University of Calgary PRISM: University of Calgary's Digital Repository Graduate Studies The Vault: Electronic Theses and Dissertations 2017 Structural Behaviour of Spatial Arch Bridges Hudecek, Martin Hudecek, M. (2017). Structural Behaviour of Spatial Arch Bridges (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/27901 http://hdl.handle.net/11023/3839 doctoral thesis University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. Downloaded from PRISM: https://prism.ucalgary.ca UNIVERSITY OF CALGARY Structural Behaviour of Spatial Arch Bridges by Martin Hudecek A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAM IN CIVIL ENGINEERING CALGARY, ALBERTA MAY, 2017 © Martin Hudecek 2017 Abstract This thesis investigates particular aspects of the structural behaviour of a new form of bridge structure called spatial arch bridge (SAB). SABs are designed to be outstanding pieces of architecture. Due to the enhancement in graphical and structural analysis software, the number of SABs is increasing. However, the complexity of SABs results in certain challenges in structural analysis and design. The unique combination of the arch, hangers, and deck result in the development of out-of-plane loads that significantly influence the structural response. This work focuses on SABs with an inferior deck suspended on flexible hangers (cables) below the arch. Three different spatial arrangements of the arch and deck are developed and analyzed to fill particular gaps in the current state of knowledge. Finite element analysis (FEA) is employed as the main analysis tool. Both linear and nonlinear parametric models are developed to address the objectives of the research. Ratios of primary and secondary geometric variables including arch rise, span, deck reach, and inclination or rotation of the parabolic arch are established to identify the trends in the structural response and to consider the effects of various types of loads. The significance of variability in the bending stiffness of the arch and the deck is studied to determine the optimal combination of these parameters that results in spatial configurations with minimal susceptibility to buckling as a function of particular types of end conditions of the deck. The work describes aspects of advanced composite materials (ACM), such as a low modulus of elasticity and time-dependent material properties in all-composite assemblies, and determines the applicability of commonly used durable structural profiles in SABs taking into account the nonlinear character of the cables and the effect of additional tensioning of the cables. The results of the large number of analyses conducted are summarized in tables accompanied with charts and schematic sketches that are intended to serve as guidelines when analyzing or designing structures similar in nature to the ones described in this work. Design criteria are proposed. Key words: Spatial arch bridges, parametric models, FEA, geometric ratios, stiffness ratios, end conditions of the deck, flexible hangers, susceptibility to buckling, additional tensioning of cables, advanced composite materials, design guidelines ii Preface The work described in this thesis assesses the structural behaviour of spatial arch bridges (SABs). These structures can be very complex and many aspects can influence their response to applied loads. The thesis is organized into eight chapters to clarify the structural behaviour of SABs in order of increasing complexity. The structural behaviour of SABs is investigated using finite element analysis (FEA), and the significance of certain variables, including geometric and stiffness ratios and material properties, is studied. Each chapter contains an introduction and sections on methodology, results, and discussion. The influence of a change in the geometric variables on structural response in the arch, deck, and cables under several loading conditions is investigated first. The revealed issues are studied in the chapters that follow. The significance of arch and deck stiffness under live loads is investigated, which provides grounds to define the susceptibility to buckling as a function of the end conditions of the deck. The application of advanced composite materials (ACMs) in SABs is examined. Additional tensioning of flexible hangers, transferring the loads from the deck to the arch, is considered in certain configuration. The arrangement of the hangers in the assumed spatial configurations and the response to dynamic loading are discussed as possible directions for future work. The appendix of the thesis provides details, such as large tables or charts, to the analyses presented in the body of text. A complete parametric input file that gathers all necessary parameters and commands is included in the appendix as well. The understanding of the structural behaviour of SABs obtained from the research described in each chapter is summarized at the end of each chapter and can be used by designers of SABs as a guideline. Design criteria are proposed for the spatial configurations studied in this thesis. The proposed guidelines and criteria are not intended to specify exact design procedures. Rather, the intention is to provide credible information that can be used while designing and analyzing these structures. iii Acknowledgements I would like to express my greatest appreciation to Dr. Nigel Graham Shrive, who guided me and offered invaluable advice throughout my doctoral studies. I would like to acknowledge and thank the following for their support: Stantec consulting Ltd. and the Natural Sciences and Engineering Research Council of Canada (NSERC), who have supported my research financially via the Industrial Postgraduate Scholarship (IPS) program. I would also like to thank Compute Canada and the University of Calgary for providing the finite element software, Abaqus. My countless thanks belong to all my colleagues, coworkers, friends, and family members who helped me throughout my studies and with revising this thesis in particular. iv Dedication With love and great memory to my parents Jarmila and Karel†, my brother Tomáš and to my wife Elissa who always supported me throughout my academic pursuit. I would like to dedicate this thesis to my daughter Sophia who is the bright light in our lives. v Table of Contents Abstract ................................................................................................................................ii Preface ............................................................................................................................... iii Acknowledgements.............................................................................................................iv Dedication ............................................................................................................................ v Table of Contents ................................................................................................................vi List of Tables .....................................................................................................................xii List of Figures and Illustrations ........................................................................................xxi List of Symbols, Abbreviations and Nomenclature ....................................................... xxxv Epigraph .............................................................................................................................xli Chapter One: Introduction and Motivation............................................................... - 1 - 1.1 Spatial Arch Bridges ................................................................................................. - 1 - 1.2 Problem Definition ................................................................................................... - 2 - 1.3 Objectives ................................................................................................................. - 4 - 1.4 Scope of Work .......................................................................................................... - 5 - 1.5 Thesis Layout............................................................................................................ - 6 - Chapter Two: Literature Review ................................................................................ - 9 - 2.1 Introduction............................................................................................................... - 9 - 2.2 Definition of Spatial Arch Bridges ........................................................................... - 9 - 2.3 History and Development of Spatial Structures ..................................................... - 10 - 2.4 Geometry of Spatial Arch Bridges.......................................................................... - 17 - 2.4.1 General............................................................................................................. - 17 - 2.4.2 Classification of Spatial Arch Bridges ............................................................ - 18 - 2.4.2.1 Spatial Arch Ribs and Spatial Shells ......................................................