Theory of Concrete-Filled Steel Tubular Structures [1st ed. 2024] 9819921694, 9789819921690

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Lin-Hai Han

Theory of Concrete-Filled Steel Tubular Structures

Theory of Concrete-Filled Steel Tubular Structures

Lin-Hai Han

Theory of Concrete-Filled Steel Tubular Structures

Lin-Hai Han Guangxi University Nanning, China Tsinghua University Beijing, China

ISBN 978-981-99-2169-0 ISBN 978-981-99-2170-6 (eBook) https://doi.org/10.1007/978-981-99-2170-6 Jointly published with China Architecture & Building Press The print edition is not for sale in China (Mainland). Customers from China (Mainland) please order the print book from: China Architecture & Building Press. © China Architecture & Building Press 2024 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

Concrete-filled steel tube (CFST) is a composite structural type formed by filling concrete into a steel tube, and the two materials can resist actions together. CFST is widely used in buildings, bridges, transportation hubs, energy infrastructures, and other constructions due to its superior mechanical properties. It has emerged as a superior structural type for main structures of the contemporary major civil engineering constructions in China. A systematic analytical theory and design technology system for CFST structure in terms of the whole life cycle has been established, which lays a foundation for its design and construction and the realization of its high performance and life-cycle safety in practice. In the past decades, the author has been teaching a course on CFST structures for senior undergraduate and postgraduate students at Tsinghua University. The author believes that it is necessary to form a teaching textbook to systematically discuss the basic theoretical and technical issues, such as the constitutive models of materials, the resistance calculation methods, the key structural detailing, and the construction techniques that support the nonlinear analysis and refined design of CFST structures. This textbook is based on a compilation of lecture notes from these years. Chapter 1 of this book discusses the basic forms, the working characteristics, and the development history of CFST structures. CFST structure has a complex loading mechanism. The high performance and mechanical complexity originate from the nonlinear confinement effect of the steel tube on the core concrete. The chapter illustrates the concept of “confinement factor”, the mechanical nature of the nonlinear confinement effect, the theoretical framework of the CFST structure analysis in terms of the whole life-cycle, and the basic principles of the CFST structure design. Typical engineering application practices of the CFST structures are also introduced. The “matching” design of the materials that make up the CFST structure is crucial to ensure its high performance. Chapter 2 of this book discusses the design principles of CFST structural materials, the determination principles of the connection materials, and the protective materials, including the anti-corrosion coatings and the fireproof coatings. In the past, based on the in-depth study on the confinement effect of the CFST, the hardening, plasticity, and softening characteristics of stress–strain relationship of the v

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core concrete in compression and the corresponding limit value of the confinement factor have been clarified, and based on this, the constitutive models of the core concrete applicable to short-term and long-term loading, cyclic loading, elevatedtemperature action, and other multiple working conditions have been established, which created the conditions for realizing CFST structural analysis in terms of the entire life cycle. For concrete-encased CFST hybrid structures, the constitutive models of the stirrup-confined concrete are further improved. Chapter 3 of this book discusses the structural analysis methods, the shrinkage and creep models of concrete, the constitutive models of steel and concrete, and the interface models between steel and concrete. Chapter 4 of this book deals with resistances of CFST members subjected to single, complex, long-term, and seismic loads. The methods of calculating vertical and lateral local bearing resistances, the influence of the cross-sectional size, the concept and determination methods of the limiting value of initial stress in the steel tube, and the limiting value of core concrete void are also discussed. CFST hybrid structure is a new structural form developed on the basis of CFST, traditional steel, and concrete structures. This type of structure takes the CFST members serving as its main members, which are in contact with and act compositely with other members or components. From the perspective of structural type classification, the CFST hybrid structure is classified as the general category of CFST structures. Chapter 5 of this book discusses the working mechanisms and the resistance calculation methods of CFST hybrid structures. The reasonable design of key joints is the basis for ensuring the reliable work of the CFST structural systems. Chapter 6 discusses the design principles and methods of beam-to-column joints, CFST chord-steel tubular web joints, detailing of the column bases and supporting joints, and fatigue design of joints. Chapter 7 of this book describes the design principle of fire resistance and detailing requirements of fire protection for CFST structures based on the coupled loadtemperature-time analysis. The design principles and methods of corrosion resistance and impact resistance for CFST structures are also introduced. Because the core concrete of CFST is concealed by the steel tube, scientific and reasonable construction methods are crucial to ensure the high quality and safety of this type of structure. Chapter 8 of this book discusses the fabrication and installation of steel tubes as well as the construction of core concrete and concrete encasement. This chapter also describes the inspection, acceptance, maintenance, and dismantling of CFST structures. Chapter 9 of this book discusses the prospects of the CFST structures. In order to facilitate the reader’s reference, the appendix of this book presents design examples for CFST hybrid structures based on GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures and other relevant national standards.

Preface

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The author’s research work has received continuous collaboration and support from colleagues in the engineering field. Mr. Yin Ye, Zhong Fan, Tingmin Mou, Weibiao Yang, Qianyi Song, and Dayan Qin have provided the authors with relevant engineering photos and information in this book. This book is an English translation of the book Theory of Concrete-Filled Steel Tubular Structures (in Chinese), published by China Architecture & Building Press in January 2023. Zhao Li, the editor from China Architecture & Building Press, has made professional and patient editing works for the publication of the Chinese version of this book. The author greatly appreciates their help toward the publication of this book. Due to the limitations of the author’s knowledge, various parts of this book can be further improved. Criticism and corrections from the readers are much appreciated! Nanning/Beijing, China February 2023

Lin-Hai Han

Introduction

Concrete-filled steel tube (CFST) is a composite structural type that is formed by filling concrete into a steel tube, and the two materials can resist actions together. It is one of the superior structural forms for the main structures of contemporary major civil engineering in China. Focusing on this critical area, the book elaborates the basic forms, the mechanical characteristics, and the typical engineering applications of CFST structures. Based on the analytical theory and design methods of CFST in terms of the entire life cycle, the CFST structural materials, including steel, concrete, connection materials, and protection materials, are discussed. The CFST structural analysis methods are addressed, including shrinkage and creep models of concrete, the constitutive models of steel and concrete, and interface models between steel and concrete. The working mechanism of CFST structures under single, complex, longterm and seismic loads, local bearing, and its size effects is elaborated. The basic concepts and determining methods of the limiting value of initial stress as well as the limiting value of core concrete void in the steel tube are discussed. The mechanical characteristics and resistance calculation methods of CFST hybrid structures, the design of CFST joints, the design principles and methods of corrosion, fire and impact resistances for CFST structures, the construction, acceptance, maintenance, and dismantling of CFST structures are also discussed. The development prospects of CFST structures are also discussed in this book. Finally, calculation examples for CFST hybrid structures are presented at the end of the book in accordance with the current national standard GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures. This book is intended to be used as a textbook by postgraduate and senior undergraduate students of civil engineering or other relevant fields. It can also be used by readers with some basic knowledge of steel structures, concrete structures, etc.

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Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Fundamental Mechanical Properties of Concrete-Filled Steel Tubular (CFST) Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Development History of Concrete-Filled Steel Tubular (CFST) Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Analytical Theory of Concrete-Filled Steel Tubular (CFST) Structures in Terms of Whole Life Cycle . . . . . . . . . . . . . . . . . . . . . . . 1.4 General Requirements for the Design of Concrete-Filled Steel Tubular (CFST) Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Typical Engineering Applications of Concrete-Filled Steel Tubular (CFST) Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 10 18 26 27

2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Connecting Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Protective Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Anti-corrosion Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Fireproof Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49 49 50 53 58 59 59 60

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Design Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Shrinkage and Creep Models of Concrete . . . . . . . . . . . . . . . . . . . . . . 3.5 Constitutive Models of Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Constitutive Models of Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Fiber-Based Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Finite Element Analysis-Based Models . . . . . . . . . . . . . . . . . .

63 63 64 67 71 76 80 80 94

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3.7 Interface Models Between Steel and Concrete . . . . . . . . . . . . . . . . . . 3.7.1 Steel Tube-Core Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.2 Steel Tube-Concrete Encasement . . . . . . . . . . . . . . . . . . . . . . . 3.7.3 Reinforcement-Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

104 104 109 110

4 Design of Concrete-Filled Steel Tubular (CFST) Members . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Design of Members Under Single Loading Conditions . . . . . . . . . . . 4.2.1 Resistance in Axial Compression and Tension . . . . . . . . . . . . 4.2.2 Bending Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Torsional Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Shear Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Design of Members Under Combined Loading Conditions . . . . . . . 4.3.1 Resistance in Combined Compression (Tension) and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Resistance in Combined Compression and Torsion . . . . . . . . 4.3.3 Resistance in Combined Bending and Torsion . . . . . . . . . . . . 4.3.4 Resistance in Combined Compression, Bending and Torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.5 Resistance in Combined Compression, Bending and Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.6 Resistance in Combined Compression, Bending, Torsion and Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Resistance for Members Under Long-Term Loading . . . . . . . . . . . . . 4.5 Hysteretic Models of Concrete-Filled Steel Tubular (CFST) Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Resistance of Members to Local Bearing . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Vertical Local Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Lateral Local Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Influence of Cross-Sectional Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Limiting Value of Initial Stress in the Steel Tube . . . . . . . . . . . . . . . . 4.9 Limiting Value of Core Concrete Void in the Steel Tube . . . . . . . . . .

115 115 116 116 128 131 133 134

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Trussed Concrete-Filled Steel Tubular (CFST) Hybrid Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Resistance in Compression and Bending . . . . . . . . . . . . . . . . . 5.2.2 Shear Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Load Characteristics Considering Effects of Whole Construction Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Design of Single-Chord Structures for Compression and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

135 142 145 147 150 154 157 159 170 170 177 180 181 184 189 189 190 191 207 208 210 213

Contents

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5.3.3 Design of Four-Chord Structures for Compression and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.4 Design of Six-Chord Structures for Compression and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.5 Design of Slender Structures for Compression and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.6 Design of Structures for Compression and Bending Under Long-term Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.7 Design of Structures for Shear . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.8 Design of Arch Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Design of Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Types of Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Beam-to-Column Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Concrete-Filled Steel Tubular (CFST) Chord to Steel Tubular Web Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Design Method of Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Beam-to-Column Joints of Concrete-Filled Steel Tubular (CFST) Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Beam-to-Column Joints of Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 Concrete-Filled Steel Tubular (CFST) Chord to Steel Tubular Web Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.4 Column Bases and Supporting Joints . . . . . . . . . . . . . . . . . . . . 6.4 Fatigue Design of Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Protective Design of Concrete-Filled Steel Tubular (CFST) Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Design of Corrosion Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Basic Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Resistance of Members Under Corrosion . . . . . . . . . . . . . . . . 7.3 Design of Fire Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Basic Principles of Fire Resistance . . . . . . . . . . . . . . . . . . . . . 7.3.2 Fire Resistance Ratings of Concrete-Filled Steel Tubular (CFST) Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Fire Resistance Ratings of Concrete-Filled Steel Tubular (CFST) Hybrid Structures . . . . . . . . . . . . . . . . . . . . . . 7.3.4 Resistance of Members During Fire . . . . . . . . . . . . . . . . . . . . . 7.3.5 Resistance of Members After Fire . . . . . . . . . . . . . . . . . . . . . . 7.3.6 Detailing Requirements of Fire Protection . . . . . . . . . . . . . . . 7.4 Design of Impact Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Basic Principles of Impact Resistance . . . . . . . . . . . . . . . . . . . 7.4.2 Design Methods of Impact Resistance . . . . . . . . . . . . . . . . . . .

226 235 242 244 249 258 263 263 264 264 265 269 269

275 283 289 296 301 301 302 302 303 305 306 308 310 313 316 324 330 330 334

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8 Construction, Inspection and Acceptance, Maintenance and Dismantling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Fabrication and Erection of Steel Structures . . . . . . . . . . . . . . . . . . . . 8.3 Placement of Core Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Construction of Concrete Encasement . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Inspection and Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6 Maintenance and Dismantling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

339 339 340 341 347 351 352

9 Prospects of Concrete-Filled Steel Tubular (CFST) Structures . . . . . . 355 Appendix A: Design Examples of Trussed Concrete-Filled Steel Tubular (CFST) Hybrid Structures . . . . . . . . . . . . . . . . . . . . . 363 Appendix B: Design Examples of Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 Appendix C: Finite Element Analysis Examples of Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid Structures . . . . . . . . . . . . . . . . . . . . . 421 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

About the Author

Prof. Lin-Hai Han (Doctor of Philosophy) has long been engaged in teaching and research in the area of structural engineering. In the past 30 years, he has focused on concrete-filled steel tubular (CFST) structures, a key research area in civil engineering, and established its life-cycle-based analytical theory, including systematic and innovative research outcomes regarding the discovery of new phenomenon, the revealing of characteristic mechanical trends, the invention of structural detailing, the development of novel experimental apparatus, and the accurate calculations of structural resistances. He has published five books, including ConcreteFilled Steel Tubular Structures: Theory and Practice, Advanced Composite and Mixed Structures: Testing, Theory and Design Approach, Fire Safety Design Theory of Steel-Concrete Composite Structures, and numerous papers in prestigious Chinese and international academic journals. The research outcomes have been applied to the design of iconic constructions in sectors related to building, highway, railway, civil aviation, energy, etc. He has presided over the drafting of ten technical standards, including the Chinese national standard GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures (both Chinese Edition and English Edition). He is also presiding over the drafting of an ISO standard Design Standard for Concrete-Filled Steel Tubular (CFST) Hybrid Structures. As the first author, he was awarded the State Natural Science Award (Second Prize) in 2019, two State Patent Awards (Excellence Prize) in 2021 xv

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About the Author

and 2022, respectively, and the Standard Technology Innovation Award (First Prize) in 2022. He was selected in the National Hundred, Thousand and Ten-Thousand Talent Program (First and Second Tiers), funded by the National Science Fund for Distinguished Young Scholars, and appointed the Changjiang Distinguished Professorship of the Ministry of Education. He currently serves as the deputy secretary of the CPC Committee of Guangxi University, the president of Guangxi University, a tenured professor at Tsinghua University, and the director of the State Key Laboratory of Featured Metal Materials and Life-Cycle Safety for Composite Structures.

Symbols

Design Actions, Action Effects and Resistances M M cd M cu N N0 Nc N cd NE N cfst N rc Nt Nu V V cd V cfst V cu V rc T T cd T cu

Bending moment Design value of bending moment Bending resistance Axial force Resistance of cross-section of the CFST hybrid structure to compression Resistance of cross-section to compression Design value of axial force Euler critical force Resistance of cross-section of the encased CFST member to compression Resistance of cross-section of the concrete encasement to compression Resistance of cross-section to tension Resistance in axial compression Shear force Design value of shear force Shear resistance of the encased CFST member Shear resistance Shear resistance of the concrete encasement Torsional moment Design value of torsional moment Torsional resistance

Material Properties Ec E c,c E c,oc E s,l

Modulus of elasticity of concrete Modulus of elasticity of core concrete in the CFST member Modulus of elasticity of concrete slab or concrete encasement Modulus of elasticity of longitudinal reinforcement xvii

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Es f f ba f bu fc f c f ck f c,c f c,oc f cu f cu,c f cu,oc fl f l f sc f scp f scy f sv ft f tk f ts fu fv fw fy f yh G Gc,c Gc,oc Gs

Symbols

Modulus of elasticity of steel Design value of tensile, compressive, and flexural strength of steel Mean bond strength Ultimate bond strength Design value of compressive strength of concrete, measured on prisms 150/300 mm Cylinder strength of concrete Characteristic value of compressive strength of concrete Design value of compressive strength of core concrete in CFST members, measured on prisms 150/300 mm Design value of compressive strength of concrete encasement, measured on prisms 150/300 mm Characteristic value of cube strength of concrete Characteristic value of cube strength of core concrete in CFST members Characteristic value of cube strength of concrete encasement Design value of tensile strength of longitudinal reinforcement Design value of compressive strength of longitudinal reinforcement Design value of compressive strength of the CFST cross-section Proportioned limit of CFST cross-section to axial compression Characteristic value of compressive strength of the CFST cross-section Design value of shear strength of the CFST cross-section Design value of tensile strength of the concrete Characteristic value of tensile strength of the concrete Splitting strength of concrete Tensile strength of steel Design value of shear strength of the steel Design value of the tensile, compressive, and flexural strength of the steel tube in the web Yield strength of steel Yield strength of stirrups Shear modulus Shear modulus of the core concrete in the CFST member Shear modulus of the concrete slab or concrete encasement Shear modulus of steel

Geometric Parameters a Ab Ac Ah Al 

Thickness of fireproof coatings Dispersed bearing area when under lateral local bearing Cross-sectional area of the core concrete in the CFST member Total cross-sectional area of the stirrups Cross-sectional area of the longitudinal reinforcement

Symbols

AL Alc Aoc As Asc Ase Asv Av Aw be B Bc C d dr ds dw D De Di H h0 hb hi Ic Is I s,h I l,h I c,h I oc,h l0 l1 lv s t te u0 α Δt

xix

Area under local bearing Direct bearing area when under lateral local bearing Cross-sectional area of concrete slab or concrete encasement Cross-sectional area of the steel tube Cross-sectional area of the CFST member Cross-sectional area of the steel tube after corrosion Cross-sectional area of stirrups Cross-sectional area of stirrup-confined concrete Cross-sectional area of a single web steel tube in trussed CFST hybrid structure Effective flange width of the concrete slab Cross-sectional width Cross-sectional width of stirrup-confined concrete Cross-sectional perimeter Diameter of the core concrete in CFST member or screwed reinforcement Mean width of the circumferential void Maximum height of the spherical-cap void Outside diameter of the steel tube in the web Outside diameter of the circular CFST member Outside diameter of the steel tube after corrosion Diameter of the core concrete in the CFST member Cross-sectional height Effective height of the cross-section along the bending direction Thickness of the concrete slab in the compression zone of the cross-section Distance between the centroids of the compression and the tension chords along the cross-sectional height Second moment of area of the core concrete in the CFST member Second moment of area of the steel tube Second moment of area of the steel tube to centroidal axis of cross-section of the CFST hybrid structure Second moment of area of the longitudinal reinforcement to centroidal axis of cross-section of the CFST hybrid structure Second moment of area of the core concrete to centroidal axis of cross-section of the CFST hybrid structure Second moment of area of the concrete slab or concrete encasement to centroidal axis of cross-section of the CFST hybrid structure Effective length of the structure Length of a single chord in an interval of the trussed CFST hybrid structure Length of stirrups Spacing of stirrups; slump; relative slip Wall thickness of the steel tube or thickness of the steel plate; time Wall thickness of the steel tube after corrosion Initial deflection Half of the projection angle of web on the plane of chord cross-section Mean wall thickness loss of the steel tube after corrosion

xx

ρ ρv ρ sv θ W sc W sc1 W sc,t

Symbols

Longitudinal reinforcement ratio Volumetric stirrup ratio Superficial stirrup ratio Angle between the diagonal web and the chord; angle between the web that transmits lateral local bearing and the chord Flexural modulus of cross-section of the trussed CFST hybrid structure Flexural modulus of cross-section of the CFST structure Torsional modulus of cross-section of the CFST structure

Coefficients and Others c

Cm kB k cr k nL kT K LC Kd n ncfst nL R Rd td th to tR T α α1 αe αs β βl βc ε εy εo

Distance between the neutral axis and the compressive edge of the cross-section; quality of cement per cubic meter; thickness of reinforced concrete cover Eccentricity adjustment coefficient at the end section Coefficient of flexural stiffness after fire exposure Long-term load coefficient Adjustment coefficient for long-term load ratio Coefficient of the resistance of the CFST column during fire Reduction coefficient of CFST members under local bearing Reduction coefficient due to void Axial load ratio; total number of chords in the trussed CFST hybrid structure; load ratio during fire Resistance coefficient of the encased CFST member Long-term load ratio Load ratio during fire Dynamic increase factor under impact Time after the end of initial wet curing Critical time when cooling Heating time ratio Fire resistance rating Temperature Coefficient of linear expansion Strength coefficient of the equivalent stress block for concrete encasement Cross-sectional steel ratio of the CFST member after corrosion Cross-sectional steel ratio of the CFST member Ratio of local bearing area; initial stress coefficient; diameter–width ratio Strength increase factor of concrete when under lateral local bearing Coefficient of concrete strength when under lateral local bearing Strain Yield strain of steel Peak uniaxial compressive strain of the core concrete in the CFST member

Symbols

εcu εl εsh ηc γm γt γu γv γ sc ϕ ϕc λ λo λv λp ξ ξe σ σo σ so τ τu χr χs μ ζc Δy Δu

xxi

Ultimate compressive strain of concrete Creep strain of concrete Shrinkage strain of concrete Amplification coefficient of bending moment Plastic development factor of the bending resistance Calculation coefficient of torsional resistance Ultimate shear deformation; coefficient of the restriction of steel tubular on concrete shrinkage Calculation coefficient of shear resistance Partial safety factor for the compressive strength of the CFST member Stability factor for the axial compression structure Stability factor for concrete slab in compression Equivalent slenderness ratio Critical slenderness ratio for the elasto-plastic buckling of structure Shear span-to-depth ratio of the calculated section Critical slenderness ratio for the elastic buckling of the structure Confinement factor Nominal confinement factor after corrosion Stress Peak uniaxial compressive stress of the core concrete in the CFST member Initial stress in the steel tube Interfacial bond stress; cross-sectional mean shear stress Bond strength Circumferential void ratio Spherical-cap void ratio Friction coefficient Adjustment coefficient of curvature Yield displacement Ultimate displacement

Chapter 1

Introduction

Key Points and Learning Objectives Key Points This chapter discusses the basic forms, the mechanical characteristics and the development history of concrete-filled steel tubes (CFST); explains the concept of the “confinement factor” of CFST and its mechanical essence; introduces the theoretical analysis framework based on the whole life cycle and the basic design principles of CFST. This chapter also introduces some typical engineering practices of CFST. Learning Objectives Comprehend the concept of “confinement factor”, the mechanical essence of the confinement effect and the basic principles of CFST design. Get familiar with the basic forms and working characteristics of CFST. Learn about the development history and the typical engineering practices of CFST structures.

1.1 Fundamental Mechanical Properties of Concrete-Filled Steel Tubular (CFST) Structures Concrete-filled steel tube (CFST) is a composite structural type that is formed by filling concrete into a steel tube, and the two kinds of materials could resist actions together. The commonly used cross-sectional shapes of CFST are shown in Fig. 1.1, where circular, square and rectangular cross-sections are most widely used in practice (shown as Fig. 1.1a–c). According to the actual requirements of the engineering projects, polygonal, circular-end rectangular and elliptical cross-sectional forms can also be adopted for CFST structures (shown as Fig. 1.1d–f).

© China Architecture & Building Press 2024 L. Han, Theory of Concrete-Filled Steel Tubular Structures, https://doi.org/10.1007/978-981-99-2170-6_1

1

2

1 Introduction

Steel tube

Steel tube

Core concrete

Steel tube

Core concrete (b) Square

(a) Circular Steel tube

Core concrete (d) Polygonal

Core concrete (c) Rectangular Steel tube

Steel tube

Core concrete (e) Circular-end rectangular

Core concrete (f) Elliptic

Fig. 1.1 Typical CFST cross-sectional shapes

The steel tube of CFST can be fabricated through hot-rolling, cold-forming or welding, etc. The steel tube can be made from carbon steel, high-strength steel, stainless steel, etc. The core concrete poured in the steel tube can be conventional concrete, high-strength concrete, self-consolidating concrete, recycled aggregate concrete, etc. CFST is a type of composite structures, the composite effects of which can be generally summarized as the following three aspects: (1) “Confinement effect” of the steel tube on core concrete Mechanical behavior of thin-walled steel tubes is sensitive to local defects, so it is not easy to make full use of the material strength and the resistance is relatively unstable. After filling the steel tube with concrete to form CFST, concrete can delay or avoid the premature local buckling of the thin-walled steel tube. At the same time, the steel tube confines the core concrete, making it in a three-dimensional compression state under the axial compression load, thus delaying the longitudinal cracking of the core concrete. The two materials complement each other and work together to make CFST have higher resistance and better ductility. Taking a circular CFST member in axial compression as an example, Fig. 1.2 shows a schematic diagram of the interaction between the steel tube and its core concrete, where p represents the interaction stress between the steel tube and its core concrete. In addition to the physical properties of the steel tube and its core concrete, the match of their geometric and physical properties will also have significant influences on the mechanical behavior of the CFST member. In short, the combination of the steel tube and its core concrete to form CFST not only makes up for the respective weaknesses of the two materials, but also enables the full utilization of the advantages of both, which is exactly the superiority of the mechanical behavior of the CFST structures.

1.1 Fundamental Mechanical Properties of Concrete-Filled Steel Tubular …

3 Steel tube

p

Core concrete

p Core concrete

Steel tube Steel tube Core concrete

p

Steel tube

Fig. 1.2 Interaction between the steel tube and its core concrete

In order to quantitatively study the change of resistance after filling concrete in a hollow steel tube, comparative tests of members in axial compression were conducted. In the test, the specimens were made of the same steel or concrete, and their dimensional information is as follows: 1) Hollow steel tube specimen: circular cross-section, the outside diameter is 114 mm, and the wall thickness is 2 mm; 2) Plain concrete specimen: circular cross-section, the diameter is 110 mm; 3) CFST specimen: circular cross-section, the outside diameter is 114 mm, and the wall thickness of the steel tube is 2 mm. The test results of the above three-type specimens in axial compression are as follows: 1) Hollow steel tube specimen: N s = 158 kN; 2) Plain concrete specimen: N c1 = 192 kN; 3) CFST specimen: N sc = 447 kN. The comparison of the resistance of three-types specimens in axial compression is shown in Fig. 1.3. The resistance of CFST in axial compression (N sc ) is higher than the sum of steel tube and core concrete alone (N s + N c1 ), reflecting the “combination” effect of “1 + 1 > 2”. The comparison of the failure modes of hollow steel tubes, plain concrete and CFST stub members is shown in Fig. 1.4. The hollow steel tube shows inwards and outwards local buckling, the plain concrete shows brittle fracture failure, and the CFST shows outwards local buckling of the steel tube, and its overall deformation capacity is better. In order to compare the change in resistance of hollow steel tubes before and after filling concrete in axial tension, comparative tests of specimens using the same steel in axial tension were carried out. 1) Hollow steel tube specimen: circular cross-section, the outside diameter is 203 mm, and the wall thickness is 3 mm. 2) CFST specimen: circular cross-section, the outside diameter is 203 mm, and the wall thickness of the steel tube is 3 mm.

4

1 Introduction

447 kN 350 kN

192 kN 158 kN

Ns

Nc1

Ns +Nc1

Nsc

Fig. 1.3 Comparison of resistance of members in axial compression

(a) Hollow steel tube

(b) Plain concrete

(c) CFST

Fig. 1.4 Failure modes of hollow steel tube, plain concrete and CFST member in axial compression

The comparison of the axial tensile load (N)-axial strain (ε) relationship between the hollow steel tube and CFST specimen is shown in Fig. 1.5. It can be seen that the tensile strength of the CFST specimen is higher than that of the hollow steel tube specimen. The failure modes of the hollow steel tube and CFST specimens in axial tension are shown in Fig. 1.6. It can be seen that when failure occurs in the specimen, the hollow steel tube shows an obvious “necking” phenomenon, while the CFST specimen shows better integrity due to the existence of core concrete, and its steel tube does not occur a “necking” phenomenon. In order to compare the change of resistance of hollow steel tubes before and after filling concrete in torsion, comparative tests of specimens using the same steel in torsion were carried out. 1) Hollow steel tube specimen: circular cross-section, the outside diameter is 203 mm, and the wall thickness is 4 mm;

1.1 Fundamental Mechanical Properties of Concrete-Filled Steel Tubular …

5

N (kN)

Fig. 1.5 Comparison of axial tensile load (N)-axial strain (ε) relationship

CFST

Hollow steel tube

ε (με)

Fig. 1.6 Failure photographs of hollow steel tube and CFST members in axial tension Hollow steel tube Necking

(a) Hollow steel tube

CFST

Necking

(b) CFST

2) CFST specimen: circular cross-section, the outside diameter is 203 mm, and the wall thickness of the steel tube is 4 mm. The comparison of the torsion (T )-torsion angle (θ ) relationship between the hollow steel tube and CFST specimen is shown in Fig. 1.7. The initial torsional stiffness of the hollow steel tube specimen is smaller, and the resistance decreases significantly after the steel tube is bent obliquely in the direction of 45°. The CFST specimen shows superior resistance and ductility. The resistance of the hollow steel tube specimen in torsion was 66 kN·m, and that of the CFST specimen was 98 kN·m, which was 48% higher than the former. The comparative failure modes of the hollow steel tube and CFST specimens are shown in Fig. 1.8. The hollow steel tube specimen shows inclined outwards buckling along 45°, while the CFST specimen maintains excellent integrity. (2) Changes of failure modes of members Compared with the hollow steel tube members, the “buckling mode” of the CFST member is obviously different due to the action of core concrete. The main “contribution” of core concrete is to delay the premature local buckling of the steel tube, so that the resistance and plastic deformation capacity of CFST members are greatly

6

1 Introduction T (kN·m) CFST

Hollow steel tube

θ (°)

Fig. 1.7 Comparison of the torsion (T )-torsion angle (θ) relationship

(a) Hollow steel tube

(b) CFST

Fig. 1.8 Failure photographs of hollow steel tube and CFST members in torsion

improved by comparison with hollow steel tubes under the conditions of the same parameters. The comparison of the failure modes of hollow steel tube, reinforced concrete and CFST stub columns in axial compression is shown in Fig. 1.9. During loading, the failure modes of members determine their resistance. CFST will not occur inwards local buckling like a hollow steel tube, and also will not occur inclined compression damage like reinforced concrete. The comparison of failure modes of hollow steel tube, concrete and CFST member in axial tension is shown in Fig. 1.10. The phenomenon of “necking” occurs when the hollow steel tube member without pouring the core concrete is subjected to axial tensile failure, as shown in Fig. 1.10a. The corresponding concrete member

1.1 Fundamental Mechanical Properties of Concrete-Filled Steel Tubular … Hollow steel tube

Outwards buckling

7

Core concrete

Concrete

Steel tube Outwards buckling

Cracks Inwards buckling

Concrete crushing

Concrete crushing

(a) Hollow steel tube

(b) Reinforced concrete

(c) CFST

Fig. 1.9 Comparison of failure modes of hollow steel tube, reinforced concrete and CFST stub columns in axial compression

is more likely to form fracture cracks during loading and eventually lead to failure, shown in Fig. 1.10b. For the CFST member, the steel tube and its core concrete can complement to each other and act together, the core concrete surface will uniformly develop microfractures perpendicular to the direction of loading, and the steel tube will not suffer “necking” failure, as shown in Fig. 1.10c. For the development of concrete cracks of plain concrete and CFST to axial tension, the failure mode of the plain concrete member is cracked in the middle section, and a main crack develops continuously until penetration during loading (Fig. 1.10b). The axial tension subjected by concrete is gradually transferred to the outer steel tube after the first crack develops in the core concrete of CFST. Therefore, when the CFST member is subjected to failure, the crack development Steel tube Steel tube

Concrete

Core concrete

Fracture cracks Microfine cracks

(a) Hollow steel tube

(b) Concrete

(c) CFST

Fig. 1.10 Comparison of failure modes of hollow steel tube, concrete and CFST member in axial tension

8

1 Introduction

Fig. 1.11 Comparison of failure modes of hollow steel tube, reinforced concrete and CFST member in bending

Inwards buckling

Steel tube

(a) Hollow steel tube Concrete Cracks

Concrete crushing

(b) Reinforced concrete Outwards buckling

Core concrete Concrete crushing

Steel tube

Cracks (c) CFST

and distribution of the core concrete along the circumferential direction are relatively uniform (Fig. 1.10c). The comparison of failure modes of the hollow steel tube, reinforced concrete and CFST member in bending is shown in Fig. 1.11. For the hollow steel tube member, the compressive area has the inwards buckling phenomenon (Fig. 1.11a). For the reinforced concrete member, the cracks in the tensile area are relatively concentrated and obvious, and there are concentrated crushing areas in the compressive area (Fig. 1.11b). For the CFST member, the steel tube in the compressive area has outwards buckling and the core concrete is crushed, while the microcracks develop in the tensile area of the core concrete (Fig. 1.11c). The comparison of failure modes of the torsional members among hollow steel tubes, reinforced concrete and CFST is shown in Fig. 1.12. For the hollow steel tube member, the steel tube is twisted obliquely along about 45°. For the reinforced concrete member, there are multiple shear diagonal cracks in the concrete. For the CFST member, the steel tube and concrete act together with no slip marks between them, and there are no obvious shear oblique cracks in the core concrete. CFST has good plasticity, toughness, high impact, earthquake, and fire resistances, and post-fire repairability due to the advantages of mutual contribution, complementary to each other and acting together between the steel tube and its core concrete. (3) Convenient placement of the core concrete During the placement of core concrete, the steel tube can be used as the formworks, which makes the placement of concrete more convenient, saves formworks, shortens

1.1 Fundamental Mechanical Properties of Concrete-Filled Steel Tubular …

Steel tube

9

Core concrete

Concrete

Steel tube

(a) Steel tube

(b) Reinforced concrete

(c) CFST

(1) Circular cross-section Steel tube

Core concrete

Concrete

Steel tube

Shearing oblique cracks

(a) Steel tube

(b) Reinforced concrete

(c) CFST

(2) Square cross-section Fig. 1.12 Comparison of failure modes of hollow steel tubes, concrete and CFST members in torsion

the construction period and reduces direct costs of construction. The convenient construction of core concrete is one of the important advantages of CFST. To sum up, CFST is a high performance structural with the advantages of the mechanical behaviour and construction. The scientific and reasonable design of CFST can achieve the high performance utilization of steel and concrete and make full use of the characteristics of high resistance, excellent plasticity, toughness, constructability, fire resistance and economy. It should be noted that each kind of structure has its own technical characteristics, and needs to be selected according to the engineering necessity. The construction of high-quality main structures is crucial to ensure the sustainable development of civil engineering. In the engineering practice of CFST, the high performance of CFST can only be achieved and guaranteed by scientific adoption and construction.

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1 Introduction

1.2 Development History of Concrete-Filled Steel Tubular (CFST) Structures The development of CFST has undergone a gradual evolution. In the 1870s, Severn Railway Bridge (UK) adopted CFST piers, which was one of the early reported structural types using CFST. At that time, the placement of core concrete inside the steel tube was to prevent corrosion. In the early days, the outer steel tube of CFST usually used seamless steel tube, normal strength hot rolled steel tube and cast steel tube, etc. And the core concrete usually used normal strength concrete. Since the 1960s, scholars have studied the mechanical behaviour of circular CFST members in combined compression and bending, the interface performance of steel tube and core concrete, etc. The members were mainly with a circular cross-section. In the 1970s to the 1980s, CFST research expanded from basic static performance gradually to seismic performance, fire resistance and long-term load performance, etc. Since the 1990s, CFST engineering applications have made great progress. Coldformed steel tubes and welded steel tubes with better mechanical properties were widely used in CFST, which made it possible to use thinner and wider size ranges of outer steel tubes. High-strength concrete (such as strength class of the concrete is higher than C60–C80) was used to make CFST further higher strength, smaller cross-section and better economy. At this stage, the application of square and rectangular CFST in engineering practice was gradually increased in order to meet the requirements of building construction. Around the 1990s, researchers further expanded the study of structural performances under single static load to combined structural performances of CFST in combined compression, bending and shear, or combined compression, bending and torsion, etc. The research on seismic performance was also further developed. At the same time, the research on square and rectangular CFST design methods made great progress and there were also research reports on CFST with thin-walled steel tubes. CFST had been applied in some high-rise buildings and bridges in the United States, Europe, and Australia, such as Two Union Square (56 stories, 226 m, circular crosssection) built in 1989 in the United States, Casselden Place (43 stories, 166 m, circular cross-section) built in 1992 in Australia, and Commerzbank Tower (56 stories, 259 m, triangular cross-section) completed in 1996 in Germany, etc. Since the twenty-first century, there have been some new trends in the research of CFST. On the one hand, CFST analysis theory has been further developed based on traditional CFST structures; on the other hand, CFST with new cross-sections (elliptical, polygonal, etc.), new materials (such as high strength and performance concrete, high-strength steel with yield strength ≥ 460 MPa, stainless steel, etc.) and new composite types (such as concrete-filled double skin steel tubular structure) have appeared one after another in order to improve the structural performance. In addition, CFST hybrid structures in which CFST members are in contact with and act compositely with conventional steel or concrete members (components) have been further developed. An overview of the development of CFST structural forms is shown in Fig. 1.13.

1.2 Development History of Concrete-Filled Steel Tubular (CFST) Structures Fig. 1.13 Schematic diagram of the development of the CFST structural forms

11

Traditional CFST stuctures New CFST structures

High Performance

CFST hybrid structures

In the past decades, new progress has been made in the research of the mechanical behaviour of CFST under long-term loading and complex loading. On this basis, the CFST analysis theory in terms of the whole life cycle has been established, which has laid the theoretical foundation for its theoretical analysis, calculation and design. It has been extended and applied to the theoretical research of new CFST members, key joints and structural systems. In addition, it has been widely applied to the refined design of large and complex CFST engineering structures. (1) Novel CFST structures The concept of traditional CFST structures has been expanded and applied to novel CFST structures, such as elliptical CFST, concrete-filled double skin steel tubular structure (CFDST), FRP-encased (fiber-reinforced polymer/plastics) CFST, stiffeners-encased CFST, steel profile-encased CFST, T-shaped CFST, prefabricated CFST and new tubes (such as stainless steel tubes and high-strength steel tubes) and/ or new core concrete materials (such as high-strength concrete, seawater sea sand concrete). Some of the new CFST structural forms are shown in Fig. 1.14. Due to the need of building appearance or structural performance, inclined CFST column members, tapered CFST members and curved CFST members are also used in actual engineering projects, as shown in Fig. 1.15a–c respectively. (2) CFST hybrid structure In recent years, large-scale infrastructure constructed in China tends to have superlong spans and towering, bear super weights, and work under severe environmental conditions. The development of matched high-performance main structures and the establishment of structural analysis theory and design technology system through design, construction and service have become a major engineering technical and scientific problem to be solved urgently. CFST hybrid structure is a new structure form developed based on traditional steel structure, concrete structure and CFST structure, which combines the CFST members and steel tubes or other types of steel profiles or reinforced concrete members (or components). Due to the “hybrid effects” among the different members (or components) in the CFST hybrid structure, they can act together and complement each other. In accordance with the current national standard GB 50083 Standard for General Terms Used in Design of Engineering Structures, such a structure form is classified as a “hybrid structure”. Compared to conventional steel structures, CFST hybrid structures have greater stiffness, better durability and lower cost. Compared to the conventional concrete structures, CFST hybrid structures have higher resistance, lighter self-weight, better seismic performance and better constructability.

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1 Introduction

Elliptical steel tube

(a) Elliptical CFST Stiffeners

FRP

Outer steel tube Steel tube Inner steel tube

(b) CFDST

Steel tube

(c) FRP-encased CFST

Steel profile

Steel tube

Steel tube

(d) Stiffeners-encased CFST (e) Steel profile-encased CFST (f) T-shaped CFST

Stainless steel tube

Spiral welded steel tube

Steel tube

(g) Prefabricated CFST

(h) Stainless CFST

Steel tube Steel plate

Steel tube

FRP

(j) Dumbbell type CFST

(i) Spiral welded CFST

(k) FRP-CFST

Fig. 1.14 Some of the new CFST members

Pentagonal steel tube

(l) Pentagonal CFST flange composite beam

1.2 Development History of Concrete-Filled Steel Tubular (CFST) Structures

Core concrete

Core concrete

(a) Inclined column

Core concrete

Steel tube

Steel tube

13

(b) Tapered member

Steel tube

(c) Curved member

Fig. 1.15 Inclined, tapered and curved CFST members

The national standard GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures was promulgated and implemented on December 1, 2021. In this technical standard, CFST hybrid structures consist of trussed CFST hybrid structures and concrete-encased CFST hybrid structures. 1) Trussed CFST hybrid structure Trussed CFST hybrid structure is the truss structure consisting of circular CFST chords and steel tube, CFST or other steel profile webs. There are two-chord, three-chord, four-chord, and six-chord trussed CFST hybrid structures, as shown in Fig. 1.16, and the chords are normally symmetrically placed. Trussed CFST hybrid structures may serve as structural members, such as truss girder systems with reinforced concrete slabs, or columns. During the construction of the trussed CFST hybrid structure, the steel components, such as the hollow steel tubes, are first erected, and the core concrete in the chords is then placed, as shown in Fig. 1.17. Prior to the hardening of concrete and the forming of CFST chords, there is initial stress in the steel tubes due to actions like construction loads. Thus, the structural safety of both the steel tubular structure during the construction stage and the trussed CFST hybrid structure during the service stage shall be ensured. 2) Concrete-encased CFST hybrid structure The concrete-encased CFST hybrid structure is a kind of hybrid structure consisting of the built-in circular CFST and the steel tube encased with reinforced concrete. The encased CFST member(s) in the concrete-encased CFST hybrid structure may be single or multiple, as shown in Fig. 1.18, and are normally symmetrically placed. For the single-chord cross-section, the CFST member is placed at the center of the cross-section with a rectangular concrete encasement, forming a solid crosssection. For the multi-chord cross-section, CFST chords are placed at the corners (four-chord type) and also mid-height of the cross-section (six-chord type) of the rectangular concrete encasement; steel tubes, or CFST or other steel profiles are

14

1 Introduction

2

2

1

1

(a) Two-chord cross-section

(b) Three-chord cross-section

2 2 1

1

(c) Four-chord cross-section

(d) Six-chord cross-section

Fig. 1.16 Cross-sections of trussed CFST hybrid structures. 1—CFST chords; 2—Webs

2

Placement of core concrete in chords

1 (a) Steel tubular structure

2 3

(b) Trussed CFST hybrid structure

Fig. 1.17 Construction process of a trussed CFST hybrid structure. 1—Steel tubular chords; 2— Webs; 3—CFST chords

used as webs to connect the CFST chords; to reduce self-weight, an internal hollow section, which may be octagonal or rectangular, is generally formed. The multi-chord concrete-encased CFST hybrid structure is indeed a derivation of the trussed CFST hybrid structure, and may be used as columns or arches. A typical construction process for the concrete-encased CFST hybrid structure consists of the erection of hollow steel tubular chords and webs, placement of core concrete in chords, installation of reinforcement, and placement of concrete encasement, as shown in Fig. 1.19. During the whole construction process, there will be complex stress and internal force redistribution in the materials and the structure, which might pose a threat to the structural safety during its design working life. Thus, the structural safety of both the steel tubular structure and the trussed CFST hybrid structure during the construction stage, and the structural safety of the

1.2 Development History of Concrete-Filled Steel Tubular (CFST) Structures

2

2

3

3

4

4

1

1

15

2 1

(a) Single-chord, solid cross-section

(b) Four-chord, rectangular crosssection with an internal hollow section

(c) Six-chord, rectangular cross-section with an internal hollow section

Fig. 1.18 Section of the concrete-encased CFST hybrid structure. 1—CFST; 2—Concrete encasement; 3—Hollow part; 4—Webs

concrete-encased CFST hybrid structure during the service stage, need to be ensured (Fig. 1.19). From the structural point of view, the CFST hybrid structure belongs to the category of CFST. (3) Beam-column joint, composite shear wall and frame structure In engineering practice, CFST frames are usually combined with reinforced concrete or steel structure to form CFST hybrid structure system, such as CFST frame-concrete shear wall, CFST frame-concrete core tube structure system and bottom CFST frameupper steel structure frame. 1) Plane K-joints of trussed CFST hybrid structure Research has been conducted on the static performance and impact resistance performance of circular and square trussed CFST hybrid structural plane K-joints. The plane K-joints of the trussed CFST hybrid structure are shown in Fig. 1.20. 3 Placement of core concrete in chords

Placement of concrete encasement

2 2 1

4 2 5

3

(a) Steel tube structure (b) Trussed CFST hybrid structure (c) Concrete-encased CFST hybrid structure

Fig. 1.19 Construction process of a concrete-encased CFST hybrid structure. 1—Steel tubular chords; 2—Webs; 3—CFST chords; 4—Concrete encasement; 5—Internal hollow section

16

1 Introduction

Steel tubular webs

Circular CFST chord (a) Circular cross-section

Steel tubular webs

Square CFST chord (b) Square cross-section

Fig. 1.20 Plane K-joints of trussed CFST hybrid structure

2) Joints of CFST column-steel beam, reinforced concrete beam and composite beam Researchers have conducted research on the static performance of square CFST column-steel beam blind bolt joints and the seismic performance of circular CFST column-steel beam outer ring plate joints, circular CFST column-steel beam blind bolt joints, square CFST column-steel beam inner spacer joints, square CFST column-composite beam joints and square CFST column-reinforced concrete beam penetration joints. The joints of CFST column-steel beam, composite beam and reinforced concrete beam are shown in Fig. 1.21. 3) Plane frames of CFST column-steel beam and steel profile reinforced concrete beam Researchers have carried out studies on the seismic performance of square CFST column-steel profile reinforced concrete beam frames, concrete-encased CFST hybrid structural columns-steel profile reinforced concrete beam frames and square CFST columns with support built-in sandwich plate-steel beam frames, and the fire resistance of CFST column-I shaped steel beam frames. The plane frames of CFST column-steel profile reinforced concrete beams and steel beams are shown in Fig. 1.22. 4) CFST frame structure Researchers have conducted studies on the seismic performance of multi-story CFST frames and high-rise CFST structures. The schematic diagrams of CFST frame structures are shown in Fig. 1.23. The scientific formulation of relevant engineering and construction technical standards is crucial to ensure the high quality development of CFST structures. At present, technical standards related to CFST structures have been promulgated and implemented at home and abroad, such as AIJ Recommendations for Design and Construction of Concrete Filled Steel Tubular Structures promulgated in 2005 in Japan, ANSI/

1.2 Development History of Concrete-Filled Steel Tubular (CFST) Structures Circular CFST colum

17

Circular CFST colum

Outer ring plate

blind bolts Steel beam

Steel beam (a) Connection with steel beam (outer ring plate)

(b) Connection with steel beam (blind bolts)

Ribbed square CFST column

Inner spacer

Steel beam

Bolts (c) Connection with steel beam (blind bolts)

Square CFST column (d) Connection with steel beam (inner spacer)

Composite beam Square CFST column

Reinforced concrete beam

(e) Connection with composite beam

(f) Connection with reinforced concrete

Square CFST column

Fig. 1.21 Joints of CFST column-steel beam, reinforced concrete beam, composite beam

AISC 360 Specification for Structural Steel Buildings promulgated in 2006 in the United States, EN 1994-1-1 Design of Composite Steel and Concrete Structures promulgated in 2004 in Europe, GB 50923-2013 Technical Code for Concrete-Filled Steel Tube Arch Bridges promulgated in 2013 and implemented in 2014 in China, GB 50936-2014 Technical Code for Concrete Filled Steel Tubular Structures promulgated and implemented in 2014 in China, GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures promulgated and implemented in 2021 in China and so on.

18

1 Introduction Steel profile reinforced concrete beam

Steel profile reinforced concrete beam

Square CFST column Concrete-encased CFST hybrid structural columns (a) Square CFST columns-steel profile reinforced concrete beam frame Steel beam Sandwich panel Square CFST column

(b) Concrete-encased CFST hybrid structural columns-steel profile reinforced concrete beam frame I shaped steel beam

Steel bracing

(c) Square CFST column with support built-in sandwich plate-steel beam frame

CFST column

(d) CFST column-I shaped steel beam frame

Fig. 1.22 Plane frames of CFST column-steel beam, steel profile reinforced concrete beam

1.3 Analytical Theory of Concrete-Filled Steel Tubular (CFST) Structures in Terms of Whole Life Cycle The whole life cycle of engineering structures includes design, construction, operation and maintenance. During the whole life cycle, the reliability of engineering structures will influence many aspects such as environment, material, information, energy and economy in the process of sustainable urbanization construction. It is necessary to design and select the engineering structure according to the engineering necessity. The construction of high-quality and long-life structures is the key to ensure the sustainable development of civil engineering, and is also one of the core foundations to achieve the overall carbon reduction goal of civil engineering. The design life of large-scale infrastructures with CFST as the main structure is usually more than 100 years, and the life cycle should safely resist frequent actions (complex stress, long-term load, steel corrosion, etc.) and occasional extreme actions (earthquake, fire, impact, etc.). Scientific and reliable analysis theory and design technology system need to be established urgently. Figure 1.24 shows the overall relationship among theoretical research, technical standard formulation and engineering practice of CFST structural performance. In terms of whole life cycle, the characteristics of analysis theory of CFST structures are generally reflected in the following three aspects: (1) comprehensive consideration of construction factors (e.g. steel tube fabrication, core concrete placement,

1.3 Analytical Theory of Concrete-Filled Steel Tubular (CFST) Structures …

19

Steel beam

Reinforced concrete floor slab

Steel beam CFST column Reinforced concrete shear wall or steel plate shear wall

(a) Multi-story CFST frame

CFST column (b) CFST frame-reinforced concrete shear wall or steel plate shear wall structure

Steel beam

CFST column

Reinforced concrete core tube CFST column (c) CFST frame-reinforced concrete core tube structure

(d) Multi-layer and high-rise CFST

Fig. 1.23 CFST frame structures

Static performance Dynamic performance CFST structure in terms of whole life cycle

Performance under short-term load Performance under long-term load Performance under cyclic load Performance under impact load Performance under fire and fire resistance rating

Fire resistance

Post-fire performance evaluation and repair

Construction stage impact

Impact of construction process on structural performance

Durability

Quality control of concrete placement

Develop technical standards

CFST structural analysis theory in terms of whole life cycle

Engineering practice

Fig. 1.24 Analysis theory and application framework of CFST structures in terms of whole life cycle

20

1 Introduction

etc.), long-term loading (e.g. concrete shrinkage and creep) and environmental effects (e.g. chloride ion corrosion, etc.); (2) analysis theory of mechanical performance of CFST structures under extreme actions (e.g. strong earthquake, fire, impact, etc.) that may lead to its destruction during the whole service life, and the analysis theory and method considering the coupling of multiple actions; (3) design principle and method of CFST structures in terms of the whole life cycle. To realize the theoretical analysis based on the life cycle, it is necessary to clarify the mechanism of the non-linear confinement effect on core concrete and the constitutive models, CFST analysis and calculation methods under multiple working conditions. (1) Concept of confinement effect The confinement effect is the source of the performance advantage and complexity of CFST structure. This effect is strongly nonlinear and the existing fixed-value confinement theory cannot be applied to accurately establish the constitutive model of core concrete, which fundamentally restricts the scientific development of this field. The fundamental problem in this field is how to accurately reveal the mechanism of the confinement effect in concept, quantify the amplitude of the confinement effect, and then propose the constitutive model of its core concrete. In the past, some scholars “borrowed” the traditional method of confining concrete with stirrups to calculate the resistance of CFST members by using the parameter “hooping index”, and some scholars also used the diameter (width) to thickness ratio of steel tubes as the basic parameter to measure the change of the confinement effect. These methods are not fully satisfied with the theoretical study of CFST structure in terms of the whole life cycle. The reasons are as follows: 1) the steel tube of CFST is generally in a three-dimensional stress state during loading and there is a tendency of local buckling, while the stirrups in the stirrup-confined concrete are in an unidirectional stress state of circumferential tension; 2) the basic performance of CFST is not only determined by the geometry and physical characteristics of the steel tube and concrete, but also by the “matching” relationship between the steel tube and concrete. It is difficult to accurately describe the confinement effect using the diameter (width) to thickness ratio of the steel tube as the basic parameter; 3) it is necessary to accurately master the changing pattern of the confinement effect under the long-term stress, cyclic stress and high temperature during the whole service life. Based on experimental research and theoretical analysis, the concept of the “confinement factor” was first proposed. Confinement factor (ξ ) is used as a basic parameter to measure the confinement effect of the steel tube on its core concrete during the service life cycle. The calculation equation for ξ is proposed as follows: ξ=

As f y fy = αs Ac f ck f ck

(1.3.1)

As Ac

(1.3.2)

αs =

1.3 Analytical Theory of Concrete-Filled Steel Tubular (CFST) Structures …

21

where, ξ αs As Ac f ck fy

confinement factor; cross-sectional steel ratio of the CFST member; cross-sectional area of the steel tube (mm2 ); cross-sectional area of the core concrete in the CFST member (mm2 ); characteristic value of compressive strength of concrete (N/mm2 ); yield strength of steel (N/mm2 ), for single load and complex stress, long-term load and seismic action conditions, the normal temperature value shall be taken. For fire and post-fire action conditions, the influence of real-time temperature and the highest temperature experienced shall be considered respectively.

Table 1.1 shows the conversion relationship between the characteristic value of compressive strength of concrete ( f ck ), strength class of concrete and cylinder compressive strength of concrete ( f c' ). As long as the strength class of concrete or characteristic value of cube strength of concrete ( f cu ) is given, the corresponding f ck , f c' and modulus of elasticity of concrete (E c ) can be determined according to this table. For a particular CFST cross-section, the confinement factor (ξ ) can reflect the influence of the geometric and physical properties of the steel and core concrete that make up the CFST section. With the increase of ξ , the greater the proportion of steel and the smaller the proportion of concrete; vice versa, with the decrease of ξ , the smaller the proportion of steel and the larger the proportion of concrete. Within general engineering parametric ranges, the influence of ξ on CFST performance is mainly shown in: with the increase of ξ , the steel tube provides stronger confinement to its core concrete during loading, and the strength and ductility of the CFST member increases; vice versa, with the decrease of ξ , the steel tube provides weaker confinement to its core concrete, and the strength and ductility of the CFST member decreases. In other words, the confinement factor can directly reflect the degree of composite effects between the steel tube and its core concrete within the general parametric ranges. The above concept of confinement factor applicable to CFST with multiple sections can accurately reveal the physical nature of the action mechanism between steel tubes and core concrete under long-term loads, complex forces, earthquake and fire conditions throughout the whole life cycle, and reasonably quantify the matching relationship between the geometric dimensions and physical properties of CFST, that is, when the section size is the same, the material strength ratio of steel tubes and Table 1.1 Conversion relationship between the strength class of concrete and f ck , f c' , E c Strength class f ck (N/mm2 ) f c'

C30

C40 20

C50 26.8

C60 33.5

C70 41

C80 48

C90 56

64

(N/mm2 )

24

33

41

51

60

70

80

E c (N/mm2 )

30,000

32,500

34,500

36,500

38,500

40,000

41,500

Note Intermediate values in the table are obtained by linear interpolation

22

1 Introduction

concrete determines the confinement effect; When the material strength is constant, the cross-sectional steel ratio determines the confinement effect. The confinement factor is a key parameter to describe the constitutive model of core concrete, which creates conditions for the scientific establishment and in-depth research of the analysis theory of new CFST structures and CFST hybrid structures. The confinement factor can also provide a basis for the conceptual design of CFST structures, such as determining the geometric characteristics of the cross-section (such as crosssectional size, steel ratio), physical parameters (material strength), optimizing the matching relationship between them, and calculating the ductility in the structural seismic design. (2) Constitutive models of core concrete In the past, the constitutive models of steel have been studied systematically by many scholars. For the core concrete in CFST, with the proposed confinement factor as the basic parameter, researchers have proposed the stress–strain relationship of the core concrete applicable to the fiber-based models and the finite element analysisbased method for various loading conditions that CFST may be subjected to during the life-cycle service. On this basis of systematic experimental studies, the stress– strain relationship model of core concrete under long-term loading is established by considering the effects of creep coefficient and shrinkage strain on the strain corresponding to the peak stress of core concrete. The stress–strain relationship model of core concrete under short-term static loading is used as the skeleton curve and the characteristics of unloading stiffness degradation and softening under cyclic stress are considered to establish the stress–strain relationship model of core concrete under cyclic stress. Considering the various stages of CFST subjected to normal temperature, elevated temperature, cooling and after elevated temperature under the action of full-range fire, the calculation method of confinement factor under (after) elevated temperature is determined on the basis of the influence pattern of temperature on the confinement effect. At the same time, considering the influence of temperature on the peak stress of core concrete and its corresponding strain, the compressive stress–strain relationship model that can describe the performance of core concrete under the change path of complex temperature is established. The schematic diagram of the stress–strain relationship model of core concrete under different confinement conditions is shown in Fig. 1.25. σ 02 and σ 01 are the peak stresses of concrete under strong and weak confinement conditions, respectively. ε02 and ε01 are the corresponding strains, respectively. Within the general engineering parametric ranges, with the increase of confinement factor (ξ ), the steel tube provides stronger confinement to its core concrete during loading, the peak stress of core concrete and the corresponding strain increase, and the stress–strain relationship after the peak stress of concrete becomes flatter. As a result, the general constitutive model of core concrete of the CFST based on the confinement factor is established, which lays the foundation for establishing the refined numerical model at the level of CFST members and structures, clarifying the

1.3 Analytical Theory of Concrete-Filled Steel Tubular (CFST) Structures … Fig. 1.25 Compressive stress (σ )-strain (ε) relationship of core concrete under different confinement conditions

23

σ σ02 σ01 Stronger confinement

Weaker confinement O

ε01 ε02

ε

failure mechanism of structures under long-term loading, complex loading, earthquake and fire conditions throughout the whole life cycle, and further establishing the corresponding calculation methods for resistance. (3) Calculation and analysis methods of CFST structures under various loading conditions It is a fundamental problem in this field to establish the damage mechanism analysis and resistance calculation methods of structures under frequent static loading and extreme loading action to provide a guarantee for the safety design of large-scale and complex CFST engineering structures. During the life-cycle service, CFST is often in a single or complex stress state such as axial compression (tension); combined compression (tension) and bending; combined compression and torsion; combined compression, bending and torsion; combined compression, bending and shear or even combined compression, bending, torsion and shear (as shown in Fig. 1.26a, where N, M, T and V represent axial force, bending moment, torque and shear force respectively). Therefore, refined finite element analysis-based models for mechanical behavior analysis of CFST members under compression (tension), bending, torsion, shear, and complex stress states are developed. The load-deformation relationship for stress states of CFST structures under axial compression (tension), bending, combined compression (tension) and bending, torsion, shear, combined compression and torsion, combined bending and torsion, combined compression, bending and torsion, combined compression, bending and shear, and combined compression, bending, torsion and shear are simulated and analyzed during the whole loading. A series of experimental studies were carried out. The section stress state and the interaction pattern of the steel tube and its core concrete during each stress stage and the mechanical characteristics of CFST members under different loading paths are clarified. The damage characteristics and ultimate limit states of CFST members under complex stress states are revealed. Based on systematic parameter analysis, the corresponding calculation methods for resistances are proposed and shown in Fig. 1.26b, where N u , M u , T u and V u represent the resistance of CFST in axial compression (tension), bending, torsion, and shear, respectively. The refined numerical analysis-based models for the mechanical performance analysis of CFST members under low cyclic loading are established for the seismic

24

M V

1 Introduction

N

T T

[V/Vu] (M,T)

(N,T)

(N,M,T) M

O N

(N,M)

(a) Loading paths

(b) Envelope surface of resistance

Fig. 1.26 CFST member under complex loading

actions that CFST may suffer during the life-cycle service. The characteristics of moment–curvature, horizontal load–displacement hysteretic relationship and damage regulations for CFST members with different cross-sections are obtained. And the load–displacement hysteretic relationship model of CFST members [as ' ' ' shown in Fig. 1.27, where A (A ), B (B ) and C (C ) represent the control points of skeleton curve] and the mathematical model of displacement ductility coefficient are proposed. Accurate fire resistance design and post-fire assessment of CFST members require the comprehensive consideration of the full-range fire process, including heating and cooling. During this process, CFST is subjected to complex time-varying actions of both loading and temperature. If the action paths are simply separated like the ' ' ' path AC D E shown in Fig. 1.28a, the stress redistribution and accumulated damage during the whole process of fire action cannot be accurately simulated and thus the fire resistance performance is overestimated. For this reason, the authors’ research team adopted the path ABCDE, which can reflect the whole process of fire action more Axial loading

Load B

Cyclic loading

C

A O

Displacement

A′ C′

B′

Fig. 1.27 Load–displacement hysteretic relationship models of CFST member

1.3 Analytical Theory of Concrete-Filled Steel Tubular (CFST) Structures … Fig. 1.28 Calculation model of CFST members during full-range fire action process. T —Temperature; εσ (σ, T )—Strain caused by stress; εth (T )—Thermal expansion strain; εc,tr (σ, T )—Transient thermal strain

25

Load

E' E

B

D Loading

Load holding surface A

C O D'

Time

Temperature action C' Temperature (a) Loading-temperature-time paths N

(b) Theoretical model

realistically, and established the theoretical model of load-deformation relationship and fire resistance ratings of CFST members under the coupling actions of loading, temperature and time (as shown in Fig. 1.28b, where “+” and “−” represent tensile strain and compressive strain, respectively). The typical failure characteristics and regulation of the load-deformation relationship for CFST members under the full process of fire are clarified. The influence of key parameters on the fire resistance ratings, typical failure characteristics and resistances of CFST columns are analyzed. The design method of resistance and fire protection of CFST members in axial compression under fire is proposed. The mathematical model for the calculation of resistance and deformation of members after fire and the hysteretic model of members in combined compression and bending are established. The damage assessment of CFST members is realized by comprehensively considering the influence of the whole process of stress and fire during service stage. The main achievements of life-cycle-based analysis theory for CFST structures, such as the constitutive models of core concrete, resistance calculation method of CFST structures under complex stress state and fire, and design methods of fire protection, are applied to the mechanical analysis and calculation of CFST engineering structures, such as high-rise/tall structures, large-span/spatial structures and heavy-weight structures. The analysis theory of CFST structures in terms of the

26

1 Introduction

whole life cycle has also laid a strong theoretical foundation for the formulation of engineering and construction technology standards for CFST structures.

1.4 General Requirements for the Design of Concrete-Filled Steel Tubular (CFST) Structures According to GB 50068 Unified standard for reliability design of building structures, the reliability design of CFST should meet the requirements of ultimate limit state, serviceability limit state and durability limit state. The limit state design should meet the following requirements when the action effects and resistances of the structure are used as the comprehensive basic variables. R−S≥0

(1.4.1)

where, R the resistance of the structure; S the action effects of the structure. The design of CFST shall include the following contents: (1) Design of the structural plans, including the structural forms and arrangement of structures; (2) Selection of materials and cross-sections; (3) Analysis of actions and their effects; (4) Verification of the ultimate limit states of the structures; (5) Detailing requirements of the structures, members, and connections; (6) Requirements for construction, transportation, erection, corrosion resistance, fire resistance, etc.; (7) Specified performance design of special structures. This book adopts the probability-based limit states design method and the design is carried out by adopting the design expressions of partial safety factors. Ultimate limit state design shall be carried out for CFST hybrid structures. Except for the design for accidental actions, serviceability limit state design shall be carried out. The design shall conform to the following requirements: (1) In the ultimate limit state design, the basic combination, the accidental action combination, or the seismic combination of load effects shall be selected; (2) In the serviceability limit state design, the normal combination, the frequent combination, or the quasi-permanent combination of load effects shall be selected. The safety classes and design working life of CFST hybrid structures shall conform to the requirements of the current national standard GB 50153 Unified Standard for Reliability Design of Engineering Structures. The safety classes of

1.5 Typical Engineering Applications of Concrete-Filled Steel Tubular …

27

CFST hybrid structures shall not be lower than those of the whole structures. When designing CFST hybrid structures, materials, structural plans and detailing shall be properly chosen so that the strength, stiffness and stability of structures can satisfy the respective requirements. The requirements for corrosion and fire resistances shall also be satisfied. The deformation and crack width of CFST shall be within the limits for structural safety and service requirements. For different engineering types, the limiting values for deformation and crack width shall conform respectively to the requirements of current relevant standards of the nation. The maximum applicable heights, the classes of seismic measure, the internal force adjustments and the detailing requirements of CFST structures shall conform respectively to the requirements for CFST structures in the current standards of the nation based on their engineering types. In the design of CFST, the levels of constructional techniques and constructional conditions need to be considered, based on which reasonable construction methods shall be chosen and technical requirements shall be drafted. In the design of CFST hybrid structures, the influence of the whole construction process on the resistance during the service stage shall be considered. Accordingly, some critical technical requirements, such as the limiting value of initial stress in the steel tube, and the limiting value of core concrete void in the steel tube, shall be set to meet the design objectives. Characteristic values of loads, partial safety factors and coefficients for combination value of actions of CFST structures shall conform respectively to the requirements of current relevant standards of the nation in accordance with the engineering types. For CFST structures directly subjected to dynamic loads, the characteristic values of the loads shall be multiplied by dynamic factors when conducting designs for the strength and stability of members, as well as the strength and fatigue of connections. The values of the dynamic factors shall be taken in accordance with the requirements of the current relevant national standards. Design values of the loads shall be used in the verification for the strength and stability of CFST structures, as well as the verification of the strength of connections; and characteristic values of the loads shall be used for the fatigue verification of CFST structures.

