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4. an Analytical Model of Buckling Panels of Steel Beams at Elevated

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4. an Analytical Model of Buckling Panels of Steel Beams at Elevated A COMPONENT-BASED APPROACH TO MODELLING BEAM-END BUCKLING ADJACENT TO BEAM-COLUMN CONNECTIONS IN FIRE A thesis submitted for the degree of Doctor of Philosophy In the Faculty of Engineering of The University of Sheffield by GUAN QUAN Department of Civil and Structural Engineering The University of Sheffield August, 2016 ACKNOWLEGEMENTS My special thanks go to Professor Ian Burgess and Dr Shan-Shan Huang for their guidance, inspiration and dedication in supervising me throughout my research project. Their continuous awareness and rich experience made this PhD project nowhere near a lofty mountain, but near a highway. My thanks also go to their financial support on my international conferences, which are great opportunities to present my own work and to communicate with worldwide researchers. The financial support provided by CSC program and by the University of Sheffield is also greatly appreciated. My thanks also go to my colleagues and friends in the Structural Fire Engineering Research Group for the precious friendship we developed; and to Dr Ruirui Sun for his continuous advice on the development of Vulcan. I would like to express my gratefulness to my family for their love, understanding and sharing during the course of my PhD. Thanks to my boyfriend Dr Jun Ye. We have been together for more than six years from Wuhan University to Zhejiang University in China and to the University of Sheffield in the UK. Thank you for your love, accompany and support. I’m glad that we are going to put an end to our PhD courses as well as our single states together. I DECLARATION I certify that this thesis submitted for the degree of Doctor of Philosophy is the result of my own research, except where otherwise acknowledged. No portion of the work presented in this thesis has been submitted for another degree or qualification to this, or any other university or institution. Guan QUAN (Signature of candidate) 28th August, 2016 II ABSTRACT The investigation of the collapse of “7 World Trade” as part of the events of 11 September 2001 in New York City (Gann, 2008) indicated that connections were among the most vulnerable elements of steel-framed or composite buildings, and their characteristics can determine whether such buildings survive in extreme scenarios such as fire. In this case total collapse of the building was triggered by the fracture of beam-to-column connections caused largely by thermal expansion of long-span beams. This emphasized the importance of investigating the complex mechanisms through which forces are transferred from the adjacent parts of a structure to the connections under fire conditions. The Cardington fire tests in 1995-96 (Newman, 2000) provided ample evidence that both shear buckling of beam webs and beam bottom-flange buckling, near to the ends of steel beams, are very prevalent under fire conditions. Both of these phenomena could affect the force distribution at the adjacent column-face connection bolt rows, and therefore the sequence of fracture of components. However, there is a distinct lack of practical research investigating the post-buckling behaviour of beams of Classes 1 and 2 sections adjacent to connections at elevated temperatures. In this PhD thesis, the development of analytical models of pure beam-web shear buckling and a combination of both beam-web shear buckling and bottom-flange buckling of beams of Classes 1 and 2 sections are reported. The analytical models are able to predict the post-buckling behaviour of the beam-end buckling panels in the vicinity of beam-column connections at elevated temperatures. A transition criterion, to distinguish between cases in which pure beam-web shear buckling occurs and those in which the instability is a combination of shear buckling and bottom-flange buckling, III has been proposed, including a calculation procedure to detect the transition length between these two buckling modes. A component-based buckling element has been created and implemented in the three-dimensional structural fire analysis software Vulcan. The influence of the buckling elements on the bolt row force redistribution of the adjacent connections has been investigated in isolated beams and a simple two- span two-floor frame. It is expected that the buckling element will be involved in more complex performance-based frame analysis for design, and that it will be used with an explicit dynamic procedure to simulate local and progressive collapse of whole buildings. IV PUBLICATIONS Journal papers: 1. Quan, G., Huang, S.-S. & Burgess, I.W., 2015. An Analytical Approach to Modelling Shear Panels in Steel Beams at Elevated Temperatures. Engineering Structures, 85, 73-82. 2. Quan, G., Huang, S.