Static strength of tubular x joints with chord fully infilled with high strength grout

STATIC STRENGTH OF TUBULAR X-JOINT WITH
CHORD FULLY INFILLED WITH HIGH STRENGTH
GROUT











CHEN ZHUO










A THESIS SUBMITTED

FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF CIVIL ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2010


i


ACKNOWLEDGEMENT

I would like to thank my supervisors Professor Choo Yoo Sang and Dr. Qian Xudong, for
their invaluable assistance in planning and executing this work, and for their patient
advice and support throughout all my research at National University of Singapore.
My thanks go to Professor J. Wardenier and Professor Peter Marshall for their helpful
discussions and valuable contributions during the Joint Industry Project (JIP).
The friendship, advice and practical assistance offered by my colleagues and friends at
Center for Offshore Research and Engineering (NUS) are grateful appreciated. In
particular, I thank Mr. Shen Wei, Mr. Wah Yifeng and Dr. Wang Zhen for their kind help
during my experimental work.
All experiments have been carried out in the Structural Engineering Laboratory of
National University of Singapore with the help of all the staff there. Special thanks are
extended to Mr.Koh, Mr. Ang and Annie for their much helpful advice during the tests.
I wish to acknowledge the research scholarship I have received from the National
University of Singapore and the funding from JIP. Their financial assistance has enabled
me to devote time to writing this thesis without the additional pressure of financial
difficulties.
Finally, my heartfelt thanks go to my parents, family and friends for their support during
the last few years.

ii


TABLE OF COTENTS

ACKNOWLEDGEMENT I
TABLE OF COTENTS II
NONMENCLATURE IX
LIST OF FIGURES XIV
LIST OF TABLES XXII
SUMMARY XXV

CHAPTER 1 INTRODUCTION 1
1.1 BACKGROUND 1
1.2 MOTIVATION 3
1.3 SCOPE AND AIMS OF RESEARCH 7
1.3.1 Scope of reserach 7
1.3.2 Main ojectives of reserach 8
1.4 CONTENTS OF CURRENT THESIS 8
CHAPTER 2 PREVIOUS RESEARCH AND DESIGN FORMULATION 10
2.1
REVIEW OF RESEARCH ON AS-WELDED CHS JOINTS 10
2.1.1 Experimental research 10
2.1.2 Numerical research 14
2.2
ANALYTICAL MODEL FOR CHS JOINTS 15
2.2.1 Punching shear model 16

iii


2.2.2 Ring Model 18
2.3 GENERAL FAILURE CRITERIA 19
2.3.1 Yura’s deformation limit 19
2.3.2 Lu’s deformation limit 21
2.3.3 Plastic limit load approach 22
2.3.4 Plastic strain limit 22
2.4 RESEARCH ON GROUTED JOINT 22
2.5 EXISTING GUIDANCE 25
2.5.1 Guidance for as-welded CHS joints 25
2.5.2 Guidance for fully grouted joint 28
2.6 SUMMARY 28
CHAPTER 3 DESCRIPTION OF TEST PROGRAM 30
3.1 OVERVIEW OF TEST PROGRAM 30
3.2 DESCRIPTION OF IN-PLANE BENDING TEST 31
3.2.1 Test specimens 31
3.2.2 Test rig and set-up for in-plane bending test 33
3.2.3 Instrumentation 35
3.3
DESCRIPTION OF AXIAL LOADING TEST 38
3.3.1 Specimens 38
3.3.2 Test rig and set up for axial loading test 40
3.3.3 Instrumentation 42
3.4
WELDING OF TEST SPECIMENS 45
3.5 MATERIAL PROPERTIES 47

iv


3.5.1 Circular Hollow Sections 47
3.5.2 Grout 48
3.6 GROUTING PROCEDURE FOR SPECIMENS 49
3.7 TEST SEQUENCE 51
3.7.1 Test order of specimens 51
3.7.2 Test procedure 52
CHAPTER 4 SUMMARY AND DISCUSSIONS OF TEST RESULTS 54
4.1 AXIAL TENSILE LOADING TEST 54
4.1.1 Failure mechanisms 54
4.1.2 Load-deflection curves 70
4.1.3 Elastic stress distributions 78
4.1.4 Ultimate strength 81
4.1.5 Comparisons with codes 84
4.1.6 Summary 85
4.2 AXIAL COMPRESSIVE LOADING TEST 87
4.2.1 Failure mechanism 87
4.2.2 Load-deflection curve 89
4.2.3 Local stress distributions 92
4.2.4 Ultimate strength 92
4.2.5 Summary 93
4.3
IN-PLANE BENDING TEST 93
4.3.1 Summary of the test observations and the failure modes 93
4.3.2 Load deflection curves 96