1.5 Typical Engineering Applications of Concrete-Filled Steel Tubular (CFST) Structures CFST can adapt to the development of modern engineering structures towards superlong span, towering, super weights and withstand severe environmental conditions, and meet the requirements of modern construction technology industrialization. It is being more and more widely used in single- and multi-story industrial plant columns, equipment frame columns, various supports, trestle columns, subway platform columns, power transmission and substation towers, trussed compression rods, piles, spatial structures, commercial plazas, high-rise and super high-rise buildings,

28

1 Introduction

towering building structures and bridge structures. This section illustrates the characteristics and possible forms of CFST structures by introducing its typical engineering applications. (1) Industrial plants Since the 1970s, CFST has been widely used as various types of plant columns. The interior view of the completed plant of the Baogang hot rolling mill is shown in Fig. 1.29. (2) Equipment frame, various supports and trestle structure In various platforms or structures, the bottom pillars are often subjected to large vertical loads, so it is more reasonable to use CFST columns. CFST is widely used in various equipment frame columns, support columns and trestle columns. The CFST coal transfer trestle column of a power plant is shown in Fig. 1.30. (3) Subway stations Fig. 1.29 Interior view of a hot rolling mill plant

Fig. 1.30 CFST coal transfer trestle

1.5 Typical Engineering Applications of Concrete-Filled Steel Tubular …

29

Fig. 1.31 Application of CFST in metro station

Subway platform columns are generally subjected to large vertical pressure. The use of CFST columns with high resistance can reduce the cross-sectional area of columns and expand the use of space. The traffic hub project of Tianjin Metro Station consists of the intersection of Tianjin Metro Lines 2, 3 and 9. The main structure of the station is a multi-layer multi-span frame structure. The main frame adopts circular CFST columns with a diameter of 1000 mm, which are connected with reinforced concrete beams at the joints. The interior view of the metro station with CFST columns is shown in Fig. 1.31. (4) Transmission and transformation towers The 500 kV network transmission and transformation project in Zhoushan City, Zhejiang Province connects Zhoushan power grid and Ningbo power grid, and the span of the main crossing section of Luotou Watercourse is 2756 m. In order to comply with the regulations, it is often necessary to increase the wall thickness of the steel tube in the design of the project, resulting in problems such as difficult processing of thick plates, layer tearing, and large mass of single piece. Therefore, the CFST structure is adopted for the Zhoushan Great Crossing tower. The height of the new sea-crossing transmission tower of Xihoumen crossing Jintang and Zezi islands is 380 m, and the weight of a single foundation is 7280 t. The concrete in the main steel tube of the tower is placed to a height of 260 m, and the maximum outside diameter of the main steel tube is 2.3 m, and its wall thickness is 28 mm. Xihoumen Great Crossing Tower with the height of 380 m was completed in October 2018. The construction process and the situation after the completion of Zhejiang Zhoushan Great Crossing Tower and Xihoumen Great Crossing Tower are shown in Figs. 1.32 and 1.33, respectively. 220 kV Tianhu-Chongxian open ring into seedling transmission line project, its length of the line is more than 10 km, with 52 bases of poles and towers, among which No. 2–14 are four-loop steel rods, No. 47–51 are double-loop steel towers, and the rest are double-loop steel rods. Due to the line corner tower being subjected to a

30

Fig. 1.32 Zhoushan Great Crossing Tower, Zhejiang

Fig. 1.33 Xihoumen Great Crossing Tower, Zhoushan, Zhejiang

1 Introduction

1.5 Typical Engineering Applications of Concrete-Filled Steel Tubular …

31

Fig. 1.34 CFDST pole

Steel tubes

Concrete

large bending moment, the tapered concrete-filled double-skin steel tubular structure (CFDST) is adopted as the main line tower through the comparison of various tower forms as shown in Fig. 1.34. CFDST has the advantages of expanded cross-section, large bending stiffness, inner hollow concrete saving, lighter self-weight and good seismic performance. (5) Piles Steel tube piles have the characteristics of convenient construction. During construction, the process of pile driving, pile cutting and soil excavation can be adopted. However, the disadvantage of using steel tube piles is the high cost. In the 1990s, the Baogang successfully tested and promoted CFST pile technology in the third phase of the project. The CFST pile has good development prospects as the foundation of important buildings such as high-rise buildings, bridges and wharves on coastal soft ground. (6) Spatial structure The roof support columns of T1 and T2 terminals of Chengdu Tianfu International Airport completed in 2021 adopt CFST. CFST column types are equal-section inclined columns, variable-section (tapered) inclined columns and variable-section straight columns. The maximum height of the columns is 29.9 m and they are all with a circular cross-section and an outside diameter of 1000–2300 mm. The steel tubes are made of Q355 steel with wall thickness of 30–45 mm and filled with C50 concrete. The engineering application for CFST in the terminals of Chengdu Tianfu International Airport is shown in Fig. 1.35.

32

1 Introduction

Fig. 1.35 CFST columns of the terminal of Chengdu Tianfu International Airport during construction process

Qingdao Jiaodong International Airport terminal has 6 floors above and below ground. The steel structure roof of the airport terminal building adopts an orthogonal four-placed four-angle cone grid with CFST columns as vertical load-bearing members. The circular CFST columns have an outside diameter of 1600–2100 mm, a wall thickness of 35–45 mm, and a height of 24.0–26.0 m. Its steel tube is made of Q355 steel and filled with C50 concrete. The engineering application of CFST in Qingdao Jiaodong International Airport terminal is shown in Fig. 1.36. The Qinghe Station Project of the new Beijing-Zhangjiakou Railway Project consists of a north–south drop-off platform, an elevated waiting floor and a main station building. The CFST column is used as the vertical load-bearing member. As a large public infrastructure serving the 2022 Winter Olympic Games, Qinghe Station has a long span and its main structure has high requirements for bearing capacity. The CFST columns with a maximum diameter of 1800 mm, Y-shaped columns and A-shaped columns are used, as shown in Fig. 1.37. The height of the CFST column is 11.2–15.3 m, its outside diameter of the steel tube is 900–1800 mm, and its wall thickness is 30–50 mm. It is made of Q390 steel and filled with C60 concrete. (7) High-rise and super high-rise buildings CFST can be used for columns and lateral force resisting systems in multi-, high-rise and super high-rise buildings. The system shown in Fig. 1.23b consists of CFST frame and reinforced concrete shear wall or steel plate shear wall, which generally constructs the outer frame first and the concrete shear wall later. The system shown in

1.5 Typical Engineering Applications of Concrete-Filled Steel Tubular …

33

Fig. 1.36 Application of CFST column in Qingdao Jiaodong International Airport Terminal

Fig. 1.23c consists of the outer CFST frame and inner reinforced concrete core tube. The inner core tube provides the main lateral stiffness, and it is generally constructed before the outer frame during construction. Compared with the steel frame, the outer CFST frame has greater rigidity and bearing capacity. The Hangzhou Ruifeng International Business Building, completed in 2001, uses square CFST columns, welded I-beams, profiled steel plate composite floor slabs and reinforced concrete shear walls. The maximum cross-section size of the square CFST column is 600 mm, with the maximum wall thickness of the steel tube as 28 mm and the minimum as 16 mm, using Q345 steel. The steel structural installation process and typical beam-to-column joints of Hangzhou Ruifeng International Business Building are shown in Fig. 1.38a, b, respectively. The office building of Beijing Fortune Plaza is located at 7 Dongsanhuan Zhong Road, Chaoyang District, Beijing, which adopts circular CFST columns. The building has 4 underground floors and 58 above-ground floors, with a total building height of 265.15 m. The CFST columns are made of circular cross-section steel tubes with the following specifications: Φ1600 × 60, Φ1300 × 35, etc. The below fifty floors are filled with C60 concrete, and the above fifty-one floors are filled with C50 concrete. The situation of CFST columns during construction process is shown in Fig. 1.39. The Z15 block project in the CBD core area of Chaoyang District, Beijing (CITIC Tower, also known as China Zun) is shown in Fig. 1.40. The building has a height of 528 m, 7 floors underground and 108 floors above ground, which adopts a mega frame-core tube structural form. The outer rectangular frame consists of multi-cavity polygonal CFST columns, giant diagonal braces, and transformation trusses. The CFST columns are located at the four corners of the building plan and are connected

34

1 Introduction

Fig. 1.37 Application of CFST in Qinghe Station of the new Beijing-Zhangjiakou Railway Project

(a) Straight column

(b) Y-shape column

(c) A-shape column

1.5 Typical Engineering Applications of Concrete-Filled Steel Tubular … Fig. 1.38 Hangzhou Ruifeng International Business Building

(a) Steel structural installation process

(b) Beam-to-column joint

Fig. 1.39 CFST columns during the construction of Beijing Fortune Plaza

35

36

1 Introduction

to the transformation trusses, giant diagonal braces and sub-frames at each section to form the lateral stiffness and bear the major lateral loads. The column base of Z15 project (China Zun) includes multi-cavity polygonal CFST columns, the underground part is wrapped with reinforced concrete, and the column is connected with encased steel plate concrete wing wall; The connection of the column base adopts a non-embedded form, the upper steel structure is anchored to the foundation through anchor bolts, and the concrete longitudinal reinforcement deeps into the foundation. The cross-sectional area at the bottom of the column base reaches 80m2 , and the design maximum axial compression and axial tension load reach 2 × 106 and 4 × 105 kN, respectively. The project is located in the 8° seismic zone, and the stress condition of the corner column under the strong earthquake Fig. 1.40 Application of CFST in the Z15 project (China Zun)

(a)

(b)

1.5 Typical Engineering Applications of Concrete-Filled Steel Tubular …

37

level is particularly important for the safety of the structure. In order to meet the demand for load-bearing, the corner column is bifurcated into two column legs at the elevation of 43.35 m, and is subjected to the action of giant diagonal braces and transfer trusses on both sides at the bifurcation. (8) Towering building structures Canton Tower is located at the intersection of Guangzhou’s Pearl River landscape axis and the city’s new central axis. The main body of the tower is 454 m high, the top steel mast is 156 m high, and the total height is 600 m. The outer frame of Canton Tower consists of 24 CFST columns with a height of about 454 m and the inner core tube is the reinforced concrete structure. The outside diameter of the 24 steel tubes is 2 m below the elevation of 5 m, and the tapered tubes with the outside diameter tapering from 2 to 1.2 m are used above 5 m, with the wall thickness of the steel tubes tapering from 50 to 30 mm from the bottom to the top. The in-filled concrete varies from C60 to C45. The outer steel tube of CFST is connected with the diagonal support to form a stable spatial structure and improve the torsional and wind resistance of the tower. The situation of Canton Tower during construction process is shown in Fig. 1.41. The Beijing Olympic Tower (shown in Fig. 1.42), completed in 2012, is located in the northern part of the Olympic Park in Chaoyang District, Beijing, which is close to the Olympic Forest Park. The tower eaves are 246.8 m high, and the height of the Olympic five rings logo at the highest point is 264.8 m. CFST is used for the tower. Fig. 1.41 Canton Tower during construction

CFST member

38

1 Introduction

(a)

(b)

Fig. 1.42 Beijing Olympic Tower

It is a towering structure with a large concentrated mass at the crown and the CFST of the tower is mainly subjected to combined compression and bending loads. (9) Bridge structures The main forms of CFST applied in bridge structures are shown in Fig. 1.43. The arch structure is mainly subjected to axial compression. When the span is large, the arch ribs will bear large axial compression. Therefore, it is reasonable to use CFST. During construction, hollow steel tube not only has the function of form and reinforcement, but also has the advantages of large stiffness, high resistance and light self-weight after its formation. Combined with the bridge turning construction process, it can achieve the goal of high strength of arch bridge materials and light self-weight of the arch ring without supporting construction. The CFST arch ribs commonly used in practical engineering can be a single CFST arch rib, a bundle, two-chord or multiple-chord trussed CFST hybrid structure, or the concrete-encased CFST hybrid structure. In the early stage, the construction method of support was adopted for the CFST arch bridge. In the later stage, the construction technology of cable-stayed buckle, self-compacting concrete placement technology and high-performance concrete control technology were adopted, and the CFST was developed rapidly.

1.5 Typical Engineering Applications of Concrete-Filled Steel Tubular …

39

CFST

Fig. 1.43 Schematic diagram of CFST applied in bridge structures

Sichuan Wangcang Donghe Bridge, which was opened to traffic in 1991, is a CFST arch bridge with a main span of 115 m. The arch rib cross-section is dumbbell type. The CFST of the upper and lower chord has an outside diameter of 800 mm and the wall thickness of the steel tube is 10 mm, adopting Q345 steel and C30 concrete. The arch axis is the suspension chain line, the arch axis coefficient is 1.543, and the rise-to-span ratio is 1/6. The bridge is one of the earliest arch bridges built with CFST in China. Guangxi Pingnan Third Bridge is located in Pingnan County, Guigang City, Guangxi Zhuang Autonomous Region, which has a main span of 575 m CFST arch. The net rise-to-span ratio is 1/4.0, the arch axis coefficient is 1.5, the radial height of the top of the arch is 8.5 m, the height of the base of the arch is 17.0 m, and the rib width is 4.2 m. The tube is filled with C70 concrete. The total mass of the arch truss of the bridge is 9000 tons, divided into 44 lifting sections, of which the mass of the heaviest section is 214 tons. The bridge started construction on August 7, 2018, and was opened to traffic on December 28, 2020. The scenarios of the Guangxi Pingnan Third Bridge during the construction process and after completion are shown in Fig. 1.44. Compared with steel arch bridges, CFST arch bridges have the advantages of saving about 50% steel, low cost and easy construction. Therefore, CFST arch bridge has become one of the main types of the arch bridge in China. According to incomplete statistics, China has built more than 500 CFST arch bridges so far, including more than 20 bridges with a main span of more than 300 m, 10 bridges with a main span of more than 400 m and 4 bridges with a main span of more than 500 m. Guangyuan Zhaohua Jialing River Bridge (as shown in Fig. 1.45) is located in Zhahua Town, Guangyuan City, Sichuan Province and crosses the Jialing River, which is a key control project of the Guangyuan-Nanchong section of the LanzhouHaikou Expressway of the national expressway network. The main span of the bridge is 364 m. The design life of the structure is 100 years and the seismic precautionary

40

1 Introduction

(a) Construction process

(b) After completion

Fig. 1.44 Guangxi Pingnan third bridge

intensity is 8°. The height difference between the bridge deck and the Jialing River is more than 120 m. The main arch rib of Guangyuan Zhahua Jialing River Bridge adopts the concrete-encased CFST hybrid structure (as shown in Fig. 1.45). The outside diameter and wall thickness of the steel tube are 457 and 14 mm, respectively, filled with C80 concrete. Compared with the scheme of original reinforced concrete continuous rigid structure bridge, the consumption of concrete is saved and the construction period is effectively shortened. The Luzhou Modaoxi Bridge (shown in Fig. 1.46) is located in Luzhou City, Sichuan Province, which is the controlling project of the Xuyong-Gulin Expressway. It crosses the natural river Modaoxi section and is in the tectonic erosion of the middle mountain terrain, which has complicated terrain. The main span of the bridge is 280 m and the maximum vertical height difference between the design elevation of

1.5 Typical Engineering Applications of Concrete-Filled Steel Tubular …

2

41

1

Fig. 1.45 Guangyuan Zhaohua Jialing river bridge. 1—CFST; 2—Reinforced concrete

the bridge and the valley floor is about 155 m. The design life of the main structure is 100 years and the seismic precautionary intensity is 7°. The Luzhou Modaoxi Bridge adopts the concrete-encased CFST hybrid structure as the main structure of the arch bridge, which can give full use of the material performance of steel and C100 highstrength concrete and the support of the steel tube. The outside diameter of the steel tube is 402 mm and its wall thickness is 12 or 16 mm. The Luzhou Modaoxi Bridge was completed in November 2015. The Jinsha River Bridge changed from a slip rope in Fengjiaping Village, Butuo County (shown in Fig. 1.47) is located in Butuo County, Liangshan Prefecture,

Fig. 1.46 Luzhou Maodaoxi Bridge during construction

42

1 Introduction

Fig. 1.47 Jinsha River Bridge replacing the original zipline in Fengjiaping Village, Butuo County

Sichuan Province. Its seismic precautionary intensity is 8°. The bridge adopts the concrete-encased CFST hybrid structure as the main arch structure. The outside diameter of the steel tube is 508 mm and its wall thickness is 16 or 24 mm, filled with C60 concrete. Compared with the reinforced concrete arch bridge scheme, this scheme saves concrete consumption and shortens the construction period. The main arch of the bridge was closed on April 12, 2017, and completed in May 2018. The Jinsha River bridge replacing the original zipline is located in Jinyang County, Liangshan Prefecture, Sichuan Province and the seismic precautionary intensity is 8°. The bridge adopts the concrete-encased CFST hybrid structure as the main arch structure which is similar to the Jinsha River Bridge changed from a slip rope in Fengjiaping Village, Butuo County. The scenario when the CFST skeleton was installed is shown in Fig. 1.48a and the scenario after the completion of the concrete encasement is shown in Fig. 1.48b. The main arch of the bridge was completed on April 26, 2017, and completed in May 2018. The Jinsha River Bridge changed from a slip rope in Fengjiaping Village, Butuo County and the Jinsha River Bridge changed from a slip rope in Xiying Group, Dupingyi Village, Jinyang County are “Cable upgrading Bridge” projects for poor areas jointly initiated by Poverty Alleviation Office of The State Council and Ministry of Transport. Guang’an Guangsheng Qujiang Bridge is located in Guang’an City, Sichuan Province, with a total length of 793 m and a main span of 320 m. The design life of the main structure is 100 years and the seismic precautionary intensity is 6°. Guan’an Guangsheng Qujiang Bridge adopts scheme of the concrete-encased CFST hybrid structure as the main structure. The outside diameter of the steel tube is 351 mm, its wall thickness is 14 or 18 mm, and C100 concrete is filled. The completed scenario of the bridge is shown in Fig. 1.49. Concrete-encased CFST hybrid structure has good applicability in bridge piers. Located in Shizi Township, Yingjing County, Sichuan Province, Ya’an Labajing Bridge is a bridge crossing Labajing Valley on Ya’an-Luzhou Expressway. It is

1.5 Typical Engineering Applications of Concrete-Filled Steel Tubular …

43

(a) Scenarios during installation of CFST skeleton

(b) Scenarios after completion of concrete encasement Fig. 1.48 Jinsha River Bridge changed from a slip rope, Xiying Group, Duoping Village, Jinyang County

Fig. 1.49 Guang’an Guangsheng Qujiang Bridge

44

1 Introduction

located in a mountainous area and has complex terrain and environment. The design service life of the main structure is 100 years, and the seismic precautionary intensity is 8°. The Labajin Bridge (as shown in Fig. 1.50) of Yalu Expressway in Sichuan Province uses the four-chord concrete-encased CFST hybrid structure as its pier column structure. Ya’an Labajin Bridge has three main piers with the span of 105–200 m. Among them, the height of pier 10# reaches 182.5 m, which becomes the world’s highest pier in the 8° seismic fortification zone (as shown in Fig. 1.50). The outside diameter of the steel tube is 1320 mm, which is filled with C30-C80 concrete. The results of the schemes comparison show that, when using concrete-encased CFST hybrid structure, the spacing of each CFST chord can be adjusted so that the smaller diameter CFST member can be used to obtain the larger cross-sectional flexural stiffness. The main pier structure has uniform stress distribution, clear force transmission path and convenient construction process. Compared with the original continuous rigid structural bridge scheme using reinforced concrete pier, Ya’an Labajin Bridge has achieved the comprehensive benefits of saving a large amount of concrete for the

1

2 (a) During the construction of high pier

(b) Schematic of high pier cross-section

(c) After the completion of the bridge

Fig. 1.50 Ya’an Labajin Bridge. 1—CFST; 2—Reinforced concrete

1.5 Typical Engineering Applications of Concrete-Filled Steel Tubular …

45

Fig. 1.51 Ya’an Heishigou bridge

pier and shortening the construction period. Since the bridge was completed on April 28, 2012, the operating condition has been kept in good condition. The bridge has withstood the Ya’an earthquake (7.0-magnitude earthquake) on April 20, 2013. Ya’an Heishigou Bridge is located in Huangyi Township, Yingjing County, Ya’an City, Sichuan Province, which is a super-large bridge (as shown in Fig. 1.51) for the Ya’an-Lugu Expressway to cross the large gully-Heishigou. The bridge deck is about 190 m from the bottom of the ditch, the main span is 200 m, the design service life of the main structure is 100 years, and the seismic fortification intensity is 8°. The maximum height of the concrete-encased CFST hybrid structure pier of the bridge is 157 m, its outside diameter of the steel tube is 1320 mm, and it is filled with C30–C80 concrete, which has achieved the comprehensive benefits of saving steel and concrete and shortening the construction period. Ya’an Heishigou Bridge was completed on April 28, 2012. Ya’an Ganhaizi Bridge is located in Shimian County, Ya’an City, Sichuan Province, as shown in Fig. 1.52. The design service life of the main structure is 100 years, and the seismic fortification intensity is 9°. Ya’an Ganhaizi Bridge has a total length of 1811 m, a total of 36 spans, and a design width of 24.5 m. Its highest pier reaches 107 m, the maximum longitudinal slope is 4% and the minimum curve radius is 356 m. The second link has a total length of 1044.7 m with a maximum span of 62.5 m. The piers and trusses of the bridge adopt the trussed CFST hybrid structure. Compared with the original reinforced concrete simple-supported girder bridge, the number of bridge spans was reduced from 51 to 36, saving the amount of pile foundation and achieving the comprehensive economic benefits of saving steel and concrete, and shortening the construction period. Ya’an Ganhaizi Bridge was completed on April 22, 2012, and has withstood the Ya’an earthquake (7.0-magnitude earthquake) on April 20, 2013. Wenchuan Keku Bridge (shown in Fig. 1.53) is located in Keku Township, Wenchuan County, Aba Prefecture, Sichuan Province, which is 50 km away from Yingxiu Town, the epicenter of the Wenchuan 5.12 earthquake. The bridge is 6431 m long, with a design life of 100 years for the main structure and a seismic fortification intensity of 9°. The CFST piers and the trussed CFST hybrid structure with the

46

1 Introduction

Fig. 1.52 Ya’an Ganhaizi bridge

(a)

(b)

Fig. 1.53 Wenchuan Keku bridge

concrete structural slab as the truss girders are adopted due to limited construction conditions in mountainous areas and the design requirements of “repairable under 9-magnitude earthquake”. This solution makes the main structure of the bridge relatively small in cross-sectional size and without reinforcement, which makes it easy to be erected by the bridge erector as a whole hole. By using CFST as the casting mold, no formwork is needed for the whole bridge during the construction stage, which greatly reduces the overhead work and facilitates the construction. Compared with the original reinforced concrete simple-supported girder bridge, the CFST hybrid structure bridge pier saves about 40% of concrete consumption and 30% of steel, and effectively shortens the construction period. Wenchuan Keku Bridge was fully completed on November 3, 2018. On August 20, 2019, under the impact of the “8.20” debris flow in Aba Prefecture, the 24 # pier column of the left side of the bridge (from Wenchuan to Malkang) was inclined by about 5°, and the WenzhouMalaba Expressway was closed accordingly, but the main structure of the bridge was intact and kept in good condition, which avoided the major accident of collapse of

1.5 Typical Engineering Applications of Concrete-Filled Steel Tubular …

47

the bridge. The right side of the bridge was released on time and unilaterally after rapid repair, providing a key channel for rescue and disaster relief. The trussed CFST hybrid structural girder with concrete structural slabs was adopted for Ya’an Ganhaizi Bridge and Wenchuan Keku Bridge, which is essentially a trussed CFST hybrid structure system. The CFST engineering practice shows that compared with reinforced concrete, the CFST does not need to install the reinforcement, erect the framework and remove the framework, and the steel tube is generally no longer equipped with reinforcement, so the concrete placement is more convenient and the placement quality of concrete is easier to guarantee; compared with steel structure, the detailing of the CFST structure is simpler, with fewer welds, and easier to fabricate. Due to the support of core concrete, thin-walled steel tubes can be used in CFST structures, so the onsite splicing and welding of the steel tube is simpler and faster, and the installation deviation is easier to correct. Due to the small self-weight of thin-walled hollow steel tube members, its transportation and lifting are more convenient. In addition, the CFST column base has few parts and short welding seams, so simple detailings can be adopted, such as directly inserted into the concrete foundation reserved cups. Exercises 1. Briefly describe the mechanical characteristics and engineering applicability of CFST structures. 2. Briefly describe the composite action mechanism between the steel tube and its core concrete in CFST structures. 3. Briefly explain why the confinement factor can be used as the basic parameter to measure the confinement effect of steel tube on its core concrete during the life-cycle service. 4. Briefly describe the design principle of “strength matching” between the steel tube and its core concrete in CFST structures. 5. Briefly describe the possible forms and characteristics of CFST structures in engineering applications.

Chapter 2

Materials

Key Points and Learning Objectives Key Points The design principles of materials for CFST structures and those of connecting materials, anti-corrosion materials and fireproof coatings are discussed in this chapter. Learning Objectives Understand the performance characteristics and design principles of materials for CFST structures. Be familiar with the design principles of connecting materials, anticorrosion materials and fireproof coatings. Learn the types and suitable conditions of materials for CFST structures.

2.1 Introduction Concrete-filled steel tube (CFST) is composed of steel and its core concrete, other materials such as reinforcement, connecting materials and protective materials are frequently used in engineering practice. During the design of CFST structures, structural materials shall be selected in accordance with the requirements of the engineering structures to realize the integrated design of CFST material-structure and ensure the structural safety throughout its life-cycle service. This chapter briefly discusses the determination principles of steel, concrete, connecting materials and protective materials for CFST structures.

© China Architecture & Building Press 2024 L. Han, Theory of Concrete-Filled Steel Tubular Structures, https://doi.org/10.1007/978-981-99-2170-6_2

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50

2 Materials

2.2 Steel According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the steel tubes of grades Q355, Q390, Q420 and Q460 are commonly used in CFST structures. The quality of the steel tube shall conform respectively to the relevant requirements of the current national standards GB/T 700 Carbon Structural Steels, GB/T 1591 High Strength Low Alloy Structural Steels, GB/T 19879 Steel Plates for Building Structure, GB/T 714 Structural Steel for Bridge and GB 50017 Standard for Design of Steel Structures. The proper choices of steel grades and quality degrees in CFST structures shall be made based on the importance of the structures, the load characteristics, the stress states, the wall thicknesses, the connection methods, and the service conditions, etc. According to the current national standard GB/T 1591 High Strength Low Alloy Structural Steels, Table 2.1 shows the strength indices for steel tube materials. When using other grades of steel than Table 2.1, it shall conform to the relevant requirements of current standards of the nation. When there is a specific necessity, weathering steel or fire-resistant steel may be used. Table 2.1 Strength indices for the design of steel tube materials Steel grades

Q355

Q390

Q420

Q460

Wall thickness of the steel tube (mm)

Design value of strength

Yield strength f y (N/mm2 )

Tensile strength f u (N/mm2 )

Tensile, compressive, and flexural strength f (N/mm2 )

Shear strength f v (N/mm2 )

≤ 16

305

175

355

470

> 16, ≤ 40 > 40, ≤ 63

295

170

345

290

165

335

> 63, ≤ 80

280

160

325

> 80, ≤ 100

270

155

315

≤ 16

345

200

390

> 16, ≤ 40

330

190

380

> 40, ≤ 63

310

180

360

> 63, ≤ 100

295

170

340

≤ 16

375

215

420

> 16, ≤ 40

355

205

410

> 40, ≤ 63

320

185

390

> 63, ≤ 100

305

175

370

≤ 16

410

235

460

> 16, ≤ 40

390

225

450

> 40, ≤ 63

355

205

430

> 63, ≤ 100

340

195

410

490

520

550

2.2 Steel

51

Table 2.2 Physical properties of steel tube materials Modulus of elasticity E (N/mm2 )

Shear modulus G (N/mm2 )

Coefficient of linear expansion α (per Mass density ρ (kg/m3 ) °C)

2.06 × 105

79 × 103

12 × 10–6

7,850

Table 2.2 shows the physical properties of steel tube materials. Longitudinally welded tubes should be employed for the steel tubes in CFST structures, and complete-penetration butt welding shall be used. The welding shall conform to the first-degree welding quality requirements of the current national standard GB 50661 Code for Welding of Steel Structures. Alternatively, seamless steel tubes may be used, and their quality shall conform to the relevant requirements of the current national standard GB/T 8162 Seamless Steel Tubes for Structural Purposes. When other types of steel tubes are used, they shall conform to the relevant requirements of the current standards of the nation. The steel tube in CFST can also be made of austenitic stainless steel. The confinement effect provided by stainless steel tube can effectively reduce the brittleness of core concrete, and increase its plasticity and ductility, while the concrete inside the tube can effectively delay or avoid the local buckling of the stainless steel tube so that the wall thickness of the latter can be properly reduced and therefore the material consumption is reduced. Stainless steel tube has the advantages of excellent appearance and improved corrosion resistance, and its application in CFST structures can reduce the engineering maintenance cost. In addition, the stainless steel tube generally has better mechanical properties at high temperatures than those of carbon steel, which makes the fire resistance of the concrete-filled stainless steel tubular structure better than the corresponding ordinary CFST structures. At present, the relatively commonly used Austenitic stainless steel matrix is mainly with Austenitic structure, which has excellent corrosion resistance, plasticity, impact resistance and weldable performance. Austenitic stainless steel is the most widely used stainless steel. Compared with carbon steel for structural use, there is no obvious yield platform in the stress–strain relationship of stainless steel materials, and the stress at 0.2% residual strain is usually defined as the nominal yield strength ( f 0.2 ). The elongation after fracture of Austenitic stainless steel can be achieved by 50–60% under tension, while that of Austenitic-ferrite duplex stainless steel is 30–40%. Figure 2.1 shows the comparison of the stress (σ )-strain (ε) relationship between carbon steel used for structure and Austenitic stainless steel, where f y is the yield strength of steel, f 0.2 is the corresponding nominal yield strength when residual strain is 0.2%, f u is the tensile strength of the steel and εu is the ultimate strain of the steel. The provision on properties of stainless steel is recommended in the standard of China Association for Engineering Construction Standardization T/CECS 952 Technical Specification for Concrete-Filled Stainless Steel Tubular Structures. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the longitudinal reinforcement in CFST hybrid structures

52

2 Materials

σ

Fig. 2.1 Stress (σ )-strain (ε) relationships of carbon steel and Austenitic stainless steel

fu Austenitic stainless steel fy=f0.2

Carbon steel

O

εu

ε

should be steel bars of Grades HRB400, HRB500, HRBF400, and HRBF500; and the stirrups should be steel bars of Grades HRB400, HRBF400, HPB300, HRB500, and HRBF500. They shall also conform to the relevant requirements of the current national standard GB 50010 Code for Design of Concrete Structures. Table 2.3 shows the basic indices of the reinforcement materials. Table 2.3 Basic indices of reinforcement material property Grade

Characteristic value of yield strength f yk (N/ mm2 )

Characteristic value of ultimate strength f stk (N/ mm2 )

Design value of tensile strength f u (N/mm2 )

Design value of Modulus of compressive elasticity E s ' strength f y (N/ (N/mm2 ) mm2 )

HPB300

300

420

270

270

2.10 × 105

HRB335

335

455

300

300

2.00 × 105

HRB400 400 HRBF400 RRB400

540

360

360

HRB500 500 HRBF500

630

435

435 '

Note For members to axial compression, the design value of compression strength f y of reinforcement shall be 400 N/mm2 when HRB500 and HRBF500 reinforcement are adopted. The design value of tensile strength f yv for transverse reinforcement should be adopted in accordance with the value of f u in the table. When used for the calculation of shear, torsion, punching shear resistance, the value > 360 N/mm2 should be taken as 360 N/mm2

2.3 Concrete

53

2.3 Concrete The selection of core concrete materials in CFST structures should be determined based on the principle of “trinity” in terms of structural characteristics, construction techniques and structural service life. As the core concrete is sealed by the steel tubes, it is difficult for extra water to be discharged, the water/blinder ratio of concrete should not be too large. Excessive shrinkage of concrete might hinder the ability of the steel tubes and the concrete to act together. Therefore, proper techniques, such as shrinkage compensation techniques, may be used when necessary to reduce the shrinkage of core concrete. Moreover, to effectively unleash the structural merits of the CFST members, the strength class of the core concrete should not be too low. The strength class of the core concrete should not be lower than C40 for CFST members in compression and shall not be lower than C30 for CFST members in tension. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the quality of concrete used in CFST hybrid structures shall conform respectively to the requirements of the current national standards GB 50010 Code for Design of Concrete Structures, and GB/T 50107 Standard for Evaluation of Concrete Compressive Strength, and shall also satisfy the following requirements: (1) Water/cement ratio of concrete should not exceed 0.45; (2) Strength class of the core concrete in CFST members shall not be lower than C30 in terms of cubic strength with prototype lengths of 150 mm; (3) For concrete-encased CFST hybrid structures, strength class of the core concrete in CFST members shall not be lower than that of the concrete encasement; and strength class of the concrete encasement shall not be lower than C30. Concrete shrinkage is the reduction of component size over time during the physical and chemical process of concrete setting and hardening, which is mainly divided into plastic shrinkage, autogenous shrinkage, drying shrinkage, temperature shrinkage and carbonization shrinkage and so on. When the core concrete of CFST structure shrinks, the core concrete is wrapped in a closed environment with the outer steel tube and there is no direct water exchange with the external environment, so the shrinkage deformation of core concrete is reduced. In addition, there is interfacial contact between steel pipe and core concrete, namely the bonding and the friction, which restrict the shrinkage of core concrete. Therefore, the total shrinkage deformation of the core concrete in the CFST structure is significantly smaller than that of the corresponding normal concrete without steel tube surrounding. Figure 2.2 shows the measured shrinkage of core concrete in steel tubes and plain concrete. The outer diameter of the circular specimen is 1000 mm, the mixture design of concrete is cement: fly ash: sand: stone: water = 400:150:816:884:160, the unit is kg/m3 , the water/blinder ratio is 0.29, and the sand ratio is 0.48. The 28-day cube strength of concrete f cu = 69.6 N/mm2 , modulus of elasticity E c = 3.71 × 104 N/mm2 . In practical CFST engineering projects, due to various reasons in terms of materials, placement process and construction activities, the core concrete void may occur

54 Fig. 2.2 Measured results of shrinkage deformation of concrete

2 Materials

ε (με)

Core concrete Plain concrete

t (day)

in CFST, which will hinder steel tube and core concrete to act together and reduce the composite effects at different degrees. The possible factors that lead to the core concrete void are excessive concrete shrinkage, defects in concrete casting (such as segregation, and non-compactness), drastic changes in ambient temperature, interface damage, etc. For CFST projects, it is necessary to ensure that there is no continuous void between the steel tube and its core concrete, the void value shall be no more than the required limitation (as discussed in Sect. 4.9 of this book). Normally, there is no additional need to add some expansion agent to the core concrete mixture. When there is a special demand, it can be properly configured according to the practical project. The amount of configuration should be based on the principle of compensating for the shrinkage of concrete. To ensure that the steel tube and core concrete are complementary to each other and have the expected composite effects, the strength class of core concrete shall reasonably match the steel grade. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, with generally used cross-sectional steel ratios, Q355 steel should be used to match with C30-C80 concrete; and Q390, Q420 and Q460 steel should be used to match with C50-C80 concrete. When there is reliable evidence, concrete with a higher strength class may also be used. The strength class of core concrete in the steel tube should conform to the requirements in Table 2.4. According to the requirements of current national technical standards, Table 2.5 shows the basic indices of concrete material properties. The mechanical properties of the CFST member are related to the confinement effect of the steel tube on its core concrete, which increases the strength, plasticity and ductility of concrete, and the support of the core concrete to the steel tube, which postpones or prevents the inwards local buckling of the steel tube. Thus, in addition Table 2.4 Strength class of core concrete in the steel tube

Steel grade

Q355

Q390, Q420 and Q460

Strength class of concrete C30–C80 C50–C80

2.3 Concrete

55

Table 2.5 Basic indices of concrete material properties Properties

Strength class of concrete C30

C35

C40

C45

C50

C55

C60

C65

C70

C75

C80

Characteristic 20.1 value of compressive strength f ck (N/mm2 )

23.4

26.8

29.6

32.4

35.5

38.5

41.5

44.5

47.4

50.2

Characteristic value of tensile strength f tk (N/mm2 ) Design value of compressive strength f c (N/mm2 )

2.01

14.3

2.20

16.7

2.39

19.1

2.51

21.1

2.64

23.1

2.74

25.3

2.85

27.5

2.93

29.7

2.99

31.8

3.05

33.8

3.11

35.9

Design value of tensile strength f t (N/mm2 )

1.43

1.57

1.71

1.80

1.89

1.96

2.04

2.09

2.14

2.18

2.22

Modulus of elasticity E c (×104 N/ mm2 )

3.00

3.15

3.25

3.35

3.45

3.55

3.60

3.65

3.70

3.75

3.80

Note The value of shear deformation modulus Gc of concrete can be used as 40% of the corresponding modulus of elasticity, and the Poisson’s ratio ν c of concrete can be taken as 0.2

to the physical properties of the steel tube and its core concrete, the match of their geometric properties and physical properties will also impose significant influences on the mechanical behavior of the CFST member. In order to realize the design concept of material-structure integration and effectively unleash the advantages of both steel tube and concrete, the design of CFST structure shall meet the basic construction requirements. The provision on the minimum outer diameter and wall thickness is to ensure the quality of concrete placement and steel tube welding, and the provision on the diameter-to-thickness ratio is to make the cold-forming process easier. Studies have shown that due to the existence of the core concrete, the stability of the steel tube is enhanced; however, the limit of the diameter-to-thickness ratio of the steel tube in the CFST member shall not be > 1.5 times that of the corresponding hollow steel tube. After a comprehensive evaluation of the mechanical behavior as well as the cost of trussed CFST hybrid structures, it is determined that the crosssectional steel ratio shall not be too large or too small, and a range of 0.06–0.20 is reasonable for practice. To ensure that the steel tube and core concrete act together in the large-scale CFST member, necessary detailing, such as stiffeners along the

56

2 Materials

inner surface of the steel tube, can be employed based on the requirements of the engineering projects. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the detailing of CFST members in CFST hybrid structures shall conform to the following requirements: (1) The outside diameter of circular steel tubes shall not be < 200 mm and the wall thickness shall not be < 4 mm. The outside(diameter-to-thickness ratio of the ) and should not be less than cross-section shall not be greater than 150 235 fy ( ) 25 235 , where f y is the yield strength of the steel tube (N/mm2 ); fy (2) The cross-sectional steel ratio of a CFST member, which shall be calculated in accordance with Eq. (1.3.2), should not be < 0.06 and shall not be > 0.20; (3) The confinement factor of the cross-section, which shall be calculated in accordance with Eq. (1.3.1), should not be < 0.6 and shall not be > 4.0; (4) When the outside diameter of the steel tube is ≥ 2000 mm, effective measures should be taken to reduce the shrinkage of the core concrete. The core concrete in CFST structure can also be recycled aggregate concrete according to engineering necessity. Recycled aggregate concrete refers to concrete mixed with recycled coarse aggregate. Recycled aggregate concrete can effectively relieve the mining pressure of sand and stone, which is in line with the sustainable development goal of engineering construction. However, recycled aggregate has initial micro-cracks and high brittleness. Compared with ordinary concrete, recycled aggregate concrete has relatively lower strength and elastic modulus, and larger shrinkage and creep. During loading, compared with ordinary concrete, the peak stress of the stress–strain relationship of recycled aggregate concrete is relatively smaller, while the peak strain is relatively larger. If recycled aggregate concrete is placed into steel tubes, its disadvantages will be improved, which promotes the utilization of recycled aggregate concrete. Figure 2.3(1) and (2) respectively show the core concrete failure modes of the stub column specimen in axial compression and the specimen in pure bending after the steel tube is stripped. In the figures, “racfst-1” and “racfst-2” represent recycled aggregate CFST specimens with replacement ratio of recycled coarse aggregate (r) of 25 and 50%, respectively. And “cfst” represents CFST specimens used for comparison. It can be seen that the failure modes of specimens are not significantly different with different replacement ratios of recycled coarse aggregate. This is mainly due to the fact that the steel tube and core concrete are complementary to each other and have strong composite effects during loading, which improves the plastic property of recycled aggregate concrete. China Association for Engineering Construction Standardization Standard T/ CECS 625-2019 Technical Specification for Recycled Aggregate Concrete-Filled Steel Tubular Structures provides the technical regulations of recycled aggregate CFST structures. The recycled aggregate concrete applicable to this regulation shall be mixed with recycled coarse aggregate concrete and natural fine aggregate, and its material property requirements are as follows: (1) Replacement ratio of recycled coarse aggregate shall not be more than 70%;

2.3 Concrete

r=0

57

r=25% r=50% r=0 r=25% r=50% (a) Circular specimen (b) Square specimen (1) Stub specimens to axial compression

(2) Specimens to pure bending Fig. 2.3 Failure modes of core concrete with different replacement ratios of recycled coarse aggregate

(2) The strength class of recycled aggregate concrete should be determined according to the characteristic value of cube strength, and its strength class shall not be higher than RC50 or lower than RC30; (3) When combined with steel tube materials, Q235 steel should be matched with RC30 recycled coarse aggregate, and Q355, Q355GJ and Q390 steel should be matched with RC40 or RC50 recycled coarse aggregate, Q420 and Q460 steel should be matched with RC50 recycled coarse aggregate; (4) For recycled coarse aggregate mixed only with class I recycled coarse aggregate, its strength indices shall conform to the relevant requirement of the current standard of nation GB 50010 Code for Design of Concrete Structures. Its modulus of elasticity shall be determined by test. When there is a lack of test data, the

58

2 Materials

Table 2.6 Modulus of elasticity of recycled aggregate concrete mixed with class I recycled coarse aggregate only (×104 N/mm2 ) Replacement ratio of recycled coarse aggregate (%)

Strength class RC30

RC35

RC40

RC45

RC50

10

2.97

3.12

3.21

3.31

3.41

20

2.93

3.08

3.18

3.28

3.37

30

2.90

3.05

3.14

3.24

3.34

40

2.87

3.01

3.11

3.20

3.30

50

2.84

2.98

3.07

3.17

3.26

60

2.80

2.94

3.04

3.13

3.22

70

2.77

2.91

3.00

3.09

3.18

Note Intermediate values in the table are obtained by linear interpolation

modulus of elasticity of recycled coarse aggregate with the replacement ratio of recycled coarse aggregate of 10–70% may be adopted according to Table 2.6; (5) The basic indices of properties of recycled aggregate concrete materials mixed with class II and III recycled coarse aggregate can be adopted according to Table 2.7. The shear modulus G c,r of recycled aggregate concrete can be taken as 40% of its corresponding modulus of elasticity; the Poisson ratio of recycled aggregate concrete νc,r can be taken as 0.2.

2.4 Connecting Materials Connecting materials for CFST structures include welding materials, connecting fastener materials, et al. For welding materials, the covered electrodes used in manual welding, the welding electrodes used in automatic or semi-automatic welding and the welding electrodes and fluxes used in submerged arc welding shall all conform to the relevant requirements of the current national standards. The quality of connecting fasteners used for CFST structures including plain bolts, high-strength bolts with a large hexagon head used in steel structures and cheese head studs shall all conform to the relevant requirements of the current national standards. Strength indices for welding seams and connecting fasteners shall refer to the relevant provisions in the current standard of nation GB 50017 Standard for Design of Steel Structures. In the design of concrete-filled stainless steel tubular structures, the selection of welding material should match the mechanical properties of the base material, and the weld metal should have excellent ductility, plasticity and crack resistance. When stainless steel is connected with dissimilar metals such as carbon steel for structural

2.5 Protective Materials

59

Table 2.7 Basic indices of properties of recycled aggregate concrete materials mixed with class II and III recycled coarse aggregate Properties

Replacement ratio of Strength class recycled coarse aggregate RC30 RC35 RC40 RC45 RC50 (%)

Characteristic value of 10 compressive strength f ck (N/ 30 mm2 ) 50

19.70 22.93 26.26 29.01 31.75

70

17.49 20.36 23.32 25.75 28.19

18.89 22.00 25.19 27.82 30.46 18.19 21.18 24.25 26.79 29.32

Characteristic value of 10 tensile strength f tk (N/mm2 ) 30

1.97

2.16

2.34

2.46

2.59

1.89

2.07

2.25

2.36

2.48

50

1.82

1.99

2.16

2.27

2.39

70

1.75

1.91

2.08

2.18

2.30

Design value of compressive 10 strength f c (N/mm2 ) 30

14.01 16.37 18.72 20.68 22.64

50

12.94 15.11 17.29 19.10 20.91

70

12.44 14.53 16.62 18.36 20.10

Design value of tensile strength f t (N/mm2 )

Modulus of elasticity E c (× 104 N/mm2 )

13.44 15.70 17.95 19.83 21.71

10

1.40

1.54

1.68

1.76

1.85

30

1.34

1.48

1.61

1.69

1.78

50

1.29

1.42

1.55

1.63

1.71

70

1.24

1.37

1.49

1.57

1.64

10

2.90

3.05

3.15

3.24

3.34

30

2.73

2.87

2.96

3.05

3.14

50

2.59

2.72

2.80

2.89

2.98

70

2.47

2.59

2.67

2.76

2.84

Note Intermediate values in the table are obtained by linear interpolation

use, low alloy steel, weathering steel or aluminum, it is necessary to pay attention to the corrosion of dissimilar metal (galvanic) joints. For fastener connections, the corrosion resistance of the bolt material shall be equivalent to the metal with the strongest corrosion resistance.

2.5 Protective Materials 2.5.1 Anti-corrosion Coatings Steel corrosion is a physical–chemical interaction process between steel and the environment that changes the properties of steel and may cause damage to the function of the structural system. When CFST structures without reinforced concrete

60

2 Materials

encasement are applied to marine and offshore structures, the outer wall of the steel tube is prone to be continuously corroded under the severe corrosive environment of seawater and marine atmosphere. However, since the inner wall of the steel tube and the core concrete of the CFST structure maintain a reliable bond, the inner wall of the steel tube is isolated from the continuous oxygen supply, so that the corrosion of the inner wall of the steel tube will not occur continually. Corrosion has obvious effects on the mechanical performance of CFST members from the following four aspects: (1) (2) (3) (4)

Reduce the cross-sectional area of the steel tube; Reduce the stiffness and resistance of the members; Reduce the confinement effect of steel tube on core concrete; Increase the risk of local buckling due to the reduction of the wall thickness of steel tube.

In practical engineering projects, anti-corrosion technical measures of CFST should be determined according to the characteristics of different corrosion environments. Common techniques include the use of protective coatings, anti-corrosion techniques, electrochemical cathodic protection, and the addition of corrosion inhibitors in relatively closed underwater areas (such as marine environments). For the CFST members without reinforced concrete encasement, the outer surface of steel tubes shall adopt anti-corrosion measures such as painting after rust removal or metal coating. Anti-rust and anti-corrosion coatings, rust removal degree of steel surfaces and the structural requirements of corrosion protection on steel structures shall conform respectively to relevant provisions in the current technical standards of the nation. The quality of anti-corrosion coatings used for CFST structures should meet the relevant provisions of the current standards of the nation. When applying anti-corrosion coating systems, the surface of the steel tube should be treated to ensure that harmful substances are removed and a surface with reliable primer adhesion is obtained. The appropriate coating system should be selected according to the corrosion environment, corrosion grade, type of surface to be painted and grade of durability requirement, etc. The coating thickness should not only reach the dry film thickness, but also avoid local over-thickness. For building structures in atmospheric corrosion, the minimum thickness of the anti-corrosion coating should also meet the relevant provisions of current standards of the nation. It should be pointed out that when the core concrete contains harmful chloride ions, the inner tube wall should also be protected against corrosion.

2.5.2 Fireproof Coatings The quality of fireproof coatings used for CFST structures shall conform the relative requirement of the current national standard GB 14907 Fire Resistive Coating for Steel Structure. Other types of fire protective materials shall conform the requirement of relevant current national standards.

2.5 Protective Materials

61

Fire protection design of CFST structure should be based on the usage, position and type of fire of buildings or structures to select the corresponding categories of fireproof coatings. Indoor hidden structural members generally use the non-reactive fireproof coating or epoxy fireproof coating; the outdoor or open CFST structure project should use outdoor fireproof coating; for marine engineering and petrochemical engineering structures, outdoor non-reactive fireproof coating or outdoor epoxy intumescent fireproof coating should be selected. Limited by the fire resistance performance of steel structures and the thermal insulation performance of the intumescent fireproof coating, relevant standards prescribe that intumescent fireproof coating should not be employed for steel members with required fire resistance ratings > 1.5 h. However, for trussed CFST hybrid structures, fire resistance ratings of 3.0 h can be reached, provided that the intumescent fireproof coatings are reasonably designed. One of the reasons is attributed to the capacities of thermal absorption and storage of the concrete in the chord steel tubes, which can delay the heating rate of the steel tubes under fire exposure. Besides, concrete in the steel tubes makes a great contribution to the bearing capacity of structures, and the stress level of the steel tubes is relatively low, also the stress redistribution between the concrete and the tubes due to the different material degradation delays the deterioration of the structural resistance. Therefore, intumescent fireproof coating can also be used in the CFST structure for airports, stations and other large-scale public infrastructure. As mentioned in Sect. 1.4 of this book, the main structure of the Qinghe Station project of the new Beijing to Zhangjiakou Railway project adopts straight columns with a maximum diameter of 1800 mm, Y-shaped columns and A-shaped columns (as shown in Fig. 1.37). The maximum fire load ratio of CFST column is up to 0.52, and the designed fire resistance is 3.0 h. Considering the factors of safety, durability, aesthetics and space efficiency, the project finally adopts the light weight, thin coating and aesthetically pleasing intumescent fireproof coating as the fire protection material of CFST column, as shown in Fig. 2.4. According to T/CECS 24-2020 Technical Specification for Application of Fire Resistive Coating for Steel Structure, in practical engineering projects, if the inspection report or the test report of fireproof coating specified the utilization of reinforcing meshing, then the meshing should be adopted during construction. The materials and the specifications of the meshing should be consistent with those used in the inspection report or the test report. The meshing material should be selected from barbed wire meshing, alkali-resistant glass fiber meshing or carbon fiber meshing. The thicknesses of the fireproof coating and crack should be effectively controlled. The penetrating crack shall not appear on fireproof coating, in order to meet the requirements in terms of airtight, thermal insulation and integrity of the fire protection.

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2 Materials

(a) Straight column

(b) Y-shaped column

Fig. 2.4 CFST columns with intumescent fireproof coatings

Exercises 1. Briefly describe the selection principles of steel in CFST structures. 2. Briefly describe the reason why the limit value of the diameter (width)-tothickness ratio of steel tubes in CFST structures is different from that in steel structures. 3. Briefly describe the main species and applicable conditions of anti-corrosion coatings and fireproof coatings for CFST structures.

Chapter 3

Analysis of Concrete-Filled Steel Tubular (CFST) Structures

Key Points and Learning Objectives Key Points This chapter discusses the structural analysis methods of CFST structure, the calculation models for shrinkage and creep of core concrete, the constitutive models for steel and concrete, and the interface models between steel and concrete. Learning Objectives Understand the basic concepts and principles of structural analysis methods for CFST structure. Familiarize with the constitutive models of steel and concrete and their applicable conditions. Understand the models of shrinkage and creep of core concrete, and the interface models between steel and concrete.

3.1 Introduction The CFST structures in this book refer to structures that use CFST members as the main load-resisting components. Among them, the CFST hybrid structures refer to the structures that combine the CFST members as the main components and other members (or components), they can act together and are complementary to each other. It is classified as CFST structures (as shown in Figs. 1.16 and 1.18). In actual engineering projects, the CFST structure is often combined with a reinforced concrete structure and steel structure to form a CFST hybrid structural system, including CFST frame-reinforced concrete, or steel plate shear wall hybrid structure system (as shown in Fig. 1.23b) and trussed CFST hybrid structural system with a reinforced concrete slab (as shown in Fig. 1.53). The mechanical characteristics of CFST members under complex loading, key joints in CFST structures, CFST hybrid structures and CFST hybrid structural systems are often calculated by structural global analysis. © China Architecture & Building Press 2024 L. Han, Theory of Concrete-Filled Steel Tubular Structures, https://doi.org/10.1007/978-981-99-2170-6_3

63

64

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

CFST structural analysis is the process of determining the action effects in CFST structure. In order to design CFST structure reasonably, it is necessary to establish the CFST structural analysis model for structural analysis. This chapter discusses the analysis method, calculation indices, shrinkage and creep models of concrete, constitutive models of steel and concrete, interaction models between steel and concrete, and other methods required by CFST structural analysis.

3.2 Methodology According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, elastic analysis, elasto-plastic analysis or experimental approaches shall be chosen for the structural analysis of CFST structures based on the structural types, material properties, and load characteristics. When using modelling software to carry out structural analysis, the results shall be verified to make sure the results are reasonable and valid before applying them to engineering designs. Global action effects shall be analyzed for CFST structures, and detailed analysis shall be carried out for local areas with particular loading conditions. Structural analysis for CFST structure shall conform to the following requirements: (1) Force equilibrium is achieved; (2) Deformation compatibility, including constraints at joints and boundaries, is satisfied; (3) Reasonable constitutive models for materials are employed; (4) Analyses are conducted for both construction and service stages. The constitutive models for materials considering the confinement effect in Sect. 3.6.1 may be employed for the elasto-plastic analysis of CFST structures using fiber-based models. The structural analysis shall properly consider the composite effects among materials and hybrid effects among members. When structures are subjected to various loading conditions during the construction and service stages, the structural analysis shall be conducted for each of the loading conditions to determine the most unfavorable load combination. Furthermore, the following requirements shall be satisfied: (1) When the structures are subjected to seldom occurred earthquakes, fire, impact, etc., the corresponding analysis shall be conducted based on current relevant standards of the nation; (2) When the effects of shrinkage and creep of concrete, support settlement, temperature variation, corrosion, etc., are significant enough to endanger the safety or serviceability of the structures, corresponding analysis of the action effects shall be conducted, and corresponding technical arrangements shall be employed to tackle the issue;

3.2 Methodology

65

(3) Structural analysis for the service stage shall consider the influence of internal force and deformation during the construction stage on the structural performance. When the structures are subjected to accidental actions, the relationships between the force and deformation (or deformation rate) are complex and generally nonlinear. Elasto-plastic or plastic theory should be employed for the analysis. The level of construction difficulty and cost of CFST hybrid structures highly depend on the construction methods. Thus, the construction plan shall be conducted during the design. The load conditions of CFST hybrid structures are quite different for the construction process and the post-construction stage. The structural analysis shall be carried out for the key construction stage in the design. In other words, the structural analysis shall be carried out for both the construction and service stages, with the influence of imperfections during the fabrication and construction reasonably considered in the calculation models. For CFST structures, the following verifications during the main construction stages shall be conducted: (1) The strength, deformation and stability of steel tubes during their fabrication, transportation and erection; (2) The strength, deformation and stability of steel structures during the placement of the core concrete; (3) The strength, deformation and stability of steel and concrete structures during the placement of the concrete encasement of concrete-encased CFST hybrid structures. For the structural analysis of the construction stages, all the actual loads and effects during the whole construction, including the installation of machines and materials, steel structures during erection, concrete during placement, installation and dismantling of temporary supporting structures, temperature variation, wind loads, other temporary construction loads, etc., shall be considered carefully. For trussed CFST hybrid structures, the whole construction stage includes the steel tube erection, core concrete placement, etc.; and for concrete-encased CFST hybrid structures, the whole construction stage also includes the reinforcement installation, placement of concrete encasement, etc. Structural analysis on CFST structures shall consider the static and dynamic effects of wind loads. For special structures, their shape factors should be determined through wind tunnel tests. Damping ratios for trussed CFST hybrid structures may be taken as 0.03 for frequently occurred earthquakes, and 0.04 for seldom occurred earthquakes; for concrete-encased CFST hybrid structures, the damping ratios may be taken as 0.045 for frequently occurred earthquakes, and 0.05 for seldom occurred earthquakes. They may also be determined through structural experiments. According to CECS 28:2012 Technical Specification for Concrete-Filled Steel Tubular Structures, the damping ratios of CFST structure for frequently occurred earthquakes may be taken as 0.05 when using reinforced concrete floor; damping ratios for frequently occurred earthquakes may be taken as 0.04 when the height of

66

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

frame-center support and frame-eccentric support structures is no more than 50 m, 0.03 when the height is > 50 and < 200 m and 0.02 when the height is not < 200 m; in addition to frame-center support and frame-eccentric support structures, damping ratios for other structures that use steel beam-concrete slab floor may be taken as 0.04. Experimental study is the most direct method to determine the structural analysis parameters. For example, the seismic simulating apparatus model test is carried out on the hybrid structure shear wall with CSFT side column and the CFST frame-core shear wall hybrid structural system, where circular and square CFST columns are used as frame columns. Figure 3.1 shows the situation during the seismic simulating apparatus model test. Fig. 3.1 Seismic simulating apparatus test model

3.3 Design Indices

67

The tested model shown in Fig. 3.1 refers to the structural design of an actual highrise building. The model consists of an outer CFST frame and a reinforced concrete shear wall located in the center. The structure height is 6.3 m with 30 floors, and the plane size of the standard layer is 2.2 m × 2.2 m. The square core tube formed by the reinforced concrete shear wall is located in the center of the model with a plane size of 1.21 m × 1.21 m. The main beam on the floor is hinged with the concrete shear wall. The model frame column section is divided into circular and square, and the outer frame and floor steel beams are welded I-shaped steel beams. Three kinds of strong motion record waves were used in the test, namely the Taft wave, EL-Centro wave and Tianjin wave. The peak horizontal acceleration was 0.2 (small earthquake), 0.4 (medium earthquake), 0.6 (large earthquake) and 0.8 g (super large earthquake). The results of the seismic simulating apparatus test showed that the two hybrid structural models with circular and square CFST columns, respectively, showed superior seismic performance. The damping ratios of the model with square CFST columns were slightly higher than those of the model with circular CFST columns. First-order damping ratios in the X and Y directions are in the range of 0.030–0.035 before the earthquake. Second-order damping ratios are smaller than those in the first order, ranging from 0.02 to 0.03. The second-order damping ratios in both directions gradually increased with the increase of earthquake intensity. After the peak earthquake input of 0.6 g, the first-order damping ratios of the model were in the range of 0.035–0.040.

3.3 Design Indices (1) Compressive strength The compressive strength is the maximum axial compressive stress that the material can bear, and it is an important calculation index to reasonably determine the resistance of CFST structure in axial compression. Under axial compression load, the working mechanisms of CFST cross-section are that steel and concrete are complementary to each other and able to act together during loading, so the confinement factor (ξ ) is adopted for compressive strength of CFST cross-section to reflect the composite effect of the steel tube and its core concrete. The specific determination method for compressive strength of CFST cross-section is described in Sect. 4.2.1 (1) of this book. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the design value of the compressive strength of circular CFST cross-section shall be calculated in accordance with the following equations: f sc =

f scy γsc

f scy = (1.14 + 1.02ξ ) f ck

(3.3.1) (3.3.2)

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3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

where, f sc design value of compressive strength of the CFST cross-section (N/mm2 ); f scy characteristic value of compressive strength of the CFST cross-section (N/ mm2 ); ξ confinement factor, shall be calculated by Eq. (1.3.1); f ck characteristic value of compressive strength of concrete, shall be determined by Table 1.1 (N/mm2 ); γsc partial safety factor for the compressive strength of the CFST members, shall be determined by Table 3.1. When using f sc as the design index for the compressive strength of the CFST cross-section in CFST hybrid structures, a reliability analysis has been carried out. After summarizing and analyzing experimental data of more than a thousand circular CFST stub columns subjected to axial compression, calculation results for CFST columns with different steel grades, concrete strength, cross-sectional steel ratios, etc., showed that the design index f sc determined by Eq. (3.3.1) can meet the reliability requirements for ductile members of the current national standard GB 50153 Unified Standard for Reliability Design of Engineering Structures. For the buildings and electric power transmission towers, highway bridges, and port engineering structures with a structural safety class of “Second”, partial safety factors for the compressive strength of CFST members are chosen in accordance with the current national standards GB 50068 Unified Standard for Reliability Design of Building Structures, GB/T 50283 Unified Standard for Reliability Design of Highway Engineering Structures, and GB 50158 Unified Standard for Reliability Design of Port Engineering Structures. For railway bridge structures, considering the ductile behavior of CFST members in axial compression, the partial safety factor is recommended to be 1.80 in accordance with the provisions on the allowable stresses of concrete and steel in the current professional standards TB 10092 Code for Design of Concrete Structures of Railway Bridge and Culvert and TB 10091 Code for Design on Steel Structure of Railway Bridge. It is worth noting that when the ambient temperature changes, the compressive strength of the CFST member will be affected. When the ambient temperature changes greatly, the influence of temperature change on the compressive strength of the CFST member may not be ignored. The decline rate of the design index of compressive strength of the CFST member can be determined through test and analysis with + 20 °C as the reference temperature. (2) Shear strength Table 3.1 Partial safety factor for the compressive strength of the CFST members (γ sc ) Structure type

Buildings

Highway bridges

Electric power transmission towers

Port engineering structures

γsc

1.20

1.40

1.20

1.20

3.3 Design Indices

69

Shear strength is the maximum shear stress borne by the material. Based on the relationship between nominal shear stress and shear strain of circular CFST cross-section to pure shear, the ultimate limit state of CFST cross-section to shear is determined and the calculation equations for its design value of shear strength ( f sv ) are thus derived. The design value of the shear strength for the circular CFST cross-section should be calculated in accordance with the following equation:   f sv = 0.422 + 0.313αs2.33 ξ 0.134 f sc

(3.3.3)

where, f sv design value of shear strength of the circular CFST cross-section (N/mm2 ); f sc design value of compressive strength of the circular CFST cross-section, shall be calculated by Eq. (3.3.1) (N/mm2 ); αs cross-sectional steel ratio, shall be calculated by Eq. (1.3.2); ξ confinement factor, shall be calculated by Eq. (1.3.1). (3) Elastic compression stiffness and elastic tension stiffness Elastic compression (tension) stiffness is the ratio of the axial force applied on the compression (tension) member during the elastic stage to the corresponding compressive (tensile) deformation. Elastic compression stiffness and elastic tension stiffness of the CFST cross-section should be calculated in accordance with Eqs. (3.3.4) and (3.3.5), respectively: (E A)c = E s As + E c,c Ac

(3.3.4)

(E A)t = E s As

(3.3.5)

where, (EA)c elastic compression stiffness of the CFST cross-section (N); (EA)t elastic tension stiffness of the CFST cross-section (N); Es modulus of elasticity of the steel tube (N/mm2 ), shall be determined in accordance with the relevant provisions of the current national standard GB 50017 Standard for Design of Steel Structures; E c,c modulus of elasticity of the core concrete (N/mm2 ), shall be determined in accordance with the relevant provisions of the current national standard GB 50010 Code for Design of Concrete Structures; As cross-sectional area of the steel tube (mm2 ); Ac cross-sectional area of the core concrete (mm2 ). Elastic compression stiffness and elastic tension stiffness of CFST hybrid structures should be calculated in accordance with Eqs. (3.3.6) and (3.3.7), respectively: (E A)c,h = ∑(E s As + E s,l Al + E c,c Ac ) + E c,oc Aoc

(3.3.6)

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3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

(E A)t,h =

∑

E s As + E s,l Al



(3.3.7)

where, (EA)c,h (EA)t,h Es E s,l E c,c E c,oc As Al Ac Aoc

elastic compression stiffness of the CFST hybrid structure (N); elastic tension stiffness of the CFST hybrid structure (N); modulus of elasticity of the steel tube (N/mm2 ); modulus of elasticity of the longitudinal reinforcement (N/mm2 ); modulus of elasticity of the core concrete (N/mm2 ); modulus of elasticity of the concrete slab or concrete encasement (N/mm2 ); cross-sectional area of the steel tube (mm2 ); cross-sectional area of the longitudinal reinforcement (mm2 ); cross-sectional area of the core concrete (mm2 ); cross-sectional area of the concrete slab or concrete encasement (mm2 ).

