The revised manual included an

additional check on plate buckling as well as plate flexure.


61

(3.12)

Where, (3.13)

(3.14)

Equations (3.11) and (3.12) were adopted from experimental tests reported by Kulak et al.

(1987), based on evidence of apparent hole elongation by bearing deformation which

occurred immediately adjacent to the bolt hole. The defined limit state of 2.4 dbtfu

provides a bearing strength which is attainable at the reasonable deformation of 1/4 in.

(approximately 6.35mm), limiting the hole ovalisation length. However, the clear

distance Le between bolt holes is used rather than the end distance e2 or the bolt spacing,

as used by Kulak et al.(1987).

Eurocode 3-1-8 (CEN, 2005b) recommends a different expression for the design bearing

resistance, as given by Equation (3.15).

(3.15)

In the case of end bolts, the αd is taken to be e2 /3db in the direction of load transfer, whilst

in the direction perpendicular to the load direction, value of k1 is given by the smallest

value of (2.8 e2 /db – 1.7) or 2.5 for the edge bolts. The recommended value of the partial

safety factor γM2 is given as 1.25.

(3.16)

The design provisions give conservative design bearing strengths, with the Eurocode

prediction being lower than of AISC-LRFD by 20%. This is partly due to the strength

reduction factor imposed by AISC-LRFD being 0.75, whereas the Eurocode uses a safety

factor of 1.25, equivalent to a 0.8 strength reduction factor. This is supported by Rex and

Easterlings’ reported experimental finding that the coefficients of variation for the plate

strength given by AISC-LRFD 13rd

Edition was 30% compared with the experimental

results, being considerably over-conservative in bearing resistance design. The best

correlation was given by AISC-LRFD 3rd

Edition with COV of 10%, followed by

Eurocode 3-1-8 with merely 11%. This value was calculated, based on the ratio of plate

strength in the tests to the predicted strengths, using the respective design guides.


62

Therefore, the plate strength recommendation by AISC-LRFD 3rd

Edition seems suitable

to be adopted in the plate strength calculation.

From the detailed FE modelling, Sarraj proposed a design bearing equation, which

classifies the bearing cases based on the plate end-distance. For bearing in tension, the

strength calculation considers a general case for all sizes of bolt, given by Equation

(3.17). For small end distance (e2 ≤ 2.0db), the value of e2 is substituted by 2.0db in this

equation. However, for bearing in compression, the bearing strength can be calculated

using Equation (3.18) for all sizes of bolt, substituting a value of 3.0db for large end-

distance case (e2 ≤ 3.0db). Otherwise the e2 value is valid.

(3.17)

(3.18)

e) Plate bearing normalised force-displacement relationship

Rex and Easterling (2003) represented the bearing component behaviour using

normalised force-displacement values, which were subsequently fitted into the equation

originated by Richard and Abbot (1975) with the resulting relationship given in Equation

(3.19). Sarraj (2007b) also adopted a similar expression, given in Equation (3.20),

adopting different curve-fit values Ψ and Ω. These curve-fit parameters were derived on

the basis of the most effective plate bearing behaviour generated from the parametric

finite element modelling.

In the case of the force-displacement relationship at elevated temperature, the curve-fit

values were defined for each corresponding temperature, according to the end-distance

limitation and bolt sizes. The summarised curve-fit values for a range of temperatures

given by Sarraj (2006b) are shown in Table 3.2 and Table 3.3. As proposed previously, in

the case of compressive bearing strength, the curve-fit values differ, depending on the

sizes of the bolts used.

(3.19)

(3.20)

(3.21)


63

The given F is the plate force [N], Fb,rd is the nominal plate strength, is the normalised

hole elongation, and β is the steel correction factor (equal to 30% elongation, and taken

equal as β=1 for typical steel).

Table 3.2 Tensile curve-fit values at different temperatures in the case of small end

distance (e2 ≤ 2.0db)

Table 3.3 Compressive curve-fit values at different temperatures in the case of large end

distance (e2 ≥ 3.0db)

f) Pre- and post-yielding regions of plate bearing component

All design standards treat end tear-out and bearing failure as a single limit state, by

providing a design equation that relates end tear-out capacity to the end distance, and by

setting an upper limit for the bearing capacity (Rex and Easterling, 2003; Salih et al.,

2010). The analytical model derived by Sarraj for plate bearing has been adopted for

For all sizes of bolt

20 1.0× fu 2.1 0.012

100 1.25× fy 2 0.008

200 1.25× fy 2 0.008

300 1.25× fy 2 0.008

400 1.0× fy 2 0.008

500 0.78× fy 2 0.008

600 0.47× fy 2 0.008

700 0.23× fy 2 0.008

800 0.11× fy 1.8 0.008

For bolts up to M20 For M24 bolts and larger

20 1.0× fy 1.7 0.011 1.7 0.008

100 1.25× fy 1.7 0.011 1.7 0.008

200 1.25× fy 1.7 0.011 1.7 0.008

300 1.25× fy 1.7 0.011 1.7 0.008

400 1.0× fy 1.7 0.009 1.7 0.008

500 0.78× fy 1.7 0.007 1.7 0.008

600 0.47× fy 1.7 0.0055 1.7 0.008

700 0.23× fy 1.7 0.0055 1.7 0.007

800 0.11× fy 1.7 0.001 1.7 0.007


64

further analysis. Based on the experimental data by Rex and Easterling (2002), a

comparison of the plate bearing characteristic has been investigated in detail, together

with Sarraj’s finite element model. The force-deflection relationship in Figure 3.12 shows

good agreement between the generated analytical model and the experimental test. The

geometrical details of the single-plate specimen tested by Rex and Easterling are; 127mm

plate width, 6.5mm thickness and 38mm end distance. The bolt fastening the plate was a

high-strength bolt with 25mm diameter. The material properties of the plate were listed as

205 kN/mm2 Elastic modulus, 307 N/mm

2 Yield stress and 452 N/mm

2 ultimate strength.

Figure 3.12 Comparison of the plate bearing component up to yield.

The incorporation of the substantiated plate bearing characteristic generally defined for

the behaviour of the plate bearing component at maximum resistance and before yielding

stage, for both the beam web and the cover plates. The behaviour of the bearing

component adopted is shown Figure 3.13, for the pre- and post-yield stages of plate

bearing.

Figure 3.13 Plate bearing characteristic for component model.

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14

Fo

rce

(kN

)

Displacement (mm)

PLATE BEARING

TEST (Rex, 2003)

FEM (Sarraj, 2006)

COMP MODEL

Fo

rce (

kN

)

Displacement (mm)

PLATE BEARING

Fbrt, max

COMPRESSIVE

TENSILE

e2

Fbr, yield

Fbrc, max


65

As the applied tensile force increases from zero, the concentration of stress develops

elastically with deformation, in the vicinity of the bolt hole. Local yielding of the plates is

subsequently initiated as maximum stresses develop at the hole edge, allowing stress

redistribution to happen around the bolt hole. In this case, the bolt is embedded in the side

of the bolt hole, and the material of the plate in the contact zone piles up, causing

ovalisation of the bolt hole.

At the initiation of plate yielding, the plate bearing characteristic tends to retain some

stiffness, generating a low rate of bearing deformation. The bearing resistance Fbrt, max is

then reached, beyond which there is a plateau until a considerable plastic range has been

exceeded. The elongation of the bolt hole is largely influenced by the ductility of the plate

material and its dimensions (thickness t and end distance e2). The ultimate limiting factor

for the plate strength, when the bolt protrudes close to the edge of the plate, is given by

the end distance e2, between the bolt hole and the plate edge. Any movement in the

opposite-direction away from the edge of the plate (compressive action) results in large

bearing deformation of the bolt hole, without the occurrence of tear-out failure, and is

taken as infinitely ductile.

The force-displacement relationship derived for the plate bearing component at ambient

temperature defines the characteristic at elevated temperature. The reduced bearing

characteristics subject to elevated temperature is shown in Figure 3.14, for tension and

compression for temperatures up to 900°C. From low temperature up to 400°C, no

significant reduction in stiffness or capacity of the bearing component is observed.

However, with the weakening of steel strength, the bearing capacity is reduced, with an

ultimate deformation limiting the hole ovalisation in tension only. The plate bearing

failure mode in a connection generally shows signs of distress through permanent plastic

deformation, but tends to be non-catastrophic, in contrast to the more brittle shearing

failure.


66

Figure 3.14 Temperature-dependent plate bearing characteristic for component model; a)

tensile and b) compressive.

3.2.2. Bolt shearing

This simulates the effect when the critical shear cross-section of a bolt becomes fully

plastic. When the equivalent plastic stress exceeds the true yield stress of the bolt, then

the residual cross section of the bolt is gradually deemed to yield, initiating the failure of

a joint. Bolt shear is generally considered to be an undesirable failure mode, because it

does not involve enough ductility to ensure a simultaneous plastic distribution of the

forces taken by the bolts, and can therefore allow progressive failure. Bolt shearing acts

across the shearing planes, which are the planes between the connected plates moving in

opposite directions, in either single- or double-shear (Figure 3.15). The bolt hole can be

defined as standard, slotted or oversized. Whilst the ideal bolt hole is a close fit to the

bole diameter, most holes have a pre-defined clearance for more practical assembly on

site.

0

20

40

60

80

100

120

140

0 10 20 30 40 50

Fo

rce (

kN

)

Displacement (mm)

-120

-100

-80

-60

-40

-20

0

-50 -40 -30 -20 -10 0

Fo

rce (

kN

)

Displacement (mm)

20 C

100 C

200 C

300 C

400 C

500 C

600 C

700 C

800 C

900 C

Tensile plate

deformation

Compressive

plate

deformation

(a)

(b)


67

Figure 3.15 a) Single-shear failure and b) Double-shear failure.

The bolt shearing strength is determined experimentally, and is approximately about

60%-80% of its ultimate tensile strength, the variation being due to the threads in the

shearing plane. This range covers values given by Eurocode 3-1-8 (CEN, 2005b) and

AISC-LRFD (AISC, 1993) to approximate the shearing capacity of a bolt. Thus, the

single-shear capacity of an individual high-strength bolt can be conservatively determined

using Equation (3.22), as given in Eurocode 3-1-8, Annex J.

(3.22)

Where,

αv is a parameter defining whether the shear plane passes through;

a) The threaded portion of the bolt, given with

αv = 0.6, for classes 4.6, 5.6 and 8.8,

αv = 0.5, for classes 4.8, 5.8, 6.8 and 10.9.

b) The unthreaded portion of the bolt (the shank), given with

αv = 0.6

The relative contributions from the shank and the threaded region are functions of the bolt

material properties and their relative areas. The deformation capacity of a threaded bolt is

strongly influenced by its threaded length within the stressed length (Owens, 1992). The

greatest shear strength is obtained when the full shank is available to resist the applied

shear load. When the threads are cut by the shear plane of the bolt, the capacity may be

reduced to as little as 70% of the full shank strength. The effect of threads in shear planes

on both strength and deformation capacity is shown in Figure 3.16. The issues of

permitting threads within shear planes are resolved by applying the factor αv and the

reduction of the deformation capacity.

Bolt

Shearing

F

F

F

F/2

F/2


68

Figure 3.16 Force-displacement graph for M20 bolt with thread or shank in shear plane

(Owens, 1992).

For the case of bolt shearing at elevated temperature, Sarraj (2007b) derived ultimate

strength reduction factors from the FE model of single lap joints using S275 steel plates,

in which each plate had thickness of 0.5db. The model was analysed for shearing capacity

at ambient and elevated temperatures. The relative deformation of high-strength Grade

8.8 bolts at their respective temperatures were measured by clamping one plate at one end

and enforcing axial displacement at the opposite end of the other plate (Figure 3.17).

Figure 3.17 Sarraj (2007b) three-dimensional finite element model of single bolted joint.

The investigation of bolt shearing capacity is based on steady-state temperatures ranging

from 100ºC to 900°C. This allows derivation of bolt shearing strength reduction factors

with respect to the shearing capacity at ambient temperature. The comparison of the

proposed factors is given in Table 3.4, in comparison to the strength reduction factors

given in Eurocode 3-1-2 (CEN, 2005a). The ultimate factor from the Eurocode is

calculated using the conversion factor for bolt shear, which in this case is taken as 0.6.

Overall, good correlation is observed between the reduction factors, with a slight

discrepancy between 100°C and 400°C.

x

z

y

0

100

200

300

0 2 4 6 8 10

Load kN

Design strength

to BS 5950 Part 1

Deformation (mm)

Design strength

to BS 5950 Part 1 Behaviour

Shank in

shear planes

Thread in

shear planes

Behaviour

234

184


69

Table 3.4 Reduction factor for bolts in shear.

a) Bolt shearing strength

The prescribed bolt strength reduction factor effectively calculates the bolt shearing

strength at increasing temperatures using Equation (3.23). The strength reduction factor is

represented by Rf, v, b, whilst As is the tensile stress area of bolt.

(3.23)

The bolt shearing force-displacement relationship is presented using Sarraj’s FE data,

which is then fitted to a modified Ramberg-Osgood (1943) expression, given in Equation

(3.24). Using this equation allows the bolt shearing strength to be defined by a continuous

function with no distinct yield point. The additional temperature-dependent parameter Ω

needs to be obtained in advance, which in this case uses the best curve-fitting values

summarised in Table 3.5.

(3.24)

Where F is the plate force [N], Fv,rd is the temperature-dependent bolt shearing strength

[N], kv,b is the temperature-dependent bolt shearing stiffness [N/mm] and n defines the

“sharpness” of the curve, which controls the curvature of the pre-yield range.

Table 3.5 Bolt shearing parameters at respective temperatures

Reduction factor,

EC3 Reduction factor

20 0.580 0.6×1.000 = 0.600

100 0.575 0.6×0.968 = 0.581

200 0.538 0.6×0.935 = 0.561

300 0.500 0.6×0.903 = 0.542

400 0.426 0.6×0.775 = 0.456

500 0.323 0.6×0.550 = 0.330

600 0.139 0.6×0.220 = 0.132

700 0.061 0.6×0.100 = 0.060

800 0.041 0.6×0.067 = 0.040

900 0.019 0.6×0.033 = 0.019


70

The bolt shearing stiffness kv,b is represented by the following temperature-dependent

expressions, given in Equation (3.25). The shear stiffness was adapted by Sarraj using

Timoshenko beam theory (Hayes, 2003), which accounts for shear deformation in

isotropic beams. The shear correction factor k was introduced to correct the strain energy

resulting from the assumption of a constant shear profile (Madhusi-Raman and Davalos,

1996). In this case it was effectively applied through the bolt section, which directly

influences the shear correction value due to the cross-sectional and material properties of

the bolts. The value of k = 0.15 was found to be suitable for bolt shearing analysis (Sarraj,

2007b).

(3.25)

with the shear modulus given as,

(3.26)

where,

∆ is relative bolt deflection [mm];

G is the shear modulus;

Eθ is the temperature-dependant Elastic Modulus given in Eurocode 3-1-2 (CEN, 2005a)

b) Pre- and post-yielding region of bolt shearing component

The shearing resistance of a bolted connection derived by Sarraj can be generally applied

to a single- or double-shear loading state, according to the number of interacting shearing

surfaces in contact. As the loading increases beyond its shearing capacity (Fbs,max), the

Reduction factor,

Bolt shearing

strength,

Bolt shearing

stiffness,

Temperature

dependant parameter,

20 0.580 145.7 184.3 2.5

100 0.575 144.4 184.3 2.8

200 0.538 128.1 165.8 2.0

300 0.500 125.6 147.4 2.2

400 0.426 107.0 129.0 2.0

500 0.323 81.1 110.6 2.0

600 0.139 34.9 57.1 1.3

700 0.061 15.32 24.0 0.6

800 0.041 10.30 16.6 0.7

900 0.019 4.77 12.4 0.02


71

edge of the plate hole ‘cuts’ into the bolt shank and causes it to lose full continuity

between its two parts. The shearing displacement at the post-yielding stage causes a

simple reduction of the residual connected bolt area. The shear area reduces linearly with

the slip of the shear planes (Figure 3.18), generating a gradual decrease of shear

resistance to zero at a shear deformation equal to the bolt diameter. This assumption is

based on the experimental test results by Yu et al. (2009) on fin-plate connections. It was

observed that its bolt failed gradually after the maximum shearing capacity was reached,

in contrast to the immediate failure previously assumed in Sarraj’s component model.

Figure 3.18 Residual area of bolt at post-yielding stage.

The bolt shearing force-displacement relationships generated for tension and compression

exhibit the same characteristic (Figure 3.19). This displacement is limited to the bolt

diameter dbs during the post-yielding stage. The bolt shearing characteristic derived for

steady-state temperatures up to 900°C can be summarised in Figure 3.20.

Figure 3.19 Bolt shearing force-displacement graph in “tension” and “compression”.

Fo

rce (

kN

)

Displacement (mm)

BOLT SHEARING

Fbs, max

COMPRESSIVE

TENSILE

dbs

Fbs, yield

Fbs, max

dbs

Residual area,

Ashear

α

Diameter, db

Bolt Bolt

Hole


72

Figure 3.20 Temperature-dependent bolt shearing characteristics.

3.2.3. Friction

The load transfer between the plate components of a bolted shear connections is initially

provided by the frictional force which is developed by the high interface pressure from

the bolt clamping forces and the friction coefficient of the plate contact surfaces (Figure

3.21). The use of preloaded bolts is highly suitable for use in slip-resistant joints, since

the frictional resistance is directly influenced by the magnitude of the bolt clamping

force. The bolts are pre-loaded close to their proof load in order to develop a large normal

force between the two connected plate surfaces. Although the friction between these

surfaces in a fully-tightened connection may contribute some percentage to the ultimate

load, the actual amount is not clear.

Figure 3.21 The friction resistance in double bolted joint

The slip resistance of a bolted joint is also proportional to the number of connected

surfaces, and therefore greater resistances can be obtained in instances where multiple

lap-joints are used. In a slip-critical joint, the slip resistance of the bolted joint is designed

at the serviceability limit state. However, for bolted joints, which transfer load by shear

and bearing, the slip is not considered as a critical factor. Joint slip may occur before or

after the working load of the connection is reached. Slip then brings the connected parts

Friction

resistance

0

50

100

150

200

0 10 20 30

Fo

rce (

kN

)

Displacement (mm)

20 C 100 C 200 C 300 C 400 C

500 C 600 C 700 C 800 C 900 C

-200

-150

-100

-50

0

-30 -20 -10 0

Fo

rce (

kN

)

Displacement (mm)

Compressive Tensile


73

into bearing on both sides of the bolt, so that the applied load is transmitted partially by

frictional resistance and partly by shearing of the steel elements (Kulak, et al., 1987).

Frank and Yura (1981) conducted an experimental test series to assess the frictional

behaviour in developing the slip loads for bolted shear connections with coated contact

surfaces. A total of 77 elemental slip tests were conducted using steel plates with blast-

cleaned steel surfaces and single bolts in double-shear. The investigation included the

effect of surface coating on the slip coefficient. The joints were fabricated from three

types of steel; A36, A572 and A514. The force-displacement response was described in

three characteristic stages (reproduced in Figure 3.22), which described the frictional

resistance as almost linear until the force approaches the maximum resistance. Beyond

the point, a sudden drop of the force occurs, followed by rapid plate slip. The response of

the curves appeared not to be affected by steel type or size of the bolt hole. However, the

characterisation of the slip behaviour based on the experimental results was not specified

by Frank and Yura (1981).

Figure 3.22 Frank and Yura typical force-displacement curve for sandblasted surface.

Rex and Easterling (2002) proposed a slip characteristic based on the simplified pre- and

post-slip behaviour, using a bi-linear relationship. The model exhibits similar basic

shapes to the previous model, but with a significant difference in the post-slip behaviour

(Figure 3.23). This representation was adopted from observation of the model introduced

by Frank and Yura (1981), coupled with the reported frictional behaviour of single bolt-

lap-plates by Karsu (1995) and Gillett (1987). The approximate plate-bolt-plate behaviour

was defined to degrade continuously to zero or negligible frictional load transfer, after the

Force, P

(kips)

Slip (mils)

SLIP LOAD

25 50

40

20 Slip

P


74

maximum resistance was exceeded. The experimental data by Gillett (1978) were used to

calculate the values of the slip load Rf initial stiffness Kfi and post-peak stiffness Kfp and

subsequently used to calculate the slip resistance using Equation (3.27). In the proposed

model, the deformation at slip was given an average absolute value of 0.0076 in

(0.19mm).

Figure 3.23 Rex and Easterling Bi-linear rational model

The slip resistance expression proposed by Rex and Easterling was based on a

modification of the AISC-LRFD 3rd

Edition (AISC, 1993) requirement for bolt-

tightening. The coefficient recommended by Fisher et al. (1978) for the value of α was

also taken into consideration. This was given as 1.0 for A325 bolts and 0.88 for A490

bolts.

(3.27)

where,

Rf = slip resistance

Abt = stressed area of bolt (usually taken as 75% of bolt gross area)

μ = coefficient of slip (obtained either by specific tests or as defined in Table 3.7)

Alternatively, the design slip resistance for preloaded bolts of Grade 8.8 (equivalent to an

A325 bolt) or 10.9 can also be calculated using the specified equation given by Eurocode

3-1-8 (CEN, 2005b) as follows:

Force, P

Displacement, (in)

Rf

kfi

0.19

kfp


75

(3.28)

where;

ks = Factor given according to the type of bolt holes (reproduced in Table 3.6),

n = Number of friction surfaces.

γM3 = partial safety factor (taken as 1.25).

The preloading force of the bolt, Fp,C, is defined in compliance to Eurocode EN 1090-2:

Requirement for the execution of steel structures (CEN, 2008). In cases where calibrated

preloading is not present, the right-hand side of Equation (3.29) is assumed to be factored

by 0.5.

(3.29)

Where,

As = Stressed area of bolt,

fu,b = design resistance of a single bolt [N].

Equations (3.27) and (3.29) clearly describe the frictional resistance as a function of the

coefficient of slip and the preload force induced by the initial tightening process. These

basic parameters vary considerably according to the design criteria, and thus a reliable

value needs to be determined to generate an accurate estimation of the frictional

resistance. A detailed overview of these parameters is given in the next section.

a) Oversized bolt holes

In order to facilitate erection, oversized holes can be of great benefit to allow tolerance in

placing the components during assembly. The nominal clearance for oversized bolts

given in Eurocode 1090-2 (CEN, 2008) for the commonly-used bolt sizes (M16 to M22)

is specified as not exceeding 4mm, and not more than 6mm for M24 bolts. A question on

the utilisation of this specification arises with regard to the performance of the

connection. If oversized holes are employed, omni-directional effects exist on the hole

tolerance. This is contrary to the case of slotted holes, where a much greater tolerance is

provided but is mainly mono-directional (Figure 3.24).


