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Local Buckling of Doubly-Symmetric I-Sections Subjected to Warping Torsion

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Local Buckling of Doubly-Symmetric I-Sections Subjected to Warping Torsion DEGREE PROJECT IN THE BUILT ENVIRONMENT, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019 Local Buckling of Doubly-Symmetric I-Sections Subjected to Warping Torsion The limitations of the Reduced Cross-Section Method under unconventional loading MIKLÓS ORI KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT Local Buckling of Doubly-Symmetric I-Sections Subjected to Warping Torsion The limitations of the Reduced Cross-Section Method under unconventional loading MIKLÓS ORI Dr. Bert Norlin (Supervisor and Examiner), KTH, ABE, Stockholm Master Thesis, 2019 KTH Royal Institute of Technology School of Architecture and Built Environment Department of Structural Engineering and Bridges SE-100 44 Stockholm, Sweden TRITA-ABE-MBT-19164 KTH ROYAL INSTITUTE OF TECHNOLOGY INFORMATION AND COMMUNICATION TECHNOLOGY Abstract In regular design practice, when it comes to conventional loading, such as uniaxial compression and bending, the local buckling of thin plates is taken care of through cross section classification. The effect of warping torsion, which also gives rise to normal stresses in the section, however, is typically not considered in the process. Present work aimed to uncover the influence of warping torsion on the phenomena of local plate buckling and to investigate the limitations of the effective width method when it was applied against its intended use. In the case of varying results, a simple correction to the calculation method was to be developed to improve accuracy. The examined I-sections were tested to failure and results were obtained with two different approaches: with finite element method and a Eurocode-based hand- calculation. The finite element models were refined to closely mimic physical experiments and their results were accepted as the true resistance of the sections, while the calculation method tried to capture the structural response in a practical, easily understandable way. The calculated results showed reasonably good accuracy with that of the finite element analysis. However, what really stood out was how similar the change in resistance was when the section parameters were manipulated. Through a properly chosen function, this allowed for the creation of an exponent that could modify the calculated results to achieve an even greater accuracy. The eccentricity of the applied load on the system was also manipulated to alter the proportion of normal stresses due to the two examined effects. It became clear that the stresses from warping in the applied calculation model were underestimated and the otherwise conservative method of effective width lost much of its safety margin when its application was extended to warping as well. Consequently, the consideration of stresses from warping in the regular design process and stability control of commonly used thin walled open sections seemed to be justified. The effective width method could not reliably cover the issue with retaining its original margin of safety. Keywords: Local plate buckling – Warping torsion – Finite element modelling - Eurocode Preface This report represents the full work of a final thesis for the Master of Science in Civil and Architectural Engineering at KTH Royal Institute of Technology. All the work was conducted at the Department of Structural Engineering and Bridges. I wish to express my gratitude to my supervisor, professor Bert Norlin, who with his continued support and understanding did not only make it possible to successfully finish my degree project but also granted me the opportunity to pursue extra-curricular exploits and therefore improve myself in my academic and professional life simultaneously. My friends and family deserve my undying gratitude for their endless support. This work and the years leading up to it would never have been possible without their care, kindness and funding. Stockholm, February 2019 Miklós Ori Table of Contents Abstract ............................................................................................................................................ 4 Preface ............................................................................................................................................. 6 1 Introduction ....................................................................................................................... 11 1.1 Background .............................................................................................................................. 11 1.2 Problem ..................................................................................................................................... 11 1.3 Applied methods .................................................................................................................... 12 1.4 Outline ....................................................................................................................................... 13 2 Theoretic Background .................................................................................................... 14 2.1 Warping torsion ..................................................................................................................... 14 2.2 Local plate buckling .............................................................................................................. 18 3 Methodology ....................................................................................................................... 23 3.1 The finite element model .................................................................................................... 23 3.1.1 Geometry ............................................................................................................................................. 23 3.1.2 Elements and meshing ................................................................................................................... 23 3.1.3 Boundary conditions ...................................................................................................................... 23 3.1.4 Material model .................................................................................................................................. 24 3.1.5 Load model ......................................................................................................................................... 24 3.1.6 Analysis ................................................................................................................................................ 24 3.2 Computation ............................................................................................................................ 25 3.2.1 Input data ............................................................................................................................................ 25 3.2.2 Geometry ............................................................................................................................................. 26 3.2.3 Cross-sectional properties ........................................................................................................... 26 3.2.4 Stresses ................................................................................................................................................ 27 3.2.4.1 Pure bending .......................................................................................................................... 28 3.2.4.2 Warping torsion ................................................................................................................... 29 3.2.5 Verification ......................................................................................................................................... 30 4 Results .................................................................................................................................. 32 5 Result Analysis .................................................................................................................. 37 5.1 Conclusions .............................................................................................................................. 38 5.2 Future of the study ................................................................................................................ 40 5.3 Correction of the results ..................................................................................................... 41 Bibliography ............................................................................................................................... 44 Appendix A ................................................................................................................................... 45 Appendix B ................................................................................................................................... 59 Introduction | 11 1 Introduction 1.1 Background The phenomenon of buckling is a well-known one in the world of structural engineering. So much so, that it is one of the most comprehensively researched and described notions in the field that has been around since the 18th century. Despite of its apparent appeal to the scientific community it could not take the heart of the engineers. Stability loss, non-linear analysis, eigenvalues and initial imperfections are as good as swears for the ears of the practicing engineer. Consequently, countless methods of calculations have been developed to simplify and work around the problem rather than face it straight on. Not denying
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