(4) Elastic flexural stiffness The elastic flexural stiffness is the ratio of the bending moment applied to the bending member in the elastic stage to corresponding the curvature. Elastic flexural stiffness of the CFST cross-section should be calculated in accordance with the following equation: E I = E s Is + E c,c Ic

(3.3.8)

where, EI elastic flexural stiffness of the CFST cross-section (N·mm2 ); I s second moment of area of the steel tube (mm4 ); I c second moment of area of the core concrete (mm4 ). Elastic flexural stiffness of CFST hybrid structures should be calculated in accordance with the following equation: (E I )h = E s Is,h + E s,l Il,h + E c,c Ic,h + E c,oc Ioc,h

(3.3.9)

where, (EI)h elastic flexural stiffness of the CFST hybrid structure (N·mm2 ); I s,h second moment of area of the steel tube to centroidal axis of cross-section of the CFST hybrid structure (mm4 ); I l,h second moment of area of the longitudinal reinforcement to centroidal axis of cross-section of the CFST hybrid structure (mm4 ); second moment of area of the core concrete to centroidal axis of cross-section I c,h of the CFST hybrid structure (mm4 ); I oc,h second moment of area of the concrete slab or concrete encasement to centroidal axis of cross-section of the CFST hybrid structure (mm4 ).

3.4 Shrinkage and Creep Models of Concrete

71

(5) Elastic shear stiffness The elastic shear stiffness is the ratio of the shear force exerted on the shear member in the elastic stage to the corresponding orthogonal angle. Elastic shear stiffness of the CFST cross-section should be calculated in accordance with the following equation: G A = G s As + G c,c Ac

(3.3.10)

where, GA Gs

Gc,c

elastic shear stiffness of the CFST cross-section (N); shear modulus of steel (N/mm2 ), shall be determined in accordance with the relevant provisions of the current national standard GB 50017 Standard for Design of Steel Structures; shear modulus of the core concrete in the CFST member (N/mm2 ), shall be determined in accordance with the relevant provisions of the current standard of nation GB 50010 Code for Design of Concrete Structures.

Elastic shear stiffness of CFST hybrid structures should be calculated in accordance with the following equation: (G A)h =

∑

 G s As + G c,c Ac + G c,oc Aoc

(3.3.11)

where, (GA)h elastic shear stiffness of the CFST hybrid structure (N); Gc,c shear modulus of the core concrete in the CFST member (N/mm2 ), shall be determined in accordance with the relevant requirements of the current national standard GB 50010 Code for Design of Concrete Structures; Gc,oc shear modulus of the concrete slab or concrete encasement (N/mm2 ), shall be determined in accordance with the relevant requirements of the current national standard GB 50010 Code for Design of Concrete Structures.

3.4 Shrinkage and Creep Models of Concrete In actual engineering projects, the design working life of CFST structure is usually 50, 100 years or even longer, and the core concrete in the steel tube is often in a state of high stress, which will cause shrinkage and creep deformation, and then occur the stress redistribution, which will change the stress of the steel tube and its core concrete. Finally, the mechanical performances of CFST structures are affected. The time-varying characteristics of core concrete of CFST members are currently the hot spot concerned by the engineering field, and also one of the core issues of the whole life-cycle-based design principle of CFST structure. In order to realize the fine analysis of CFST structure considering time-varying characteristics, it is necessary to establish accurate shrinkage and creep models of core concrete.

72

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

(1) Shrinkage Model The shrinkage mechanism of concrete is discussed in Sect. 2.3 of this book. The shrinkage deformation of core concrete in CFST members is similar to that of plain concrete, but the value and deformation rate at the early stage of shrinkage of the former are much smaller. The cross-section size has a great influence on the shrinkage deformation of the core concrete. With the increase of the cross-section size, the longitudinal and transverse shrinkage deformation of the core concrete shows a decreasing trend. The main reason is that the cross-section size has a great influence on the migration rate of water inside the core concrete and the diffusion rate to the steel tube wall. The shrinkage model of plain concrete is given by the American Concrete Institute standard ACI 209R-92. Through the analysis of the test results of core concrete shrinkage in CFST members, it is found that the value of shrinkage deformation calculated by this model is generally greater than that of the test results. Therefore, based on the analysis of the shrinkage mechanism of core concrete in CFST members, the confinement effect of steel tube on core concrete shrinkage is comprehensively considered and the correction factor (γu ) for the confinement of steel tube on the core concrete shrinkage is proposed through the regression analysis of the test results based on the concrete shrinkage model presented in ACI 209R-92. The calculation equations for the shrinkage strain (εsh )t of the core concrete in the CFST member are proposed by GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures as follows: (εsh )t =

(3.4.1)

(εsh )u = 780γcp γλ γvs γs γψ γc γα γu

(3.4.2)

γvs = 1.2e−0.00472V /S

(3.4.3)

γs = 0.89 + 0.00161s

(3.4.4)

 γψ =

where,

td (εsh )u 35+td

0.30+0.014ψ (ψ ≤ 50) 0.90+0.002ψ (ψ > 50)

(3.4.5)

γc = 0.75 + 0.00061c

(3.4.6)

γα = 0.95 + 0.008αv

(3.4.7)

γu = 0.0002D + 0.63

(3.4.8)

3.4 Shrinkage and Creep Models of Concrete

73

td time after shrinkage is considered, i.e., after the end of initial wet curing (d); (εsh )u ultimate shrinkage strain of concrete (με). γcp shrinkage correction factor for initial wet curing, shall be determined in accordance with Table 3.2; γλ correction factor for relative humidity, which is set as 0.3 for the core concrete; γvs correction factor for volume-to-surface ratio (V /S, unit: mm); γs correction factor for concrete slump; s concrete slump (mm); γψ correction factor for fine aggregate; ψ ratio of the fine aggregate to total aggregate by weight in percent; γc correction factor for cement content; c quality of cement per cubic meter (kg/m3 ); γα correction factor for air content; αv air content in percent; γu correction factor for restriction to the core concrete shrinkage due to the steel tube; D outside diameter of the steel tube (mm). Equation (3.4.2) is applicable for members with an outside diameter (D) of steel tubes in the range of 200–1200 mm. In engineering applications, the core concrete shrinkage may be predicted and appropriate construction measures may be taken to reduce the shrinkage. According to the necessity of engineering, the long-term performance test of core concrete in the CFST column of an engineering project for 2100 days was carried out. The cross-section size of the test chamber is about 2000 mm, using C70 concrete, and the water-to-binder ratio of concrete is 0.28. Figure 3.2 shows the comparison of core concrete shrinkage in steel tubes at the two measuring points between the measured results and the calculated results using the above model, where the results are generally consistent with each other. (2) Creep Model Concrete creep is the strain of the concrete that increases with time under sustained action. The influence factors of concrete creep are mainly divided into internal and external factors. The internal factors include cement variety, aggregate content and water-to-binder ratio. External factors include loading age, loading stress ratio (ratio of loading stress to concrete strength), the time since the application of load, ambient relative humidity, and structure size, etc. When calculating the deformation of CFST structures under long-term load, the creep model of core concrete shall be determined first. Table 3.2 Shrinkage correction factor for initial wet curing γcp Curing time (d)

1

3

7

14

28

90

γcp

1.2

1.1

1.0

0.93

0.86

0.75

Note Intermediate values in the table are obtained by linear interpolation

74

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

εsh (με)

εsh (με)

Measured Calculation t=28d

t (d)

120 100 80 60 40 20 0

Measured Calculation

t=28d

0

600

1200 1800 2400 t (d)

(b) Point 2

(a) Point 1

Fig. 3.2 Measured results of shrinkage strain (εsh )–time (t) of concrete

Due to the deformation compatibility between the steel tube and the core concrete, the external load carried by the core concrete continuously changes under long-term load. Therefore, this loading process should be properly considered when analyzing the deformation under long-term load. Through the comparison and analysis of the previous calculation methods of long-term load, the age-adjusted effective modulus method can be used to calculate the creep of CFST structure under long-term load. According to ACI 209R-92 and the age-adjusted effective modulus method, the creep strain of concrete under long-term load presented in Han (2016) should be determined according to the following equations: σ (t0 ) φ(t, t0 ) + ε1 (t) = E(t0 )  φ(t, t0 ) =

t t0

∂σ (τ ) 1 + φ(t, τ ) · dτ ∂τ E(τ )

 (t − t0 )0.6 φu 10 + (t − t0 )0.6

(3.4.9)

(3.4.10)

φu = 2.35γc,t0 γc,RH γc,vs γc,s γc,ψ γc,α

(3.4.11)

γc,t0 = 1.25t0−0.118

(3.4.12)

γc,RH = 1.27 − 0.67h

(3.4.13)

γc,VS =

 2 1 + 1.13e[−0.0213(V /S)] 3

γc,s = 0.82 + 0.00264s

(3.4.14) (3.4.15)

3.4 Shrinkage and Creep Models of Concrete

75

γc,ψ = 0.88 + 0.0024ψ

(3.4.16)

γc,α = 0.46 + 0.09αv

(3.4.17)

where, ε1 (t) t0 σ (t 0 ) E(t 0 ) φ(t, t0 ) φu γc,t0 γc,RH γc,VS γc,s s γc,ψ ψ γα αv

creep strain of concrete at time t (με); the age of concrete at loading (d); concrete stress at time t 0 (N/mm2 ); modulus of elasticity of concrete at time t 0 (N/mm2 ); creep coefficient; ultimate creep coefficient; the age of loading factor for creep; ambient relative humidity factor, the ambient relative humidity (h) of this book is taken as 90%; correction factor for volume-to-surface ratio (V /S, unit: mm); correction factor for concrete slump; concrete slump (mm); correction factor for fine aggregate; ratio of the fine aggregate to total aggregate by weight in percent; correction factor for air content; air content in percent.

Taking the experimental study of CFST members in compression under longterm load as an example, the time-history curves of the longitudinal strain predicted by the creep model are in good agreement with the experimental results (Fig. 3.3). Long-term load ratio nL = 0.58–0.68, yield strength of the steel tube f y = 293.5 N/ mm2 , and cube strength of core concrete f cu = 34.3 N/mm2 .

Fig. 3.3 Longitudinal strain (εl )–time (t) relationship of CFST specimens

76

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

3.5 Constitutive Models of Steel The finite element analysis-based method or fiber-based models can be used in the full-range analysis of the load-deformation relationship for CFST structure. The finite element method is a numerical analysis method that discretizes the continuous solution domain into finite elements and approximates the real physical system with the approximate solution of finite elements under given constraints. The fiber-based model is a simplified numerical analysis method compared with the finite element method. In the calculation and analysis of this method, it is assumed that the longitudinal stress at any point on the section only depends on the longitudinal fiber strain at that point, and that there is no relative slip between the steel and concrete. The finite element method and the fiber-based models have their own characteristics. The finite element method is universal and can investigate the interaction between steel tube and core concrete under the full-range loading in detail, which is beneficial to reveal the mechanical essence of CFST members comprehensively, while it is relatively complicated and costs a large amount of calculation. The fiber model method is simple and practical, but it is not convenient to analyze the interaction between steel tube and concrete during full-range loading. The key to the scientific and effective application of the finite element method and fiber-based models is to reasonably determine the constitutive models for the steel and concrete in CFST members. The constitutive model is a mathematical model reflecting the mechanical properties of materials and is an important basis for the calculation of structural strength and deformation. The steel constitutive models in this book mainly cover four working conditions: monotonic load, cyclic load, elevated temperature and post-elevated temperature. The same steel constitutive model was used in the finite element method and fiber-based models. (1) Monotonic Load According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the uniaxial monotonic stress (σ )–strain (ε) relationship of steel tubes and reinforcement should be determined in accordance with the following equation:

3.5 Constitutive Models of Steel

77

σ=

ε ≤ εy Esε f y + 0.01E s (ε − εy ) ε > εy

(3.5.1)

where, E s modulus of elasticity of steel (N/mm2 ); f y yield strength of steel (N/mm2 ); εy yield strain of steel. (2) Cyclic Load According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the skeleton curve of the stress (σ )–strain (ε) relationship of steel under cyclic load (Fig. 3.4) should be determined by Eq. (3.5.2), and the modulus of the softening stage should be determined with Eq. (3.5.1):  Eb =

f y +σd εy +εd

1.65εy < εd ≤ 6.11εy

0.1E s εd > 6.11εy

(3.5.2)

where, E b modulus of elasticity of the softening stage de and the corresponding antisymmetric stage d' e' (N/mm2 ); E s modulus of elasticity of steel (N/mm2 ); σ d stress at point d when the softening stage begins (N/mm2 ), point d is on the straight line parallel to ab; εd strain at point d when softening stage begins; εy yield strain of steel. When ε ≤ εy , the loading or unloading modulus is the elastic modulus E s ; moreover, if steel begins to unload before the hardening stage ab, the Bauschinger effect Fig. 3.4 Stress (σ )–strain (ε) hysteretic relationship of the steel tube

78

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

Fig. 3.5 Stress (σ )–strain (ε) hysteretic relationship of the reinforcement

is not considered. On the contrary, if steel begins to unload in the hardening stage ab, the Bauschinger effect needs to be considered. The skeleton curve of the stress (σ )–strain (ε) relationship of reinforcement under cyclic load (Fig. 3.5) should be determined by Eq. (3.5.1); after the stress is unloaded to zero with the elastic modulus, if the reinforcement does not yield during reloading, then the reloading path should point to the original yield point of the reinforcement; if the reinforcement yields during reloading, then the reloading path should point to the maximum strain point during the loading history. Referring to the current national standard GB 50010 Code for Design of Concrete Structures, if reinforcement begins to unload before the hardening stage (ab), the Bauschinger effect needs not to be considered and the loading and unloading modulus is taken as the elastic modulus E s ; if reinforcement begins to unload in the hardening stage (ab), the Bauschinger effect needs to be considered and the stress unloads to zero with the elastic modulus E s . In the reloading stage, the curve is a straight line directed at the original yield point (da' ) or the maximum strain point during the loading history (d' c), and then it keeps loading following the skeleton curve. (3) At elevated temperature The stress–strain relationship model of steel at the elevated temperature given by Lie and Denham (1993) has been applied and verified in the study of the fire resistance of reinforced concrete members and CFST members. The stress (σ )–strain (ε) relationship of steel tube and reinforcement at elevated temperature is shown in Fig. 3.6, and should be determined in accordance with the following equations:

σ =

⎧ ⎨ ⎩

f (T,0.001) ε 0.001 f (T ,0.001) εp 0.001

ε ≤ εp



+ f T , (ε − εp + 0.001) − f (T, 0.001) ε > εp

(3.5.3)

3.5 Constitutive Models of Steel Fig. 3.6 Stress (σ )–strain (ε) relationship of steel at elevated temperature

79

σ T=20 T=300 T=500 T=600 T=900 O

εp = 4 × 10−6 f y

ε (3.5.4)

  √ f (T , 0.001) = (50 − 0.04T ) × 1 − e[(−30+0.03T ) 0.001] × 6.9

(3.5.5)

  f T , εsσ − εp + 0.001 = (50 − 0.04T )   √ × 1 − e[(−30+0.03T ) εsσ −εp +0.001] × 6.9

(3.5.6)

where, σ ε T fy

stress (N/mm2 ); strain; temperature of steel (°C); yield strength of steel (N/mm2 ).

(4) After elevated temperature The mechanical performance of steel after elevated temperature is related to the steel types, the duration of elevated temperature, the cooling method and other factors. It is generally believed that the internal metallography structure of steel changes at elevated temperature, and the strength and modulus of elasticity decrease with the increase of temperature. Its strength has a greater degree of recovery after cooling. The study of post-fire mechanical performance of CFST members shows that the stress–strain relationship of structural steel subjected to natural cooling using bilinear model is in good agreement with the measured results. Stress (σ )–strain (ε) relationship of steel tube and reinforcement after elevated temperature was presented in Han et al. (2022), and should be determined in accordance with the following equations:

80

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

σ =  f yp (Tmax ) =

E sp (Tmax )ε

 ε ≤ εyp (Tmax ) ' (Tmax ) ε − εyp (Tmax ) ε > εyp (Tmax ) f yp (Tmax ) + E sp

(3.5.7)

◦ fy   Tmax ≤ 400 C f y 1 + 2.33 × 10−4 (Tmax − 20) − 5.88 × 10−7 (Tmax − 20)2 Tmax > 400 ◦ C

(3.5.8) εyp (Tmax ) = f yp (Tmax )/E sp (Tmax )

(3.5.9)

E sp (Tmax ) = E s

(3.5.10)

' E sp (Tmax ) = 0.01E sp (Tmax )

(3.5.11)

where, σ ε εyp (T max ) fy f yp (T max ) Es E sp (Tmax ) T max

stress (N/mm2 ); strain; yield strain of steel after cooling from maximum temperature T max ; yield strength of steel (N/mm2 ); yield strength of steel after elevated temperature (N/mm2 ); modulus of elasticity of steel (N/mm2 ); modulus of elasticity of steel after cooling from maximum temperature T max (N/mm2 ); maximum temperature (°C).

3.6 Constitutive Models of Concrete The constitutive models of concrete mainly cover four working conditions: monotonic loading, cyclic loading, at elevated temperature and after elevated temperature (Fig. 3.7).

3.6.1 Fiber-Based Models According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, when analyzing the CFST structures with fiber-based models, the confinement effect of the steel tubes on its core concrete shall be considered for CFST members. For concrete-encased CFST hybrid structures, concrete encasement consists of unconfined concrete and stirrup-confined concrete, as shown in Fig. 3.8a, b, respectively.

3.6 Constitutive Models of Concrete Fig. 3.7 Stress (σ )–strain (ε) relationship of steel after elevated temperature

81

σ Tmax=20 Tmax=600 Tmax=900

O

(a) Single-chord

ε

(b) Four-chord

Fig. 3.8 Schematic diagram of components and partition of materials in cross-sections of concreteencased CFST hybrid structures. 1—Core concrete; 2—Steel tubes; 3—Stirrup-confined concrete; 4—Longitudinal reinforcement; 5—Stirrups; 6—Unconfined concrete; 7—Internal hollow section

(1) Monotonic compression and tension 1) Stress (σ )–strain (ε) relationship for concrete of circular CFST member to monotonic compression. The essence of concrete is characterized by the nonuniformity of material composition and the existence of natural micro-cracks. This characteristic of concrete determines the complexity of its working performance. The core concrete of CFST is confined by the outer steel tube and there is an interaction between the steel tube and its concrete, which further complicates the working performance of the core concrete.

82

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

The loading characteristic of core concrete of CFST in axial compression is that the lateral pressure is passive. In the early stage of loading, concrete is generally under uniaxial compression state. With the increase of the longitudinal deformation of concrete, its coefficient of transverse deformation will increase continuously. When it exceeds the coefficient of transverse deformation of the steel, the interaction force will be generated between the steel tube and its core concrete, and the concrete will be under triaxial compressive stress state. By sorting out and analyzing the test results of CFST stub columns to axial compression, it is found that within the general parametric ranges, the characteristic of the σ − ε relationship of core concrete is related to concrete itself as well as the confinement factor (ξ ), which is mainly shown in: with the increase of ξ , the steel tube provides stronger confinement to its core concrete during loading, the peak stress of core concrete and the corresponding strain increase, and the stress–strain relationship after the peak stress of concrete occurs latter, even not occur; vice versa, with the decrease of ξ , the steel tube provides weaker confinement to its core concrete, the stress–strain relationship after the peak stress of concrete occurs earlier, and the decreasing trend of the decreasing phase increase. Based on the above understanding, the influence of concrete strength and confinement factor (ξ ) is investigated by checking and analyzing the experimental results of a large number of CFST stub columns to axial compression. The proposed longitudinal stress (σ )–strain (ε) relationship model of the core concrete of circular CFST member was presented in Han (2016), and should be determined in accordance with the following equations: y = 2x − x 2 (x ≤ 1)  y=

1 + q(x 0.1ξ − 1) (ξ ≥ 1.12) (x > 1) x (ξ < 1.12) β(x−1)2 +x

(3.6.1.1)

(3.6.1.2)

x=

ε εo

(3.6.1.3)

y=

σ σo

(3.6.1.4)



  24 0.45 ' σo = 1 + (−0.054ξ + 0.4ξ ) fc f c'    ' f εo = εcc + 1400 + 800 c − 1 ξ 0.2 24 

2

εcc = 1300 + 12.5 f c' q=

ξ 0.745 2+ξ

(3.6.1.5)

(3.6.1.6) (3.6.1.7)

(3.6.1.8)

3.6 Constitutive Models of Concrete

83

[0.25+(ξ −0.5)7 ] '2  β = 2.36 × 10−5 f c × 3.51 × 10−4

(3.6.1.9)

where, σ ε ξ f c'

stress (N/mm2 ); strain (με); confinement factor, shall be calculated by Eq. (1.3.1); cylinder strength of concrete (N/mm2 ), shall be determined in accordance with Table 1.1.

It can be seen from the above equations that when x ≤ 1, that is, before the core concrete reaches the peak stress (σ o ), the σ − ε relationship is similar to the plain concrete in form. When x > 1, the σ − ε relationship of the core concrete changes as the confinement factor (ξ ) changes. Figure 3.9 shows the typical σ − ε relationship of core concrete of CFST members. When ξ > ξ0 , the σ − ε relationship curve still does not appear to decrease after the concrete stress reaches σ o ; When ξ ≈ ξ0 , the σ − ε relationship tends to be flat after the concrete stress reaches σo . And when ξ < ξ0 , the σ − ε relationship will decrease after the concrete stress reaches σ o . By analysis and arrangement of the experimental results, it is found that for circular CFST members, ξ0 ≈ 1.12. 2) The uniaxial monotonic compressive stress (σ )–strain (ε) relationship of stirrupconfined concrete (Fig. 3.8) in concrete-encased CFST hybrid structures should be determined in accordance with the Eqs. (3.6.1.10)–(3.6.1.16). The ascending branch of the stress–strain relationship of stirrup-confined concrete encasement is formulated by a second-order parabola, while the descending branch is simplified to be linear. Peak stress σ o , peak strain εo , and the descending rate E des proposed by Hoshikuma et al. (1997) for stirrup-confined concrete are adopted.  y=

2x − x 2 ε ≤ εo 1 − Eσdes (ε − εo ) ε > εo o

(3.6.1.10)

ε εo

(3.6.1.11)

x=

Fig. 3.9 Stress (σ )–strain (ε) relationship of the core concrete

84

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

y=

σ σo

(3.6.1.12)

  ρv f yh σo = f c' 1 + 0.73 ' fc

(3.6.1.13)

ρv f yh f c'

(3.6.1.14)

εo = 2450 + 12,200 Asvlv Av s

(3.6.1.15)

11.2 f c'2 ρv f yh

(3.6.1.16)

ρv = E des = where, σ ε f c' f yh ρv Asv lv Av s

stress (N/mm2 ); strain (με); cylinder strength of concrete (N/mm2 ), shall be determined in accordance with Table 1.1; yield strength of stirrups (N/mm2 ); volumetric stirrup ratio; cross-sectional area of stirrups (mm2 ); length of stirrups (mm); cross-sectional area of stirrup-confined concrete (mm2 ); spacing of stirrups (mm).

3) The uniaxial monotonic compressive stress (σ )–strain (ε) relationship proposed by Attard and Setunge (1996) was adopted to describe the unconfined concrete (Fig. 3.8) in concrete-encased CFST hybrid structures, and should be determined in accordance with the following equations: y=

Ax + Bx 2 1 + C x + Dx 2

(3.6.1.17)

x=

ε εo

(3.6.1.18)

y=

σ σo

(3.6.1.19)

σo = f c'

(3.6.1.20)

4,260,000 f c' √ E c 4 f c'

(3.6.1.21)

εo =

3.6 Constitutive Models of Concrete

⎧⎧ ⎪ A = Ecf ε' o ⎪ ⎪ ⎪ c ⎪ ⎪ ⎨ ⎪ ( A−1)2 ⎪ B = −1 ⎪ ⎪ 0.55 ⎪⎪ ⎪ ⎪ C = A − 2 ⎪ ⎪ ⎪⎪ ⎩ ⎨ D = B + 1 ⎧ f i (εi −εo )2 ⎪ ⎪ A = ε ε f '− f ⎪ ⎪ ⎪ i o( c i) ⎪ ⎪ ⎨ ⎪ ⎪ B = 0 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ C = A−2 ⎪ ⎩ ⎪ ⎩ D=1

85

(ε ≤ εo ) (3.6.1.22) (ε > εo )

f i = f c' [1.41 − 0.17 ln( f c' )]

(3.6.1.23)

εi = εo [2.5 − 0.3 ln( f c' )]

(3.6.1.24)

where, σ stress (N/mm2 ); ε strain (με); f c' cylinder strength of concrete (N/mm2 ), shall be determined in accordance with Table 1.1; E c modulus of elasticity of concrete (N/mm2 ). 4) Under long-term loading, the constitutive model of concrete will be affected by shrinkage and creep, as shown in Fig. 3.10. The creep coefficient of concrete φ(t, t0 ) under long-term load can be determined in accordance with Eq. (3.4.10). 5) The monotonic tensile stress (σ )–strain (ε) relationship of concrete presented in Shen et al. (1993) was adopted, and should be determined in accordance with the following equations: Fig. 3.10 Concrete stress (σ )–strain (ε) relationship considering shrinkage and creep σ o —Peak stress of concrete without long-term loading; σ (t 0 )—Concrete stress at t 0 ; ε(t 0 )—Total strain of concrete at t 0 ; φ(t, t0 )—Creep coefficient of concrete under long-term loading

86

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

 y=

1.2x − 0.2x 6 (x ≤ 1) x (x > 1) 0.31σ 2 (x−1)1.7 +x

(3.6.1.25)

p

x=

ε εp

(3.6.1.26)

y=

σ σp

(3.6.1.27)

σp = 0.26(1.25 f c' )2/3

(3.6.1.28)

εp = 43.1σp

(3.6.1.29)

where, σ p peak tensile stress (N/mm2 ); εp strain corresponding to peak tensile stress (με); f c' cylinder strength of concrete (N/mm2 ), shall be determined in accordance with Table 1.1. (2) Cyclic loading The stress (σ )–strain (ε) relationship of concrete under cyclic loading presented in Han (2016) is shown in Fig. 3.11, and the unloading and reloading paths should be calculated in accordance with the following equations: 1) For compressive unloading and reloading, the following equations should be applied: εB =

σo εA − σA ε1 σo + σA

ε1 = 0.5εo σC =

(3.6.1.30) (3.6.1.31)

0.75σo (εA − εB ) 0.75ε1 + εB

(3.6.1.32)

D1 εA − D2 εB − σC D1 − D2

(3.6.1.33)

εD =

σD = D2 (εD − εB ) D1 = D2 =

(3.6.1.34)

3σo + σC 3ε1 + εA

(3.6.1.35)

0.2σo 0.2ε1 + εB

(3.6.1.36)

3.6 Constitutive Models of Concrete

87

Fig. 3.11 Stress (σ )–strain (ε) hysteretic relationship of concrete

where, εB σC εD σD

residual strain when stress is unloaded to zero (με); stress at point C during reloading (N/mm2 ); strain at point D during unloading (με); stress at point D during unloading (N/mm2 ).

2) For tensile unloading and reloading, the following equations should be applied:   0.9εo (3.6.1.37) εH = εG 0.1 + εo + |εG |   |εH |/εo − 4 (3.6.1.38) σcon = 0.3σW 2 + |εH |/εo + 2 σw = σo εh ≤ εo loading and unloading through G - I - J σw = σA εh > εo loading and unloading through G - I' - C - E   2ε σ = σcon 1 − (εH ≤ ε < 0) εH + ε   σ = σcon 1 −  σ = σcon 1 −

(3.6.1.39) (3.6.1.40)

ε 2ε εo  + εo +ε σo 0 ≤ ε < εo loading and unloading through G - I - J ε + 2ε σ 0 ≤ ε < ε loading and unloading through G - I' - C - E A εA εA +ε C

(3.6.1.41) where,

88

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

εH strain at point H when effect of cracked surface begins (με); σ con stress at point I or I' when strain is zero during reloading (N/mm2 ); εh maximum compressive strain during the loading history (με). In the compressive unloading and reloading curves shown in Fig. 3.11, when compressive strain ε ≤ 0.55εo , the loading and unloading modulus is the elastic modulus; when ε > 0.55εo , the unloading and reloading paths are determined using the “focus point method”, where εo is the peak strain of the skeleton curve of concrete, and σ o is the corresponding stress. The stress values of the focus points F1 , F2 , F3 , and F4 are 0.2σ o , 0.75σ o , σ o , and 3σ o , respectively. For instance, if the unloading starts from point A on the skeleton curve, and continues through path A–D–B, where B is the intersect point between line AF3 and ε axis, C is the point on the extension line of BF2 where the strain equals to εA , D is the intersect point of CF4 and the extension line of BF1 , and the residual strain when unloading to σ = 0 is εB . If the unloading exceeds point B and reloading begins, the reloading curve will go through B–C–E, where E is the point on the skeleton curve where the strain is 1.15 εA . For the unloading exceeds point B and reloading reversely, when the maximum tensile strain during the loading history ε ≤ εp , i.e., the  tensile  concrete is not cracked, the stress and strain develop through BF, where F εp , σp is the point on the skeleton curve corresponding to the tensile stress; when the maximum tensile strain during the loading history ε > εp , the stress and strain develop through BG, where G(εG , σG ) is the point on the skeleton curve corresponding to the maximum tensile strain. In the tensile unloading and reloading paths, when the strain at the unloading point ε ≤ εp , the unloading modulus is taken as the elastic modulus and then the path goes to reverse reloading; when ε > εp , a curve function is used to describe the unloading and reloading paths. For instance, when the unloading begins at point G in the softening stage, considering the effect of cracked surface, the unloading first follows a straight line to point H, where H is the starting point of the effect of cracked surface. When the maximum compressive strain during the loading history εh ≤ εo the unloading and reloading go through G–I–J; when the maximum compressive strain during the loading history εh > εo , the unloading and reloading go through G–I' –C–E. If the unloading starts at any point on GI, the unloading path then is the straight line between the unloading point and point G. (3) At elevated temperature 1) The stress (σ )–strain (σ ) relationship of core concrete of circular CFST member at elevated temperature presented in Han et al. (2022) (as shown in Fig. 3.12) should be calculated in accordance with the following equations: y = 2x − x 2 x ≤ 1  y=

1 + q(x 0.1ξh − 1) ξ ≥ 1.12 x >1 x ξ < 1.12 β(x−1)2 +x

(3.6.1.42)

(3.6.1.43)

3.6 Constitutive Models of Concrete Fig. 3.12 Stress (σ )–strain (ε) relationship for concrete at elevated temperature

89

σ

T=20

T=300 T=500

T=600 T=900 O

ε (a) Core concrete

σ T=20 T=300 T=500 T=600

T=800 O

ε (b) Stirrup-confined concrete

σ

T=20 T=300 T=500

T=600 T=800 O (c) Unconfined concrete

ε

90

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

x=

ε εo (T )

(3.6.1.44)

y=

σ σo (T )

(3.6.1.45)



  σo (T ) = 1 + −0.054ξh2 + 0.4ξh ·



24 f c'

0.45  · 1−

T 1000

9.55 

· f c' (T ) (3.6.1.46)

f c'

f c' (T ) =

1 + 1.986 · (T − 20)3.21 × 10−9    ' fc − 1 · ξh0.2 εo (T ) = εcc (T) + 1400 + 800 · 24   −4 · 1.03 + 3.6 × 10 · T + 4.22 × 10−6 · T 2

(3.6.1.47)

(3.6.1.48)

    εcc (T ) = 1.03 + 3.6 × 10−4 · T + 4.22 × 10−6 · T 2 · 1300 + 12.5 · f c' (3.6.1.49) q=

ξh0.745 2 + ξh

  7 0.25+(ξh −0.5)

  β = 2.36 × 10−5

ξh =  f y (T ) =

(3.6.1.50)

· f c'2 · 3.51 × 10−4

As f y (T ) Ac f ck

fy 0.91 f y 1+6.0×10−17 (T −10)6

(3.6.1.51) (3.6.1.52)

T < 200 ◦ C T ≥ 200 ◦ C

(3.6.1.53)

where, σ o (T ) εo (T ) As Ac f ck f c'

peak stress of concrete at T (N/mm2 ); peak strain of concrete at T (με); cross-sectional area of the steel tube (mm2 ); cross-sectional area of the core concrete in the CFST member (mm2 ); characteristic value of compressive strength of concrete (N/mm2 ); cylinder strength of concrete (N/mm2 ), shall be determined in accordance with Table 1.1; f c' (T ) cylinder strength of concrete at T (N/mm2 ); fy yield strength of steel (N/mm2 ); f y (T ) yield strength of steel at T (N/mm2 ); T temperature (°C);

3.6 Constitutive Models of Concrete

ξh

91

confinement factor at T, shall be determined in accordance with Eq. (3.6.1.52).

2) The stress (σ )–strain (ε) relationship of stirrup-confined concrete of concreteencased CFST hybrid structures at elevated temperature presented in Han et al. (2022) should be determined in accordance with the following equations:  y=

1−

2x − x 2 ε ≤ εo (T ) − εo (T )) ε > εo (T )

E des (ε σo (T )

(3.6.1.54)

x=

ε εo (T )

(3.6.1.55)

y=

σ σo (T )

(3.6.1.56)

⎧ ' ◦ ◦ ⎨ fc  T −20  0 C◦< T < 450 C◦ ' ' f c (T ) = f c 2.011 − 2.353 1000 450 C ≤ T ≤ 874 C ⎩ 0 T > 874 ◦ C σo (T ) = f c' (T )(1 + 0.73 εo (T ) = 2450 + 12,200

ρv f yh (T ) ) f c' (T )

ρv f yh (T ) +6T + 0.04T 2 f c' (T )

ρv = E des =

Asvlv Av s

11.2 f c' (T )2 ρv f yh (T )

(3.6.1.57)

(3.6.1.58) (3.6.1.59) (3.6.1.60)

(3.6.1.61)

where, temperature (°C); T f c' (T ) cylinder strength of concrete at T (N/mm2 ); f yh (T ) yield strength of stirrup at T (N/mm2 ), shall be determined in accordance with Eq. (3.6.1.53); εo (T ) peak strain of concrete at T (με); σo (T ) peak stress of concrete at T (N/mm2 ); ρv volumetric stirrup ratio; Asv cross-sectional area of stirrups (mm2 ); lv length of stirrups (mm); cross-sectional area of stirrup-confined concrete (mm2 ). Av 3) The stress–strain relationship model for concrete at elevated temperature proposed by Lie and Denham (1993) was adopted for unconfined concrete outside

92

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

concrete-encased CFST hybrid structure (as shown in Fig. 3.12), and should be determined in accordance with the following equations:

σ =

 ⎧ 2   ⎪ εo (T )−ε ' ⎪ f (T ) 1 − εo (T ) ε ≤ εo (T ) ⎪ ⎪ ⎨ c  ⎪ 2   ⎪ ⎪ ε−εo (T ) ' ⎪ ⎩ f c (T ) 1 − 3εo (T ) ε > εo (T ) εo (T ) = 2500 + 6T + 0.04T 2

(3.6.1.62)

(3.6.1.63)

where, T εo (T ) f c'

temperature (°C); peak strain of concrete at T (με); cylinder strength of concrete (N/mm2 ), shall be determined in accordance with Table 1.1; f c' (T ) cylinder strength of concrete at T (N/mm2 ), shall be determined in accordance with Eq. (3.6.1.57).

(4) After elevated temperature 1) Stress (σ )–strain (ε) relationship of core concrete of circular CFST member after elevated temperature presented in Han et al. (2022): Considering the influence of elevated temperature, εo and σ o in the stress–strain relationship of core concrete at ambient temperature [Eqs. (3.44) and (3.45)] are modified: 2 εo (Tmax ) = εo [1 + (1500Tmax + 5Tmax ) × 10−6 ]

σo (Tmax ) =

σo 1 + 2.4(Tmax − 20)6 × 10−17

(3.6.1.64) (3.6.1.65)

where, T max σo σo (Tmax ) εo (T max )

maximum temperature (°C); peak stress of concrete at ambient temperature (N/mm2 ); peak stress of concrete after elevated temperature (N/mm2 ); peak strain of concrete after elevated temperature (με).

2) The stress (σ )–strain (ε) relationship of stirrup-confined concrete in concreteencased CFST hybrid structure after elevated temperature exposure presented in Han et al. (2022) shall be determined in accordance with the following equations:  y=

2x − x 2 ε ≤ εo (Tmax ) E des (T )] ε > εo (Tmax ) − ε 1 − σo (T [ε o max max ) x=

ε εo (Tmax )

(3.6.1.66) (3.6.1.67)

3.6 Constitutive Models of Concrete

93

y=

σ σo (Tmax )

σo (Tmax ) = f c' (Tmax )(1 + 0.73 εo (Tmax ) = 2450 + 12,200

(3.6.1.68) ρv f yh ) f c'

ρv f yh (Tmax ) 2 + 6Tmax + 0.04Tmax f c' (Tmax )

⎧ ' 0 ◦ C < Tmax ≤ 500 ◦ C ⎨ f c (1 − 0.001Tmax ) ' ' f c (Tmax ) = f c (1.375 − 0.00175Tmax ) 500 ◦ C < Tmax ≤ 700 ◦ C ⎩ 0 Tmax > 700 ◦ C ρv = E des =

Asvlv Av s

11.2 f c' (Tmax )2 ρv f yh

(3.6.1.69) (3.6.1.70)

(3.6.1.71)

(3.6.1.72)

(3.6.1.73)

where, T max f c'

maximum temperature (°C); cylinder strength of concrete (N/mm2 ), shall be determined in accordance with Table 1.1; f c' (Tmax ) cylinder strength of concrete after cooling from T max (N/mm2 ); f yh yield strength of stirrups (N/mm2 ); f yh (T max ) yield strength of stirrups after cooling from T max (N/mm2 ); εo (T max ) peak strain of concrete after cooling from T max (με); σ o (T max ) peak stress of concrete after cooling from T max (N/mm2 ); volumetric stirrup ratio; ρv Asv cross-sectional area of stirrups (mm2 ); length of stirrups (mm); lv Av cross-sectional area of stirrup-confined concrete (mm2 ). 3) The stress (σ )–strain (ε) relationships of unconfined concrete in concrete-encased CFST hybrid structures after elevated temperature was presented in Han et al. (2022), and should be determined in accordance with the following equations: ⎧   2  ⎪ εo (Tmax )−ε ' ⎪ ε ≤ εo (Tmax ) ⎨ f c (Tmax ) 1 − εo (Tmax )  (3.6.1.74) σ =  2  ⎪ o (Tmax ) ⎪ ε > εo (Tmax ) ⎩ f c' (Tmax ) 1 − ε−ε 3εo (Tmax ) 2 εo (Tmax ) = 2500 + 6Tmax + 0.04Tmax

where,

(3.6.1.75)

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3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

T max maximum temperature (°C); εo (T max ) peak strain of concrete after cooling from T max (με); f c' (Tmax ) cylinder strength of concrete after cooling from T max (N/mm2 ), shall be determined in accordance with Eq. (3.6.1.71); f c' cylinder strength of concrete (N/mm2 ), shall be determined in accordance with Table 1.1.

3.6.2 Finite Element Analysis-Based Models The finite element analysis software ABAQUS possesses nonlinear analysis function. As an example, this section introduces the determination method of concrete constitutive model needed to analyze the working mechanism of CFST members based on this software platform. There are three main factors of the constitutive model for concrete has: (1) yield surface, which defines the boundary of the loading and strengthening zone; (2) strengthening/softening law, which defines the change of loading surface and the change of material strengthening characteristics during plastic flow; (3) flow law, which is related to plastic potential function and defines the plastic stress–strain relationship in incremental form. Plastic damage models are widely used to simulate the mechanical properties of quasi-brittle materials such as concrete under compression, tension, bending, shear and cyclic loading. The yield surface was proposed by Lubliner et al. (1989), and Lee and Fenves (1998), which was presented in the ABAQUS documentation, and can be determined in accordance with the following equations: F=

   1 √ 3J2 + α I1 + β(σmax ) − γ (−σmax ) − σc ε˜ cpl 1−α σb0 σ

−1

σc0

−1

α= 2σc0b0 β=

(3.6.2.1)

(3.6.2.2)

σb0 (1 − α) − (1 + α) σc0

(3.6.2.3)

3(1 − K c ) 2K c − 1

(3.6.2.4)

γ = where, σ b0 σ c0 pl σc (˜εc ) Kc

peak stress under biaxial compression (N/mm2 ); peak stress under uniaxial compression (N/mm2 ); effective cohesive stress of concrete (N/mm2 ); the ratio of the second stress invariants on the tension and compression meridians, which is approximately a constant for concrete with a value of 2/3.

3.6 Constitutive Models of Concrete

95

(1) Monotonic load 1) Core concrete Based on the calculation and analysis of a large number of circular CFST specimens to axial compression, considering theinfluence of confinement  factor (ξ ) and the cylinder strength of concrete f c' , the stress (σ )–strain (ε) relationship of core concrete suitable for finite element analysis was presented in Han (2016), and should be calculated in accordance with the following equations:  y=

2x − x 2 (x ≤ 1) x (x > 1) βo (x−1)η +x

(3.6.2.5)

x=

ε εo

(3.6.2.6)

y=

σ σo

(3.6.2.7)

σ0 = f c'

(3.6.2.8)

εo = εc + 800ξ 0.2

(3.6.2.9)

εc = 1300 + 12.5 f c'

(3.6.2.10)

η=2

(3.6.2.11)

[0.25+(ξ −0.5)7 ]  ' 0.5  · fc β0 = 2.36 × 10−5 · 0.5 ≥ 0.12

(3.6.2.12)

where, σ stress (N/mm2 ); σ0 peak stress (N/mm2 ); ε strain (με); εo strain corresponding to peak stress (με); ξ confinement factor, shall be calculated by Eq. (1.3.1); f c' cylinder strength of concrete (N/mm2 ), shall be determined in accordance with Table 1.1. The characteristic of Eqs. (3.6.2.5)–(3.6.2.12) is that when x ≤ 1, before the core concrete reaches the peak stress (σ o ), the stress (σ )–strain (ε) is similar to the plain concrete in form. When x > 1, in the equations of the decreasing branch of the curve, the coefficient β 0 is a variable related to the confinement factor (ξ ), so the σ − ε relationship of the core concrete changes with ξ .

96

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

2) The uniaxial monotonic compressive stress (σ )–strain (ε) relationship of stirrup-confined concrete was presented in Han et al. (2017), and should be determined in accordance with the following equations:

σ =

⎧ ⎪ ⎨ σo ⎪ ⎩

k·

ε εo

k − 1 + ( εεo )k

ε ≤ εo

σo − E des (ε − εo ) ε > εo σo = f c'

(3.6.2.14)

εo = 2450 + 12,200 k=

where, σ σ0 ε εo εc,0.85 Av Asv Bc Ec f c'

Ec Ec −

Asv lv f yh Av s f c'

σo εo

0.15σo εc,0.85 − εo / Asv lv Bc + εo = 225,000 Av s s E des =

εc,0.85

(3.6.2.13)

(3.6.2.15) (3.6.2.16) (3.6.2.17)

(3.6.2.18)

stress (N/mm2 ); peak stress (N/mm2 ); strain (με); strain corresponding to peak stress (με); strain corresponding to stress decreased to 85% peak value (με); cross-sectional area of stirrup-confined concrete (mm2 ); cross-sectional area of stirrups (mm2 ); cross-sectional width of stirrup-confined concrete (mm2 ); modulus of elasticity of concrete (N/mm2 ); cylinder strength of concrete (N/mm2 ), shall be determined in accordance with Table 1.1; f yh yield strength of stirrups (N/mm2 ); lv total length of stirrups (mm); s spacing of stirrups (mm). 3) For unconfined concrete, the monotonic compressive stress (σ )–strain (ε) relationship is the same as that of the fiber-based models in Sect. 3.6.1. 4) Under the influence of the time-varying effect, the strain of concrete confined by steel tube and stirrups will increase and the equivalent stiffness will decrease, while the stiffness of steel tube and longitudinal reinforcement will remain basically unchanged, thus causing the load to transfer to the steel tube and longitudinal reinforcement. In this process, the stress of the

3.6 Constitutive Models of Concrete

97

confined concrete decreases and the strain increases, and the deformation of the whole component increases gradually. For confined concrete, this process is not only different from the creep process of plain concrete under constant load, but also different from the creep relaxation process under constant deformation. The effective modulus method of age-adjustment can comprehensively reflect the internal force redistribution process. The calculation methods of creep strain are shown in Eqs. (3.4.9) and (3.4.10). (2) Cyclic loading The stress–strain relationship of concrete under cyclic loading presented in the ABAQUS documentation is shown in Fig. 3.13. For cyclic loading, a damage index d can be introduced to reduce the elastic stiffness matrix of concrete, to reflect the degradation of elastic stiffness caused by concrete damage during tension and compression. The damage index d changed from 0 (no damage) to 1 (complete damage). (1 − d) represents the ratio of the effective bearing area (total damage reduction area) to total crosssectional area. In the case of no damage, d = 0 and the effective stress is equivalent to Cauchy stress. In this case, the skeleton curve of concrete is described in Sect. 3.6.2 (1); when damage occurs, only the effective stress area bears the external load. Under cyclic loading, when a concrete section is recompressed after a dilated crack, the fracture surface effect of aggregate occlusion will occur on the cracked surface, so that a considerable part of compressive stress can be transferred before the cracked surface is completely closed. Taking uniaxial cyclic loading as an example, Eqs. (3.6.2.19) to (3.6.2.24) are used to define

Fig. 3.13 Stress (σ )–strain (ε) relationship of concrete under cyclic loading

98

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

the total damage index under cyclic loading. ωt and ωc are the restoration coefficients of tensile and compression stiffness respectively, which are used to control the behavior of cracks before and after closure of crack, and they can vary from 0 to 1. When ωt = 0, it is considered that the ratio of tensile stiffness to compressive unloading stiffness is (1 − d t ) when the compressed concrete is unloaded and in tensioned again. When ωt = 1, it is considered that when the cracked concrete is compressed again, the compression stiffness fully recovers. The default values in this book are ωt = 0 and ωc = 1. σ = E d (ε − εpl )

(3.6.2.19)

E d = (1 − d)E 0

(3.6.2.20)

(1 − d) = (1 − sc dt )(1 − st dc )

(3.6.2.21)

st = 1 − ωtr ∗ (σ 11 )

(3.6.2.22)

sc = 1 − ωc (1 − r ∗ (σ 11 ))

(3.6.2.23)

∗

r (σ 11 ) =



1 σ 11 > 0 0 σ 11 < 0

(3.6.2.24)

where, εpl σ 11 E0 dc dt ωt ωc

plastic strain; uniaxial effective stress (N/mm2 ); initial (without considering damage) elastic stiffness matrix (N/mm2 ); damage index of concrete under compression; damage index of concrete under tension; coefficient of recovery of tensile stiffness, 0 ≤ ωt ≤ 1; coefficient of recovery of compressive stiffness, 0 ≤ ωc ≤ 1.

The loading and unloading criteria for concrete under cyclic loading adopt the “focus point method” model. When concrete is unloaded and then reverse loaded, its unloading and reloading paths approximately point to a certain “focus point” in space. As shown in Fig. 3.14a, when concrete is unloaded under compression and then reverse loaded, all the loading and unloading paths are approximately pointing to space R((n c σc0 )/E c , n c σc0 ), where nc is the damage index coefficient of concrete under compression, σc0 is the peak stress of concrete in compression, and E c is the initial modulus of elasticity of concrete. As shown in Fig. 3.14b, when concrete is unloaded by tension and then reverse loaded, when the concrete strain (εt ) is greater than the strain corresponding to the peak tensile stress of concrete (εt0 ), it is unloaded and reloaded

3.6 Constitutive Models of Concrete

99

Fig. 3.14 Stiffness degradation of concrete during loading and unloading

according to the initial elastic stiffness. When εt is less than εt0 , the loading and unloading paths approximately point to the space Z((n t σt0 )/E c , n t σt0 ), where nt is the tensile damage index coefficient of concrete, σt0 is the peak stress of concrete in tension and E c is the initial modulus of elasticity of concrete. According to the above loading and unloading criteria, the damage indexes of concrete in compression and tension under uniaxial stress are determined as follows: dc = 1 −

(σc + n c σc0 ) ≥0 E c (n c σc0 /E c + εc )

(3.6.2.25)

dt = 1 −

(σt + n t σt0 ) ≥0 E c (n t σt0 /E c + εt )

(3.6.2.26)

where, dc dt σc σt σc0 σt0 εc εt εc0 εt0 nc

damage index of concrete in compression; damage index of concrete in tension; stress of concrete in compression (N/mm2 ); stress of concrete in tension (N/mm2 ); peak stress of concrete in compression (N/mm2 ); peak stress of concrete in tension (N/mm2 ); strain of concrete in compression; strain of concrete in tension; strain corresponding to peak stress of concrete in compression; strain corresponding to peak stress of concrete in tension; damage index coefficient of concrete in compression, for core concrete, nc = 2 and for unconfined concrete, nc = 1;

100

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

nt

damage index coefficient of concrete in tension, for core concrete, nt = 1 and for unconfined concrete, nt = 1.

(3) At elevated temperature 1) The stress (σ )–strain (ε) relationship of core concrete of circular CFST member at elevated temperature was presented in Han et al. (2022), and should be determined in accordance with the following equations:  y=

2x − x 2 x ≤ 1 x x >1 βo (x−1)2 +x

(3.6.2.27)

x=

ε εo (T )

(3.6.2.28)

y=

σ σo (T )

(3.6.2.29)

εo (T ) = (εcc + 800ξh0.2 ) · (1.03 + 3.6 × 10−4 T + 4.22 × 10−6 T 2 ) (3.6.2.30)

f c' (T ) =

σo (T ) = f c' (T )

(3.6.2.31)

εcc = 1300 + 12.5 f c'

(3.6.2.32)

f c'

(3.6.2.33)

1 + 1.986 × 10−9 × (T − 20)3.21

βo = (2.36 × 10−5 )[0.25+(ξh −0.5) ] ( f c' )0.5 × 0.5 ≥ 0.12 7

where, σ ε T σ o (T ) εo (T ) ξh

(3.6.2.34)

stress (N/mm2 ); strain (με); current temperature (°C); peak stress of concrete at T (N/mm2 ); peak strain of concrete at T (με); confinement factor at T, shall be calculated in accordance with Eq. (3.6.1.52); f c' cylinder strength of concrete at ambient temperature (N/mm2 ), shall be determined in accordance with Table 1.1; fy yield strength for steel of steel tube (N/mm2 ); f c' (T ) cylinder strength of concrete at T (N/mm2 ); f y (T ) yield strength for steel of steel tube at T (N/mm2 ), shall be calculated in accordance with Eq. (3.6.1.53).

3.6 Constitutive Models of Concrete

101

2) The stress (σ )–strain (ε) relationship of stirrup-confined concrete in concrete-encased CFST hybrid structure at elevated temperature was presented in Han et al. (2022), and should be determined in accordance with the following equations:  σ =

k(T )

ε

σo (T ) k(T )−1+(εo (Tε )

ε ≤ εo (T )

k(T ) εo (T ) )

σo (T ) − E des (T )(ε − εo (T )) ε > εo (T ) σo (T ) = f c' (T )

f c' (T )

=

⎧ ⎨ ⎩

f c'

(3.6.2.36)

◦ f c' < T < 450 ◦ C

 T −20  0 C ◦ 2.011 − 2.353 1000 450 C ≤ T ≤ 874 ◦ C (3.6.2.37) 0 T > 874 ◦ C

k(T ) = εo (T ) = 2450 + 12,200

E c (T ) E c (T ) −

εc,0.85 = 225,000

σo (T ) εo (T )

Asv · lv · f yh (T ) + 6T + 0.04T 2 Av · s · f c' (T )

E des (T ) =

where, σ ε σ o (T ) εo (T ) Asv Av Bc E c (T )

(3.6.2.35)

Asv · lv Av · s

/

0.15σo (T ) εc,0.85 − εo (T )

Bc + εo (T ) + 6T + 0.04T 2 s

(3.6.2.38)

(3.6.2.39) (3.6.2.40)

(3.6.2.41)

stress (N/mm2 ); strain (με); peak stress of concrete at T (N/mm2 ); peak strain of concrete at T (με); cross-sectional area of stirrups (mm2 ); cross-sectional area of stirrup-confined concrete (mm2 ); cross-sectional width of stirrup-confined concrete (mm2 ); modulus of elasticity of concrete at T (N/mm2 ), which shall be determined in accordance with ACI 318 at ambient temperature and with ACI 216.1 during heating stage; f c' cylinder strength of concrete at ambient temperature (N/mm2 ), shall be determined in accordance with Table 1.1; f c' (T ) cylinder strength of concrete at T (N/mm2 ), shall be calculated in accordance with Eq. (3.6.1.57); f yh (T ) yield strength of stirrups at T (N/mm2 ), shall be calculated in accordance with Eq. (3.6.1.57); lv total length of stirrups (mm);

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3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

s spacing of stirrups (mm); T temperature (°C). 3) The constitutive model for unconfined concrete at elevated temperature based on the finite element method is the same as the corresponding constitutive model based on fiber-based models (Sect. 3.6.1). (4) After elevated temperature 1) The stress (σ )–strain (ε) relationship of core concrete of circular CFST member after elevated temperature was presented in Han et al. (2022), and should be determined in accordance with the following equations:  y=

2x − x 2 (x ≤ 1) x (x > 1) β (x−1)2 +x

(3.6.2.42)

o

x=

ε εo (Tmax )

(3.6.2.43)

y=

σ σo (Tmax )

(3.6.2.44)

σo (Tmax ) = f c' (Tmax )

(3.6.2.45)

εo (Tmax ) = εcc2 + 800ξ 0.2

(3.6.2.46)

     εcc2 = 1300 + 12.5 f c' · 1 + 1500Tmax + 5T 2max × 10−6 (3.6.2.47) f c' (Tmax ) =

f c' 1 + 2.4(Tmax − 20)6 × 10−17

βo = (2.36 × 10−5 )[0.25+(ξh −0.5) ] ( f c' )0.5 · 0.5 ≥ 0.12 7

(3.6.2.48) (3.6.2.49)

where, σ o (T max ) peak stress of concrete after cooling form T max (N/mm2 ); εo (T max ) peak strain of concrete after cooling form T max (με); ξ confinement factor at ambient temperature, shall be calculated in accordance with Eq. (1.3.1); f c' cylinder strength of concrete at ambient temperature (N/mm2 ), shall be determined in accordance with Table 1.1; f c' (T max ) cylinder strength of concrete after cooling form T max (N/mm2 ); T max maximum temperature (°C). 2) The stress (σ )–strain (ε) relationship of stirrup-confined concrete in concrete-encased CFST hybrid structure after elevated temperature was presented in Han et al. (2022), and should be determined in accordance with the following equations:

3.6 Constitutive Models of Concrete

 σ =

103

σo (Tmax ) k(T

k(Tmax )· εo (Tεmax )

k(Tmax ) ε max )−1+( εo (Tmax ) )

ε ≤ εo (Tmax )

σo (Tmax ) − E des · (ε − εo (Tmax )) ε > εo (Tmax ) σo (Tmax ) = f c' (Tmax )

εo (Tmax ) = 2450 + 12,200

E c (Tmax ) E c (Tmax ) −

E des (Tmax ) =

where, σ o (T max ) εo εo (T max ) T max Acc Ah Bc f c' (T max )

Ah · lh Acc · s

/

(3.6.2.51)

Ah · lh · f yh (Tmax ) 2 + 6Tmax + 0.04Tmax Acc · s · f c' (Tmax ) (3.6.2.52)

k(Tmax ) =

εc,0.85 = 225,000

(3.6.2.50)

σo (Tmax ) εo (Tmax )

0.15σo (Tmax ) εc,0.85 − εo (Tmax )

(3.6.2.53)

(3.6.2.54)

Bc 2 + εo (Tmax ) + 6Tmax + 0.04Tmax (3.6.2.55) s

peak stress of concrete after cooling from T max (N/mm2 ); peak strain of concrete at ambient temperature (με); peak strain of concrete after cooling from T max (με); maximum temperature (°C); cross-sectional area of stirrup-confined concrete (mm2 ); cross-sectional area of stirrups (mm2 ); cross-sectional height of stirrup-confined concrete (mm2 ); cylinder strength of concrete after cooling from T max (N/mm2 ), shall be determined in accordance with Eq. (3.6.1.71); E c (T max ) modulus of elasticity of concrete after cooling from T max (N/ mm2 ); lh total length of stirrups (mm); s spacing of stirrups (mm). 3) The constitutive model for unconfined concrete after elevated temperature based on the finite element analysis-based method is the same as that based on fiber-based models (Sect. 3.6.1).

104

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

3.7 Interface Models Between Steel and Concrete 3.7.1 Steel Tube-Core Concrete The interface behavior of the interface between steel tube and concrete is related to the shrinkage of core concrete and the stress state of the CFST member. The shrinkage of the core concrete will make it “stripping” from the steel tube, while the core concrete will produce “expansion” deformation in compression, to “compensate” the “stripping” deformation due to the above shrinkage. When the “expansion” deformation is larger than the “stripping” deformation, the steel tube and the core concrete can be complementary to each other and act together, which means core concrete is confined by the steel tube and in a triaxial compression state, and its longitudinal cracking is effectively delayed. The mechanical performance of the interface between the steel tube and core concrete depends on the bond behavior between the steel tube and concrete, and also on the friction between the core concrete and the steel tube wall during the loading of CFST member, and this friction will be enhanced with the increase of the interaction between the steel tube and its concrete. Figure 3.15 shows the composition of interfacial bond stress (τ ) between the steel tube and its core concrete. When the push-out load is small, relative slip does not occur between the steel tube and core concrete. The bond stress (τ ) mainly consists of chemical adhesion force (τ c ) and macro-interlocking force (τ m ), where τ c results from adhesion between the inner wall of the steel tube and the cement paste of the core concrete, and τ m is caused by the contact between the uneven part of the inner wall of the steel tube and the core concrete. The bond strength (τ u ) between steel tube and concrete is the average bond strength between steel tube and concrete in a certain length range. When the bond stress increases to the bond strength (τ u ), a relative slip occurs between the steel tube and the core concrete, and then τ is contributed by the friction resistance (τ f ) Push-out load N

Push-out load N

Push-out load N

Interface

Chemical adhesion force

Macro-interlocking force

Friction

σN

τc σN τm

τc

Steel tube

Core concrete

(a) Chemical adhesion force τc

τf

τf

τm

Slip plane

(b) Macro-interlocking force τm

(c) Friction τf

Fig. 3.15 Composition of bond stress (τ ) at the interface between steel tube and core concrete

3.7 Interface Models Between Steel and Concrete

105

between the steel tube and the core concrete. The value of τ f is mainly determined by the friction coefficient (μ) and the normal stress at the interface (σ N ), and μ is related to the roughness of the interface. σ N is the confined stress of the steel tube on the core concrete caused by the transverse expansion of concrete. After relative slip between steel tube and core concrete, on the one hand, shear stress of concrete in contact with the bulge in the inner wall of the steel tube is more than its shear strength, so shear failure occurs, cracks develop in the concrete near the slip surface and broken concrete fills the hollow of the steel tube, which reduce the concave and convex height difference at the surface of the steel tube and decreases μ continuously. On the other hand, σ N increases with the confinement force, and the magnitude of τ f fluctuates to some extent. When the concrete is pushed out along the slip surface, the friction coefficient of the interface tends to be stable, and τ f increases with the increase of σ N . (1) Coulomb friction model The contributions of interfacial adhesion force and friction force to interfacial shear stress transfer are different, so the influences of both forces should be considered in order to simulate the interface performance reasonably. The Coulomb friction model (as shown in Fig. 3.16) can be used to simulate the tangential force transfer of interface between the steel tube and the core concrete, which means the interface can transfer shear stress until the shear stress reaches the critical value τ crit and relative sliding occurs between interfaces. The equations allowing “elastic sliding” was adopted in the calculation, and the interface shear stress remained constant as τ crit during sliding. τ crit is proportional to the contact pressure of interface (p) and not less than the bond strength of interface (τ u ) (as shown in Fig. 3.17), namely: τcrit = μ · p ≥ τu

Fig. 3.16 Coulomb friction model

(3.7.1.1)

106

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

Fig. 3.17 Interfacial critical shear stress

where, τ crit critical shear stress of interface (N/mm2 ); μ friction coefficient of interface, general range of the value is between 0.2 and 0.6; p contact compressive stress of interface (N/mm2 ); τ u bond strength of interface (N/mm2 ). The main factors affecting the bond strength between the steel tube and its core concrete are: the cross-section type of members, the age and strength of concrete, the ratio of diameter-to-thickness of steel tube, the slenderness of members and the way of concrete placement. For actual engineering projects, after the completion of design procedure of CFST member, its geometric parameters (such as cross-sectional shape, ratio of diameter-to-thickness of the steel tube, slenderness, etc.) and physical parameters (such as concrete strength) tend to be certain, so the influence of the quality of concrete placement on the bond strength between steel tube and concrete is particularly important. The bond strength (τ u ) is linearly correlated with t/D2 . The bond strength of the interface for circular CFST members was proposed by Lyu et al. (2021), and should be calculated in accordance with Eq. (3.7.1.2). ⎧ ⎪ ⎨

  0.225    Dt 2 ≤ 0.000032 τu = t t ⎪ ⎩ 0.071 + 4900 D2 D2 > 0.000032 where, τ u bond strength between steel tube and concrete (N/mm2 ); D outer diameter of the circular CFST cross-section (mm); t wall thickness of the steel tube (mm).

(3.7.1.2)

3.7 Interface Models Between Steel and Concrete

107

(2) Simplified model of average bond stress-relative slip The experimental results show that the average bond stress-relative slip relationship curve between steel tube without special treatment on the surface and core concrete can be divided into ascending stage and smooth branch, and the shape of ascending stage is similar to the bond stress-relative slip relationship curve between reinforcement and concrete. The bond stress-relative slip model between reinforcement and concrete was presented in FIB MC 2010. The simplified model of the average bond stress (τ )–relative slip (s) relationship for the interface without special treatment between the steel tube and its core concrete is shown in Fig. 3.18, and the mathematical expression is shown in Eq. (3.7.1.3). τ=

  η τu ss0 (0 ≤ s ≤ s0 ) τu

(3.7.1.3)

(s > s0 )

  D τu = k 3.56 × 10−3 f cu + 0.4 f (λ) f ( ) t

(3.7.1.4)

f (β) = 1.28 − 0.28β

(3.7.1.5)

f (λ) = 1.36 − 0.09 ln(λ)

(3.7.1.6)

 f

D t



 = 1.35 − 0.09 ln

D t



where, τ τu

average bond stress between steel tube and concrete (N/mm2 ); bond strength between steel tube and concrete (N/mm2 );

Fig. 3.18 The average bond stress (τ )–relative slip (s) relationship between steel tube and core concrete

(3.7.1.7)

108

k η D t s λ f cu

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

coefficient, when the core concrete is normal concrete, k = 1.0; when the core concrete is self-compacting high-performance concrete, k = 1.5; coefficient, can be taken as 0.6; outer diameter of circular CFST cross-section (mm); wall thickness of steel tube (mm); relative slip between steel tube and concrete (mm); slenderness, λ = 4L/d for circular CFST member, where L is the calculated length of the specimen; characteristic value of cube strength of concrete (N/mm2 ).