76

Figure 3.24 Direction of bolt deformation for; a) oversized bolt hole and b) slotted bolt

hole

The displacement has been treated in accordance with the consideration of the bolt slip as

a serviceability criterion. However, the reduction of bolt capacity is also of concern. As

bolt holes become larger relative to the bolt diameter during loading, the amount of

material available to resist the force in the bolt is reduced. As a result, the amount of bolt

elongation (and pre-tension) is less than if a standard clearance were present (Kulak, et

al., 1987). Thus, a reduction factor is used to account directly for the possible reduction of

bolt pretension or change of contact surface stresses around the bolt hole in calculation of

slip resistance (Stankevicius, et al., 2009). This factor is adopted by the Eurocode 3-1-8

(CEN, 2005b) and the Research Council on Structural Connections (RCSC, 2004)

specifications as the values of ks shown in Table 3.6.

Table 3.6 Values of ks

Description Class

Bolts in normal holes 1.0

Bolts in either oversized holes or slotted holes with the axis of

the slot perpendicular to the direction of load transfer. 0.85

Bolts in long slotted holes with the axis of the slot

perpendicular to the direction of load transfer. 0.7

Bolts in short slotted holes with the axis of the slot parallel to

the direction of load transfer 0.76

Bolts in long slotted holes with the axis of the slot parallel to

the direction of load transfer 0.63

Clearance

hole

Gap

Bolt

Gap

Bolt

(a)

Gap

Bolt

Gap

Bolt

Clearance

hole

(b)

Omni-

direction

Mono-

direction


77

b) Slip coefficient

The slip coefficient varies according to the joint type and the surface characteristics of the

connected plates (Kulak, et al., 1987), which can be determined experimentally for

designing slip-critical connections. It is of prime importance to determine the slip

coefficient values for an accurate evaluation of the frictional resistance. The contact

surfaces are prepared to improve the coefficient of friction in the design. Eurocode 1090-

2 (CEN, 2008) provides a representation of slip coefficient values, given in Table 3.7,

according to the classification of the surface treatment.

Table 3.7 Classification of surfaces assumed for the use of slip coefficient values.

Surface treatment Class Slip factor, μ

Surface blasted with shot or grit with loose rust removed,

not pitted

A 0.50

Surfaces blasted with shot or grid:

a) Spray-metalized with a aluminium or zinc based

product;

b) With alkali-zinc silicate paint with a thickness of

50μm to 80μm

B 0.40

Surfaces cleaned by wire-brushing or flame cleaning, with

loose rust removed

C 0.30

Surfaces as rolled D 0.20

Sarraj (2007b) proposed that the maximum friction resistance shall be calculated with the

expression given in Equation (3.30), for M20 bolts of Grade 8.8 or 10.9. The friction

component was investigated by analysing finite element lap joints models with two

different values of friction coefficient; 0.25 and almost zero. Based on the finite element

model, the friction behaviour was simplified to the two straight lines with a triangular

relationship (Figure 3.25) adopted by Rex and Easterling (2002). The force-deflection

relationship was subsequently derived in terms of the maximum deflection Δsf and

ultimate deflection Δsu. The equation proposed by Rex and Easterling was adapted for the

M20 bolt size, which is commonly used in European construction. The ultimate

deformation Δsu can be calculated based on the post-slip behaviour, which relates the

stiffness to the combined thickness of the connected plates tp1 and tp2, as given in

Equation (3.32).


78

(3.30)

Yield deflection,

(3.31)

Ultimate deflection,

(3.32)

Where,

tp1 = thickness of cover plate

tp1 = thickness of beam web

Figure 3.25 Sarraj’s frictional force-displacement relationship

The initial stiffness kfi and the post-slip stiffness kfp are given by the relationships given in

Equations (3.33) and (3.34).

(3.33)

(3.34)

c) Pre- and post-yielding regions of friction component

In this research, a rational representation of this characteristic is defined through the pre-

and post-slip behaviour of a connection (Figure 3.26). The representation follows the

basic shape observed by Frank and Yura (1981), amended to take account of the frictional

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14 16 18 20

Displacement, Δ (mm)

kfi

kfp

Force, F (kN)

Δsu Δsf

Fs,rd FE Model

Mathematical

model


79

behaviour observed in the experimental results from Yu et al. (2009) and Hirashima et al.

(2010). It was observed for both cases that high frictional stresses develop immediately

after the commencement of an experiment. Therefore, in this model, the initial stiffness of

the pre-slip region is determined fairly arbitrarily, assuming the friction force reaches its

peak at 10% of the bolt-hole clearance, simulating the dynamic frictional force that is

resisted by the connected plate at initial stage of loading. The maximum friction

resistance Ffric, max then persists as a plateau until the bolt makes positive contact with bolt

hole edge. When the bolt slips dslip, the load is carried partly by bearing and partly by

friction. Thus, the post-slip resistance degrades gradually with movement, indicating the

static frictional force that remains on the connection.

Figure 3.26 Friction force-displacement curve at ambient temperature

Essentially, the reduction of the friction characteristics with temperature is assumed to

depend on the elastic modulus reduction factor. These characteristics derived for steady-

state temperatures up to 900°C can be summarised in Figure 3.27, for both in tension and

compression. The frictional resistance is controlled by the normal force between the plate

surfaces, caused by bolt tension, and this is assumed to be generally based on elastic bolt

behaviour. It was observed by Kirby’s (1995) test that the degradation of shear forces at

high temperature reduces at the same rate as the tensile force. In other experimental

research by Liang (2006), it was reported that during the high-clamping-force stage

(approximately up to 300°C), large slip marks in the vicinity of the bolt holes indicated

that active contact is made due to expansion of the connected plates. With increased

temperature, the slip marks reduced, and almost vanished at approximately 800°C. Thus,

the rapid drop of slip resistance at high temperature also follows the loss of tension in the

Fo

rce (

kN

)

Displacement (mm)

FRICTION

Ffric, max

COMPRESSIVE

TENSILE

Ffrict, max

dslip


80

bolts, which is consistent with the rapid reduction of tensile strength when the bolt is

heated above its estimated tempering temperature (Liang, 2006)

Figure 3.27 Temperature-dependent friction force-displacement curve

3.3. Behaviour of equivalent bolt-row component

The key components identified in the last section form the equivalent bolt-row

components of a fin-plate connection, which are listed as bearing of plates/beam web,

shearing of bolts, and friction. The so-called equivalent bolt-row characteristic is first

explained for a single-bolted joint, and is subsequently extended for multi-bolt rows. In

the framework of the component model, these elemental parts are known as

“components”, from which the deformation characteristic is represented by nonlinear

force-displacement relationship. The fundamental force-displacement relationship of a lap

joint can be best explained using a typical monotonic friction-bearing characteristic. The

individual characteristics are explained in Figure 3.28, which illustrates, for tension and

compression, the response of the joint. The evaluation and derivation of pre-yielding

failure criterion in each component account for the post-yielding behaviour, respective to

the geometrical and mechanical behaviour of the components.

-60

-40

-20

0

-30 -20 -10 0

Fo

rce (

kN

)

Displacement (mm)

0

20

40

60

0 10 20 30

Fo

rce (

kN

)

Displacement (mm)

20 C 100 C 200 C 300 C 400 C

500 C 600 C 700 C 800 C 900 C

Tensile Compressive


81

Figure 3.28 Force-displacement characteristics for single-bolted joint components.

The load capacity of an equivalent bolt-row is predominantly determined by the assembly

of its springs, from which the weakest individual component spring initiates the failure.

The ultimate fracture or failure criterion adopted for any bolted joint follows its weakest

component characteristic. In order to simulate the force transfer in a bolted joint, the

individual components are arranged with the primary components arranged in series to

form an equivalent component. The frictional resistance between the plates contributes to

a large increase of the joint capacity for equal displacement of the primary components,

particularly in the early loading stage. Therefore, a rational approach to the frictional

component is to consider it as acting in parallel to the primary components.

The equivalent bolt-row component of a single-bolted lap-joint can be depicted as Figure

3.29 in which the dotted lines represent a bolted joint with no hole clearance. However,

the utilisation of high-strength bolts in an oversized bolt holes requires essential

consideration of the bolt slip in the clearance hole. The consideration of this slip effect in

a bolted joint may compromise the overall analytical procedure if neglected, because the

pre-tightening of bolts and the resulting friction diminishes only after major slip. In this

research, the slip influence is incorporated by shifting the origin of the component curve

horizontally by a finite displacement, so that the initial frictional displacement is

eliminated. This initial displacement is the clearance distance between the bolt and bolt

hole edge Δhole.

Cover plate in bearing Beam web in bearing

Bolt in Shear Friction

+ +

+ +

- -

- -

Single-bolted lap joint


82

Figure 3.29 Equivalent bolt-row component of a bolted lap joint

The non-linear response of a fin-plate connection falls into three primary regions: friction

plateau, non-linear bearing and post-yield failure. This behaviour can be explained with

the aid of the bolted joint illustration in Figure 3.30. At the initial stage of loading, the

bolt is assumed to be installed centrally in the plate bolt holes, carrying no active forces

on the mechanical or frictional components (indicated as Stage 1). The load is then

transferred by frictional stress at the plate surfaces, marked as the friction plateau in Stage

2. The frictional resistance is treated independently, in parallel to the force-displacement

relationship of the mechanical components. When the load exceeds the frictional

resistance Ffric, a large relative displacement δslip occurs, and the bolt comes into contact

with the bolt edges. In the case of multi-row bolted joints, the bolts positioned furthest

away from the centre of rotation usually come into contact with the hole walls first, and

are therefore described as the critical bolts. The critical bolts initiate the stage of bearing

against the walls of the bolt hole after a major slip has occurred. The connection then

behaves elastically with increasing load (Stage 3) until the stress in any of the individual

components reaches the yield strength of the material. This then deforms plastically

(Stage 4), by either bolt shear or plate bearing, depending upon their pre-defined

characteristics. Thus, for a row of components, both elastic and inelastic behaviour of

components may act simultaneously, but the yielding of the weakest component denotes

the beginning of inelastic action of the row as a whole.

Original loading

curve

Modified

loading curve

Δhole


83

Figure 3.30 The non-linear response of a bolted lap joint

3.4. Summary

This chapter has described the characterisation of the component elements that has been

identified for fin-plate connections. In order to represent the behaviour of individual

components accurately, the maximum resistance has been compared with previous

experimental and analytical results. For each component, the post-yielding characteristic

has been defined on the basis of its actual failure behaviour, coupled with experimental

evidence. Several important points can be drawn based on the assessment of the fin-plate

connections primary components.

The limiting parameter for the plate bearing component is the end distance e2 of the

plate. This indicates an ultimate tear-out yielding failure of the plate. The influence

F

δ

δ

δ

δ

F

F

F

Stage 2

Stage 3

Stage 4

Ffric

Feq, max

δslip

Feq, yield

Ffric

Feq, max

δfract

δmax

δslip

Stage 1

Friction

plateau


84

of this parameter is incorporated with two cases; small end distance (e2 ≤ 2.0db) and

large end distance (e2 ≥ 3.0db) based on Sarraj (2007b) FE investigation. However,

tear-out of the plate is effectively only valid for the plate behaviour in tension, as the

plate in compression (pushing towards the supporting member) is not subjected to

any end distance limitation.

The ‘brittle’ failure of a fin-plate connection is defined by the shearing of bolts in the

bolted connections. The maximum resistance of this component is given by the

Eurocode 3-1-8 (CEN, 2005b), which being approximately 60%-80% of its ultimate

tensile strength. This failure mode is undesirable as it affects the integrity of the

structural system, having inadequate ductility to ensure simultaneous plastic

distribution of the forces taken by the bolts, and therefore allowing a progressive

failure. A fully detached plate due to the shearing of the bolt is represented by the

residual connected bolt area, after the displacement at maximum shearing resistance

is reached.

The friction characteristic of the plates is of prime importance particularly for the

bolted connection utilising high-strength preloaded bolts. The maximum friction

resistance is immediately achieved to overcome the static friction between the

connected plates. When slip occur`s, this resistance somewhat reduces and remain

with constant rate.

The assembly of the individual elements form the equivalent component, representing

single bolted lap-joint. The maximum capacity of the bolted joint is determined by the

weakest component, in either of these individual components. The limiting parameter,

defining the bolted joint ultimate failure subsequently follows that of the weakest

component.

Chapter 4: Component-based model for fin-plate connection

85

4. COMPONENT-BASED MODEL FOR FIN-PLATE

CONNECTION

The incorporation of actual joint flexibility into routine design practice implies the use of

appropriate analytical methods and computational tools. In current design terms, the

actual flexibility of semi-rigid connections, as compared to the traditional approaches of

treating connections as perfectly pinned or completely fixed, can substantially alter the

internal force distribution in the structure. The flexibility of a connection can be

reasonably established by concentrating attention on the beam-column interface. In this

localised region, the overall joint behaviour is the result of contributions from several

sources of flexibility located in different positions, and the discretisation of the structure

needs to identify the most important of these. Fortunately, Eurocode 3-1-8 (CEN, 2005b)

has provided a realistic way of incorporating connection behaviour within “semi-rigid”

construction into the design process, using the component-based method. This approach

allows the assessment of the individual contributions from different zones to the joint

flexibility, to provide complete joint characteristics. The implementation of the

recommended ‘component’ procedure in the Eurocode is inclined towards endplate

connections, following long development by many researchers (Zoetemeijer, 1983;

Tschemmernerg & Humer, 1988; Jaspart, 2000). For other types of connections, only the

maximum resistances of the active components are recommended, which falls short of the

characterisation needed to assemble the component behaviour into full connection

models. On top of this, none of the proposed component models currently available in

the literature is sufficiently sophisticated to adequately simulate the behaviour of fin-plate

connections in a framed structure subjected to a complete heating and cooling sequence.

4.1. Arrangement of a single bolted joint component model

The active components of fin-plate connection behaviour have already been identified.

The basics of component-based models have been developed with Sarraj’s finite element

models and Yu’s experimental results. In this chapter, the active behaviour of a general

fin-plate connection is represented by ‘component springs’, and these are assembled in an

arrangement that gives the best representation of the connection. As described in the

previous chapter, the representation of fin-plate connection behaviour is based on that of

a single-bolt-row bolted joint. Thus, the component-based connection model is first

described for a bolted lap-joint, comprised of three fundamental components arranged as

springs in series, using two-noded spring elements with no physical length. The


86

assembled model consists of components representing the fin-plate in bearing, bolt in

shearing and beam web in bearing, as illustrated in Figure 4.1. This model also accounts

for friction using a spring in parallel with this basic spring series.

Figure 4.1 Component-based model for a single-bolted lap-joint

In order to account for the usual case where bolt holes are larger than the bolts,

modifications have been made to the component model to represent slip behaviour. The

free slip phase has been considered independently, which is indicated by the activation of

the assembled component behaviour only when the gap closes in either the tension or

compression spring row. If a bolt is presumed initially to be installed centrally in the bolt

holes of both connected plates then it needs a finite relative movement between the plates

to produce positive contact.

4.1.1. Equivalent component for single bolt-row

The arrangement of the component model demonstrates that, during a complete analysis,

tension and compression do not follow the same lines of action. When the connection is

loaded either in tension or compression, the contact achieved by closing the gap activates

the component model. The load capacity is predominantly determined by the assembly of

springs, from which the weakest individual component spring initiates failure. The

determination of the post-yield behaviour of the equivalent bolt-row component can be

defined by reference to its dominant individual component. A summary of the equivalent

bolt-row components in bearing or shearing failure is given in Table 4.1 for tensile

components and in Table 4.2 for compressive components. The second columns of these

Tables generate the final equivalent bolt-

End distance

Bolt

Shear

Beam Web

bearing

(Tension)

Cover-plate

bearing

(Tension)

Cover-plate

bearing

(Compression)

Beam Web

bearing

(Compression)

Friction (slip)

Contact

elements


87

Table 4.1 Tensile equivalent bolt-row component of a single bolted joint

Type of failures

Tensile assembly

Plate bearing failure

(weak plate/strong bolt)

Bolt shearing failure

(weak bolt/strong plate)

δ

Cover-plate bearing

(Tension)

Beam Web bearing

(Tension)

Bolt

Shear

Friction (slip)

δ

F

Feq, max

F

δ

F

δ

+

Feq, max

F

δ

F

δ

F

δ

+

Friction Lap joint

Lap joint Friction


88

Table 4.2 Compressive equivalent bolt-row component of a single bolted joint

Type of failures

Compressive assembly

Plate bearing failure

(weak plate/strong bolt)

Bolt shearing failure

(weak bolt/strong plate)

δ

Cover-plate bearing

(Compression)

Beam Web bearing

(Compression)

Bolt

Shear

Friction (slip)

+

+ Feq, max

Feq, max

F

δ

F

δ δ

F

δ δ

F

δ

F

F

Friction

Friction

Lap joint

Lap joint


89

row components, in cases where either the plate bearing component or the bolt shearing

component is the weakest. The adopted force-displacement characteristic changes

according to those of its components.

For the case of ductile failure, the plate-in-bearing component allows large bearing

deformation, after it reaches its maximum bearing resistance. For a brittle failure mode,

the bolt shear is assumed to rapidly reduce the shearing capacity in proportion to the

residual bolt area. Assembly of the identified characteristics forms the fundamental

behaviour of the bolted joint. The force-displacement relationship of each component

characteristic is then programmed in Vulcan in order to investigate the overall response of

the fin-plate connection.

4.2. Application of fin-plate connection in Vulcan

The developed joint elements in Vulcan can be described as effectively a black box,

whose characteristics are customised to the behaviour of the particular joint, and readily

allow it to be positioned at the intersection of any primary structural members. This

analytical tool consists of an assembly of spring elements, representing the component

springs which are interconnected with rigid links, in between two-noded points. The lap-

joint component can be detailed according to their lines of action that act in series;

namely, (i) fin-plate in bearing (tension), (ii) beam web in bearing (tension), (iii) bolt in

shear, (iv) beam web in bearing (compression) and (v) fin-plate in bearing (compression)

in each given bolt-row. A friction spring (vii) is incorporated, in parallel to the lap-joint

component springs. An additional vertical (vi) shear spring for each given bolt-row, is

included to transfer the vertical reaction from one node to the other. The positioning of

the lap-joint can be illustrated as given in Figure 4.2.

Figure 4.2 Arrangement of component model in a bolted lap-joint

0mm

(vii)

(iv)

(vi)

(v)

(i) (ii)

(iii) Fin plate

Beam web

Lap-joint

component


90

Meanwhile, the arrangement of fin-plate connection model in a beam-column setup for

multiple bolt rows can be illustrated in Figure 4.3. In consideration for contacts made by

the beams-end and the column face at high rotation, additional springs are included at the

upper (viii) and lower (xi) beam flanges.

Figure 4.3 Beam-to-column arrangement of fin-plate connection in Vulcan

The modelling procedure requires textual input data which precisely describes the model.

The geometry of fin-plate connections allows multiple bolt-rows. In a non-linear Vulcan

analysis the bolt group equilibrium simply forms part of the establishment of global

equilibrium for the whole structural model. A minimum requirement of two bolt-rows is

generally adopted to satisfy this equilibrium requirement. The following assumptions are

made to allow for the effect of groups of bolt-rows in fin-plate connections (Figure 4.4).

The connection element is assumed to be positioned at the centreline axis of the

beam section. Thus, any bolt-rows in the connection have an offset from this

point. Prior to large rotation, during its elastic stage, the bolt group rotates about

its elastic “centroid”.

The connection’s centre of rotation changes its position when the gap between

one or other of the beam’s flanges and the column face closes. This point is

shifted to the lower flange of the beam. This point is also referred to as the

instantaneous centre of rotation.

(viii)

0mm

M

N V

(xi)

BEAM

COLUMN

Lap joint, n Bolt row n

i j


91

Figure 4.4 Position of the centre of rotation of the connection

4.3. Development of finite element software Vulcan

The finite element software Vulcan is a dedicated specialist program for thermo-structural

analysis, developed at the University of Sheffield since 1990 (Wang, 2002). This program

was originally based on the software called Instaf written by El-Zanaty and Murray

(1983) which was capable of analysing two-dimensional behaviour of steel frames at

ambient temperature (Bailey, 1995; Shepherd, 1999). Initial development of a semi-rigid

connection facility in the finite element software was initiated by Bailey (1995),

extending developments by Najjar (1994) and Saab (1990). The software was later

renamed Vulcan to reflect the considerable extent of development and improvement from

the original version. At each development stage the software was extensively validated

against available experimental results, including all seven fire tests conducted at

Cardington. Most recently, the software was further refined with the development of a

simple component-based connection element by Block (2006) for bolted, extended and

flush, endplate connections. The research work presented herein is based on the

connection approaches by Bailey and Block, and extends the capabilities of Vulcan to the

use of fin-plate connections in the framework of the component-based method.

4.3.1. General solution procedure in Vulcan

A finite element solver is generally prescribed for use in nonlinear problems, which

include structural analysis at elevated temperature. The nonlinearity refers to geometric

and material changes in the model, which themselves cause major changes in incremental

stiffness during the process of heating and cooling. At high temperature, the changes in

shape and the constitutive relationships are more pronounced, in contrast to the high

stresses which are the main effect at ambient temperature.

lbd

Forced centre

of rotation

(a) Elastic (b) Fully plastic

fb1,e fb1,p

fb3,e fb3,p

fb2,e

fb2,e

ln

M

b1

b2

b3

bf fbf ,e fbf ,p

Free centre

of rotation


92

a) Iteration schemes

In order to deal with the problem of the high degree of nonlinearity at elevated

temperature, the iterative solution in Vulcan adopts the Newton-Raphson (Chen and Lui,

1987; Shepherd, 1999) method. Following the standard finite element procedure, the

stiffness relationship is given in Equation (4.1).

(4.1)

Where

F, d = vector of forces and displacement respectively;

[K] = stiffness matrix.

In linear analysis, the assumption follows that changes in stiffness are small, so that a

constant stiffness may be assumed from the undeformed state. On the contrary, a

nonlinear analysis requires careful consideration of the change in stiffness matrix, which

must be updated as the nonlinear solver progresses through an iterative solution process.

This relationship can be represented by Equation (4.2).

(4.2)

Where,

ΔF = vector of out-of-balance forces;

Δd = vector of incremental displacement.

[K] = tangent stiffness matrix.

As for finite element solution for continuum problems, the physical extent of the model is

generally subdivided into elements, connected at nodal points whose original positions

form the reference state for displacements. The nodes are generally placed at the centroid

of the section, and the reference state remains fixed for calculations at ambient

temperature. The displacements at these points (the degrees of freedom) are generally the

basic unknown parameters in the finite element modelling.

(4.3)

The methodology of a Newton-Raphson model can be described with the aid of Figure

4.5. Considering a case where the initial temperature T1 is equal to 20°C, the

displacement at the first iteration is zero, resulting in zero value for elastic stiffness and

internal force, based on Equation (4.2). The vector for out-of-balance force at 20°C

corresponds to the first incremental value of external force. The total displacement Δr+1


93

for the next iteration is calculated as the sum of the incremental displacement and the

total displacement from the previous iteration. These values, in the context of a set of

shape functions, define the state of strain throughout all the elements. With the

displacement estimation, the out-of-balance force can be evaluated, as well as the tangent

stiffness for the subsequent iteration. The out-of-balance force vector corresponds to the

imbalance between the internal and external forces, and hence an increment in the nodal

displacement is required. The corrective process of updating the nodal point displacement

is repeated until the unbalanced forces have been reduced to within a specified tolerance

limit. Based from the updated nodal displacement, the stiffness matrix is re-evaluated

using updated values of the tangent stiffness at the new level of displacement.

