@phdthesis{oai:sucra.repo.nii.ac.jp:00018921,
 author = {Mahmudur, Rahman},
 month = {},
 note = {xv, 168 p., The strengths of longitudinally continuous stiffened steel plates under uniaxial compression were investigated by employing a combination of numerical and probabilistic approaches. The probabilistic compressive strengths were obtained for two different limit states, i.e. the Ultimate Limit State (ULS) and the Serviceability Limit State (SLS). For slender stiffened plates, the SLS is particularly important because large out-of-plane deflection occurs due to elastic buckling, before reaching the ultimate strength. Due to lack of specific criteria to determine the compressive strength at SLS, a rational criterion has been proposed based on elastic buckling strength and fabrication tolerance.

Three different stiffened plate models with three, two, and one flat plate longitudinal stiffeners, corresponding to Model-1, Model-2, and Model-3 were considered for the study, where Model-1 and Model-2 shows column-like behavior (small post-buckling strength) and Model-3 exhibits plate-like behavior (significant post-buckling strength reserve). The plates of both normal and high-performance steel (SBHS) were taken into account, and their thickness was varied from 10 to 90 mm. The compressive strengths at ULS and SLS were determined from nonlinear elasto-plastic finite element analysis (FEA), where both material and geometric nonlinearity were taken into account. As a source of variability of the compressive strengths, variation of the initial out-of-plane deflection and residual stress were considered simultaneously in the FEA. The probabilistic distribution of the compressive strengths for Model-1 and Model-2 were obtained through Monte Carlo simulations in association with the response surface method. The response surface function is a second order polynomial of the independent random variables, i.e. the initial out-of-plane deflections and the residual stresses. For Model-3, an approximate estimation procedure was followed to obtain the first-order mean values. The first order variances were also estimated approximately, employing the Taylor series finite difference (TSFD) method. Based on the obtained probabilistic information, partial safety factors were proposed, considering the mean value strengths as the nominal strengths, as an example.

The study results were compared with different design codes e.g. JSHB, AASHTO, Eurocode, and Canadian Code. Comparing to the ULS strengths for Model-1 and Model-2 with a 5% non-exceedance probability indicate that the JSHB, AASHTO, and Canadian Code provides significantly conservative design, specifically for stiffened plates with high reduced slenderness parameters. However, in the middle range of reduced slenderness parameters, AASHTO and Canadian Code predicts overestimated strengths for Model-3. All of the three Models showed better agreement with the Eurocode than other design specifications. Nevertheless, a scope for improvement of the Eurocode was addressed by considering continuous stiffened panels (in the longitudinal direction) rather than an isolated panel. The uniqueness of this research is that the effect of thick plates and SBHS steels were included. Furthermore, rather than deterministic strengths, probabilistic strengths are provided for column-like behavior and plate-like behavior, which can be used as an important reference for developing a reliability-based design strength curve., Acknowledgements..........................................................................................................iv
Abstract...............................................................................................................................vi
Table of Contents .......................................................................................................... viii
List of Figures....................................................................................................................xi
List of Tables ....................................................................................................................xv
Chapter 1: Introduction .................................................................................................. 17
1.1 General........................................................................................................................... 17
1.2 Historic steel box girder bridge collapse ....................................................................... 18
1.3 Code provisions for buckling strength........................................................................... 20
1.3.1 JSHB....................................................................................................................... 20
1.3.2 AASHTO................................................................................................................ 22
1.3.3 Canadian Code........................................................................................................ 24
1.3.4 Eurocode................................................................................................................. 25
1.4 Basic concept of reliability-based design ...................................................................... 26
1.5 Identification of problems ............................................................................................. 28
1.6 Research objectives and scope ...................................................................................... 29
1.7 Outline of the dissertation ............................................................................................. 30
Chapter 2: Probabilistic compressive strength of stiffened steel plates exhibiting column-like behavior: ULS and SLS............................................................................ 33
2.1 Introduction ................................................................................................................... 33
2.2 Description of the models for numerical analysis......................................................... 35
2.2.1 Geometric configuration......................................................................................... 35
2.2.2 Boundary conditions............................................................................................... 36
2.2.3 Material model........................................................................................................ 37
2.3 Deterministic finite element analysis (FEA) ................................................................. 38
2.3.1 Elastic buckling analysis ........................................................................................ 38
2.3.2 Nonlinear elasto-plastic analysis............................................................................ 40
2.3.3 Effect of initial local out-of-plane deflection ......................................................... 42
2.3.4 Parametric study ..................................................................................................... 43
2.4 FEA results and response surface for ULS.................................................................... 45
2.4.1 ULS and stress-strain curves .................................................................................. 45
2.4.2 Effect of variation of initial imperfections............................................................. 46
2.4.3 Response surface for ULS ...................................................................................... 48
2.5 FEA results and response surface for SLS .................................................................... 51
2.5.1 The SLS and its determination criteria ................................................................... 51
2.5.2 Effect of variation of initial imperfection............................................................... 54
2.5.3 Response surface for SLS....................................................................................... 5
2.6 Probabilistic analysis and PSFs..................................................................................... 56
2.6.1 Monte Carlo simulation (MCS).............................................................................. 56