The load-relative slip curve calculated by Eq. (3.7.1.3) is in good agreement with the test results, and the calculated results are generally safe. Under (after) elevated temperature, the bond of the interface between steel and concrete will be affected by the action of elevated temperature, thus showing different properties from that at room temperature. For the steel-core concrete interface, the influence of elevated temperature mainly shows on the average bond strength and the corresponding ultimate slip in the average bond stress (τ )–relative slip (s) model. The test results show that, with the increase of temperature, the bond strength (τ uT ) of the interface between steel and concrete decreases at (after) elevated temperature, while the corresponding ultimate slip (suT ) increases. Based on the average bond stress (τ )–relative slip (s) relationship model of the interface between steel tube and core concrete at room temperature, the bond strength between steel tube and concrete encasement at (after) elevated temperature given by Table 3.3 and change coefficient for ultimate slip (k τT and k ST ) are used to consider the influence of elevated temperature. By replacing τ u and s0 in Eq. (3.7.1.3) with kτ T · τu and kST · s0 , the average bond stress (τ )–relative slip (s) relationship model of the interface between steel tube and its core concrete at and after elevated temperature can be obtained. Table 3.3 Value of coefficients k τT and k ST Interface temperature

0 ≤ T ≤ 100°C

100°C < T ≤ 400°C

400°C < T ≤ 600°C

At elevated temperature

kτ T

1 + 1.22 × 10−3 T

1.205 − 0.83 × 10−3 T

2.619 − 4.365 × 10−3 T

k ST

1 − 0.606 × 10−3 T

0.656 + 1.017 × 10−3 T

− 7.641 + 21.76 × 10−3 T

kτ T

1 + 0.49 × 10−3 T

1.326 − 2.767 × 10−3 T

0.657 − 1.095 × 10−3 T

k ST

1 − 3.49 × 10−3 T

0.239 + 4.12 × 10−3 T

1.887

After elevated temperature

3.7 Interface Models Between Steel and Concrete

109

3.7.2 Steel Tube-Concrete Encasement Reasonable determination of the bond strength of the interface between CFST and concrete encasement is an important basis for structural analysis and calculation of concrete-encased CFST hybrid structure during loading. Based on the push-out test with the same concrete strength ( f cu = 72 N/mm2 ), the bond stress (τ )–slip (s) relationship was obtained (as shown in Fig. 3.19). The test results show that the bond strength between steel tubes and concrete encasement of concrete-encased CFST hybrid structure is 2.96–4.44 N/mm2 , which is generally equivalent to the bond stress between steel tubes and core concrete. The bond strength of inner CFST and the outer reinforced concrete encasement can be calculated in accordance with Eq. (3.7.1.2). The bond stress (τ )–slip (s) relationship at and after elevated temperature was presented in Han et al. (2022), and may be calculated in accordance with Eq. (3.7.2.1). / ⎧ s τoT 4 soT ⎪ ⎪ ⎪ ⎨ 2 2T s + k3T s τ = k1T + k(s−s uT )(τuT −τcrT ) ⎪ τuT − ⎪ ⎪ (scrT −suT ) ⎩ τcrT

(0 ≤ s ≤ soT ) (soT < s ≤ suT ) (suT < s ≤ scrT ) (s > scrT )

(3.7.2.1)

soT = 0.00018tkST

(3.7.2.2)

suT = 0.0525tkST

(3.7.2.3)

scrT = 0.625tkST

(3.7.2.4)

2 k1T = τuT − k2T suT − k3T suT

(3.7.2.5)

Fig. 3.19 Comparison of bond stress (τ )–slip (s) relationship

110

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

2suT (τuT − τoT ) (suT − soT )2

(3.7.2.6)

(τuT − τoT ) (suT − soT )2

(3.7.2.7)

τoT = 0.252 f t kτ T

(3.7.2.8)

  0.096c τuT = 0.378 + + 10ρsv f t kτ T t

(3.7.2.9)

τcrT = 0.171 f t kτ T

(3.7.2.10)

f t = 0.23 f cu2/3

(3.7.2.11)

k2T =

k3T =

where, τ s t c ρ sv f cu k τT k ST

bond stress between the concrete encasement and the steel tube (N/mm2 ); the relative slip between concrete encasement and steel tube (mm); wall thickness of steel tube (mm); thickness of reinforced concrete protective layer (mm), c; superficial stirrup ratio, ρsv ≤ 0.01727; cube strength of concrete (N/mm2 ); the change coefficient of bond strength at (after) elevated temperature, shall be determined in accordance with Table 3.3. the change coefficient of ultimate value of slip at (after) elevated temperature, shall be determined in accordance with Table 3.3.

Taking c = 30 mm, f cu = 60 N/mm2 , ρ sv = 0.13% as an example, Fig. 3.20 shows the τ − s relationship curve between steel tube and concrete encasement at and after elevated temperature.

3.7.3 Reinforcement-Concrete Interface bond problems also exist between longitudinal reinforcement and concrete encasement in concrete-encased CFST hybrid structures, and the variation pattern of bond strength can be referred to reinforced concrete structures. There are many factors that affect the bond performance, such as the strength and gradation of concrete, the diameter of the anchor bar, strength, deformation index, shape parameter, stirrup configuration, lateral pressure, and so on. According to the current national standard GB 50010 Code for Design of Concrete Structures, the bond stress-slip constitutive relationship between concrete and hot

3.7 Interface Models Between Steel and Concrete

111

Fig. 3.20 Bond stress (τ )–relative slip (s) relationship between steel tube and concrete encasement at and after elevated temperature Fig. 3.21 Bond stress (τ )–relative slip (s) relationship between reinforcement and concrete

rolled ribbed steel bar is shown in Fig. 3.21, and the key parameters are determined in accordance with Eqs. (3.7.3.1)–(3.7.3.5). (1) Linear branch: τ = k1 s

0 ≤ s ≤ scr

(3.7.3.1)

(2) Splitting branch: τ =τcr + k2 (s − scr )

scr < s ≤ su

(3.7.3.2)

su < s ≤ sr

(3.7.3.3)

(3) Descending branch: τ =τu + k3 (s − su ) (4) Residual branch: τ =τr s > sr

(3.7.3.4)

112

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

(5) Unloading branch: τ = τun +k1 (s − sun )

(3.7.3.5)

where, τ s k1 k2 k3 τ un sun

bond stress between concrete and hot rolled steel bar (N/mm2 ); relative slip between concrete and hot rolled steel bar (mm); slope of linear stage (N/mm3 ); slope of splitting stage (N/mm3 ); slope of descending stage (N/mm3 ); bond stress at unloading point (N/mm2 ); relative slip at unloading point (mm).

The bond stress (τ )–slip (s) relationship between concrete and hot rolled steel bar should be determined in accordance with the following equations: ⎧ / s ⎪ τsT 4 sST ⎪ ⎪ ⎪ √ ⎪ ⎪ ⎨ k1T + k2T 4 s τ = k3T + k4T s − k5T s 2 ⎪ ⎪ (s−suT )(τuT −τrT ) ⎪ ⎪ ⎪ τuT − (srT −suT ) ⎪ ⎩ τrT

(0 ≤ s ≤ sST ) (sST < s ≤ scrT ) (scrT < s ≤ suT ) (suT < s ≤ srT ) (s > srT )

(3.7.3.6)

sST = 0.0008dkST

(3.7.3.7)

scrT = 0.0240dkST

(3.7.3.8)

suT = 0.0368dkST

(3.7.3.9)

srT = 0.540dkST

(3.7.3.10)

√ k1T = τcrT − k2T 4 scrT

(3.7.3.11)

τcrT − τsT k2T = √ √ 4 scrT − 4 ssT

(3.7.3.12)

2 k3T = τuT − k4T suT + k5T suT

(3.7.3.13)

k4T =

2suT (τuT − τcrt ) (suT − scrt )2

(3.7.3.14)

(τuT − τcrT ) (suT − scrT )2

(3.7.3.15)

k5T =

3.7 Interface Models Between Steel and Concrete

113

τsT = 1.01 f ts kτ T

(3.7.3.16)

/   c f ts kτ T τcrT = 1.01 + 1.54 d /   c (1 + 8.5ρsv ) f ts kτ T τuT = 1.01 + 1.54 d /   c (1 + 8.5ρsv ) f ts kτ T τrT = 0.29 + 0.43 d

(3.7.3.17)

(3.7.3.18)

(3.7.3.19)

f ts = 0.19 f cu3/4

(3.7.3.20)

where, τ s f ts d c f cu ρ sv k τT k ST

bond stress between concrete and hot rolled ribbed steel bar (N/mm2 ); the relative slip between the concrete and hot rolled steel bar (mm); splitting strength of concrete (N/mm2 ); diameter of the screwed reinforcement (mm); thickness of reinforced concrete protective layer (mm); cube strength of concrete (N/mm2 ); superficial stirrup ratio; change coefficient of bond strength at (after) elevated temperature, shall be determined in accordance with Table 3.4; change coefficient of ultimate slip at (after) elevated temperature, shall be determined in accordance with Table 3.4.

Taking d = 20 mm, c = 30 mm, f cu = 60 N/mm2 , ρ sv = 0.13% as an example, Fig. 3.22 shows the τ − s relationship between reinforcement and concrete at and after elevated temperature. Table 3.4 Value of coefficients k τT and k ST Coefficient At elevated temperature

After elevated temperature

0 ≤ T ≤ 400 °C 400 °C < T ≤ 700 °C 0 ≤ T ≤ 400 °C 400 °C < T ≤ 700 °C k τT

1 + 0.283 × 10−3 T

1.925 − 2.03 × 10−3 T

1 − 0.535 × 10−3 T

1.581 − 1.987 × 10−3 T

k ST

1 + 3.376 × 10−3 T

− 1.205 + 8.887 × 10−3 T

1 + 7.325 × 10−3 T

− 3.11 + 17.56 × 10−3 T

114

3 Analysis of Concrete-Filled Steel Tubular (CFST) Structures

Fig. 3.22 The bond stress (τ )–relative slip (s) relationship between reinforcement and concrete at and after elevated temperature

Exercises 1. Compare the shrinkage and creep of core concrete between CFST and ordinary concrete. 2. Briefly describe the principles of determining constitutive models for core concrete of CFST structures. 3. Briefly describe the basic principles and calculation process of fiber-based models for CFST structures. 4. Briefly describe the methods of determining the interface models between various materials of CFST structures.

Chapter 4

Design of Concrete-Filled Steel Tubular (CFST) Members

Key Points and Learning Objectives Key Points This chapter discusses the calculation methods of resistances of CFST members under single load, complex load, long-term load, and cyclic load, and the concept and determination methods of resistances of the vertical and lateral local bearing, size effect, limiting value of initial stress in the steel tube, and the limiting value of core concrete void. Learning Objectives Master the working principle of CFST members and the calculation method of the resistance of CFST members under a single load. Be familiar with the calculation methods of the resistances of CFST members under complex load, long-term load and cyclic load, and the concepts and determination methods of size effects, limiting value of initial stress in the steel tube, limiting value of core concrete void. Understand the full-range mechanical performance of CFST members under single load, complex load, long-term load, cyclic load, and vertical and lateral local bearing.

4.1 Introduction Resistance of a CFST member is the maximum internal force that the member can withstand, or the internal force when it reaches the deformation that is not suitable for further loading. To clarify the life-cycle-based mechanical performance and calculation method of resistance of CFST members is the basis of the reasonable design of such structures. The study shows that the mechanical performance of CFST members vary with the type of loads (short-term load, long-term load, cyclic load, local bearing, etc.), loading path, size effect, construction process and initial structural imperfection. In this chapter, the working principle and calculation methods for resistances © China Architecture & Building Press 2024 L. Han, Theory of Concrete-Filled Steel Tubular Structures, https://doi.org/10.1007/978-981-99-2170-6_4

115

116

4 Design of Concrete-Filled Steel Tubular (CFST) Members

of CFST members under single load, complex load, long-term load, cyclic load, and local bearing are described, and the basic concepts and determination principles of the effects of size effects, the limiting value of initial stress in the steel tube, and limiting value of core concrete void are discussed.

4.2 Design of Members Under Single Loading Conditions 4.2.1 Resistance in Axial Compression and Tension Resistance in axial compression (tension) of the CFST member refers to the maximum axial compression (axial tension) force that the CFST member can resist, or the axial compression (axial tension) force when it reaches a deformation that is not suitable for further loading. (1) Resistance of cross-section to axial compression For CFST stub members to axial compression, Fig. 4.1 shows a typical σ sc − ε relationship, where σ sc is the nominal compressive stress of CFST member (= N/ Asc , where N is the axial compression force; Asc = As + Ac , Asc is the cross-sectional area of CFST member; As and Ac are the cross-sectional areas of the steel tube and the core concrete in the steel tube, respectively). The research shows that the basic shape of the σ sc − ε relationship curve for CFST members is closely related to the confinement factor (ξ ). When ξ > ξ o (ξ o is the limiting value of confinement factor), the curve has a hardening stage, and the larger ξ is, the greater the hardening of the curve; when ξ ≈ ξ o , the later stage of the curve basically tends to be flat; when ξ < ξ o , the curve enters into a descending stage after reaching a peak value, and with the decrease of ξ, the descending decreases, and the descending stage appears earlier. The ξ o is related to the cross-sectional shape of CFST member: for circular cross-section, ξ o ≈ 1.0; for square and rectangular cross-section, ξ o ≈ 4.5. The characteristics of the σ sc − ε relationship curve are as follows: 1) Elastic stage (OA): the steel tube and the core concrete are generally separately stressed, and point A is roughly the beginning of the elasto-plastic stage of the steel. 2) Elasto-plastic stage (AB): micro-cracks of core concrete are developing under the action of longitudinal compression, so that the coefficient of transverse deformation exceeds the steel Poisson’s ratio, which will induce interaction force between the steel tube and its core concrete, that is, the confinement effect of steel tube on the core concrete, and with the increase of longitudinal deformation, this confinement effect increases. At point B, the steel has entered the elastoplastic stage, the stress of which has reached yield strength, the longitudinal compressive stress of concrete can generally reach the peak stress. 3) Plastic hardening stage (BC): the distance between the end point C of the hardening stage and point B is related to ξ . With the decrease of the ξ, the point B

4.2 Design of Members Under Single Loading Conditions

σsc(=N/Asc)

ξ>ξo BC

fscy fscp

117

A

O εscp εscy

ξ=ξo ξ 1.2) 0.808bknL

(4.4.3)

a=

λ 100

(4.4.4)

4.5 Hysteretic Models of Concrete-Filled Steel Tubular (CFST) Members

b = ξ 0.05  knL =

(a ≤ 0.4) 1 − 0.07n L 0.98 − 0.07n L + 0.05a (a > 0.4) nL =

NL Nu

159

(4.4.5)

(4.4.6) (4.4.7)

where, N design value of axial compression (N); k cr long-term load coefficient, set as 1.0 when k cr is > 1.0; N u resistance of the CFST member in axial compression (N), shall be calculated by Eq. (4.2.1.9); k nl adjustment coefficient for long-term load ratio, taken as 1.0 when it is > 1.0; λ slenderness ratio of the member, shall be determined by Eq. (4.2.1.5); ξ confinement factor, shall be calculated by Eq. (1.3.1); nL long-term load ratio; N L long-term axial compression (N) in the CFST member, shall be determined with quasi-permanent combination of loads.

4.5 Hysteretic Models of Concrete-Filled Steel Tubular (CFST) Members The earthquake is an action that the CFST member may experience during its lifecycle service. Studying the hysteretic characteristic of the bending moment (M)curvature (φ) and the horizontal load (P)-horizontal displacement (Δ) of the CFST member and determining the restoring force model is one of the most important prerequisites for elasto-plastic seismic response analysis of CFST members. A necessary prerequisite for the full-range analysis of bending moment (M)curvature (Δ) and horizontal load (P)-horizontal displacement (Δ) relationship curves for the CFST member under cyclic loading is the determination of stress–strain models for steel and core concrete under cyclic loading, as described in Sects. 3.5 and 3.6 of this book. (1) Bending moment (M)-curvature (φ) behavior Figure 4.34 shows a typical bending moment (M)-curvature (φ) relationship curve for CFST members in combined compression and bending under constant axial loading, which can be generally divided into the following stages: (a) OA stage. At this stage, M − φ relationship curve is basically linear, a part of the cross-section is in the unloading state, and the concrete stiffness is large. Since the stress of concrete under loading is close to the compressive strength of concrete, the confinement effect has been generated. When the axial load

160

4 Design of Concrete-Filled Steel Tubular (CFST) Members

M

Fig. 4.34 Hysteretic relationship of M − φ of member in combined compression and bending

B A C

O E

(b)

(c)

(d)

(e)

(f)

F

D

ratio (n) is small, the steel tube is always in the elastic state. At point A, the outermost fiber in the compression zone of the steel tube begins to yield, and tensile stress begins to appear in the unloading zone. AB stage. The M − φ relationship is nonlinear, and the cross-section is in an elasto-plastic state. With the increase of the external bending moment, the yield area of the steel tube in the compression zone increases, and the stiffness decreases continuously. BC stage. Unloading from point B, the M − φ relationship is basically linear, and the unloading stiffness is generally the same as that of the OA stage. The part of the cross-section in the tension state due to unloading turns into the compression state, while the original loading part is in the compressive unloading state. The bending moment at point C is unloaded to zero, but there is stress on the steel tube and concrete of the whole cross-section due to the action of axial force. Due to the plastic deformation of both steel and concrete resulting in residual strain, there is a residual positive curvature on the cross-section at point C. CD stage. The cross-section starts to be backloaded, M − φ relationship is still basically linear, and the steel tube is in the elastic state. The outermost fiber of the steel tube in the compression zone at point D begins to yield, and the tensile stress begins to occur in the part cross-section of concrete. DE stage. The cross-section is in the elasto-plastic stage. With the increase of the yield area of the steel tube in the compression zone, the stiffness of the cross-section gradually decreases. EF stage. The working condition is similar to that of the BE stage with a small slope of M − φ. Although there are still new areas of the cross-section entering the plastic state at this time, it has little influence on the stiffness of the crosssection due to this part of the zone close to the centroid. Steel entering the hardening stage has a certain stiffness, and the concrete in the compression zone also has a certain stiffness due to the influence of the confinement effect, so the whole cross-section can still maintain a certain stiffness.

The characteristic of the skeleton curve of the M − φ relationship for CFST members in combined compression and bending is that there is no steep descending stage, the corner ductility is good, and its shape is similar to the performance of the steel member without local instability. This is because the concrete in the CFST

4.5 Hysteretic Models of Concrete-Filled Steel Tubular (CFST) Members

161

M

Fig. 4.35 The hysteretic model of bending moment (M)-curvature (φ)

3 A

Ms 5

B

D

My

1

4 Kp

1

C

Ke

2

1 O

y

2

5

A 1 C

4

3

B

D

member is restrained by the steel tube, and the failure of the member due to the premature crushing of the concrete will not occur during loading. In addition, the existence of concrete can avoid or delay the premature local buckling of steel tubes. The steel tubes and its core concrete are complementary to each other and have strong composite effects, so that the properties of steel and concrete can be fully developed. The M − φ relationship curve shows the characteristic of good stability, full curve pattern, no obvious stiffness degradation or pinching phenomenon, and good energy dissipation. The hysteretic model of M − φ for the circular CFST member was presented in Han (2016), and can be described by the trilinear model shown in Fig. 4.35, where five parameters need to be determined: elastic stiffness (K e ), yield bending moment (M y ), bending moment corresponding to point A (M s ), yield curvature (φ y ), and stiffness at the third stage (K p ). 1) Elastic stiffness (K e ) Elastic stiffness K e shall be approximately calculated in accordance with the following equation: K e = E s Is + 0.6E c Ic where, Ke Es ls Ec lc

elastic stiffness (N·mm2 ); modulus of elasticity of steel (N/mm2 ); second moment of area of the steel tube (mm4 ); modulus of elasticity of concrete (N/mm2 ); second moment of area of the core concrete (mm4 ).

(4.5.1)

162

4 Design of Concrete-Filled Steel Tubular (CFST) Members

M

Fig. 4.36 Determination method of yield bending moment (M y )

C'

B My Kp Ms

C

A Ke

O

y

2) Yield bending moment (M y ) The M − φ relationship of circular CFST member is characterized by: when the axial load ratio is relatively small, the curve has a hardening phenomenon, while in other cases, the descending stage may occur on the curve. M y is the bending moment at the peak point, as shown in Fig. 4.36, where the dashed line is the numerical calculation result. The yield bending moment of circular CFST members on the M − φ relationship is mainly related to the cross-sectional steel ratio (α s ), concrete strength ( f cu ) and axial load ratio (n). The equations are as follows: A1 · c + B1 · Mcu (A1 + B1 ) · ( p · n + q)  −0.137 (b ≤ 1) A1 = 0.118b − 0.255 (b > 1)  −0.468b2 + 0.8b + 0.874 (b ≤ 1) B1 = 1.306 − 0.1b (b > 1)  0.566 − 0.789b (b ≤ 1) p= −0.11b − 0.113 (b > 1)  1.195 − 0.34b (b ≤ 0.5) q= 1.025 (b > 0.5) My =

(4.5.2)

(4.5.3)

(4.5.4)

(4.5.5)

(4.5.6)

where, M cu bending resistance (N·mm), shall be determined in accordance with Eq. (4.2.2.6); b coefficient, taken as α s /0.1; c coefficient, taken as f cu /60, where f cu is cube strength of concrete (N/mm2 ).

4.5 Hysteretic Models of Concrete-Filled Steel Tubular (CFST) Members

163

3) Bending moment corresponding to point A (M s ) Equation for the bending moment corresponding to point A (M s ) is as follows: Ms = 0.6My

(4.5.7)

4) Curvature (φ y ) Curvature (φ y ) corresponding to yield bending moment (M y ) is mainly related to f cu and n, and the equation is as follows: φy = 0.0135(c + 1) · (1.51 − n)

(4.5.8)

where, φ y curvature corresponding to yield bending moment (My); c coefficient, taken as f cu /60, where f cu is cube strength of concrete (N/mm2 ); n axial load ratio, shall be calculated in accordance with Eq. (4.3.5.1). 5) Stiffness at the third stage (K p ) The calculation results show that stiffness at the third stage (K p ) of the bending moment–curvature relationship for circular CFST members is divided into two cases: greater than zero (positive stiffness) and less than zero (negative stiffness). The parameter study indicates that the confinement factor (ξ ), axial load ratio (n) and concrete strength ( f cu ) are the main parameters affecting K p . Through regression analysis of numerical results, the equation of K p is given as follows: K p = αdo · K e αdo =

αd 1000

(4.5.9) (4.5.10)

The coefficient αd shall be determined as follows: when confinement factor ξ > 1.1:  2.2ξ + 7.9 (n ≤ 0.4) αd = (4.5.11) (7.7ξ + 11.9) · n − 0.88ξ + 3.14 (n > 0.4) where, n axial load ratio, shall be calculated in accordance with Eq. (4.3.5.1); ξ confinement factor, shall be calculated in accordance with Eq. (1.3.1). When confinement factor ξ ≤ 1.1:  αd =

A · n + B (n ≤ n o ) C · n + D (n > n o )

(4.5.12)

164

4 Design of Concrete-Filled Steel Tubular (CFST) Members

n o = (0.245ξ + 0.203) · c−0.513

(4.5.13)

A = 12.8c · (ln ξ − 1) − 5.4 ln ξ − 11.5

(4.5.14)

B = c · (0.6 − 1.1 ln ξ ) − 0.7 ln ξ + 10.3

(4.5.15)

C = (68.5 ln ξ − 32.6) · ln c + 46.8ξ − 67.3

(4.5.16)

D = 7.8ξ −0.8078 · ln c − 10.2ξ + 20

(4.5.17)

where, c coefficient, taken as f cu /60, where f cu is cube strength of concrete (N/mm2 ); n axial load ratio, shall be calculated in accordance with Eq. (4.3.5.1); ξ confinement factor, shall be calculated in accordance with Eq. (1.3.1). 6. Softening stage of the Model For the bending moment–curvature hysteretic model of circular CFST member shown in Fig. 4.35, when unloaded from point 1 or 4, the unloading line will be unloaded according to elastic stiffness K e and backloaded to point 2 or 5. The ordinate load values of points 2 and 5 were taken as 0.2 times of that of points 1 and 4, respectively. When the reverse loading was continued, the model entered the softening stage 23' or 5D' , and points 3' and D' were on the extension of the OA line, whose ordinate values were the same as points 1(or 3) and 4(or D), respectively. Subsequently, the loading path was carried out along 3' 1' 2' 3 or D' 4' 5' D, and the softening segments 2' 3 and 5' D were determined in a similar way as 23' and 5D' , respectively. (2) Hysteretic performance of horizontal load (P)-horizontal displacement (Δ) Figure 4.37 shows the typical failure mode of hysteretic performance of the circular CFST member under horizontal load (P)-horizontal displacement (Δ). As shown in Fig. 4.37a, obvious inwards and outwards buckling occurs in the steel tube under cyclic loading. As shown in Fig. 4.37b, the failure mode of the CFST member is compression-bending failure, and outwards buckling deformation occurs at the upper and lower parts of the cross-section under cyclic loading. Figure 4.38 shows the measured P − Δ relationship of circular CFST specimens under different axial load ratios (n). When n is small, the skeleton curve of the hysteretic curve basically keeps horizontal during the late loading stage, and there is no obvious descending stage. When n is larger, an obvious descending stage appears, indicating that the ductility of the specimen tends to decrease with the increase of axial load ratio. The P − Δ relationship is relatively full with no obvious pinching phenomenon. The trilinear model presented in Han (2016) shown in Fig. 4.39 can be adopted as the P − Δ hysteretic model for CFST members, where point A is the end point of

4.5 Hysteretic Models of Concrete-Filled Steel Tubular (CFST) Members Fig. 4.37 Failure modes of hollow steel tube specimen and CFST specimen

165

Inwards local buckling

(a) Hollow steel tube specimen

Outwards local buckling

(b) CFST specimen

elastic stage of skeleton curve, whose horizontal load is 0.6Py ; point B is the peak point of skeleton curve, whose horizontal load is Py . The softening problem during reloading still needs to be considered in the model. The parameters for the model include: elastic stiffness (K a ), maximum horizontal load (Py ) and its corresponding displacement (Δp ), and stiffness in the third stage (K T ). 1) Elastic stiffness (K a ) Because axial load ratio (n) has little effect on the elastic stiffness of the member to combined compression and bending, the elastic stiffness can be determined according to the corresponding calculation method of stiffness of members to pure bending. The equation of elastic stiffness K a is as follows: Ka =

3K e L 31

(4.5.18)

where, K a elastic stiffness of member to combined compression and bending (N/mm); K e elastic stiffness of member to pure bending (N·mm2 ), should be calculated in accordance with Eq. (4.5.1); L 1 effective length, taken as L/2 (mm).

166

4 Design of Concrete-Filled Steel Tubular (CFST) Members

P (kN)

P (kN)

Δ (mm)

Δ (mm)

(a) n=0

(b) n=0.2

P (kN)

P (kN)

Δ (mm)

(c) n=0.4

Δ (mm)

(d) n=0.6

Fig. 4.38 Load (P)-deformation (Δ) hysteretic relationship of members in combined compression and bending

Fig. 4.39 Hysteretic model of horizontal load (P)-horizontal displacement (Δ)

4.5 Hysteretic Models of Concrete-Filled Steel Tubular (CFST) Members

167

2) Maximum horizontal load (Py ) and its corresponding displacement (Δp ) The value of Py is mainly related to the axial load ratio (n) and confinement factor (ξ ), where: 

 a=

1.05a · MLcu1 a · (0.2ξ + 0.85) ·

(1 < ξ ≤ 4) (0.2 ≤ ξ ≤ 1)

(4.5.19)

0.96 − 0.002ξ (0 ≤ n ≤ 0.3) (1.4 − 0.34ξ ) · n + 0.1ξ + 0.54 (0.3 < n < 1)

(4.5.20)

Py =

Mcu L1

where, M cu bending resistance of member (N·mm), shall be calculated in accordance with Eq. (4.2.2.6); n axial load ratio, shall be calculated in accordance with Eq. (4.3.5.1); ξ confinement factor, shall be calculated in accordance with Eq. (1.3.1). The displacement (Δp ) corresponding to the maximum horizontal load is mainly related to yield strength of steel ( f y ), slenderness ratio (λ) and axial load ratio (n). The specific equation is as follows: Δp =  f 1 (n) =

6.74[(ln r )2 − 1.08 ln r + 3.33] · f 1 (n) Py · (8.7 − s) Ka

1.336n 2 − 0.044n + 0.804 (0 ≤ n ≤ 0.5) 1.126 − 0.02n (0.5 < n < 1)

(4.5.21)

(4.5.22)

s=

fy 345

(4.5.23)

r=

λ 40

(4.5.24)

where, Δp displacement corresponding to maximum horizontal load (mm); Py maximum horizontal load (N), shall be calculated in accordance with Eq. (4.5.19); K a elastic stiffness (N/mm), shall be calculated in accordance with Eq. (4.5.18); f y yield strength of steel (N/mm2 ); n axial load ratio, shall be calculated in accordance with Eq. (4.3.5.1); λ slenderness ratio, shall be calculated in accordance with Eq. (4.2.1.5). 3) Stiffness of BC stage (K T ) Stiffness of BC stage K T shall be determined in accordance with the following equations:

168

4 Design of Concrete-Filled Steel Tubular (CFST) Members

KT =

0.03 f 2 (n) · f (r, αs ) · K a (c2 − 3.39c + 5.41) c=

 f 2 (n) =  f (r, αs ) =

f cu 60

3.043n − 0.21 (0 ≤ n ≤ 0.7) 0.5n + 1.57 (0.7 < n < 1)

(8αs − 8.6)r + 6αs + 0.9 (r ≤ 1) (15αs − 13.8)r + 6.1 − αs (r > 1)

(4.5.25) (4.5.26)

(4.5.27)

(4.5.28)

where, Ka f cu n r αs

elastic stiffness (N/mm), shall be calculated in accordance with Eq. (4.5.18); cube strength of concrete (N/mm2 ); axial load ratio, shall be calculated in accordance with Eq. (4.3.5.1); coefficient, shall be calculated in accordance with Eq. (4.5.24); cross-sectional steel ratio, shall be calculated in accordance with Eq. (1.3.2).

4) Softening stage of the model In the P − Δ hysteretic model shown in Fig. 4.39, when unloading from point 1 or 4, the unloading line will be unloaded according to the elastic stiffness K a , and the load will be reversed to 2 or 5 points, where the ordinate load value of 2 and 5 points is 0.2 times of the ordinate load value of 1 and 4 points, respectively. When continuing reversing loading, the model enters the softening part 23' or 5D' , and points 3' and D' are on the extension of the OA line, whose ordinate values are the same as points 1 (or 3) and 4 (or D), respectively. Subsequently, the loading path was carried out along 3' 1' 2' 3 or D' 4' 5' D, and the softening parts 2' 3 and 5' D were determined in a similar way as 23' and 5D' , respectively. 5) Displacement ductility factor (μ) The displacement ductility coefficient of the CFST member can be defined as: μ=

Δu Δy

(4.5.29)

where, μ displacement ductility factor; Δy yield displacement (mm); Δu ultimate displacement (mm). There is no obvious yield point in the P − Δ curve of CFST member. Yield displacement (Δy ) is taken as the displacement at the intersection of the elastic stage of the P − Δ skeleton curve and the tangent of the crossing peak point. The ultimate

4.5 Hysteretic Models of Concrete-Filled Steel Tubular (CFST) Members Fig. 4.40 Skeleton curve of P − Δ relationship

169

P B

Py 0.85Py

KT

A

1

C

Ka 1 O

Δp

Δy

Δu

Δ

displacement (Δu ) is taken as the corresponding displacement when the bearing capacity decreases to 85% of the resistance, as shown in Fig. 4.40. The equations of Δy and Δu are as follows: Δy =

Py Ka

Δu = Δp − 0.15

(4.5.30) Py KT

(4.5.31)

where, Δy Δp Δu Ka KT

yield displacement (mm); displacement corresponding to maximum horizontal load (mm); ultimate displacement (mm); elastic stiffness (N/mm), shall be calculated in accordance with Eq. (4.5.18); stiffness of BC stage (N/mm), shall be calculated in accordance with Eq. (4.5.25).

Displacement ductility coefficient (μ) of the CFST member is related to material strength, axial load ratio, slenderness ratio and cross-sectional steel ratio. With the increase of axial load ratio, slenderness ratio and cube strength of concrete, the displacement ductility coefficient gradually decreases. With the increase of crosssectional steel ratio, the displacement ductility coefficient increases. In the general range of parameters, the displacement ductility coefficients of CFST columns are generally > 3, and most of them are above 4.

170

4 Design of Concrete-Filled Steel Tubular (CFST) Members

4.6 Resistance of Members to Local Bearing 4.6.1 Vertical Local Bearing Local bearing is a common loading state in engineering structures, which is, the area of the force is less than the cross-sectional area or bottom area of the supporting member. For example, there are local bearing in the bearing structural support, the joint of the assembly column, the rigid frame, the hinge support of the grid or the arch structure, the anchorage area of the post-tensioned prestressed concrete member, and even the compression area of the section after the crack of the bending member. Figure 4.41 shows the diagram of local bearing of CFST member, where N is axial compression, AL is the area of local bearing, and Ac is the cross-sectional area of core concrete. The ratio of local bearing area is defined as: β=

Ac AL

(4.6.1.1)

where, β ratio of local bearing area; Ac cross-sectional area of core concrete (mm2 ); AL direct bearing area when under lateral local bearing (mm2 ). Under the action of local compressive load, the steel tube of CFST member can provide a certain confinement effect on core concrete, to improve the plasticity of core concrete and make the failure mode of CFST member different from that of plain concrete. For CFST members, a continuous process of subsidence occurs in the loaded plate. The concrete around the loading plate occurs shear failure, and the aggregates are crushed. The cracks in the core concrete fully develop, and the concrete around the end-loaded plate is broken and uplifted. However, the cracks development Fig. 4.41 Vertical local bearing

Ac

AL N

4.6 Resistance of Members to Local Bearing Fig. 4.42 N LC − Δ relationship under local bearing

171

NLC

or B C A

(

and

Or (

and

D D ) ) D

and

O

Δ

of plain concrete members are more concentrated, and the characteristics of brittle failure are obvious. Figure 4.42 shows the typical N LC − Δ relationship of CFST member to local bearing obtained by calculations, where N LC is the local bearing of CFST and Δ is the longitudinal deformation of the local bearing zone. In addition to the confinement factor (ξ ), the basic shape of the N LC − Δ relationship of CFST member is greatly related to the ratio of the local bearing area (β). As β increased, the magnitude of the descending stage of the curve decreased, and the descending stage occurred later or even did not occur. From the local bearing test of plain concrete and CFST specimens, it can be seen that when β > 9, the descending stage almost did not occur. The characteristics of the N LC − Δ relationship for local bearing are as follows: (1) Elastic stage (OA): The steel tube and core concrete are in the elastic stage. At this stage, the steel tube basically has no restraint on the core concrete. At point A, the steel reaches the proportional limit. (2) Elasto-plastic stage (AB): In this stage, the micro-cracks of the core concrete will gradually develop under the action of longitudinal pressure, the transverse deformation coefficient will increase, and the confinement effect of steel tube on the core concrete will gradually increase. The steel tube in the local bearing zone at point B usually enters the plastic stage, and the longitudinal compressive stress of concrete also reaches the peak value. (3) Plastic hardening stage (BC): The BC stage is mainly related to the confinement factor (ξ ), and the smaller ξ or β is, the closer B and C are. When ξ is larger or β is larger, the hardening stage of the curve can maintain the trend of continuous growth. (4) Descending stage (CD): The larger the β, the descending stage of the curve is smoother, or even no descending stage. In Fig. 4.42, the value of ξ o is related to the cross-sectional shape of CFST member: for circular cross-section, ξ o ≈ 1.

172

4 Design of Concrete-Filled Steel Tubular (CFST) Members

Reduction coefficient of resistance in local bearing (K LC ) is defined as the ratio of the resistance of CFST member in local bearing to the resistance of CFST in axial compression: K LC =

NuLC Nu

(4.6.1.2)

where, K LC reduction coefficient of resistance when under local bearing; N uLC resistance of CFST member to local bearing (N); Nu resistance of CFST in axial compression (N). (1) CFST member without end plate Figure 4.43 shows the development of concrete cracks near the local bearing plate. It can be seen that cracks of concrete distribute uniformly. As the ratio of the local bearing area decreases, the cracks of the concrete near the local bearing zone at the end become finer, which indicates that the composite effect is more fully developed. With the increase of the ratio of local bearing area, fewer and coarseer cracks develop, and the cracking phenomenon is more similar to that of plain concrete. However, according to the failure mode of specimens with a ratio of the local bearing area of 25 (as shown in Fig. 4.43), though the local bearing area is relatively small and far away from the steel tube, the splitting failure still does not occur like plain concrete, indicating that the confinement effect of steel tube on core concrete is still effective. The equations for the reduction coefficient of resistance of circular CFST without end-plate member to local bearing were proposed by Han (2016), and should be calculated as follows: K LC = A0 · β + B0 · β

0.5

+ C0

A0 = (−0.18ξ 3 + 1.95ξ 2 − 6.89ξ + 6.94) × 10−2

(a) β =1.4

(b) β 9

(c) β 16

(d) β 25

Fig. 4.43 Failure mode of the ends of specimens to local bearing

(4.6.1.3) (4.6.1.4)

(e) β 16 plain concrete

4.6 Resistance of Members to Local Bearing

173

B0 = (1.36ξ 3 − 13.92ξ 2 + 45.77ξ − 60.55) × 10−2

(4.6.1.5)

C0 = (−ξ 3 + 10ξ 2 − 33.2ξ + 150) × 10−2

(4.6.1.6)

where, A0 , B0 , C 0 coefficient, shall be determined in accordance with Table 4.3; ξ confinement factor, shall be calculated in accordance with Eq. (1.3.1); β ratio of local bearing area, shall be determined in accordance with Eq. (4.6.1.1). (2) CFST member with end plate The overall mechanical performance of the CFST member can be improved by setting the end plate with certain stiffness at the end of the CFST member. The influence of the end plate on the resistance of the CFST member to local bearing is mainly reflected in two aspects. First, the deformation of the end of the steel tube is constrained, which is conducive to improving the confinement effect of the steel tube. What’s more, the diffusion effect of the end plate on the local bearing force makes the force transmitted to the top of the member more uniform, increases the actual bearing area, improves the resistance of the member due to the strengthening of the confinement effect of the steel tube. Figure 4.44 shows the local bearing force (N)-displacement (Δ) relationship of the CFST specimen with an end plate. It can be seen that with the increase of end plate thickness (t a ), the resistance of the specimen to local bearing increases. For specimens with different ratios of local bearing area (β) and cross-section shape, the variation law of local bearing resistance with end-plate stiffness is different. The increase of the end plate thickness (t a ) has no obvious effect on the local compressive stiffness of the member. The equations for the reduction coefficient K LC of resistance of circular CFST to local bearing with end plate were proposed by Han (2016), and should be calculated as follows: K LC = ( A0 · β + B0 · β 0.5 + C0 ) · (D0 · n 2r + E 0 · n r + 1) ≤ 1  n r = 1.1 ·

E s · ta3

(4.6.1.7)

0.25

E · D3

A0 = (−0.17ξ 3 + 1.9ξ 2 − 6.84ξ + 7) × 10−2

(4.6.1.8) (4.6.1.9)

B0 = (1.35ξ 3 − 14ξ 2 + 46ξ − 60.8) × 10−2

(4.6.1.10)

C0 = (−1.08ξ 3 + 10.95ξ 2 − 35.1ξ + 150.9) × 10−2

(4.6.1.11)

−0.273

−0.410

1.358

B0

C0

1.258

0.018

1

0.040

0.5

A0 1.193

−0.186

0.004

1.5

1.156

1.139

−0.119

−0.009

−0.005 −0.138

2.5

2

Note Intermediate values in the table are obtained by linear interpolation

Coefficient

ξ

Table 4.3 Coefficients A0 , B0 , C 0

1.134

−0.118

−0.010

3

1.134

−0.126

−0.010

3.5

1.132

−0.132

−0.009

4

1.120

−0.125

−0.010

4.5

1.090

−0.097

−0.013

5

174 4 Design of Concrete-Filled Steel Tubular (CFST) Members

4.6 Resistance of Members to Local Bearing Fig. 4.44 Local bearing force (N)-displacement (Δ) relationship of CFST specimen with end plate

175

(kN) ta=12mm ta=5mm ta=2mm

(mm)

D0 = (−0.53β − 54β 0.5 + 46) × 10−2

(4.6.1.12)

E 0 = (6β + 62β 0.5 − 67) × 10−2

(4.6.1.13)

E=

E s As + E c Ac Asc

(4.6.1.14)

where, Ac As Asc D ta Es Ec A0 , B0 , C 0 D0 , E 0 β ξ

cross-sectional area of the core concrete (mm2 ); cross-sectional area of the steel tube (mm2 ); cross-sectional area of the CFST member (mm2 ); outside diameter of the CFST member (mm); thickness of end plate (mm); modulus of elasticity of steel (N/mm2 ); modulus of elasticity of concrete (N/mm2 ); coefficient, shall be determined in accordance with Table 4.4. coefficient, shall be determined in accordance with Table 4.5; ratio of local bearing area, shall be determined in accordance with Eq. (4.6.1.1); confinement factor, shall be calculated in accordance with Eq. (1.3.1).

Therefore, resistance of CFST member to local bearing (N uLC ) should conform to Eq. (4.6.1.15) and be calculated in accordance with Eq. (4.6.1.16):

where,

NLd ≤ NuLC

(4.6.1.15)

NuLC = K LC · Nu

(4.6.1.16)

−0.275

−0.411

1.360

B0

C0

1.257

0.019

1

0.040

0.5

A0 1.192

−0.187

0.004

1.5

1.159

1.147

−0.122

−0.009

−0.004 −0.140

2.5

2

Note Intermediate values in the table are obtained by linear interpolation

Coefficient

ξ

Table 4.4 Coefficient A0 , B0 , C 0

1.150

−0.124

−0.010

3

1.159

−0.134

−0.010

3.5

1.166

−0.144

−0.008

4

1.163

−0.143

−0.008

4.5

1.142

−0.121

−0.010

5

176 4 Design of Concrete-Filled Steel Tubular (CFST) Members

4.6 Resistance of Members to Local Bearing

177

Table 4.5 Coefficient D0 , E 0 ξ

2

4

6

8

10

12

14

16

Coefficient D0 −0.314 −0.641 −0.895 −1.110 −1.301 −1.474 −1.635 −1.785 E0

0.327

0.810

1.209

1.564

1.891

2.198

2.490

2.770

Note Intermediate values in the table are obtained by linear interpolation

N Ld design value of local bearing of CFST member (N); N uLC resistance of CFST to local bearing (N); K LC reduction coefficient of local bearing resistance of circular CFST member with end plate, shall be calculated in accordance with Eq. (4.6.1.7); resistance of CFST member in axial compression, shall be calculated in Nu accordance with Eq. (4.2.1.9).

4.6.2 Lateral Local Bearing Chord and web connections of trussed CFST hybrid structural K-joints may exhibit local bearing failure of core concrete. The lateral local bearing force transmitted by the webs can be effectively dispersed and transmitted in the chord concrete, as shown in Fig. 4.45. For chords and webs with circular cross-sections, the loading path of the lateral local compressive stress along the transverse direction of the chord is controlled by the circular cross-section edge and the web-to-chord diameter ratio. When the web-to-chord diameter ratio is relatively large, the lateral compressive stress will soon reach the edge of the chord concrete and steel tube; which is therefore ignored in the force transmission diagram for safety, and only the transmission path of the lateral local compressive stress along the longitudinal direction is considered. In addition, with the change of the angle θ between the web and the chord, the dispersing direction and slope of the lateral local compressive stress in the chord concrete will change; through experiments and finite element analysis, the stress transfer direction is simplified to be symmetrically transferred at a slope of 2:1 (horizontal: vertical). The mechanical behavior of CFST members under lateral local bearing is complex. The research shows that the typical failure modes of joint area of CFST member to local bearing are plastic failure of steel tubes and collapse of core concrete. Due to the composite effect of steel tube and core concrete, CFST member subjected to lateral local bearing force shows good resistance and ductility. Figure 4.46 shows the comparison of failure modes of CFST member and hollow steel tube under lateral local bearing. Figure 4.47 shows the comparison of typical failure modes of CFST specimens and corresponding hollow steel tube and plain concrete specimens under lateral local bearing.

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4 Design of Concrete-Filled Steel Tubular (CFST) Members

NLF

1

NLF 1

(a) Longitudinal section view 1

Ab

Alc dw

θ

2

2

D

dw

D

D

dw

D

(c) Top view

(b) Side section view

Fig. 4.45 Lateral local bearing force transmission of core concrete in the joint area. 1—CFST chords; 2—Steel tubular webs; N LF —Design value of lateral local bearing force on the chord in joint zone; D—Outside diameter of the chord bearing lateral force; d w —Outside diameter of the web transmitting lateral force; Ab —Dispersed bearing area when under lateral local bearing; Alc — Direct bearing area when under lateral local bearing, taking as cross-sectional area of a solid web with the same outside diameter; θ—Angle between the chord and the web that transmits lateral local bearing

Tearing of steel tube

Buckling failure of the steel tube Plastic failure of the steel tube (b) Hollow steel tube specimen (a) CFST specimen Fig. 4.46 Failure modes of CFST member and hollow steel tube to lateral local bearing

According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the resistance of the connection between a chord of a K-joint and a web with a circular cross-section in CFST members to lateral local bearing shall satisfy the inequality in Eq. (4.6.2.1), and should be calculated in accordance with Eq. (4.6.2.2): NLF ≤ NuLF

(4.6.2.1)

4.6 Resistance of Members to Local Bearing Tearing of steel tube surface

Fillet weld

179

Inwards buckling

Outwards buckling

Core concrete gushing Fillet weld (b) Hollow steel tubular member

(a) CFST member

Concrete cracking

(c) Plain concrete member

(1) Member to diagonal loading Tearing steel tube surface

Inwards buckling

Core concrete gushing

Plastic distortion (a) CFST member

Concrete cracking

Lateral deformation (b) Hollow steel tubular (c) Plain concrete member member (2) Member to vertical loading

Fig. 4.47 Failure modes of member to lateral local bearing

NuLF = βc βl f c /

Alc sin θ

(4.6.2.2)

βl =

Ab Alc

(4.6.2.3)

Alc =

πdw2 4

(4.6.2.4)

Alc + 2dw D sin θ

(4.6.2.5)

Ab = where, N LF N uLF fc θ βl Alc D dw Ab βc

design value of lateral local bearing force on the chord in joint zone (N); resistance of the chord to lateral local bearing (N); design value of compressive strength of concrete (N/mm2 ); angle between the chord and the web that transmits lateral local bearing; strength increase factor of concrete when under lateral local bearing; direct bearing area when under lateral local bearing, taking as cross-sectional area of a solid web with the same outside diameter (mm2 ); outside diameter of the chord bearing lateral force (mm); outside diameter of the web transmitting lateral force (mm); dispersed bearing area when under lateral local bearing (mm2 ); coefficient of concrete strength when under lateral local bearing, shall be determined in accordance with Table 4.6.

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4 Design of Concrete-Filled Steel Tubular (CFST) Members

Table 4.6 Coefficient of concrete strength when under lateral local bearing / Alc f y 0.4 0.8 1.2 1.6 2.0

≥ 3.0

Ab f ck

βc

1.07

1.22

1.47

1.67

1.87

2.00

Note Intermediate values in the table are obtained by linear interpolation

4.7 Influence of Cross-Sectional Size In order to illustrate the applicability of the equations given in Sects. 4.2 and 4.3 for resistance of CFST members with large cross-sectional sizes in axial compression and in combined compression and bending, respectively, the experimental results of different researchers were collected and analyzed. Figure 4.48 shows the D − k relationship between test results of circular CFST members to axial compression, where k = Nue /Nuc , Nue is the test value and Nuc is the calculation value [Eq. (4.9)]. The characteristic value of material strength is used in the calculation. The outside diameter of the cross-section of the member varies from 76.4 to 1020 mm. It can be seen that most of the test data is concentrated on the area with an outside diameter of the cross-section below 200 mm. When the outside diameter of the cross-section (D) is between 76.4 and 200 mm, the value of k generally varies between 0.95 and 1.25. When the outside diameter of the crosssection (D) is between 200 and 1020 mm, the value of k generally varies between 1.0 and 1.1. The mean value and mean square deviation of the ratio of all test results to calculated results are 1.065 and 0.095, respectively. The mean value and mean square deviation of the outside diameter of the cross-section (D) above 250 mm were 1.084 and 0.058, respectively. It can be seen from the comparison in Fig. 4.48 that the calculated results are generally agreed with the test results and tend to be safe. For CFST members in combined compression and bending, the D −k relationship is shown in Fig. 4.49, k = N ue /N uc , where N ue is the experimental value and N uc is the calculated value, which could be determined in accordance with Eqs. (4.3.1.8)

k=1.0

D (mm) Fig. 4.48 D − k relationship of member to axial compression

4.8 Limiting Value of Initial Stress in the Steel Tube

181

k=1.0

D (mm) Fig. 4.49 D − k relationship of members in combined compression and bending

and (4.3.1.9). As the D − k relationship shown in Fig. 4.49, the range of the outside diameter of the specimen’s cross-section is 76–450 mm. The k values of all the tests were basically between 0.9 and 1.2, and the mean value and mean square deviation values were 1.072 and 0.159, respectively. The mean value and mean square deviation of the data with the outside diameter of the cross-section above 200 mm are 1.159 and 0.150, respectively. The calculated results are generally safe.

4.8 Limiting Value of Initial Stress in the Steel Tube The load action effects of construction and service stages should be considered comprehensively in the life-cycle-based design method of the CFST member. Taking the CFST column in practical high-rise buildings as an example, the hollow steel tube is usually installed first, then the beam is installed, and the floor is constructed. In order to speed up the construction and improve the work efficiency, the hollow steel tube column is usually installed first, and then the concrete is placed into the hollow steel tube. Figure 4.50 schematically shows the construction of the CFST column in a typical multi-story and high-rise building. In this way, the initial compressive stress (hereinafter referred as initial stress in the steel tube) along the longitudinal direction will occur in the steel tube due to the construction load and the dead weight of wet concrete before the concrete setting and forms CFST member together with the steel tube. During the construction of CFST arch bridges, the hollow steel tube arch ribs are usually installed first, and then the concrete inside the steel tube is placed, which also causes the initial stress in the steel tube. Reasonable determination of the influence of initial stress in the steel tube on the mechanical performance of the CFST member is of great significance for the safe and reasonable application of the CFST member and the construction organization. The initial stress in the steel tube is the stress in the steel tube of the CFST member before the steel tube and concrete act together. The influence coefficient of initial stress (β) is shown in Eq. (4.8.1).

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4 Design of Concrete-Filled Steel Tubular (CFST) Members

Fig. 4.50 Pumping and placement of core concrete

Composite floor slabs

Hollow steel tube

Wet concrete in steel tube

Concrete pumps Steel beam

β=

σso ϕs · f y

σso =

Np As

(4.8.1) (4.8.2)

where, σ so Np As ϕs

initial stress in the steel tube (N/mm2 ); initial load applied to the steel tube (N); cross-sectional area of the steel tube (mm2 ); stability factor for the hollow steel tube in compression, shall be determined with the current national standard GB 50017 Standard for Design of Steel Structures.

Figure 4.51 shows the typical N − um relationship of CFST members in combined compression and bending with and without considering the impact of the initial stress in the steel tube, where N uo and umu are the resistance and its corresponding deformation of the member without initial stress in the steel tube, respectively; N up and umup are the resistance and its corresponding deformation with initial stress in the steel tube, respectively. It can be seen in Fig. 4.51 that when there is initial stress in the steel tube, the resistance of member decreases, its corresponding deformation value increases, and the elastic stiffness of member also decreases. The initial stress in the steel tube has an impact on the resistance of CFST members. The existence of initial stress in the steel tube can reduce the resistance of the CFST member by about 20% at most. Therefore, the influence of initial stress in the steel tube on the resistance of the CFST member should be reasonably considered. The main parameters affecting the resistance coefficient (k p ) are the coefficient of initial stress in the steel tube (β), the slenderness ratio of the member (λ) and load

4.8 Limiting Value of Initial Stress in the Steel Tube Fig. 4.51 Typical N − um relationship

183

N Nuo Nup

Steel tube without initial stress Steel tube with initial stress

umu

O

umup

um

eccentricity (e/r). The calculation of k p was proposed by Han (2016), and shall be in accordance with the following equations: kp = 1 − f (λ) · f  f (λ) =



r

·β

(λo ≤ 1) 0.17λo − 0.02 −0.13λ2o + 0.35λo − 0.07 (λo > 1) λo =

e f( ) = r

e

λ 80

 2     0.75 re − 0.05 re + 0.9  re ≤ 0.4 e > 0.4 −0.15 re + 1.06 r

(4.8.3)

(4.8.4) (4.8.5)

(4.8.6)

where, f (λ) f (e/r) β λ e/r

function considering the influence of slenderness ratio (λ); function considering the influence of load eccentricity (e/r); coefficient of initial stress, shall be calculated in accordance with Eq. (4.8.1); slenderness ratio, shall be determined in accordance with Eq. (4.2.1.5); load eccentricity, r = D/2 for circular CFST member.

According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the limiting value of initial stress in the steel tube of a CFST member due to the construction loads shall be 35% of the critical stress value corresponding to the resistance of the hollow steel tube. When the initial stress of the steel tube in the CFST member is lower than the limiting value, the influence of construction load on the resistance of the completed structures may be ignored; otherwise, the influence shall be considered.

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4 Design of Concrete-Filled Steel Tubular (CFST) Members

The stress in the hollow steel tube is calculated according to the load of core concrete in the construction stage, and the initial stress has little influence on the resistance of the CFST member in compression. However, due to the existence of initial stress, the elasto-plastic stage of CFST member will be advanced, and the combined tangent modulus of the elasto-plastic stage will be changed, thus affecting the stability of the structure. The critical stress corresponding to the resistance of the hollow steel tube is ϕ s f , where ϕ s is the stability factor of the hollow steel tube, and f is the design value of steel tube material strength. When the initial stress in the steel tube caused by construction load in CFST member is equal to or greater than the limiting value, the influence of initial stress in the steel tube and initial deformation caused by construction load on structural resistance after construction cannot be ignored.

4.9 Limiting Value of Core Concrete Void in the Steel Tube For CFST members in actual engineering projects, as a result of concrete material preparation, casting process and quality control, voids may occur in core concrete, which will affect the interaction and co-working performance of steel tube and its core concrete and the resistance of the CFST member. In practical engineering projects, due to concrete shrinkage and construction issues, circumferential void (Fig. 4.52a) and spherical-cap void (Fig. 4.52b) might develop in the cross-sections of vertical members and horizontal members, respectively. The influence of circumferential void on the resistance and stiffness of CFST members is significant compared with sphere-cap void under the same void ratio. When the void is within a limiting value, its influence on the structural resistance is moderate and may be neglected. Therefore, the concept of limiting value of core concrete void in the steel tube is proposed and used. (1) Core concrete in CFST members shall not have a continuous circumferential void along its periphery. When it has a local circumferential void (Fig. 4.53a), the limiting value of concrete void ratio in the steel tube shall be 0.025% and the circumferential void ratio of shall be calculated in accordance with the following equation: Fig. 4.52 Schematic diagram of concrete voids in the steel tube. 1—Circumferential void; 2—Spherical-cap void; 3—Steel tube; 4—Core concrete

2

1

4

3

(a) Circumferential void

3

4 (b) Spherical-cap void

4.9 Limiting Value of Core Concrete Void in the Steel Tube

1

3

2 3

dr

ds≤5mm

Fig. 4.53 Schematic diagram of the voids in CFST members. 1—Circumferential void; 2—Spherical-cap void; 3—Steel tube; 4—Core concrete

185

4

4

D

D (a) Circumferential void

χr =

dr D

(b) Spherical-cap void

(4.9.1)

where, χ r circumferential void ratio; d r mean width of the circumferential void (mm); D outside diameter of the steel tube (mm). As shown in the experimental studies of CFST members in compression with circumferential voids, when the void ratio is lower than 0.025%, the reduction of resistance caused by void is relatively low, and may be neglected. When the void ratio is equal to or > 0.025%, the composite effects between the steel tube and concrete cannot be fully developed, and additional measures shall be employed to ensure that steel tube and concrete act together. (2) When the core concrete has a local spherical-cap void (Fig. 4.53b), the limiting value of concrete void ratio in the steel tube shall be 0.6%, and the void height shall not be > 5 mm. The spherical-cap void ratio shall be calculated in accordance with the following equation: χs =

ds D

(4.9.2)

where, χ s spherical-cap void ratio; d s maximum height of the spherical-cap void (mm); D outside diameter of the steel tube (mm). When the spherical-cap void ratio is > 0.6%, the support effect of core concrete to the steel tube is weakened, and the resistance and stiffness of CFST members are notably affected. Therefore, the concrete void shall be filled. When the void ratio of CFST members is lower than 0.6%, but the void height of CFST members is > 5 mm, the void shall also be filled. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the design value for resistance of cross-section of CFST

186

4 Design of Concrete-Filled Steel Tubular (CFST) Members

members with spherical-cap void to compression may be calculated in accordance with the following equations:

 f (ξ ) =

Nug = K d Nc

(4.9.3)

K d =1 − f (ξ )χs

(4.9.4)

1.42ξ + 0.44 (ξ ≤ 1.24) 4.66 − 1.97ξ (ξ > 1.24)

(4.9.5)

where, N ug design value for resistance of cross-section of single CFST member with spherical-cap void to compression (N); N c design value for resistance of cross-section of single CFST member to compression (N); K d reduction coefficient due to void, set as 1.0 when it is > 1.0; χ s spherical-cap void ratio, shall be determined in accordance with Eq. (4.9.2). A circular CFST column used in a practical project is taken as an example to verify the calculation. The CFST column with outside diameter (D) of 1600 mm was used in this project. The detection of engineering structure found that there was local small void in the steel tube and concrete, and the maximum void width d r = 0.05– 0.1 mm. According to Eq. (4.9.1), the void ratio χ r = 0.00313–0.00625%, which is less than the limiting value of concrete void of 0.025% and meets the requirements. The CFST column meets the requirements of resistance. Figure 4.54 shows the transverse cutting of CFST member after the interface performance model test of steel tube-core concrete according to an actual project. The steel tube has a maximum cross-section of φ1600 × 60 and is filled with C60 normal concrete. This project adopts the pumping jacking method to carry out CFST construction. The maximum concrete pumping height is 265.15 m. The measured results show that the compactness of the interface between core concrete and steel tube is good, and only a 0.1 mm gap is observed in a small local area. Exercises 1. Briefly introduce the characteristics of the stress–strain relationship for CFST stub column to axial compression, and analyze the influence of confinement factor. 2. Briefly introduce the main factors that affect the axial force-bending moment relationship of CFST members to combined compression and bending. 3. Briefly introduce the principle of determining the restoring force model of CFST members. 4. Briefly introduce the concept and determination method of limiting value of initial stress in the steel tube and the limiting value of core concrete void of CFST member.

4.9 Limiting Value of Core Concrete Void in the Steel Tube

Core concrete

187

Core concrete

Interface

Interface

Steel tube wall

Steel tube wall (a) D=1300mm

(b) D=1600mm Steel tube wall

Core concrete

0.1mm gap localized at the interface between steel tube and core concrete

(c) Local gap of 0.1mm (D=1300mm) Fig. 4.54 Interface between the steel tube and its core concrete

Chapter 5

Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

Key Points and Learning Objectives Key Points This chapter describes the working mechanism of trussed CFST hybrid structures and concrete-encased CFST hybrid structures, and introduces the calculation methods of resistances of CFST hybrid structures. Learning Objectives Understand the characteristics and typical failure modes of trussed CFST hybrid structures and concrete-encased CFST hybrid structures during full-range loading. Be familiar with the calculation methods for the resistances of trussed CFST hybrid structures and concrete-encased CFST hybrid structures. Learn the detailing requirements of CFST hybrid structures.

5.1 Introduction In recent years, CFST hybrid structures have emerged as a superior structural type for the construction of large-scale infrastructure. The objective of the technical standard GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures in Chinese and English promulgated in 2021 is to implement the relevant technical and economic requirements of the state in concrete-filled steel tubular (CFST) hybrid structures, by using advanced technology, and ensuring safety, reasonableness, economy, and good quality of the structures. The technical standard is applicable to the design, construction and acceptance of CFST hybrid structures in buildings, railways, highways, electric power transmission, port engineering, etc. Based on this technical standard, this chapter discusses the basic working principles and design methods of CFST hybrid structures. © China Architecture & Building Press 2024 L. Han, Theory of Concrete-Filled Steel Tubular Structures, https://doi.org/10.1007/978-981-99-2170-6_5

189

190

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

5.2 Trussed Concrete-Filled Steel Tubular (CFST) Hybrid Structures Trussed CFST hybrid structures is a trussed structure that consists of circular CFST chords and steel tube, CFST or other steel profile webs. There are two-chord, three-chord, four-chord, and six-chord trussed CFST hybrid structures, as shown in Fig. 1.16, and the chords are normally symmetrically placed. Compared with trussed hollow steel tubular structures, trussed CFST hybrid structures have the advantages of good integrity, high resistance, spatial stiffness and deformation resistance, excellent stability performance, low economic cost and easy to perform fire protection. Therefore, trussed CFST hybrid structures are widely used in marine engineering, bridge engineering and building structures. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the limiting values of slenderness ratios for the chords of trussed concrete-filled steel tubular (CFST) hybrid structures shall conform to the relevant requirements of the current national standard GB 50936 Technical Code for Concrete Filled Steel Tubular Structures; the limiting values of slenderness ratios for the webs shall conform to the relevant requirements of the current national standard GB 50017 Standard for Design of Steel Structures. For trussed CFST hybrid structures subjected to eccentric loads, diagonal webs should be used; and when the distances between the chords are relatively small or there are some functional requirements, horizontal webs may be used. The detailing of the webs of trussed CFST hybrid structures shall conform to the following requirements: (1) The webs should use circular hollow steel tubes or CFST members, and other types of steel profiles may also be used; (2) The axes of diagonal webs should intersect at the centroid of the joint; when the eccentricity of the webs is inevitable, Provision 6.3.3(2) of this book shall be satisfied; when using gap K-joints, the clear distance between the web ends should not be less than the summation of the wall thicknesses of the two webs; (3) The distance between the centroids of horizontal webs should not be greater than 4 times the distance between the centroids of chords; the cross-sectional area of the hollow steel tubular web should not be less than 1/5 of that of the single chord; (4) The intersecting weld between web and chord shall be continuous welding and have a smooth transition; where webs overlap each other, overlapped webs shall be welded to the lapped webs along the lap edges; (5) Other detailing requirements of connections between chords and webs, calculation of the weld strength and the tensile strength of chord at joint location shall conform to the relevant requirements of the current national standard GB 50017 Standard for Design of Steel Structures. The schematic diagram of the web forms of trussed CFST hybrid structures is shown in Fig. 5.1. The hollow steel tubular webs may be filled with concrete if

5.2 Trussed Concrete-Filled Steel Tubular (CFST) Hybrid Structures 2

1

1

3 (a) Trussed structure with diagonal webs

191

3 (b) Trussed structure with horizontal webs

Fig. 5.1 Webs in trussed CFST hybrid structures, 1—CFST chords; 2—diagonal webs; 3—horizontal webs

necessary. The detailing requirements for the horizontal webs are to ensure that the webs have enough linear stiffness. The resistance of whole structures as well as the chords and webs shall be calculated in the resistance design of trussed CFST hybrid structures. The equivalent slenderness ratios of the structures shall be determined with a global structural analysis, and the equivalent slenderness ratios of axial compression structures may be determined in accordance with the current national standard GB 50936 Technical Code for Concrete Filled Steel Tubular Structures. In addition, the resistance of the structures may be determined with a global structural analysis.

5.2.1 Resistance in Compression and Bending (1) Resistance in axial compression Typical failure modes of two- and three-chord trussed CFST hybrid structures are shown in Fig. 5.2 (1) and Fig. 5.2 (2), where no out-of-plane instability occurred and the specimens acted together well in general. The specimen with horizontal webs occurred failure at the end section where the webs were connected to the chords, while the specimen with diagonal webs occurred failure at the middle section where the chords reached the resistance in compression. Figure 5.2 (3b) shows the trussed hollow steel tubular structure compared with the trussed CFST hybrid structures as shown in Fig. 5.2 (3a). During loading, severe local buckling occurred in the chord. Compared with the hollow steel tubular specimens, the CFST specimens possess more than 60% higher resistance and higher elastic stiffness. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the resistance of trussed CFST hybrid structures with identical chords in axial compression shall conform to the following requirements: 1) When the long-term load effects are not considered, the resistance of trussed CFST hybrid structures in axial compression shall satisfy the inequality in Eq. (5.2.1.1), and should be calculated in accordance with Eq. (5.2.1.2): N ≤ Nu

(5.2.1.1)

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5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

Outward local buckling

(a) CFST

Inward local (b) Hollow steel tube buckling (1) Specimen with horizontal webs

(2) Specimen with diagonal webs

(3) Chord

Fig. 5.2 Failure modes of trussed CFST hybrid structures in compression

Nu = ϕ

∑

Nc

(5.2.1.2)

where, N Nu Nc ∑ ϕ

Nc

design value of axial compression (N); resistance of the trussed CFST hybrid structure in axial compression (N); resistance of cross-section of a single chord to compression(N), shall be calculated in accordance with Eq. (4.2.1.3); summation of resistances of cross-sections of chords to compression (N); stability factor for the axial compression structure (taken as the lesser of the two values for the two principal axes), shall be calculated with the equivalent slenderness ratio of the structure by Eq. (4.2.1.10).