Figure 4.5 Newton-Raphson procedure

At higher temperature, the nonlinearity aspect is increased in the sense that the stress-

strain curve changes to reflect the reduction of strength and stiffness, depicted as curve T2

in Figure 4.5. The displacements from the previous equilibrium state are used as the

starting point for the process at the next, incremented, temperature. The analysis at

elevated temperature is performed with increments of temperature pre-defined by the

user. At a temperature where no solution can be found, the temperature step is bisected

and added to the previous successful temperature to refine the analysis; this can be carried

out successively to a pre-determined lower limit on the temperature step size.

Force, F

Displacement, Δ

T1

T2

K1

K2 K3

Δr1 Δr2 Δr3 Δr4

Internal force calculated

from total displacement

(Δr1 + Δr1)

Out-of-balance force calculated

from total displacement

(Δr1 + Δr1)

EXTERNAL LOAD

T2 > T1

K4


94

b) Convergence criteria failure indication

The Newton-Raphson procedure is often preferred for nonlinear problems, due to its

effectiveness and fast solution. A numerical solution using this procedure is obtained

when the convergence criteria are satisfied. The convergence check is based on the

magnitudes of the out-of balance forces. The closeness of the approximation to the true

solution values depends on the tolerance limit pre-defined by the user. In particular cases

the tolerance value should be appropriately justified, because high tolerance can cause

unacceptable inaccuracy in the results obtained, whilst low tolerance imposes an

unnecessary increase in the iterations to convergence.

However, the disadvantage of this procedure is that its capability is limited to positive

definite tangent stiffnesses. If the tangent stiffness of any of the degrees of freedom

becomes negative, then the structure becomes unstable and solution becomes impossible.

The program is terminated and the critical value is assumed to have been reached,

defining the point as failure/fracture. An approximate solution using the finite element

method, based on assumed displacement fields, does not generally satisfy all the

requirements of equilibrium or compatibility which are satisfied by an exact theory-of-

elasticity solution. However, relatively few problems exist which are amenable to exact

solution, and for most problems the finite element method gives a practical, reasonable

and logical approximation.

4.3.2. Derivation of the component-based stiffness matrix model

The component-based connection model is incorporated in Vulcan by modifying the

formation of the tangent stiffness matrix in the existing software. A programmed

subroutine has been written using Fortran, and interacts with the existing spring element

facility for semi-rigid connections, the subroutine SEMIJO. This subroutine generates the

necessary incremental displacement vectors for the connection elements and updates the

stiffness matrix and force vector.

The assembly of the spring components is presented in a simplified version, in which the

active components for a bolted joint are grouped as a “lap-joint” at each bolt-row. For

every lap-joint component, a friction spring is positioned in parallel to the lap-joint group.

A highly simplified version of the model consists of; horizontal bolt-rows represented as

single lap-joints with friction, the beam flange/column face contact, and a vertical shear

spring, as shown in Figure 4.6.


95

Figure 4.6 Simplified model of fin-plate connection component–based model

The stiffness matrix of the component model is derived on the basis of a two-noded

spring element with zero length (Figure 4.7). In order to establish the stiffness matrix of

the component elements, each degree of freedom at the nodes is displaced individually in

three degrees of freedom (two translational u, w and one rotational θ) at each node.

Figure 4.7 Degrees-of-freedom of a two-noded spring element

The deformation modes for nodes i and j are illustrated in Table 4.3.. The derivation of

the stiffness matrix is explained in the right-hand column. The forces and moments

generated for the whole connection element are shown in the middle column. The spring

forces are reaction forces which act in the opposite direction to the applied displacement.

Mode 1 considers the application of a unit horizontal translation u at node i while other

degrees of freedom are fixed. The total stiffness generated is given by the sum of the

X

Y

Node i Node j

Connection spring elements

Beam elements

i

Spring elements

of zero length

X

θj,z

vj

uj

wj

θj,y

Z Y

θj,x

j

Vj ,wj

Nj ,uj

Mj ,θj Mi ,θi

Ni ,ui

Vi, wi

i j

Beam flange

Shear

Friction

0mm length

Lap-joint


96

stiffnesses in springs k1 and k3. However, for the case where the stiffnesses of the two

parallel springs are not equal, a reaction moment Mi is generated by the translation ui. The

vertical translation considered in Mode 2, generates only shear forces in the spring k2. In

Mode 3, node i is rotated by a unit angle ϕ. The forces developed in the springs are

caused by the tensile and compressive actions of the springs, corresponding to their

positions relative to the nodal point. By satisfying the moment equilibrium at the nodal

point, the resulting stiffness of the reaction moment Mi is given by k1 and k3. If the

stiffnesses of the springs are not equal, a normal reaction force Ni is then generated by the

rotation ϕ.

Table 4.3 Deformation modes of the connection element

Translation Forces generated Stiffness matrix

generated

MODE 1

Force equilibrium;

Reaction moment, with

two unequal springs ;

Node i;

Node j;

Node i;

Node j;

MODE 2

Force equilibrium;

Node i;

Node j;

δ2,i

wi =1

δ1,i

δ3,i

ui =1


97

MODE 3

Force equilibrium;

Reaction moment

Node i;

Node j;

Node i;

Node j;

By solving for the global force and moment equilibrium of the whole element using

Equations (4.4)-(4.6), their influences on the degrees of freedom at node i can be

calculated.

Horizontal equilibrium;

(4.4)

Vertical equilibrium;

(4.5)

Moment equilibrium;

(4.6)

δ1,i

δ3,i

θi =1


98

The derivation procedure for the stiffness matrix has been described in detail. The

symmetric stiffness matrix of the connection element in two dimensions is shown below,

on the basis of a two-noded point element.

The implementation of the tangent stiffness matrix in Vulcan, however, requires

consideration of a third dimension to be introduced. At this stage, the out-of plane and

torsional DOFs are assumed to be rigid, and there is no interaction between them. These

are assumed to be of minor importance in a steel-framed building, which may be

disregarded in the design analysis. Therefore, considerating three-dimensional cases, the

final tangent stiffness matrix of the connection element can be detailed as;

As described in Figure 4.6, a single bolt-row consists of a lap-joint and a friction spring.

Thus, the upper spring k1 which represents the number of horizontal bolt-rows, substitutes

for the sum of the stiffnesses of the lap-joint and friction spring.


99

In these equations, n is the number of component bolt-rows, and the indices “lap” and

“bfl” indicate the lap-joint assembly and beam flange spring respectively. The index s

indicates the shear spring. Due to the simplicity of this mechanical model, the tangent

stiffness can be incorporated into Vulcan using its existing spring element infrastructure.

The properties of the vertical shear spring component are currently defined to exhibit

similar characteristics to those of the axial bolt-row component. This assumption is made

in an attempt to investigate the influence of combined forces on each bolt-row. The shear

springs, which react to the applied shear force are assumed to be subjected to an equal

distribution of the vertical direct shear. Therefore, the vertical component is a function of

the number of bolt-rows in the connection.

4.3.3. Validation of the stiffness matrix in Vulcan

A number of simple tests using the implemented two-noded spring model, shown in

Figure 4.8, have been conducted using Vulcan. Using an iterative process, the results can

be generated at each load increment. In this case the loading of a spring is defined in 20

increments. Simple tests are performed in three loading conditions, varying the

deformation and rotation of the spring model. The forces are applied on node j, whilst

node i is assumed to be fully fixed.

(4.7)

(4.8)

(4.9)

(4.10)


100

Figure 4.8 Two-noded spring element

In order to validate the results produced by the model, linear representations have been

adopted for the force-displacement characteristics of the spring elements. The

displacements of this simplified model can be manually calculated by utilising similar

expressions to those in the stiffness matrix given in Equations (4.4)-(4.6). For each bolt-

row, the two parallel springs are assembled in the form of an equivalent spring, whose

stiffness is given by the total of the stiffnesses of the individual springs. In this case, the

total stiffness of the upper and lower horizontal bolt-row springs is represented by k1,tt and

k2,tt .

For Case 1 (Nj = 200 kN), consider the component elements subjected only to tension

force. The vertical spring is assumed to be uncoupled, and therefore the deformation uj

and rotation ϕj can be described using the following equations;

Deformation,

Rotation,

Vj

Nj

Mj

i j ks

Stiffnesses;

k1,a = k1,b = k2,a = k2,b = 5000 N/mm2

ks = 10000 N/mm2

Length, l1 = 100mm

l2 = 150mm

Force, Nj = 200 kN

Vj = 100 kN

Moment, Mj = 100kNm

k1,a

k1,b

k2,a

k2,b

l2

l1


101

The theoretical deformation and rotation can be compared against the resultant output of

node j from Vulcan, shown in Figure 4.9.

Figure 4.9 Displacement and rotation of node j (Case 1)

For Case 2 (Mj = 100kNm), in addition to the axial load, the component element is also

subjected to moment applied at node j.

Deformation,

Rotation,

Figure 4.10 Displacement and rotation of node j (Case 2)

0

50

100

150

200

250

0 5 10 15

No

rmal

Fo

rce

(kN

)

Displacement (mm)

Manual

Vulcan 0

50

100

150

200

250

-1 -0.8 -0.6 -0.4 -0.2 0

No

rmal

Fo

rce

(kN

)

Rotation (deg)

Manual

Vulcan

0

50

100

150

200

250

0 5 10 15 20

No

rmal

Fo

rce

(kN

)

Displacement (mm)

Manual

Vulcan 0

20

40

60

80

100

120

0 5 10 15 20

Mo

men

t (k

Nm

)

Rotation (deg)

Manual

Vulcan


102

The theoretical calculated results can again be compared against Vulcan (Figure 4.10). In

Case 3, where the vertical force is applied (Vj = 100 kN), both the calculated value and

Vulcan show a displacement of 10mm. This can be directly calculated, assuming that the

vertical spring is uncoupled. Exact comparison signifies that the spring element

incorporated in Vulcan is generating the correct elastic displacements, according to the

finite element equilibrium requirement.

4.4. Load reversal of component model

The constitutive relationships of many materials demonstrate inelastic behaviour when

the applied stress (or strain) exceeds a certain limit, which in return results in a change in

the stress-strain relationship during unloading. In this phase, the stress-strain curve is no

longer unique, as it was in the loading phase. Unloading can occur due to second-order

effects, often linked to large displacements in structural members. The occurrence of

unloading in connections is commonly found in fire situations, due to the effects of

thermal expansion and contraction, and the transient character of the heating, which cause

beam-to-column connections to experience changing combinations of axial forces and

moments (Franssen, 1990). In order to respond correctly to such force reversals, a

loading-unloading approach needs to be realistically included in the force-displacement

curves for individual connection elements.

Strain reversal can be caused by cooling behaviour, to the extent that there is a possibility

that the structural integrity of the frame can be jeopardised during the cooling phase.

This is supported by evidence of localised failure in connections due to the occurrence of

high axial tensile forces during cooling (Bailey, et al., 1996). In cases where structural

members and assemblies are minimally damaged in fire, an assessment of reusability and

the possibility of remedial action needs to be performed. Although the necessary

assessment can partly be carried out by visual inspection, in members with significant

distortion it requires specific consideration of the residual stresses developed during the

whole period of fire exposure (El-Rimawi, et al., 1996). Any permanent strain imposed

on the damaged member may possibly alter its material characteristics, and so a detailed

evaluation is required to restore the structural frame to the equivalent of its undamaged

state.


103

4.4.1. Masing rule approach

The classic Masing rule (Masing, 1923) approach has been reviewed to successfully

simulate the behaviour of connection elements subjected to strain reversal (Bailey, 1995;

El-Rimawi, 1996; Block, 2006, Santiago et al., 2008). This concept was firstly developed

in materials science for metallic materials. However, Gerstle (1988) extended its

application as a result of experimental validation on top-and-seat angle connections under

load cycling. It was observed that, after the loading of connections along their non-linear

path, unloading or moderate moment reversal takes place along a linear path with a slope

of similar initial stiffness to the loading curve (Figure 4.11). Thereafter, the connection

response proceeds elastically, in that it initially ‘unloads’ with its initial elastic loading

stiffness. The Masing approach seems an appropriate way to represent elasto-plastic

connection behaviour, where it is necessary to consider the unloading or cyclic behaviour

of a connection.

Figure 4.11 Loading-initial-unloading sequence in typical force-displacement graph

(Azinamimi, et al., 1987)

In the context of the component-based method, the classic Masing rule is adapted so that

each individual component will respond realistically to load reversals. The unique force-

displacement relationship of the loading curve is referred to as the skeleton curve, whilst

the unloading curve is the hysteresis curve. The form of this hysteresis curve, from the

point at which strain reversal occurs, (Figure 4.12) is the skeleton curve, scaled by a

factor of two and reversed in direction, generating a permanent reference deformation at

the point where it intersects the zero-force axis. Block (2006) has described the force-

displacement relationships of the loading and unloading curves as;

Loading (Skeleton) curve; (4.11)

Fo

rce,

F

Displacement, δ

LOAD

UNLOAD

k

k

1

1 Unloading

path

Loading

path


104

Unloading (Hysteresis) curve;

(4.12)

Where δA and FA are respectively the displacement and the force at the unloading point

(c).

Figure 4.12 Hysteresis behaviour using a modified Masing Rule.

The applicability of this approach for fin-plate connections, however, requires

modification (Figure 4.12) to the typical Masing rule. The primary concern of this

modification in a shear connection is the utilisation of preloaded bolts. In order to achieve

a more justifiable simulation of the behaviour, consideration of the initial bolt-slip phase,

as well as the unloading path into the opposite quadrant (from between tension to

compression) is included. The modifications involve two rules;

Rule 1: (Incomplete unloading loop). When the model establishes contact, it gradually

picks up strength until the force is reversed, and its unloading path is characterised by a

permanent displacement δPL. The unloading (hysteretic) response proceeds from point (c)

until the resistance reduces to zero, at point (d) in Figure 4.12. Beyond this point there is

no further unloading, but the deflection reduces until it has reversed both the permanent

deformation (d)-(b), and a single original bolt-hole clearance (b)-(a). This phenomenon

can be physically visualized as the bolt changing its direction, following its ideal route to

the original centre of bolt-hole.

F

δ

TENSION (+ve)

COMPRESSION (-ve)

Skeleton

curve,

ε = f(σ)

δPL

Slip phase

a b e

c

d

f

g

δ' Hysteresis

curve,

ε = f(σ)

2 2

F'


105

Rule 2: (Opposite direction bolt-slip phase). Under continuous force reversal, the force in

the opposite quadrant is only established when positive contact between the bolt and the

bolt-hole wall is made, shown at point (e).

The rules applied to the load-reversal curve are largely reflected by the frictional stresses

which are generated between the plate surfaces of the shear connection. The movement

generated during the free-slip phase prior to positive contact between the bolt holes (in

both directions) requires finite frictional resistance. This explains the truncation and

redirection of the unloading curve when the force decreases to zero at point (d). For a fin-

plate connection this assumption is reasonable, as the main concern of this approach

during the unloading phase is the definition of the permanent displacement δPL.

4.4.2. Modified Masing Rule at elevated temperatures

In a building fire, the reduction of strength and stiffness of the structural materials can be

uniquely defined using a series of force-displacement curves which are a function of

temperature. Plastic deformations are likely to occur due to the effect of the material

weakening at high temperatures. In the case of varying temperature, this application

becomes more complicated, particularly in dealing with the loading-unloading cycle of

the connection’s component characteristics, which are temperature dependent. Thus, the

concept of a Reference point (Figure 4.13) has been introduced to predict the relationship

between the component’s force-displacement curves as temperatures change. This

explains that the plastic permanent deformation, rather than the maximum force level, is

the variable which defines the current force-displacement history at a change of

temperature.


106

Figure 4.13 The force-displacement relationship incorporating unloading phase with

temperature change.

The permanent plastic deformation, which is recalculated after each temperature change,

is considered as unaffected if the temperature changes during the unloading stage. At

initial temperature T1, loading of the component to F1 results in a permanent displacement

δP,T1, generally referred as the reference point.

(4.13)

The position of the reference point is used as an indication of whether further loading

occurs at the next load step or temperature step. This is determined by comparing the

updated permanent displacement with that at the previous step. A higher permanent

displacement indicates that the component’s loading path follows the skeleton curve, and

thus the absolute value of the reference point is updated from the current equilibrium

state. If the value is lower, the unloading curve at the new temperature is followed. At this

point, the stored value of permanent displacement is used to define the unique unloading

curve for the temperature T2, in order to ensure that the unloading curve for a new

temperature intersect the previous unloading path at the zero-force axis. Thus, each force-

displacement curve at different temperatures necessarily has to unload completely

through the same reference point.

The intersection point between the newly updated loading and unloading curves needs to

be defined. Due to the non-linearity of the curves, the solution can be found from

Equation (4.14) using an iterative method.

Force

Displacement

δP , T1 ( Reference point)

T1

T2

T1< T2

F1> F2

Intersection

point

Loading curve

fδ, load, T1 (F) and

fδ, load, T2(F)

Loading curve

fδ, Unload, T1 (F) and

fδ, Unload, T2(F)

F1

F2


107

(4.14)

Once the force Finter at the intersection point is known, then the displacement δinter at this

force can be defined through the form of the loading curve at temperature T2, using

Equation (4.15). Subsequently, for any trial displacement given to the connection

element, for instance δ2 (Equation (4.16), the appropriate force can be calculated using

Equation (4.17), relative to the intersection point.

(4.15)

(4.16)

(4.17)

By defining the curve generated from this point, complex reloading and unloading can be

avoided. The permanent plastic displacement which is recalculated after each temperature

change is the variable describing the complete force-displacement history instead of the

maximum force level. The main assumption about the reference point concept is that the

permanent strain of each spring remains unaffected by the change of temperature.

4.5. Influence of combined action on connection elements

The importance of tying capacity in structural steel connections is reflected by the tying

capacity requirements imposed in the design code BS 5950-1 (BSI, 2001). However, the

necessary check on tying capacity is performed as an isolated action in the

recommendations of the Green Book (BCSA, 1991), whereas in reality a combination of

shear force and moment (or rotation) are present in actual structures, in addition to the

tying forces. The tying capacity of a connection is even more significant in the event of a

fire, because it may have to transfer significant forces to adjacent structural members,

while simultaneously being subjected to high rotations. It is important under these

circumstances that it maintains its structural integrity. According to Burgess (2012), the

co-existence of moment and shear forces with normal force may affect the tying forces in

individual bolts, which may prevent uniform distribution of the resultant tying force

between the bolts, thus significantly reducing the tying capacity.

Most research on the component-based model ignores the contribution of the shear

“spring” by setting its component to be rigid. However its real influence on the

connection behaviour is in need of detailed investigation. The vertical action developed


108

by Block (2006) using a single shear spring as an aggregate characteristic for all bolt-

rows, may not be the best representation of the connection’s response in fire. This follows

the evidence that the net forces taken by each bolt-row do not necessarily result in parallel

yield displacement patterns (Figure 4.14).

Figure 4.14 Actual displacement pattern of bolt-rows

A degree of complexity arises when modelling fin-plate connections in this combined

action of horizontal and vertical forces with moment. The position of the bolts in their

holes, variations in hole and bolt diameter, as well as the loading method and sequence

can all affect the forces acting on individual bolts. This situation is statically

indeterminate.

Kulak et al. (1987) adequately represented the strength of a bolt subjected to combined

shear and tension, resulting from externally applied load, as being closely defined by an

elliptical interaction curve (Figure 4.15), which is analogous to the Von Misses failure

criterion. The relationship of the tensile capacity to the shear imposed on a bolt, and vice

versa, can be determined using the following expression;

(4.18)

Where,

x is the ratio of the calculated shear stress to tensile strength of the bolt,

y is the ratio of calculated tensile stress to tensile strength of the bolt,

G is the ratio of the shear strength to the tensile strength of the bolt.

Column

Arbitrary bolt

displacement


109

Figure 4.15 Kulak’s elliptical curve model

In this model, for each given bolt-row, the shear components are represented by vertical

springs (Figure 4.16). The deformation parallel to the shear direction is smaller than the

tensile deformation. In order to generate the effect of the combination of forces, together

with high rotation, the vertical shear is distributed equally between the bolt holes, and the

combined normal force and moment create horizontal forces at each of the bolt holes.

The magnitudes of these horizontal forces have to be such as to create equilibrium while

also being kinematically compatible with the movement and rotation of the beam end

relative to the fin plate.

Figure 4.16 Component-model for combined forces in multiple bolt-rows

If the external vertical shear force runs through the centroid of the group of bolts, it is

referred to as equivalent shear force, which causes equal vertical translation of the bolts

(Figure 4.17). In the usual case, the axial and vertical components are uncoupled and

treated individually. For the case of arbitrary bolt displacements, the inclined translation

is assumed to represent the actual movement of the bolts, and changes relative to the

degree of rotation, at every loading step.

i j

θ

Mj

Nj

Vj

Ten

sile

str

ess

Ten

sile

str

eng

th

1.0

Shear stress

Tensile strength

1.0


110

Figure 4.17 Vertical and horizontal translations of the bolts.

Figure 4.18 Uniaxial component, Fu of the bolt

The actual behaviour of a resultant force component at a bolt hole can be depicted as

shown in Figure 4.18, with respect to its vertical and horizontal components. The

combined action on each bolt can then be calculated, by effectively reducing the capacity

of the horizontal tying forces Fx (Figure 4.19) with respect to the vertical shear

component Fv. The failure envelope represents the yield surface at a given bolt hole. The

initial yield surface is symmetric with respect to the initial centre of the bolt hole. When

the horizontal and vertical force components are treated individually, the yield surface is

depicted as “available” capacity. However, the combined effect of these components

results in an actual capacity which is less than this. Thus, uncoupling these components

may overestimate the actual capacity of the bolt components. At each bolt-row, the

vertical component for each bolt in the connection is given as;

(4.19)

Subsequently, the reduced horizontal capacity can be identified using Equation (4.20),

with respect to the uniaxial capacity Fu of each active component at each bolt-row.

(4.20)

Fx

V/n

I

II

III

IV

V

+ =

Uniaxial

component Equivalent

shear force


111

Figure 4.19 The failure envelopes for the actual and available, resistance capacities of

components

This assumption of a reduced horizontal strength seems justifiable, particularly

considering the significance of the large rotations of the bolts during a fire. The

incorporation of the component model in Vulcan can be sequentially described with the

aid of the flow chart shown in Figure 4.20.

FV

FX

Bolt hole

Failure

envelope

Available

Actual

FX

Fu Fv

θ


112

Figure 4.20 Implementation of Masing Rule in Vulcan

NO

YES

YES

NO

Update

reference

point

Force returned to VULCAN

INITIALISE DISPLACEMENT, D

Calculate frictional force, FSLP

and stiffness, KSLP D ≥ slip phase

(bolt clearance hole)

Calculate lap-joint forces, FSER and

stiffness, KSER (loading curve)

Calculate displacement, DUNL and

stiffness, KUNL (unloading curve)

Calculate permanent deformation, DREF

DREF = D - DUNL

Check for unloading,

DREF < OLDDREF

‘UNLOAD’?