v


4.3.3 Ultimate strength 100
4.3.4 Comparison with design codes 101
4.3.5 Local stress distributions in elastic range 103
4.3.6 Discussions of test results 105
CHAPTER 5 NEW ANALYTICAL MODELS FOR FULLY GROUTED JOINTS
107
5.1 INTRODUCTION 107
5.2 ANALYTICAL FAILURE MODEL FOR A FULLY GROUTED X-JOINT SUBJECTED TO AXIAL
TENSILE LOADING
108
5.2.1 Summary of the failure mechanism 108
5.2.2 Review of Analytical models for as-welded joints 114
5.2.3 A modified punching shear model for fully grouted X-joints 117
5.2.4 New equations for the ultimate strength of fully grouted X-joints 120
5.2.5 Comparisons between the test results and the predictions from proposed
equations 125
5.3
ANALYTICAL FAILURE MODEL FOR THE FULLY GROUTED JOINT SUBJECTED TO IPB132
5.3.1 Summary of the failure mechanism of fully grouted X-joints subjected to IPB
132
5.3.2 New analytical failure model for fully grouted X-joint subjected to IPB 135
5.3.3 Comparisons between the test results and the predictions from the proposed
equations 137
5.4
SUMMARY 145

vi


CHAPTER 6 THE BASES AND THE VERIFICATIONS OF THE FE ANALYSES
147
6.1 NUMERICAL PROCEDURES 147
6.1.1 Modeling with PATRAN 148
6.1.2 Analysis with ABAQUS 148
6.2 MATERIAL PROPERTIES 149
6.2.1 Steel 149
6.2.2 Grout 150
6.3 CONVERGENCE ANALYSIS 152
6.4 BOUNDARY CONDITIONS 154
6.5 CONTACT DEFINITION 158
6.6 ELEMENT TYPE 162
6.7 PROFILE OF WELDS 164
6.8 VERIFICATION OF FE ANALYSIS 166
6.8.1 Failure mechanism 166
6.8.2 Load-deformation curves 167
6.8.3 Ultimate strength 171
6.9
SUMMARY 173
CHAPTER 7 FE ANALYSES OF GROUTED TUBULAR JOINTS USING
CONTINUUM DAMAGE MECHANICS APPROACH 174
7.1 INTRODUCTION 174
7.2
BACKGROUND TO CONTINUUM DAMAGE MECHANICS (CDM) 174
7.3 EFFECT OF STRESS TRIAXIALITY 178

vii


7.4 DAMAGE MODEL IN ABAQUS 181
7.5 STUDY ON THE EFFECT OF Ε
D
, U
F
0
AND D
C
184
7.6 DETERMINATIONS OF THE MATERIAL CONSTANTS 186
7.6.1 Determinaitons of the material constants 187
7.6.2 Effect of the element size 189
7.7 VERIFICATION OF FE ANALYSES ADOPTED CDM APPROACH 191
7.8 EFFECT OF LOADING RATE 194
7.9 TECHNIQUE TO IMPROVE THE CALCULATION EFFICIENCY 196
7.10 SUMMARY 197
CHAPTER 8 PARAMETRIC STUDY BY FINITE ELEMENT METHOD (FEM)
198
8.1 INTRODUCTION 198
8.2 SCOPE OF PARAMETRIC STUDY 199
8.3 FE CONSIDERATIONS 200
8.4 FAILURE CRITERIA 200
8.5
RESULTS FOR AXIAL LOADING 201
8.5.1 Failure mechanism 201
8.5.2 Effect of joint parameters 203
8.5.3 Verification of design equations 205