-S. and Burgess, I.W., 2016. Component-Based Model of Buckling Panels of Steel Beams at Elevated Temperatures. Journal of Constructional Steel Research, 118, 91–104. 3. Quan, G., Huang, S.S. and Burgess, I.W., 2016. Parametric Studies on the Component-Based Approach to Modelling Beam Bottom Flange Buckling at Elevated Temperatures. Acta Polytechnica,56(2), 132–137. 4. Quan, G., Huang, S.-S. and Burgess, I.W., 2016. The Behaviour and Effects of Beam- End Buckling in Fire using a Component-Based Method. Acc. Engineering Structures. Conference papers: 1. Quan, G., Huang, S.-S. and Burgess, I.W., 2014. Shear Panel Component in the Vicinity of Beam-Column Connections in Fire. Proc. Structures in Fire Conference, Shanghai, China, 827-835. 2. Quan, G., Huang, S.-S. and Burgess, I.W., 2014. Shear Panel in the Vicinity of Beam- Column Connections - Component-Based Modelling. Proc. Eurosteel 2014, Naples, Italy, 218-225. 3. Quan, G., Huang, S.-S. and Burgess, I.W., 2015. A Parametric Investigation of the Transition Between Beam-Web Shear Buckling and Bottom-Flange Buckling at Elevated Temperatures, Proc. CONFAB 2015, Glasgow, UK, 273-278. 4. Quan, G., Huang, S.S. and Burgess, I.W., 2015. A Component-Based Approach to Modelling Beam Bottom Flange Buckling at Elevated Temperatures, Proc. ASFE 2015, Dubrovnik, Croatia, 19-24. 5. Quan, G., Huang, S.S. and Burgess, I.W., 2016. Component-Based Element of Beam Local Buckling Adjacent to Connections in Fire. Proc. Structures in Fire Conference, Princeton, USA, 352-359. V TABLE OF CONTENTS ACKNOWLEGEMENTS ................................................................................................ I DECLARATION .......................................................................................................... II ABSTRACT ............................................................................................................... III PUBLICATIONS ......................................................................................................... V TABLE OF CONTENTS ............................................................................................... VI 1. ......................................................................................................................... 1 INTRODUCTION ........................................................................................................ 1 1.1 BACKGROUND 2 1.2 RESEARCH MOTIVATIONS 7 1.3 SCOPE OF THIS RESEARCH 9 2. ....................................................................................................................... 11 LITERATURE REVIEW .............................................................................................. 11 2.1 MATERIAL PROPERTIES 12 2.2 FIRE RESISTANCE DESIGN METHODS 15 2.3 RESEARCH INSPIRED BY CARDINGTON FIRE TESTS 17 2.3.1 The Cardington Fire Tests .......................................................................................... 17 2.3.2 Steel beam and concrete slab research inspired by the Cardington Fire Tests ......... 19 2.4 FRAME NUMERICAL MODELLING 21 2.5 PROGRESSIVE COLLAPSE OF WTC7 BUILDING 24 2.6 JOINT MODELS 25 2.7 SHEAR BUCKLING OF PLATE GIRDERS 29 2.8 BOTTOM-FLANGE BUCKLING YIELD LINE MODELS 31 2.9 CONCLUSION 34 3. ....................................................................................................................... 36 AN ANALYTICAL APPROACH TO MODELLING SHEAR PANELS IN THE POST-BUCKLING STAGE AT ELEVATED TEMPERATURES ..................................................................... 36 3.1 INTRODUCTION 37 3.2 DEVELOPMENT OF ANALYTICAL MODEL 37 3.2.1 The deflection at mid-span ........................................................................................ 41 3.2.2 Shear resistance of the beam .................................................................................... 43 3.3 VALIDATION AGAINST FINITE ELEMENT MODELLING 53 3.4 CONCLUSION 58 4. ....................................................................................................................... 60 COMBINING THE EFFECTS OF SHEAR BUCKLING AND BOTTOM-FLANGE BUCKLING IN THE POST-BUCKLING STAGE ................................................................................... 60 4.1. INTRODUCTION 61 4.2. DEVELOPMENT OF ANALYTICAL MODEL 64 4.2.1 Pre-buckling stage and plateau.................................................................................. 65 VI 4.2.2 Post-buckling stage ................................................................................................... 65 4.3 VALIDATION AGAINST FINITE ELEMENT MODELLING 78 4.3.1 Validation of FE model against experimental results................................................ 78 4.3.2 Comparison between the proposed analytical model, Dharma’s model and FEA ... 84 4.3.3 Integration into a full beam model ..........................................................................
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