Temperature

Tn+1

Calculate intersection point from

DREF

Solve iteratively due to nonlinear

characteristic for FINTER between the

loading and unloading curves at Tn+1

D = DUNL – DREF

Calculate FTn+1 from the unloading

curve with respect to DTn+1

DTn+1 = DINTER- D

Calculate force, FSER on the unloading

curve at displacement DTn+1 relative

to the intersection point

FSER = FINTER- FTn+1

FSLP FSER


113

4.6. Summary

This chapter has presented the incorporation of the developed component model in

Vulcan. In general, the application of the method involves the characterisation of

nonlinear components, which are assembled as extensional two-noded ‘spring’ elements

and rigid links. This can then be extended to include multiple bolt rows for fin-plate

connections. In order to incorporate the connection element in the finite element solution

processor, the generic stiffness matrix of the connection element has been derived. The

nonlinear force-displacement characteristic of individual components described in

Chapter 3 is used to predict the behaviour of the whole connection. At high temperatures,

these springs are subjected to declining strength and stiffness of the connection

characteristics.

The solution procedure using Vulcan is limited by its incapability to deal with negative

stiffness, being a static solver. This is somewhat unfortunate as the component model

should be able to predict the connection response even after the maximum capacity has

been reached or any failure occurs in the connection component. To deal with this issue,

the connection component adopts a high ductility assumption to possibly simulate the real

connection response either in isolation or in global frames.

In order to consider the complicated load-reversal at high temperature, the force

transitions are applied using the Masing Rule relative to positive contact between the bolt

and plate. The essential concept of this method is the utilisation of the ‘Reference Point’

and ‘Permanent Displacement’, particularly at elevated temperatures. By assuming that

the reference point is unaffected by the temperature change, the complex loading and

unloading cycle of the connection element has been made possible.

The influence of vertical shear component has also been considered in the component

model. Contrary to Block (2007) shear model, the shear spring is coupled with the

horizontal spring components, in order to investigate the reducing effect of the horizontal

spring capacity due to the uniaxial forces acting on the bolts. The incorporation of the

loading and unloading approach and the consideration of combination forces have been

successfully implemented in Vulcan, and will be further discussed in next chapter.

Chapter 5: Application of component-based model

114

5. APPLICATION OF COMPONENT-BASED MODEL

The component-based model is applicable to a broad spectrum of connection parameters

and types. The versatility of this method allows unrestricted application, provided that the

fundamental behaviour of one generic connection type can be realistically represented

either empirically or experimentally. Since the generation of the component model has

been described in the previous chapters, it is now necessary to investigate the

applicability of the component model to real connection response. The assessment will

provide an improved understanding of overall connection performance, including

consideration of the structural interaction within simple isolated joints and global

structural frames. In this chapter, the developed model is validated against available

experimental results, and is subsequently extended to parametric studies on the influence

of connection behaviour.

5.1. Single-bolted connection behaviour

As the generation of the component-based model for the fin-plate connection is derived

from a single lap-joint’s behaviour, the validation of this behaviour against actual

response is an important step in guaranteeing the accuracy and consistency of the

proposed component model. Richard et al. (1980) investigated this relationship using the

test specimen detailed in Figure 5.1, consisting of two 3/8” (9.53mm) plates of ASTM

A36 steel, connected by a 3/4” (19.05mm) diameter ASTM A325 high-strength bolt. The

bolt hole was an over-sized standard hole according to AISC-LRFD (AISC, 1993). The

yield strength of the plate and bolt are defined on the basis of nominal values, as it was

not reported by Richard.

Figure 5.1 Richard et al. (1980) single lap-joint specimen geometry and dimensions.

3.75in/

95.3mm

13/16in

Bolt

3 in/

76.2mm

6.75 in/171.45mm

Plate 1 Plate 2

4 i

n/1

01

.6m

m


115

Richard also represented non-linear force-displacement behaviour of a single bolt lap-

joint with a continuous parametric equation. This equation uses four parameter functions;

(K, Kp, Ro and N), dependent upon the connection geometry, stiffness and strength. The

Richard Function can then be derived by the combination of these parameters. The

curves generated were used to describe the structural behaviour of welds, double framing

angles and bolts in single and double shear (El-Salti, 1992).

(5.1)

Where,

R= Force (or Stress)

Δ= Deformation

K = Initial elastic stiffness

Kp = Plastic stiffness

Ro = Reference Load

N = Curvature parameter

A comparison of the generated component model (indicated by CM) against the

experimental result is given in Figure 5.2. The dotted line represents the analytical curve

produced by Richard using the expression given in Equation (5.1). The force-

displacement relationship of a bolted single plate indicates good agreement, with a slight

discrepancy in the elastic range. The overall capacity of the component model suggests a

more conservative response, being slightly lower than the analytical model by a mere

4.3%. In other research, Hu (2011) also created a 3D finite element model using Abaqus,

which provided good agreement with test results. The displacement of the component

model, however, requires to be shifted in line with the free slip present in order to

illustrate the actual behaviour of the bolted joint. The active response of the bolted joint is

only established after positive contact between the bolt and the bolt hole walls.


116

Figure 5.2 Force-displacement comparison curves

5.2. Multi-bolt-row fin-plate connection behaviour

The application of the component model to fin-plate connections can be performed by

simply replicating the single-bolted model on multiple bolt rows. The investigations of

the fin-plate connection behaviour are herein considered according to different cases;

subjected both to pure axial force and combined forces.

5.2.1. Fin-plate connection subjected to axial force

A series of fin-plate connection tests was carried out by Hu (2011) for ambient and

elevated temperatures. The loading and temperature conditions imposed on the test

specimens were intended to permit investigation of the connection behaviour and the key

limit states experienced during a fire. The connections were tested at four high

temperatures; 400°C, 500°C, 550°C and 700°C, in addition to the ambient temperature

20°C. By utilising an electric furnace, the heating conditions were defined to be thermally

steady-state, and the testing was displacement-controlled at a rate of 0.05in/min. The

material properties for the connection components were experimentally determined, as

given in Table 5.1.

Table 5.1 Measured material properties at ambient temperature

Connection part Yield strength(N/mm2) Ultimate strength(N/mm

2)

Beam ASTM A992

W12×26 406 518

A36 Fin-plate 303 452

A 325 Bolts Not measured 961

0

20

40

60

80

100

120

140

160

180

-5 0 5 10 15 20

Fo

rce

(kN

)

Displacement (mm)

FE Model (Hu, 2011)

Analytical model (Richard,1980)

CM

3/4" A325 Bolt

3/8" A36 Plates


117

The test specimens were cut from an ASTM A992 W12×26 structural steel section, and

connected to a 3/8 inch (9.53mm) thick fin-plate. The assembly of the beam section and

fin-plate were both welded to two thick base plates by 1/4 inch (6.25mm) fillet welds at

both ends. The connection dimensions were specified according to the recommendations

of the AISC Manual (AISC, 2006). The test setup details were as shown in Figure 5.3.

Using similar arrangements, the tests were performed in two phases; subjected to normal

tension and to inclined tension. However, in this thesis, only the normal tension case will

be investigated further.

Figure 5.3 Hu (2011) test setup and specimen detail.

A load controller was used to control the crosshead displacement of the machine. The

furnace was supported by a motor-driven lift system to facilitate its movement within the

testing frame. The test machine measured and recorded the vertical displacement of the

upper loading head, which was considered to be the total displacement in the tests. In the

case of the test subjected to normal tension, the base plate displacements were measured

by the displacement transducers attached to the two stainless steel rods protruding out of

the furnace.

The test arrangement was simulated using the component model and this was compared

with respect to the force-deflection response of the specimen. In general, good

comparisons were achieved for both ambient (Figure 5.5) and elevated temperatures

(Figure 5.6). In order to provide clear evaluation of the actual connection response, the

curves were shifted to eliminate the effect of the initial slip phase. For all cases, the

1-1/4” 3-1/4”

3”

3”

10”

Furnace

TEST SPECIMEN

Displacement

Transducers


118

connection response was only modelled until the maximum resistance was reached, as the

current static solution process is limited to positive stiffness. At 20°C, the experimental

evidence showed bearing/tear-out failure at the bolt holes in the beam web (Figure 5.4)

with little deformation observed in the bolts themselves. This is consistent with the

response given by the component model, which established plate yielding in the beam

web to be the dominant failure mode.

Figure 5.4 (a) Tear-out failure in the beam web (b) Deformation in the bolts

Figure 5.5 Force-displacement response for connection subjected to normal tension

(Ambient temperature)

At all elevated temperatures, the weakest component identified in the component model is

bolt shear. With the exception of the temperature case at 400°C, fracture of the bolt was

the only connection failure mode observed. At 400°C, the test specimen failed by beam

web tear-out failure, but with noticeable bolt shear deformation. Thus, as the component

model is incapable of establishing a mixed-failure mode, either failure characteristic can

be considered the dominant failure mode. Moreover, the maximum resistance of the beam

web and bolt components indicated only 9.4% difference.

0

50

100

150

200

250

300

350

400

-10 0 10 20 30

Fo

rce

(kN

)

Displacement (mm)

Test (Hu, 2011)

CM T20


119

Figure 5.6 Force-displacement response for connection subjected to normal tension

(elevated temperatures)

5.2.2. Fin-plate connection subjected to inclined force

A series of experimental tests were carried out by Yu et al. (2009) to investigate the

robustness of steel connections at elevated temperatures. Four types of connection were

studied; flush endplates, flexible endplates, fin-plates and web cleats. A detailed

description of the tests in an electric furnace with internal capacity of 1.0m3

is shown

schematically in Figure 5.7. A UB 305×165×40 section support-beam was connected to

one flange of a UC 254×89 section column, and positioned such that the whole specimen

was tilted by 25° above the horizontal axis in the furnace. Each specimen was gradually

heated to a specified temperature and loaded to failure at this constant temperature using

a special loading system. The loading jack was rigidly connected to the lower beam of the

reaction frame and connected to the specimen using an assembly of three 26.5mm

diameter 1030 Grade Macalloy link bars. The furnace bar, link bar and jack bar were each

connected to a central pin at one end, with their opposite ends connected to the test

member, the jack and a fixed pin on the reaction frame respectively. The loading jack was

displacement-controlled and functioned by pulling the central pin downward during the

loading process, thus applying an inclined tensile force to the beam end through the

furnace bar. The angle between the furnace bar and the beam axis determined the

inclination of the tying force applied, and therefore the ratio of the tying and shear forces.

This arrangement was designed to enable large rotation of the connection, relative to the

supported column.

0

50

100

150

200

250

300

350

-5 0 5 10 15 20

Fo

rce

(kN

)

Displacement (mm)

CM T400

Test (Hu, 2011)

CM T500

Test (Hu, 2011)

CM T550

Test (Hu, 2011)

CM T700

Test (Hu, 2011)


120

Figure 5.7 Yu et al. (2009) test setup

The connection tests were performed at a very slow deflection rate and were

progressively loaded to fracture over about 90 minutes. Measurement of the force was

achieved using strain-gauges attached to the loading bars. Meanwhile, the deformations

of the specimens were measured using a digital camera placed in front of the

100mm×200mm observation window, in the front door of the furnace. Rotations and

displacements were calculated from the movements of targets marked on the column and

beam specimens.

One fin-plate detail will now be considered from this test series, using test results at both

ambient and elevated temperatures. The detailing of the beam-to-column member and

connection are illustrated in Figure 5.8. The steel beams and fin-plates were both S275

Grade whilst the column was of S355 Grade steel. Standard coupon tests were performed

on the test specimens to determine their properties at ambient temperature; however the

properties at elevated temperature were not tested directly. The material properties were

given as; Young’s Modulus 176.35 kN/mm2, yield strength 356 N/mm

2 and ultimate

strength 502 N/mm2.

Load jack

Reaction frame

Electrical furnace

Macalloy

bars

Tested

connectio

n

Reaction

frame

Support beam

α

Furnace bar Link

bar Jack

bar


121

Figure 5.8 Geometry of the test specimen

The fin-plate used was 200mm deep × 8mm thick with three rows of bolts, designed in

accordance with UK design recommendations (BCSA, 1991). Twelve fin-plate

connection specimens with a single column of bolts were tested, plus an additional two

specimens with a double column of bolts, as shown in Figure 5.9. The bolts used were

fully threaded Grade 8.8 M20 and M24 bolts. At both ambient and elevated temperatures,

the connections were loaded by forces at initial inclination angles of 35° and 55º;

however the nominal angle varied during the test, depending on the assembled

configuration of the loading system.

Figure 5.9 Detailing of the tested fin-plate connection

In this validation, the experimental setup of a beam-to-column fin-plate connection is

simulated using the developed component-based model in Vulcan, and compared to the

test results. The results shown are for applied force with initial inclinations of =35° at

ambient (Figure 5.10) and elevated temperatures (Figure 5.11). On the whole, the

responses of the component-based model achieved close agreement with the test results,

particularly during the loading phase. It can be observed from the results that the simple

models exhibit similar load-sharing sequences, which can be detailed in stages;

Stage 1 The first bolt contacts the edges of the bolt holes of the connected plates. The

model initially experiences a slip stage of up to about 2° rotation with frictional

resistance only.

200mm

50 50

40mm

60mm

60mm

40mm

50 50 50

51.7mm

F

α

320mm

300mm

400mm 90mm

40mm

10mm


122

Stage 2 When one or two bolts have come into positive contact with their hole edges, the

resistance gradually increases until the top bolts reach their maximum

resistance. Subsequently, the bottom flange comes into contact with the column

face, resulting in stiffer deformation response.

Stage 3 The bottom bolt unloads, and undergoes a short free-slip phase. The applied force

rises again as the bottom bolt changes the direction of its force by contacting the

opposite edges of its bolt hole. The connection reaches its maximum resistance

when either the bottom bolt reaches its ultimate load, or the first bolt has

excessively deformed or fractured.

Figure 5.10 Force-rotation comparisons at loading angle 35° at ambient temperature

0

50

100

150

200

250

0 2 4 6 8 10 12

Fo

rce

(kN

)

Rotation (deg)

M20-8.8-3 bolt

Abaqus (Yu, 2009)

Test 35(Yu, 2009)

CM T20-35


123

Figure 5.11 Force-rotation comparisons at loading angle 55° at ambient temperature

In addition to the experimental tests, Yu et al. (2009) also generated a component model

using the finite element software Abaqus. The reason for the form of response of the

substantiated model is that, as the model is loaded, the geometry change causes the

relationship between the forces and rotational displacements to be non-linear.

Subsequently, second-order geometric effects are taken into account in the Vulcan

analysis, which may create increased moments. The distinct discrepancy between the

component models’ curves can be purely focused on the initial stage of loading, and is

caused by the frictional effect in the model. The friction model in Abaqus was generated

according to the triangular model of Sarraj (2007b). The friction component in the newly

developed component-based model is established using the recommendation of Eurocode

3-1-8 (CEN, 2005b), coupled with experimental observation, to define the overall

behaviour of the component. The frictional resistance enables a more realistic prediction

by its consideration of the number of friction surfaces and the detailing of the bolt holes.

Yu’s model considered two ductility cases based on the post-resistance behaviour of the

bolts, which are listed as; infinite and finite ductility. In the current model, similar

assumptions are adopted, but with a high-ductility case rather than infinite ductility, in

order to simulate the progressive connection failure observed in the tests. Using static

analysis, the response of the connection could be generated until the top two bolts in

combination reached their maximum resistance, and the bottom bolt was stress-free

(indicated by circles in all cases). Beyond this point, the analysis terminated, unless the

infinite ductility assumptions was adopted for bolts.

0

20

40

60

80

100

120

140

160

180

0 5 10 15

Fo

rce

(kN

)

Rotation (deg)

M20-8.8-3 bolt

Abaqus (Yu, 2009)

Test (Yu, 2009)

CM T20-55


124

The idealised force-displacement characteristic of a fin-plate connection follows the post-

yield behaviour of its weakest component, which in this case refers to bolt shearing. The

ultimate fracture of the connection is defined by the residual cross-sectional area of the

bolt. However, the computational limitation of static solvers prohibits further analysis

when dealing with instability caused by negative stiffness. This limitation, however, can

be resolved by utilising a dynamic solver during the unstable phase, or by using

displacement control of the static case. Either approach is possible, particularly the

former, but this is out of the scope of this research.

By adopting a high-ductility connection model, the static analysis can be extended to

model the complete connection response. Additionally, the unloading process can be fully

mobilised while adopting the declining bolt shear resistance assumption in the component

model. Also, in most experimental bolted joint tests conducted (Hirashima et al., 2007),

the ductility of bolts in shear is seen to increase considerably at high temperatures. The

conservative ductile fracture characteristics of the bolts allow the third bolt row to

proceed to unload in the opposite direction, whilst the top two bolts have yielded beyond

their maximum resistance. This consideration provides a considerably more refined

comparison to the test results, as compared to Yu’s model towards the end of the loading

stage at either ambient or elevated temperature.

5.3. Application of component model at elevated temperature

The wide range of Yu’s experimental data at elevated temperature allows the validation

of simulations using the component-based model in Vulcan. Using the electric furnace,

three elevated steady-state temperatures of 450°C, 550°C and 650°C were applied in the

experiments. They represent the temperature range within which the properties of both

the structural and bolt steels are subjected to rapid degradation during fire. The

connection was also subjected to the combinations of shear and tying forces

corresponding to angle α of 35° and 55°, similar to the ambient-temperature tests. The

results are shown in Figure 5.12 and Figure 5.13.


125


steady state temperature

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

Fo

rce

(kN

)

Rotation (deg)

M20-8.8-3 bolt

Abaqus (Yu,2009)

Test (Yu, 2009)

CM T450-35

0

10

20

30

40

50

60

0 2 4 6 8 10 12

Fo

rce

(kN

)

Rotation (deg)

M20-8.8-3 bolt

Abaqus (Yu, 2009)

Test (Yu, 2009)

CM T550-35

0

10

20

30

0 2 4 6 8 10 12

Fo

rce

(kN

)

Rotation (deg)

M20-8.8-3 bolt

Abaqus (Yu, 2009)

Test (Yu, 2009)

CM T650-35


126


steady state temperature

0

20

40

60

80

100

0 2 4 6 8 10 12

Fo

rce

(kN

)

Rotation (deg)

M20-8.8-3 bolt

Abaqus (Yu, 2009)

Test (Yu, 2009)

CM T450-55

0

10

20

30

40

50

0 2 4 6 8 10 12

Fo

rce

(kN

)

Rotation (deg)

M20-8.8-3 bolt

Abaqus (Yu, 2009)

Test (Yu, 2009)

CM T550-55

0

10

20

30

0 2 4 6 8 10 12

Fo

rce

(kN

)

Rotation (deg)

M20-8.8-3 bolt

Abaqus (Yu, 2009)

Test (Yu, 2009)

CM T650-55


127

At elevated temperatures, the responses of the component model have to be shifted to be

directly compared to the tests. This is because of the varied initial slip distances that can

occur, depending on the process used to assemble the bolts, and the initial relative

positions of the bolts and the gap between the beam end and the column face. The

component model defaults to nominal (or recommended) values for all these parameters.

Thus, the connection’s curve has to be shifted along the rotation axis to be directly

comparable with test results.

The predicted maximum resistance is higher than was observed in the tests, which is to be

expected, as it is mainly caused by successive failures of the bolts beyond their nominal

resistances. The responses of the component model used in these comparisons are over-

strong because the bolt-shear component used is assumed to follow the simplified

assumption of the high-ductility case beyond its ultimate resistance. The static analysis

terminates at the stage when the top two bolts in combination reach their maximum

resistance, when the bottom bolt is still stress-free. The component model however is able

to produce relatively close predictions of the fin-plate connection behaviour when

appropriate criteria are adopted. The summary of the maximum rotation and the failure

modes observed in the tests and predicted by the component model are given in Table 5.2.

Table 5.2 Comparison of the test and component model deformation response.

Specimen

Max resistance (kN) Max rotation

(degree)

Dominant failure

mode

Tests CM %Diff Tests CM %Diff Tests CM

20-35 185.11 186.74 0.9 7.81 9.74 24.7

Visible

plate

bearing,

followed

by one bolt

fractured

Bolt

shear

450-35 84.47 129.58 53.4 6.24 8.08 29.5 Bolt shear Bolt

shear

550-35 38.46 52.35 36.1 7.12 8.41 18.1 Bolt shear Bolt

shear

650-35 19.3 26.58 37.7 7.37 7.14 3.1 Bolt shear Bolt

shear

20-55 145.95 146.2 0.2 11.11 14.69 32.2 Two bolts

sheared

Bolt

shear

450-55 70.69 91.62 29.6 6.09 7.32 20.2 Bolt shear Bolt

shear

550-55 34.81 45.26 30.0 6.56 7.34 11.9 Bolt shear Bolt

shear

650-55 17.73 22.45 26.6 6.26 6.35 1.4 Bolt shear Bolt

shear


128

5.4. Force and displacement of connections.

Detailed analysis of the active components is possible when applying the component-

based model. The response of every component can be traced, at every loading step, by

plotting the non-linear force-displacement graphs (Figure 5.14). The case adopted in this

section is at ambient temperature (T=20°C) with an applied load angle =35°. Bolts B1

and B2 are loaded in tension beyond their maximum resistance, which results individual

bolt curves with negative stiffness. An extended failure phase is possible with the

assumption of a high-ductility characteristic, for which the ultimate fracture of a bolt is

not equivalent to a displacement equal to the bolt diameter.

Conversely, for the bolt B3, loaded in compression, a different route is adopted. From the

results generated, the implementation of both loading and unloading characteristics can

be clearly demonstrated by the behaviour of bolt B3, as shown in Figure 5.15. The bolt

has reached its plastic phase, and this has caused permanent deformation to the bolt. The

lower beam flange can be distinctly observed to function only in compression, which is

initiated when the gap between the beam-end and the column face closes. Beyond this,

the lower beam flange acts as a pivot, reducing the overall deformation of the top bolts

due to its high stiffness.

Figure 5.14 Force-displacement curves of individual bolts, and the column flange

component.

-200

-150

-100

-50

0

50

100

150

-20 -10 0 10 20 30

Fo

rce

(kN

)

Displacement (mm)

B1 B2 B3 BF

Tension

Compression


129

Figure 5.15 Partial unloading of bottom bolt (B3)

A complete analysis of the components is explained in terms of the change in the bolt

forces (Figure 5.16), relative to the external applied load FL. Additionally, an illustration

of the bolt displacement at each row is provided to show the configuration changes of the

bolts in the fin-plate, emphasizing the dB3 behaviour which is able to properly describe the

sequence of the loading-unloading cycle. The critical bolt forces, FB1 and FB2, are the

highest, and hence the first to come into contact with the bolt hole circumference. With

increased loading, at approximately FL = 49kN, the compressive lower beam flange

spring is activated, following large rotation of the connection. The contact established

initiates the much stiffer response shown previously for other cases. Almost immediately,

a corresponding unloading of B3 can be observed. The bolt B3 is initially loaded in

compression until irreversible plastic deformation occurs, and subsequently unloads,

following the pre-defined free-slip route into the tensile phase. All the bolt rows then

displace with respect to the instantaneous point of rotation (in this case: lower beam

flange). The uppermost bolt B1 displaces extensively, exceeding the bolt diameter, which

is in agreement with the test results showing evident bolt shearing failure. Bolt B2 carries

the lowest relative force, delaying contact with the bolt hole circumference until an

external force FL of approximately 78kN.

