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 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. i TABLE OF COTENTS ACKNOWLEDGEMENT .I TABLE OF COTENTS . II NONMENCLATURE . IX LIST OF FIGURES . XIV LIST OF TABLES . XXII SUMMARY .XXV CHAPTER INTRODUCTION . 1.1 BACKGROUND 1.2 MOTIVATION 1.3 SCOPE AND AIMS OF RESEARCH 1.3.1 Scope of reserach . 1.3.2 Main ojectives of reserach . 1.4 CONTENTS OF CURRENT THESIS CHAPTER 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 ii 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 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 iii 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 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 iv 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 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 v CHAPTER 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 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 vi 7.4 DAMAGE MODEL IN ABAQUS . 181 7.5 STUDY ON THE EFFECT OF ΕD , UF0 AND DC 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 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 vii 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 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 viii NONMENCLATURE A: Cross-sectional area of brace member Be: Effective width C: Damage constant in McClintock-R.T. 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To determine the three independent components of plane strain, three linearly independent strain measures are needed, i.e., three strain gages positioned in a rosette-like layout. 252 Appendices Figure A-2 Typical layout of rosette Consider a strain rosette attached on the surface with an angle α from the x-axis. The rosette itself contains three strain gages with the internal angles β and γ, as illustrated on Figure A-2. Suppose that the strain measured from these three strain gages are εa, εb, and εc, respectively. The following coordinate transformation equation is used to convert the longitudinal strain from each strain gage into strain expressed in the x-y coordinates, (A.2) Applying this equation to each of the three strain gages results in the following system of equations, (A.3) These equations are then used to solve for the three unknowns, εx, εy, and εxy. Note: The above formulas use the strain measure εxy as opposed to the engineering shear strain γxy. To use γxy, the above equations should be adjusted accordingly. 253 Appendices The free surface on which the strain rosette is attached is actually in a state of plane stress, while the formulas used above are for plane strain. However, the normal direction of the free surface is indeed a principal axis for strain. Therefore, the strain transform in the free surface plane can be applied. Special Cases of Strain Rosette Layouts Case 1: 45º strain rosette aligned with the x-y axes, i.e., a = 0º, b = g = 45º. Figure A-3 45º strain rosette For case 1: σ 21 = E ⎡ε a + ε c ± ⎢ ⎣ −ν +ν σ mises = (σ −σ2 ) + (σ 2 ⎤ 2(ε a − ε b ) + 2(ε b − ε c ) ⎥ ⎦ −σ3 ) + (σ − σ1 ) (A.3) Case 2: 60º strain rosette, the middle of which is aligned with the y-axis, i.e., a = 30º, b = g = 60º. Figure A-4 60º strain rosette 254 Appendices Principal Directions, Principal Strain The normal strains (εx’, εy’) and the shear strain (εx’y’) vary smoothly with respect to the rotation angle q, in accordance with the transformation equations given above. There exist a couple of particular angles where the strains take on special values. First, there exists an angle θp where the shear strain εx’y’ vanishes. That angle is given by, (A.4) This angle defines the principal directions. The associated principal strains are given by, (A.5) The transformation to the principal directions with their principal strains can be illustrated as follow: Figure A-5 Transformation of strains from given coordinates to principal directions Maximum Shear Strain Direction Another important angle, θs, is where the maximum shear strain occurs and is given by, 255 Appendices (A.6) The maximum shear strain is found to be one-half the difference between the two principal strains, (A.7) The transformation to the maximum shear strain direction can be illustrated as follow: Figure A-6 Transformation of strains to maximum shear strain 256 Appendices Appendix B Conversion of Engineering Strain & Stress The relationship between true strain and nominal strain is established by expressing the nominal strain as: ε nom = l − l0 l l l = − = −1 l0 l0 l0 l0 (B.1) Adding unity to both sides of this expression and taking the natural log of both sides provides the relationship between the true strain and the nominal strain: (B.2) ε = ln(1 + ε nom ) The relationship between true stress and nominal stress is formed by considering the incompressible nature of the plastic deformation and assuming the elasticity is also incompressible, so l A0 = lA (B.3) The current area is related to the original area by A=A l0 l (B.4) Substituting this definition of σ= ⎛ l F F l = = σ nom ⎜⎜ A A0 l ⎝l0 where into the definition of true stress gives ⎞ ⎟ ⎟ ⎠ (B.5) l can also be written as ( + ε nom ) l0 Making this final substitution provides the relationship between true stress and nominal stress and strain: σ = σ nom (1 + ε nom ) (B.6) 257 Appendices Appendix C Verification of Recorded Loading C.1 In-Plane Bending Test The comparisons between calculated moments in monitored cross sections based on measured strain and those based on recorded global load are shown in Figure C-1. The close correlation between measure moment and calculated moment in elastic range proves the validity of recorded global load. 1200 400 300 M1_measured M2_measured M3_Measured M4_Measured