lateral torsional buckling of wood i-joist

201 Pages·2016·4.65 MB·English

LATERAL TORSIONAL BUCKLING OF
WOOD I-JOIST

BY
RÉMI ST-AMOUR

A THESIS SUBMITTED TO THE
FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
MASTER OF APPLIED SCIENCE IN CIVIL ENGINEERING

OTTAWA-CARLETON INSTITUTE FOR CIVIL ENGINEERING
FACULTY OF CIVIL ENGINEERING
UNIVERSITY OF OTTAWA
© RÉMI ST-AMOUR, OTTAWA, CANADA 2016
ABSTRACT
Engineered wood I-joists have grown in popularity as flooring and roofing structural
systems in the past 30 years, replacing solid sawn lumber joists. Typical wood I-joists are
manufactured with a very slender section, which is desirable to achieve higher flexural
capacities and longer spans; however, this makes them susceptible to lateral torsional
buckling failure. Continuous beam spans and uplift forces on roof uplift are potential
scenarios where lateral instability can occur and reflects the need to investigate the lateral
torsional buckling behavior of wood I-joists. Within this context, the present study
conducts an experimental investigation on the material properties and the critical buckling
load of 42 wood I-joist specimens. A 3D finite element model is built using the
experimentally determined material parameters to effectively predict the observed
buckling behavior of the specimens while also accounting for initial imperfections in the
joists. The adequacy of other analytical models to predict the critical buckling load of wood
I-joists are also investigated. It is demonstrated that the American design standard
underestimates the critical buckling load of wood I-joists while the classical theory
provides an adequate estimate of the buckling capacity. Furthermore, the effects of initial
imperfections on the lateral torsional buckling behavior are discussed. The developed and
verified FE model is used to reproduce the nonlinear buckling behavior of the wood I-joist
and also to provide an accurate estimate of the lateral torsional buckling capacity using the
linear buckling analysis.

II
ACKNOWLEDGMENT
I would like to express my sincere gratitude towards my research director, Dr. Ghasan
Doudak, whose advice and guidance allowed me to develop my expertise in timber
engineering and complete this research.
I can never thank enough colleagues that provided crucial help during my research
especially, Mr. Yang Du, Mr. Qiuwu Xiao, Mr. Dominic Cote, Ms. America Lopez, Mr.
Arthur Manieri, Mr. Benoît Pelletier and Mr. Christian Viau.
Finalement, je veux exprimer ma profonde reconnaissance à l’égard de ma mère et de mon
père pour voir cru en moi ainsi que pour leur appui tout au long de mes études
universitaires.