-60

-50

-40

-30

-20

-10

0

-3 -2 -1 0

Fo

rce

(kN

)

Displacement (mm)


130

Figure 5.16 Loading and unloading sequence

5.5. Parametric study

The investigation of the connection’s response is extended by performing parametric

studies on the key components which influence the overall behaviour of the beam-column

connection. Therefore, further study concentrates on the influence of the connection

detailing on the overall connection performance.

5.5.1. Influence of the bolt grade and sizes

At both ambient and elevated temperatures, an investigation of the effect of utilising

stronger bolts has been performed using different bolt grades and diameter sizes. This

study concurs with the design recommendation to avoid undesirable brittle failure in

-20

-10

0

10

20

30

0 20 40 60 80 100 120 140

Dis

pla

cem

en

t (m

m)

External Force (kN)

-200

-150

-100

-50

0

50

100

150

0 20 40 60 80 100 120 140

Fo

rce (

kN

)

External Force (kN)

B1

B2

B3

BF

FB1

FB2

FB3

FBF

dB1

dB2 dB3

dBF


131

connections; moreover, it has been observed in many tests that the primary connection

failure is bolt shearing failure. In the context of component model, the properties of the

bolts determine their shearing resistance, which then characterises the primary failure

modes of the connections. Comparisons to experimental results has been made where

these are available, otherwise a computational analysis has been carried out over a wider

range of evaluation. In general, the overall behaviour of the connection in terms of

capacity and maximum rotation has been adequately predicted by the component model,

giving close agreement to the experimental results.

Two commonly used bolt sizes, M20 and M24, are adopted and compared to the tests,

with respect to connection force-rotation relationships (Figure 5.17). It is evident that the

maximum resistance of fin-plate connections can be increased by using larger bolt

diameters. Additionally, the dominant failure mode also changes from brittle to ductile

failure with an increase of the bolt shearing capacity. At ambient temperature, the effect

of utilising an M24 bolt is merely to increase the capacity by 20.3% compared with that

given using M20 bolts. The component model, however, is capable of generating higher

maximum resistances, depending on the ductility assumption adopted for the bolt

components.

At elevated temperature, a significant increase of the connection resistance has been

observed when utilising M24 bolts (Figure 5.18). The enhancement of the connection

capacity for a test performed at temperature 550°C reached 92.7% relative to that for

M20 bolts. This is explained by the fact that bolts increase their ductility when exposed

to high temperatures, thus providing higher resistance to the connection by allowing

larger beam-end rotation.


132

Figure 5.17 Force-displacement response for ambient temperature with load angle 35°

Figure 5.18 Force-displacement response for T=550°C with load angle 35°

For varying bolt properties, three bolt Grades (4.6, 8.8 and 10.9) have been considered.

The loading patterns of the connections with bolt Grades 8.8 and 10.9 are generally

similar, with small discrepancies as shown in Figure 5.19. However, the maximum

resistance when using bolt Grade 10.9 increases by approximately 15.1% as compared

with that of Grade 8.8 at ambient temperature.

At elevated temperatures, rather unusual behaviour was observed in the tests using bolt

Grade 10.9. The top bolt appears to experience premature failure at much lower resistance

than the two lower bolts. This is shown in Figure 5.20, which shows that the maximum

resistance of the connection occurs at a second peak point, indicating the failure of the

second bolt row. This limit is enhanced by 45.3% relative to that for bolt Grade 8.8. The

0

50

100

150

200

250

0 2 4 6 8 10 12

Fo

rce

(kN

)

Rotation (deg)

T20-35 M20-8.8, YU Test

M24-8.8, YU Test

M20-8.8, CM

M24-8.8, CM

0

20

40

60

80

100

0 5 10 15

Fo

rce

(kN

)

Rotation (deg)

T550-35 YU Test, M20-8.8

Yu Test, M24-8.8

CM, M20-8.8

CM, M24-8.8


133

component model, however, is capable of predicting the peak resistance of the first (top)

bolt row, if this performs as anticipated. In all cases, the component model generally

generates good agreement, predicting the connection’s maximum resistance as well as

simulating the underlying mechanism throughout the loading-unloading sequence.

The large discrepancy shown for connections using bolt Grade 10.9, in terms of the

connection’s maximum resistance, is explained by the unusual early failure of the top

bolts during the tests, at a lower applied force than that at which the other two bolts fail.

This was observed with the peak resistance reached at failure of the middle bolt rather

than that of the top bolt. The component model, however, is able to generate the

predicted maximum capacity of the connection in the normal case of perfectly-

functioning top bolt performance.

In all cases, the use of stronger bolt properties generally increases the capacity of the

connection. Significant enhancement of capacity can be achieved, particularly at high

temperatures. Although the strength and stiffness of the bolt decreases with increasing

temperature the steel becomes softer, thus allowing the bolt to behave in a more ductile

manner. This was observed in Yu’s (2009) double-shear test on A325 and A490 bolts

(equivalent to property classes Grade 8.8 and 10.9 respectively). At temperatures between

500°C to 700°C, parallel abrasion marks were visible on the bolt failure surfaces, which

indicate the shearing failure that occurred and the high ductility of bolts at these

temperature levels.

Figure 5.19 Force-displacement response for ambient temperature with load angle 35°

0

50

100

150

200

250

300

0 2 4 6 8 10 12 14 16

Fo

rce

(kN

)

Rotation (deg)

T20-35 M20-10.9, YU Test

M20-10.9, CM

M20-8.8, YU Test

M20-8.8, CM

M20-4.6, CM


134

Figure 5.20 Force-displacement response for T=550°C with load angle 35°

5.5.2. Influence of the connection position with respect to neutral axis

In order to achieve the required flexibility in the fin-plate connection, restraint has been

investigated with respect to the connection’s position on the beam web. The

recommended position of the connection according to the Green Book (BCSA, 1991) is

to be positioned near to the top flange to provide adequate positional restraint. The range

of distances has been defined relative to the neutral axis of the beam from the beam top

flange. Four cases are generated; three of those are arranged in the top portion of the

beam web, and one case is positioned so that the middle bolt is aligned on the beam

neutral axis (Figure 5.21). All the connections have identical configuration and detailing,

and are subjected to ambient (T=20°C) and elevated (T=550°C) temperatures.

Figure 5.21 Position of connection in respect to top beam flange

In general, the maximum resistance of the connection can be achieved by positioning the

connection as close as possible to the upper beam flange. Moving the connection

downward towards the neutral axis causes a reduction of the connection resistance.

0

20

40

60

80

100

0 5 10 15

Fo

rce

(kN

)

Rotation (deg)

T550-35

M20-10.9, Yu Test

M20-10.9, CM

M20-8.8, Yu Test

M20-8.8, CM

M20-4.6, CM

40mm

30

3.4

mm

20mm

NA NA

10mm 51.7mm

T=20°C TP3 TP1 TP2 TP4

T=550°C TP7 TP5 TP6 TP8


135

However, it is observed that the rotational ductility of the connection increases as this

distance increases. High flexibility of the connection is favourable to accommodate the

end rotation demanded of a simply supported beam. The ultimate resistance of the

connection is shown in Figure 5.24 with respect to its distance from the upper beam

flange

Figure 5.22 Force-rotation response for ambient temperature with varying connection

positions (shown in Figure 5.21)

Figure 5.23 Force-rotation response for T=550°C with varying connection positions

(shown in Figure 5.21)

0

50

100

150

200

250

0 5 10 15 20

Fo

rce

(kN

)

Rotation (deg)

M20-8.8-3 bolts

TP1-T20

TP2-T20

TP3-T20

TP4-T20

0

20

40

60

80

100

0 5 10 15 20

Fo

rce

(kN

)

Rotation (deg)

M20-8.8-3bolts

TP5-T550

TP7-T550

TP8-T550

TP6-T550


136

Figure 5.24 Comparison of maximum resistances for T=20°C and T=550°C

Due to the beam end rotations, the main concern is then the bolt capacity, which may

significantly affect the overall connection capacity. If it is assumed that the vertical shear

force is equally distributed between the total number of bolt rows, the horizontal

component is now investigated. The magnitudes of the horizontal bolt forces are a

function of each bolt’s location with respect to the centroidal axis of the beam. As the

distance to this axis increases, the horizontal force acting on the bolt increases.

Figure 5.25 Forces and displacements of bolts for T=20°C and T=550°C (refer Figure

5.21)

0

50

100

150

200

250

300

0 10 20 30 40 50 60

Max

imum

Res

ista

nce

(kN

)

Position of bolt(mm)

T = 20 C

T = 550 C

0

50

100

150

Bo

lt F

orc

e (k

N)

TP1

TP2

TP3

TP4

T20

0

10

20

30

40

50

Bo

lt F

orc

e (k

N)

T550

TP5

TP6

TP7

TP8

0

10

20

30

40

50

60

70

0 100 200 300

Bo

lt D

isp

alce

men

t (m

m)

External Force (kN)

0

10

20

30

40

50

60

70

0 50 100

Bo

lt D

isp

lace

men

t (k

N)

External Force (kN)


137

The internal bolt forces and the displacements of the critical bolts (those furthest from the

neutral axis) are shown in Figure 5.25, against the applied external force. At both ambient

and elevated temperatures, the top bolt reaches its maximum resistance of 121.9 kN and

36.1kN respectively, and subsequently follows the “downhill” failure curve of the

governing component. It is evident that with greater lever arm from the neutral axis, a

bolt attracts a higher force. For models TP1 and TP5, the bolt yields in a more ductile

manner, this allows a much higher failure force on the connection to be achieved.

Conversely, the bolts nearest to the neutral axis are subjected to low horizontal forces.

The directions of the bolt forces to resist mainly moment are shown in Figure 5.26. Two

examples of the bolt movements, in Models TP5 and TP8 at elevated temperature are

shown in Figure 5.27. The bolt movements are plotted relative to their positions in the

connection; with the origin on the Y-axis indicating the neutral axis of the beam. The

plots illustrate that the bolt group initially rotates about its centreline, satisfying the

equilibrium state by moving as if they were connected by a solid structure. This

movement is essentially caused by the beam-end rotation and is a function of the distance

from the neutral axis of the beam. The top bolts for both models are shown as displacing

considerably beyond the maximum resistance. However, this is largely a result of the

infinitely ductile bolt shear model used. The middle and lower bolts accommodate

further rotation of the beam-end. Model TP8 shows lower displacement by 2.8% and

6.9% than model TP5 respectively.

Figure 5.26 Direction of horizontal forces on the bolt.

The position of the connection on the beam web determines the rotational ductility of the

beam-column connection model. The capacity of a connection depends on the critical

bolts’ distance from the neutral axis, and this also modifies the connections’ overall

ductility in rotation.

Support side Beam side

Force is positive

toward the beam + ve

-ve

Force is negative

toward the support


138

Figure 5.27 Movements of bolt group for a) Model TP5 and b) Model TP8

5.5.3. Influence of loading angle

The inclined tying force, which is represented by the loading angle, is a fairly realistic

way of simulating the combination of beam-end shear, tying and moment forces in the

later stages of heating by a real fire. The varying loading angle specified in the tests

generates a set ratio of tying to shear force. A smaller loading angle, of 35°, allows higher

tying capacity of the connection than that for the higher angle of 55°, because it leads to a

smaller proportion of shear force. The angle also influences the resultant force, with 35°

generating lower moment at the bolt assembly, thus enhancing the overall connection

capacity.

Figure 5.28 Comparison force-rotation curve with loading angle 35°-55°

The robustness requirement of the shear connection includes their capability to carry the

tying forces, in addition to the vertical shear load applied parallel to the column.

Therefore, the investigation of the combined action of the horizontal and vertical forces is

carried out relative to the inclined force adopted in the experiments. The incorporation of

-40

-20

0

20

40

60

80

100

120

-20 0 20 40 60

Po

stio

n o

f b

olt

(m

m)

Bolt Displacement (mm)

Top bolt

Middle Bolt

Lower bolt -80

-60

-40

-20

0

20

40

60

80

-20 0 20 40 60

Po

stio

n o

f b

olt

(m

m)

Bolt Displacement (mm)

Top bolt

Middle bolt

Lower bolt

0

50

100

150

200

250

0 5 10 15 20 25

Fo

rce

(kN

)

Rotation (deg)

M20-8.8-3 bolt CM T20-55

Test 55(Yu, 2009)

CM T20-35

Test 35(Yu, 2009)


139

this action has been detailed in Chapter 4, which entail the representation of the reduced

horizontal bolt forces with the inclusion of the vertical shear component. The force-

rotation of the component model response at temperature T=550°C is shown in Figure

5.29. The coupled forces model indicates the consideration of horizontal and vertical

forces that is coupled, hence reducing the individual bolt capacity and thus the overall

connection. However, the capacity reduction shown here is not significantly influenced

by the consideration of coupling the forces on the bolt row.

Figure 5.29 The force-rotation response of combined forces at temperature 550°C

5.6. Application of the fin-plate connection element

The development of the component model has been described and validated with

previously available experimental results. A brief application of the connection element

will now be conducted to investigate the behaviour of fin-plate connections in isolation

and in a global frame analysis.

5.6.1. Influence of connection in isolated beam

The behaviour of a fin-plate connection will be investigated in the context of a typical

beam in isolation. The connection element is incorporated at the beam-end connections in

the form of non-linear characteristics representing the components of a fin-plate

connection. Analysis is conducted for a typical beam used in building construction. An

example beam 7m long is adopted, with Universal Beam section 454×152×60. A

uniformly distributed load is applied to the beam, which corresponds to 0.6 load ratio.

The connection element has been designed, according to the ‘Green Book’ (BCSA, 1991)

for the adopted loading and member size. The details of the fin-plate connection are

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10

Fo

rce

(kN

)

Rotation (deg)

M20-8.8-3 bolt

Uncoupled forces

Coupled forces


140

shown in Figure 5.30, with a plate thickness of 10mm. The end clearance between the

bottom beam flange and the column face is 10mm. The two usual scenarios for a

connection in normal construction are relatively rigid and flexible. The supporting

member components such as the flange of a column or a plate embedded in a reinforced

concrete wall are relatively rigid. Connections to one side of a column web or a beam

web are very flexible. In this chapter, only the relatively rigid case is considered.

Figure 5.30 (a) Detailing of the connection element (b) The arrangement of the isolated

beam with connection elements.

The connection response is firstly studied in terms of the midspan deflection of the beam

member. Two cases are compared, with end restraint (AX), and without end restraint (N-

AX), as shown in Figure 5.31. In the AX case, the beam experiences restraint provided by

the adjacent structure, while in the latter case (N-AX), the beam is allowed to expand in

the longitudinal direction and experiences pure bending behaviour and rotation of the

connection element. The beams are subjected to uniform heating. The isolated beam

responses for the two cases show that they exhibit relatively similar low levels of

deflection before reaching temperature 265°C. Beyond this, the central deflection in the

AX model increases at a much faster rate. The connection is subjected to high moment,

and high compressive axial force caused by restrained thermal expansion. As the

compressive force is reduced, the rate of deflection also reduces.

40mm

80mm

80mm

80mm

40mm

320mm

50mm 50mm

UB 454 ×152 × 60

W (kNm)

7000mm

AX

N-AX

(a)

(b)

Spring

element


141

Figure 5.31 Midspan deflection of the beam

The connection element is subjected to a combination of shear and moment, as a result of

the loading applied to the beam. The behaviour of the connection strongly depends on the

location of the point of contraflexure, at which the bending moment is zero. This location

depends on the rotational stiffness and strength of the fin-plate connection. As shown in

Figure 5.32, as the applied temperature increases, the end moment increases. When the

end moment exceeds the yield moment capacity of the connection, the rotational stiffness

of the connection decreases, which results in redistribution of the end moments towards

the midspan of the beam. During the heating of the connection element, the contraflexure

point moves towards the supports, thus decreasing the fixed-end moment in the beam.

This behaviour shows the fin-plate connection acting more like a pin connection, as it

experiences more yielding and loss of rotational stiffness. The location of the

contraflexure point primarily depends on the depth of the fin-plate, the amount of

slippage in the bolts and the rotational stiffness of the supporting member (in this case,

rigid).

Figure 5.32 End moment in the connection for axially restrained.

-1200

-1000

-800

-600

-400

-200

0

0 200 400 600 800

Def

lect

ion (

mm

)

Temperature(C)

N-AX

AX

-200

-150

-100

-50

0

50

0 200 400 600 800

Mo

men

t (k

Nm

)

Temperature(C)

AX


142

Figure 5.33 Change of contraflexure point in beam during loading

5.6.2. Influence of the applied load ratio

The beam studied above is subjected to a load ratio of 0,6. In order to investigate a

practical case, it is necessary to estimate an appropriate load-ratio, not so low that it only

induces nominal moments within the connection, or so high as to result in rapid

premature failure. The load ratio is defined as the ratio between the applied loading at

Fire Limit State and the load capacity of the beam at ambient temperature.

The influence of the load ratio on the performance of the generated model is shown in

Figure 5.34. The load ratio is plotted in the range 0.3-0.8 against the “failure temperature”

of the beam. The term “failure temperature” is here defined as the temperature at which

the beam reaches a limiting deflection of span/30, which is a familiar limit taken from

standard furnace testing of beams. This is a very simplistic criterion in the context of

connection response.

The figure also shows the case where the temperature of the connection is lower than the

beam temperature. The use of a lower connection temperature has been recommended by

Lawson (1990), as 70% of the lower beam flange temperature, and is based on a series of

furnace tests using the ISO standard time-temperature regime (ISO834, 1975) . However,

this contradicts the temperature distributions recorded by Leston-Jones (1997) in his bare-

steel joint tests utilising end-plate connections. The temperature difference showed little

variation in these tests, being 98% of the lower beam flange temperatures. However, the

latter tests used a beam-to-column connection totally enclosed within a furnace, whereas

the earlier tests used a concrete slab supported on the beam’s top flange as the ceiling of

the furnace, causing very different conditions for the incident heat flux around the

connections. The connection temperature adopted in this study is defined, assuming a

supported concrete slab, as uniform but at 80% of the uniform beam temperature.

At service load

At yield point

At collapse

Contraflexure

point


143

Figure 5.34 Influence of load ratio on different connection temperatures.

Figure 5.35 Top bolt forces of the connection (critical bolts).

Figure 5.36 Force-displacement graph of the bolt component for case (a) LR= 0.3; (b)

LR= 0.7

Superficially this suggests that lower connection temperatures can enhance the beam

performance quite significantly at medium-to-high load ratios. However, this is based

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

500 600 700 L

oad

Rat

io

Failure Temparatures(C)

Tc=1.0Tb

Tc=0.8Tb

-200

-150

-100

-50

0

50

100

150

0 100 200 300 400 500 600

Fo

rce

(kN

)

Temperature ( C)

LR =0.3 LR =0.4 LR =0.5 LR =0.6 LR =0.7

-200

-150

-100

-50

0

50

100

150

-40 -20 0 20

Fo

rce

(kN

)

Displacement

B-1 B-2

B-4 B-3

-200

-150

-100

-50

0

50

100

150

-20 0 20 40 60 80

Fo

rce

(kN

)

Displacement

B-1 B-2

B-3 B-4


144

entirely on beam deflection, and takes no account of the real possibility of fracture of

elements of the connections.

The influence of the load ratio on the connection can be explained with the bolt forces in

the connection for the case with lower connection temperature. Figure 5.35 shows the bolt

forces, farthest away from the centreline of the connection (critical bolts). For all case, the

bolt forces increases with temperature increase, but the unloading point of the loaded

connection varies considerably, with different load ratios. As shown before, the critical

temperature varies slightly with different load ratios. However, the loading level (in terms

of magnitude) on the connection defined the behaviour of the whole connection. This is

shown in Figure 5.36 for two cases; with low load ratio 0.3 and high load ratio 0.7. The

unloading of the bolt component is more obvious for LR =0.7, as it starts to unload

temperature, T=354°C, whilst for LR=0.3 the connection unloads later at T=451°C.

Because the connection was loaded at low level, the inelastic behaviour in the connection

is delayed, and subsequently an improved critical temperature.

5.7. Connection response on two-dimensional sub-frame.

The development of the component-based model has been successfully validated in the

previous sections. Having defined the behaviour of the fin-plate connections at elevated

temperatures in isolation, it is now necessary to consider the significance of the influence

of continuity between structural members in frameworks. This can be achieved by simply

implementing the component model in a typical sub-frame arrangement, as a way of

assessing how the global structural response is affected by the interaction between the

structural members and the connection’s component assembly. The analysis of sub-

frames is preferable to complete structures, because they facilitate the computation in

terms particularly of runtimes and preparation times. A symmetric sub-frame model

representing a restrained “rugby goal post” frame has been adopted for this study. Similar

frame models have been used by Leston-Jones (1997), Al-Jabri (1999) and Block (2006)

on other types of connection, and have provided good predictions of the whole-frame

structural behaviour. However, this model has the disadvantage of being based on a

plane-frame model, and therefore neglects any, potentially significant, influence of out-

of-plane connectivity and slab action.

The response of the sub-frame is investigated using two different temperature

distributions on the connection, in order to represent the effect of the higher massivity in

the connection region than in the open beam span. The frame arrangement (Figure 5.37)


145

consists of a UB 254×102×22 beam section with span 5.5m, and column sections UC 203

×203×71. The detailed selection of these sections for ambient-temperature at Ultimate

Limit State conditions is given in the Appendix, assuming the building is of residential

type. The restraint conditions at the beam ends are defined to prevent horizontal

displacement, whilst the columns are allowed to displace vertically. A uniformly

distributed line loading is applied to the beam, generating a load ratio of 0.6 with respect

to the assumed simply supported conditions. Additionally, a point load of 1324 kN has

been placed on the top of the column, generating the same load ratio in the lower column,

when combined with the beam reactions.

The heating regimes on the structural members are defined individually, assuming that

the fire compartment coincides with the middle bay. However, the temperature

distributions across the beam sections are assumed to be uniformly distributed. The

lower-storey columns are defined to reach only 50% of the beam temperature, assuming

that they are fully protected, but leaving the joint zone exposed to the fire. Thus, a much

higher temperature is defined at the connection compared to the column, but this is lower

than the temperature of the heated beam, due to the higher massivity and low exposed

surface area in the vicinity of the joint.

Figure 5.37 Two-dimensional subframe model

2750mm 5500mm

35

00

mm

3

50

0m

m

Midspan

1.0T

20°C

0.8T


146

The connection response in the sub-frame arrangement is investigated mainly on the basis

of the mid-span deflection in the heated bay and the connection’s internal forces. The

mid-span deflection shown in Figure 5.38 is compared to the nominal cases of pinned and

rigid connections, which would provide a solution envelope if the developed connection

element were semi-rigid only in the rotational sense. The beam deflection starts to

increase from about 200°C, and is largely caused by the major-axis thermal buckling due

to the compression force caused by restrained thermal expansion. The deflection rate then

increases rapidly in the temperature range 400°C to 700°C, until the frame loses its

stability and fails by ‘run-away’. This form of response can be anticipated, given the

reduction of the material mechanical properties described in Chapter 2. The case with the

arrangement tested as a rigidly-jointed frame is observed to provide significant

enhancement in response in the middle range of temperatures as compared to the pinned

connections, but the eventual failure temperatures for each of these two idealised cases

will be almost identical, being based on catenary tension failure of the beam section.