2.6.2 Proposal for PSFs ................................................................................................... 59
2.7 Discussion...................................................................................................................... 60
2.8 Conclusion..................................................................................................................... 63
Chapter 3: Probabilistic column-like compressive strength considering the effect of longitudinal edge support: ULS and SLS .............................................................. 65
3.1 Introduction ................................................................................................................... 65
3.2 Deterministic FEA......................................................................................................... 67
3.2.1 Model geometry, boundary conditions, and material model.................................. 67
3.2.2 Elastic buckling analysis ........................................................................................ 69
3.2.3 Verification of the nonlinear FEA result ................................................................ 70
3.2.4 Mesh size dependency analysis.............................................................................. 72
3.2.5 Effect of local initial out-of-plane deflection ......................................................... 73
3.2.6 Parametric study ..................................................................................................... 75
3.3 FEA results for ULS...................................................................................................... 75
3.3.1 Effect of reduced slenderness parameter RR........................................................... 76
3.3.2 Effect of plate thickness ......................................................................................... 76
3.3.3 Effect of material grade .......................................................................................... 77
3.4 FEA results for SLS....................................................................................................... 78
3.4.1 Variation of buckling modes for slender plates...................................................... 78
3.4.2 Normalized stress vs. out-of-plane deflection curves............................................. 79
3.4.3 SLS determination criterion ................................................................................... 80
3.5 Probabilistic analysis..................................................................................................... 81
3.5.1 Response surface: ULS and SLS............................................................................ 81
3.5.2 Monte Carlo simulation (MCS): ULS and SLS ..................................................... 85
3.5.3 Partial safety factors: ULS and SLS....................................................................... 87
3.6 Discussion...................................................................................................................... 88
3.7 Conclusion..................................................................................................................... 90
Chapter 4: Probabilistic compressive strength of stiffened plates exhibiting plate-like behavior: ULS and SLS........................................................................................... 91
4.1 Introduction ................................................................................................................... 91
4.2 Selection of stiffened plate models................................................................................ 93
4.3 Numerical analysis ........................................................................................................ 95
4.3.1 Model geometry, boundary conditions, and material model.................................. 95
4.3.2 Elastic buckling analysis ........................................................................................ 96
4.3.3 Nonlinear elasto-plastic FEA.................................................................................. 97
4.3.4 Nonlinear FEA result for ULS................................................................................ 98
4.3.5 Nonlinear FEA result for SLS ................................................................................ 99
4.3.6 Effect of local initial out-of-plane deflection ....................................................... 100
4.3.7 Parametric analysis............................................................................................... 101
4.4 Experimental verification ............................................................................................ 102
4.4.1 Experimental model.............................................................................................. 102
4.4.2 Initial out-of-plane deflection measurement......................................................... 103
4.4.3 Measurement of residual stress............................................................................. 104
4.4.4 Test setup.............................................................................................................. 105
4.4.5 Numerical simulation of the experimental model ................................................ 106
4.4.6 Result verification ................................................................................................ 107
4.5 Approximate solution for probabilistic strengths: ULS and SLS................................ 109
4.5.1 Estimation of first order mean and first order variance........................................ 110
4.5.2 Probabilistic compressive strengths: ULS and SLS ............................................. 112
4.5.3 Partial safety factors: ULS and SLS..................................................................... 113
4.6 Discussion.................................................................................................................... 114
4.7 Conclusion................................................................................................................... 116
Chapter 5: Summary and recommendations for future study .............................. 119
5.1 Summary...................................................................................................................... 119
5.2 Recommendations for future study ............................................................................. 122
References ....................................................................................................................... 124
APPENDIX A.................................................................................................................. 130
Detailed dimensions of the Model-1 stiffened plates........................................................ 130
APPENDIX B .................................................................................................................. 131
Detailed dimensions of the Model-2 stiffened plates........................................................ 131
APPENDIX C.................................................................................................................. 132
Detailed dimensions of the Model-3 stiffened plates........................................................ 132
APPENDIX D.................................................................................................................. 133
FEA Results for Model-1 .................................................................................................. 133
APPENDIX E .................................................................................................................. 151
FEA Results for Model-2 .................................................................................................. 151
APPENDIX F................................................................................................................... 166
FEA Results for Model-3 .................................................................................................. 166, 主指導教員 : 奥井義昭, text, application/pdf},
 school = {埼玉大学},
 title = {Reliability-based design for buckling strength of stiffened steel plates : ultimate and serviceability limit states},
 year = {2019},
 yomi = {マフムダ, ラーマン}
}