III
TABLE OF CONTENTS

CHAPTER 1 INTRODUCTION ....................................................................................... 1
1.1 Description of the problem ................................................................................... 1
1.1.1 Constitutive material properties of wood I-joists.......................................... 2
1.1.2 Behavior of I-shaped beams subjected to lateral instability ......................... 4
1.1.3 Canadian design standard for steel construction ........................................... 8
1.1.4 American design standard for wood construction ........................................ 8
1.1.5 Twisting of I-beams ...................................................................................... 9
1.1.6 Transformed section properties for composite I-beams .............................. 10
1.2 Research objectives ............................................................................................ 10
1.3 Methodology ...................................................................................................... 12
1.4 Outline of the thesis............................................................................................ 13
CHAPTER 2 LITERATURE REVIEW .......................................................................... 14
2.1 Lateral instability of wood beams ...................................................................... 14
2.2 Lateral instability of wood I-joists ..................................................................... 18
2.2.1 Mechanical properties ................................................................................. 18
2.2.2 Lateral instability ........................................................................................ 19
2.3 Summary ............................................................................................................ 21
CHAPTER 3 SENSITIVITY ANALYSIS ...................................................................... 23
3.1 General ............................................................................................................... 23
3.1.1 Convention used for this study ................................................................... 23
3.2 Model description ............................................................................................... 24
3.2.1 Cross-section dimensions............................................................................ 25
3.2.2 Element type ............................................................................................... 25
3.2.3 Mesh ............................................................................................................ 25
3.2.4 Material properties ...................................................................................... 26
3.2.5 Boundary conditions ................................................................................... 28
3.2.6 Load application.......................................................................................... 28
3.2.7 Eigenvalue buckling analysis ...................................................................... 29
3.3 Validation with the theoretical solution ............................................................. 30
3.4 Results of the sensitivity analysis....................................................................... 30
CHAPTER 4 EXPERIMENTAL PROGRAM................................................................ 34
4.1 Specimen description ......................................................................................... 34
4.2 Testing program ................................................................................................. 37
4.2.1 I-joist lateral flexural stiffness .................................................................... 38
4.2.2 I-Joist torsional rigidity ............................................................................... 40
4.2.3 Lateral torsional buckling capacity ............................................................. 42
4.2.4 Flange longitudinal modulus of elasticity ................................................... 46
4.2.5 Flange torsional shear modulus .................................................................. 46
4.2.6 Web transverse modulus of elasticity ......................................................... 47
4.2.7 Flexural capacity ......................................................................................... 48
IV
CHAPTER 5 EXPERIMENTAL RESULTS .................................................................. 50
5.1 General ............................................................................................................... 50
5.2 Mechanical properties ........................................................................................ 50
5.2.1 I-joist lateral flexural stiffness .................................................................... 50
5.2.2 I-joist torsional rigidity ............................................................................... 51
5.2.3 Wood I-joist components tests .................................................................... 53
5.2.4 Determination of the web torsional stiffness .............................................. 55
5.2.5 Lateral torsional buckling capacity ............................................................. 55
5.2.6 Ultimate flexural capacity ........................................................................... 60
CHAPTER 6 FINITE ELEMENT MODELLING .......................................................... 63
6.1 General ............................................................................................................... 63
6.2 Linear and nonlinear analysis ............................................................................. 63
6.3 Model description ............................................................................................... 65
6.3.1 Elements details .......................................................................................... 65
6.3.2 Material parameters .................................................................................... 66
6.3.3 Mesh detail .................................................................................................. 67
6.3.4 Boundary conditions and load application .................................................. 68
6.4 Eigenvalue analysis procedure ........................................................................... 70
6.5 Nonlinear analysis procedure ............................................................................. 72
6.5.1 Imperfection sensitivity analysis................................................................. 76
CHAPTER 7 DISCUSSION ........................................................................................... 78
7.1 General ............................................................................................................... 78
7.2 Experimental investigation of the wood I-joist mechanical properties .............. 78
7.2.1 Sensitivity analysis...................................................................................... 78
7.2.2 Longitudinal modulus of elasticity determination ...................................... 79
7.2.3 Determination of the flange shear modulus ................................................ 82
7.3 Investigation of the lateral torsional buckling capacity ..................................... 83
7.3.1 Experimental buckling displacements ........................................................ 83
7.3.2 Models for predicting the critical buckling load of wood I-joist ................ 85
7.3.3 Experimental critical buckling load and model predictions comparison .... 88
7.3.4 Experimental buckling displacements and nonlinear FEA comparison ..... 92
7.4 Ultimate flexural capacity .................................................................................. 95
CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS .................................... 96
8.1 Summary and conclusions .................................................................................. 96
8.2 Recommendations for further research .............................................................. 97
REFERENCES ................................................................................................................ 98
APPENDIX A ................................................................................................................ 103
APPENDIX B ............................................................................................................... 188