Incorporating the component model, which attempts to represent the stiffness and

strength at any temperature of each component, results in a significantly lower failure

temperature. This is in accordance with the logic that the fin-plate connection, as a

simple connection, possesses limited stiffness and strength. Its performance is relatively

poor at elevated temperatures, when subjected to combined tying, moment and shear

forces.

This comparison has considered a case in which the connection temperature is equal the

temperature of the heated beam. Incorporating a more realistic fire scenario and its likely

effect on the connection temperature should result in an enhancement of the frame

response compared to this case.

Figure 5.38 Vertical displacement of the mid-span at the heating bay

-1200

-1000

-800

-600

-400

-200

0

0 200 400 600 800 1000 1200

Def

lect

ion(m

m)

Temperature ( C)

Tc = 1.0 Tb

Rigid

Pinned


147

A comparison of deflection responses is given for cases with different connection

temperatures in Figure 5.39. In the case where the connection temperature is equal to the

beam temperature (Tc=1.0Tb) the beam failure temperature is approximately 100°C

lower than for the case with a cooler connection temperature (Tc=0.8Tb). The overall

performance of the fin-plate connection is particularly improved in the range of

temperature during which the rate of weakening of the material becomes large. The rate

of deflection reduces beyond temperature 700°C, which can be attributed to the restraint

provided by the column having initially accelerated the rate of deflection. The thermal

expansion decreases at this stage, and the column provides a degree of restraint until the

connection components’ capacity has reduced sufficiently to proceed to ‘run-away’. This

form of connection response can be seen to be highly influenced by the connection’s

heating rate.

Figure 5.39 Vertical displacement at mid-span with two connection temperature regimes

The connection rotations for these two cases are shown in Figure 5.40. With the

temperature equal to that of the beam, connection failure occurs due to the combination of

high compressive forces and the material strength reduction, with the curves diverging at

a beam temperature of 523°C. High rotation causes significant deformation of the bolts in

the connection, particularly the top bolt; this applies to both cases.

-800

-700

-600

-500

-400

-300

-200

-100

0

0 200 400 600 800 1000 1200

Def

lect

ion(m

m)

Temperature ( C)

Tc = 0.8 Tb

Tc = 1.0 Tb


148

Figure 5.40 Rotation response of the connection element

In the framework of the component model, the failure sequence of the connection can be

explained in detail in terms of the effects on its components. The detailed variation of the

component forces in the connection, for the case where Tc=0.8Tb, is shown in Figure

5.41. The forces shown here are those of the three bolts and the bottom beam flange

contact component. In order to illustrate the different stages of the behaviour at each of

the component bolt rows and the lower flange contact point, the force variation for each

of these components is re-plotted with annotation on Figure 5.43.

Figure 5.41 Component forces in the connection (Tc=0.8Tb).

The positions of the bolts in the fin-plate connection vary with respect to the centreline of

the plate depth, and this determines the effect of connection rotation on the bolt force.

Bolt Row 1 may be seen as critical, being positioned furthest away, both from the

centreline and from the bottom flange contact point, and therefore tends to experience the

highest movements. Throughout the heating, all bolts in the connection follow through a

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200

Ro

tati

on (

deg

)

Temperature ( C)

Tc = 0.8 Tb

Tc = 1.0 Tb

-250

-200

-150

-100

-50

0

50

100

150

0 200 400 600 800 1000

Co

mp

onen

t F

orc

es (

kN

)

Bolt row 1 Bolt row 2 Bolt row 3 Bot B/flange

Compression

Temperature (ºC)

Tension


149

cycle of loading and unloading, as explained in Chapter 5. However, only Bolt Rows 2

and 3 experience permanent deformation from the start of heating, subsequently

following the slip-unloading route while changing the direction of the force. This is

shown by “plateau” responses in their compressive curves, which indicate the free slip

phase of the bolts. Bolt Row 1 unloads elastically and therefore no permanent

deformation is observed in this bolt in the initial phase. Nevertheless, the displacement of

Bolt Row 1 later shows significant yielding of the beam web, without any brittle failure

of the bolts. The deformation of the plate in bearing, however, has been exaggerated in

this study by assuming a high-ductility connection.

At temperature 307.5°C the bottom beam flange comes into contact with the column face,

which causes an increased compressive force imposed by the beam flange component.

This component has been defined to function only in compression, and only activates

when positive contact is made. When established, contact increases the stiffness of the

overall connection response significantly, since rotation is now about the contact point

rather than the centroid of the bolt rows. This response may advantageously enhance the

capacity of a connection, by reducing the rates of deformation of its individual

components, although reversal of movement at the lower bolt rows may temporarily

reduce the stiffness.

The deformations of each of the component rows as the beam temperature increases are

shown in Figure 5.42 for the case with Tc=0.8Tb.

Figure 5.42 Component displacements in the connection (Tc=0.8Tb).

-20

0

20

40

60

80

0 200 400 600 800 1000

Dis

pla

cem

ent

(mm

)

Bolt row 1 Bolt row 2

Bolt row 3 Bot B/flange


150

Figure 5.43 Force-displacement graphs of the components

The axial forces in the connection (and the heated beam) for the two cases generally

exhibit the same response at low temperatures. However, as the beam and connection

weaken according to the heating rate, the comparison becomes more pronounced. From

Figure 5.44, the changes of internal force as temperatures rise can be clearly explained.

At low temperatures, a large compressive axial force, imposed by the thermal expansion

of the beam, is formed in the connection.

Figure 5.44 Axial forces in the connection

-300

-250

-200

-150

-100

-50

0

50

100

0 200 400 600 800 1000

Fo

rce(

kN

)

Temperature ( C)

Tc = 0.8 Tb

Tc = 1.0 Tb

-150

-100

-50

0

50

-20 0 20 40

Fo

rces

(kN

)

Displacement (mm)

Bolt row 3

-250

-200

-150

-100

-50

0

-15 -10 -5 0

Fo

rces

(kN

)

Displacement (mm)

Bot B/flange

-50

0

50

100

-10 40 90

Fo

rces

(kN

)

Displacement (mm)

Bolt row 1

-100

-50

0

50

100

-10 40

Fo

rces

(kN

)

Displacement (mm)

Bolt row 2


151

The connection element behaves similarly to the whole structure when using the

symmetric boundary condition; a high level of axial restraint is caused by adjacent

structural members preventing axial movement of the beam ends. This compressive

action causes major-axis buckling, increasing the deflection at the mid-span of the heated

beam. The kink at 311°C can be explained by the initiation of contact between the lower

beam flange and the column face, as explained previously for the component bolt forces.

Therefore, there is an increase of connection stiffness after positive contact has been

made. At higher temperatures, the compressive force in the connection changes to tensile

force, which derives from catenary action of the beam. This tensile force increases until

the beam loses its capacity and eventually fails. The variation of moment of the

connection and the middle of the heated beam is presented in Figure 5.45.

Figure 5.45 Change of bending moment during heating phase.

5.8. Summary

In this chapter, the validation of the component model has been carried out against

available experimental tests. The proposed connection element compares well to the tests

results, for the cases where the connection is subjected to axial force and inclined force at

ambient and elevated temperatures. Although the component model predicted higher

maximum resistance of the connection, the yielding pattern during loading and heating

has been well captured. This sequential response of the connection has been described in

the context of the individual component forces and relative movement.

-60

-40

-20

0

20

40

60

0 200 400 600 800 1000

Mo

men

t (k

Nm

)

Temperature ( C)

Tc = 0.8 Tb (conn) Tc = 0.8 Tb(midspan)

Tc = 1.0 Tb (conn) Tc = 1.0 Tb (midspan)


152

The high resistance prediction is explained by the adoption of the ductility assumption in

the component model. This assumption is conservative in predicting the final fracture or

yielding in connection, however, it allows the individual component to proceed into full

cycle of loading and unloading phase during the course of heating. The consideration of

the combination forces has shown that only slight reduction has been made to the

connection response.

The validated component model is extended to study the behaviour of structural member

in isolation and sub-frame. In the sub-frame study investigation above, the real behaviour

of fin-plate connection in a frame structure has been closely simulated. Significant

reversals of forces during the heating phase can be generated. The logical and realistic

response provided using the component method also demonstrates the reliability of this

method for practical application.

Chapter 6: Component-based model for moment resisting beam-splice connection

153

6. COMPONENT-BASED MODEL FOR MOMENT-

RESISTING BEAM-SPLICE CONNECTION

Steel moment-resisting framed buildings are assumed to develop their ductility through

the development of yielding in their beam-column connections. Many engineers believe

that it is possible to withstand large deformations without significant degradation in

strength, and without the development of instability and collapse. However, evidence of

unforeseen connection failures in different types of hazard (earthquake, blast and fire) has

challenged this paradigm, raising questions about the adequacy of moment-resisting

connection design in building code provisions. Even before the destructive fires in the

WTC7 building, and following the 1994-Northridge and 1995-Kobe earthquakes,

substantial effort was being made to represent the realistic behaviour of such connections.

The framing system type identified in these catastrophic events is widely utilised in the

USA and Japan, where it provides a popular solution for buildings in highly seismic

regions. This is known as a “column-tree” system (Astaneh, 1997), and needs to utilise its

beam-splices as major elements in design. The beam-splices act as ductile ‘fuses’, and

limit the magnitudes of the internal forces, including bending moments, which can be

developed in the frame, which makes them an ideal type of connection in both fire and

earthquake scenarios. Depending on the rotational strength and stiffness of these splices,

the structural frame can behave either as ‘rigid’ or semi-rigid’. Semi-rigidity can be

beneficial at high temperature, when redistribution of forces from beams to other

structural members is critical, influencing the survival time of the whole framing system.

This chapter adapts the component-based approach to characterise the moment-resisting

connection behaviour of beam-to-beam-splices in fire. It will be seen that the method is

capable of capturing the key features of the overall connection interaction in a realistic

manner, based on the underlying mechanics, and can be verified with evidence from

experimental data.

6.1. Beam splice connection design philosophy

In extreme events, very high demands for local and global deformation are imposed on

structural elements, connections and details. Connections between members, in particular,

are anticipated to be the regions where the material is exposed to inelastic deformations,

which consequently influence local ductility requirements and frame performance. The

beam-splices, as the key elements in column tree systems, need to be designed

appropriately in order not to compromise the strength of the beams. The beam-splice


154

connections most often used are either welded, field-bolted or a mixture of bolted and

welded elements. However, the advantages of using column-tree systems can be fully

utilised using fully bolted splices. Thus, this analysis concentrates on the bolted

connections. Plate splices, shown in Figure 6.1, can be either single- or double-plated,

the arrangement being repeated on each side of the joint. The use of double plates in

general reduces the number of bolts and shortens the lengths of plate splices. The web

splices normally employ double plates to stiffen the web out-of-plane and to utilise the

double-shear capacity of the bolts. The design philosophy (BCSA, 2002) for this type of

connection is that the flange splices are designed to resist most of the applied moment.

The web splice carries transverse shear, which is assumed to be distributed equally

between the bolts. Additionally, any axial force in the beam is divided equally between

the flanges.

Figure 6.1 Forces in splice connection

Connections in general should possess the characteristics of both strength and ductility,

which in this context refers to their ability to articulate plastically at some stage of the

loading cycle without failure, and this is governed by the ductilities of their parts. The

ductility of a joint reflects the length of the yield plateau in its moment-rotation response,

which is provided mainly by its capacity for plate yielding and bearing deformation at its

bolt holes. Failure criteria are introduced for each individual component to facilitate the

simulation of its behaviour at different temperatures, including final fracture. The design

procedure classifies failure modes into ‘ductile’ and ‘brittle’, and attempts to ensure that

ductile failure modes will precede the brittle ones. In this study only the dominant failure

modes (bearing of plates and bolt shear) are considered, on the basis of previous test

results and analytical research (Sarraj, 2007b; Yu, et al., 2009).

N

M V

V M

N

T T

C C


155

6.2. Mechanical model development

In developing the mechanical model of a connection, a comprehensive understanding of

the general behaviour of the connection is necessary. For splice connections, the

utilisation of preloaded bolts can transfer force, initially through frictional resistance and

subsequently through bearing stresses. It is assumed in this research that the bolts are

subjected to forces acting through their centroids. In the initial stage of loading, the bolts,

which are presumed to be installed centrally, do not carry any force. The load is solely

transferred by frictional resistance at the contact surfaces of the plates. When the load

exceeds the frictional resistance, large relative displacement occurs, and the bolt comes

into positive contact with the bolt hole edges. This displacement is caused by a finite slip,

ranging from zero to two hole clearances. The positions of the bolts in their respective

holes during the assembly process define their slip ranges. The bolts positioned furthest

away from centre of rotation usually come into contact with the hole walls first, and are

therefore the critical bolts. These then deform plastically, either by bolt shear or plate

bearing, and eventually fracture. Overall, the connection behaves elastically with

increasing load until the stress in either a bolt or a plate reaches the yield strength of the

material. Beyond this stage, the maximum resistance of the aggregate bolt-row

characteristic is controlled by that of its weakest component. Thus, the post-yield failure

characteristic follows the dominant component. It should be noted that the initial

frictional resistance diminishes somewhat when slip occurs in a bolt row.

Commonly used beam-splice connections consist of splice plates, which are lapped across

the two connected beams and bolted to either side of the web and flanges. In a component

model framework, the active zones for such a splice connection cover the region where

the two members are interconnected and where the set of physical components

mechanically fasten the connected elements, as shown in Figure 6.2.

Figure 6.2 A bolted double-splice butt joint.

Contact elements

End distance


156

Characterisation of these active zones is based on the force transfer across a bolted

double-splice butt joint between in-line connected members. Within each zone, several

sources of deformation can be identified, which in this case refer to the frictional, bearing

and shearing resistance of the connected plates and bolts.

6.2.1. Proposed component-based model

It can be seen that the fundamental concept is comparable to that for fin-plate

connections. Thus, the component model derived for a single lap joint (explained in

Chapter 4) can be extended to use for butt joint connections. The assembly of the primary

lap joint (Figure 6.3) can be summarised as consisting of;

a) Cover-plate in bearing (Tension)

b) Cover-plate in bearing (Compression)

c) Beam web in bearing (Tension)

d) Beam web in bearing (Compression)

e) Bolt in shearing

f) Friction (slip)

Figure 6.3 Component model of single bolted lap-joint.

Figure 6.4 Component-based model of two-bolt row subjected to (a) tension; (b)

compression

(a)

δ

(b)

δ

M

(e)

(c) (a)

(b) (d)

(f)


157

When the connection is loaded either in tension or compression (Figure 6.4), the contact

achieved by closing the gap, δ activates one or other series of three components. The

equivalent characteristic of the active series follows the failure characteristics of its

weakest individual component.

6.3. Validation of lap-joint connection using preloaded bolts

In shear-bolted joints, one primary factor influencing the performance can be distinctively

established as the frictional forces. The use of high strength friction grip bolts requires

pre-stressing of the bolts, which allows the force transfer mechanism to be carried largely

by the frictional forces. Pre-loaded bolts are commonly used in these connections, which

give a high probability of structural failure in instances where slip occurs.

Lap-bolted joint tensile tests were carried out at Chiba University (Hirashima et al.,

2007), Japan to obtain the relationship of the shear characteristics of high strength bolts.

The tests were performed for single- and double-bolted joints at ambient and elevated

temperatures. The test specimen setup is illustrated in Figure 6.5. The steel grades were

SN 490B for the plates and F10T for the high-strength friction grip bolts, according to the

Japanese Industrial Standard (JIS, 2008). An interval of 600mm is taken as reference

point for the displacement measurement. At both ends, an M24 nut is welded on both

sides of the test specimen. The bolts were tested in two sizes with oversized bolt holes;

M16 in 18mm bolt holes and M20 in 22mm bolt holes respectively.

The test specimen was positioned in an electric furnace (Figure 6.6) with internal

dimensions of 1100mm length, 800mm width and 700mm depth. The right-hand side of

the specimen was attached to a column, whilst the left-hand side was connected to a

manual loading jack. The specimen was loaded at a steady-state condition according to

the specified temperatures. The specimen was designed considering the plate thickness,

width and bolt spacing, so that the high-strength bolts were loaded until they fractured.

The displacement gauge was installed outside the furnace, and connected to the M24 nuts

by four stainless steel rods. The temperature was controlled using six temperature gauges

which were installed within the 600mm reference length. The specimen was heated at

about 10°C per minute, and loaded 1-1.5 hours after it had been kept constant. The

specimen was tested at both ambient and elevated temperatures (400ºC, 500ºC, 600ºC and

700ºC).


158

Figure 6.5 Hirashima et al. (2007) lap-joint test specimen

Figure 6.6 Arrangement of the test specimen inside the electric furnace.

The force-displacement relationship of the bolted lap joint tests is compared with the

predictions of the component model (Figure 6.7-Figure 6.8). The test is represented with

dotted lines whilst the component models follow the full lines. The specimen’s

displacement in the test is the average displacement measured between the measurement

points. In this validation, only double-bolted lap joint cases are investigated further, in

order to extend the lap-joint behaviour to beam splice connections. The component model

has shown reasonable agreement with the test results, particularly at elevated

temperatures. At ambient temperature, the yielding of the plate from the model is less

than that in the test. This is largely because the component characteristics follow the

principles of Eurocode 3-1-8 (CEN, 2005b).

Test specimen

770mm 860mm

1640mm

10mm

55

55

55

55

55

55

50 200 260 40 40

600mm

19mm 12mm

Bolt M16 or M20


159

In this model, the influence of initial friction between the plates has been reasonably well

captured using the component model characteristics. At initial loading, the force is solely

resisted by the frictional stress between the connected plates, thus explaining the increase

of force at low displacement followed by a “plateau”. Subsequently, after slip occurs, the

transition into bearing joint behaviour increases the stiffness according to the bolted lap-

joint characteristics. In general, the component model is capable of simulating the lap-

joint response at both ambient and elevated temperatures.

Figure 6.7 Force- deflection response of double-bolted joint with M16 bolt.

Figure 6.8 Force- deflection response of double-bolted joint with M20 bolt.

6.4. Beam-splice component model validation

An experimental study on I-section steel beam incorporating high-strength bolted splice

joints was performed, following the lap-joint connection test performed in Chiba

University (Hirahima, et al., 2010). The moment-resisting beam-splice connections were

subjected to ambient and increasing temperatures. The experiments investigated both the

temperature distributions within the connected zones of the beams and the structural

0

100

200

300

0 2 4 6

Fo

rce(

kN

)

Displacement (mm)

T=400 C

T=500 C

T=600 C

T=700 C

T=20 C

0

100

200

300

400

0 2 4 6 8

Fo

rce(

kN

)

Displacement (mm)

T=400 C

T=500 C

T=600 C

T=700 C

T=20 C


160

behaviour of the moment-resisting connections at these high temperatures. Four

specimens using beam-splice connections with different details and loading were tested.

Only three of the tests, with the more significant arrangements, are studied here, since the

objective of this study is to understand the influence of fire on moment-resisting

connection response. Details of the differences between the selected specimens are given

in Table 6.1.

Table 6.1 Test detailing for different arrangement.

Specimen

Connection type of

moment-resisting

connection

Number of HSFG

bolts Constant

load Pc

(kN)

Fire

protection Flange Web

Test 2

Partial-strength

4 8 121.9 kN

12.5mm

ceramic

fibre

blanket.

In region e,

a double

layer was

applied.

Test 3 Full-strength

8 8

Test 4 8 8 61.0 kN

The schematic setup of a test is given in Figure 6.9, showing the symmetric test setup.

The complete span between supports was 4.2m. The load Pc was applied mainly through

two jacks near mid-span, with the forces given in Table 6.1. Two additional jacks Pe at

the ends of the cantilevers (Position a) were used to attempt to maintain zero rotation at

the supports throughout the test. In order to control lateral buckling and twisting of the

beam during heating, a stabilising system was set up at the point of contraflexure

(indicated as e). The connection details are shown in Figure 6.10. The distinction

between the partial-strength (Test 2) and full-strength (Test 3 and 4) connections rests

primarily on the number of bolts in the beam flanges.


161

Figure 6.9 The symmetric test setup

Figure 6.10 Connection details for (a) Test 2 (b) Tests 3 and 4

6.4.1. Material properties

Details of the material properties and section of the structural member are given in Table

6.2. The yield and ultimate stresses were measured from tensile coupon tests from the test

specimens, with nominal grades of SN 400B for the beam and F10T for the bolts,

according to the Japanese Industrial Standard (JIS, 2008). The degradation of strength of

the structural members was based on the reduction factors defined from the experimental

results depicted in Figure 6.11 for SN 400B and F10T. These are compared with

recommendations of EC3-1-2 (CEN, 2005a). It can be observed that the experimental

reduction curve employed is more pronounced in the early heating stage, whilst at higher

temperatures it follows closely the EC3 curve. The details of the material properties

measured from the coupon tests on the steel and bolts are given in Table 6.3 and Table

6.4 respectively.

60 4

0

60

60

40

26

0m

m

40 40

10

40 40

60 4

0

60

60

40

26

0m

m

40 60 40 40 60 40

290mm

10

170mm (a) (b)

400 1000 400 4200 250 450 1150

b c d e f e a d c b a

Dh1

Dh2

D4 D3 D2 D1

D2 D3 D4

1000 250 450 1150

Pe Pc

Loading Frame

Insulation

board Support

Load cell


162

Table 6.2 Section properties of structural members.

Sections Dimensions(mm)

Yield

Stress, fy

(N/mm2)

Tensile

strength, fu

(N/mm2)

Elongat

ion (%)

Beam I-section steel beam 350 × 175 × 11 × 7 308 446 31

Cover

plates

Flange (Test 2) 170 × 175 × 9.0

170×70 × 9.0

393 456 28

Web (Test 2) 260 × 170 × 6.0 *

Flange (Tests 3 & 4) 290 × 175 × 9.0

290 × 70 × 9.0

Web (Tests 3 & 4) 260 × 170 × 6.0 *

Bolt Flange 16 × 60 1043 1083 19

Web 16 × 55 1019 1057 19

* Coupon tests were only performed on 9mm plate; assumed the same for 6mm plate.

Figure 6.11 Strength reduction factors for a) SN 400B steel b) F10T bolts.