2) When the axial compression of a single CFST chord caused by permanent load accounts for 50% or higher of its total axial compression, the influence of longterm load on the structural stability shall be considered. When the long-term load effects are taken into account, the resistance of trussed CFST hybrid structures in axial compression shall satisfy the inequality in Eq. (5.2.1.3), and the long-term load coefficients should be calculated in accordance with Eq. (5.2.1.4): N ≤ kcr Nu  ⎧ 2 − 0.4a + 1 b2.5a knL (a ≤ 0.4) ⎨ 0.2a  kcr = 0.2a 2 − 0.4a + 1 bknL (0.4 < a ≤ 1.2) ⎩ (a > 1.2) 0.808bknL

(5.2.1.3)

(5.2.1.4)

5.2 Trussed Concrete-Filled Steel Tubular (CFST) Hybrid Structures

λ 100

(5.2.1.5)

b = ξ 0.05

(5.2.1.6)

a=

knL =

193

(a ≤ 0.4) 1 − 0.07n L 0.98 − 0.07n L + 0.05a (a > 0.4) nL =

NL Nu

(5.2.1.7) (5.2.1.8)

where, N k cr Nu k nL λ ξ nL NL

design value of axial compression (N); long-term load coefficient, set as 1.0 when k cr is greater than 1.0; resistance of the trussed CFST hybrid structure in axial compression (N); adjustment coefficient for long-term load ratio, taken as 1.0 when it is greater than 1.0; equivalent slenderness ratio of the structure, shall be determined by global analysis of the structure; confinement factor, shall be calculated by Eq. (1.3.1); long-term load ratio; long-term axial compression (N) in the trussed CFST hybrid structure, shall be determined with quasi-permanent combination of loads.

(2) Bending resistance The research shows that there were two types of failure modes of the trussed CFST hybrid structures in bending without concrete slabs: (1) flexural failure of beam: the specimens undergo the global large deflection, exhibit good ductility and integrality, and the joint has no local failure characteristics; (2) joint failure in the flexural-shear span: in addition to the overall deflection, with the increasing load, joint failure eventually occurs in the shear span area, including tearing of the welding in the zone of joints to tension or tearing of the chord and chord buckling in the zone of joints to compression. The two types of failure modes are shown in Fig. 5.3a, b, respectively. During the full-range loading, the load (M)-mid-span deflection (um ) relationship of the trussed CFST hybrid structures to bending is shown in Fig. 5.4, which can be generally divided into three stages: 1) Elastic stage (OA) The M-um relationship of trussed CFST hybrid structures is basically linear at this stage. When the maximum longitudinal fiber strain of the steel tube to tension of the lower chord reaches the proportional strain, the cross-section reaches the critical state of elasticity and plasticity (point A) and its corresponding bending moment is called the elastic bending moment (M e ).

194

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

(a) Global flexural failure

(b) Local failure of joint in the flexural-shear zone

(c) Flexural failure of member with reinforced concrete slab

Fig. 5.3 Failure modes of trussed CFST hybrid structures to bending Fig. 5.4 Bending (M)–mid-span deflection (um ) relationship

M C

Mu My

Me O

B

A

um

2) Elasto-plastic stage (AB) When the bending moment in the cross-section reaches about 0.4–0.5M u , the Mum relationship enters the elasto-plastic stage, no longer showing a linear relationship, and the bending stiffness of the member gradually becomes smaller. With the increase of the load, the global deformation of the member develops continuously, and the steel tube subjected to tension of the lower chord gradually enters the yield stage, but the maximum deflection in the span of the member is still relatively small. When the cross-sectional strain of the upper and lower chords reaches the yield strain of steel, the elasto-plastic stage ends at this point (point B), and its corresponding bending moment is called the yield bending moment (M y ). 3) Plastic stage (BC)

5.2 Trussed Concrete-Filled Steel Tubular (CFST) Hybrid Structures

195

As the load continues to increase, the steel tube of the lower chord in the middle span gradually enters the hardening stage, and the cross-sectional flexural stiffness decreases rapidly. When the M-um relationship is at the plateau stage, the resistance of the member does not change much, the global deformation develops rapidly, and plastic deformation becomes apparent. After the maximum longitudinal fiber strain (at the outer edge of the lower surface of the steel tube to tension of the lower chord) reaching εu (to avoid excessive plastic strain, take εu = 0.01), the member enters the failure stage, and its corresponding bending moment at the point C is called the ultimate bending moment (M u ). At this time, the maximum longitudinal fiber strain at the outer edge of the concrete to compression of the upper chord reaches or exceeds the ultimate compressive strain of the concrete (εcu ). Based on the experimental study, finite element analysis and theoretical analysis, the calculation method for resistance of trussed CFST hybrid structures to bending was determined. The basic assumptions include: (1) ignoring the direct contribution of the concrete to tension in the chord to the global banding resistance; (2) ignoring the direct contribution of the web to the global banding resistance; (3) the neutral axis is located within the height of the web. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the bending resistance of trussed CFST hybrid structures without concrete slab and with identical compression chords shall satisfy the inequality in Eq. (5.2.1.9), and should be calculated in accordance with Eq. (5.2.1.10): M ≤ Mu

(5.2.1.9)

∑ ∑  Mu = min ϕ Nc , Nt h i

(5.2.1.10)

where, M M∑ u ϕ ∑ Nc Nt Nt hi

design value of bending moment (N·mm); bending resistance (N·mm); summation of resistances of chords in axial compression (N); summation of resistances of cross-sections of chords to tension (N); resistance of cross-section of a single chord to tension (N), shall be calculated by Eq. (4.2.1.20); distance between the centroids of the compression and the tension chords along the cross-sectional height (mm).

An experimental study of trussed CFST hybrid structures with concrete slabs on the upper chord was carried out, and the typical failure mode of the specimen is shown in Fig. 5.3c. The concrete slab and trussed CFST hybrid structures can act together during full-range loading; the existence of the concrete slab changes the loading path of the internal forces, increases the strain developments of the webs, and enhances the global rigidity and resistance of structures; under positive bending moment, the bending resistance is increased by 16–20%; when the resistance is

196

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

reached, the neutral axis moves upward and is within the cross-section of steel tube of the upper chord. Trussed CFST hybrid structures and concrete slabs can be used to form a hybrid structural system. To ensure that they can act together, related calculations have to be carried out based on the shear force between them, and corresponding detailing, such as encasing the compression chords into the concrete slab, or using shear connectors, has to be applied. Welded studs should be adopted as shear connectors; perfobond connectors, channel connectors and other types of reliable shear connectors may also be used. The concrete slab may also be pre-stressed to ensure the integrity between the it and the main truss girder. When considering the bending resistance of trussed CFST hybrid structures with concrete slab, it is classified in accordance with the first-type cross-section and the second-type cross-section, and the calculation equations for bending resistance are provided, respectively. The basis for the classification of cross-section types can be understood as follows: in the positive moment zone, with the increase of the bending moment, the neutral axis of the trussed CFST hybrid structures with concrete slab keeps moving upward. When the neutral axis is located within the height of the webs, some of the CFST chords are in compression, which can thus exploit the structural merits of CFST members in compression. This is the first type of cross-section. When the neutral axis moves upward and is above the compression chords, the chords are mainly in tension, so that the advantages of CFST members with good compression performance cannot be fully exploited. This is the second type of cross-section. The composite effect between concrete slabs and trussed CFST hybrid structures should be considered in the design of trussed CFST hybrid structures with concrete slabs under the action of a positive moment. In the section of the negative moment, the contribution of reinforcement in the slab to the resistance can be considered according to the practical needs of the project. The calculation method for bending resistance of cross-section of trussed CFST hybrid structures without concrete slab is derived based on experimental studies, finite element simulations and theoretical analyses. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the following provisions shall be satisfied: 1) The calculation of the bending resistance of structures in the positive moment zone shall conform to the following requirements: a) When the inequality in the following equation is satisfied, the bending resistance of the structures should be calculated in accordance with the first-type of cross-section shown in Fig. 5.5a: ∑ ∑ ∑ Asc ≤ (1.1 − 0.4αs ) f ϕc ( be h b f c + Al' fl' ) + ϕsc f sc As (5.2.1.11) where, ϕc

stability factor for the concrete slab in compression, shall be calculated in accordance with the current national standard GB 50010 Code for Design

5.2 Trussed Concrete-Filled Steel Tubular (CFST) Hybrid Structures

Dt

M

H

Dc

7

3 4

Dc hn

hb

1

xn

φc∑behbfc

5

6

φscfsc∑As

hi

φcf l'Al'

197

∑Nt

Dt

2 (a) First-type cross-section

7

Dc hn

Dc M

H

3 4

Dt

f ∑Asc-t

hb

1

hi

φc∑behbfc

5

6 φscfsc∑Asc-

xn

φcf l'Al'

∑Nt

2

Dt

(b) Second-type cross-section

Fig. 5.5 Schematic diagram of cross-sections of trussed CFST hybrid structures with concrete slab, 1—compression chords; 2—tension chords; 3—neutral axis; 4—webs; 5—concrete slab; 6— longitudinal reinforcement; 7—concrete encasement of chords

be

∑ hb fc Al' fl' ϕsc f sc

be

of Concrete Structures, where the effective length should be taken as the interval length l 1 ; effective flange width of the concrete slab corresponding to a single chord (mm, the chord can be seen as the beam of a slab-beam system), shall be calculated in accordance with the current national standard GB 50010 Code for Design of Concrete Structures; summation of effective flange widths of concrete slab (mm); if there is overlap, the overlapped part is only counted once; thickness of the concrete slab in the compression zone of the cross-section (mm); design value of compressive strength of concrete in the slab (N/mm2 ); total cross-sectional area of the longitudinal compression reinforcement (mm2 ); design value of compressive strength of the longitudinal reinforcement (N/ mm2 ); stability factor for the compression chord, the effective length should be set as 90% of the interval length; design value of compressive strength for the compression CFST chord (N/ mm2 ), shall be calculated by Eq. (3.3.1) of this standard;

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5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

∑

Asc summation of cross-sectional areas of compression chords (mm2 ); f design value of compressive, tensile and flexural strength of steel of the tension chord (N/mm2 ); ∑ As summation of cross-sectional areas of steel tubes in tension chords (mm2 ). (b) When the inequality in Eq. (5.2.1.11) is not satisfied, the bending resistance of the structures should be calculated in accordance with the second-type crosssection shown in Fig. 5.5b. 2) The bending resistance of the structures in negative moment zones should be calculated with the contribution of the steel reinforcement in the slab considered, and may also be calculated in accordance with Eq. (5.2.1.10). 3) The bending resistance of trussed CFST hybrid structures with concrete slab and with identical compression chords as well as identical tension chords, and having the first-type cross-section, should be calculated in accordance with the following equation: Mu = ϕc (

∑

be h b f c +

Al' fl' )



hb Dt − H− 2 2

+ ϕsc f sc

∑

Asc h i (5.2.1.12)

where, Mu fc Al' fl' H Dt hb f sc ∑ hi

Asc

bending resistance (N·mm); design value of compressive strength of concrete in the slab (N/mm2 ); total cross-sectional area of the longitudinal compression reinforcement (mm2 ); design value of compressive strength of the longitudinal reinforcement (N/ mm2 ); total height of the cross-section (mm); outside diameter of the tension chord steel tube (mm); thickness of the concrete slab in the compression zone of the cross-section (mm); design value of compressive strength of the compression chord (N/mm2 ), shall be calculated by Eq. (3.3.1) of this standard; summation of cross-sectional areas of compression chords (mm2 ); distance between the centroids of the compression and the tension chords along the cross-sectional height (mm).

4) The bending resistance of trussed CFST hybrid structures with concrete slab and with identical compression chords as well as identical tension chords, and having the second-type cross-section should be calculated in accordance with the following equations:

5.2 Trussed Concrete-Filled Steel Tubular (CFST) Hybrid Structures

199



Dt 1 ∑ Asc - t (h n + Dc − xn ) − xn + σs As H − 2 2 ∑ ∑ 1 hb Asc-c (xn − h n ) be h b f c + Al' fl' )(xn − ) + ϕsc σsc +ϕc ( 2 2 (5.2.1.13) ∑ ∑ ∑ ϕc ( be h b f c + Al' fl' ) + ϕsc f sc As Asc-c = (1.1 − 0.4αs ) f ∑ + f Asc-t (5.2.1.14) Mu = (1.1 − 0.4αs ) f

∑

hn = H − hi − when h n < xn ≤ h n +

Dt Dc − 2 2

(5.2.1.15)

Dc 2

Dc + h n − xn Dc2 arccos 2 Dc 4 2

/ 2

2 Dc Dc Dc + h n − xn + h n − xn − − 2 2 2   Dc + h n − xn 2 Asc-t = π − arccos Dc t Dc

Asc-c =

(5.2.1.16)

(5.2.1.17)

2

Dc < x n < h n + Dc 2   xn − D2c − h n Dc2 Asc-c = π − arccos Dc 4 2 /

2

2 Dc Dc Dc − hn + h n − xn + xn − − 2 2 2

when h n +

Asc-t = arccos σsc = σs =

E scp where,

xn −

Dc 2 Dc 2

− hn

Dc t

εcu 1 E scp (xn − h n ) 2 xn

1 εcu E s (h n + Dc − xn ) ≤ f 2 xn   f [0.192 235 + 0.488] f sc = 3.25 × 10−6 f

(5.2.1.18)

(5.2.1.19) (5.2.1.20) (5.2.1.21)

(5.2.1.22)

200

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

αs Dc H ϕsc

cross-sectional steel ratio, shall be calculated by Eq. (1.3.2); outside diameter of the compression chord steel tube (mm); total height of the cross-section (mm); stability factor for the compression chord, should be calculated by Eq. (4.2.1.10), the effective length should be set as 90% of the interval length; distance between the upper point of the compression chord and the upper surface of the concrete slab (mm); distance between the upper surface of the structure and the neutral axis (mm); modulus of elasticity of steel (N/mm2 ); ultimate compressive strain of concrete, shall be determined in accordance with the current national standard GB 50010 Code for Design of Concrete Structures; wall thickness of the steel tube in the compression chord (mm); design value of tensile, compressive and flexural strength of the steel tube (N/ mm2 ).

hn xn Es εcu t f

(3) Resistance in combined compression and bending According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, when trussed CFST hybrid structures with identical chords are subjected to the combined actions of compression and bending, the resistance in combined compression and in-plane bending should conform to the following equations: NB = ϕ MB = ϕ

1) when

M N

≤

∑

∑

>

∑

Nt

(5.2.1.23)

Nt r t

(5.2.1.24)

rc =

Nuc2 hi Nuc1 + Nuc2

(5.2.1.25)

rt =

Nuc1 hi Nuc1 + Nuc2

(5.2.1.26)

N ∑

Asc

+

NE = M N

Nc r c +

∑

MB : NB

ϕ f sc

2) when

Nc −

MB : NB

M



 ≤1 Wsc 1 − ϕ NNE f sc π2

(5.2.1.27)

∑

(E A)c λ2

(5.2.1.28)

5.2 Trussed Concrete-Filled Steel Tubular (CFST) Hybrid Structures

−N +

M  rc 1 −

N NE

 ≤ (1.1 − 0.4αs )

∑

201

As f

(5.2.1.29)

where, N M NB MB rc rt Nuc1 , Nuc2 ϕ ∑ ∑ Asc As N ∑c Nc N

∑t

Nt

W sc f sc NE (EA)c λ

design value of axial force (N); design value of bending moment (N·mm); axial force corresponding to the equilibrium point of tension and compression limit in N-M correlation curve of resistance (N); bending moment corresponding to the equilibrium point of tension and compression limit in N-M correlation curve of resistance (N·mm); distance between the cross-sectional center of gravity and the centroidal axis for the chord in compression zone (mm); distance between the cross-sectional center of gravity and the centroidal axis for the chord in tension zone (mm); summation of resistances to compression of chords in compression zone and chords in tension zone of the trussed CFST hybrid structure, respectively (N); stability factor for the axial compression structure, shall be calculated with the equivalent slenderness ratio of the trussed CFST hybrid structure by Eq. (4.2.1.10); summation of cross-sectional areas of all chords (mm2 ); summation of cross-sectional areas of steel tubes of all chords (mm2 ); resistance of cross-section of a single chord to compression (N); summation of resistances of cross-section to compression of all compression chords (N); resistance of cross-section of a single chord to tension (N); summation of resistances of cross-section to tension of all tension chords (N); flexural modulus of cross-section of the structure (mm3 ); design value of compressive strength of a single CFST chord (N/mm2 ), shall be calculated by Eq. (3.3.1) of this standard; Euler critical force calculated using equivalent slenderness ratio of the structure (N); elastic compression stiffness of cross-section of a single chord (N); equivalent slenderness ratio of the structure.

3) When the equivalent slenderness ratio is greater than 120, the resistance of trussed CFST hybrid structures in combined compression and in-plane bending should also satisfy the inequality in the following equation: ϕ f sc

N ∑

Asc

+

M ∑ rc (1.1 − 0.4αs ) f As (1 −

N ) NE

≤1

(5.2.1.30)

202

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

(4) Resistance of curved trussed CFST hybrid structures. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the resistance of curved trussed CFST hybrid structures (Fig. 5.6) in axial compression should conform to the requirements of Eqs. (5.2.1.27), (5.2.1.29) and (5.2.1.30). The design value of the bending moment caused by the initial deflection of structures should be calculated in accordance with the following equation: M = N u0

(5.2.1.31)

where, M design value of bending moment (N·mm); N design value of axial force (N); y

N

x

x l1

y 4 rt hi

rc

b

A-A (two-chord) y α

x

u0 L

rc

A

A

y

x 4 rt

hi A-A (three-hord) y

1 2 b

3

x

x rc

N

y 4 rt hi

A-A (four-chord)

Fig. 5.6 Curved trussed CFST hybrid structures in combined compression and bending, 1—chords in compression zone; 2—chords in tension zone; 3—webs; 4—cross-sectional center of gravity; L— Distance between the center points of sections at both ends; u0 —Initial deflection; hi —Distance along the cross-sectional height between the centroids of compression and the tension chords; b—Distance between the center points of chords out of the plane of bending moment; l 1 —Interval length; r c , r t —Distance between the cross-sectional center of gravity and centroidal axes for chords in compression zone and tension zone, respectively; α—Half of the projection angle of web on the plane of chord cross-section

5.2 Trussed Concrete-Filled Steel Tubular (CFST) Hybrid Structures

203

u0 initial deflection of the curved trussed CFST hybrid structure (mm), defined as the vertical distance between the centroid of the middle section and the connecting line for the centroids of end sections. For the curved trussed CFST hybrid structures in compression at both ends, the second-order effect of axial force on the mid-span segment is most significant; meanwhile, because the shear force has the greatest influence on the end joints, the shear force will also cause internal force in the chords. Therefore, it is necessary to verify the resistances of the chords in the middle and end sections. For structures with horizontal webs, if the shear force near the mid-span section is ignored, the chords are axially loaded, the same as the chords of the structures with diagonal webs. Therefore, the resistance of the structures may be verified in accordance with the axial force structures with the same structural length and interval width. The design value of axial compression force and bending moment of curved trussed CFST hybrid structures with identical CFST chords shall satisfy the following provisions: 1) The design values of the axial force and the bending moment of CFST chords of curved trussed CFST hybrid structures with identical chords should conform to the following requirements:  Ncd,1 =

N1t n1

0

(n 1 > 0) (n 1 = 0)

(5.2.1.32)

⎧ ⎨ N2t (n 2 > 0) n2 = ⎩ 0 (n 2 = 0)

(5.2.1.33)

N1t =

N u0 Nrt  +  h h 1 − NNE

(5.2.1.34)

N2t =

N u0 Nrc  −  h h 1 − NNE

(5.2.1.35)

Ncd,2

where, N Ncd,1 Ncd,2 N1t

design value of axial force in the curved structure (N), taken as positive in compression and negative in tension; design value of axial force for a single chord in compression zone of the curved structure (N); design value of axial force for a single chord in tension zone of the curved structure (N); design value of summation of axial forces of all chords in compression zone of the curved structure (N);

204

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

N2t

design value of summation of axial forces of all chords in tension zone of the curved structure (N); numbers of chords of curved trussed CFST hybrid structures in compressive and tension zones, respectively; distance between the centroids of chords (mm); Euler critical force calculated using equivalent slenderness ratio of the structure (N), shall be calculated by Eq. (5.2.1.28); distance between the cross-sectional center of gravity and centroidal axes for chords in compression zone and tension zone, respectively (mm); initial deflection of the curved trussed CFST hybrid structure (mm), defined as the vertical distance between the centroid of middle section and the connecting line for the centroids of end sections.

n1, n2 h NE rc , rt u0

2) When the curved trussed CFST hybrid structures with horizontal webs are under axial force, the design values of the axial force and the bending moment of the chords at the ends of the structures should be calculated in accordance with the following equations: N n

(5.2.1.36)

N u0 l1 π · · m b L 1 − NN E

(5.2.1.37)

Ncd = Mcd = where

N cd design value of axial force for a single chord at the ends of the curved structure (N); M cd design value of bending moment for a single chord at the ends of the curved structure (N·mm); design value of axial force for the curved structure (N); N n total number of chords; l1 interval length (mm); m parameter related to the number of chords, for two-chord, four-chord and sixchord structures, mb is 2, 4 and 6, respectively; for three-chord structure, mb is 4cosα, where α is half of the projection angle of web on the plane of chord cross-section; L distance between the centroids of two end sections of the curved structure (mm); u 0 initial deflection of the curved trussed CFST hybrid structure (mm), defined as the vertical distance between the centroid of middle section and the connecting line for the centroids of end sections. 3) The design value of the axial force for the end chords of axially loaded curved trussed CFST hybrid structures with diagonal webs should be calculated in accordance with the following equation:

5.2 Trussed Concrete-Filled Steel Tubular (CFST) Hybrid Structures

Ncd =

205

N 2π N u0 + · n L tan θ 1 − NN E

(5.2.1.38)

where, N cd design value of axial force for the end chord (N); θ angle between the diagonal web and the chord. Compared to straight trussed CFST hybrid structures, the loading condition of curved trussed CFST hybrid structures is more complex and the accurate internal force distributions shall be derived through a global structural analysis. (5) Resistance of web When the outside diameter of the webs is small or the number of webs is not sufficient, the webs of curved CFST structures may reach the resistance earlier than the chords, leading to premature failure of the structures. Therefore, it is necessary to verify the resistances of the webs. The shear force of straight trussed CFST hybrid structures in axial compression is jointly carried by the webs that are subjected to the shear force. The calculation is based on the relevant provisions of the current national standard GB 50017 Standard for Design of Steel Structures. It is assumed that the deflection curve of the curved trussed CFST hybrid structures is approximately a half-sine wave during the process of deflecting in compression at the ends, and the maximum shear forces at both ends are derived (Fig. 5.8). All webs are designed in accordance with the most unfavorable conditions (Fig. 5.7). The design of resistances of webs in trussed CFST hybrid structures shall conform to the relevant provisions of the current national standard GB 50017 Standard for Design of Steel Structures. When bearing axial force and the chords are identical, the load carried by the webs of the trussed CFST hybrid structures may be calculated in accordance with the following equations: 1) The shear force of webs in straight trussed CFST hybrid structures in axial compression at both ends may be calculated in accordance with the following equation: N

Fig. 5.7 Shear force distribution of the curved trussed CFST structure, 1—gravity axis

Vmax L/2

1

u0 L/2

z

N

x

Vmax

206

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

Construction load Place the core concrete in the steel tube and arrange the webs

(a) Hollow steel tube

Self-weight of concrete and construction load, etc. Install reinforcement

(b) CFST skeleton

Self-weight of reinforcement and construction load, etc.

Loads in the service stage

Place the concrete encasement

(c) CFST skeleton and external reinforcement

(d) Concrete-encased CFST hybrid structure

Fig. 5.8 Schematic diagram of construction process for concrete-encased CFST hybrid structure

V =

∑(Asc f sc ) 85

(5.2.1.39)

where, V summation of design values of shear force of all webs (N); f sc design value of axial compression strength of a single CFST chord (N/mm2 ), shall be calculated by Eq. (3.3.1) of this standard; Asc cross-sectional area of the compression chord (mm2 ). 2) When curved trussed CFST hybrid structures are subjected to axial compression force at both ends, the design value of maximum shear force in the webs may be calculated in accordance with the following equation: Vwm =

N u0 π · L 1 − NN E

(5.2.1.40)

where, V wm design value of maximum shear force in webs (N); distance between the center points of end sections of the curved trussed CFST L hybrid structure (mm), shown in Fig. 5.6; N design value of axial force (N); N E Euler critical force (N) calculated using the equivalent slenderness ratio of the structure, shall be calculated by Eq. (5.2.1.28); u0 initial deflection of the curved structure (mm), defined as the vertical distance between the centroid of middle section and the connecting line for the centroids of end sections, as shown in Fig. 5.6 3) When curved trussed CFST hybrid structures with horizontal webs are subjected to axial compression force at both ends, the design value of the maximum bending moment in the webs may be calculated in accordance with the following equation:

5.2 Trussed Concrete-Filled Steel Tubular (CFST) Hybrid Structures

Mwd =

l1 · Vwm mb

207

(5.2.1.41)

where, M wd design value of maximum bending moment in webs (N·mm); l1 interval length (mm); mb parameter related to the number of chords, for two-chord, four-chord and sixchord structures, mb is 2, 4 and 6, respectively; for three-chord structure, mb is 4cosα, where α is half of the projection angle of web on the plane of chord cross-section (Fig. 5.6) 4) When curved trussed CFST hybrid structures with diagonal webs are subjected to axial compression at both ends, the design value of the maximum axial force in the webs may be calculated in accordance with the following equation: Nwd =

1 · Vwm m sin θ

(5.2.1.42)

where, N wd design value of maximum axial force in webs (N); θ angle between the axis of the diagonal web and the axis of the chord; m parameter related to the number of chords, for two-chord, three-chord, fourchord and six-chord structures, m is 1, 2cosα, 2 and 3, respectively, where α is half of the projection angle of web on the plane of chord cross-section Fig. 5.6.

5.2.2 Shear Resistance According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the shear resistance of trussed CFST hybrid structures shall satisfy the following inequality: V ≤ Vu

(5.2.2.1)

where, V design value of shear force (N); V u shear resistance of the trussed CFST hybrid structure (N). The shear resistance of trussed CFST hybrid structures with horizontal webs shall be taken as the lesser of the resistances of webs subjected to flexural-shear failure and chords subjected to shear failure. In the case of flexural-shear failure of webs, the calculation of resistance of the webs shall conform to the relevant provisions of the current national standard GB 50017 Standard for Design of Steel Structures; in the

208

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

case of shear failure of chords, the shear resistance of structures may be calculated in accordance with the following equation: Vu = 0.9

∑

Vcu

(5.2.2.2)

where, Vcu shear resistance of a single CFST chord (N), should be calculated by Eq. (4.2.4.3). In Provision (5) in Sect. 5.2.1 of this book, the design value of shear force in the webs is provided, but it is only a shear value to limit the instability failure for a single chord of the structures; when bearing external shear force, the shear force of the webs shall be derived through a global structural analysis. For the trussed CFST hybrid structures with diagonal webs, the external shear force is mainly carried by the webs, and the shear resistance is determined by the resistances to compression and tension of the webs, rather than the shear resistance of the chords. The calculation of resistance of the webs shall conform to the relevant provisions of the current national standard GB 50017 Standard for Design of Steel Structures.

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid Structures The concrete-encased CFST hybrid structure consists of the built-in circular CFST part and concrete encasement. The single or multiple CFST chords are usually symmetric in concrete-encased CFST hybrid structure, as shown in Fig. 1.18. The concrete-encased CFST hybrid structure can be used as columns or arch structures, etc. Based on the experimental research and theoretical analysis, the damage mechanism and failure characteristics of the concrete-encased CFST hybrid structures to compression (tension), bending, torsion, shear, complex force, long-term load, cyclic load and impact load have been revealed, the calculation methods of structural resistance in complex force condition and long-term load are proposed, and the design methods of seismic and impact resistance are established, which provides the technical basis for the scientific design of concrete-encased CFST hybrid structure. Concrete-encased CFST hybrid structure shall conform to the following provisions: (1) The effective length of concrete-encased CFST hybrid structures shall conform to the relevant requirements of the current national standard GB 50010 Code for Design of Concrete Structures, and the radius of gyration should be calculated

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

209

as that for a composite cross-section. The global slenderness ratios of concreteencased CFST hybrid structures shall not be greater than 60. The global slenderness ratios of the concrete-encased CFST hybrid structures may be calculated in accordance with the methods for the corresponding reinforced concrete structures. In order to simplify the calculation, the contribution of the webs of the encased CFST members may be ignored. (2) During the construction stage of core concrete placement in the steel tube, the maximum compressive stress in the steel tube caused by the construction load shall not be greater than 35% of the corresponding critical stress value of the resistance of the hollow steel tube. (3) The thickness of the cover of the concrete encasement shall conform to the relevant requirements of the current national standard GB 50010 Code for Design of Concrete Structures. (4) The longitudinal reinforcement ratio of the concrete encasement shall be calculated in accordance with Eq. (5.2.2.2). It shall be determined based on the engineering types, and conform respectively to the relevant requirements of the current standards of the nation GB 50010 Code for Design of Concrete Structures, GB 50011 Code for Seismic Design of Buildings, GB 50111 Code for Seismic Design of Railway Engineering, or JTG/T 2231-01 Specifications for Seismic Design of Highway Bridges. ρ=

Al Aoc

(5.3.1)

where, ρ longitudinal reinforcement ratio; Al total cross-sectional area of the longitudinal reinforcement (mm2 ); Aoc cross-sectional area of the concrete encasement (mm2 ). The cross-sectional area of CFST members is excluded when calculating the longitudinal reinforcement ratio. Based on engineering experiences, the longitudinal reinforcement ratio of the concrete-encased CFST hybrid structures may be lower than that of conventional reinforced concrete structures. Therefore, the longitudinal reinforcement ratio may be controlled to be within 5%. In accordance with the current national standard GB 50011 Code for Seismic Design of Buildings, the minimum longitudinal reinforcement ratio is 0.5% for the seismic measure of Class IV; the minimum longitudinal reinforcement ratio of the reinforced concrete pier is 0.5% in accordance with the requirements of the current national standard GB 50111 Code for Seismic Design of Railway Engineering; the minimum longitudinal reinforcement ratio is 0.6% in accordance with the requirements of the current standard of the nation JTG/T 2231-01 Specifications for Seismic Design of Highway Bridges. When the CFST members take a relatively large portion of the whole crosssection, further special studies need to be conducted to determine the approximate longitudinal reinforcement ratio.

210

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

(5) Based on previous studies, the arrangement of stirrups in the concrete encasement shall conform to the relevant requirements of the current national standard GB 50010 Code for Design of Concrete Structures. In seismic design, the relevant requirements of the current standards of the nation GB 50011 Code for Seismic Design of Buildings and JTG/T 2231-01 Specifications for Seismic Design of Highway Bridges shall also be satisfied. (6) The outside dimensions and layout of steel webs in the concrete-encased CFST hybrid structures shall conform to the requirements of the cover thickness of the concrete encasement. (7) The resistance of concrete-encased CFST hybrid structures with more than six chords or other complicated situations may be determined through a global structural analysis. For example, fiber-based model can be used to analyze and calculate the resistance of the structure, where the corresponding models of steel and concrete given in Chap. 3 can be adopted. (8) For single-chord concrete-encased CFST hybrid structures, the ratio of the outside diameter of the CFST member (D) to the width of the structural crosssection (B), defined as outside diameter-to-sectional width ratio (D/B), should not be less than 0.5 and not be greater than 0.75; and for multiple-chord concreteencased CFST hybrid structures, the outside diameter-to-sectional width ratio (D/B) should not be less than 0.15 and not be greater than 0.25.

5.3.1 Load Characteristics Considering Effects of Whole Construction Process The concrete-encased CFST hybrid structures are affected by its self-weight, the sequence of construction and the load during the construction process, initial stress may occur in the inner steel tube, core concrete and outer reinforced concrete, which may affect the magnitude and distribution of the stress of each component in the cross-section. The construction process of concrete-encased CFST hybrid structure can be generally divided into the following processes: (1) Install the skeleton of the steel tube; (2) Place the core concrete in the steel tube to form the CFST skeleton; (3) Construct the concrete encasement outside the CFST. The sequence of concrete placement can be divided into two types. One is stepby-step pouring, that is, after completing the construction of the CFST structure, install the reinforcement and place the concrete encasement. The other is to place the core concrete and concrete encasement at the same time after the installation of reinforcement. Thus, the concrete-encased CFST hybrid structures stiffened mixed structure is formed after the construction of concrete encasement. In this process, the safety of the structure during the “two-stage” must be ensured, that is, (1) the construction stage: the safety of steel tube skeleton and CFST skeleton under the action of construction load and self-weight of structure; (2) serviceability stage:

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

211

the safety of the concrete-encased CFST hybrid structure under the loads in the serviceability stage such as self-weight, service load and hazardous load. The concrete-encased CFST hybrid structures will be affected by the construction load, which not only occurs during the construction process, but also during the service life. Because of the strong nonlinearity of the concrete material and the confinement effect of the steel tube and the reinforcement on the concrete, the shrinkage and creep performance of the concrete under long-term loading can be improved; the reinforcement and the steel tube are generally in the linear elastic stage during the service stage, and the constitutive model of concrete is less affected by the long-term loading. However, the shrinkage and creep of the concrete make part of the load transfer to the reinforcement and the steel tube, which further increases the deformation of the reinforcement and steel tube in the service stage. Concrete-encased CFST hybrid structure consists of steel and concrete materials, the concrete material is divided into three regions according to the degree of confinement (as shown in Fig. 3.8), that is, core concrete inside the steel tube, confined concrete outside the steel tube and inside the stirrups, and unconfined concrete outside the stirrups. Therefore, quantitative analysis of the mechanical performance of the concrete-encased CFST hybrid structure during the whole construction process is particularly complicated. Taking the concrete-encased CFST hybrid structure to axial compression load as an example, the loading process can be summarized as follows: (1) Install the hollow steel tube and place core concrete (Fig. 5.8a). The steel tube is subjected to self-weight, construction load and weight of wet core concrete. At this stage, initial stress will be generated in the steel tube, so the stability of the steel tube structure should be verified. (2) After the initial setting of the core concrete, the CFST skeleton structure is formed, which jointly bears the loads generated during the construction of the concrete encasement (Fig. 5.8b, c). The stability of the CFST skeleton structure should be verified in this stage. (3) After placing the concrete encasement, the concrete-encased CFST hybrid structure is formed, where the built-in CFST part and the concrete encasement part are jointly subjected to loads in the service stage (Fig. 5.8d). Figure 5.9 shows a comparison of the axial compression load (N)-axial compression strain (ε)-time (t) relationship considering the whole construction process and the effect of long-term load. In the figure, the curve OABCDEF is the case of the effect of the whole construction process and long-term loading: (1) OA stage: the structure is subjected to the action of self-weight and service load, and is generally in the elastic stage. (2) AB stage: In the service stage, the loads borne by the structure keep unchanged, but the longitudinal strain gradually increases with the duration of load holding time (t). Due to the time-varying characteristics of the concrete material and the influence of the confinement by the steel tube, the shrinkage and creep strains increase nonlinearly during the load-holding stage, and the increasing is faster during 90d load-holding, and it gradually decreases thereafter;

212

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures N C' (0,Nu,εu)C'' (0,Nul,εul)

The loading path Nu Nul without the consideration of the whole construction The loading path with the consideration of the whole construction process

D'(0,N'u,ε'u) D''(0,N'ul,ε'ul) E''(0,N'ul,ε''ul) E' (0,N'u,ε''u) F' F'' C (tl,Nul,εul)

O'(0,Nl,0)

A (0,Nl,ε0)

ε'

B'' (0,Nl,εl) D (tl,N'ul,ε'ul)

E(tl,N'ul,ε''ul) F

(tl,Nl,0)

B(tl,Nl,εl)

t' O (0,0,0)

tl

(tl,0,εl)

εl

εu

εul

ε'ul

ε''ul

ε

(tl,0,εul) (tl,0,ε'ul) (tl,0,ε''ul)

t

Fig. 5.9 Axial compression load (N)-axial compressive strain (ε)-holding time (t) path. N—Axial compression load; ε—Axial compressive strain; εl —Axial compressive strain of the structure in service stage; εu —Axial compressive strain corresponding to the structural resistance without the consideration of the whole construction process and long-term load effects; ε ul —Axial compressive strain corresponding to the structural resistance with the consideration of the whole construction process and long-term load effects; t—Holding time; t 1 —Load-holding time of the structure in normal use stage; N l —The self-weight and service load of the structure; N u —The resistance of the structure without the consideration of the whole construction process and long-term load effects; N ul —The resistance of the structure with the consideration of the whole construction process and long-term load effects

(3) BCDEF stage: In the failure stage, the load gradually increases until it reaches the structural resistance (point C). After that, due to the collapse of the concrete encasement and the buckling of the longitudinal reinforcement, the concrete encasement gradually loses the resistance, so the resistance of the structure enters descending stage (CD stage). After declining to point D, the structural resistance is mainly contributed by the inner CFST part, then the platform stage (DE) is formed; with the failure of the CFST part, the resistance of the structure further decreases and the final failure occurs (point F). In Fig. 5.9, the curves OAC' D' E' F' are the cases without considering the whole construction process or long-term load effects. It can be found by comparison, that the resistance (N ul ) and structural stiffness of concrete-encased CFST hybrid structure are reduced after considering the whole construction process and long-term load. When the age of concrete at loading is short (e.g., the curing time of core concrete is less than 7 d), the effects of the whole construction process and long-term load are

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

213

more significant, resulting in greater creep deformation and thus a more significant reduction in stiffness during the service stage. Therefore, the influence of the whole construction process and long-term load cannot be ignored in the design of the concrete-encased CFST hybrid structure. Realize the fine simulation and analysis of the concrete-encased CFST hybrid structure considering the influence of the whole construction process, and obtaining the calculation results which can provide a quantitative basis for the construction design and operation and maintenance, are the key techniques to ensuring life-cycle safety during the whole construction process and full-range loading.

5.3.2 Design of Single-Chord Structures for Compression and Bending Figure 1.18a schematically shows the cross-section of the single-chord concreteencased CFST hybrid structure. (1) Axial compression performance Figure 5.10 shows a schematic diagram of the typical failure mode of single-chord concrete-encased CFST hybrid structure to axial compression. At the middle of the length of the members, the bulge of reinforced concrete encasement and embedded circular CFST member, the buckling of longitudinal reinforcement occur, but the external bulging of embedded circular CFST member is not as significant as the reinforced concrete encasement. Figure 5.11 shows the typical axial force (N)-axial strain (ε) relationship curve and the distribution of internal forces of each member for a single-chord concreteencased CFST hybrid structure. The whole curve can be divided into five stages according to five characteristic points, which are: point A, the steel tube starts to enter the elasto-plastic stage; point B, the unconfined concrete outside the stirrups

(a) Concrete encasement (b) Reinforcement

(c) Steel tube

(d) Core concrete

Fig. 5.10 Failure modes of concrete-encased CFST hybrid structure to axial compression

214 Fig. 5.11 Axial force (N)-axial strain (ε) relationship of concrete-encased CFST hybrid structure

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures Whole section Unconfined concrete Stirrup-confined concrete Core concrete Steel tube Longitudinal reinforcement

Ν (kN) 10000 B

8000

C D

A

6000

E

4000 2000 0 0

2000

4000

6000

8000 ε (με)

reaches its strength; point C, the whole section reaches the ultimate load (N u ); point D, the calculations are stopped because the axial force enters a plateau stage. (2) Performance in combined compression and bending There are two main failure types of the single-chord concrete-encased CFST hybrid structure subjected to combined compression and bending, which are small eccentric compression and large eccentric compression. When large eccentric compression failure occurs, the reinforced concrete encasement collapses and the tensile edge fibers of the steel tube yield. When small eccentric compression failure occurs, the reinforced concrete encasement collapses and the tensile edge fibers do not yield. For the single-chord concrete-encased CFST hybrid structure with small eccentric compression failure, cracks start to occur in the tension zone of concrete concentrated in the middle area when the axial force is close to the ultimate load (N u ), as shown in Fig. 5.12a. For the single-chord concrete-encased CFST hybrid structure with large eccentric compression failure, cracks start to appear in the tension zone of the concrete when the axial force reaches about 0.2N u , and the distribution range of cracks is larger than that of the small eccentric compression failure, but the range of concrete collapse in the compression zone is smaller than that of the small eccentric compression failure, as shown in Fig. 5.12b. As shown in Fig. 5.13, the N/N u -M/M u correlation for single-chord concreteencased CFST hybrid structure can be generally divided into two stages: 1) when small eccentric compression failure occurs, M/M u increases with decreasing N/N u ; 2) when large eccentric compression occurs, M/M u decreases with decreasing N/ N u . When comparing the N/N u -M/M u correlation curves of single-chord concreteencased CFST hybrid structure to that of reinforced concrete structures, the shapes of both are consistent, but the N b /N u and M b /M u of the single-chord concreteencased CFST hybrid structure are smaller than those of the corresponding reinforced concrete structure at the critical failure.

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

Steel tube

Steel tube

Longitudinal reinforcement

Longitudinal reinforcement

Concrete cracking

Concrete cracking

Concrete crushing

(a) Small eccentric compression

215

Concrete crushing

(b) Large eccentric compression

Fig. 5.12 Failure mode of concrete-encased CFST hybrid structure in combined compression and bending N/Nu

Concrete-encased CFST hybrid structure

1.0

Reinforced concrete structure

Nb/Nu Nb/Nu

Small eccentric compression failure Critical failure Large eccentric compression failure

O

1.0

Mb/Mu

Mb/Mu

M/Mu

Fig. 5.13 N/N u -M/M u relationship of the concrete-encased CFST hybrid structure, N—Compressive resistance of member to combined compression and bending; M—The bending moment corresponding to N (=N(e + um ), where e is initial eccentricity, and um is the mid-span deflection of the member when N is reached); N u —Resistance in axial compression; M u —Bending resistance; N b —Compressive resistance of member to combined compression and bending in case of critical failure; M b —The bending moment corresponding to N b in case of critical failure.

(3) Bending performance The typical failure mode of single-chord concrete-encased CFST hybrid structure is a flexural failure, and the concrete cracks are mainly vertical flexural cracks. Figure 5.14 gives the typical bending moment (M)-curvature (φ) relationship for single-chord concrete-encased CFST hybrid structure, which can be divided into three stages in general: 1) Elastic stage (OA). At this stage, the member is in the elastic stage, the concrete encasement starts to show obvious vertical flexural cracks at point A, and the stiffness of the member starts to decrease.

216

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

M C B

A

D

E

Point A：Concrete encasement cracks Point B：The tensile longitudinal reinforcement yields Point C：The tensile edge of steel tube yields Point D：The compressive edge of steel tube yields Point E：Strain at the tensile edge of steel tube reaches 0.01

O

φ

Fig. 5.14 Typical bending moment(M)-curvature(φ) relationship of the single-chord concreteencased CFST hybrid structure

2) Elasto-plastic stage (ABC). At point B, the tensile longitudinal reinforcement yields, and the stiffness of the member is further reduced; the tensile edge of the steel tube begins to yield near point C. 3) Plastic stage (CDE). At point D, the compressive edge of the steel tube starts to yield. At point E, the strain at the tensile edge of the steel tube reaches 0.01, and the bending moment is generally unchanged, so the bending moment corresponding to point E is taken as the ultimate bending moment of the single-chord concrete-encased CFST hybrid structure. (4) Axial tension performance Figure 5.15 shows the typical failure modes of CFST members, reinforced concrete members and the concrete-encased CFST hybrid structure to axial tension. Tensile failure for concrete-encased CFST hybrid structure is as cracking of external concrete by full section, steel tube cracking in tension and concrete encasement cracking in tension. Compared with reinforced concrete members, the concrete-encased CFST hybrid structure has a more uniform distribution of concrete cracks. The tensile failures phenomena of concrete-encased CFST hybrid structure include the tensile cracking of the full cross-section of concrete encasement, the tensile cracking of the steel tube and the tensile cracking of concrete encasement. Compared with reinforced concrete members, concrete cracks of the concreteencased CFST hybrid structure are more evenly distributed. Figure 5.16 shows the measured tensile load (N)-strain (ε) relationship for the concrete-encased CFST hybrid structure specimens. It can be seen that the tensile resistance of concrete-encased CFST hybrid structure (cecfst) specimen is significantly higher than that of concrete-filled steel tubular specimens (cfst) and reinforced concrete specimens (rc). (5) Calculation of resistances

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

(a) Plain concrete structure

(c) Reinforced concrete structure

(b) CFST structure

217

(d) Concreteencased CFST hybrid structure

Fig. 5.15 Failure modes of the structures to axial tension N (kN)

N (kN) cecfst-2b-2

cecfst-2b-1

rc-2

cecfst-2b-2

cfst-1

cfst-2 ε (με)

ε (με) (a) Comparison with reinforced concrete structure

(b) Comparison with CFST member

Fig. 5.16 Tensile load (N)-strain (ε) relationship

The following provisions are given by GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures: 1) The resistance of cross-section of single-chord concrete-encased CFST hybrid structures to compression shall satisfy the inequality in Eq. (5.3.1) and should be calculated in accordance with Eq. (5.3.2.1): N ≤ N0

(5.3.2.1)

N0 = 0.9(Nrc + Ncfst )

(5.3.2.2)

Nrc = f c,oc Aoc + fl' Al

(5.3.2.3)

Ncfst = f sc Asc

(5.3.2.4)

218

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

where, N N0 N cfst N rc f c,oc Aoc fl' Al f sc Asc

design value of axial compression in the cross-section of the concrete-encased CFST hybrid structure (N); resistance of cross-section of the concrete-encased CFST hybrid structure to compression (N); resistance of cross-section of the encased CFST member to compression (N); resistance of cross-section of the concrete encasement to compression (N); design value of compressive strength of the concrete encasement (N/mm2 ); cross-sectional area of the concrete encasement (mm2 ); design value of compressive strength of the longitudinal reinforcement (N/ mm2 ); cross-sectional area of the longitudinal reinforcement (mm2 ); design value of compressive strength of encased CFST cross-section (N/mm2 ), shall be calculated by Eq. (3.3.1) of this standard; cross-sectional area of the encased CFST member (mm2 ).

2) When the neutral axis is located within the height of the cross-section, the resistance of cross-section of single-chord concrete-encased CFST hybrid structures to combined compression and bending shall satisfy the following inequalities: ' N ≤ Nrc' + Ncfst

(5.3.2.5)

M ≤ Mrc + Mcfst

(5.3.2.6)

where, N M Nrc' M rc ' Ncfst

M cfst

design value of axial compression in the cross-section of the concrete-encased CFST hybrid structure (N); design value of bending moment in the cross-section of the concrete-encased CFST hybrid structure (N·mm); compression resistance of cross-section of the concrete encasement to combined compression and bending (N); bending resistance of cross-section of the concrete encasement to combined compression and bending (N·mm); compression resistance of cross-section of the encased CFST member to combined compression and bending (N); bending resistance of cross-section of the encased CFST member to combined compression and bending (N·mm).

The assumptions for the resistance of cross-section to combined compression and bending include: (a) The plane section remains plane after deformation; (b) the ultimate compressive strain of the concrete in the normal section is εcu , and when the strength class of concrete is not   higher than C50, it is set as 0.0033; otherwise, it is set as 0.0033 − f cu,oc − 50 × 10−5 , where f cu,oc is the characteristic value

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

219

of cube strength of the concrete encasement (N/mm2 ); (c) the tensile strength of concrete is neglected; (d) the ultimate strain of the longitudinal reinforcement and the steel tube shall not be greater than 0.01, and (e) the stresses of the longitudinal reinforcement and the steel tube is taken as the products of corresponding strains and elastic modulus, and shall satisfy the following inequalities: |σl | ≤ fl

(5.3.2.7)

|σs | ≤ f

(5.3.2.8)

where, σl σs f fl

stresses of the longitudinal reinforcement (N/mm2 ); stresses of the steel tube (N/mm2 ); design value of tensile, compressive and flexural strength of steel (N/mm2 ); design value of tensile strength of the longitudinal reinforcement (N/mm2 ).

3) The resistance of cross-section of the concrete encasement of single-chord concrete-encased CFST hybrid structures (Fig. 5.17) to compression and the corresponding bending resistance of the cross-section should conform to the following equations: Nrc' = α1 f c,oc Ae,oc + Mrc = α1 f c,oc Ae,oc

∑

σli Ali

(5.3.2.9)

∑

H H σli Ali − xe,oc + − xli 2 2

(5.3.2.10)

c − xli c

(5.3.2.11)

σli = E s εcu

|σli | ≤ fl

(5.3.2.12)

where Nrc' Mrc Ae,oc

Al i εcu

compression resistance of cross-section of the concrete encasement to combined compression and bending (N); bending resistance of cross-section of the concrete encasement to combined compression and bending (N·mm); area of equivalent stress block of concrete encasement (mm2 ), the height of the equivalent stress block is β 1 c, β 1 is the height coefficient of equivalent stress block for concrete encasement, set as 0.80 when strength class of concrete is not higher than C50; 0.74 for C80; calculated by linear interpolation for concrete between C50 and C80; cross-sectional area of the i-th longitudinal reinforcement (mm2 ); ultimate compressive strain of concrete at the compressive edge;

0.5D

0.5D

Ae,oc

0.3D

β1c

(H-D)/2 H

D

B B-D

0.3D

(H-D)/2

H

D

B (B-D)/2 0.3D 0.4D 0.3D (B-D)/2

(H-D)/2

H

B

D

(H-D)/2

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

0.3D 0.4D 0.3D

220

(a) Section simplification α1fc,ocAe,oc N'l

xli

εli

c

εcu

1

Mrc N'rc 2

εli

(b) Strain distribution

Nl

(c) Force equilibrium

Fig. 5.17 Resistance of cross-section of the concrete encasement, 1—Neutral axis; 2—Centroidal axis; B—Cross-sectional width; c—Distance between the neutral axis and the compressive edge of the cross-section; H—Cross-sectional height; N l —Axial force of longitudinal reinforcement in tension zone; N’l —Axial force of longitudinal reinforcement in compression zone; Eli —Strain of the i-th longitudinal reinforcement; εcu —Ultimate compressive strain of concrete

c x e,oc x li σli fl α1

distance between the neutral axis and the compressive edge of the cross-section (mm); distance between the compressive edge and the centroid of the equivalent stress block of the concrete encasement (mm); distance between the i-th longitudinal reinforcement and the compressive edge of the cross-section (mm); stress of the i-th longitudinal reinforcement (N/mm2 ), taken as positive in compression and negative in tension; design value of tensile strength of the longitudinal reinforcement (N/mm2 ); strength coefficient of the equivalent stress block for concrete encasement, set as 1.0 when strength class of concrete is not higher than C50; 0.94 for C80; calculated by linear interpolation for concrete between C50 and C80.

In calculation, the compressive stress may be defined as positive, and the tensile stress as negative. The sign of the longitudinal reinforcement stress may be determined by its position. 4) The resistance of cross-section of the CFST member in single-chord concreteencased CFST hybrid structures to compression and the corresponding bending

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

221

resistance of the cross-section should be calculated in accordance with the following equations: ' Ncfst = Nc' + Ns'

(5.3.2.13)

Mcfst = Mc + Ms

(5.3.2.14)

where, ' Ncfst compression resistance of cross-section of the encased CFST member to combined compression and bending (N); M cfst bending resistance of cross-section of the encased CFST member to combined compression and bending (N·mm); Nc' compression resistance of cross-section of the core concrete in the CFST member to combined compression and bending (N); Mc bending resistance of cross-section of the core concrete in the CFST member to combined compression and bending (N·mm); Ns' compression resistance of cross-section of the steel tube in the CFST member to combined compression and bending (N); Ms bending resistance of cross-section of the steel tube in the CFST member to combined compression and bending (N·mm).

(a) The resistance of cross-section of the core concrete in the CFST member to compression and the corresponding bending resistance should be calculated in accordance with the following equations (Fig. 5.18; Tables 5.1 and 5.2):

Mc = αco Ac,c σe,c (0.5H − xe,c )

(5.3.2.16)

−Di ) 0.12 c−0.5(H + 0.73 [0.5(H − Di ) ≤ c < 0.5(H + Di )] Di −c −0.3 HH−D + 1 [0.5(H + Di ) ≤ c ≤ H ] i (5.3.2.17)

Fig. 5.18 Resistance of cross-section of the core concrete in the CFST member, 1—neutral axis; 2—point A.

B

1

εcu Ac,c

2

εe,c Di

1

xe,c c

αco =

(5.3.2.15)

H



Nc' = αco Ac,c σe,c

222

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

Table 5.1 Peak uniaxial compressive stress (σ o ) of core concrete in the CFST member (N/mm2 ) Strength class of concrete

Confinement factor ξ 0.6

1.0

1.5

2.0

2.5

3.0

3.5

4.0

C30

20.9

23.1

25.4

27.1

28.5

29.4

29.8

29.8

C40

28.1

30.6

33.4

35.5

37.1

38.1

38.6

38.6

C50

34.4

37.2

40.3

42.7

44.5

45.7

46.3

46.3

C60

42.1

45.4

48.9

51.6

53.6

54.9

55.6

55.6

C70

49.1

52.6

56.4

59.4

61.6

63.1

63.8

63.8

C80

56.8

60.7

64.8

68.1

70.4

72.1

72.8

72.8

Note Intermediate values in the table are obtained by linear interpolation

Table 5.2 Peak uniaxial compressive strain (εo ) of core concrete in the CFST member (με) Strength class of concrete

Confinement factor ξ 0.6

1.0

1.5

2.0

2.5

3.0

3.5

4.0

C30

2900

3000

3100

3200

3300

3300

3400

3500

C40

3200

3400

3600

3700

3800

3800

3900

4000

C50

3600

3800

3900

4100

4200

4300

4300

4400

C60

4000

4200

4400

4600

4700

4800

4900

5000

C70

4400

4700

4900

5000

5200

5300

5400

5500

C80

4800

5100

5400

5500

5700

5800

5900

6000

Note Intermediate values in the table are obtained by linear interpolation



εe,c 2 σe,c εe,c − =2 σo εo εo

(5.3.2.18)

c − xe,c (5.3.2.19) c

⎧ c − 0.5H + 0.5Di ⎪ ⎪ −0.04 + 0.46 ⎪ ⎪ Di ⎨ [0.5(H − Di ) ≤ c < 0.5(H + Di )] H − Di = ) + (c − 0.5H + 0.5D i ⎪ ⎪ 2   ⎪ ⎪ ⎩ −0.16 H −c + 0.5 D + H −Di [0.5(H + Di ) ≤ c ≤ H ] i H −Di 2 εe,c = εcu

xe,c

(5.3.2.20) where, Nc' Mc

compression resistance of cross-section of the core concrete in the CFST member to combined compression and bending (N); bending resistance of cross-section of the core concrete in the CFST member to combined compression and bending (N·mm);

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

223

Ac,c compressive cross-sectional area of the core concrete in the CFST member (mm2 ), 0 ≤ Ac,c ≤ Ac ; σ e,c fiber stress of concrete at equivalent point A (N/mm2 ), σ e,c ≤ σ o ; x e,c distance between the equivalent point A in the compressive area and the compressive edge of the cross-section (mm) (Fig. 5.18); αco height coefficient of the compressive area; Di diameter of the core concrete in the CFST member (mm); εe,c fiber strain of concrete at the equivalent point A; εcu ultimate compressive strain of concrete at the compressive edge; σ o peak uniaxial stress of the core concrete (N/mm2 ), shall be determined with Table 5.1; εo peak uniaxial compressive strain of the core concrete, shall be determined with Table 5.2. (b) The resistance of cross-section of the steel tube to compression and the corresponding bending resistance should be calculated in accordance with the following equations: Ns' = kl f As

(5.3.2.21)

Ms = k 2 f A s D

(5.3.2.22)

⎧ D c 2 c D ⎪ ⎪ (2.8 − 4.2)( ) − 7.9 − 4.6 ⎪  ⎪ H H H  ⎨

0.38H 0.5 ≤ Hc ≤ 1 345 D k1 = +(1.6 − 2.9) ⎪ ⎪ ⎪ H ⎪   fy c  ⎩ −3.0 HD + 4.6 Hc + 1.5 HD − 2.3 < 0.5 H  c 2 c k2 = m 1 + m2 + m3 H H   2   −5.3 HD + 6.7 HD − 1.8 0.5 ≤ Hc ≤1  m1 =  2 c < 0.5 −22.2 HD + 29.4 HD − 12 H   2   9.1 HD − 11.8 HD + 0.6 345 + 2.3 0.5 ≤ c ≤ 1 fy H   m2 =  2 c < 0.5 13.7 HD − 19.4 HD − 0.76 345 + 9.7 H fy  m3 =

 2   −3.9 HD + 5.3 HD − 0.46 345 − 0.7 0.5 ≤ c ≤ 1 fy H    2 c < 0.5 −2.1 HD + 3.5 HD + 0.22 345 − 1.9 H fy

(5.3.2.23)

(5.3.2.24)

(5.3.2.25)

(5.3.2.26)

(5.3.2.27)

where: Ns'

compression resistance of cross-section of the steel tube in the CFST member to combined compression and bending (N);

224

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

Ms

bending resistance of cross-section of the steel tube in the CFST member to combined compression and bending (N·mm); calculation coefficients, for k 1 , taken as 1.0 when it is greater than 1.0, and −1.0 when it is less than −1.0; for k 2 , taken as 0 when it is less than 0; cross-sectional area of the steel tube (mm2 ); design value of tensile, compressive and flexural strength of the steel tube (N/mm2 ); yield strength of the steel tube (N/mm2 ).

k1, k2 As f fy

5) When the neutral axis is located beyond the cross-sectional height, the bending resistance of cross-section of single-chord concrete-encased CFST hybrid structures to combined compression and bending shall satisfy the inequality in the following equations: M ≤ Mu,N Mu,N =

N0 − N Mu,H N0 − Nu,H

(5.3.2.28) (5.3.2.29)

where, M u,N bending resistance of cross-section taking into account axial compression N (N·mm); N u,H compression resistance of cross-section when the distance c between the neutral axis and the compressive edge is equal to the sectional height H (N), shall be calculated in accordance with Eqs. (5.3.2.25) and (5.3.2.26); M u,H bending resistance of cross-section when the distance c between the neutral axis and the compressive edge is equal to the sectional height H (N·mm), shall be calculated in accordance with Eqs. (5.3.2.25) and (5.3.2.26); N0 resistance of cross-section to compression (N), shall be calculated by Eq. (5.3.2.22). The equivalent compressive area method is applied in accordance with the current national standard GB 50010 Code for Design of Concrete Structures. The internal force and bending moment contributions of the steel tube and the core concrete are analyzed, and the distance between the equivalent point A and the compressive edge of the cross-section, the height coefficient of the compressive area, and the coefficient for the steel tube, are determined based on the mechanical analysis to simplify the calculation. The variable c can be calculated based on the assumption that the resistance of the equivalent compressive area is equal to the design value of the axial force. Then the calculations are classified into two conditions: c ≤ H, and c > H, in accordance with the location of the neutral axis. For the first condition (c ≤ H), the resistance of cross-section of concrete-encased CFST hybrid structures to combined compression and bending can be calculated

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

225

N

Fig. 5.19 N-M relationship

Nu

c>H (Mu,H,Nu,H), c=H c H), to simplify the calculation, the segment where c > H in the N-M relationship (Fig. 5.19) is assumed as a straight line. 6) Tensile strength of the cross-section of the concrete encasement may be neglected in calculating the resistance of cross-section of single-chord concrete-encased CFST hybrid structures to tension. The resistance is calculated as the summation of those of the CFST cross-section and the longitudinal reinforcement. The following requirement shall be satisfied: N ≤ Nrc,t + Ncfst,t

(5.3.2.30)

Nrc,t = fl Al

(5.3.2.31)

Ncfst,t = (1.1−0.4αs ) As f

(5.3.2.32)

where. N N rc,t N cfst,t Al As

design value of axial tension in the cross-section of the concrete-encased CFST hybrid structure (N); resistance of cross-section of the concrete encasement to tension (N); resistance of cross-section of the encased CFST member to tension (N); cross-sectional area of the longitudinal reinforcement (mm2 ); cross-sectional area of the steel tube (mm2 );

226

αs fl f

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

cross-sectional steel ratio of the CFST member, shall be calculated by Eq. (1.3.2) of this standard; design value of tensile strength of the longitudinal reinforcement (N/mm2 ); design value of tensile strength of the steel tube (N/mm2 ).

5.3.3 Design of Four-Chord Structures for Compression and Bending The cross-sectional illustration of the four-chord concrete-encased CFST hybrid structure is shown in Fig. 1.18b. The failure mode of the four-chord concrete-encased CFST hybrid structure to axial compression generally shows the crush and scaling of the concrete encasement (shown in Fig. 5.20a), which is similar to that of reinforced concrete specimens (shown in Fig. 5.20b). The failure mode of the internal hollow shows that the crush of concrete in the middle part, while the other parts are intact. In the spalling part of the concrete encasement, the steel tube bends, while the core concrete remains intact due to the restraint of the steel tube. The longitudinal deformation of concrete, longitudinal reinforcement and steel tube are coordinated during the full-range loading process. The buckling of steel tube occurs at the scaling position of concrete encasement, while the core concrete remains intact due to the confinement of steel tubes. The longitudinal deformation of concrete, longitudinal reinforcement and steel tubes was coordinated and consistent during the whole process of stress. The failure mode of concrete-encased CFST hybrid structure to combined compression and bending shows flexural cracks and crushing of concrete, as shown in Fig. 5.21. Significant bending deformation occurs in the inner CFST, but due to the confinement of the encased concrete and the support of core concrete, local buckling

Hollow part

(a) Concrete-encased CFST hybrid structure

(b) Reinforced concrete structure

Fig. 5.20 Failure mode of the structures in axial compression

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

227

does not occur in the steel tube; due to the confinement of the steel tube, the core concrete is in a confining pressure state. The core concrete remains intact until the failure occurs, and the inner CFST and the concrete encasement can keep working together. The following provisions are given by GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures: (1) The resistance of cross-section of four-chord concrete-encased CFST hybrid structures to compression is calculated as the summation of the resistances of the cross-sections of encased CFST members and concrete encasement, which shall satisfy the inequality in Eq. (5.3.3.1), and should be calculated in accordance with Eq. (5.3.3.2). The calculating assumptions for the resistance of four-chord structures are the same as that of single-chord structures. N ≤ N0

(5.3.3.1)

N0 = 0.9(Nrc + Ncfst )

(5.3.3.2)

Nrc = f c,oc Aoc + fl' Al

(5.3.3.3)

Ncfst =

∑

f sc,i Asc,i

(5.3.3.4)

where, N N0 N rc N cfst f c,oc Aoc

design value of axial compression in the cross-section of the concrete-encased CFST hybrid structure (N); resistance of cross-section of the concrete-encased CFST hybrid structure to compression (N); resistance of concrete encasement to compression (N); resistance of cross-sections of encased CFST members to compression (N); design value of compressive strength of the concrete encasement (N/mm2 ); cross-sectional area of the concrete encasement (mm2 );

(a) Concrete encasement crushes

(b) Steel tube

(c) Core concrete of embedded CFST

Fig. 5.21 Failure mode of the member to combined compression and bending

228

fl' Al f sc,i Asc,i

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

design value of compressive strength of the longitudinal reinforcement (N/ mm2 ); cross-sectional area of the longitudinal reinforcement (mm2 ); design value of compressive strength of cross-section of the i-th CFST member (N/mm2 ); cross-sectional area of the i-th CFST member (mm2 ).