8.5.4 Improvements in strength compared to as-welded joints 206
8.5.5 Representation of joint stiffness 209
8.6
RESULTS FOR IPB 213
8.6.1 Failure mechanism 213


viii


8.6.2 Effect of joint parameters 215
8.6.3 Verification of design equation 217
8.6.4 Improvement in strength comparing with as-welded joints 218
8.6.5 Representation of joint stiffness 219
8.7
RESULTS FOR OPB 222
8.7.1 Failure mechanism 222
8.7.2 Effect of joint parameters 224
8.7.3 Verification of design equation 226
8.7.4 Improvement in strength comparing with as-welded joints 227
8.7.5 Representation of joint stiffness 228
8.8
SUMMARY 231
CHAPTER 9 CONCLUSIONS 234
9.1 MAIN FINDINGS 234
9.1.1 Experimental investigations on the behavior of fully grouted joints 234
9.1.2 New analytical failure model 236
9.1.3 Application of CDM approach in analyses of tubular joints 238
9.1.4 Numerical investigations on the static behavior of fully grouted joints 239
9.2

FUTURE WORK 241
REFERENCES 243
APPENDIX A TRANSFORMATION OF STRAIN MEASUREMENTS 252
APPENDIX B CONVERSION OF ENGINEERING STRAIN & STRESS 257
APPENDIX C VERIFICATION OF RECORDED LOADING 258


ix



NONMENCLATURE

A: Cross-sectional area of brace member
B
e
: Effective width
C: Damage constant in McClintock-R.T. Model
C
1
& C
3
: Chord load factor coefficients
D
0
: outer diameter of chord
D
n
, D: Damage parameter
D

c
: Critical value of damage at macro crack initiation
E: Young’s Modulus
E: Young’s Modulus
F
a
: Allowable compressive stress in column
F
b
: Allowable bending stress
FS: Factor of safety
F
u
: Ultimate stress of chord
F
y
: Yield stress of chord
K: General material hardening parameters
K
a
: Effective brace-to-chord intersection length factor
L: Characteristic length of element
L
0
: length of chord
M: General material hardening parameters
M
BY
: Moment at which full cross section yielding occurred in braces.

M
c
: Nominal axial load in the chord


x



M
crack
: Moment at which first noticeable surface crack was observed
M
max
: Maximum recorded moment during a test
M
P
: Plastic moment capacity of joint
M
PC
: Plastic moment capacity in the chord
M
s
: Moment corresponding to the serviceability limit
M
u
: Ultimate moment capacity of joint
M
y
: Elastic moment capacity of joint

M
y
: First chord yield moment
P: Axial load in brace
P
BY
: Axial load corresponding to brace yielding. The corresponding
P
c
: Nominal axial load in the chord
P
crack
: Axial load corresponding to crack initiation
P
DL
: Axial load corresponding to deformation limit of 0.03D
0
P
max
: Maximum axial load recorded during test
P
s
: Axial load corresponding to the serviceability limit
P
SL
: Axial load corresponding to serviceability limit of 0.01D
0

P
u

,: Ultimate axial capacity of joint
P
YC
: Yield axial capacity of chord
Q
f
: Chord stress modifier
Q
u
: Geometry modifier
S: Plastic section modulus of brace member
S
0
: Material and temperature dependent parameters
T
0
: thickness of chord


xi



T
p
: Tensile force along brace-to-chord intersection
W
e
: Elastic work
W

p
: Plastic work
V
p
: Shear force along brace-to-chord intersection
c: Joint elastic range factor
c
1
: Effective distance factor between brace saddles
d: outer diameter of brace
f
a
: Axial stress in eccentrically compressed column
f
y
: Yield stress of brace
f
u
: Ultimate stress of brace
f
b
: Bending stress in eccentrically compressed column
f
op
: Chord stress as results of additional axial force or bending moment
k: Hardening parameter of chord material
k
0
: Initial joint stiffness
k

n
: Joint stiffness in plastic stage w
k
T
: Tensile force portion factor
k
V
: Shear force portion factor
m: Hardening parameter of chord material
m
p
: Plastic moment per unit length of chord
n: Joint stiffness hardening factor
p: equivalent plastic strain (p= (2/3ε
p
:ε
p
)
1/2
)
p
d
: Damage strain threshold
p
R
: Fracture strain
s
0
: Material and temperature dependent parameters