Table 6.3 Material properties of steel grade SN 400B

,aE ,pf ,yf ,y ,uf ,u

[°C] [N/mm2] [N/mm

2] [N/mm

2] [N/mm

2]

0 205000 282 292 0.01 446 0.15

100 205000 269 282 0.01 444 0.15

200 184500 267 285 0.01 522 0.15

300 164000 209 268 0.01 515 0.15

400 143500 181 246 0.01 423 0.15

500 123000 160 206 0.01 296 0.15

600 63550 109 122 0.01 166 0.15

700 26650 62 64 0.01 84 0.15

800 18450 33 37 0.01 55 0.15

900 13940 9 14 0.01 19 0.15

1000 9225 6 9 0.01 14 0.15

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 200 400 600 800 1000

Red

uct

ion

fac

tor

ky,θ

Temperature [ C]

TEST

CEN(2005b)

AIJ(2008)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 200 400 600 800 1000

Red

uct

ion

fac

tor

kb

,θ

Temperature [ C]

TEST

CEN(2005b)

AIJ (2008)


163

Table 6.4 Material properties of bolts (F10T)

,aE ,pf ,yf ,y ,uf ,u

[°C] [N/mm2] [N/mm

2] [N/mm

2] [N/mm

2]

0 205000 1110 1168 0.04 1178 0.2

100 205000 950 1070 0.04 1080 0.2

200 184500 950 1125 0.04 1135 0.2

300 164000 910 1086 0.04 1096 0.2

400 143500 689 776 0.03 786 0.2

500 123000 416 500 0.02 510 0.3

600 63550 209 259 0.02 269 0.6

700 26650 62 125 0.02 135 0.8

800 18450 57.9 67 0.02 77 0.8

900 13940 28.5 33 0.02 43 0.8

1000 9225 0.8 1 0.02 6 0.8

6.4.2. Temperature distribution

The furnace fire curve adopted in the test was the ISO 834 (ISO834, 1975) standard fire

heating curve, shown in Figure 6.12 for Test 3. This fire protection was varied between

zones along the beam, resulting in a differential temperature distribution. The different

zones of fire protection are denoted as a to f in Figure 6.9.

Figure 6.12 ISO 834 Temperature curve for Test 3

The temperature details of four zones; mid-span, support, joint and in between joint and

support, are shown in Figure 6.13-Figure 6.16, corresponding to their insulation details.

The thermal gradients across the beam depth, however, were caused by the presence of

the 100mm thick ALC (autoclaved lightweight concrete) panel, supported on the upper

flange, which resulted in about 160°C temperature difference between the bottom and top

flanges at 60 minutes. To represent the shielding and heat-sink effects of a normal-weight

concrete slab on the top flange temperature in more realistic construction, a ceramic fibre

0

200

400

600

800

1000

1200

0 30 60 90 120 150

Tem

per

ature

( )

Time(min)

ISO 834

Temperature

curve

Heating

stopped


164

blanket (130 kg/m3 at 12.5mm thickness), with fire resistance rating of about 1 hour, was

used to provide some insulation to the top flange of the beam. The average temperatures

measured in the test at the positions; support, mid-span and joint, are shown in Figure

6.17.

At point f

Additional layer of 12.5mm

fire protection covering the

whole section

Figure 6.13 Fire protection scheme on mid-span section.

At point c


protection applied on the

bottom section.

Figure 6.14 Fire protection scheme on support section.

At point d

Nominal fire protection

Figure 6.15 Fire protection scheme at joint section.

0

200

400

600

800

1000

0 50 100 150

Tem

per

ature

( C

)

Time (min)

MID-SPAN Mid-1

Mid-2

Mid-3

Mid-4

Mid-5

Mid-6

0

200

400

600

800

0 50 100 150

Tem

per

ature

( C

)

Time (min)

SUPPORT Sup-1

Sup-2

Sup-3

Sup-4

Sup-5

Sup-6

0

200

400

600

800

0 50 100 150

Tem

per

ature

( C

)

Time (min)

JOINT Joi-1

Joi-2

Joi-3

Joi-4

Joi-5

Joi-6

① ② ③

④ ⑤ ⑥

② ① ③

④ ⑤ ⑥

① ②

③

④ ⑤ ⑥


165

At point e


fire protection covering the

whole section

Figure 6.16 Fire protection scheme on section between joint and mid-span.

Figure 6.17 Average temperatures at position (a) support (b) mid-span (c) joint

6.5. Implementation in Vulcan

The implementation in Vulcan of the component method to the beam-splice connection

arrangement follows the splice connection design; which requires that the beam flanges

0

100

200

300

400

500

600

0 50 100 150

Tem

per

ature

( C

)

Time (min)

JOINT-MIDSPAN

Joi-Mid-3

0

100

200

300

400

500

600

700

800

900

0 30 60 90 120 150

Tem

per

atu

re (

°C)

Time (min)

Test 2

Test 4

Test 3

(b) MID-SPAN

0

100

200

300

400

500

600

700

800

900

0 30 60 90 120 150 Time (min)

Tem

per

atu

re (

°C)

Test 2

Test 4

Test 3

(a) SUPPORT

0

100

200

300

400

500

600

700

800

900

0 30 60 90 120 150

Tem

per

atu

re (

°C)

Time (min)

Test 2

Test 3

Test 4

(c) JOINT

③


166

must transmit both applied moments and shear acting in either direction. The transverse

shear however, is fully resisted by the web plate and uniformly distributed across the web

bolts which are equally spaced.

In this experiment, the beam splice connection utilises double-lap splice-plates on either

side of the beam flange or web, with a double column of bolts (Figure 6.18a) for Tests 3

and 4. The component model incorporates this arrangement so that the displacements of

these bolts are added in parallel for each bolt row (Figure 6.18b), and therefore the

relative displacements are considered for these bolts. For the case where a single-column

bolt row was defined (Test 2), the spring model is simply reduced according to the

number of bolts. A highly simplified component arrangement is shown in Figure 6.18d,

which consists of two springs in series representing the bolts on the connected beams,

without friction.

Figure 6.18 Simplified component model arrangement for double-splice butt-joint

The simplified arrangement can now be assembled as a complete structural component.

Figure 6.19 illustrates the positions of the assembled components which connect the

beams to one another. The component model representing the beam splice connection is

shown in a zero-length region.

F F

δ

(a) Double-splice butt-joint

(b) Component-model for double-splice butt-joint

One bolt

F F

δ δ

(c) Simplified butt-joint

Two bolts in parallel

(d) Simplified component model

F

F F

δ


167

Figure 6.19 Arrangement of one bolt row component model in beam splice connection.

0mm

Row n

V

M

N N V

M


168

Essentially, the springs in a bolt row are set-up in series, representing a web bolt row on

either side of the beam gap with net stiffness klap,n. The index ‘lap’ refers to a single bolt

row, which can be extended to multiple (n) bolt rows. In order to include the effect of the

friction between the double plates, a parallel friction spring is added to each bolt-lap

spring, represented by stiffness kslip,n. The upper and lower beam flange springs, kbf,

upper/lower account for both positive compressive contact between the beam flanges and the

tensile behaviour of the flange bolt rows, including friction.

The complete arrangement of the component model for the beam splice connection

adopted in the experiment is illustrated in Figure 6.20. The springs on the top (kbf,1)and

bottom (kbf,2) beam flanges include either two or four bolts on either side of the gap

between the connected beam, whilst on the beam web each spring includes two bolts for

each bolt row. The springs correspond to the defined number of bolt rows in the test, of

which there were four, (kw,1-kw,4). In addition to the bolt components, the lower beam

flange spring also takes into account any occurrence of large rotation in the beam. A

compressive lower spring component is activated once the clearance gap between the

connected lower flanges has nearly closed, indicating that positive contact is in the

process of being made, due to large change of rotation between the beam

ends.

Figure 6.20 Component-based model arrangement in Vulcan. (Note that u1 is the relative

mean displacement across the whole connection).

6.5.1. Individual component spring characteristic

The identification of active components in the beam splice connection has been explained

in the previous section. The essential element in the framework of the component model

is the nonlinear spring characterisation of the individual components, whose

characteristics will be shown. The temperature-dependent springs defined in this

experiment follow the spring characteristics explained in Chapter 3 for the components;

0mm

θ u

θ

w


169

plate in bearing, bolt shearing and friction. The force-displacement characteristics given

in Figure 6.21- Figure 6.25 define the components of the various parts of the beam splice.

Figure 6.21 Tensile force-displacement characteristic for cover plate and beam flange in

bearing.

Figure 6.22 Tensile force-displacement characteristic for cover plate and beam web in

bearing.

Figure 6.23 Compressive force-displacement characteristic for cover plate and beam

flange in bearing.

0

100

200

300

400

0 10 20 30 40 50

Fo

rce

(kN

)

Displacement (mm)

Cover plate (flange) in bearing

0

50

100

150

200

250

0 10 20 30 40 50

Fo

rce

(kN

)

Displacement (mm)

Beam flange in bearing

T = 20 C T = 100 C T = 200 C T = 300 C

T = 400 C T = 500 C T = 600 C T = 700 C

0

50

100

150

200

250

0 10 20 30 40 50

Fo

rce

(kN

)

Displacement (mm)

Cover plate (web) in bearing

0

50

100

150

0 10 20 30 40 50

Fo

rce

(kN

)

Displacement (mm)

Beam web in bearing

-400

-300

-200

-100

0

-40 -30 -20 -10 0

Fo

rce

(kN

)

Displacement (mm)

Cover plate (flange) in bearing -250

-200

-150

-100

-50

0

-40 -30 -20 -10 0

Fo

rce

(kN

)

Displacement (mm)

Beam flange in bearing


170

Figure 6.24 Compressive force-displacement characteristic for cover plate and beam web

in bearing.

The tensile and compressive plate bearing components are detailed for both the cover

plate and the beam web, with different thicknesses of 11mm and 9mm respectively. The

limiting parameter for ultimate yielding in plate bearing under tension is the end distance

of the cover plate, which in this test was equal to 40mm.

For the bolt shearing component, the limiting parameter for the ultimate bolt

displacement is the bolt diameter, which was 16mm in the tests. When the maximum

resistance of the bolt shearing component is reached, shearing beyond this displacement

is calculated with respect to the residual area of the bolt. Therefore, total shear failure of

the bolt is defined when the displacement is equal to the diameter of the bolt.

Figure 6.25 Tensile and compressive force-displacement characteristic bolt shearing

component.

-250

-200

-150

-100

-50

0

-40 -30 -20 -10 0

Fo

rce

(kN

)

Displacement (mm)

Cover plate (web) in bearing -150

-100

-50

0

-40 -30 -20 -10 0

Fo

rce

(kN

)

Displacement (mm)

Beam web in bearing

T = 20 C T = 100 C T = 200 C T = 300 C

T = 400 C T = 500 C T = 600 C T = 700 C

0

50

100

150

200

0 5 10 15 20

Fo

rce

(kN

)

Displacement (mm)

-200

-150

-100

-50

0

-20 -15 -10 -5 0

Fo

rce

(kN

)

Displacement (mm)

T = 20 C T = 100 C T = 200 C T = 300 C

T = 400 C T = 500 C T = 600 C T = 700 C


171

6.6. Component model validation

The component model incorporated in Vulcan represents the beam-to-beam experimental

setup, with the real boundary conditions of the test. In the model, full rotational restraint

is provided at the support to simulate the constant zero rotation which is maintained

during the tests. An “axis of symmetry” boundary condition is applied at the right-hand

end of the model (Position f), to represent the mirror-image arrangement of the right-hand

half of the beam arrangement. The three tests conducted are examined here in terms of

the deflection at mid-span, and the distribution of bending moment at several main

positions along the beam, with respect to temperature increase. The temperature axis

shows the mean temperature in the section at the mid-span of the beam. In these graphs

the dotted lines indicate the test results, while the full lines are the analytical results using

the component models for the splice connections.

6.6.1. Deflection at mid-span

In general, very reasonable agreement can be seen between the tests and the analytical

models using the component elements, in terms of the mid-span deflection. The

component models generally exhibit a similar loading pattern, with large deformation

forming a plastic hinge, which eventually fails in a ‘runaway’ stage (Figure 6.26-Figure

6.28). The bending moment is carried mainly by the flanges, and so the number of bolts

in each flange splice is a major influence on the connection strength. The term ‘failure’ in

this model can be defined as either the occurrence of beam failure by runaway, or the

fracture of any component the connection. In the early heating stage, the forces in the

bolts are transferred primarily by frictional resistance until the slip resistance is exceeded,

when slip occurs. The forces are then resisted by the bearing and shear characteristics of

the bolt component assembly.

In Test 2, a significant rotation caused a very obvious bearing contact of the lower beam

flanges at a beam temperature of 713.5°C. In this test the failure of the beam caused

considerable shearing deformation of the bolts through the beam upper flange, followed

by large bearing deformation of the beam web’s tension zone. With increased numbers of

bolts in the beam flanges (Test 3), the failure of the beam was delayed slightly, to the

higher temperature of 725.5°C. After positive contact between the lower beam flanges

was made, at high rotation, they experienced a high compressive force, which

subsequently generated higher bolt deformation in the upper beam flange due to this

lowering of the centre of rotation at the connection. The beam specimen in Test 4 failed at


172

a critical temperature of 818°C, at only half the loading of Test 3. This arrangement

experienced a much larger mid-span deflection because of the higher temperature, and the

connection components were more highly deformed.

Figure 6.26 Mid-span deflection of Test 2


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173


6.6.2. Moment distribution

The variation of bending moment at three different positions along the beam span is

depicted in Figure 6.30-Figure 6.322 for each of the three tests; the positions are shown

on Figure 6.29. The legend CM-3(c) indicates the component model for a given Test

number, for three positions; c for support, d for joint and f for mid-span. The analytical

results at the other positions provide a general view of the change of bending moment at

the joint and mid-span during the transient heating. The fixed-end bending moment at the

support location (Position c) is directly comparable to the test measurement, which is

shown for two cases; ‘actual’ and ‘error’. The ‘error’ case accounts for the error made

during the initial set-up of these experiments, which caused the initial moment to be 25%

larger than the theoretical value of 120.8kNm.

The discrepancy shown between the analytical and test results for all tests at the support

was mainly due to this error, which generated a lower moment within the component

model at the initial loading stage. This accounts for the difference between the results of

the test and the component model. It also contributes to the small difference in deflection

at ambient temperature. During the tests, it was intended to keep the beam rotation at the

support constant at zero, using the loading jack Pe. However, it was later observed that

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(m

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COMP MODEL

TEST


174

this initial rotation had actually been approximately 0.0023 radian, and this value was

used throughout the tests.

The hogging moment measure in the test was measured from the reaction force at the load

cell positioned at the end of the beam test specimen (Figure 6.9). The gradual increase of

the moment during early stage of heating is due to the thermal gradient across the beam

section. Essentially, the hogging bending strains induced by rotational restraint at the

beam support have to counteract the thermal strains due to the temperature gradient

through the section depth. This leads to the formation of a large hogging moment across

the span during heating which counteracts the thermal bowing of the beam. In the case

where the section temperature gradient is higher, a larger hogging moment is formed.

This is consistent with the sectional temperature data shown in Section 6.4.2.

Subsequently, as the thermal gradient reduces, the additional hogging moment also

decreases.

Figure 6.29 Positions at which moments are plotted in Figures 6.30-6.32

b c d e f a

CM-n(c)-support

CM-n(d)-joint

CM-n(f)-mid-span


175

Figure 6.30 Moment distribution along the beam

for Test 2

Figure 6.31 Moment distribution along the beam

for Test 3

Figure 6.32 Moment distribution along the beam for

Test 4

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Error-CM-2(c) Actual-CM-2(c)

TEST 2

TEST 2

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TEST 3

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TEST 4

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TEST 4


176

6.6.3. Change of connection bolt axial forces and displacements

In this section, the change of individual bolt forces with temperature is detailed for only

Test 2. The force shown for each bolt row represents the total axial force transmitted

between the connected beams at this row, which has been simplified as an arrangement of

springs in series, as shown in Figure 6.18. In the beam splice connection, it is evident

from the graphs shown that the moment is mainly resisted by the flanges of the beam.

Most design recommendations (BCSA, 2002; AISC, 1999) assume that the flange splices

must carry all of the moment at the location of the flange splice. However, Green and

Kulak et al. (1987) found this to be a conservative assumption because the web splice

also has the capacity to transfer some of the moment, which is also verified here.

The axial forces for each row are shown in Figure 6.33, with increasing connection

temperatures. The axial force on each bolt row, produced by the bending moment,

increases proportionally with the distance of the bolt from the centreline of the splice

connection, which in this case coincides with the beam neutral axis. The critical bolts,

therefore, are those furthest away from this axis. In the region where both moment and

shear are present, it can be seen that both the bolts in the flange and the web carry

symmetric axial forces in the tension and compression zones. In general, the flange splice

forces (UP B/FL-1, UP B/FL-2, BOT B/FL-1 and BOT B/FL-2) follow a similar trend to

the bending moment curve. The axial force increases until the friction component enters

the ‘plateau’ region at Point 1, beyond which the reduction of the forces is more apparent.

This is consistent with the reduction of elastic modulus of the steel, which governs the

characteristics of the friction component. Although an increase of the web forces can be

observed, because of the proportion of the moment resisted by the flange splices is much

higher, the resistance reduction dictates the magnitude of the overall bolt forces. At Point

2, the friction forces on the bolts Web 1 and Web 4 enter the plateau phase, closely

followed by Web 2 and Web 3 at Point 3. The compressive beam flange (COMP B/FL)

force increases from temperature 579°C, initiated by the positive contact made by the

lower beam flanges.


177

Figure 6.33 Axial bolt-row forces on the beam splice connection

The forces on the flange splices are mainly resisted by the friction component (Figure

6.34) during the heating phase. This is due to the utilisation of high-strength friction grip

bolts in the splice connection, which define the behaviour of the connection as

predominantly a slip-critical joint. However, at later stages, the lap-jointed component

(plate bearing and bolt shear) starts to pick up strength as the frictional resistance reduces

with temperature. This explains the increasing bolt forces on the beam web at

temperatures beyond 517°C.

Figure 6.34 The friction and lap-joint forces on the flange splice.

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Fo

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(kN

)

Temperature ( C)

UP B/FL-1

UP B/FL-2

Web 1

Web 2

Web 3

Web 4

BOT B/FL-1

BOT B/FL-2

COMP B/FL

3 2 1 Web 1

Web 2

Web 3

Web 4

UP b/fl 1,2

BOT b/fl 1,2

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178

The displacements between the bolt components are shown in Figure 6.35. The

displacement of the bolt-row on the tensile beam flange is less than on the compressive

flange, due to the rotation of the beam which closes the gap between the lower beam

flanges. The contact made shifts the centre of rotation down to the lower beam flange

position. Thus, a slight decrease of the rate of displacement between the upper flanges

can be observed due to the increase of lever arm of the top bolts.

Figure 6.35 Bolt displacements on the beam splice connections

The behaviour of the flange splices is investigated further for Tests 2 and 3. In Test 3, the

bolts on the flange splice were doubled on either side of the beam gap. The force-

displacement relationships for the upper beam flange in the two tests are shown in Figure

6.36. Test 2 was designed as a partial-strength connection, with a capacity ratio

(connection moment capacity/beam moment capacity) of 0.73, whilst Test 3 had full

strength. When these two tests were subjected to the same loading of 122kN, the force

carried on the upper flange splice in Test 2 can be seen to be higher than that for Test 3.

From this graph, the displacement of the bolt progresses until it reaches a maximum of

12.1mm, when a residual 25% remains of the bolt diameter. This indicates that the bolts

are highly sheared, and failure due to upper plate distortion is unlikely (Figure 6.37a).

However, the case where the upper flange bolt breaks is badly represented by the

assumption of high ductility. If the solution process is able to deal with the negative

stiffness of the downhill component curves, simulating the actual bolt behaviour more

accurately (Figure 6.37b) is quite possible.

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Dis

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cem

ent(

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)

Temperature ( C)

UP B/FL-1

UP B/FL-2

Web 1

Web 2

Web 3

Web 4

BOT B/FL-1

BOT B/FL-2

COMP B/FL

Tension

Compression


179

Figure 6.36 Comparison of predicted upper beam flange forces for Tests 2 and 3.

Figure 6.37 Bolt behaviour on upper flange splice.

6.6.4. Component characteristic

The key component governing the connection’s behaviour has been identified in the last

section as the friction component. Therefore, the influence of the friction component

characteristic will be further investigated both locally and globally. Three different

configurations of the friction component are defined (Figure 6.38), which can be

summarized as;

a) Frict-A: This friction characteristic has been adopted in this research. On loading

of the connection, the maximum resistance is immediately achieved at

approximately 10% of the displacement of the clearance gap between the bolt

hole and the bolt. Subsequently, it enters a brief ‘plateau’ stage and then reduces

its resistance gradually while slip is occurring.

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(kN

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Upper beam flange-1

Test 2

Test 3

Shear force

(b) Bolt breaking at Upper

flange in Test 2

Shear force

(a) Distortion of upper flange plate


180

b) Frict-B: Initial behaviour before slip follows the characteristic of Frict-A.

However, the maximum resistance is retained with no reduction after slip occurs.

c) Frict-C: This friction behaviour was proposed by Sarraj (2007b), using a

triangular characteristic which gradually increases until slip occurs. The

maximum resistance then reduces linearly to zero force.

Figure 6.38 Friction component (a) Frict-A; (b) Frict-B and (c) Frict-C.

The influence of the frictional behaviour is investigated for Test 3. Firstly, the mid-span

deflection of the tested beam is compared in Figure 6.39 using these three friction

characteristics. The deflection trends at mid-span for Frict-A and Frict-B are observed to

behave very similarly. Even the failure temperatures at maximum deflection only differ

by 2°C. However, more obvious deflection behaviour can be observed for Frict-C, which

generated approximately 9.5% higher deflection that the other two models during the

initial heating phase.

Figure 6.39 Mid-span deflection comparison for Test 3.

The resultant deflection trend can be explained further by showing the individual

component forces on the beam-splice connection. The axial bolt forces on the upper beam

flange for these friction cases are shown in Figure 6.40. For Frict-A and Frict-B, similar

behaviour is seen until the analysis stops. This is consistent with the upper flange bolt-

Fo

rce

(kN

)

Displacement (mm)

(a)

Fo

rce

(kN

)

Displacement (mm)

(b)

Fo

rce

(kN

)

Displacement (mm)

(c)

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Frict-A

Frict-B

Frict-C

TEST 3


181

row behaviour explained in the previous section, which enters the plateau stage when its

force decreases. The individual behaviour of these two cases could not be captured, as

slip occurs at a very late stage of the analysis. More interesting are the bolt-row force

with the Frict-C model, which is evidently much lower, even though a relatively similar

pattern of behaviour is followed. This is consistent with the higher deflection at mid-span

of this model. Following the weakening of the steel, the initiation of force reduction can

be observed to be at approximately the same temperature.

Figure 6.40 Comparison of the bolt forces on upper flange splice.

The study of the friction component reflects the importance of friction on the slip-critical

behaviour of this type of beam-splice connection. All the friction models behave

adequately, with no occurrence of slip during the ambient-temperature serviceability

range.

6.6.5. End restraint of beams

Predicting the influence of end restraint of a beam under fire conditions is complex due to

the fire-induced forces developed during the course of heating. These fire-induced

restraint forces can influence the behaviour of the beam and consequently alter its failure

pattern. In practice beams are often designed as simply supported, even though their

physical connections are likely to provide significant end-fixity. This consideration can

be viewed as over-conservative and inaccurate, particularly for the case when structural

members are subjected to fire. This perspective was further reinforced during the

Cardington tests (Usmani, et al., 2001). The assessment of structural members in isolation

neglects the importance of structural continuity with adjacent members, providing axial

and rotational restraint to the beam. Significant internal stresses can develop due to

restraining the free thermal strain of a beam. Combined with high-temperatures in the

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Up

per

Fla

nge

Fo

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)

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Frict-A

Frict-B

Frict-C


182

steel, these restraints may affect the fire resistance times of the beams, and consequently

the survival time of the overall structural frame.