(2) When the neutral axis is located within the height of the cross-section, the resistance of cross-section of four-chord concrete-encased CFST hybrid structures to combined compression and bending shall satisfy the following inequalities ' N ≤ Nrc' + Ncfst

(5.3.3.5)

M ≤ Mrc + Mcfst

(5.3.3.6)

where, N M Nrc' ' Ncfst

M rc M cfst

design value of axial compression in the cross-section of the concrete-encased CFST hybrid structure (N); design value of bending moment in the cross-section of the concrete-encased CFST hybrid structure (N·mm); compression resistance of cross-section of the concrete encasement to combined compression and bending (N); compression resistance of cross-sections of encased CFST members to combined compression and bending (N); bending resistance of cross-section of the concrete encasement to combined compression and bending (N·mm); bending resistance of cross-sections of encased CFST members to combined compression and bending (N·mm).

The calculating assumptions for four-chord structures for compression and bending are the same as that (5) in Sect. 5.3.2 of this book. (3) The resistance of cross-section of the concrete encasement in four-chord concrete-encased CFST hybrid structures (Fig. 5.22) to compression and the corresponding bending resistance of the cross-section should be calculated in accordance with the following equations: ∑ Nrc' = α1 f c,oc Ae,oc + σli Ali (5.3.3.7) Mrc = α1 f c,oc Ae,oc

∑

H H σli Ali − xe,oc + − xli 2 2

(5.3.3.8)

c − xli c

(5.3.3.9)

σli = E s εcu

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

tc

ac

B B-2D

D 2ac

H H-2tc

2tc

ac tc-ac

tc

tc

H H-2tc

H H-2tc

tc

B D B-2ac-2D D

ac

D

Ae,oc H-2(ac+D) βlc

tc

tc-ac ac

B B-2tc

D ac

tc

229

(a) Section simplification

εcu

α1fc,ocAe,oc c

N'l

xli

1

εli

Mrc N'rc

2 Nl

(b) Strain distribution

(c) Force equilibrium

Fig. 5.22 Resistance of cross-section of the concrete encasement, 1—neutral axis; 2—centroidal axis; B—Cross-sectional width; c—Distance between the neutral axis and the compressive edge of the cross-section; H—Cross-sectional height; N l —Axial force of longitudinal reinforcement in tension zone; N’l —Axial force of longitudinal reinforcement in compression zone; t c —Distance between the edge of the internal hollow section and the outside edge of the concrete encasement; ac —Distance between the outside edge of the steel tube and the outside edge of the concrete encasement; Eli —Strain of the i-th longitudinal reinforcement; εcu —Ultimate compressive strain of concrete

|σli | ≤ fl

(5.3.3.10)

where, Nrc' Mrc Ae,oc

Ali εcu c

compression resistance of cross-section of the concrete encasement to combined compression and bending (N); bending resistance of cross-section of the concrete encasement to combined compression and bending (N·mm); area of equivalent stress block of concrete encasement (mm2 ), the height of the equivalent stress block is β 1 c, β 1 is the height coefficient of equivalent stress block for concrete encasement, set as 0.80 when strength class of concrete is not higher than C50; 0.74 for C80; calculated by linear interpolation for concrete between C50 and C80; cross-sectional area of the i-th longitudinal reinforcement (mm2 ); ultimate compressive strain of concrete at the compressive edge; distance between the neutral axis and the compressive edge of the cross-section (mm);

εcu εs1

xs1

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

Ns1

c

230

Ms N's

xs2

1

εs2

(a) Strain distribution

2 Ns2

(b) Force equilibrium

Fig. 5.23 Resistance of cross-sections of steel tubes, 1—neutral axis; 2—centroidal axis; N s1 — Axial force of steel tubes close to the compressive edge; N s2 —Axial force of steel tubes away from the compressive edge; εsl —Strain of the centroid of steel tubes close to the compressive edge; εs2 — Strain of the centroid of steel tubes away from the compressive edge; ε cu —Ultimate compressive strain of concrete

xe,oc distance between the compressive edge and the centroid of the equivalent stress block of the concrete encasement (mm); distance between the centroid of the i-th longitudinal reinforcement and the x li compressive edge of cross-section (mm); stress of the i-th longitudinal reinforcement (N/mm2 ), taken as positive in σ li compression and negative in tension; strength coefficient of the equivalent stress block for concrete encasement, set α1 as 1.0 when strength class of concrete is not higher than C50; 0.94 for C80; calculated by linear interpolation for concrete between C50 and C80. (4) The resistance of cross-sections of the symmetrically encased CFST members in four-chord concrete-encased CFST hybrid structures (Fig. 5.23) to compression and the corresponding bending resistance of the cross-sections should be calculated in accordance with Eqs. (5.3.3.11) and (5.3.3.12), respectively, and shall conform to the following requirements: ' = Nc' + Ns' Ncfst

(5.3.3.11)

Mcfst = Mc + Ms

(5.3.3.12)

where, ' Ncfst compression resistance of cross-sections of encased CFST members to combined compression and bending (N); Mcfst bending resistance of cross-sections of encased CFST members to combined compression and bending (N·mm); compression resistance of cross-sections of the core concrete to combined Nc' compression and bending (N); compression resistance of cross-sections of steel tubes to combined compresNs' sion and bending (N);

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

Mc

231

bending resistance of cross-sections of the core concrete to combined compression and bending (N·mm); bending resistance of cross-sections of steel tubes to combined compression and bending (N·mm).

Ms

1) The resistance of cross-sections of steel tubes to compression and the corresponding bending resistance should be calculated in accordance with Eqs. (5.3.3.13) and (5.3.3.14), respectively (Fig. 5.23): Ns' = 2σs1 As1 + 2σs2 As2 Ms = 2σs1 As1 (0.5H − xs1 ) + 2σs2 As2 (0.5H − xs2 )

(5.3.3.13) (5.3.3.14)

where, Ns' Ms As1 As2 x s1 x s2 σ s1 σ s2

compression resistance of cross-sections of steel tubes to combined compression and bending (N); bending resistance of cross-sections of steel tubes to combined compression and bending (N·mm); cross-sectional areas of steel tubes close to the compressive edge (mm2 ); cross-sectional areas of steel tubes away from the compressive edge (mm2 ); distance between the compressive edge and the centroid of the steel tube close to the compressive edge (mm); distance between the compressive edge and the centroid of the steel tube away from the compressive edge (mm); stress of centroid of the steel tube close to the compressive edge (N/mm2 ), taken as positive in compression and negative in tension; stress of centroid of the steel tube away from the compressive edge (N/mm2 ), taken as positive in compression and negative in tension.

2) In accordance with whether the location of the neutral axis crosses the core concrete close to or away from the compressive edge of the cross-section, the resistance of cross-sections of the core concrete to compression and the corresponding bending resistance should conform to the following requirements: (a) When (H-aci ) ≤ c ≤ H, the core concrete is all in compression (Fig. 5.24), the resistance should be calculated in accordance with the following equations: Nc' = 2σc1 Ac1 + 2σc2 Ac2 Mc = 2σc1 Ac1 (0.5H − xc1 ) + 2σc2 Ac2 (0.5H − xc2 ) where,

(5.3.3.15) (5.3.3.16)

Nc1 Mc

xc2 c

H aci Di H-2aci-2Di Di

εcu εc1

xc1

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

aci

232

N'c

εc2 1 (a) Strain distribution

2 Nc2

(b) Force equilibrium

Fig. 5.24 Resistance of cross-section of the core concrete [(H-aci ) ≤ c ≤ H], 1—neutral axis; 2—centroidal axis; H—Cross-sectional height; aci —Distance between the outside edge of the core concrete and the outside edge of the concrete encasement; c—Distance between the neutral axis and the compressive edge of the cross-section; N c1 —Axial force of the core concrete close to the compressive edge; N c2 —Axial force of the core concrete away from the compressive edge; εc1 — Strain of centroid of the core concrete close to the compressive edge; εc2 —Strain of centroid of the core concrete away from the compressive edge; εcu —Ultimate compressive strain of concrete

Nc' Mc Ac1 Ac2 x c1 x c2 σ c1 σ c2

compression resistance of cross-sections of the core concrete to combined compression and bending (N); bending resistance of cross-sections of the core concrete to combined compression and bending (N·mm); cross-sectional area of the core concrete close to the compressive edge (mm2 ); cross-sectional area of the core concrete away from the compressive edge (mm2 ); distance between the compressive edge and the centroid of the core concrete close to the compressive edge (mm); distance between the compressive edge and the centroid of the core concrete away from the compressive edge (mm); stress of the centroid of the core concrete close to the compressive edge (N/ mm2 ), shall be calculated by Eq. (5.3.2.18) stress of the centroid of the core concrete away from the compressive edge (N/ mm2 ), shall be calculated by Eq. (5.3.2.18).

(b) When (H-Di -aci ) < c < (H-aci ), the neutral axis is located within the core concrete away from the compressive edge. The tensile strength of the core concrete away from the compressive edge should not be considered (Fig. 5.25), and the resistance should be calculated in accordance with the following equations: Nc' = 2σc1 Ac1 + 2σe,c2 Ac,c2 Mc = 2σc1 Ac1 (0.5H − xc1 ) + 2σe,c2 Ac,c2 (0.5H − xe,c2 ) xe,c2 = 0.54c + 0.46H − 0.5Di − 0.46aci

(5.3.3.17) (5.3.3.18) (5.3.3.19)

xc1

εcu εc1

3

Mc N'c

εe,c2 Ac,c2

233

Nc1

xe,c2 c

H aci Di H-2aci-2Di Di

aci

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

2 Nc2

1

(a) Strain distribution

(b) Force equilibrium

Fig. 5.25 Resistance of cross-section of the core concrete [(H-Di -aci ) < c < (H-aci )], 1—neutral axis; 2—centroidal axis; 3—equivalent point A; H—Cross-sectional height; aci —Distance between the outside edge of the core concrete and the outside edge of the concrete encasement; c—Distance between the neutral axis and the compressive edge of the cross-section; εc1 —Strain of centroid of the core concrete close to the compressive edge; εe,c2 —Strain of the core concrete at equivalent point A away from the compressive edge; εcu —Ultimate compressive strain of concrete

where, Ac,c2 compressive area of the core concrete away from the compressive edge (mm2 ); x e,c2 distance between the compressive edge and the equivalent point A of the core concrete away from the compressive edge (mm); σ e,c2 stress of the core concrete at the equivalent point A away from the compressive edge (N/mm2 ), shall be calculated by Eq. (5.3.2.18). (c) When (Di + aci ) ≤ c ≤ (H–Di –aci ), the neutral axis is located between the core concrete that is away from and close to the tensile edge. The tensile strength of the core concrete away from the compressive edge should not be considered (Fig. 5.26), and the resistance of cross-section should be calculated in accordance with the following equations: Nc' = 2σc1 Ac1

(5.3.3.20)

Mc = 2σc1 Ac1 (0.5H − xc1 )

(5.3.3.21)

where: Ac1 cross-sectional area of the core concrete close to the compressive edge (mm2 ); x c1 distance between the compressive edge and the centroid of the core concrete close to the compressive edge (mm); σ c1 stress of centroid of the core concrete close to the compressive edge (N/mm2 ), shall be calculated by Eq. (5.3.2.18). (d) When aci < c < (Di + aci ), the neutral axis is located within the core concrete close to the compressive edge. The tensile strength of the core concrete close to

Nc1

c

H aci Di H-2aci-2Di Di

εcu εc1

xc1

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

aci

234

Mc

1

N'c

(a) Strain distribution

2

(b) Force equilibrium

Fig. 5.26 Resistance of cross-section of the core concrete [(Di + aci ) ≤ c ≤ (H-Di -aci )], 1—neutral axis; 2—centroidal axis; H—Cross-sectional height; aci —Distance between the outside edge of the core concrete and the outside edge of the concrete encasement; c—Distance between the neutral axis and the compressive edge of the cross-section; εc1 —Strain of centroid of the core concrete close to the compressive edge; εcu —Ultimate compressive strain of concrete.

the compressive edge should not be considered (Eq. 7.12), and the resistance of cross-section should be calculated in accordance with the following equations (Fig. 5.27). Nc' = 2σe,c1 Ac,c1

(5.3.3.22)

Mc = 2 Ac,c1 σe,c1 (0.5H − xe,c1 )

(5.3.3.23)

xe,c1 = 0.46c + 0.04Di + 0.54aci

(5.3.3.24)

Ac,c1

εcu εe,c1 1

(a) Strain distribution

Nc1

c

3

xe,c1

H aci Di H-2aci-2Di Di

aci

where,

Mc N'c

2

(b) Force equilibrium

Fig. 5.27 Resistance of cross-section of the core concrete [aci < c < (Di + aci )], 1—neutral axis; 2—centroidal axis; 3—point B; H—Cross-sectional height; aci —Distance between the outside edge of the core concrete and the outside edge of the concrete encasement; c—Distance between the neutral axis and the compressive edge of the cross-section; ε e,c1 —Strain of the core concrete at the equivalent point B close to the compressive edge; εcu —Ultimate compressive strain of concrete

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

235

Ac,c1 cross-sectional area of the compressive core concrete close to the compressive edge(mm2 ); x e,c1 distance between the compressive edge and the equivalent point B of the core concrete close to the compressive edge (mm); σ e,c1 stress of the core concrete at the equivalent point B close to the compressive edge (N/mm2 ), shall be calculated by Eq. (5.3.2.18). (5) When the neutral axis is located beyond the height of the cross-section, the bending resistance of cross-section of four-chord concrete-encased CFST hybrid structures to combined compression and bending shall satisfy the inequality in Eq. (5.3.3.25), and should be calculated in accordance with Eq. (5.3.3.26): M ≤ Mu,N Mu,N =

N0 − N Mu,H N0 − Nu,H

(5.3.3.25) (5.3.3.26)

where, N u,H compression resistance of cross-section calculated in accordance with (2) in Sect. 5.3.3 of this book when the distance c between the neutral axis and the compressive edge is equal to the sectional height H (N); M u,H bending resistance of cross-section calculated in accordance with (2) in Sect. 5.3.3 of this book when the distance c between the neutral axis and the compressive edge is equal to the sectional height H (N·mm); M u,N bending resistance of cross-section taking into account axial compression N (N·mm); resistance of cross-section to compression calculated in accordance with (1) N0 in Sect. 5.3.3 of this book (N). (6) For the verification of the resistance of cross-section to combined compression and bending, distance (c) between the neutral axis and the compressive edge of cross-section may be calculated by assuming that the design value of axial compression is equal to the resistance of cross-section to compression. If c ≤ H, the bending resistance (M u ) of cross-section should be calculated in accordance with (2) in Sect. 5.3.3 of this book. If c > H, the bending resistance (M u ) of cross-section should be calculated in accordance with (5) in Sect. 5.3.3 of this book.

5.3.4 Design of Six-Chord Structures for Compression and Bending The cross-section of the six-chord concrete-encased CFST hybrid structure is shown in Fig. 1.18c. The typical failure mode of the six-chord concrete-encased CFST

236

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

(a) Crushing of the concrete encasement

(b) Buckling of the inner longitudinal reinforcement and the steel tube

Fig. 5.28 Failure modes of six-chord concrete-encased CFST hybrid structure to axial compression

hybrid structure under axial compression is shown in Fig. 5.28. The concrete encasement of the specimen is generally crushed at the mid-span section, with some concrete spalling on both the outer and inner surfaces, which is consistent with the failure mode of the conventional reinforced concrete specimen to axial compression. After removing the outer concrete, it is found that the internal longitudinal reinforcement and steel tube show the phenomenon of compression buckling. The core concrete has no crushing phenomenon due to the confinement effect of the steel tube, and generally remains intact. For the six-chord concrete-encased CFST hybrid structure in bending, as shown in Fig. 5.29, there are obvious vertical flexural cracks at the bottom of the pure bending section with concrete spalling. Shear diagonal cracks without penetration occurs at the bottom of the flexural-shear section, and concrete crushes at the top of the pure bending section. The bottom of the steel tube of the lower chord yields in tension and fractured near the mid-span area; due to the support of concrete, the steel tube does not show obvious local buckling, and the global flexural deformation is dominant. The strain distribution of concrete encasement, steel tube and reinforcement along the height of the mid-span cross-section of a six-chord concrete-encased CFST hybrid structure (as shown in Fig. 5.30) generally conforms to the plane section assumption. Therefore, based on the plane section assumption, the calculation method for the bending resistance of the six-chord concrete-encased CFST hybrid structure can be determined. The following provisions are given by GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures: (1) The resistance of cross-section of six-chord concrete-encased CFST hybrid structures to compression shall conform to the requirements of (1) in Sect. 5.3.3 of this book.

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

237

(a) Concrete encasement

(b) Inner steel tube

(c) Core concrete of the embedded CFST

Fig. 5.29 Failure modes of six-chord concrete-encased CFST hybrid structure to bending Fig. 5.30 Strain distribution of concrete encasement along the cross-sectional height

Relative height of the concrete encasement 0.27Mu 0.53Mu 0.75Mu

ε (με)

(2) When the neutral axis is located within the height of the cross-section, the resistance of cross-section of six-chord concrete-encased CFST hybrid structures to combined compression and bending shall satisfy the following inequalities: ' N ≤ Nrc' +Ncfst

(5.3.4.1)

M ≤ Mrc + Mcfst

(5.3.4.2)

where, N

design value of axial compression in the cross-section of the concrete-encased CFST hybrid structure (N);

238

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

M Nrc' ' Ncfst

M rc M cfst

design value of bending moment in the cross-section of the concrete-encased CFST hybrid structure (N·mm); compression resistance of cross-section of the concrete encasement to combined compression and bending (N); compression resistance of cross-sections of encased CFST members to combined compression and bending (N); bending resistance of cross-section of the concrete encasement to combined compression and bending (N·mm); bending resistance of cross-sections of encased CFST members to combined compression and bending (N·mm).

The calculating assumptions for the six-chord structures for compression and bending are the same as that in (5) in Sect. 5.3.2 of this book. (3) The resistance of cross-section of the concrete encasement of six-chord concrete-encased CFST hybrid structures (Fig. 5.31) to compression and the corresponding bending resistance of the cross-section should be calculated in accordance with the following equations:

tc

D

Ae,oc

βlc

D ac

B B-2D

ac D

H

H-2tc tc

H

D D ac

B B-2tc

tc

D ac

tc H-2tc tc

H

tc

tc

B-2tc

H-2ac-2D

B tc

(a) Section simplification εcu c

βlc

α1fc,ocAe,oc N'l Mrc xli

1 2 εli

(b) Strain distribution

N'rc

2 Nl

(c) Force equilibrium

Fig. 5.31 Resistance of cross-section of the concrete encasement, 1—neutral axis; 2—centroidal axis; B—Cross-sectional width; c—Distance between the neutral axis and the compressive edge of the cross-section; H—Cross-sectional height; N l —Axial force of longitudinal reinforcement in tension zone; N’l —Axial force of longitudinal reinforcement in compression zone; t c —Distance between the edge of the internal hollow section and the outside edge of the concrete encasement; ac —Distance between the outside edge of the steel tube and the outside edge of the concrete encasement; Eli —Strain of the i-th longitudinal reinforcement; εcu —Ultimate compressive strain of concrete

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

Nrc' = α1 f c,oc Ae,oc + Mrc = α1 f c,oc Ae,oc (0.5H − xe,oc ) + σli = E s εcu

∑

∑

σli Ali

σli Ali (0.5H − xli )

c − xli c

|σli | ≤ fl

239

(5.3.4.3) (5.3.4.4) (5.3.4.5) (5.3.4.6)

where, Nrc' Mrc Ae,oc

Ali εcu c x e,oc x li σ li α1

compression resistance of cross-section of the concrete encasement to combined compression and bending (N); bending resistance of cross-section of the concrete encasement to combined compression and bending (N·mm); area of equivalent stress block of concrete encasement (mm2 ) the height of the equivalent stress block is β 1 c, β 1 is the height coefficient of equivalent stress block for concrete encasement, set as 0.80 when strength class of concrete is not higher than C50; 0.74 for C80; calculated by linear interpolation for concrete between C50 and C80; cross-sectional area of the i-th longitudinal reinforcement (mm2 ); ultimate compressive strain of concrete at the compressive edge; distance between the neutral axis and the compressive edge (mm); distance between the compressive edge and the centroid of the equivalent stress block of the concrete encasement (mm); distance between the centroid of the i-th longitudinal reinforcement and the compressive edge (mm); stress of the i-th longitudinal reinforcement (N/mm2 ), taken as positive in compression and negative in tension; strength coefficient of the equivalent stress block for concrete encasement, set as 1.0 when strength class of concrete is not higher than C50; 0.94 for C80; calculated by linear interpolation for concrete between C50 and C80.

(4) The resistance of cross-sections of symmetrically encased CFST members in six-chord concrete-encased CFST hybrid structures to compression and the corresponding bending resistance of the cross-sections should be calculated in accordance with Eqs. (5.3.4.7) and (5.3.4.8), and shall conform to the following requirements:

where,

' Ncfst = Nc' + Ns'

(5.3.4.7)

Mcfst = Mc + Ms

(5.3.4.8)

240

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

' Ncfst compression resistance of cross-sections of encased CFST members to combined compression and bending (N); Mcfst bending resistance of cross-sections of encased CFST members to combined compression and bending (N·mm); Nc' compression resistance of cross-sections of the core concrete to combined compression and bending (N); Ns' compression resistance of cross-sections of steel tubes to combined compression and bending (N); Mc bending resistance of cross-sections of the core concrete to combined compression and bending (N·mm); Ms bending resistance of cross-sections of steel tubes to combined compression and bending (N·mm).

1) The resistance of cross-sections of steel tubes to compression and the corresponding bending resistance should be calculated in accordance with the following equations (Fig. 5.32): Ns' = 2σs1 As1 + 2σs2 As2 + 2σs3 As3

(5.3.4.9)

Ms = 2σs1 As1 (0.5H − xs1 ) + 2σs2 As2 (0.5H − xs2 ) + 2σs3 As3 (0.5H − xs3 ) (5.3.4.10) where, Ns'

compression resistance of cross-sections of steel tubes to combined compression and bending (N);

xs1

εcu Ns1

1

xs2

xs3

c

εs1

εs3

N's

2 Ns3

εs2

(a) Strain distribution

Ms

Ns2

(b) Force equilibrium

Fig. 5.32 Resistance of cross-sections of steel tubes, 1—neutral axis; 2—centroidal axis; N s1 — Axial force of steel tubes close to the compressive edge; N s2 —Axial force of steel tubes away from the compressive edge; N s3 —Axial force of steel tubes in the middle position; N s ' —Axial force of steel tubes; M s —Bending moment of steel tubes; εs1 —Strain of the centroid of steel tubes close to the compressive edge; εs2 —Strain of the centroid of steel tubes away from the compressive edge; εs3 —Strain of the centroid of steel tubes in the middle position; εcu —Ultimate compressive strain of concrete

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

241

M s bending resistance of cross-sections of steel tubes to combined compression and bending (N·mm); As1 cross-sectional areas of steel tubes close to the compressive edge (mm2 ); As2 cross-sectional areas of steel tubes away from the compressive edge (mm2 ); As3 cross-sectional areas of steel tubes in the middle position (mm2 ); x s1 distance between the compressive edge and the centroids of steel tubes close to the compressive edge (mm); x s2 distance between the compressive edge and the centroids of steel tubes away from the compressive edge (mm); x s3 distance between the compressive edge and the centroids of steel tubes in the middle position (mm); σ s1 stress of the centroids of steel tubes close to the compressive edge (N/mm2 ), taken as positive in compression and negative in tension; σ s2 stress of the centroids of steel tubes away from the compressive edge (N/mm2 ), taken as positive in compression and negative in tension; σ s3 stress of centroid of steel tubes in the middle position (N/mm2 ), taken as positive in compression and negative in tension. 2) The resistance of cross-sections of the core concrete to compression and the corresponding bending resistance should be calculated in accordance with the following equations: Nc' = Mc =

∑

∑

σci Aci

(5.3.4.11)

σci Aci (0.5H − xci )

(5.3.4.12)

where, Nc' compression resistance of cross-sections of the core concrete to combined compression and bending (N); M c bending resistance of cross-sections of the core concrete to combined compression and bending (N·mm); Aci cross-sectional areas of core concrete fibers (mm2 ); σ ci stress of the core concrete fiber (N/mm2 ), shall be calculated by Eq. (5.3.2.18); x ci distance between the centroid of the core concrete fiber and the compressive edge (mm). (5) When the neutral axis is located beyond the height of the cross-section, the bending resistance of cross-section of six-chord concrete-encased CFST hybrid structures to combined compression and bending shall satisfy the inequality in Eq. (5.3.4.13), and should be calculated in accordance with Eq. (5.3.4.14): M ≤ Mu,N

(5.3.4.13)

242

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

Mu,N =

N0 − N Mu,H N0 − Nu,H

(5.3.4.14)

where, N u,H compression resistance of cross-section (N), calculated by (2) in Sect. 5.3.4 when the distance c between the neutral axis and the compressive edge is equal to the sectional height H; M u,H bending resistance of cross-section (N·mm), calculated by (2) in Sect. 5.3.4 when the distance c between the neutral axis and the compressive edge is equal to the sectional height H; M u,N bending resistance of cross-section taking into account axial compression N (N·mm); N0 resistance of cross-section to compression (N), calculated by (1) in Sect. 5.3.4. (6) For the verification of the resistance of cross-section to combined compression and bending, distance (c) between the neutral axis and the compressive edge of cross-section may be calculated by assuming that the design value of axial compression is equal to the resistance of cross-section to compression. If c ≤ H, the bending resistance (M u ) of cross-section should be calculated in accordance with (2) in Sect. 5.3.4 of this book; if c > H, the bending resistance (M u ) of cross-section should be calculated in accordance with (5) in Sect. 5.3.4 of this book.

5.3.5 Design of Slender Structures for Compression and Bending The following provisions are given by GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures: (1) The resistance of slender concrete-encased CFST hybrid structures in axial compression should be calculated in accordance with the following equation: Nu = 0.9ϕ(Nrc + Ncfst )

(5.3.5.1)

where, Nu N rc N cfst ϕ

resistance of cross-section of the concrete-encased CFST hybrid structure to compression (N); resistance of cross-section of the concrete encasement to compression (N); resistance of cross-sections of encased CFST members to compression (N); stability factor for the concrete-encased CFST hybrid structure, shall be calculated using the structural slenderness ratio in accordance with the current national standard GB 50010 Code for Design of Concrete Structures.

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

243

(2) Structural slenderness ratio (λ) of concrete-encased CFST hybrid structures in combined compression and bending should be calculated in accordance with Eq. (5.3.5.2). When the structural slenderness ratio (λ) satisfies the inequality in Eq. (5.3.5.3), the effects of the secondary moment may be neglected. Otherwise, the effects of the secondary moment should be considered in accordance with (3) in Sect. 5.3.5 of this book. λ=

l0 i

λ ≤ 34 − 12

(5.3.5.2) M1 M2

(5.3.5.3)

where, M 1 , M 2 design value of bending moment of two end sections about the same axis based on structural elastic analysis taking into account the influence of lateral deflection (N·mm). The absolute value of M 1 is lower than that of M 2 . When the structure is under single-curvature bending, M 1 /M 2 is positive. Otherwise M 1 /M 2 is negative; l0 effective length of the structure (mm), shall be determined in accordance with the current national standard GB 50010 Code for Design of Concrete Structures; i radius of gyration in the eccentric loading direction (mm). When the slenderness ratio λ satisfies the inequality in Eq. (5.3.5.3), the N u considering the secondary moment is lower than the N u without considering the secondary moment, and the reduction is within 10%. (3) Considering the secondary moment effects, the design value of bending moment for the critical cross-sections of structures in combined compression and bending should be calculated in accordance with the following equations: M = C m ηc M 2 M1 M2 2 l0 1 ηc = 1 + ζc ei 1300 h 0 H Cm = 0.7 + 0.3

 ζc =

0.5( f c,oc Aoc + f c,c Ac ) i + 13.6e + 0.1 Nu ∑ l0 0.5[ f c,oc Aoc + ( f c,c Ac )] 6.7ei + l0 + 0.1 Nu

(single-chord) (four-chord and six-chord)

(5.3.5.4) (5.3.5.5)

(5.3.5.6)

(5.3.5.7)

where, M

design value of bending moment of the critical cross-section (N·mm);

244

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

M 1, M 2

design value of bending moment of two end sections about the same axis based on structural elastic analysis taking into account the influence of lateral deflection (N·mm). The absolute value of M 1 is lower than that of M 2 . When the structure is under single-curvature bending, M 1 /M 2 is positive. Otherwise M 1 /M 2 is negative; Cm eccentricity adjustment coefficient at the end sections, set as 0.7 when it is lower than 0.7; ηc amplification coefficient of bending moment; ei initial eccentricity (mm), including additional eccentricity ea , ei = ea + M2 , where N is the design axial compression (N) corresponding to the N design bending moment M 2 ; ea additional eccentricity (mm), set as the greater value of 20 mm and the 1/30 of cross-sectional size in bending direction; H cross-sectional height (mm); h0 effective height of the cross-section along the bending direction (mm), measured as the distance between the action point of the tensile reinforcement force and the compressive edge; ζc adjustment coefficient of curvature, set as 1.0 when it is greater than 1.0; cross-sectional area of the core concrete (mm2 ); Ac cross-sectional area of the concrete encasement (mm2 ); Aoc design value of compressive strength of the core concrete (N/mm2 ); f c,c f c,oc design value of compressive strength of the concrete encasement (N/ mm2 ); ∑ ( f c,c Ac ) summation of resistance of core concrete of four-chord and six-chord structures to compression (N). The secondary moment effects are considered by increasing the eccentricity, and the adjustment coefficient of curvature is different from that of reinforced concrete structures.

5.3.6 Design of Structures for Compression and Bending Under Long-term Loading In practical engineering projects, concrete-encased CFST hybrid structure is often in load-resisting state. The increase of structural deformation and reduction of resistance of this structure due to shrinkage and creep of concrete cannot be ignored. Compare and clarify the internal forces and deformations of three types of specimens, namely, CFST, reinforced concrete and concrete-encased CFST hybrid structure with the same axial compression resistance under monotonic short-term loading. Figure 5.33 shows the full-range load (N)-strain (ε) relationship including the initial loading stage (OA), long-term loading stage (AB) and failure stage (BCD).

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid … Fig. 5.33 Load(N)-strain(ε) relationship with long-term loading

245

N (kN) C D

A B

O

ε (με)

Due to the shrinkage and creep of concrete, the deformation of the concreteencased CFST hybrid structure in the long-term loading stage is greater than that of the corresponding CFST structure, and its resistance is lower than that of the corresponding CFST structure. The concrete deforms outwards under the long-term load, and the concrete is confined by the stirrups and the steel tube, so that the concrete is in a triaxial compressive state, thus reducing the influence of long-term load on the modulus of elasticity of concrete. Compared with the reinforced concrete structure with the same axial compression resistance, the deformation of the concrete-encased CFST hybrid structure is reduced during the long-term loading stage. When the concrete-encased CFST hybrid structure with long-term loading fails under axial compression, the concrete encasement is crushed and spalled, and the longitudinal reinforcement is buckled, while the integrity of the embedded CFST remains good. Under long-term loading, shrinkage and creep develop in the concrete encasement and core concrete, which leads to internal force redistribution, and the variations of the stresses of steel and concrete. Moreover, the secondary moment effects enlarge the bending moment, which reduces the resistance of structures. The key parameters affecting the descent stage include: structural effective slenderness ratio, crosssectional steel ratio of the CFST member, longitudinal reinforcement ratio of concrete encasement, eccentricity ratio, and the strength class of concrete encasement. According to the results of experimental research and finite element analysis, the method of resistance of concrete-encased CFST hybrid structure under complex stress state can be obtained, and the calculation table of long-term load coefficient k cr is proposed (Table 5.3). The following provisions are given by GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures: (1) Axial compression resistance of concrete-encased CFST hybrid structure to long-term load should be calculated in accordance with the following equation: NuL = kcr Nu where,

(5.3.6)

1.000 1.000

0.63

0.75

0.953 0.985 0.989

0.50

0.63

0.75

20

0.50

0.723

0.697

0.669

0.820

0.790

0.772

1.000

1.000

0.996

1

0.796

0.768

0.740

0.903

0.871

0.848

1.000

1.000

1.000

3

0.5

0.699

1

0.769

0.998

0.992

0.968

3

0.824

1.000

0.999

0.997

5

0.673

0.942

0.924

0.905

1

0.745

0.986

0.972

0.943

3

Longitudinal reinforcement ratio ρ (%)

0.5

Outside diameter-to-sectional width ratio D/B

Slenderness ratio λ

40

0.829

0.789

0.765

0.976

0.960

0.936

1.000

1.000

1.000

5

0.858

0.823

0.798

0.955

0.926

0.905

1.000

1.000

1.000

5

0.798

0.999

0.997

0.985

5

Load eccentricity-to-radius of gyration ratio e/r 0

0.773

0.682

0.75

0.733

0.647

0.701

0.929

0.63

0.864

0.75

0.904

0.625

0.829

0.63

0.877

1.000

1.000

1.000

3

0.50

0.808

0.50

Strength class of concrete encasement C60

60

40

1.000

0.50

20

1

Longitudinal reinforcement ratio ρ (%)

0

0.5

Load eccentricity-to-radius of gyration ratio e/r 0

Outside diameter-to-sectional width ratio D/B

Slenderness ratio λ

Strength class of concrete encasement C30

Table 5.3 Long-term load coefficients k cr for single-chord concrete-encased CFST hybrid structures

0.705

0.917

0.912

0.882

1

1.0

0.815

0.781

0.756

0.872

0.835

0.808

1.000

1.000

0.973

1

1.0

0.779

0.951

0.933

0.902

3

0.887

0.858

0.824

0.934

0.905

0.880

1.000

1.000

0.982

3

(continued)

0.820

0.976

0.959

0.941

5

0.940

0.905

0.879

0.965

0.947

0.927

1.000

1.000

0.998

5

246 5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

0.566 0.591

0.75

0.729

0.691

0.665

0.864

0.845

5

0.629

0.604

0.575

0.724

0.693

1

0.698

0.668

0.644

0.797

0.769

3

0.952 0.985 0.989

0.50

0.63

0.75

20

0.5

0.677

1

0.746

0.998

0.992

0.968

3

0.800

1.000

0.999

0.997

5

0.651

0.941

0.923

0.904

1

0.723

0.985

0.971

0.942

3

Longitudinal reinforcement ratio ρ (%)

0.5

Outside diameter-to-sectional width ratio D/B

0.50

0.676

0.641

0.610

0.819

0.795

3

0.761

0.723

0.698

0.845

0.819

5

0.773

0.999

0.996

0.984

5

Load eccentricity-to-radius of gyration ratio e/r 0

0.538

0.63

0.751

0.50

0.715

0.75

1

Slenderness ratio λ

40

0.5

Longitudinal reinforcement ratio ρ (%)

0

Load eccentricity-to-radius of gyration ratio e/r 0

0.63

Outside diameter-to-sectional width ratio D/B

Strength class of concrete encasement C80

60

Slenderness ratio λ

Strength class of concrete encasement C30

Table 5.3 (continued)

0.683

0.916

0.911

0.881

1

1.0

0.717

0.691

0.661

0.764

0.732

1

1.0

0.755

0.950

0.932

0.901

3

0.787

0.757

0.729

0.826

0.802

3

(continued)

0.794

0.975

0.958

0.940

5

0.841

0.806

0.783

0.857

0.837

5

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid … 247

0.5

0.499 0.526 0.549

0.63

0.75

0.728

0.50

0.693

0.75

1

0.629

0.596

0.567

0.795

0.771

3

0.678

0.643

0.619

0.838

0.820

5

0.584

0.561

0.535

0.702

0.672

1

0.649

0.620

0.598

0.773

0.745

3

Longitudinal reinforcement ratio ρ (%)

0

0.708

0.672

0.648

0.820

0.794

5

Load eccentricity-to-radius of gyration ratio e/r 0

0.63

Outside diameter-to-sectional width ratio D/B

0.665

0.642

0.614

0.740

0.708

1

1.0

0.730

0.702

0.677

0.801

0.778

3

0.781

0.748

0.727

0.831

0.811

5

Note e is the load eccentricity, for strong axis bending, r 0 = H/2; for weak axis bending, r 0 = B/2. The intermediate values in the table are obtained by linear interpolation

60

Slenderness ratio λ

Strength class of concrete encasement C30

Table 5.3 (continued)

248 5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

249

N uL resistance of the concrete-encased CFST hybrid structure in axial compression considering long-term load effects (N); N u resistance of the concrete-encased CFST hybrid structure in axial compression (N), should be calculated by (1) in Sect. 5.3.5 of this book; k cr long-term load coefficient. (2) The long-term load coefficients (k cr ) should conform to Tables 5.3, 5.4 and 5.5 of this standard. 1) The long-term load coefficients for single-chord concrete-encased concrete-filled steel tubular (CFST) hybrid structures should conform to Table 5.3. 2) The long-term load coefficients for four-chord concrete-encased CFST hybrid structures with identical encased CFST members should conform to Table 5.4. 3) The long-term load coefficients for six-chord concrete-encased CFST hybrid structures with identical encased CFST members should conform to Table 5.5.

5.3.7 Design of Structures for Shear The shear resistance of concrete-encased CFST hybrid structures is the summation of the shear resistances of concrete encasement and the encased CFST members. The concrete encasement has similar shear resistance to conventional reinforced concrete structures. The shear resistance contributions of the encased CFST members are threefold: (1) the shear resistance of the encased CFST members themselves; (2) the dowel action of continuous CFST members similar to that of longitudinal reinforcement; (3) similar to reinforcement, CFST can resist vertical shear force, effectively inhibit the generation and development of concrete cracks and improve the bite force of aggregate concrete encasement. Failure mode of concrete-encased CFST hybrid structure to combined bending moment and shear force: (1) Diagonal compression failure (Fig. 5.34a), corresponding to the shear-to-span ratio av /B = 0.75 (av is the length of the flexural-shear section, B is the section width). The failure modes show that the concrete oblique crushing along the loading point and the direction of the support line, like the stub column in oblique compression. Because the load borne by the component is mainly controlled by the concrete compressive stress, the failure mode is the compressive brittle failure. (2) Shear-compression failure (Fig. 5.34b), corresponding to the shear-span ratio av /B = 1.2–2. The failure mode is shear brittle failure, which shows that the shear diagonal cracks appear in the flexural-shear section, the concrete at the top of the diagonal cracks is crushed under the combined action of shear and compression, while the vertical flexural cracks in the pure bending section develop slowly.

1.000 1.000

0.20

0.25

0.956 0.962 1.000

0.15

0.20

0.25

20

0.15

0.720

0.691

0.683

0.854

0.837

0.835

1.000

1.000

1.000

1

0.805

0.770

0.767

0.909

0.890

0.889

1.000

1.000

1.000

3

0.5

0.764

1

0.811

1.000

0.974

0.972

3

0.886

1.000

1.000

1.000

5

0.728

0.953

0.932

0.927

1

0.786

1.000

0.941

0.939

3

Longitudinal reinforcement ratio ρ (%)

0

Outside diameter-to-sectional width ratio D/B

Slenderness ratio λ

40

0.888

0.853

0.850

0.976

0.952

0.949

1.000

1.000

1.000

5

0.880

0.849

0.846

0.954

0.936

0.935

1.000

1.000

1.000

5

0.859

1.000

1.000

1.000

5

Load eccentricity-to-radius of gyration ratio e/r 0

0.811

0.722

0.25

0.768

0.701

0.762

0.929

0.20

0.877

0.25

0.904

0.692

0.866

0.20

0.902

1.000

1.000

1.000

3

0.15

0.862

0.15

Strength class of concrete encasement C60

60

40

1.000

0.15

20

1

Longitudinal reinforcement ratio ρ (%)

0

0.5

Load eccentricity-to-radius of gyration ratio e/r 0

Outside diameter-to-sectional width ratio D/B

Slenderness ratio λ

Strength class of concrete encasement C30

Table 5.4 Long-term load coefficients k cr for four-chord concrete-encased CFST hybrid structures

0.729

0.943

0.877

0.874

1

1

0.776

0.744

0.733

0.878

0.833

0.830

1.000

0.970

0.971

1

1

0.785

0.945

0.883

0.882

3

0.861

0.816

0.811

0.929

0.888

0.882

1.000

0.976

0.971

3

(continued)

0.853

0.977

0.954

0.950

5

0.921

0.891

0.887

0.964

0.948

0.946

1.000

1.000

1.000

5

250 5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

0.601 0.623

0.25

0.780

0.748

0.746

0.907

0.889

5

0.627

0.593

0.583

0.758

0.736

1

0.704

0.672

0.668

0.831

0.788

3

0.957 0.961 1.000

0.15

0.20

0.25

20

0.5

0.750

1

0.795

1.000

0.978

0.974

3

0.869

1.000

1.000

1.000

5

0.713

0.954

0.932

0.928

1

0.770

1.000

0.941

0.939

3

Longitudinal reinforcement ratio ρ (%)

0

Outside diameter-to-sectional width ratio D/B

0.15

0.711

0.667

0.665

0.859

0.813

3

0.775

0.743

0.742

0.889

0.861

5

0.843

1.000

1.000

1.000

5

Load eccentricity-to-radius of gyration ratio e/r 0

0.592

0.20

0.801

0.15

0.770

0.25

1

Slenderness ratio λ

40

0.5

Longitudinal reinforcement ratio ρ (%)

0

Load eccentricity-to-radius of gyration ratio e/r 0

0.20

Outside diameter-to-sectional width ratio D/B

Strength class of concrete encasement C80

60

Slenderness ratio λ

Strength class of concrete encasement C30

Table 5.4 (continued)

0.713

0.944

0.877

0.874

1

1

0.682

0.641

0.634

0.779

0.733

1

1

0.768

0.945

0.884

0.883

3

0.762

0.722

0.715

0.836

0.791

3

(continued)

0.835

0.980

0.953

0.951

5

0.815

0.790

0.789

0.878

0.856

5

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid … 251

0.5

0.563 0.571 0.592

0.20

0.25

0.785

0.15

0.753

0.25

1

0.677

0.635

0.633

0.843

0.797

3

0.743

0.712

0.711

0.891

0.872

5

0.595

0.563

0.553

0.744

0.720

1

0.670

0.639

0.635

0.815

0.773

3

Longitudinal reinforcement ratio ρ (%)

0

0.738

0.707

0.706

0.871

0.845

5

Load eccentricity-to-radius of gyration ratio e/r 0

0.20

Outside diameter-to-sectional width ratio D/B

0.646

0.608

0.600

0.762

0.718

1

1

0.723

0.685

0.679

0.818

0.773

3

0.775

0.752

0.749

0.860

0.838

5

Note e is the load eccentricity, for strong axis bending, r 0 = H/2; for weak axis bending, r 0 = B/2. The intermediate values in the table are obtained by linear interpolation

60

Slenderness ratio λ

Strength class of concrete encasement C30

Table 5.4 (continued)

252 5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

1.000 1.000

0.20

0.25

0.938 0.942 1.000

0.15

0.20

0.25

20

0.15

0.710

0.682

0.674

0.831

0.818

0.816

0.999

0.999

0.999

1

0.801

0.766

0.763

0.906

0.879

0.876

1.000

1.000

1.000

3

0.5

0.750

1

0.808

1.000

0.969

0.967

3

0.890

1.000

1.000

1.000

5

0.716

0.941

0.910

0.908

1

0.783

0.990

0.936

0.934

3

Longitudinal reinforcement ratio ρ (%)

0

Outside diameter-to-sectional width ratio D/B

Slenderness ratio λ

40

0.893

0.860

0.858

0.979

0.954

0.953

1.000

1.000

1.000

5

0.881

0.854

0.851

0.955

0.942

0.934

1.000

1.000

1.000

5

0.863

1.000

1.000

1.000

5

Load eccentricity-to-radius of gyration ratio e/r 0

0.808

0.712

0.25

0.766

0.690

0.760

0.927

0.20

0.871

0.25

0.902

0.681

0.855

0.20

0.900

1.000

1.000

1.000

3

0.15

0.851

0.15

Strength class of concrete encasement C60

60

40

1.000

0.15

20

1

Longitudinal reinforcement ratio ρ (%)

0

0.5

Load eccentricity-to-radius of gyration ratio e/r 0

Outside diameter-to-sectional width ratio D/B

Slenderness ratio λ

Strength class of concrete encasement C30

Table 5.5 Long-term load coefficients k cr for six-chord concrete-encased CFST hybrid structures

0.717

0.925

0.856

0.854

1

1

0.768

0.734

0.723

0.838

0.820

0.816

0.934

0.950

0.949

1

1

0.781

0.933

0.877

0.876

3

0.855

0.813

0.808

0.922

0.881

0.876

1.000

0.965

0.961

3

(continued)

0.855

0.971

0.954

0.952

5

0.921

0.894

0.892

0.965

0.951

0.943

1.000

1.000

1.000

5

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid … 253

0.591 0.615

0.25

0.783

0.754

0.753

0.909

0.893

5

0.617

0.584

0.575

0.748

0.722

1

0.701

0.668

0.666

0.825

0.785

3

0.939 0.943 1.000

0.15

0.20

0.25

20

0.5

0.736

1

0.792

1.000

0.971

0.968

3

0.873

1.000

1.000

1.000

5

0.701

0.942

0.911

0.909

1

0.767

0.992

0.937

0.935

3

Longitudinal reinforcement ratio ρ (%)

0

Outside diameter-to-sectional width ratio D/B

0.15

0.707

0.666

0.663

0.853

0.810

3

0.778

0.745

0.745

0.887

0.865

5

0.846

1.000

1.000

1.000

5

Load eccentricity-to-radius of gyration ratio e/r 0

0.581

0.20

0.789

0.15

0.755

0.25

1

Slenderness ratio λ

40

0.5

Longitudinal reinforcement ratio ρ (%)

0

Load eccentricity-to-radius of gyration ratio e/r 0

0.20

Outside diameter-to-sectional width ratio D/B

Strength class of concrete encasement C80

60

Slenderness ratio λ

Strength class of concrete encasement C30

Table 5.5 (continued)

0.701

0.926

0.857

0.856

1

1

0.675

0.633

0.625

0.769

0.721

1

1

0.764

0.935

0.878

0.877

3

0.755

0.718

0.713

0.828

0.786

3

(continued)

0.837

0.972

0.956

0.954

5

0.814

0.794

0.792

0.874

0.857

5

254 5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

0.5

0.554 0.562 0.586

0.20

0.25

0.774

0.15

0.741

0.25

1

0.675

0.634

0.632

0.835

0.794

3

0.746

0.718

0.717

0.885

0.874

5

0.587

0.556

0.546

0.734

0.708

1

0.667

0.636

0.633

0.809

0.770

3

Longitudinal reinforcement ratio ρ (%)

0

0.740

0.711

0.710

0.869

0.848

5

Load eccentricity-to-radius of gyration ratio e/r 0

0.20

Outside diameter-to-sectional width ratio D/B

0.639

0.600

0.592

0.752

0.706

1

1

0.718

0.682

0.676

0.810

0.769

3

0.773

0.755

0.752

0.855

0.840

5

Note e is the load eccentricity, for strong axis bending, r 0 = H/2; for weak axis bending, r 0 = B/2. The intermediate values in the table are obtained by linear interpolation

60

Slenderness ratio λ

Strength class of concrete encasement C30

Table 5.5 (continued)

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid … 255

256

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

(a) Diagonal compressive failure (av/B=0.75)

(b) Shear-compression failure (av/B=1.5)

(c) Flexural failure (av/B=3)

Fig. 5.34 Failure modes of the specimens under bending moment and shear force

(3) Flexural failure (shown in Fig. 5.34c), corresponding to the shear-to-span ratio av /B = 3. The failure mode shows that obvious distribution of vertical flexural cracks appear in the pure bending section, and the concrete of top of the compression zone is crushed, and no through shear diagonal cracks are formed in the bending-shear section. The cross-section of the specimen is shown in Fig. 1.18b. The cross-section of the concrete encasement is square, the side length is 300 mm, the outer diameter of the embedded CFST is 60 mm, and its wall thickness is 3 mm. The steel grade of encased steel tube is Q355. The strength class of core concrete is C60, and concrete encasement is C30. Figure 5.35 shows the shear force (V )-deflection at the loading point (up ) relationship. The corresponding failure modes are diagonal compression failure, shear-compression failure and flexural failure. For the specimen in diagonal compression failure (av /B = 0.75), point A1 is the beginning of visible diagonal cracks in the flexural-shear section, point B2 is the beginning of vertical cracks in the pure bending section, and at point C1 the load reaches V u . For the specimen in shear-compression failure (av /B = 1.5), point A2 is the beginning of visible diagonal cracks in the flexural-shear section, point B2 is the formation of through diagonal cracks in the flexural-shear section, when the stiffness is reduced, and at point C2 the load reaches V u . For the specimen in flexural failure (av /B = 3), point A3 is the beginning of the visible vertical flexural cracks in the pure bending section, at point B3 the tensile steel tube in the pure bending section yields, and at point C3 the load reaches V u .

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid … Fig. 5.35 Typical V-up relationship with various shear-span ratio (av /B), av —Length of flexural-shear span; B—Width of cross-section; V —Shear force; up —Deflection at the loading point

257

V (kN) 800 C1

600

B1

400

B2

a v/B=0.75 C2

a v/B=1.5 C3

200A 1 A 2 B3 A3 0 0

10

20

30

a v/B=3

40

50 up (mm)

The following provisions are given by GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures: (1) The shear resistance of concrete-encased CFST hybrid structures in bending is the summation of the shear resistances of concrete encasement and the encased CFST members, and shall satisfy the inequality in the following equation: V ≤ Vrc + Vcfst

(5.3.7.1)

where, V design value of shear force (N); V rc shear resistance of the concrete encasement (N); V cfst shear resistance of encased CFST members (N). Equation (5.3.7.1) provides the shear resistance of cross-section of concreteencased CFST hybrid structures in bending. Shear resistance of cross-section of concrete-encased CFST hybrid structures in eccentric compression or eccentric tension shall be studied individually. (2) The shear resistance of the concrete encasement shall conform respectively to the requirements of the current standards of the nation JTG 3362 Specifications for Design of Highway Reinforced Concrete and Prestressed Concrete Bridge and Culvert and TB 10002 Code for Design on Railway Bridge and Culvert. The shear resistance of the concrete encasement shall be calculated in accordance with the following equations: / √ (5.3.7.2) Vrc = 0.45Aoc (2 + 60ρ) f cu,oc ρsv f v ρsv =

Asv sB

where, V rc

shear resistance of the concrete encasement (N);

(5.3.7.3)

258

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

Aoc ρ

cross-sectional area of the concrete encasement (mm2 ); tensile longitudinal reinforcement ratio in the inclined section, set as 2.5% when it is greater than 2.5%; characteristic value of cube strength of the concrete encasement (N/mm2 ); stirrup ratio in inclined section; cross-sectional area of stirrups (mm2 ); spacing of stirrups (mm); cross-sectional width (mm); design value of tensile strength of stirrups (N/mm2 ).

f cu,oc ρ sv Asv s B fv

(3) The contribution of CFST to the shear resistance of concrete-encased CFST hybrid structure is considered in favor of safety, and the dowel action of CFST part and restraining the start and development of concrete cracking is neglected in the calculation. The shear resistance of the encased CFST should be calculated in accordance with the following equation: Vcfst =

∑

0.9(0.97 + 0.2 ln ξi )Asc,i f sv,i

(5.3.7.4)

where, V cfst ξi Asc,i f sv,i

shear resistance of the encased CFST members (N); confinement factor of the i-th encased CFST member; cross-sectional area of the i-th encased CFST member (mm2 ); design value of shear strength of the i-th encased CFST cross-section (N/mm2 ).

(4) Due to the continuity of steel tubes, they can resist vertical shear and longitudinal tensile (or compressive) forces at the same time, effectively resisting shear force, making the shear resistance of concrete-encased CFST hybrid structure significantly improved. The study showed that, within general engineering parametric ranges, for single-chord concrete-encased CFST hybrid structures subjected to combined bending moment, axial force and shear force, when the shear span-todepth ratio of the calculated section λv (=M/(Vh0 )) is not less than 1.5, and the outside diameter-to-sectional width ratio (D/B) ratio is not less than 0.5, and the reinforcement placement of concrete encasement conforms to the requirements of the current national standard GB 50011 Code for Seismic Design of Buildings, the influence of shear force on the resistance in combined compression and bending may be neglected.

5.3.8 Design of Arch Structures Arch structures are structures with arches as the load-bearing system. Arch structures have been widely used in practical engineering projects due to their clear force transmission mechanism, simple and clear structure, and remarkable economic efficiency.

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

259

Figure 5.36 shows the construction process of concrete-encased CFST hybrid arch structures. First, the trussed steel tube arch is constructed, then the core concrete is placed to form the CFST arch rib, and finally the concrete encasements are constructed. In order to study the mechanical performance of concrete-encased CFST hybrid arch structures, the experimental study has been carried out in Tsinghua University. For the arch structures in the form of fixed arches with non-uniform cross-sections, the axes are selected as suspension chain lines. The vector height f is 2.5 m, the span L is 10 m, and the vector-to-span ratio is 1/4 (Fig. 5.37). The concrete encasement adopts single box and single chamber section, and the outer section and hollow section are rectangular. The outer section width is kept constant at 120 mm as the outer section position rises, and the outer section height gradually decreases from 220 mm (arch foot) to 137 mm (arch top). The strength class of the concrete encasement is C50 concrete with a 5 mm thickness protective layer. φ4 cold-drawn reinforcement is used for longitudinal reinforcement and stirrups. Longitudinal reinforcement is arranged inside and outside. The spacing of the stirrups is 50 mm, and the spacing of the encrypted area at the loading end is 25 mm. The outer diameter of the four corners and two round CFST at the waist are 12 mm, and the wall thickness is 2 mm. The steel tube is filled with high-strength cement mortar. The full-range loading curve of the concrete-encased CFST hybrid arch structures can be generally divided into four stages (Fig. 5.37): Lifting device A A

A

Steel support Steel tube Arch foot support

CFST arch rib

A A-A section

A-A section A

A CFST arch rib A Concrete encasement

A Concrete-encased CFST hybrid arch

A-A section

A-A section

Fig. 5.36 Construction process of the concrete-encased CFST hybrid arch structures Fig. 5.37 Measured load (P)-vertical displacement (uy ) relationship

P (kN) 2P

C

100

B

80

L/4 L/4 L/4 L

D

60

P P P P P 2P

A

40 20

E

F

0 0

10

20

30

40

50

uy(mm)

f

L/4

260

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

(1) Elastic stage (before point A): in the early stage of loading, the structure is linear elastic, the concrete starts to crack at point A. (2) Elasto-plastic stage (AB stage): structural stiffness has been reduced, concrete cracks continue to appear and develop. Crack width gradually becomes larger and the steel tube yields at point B. (3) Plastic hardening stage (BC stage): the vertical displacement of the structure increases rapidly. At point C, it reaches the limiting state, and the concrete encasement and the inner CFST can work together. (4) Descending stage (CD stage): The load decreases, the displacement of the structure increases. The concrete encasement continues to collapse and spall, the steel tube of encased CFST yields, and the structure fails. Before point C, the load applied on the concrete-encased CFST hybrid arch structures are increasing, where cracks appear and develop on the surface of concrete encasement; the CD stage is the stable descending stage, where structure shows some ductility. The reinforced concrete encasement and the encased CFST can act together during the full-range loading, and the encased CFST improves the ductility of the whole structure. As shown in Fig. 5.38, the loading point of the concrete-encased CFST hybrid arch structure model is near the left side of 1/8 span. The concrete encasement collapses and spalling, the longitudinal reinforcement and the encased CFST buckles obviously, the core concrete of the encased CFST remains intact, and there is no obvious slip between the reinforced concrete encasement and the encased CFST. The encased CFST and the reinforced concrete encasement can work together and the encased CFST can restrain the cracks development of the reinforced concrete encasement. Based on experimental research and finite element analysis, the calculation method for the resistance of concrete-encased CFST hybrid arch structures has been determined. The following provisions are given by GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures:

Buckling of longitudinal reinforcement Concrete crushes

Remove the concrete encasement Buckling of steel tube

Concrete cracks

Fig. 5.38 Failure modes of the concrete-encased CFST hybrid arch structures

5.3 Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid …

261

(1) In-plane and out-of-plane global stabilities for concrete-encased CFST hybrid arch structures shall be verified. When verifying the in-plane global stability, the equivalent beam-column method may be used. For the concrete-encased CFST hybrid arch structures, the arches shall be calculated as equivalent beamcolumn structures for the verification of the in-plane stability in accordance with the requirements of the current national standard GB 50923 Technical Code for Concrete-Filled Steel Tube Arch Bridges. The critical cross-sections include the cross-sections at the top, 3/8 span, 1/4 span and bases of the arches. Global structural analysis needs to be conducted for complex arches with super-large span or non-uniform cross-sections to determine the critical cross-sections and to carry out the corresponding calculations. (2) For fixed arches, two-hinged arches, and three-hinged arches, the effective lengths of the equivalent beam-columns shall be 0.36S, 0.54S, and 0.58S, respectively, where S is the length of the arch axis. The actions at the ends and the dimensions of the cross-sections for verification of the beam-columns shall be taken as the internal forces and dimensions of the critical cross-sections. For complex arches with super-large span and non-uniform cross-sections, the equivalent cross-sections of the arches may be used as the cross-sections for verification. The effective length and the internal force shall be calculated by a global structural analysis. The calculation method for the in-plane stability resistance of concrete-encased CFST hybrid arch structures can be summarized as follows: 1) Determine the form of load action and conduct the first-order elastic analysis. 2) Select the most unfavorable section as critical cross-sections to verify the resistance of the structure. 3) Verify the resistance of each critical cross-sections in combined compression and bending by using the equivalent beam-column method. The cross section of the equivalent beam-columns is the same as the critical cross-sections. Determine whether each critical cross-section satisfies the following equations. N ≤ ϕ Nu

(5.3.8.1)

ηc M ≤ Mu

(5.3.8.2)

where, Nu ϕ Mu ηc

resistance of the equivalent beam-columns in axial compression; stability factor; bending resistance of the equivalent beam-columns; amplification coefficient of bending moment.

(4) When verifying the shear resistance of critical cross-sections, determine whether each critical cross-section satisfies the following equation in turn.

262

5 Design of Concrete-Filled Steel Tubular (CFST) Hybrid Structures

V ≤ Vu

(5.3.8.3)

where, V u shear resistance of the equivalent beam-columns. Exercises 1. Briefly describe the concept and main cross-section forms of CFST hybrid structures. 2. Briefly describe the mechanism of hybrid effect for CFST hybrid structures. 3. Briefly describe key points for design of trussed CFST hybrid structures. 4. Briefly describe key points for design of concrete-encased CFST hybrid structures. 5. Taking the concrete-encased CFST hybrid structure as an example, briefly describe the influence of construction process on the mechanical performance of CFST hybrid structures.

Chapter 6

Design of Joints

Key Points and Learning Objectives Key Points This chapter introduces the design principles and methods of beam-to-column joints, CFST chord-steel tubular web connection joints in CFST structures, the detailing requirements of column bases and supporting joints, and the design methods for fatigue resistance of joints. Learning Objectives Understand the design principles and methods for the beam-to-column joints, CFST chord-steel tubular web connection joints in CFST structures. Be familiar with the design method for fatigue resistance of joints. Learn the types and detailing forms of the beam-to-column joints and CFST chord-steel tubular web connection joints, as well as the detailing of the column bases and supporting joints.

6.1 Introduction Reasonably determining the calculation methods for the mechanical index and detailing of key joints is particularly crucial for the design of CFST structures. The joints in CFST structures include beam-to-column joints, CFST chord-steel tubular web connection joints, column base connection joints, etc. Design of the joints in CFST structures shall conform to the requirements of strength, stiffness, stability and seismic performance. It shall ensure that the force can be transferred effectively and that the steel and its core concrete can act together. It shall also take into account the ease of manufacturing, erection and placement of the core concrete.

© China Architecture & Building Press 2024 L. Han, Theory of Concrete-Filled Steel Tubular Structures, https://doi.org/10.1007/978-981-99-2170-6_6

263

264

6 Design of Joints

6.2 Types of Joints 6.2.1 Beam-to-Column Joints According to the load characteristics, the beam-to-column joints in CFST frame structures are mainly divided as the following types: (1) Hinged joint: The beam only transfers the support reaction to the CFST column; (2) Semi-rigid joint: the angle between the beam and the axis of the CFST column changes during the loading, which means there is relative angular displacement and it may cause internal force redistribution; (3) Rigid joint: The angle between the beam and the axis of the CFST column remains unchanged during the loading. In the case of the hinged joint, for example, the beam transmits only the support reaction force to the CFST column, so it is necessary to set a bracket to transmit the shear force. The shear force at the end of the beam is transferred to the CFST column through the welding of the web or the welding of the vertical steel plate to the column, as shown in Fig. 6.1, where L is the length of the vertical welding; when the beam is an I-section steel beam, L is taken as the height of the web of the beam; when the bracket is welded to the tube wall used to transfer the shear force, L is taken as the height of the rib of the bracket; and V is the shear force of joint. The detailing of forms for two hinged joints is given in Fig. 6.2. For the semi-rigid joint, due to the change of the angle between the beam and the axis during the loading, there will be a redistribution of internal forces in the structure. The loading condition of the structure is complicated and the deformation is large, so specific analysis shall be carried out for the application of practical engineering projects. Rigid joint is one of the most widely used joints in China. The key points for the design of detailing of this type of joint are: during the loading process, the angle Fig. 6.1 Transfer of the vertical shear force. 1—CFST column

1

L

V

6.2 Types of Joints

265

1

1 3

3

A

A

B

B

2

A-A (a) Type1

2

B-B (b) Type2

Fig. 6.2 Forms of hinged joints. 1—CFST; 2—Steel beam; 3—bolt

between the beam and the axis of the CFST column should always remain unchanged. The bending moment, axial force and shear force at the end of the beam are safely and reliably transmitted to the CFST column through reasonable detailing.

6.2.2 Concrete-Filled Steel Tubular (CFST) Chord to Steel Tubular Web Joints Overlap K-joint, gap K-joint, KT-joint, multiplanar TT-joint and multiplanar KK-joint in trussed CFST hybrid structures are shown in Fig. 6.3. K-joints are commonly used in trussed CFST hybrid structures. The detailing of the joints and connections in trussed CFST hybrid structures should be simple enough and the loading conditions of the structures shall be clearly defined. The centerlines of loaded members should intersect at one point. These joints can be classified as hinged joint, rigid and semi-rigid joint according to the initial rotational stiffness. Hinged joint does not transmit bending moments and allows rotation in the connection zone of web and chord within the range of design value of load. Rigid joint can sufficiently transmit loads such as bending moment

266

6 Design of Joints

1

2

2 1

(a) Overlap K-joint

2

1

2 1

(b) Gap K-joint 2

2

1

1 (c) KT-joint

2

2 1

2

1

2

1 (d) Multiplanar TT-joint

1 (e) Multiplanar KK-joint

Fig. 6.3 Typical forms of joints in trussed CFST hybrid structures. 1—CFST chords; 2—Steel tubular webs

6.2 Types of Joints

267

and axial force. The initial rotational stiffness of the joint zone is much higher than that of the rod. The performance of semi-rigid joints is in between the above two. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, for the welded intersecting joints of trussed CFST hybrid structures (Fig. 6.3), the steel tubular webs shall be connected along the intersecting lines by butt welds with groove or fillet welds, and the welding consumables shall match the grade of the steel tubes. The design of the welds of intersecting joints of trussed CFST hybrid structures may be conducted in accordance with the approaches for intersecting joints of hollow steel tubes. When the angle between the web and the chord is less than 60°, considering that it is difficult to ensure the weld quality by using fillet welds at the root of the intersecting line, butt weld with groove connection should be adopted. For the plane K-joints and N-joints where webs overlap, when the two webs have different diameters, the web with a greater diameter shall be directly welded to the chord, while the web with a smaller diameter shall be overlapped to the web with the greater diameter. When the two webs have the same diameter, the web carrying a greater force shall be welded directly to the chord while the web carrying a lower force shall be overlapped to the web carrying a greater force. In some tower structures, when the webs and chords in the joints of trussed CFST hybrid structures are connected by gusset plates and bolts, the insert plates at the ends of the webs may adopt U-plates, through-plates, T-plates or cross-plates (Fig. 6.4). The opening gap of the U-plates may be 2–3 mm greater than the thickness of the gusset plates. The weld length of the plates inserted into the steel tubes shall be determined in accordance with the internal force calculation. In order to prevent the out-plane instability of the joint and enhance its resistance, when the joint of trussed CFST hybrid structures is connected by gusset plates, ring or sector-shaped stiffeners may be set on both sides of the gusset plates (Fig. 6.5), and the corresponding central angle should not be less than 30°. Adjacent stiffeners in the same plane shall be connected to form a single piece. When the ratio √ of the length of the free edge of the gusset plate to its thickness is greater than 60 235/ f y , a flanged edge should be used or longitudinal stiffeners should be set. The calculation for resistance of the gusset plates shall conform respectively to the relevant requirements of the current standards of the nation GB 50017 Standard for Design of Steel Structures and DL/T 5486 Technical Code for Design of Tower Structures of UHV Overhead Transmission Line.