xii



t: thickness of brace
u
f
: Effective plastic displacement at fracture
u
f
0
: one dimensional plastic displacement at fracture
α: the ratio of chord length to chord diameter(L
0
/D
0
)
β: the ratio of brace diameter to chord diameter (d/D
0
)
δ: Chord deformation
δ
brace
: Brace elongation
ε: True strain
ε
d
: Uni-axial damage strain threshold
ε

p
: Plastic strain tensor;
ε
R
: Uni-axial strain at fracture
ε
y
: chord yielding strain
φ : Joint rotation
φ: Stress reduction factor for axial loaded column
γ: the ratio of chord diameter to twice of chord thickness(D
0
/2T
0
)
λ: Ratio of plastic work to elastic work
τ: the ratio of brace thickness to chord thickness
τ
max
: Maximum shear stress in chord
θ: the angle between brace and chord axis
θ
yura
: Yura’s deformation limit
σ
~
: Effective stress
σ
1
& σ

2
: Principle stresses
σ
cu
: Compressive strength grout


xiii



σ
eq
: Mises equivalent stress
σ
H
: hydrostatic stress
σ
nom
: Average tensile stress in brace
σ
tu
: Tensile strength of grout
σ
τ
: Normal stress
Ψ: Local dihedral angle
ν: Poisson’s ratio
ρ: density of the material in the element
∆: Global displacement at the loading point

∆
BY
: Joint deformation corresponding to P
BY

∆
crack
: Joint deformation corresponding to P
crack
∆
max
: Joint deformation corresponding to P
max

∆t: Maximum stable time increment size limit
∆
yura:
Yura’s chord deformation limit










xiv

LIST OF FIGURES

Figure 1-1Typical jacket and jack-up Platforms 1
Figure 1-2 Typical tubular joint and definition of symbols 2
Figure 1-3 Pile-to-sleeve connections 3
Figure 1-4 Grout-filling of tubular member 5
Figure 1-5 Grouted tubular joint 5
Figure 2-1 Punching shear model 16
Figure 2-2 Ring model (Wardenier, 2002) 18
Figure 3-1 X1/X1-G configuration and dimensions 32
Figure 3-2 X2/X2-G configuration and dimensions 32
Figure 3-3 A schematic isometric view of the 10,000 kN test rig 34
Figure 3-4 Set-up of in-plane bending test 34
Figure 3-5 Typical lay-out of single element gauges on braces 36
Figure 3-6 Typical lay-out of rosette gauges on chord 37
Figure 3-7 Typical transducer lay out 38
Figure 3-8 As-welded and fully grouted joint configuration and dimensions 39
Figure 3-9 Test set-up for compressive test 41
Figure 3-10 Test set-up for tensile test 42
Figure 3-11 Lay-out of rosette gauges 44
Figure 3-12 Lay-out of single element gauges 44
Figure 3-13 Lay-out of transducer 45


xv

Figure 3-14 Welded Tubular Connections – Shielded Metal Arc Welding (AWS D1.1,
1998) 46
Figure 3-15 Equipment used for grouting 50
Figure 3-16 the displacement of water by the injected grout 51
Figure 4-1 Chord yielding of X3 during Test 55
Figure 4-2 Brace yielding during test 55
Figure 4-3 Failure shape of X3 56
Figure 4-4 Failure shape of X5 57
Figure 4-5 Chord yielding during test 57
Figure 4-6 Crack initiation 58
Figure 4-7 Failure shape of X4 after test 58
Figure 4-8 Failure shape of X6 after test 59
Figure 4-9 Failure shape of X7 after test 59
Figure 4-10 First yielding along brace-to-chord intersection 61
Figure 4-11 Brace yielding of fully grouted joints 61
Figure 4-12 Typical failure shape fully grouted joint with β=1.0 62
Figure 4-13 Typical failure shape fully grouted joint with β=0.7 63
Figure 4-14 Comparisons between chord deformation (β=0.7) 65
Figure 4-15 Comparison between yielding patterns – over all (β=0.7) 66
Figure 4-16 Comparison between yielding patterns – close-up (β=0.7) 66
Figure 4-17 Crack orientation in as-welded joints (β=0.7) 67
Figure 4-18 Crack orientation in fully grouted joints (β=0.7) 67
Figure 4-19 Comparisons between chord deformation (β=1.0) 68