V
LIST OF TABLES
Table 3-1: Reference model mechanical properties .......................................................... 27
Table 3-2 Finite element model response to material properties fluctuations .................. 32
Table 4-1 Wood I-joist specimen breakdown and moisture content ................................ 35
Table 4-2 Test program ..................................................................................................... 37
Table 5-1 Torsional rigidity of 0.4m wood I-joists........................................................... 52
Table 5-2 Torsional rigidity of 0.6m wood I-joists........................................................... 52
Table 5-3 Component mechanical properties of sample #1 .............................................. 53
Table 5-4 Component mechanical properties of sample #5 .............................................. 54
Table 5-5 Component mechanical properties of sample #16 ............................................ 54
Table 5-6 Average out-of-straightness of the top flange for each tested sample group ... 56
Table 5-7 Lateral torsional buckling capacity (kN) .......................................................... 56
Table 5-8 Ultimate flexural capacity, corresponding deflections and failure modes ....... 61
Table 6-1 Specimen flange modulus of elasticity input parameters ................................. 66
Table 6-2 Wood I-joist FE models mesh details ............................................................... 68
Table 6-3 Eigenvalue buckling analysis results ................................................................ 70
Table 6-4 Out-of-straightness of specimen compression flange....................................... 73
Table 6-5: Imperfection sensitivity FE model material parameters .................................. 76
Table 7-1 MOE comparison for uncut wood I-joist and component testing ................... 81
Table 7-2 Effect of the inelastic deformations on the MOE ............................................. 81
Table 7-3 FEA derived and Design Standards moment gradient and load eccentricity
factors ................................................................................................................................ 87
Table 7-4 Sample group #5 Experimental buckling capacity Vs. predictions .................. 89
Table 7-5 Sample group #6 Experimental buckling capacity Vs. predictions .................. 90
Table 7-6 Sample group #7 Experimental buckling capacity Vs. predictions .................. 90
Table 7-7 Sample group #8 Experimental buckling capacity Vs. predictions .................. 91
Table 7-8 Sample group #16 Experimental buckling capacity Vs. predictions ................ 91
Table A-1: Buckling displacements of specimen 1-5 ..................................................... 104
Table A-2 Buckling displacements of specimen 2-5 ...................................................... 106
Table A-3 Buckling displacements of specimen 3-5 ...................................................... 108
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Table A-4 Buckling displacements of specimen 4-5 ...................................................... 110
Table A-5 Buckling displacements of specimen 5-5 ...................................................... 112
Table A-6 Buckling displacements of specimen 6-5 ...................................................... 114
Table A-7 Force and displacements of specimen 7-5 ..................................................... 116
Table A-8 Buckling displacements of specimen 8-5 ...................................................... 118
Table A-9 Buckling displacements of specimen 9-5 ...................................................... 120
Table A-10 Buckling displacements of specimen 10-5 .................................................. 122
Table A-11 Buckling displacements of specimen 1-6 .................................................... 124
Table A-12 Buckling displacements of specimen 2-6 .................................................... 126
Table A-13 Buckling displacements of specimen 3-6 .................................................... 128
Table A-14 Buckling displacements of specimen 4-6 .................................................... 130
Table A-15 Buckling displacements of specimen 5-6 .................................................... 132
Table A-16 Buckling displacements of specimen 1-7 .................................................... 134
Table A-17 Buckling displacements of specimen 2-7 .................................................... 136
Table A-18 Buckling displacements of specimen 3-7 .................................................... 138
Table A-19 Buckling displacements of specimen 4-7 .................................................... 140
Table A-20 Buckling displacements of specimen 5-7 .................................................... 142
Table A-21 Buckling displacements of specimen 1-8 .................................................... 144
Table A-22 Buckling displacements of specimen 2-8 .................................................... 146
Table A-23 Buckling displacements of specimen 3-8 .................................................... 148
Table A-24 Buckling displacements of specimen 4-8 .................................................... 150
Table A-25 Buckling displacements of specimen 5-8 .................................................... 152
Table A-26 Buckling displacements of specimen 6-8 .................................................... 154
Table A-27 Buckling displacements of specimen 7-8 .................................................... 156
Table A-28 Buckling displacements of specimen 8-8 .................................................... 158
Table A-29 Buckling displacements of specimen 9-8 .................................................... 160
Table A-30 Buckling displacements of specimen 10-8 .................................................. 162
Table A-31 Buckling displacements of specimen 11-8 .................................................. 164
Table A-32 Buckling displacements of specimen 1-16 .................................................. 166
Table A-33 Buckling displacements of specimen 2-16 .................................................. 168
Table A-34 Buckling displacements of specimen 3-16 .................................................. 170
VII
Table A-35 Buckling displacements of specimen 4-16 .................................................. 172
Table A-36 Buckling displacements of specimen 5-16 .................................................. 174
Table A-37 Buckling displacements of specimen 6-16 .................................................. 176
Table A-38 Buckling displacements of specimen 7-16 .................................................. 178
Table A-39 Buckling displacements of specimen 8-16 .................................................. 180
Table A-40 Buckling displacements of specimen 9-16 .................................................. 182
Table A-41 Buckling displacements of specimen 10-16 ................................................ 184
Table A-42 Buckling displacements of specimen 11-16 ................................................ 186
Table B-1: Lateral flexural stiffness of wood I-joists ..................................................... 188