The component model is used to investigate this effect, in the context of the beam-splice

connection tests, by changing the boundary conditions at the beam-end support positions.

A comparison of mid-span deflections, firstly for the cases with complete axial restraint

and with freedom to move axially, is shown in Figure 6.41-Figure 6.43, for each test

specimen. The legend CM-2-AX indicates results generated by the component model, for

Test 2 with axial restraint. The case with no axial restraint is indicated with NAX.

In general terms, axial restraint influences the deflection rate of the structural beam in

response to the developing fire. The trend shown in all the models is that the mid-span

deflection increases with time, but for the cases with axial restraint CM-2-AX, CM-3-AX

and CM-3-AX the deflection rate is more pronounced before failure of the beam. In the

early stages of fire exposure, thermal expansion strain is induced in the beam member;

this produces increased length, as well as curvature induced by the temperature gradient

across the section depth. Because of the translational restraint to thermal expansion at the

beam’s ends, the mean thermal strain in particular causes two effects; firstly an axial

force which causes some reduction of the net thermal strain, and secondly a lateral

curvature which allows the elongated length of the beam to fit between its original end

positions. Neither of these effects occur in the case where the ends are free to translate.

For Test 2 (Figure 6.41), in which a partial-strength splice connection is considered, the

deflection reached a limiting value at a much lower temperature (T = 640.5°C) than for

the equivalent full-strength connection (T=705°C). In the cases considered, the ultimate

capacities of the connections are hardly influenced by the initially high deflection rates

caused by axial restraint. However, a larger discrepancy is observed for the model (CM-

2-AX) with the partial-strength connection.


183

Figure 6.41 Partial-strength connection (Test 2)

Figure 6.42 Full-strength connection (Test 3)

Figure 6.43 Full-strength connection (Test 4)

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CM-2-NAX

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TEST 3

CM-3-AX

CM-3-NAX

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CM-4-AX

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184

Under fire exposure, the restrained beam produces a different internal response which can

be explained in stages. The initial development of axial force is due to resistance to the

thermal expansion strain, which results in high compressive stress. This force is

dominated by the almost-elastic response when the beam expands as a result of heating.

This force continues to increase until the net thermal lengthening of the beam is

overtaken by the net shortening due to increased curvature as the beam loses bending

strength. As the temperature increases, the weakening of the steel causes an increased rate

of mid-span deflection. The compressive axial force gradually changes to tension until the

connection fails. If no failure occurs in the connection, the beam enters its catenary phase

in which tensile force develops in the beam and the load-bearing mechanism changes to a

cable-like one, until failure occurs in either the beam or its connections.

Figure 6.44 Axial forces for the case with end restraint.

6.6.6. Position of connection with respect to the beam

Current recommendations for design of splice connections include the principle that the

flange splices must be capable of carrying all of the bending moment at the location of

the splice. Although the design guides (BCSA, 2002; AISC, 2005) enforce no limitation

on the location of the splice connection, it is recommended that the beam web-splice

should have enough strength to resist the shear force at the position of the splice, when it

is located at the contraflexure point. This is because the contraflexure point migrates as

the applied load changes during the life of the structure (Ibrahim, 1995; Astaneh, 2005). It

may be necessary to rely on the flanges to make a contribution when there is a different

relationship between the shear force and bending moment at the connection. However,

this assumption is considered to be conservative, as the web splice also has the capacity

to transfer some moment. The shear capacity of a beam splice reduces if the web is

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Axia

l F

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e (k

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Test 3

Test 4


185

required to carry moment in addition to the shear (Green and Kulak, 1987). Therefore, the

influence of positioning the splice connection in a region where both shear and moment

are present under normal conditions is investigated in this section. Possible locations of

the beam splice connection along the beam are shown in Figure 6.45, including the

position of the contraflexure point (Lc-3) and the actual position of the connection in the

tests.

Figure 6.45 Positions of connection along the beam span

The moments generated at these connection positions are plotted (Figure 6.46-Figure

6.48) based on the moments on the support, joint and mid-span zones. At Lc-1, the

moment in the connection is highest, reaching 171kNm. At this point, the moment is

combined with shear at the connection. Similar force combinations are also identified at

position Lc-2 (The actual test connection position), but with much lower moment and the

same magnitude of shear force. The critical temperatures at which the connection failure

occurs for the case with the highest moment are the lowest, at 719.25°C. This is because

the moment imposed on the connection induces large axial forces on the flange splices,

and therefore decreases the failure temperature of the connection.

Position Lc-3 indicates the contraflexure point, for which the initial moment is nearly

zero. However, during the heating phase the moment increases due to the temperature

gradient across the cross-section, and to the rotational restraint at the support. The critical

temperature is increased when the connection is subjected to high shear force and low

bending moment. This suggests that the flange splices have not reached their maximum

b c d e f a

74kNm

120.84kN

m

Lc -1 = 225mm

Lc -2 = 450mm

Lc -3 = 990.6mm

Lc - 4 = 1325mm

Lc -1 Lc -3 Lc -4


186

capacity, thus allowing a longer survival time with lower moment. At Lc-4, the

connection is subjected to pure sagging moment.

Figure 6.46 Bending Moment in connection for various connection positions

Figure 6.47 End moment at support for various connection positions

Figure 6.48 Bending moment at mid-span for various connection positions

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Mo

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Lconn-1 Lconn-2 Lconn-3 Lconn-4

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Lsupp-3 Lsupp-4

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187

The behaviour of the splice can be described in terms of the adequacy of moment

resistance of the flanges. When the flanges can carry the total applied moment, the beam

and the splice will initially deform elastically with no relative displacement between

them. The web splice also makes an elastic contribution to the bending moment and the

applied shear. However, when the moment in the flange has reached its capacity as a slip-

critical connection, the flange plates will then slip. The web splice prevents the beam

undergoing any vertical slip deformation at this point. When the applied shear exceeds

the slipping shear capacity of the web bolts, major slip will occur. This indicates that,

with further loading, the beam will undergo some vertical slip at the location of the flange

splice (explained with Figure 6.37).

The load-carrying capacity of the flange splices is reduced in the presence of shear force.

In addition to this reduced capacity, if the connection is positioned in a region where the

bolt forces due to shear are comparable to those due to moment, the bending capacity is

further decreased. This is evident in the failure of WTC 5 building, for which the failure

of column-tree connections appeared to be due to combinations of vertical shear together

with tensile forces resulting from catenary sagging of the beams. The existence of high

shear load was attributable to the loads from collapsing upper floors.

6.7. Summary

A practical model for beam-splice connections has been developed for analysis of the

global behaviour of frames in fire. This has been shown to give good comparison with the

experimental data from three large-scale furnace tests. It can be seen that the rotational

behaviour and moment capacity of the connection depend essentially on its detailing,

particularly on the numbers of high-strength bolts used and the frictional resistance which

they generate. The partial-strength connection model of Test 2 managed to achieve a

fairly similar fire resistance, in terms of both temperature and time, to the full-strength

Test 3. The full-strength connection (Tests 3 and 4) is not the critical part of the beam at

ambient temperature, and plastic hinges should occur in the I-section instead. The use of

high-strength preloaded bolts dominates the load path of the splice connection, by

generating frictional resistance through the specified tensions in the bolts. At high

temperature, the contact pressures of the bolts are reduced, causing a reduction of the

friction resistance; it has been assumed here that the bolts remain in elastic tension, and

so the reduction of friction is controlled by the steel modulus reduction factor. This is

clearly a simplification of a combination of factors which affect the frictional resistance,

but seems adequate. When frictional resistance has been sufficiently dissipated, the bolts


188

begin to function as bearing bolts, and this may allow the connection to become the

critical part of the beam. The component-based model shows that the way the frictional

resistance degrades at elevated temperatures highly influences the overall response of the

splice connection, compared with its ambient-temperature performance. The component-

based methodology provides sufficient flexibility to allow realistic modelling of such

interactions between individual components within connections of this type.

Chapter 7: Conclusion and Recommendations

189

7. CONCLUSIONS AND RECOMMENDATIONS

Over the past three decades, structural steel connection design has been extensively

investigated, particularly with reference to their moment-rotation characteristics. The

assessment of connection response based on the realistic modelling of actual

characteristics has generated much interest, because of the enhanced structural

performance which they give compared with the traditional idealised connection

characteristics at elevated temperatures. Such information is needed by the growing

library of computational tools in order to make them independent of the availability of

test data. From the structural fire engineering perspective, designing for robust

connections is more justifiable and rational than prescribing unnecessary fire protection

for the connections. With the aim of achieving more robust connection design, a large

variety of possible connection details can be investigated in an attempt to enhance the

integrity of whole structures in fire.

7.1. Summary of the completed works

Fin-plate connections possess limited strength and stiffness, regardless of their practical

advantages in steel building constructions. The desirable characteristics of this connection

type concern its ability to act as a pin while transferring the end shear reaction of a beam

to its support without generating any large moments. In many cases, axial force is also

present in the connection, and this effect is further aggravated when subjected to elevated

temperatures. The limited performance of this type of connection can be enhanced by

ensuring that it has sufficient ductility at the fire limit state. Thus, the ductility of this

connection type has been a key feature of this thesis. The primary objective of the

research has been to facilitate the inclusion of the fin-plate connection’s joint behaviour

into global structural analysis as part of the performance-based structural fire engineering

design, in the framework of a component-based approach. The implementation of this

approach can be detailed in three successive stages, described in the following sections.

7.1.1. Characterisation of the component’s elements

This initial stage gives an overview fundamental behaviour of the fin-plate connections.

The identification of the component element has been derived on the basis of its

behaviour as an isolated connection, concentrating on the bolted lap-joint as its simplest

form. The active components of a fin-plate connection include the bearing and frictional

behaviour of the plates, as well as shearing of the bolts. The principles and calculation


190

procedure of these individual components have been described from previous

experimental studies, and compared against the recommended design procedures of the

Eurocodes and AISC.

The characteristic of the components determine the overall capacity of the connection.

While most previous researches have defined the maximum resistance of these

components, only a few have performed thorough investigations of the failure

characteristics. It is of importance to establish sufficient ductility of the whole connection

behaviour, maximising the contribution of each component. The characteristics described

for each component therefore incorporate its ‘down-hill’ behaviour, extending beyond the

maximum force capacity. The plate bearing deformation capacity is controlled by its end

distance. However, for the bolt shearing component, the bolt diameter determines its

deformation capacity.

Previous researchers (Rex and Easterling, 2003; Sarraj, 2007b) have under-estimated the

effect of frictional behaviour in the plates. This is supported by experimental evidence

from Yu et al. (2009) and Hirashima et al. (2010), which have shown significant

influence of the plate friction particularly during the initial stage of loading. The friction

characteristic has been simulated, and validated against experimental results.

The main concern in at this initial stage was the representation of the behaviour of the

identified components. While the desirable failure mode recommended in the design

guide is yielding of the plates, there are cases where a weaker bolt dominates the failure

of the connection. The behaviour of bolts at high temperatures also suggests that they

may perform in more ductile manner in fire.

7.1.2. Development of the fin-plate connection component method

The mechanical model for fin-plate connections involves an assembly process for the

identified components, as part of the main component of a bolt row. The individual

components are represented by nonlinear spring elements in series, and these are then

combined into one effective spring. The maximum resistance of this spring is determined

by the weakest component in this series. The assembly can be developed to include

multiple-bolt-row cases, in which the effective bolt row spring will be multiplied

accordingly. Additional vertical spring has also been considered, which was postulated to

be fairly rigid by previous research (Block, 2006; Hu, 2009).


191

The developed component model has been successfully incorporated into the finite

element software Vulcan. The implementation of the component model requires the

stiffness matrix of the spring elements to be derived, and this has been validated against

simple hand calculation. In the course of a fire, internal force reversal has been

considered by including the loading-unloading stage. During this development, the

primary points found were;

The classic Masing rule can be applied to describe the unloading behaviour of the

connection element. However, modifications have to be made when considering

the critical slip behaviour of bolts in fin-plate connections.

The ‘reference point’ concept adopted to represent the permanent deformations of

the components is justifiable, and is particularly useful when dealing with the

permanent deformations at changing temperatures.

With the addition of the vertical component to the component model, it has been possible

to investigate the influence of combined forces acting on individual bolt rows. The

capacity of a bolt is assumed to be reduced in the presence of a vertical component.

However, validating the combined case against actual experimental tests has so far shown

insignificant reduction of the bolt capacity.

7.1.3. Application of the fin-plate component model

As the developed component model was derived on the basis of the basic behaviour of a

bolted lap-joint in isolation, the model has been further extended to use in a moment-

resisting connection. Using similar loading approach, the component model has been

successfully implemented for beam-to-beam beam splice connection.

The developed component model has been validated against experimental data, and

compares well for most cases. The importance of the combination effect of the tying force

and shear force has been investigated, both on the whole connection and individual

elements. While certain limitations still exist, because of the nature of conventional quasi-

static analysis, the component model has been able to generate very reasonable

predictions of the connection response. This has been possible to perform such analysis

using the postulated high-ductility behaviour of individual components of the connection.

From the parametric studies, the use of higher property class bolts generally increases the

capacity of the connection, particularly at high temperatures. Although the strength the

bolt reduced with increasing temperature, the bolt behaves in a more ductile manner as


192

the steel becomes softer, thus increasing its ductility when exposed to high temperatures.

The effect of utilising an M24 bolt increases the connection capacity by 20% compared

with that given using M20 bolts for ambient temperature. Conversely, for elevated

temperature, a significant increase of the connection resistance has been observed,

reaching an enhancement of 92% at temperature 550°C. For varying bolt properties, the

increase of connection resistance followed a similar pattern to that using larger bolt

diameters. The maximum resistance when using bolt Grade 10.9 increases by

approximately 15% as compared with that of Grade 8.8 at ambient temperature and 45%

at elevated temperature. In all cases, bolt shear fracture tends to govern the failure of fin

plate connections at elevated temperatures.

In terms of fin-plate beam-column connections, the maximum resistance of the

connection can be achieved by arranging the connection as close as possible to the upper

beam flange. Moving the connection downward, towards the neutral axis, causes a

reduction of the connection resistance. However, it is observed that the rotational ductility

of the connection increases as the fin-plate is moved towards the beam’s centreline.

A study on connection behaviour in beam-column sub-frame has also been performed,

which was motivated by the known fact that the connection performance may be

enhanced by the structural continuity provided by adjacent beams, columns and floor

slabs. The connection element appears to behave logically when exposed to the

combination of bending, shear and axial force during the heating phase.

The developed component model has all the properties necessary to predict realistic

connection behaviour, both in isolation and in global frame analysis. The successful

application of the component model to different types of connections establishes the

versatility and reliability of this approach to represent the behaviour of connections at

ambient and elevated temperatures.

7.2. Recommendation for further work

Some relevant issues have been identified during this research that could possibly set

directions to further improvements to the developed component model for fin-plate

connections. These gaps and shortfalls mainly concern knowledge about connection

behaviour in fire, particularly on the characteristics of the connection elements, which

could not be properly addressed due to limited time and resources.


193

7.2.1. Component detailing

a) Available resources on the design details for bolt shear characteristics in fire

condition are scarce, particularly on double columns of bolts. Therefore, an

extension of research on this behaviour could produce additional evaluation data for

the proposed bolt-shear component.

b) The fin-plate weld on beam-to-column connections has been designed to avoid

failure according to design recommendation by the Eurocodes. However, brittle

failure caused by an “unzipping” action of the weld could cause premature failure of

the beam connection. Although there is a slim chances of this failure occurring for

normal details, but evidence of failures in the Cardington test and Wald (2005) test

show that it can happen in fire conditions.

7.2.2. Overall connection response

a) The currently developed model has defined the vertical shear component according

to a characterisation similar to the horizontal component. Consideration of the

possibility of the occurrence of vertical bolt tear-out failure, in the case of inadequate

bolt-pitch distance has been ignored. Thus, an improved and more detailed vertical

shear component is needed to enhance the model.

b) The effect of the shear deformation of the beam-end shear panel can influence the

connection either positively or negatively. Considering a frame in fire, some shear

yielding of the shear panel zones of beams can relieve the amount of plastic

deformation that must be accommodated in other regions of the frame. This happens

when the inelastic deformation of the connection when yielding is balanced between

the panel zone and other connection elements. Conversely, excessive shear

deformation of the panel zone may induce large secondary stresses into connections,

which may degrade their performance; increasing the force on the top bolt row, and

cause undesirable failure. Incorporating this effect would require a separate

component model for the shear panel, in addition to the existing model. This study

will necessarily enhance the understanding of fin-plate connection performance

coupled with that of the connected structural members.

c) Influence of composite action

Inclusion of details of the composite action between the beam and the slab may

be of great benefit in optimising the overall response of connection. For


194

example, it may delay the compressive contact of the lower beam flange and

column face.

Further extension of the component model to include the concrete slab in a

composite connection could enable more realistic modelling of the general

behaviour of composite buildings.

In parallel to this research, experimental tests on the concrete-filled tubular

columns utilising fin-plate connection have been conducted at the University of

Sheffield. They have extra flexibility because of their welding to the column

wall. Hence, another area of work should be considered and performed on fin-

plate connections.

7.3. Concluding remark

A component-based connection model has been shown to allow the behaviour of

connections to be included in practical global thermo-structural analysis, provided that

knowledge about the characteristics of key components is available from test data,

numerical simulation or analytical models. At this stage, a component model for fin-plate

connections has been developed, and successfully incorporated in Vulcan. The stiffness

matrix of the model has been derived to generate the connection’s response to

combinations of forces and displacements, and has subsequently been validated both at

ambient and elevated temperatures. This component model, when embedded in Vulcan,

allows direct analysis of whole structures or large substructures in fire, including of the

interactions between realistic connection behaviour and that of the adjacent structural

members.

A major modification to the model, which helps it to represent the real situation in fire,

allows the lower beam flange to come into contact with the column face when the

connection has undergone large rotation, sometimes in combination with either

compressive of tensile beam axial force. It has been found that the complex nature of load

reversal during a fire can be represented by adapting the Masing Rule, but with

modification of the initial slip phase to account for the case where bolt hole diameter are

larger than those of the bolts. As part of the global structural assembly of beam-column

and connection elements, the component-based model guarantees that the connection

deformations are accounted for within the equilibrium of the whole assembly. This can be

beneficial not only in design but also with assisting in the interpretation of experimental

and analytical responses of connections within structures in fire.

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Appendix

206

APPENDIX

A.1 Beam-to-column fin-plate connection configuration

Detailing of the beam-column;

Column size UC 254 × 254 × 89

Steel grade(column) S 355

Beam size UB 305 ×165 × 40 × 6

Steel grade (beam) S 275

Detailing of the fin-plate connection;

Diameter of the bolt, db = 20mm (M20 Grade 8.8)

Fin-plate (Grade S275);

Thickness, tf = 8mm (≤ 0.5db)

Length, l = 200mm (> 0.6D for 305 UB)

Depth, = 100mm

Clearance gap, = 10mm

Fin-plate connection design method (BCSA, 2002)

Shear strength of the bolts

From capacity table in H.27 in yellow pages;

Connection shear capacity = 113kN > 100kN

For single line of bolts;

Resultant force on outermost bolt due to direct shear and moment;

Direct force per bolt,

Eccentric bending moment,

Modulus of bolt group,

Force on the outermost bolt due to moment,

Appendix

207

Resultant force per bolt,

For 305 x 165 x 40 UB Grade S275

Bearing capacity of bolt,

Therefore,

Bolt group shear strength,

a) Shear strength of the plate

Shear area,

Net area,

Plain shear capacity of fin plate,

Block shear capacity of fin plate,

(where k = 0.5, and

Appendix

208

Therefore,

Shear capacity of fin plate,

b) Shear and bending interaction

Shear criteria for bending;

Eccentric moment,

Fin-plate connection design method (EC3-1-8, 2005b; EC3-1-1, 2005d)

Partial safety factors

γMO = 1.0

γM2 = 1.25 (for shear resistance at ULS)

γM,u = 1.1 (for tying resistance at ULS)

a) Joint shear resistance

Bolts in shear

Shear resistance of a single bolt Fv,Rd given in Table 3.4 (EC3-1-8)

Appendix

209

Where; αV = 0.6 for Class 8.8 bolts

For a single vertical line of bolts, α = 0

Therefore,


For a single vertical line of bolts, α = 0 and β = 0.42.

The bearing resistance of a single bolt, Fb,Rd,ver is given in Table 3.4 (EC3-1-8);

Where;

Therefore,

Similarly, for horizontal bearing resistance, Fb,Rd,hor

Appendix

210

Beam web in bearing


The bearing resistance of a single bolt, Fb,Rd,ver is given in Table 3.4 (EC3-1-8);

Where;

Therefore,

Similarly, for horizontal bearing resistance, Fb,Rd,hor

b) Joint tying resistance

Bolts in shear

Appendix

211

Where,



The bearing resistance of a single bolt, Fb,Rd,hor is given in Table 3.4 (EC3-1-8);

Where;

Therefore,

Beam web in bearing


The bearing resistance of a single bolt, Fb,Rd,hor is given in Table 3.4 (EC3-1-8);

Where;

Appendix

212

Therefore,

c) Ductility check

If then

From the summary table

Since , therefore the ductility is ensured.

Appendix

213

A.2 Design of beam section

Characteristic floor loading

Permanent action, gk 3.5kN/m2

Variable action, qk 2.0/m2

Floor geometry;

Beam span, L =7.0m

Spacing of beam = 6.0m

Material properties;

Steel grade, fy = 275 N/mm2

Elastic Modulus , Ea = 210000N/mm2

Capacity of the section at ambient temperature

The beam section chosen is 454×152×60 UB, which is Class 1 section.

At ultimate limit state (ULS)

Partial factors for actions is obtained from EN 1990, Table A1.2 (B)

Partial factor for permanent actions γG 1.35

Partial factor for permanent action γQ 1.5

Reduction factor ξ 0.85

Design value of combined actions on beams,

γG Gk + γQ Qk

= (1.35 × 3.5)* 6.0 + (1.35 × 2.0)*6.0

= 28.35+16.2

= 44.55kN/m

Design moment and shear force

Maximum design moment MED occurs at mid-span, and for bending about major axis is:

Appendix

214

Maximum design shear VED occurs at mid-span, and for bending about major axis is:

Moment resistance of chosen section, 454×152×60 UB,

Plastic modulus, Wpl = 1287.0 cm3

Moment capacity, Mpl, Rd = Wpl × fy

= 353.9kNm (Mpl, Rd > Msd, OK)

Shear resistance

Shear area , Av = 3931.mm2

Shear capacity, Vpl, Rd = Av ( fy / √3)

= 624.3 kNm (Vpl, Rd > Vsd, OK)

Design loading in fire

Design moment at the fire limit state ( EN 1993-1-2, Cl 2.4.2)

Where;

Combination factor, Ψ1,1 = 0.5

For Gk = 3.5 kN/m2 , Qk = 2.0 kN/m

2

Appendix

215

Reduction factor,

Therefore,

Design moment in fire, Mfi, d = 0.57×318.35

= 181.46 kNm

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