xvi



Figure 4-20 Comparisons between yielding patterns (β=1.0) 69

Figure 4-21 Crack orientation in as-welded joints (β=1.0) 69
Figure 4-22 Crack orientation in fully grouted joints (β=1.0) 69
Figure 4-23 Breakdown of the global displacement 71
Figure 4-24 Comparison of measured and calculated chord deformation 72
Figure 4-25 X3 & X3-G-T (β=1.0, γ=12.96) 74
Figure 4-26 X5 & X5-G-T (β=1.0, γ=20.25) 74
Figure 4-27 X4 & X4-G-T (β=0.7, γ=12.96) 75
Figure 4-28 X6 & X6-G-T (β=0.7, γ=20.25) 75
Figure 4-29 X7 & X7-G-T (β=0.7, γ=28.56) 75
Figure 4-30 Normalized chord deformation of fully grouted joints (β=1.0) 77
Figure 4-31 Stress distribution in brace cross section near joint (β=1.0) 79
Figure 4-32 Stress distribution in brace cross section near joint (β=0.7) 79
Figure 4-33 Stress distribution in chord along brace-to-chord intersection (β=1.0) 80
Figure 4-34 Stress distribution in chord along brace-to-chord intersection (β=0.7) 80
Figure 4-35 Static capacity improvements of fully grouted joints 83
Figure 4-36 Comparison between test results and joint strength equation (as-welded joint)
84
Figure 4-37 Comparison between test results and joint strength equation (fully grouted
joint) 85
Figure 4-38 Failure shape of X6-G-C 88
Figure 4-39 Infilled grout after test 89
Figure 4-40 Column in compression 90


xvii



Figure 4-41 Global load-displacement curve 91
Figure 4-42 Mises stress distribution in the chord along the brace-to-chord intersection 92

Figure 4-43 Grout conditions after test 96
Figure 4-44 Failure conditions of specimens (with cut-sections) 94
Figure 4-45 Bending moment distribution along brace axes 97
Figure 4-46 IPB Moment versus rotation curves 98
Figure 4-47 Static capacity improvements of fully grouted joints under IPB 101
Figure 4-48 Stress distribution in the chord along the brace-to-chord intersection with
brace under IPB 103
Figure 5-1 Deformation pattern of as-welded X-joints at failure 110
Figure 5-2 Deformation pattern of fully grouted X-joints at failure 110
Figure 5-3 Chord plastification of joints 111
Figure 5-4 Elastic stress distribution in an X-joint 113
Figure 5-5 Ring model 115
Figure 5-6 Punching shear model 115
Figure 5-7 Modified Punching Shear Model 118
Figure 5-8 Calculation of V
p
and T
p
119
Figure 5-9 Distribution of Dihedral Angle Ψ (θ=90
o
) 121
Figure 5-10 Distributions of k
T
and k
V
against β 125
Figure 5-11 Non-dimension ultimate load against β 127
Figure 5-12 Non-dimension ultimate load against γ 130
Figure 5-13 Illustraton of the proposed equation for brace axil tension 131

Figure 5-14 Comparison between test data and proposed equations 131


xviii



Figure 5-15 Shifting of rotation center 133
Figure 5-16 Elastic stress distribution in an X-joint subjected to IPB 134
Figure 5-17 Stress distributions in punching model under IPB for as-welded X- joint . 135
Figure 5-18 Stress distributions in punching model under IPB for fully grouted X-joint
137
Figure 5-19 Maximum bending moment against β 141
Figure 5-20 Maximum bending moment against γ 142
Figure 5-21 Illustration of the proposed equation for IPB 143
Figure 5-22 Comparison between test data and predictions 145
Figure 6-1 Typical FE Model of joints for different loading conditions 148
Figure 6-2 Material input for steel 150
Figure 6-3 Material input for grout 151
Figure 6-4 Comparisons between material models for grout 152
Figure 6-5 Mesh scheme for convergence analysis 152
Figure 6-6 Convergence study of FE models 154
Figure 6-7 Boundary condition for X-join subjected to axial loading 155
Figure 6-8 Loading conditions for bending 155
Figure 6-9 Boundary condition for X-join subjected to IPB 156
Figure 6-10 Boundary condition for X-join subjected to IPB 157
Figure 6-11 Pure bending conditions for FE models 158
Figure 6-12 Comparison between the loading conditions 158
Figure 6-13 The gap between the chord and the in-filled grout 160
Figure 6-14 Comparisons of contact conditions 162