268

6 Design of Joints

2

A

A

2

1

A-A

B

2

C

C

1

1

B-B

(b) Through-plate connection

(a) U-plate connection 2

B

C-C

2

D

E

D

E

1

D-D -

1

E-E

(d) Cross-plate connection

(c) T-plate connection

Fig. 6.4 Detailing of different forms of inserted plate connections. 1—bolts; 2—webs

2 A

A

1 1 A-A

Fig. 6.5 Detailing of the gusset plate connection. 1—through plates; 2—stiffeners

6.3 Design Method of Joints

269

6.3 Design Method of Joints 6.3.1 Beam-to-Column Joints of Concrete-Filled Steel Tubular (CFST) Structures The use of the stiffening ring is a common form of beam-to-column joints of CFST structures, as shown in Fig. 6.6. This form of the joint is safe and reliable, and it is also convenient for core concrete placement. The engineering practice of CFST structures proves that the strengthening rings can act together with the CFST columns, and reliably transfer the internal force of the beams to the steel tubes, and then to the entire columns. Moreover, the existence of the strengthening rings makes the tube walls uniformly stressed, prevents local stress concentration, improves the force performance of the joint, and enhances the stiffness of the joints. When the beam is the welded I-steel beam, the upper and lower flange plates at the end of the beam are gradually widened as they approach the column, and they are connected with the column to enclose the column to form a stiffening ring. The bending moment and axial force at the beam end are carried by the upper and lower stiffening ring. The shear force is transmitted to the column by the web through the welding. To facilitate the assembly and connection on site, the beam ends are welded together with the stiffening ring and column sections to form small pieces of steel beams. For on-site construction, the two are welded together with the same strength. To facilitate construction, the web can be connected with high-strength bolts. When the diameter of the steel tube is large, the detailing of the inner stiffening ring can also be adopted in accordance with the necessity of engineering projects. According to DL/T 5085-2021 Code for Design of Steel–Concrete Composite Structure and DBJ/T 13-51-2010 Technical Specification for Concrete-Filled Steel Tubular Structures, there are generally four forms of plane stiffening ring plate for rigid joints in circular CFST structure, as shown in Fig. 6.6 (1). There are generally three forms of plane stiffening ring plate for rigid joints in square CFST structure, as shown in Fig. 6.6 (2). Type III and IV shown in Fig. 6.6 (1) and Type II stiffening ring plate shown in Fig. 6.6 (2) have a smooth profile and no obvious stress concentration. In practical engineering projects, the fabrication and welding quality of the stiffening ring plate should be ensured to reduce the influence of residual stress and imperfection and avoid stress concentration. Flexural failure at the beam end and failure of combined compression and bending at the column end are typical failure modes of steel beam-to-CFST column joints under cyclic loading, as shown in Fig. 6.7 (1a) and (2a), respectively. The corresponding measured load (P)-displacement (Δ) relationships of the joints are shown in Figs. 6.7 (1b, 1c) and (2b, 2c), respectively. When the joint with failure at the beam end reaches the peak load, the lower flange of the steel beam buckles, the resistance begins to decline after reaching the peak load, and the degree of decline is related to that of buckling of the steel beam; When the joint with failure at the column end reaches the peak load, the steel tube

270

6 Design of Joints

1

1 b

t

b

t

t1

t1 bs D

bs D

(a) Type Ⅰ

(b) Type Ⅱ

1

1

α=45°

α=45°

≤30° t

b

t t1

b

t1

bs D

bs D

(c) Type Ⅲ

(d) Type Ⅳ

hs

≤30°

t

t

t

t1

t1

(a) Type Ⅰ

t1

tf

tf bs B

hs

1

hs

1

hs

hs

1

hs

(1) Joints with stiffening ring plate in circular CFST structures

bs B

bs B (b) Type Ⅱ

tf

(c) Type Ⅲ

(2) Joints with stiffening ring plate in square CFST structures

Fig. 6.6 Steel beam to CFST column joints with stiffening ring. 1—stiffening ring; D—Outside diameter of steel tube for circular CFST member or outside length of long side of steel tube for rectangular CFST member; B—Length of outer edge of steel tube for square CFST member or length of outer edge of short side of steel tube for rectangular CFST member; b—width of critical section of stiffening ring; bs —Flange width of steel beam; hs —Plan dimensions of rectangular CFST with stiffening ring; t 1 —Thickness of stiffening ring; t f —Flange thickness of steel beam

6.3 Design Method of Joints

271

in compression bulges, the resistance of the joint begins to decline slowly, the steel tube bulges and straightens repeatedly. When the beam is a precast reinforced concrete beam, the form of the joint shown in Fig. 6.8 can be used. The stiffening ring plate should be able to resist the bending moment and axial force at the end of the beam. The steel bracket (or web) should be able to resist the shear force at the end of the beam, and the stiffening ring plate

(a) The concrete around the steel tube was crushed and the floor slab concrete cracked

(b) The lower flange and ring plate buckled, the web slipped or buckled, and the weld was fractured.

(1) Flexural failure occurred at beam end

(a) The column was globally bent, and the concrete of the floor slab was cracked

(b) the steel tube buckled

Fig. 6.7 Failure modes of CFST joints and corresponding load (P)-displacement (Δ) relationship

272

6 Design of Joints

P (kN) 150 100 50 0 -50 -100 -150 -100

-50

0

-150 -100

100 Δ (mm)

50

0

-50

50

100 Δ (mm)

Fig. 6.7 (continued)

should be directly welded to the pre-embedded steel plate at the end of the beam or the main reinforcement in the beam. When the beam is reinforced concrete member, it can be realized by using continuous double beams or detailing of partial widening of the beam end so that the longitudinal reinforcement is continuously wrapped around the steel tube according to the specific conditions of the project. In the case of joint with an open bracket, the upper stiffening ring is generally subjected to tensile force and the bracket to shear force under the load at the end of the beam. The joint can also be in the form of a concealed bracket (web), which transmits forces in the same way as the joint with open bracket. When steel beam joint or reinforced concrete beam joint is adopted, the hysteresis characteristics, ductility coefficients and strength reserves are much higher than

6 6

2 A 1 1 5 5

4

A A A

3 (a) Joint with open bracket

(b) Joint with concealed bracket

Fig. 6.8 Reinforced concrete beam to CFST column joints with stiffening ring. 1—CFST column; 2—reinforcement concrete beam; 3—open bracket; 4—concealed bracket; 5—outer stiffening ring plate; 6—pre-embedded steel plate

6.3 Design Method of Joints

273

those of reinforced concrete frame joint under low-frequency cyclic loads. The joint cores usually do not fail and the plastic hinge locations at the beam ends are easily controlled, provided that the calculation and structural requirements of the beam ends are satisfied. Therefore, it is easier to achieve the seismic design requirement of “strong columns and weak beams, the stronger joints” by using steel beam or reinforced concrete steel to CFST columns joint with a stiffening ring. For reinforced concrete beam joint, the design of reinforcement at the end of the beam should satisfy the requirements of the current national standard GB 50010 Code for the Design of Concrete Structures, provided that the main reinforcement in the beam is reliably welded and anchored to the ring plate. The design of the joints of the frame structure located in the seismic zone shall satisfy the following requirements: (1) Adopt Type III and IV shown in Fig. 6.6 (1) or Type II shown in Fig. 6.6 (2) steel beam joint with stiffening ring or inner diaphragm. (2) When concrete beam joints are adopted, the design of the beam end shall satisfy the relevant requirements of the current national standard GB 50011 Code for Seismic Design of Buildings and GB 50010 Code for Design of Concrete Structures. (3) The verification of seismic performance of the stiffening ring plate can refer to the relevant provisions for steel structures of the current national standard GB 50011 Code for Seismic Design of Buildings. (4) The joint shall satisfy the following requirements: 1) The shape of the stiffening ring plate shall be smooth and free of cracks and nicks; 2) The horizontal weld between the steel tubes of the joint and the steel tube of the CFST column shall be of the same strength grade as the base material; 3) The butt weld between the stiffening ring plate and the flange of the steel beam shall adopt a penetration groove weld. (5) Avoid welding seams in the maximum stress area where plastic hinges may occur. The practical design of joints of CFST structures can be divided into the following processes: determination of joint design principles, selection of joint forms, joint calculation and selection of detailing. The calculation of joint generally includes: (1) (2) (3) (4)

Calculation of strength of joint; Verification of the flexural and shear strength of the joint itself; Calculation of joint plate (such as stiffening ring plate); Verification of the bond strength between the steel tube and core concrete in the joint zone.

274

6 Design of Joints

The detailing requirements of the stiffening ring plate are as follows: (1) 0.25 ≤ bs /D(B) ≤ 0.75; (2) For circular CFST member (shown in Fig. 6.6): 0.1 ≤ b/D ≤ 0.35, and b/t 1 ≤ 10; (3) For square CFST member (shown in Fig. 6.6): t1 ≥ tf ; in addition, for type I stiffening ring plates, hs /B ≥ 0.15t f /t 1 ; and for type II stiffening ring plates, hs / B ≥ 0.1t f /t 1 , where t f is the flange thickness of the steel beam connected with the ring plate. Where, D is the outer diameter of the steel tube of the circular CFST member; B is the outer width of the steel tube of the square CFST member; b is the width of the critical section of the stiffening ring plate; bs is the width of the stiffening ring plate; hs is the plane dimension of the stiffening ring plate of rectangular CFST member; t 1 is the thickness of the stiffening ring plate; t f is the thickness of the flange of the steel beam. In order to ensure that the shear force at the beam end can be effectively transferred from the steel tube to the core concrete, it is necessary to ensure that there is sufficient bond strength between the steel tube and the concrete. It is assumed that the bond stresses are uniformly distributed in the range between the midpoints of the upper and lower floor columns, as shown in Fig. 6.9. According to AIJ (2008), it is calculated as: ΔNic ≤ ψ · l · f a

Fig. 6.9 Stress transfer path. 1—beam; 2—column

(6.3.1.1)

6.3 Design Method of Joints

275

where, ΔN iC the axial force transmitted to the column by the floor beam of the i-th floor connected to the column (N), should be determined according to the axial force-moment curve of the CFST member; ψ cross-section circumference of steel tube inner surface (mm); l length between the midpoints of the upper and lower floor columns (mm); design value of the bond strength between the steel tube and concrete fa (N/mm2 ), for circular CFST member, f a = 0.225 N/mm2 ; for square and rectangular CFST member, f a = 0.15 N/mm2 . ΔN iC is determined as follows: Assume that the summation of shear force at the beam end is ΔN, N 1 is the axial compression applied on the column: (1) When N 1 ≥ 0.85f c Ac , the shear force at the end of the beam is resisted by the steel tube, and the bond strength between the steel tube and the concrete does not need to be verified; (2) When N 1 < 0.85f c Ac , and N 1 + ΔN 1 > 0.85f c Ac , ΔNiC = (N1 + ΔN1 ) − 0.85 f c Ac

(6.3.1.2)

(3) When N 1 + ΔN 1 < 0.85f c Ac , ΔNiC = ΔN1

(6.3.1.3)

In the practical calculation, if the bond strength does not satisfy the requirements, measures such as internal spacers or studs can be set in the inner wall of the steel tube in the joint zone as necessary to ensure the effective transmission of the shear force at the end of the beam.

6.3.2 Beam-to-Column Joints of Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid Structures Concrete-encased CFST hybrid structural columns can be connected to steel beams and reinforced concrete beams to form connection joints. Based on the experimental study of the reinforced concrete beam to concrete-encased CFST hybrid structural column joint, the failure mode can be divided into four categories, as shown in Fig. 6.10 (1a), (2a), (3a), (4a), which are: (1) flexural failure at the end of the reinforced concrete beam; (2) shear failure at the end of the reinforced concrete beam; (3) compression-flexural failure at the end of concrete-encased CFST hybrid structural column; (4) shear failure at the core zone of the joint. For flexural failure at the end of the beam, the concrete in the compression zone at the end of the beam

276

6 Design of Joints

crushes, the longitudinal reinforcement of the beam is bent under compression, and the resistance decreases obviously. For shear failure at the end of the beam, the main diagonal crack appears at the end of the beam, which cannot be completely closed when reverse loading. For compression-flexural failure at the end of the column, the concrete at the end of the column appears spalling, and horizontal penetration cracks are formed. For the shear failure at the core zone, the concrete in the core zone has an obvious peeling and spalling phenomenon. The load at beam end (P)-displacement (Δ) relationships for the four typical failure modes are shown in Fig. 6.10 (1b), (2b), (3b), and (4b), respectively. The P-Δ curve is generally linear from the application of axial force to yield load through loading at the end of the beam. At this stage, multiple transverse cracks appear on the surface of the slab, and the cracks can be closed at the reverse loading. When loading to the elasto-plastic stage, concrete cracks appear at the location corresponding to the failure mode, accompanied by the spalling of concrete and the yield of reinforcement. A certain reduction in the loading stiffness of the P-Δ curve occurs. After reaching the peak load, the structure enters the failure stage, and the resistance and stiffness decrease significantly under different loading cycles. The specimens with shear failure at the core zone and beam end deteriorate rapidly, and the cracks cannot be closed when reverse loading. The restoring force model for the seismic performance of the core zone of the beam-to-column joint of the concrete-encased CFST hybrid structure includes the skeleton curve and the hysteretic criterion, and is shown in Fig. 6.11. The key parameters of the skeleton curve were proposed by Han (2016), and should be calculated by the following equations. The stiffness of the descending stage (K d ) is proportional to the initial loading stiffness, and the ratio (K d / K a ) is about 0.01. K a = K core + K out + K s

(6.3.2.1)

K core = (0.26ξ + 0.47)(ρv,j + 0.12)G core Acore

(6.3.2.2)

  K out = 2.7ρv,j + 0.1 G out Aout

(6.3.2.3)

K s = 0.35G s As,v

(6.3.2.4)

Vy = 0.7Vu

(6.3.2.5)

γu = (−17ρv,j + 1) sin(2θp )(1300 + 12.5 f c' + 800ξ 0.2 ) × 10−6 where, initial loading stiffness of core zone (N/mm); Ka K core initial loading stiffness of core concrete (N/mm);

(6.3.2.6)

6.3 Design Method of Joints

277

Fig. 6.10 Failure modes of joint of concrete-encased CFST hybrid structural specimens and the corresponding load (P)-displacement (Δ) relationship

278

6 Design of Joints

Fig. 6.10 (continued) Vj

Fig. 6.11 Restoring force model V j -γ j of core zone of joint

B

Vu Vy

2′

4′

O

C′

1

Kd

A

3

1

C

K 1 a 2

1 γu

4

Kr

γj

A′ 3′

1′ B′

K out Ks Acore Aout As,v Gcore Gout Gs ρ v,j Vy Vu γu θp ξ

initial loading stiffness of concrete encasement (N/mm); initial loading stiffness of steel tube (N/mm); cross-sectional area of core concrete (mm2 ); cross-sectional area of concrete encasement (mm2 ); cross-section area of the fin to shear (mm2 ); shear modulus of core concrete (N/mm2 ); shear modulus of concrete encasement (N/mm2 ); shear modulus of steel tube (N/mm2 ); volumetric stirrup ratio of the core zone; yield shear force (N); shear resistance (N); ultimate shear deformation; the angle between diagonal and horizontal line of core concrete in core zone; confinement factor, shall be calculated in accordance with Eq. (1.1).

6.3 Design Method of Joints

279

The unloading and reloading processes need to be defined in the hysteretic criterion shown in Fig. 6.11. When the shear force in the core zone is less than the yield shear force (V y ), i.e. within the range of A' A, the core zone is loaded and unloaded linearly according to the initial loading stiffness (K a ). When the shear force in the core zone is greater than the yield shear force (V y ) and less than the shear resistance (V u ), i.e. within the range of B' B, the unloading stiffness (K r ) of the core zone is the same as the initial loading stiffness (K a ). After unloading linearly until the shear force is 0, the reloading process is loaded parabolically (e.g. 121' 2' ). When the shear deformation in the core zone is greater than the ultimate shear deformation (γ u ), i.e. the resistance is reduced by the stiffness of descending stage (K d ), the unloading stiffness (K r ) is discounted by the shear deformation at the unloading point. The reloading process is loaded parabolically, pointing to the opposite direction of the historical maximum load point (e.g. 343' 4' ). After that, if the loading is continued, it is loaded according to the skeleton curve. If unloading, unloading linearly is carried out according to the unloading stiffness calculated by Eq. (6.3.2.7).  Kr =

K  ζa γu γr

|γr | ≤ |γu | K a |γr | > |γu |

(6.3.2.7)

where, Kr Ka γr γu Nc ζ

unloading stiffness of the core zone (N); initial loading stiffness of core zone (N); shear deformation at unloading point; ultimate shear deformation; resistance of cross-section of CFST (N); parameters for correction of unloading damage, taken as 1.0.

According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, in frame structures, the rigid joints of concrete-encased CFST hybrid structural columns and the I-section steel beams shall conform to the following requirements: (1) Ring plate connections should be used; (2) The extension length of the ring plate flanges and vertical stiffening plates shall satisfy the joint construction requirements of the steel beams; (3) The flange and web of the steel beams shall be connected to the ring plates and the vertical stiffening plates respectively on site (Fig. 6.12). The beam-to-column rigid joints may adopt the form of steel beam ring plate joints shown in Fig. 6.12. The beam-to-column rigid joints which adopt the stiffening ring are safe and reliable, and it is also convenient for core concrete placement. The engineering practice of CFST structures proves that the stiffening rings can act together with the CFST columns, and reliably transfer the internal force of the beams to the steel tubes, and then to the entire columns. Moreover, the existence of the stiffening

280

6 Design of Joints

7

1 A

3 5 6

1

7

6 4

3

A

2

A––A

2

4 5

Fig. 6.12 Steel beam-to-column ring plate joint. 1—column; 2—Steel beam; 3—longitudinal reinforcement; 4—Steel tube; 5—ring plate; 6—vertical stiffening plates; 7—stirrups

rings makes the tube walls uniformly stressed, prevents local stress concentration, improves the force performance of the joint, and enhances the stiffnesses of the joints. In frame structure, the rigid joints of concrete-encased CFST hybrid structural columns and reinforced concrete beams shall conform to the following requirements: (1) When the spacing between the longitudinal reinforcement on both sides of the beam is greater than the outer diameter of the steel tube, it should use the detailing of the stiffening ring and stiffened I-section steel beam connections, as shown in Fig. 6.13a; (2) When the spacing between the longitudinal reinforcement on both sides of the beam is smaller than the outer diameter of the steel tube, it should make the longitudinal reinforcement bypass the steel tube. When a stiffening ring plate is used for connection, as shown in Fig. 6.13b, it should prefabricate the ring plate on the steel tube and weld the longitudinal reinforcement inside the reinforced concrete beam to the surface of the ring plate during construction. In the case of rigid beam-column joints, when the beam is reinforced concrete beam, in order to ensure that the force is reliably transmitted to the encased CFST, the beam-to-column rigid joint may be constructed with stiffened I-section beam. The stiffened I-section steel can make the plastic hinge of the beam end move outward, thereby effectively protecting the joint zone. Experimental results of concreteencased CFST hybrid structural column-reinforced concrete beam joints show that the stiffening ring plate connection joint can effectively transfer the load from the longitudinal reinforcement to the steel tube. Within the appropriate parametric ranges, joint failure will not occur. Joints are crucial to the seismic design of concrete-encased CFST hybrid structures. In the frame structures, both the steel beam joints and the reinforced concrete beam joints shall conform to the resistance calculation and detailing requirements to ensure that the core of the joints will not be damaged prematurely. The seismic design of beam-to-column joints shall conform to the following requirements:

6.3 Design Method of Joints

281 3

1

7

2

7

A

1

2

3

A

5

4

6

6

5

4 A––A

(a) When the spacing between the longitudinal reinforcement of the beam is greater than the outer diameter of steel tube 3

7

1

1 7

2

3

2

A

A

7

7 4

5 4

5 A––A

(b) When the spacing between the longitudinal reinforcement of the beam is less than the outer diameter of steel tube Fig. 6.13 Reinforced concrete beam-to-column joint. 1—column; 2—reinforced concrete beam; 3—longitudinal reinforcement; 4—Steel tube; 5—stiffening ring plate; 6—stiffened I-section steel; 7—stirrups

(1) When steel beams are used, the design of the beam end cross-section shall conform respectively to the relevant requirements of the current standards of the nation GB 50011 Code for Seismic Design of Buildings, GB 50017 Standard for Design of Steel Structures, and JGJ 99 Technical Specification for Steel Structure of Tall Building; (2) When reinforced concrete beams are used, the seismic verification of the stiffening ring plate shall conform to the requirements for steel structures in the current professional standard GB 50011 Code for Seismic Design of Buildings; (3) The shape of the stiffening ring plate shall be smooth and free of cracks and nicks; the horizontal weld between the steel tubes of the joint and the steel tubes of the column shall be of the same strength grade as the base material; the butt weld of the stiffening ring plate and the flange of the steel beam shall adopt penetration groove weld; (4) The diameter and spacing of the stirrups in the joints shall conform to the requirements of the current national standard GB 50011 Code for Seismic Design of Buildings;

282

6 Design of Joints

(5) The thickness of the ring plate in a joint shall be greater than the lesser value between 10 mm and the wall thickness of the steel tube. The width of the ring plate shall be greater than 40 mm and conform to the requirements of steel welding length. The yield strength of the ring plate steel shall not be lower than that of the steel tube and should not be lower than 355 N/mm2 . The welding process shall conform to the requirements of the current professional standard JGJ 18 Specification for Welding and Acceptance of Reinforcing Steel Bars; (6) When the longitudinal reinforcement of the beams and the steel tube are connected by a reinforcement connector, the connection length of the longitudinal reinforcement in the reinforcement connector shall not be less than the diameter of the longitudinal reinforcement, and the mechanical connection process shall conform to the relevant requirements of the current professional standard JGJ 107 Technical Specification for Mechanical Splicing of Steel Reinforcing Bars. The transverse connections between the steel tubes in the multi-chord concreteencased CFST hybrid structural columns shall conform to the corresponding detailing requirements. The built-in gusset plates of CFST members should be welded, and the gusset plates and the cross webs should be connected by bolts (Fig. 6.14). The design of the joint detailing between the encased CFST members of multichord concrete-encased CFST hybrid structures and the transverse bracings shall conform to the stiffness requirements of the structures, and no blind spots of concrete placement shall exist. The design, fabrication, manufacturing, splicing and acceptance of the joints of multi-chord concrete-encased CFST hybrid structural columns must conform to the requirements of relevant standards. The steel tube columns and connectors are to be processed in sections in the factory. After the pre-assembly of the sections is completed, they are to be dissembled into erection sections or unit parts and transported to the site for erection. The gusset plates are to be assembled in the factory, and to be pre-assembled with the bolt gusset plates before leaving the factory.

1 7 2

A 3 5 7 2

4

1 A

7

2

4 3

6

A-A

Fig. 6.14 Connection of steel tubes in a multi-chord column. 1—Steel tube; 2—cross webs; 3— Gusset plates; 4—splice bolts; 5—longitudinal reinforcement; 6—stirrups; 7—batten plates

6.3 Design Method of Joints

283

6.3.3 Concrete-Filled Steel Tubular (CFST) Chord to Steel Tubular Web Joints The CFST chord and the steel tubular web connection joint (like K-joint, N-joint, T-joint, Y-joint, and X-joint) are the key to the mechanical performance of trussed CFST hybrid structure system. Due to the core concrete filled in the steel tube of the chords, the steel tube and core concrete are complementary to each other and act together, which can effectively avoid the common punching shear failure and plastic failure on the surface of the chords in hollow steel tubular joints. (1) K-joint and N-joint There are two types of failure modes of hollow steel tubular K-joint, (1) plastic failure of the chord surface, that is, inward buckling failure of the chord at the web in compression; (2) punching shear failure of the chord, that is, tensile punching shear of the chord surface at the web in tension. Filling the core concrete in the K-joint can effectively reduce the inward buckling deformation of the chord steel tube and transfer the lateral load of the web to a larger area, which delays the development of plastic deformation of the surface of the chord and improves the resistance and ductility of CFST chord to steel tubular web joints. There are generally five typical failure modes CFST chord-steel tubular webs K-joint, i.e. plastic failure of chord surface, punching shear failure of chord surface, tensile failure of tensioned webs, local buckling of compressed webs and local bearing failure of core concrete, as shown in Fig. 6.15. For the failure modes shown in Fig. 6.15a, d, e, the resistance of the joints is calculated as shown in Table 6.1. For the failure modes shown in Fig. 6.15b, c, because the core concrete can effectively restrain the tensile plastic deformation of the chord, it is safer to apply the provisions for calculating the tensile fracture for the web and the welding of the trussed hollow steel tubular joint to the corresponding CFST joint, which can be carried out according to the relevant provisions of the current national standard GB 50017 Standard for design of steel structures. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, to guarantee welding convenience and construction quality of the plane K-joint of the trussed CFST hybrid structures, to ensure the realization of the various performances specified in the calculation. The detailing of the intersecting welded plane K-joints and N-joints of trussed CFST hybrid structures shall conform to the following requirements: 1) Web shall not be inserted into the chord at the connection between the web and chord; 2) Eccentricity should be avoided at the connection of web and chord; and when eccentricity is unavoidable, the eccentricity shall satisfy the following inequalities (Fig. 6.16): −0.55 

e  0.25 D

(6.3.3.1)

284

6 Design of Joints

Tensile force F

Compressive force F 2

Compressive force F

2

2

2

Tensile force F

1

1

(b) Punching-shear failure of the butt joints

(a) Plastic failure of the chord surface Compressive force F Tensile force 2 2

Compressive Tensile force F force F 2

2 1

1

(d) Local buckling of the web to compression

(c) Tensile failure of the web to tension

Compressive force F 2

Tensile force F 2 1

(e) Local compressive failure of core concrete Fig. 6.15 Typical failure modes of K-joint. 1—CFST chord; 2—hollow steel tubular web

where, e load eccentricity (mm), as shown in Fig. 6.16; D outside diameter of the chord steel tube (mm). In the analysis of internal force, trussed CFST hybrid structures may be seen as hinged structural systems under certain conditions, so eccentricity at the joint shall be avoided as much as possible. If the eccentricity is unavoidable while not exceeding the limit of Eq. (6.3.3.1), the bending moment caused by the eccentricity may not be considered when calculating the resistance of the joints and the tension chords, but shall be considered when calculating the resistance of the compression chords. Lapped connections shall conform to the requirements of the current national standard GB 50017 Standard for Design of Steel Structures. 3) For the plane K-joints and N-joints overlapped by the web, the overlap ratio (ηov ) may be calculated in accordance with Eq. (6.3.3.2), and shall not be less than 25%, or greater than 100%.

6.3 Design Method of Joints

285

Table 6.1 Design of the CFST chord to the steel tubular web joint Failure mode Plastic failure of chord surface

Calculation method for resistance √ A2 A1 Nuc = 2ks f ck sin θ A1

Range of detailing 0.8 < β ≤ 1.5; 50 < γ ≤ 100

Local buckling of web to compression

Nuc = kw f yw π tw (dw − tw ) 0.2 ≤ β ≤ 0.8; 10 ≤ γ ≤ 50

Local compression failure of core concrete

A1 Nuc = 2 f ck sin θ

√

γ > 50

A2 A1

Note N uc —The resistance of the member determined by calculation (N); A1 —Area of lateral compression bar of the composite member (mm2 ); A2 —Dispersed bearing area of the composite member to lateral compression (mm2 ); d w —Outside diameter of steel tubular webs (mm); f ck —The characteristic value of compressive strength of concrete (N/mm2 ); f yw —The yield strength of the steel tubular web (N/mm2 ); k s —Reduction factor of resistance in case of plastic failure of the chord surface; k w —Reduction factor of resistance in case of local buckling of the web to compression; t w —Wall thickness of steel tube for web (mm); θ—Angle between web and chord (°); β—Ratio of outside diameter of steel tube of web to that of chord; γ —The ratio of the outside diameter to wall thickness of the steel tube for the chord

a

a e e=0

e>0 (a) Gap K-joint

1

(b) Gap N-joint

2

A' q p

2

B

B

e

A

1

A

e 0.3

k1 (Co − 1) + 1 Co ≤ 1 f (Co ) = k2 (Co − 1) + 1 Co > 1

k3 (λo − 1) + 1 λo ≤ 1.5 f (λo ) = λo > 1.5 k 4 λo + k 5

k6 (1 − n o )2 + k7 (1 − n o ) + 1 n o ≤ 1 f (n o ) = 1 no > 1

(7.3.5.4)

(7.3.5.5)

(7.3.5.6)

(7.3.5.7)

k1 = 0.13to

(7.3.5.8)

k2 = 0.14to3 − 0.03to2 + 0.01to

(7.3.5.9)

k3 = −0.08to

(7.3.5.10)

k4 = 0.12to

(7.3.5.11)

k5 = 1 − 0.22to

(7.3.5.12)

7.3 Design of Fire Resistance

319

k6 =

k7 =

−0.4to −2.7to2 + 0.64to − 0.1

to ≤ 0.2 to > 0.2

(7.3.5.13)

0.06to 1.2to2 − 1.83to + 0.33

to ≤ 0.2 to > 0.2

(7.3.5.14)

th tR

(7.3.5.15)

C 1256

(7.3.5.16)

λo =

λ 40

(7.3.5.17)

no =

n 0.6

(7.3.5.18)

to = Co =

where, kr C λ R to th tR

influence coefficient of resistance of CFST column after fire exposure; cross-sectional perimeter (mm); slenderness ratio of the structure; load ratio; heating time; heating time to the maximum fire temperature (s); fire resistance ratings (s).

It can be seen that, if the CFST member and the time of exposure to fire (t) are given, the influence factor of resistance of the member after the force, temperature and time path AA' B' C' D' E' shown in Fig. 7.3 can be easily calculated by Eq. (7.3.5.4) Then the resistance of the CFST member after the fire exposure can be calculated by the following equation: Nu (t) = kr · Nu

(7.3.5.19)

where, Nu resistance of CFST at ambient temperature (N); N u (t) resistance of CFST column after fire exposure (N); kr influence coefficient of resistance of CFST column after fire exposure. The influence coefficient of resistance k r of CFST column after fire exposure can also be determined in accordance with Table 7.4. (2) Residual deformation (umt )

320

7 Protective Design of Concrete-Filled Steel Tubular (CFST) Structures

Table 7.4 Influence coefficient of resistance k r of circular CFST column after fire exposure λ

C Heating time ratio t o (mm) 0.1

0.2

0.3

Load ratio R 0.2 20 942

0.6

0.8

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

0.978 0.989 0.992 0.992 0.956 0.979 0.983 0.983 0.837 0.923 0.975 0.975

1884

0.982 0.993 0.995 0.995 0.964 0.986 0.991 0.991 0.847 0.934 0.987 0.987

2826

0.982 0.994 0.996 0.996 0.965 0.987 0.992 0.992 0.850 0.936 0.99

3768

0.983 0.994 0.997 0.997 0.966 0.989 0.994 0.994 0.853 0.939 0.993 0.993

4710

0.984 0.995 0.997 0.997 0.968 0.990 0.995 0.995 0.855 0.942 0.996 0.996

5652

0.984 0.995 0.998 0.998 0.969 0.992 0.997 0.997 0.858 0.945 0.999 0.999

6280

0.985 0.996 0.998 0.998 0.970 0.993 0.997 0.997 0.860 0.947 1.000 1.000

40 942

0.99

0.974 0.985 0.988 0.988 0.949 0.971 0.976 0.976 0.828 0.912 0.964 0.964

1884

0.978 0.989 0.991 0.991 0.956 0.978 0.983 0.983 0.837 0.923 0.975 0.975

2826

0.978 0.990 0.992 0.992 0.957 0.980 0.984 0.984 0.840 0.925 0.978 0.978

3768

0.979 0.990 0.993 0.993 0.959 0.981 0.986 0.986 0.843 0.928 0.981 0.981

4710

0.980 0.991 0.993 0.993 0.960 0.982 0.987 0.987 0.845 0.931 0.984 0.984

5652

0.980 0.991 0.994 0.994 0.961 0.984 0.989 0.989 0.848 0.934 0.987 0.987

6280

0.981 0.992 0.994 0.994 0.962 0.985 0.990 0.990 0.849 0.936 0.989 0.989

60 942

0.970 0.981 0.984 0.984 0.941 0.963 0.968 0.968 0.818 0.901 0.952 0.952

1884

0.974 0.985 0.987 0.987 0.948 0.970 0.975 0.975 0.827 0.911 0.963 0.963

2826

0.974 0.986 0.988 0.988 0.950 0.972 0.976 0.976 0.830 0.914 0.966 0.966

3768

0.975 0.986 0.989 0.989 0.951 0.973 0.978 0.978 0.832 0.917 0.969 0.969

4710

0.976 0.987 0.989 0.989 0.952 0.974 0.979 0.979 0.835 0.920 0.972 0.972

5652

0.976 0.988 0.990 0.990 0.954 0.976 0.981 0.981 0.837 0.923 0.975 0.975

6280

0.977 0.988 0.990 0.990 0.955 0.977 0.982 0.982 0.839 0.924 0.977 0.977

80 942

λ

0.4

0.976 0.987 0.990 0.990 0.953 0.975 0.980 0.980 0.833 0.917 0.969 0.969

1884

0.980 0.991 0.993 0.993 0.960 0.982 0.987 0.987 0.842 0.928 0.981 0.981

2826

0.980 0.992 0.994 0.994 0.961 0.983 0.988 0.988 0.845 0.931 0.984 0.984

3768

0.981 0.992 0.995 0.995 0.962 0.985 0.990 0.990 0.848 0.934 0.987 0.987

4710

0.982 0.993 0.995 0.995 0.964 0.986 0.991 0.991 0.850 0.937 0.990 0.990

5652

0.982 0.993 0.996 0.996 0.965 0.988 0.993 0.993 0.853 0.939 0.993 0.993

6280

0.983 0.994 0.996 0.996 0.966 0.989 0.993 0.993 0.854 0.941 0.995 0.995

C Heating time ratio t o (mm) 0.4

0.5

0.6

Load ratio R 0.2 20 942 1884

0.4

0.6

0.8

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

0.677 0.826 0.919 0.919 0.524 0.737 0.863 0.863 0.380 0.655 0.807 0.807 0.689 0.840 0.934 0.934 0.537 0.755 0.884 0.884 0.392 0.677 0.834 0.834 (continued)

7.3 Design of Fire Resistance

321

Table 7.4 (continued) λ

C Heating time ratio t o (mm) 0.4

0.5

0.6

Load ratio R 0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

2826

0.693 0.846 0.940 0.940 0.543 0.764 0.894 0.894 0.399 0.689 0.849 0.849

3768

0.697 0.851 0.946 0.946 0.549 0.772 0.904 0.904 0.407 0.702 0.865 0.865

4710

0.702 0.856 0.952 0.952 0.555 0.780 0.913 0.913 0.414 0.715 0.881 0.881

5652

0.706 0.861 0.957 0.957 0.561 0.789 0.923 0.923 0.422 0.728 0.897 0.897

6280

0.709 0.864 0.961 0.961 0.565 0.794 0.930 0.930 0.427 0.736 0.907 0.907

40 942

0.667 0.813 0.904 0.904 0.514 0.723 0.846 0.846 0.371 0.640 0.788 0.788

1884

0.678 0.827 0.920 0.920 0.527 0.740 0.866 0.866 0.383 0.661 0.814 0.814

2826

0.682 0.832 0.925 0.925 0.532 0.749 0.876 0.876 0.390 0.673 0.830 0.830

3768

0.686 0.837 0.931 0.931 0.538 0.757 0.886 0.886 0.397 0.686 0.845 0.845

4710

0.691 0.842 0.937 0.937 0.544 0.765 0.895 0.895 0.405 0.698 0.860 0.860

5652

0.695 0.847 0.942 0.942 0.550 0.773 0.905 0.905 0.412 0.711 0.876 0.876

6280

0.697 0.851 0.946 0.946 0.554 0.779 0.912 0.912 0.417 0.719 0.886 0.886

60 942

0.656 0.800 0.890 0.890 0.504 0.708 0.829 0.829 0.362 0.624 0.769 0.769

1884

0.667 0.814 0.905 0.905 0.516 0.726 0.849 0.849 0.374 0.645 0.795 0.795

2826

0.671 0.819 0.911 0.911 0.522 0.734 0.859 0.859 0.381 0.657 0.810 0.810

3768

0.675 0.824 0.916 0.916 0.528 0.742 0.868 0.868 0.388 0.669 0.825 0.825

4710

0.680 0.829 0.922 0.922 0.533 0.750 0.878 0.878 0.395 0.681 0.840 0.840

5652

0.684 0.834 0.927 0.927 0.539 0.758 0.887 0.887 0.402 0.694 0.855 0.855

6280

0.686 0.837 0.931 0.931 0.543 0.763 0.893 0.893 0.407 0.702 0.865 0.865

80 942

0.672 0.820 0.911 0.911 0.519 0.730 0.854 0.854 0.375 0.647 0.798 0.798

1884

0.684 0.834 0.927 0.927 0.532 0.748 0.875 0.875 0.387 0.669 0.824 0.824

2826

0.688 0.839 0.933 0.933 0.538 0.756 0.885 0.885 0.395 0.681 0.840 0.840

3768

0.692 0.844 0.938 0.938 0.544 0.764 0.895 0.895 0.402 0.694 0.855 0.855

4710

0.696 0.849 0.944 0.944 0.550 0.773 0.904 0.904 0.409 0.707 0.871 0.871

5652

0.700 0.854 0.950 0.950 0.556 0.781 0.914 0.914 0.417 0.719 0.886 0.886

6280

0.703 0.857 0.953 0.953 0.560 0.787 0.921 0.921 0.422 0.728 0.896 0.896

Note Intermediate values in the table are obtained by linear interpolation

The main factors affecting the residual deformation (umt ) of the CFST column after the fire exposure include: the heating time ratio (t o ), the cross-sectional size (crosssectional perimeter C), the slenderness ratio (λ), the load eccentricity (e/r), the load ratio (R) and the thickness of the fireproof coating (a). With the six parameters t o , C, λ, e/r, n and a as the basic variables, the equations for the calculation of umt for circular CFST were presented in Han et al. (2022), and should be calculated in accordance with the following equations:

322

7 Protective Design of Concrete-Filled Steel Tubular (CFST) Structures

u mt = f (to ) · f (λo ) · f (Co ) · f (n o ) · f (a) + f (eo )

(7.3.5.20)



0 to ≤ 0.2 2 77.25to − 19.1to + 0.73 0.2 < to ≤ 0.6

−1.05λ2o + 3.3λo − 1.25 λo ≤ 1.5 f (λo ) = λo > 1.5 u 1 λ2o + u 2 λo + u 3

u 4 (Co − 1) + 1 Co ≤ 1 f (Co ) = u 5 (Co − 1) + 1 Co > 1

2.34n 2o − 1.8n o + 0.46 n o ≤ 1 f (n o ) = no > 1 2.1(n o − 1) + 1  a 3  a 2  a +1 f (a) = −6.35 + 12.04 − 6.29 100 100 100 (non-reactive fireproof coating)

f (to ) =

f (a) = −0.24

 a 3  a 2  a + 1 (cement) + 0.97 − 1.64 100 100 100

eo ≤ 0.3 u 6 eo f (eo ) = u 7 eo + u 8 eo > 0.3

u5 =

u6 =

(7.3.5.21)

(7.3.5.22)

(7.3.5.23)

(7.3.5.24)

(7.3.5.25) (7.3.5.26)

(7.3.5.27)

u 1 = −2.77to + 2.49

(7.3.5.28)

u 2 = 11.78to − 11.38

(7.3.5.29)

u 3 = −11.44to + 12.81

(7.3.5.30)

u 4 = −2.2to + 2.44

(7.3.5.31)

6to − 1.2 −2.78to + 2.32

to ≤ 0.4 0.4 < to ≤ 0.6

(7.3.5.32)

4.85to −46.3to + 10.23

to ≤ 0.2 0.2 < to ≤ 0.6

(7.3.5.33)

u 7 = 171.03to2 − 12.72to

(7.3.5.34)

u 8 = 0.3(u 6 − u 7 )

(7.3.5.35)

7.3 Design of Fire Resistance

323

th tR

(7.3.5.36)

C 1256

(7.3.5.37)

λo =

λ 40

(7.3.5.38)

no =

n 0.6

(7.3.5.39)

e r

(7.3.5.40)

to = Co =

eo = where, umt C λ R to th tR eo e r

residual deformation of CFST column after fire exposure (mm); cross-sectional perimeter (mm); slenderness ratio of the member; load ratio; heating time ratio; heating time to the maximum fire temperature (s); fire resistance ratings (s); load eccentricity; axial load eccentricity (mm); for circular CFST member, r = D/2, where D is the outer diameter of steel tube of circular CFST member (mm).

(3) Influence coefficient of flexural stiffness after fire exposure (k B ) The influence coefficient of flexural stiffness of CFST after fire exposure (k B ), force, temperature and time path is defined as AA' B' C' D' E' in Fig. 7.3, expressed as follows: kB =

K c (t) Kc

(7.3.5.41)

where, kB influence coefficient of flexural stiffness after fire exposure; Kc flexural stiffness of CFST member at ambient temperature; K c (t) flexural stiffness of CFST member after fire exposure. The parameters affecting k B are mainly the time of exposure to fire (t), crosssectional perimeter (C) and cross-sectional steel ratio (α s ) of CFST members, and the calculation equations for the influence coefficient of flexural stiffness after fire exposure k B of circular CFST members presented in Han et al. (2022) are as follows:

324

7 Protective Design of Concrete-Filled Steel Tubular (CFST) Structures



(1 − 0.18to − 0.032to2 ) · f (αo ) · f (Co ) to ≤ 0.6 (−0.077 ln to + 0.842) · f (αo ) · f (Co ) to > 0.6

a · (αo − 1) + 1 αo ≤ 1 f (αo ) = αo > 1 1 + b · ln(αo )

to ≤ 0.3 0.3to2 + 0.17to a= 0.11 · ln(100to ) − 0.296 to > 0.3

to ≤ 0.3 0.17to2 + 0.09to b= 0.059 · ln(100to ) − 0.159 to > 0.3

c · (Co − 1)2 + d(Co − 1) + 1 Co ≤ 1 f (Co ) = Co > 1 e · ln(Co ) + 1

3 5to − 3.3to2 + 0.1to to ≤ 0.3 c= 0.12to2 − 0.32to − 0.047 to > 0.3

0.16to2 − 0.026to to ≤ 0.45 d= 0.018to + 0.013 to > 0.45

to ≤ 0.45 0.039to2 + 0.07to e= 0.034 · ln(100to ) − 0.09 to > 0.45

kB =

(7.3.5.42)

(7.3.5.43)

(7.3.5.44)

(7.3.5.45)

(7.3.5.46)

(7.3.5.47)

(7.3.5.48)

(7.3.5.49)

αs 0.1

(7.3.5.50)

to = 0.6t

(7.3.5.51)

αo =

Co =

C 1884

(7.3.5.52)

where, kB t C αs

influence coefficient of flexural stiffness after fire exposure; time of exposure to fire (h); cross-sectional circumference (mm); cross-sectional steel ratio, shall be calculated in accordance with Eq. (1.3.2).

7.3.6 Detailing Requirements of Fire Protection (1) Fireproof coatings According to GB 51249-2017 Code for Fire Safety of Steel Structures in Buildings, fire protection measures should be taken for CFST columns based on load ratio (R) and resistance coefficient during fire (k T ) in accordance with the following provisions:

7.3 Design of Fire Resistance

325

1) when R < 0.75k T , fire protection measures can not be taken; 2) when R ≥ 0.75k T , fire protection measures shall be taken. If the value of resistance coefficient (k T ) of the CFST column without fire protection cannot satisfy the design requirements, the outer steel tube shall be protected with effective fireproof measures according to the design requirements. Commonly used fireproof coatings are cement mortar, non-reactive fireproof coating for steel structures. Non-reactive fireproof coating for steel structures, the performance of fireproof coatings should comply with the current national standard GB 14907 Fire Resistive Coating for Steel Structure and T/CECS 24-2020 Technical Specification for Application of Fire Resistive Coating for Steel Structure. Limited by the fire resistance performance of steel structures and the thermal insulation performance of the intumescent fireproof coating, the technical standards such as GB 51249 Code for Fire Safety of Steel Structures in Buildings prescribe that intumescent fireproof coating should not be employed for steel members with required fire resistance ratings greater than 1.5 h. However, CFST structures have relatively better fire performance. One of the reasons is the capacities of thermal absorption and storage of the concrete in the chord steel tubes, which can delay the heating rate of the steel tubes under fire exposure. Besides, concrete in the steel tubes makes a great contribution to the bearing capacity of structures, and the stress level of the steel tubes is relatively low, also the stress redistribution between the concrete and the tubes due to the different material degradation delays the deterioration of the structural resistance. Where the fireproof coating for steel structures is used for the protection of CFST structures, the intumescent fireproof coating may be used when the design fire resistance rating does not exceed 3.0 h, while non-reactive fireproof coating should be used when the design fire resistance rating exceeds 3.0 h. The state of the CFST specimens protected by intumescent fireproof coating for steel structures after fire is shown in Fig. 7.9. The fireproof coating reacted normally with carbonized foam during the test. The coating has an uneven distribution of different degrees of cracking phenomenon, and the global integrity of the fireproof coating does not appear to be a flaking phenomenon. There are many types of intumescent fireproof coatings for steel structures, with vastly different performances. When intumescent fireproof coating for steel structures is used for CFST structures, the following requirements shall be satisfied: 1) The thickness of the fireproof coating shall be determined by fire tests. When there are reliable references, it may also be determined based on calculation. Test methods shall conform to the requirements of the current national standard GB/T 9978.1 Fire-Resistance Tests—Elements of Building Construction—Part 1: General Requirements; 2) The intumescent fireproof coating shall be used in conjunction with the anticorrosion coating; 3) The intumescent fireproof coating shall conform to the relevant requirements for durability. In accordance with the requirements of the current national standard GB/T 9978.1 Fire-Resistance Tests—Elements of Building Construction—Part 1: General

326

7 Protective Design of Concrete-Filled Steel Tubular (CFST) Structures

Fig. 7.9 Failure mode of specimen with intumescent fireproof coating for steel structures

Requirements, conducting the standard fire test of full-scale or reduced-scale specimens under loading conditions is the most direct method to determine whether CFST structures under a specific load level and protected by a certain thickness of fireproof coating meet the fire resistance design requirements. On the other hand, for the CFST structures protected by the intumescent fireproof coatings, the fire resistance ratings are related to the critical temperature at the time of failure. After the critical temperature of the structure is obtained through a test or theoretical analysis, the base material may also be selected accordingly. The fire resistance test can be carried out in accordance with the current national standards GB 14907 Fire Resistive Coating for Steel Structure and GB/T 9978.1 Fire-Resistance Tests—Elements of Building Construction—Part 1: General Requirements to determine the thickness of the fireproof coatings. Based on engineering experiences, the thickness of the intumescent fireproof coating generally is not less than 1.5 mm. The thickness of the fireproof coating for CFST columns is an important parameter affecting its performance. So, it is important to determine the appropriate thickness of the fireproof coating. The results show that the main parameters affecting the thickness of the fireproof coating (a) of CFST columns include: the load ratio (R), the fire resistance ratings (t), cross-sectional size (e.g. cross-sectional perimeter C) and the slenderness ratio of the column (λ). For the circular CFST column with time of exposure to fire not more than 3.0 h under standard fire, the design value of the thickness of the fireproof coating was presented in Han et al. (2022), and can be calculated according to the following equations. 1) When the protective layer is metal mesh with M5 cement mortar: 

di = kLR (135 − 1.12λ) 1.85t − 0.5t 2 + 0.07t 3 C 0.0045λ−0.396

(7.3.6.1)

7.3 Design of Fire Resistance

kLR =

327

⎧ R−kT ⎪ ⎨ 0.77−kT

1 3.618−0.15t−(3.4−0.2t)R ⎪ ⎩ (2.5t + 2.3) R−kT 1−kT

R < 0.77 R ≥ 0.77 and kT < 0.77 kT ≥ 0.77

(7.3.6.2)

2) When the fireproof coating is non-reactive fireproof coating for steel structures: di = kLR (19.2t + 9.6)C 0.0019λ−0.28

kLR =

⎧ R−kT ⎪ ⎨ 0.77−kT

1 3.695−3.5R ⎪ ⎩ 7.2t R−kT 1−kT

R < 0.77 R ≥ 0.77 and kT < 0.77 kT ≥ 0.77

(7.3.6.3)

(7.3.6.4)

where, di kT R t C λ kLR

thickness of the fireproof coating (mm); resistance coefficient of CFST column during fire; load ratio; time of exposure to fire (h); cross-sectional perimeter (mm); slenderness ratio; calculation coefficient, when the value is greater than 1.0, take kLR = 1.0; when the value is less than 0, take kLR = 0.

For non-standard fires, the time of exposure to fire t in Eqs. (7.3.6.1) and (7.3.6.3) should be taken as the equivalent time of exposure. The equivalent time of exposure may be calculated in accordance with the relevant provisions of the current national standard GB 51249 Code for Fire Safety of Steel Structures in Buildings. Adopting the above equation to verify the fire resistance ratings and design of fire protection for CFST members according to the current national standard GB 512492017 Code for Fire Safety of Steel Structures in Buildings, the following conditions shall be satisfied: 1) Steel tubes should be made of Q235, Q345, Q390 and Q420 steel, strength class of the concrete is C30-C80, and the cross-sectional steel ratio is 0.04–0.20; 2) Slenderness ratio of the column should be 10–60; 3) Cross-sectional outer diameter of the circular CFST column should be 200– 1400 mm, the cross-sectional eccentricity ratio e/r should be 0–3.0 (e is the load eccentricity, and r is the outer diameter of the steel tube). For trussed CFST hybrid structure, the fire resistance ratings of the calculated unprotected trussed CFST hybrid structure does not satisfy the design requirements, effective fireproof measures should be taken according to the design requirements of its outer steel tube. The results of the fire test of trussed CFST hybrid structures show that under the same load ratio during fire, fire heating curve, chord size and material conditions, the fire resistance ratings of trussed CFST hybrid structures are slightly lower than those of the CFST members corresponding to the chords due

328

7 Protective Design of Concrete-Filled Steel Tubular (CFST) Structures

to the thermal deformations of the webs. Therefore, the chord of the trussed CFST hybrid structures may be protected against fire with 1.2 times the thickness of the fireproof coatings of the CFST members, resulting in a conservative design. When using non-reactive fireproof coatings or welded fabric with grout as fire protection measures, the fireproof coating thickness of the CFST chord may be determined in accordance with the relevant provisions of the current national standard GB 51249 Code for Fire Safety of Steel Structures in Buildings. When there is a reliable basis, steel mesh may also be added to the coating to enhance the strength of the coating structure in the joint zone and to ensure the reliability and stability of the coating during fire conditions. For non-reactive fireproof coatings, galvanized iron wire mesh or alkali-resistant glass fiber mesh is usually used. Intumescent fireproof coatings usually use alkali-resistant glass fiber mesh. The mesh measures adopted in the actual project shall be consistent with the measures in the inspection report or test report. (2) Vent holes Under high temperature, the free water and decomposition water in the core concrete will evaporate. In order to ensure the timely distribution of water vapor in the core concrete and the safe working of the structure, it is necessary to set vent holes in the steel pipe concrete columns. GB 51249-2017 Code for Fire Safety of Steel Structures in Buildings stipulates that vent holes with a diameter of 20 mm should be set in each floor of steel pipe concrete columns. Vent holes should be arranged one at the top and one at the bottom of each floor where the column intersects the floor slab, and the distance between vent holes and the floor slab (d v ) should be 100 mm, and should be arranged anti-symmetrically along the column body as shown in Fig. 7.10. When the floor height is greater than 6 m, vent holes should be added, and vent holes along the column height direction spacing should not be greater than 6 m. Fire resistance tests of CFST hybrid structures show that if there are not proper vent holes, the water vapor generated by the core concrete in steel tube during fire will easily cause the steel tube to tear up and the core concrete to spall, accelerating the destruction of CFST hybrid structures. Therefore, for CFST hybrid structures, proper number of vent holes shall be persevered to ensure the smooth discharge of water vapor at high temperatures.

1 dv

2

dv

Fig. 7.10 Schematic diagram of positions of vent holes in the CFST structures. 1—Vent holes; 2—Profiled steel sheet; 3—CFST column; 4—Concrete slab; 5—Steel beam

3

4

5

7.3 Design of Fire Resistance

329

≤ 4m 1

1

2

2

1

1

1

3

3

1 1

1

1

1

Fig. 7.11 Schematic diagram of positions of vent holes in the trussed CFST hybrid structure. 1—Vent holes; 2—CFST chords; 3—Webs

The chords of the trussed CFST hybrid structures shall set vent holes with a diameter of not less than 20 mm. The vent holes shall be arranged anti-symmetrically along the chord and shall avoid the joint zone. The longitudinal spacing of the vent holes should not exceed 4 m (Fig. 7.11). Vent holes with a diameter of not less than 20 mm shall be set on the steel tubes encased in the concrete-encased CFST hybrid structures. The arrangement of the vent holes shall ensure that the core concrete is connected to the outside air, and the water vapor inside the steel tubes can be smoothly discharged during fire. Vent holes should be arranged at the top and bottom of the intersection of each floor column and floor slab. The distance between the vent holes and the floor slab or the steel beam (d v ) shall be 100–200 mm, and the vent holes should be arranged anti-symmetrically along the column (Fig. 7.12). In engineering practices for concrete-encased CFST hybrid structures, the vent holes on steel tubes are reliably connected with one end of steel pipes, PVC tubes, or ceramic tubes, etc., and the other end of the tubes reach the external surface of the structure through the concrete encasement.

dv

1

dv

Fig. 7.12 Schematic diagram of positions of vent holes in the concrete-encased CFST hybrid structure. 1—Vent holes; 2—Encased CFST member; 3—Concrete encasement; 4—Steel beam; 5—Floor

2

1 3

5

4

330

7 Protective Design of Concrete-Filled Steel Tubular (CFST) Structures

7.4 Design of Impact Resistance During the life-cycle service of CFST structures, they may be threatened by impact hazards, such as vehicle or ship impact, rockfall impact, and mudflow impact, etc. Therefore, it is of great engineering practical value to understand the working mechanism of CFST structures under impact and to determine the design method of impact resistance based on it.

7.4.1 Basic Principles of Impact Resistance The comparison of the failure mode of CFST members under lateral impact is shown in Fig. 7.13. The global lateral bending deformation of the hollow steel tubular member in Fig. 7.13a is small. The local deformation near the impact area is large and even the whole section is flattened. In Fig. 7.13b, the CFST member has obvious overall lateral bending deformation, and the local deformation near the impact area is relatively small compared with the hollow steel tubular member. The core concrete at the bottom of the impact area is cracked under tension, but maintains good integrity. The failure mode of the CFST specimen clearly shows the synergistic complementarity between the steel tube and the core concrete under the lateral impact loading: on one hand, the mechanical performance of the steel tube are fully utilized due to the supporting effect of the core concrete, which can delay or avoid the premature local buckling of the steel tube. The structure has an obvious plastic hinge region, which effectively dissipates the impact energy. On the other hand, due to the confinement effect of the outer steel tube, the core concrete does not show premature serious failure, which can also improve the deformation capacity and energy dissipation capacity of the specimen. CFST structures in practical engineering are subjected to a variety of impact conditions, taking the loading condition of “long-term load + steel tube corrosion + impact” as an example. In this case, the loading path of the structure is shown in Fig. 7.14. The load action can be divided into three stages: Stage ➀ (O-A-B): the CFST column is first axially loaded to the normal service load (N 0 ). Then for a period of time (0 − t 1 , which can last for several years to decades), the member is subjected to the constant long-term load and suffers from corrosion. Stage ➁ (B-P-C): at the moment t 1 , the member is subjected to lateral impact, and the impact load timehistory curve is shown in B-P-C. The impact load reaches the peak point P at t 2 . The total duration of the impact is t 3 − t 1 (usually in the tens of microseconds to seconds). Stage ➂ (C-D): at the end of the impact, the member is axially loaded to failure in order to determine its axial residual resistance (N u ). Four comparative cases are designed and calculated under the following conditions: case 1: the member is not subjected to long-term load, corrosion and impact, and is directly loaded in axial compression to failure; case 2: the member is subjected

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331

(a) Hollow steel tubular specimen

Core concrete

(b) CFST specimen Fig. 7.13 Comparison of failure modes between hollow steel tubular and CFST specimens under impact loading Long-term load

Axial force

Axial force

Impact

Corrosion (chloride)

(a) Loading process N Nu

D (0,t4,Nu) B(0,t1,N0)

A(0,0,N0)

O

t1

t2

P(Fp,t2,N0)

C(0,t3,N0)

t3 t

Fp F

(b) Axial force (N) impact load (F) time (t) relationship

Fig. 7.14 “Long-term load + steel tube corrosion + impact load” loading path

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7 Protective Design of Concrete-Filled Steel Tubular (CFST) Structures N (kN) 10000

D1 D3

7500

D2 D4

5000 A 2500

0

0

C' B

C Example 1 Example 2 Example 3 Example 4

5

10

15

20

25

ua (mm)

Fig. 7.15 Axial load (N)-displacement (ua ) relationship

to impact; case 3: the member is subjected to long-term load and corrosion; case 4: the member is subjected to long-term load, corrosion and impact. All members are axially loaded in the final stage until failure. The basic calculation conditions are: the outside diameter of the steel tube of the CFST member is 400 mm, the wall thickness of the steel tube is 9.3 mm, the length of the member is 4000 mm, the steel tube adopts Q355 steel, and the core concrete adopts C60 concrete. Figure 7.15 shows the axial load (N)-displacement (ua ) relationship of the member for different cases. The axial load fluctuates during the impact phase. During the axial loading stage (O-A), all curves coincide. After that, cases 2, 3 and 4 enter the corrosion or impact stage, where the axial load of the member remains unchanged and the axial displacement continues to develop. It can be seen that the development of the axial displacement of the member under corrosion + impact loading (Example 4) is significantly greater than that of only corrosion or impact. This is due to the fact that the corrosion reduces the impact resistance of the member, so that the lateral deflection increases under the impact load, resulting in a larger axial displacement. It can be seen from Fig. 7.15 that the resistance of the member (N u ) can be obtained. The figure shows that corrosion and impact cause different degrees of resistance reduction of the member in axial compression. For example, the compression resistance of the member is reduced by 25% due to impact (Example 2), 11% due to long-term load and corrosion (Example 3), and 45% due to coupled action (Example 4). The reduction of the compression resistance of the member under long-term load, corrosion and impact load shows the coupling effect of three different loads: corrosion causes the reduction of the wall thickness of the steel tube of the member, which leads to the reduction of the impact resistance of the CFST column. Therefore, under the same impact energy, the lateral deflection in the mid-span of the corroded member increases. Due to the second-order effect of the axial long-term load, a larger bending moment is generated in the mid-span. At the same time, the cross-sectional steel ratio

7.4 Design of Impact Resistance

333

of the member is reduced due to corrosion, and the compression resistance of the member decreases significantly due to the combined action. The encased CFST is integrally bent and deforms without local buckling of the steel tube. The core concrete shows uniform cracks on the tensile side and maintains good integrity. The concrete encasement of the concrete-encased CFST hybrid structure can play an energy dissipating role when it is subjected to impact, which prevents the encased CFST from yielding prematurely. At the same time, the encased CFST as the core skeleton can ensure the residual resistance of the structure after the impact load and the repairability after the hazard (Fig. 7.16). Figure 7.17 shows the full-range loading-time relationship of the concrete-encased CFST hybrid structure under impact. According to the characteristics of the impact force time-history curve, it can be divided into three stages as follows: (1) Peak stage (OAA' ): At the moment corresponding to point O, the drop hammer contacts with the member, and the impact load then increases rapidly, reaches Concrete encasement

Encased CFST

Cracks

Core concrete

Fig. 7.16 Failure mode of concrete-encased CFST hybrid structure under impact

F

Δ

A

B

B

A' A

C O

A'

(a) Impact load (F)-time (t) history

C

t

O

t

(b) Mid-span deflection (Δ)-time (t) history

Fig. 7.17 Full-range loading of concrete-encased CFST structure under impact

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7 Protective Design of Concrete-Filled Steel Tubular (CFST) Structures

the peak at point A, and then drops rapidly to near zero. At this time, the drop hammer almost separates from the member. It can be seen from Fig. 7.17b that, the development of mid-span deflection at this stage is limited, and the member mainly produces local deformation in the impact zone. (2) Platform stage (A' B): After the initial impact, the hammer and the member move downward together. The plastic deformation of the member is fully developed. At this stage, the impact load is kept near a constant value and the mid-span deflection is fully developed and reaches peak value. (3) Descending stage (BC): The impact load decreases gradually in the BC stage and reaches zero at the corresponding point C. The mid-span deflection also decreases with the recovery of the elastic deformation of the specimen.

7.4.2 Design Methods of Impact Resistance CFST structure mainly has a flexural failure under impact, so the important index of impact resistance is its dynamic flexural strength. Based on the results of the parametric analysis, the practical equation for calculating the dynamic bending strength of the cross-section of the CFST structure can be obtained by regression analysis. According to GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the bending resistance of CFST structures subjected to impact shall satisfy the inequality in the following equation: Md ≤ R d Mu

(7.4.2.1)

where, M d design value of impact bending moment (N mm), when CFST hybrid structures are impacted by vehicles, ships, etc., the design impact loads may be determined in accordance with the relevant provisions in the current professional standard JTG/T 3360-02 Specifications for Collision Design of Highway Bridges; Rd dynamic increase factor under impact; M u static bending resistance (N mm), should be calculated by Eq. (4.2.2.6) of this book for the CFST chord, and in accordance with the relevant requirements in Sects. 5.3.2–5.3.4 of this book for concrete-encased CFST hybrid structures. The main factors affecting the dynamic increase factor under impact Rd include: steel strength ( f y ), cross-sectional steel ratio (α), cross-sectional diameter (D) and impact velocity (V 0 ). Based on the regression analysis, a practical equation for the dynamic increase factor under impact Rd is obtained, as shown in Eqs. (7.4.2.2), (7.4.2.7) and (7.4.2.19). (1) CFST chord Rd = 1.49 f 1 f 2 f 3 f 4

(7.4.2.2)

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335

f 1 = −4.00 × 10−7 f y2 + 8.00 × 10−5 f y + 1.02

(7.4.2.3)

f 2 = −3.66αs2 − 0.896αs + 1.13

(7.4.2.4)

f 3 = 7.00 × 10−7 D 2 − 1.30 × 10−3 D + 1.40

(7.4.2.5)

f 4 = −1.00 × 10−3 V02 + 5.08 × 10−2 V0 + 0.385

(7.4.2.6)

where, Rd fy αs D V0 f 1, f 2, f 3, f 4

dynamic increase factor for the CFST chord under impact; yield strength of the steel tube (N/mm2 ); cross-sectional steel ratio of chord; outside diameter of the chord steel tube (mm); impactor velocity (m/s); coefficients.