M1,3_calculated M2,4_calculated 200 100 Bending Moment(kN.m) 100 200 Global Load P(kN) Global Load P(kN) 500 900 600 M1_measured M2_measured M3_measured M4_measured M1,3_calculated M2,4_calculated 300 300 X1 800 X1-G 1600 900 600 M1_measured M2_measured M3_measured M4_measured M1,3_calculated M2,4_calculated 300 0 Bendign Moment(kN.m) 200 400 600 Global Load P(kN) 1200 Global Load P(kN) Bendign Moment(kN.m) 200 400 600 1200 800 M1_measured M2_measured M3_measured M4_measured M1,3_calculated M2,4_calculated 400 800 X2 0 Bendign Moment(kN.m) 500 1000 1500 2000 X2-G Figure C-1 C.1 Axial loading Test The comparisons between calculated axial load in monitored cross sections of braces based on measured strain and those based on recorded global load are shown in Figure C- 258 Appendices 2. The close correlation between measure axial load and calculated axial load in elastic range proves the validity of recorded global load. 4500 Load_record Load_Section Load_Section Load_Section 5000 Load_record Load_Section Load_Section Load_Section 4000 Load(kN) Load(kN) 6000 3000 3000 2000 1500 1000 Measured Load(kN) 0 1000 2000 3000 4000 Measured Load(kN) 0 5000 X3 1500 600 300 600 900 1200 1200 1500 600 1200 1800 2400 3000 X4-G-T 3600 Load(kN) Load(kN) Measured Load(kN) Load_record Load_Section Load_Section Load_Section Load_Section 3000 5000 1800 X4 4000 4000 600 Measured Load(kN) 3000 Load_record Load_Section Load_Section Load_Section 2400 Load(kN) Load(kN) 3000 900 300 2000 X3-G-T Load_record Load_Section Load_Section Load_Section 1200 1000 2000 1000 Load_record Load_Section Load_Section Load_Section Load_Section 2700 1800 900 Measured Load(kN) 0 1000 2000 3000 X5 Measured Load(kN) 4000 900 1800 2700 3600 X5-G-T 259 Appendices Load_record Load_Section Load_Section Load_Section 600 Load_record Load_Section Load_Section Load_Section 2000 1500 Load(kN) Load(kN) 800 400 1000 200 500 Measured Load(kN) 0 200 400 600 Measured Load(kN) 800 X6 1500 2000 Load_record Load_Section Load_Section Load_Section 3000 2400 Load(kN) Load(kN) 600 1000 X6-G-T Load_record Load_Section Load_Section Load_Section 800 500 400 1800 1200 200 600 Measured Load(kN) 0 200 400 600 Measured Load(kN) 800 X7 600 1200 1800 2400 3000 X7-G-T Figure C-2 260 [...]... objectives of research The main objectives of the present research are: • To identify the effects of presence of infilled grout on the static behavior of tubular joints • To investigate the load transfer and failure mechanisms of fully grouted X- joints under different loading conditions • To develop a new failure model for fully grouted X- joints and provide practical design equations for the design of fully. .. for strengthening or repairing, tubular members normally are fully grouted Besides, in many cases, the internal space of a pile is also filled with grout, which practically formed a fully grouted joint Thus, present study only focuses on fully grouted joints Besides, an X- tubular joint configuration has been chosen to establish the basis for the understanding of the behaviors of fully grouted joints. .. 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 k0 211 Figure 8-10 Distribution of kn 212 Figure 8-11 The value of c against β 213 Figure 8-12 Failure of fully grouted joint subjected to IPB 214 xx Figure 8-13 Joint strength against β ... 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) ... use of a grouted tubular member provides an attractive alternative Offshore works are minimized and the fabrication tolerances as well as the lack of fit are easily accommodated in grouting A grouted tubular member is the one filled with cement grout materials, forming a composite load-carry section, as shown in Figure 1-4 With the presence of the infilled grout in the tubular member, a new type of tubular. .. ultimate strength analyses of offshore structures The whole study comprises two parts: the experimental investigations and the numerical simulations Two series of experimental investigations have been conducted on the fully grouted X- joints under brace axial loading and in-plane bending respectively A total number of 15 large scale tubular joints have been tested up to failure Some unique xxv characteristics... technical literature for this type of joints Most of the researches in this subject have been conducted the individual joints commissioned by the Oil and Gas Companies with their geometries specific to the offshore platform joints requiring strengthening The objective of the present study is, therefore, to extend the understanding of the static behavior of fully grouted tubular joints and develop an effective... load in the chord Pcrack: Axial load corresponding to crack initiation PDL: Axial load corresponding to deformation limit of 0.03D0 Pmax: Maximum axial load recorded during test Ps: Axial load corresponding to the serviceability limit PSL: Axial load corresponding to serviceability limit of 0.01D0 Pu,: Ultimate axial capacity of joint PYC: Yield axial capacity of chord Qf: Chord stress modifier Qu:... design of fully grouted X- joints • To establish a consistent modeling procedure for the FE analyses of fully grouted joints which can include the crack initiation and failure mode in the chord • To generalized the load-deformation characteristics of the fully grouted X- joint under different loading conditions 1.4 Contents of current thesis The whole study comprises of two parts: the experimental investigations... 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 kn and n for fully grouted joint subjected . 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. 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. 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