xix



Figure 6-15 Comparisons of element type for fully grouted joints 163
Figure 6-16 Comparisons of element type for as-welded joints 163
Figure 6-17 Welding Profile in FE model 164
Figure 6-18 FE models with different weld size 165
Figure 6-19 Comparisons between FE models with different weld size 165
Figure 6-20 Comparisons between failure shape of FE model and corresponding
specimen (IPB) 167
Figure 6-21 Comparisons between failure shape of FE model and corresponding
specimen (Axial) 167
Figure 6-22 X1 & X1-G subjected to IPB (β=0.8, γ=16.8) 168
Figure 6-23 X2 & X2-G subjected to IPB (β=1.0, γ=9.5) 168
Figure 6-24 Fully grouted joint (DT2) subjected to OPB (β=0.7, γ=12.7) 168
Figure 6-25 X3 & X3-G-T subjected to axial loading (β=1.0, 12.96) 169
Figure 6-26 X4 & X4-G-T subjected to axial loading (β=0.7, 12.96) 169
Figure 6-27 X5 & X5-G-T subjected to axial loading (β=1.0, 20.25) 170
Figure 6-28 X6 & X6-G-T subjected to axial loading (β=0.7, 20.25) 170
Figure 6-29 X7 & X7-G-T subjected to axial loading (β=0.7, 28.56) 170
Figure 7-1 Softening behavior of materials 175
Figure 7-2 Damaged element (Lemaitre, 1985) 177
Figure 7-3 Influence of triaxiality on strain to rupture for A508 steel (Lemaitre, 1985) 180
Figure 7-4 p
d
vs. σ
H

/σ
eq
curve defined in ABAQUS 182
Figure 7-5 Three-dimensional model for the coupon specimen 184
Figure 7-6 Failure pattern of the FE model for the coupon specimen 185


xx



Figure 7-7 Effect of ε
d
and u
f
0
(in mm) on the static behavior of the coupon specimen. 186
Figure 7-8 Effect of D
c
on the static behavior of the coupon specimen 186
Figure 7-9 Illustration of true stress-strain curve adopted for analyses 188
Figure 7-10 Comparison of experimental and analytical nominal stress-strain diagram 189
Figure 7-11 FE model of the grouted X-joint 191
Figure 7-12 Failure of X-joint subjected to IPB 192
Figure 7-13 Failure of X-joint subjected to axial loading 192
Figure 7-14 Comparison of FE and experimental results (IPB) 194
Figure 7-15 Comparison of FE and experimental results (Axial loading) 193
Figure 7-16 Comparison of joint response using different time duration 195
Figure 7-17 KE/IE distribution along time duration 196
Figure 8-1 Loading conditions for joints subjected to IPB and OPB 200

Figure 8-2 Equivalent plastic strain (PEEQ) distributions in joints 203
Figure 8-3 Joint strength against β 204
Figure 8-4 Joint strength against γ 205
Figure 8-5 Comparison between FE data and proposed equations 206
Figure 8-6 Strength enhancement variation with respect to β and γ 207
Figure 8-7 Load deformation characteristic of fully grouted joints 209
Figure 8-8 The logarithm of load deformation characteristic of fully grouted joints 209
Figure 8-9 Distribution of k
0
211
Figure 8-10 Distribution of k
n
212
Figure 8-11 The value of c against β 213
Figure 8-12 Failure of fully grouted joint subjected to IPB 214


xxi



Figure 8-13 Joint strength against β 215
Figure 8-14 Joint strength against γ 216
Figure 8-15 Comparison between test data and proposed equations 217
Figure 8-16 Strength enhancement variation with respect to β and γ 218
Figure 8-17 Distribution of k
0
220
Figure 8-18 Distribution of k
n