VIII
LIST OF FIGURES
Figure 1-1 Wood orthotropic principal axes ....................................................................... 3
Figure 1-2 I-section undergoing lateral torsional buckling (Kala, 2013) ........................... 7
Figure 1-3 Lateral buckling of theoretical and realistic I-beams ........................................ 7
Figure 3-1 Convention used for the principal axes of wood I-joist .................................. 24
Figure 3-2 Finite element model mesh ............................................................................. 26
Figure 3-3 Inactive translational DOFs (RED arrows) at each end of a simply supported
wood I-joist ....................................................................................................................... 28
Figure 3-4 Loaded nodes at each end of a simply supported wood I-joist subjected to a
uniform moment about its strong axis .............................................................................. 29
Figure 3-5 Responses of the critical moment to material properties fluctuations ............ 33
Figure 3-6 Sensitivity study buckled mode shape ............................................................ 33
Figure 4-1 I-joist cross section dimensions (mm)............................................................. 36
Figure 4-2 Web continuity joint and flange continuity joint ........................................... 36
Figure 4-3 I-joist lateral flexural stiffness test configuration ........................................... 39
Figure 4-4 I-joist lateral flexural stiffness laboratory test ................................................ 39
Figure 4-5 I-joist torsional rigidity test configuration ...................................................... 41
Figure 4-6 I-joist torsional rigidity test laboratory setup .................................................. 41
Figure 4-7 Schematic drawings of the lateral torsional buckling test configuration ........ 43
Figure 4-8 Lateral torsional buckling test end supports design and its restrained DOFs . 44
Figure 4-9 Lateral torsional buckling end support apparatus ........................................... 44
Figure 4-10 Lateral torsional buckling load transfer device design ................................. 45
Figure 4-11 Lateral torsional buckling test loading apparatus .......................................... 45
Figure 4-12 Flange longitudinal modulus of elasticity laboratory test setup.................... 46
Figure 4-13 Flange torsional shear modulus laboratory test setup ................................... 47
Figure 4-14 Web transverse modulus of elasticity test configuration .............................. 48
Figure 4-15 Ultimate flexural schematic drawing ............................................................ 49
Figure 4-16 Ultimate flexural capacity laboratory test setup............................................ 49
Figure 5-1 Lateral torsional buckling test deformations in the elastic and inelastic range57
Figure 5-2 Characteristic failure mechanism at collapse load .......................................... 57
IX
Figure 5-3 Force-lateral displacement curve of specimens in sample group #6 ............... 58
Figure 5-4 Force-angular displacement curve of specimens in sample group #6 ............. 58
Figure 5-5 Force-vertical displacement curve of specimens in sample group #6 ............. 59
Figure 5-6 Force-lateral displacement curve of specimens in sample group #6 ............... 59
Figure 5-7 Load-deflection curves for ultimate flexural capacity .................................... 60
Figure 5-8 Ultimate flexural capacity of I-joist sample #8 ............................................... 61
Figure 5-9 Failure modes of the 0.4m I-joists, Tension (left) and compression (right) ... 62
Figure 5-10 Failure mode of the 0.6m I-joists (Web distortion) ....................................... 62
Figure 6-1 Typical load-displacement curves from wood I-joist LTB test ...................... 65
Figure 6-2 Modeling of the boundary conditions ............................................................. 69
Figure 6-3 Location of the boundary conditions along the I-joist FE model.................... 69
Figure 6-4 First buckling mode shape of the wood I-joist FE models.............................. 71
Figure 6-5 Initial imperfection geometry incorporated in the wood I-joist FE models .... 72
Figure 6-6 FE nonlinear geometric analysis ..................................................................... 74
Figure 6-7 Linear and geometric nonlinear analysis of wood I-joist specimen #4 of sample
group 8 .............................................................................................................................. 75
Figure 6-8 Effect of initial imperfections on the non-linearity of a typical wood I-joist
model................................................................................................................................. 77
Figure 7-1 Length study on the torsional rigidity of entire wood I-joist specimens......... 83
Figure 7-2 Experimental lateral buckling behavior of some wood I-joist specimen ........ 85
Figure 7-3 Comparison between FE and proposed moment gradient and load eccentricity
factors ................................................................................................................................ 87
Figure 7-4 Experimental CBLs Vs. model predictions for the wood I-joist specimens ... 89
Figure 7-5 Buckling displacements of specimen 5-5 ........................................................ 93
Figure 7-6 Buckling displacements of specimen 4-16 ...................................................... 94
Figure 7-7 Buckling displacements of specimen 1-8 ........................................................ 94
Figure 7-8 0.4m I-joist flexural capacity as a function of the span .................................. 95
Figure A-1 Buckling displacements of specimen 1-5 ..................................................... 105
Figure A-2 Buckling displacements of specimen 2-5 ..................................................... 107
Figure A-3 Buckling displacements of specimen 3-5 ..................................................... 109
Figure A-4 Buckling displacements of specimen 4-5 ..................................................... 111
Figure A-5 Buckling displacements of specimen 5-5 ..................................................... 113
X