221
Figure 8-19 The value of c against β 222
Figure 8-20 Failure of fully grouted joint subjected to OPB 223
Figure 8-21 Joint strength against β 224
Figure 8-22 Joint strength against γ 225
Figure 8-23 Comparison between test data and proposed equations 226
Figure 8-24 Strength enhancement variation with respect to β and γ 227
Figure 8-25 Distribution of k
0
229
Figure 8-26 Distribution of k
n
230
Figure 8-27 The value of c against β 231




xxii



LIST OF TABLES

Table 2-1 Geometry range for Yura’s database 12
Table 2-2 Geometry range for Kurobane’s database (brace axial load) 12
Table 2-3 Summary of previous grouted joint tests 25
Table 2-4 Chord strength factor Q
u
for X-joint 27

Table 2-5 Chord stress factor Q
f
for X-joint 27
Table 2-6 Chord load factor coefficients C
1
and C
3
(Pecknold et al, 2007) 27
Table 2-7 Q
u
factor for grouted joint (Pecknold et al, 2007) 28
Table 3-1 Test matrix for X- joints subjected to in-plane bending moment - Specimen
Designation
1
31
Table 3-2 Test matrix for X- joints subjected to axial loading - Specimen Designation 31
Table 3-3 Nominal dimensions for X-joints subjected in-plane bending 31
Table 3-4 Summary of the actual dimensions 33
Table 3-5 Nominal dimensions for fully grouted and corresponding as-welded joints 39
Table 3-6 Measured dimensions for specimens 40
Table 3-7 Measured weld size 46
Table 3-8 Mechanical properties of steel tubes for stage 1 referenced by test specimen. 47
Table 3-9 Mechanical properties of steel tubes for stage 2 referenced by section
specification 48
Table 3-10 Material properties of grout for specimens at phase 1 (in-plane bending test)
49
Table 3-11 Material properties of grout for specimens at phase 2 Axial loading test) 49


xxiii

Table 3-12 Specimen specifications and test date for in-plane bending test 51
Table 3-13 Specimen specification and test date for axial loading test 52
Table 4-1 Summary of ultimate strength of specimens subjected to axial tensile loading82
Table 4-2 Summary of ultimate strength of specimens subjected to axial compressive
loading 93
Table 4-3 Ultimate strength and failure modes of specimen 100
Table 4-4 Comparison between test results and prediction of design codes 102
Table 5-1 Current database for X and T joints subjected to axial tensile load 126
Table 5-2 Comparison between test data and proposed equations 132
Table 5-3 Current database for the ultimate load of X- and T-joints subjected to IPB 139
Table 5-4 Current database for the ultimate load of X- and T-joints subjected to OPB. 140
Table 5-5 Comparison between test data and predictions (IPB) 144
Table 5-6 Comparison between test data and predictions (OPB) 144
Table 6-1 Convergence analysis of fully grouted joint subject to in-plane bending (IPB)
153
Table 6-2 Convergence analysis of as-welded joint subject to in-plane bending (IPB). 153
Table 6-3 Convergence analysis of fully grouted joint subject to axial tensile loading. 153
Table 6-4 Convergence analysis of as-welded joint subject to axial tensile loading 154
Table 6-5 Parameters of the specimen for the FE verification of OPB loading case 166
Table 6-6 Comparison of ultimate strength between FE and test 171
Table 6-7 Comparison between test ultimate strengths and FE predictions at deformation
limit 172
Table 7-1 Effect of element size 190


xxiv

Table 7-2 Identified damage parameters 190
Table 7-3 Comparison of experimental and numerical strength 194
Table 8-1 Scope of parametric study 199
Table 8-2 Failure mode of fully grouted joint under brace axial tension 202
Table 8-3 Comparison between ultimate strength by proposed equations and FE analyses
206
Table 8-4 Initial stiffness of fully grouted joints subjected to brace axial tensile loading
211
Table 8-5 of k
n
and n for fully grouted joint subjected to brace axial tensile loading 212
Table 8-6 Failure mode of fully grouted joint subjected to IPB 214
Table 8-7 Comparison between ultimate strength by proposed equations and FE analyses
218
Table 8-8 Initial stiffness for fully grouted joint subjected to IPB 220
Table 8-9 of k
n
and n for fully grouted joint subjected to brace axial tensile loading 221
Table 8-10 Failure mode of fully grouted joint subjected to IPB 223
Table 8-11 Comparison between ultimate strength by proposed equations and FE
analyses 226
Table 8-12 Initial stiffness for fully grouted joint subjected to IPB 229
Table 8-13 of k
n
and n for fully grouted joint subjected to brace axial tensile loading 230