Equation (7.4.2.2) is the dynamic increase factor for a pinned single circular CFST member under lateral impact of a rigid body at midspan. For other conditions, such as impact on multiple chords or webs, and impact by deformable impactors like trucks, etc., the equation may be adopted for conservative designs. Equation (7.4.2.2) is applicable when the impactor velocity is from 10 to 28 m/s. f 1 , f 2 , f 3 , and f 4 are the coefficients that consider the influence of yield strength of the steel tube, cross-sectional steel ratio, outside diameter-to-sectional width ratio, and the impactor velocity, respectively. (2) Single-chord concrete-encased CFST hybrid structures Rd = 1.52γm γg γv γn

(7.4.2.7)

γm = m 1 m 2 m 3 m 4

(7.4.2.8)

2 m 1 = 1.27 × 10−4 f cu,oc − 1.39 × 10−2 f cu,oc + 1.36

(7.4.2.9)

2 m 2 = −7.24 × 10−6 f cu,c + 1.69 × 10−3 f cu,c + 0.925

(7.4.2.10)

m 3 = −2.31 × 10−4 f yl + 1.07

(7.4.2.11)

m 4 = 3.37 × 10−4 f y + 0.883

(7.4.2.12)

γg = g1 g2 g3

(7.4.2.13)

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7 Protective Design of Concrete-Filled Steel Tubular (CFST) Structures

g1 = −5.92ρ + 1.06

(7.4.2.14)

g2 = 0.235αs + 0.978

(7.4.2.15)

 2 D D g3 = −0.238 + 7.70 × 10−2 + 1.02 B B

(7.4.2.16)

γv = −7.50 × 10−3 V02 + 0.136V0 + 0.354

(7.4.2.17)

γn = 3.08n 2 − 1.47n + 1.16

(7.4.2.18)

(3) Four-chord and six-chord concrete-encased CFST hybrid structures with identical encased CFST members Rd = 0.61γm γg γv γn

(7.4.2.19)

γm = m 1 m 2 m 3 m 4

(7.4.2.20)

2 m 1 = 5.78 × 10−5 f cu,oc − 4.64 × 10−3 f cu,oc + 1.10

(7.4.2.21)

2 m 2 = −4.89 × 10−5 f cu,c + 4.51 × 10−3 f cu,c + 0.905

(7.4.2.22)

m 3 = −1.33 × 10−6 f yl2 + 7.44 × 10−4 f yl + 0.898

(7.4.2.23)

m 4 = −7.26 × 10−4 f y + 1.25

(7.4.2.24)

γg = g1 g2 g3

(7.4.2.25)

g1 = 566ρ 2 − 12.6ρ + 1.07

(7.4.2.26)

g2 = −2.33αs + 1.23

(7.4.2.27)

D + 1.54 B

(7.4.2.28)

g3 = −2.74

γv = −7.00 × 10−3 V02 + 0.105V0 + 0.673

(7.4.2.29)

γn = 6.43n 2 − 4.22n + 1.71

(7.4.2.30)

7.4 Design of Impact Resistance

337

where, Rd f cu,oc f cu,c f yl fy ρ αs D B V0 n

dynamic increase factor for the concrete-encased CFST hybrid structure under impact; characteristic value of cube strength of the concrete encasement (N/mm2 ); characteristic value of cube strength of the core concrete (N/mm2 ); yield strength of the longitudinal reinforcement (N/mm2 ); yield strength of the steel tube (N/mm2 ); longitudinal reinforcement ratio; cross-sectional steel ratio of CFST members, shall be calculated by Eq. (1.3.2) of this standard; outside diameter of the chord steel tube (mm); cross-sectional width (mm); impactor velocity (m/s); axial load ratio, defined as the ratio between the design axial compression and the resistance of cross-section of the concrete-encased CFST hybrid structure to compression.

Equations (7.4.2.7) and (7.4.2.19) are the dynamic increase factors for pinned single-chord, four-chord and six-chord concrete-encased CFST hybrid structures under lateral impact of a rigid body at midspan, respectively. Equations (7.4.2.7) and (7.4.2.19) are applicable when the impactor velocity is lower than 12 m/s and the axial load ratio is less than 0.6. m1 , m2 , m3 , m4 , g1 , g2 , g3 , γ v and γ n are the coefficients that consider the influence of the strength of core concrete, the strength of concrete encasement, the yield strength of longitudinal reinforcement, the yield strength of the steel tube, the longitudinal reinforcement ratio, the cross-sectional steel ratio of CFST members, the outside diameter-to-sectional width ratio, the impactor velocity, and the axial load ratio of the concrete-encased CFST hybrid structures, respectively. Exercises 1. Briefly describe the similarities and differences between the influence of chloride corrosion on hollow tubular structures and CFST structures. 2. Briefly describe the influence of chloride corrosive environment on the mechanical performance of CFST structure and the corresponding design methods of corrosion resistance. 3. Briefly describe the influencing factors and pattern of the mechanical performance of CFST columns during fire and after fire exposure. 4. Briefly describe the design methods of fire resistance and the corresponding detailing for CFST structures. 5. Briefly describe the main design principles and methods of impact resistance of CFST structures.

Chapter 8

Construction, Inspection and Acceptance, Maintenance and Dismantling

Key Points and Learning Objectives Key Points This chapter describes the fabrication and erection of steel tubes, the placement of core concrete and concrete encasement, and the inspection, acceptance, maintenance and dismantling of CFST structures. Learning Objectives Familiarize with the method and process of fabrication and erection of steel tubes, and placement of core concrete and concrete encasement. Learn the requirements and regulations of inspection, acceptance, maintenance and dismantling of CFST structures.

8.1 Introduction The construction of concrete-filled steel tubular (CFST) structure includes the fabrication and erection of the steel tube and the construction of core concrete. For concrete-encased CFST hybrid structure, the placement of concrete encasement is also required. The construction quality of CFST structures shall conform to the relevant requirements of the current national standard GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures. Before the construction of CFST structures, construction management design shall be carried out, and technical documents like the corresponding special construction plans shall be prepared. The construction plans shall sufficiently consider the safety for the fabrication and erection of structures, and the placement of core concrete in CFST members and concrete encasement. The construction of CFST structures shall also conform to the requirements of relevant national laws and regulations regarding environmental protection. © China Architecture & Building Press 2024 L. Han, Theory of Concrete-Filled Steel Tubular Structures, https://doi.org/10.1007/978-981-99-2170-6_8

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8 Construction, Inspection and Acceptance, Maintenance and Dismantling

This chapter briefly discusses the fabrication and erection of steel structures, the construction of core concrete and concrete encasement, the inspection and acceptance, the maintenance and dismantling related to CFST structures.

8.2 Fabrication and Erection of Steel Structures Detailing design drawings shall be prepared for the fabrication of steel tubes for CFST structures based on the design and construction drawings. The segmentation and connection schemes for steel tubes shall be determined based on the production conditions, on-site construction conditions, transportation requirements, lifting capacities, erection conditions and erection methods. Assessment of the welding techniques shall be carried out for steel tube fabrication. Technical documents or plans for fabrication shall be determined based on the design documents, detailed drawings and experimental results. Curved steel tubes may be produced through cold bending, hot bending, etc. The produced curved steel tubes shall have smooth surfaces, without indentations and folds visible to the naked eye. The deviation of the bending shall conform to the requirements of the current national standard. To ensure that the material properties of steel remain unchanged, the stress caused by the deformation during production shall be controlled. The production length of steel tubes may be determined based on the transportation and lifting capacities. The steel tubes shall be welded using butt penetration welding. The weld quality levels and the joints of the tube units shall conform to the relevant requirements of the current national standards. For neighboring tubes, the longitudinal welding shall be staggered with a minimum distance (in the arch direction) no less than 5 times the wall thickness of the steel tube and 200 mm. The welding of steel tubes shall strictly follow the welding methods, technical parameters, and welding sequence required by the welding technical instructions. Figure 8.1 shows the butt joint of the outer steel tube of the CFST column. During the fabrication of the steel tubes, the surfaces may not be protected, but they shall not be placed in humid environments for a long period. After the steel tubes are fabricated, the debris inside the steel tube shall be cleaned. Mechanical or manual derusting may be used. The internal surfaces of the steel tubes in trussed CFST hybrid structures and the outer surfaces of the steel tubes in concrete-encased CFST hybrid structures shall have no visible greasy dirt, oxide, rust or other dirt that are not firmly attached. For the transportation and hoisting of steel tubes, the deformation limits of the members shall be set. The lifting points and lifting plans shall be determined based on the verification of the strength and stability of the steel tubular member, and temporary strengthening measures shall be taken when necessary. For concrete-encased threechord, four-chord, and six-chord trussed CFST hybrid structures, diaphragms shall be set at locations with relatively large transverse load and the ends of the transported element. The distance between the diaphragms shall not be greater than 8 m and 9

8.3 Placement of Core Concrete

341

Fig. 8.1 Butt joint of the outer steel tube of the CFST column

times the size of the longer edge of the cross-section. The steel tubes shall be sealed at the ends when lifting. After the erection and adjustment, temporary restraining measures shall be taken. For prefabricated trussed CFST hybrid structures, construction verifications shall be carried out for the lifting, transportation, erection, etc. The strength of the core concrete before lifting shall conform to the requirements of design instructions. The strength shall not be lower than 75% of the design strength when there is no specific design requirement. During the erection of the steel tubes of CFST arches or concrete-encased CFST hybrid arches, their deformation under construction load shall be reduced. The lifting points and lifting plans shall be determined based on the verification of the strength and stability of the members. If the verification fails to satisfy the requirements, temporary strengthening measures shall be taken. After the steel tubular segments are erected, they shall be adjusted timely, and temporary restraining measures shall be taken. Figure 8.2 shows the CFST arch of a long-span arch bridge during construction.

8.3 Placement of Core Concrete For the core concrete, the strength and compactness should be fully considered to ensure the design strength of the concrete, and make the core concrete and steel tube fully act together. The study based on typical engineering projects shows that the quality control of concrete can be achieved by placing the core concrete of the CFST structure according to the “trinity” process control concept. The placement of core concrete has the feature of concealment. So, construction process control is

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8 Construction, Inspection and Acceptance, Maintenance and Dismantling

Fig. 8.2 CFST arch of a long-span arch bridge during construction

especially important to make sure that the quality control of concrete construction can be achieved by controlling the construction process. To ensure smooth construction and structural safety, the placement of core concrete should be carried out after the erection and acceptance of steel tubes. This is because it is difficult or even impossible to adjust the structures later if concrete is placed first. The debris and water inside the steel tube shall be cleaned before concrete placement to avoid their unfavorable influence on the compactness, homogeneity and steel–concrete interface. During the placement, the fresh concrete attached upon the outside of the steel tube shall also be cleaned timely to avoid unfavorable influence on the placement of concrete encasement. It is strictly forbidden to add water during the process of transportation, conveying and placing. Concrete scattered during the process of transportation, conveying and placing is strictly forbidden to be used for the placement of CFST members. The placement of core concrete should employ the pumping and jacking-up method, manually placing and vibrating method, buried-pipeline placement method, and high-positioned dropping method. Pumping and jacking-up method should be employed for CFST arches. Before concrete placement, concrete mixing design and placement technical experiments shall be carried out in accordance with the design requirements, based on which the placement techniques and technical measures shall be determined, and the specified construction plans shall be drafted. The pumping and jacking-up method, manually placing and vibrating method, buried-pipeline placement method, and high-positioned dropping method are the mature methods in the

8.3 Placement of Core Concrete

343

Fig. 8.3 Pumping and jacking-up method. 1—steel tube; 2—core concrete; 3—pumping pipeline; 4—high pressure pipe valves; 5—pump pipe; 6—moving gate; 7—bayonet; 8—round hole of the same diameter; 9—concrete pump vehicle; 10—mixer-lorry

construction of CFST structures. Among these methods, the pumping and jackingup method is the easiest to control placement quality. Independent of the method adopted, the strength, compactness and homogeneity of concrete are to be ensured. For important engineering projects, reference specimens for CFST hybrid structures shall be preserved for quality inspection. (1) Pumping and jacking-up method The concrete is pumped into the steel tube from bottom to top by the pumping pressure. The concrete is compacted by its own weight and pumping pressure, as shown in Fig. 8.3. When using the pumping and jacking-up method, the mixture design of concrete shall be controlled based on the requirements of construction management design, the placement duration, the initial setting time of concrete, and the slump loss of concrete. The placement of concrete should be continuous. When using the pumping and jacking-up method, a jacking hole with a valve preventing the backflow of concrete can be opened at the proper location of the steel tube. The jacking hole is composed of the bayonet, moving gate and pumping pipeline. During pumping, the bayonet is connected to the pump through a draft tube, and concrete is continuously pumped into the steel tube from the bottom to the top, and there is normally no need for additional vibrating. The valve preventing the backflow of concrete can be removed after the final setting of the concrete. The size of the steel tube should be greater than or equal to twice the inner diameter of the pumping pipeline. The top of the steel tube and the internal partition should be equipped with overflow holes and air venting holes. The strength of the tube wall at the lower entrance of the member adopting the pumping and jacking-up method should be verified. After the placement is completed, the pressure should be stabilized for 2–3 min before closing the stop valve and removing the pumping pipeline. (2) Manually placing and vibrating method

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8 Construction, Inspection and Acceptance, Maintenance and Dismantling

Fig. 8.4 Manually placing and vibrating method. 1—Steel tube; 2—placement pipeline; 3— vibrator; 4—construction joint of concrete; 5—mortar of the same strength class as concrete, 100–150 mm thick; H—effective working range of vibrator or 2–3 m

The concrete is placed into the steel tube from the top to the bottom and vibrated with a vibrator to make the concrete compact, as shown in Fig. 8.4. Depending on the diameter of the tube and working conditions, it is more convenient to use this method when the diameter of the tube is larger than 350 mm. When using the manually placing and vibrating method, the erection of the hollow steel tube is fixed in place and before concrete placement, a layer of mortar of the same strength class as the concrete with a thickness of 100–150 mm, is generally placed first, in order to close the bottom of the tube and make the aggregates of the freefalling concrete to not bounce. The manually placing and vibrating method should be carried out section by section. After placing a certain amount of concrete, the internal or external vibrator should be used to vibrate. The height of each placement shall not be greater than the effective working range of the vibrator or 2–3 m. When the outer diameter of the steel tube is greater than 350 mm, the internal vibrator can be used for vibrating. The time of each vibrating should be 15–30 s, and the height of each placement should not be greater than 2 m. When the outer diameter of the steel tube is less than 350 mm, the external vibrator attached to the steel tube can be used for vibrating. The position of external vibrating should be adjusted with the process of concrete placement. (3) Buried-pipeline placement method The concrete is placed into the steel tube through the pipeline, and the end of the pipeline is buried in the concrete to a certain depth during the construction process. The concrete is placed at the same time as the pipeline is lifted. The concrete is filled

8.3 Placement of Core Concrete

345

continuously by the self-weight of the concrete to make the concrete compact, as shown in Fig. 8.5. When this method is used, the vertical distance from the bottom of the lower port of the pipeline before placing should not be less than 300 mm. When the erection of the hollow steel tube is fixed in place and before the concrete is placed, a layer of mortar with the same strength class as the concrete and thickness of 100–150 mm is usually placed first. In the process of placing, the depth of the lower port of pipeline buried in the concrete should be 1 m. The side gap between the pipeline and the horizontal spacer placing hole in the steel tube should not be less than 50 mm. When the pumping method is adopted for concrete placement, it is not appropriate to vibrate at the same time. The lifting speed of pipeline should be compatible with the rising speed of concrete in the steel tube. (4) High-positioned dropping method

300mm

The concrete is placed into the steel tube through a certain throwing height, making full use of the kinetic energy when the concrete falls to make the concrete compact. This method is generally applicable to the case where non-self-compacting concrete is used, the outer diameter of the steel tube is more than 350 mm, and the height of the fall is not less than 4 m and not more than 12 m, as shown in Fig. 8.6. A placing experiment shall be carried out before construction to test the working ability of the concrete. The high-positioned dropping method can be carried out by means of

Fig. 8.5 Buried-pipeline placement method. 1—Steel tube; 2—placing pipeline; 3—concrete construction joints; 4—mortar of the same strength class as concrete, 100–150 mm thick; 5—first concrete placement; 6—second concrete placement

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8 Construction, Inspection and Acceptance, Maintenance and Dismantling

2

Fig. 8.6 High-positioned dropping method. 1—Steel tube; 2—concrete hopper

4m

1

conveying by pipeline or dropping from the hopper. The size of the feed opening should be 100–200 mm smaller than the diameter of the steel tube to facilitate the discharge of air inside the tube. For the section where the drop height is less than 4 m, the internal vibrator shall be used to properly vibrate. When using the hopper dropping method, the amount of concrete to be dropped at one time should be about 0.7 m3 , and it shall be ensured that there is no bleeding and segregation in the concrete dropped into place. The mixture design of concrete shall be determined through experiments based on the construction techniques, strength and slump requirements. If there are intervals, the interval time shall not be longer than the initial setting time of concrete. When construction joints are required to be formed for core concrete, the joints shall be set at places where it is easy to fix the joints, and the steel tube shall be temporarily sealed. The butt weld shall be higher than the concrete joint for at least 500 mm, to avoid the influence of welding heat on the quality of concrete. When using the manually placing and vibrating method, buried-pipeline placement method, or highpositioned dropping method for concrete construction, a layer of cement plaster with a thickness of 100–150 mm shall be first placed if the placed concrete has reached final setting. When the concrete is placed on the top of the steel tube, the concrete may be allowed to overflow slightly and then fasten the interlayer diaphragm or top plate with vent holes tightly on the pipe end. Spot welding shall be performed simultaneously. Until the concrete strength reaches 50% of the design value, the welding of the interlayer diaphragm or top plate shall be repaired in accordance with the design requirements. The concrete may also be placed to a position slightly lower than the top of the steel tube. After the concrete strength reaches 60% of the design value, mortar of the same strength grade needs to be filled in, and weld the interlayer diaphragm or top plate subsequently. According to the provisions of GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the placement of core concrete shall conform to the following requirements:

8.4 Construction of Concrete Encasement

347

(1) The placing concrete shall have a good workability, without any segregation or bleeding; (2) Proper technical measures should be taken to reduce the hydration heat, to compensate the shrinkage based on the circumstances; (3) Before the placement of concrete, the welding quality of the steel tube, the equipment at site, and the quality and quantity of materials shall be inspected. The mixing and placement machines shall be jointly tried. And the internal surface of the steel tubes shall be cleaned; (4) A stable time period shall be chosen for the placement based on the design requirements. The temperature shall be higher than 5 °C. When the environmental temperature is higher than 30 °C, and the temperature of the steel tube surface is higher than 60 °C, measures should be taken to lower the temperature. The temperature of concrete in the form should not be higher than 35 °C. During the construction of mass concrete, the temperature of concrete in the form should not be higher than 30 °C. When the diameter of the steel tube is less than 400 mm, self-compacting concrete should be used for the core concrete. The post-placement holes, pumping holes, and vent holes of the core concrete placement shall be sealed in accordance with the design requirements, and the surface shall be smooth, and the cleaning shall be conducted on the surface together with the anti-corrosion. Core concrete in CFST members shall be compact, and the void between the steel tube and its core concrete shall not be greater than the limiting value of core concrete void in the steel tube (as described in Sect. 4.9 of this book). Otherwise, the void shall be filled. When core concrete in the steel tubes is placed in batches for concrete-encased CFST hybrid arch structures, the concrete placement technology shall be formulated in accordance with the design requirements, and the workability and placement temperature of concrete shall be strictly controlled; only after the concrete in the steel tube reaches more than 70% of the design value of strength can the concrete placement in the next segment of the same arch rib be conducted.

8.4 Construction of Concrete Encasement Before the construction of the concrete-encased CFST hybrid structures (shown in Fig. 1.19), the construction scheme and construction technology shall be determined in accordance with the construction characteristics of structures and field conditions, and various preparations shall be made. The concrete engineering of CFST hybrid structures includes concrete engineering for the concrete slab of trussed CFST hybrid structures and the concrete encasement of concrete-encased CFST hybrid structures. The steel reinforcement and formwork engineering of outer steel tubes shall be carried out after the construction and acceptance of encased hollow steel tubes or

348

8 Construction, Inspection and Acceptance, Maintenance and Dismantling

CFST members, and derusting and other cleaning work shall be carried out for the outer surfaces of the steel tubes before construction. Before the fabrication of the reinforcement, the connecting detailing of reinforcement and steel structures shall be inspected and documented. All the connections to the steel structures should be fabricated in the factory. Before the installation of formwork, the contact surface between the formwork and concrete shall be cleaned and coated with a release agent, and the release agent shall not pollute the steel reinforcement, contact point of concrete and outer surface of the steel tube. The construction of concrete encasement may be later than the construction of core concrete in steel tubes, or they may be constructed at the same time. When they are constructed at the same time, the design department shall recheck the strength and stability of the hollow steel tube. Single layer placement or multi-layer placement may be used for the concrete encasement. If multi-layer placement is adopted, the design department shall calculate the resistance and stability of structures in the construction stage, and put forward the placement layers and loading procedures of concrete-encased steel tube. The construction department shall carry out construction in accordance with the construction loading procedure specified in the design. The workability of the concrete encasement shall be selected in accordance with the placement method and vibration conditions. Waterproof, drainage detailing shall be taken for the connection of steel members and CFST structure. Figure 8.7 shows the construction of the concrete encasement for a bridge abutment. During the construction of CFST arch in concrete-encased CFST hybrid arch structures, openings in the steel tube and welding of temporary structures shall be

1

1

2

Fig. 8.7 Construction of concrete encasement. 1—CFST; 2—reinforced concrete

8.4 Construction of Concrete Encasement

349

subject to design approval, and structural reinforcement measures shall be taken. When cutting out the temporary steel members for construction, damage to the steel tubular arch is forbidden. For the construction of concrete encasement in concrete-encased CFST hybrid arch structures, the concrete placement should be divided into three or two rings and it should be carried out at 4–8 locations simultaneously. At each placement location of the concrete encasement of the main arch, there shall have at least formworks for two adjacent sections first installed, and construction joints (Figs. 8.8 and 8.9) shall be set. When concrete-encased CFST hybrid structures are used in the longspan concrete-encased CFST hybrid arch structures, in order to reduce the amount of steel tubes used, play the composite action of the cross-section in the construction stage, and reduce the steel tube stress in the placement phase of concrete-encased steel tube, one-off placement should not be adopted, concrete shall be placed in the way of sub-ring, and the placement of the next ring shall not be carried out until the concrete of the previous ring reaches the design strength. Figure 8.10 shows the construction of the concrete encasement for the main arch.

(a) Construction of the trussed CFST hybrid rid

(b) Construction of the first ring of concrete encasement: bottom part

(c) Construction of the second ring of concrete encasement: web part

(d) Construction of the third ring of concrete encasement: top part

Fig. 8.8 Schematic diagram for three-ring construction joints of the concrete encasement of the main arch

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8 Construction, Inspection and Acceptance, Maintenance and Dismantling

(a) Construction of the trussed CFST hybrid rid

(b) Construction of the first ring of concrete encasement: bottom and side web parts

(c) Construction of the second ring of concrete encasement: top and middle web parts Fig. 8.9 Schematic diagram for two-ring construction joints of the concrete encasement of the main arch

Fig. 8.10 Construction of the concrete encasement for the main arch

8.5 Inspection and Acceptance

351

8.5 Inspection and Acceptance In addition to the general requirements of the quality inspection and acceptance of CFST hybrid structures project, the inspection and acceptance of fire protection engineering shall also conform respectively to the relevant requirements of the current national standards. The allowable errors of erection, welding, the inspection of the quality of the outer and internal surface, the welding grade as well as the damage detection requirements of steel structures shall conform to the requirements of the current national standards. According to the provisions of GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, the compactness of the core concrete placement in the steel tube may be inspected by tapping, ultrasonic, impact-echo and other methods, and shall conform to the following requirements: (1) The inspections shall not be less than 4 times. The inspections should be carried out on 3 d, 7 d and 28 d after placement and before acceptance; (2) Check points may be selected according to the actual conditions of the projects in the manual tapping check. When the result of the manual tapping check is abnormal, the density of check points shall be increased to determine the ultrasonic detection range; (3) When an abnormality is found in the ultrasonic check, a drill hole re-examination shall be conducted. Each construction of the concrete encasement shall be carried out after the quality inspection of the previous process. Self-inspection, mutual inspection, and handover inspection shall be carried out. Quality problems found during the inspection shall be dealt with immediately. The appearance quality of the CFST structure shall not have serious imperfection or dimensional deviation which affects the performance and function of the structure. Solid quality inspection shall be carried out on representative parts involved in the safety of CFST structures. The following documents and records shall be provided during the acceptance of CFST structures subdivision project: (1) Project drawings, design changes and relevant design documents; (2) Quality certificate and performance test report of the raw materials; (3) Welding material product certificates, welding process documents and baking records; (4) Welder qualification certificate and welding scope; (5) Welding seam ultrasonic flaw detection or radiographic flaw detection report and record; (6) Inspection record of connection joint; (7) Record of concrete construction; (8) Performance test report of concrete specimens; (9) Inspection records of mandatory provisions test items and supporting documents;

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8 Construction, Inspection and Acceptance, Maintenance and Dismantling

(10) Acceptance record of concealed work; (11) Quality acceptance record of each sub-project and the quality acceptance record of each inspection lot; (12) Technical data, handling plan and acceptance records of major project quality and technical issues. The strength class, workability, and shrinkage characteristics of the core concrete in the steel tube of the CFST structures shall conform to the design requirements and current relevant standards of the nation. The curing method and time of the core concrete in the steel tube of CFST structures after placement shall conform to the requirements of the special construction plan. The state implements a fire safety acceptance system for special construction projects, and the fire safety acceptance of the special construction projects shall be conducted in accordance with the current relevant requirements. According to the provisions of GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures, when CFST structures are used in special construction projects, the constructor shall apply to the fire department for fire protection acceptance and submit the following materials: (1) Application form for fire protection acceptance; (2) Acceptance report of project completion; (3) Completion drawings of construction projects involving fire protection.

8.6 Maintenance and Dismantling Users of CFST structures shall establish a life-cycle based structural service and maintenance management system according to the structural safety level, structural type, design working life and service environment. Maintenance shall comply with the principle of prevention and combination of routine maintenance, periodic inspection and identification. CFST structure should be analyzed and calculated before dismantling. The construction unit shall prepare dismantling plans and safe operation procedures, adopt safe and green dismantling technology and reduce noise, dust, sewage, vibration and impact. Waste shall be removed in time to reduce the influence on the surrounding environment. Dismantling works should be approved in accordance with the prescribed procedures and technical briefing should be given to the operators to ensure the safety of the dismantling process. (1) Maintenance For daily maintenance of CFST structure, structural damage and changes in service load, etc. should be checked. The appearance of steel pipe concrete structure should focus on cracks, deflection, freezing and thawing, corrosion, corrosion of reinforcement, peeling of protective layer, water leakage, uneven settlement and damage such as man-made openings and breakage. For the concrete-encased CFST hybrid

8.6 Maintenance and Dismantling

353

structure in coastal or acidic environment, the neutralization and corrosion condition of the concrete encasement surface should be inspected. For structures in harsh environments, targeted maintenance programs should be developed. For structures subject to erosive media and structural parts that cannot be repainted during their service life, protective measures of enclosing and wrapping should be taken to enclose the cladding. In the design of detailing for structure, the dead ends or recesses where moisture and dust can accumulate shall be reduced. For concreteencased CFST hybrid structure, there shall be technical measures to prevent concrete cracking and infiltration. (2) Dismantling The dismantling of CFST structures should be analyzed according to the short-term working conditions, with the same safety requirements as in the construction stage. The worst possible scenarios for the dismantling process shall be considered. The change of constraint conditions shall be considered at each stage of dismantling. The stability and risks of the remaining structure should be analyzed, and the dismantling plan for the next stage should be adjusted and determined. No disassembly of the structure should be carried out at the dismantling site. Measures should be taken to ensure the stability of the remaining structure during the dismantling construction. If the partial dismantling affects the safety of the structure, it shall be reinforced before dismantling. When dismantling large and complex structures, the simulation and calculation analysis for dismantling construction should be carried out. For the reusable CFST members, its service life and maintenance methods should be considered. The dismantled steel tube and reinforcement shall be recycled and reused. Exercises 1. What are the types of steel tubes usually used in CFST structures? Take one of them as an example, and briefly explain its fabrication process. 2. Briefly describe the basic methods and applicable conditions for core concrete placement in CFST structures. 3. Briefly describe the key points of quality inspection of CFST construction. 4. Briefly describe the key technologies in the whole process of construction of concrete-encased CFST hybrid structures.

Chapter 9

Prospects of Concrete-Filled Steel Tubular (CFST) Structures

Key Points and Learning Objectives Key Points This chapter discusses the future of CFST structures. Learning Objectives Be familiar with the theoretical research framework of CFST structures in terms of their entire life cycle. Learn about the new trends in the development of CFST structures. As mentioned before, CFST structure has become one of the superior structural types of large-scale infrastructure constructed in China. The main reasons can be generally summarized as follows to: (1) High material compatibility. The steel tube and its core concrete have the confinement effect and are complementary to each other, which is conducive to effectively unleashing the structural merits of the CFST members. The reasonable ‘matching’ of materials promotes the efficient application of thin-walled steel tubes and high-strength concrete. (2) High structural performance. CFST structure has high strength and ductility, excellent seismic and fire resistance. Compared with the traditional reinforced concrete structure, the dispersion of indices for mechanical performance is relatively smaller and the structure has good reliability. (3) Reduced resource consumption. For load-bearing members with the same resistance, the use of CFST columns can save up to 50% of concrete compared with the corresponding reinforced concrete, and the construction is faster. Compared with the corresponding steel members, CFST can save up to 50% of steel and increase the fire resistance ratings by 2–3 times, which meets the requirements for sustainable development in civil engineering. (4) Suitable for engineering structures under extreme conditions. In recent years, large-scale infrastructure constructed in China tends to have super-long span, © China Architecture & Building Press 2024 L. Han, Theory of Concrete-Filled Steel Tubular Structures, https://doi.org/10.1007/978-981-99-2170-6_9

355

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9 Prospects of Concrete-Filled Steel Tubular (CFST) Structures

have towering height, bear super weight and long-term work under severe environmental conditions. The safety design of such main structures is facing unprecedented challenges. The use of CFST structure in accordance with the necessity of engineering projects can take advantage of its technical characteristics and economic merits, thus providing a new approach for the construction of CFST main structure under supernormal conditions. It should be noted that even with the existence of the confinement effect, the core concrete in CFST is still a non-homogeneous and nonlinear material. The mechanical properties of the core concrete are complex and change over time, with large dispersion of performance indices. The mechanical properties of CFST are complicated due to the diversity of “matching” between the steel tubes and the core concrete. Besides the above, the development of CFST structure in recent years has shown some new trends, such as the application of high-strength steel, stainless steel, hightoughness concrete, etc. In order to further improve the utilization rate of materials, improve the structural performance and reduce the cost of the project. The introduction of these new materials will bring new challenges to the research and practical application of CFST structures. In addition, how to further improve the comprehensive disaster resistance of CFST structures, achieve accurate life-cycle-based monitoring and damage identification of CFST structures, and build a more complete, high-performance, diversified and environment-friendly modern construction technology system for CFST structures are also issues that need to be further studied by practitioners in the field of civil engineering. The following is a brief outlook on the development of CFST structures. 1. Novel CFST structures High strengthening of materials is an important development trend in the field of CFST. The confinement effect of steel tubes on core concrete improves the plasticity and ductility of the latter, providing an effective way for the application of highstrength concrete. To improve the utilization efficiency of the construction materials, it is necessary to carry out in-depth research on the design principles of high-strength CFST and the corresponding CFST hybrid structures composed of high-strength steel (with yield strength higher than 460 MPa) and high-strength concrete (e.g., strength class C90 or higher) simultaneously. Steel tubes can also be combined with different steel to form a CFST structure with superior performance, such as a double-layer steel tube structure with outer stainless steel and inner carbon steel layers (as shown in Fig. 9.1). This type of structure combines the aesthetical advantage and the durability of stainless steel with the excellent mechanical properties and economic benefit of CFST. The key to the design is to ensure that the stainless steel layer and the carbon steel layer can deform and work together during the whole loading process. Core concrete can be made of first, second, or even multi-generation recycled aggregate concrete. When recycled aggregate concrete is used in the structure, the problems such as relatively large shrinkage, creep, accumulation of initial damage,

9 Prospects of Concrete-Filled Steel Tubular (CFST) Structures

357 Core concrete

Core concrete

Carbon steel (base layer) Carbon steel (base layer) Stainless steel (composite layer)

(a) Circular cross-section

Stainless steel (composite layer)

(b) Square cross-section

Fig. 9.1 Stainless steel-carbon steel double concrete-filed steel tubular member

reduced deformability and durability, and large dispersion in terms of mechanical properties needs to be tackled. When it is filled in the high-strength steel tube to form a recycled aggregate concrete filled high-strength steel tubular member with two materials bearing external loads together, the composition of the two materials can effectively compensate for the imperfection in mechanical properties: the confinement effect of the high-strength steel tube can effectively improve the plasticity and ductility of the recycled aggregate concrete, at the same time, the core recycled aggregate concrete can delay the local buckling of the high-strength steel tube. Systematic studies of recycled aggregate concrete-filled high-strength steel tubular structures are yet to be carried out. The adoption of new materials and structural detailing will bring innovation to the design principles of CFST structures and create favorable conditions for the realization of the material-structure integration design objectives. In the future, it is necessary to develop the corresponding technical standards for new CFST structures based on systematic research and engineering practice. 2. The comprehensive disaster resistance of CFST structures Modern CFST structures face higher requirements in terms of the ability to resist disasters, such as long-span power transmission towers and offshore production platforms in marine environments. The structures are required to better adapt to the long-term combined action of both loads and environment, and to satisfy the necessities of safety, applicability, durability and post-disaster recoverability during life-cycle service. In terms of the life-cycle-based design principles of CFST structures considering extreme hazards, the key fundamental scientific issues still need to be further studied, such as the failure mechanism of structures under explosion, impact and coupled multi-hazard, the mechanical principle of structures under longterm loading and corrosion, which includes the bond behavior of material interfaces under coupled multi-hazard, and the working mechanism and design methods for structures to combine long-term loading and multi-hazard, etc.

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9 Prospects of Concrete-Filled Steel Tubular (CFST) Structures

Figure 9.2 shows the blast resistance tests of CFST members. The existence of the core concrete can significantly enhance the blast resistance of the CFST specimens. Local inwards buckling deformation and even tear openings were observed in the hollow steel tube member. After the concrete is filled, the steel tube is effectively supported by its core concrete under the action of explosion load, and the integrity of the CFST member remains good. The mechanism of interaction between the steel tube and its core concrete under blast load is complex, and the working mechanism under coupled action of long-term load and other effects also needs to be rationally revealed. 3. Life-cycle-based monitoring of large and complex CFST structures Taking comprehensive consideration of the whole construction process into account and establishing the theories, methods and key technologies for monitoring the safety of CFST structures during life-cycle service is crucial to guarantee their life-cycle safety. The specific contents of life-cycle-based monitoring include the material interface performance, stress change, concrete shrinkage and creep deformation, local deformation of the structure, and the overall deformation of the structure. 4. Damage identification for CFST structures CFST structures will be damaged to different degrees after long-term service or suffering from severe earthquake, fire, impact, debris flow or other disaster loads, etc. The accurate identification of structural damage is a prerequisite for structural safety assessment, repair and strengthening design after damage. At present, in terms of research on CFST damage identification, it is still necessary to systematically carry out damage tests on CFST specimens, identify damage parameters, and establish damage evaluation models, etc. Figure 9.3 generally gives the flow chart for the study of life-cycle-based CFST structural analytical theory and design methodology. CFST structure is an optimized product of a set of comprehensive factors such as safety, applicability, serviceability and constructability of the structure. The scientific and reasonable adoption and design of CFST structure satisfy the needs of modern engineering structure development and economical society, which enables the unity of excellent economical and structural efficiency and contributes to the sustainable development of the national economy. It is believed that with the continuous advancement of scientific research and engineering practice, a more refined life-cycle design methodology, monitoring theory and technical system for the CFST structures can be established, which will further promote the high-quality and sustainable development of CFST structures.

9 Prospects of Concrete-Filled Steel Tubular (CFST) Structures Fig. 9.2 Blast resistance test of hollow steel tubular and CFST specimens

359

Sensor Grain

Specimen

Reinforced concrete rigid anchor pier (a) Experimental device

(b) Failure mode of circular hollow steel tubular specimen

(c) Failure mode of circular CFST specimen

(d) Failure mode of square CFST specimen

High Performance

Hybrid effect

Long-term Complex loading loading Seismic action

Fire action

Impact action

Extreme loadings

…

Freezing and thawing cycle

Corrosive action

…

Environmental actions

Critical loading conditions throughout the entire service life of the structure

Material constitutive models

…

Life-cycle-based analytical theory and design technology of CFST structures

Interface models between steel and concrete

Confinement effect

Composite effect

CFST Hybrid structure

Frequent static loadings

Fig. 9.3 Flow chat of life-cycle-based theory and research on CFST structures

CFST structure with new materials

Traditional CFST structure

CFST structure

360 9 Prospects of Concrete-Filled Steel Tubular (CFST) Structures

9 Prospects of Concrete-Filled Steel Tubular (CFST) Structures

361

Exercises 1. Briefly describe the development trends of CFST structures. 2. Based on new materials, new technologies and new detailing, try to improve or propose a new CFST structure and discuss its advantages, disadvantages and potential applications. 3. Describe your understanding on the fundamental theory and the key technologies for the life-cycle-based performance enhancement of CFST structures.

Appendix A

Design Examples of Trussed Concrete-Filled Steel Tubular (CFST) Hybrid Structures

Combined with engineering practices, the Appendix gives calculation examples of the resistance of trussed CFST hybrid structure and concrete-encased CFST hybrid structure, respectively, and gives the finite element analysis examples of concreteencased CFST hybrid structure. The calculation and analysis were mainly carried out in accordance with GB/T 51446-2021 Technical Standard for Concrete-Filled Steel Tubular Hybrid Structures (hereinafter referred to as the Standard). The resistance of trussed CFST hybrid structure with and without concrete slab is calculated, respectively. In accordance with the structural size, material mechanical property and other parameters of a practical project, three examples are designed as shown in Table A.1 in the Appendix. Among them, Examples 1 and 2 are three-chord without concrete slab (as shown in Fig. A.1 in the Appendix). Four-chord trussed CFST hybrid structure (as shown in Appendix Fig. A.2). Example 3 is a four-chord trussed CFST hybrid structure with concrete slab (as shown in Appendix Fig. A.3). From Examples 1 to 3, the length of chords in an interval are 3000 mm, 7750 mm and 3000 mm respectively. The steel tube of the CFST chords and the web are all in the form of circular crosssection. In Example 3, the strength class of the concrete slab is C40, and its thickness hb is 150 mm. The inner width of the concrete slab between the two chords of CFST to compression bf is 1300 mm, the width of the concrete encasement of the chord to compression in the concrete slab bt is 900 mm, and the flange width of the extended section of the concrete slab bm is 950 mm.

© China Architecture & Building Press 2024 L. Han, Theory of Concrete-Filled Steel Tubular Structures, https://doi.org/10.1007/978-981-99-2170-6

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364

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

Table A.1 The geometric dimensions of a trussed CFST hybrid structure Example

Steel tube of the upper chord d × t (mm)

Steel tube of the lower chord D × t (mm)

Steel tube of the web dw × tw (mm)

Grade of steel

Strength class of the core concrete in chord

Distance between the centroids of the chord h (mm)

Example 1

720 × 20

720 × 20

392 × 18

Q355

C50

2000 × 2000

Example 2

1400 × 30

1400 × 30

850 × 18

Q420

C70

8500 × 8500

Example 3

450 × 15

700 × 20

273 × 12

Q355

C50

1875 × 1875

h

Fig. A.1 Cross-section of the three-chord trussed CFST hybrid structure. 1—CFST chord; 2—web 2

1 h

h

Fig. A.2 Cross-section of the four-chord trussed CFST hybrid structure. 1—CFST chord; 2—web 2

1 h

bt

bm

hb

bf

4 2

5 3

h

Fig. A.3 Cross-section of the four-chord trussed CFST hybrid structure with concrete slab. 1—Chord in tension; 2—chord in compression; 3—web; 4—concrete slab; 5—concrete encasement of the chord

1 h

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

365

A.1 Detailing (1) Detailing of the CFST chord The calculation results of CFST chord detailing are shown in Appendix Table A.2, which satisfy the requirements of the Standard for ratio of diameter to thickness, cross-sectional steel ratio and confinement factor of CFST chord. (2) Detailing of the web Calculation results of web detailing are shown in Appendix Table A.3, which can meet the requirements of the Standard for ratio of the distance between the centroids of horizontal webs to that of the chords, and ratio of the cross-sectional area of hollow steel tubular web to that of the chord. (3) Materials matching As given in Appendix Table A.4 for the grades of steel tubes and strength class of concrete, all calculation examples meet the requirements of the Standard for the strength matching relationship between the steel tubes and its core concrete. Table A.2 Calculation for the detailing of chord Example

Ratio of diameter to thickness

Limiting value of the Cross-sectional steel ratio of diameter to ratio thickness

Confinement factor

Example 1

36

≥ 17.03, ≤ 102.17

0.12

1.29

Example 2

46.67

≥ 14.69, ≤ 88.13

0.09

0.82

The upper chord in Example 3

30

≥ 16.55, ≤ 99.30

0.15

1.62

The lower chord in Example 3

35

≥ 17.03, ≤ 102.17

0.12

1.33

Table A.3 Calculation of web detailing Example

Ratio of the distance between the centroids of horizontal webs to that of the chords

Ratio of the cross-sectional area of hollow steel tubular web to that of the chord

Example 1

1.5

0.48

Example 2

0.91

0.36

Example 3

1.6

0.23

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Appendix A: Design Examples of Trussed Concrete-Filled Steel …

Table A.4 Structural material

Example

Grade of the steel

Strength class of the concrete

Example 1

Q355

C50

Example 2

Q420

C70

Example 3

Q355

C50

A.2 Calculation Indices (1) Strength calculation indices The design values of resistance of cross-section of CFST to axial compression or shear are calculated in accordance with Sect. 5.2 of the Standard. Take the CFST chord of Example 1 as an example: The characteristic value of compressive strength of CFST cross-section f scy (Eq. 3.3.2 of this book), the design value of compressive strength of CFST crosssection f sc (Eq. 3.3.1 of this book), and the design value of shear strength of CFST cross-section f sv (Eq. 3.3.3) are calculated as follows: f scy = (1.14 + 1.02ξ ) f ck = (1.14 + 1.02 × 1.29) × 32.4 = 79.6 N/mm2 f sc =

f scy 79.6 = 56.9 N/mm2 = γsc 1.40

f sv = (0.422 + 0.313αs2.33 )ξ 0.134 f sc = (0.422 + 0.313 × 0.122.33 ) × 1.290.134 × 56.9 = 25.0 N/mm2 where, γ sc is calculated by taking highway bridge structures as an example, and is 1.40. The calculation results of each example are summarized in Appendix Table A.5. (2) Calculation indices of stiffness In accordance with Sect. 5.2 of the Standard, the elastic compression stiffness, elastic tension stiffness, elastic flexural stiffness and elastic shear stiffness of trussed CFST hybrid structure are calculated. Take Example 1 as an example: Elastic compression stiffness (EA)c,h (Eq. 3.3.6 of this book), elastic tension stiffness (EA)t,h (Eq. 3.3.7 of this book), elastic flexural stiffness (EI)h (Eq. 3.3.9 of this book), the elastic shear stiffness (GA)h (Eq. 3.3.10 of this book) of trussed CFST hybrid structure are calculated as follows:

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

367

Table A.5 Design value of strength of CFST cross-section Example

Chord Design value of compressive Design value of shear strength strength of CFST cross-section of CFST cross-section f sv f sc (N/mm2 ) (N/mm2 )

Example 1

56.9

25.0

Example 2

62.8

25.9

The upper chord in Example 3 64.6

29.3

The lower chord in Example 3 57.8

25.5

Table A.6 Stiffness of cross-section Example

Elastic compression stiffness (EA)c,h (kN)

Elastic tension stiffness (EA)t,h (kN)

Elastic flexural stiffness (EI)h (kN m2 )

Elastic shear stiffness (GA)h (kN)

Example 1

6.47 × 107

2.72 × 107

6.03 × 107

2.54 × 107

Example 2

3.15 × 108

1.06 × 108

5.74 × 109

1.24 × 108

Example 3

1.17 ×

2.60 ×

5.41 ×

3.73 × 107

108

107

106

(E A)c,h = ∑(E s As + E s,l Al + E c,c Ac ) + E c,oc Aoc = 3 × (206,000 × 43,960 + 0 + 34,500 × 362,984) + 0 = 6.47 × 107 kN (E A)t,h = ∑(E s As + E s,l Al ) = 3 × (206,000 × 43,960 + 0) = 2.72 × 107 kN (E I )h = E s Is,h + E s,l Il,h + E c,c Ic,h + E c,oc Ioc,h = [2 × 206,000 × (2.22 × 1010 ) + 206,000 × (8.08 × 1010 )] + 0 + [2 × 34,500 × (1.72 × 1011 ) + 34,500 × (6.56 × 1011 )] + 0 = 6.03 × 107 kN m2 (G A)h = ∑(G s As + G c,c Ac ) + G c,oc Aoc = 3 × (79,000 × 43,960 + 13,800 × 362,984) + 0 = 2.54 × 107 kN The calculation results of each example are summarized in Appendix Table A.6.

368

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

A.3 Calculation of Resistance A.3.1 Calculation of Resistance in Axial Compression In accordance with Sects. 6.1 and 6.2 of the Standard, the resistance of trussed CFST hybrid structure without concrete slab in axial compression is calculated. Calculation conditions: The actual length L of the structure in Examples 1 and 2 is 40,000 mm and 223,784 mm respectively. Example 1 is taken as an example for calculation: Step 1: Calculate the equivalent slenderness ratio λ of the trussed CFST hybrid structure. In accordance with the provisions of Sect. 6.1 of the Standard, the equivalent slenderness ratio λ of structure in axial compression is calculated in accordance with the current national standard GB 50936 Technical Code for Concrete Filled Steel Tubular Structures: Second moment of area of the trussed CFST hybrid structure: Isch = 1.12 × 1012 mm4 Flexural modulus of the trussed CFST hybrid structure: Wsch = 8.40 × 108 mm3 Slenderness ratio of the trussed CFST hybrid structure: λx = √

l0 ∑ Isch / Asc

40,000 =√ 12 1.12 × 10 /[3 × (362,984 + 43,960)] = 41.76 where the effective length l0 is the same as the actual length L of the structure. The equivalent slenderness ratio of the trussed CFST hybrid structure: / λ=

λ2x + 200 /

=

Asc Aw

41.762 + 200 ×

= 74.79

362,984 + 43,960 21,138.48

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

369

Step 2: In accordance with Sect. 6.2 of the Standard, calculate the stability factor ϕ of the trussed CFST hybrid structure in axial compression. Critical slenderness ratio for the elasto-plastic buckling of structure (Eq. 4.2.1.17 of this book): /

420ξ + 550 (1.02ξ + 1.14) f ck / 420 × 1.29 + 550 =π× (1.02 × 1.29 + 1.14) × 32.4

λo = π

= 11.64 Critical slenderness ratio for the elastic buckling of the structure (Eq. 4.2.1.16 of this book): 1743 1743 = 93.84 λp = √ = √ fy 345 )] ( )0.3 ( [ ( 25 235 αs )0.05 · d = 13,000 + 4657 ln · fy f ck + 5 0.1 )] ( )0.3 ( ) [ ( 25 235 0.12 0.05 × = 13,000 + 4657 × ln × 345 32.4 + 5 0.1 = 10,026.72 −d (λp + 35)3 10,026.72 =− (93.84 + 35)3 = −0.0047

e=

1 + (35 + 2λp − λ0 )e (λp − λo )2 1 + (35 + 2 × 93.84 − 11.64) × (−0.0047) = (93.84 − 11.64)2 −6 = 1.20 × 10

a=

b = e − 2aλp = −0.0047 − 2 × (1.20 × 10−6 ) × 93.84 = −0.0049

370

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

c = 1 − aλ2o − bλo = 1 − 1.20 × 10−6 × 11.642 − (−0.0049) × 11.64 = 1.06 The equivalent slenderness ratio of the structure λ0 < λ < λp , so the stability factor of the trussed CFST hybrid structure (Eq. 4.2.1.10 of this book) ϕ = aλ2 + bλ + c = 0.700. Step 3: Calculation of resistance of trussed CFST hybrid structure in axial compression. Resistance of cross-section of the single-chord to axial compression (Eq. 4.2.1.3 of this book): Nc = f sc Asc = 56.9 × (362,984 + 43,960) = 2.32 × 104 kN Resistance of the trussed CFST hybrid structure in axial compression (Eq. 5.2.1.2 of this book): Nu = ϕ

∑

Nc

= 0.700 × (3 × 2.32 × 107 ) = 4.87 × 104 kN Similarly, the calculation result indicates that the resistance in axial compression of Example 2 is 1.91 × 105 kN.

A.3.2 Calculation of Bending Resistance In accordance with Sect. 6.2 of the Standard, the bending resistance of threechord trussed CFST hybrid structure without concrete slab and trussed CFST hybrid structure with concrete slab are calculated. (1) Trussed CFST hybrid structure without concrete slab Take Example 1 as an example for calculation: Resistance of cross-section of the single-chord CFST structure in tension (Eq. 4.2.1.20 of this book):

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

371

Nt = (1.1 − 0.4αs ) f As = (1.1 − 0.4 × 0.12) × 295 × 43,960 = 1.36 × 104 kN Bending resistance of the trussed CFST hybrid structure without concrete slab (Eq. 5.2.1.10 of this book): { ∑ ∑ } Mu = min ϕ Nc , Nt h i = 8.16 × 104 kN m Similarly, the bending resistance of Example 2 can be calculated, which is 1.62 × 106 kN m. (2) Trussed CFST hybrid structure with concrete slab Step 1: Determine the cross-section type The compression stability factor of concrete slab ϕ c is calculated in accordance with the current national standard GB 50010 Code for Design of Concrete Structures. l1 /hb = 3000/150 = 20, so ϕ c = 0.75. The effective width of the flange bm1 , bm2 of the overhang end and middle section of concrete slab is calculated in accordance with the current national standard GB 50010 Code for Design of Concrete Structures, bm1 = bm2 = l 1 /3 = 1000 mm. This value is larger than the actual width of the flanges of the overhang end and middle section of the concrete slab, so the effective width of concrete slab corresponding to the single chord is be = bm1 + bm2 + bt = 2500 mm. The stability factor of the chord in compression ϕ sc = 0.945 is calculated by the same method as in Sect. A.3.1. [∑ ] ∑ ∑ Asc = 3.02 × 104 kN > (1.1 − 0.4αs ) f be h b f c + Al' fl' + ϕsc f sc ϕc As = 2.65 × 104 kN Therefore, the bending resistance of the structure should be calculated in accordance with the second-type cross-section. Step 2: Calculate the bending resistance The ultimate compressive strain of concrete is calculated in accordance with the current national standard GB 50010 Code for Design of Concrete Structures. In accordance with Eqs. (6.2.5.2)–(6.2.5.10) in the Standard (Eqs. 5.2.1.14– 5.2.1.22 of this book of this book) in the standard, calculate x n , Asc-c , Asc-t , σ sc and σ s :

372

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

[0.192( f /235) + 0.488] f sc 3.25 × 10−6 f [0.192 × (305/235) + 0.488] × 64.6 = 3.25 × 10−6 × 305 = 4.80 × 104 N/mm2

E scp =

So x n = 630 mm. Because h n + Dc /2 < xn < h n + Dc , the Asc-c and Asc-t respectively in accordance with Eqs. (6.2.5.6) and (6.2.5.7) in the Standard (Eqs. 5.2.1.18 and 5.2.1.19 of this book). Asc-c = 1.51 × 105 mm2 Asc-t = 4.34 × 103 mm2 εcu 1 E scp (xn − h n ) 2 xn 1 0.0033 × (630 − 225) = × (4.80 × 104 ) × 2 630 = 50.9 N/mm2

σsc =

1 εcu E s (h n + Dc − xn ) 2 xn 0.0033 1 × (225 + 450 − 630) = × 206,000 × 2 630 = 24.3 N/mm2 ≤ f

σs =

The bending resistance of the second-type cross-section of the trussed CFST hybrid structure with concrete slab is calculated in accordance with Eq. (6.2.5.1) of the Standard (Eq. 5.2.1.13 of this book), which can be obtained as follows: Mu = 5.38 × 104 kN m

A.3.3 Calculation of the Resistance in Combined Compression and Bending In accordance with Sect. 6.2 of the Standard, the resistance in combined compression and bending of three-chord trussed CFST hybrid structure without concrete slab is verified.

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

373

Calculation conditions: the design value of axial force N = 20,000 kN, the initial deflection of the middle span of the structure u0 = 100 mm, the distance of the center points of the sections at both ends of Examples 1 and 2 is 40,000 mm and 223,784 mm, respectively. Example 1 is taken as an example for calculation: Distance between the cross-sectional center of gravity and centroidal axes for chords in compression zone (Eq. 5.2.1.25 of this book): rc =

Nuc2 h i = 666.67 mm Nuc1 + Nuc2

Distance between the cross-sectional center of gravity and centroidal axes for chords in tension zone (Eq. 5.2.1.26 of this book): rt =

Nuc1 h i = 1333.33 mm Nuc1 + Nuc2

Axial force corresponding to the equilibrium point of tension and compression limit in N-M correlation curve of resistance (Eq. 5.2.1.23 of this book): ∑

NB = ϕ

Nc −

∑

Nt

= 0.700 × 2 × (2.32 × 104 ) − 1.36 × 104 = 1.89 × 104 kN Bending moment corresponding to the equilibrium point of tension and compression limit in N-M correlation curve of resistance (Eq. 5.2.1.24 of this book): MB = ϕ

∑

Nc r c +

∑

Nt r t

= [0.700 × 2 × (2.32 × 104 ) × 666.67 + (1.36 × 104 ) × 1333.33]/1000 = 3.98 × 104 kN m Euler critical force calculated using equivalent slenderness ratio of the structure (Eq. 5.2.1.28 of this book): NE = π 2

∑

(E A)c /λ2

= π 2 × 2 × (2.16 × 1010 )/74.792 = 7.62 × 104 kN The design value of bending moment caused by the initial deflection of the structure (Eq. 5.2.1.31 of this book): M = N · u 0 = 2000 kN m

374

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

B Because u = M = 0.1 m < M = 2.11 m, verify the resistance in N NB combined compression and bending in accordance with Eq. (6.2.6.5) of the Standard (Eq. 5.2.1.27 of this book):

N ∑

M Wsc (1 − ϕ N /NE ) f sc 20,000 × 103 = 0.700 × 56.9 × (3 × 406,944) 20,000 × 103 × 100 [ ( ) ( )] + 8.40 × 108 × 1 − 0.700 × 2 × 107 / 7.62 × 107 × 56.9

ϕ f sc

Asc

+

= 0.46 ≤ 1 Example 1 satisfies the requirements of the Standard for stable resistance in combined compression and bending. Similarly, the resistance in combined compression and bending of Example 2 satisfies the requirements of the Standard.

A.3.4 Calculation for the Resistance of the Single Chord In accordance with Prevision 6.2.9 of the Standard, the resistance to axial tension, axial compression, bending, combined compression and bending, combined tension and bending, shear, torsion, combined compression and torsion, combined compression, bending and torsion, combined compression, bending and shear, and combined compression, bending, torsion and shear of the single chord in a three-chord trussed CFST hybrid structure without concrete slab can be calculated. Calculation condition for resistance in combined compression and bending: compression force N = 5000 kN, bending moment M = 500 kN m; Calculation condition for resistance in combined tension and bending: tension force N = 4000 kN, bending moment M = 500 kN m; Calculation condition for resistance in combined compression and torsion: compression force N = 9000 kN, torsional moment T = 1000 kN m; Calculation condition for resistance in combined compression, bending and torsion: compression force N = 4000 kN, bending moment M = 500 kN m, torsional moment T = 1000 kN m; Calculation condition for resistance in combined compression, bending and shear: compression force N = 4000 kN, bending moment M = 500 kN m, shear force V = 2000 kN; Calculation condition for resistance in combined compression, bending, torsion and shear: compression force N = 4000 kN, bending moment M = 500 kN m, torsional moment T = 1000 kN m, shear force V = 2000 kN.

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

375

(1) Calculation of resistance of a single CFST chord in axial compression and tension (Sect. 4.2.1 of this book). Take CFST chord of Example 1 as an example. The resistance of the chord in axial compression (Eq. 4.2.1.9 of this book) and resistance to axial tension (Eq. 4.2.1.20 of this book) are as follows: ϕ Nc = 0.987 × 2.32 × 104 = 2.29 × 104 kN Nt = 1.36 × 104 kN Similarly, it can be calculated that the resistance of a single chord in Example 2 are 9.03 × 104 kN and 4.87 × 104 kN, respectively. (2) Calculation of bending resistance of a single CFST chord (Sect. 4.2.2 of this book) Take CFST chord of Example 1 as an example. The flexural modulus of the chord cross-section (Eq. 4.2.2.1 of this book) and plastic development factor of the bending resistance (Eq. 4.2.2.7 of this book): Wscl = π × 7203 /32 = 3.66 × 107 mm3 γm = 1.1 + 0.48 ln(ξ + 0.1) = 1.1 + 0.48 × ln(1.29 + 0.1) = 1.26 Bending resistance of the chord (Eq. 4.2.2.6 of this book): Mcu = γm Wsc1 f sc = 1.26 × (3.66 × 107 ) × 56.9 = 2.62 × 103 kN m Similarly, the bending resistance of a single chord in Example 2 is 1.79 × 104 kN m. (3) Verification of the resistance of CFST chord in combined compression and bending (Sect. 4.3.1 of this book) Take the CFST chord of Example 1 as an example to verify: Step 1: Verify the resistance of cross-section to combined compression and bending η0 = 0.1 + 0.14ξ −0.84 = 0.1 + 0.14 × 1.29−0.84

376

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

= 0.21 ς0 = 1 + 0.18ξ −1.15 = 1 + 0.18 × 1.29−1.15 = 1.13 2(ς0 − 1) η0 2 × (1.13 − 1) = 0.21 = 1.24

c=

1 − ς0 η02 1 − 1.13 = 0.212 = −2.95

b=

a = 1 − 2η0 = 1 − 2 × 0.21 = 0.58 Ncd /Nc = 0.22 < 2η0 , so the resistance of cross-section to combined compression and bending is verified in accordance with Eq. (6.2.9.8) of the Standard (Eq. 4.3.1.2 of this book): 2 −bNcd cNcd Mcd 2.95 × (5 × 106 )2 1.24 × (5 × 106 ) 5 × 108 − + = − + Nc2 Nc Mcu (2.31 × 107 )2 2.31 × 107 2.62 × 109

= 0.06 ≤ 1 Cross-sectional resistance satisfies the requirements of the Standard. Step 2: Verify the resistance in combined compression and bending 2(ς0 − 1) η0 2 × (1.13 − 1) = 0.21 = 1.24

c=

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

377

NcE = π 2 (E A)c /λc2 = π 2 × (2.16 × 1010 )/152 = 9.47 × 105 kN ) N cd d = 1 − 0.4 NcE ) ( 5 × 106 = 1 − 0.4 × 9.47 × 105 × 1000 = 1.00 (

1 − ς0 ϕ 3 η02 1 − 1.13 = 0.9873 × 0.212 = −3.07

b=

a = 1 − 2ϕ 2 η0 = 1 − 2 × 0.9872 × 0.21 = 0.59 Because Ncd /Nc = 0.22 < 2ϕ 3 η0 , the resistance in combined compression and bending is verified in accordance with Eq. (6.2.9.15) in Standard (Eq. 4.3.1.9 of this book): 2 −bNcd cNcd 1 Mcd 3.07 × (5 × 106 )2 1.24 × (5 × 106 ) − + = − 2 7 2 Nc Nc d Mcu (2.31 × 10 ) 2.31 × 107 1 5 × 108 + = 0.07 ≤ 1 · 1.00 2.62 × 109

The resistance in combined compression and bending satisfies the requirements of Standard. Resistance of chord in combined compression and bending satisfies the requirements of the Standard. Similarly, Example 2 shows that resistance of single chord in combined compression and bending resistance meet the requirements of the Standard. (4) Verification of the resistance of the single CFST chord in combined tension and bending (Sect. 4.3.1 of this book) Take the CFST chord of Example 1 as an example to verify (Eq. 4.3.1.15 of this book):

378

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

5 × 108 Ntd Mcd 4 × 106 + + = (1.1 − 0.4αs ) f As Mcu (1.1 − 0.4 × 0.12) × 295 × 43,960 2.62 × 109 = 0.48 ≤ 1 Resistance in combined tension and bending satisfies the requirements of the Standard. Similarly, the resistance in combined tension and bending of a single chord in Example 2 satisfies the requirements of the Standard. (5) Calculation of shear resistance of a single CFST chord (Sect. 4.2.4 of this book) Take the CFST chord of Example 1 as an example for calculation (Eqs. 4.2.4.3 and 4.2.4.4 of this book): γv = 0.97 + 0.2lnξ = 0.97 + 0.2 × ln1.29 = 1.02 Vcu = γv Asc f sv = 1.02 × 406,944 × 25.0 = 1.04 × 104 kN Similarly, the shear resistance of a single chord in Example 2 is 3.71 × 104 kN. (6) Calculation of torsional resistance of a single CFST chord (Sect. 4.2.3 of this book) Take the CFST chord of Example 1 as an example for calculation (Eqs. 4.2.3.2– 4.2.3.4 of this book): Wsc,t = 7.33 × 107 mm3 γt = 1.294 + 0.267lnξ = 1.294 + 0.267 × ln1.29 = 1.36 Tcu = γt Wsc,t f sv = 1.36 × (7.33 × 107 ) × 25.0 = 2.49 × 103 kN m Similarly, it can be calculated that the torsional resistance of a single chord in Example 2 is 1.73 × 104 kN m.

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

379

(7) Verification of resistance of a single CFST chord in combined compression and torsion (Sect. 4.3.2 in this book) Take the CFST chord of Example 1 as an example to verify: Step 1: Verify the resistance of cross-section to combined compression and torsion (Eq. 4.3.2.1 of this book) (

Ncd Nc

)2.4

( +

Tcd Tcu

)2

( =

9 × 106 2.32 × 107

)2.4

( +

109 2.49 × 109

)2 = 0.26 ≤ 1

Step 2: Verify the resistance in combined compression and torsion (Eq. 4.3.2.2 of this book) (

Ncd ϕ Nc

)2.4

( +

Tcd Tcu

)2

( =

9 × 106 0.987 × 2.32 × 107

)2.4

( +

109 2.49 × 109

)2 = 0.27 ≤ 1

Resistance in combined compression and torsion satisfies the requirements of the Standard. Similarly, the resistance of a single chord in compression and torsion in Example 2 satisfies the requirements of the Standard. (8) Verification of resistance of a single CFST chord in combined compression, bending and torsion (Sect. 4.3.4) Take the CFST chord in Example 1 as an example to verify: ) Ncd d = 1 − 0.4 NcE ) ( 4 × 106 = 1 − 0.4 × 9.47 × 108 = 1.00 (

β=

Tcd = 0.40 Tcu

ςe = (1 − β 2 )0.417 ς0 = (1 − 0.402 )0.417 × 1.13 = 1.05 ηe = (1 − β 2 )0.417 η0 = (1 − 0.402 )0.417 × 0.21 = 0.20

380

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

2(ςe − 1) ηe 2 × (1.05 − 1) = 0.20 = 0.50

c=

1 − ςe ϕ 3 ηe2 1 − 1.05 = 0.9873 × 0.202 = −1.30

b=

a = 1 − 2ϕ 2 η0 = 1 − 2 × 0.9872 × 0.21 = 0.59 [ ( )2 ]0.417 Ncd /Nc = 0.17 < 2ϕ η0 1 − TTcdcu = 0.38, verify the resistance in 3

combined compression, bending and torsion in accordance with Eq. (6.2.9.32) in Standard (Eq. 4.3.4.2 of this book): [

]2.4 ( ) ) 1 Mcd Ncd Tcd 2 + −c + Nc d Mcu Tcu ) ( 2 4 × 106 = 1.30 × 2.32 × 107 ) ]2.4 ( 1 5 × 108 4 × 106 + · −0.50 × 2.32 × 107 1.00 2.62 × 109 ) ( 2 109 + = 0.17 ≤ 1 2.49 × 109 (

Ncd −b Nc [

)2

(

Resistance in combined compression, bending and torsion satisfies the requirements of the Standard. Similarly, Example 2 shows that resistance of a single chord in combined compression, bending and torsion satisfies the requirements of the Standard. (9) Verification of resistance of a single CFST chord in combined compression, bending and shear (Sect. 4.3.5 of this book) Take the CFST chord of Example 1 as an example to verify: Ncd /Nc = 0.17 < 2ϕ 3 η0 [1 − ( VVcucd )2 ]0.417 = 0.40, verify the resistance in combined compression, bending and shear in accordance with Eq. (6.2.9.41) of

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

381

Standard (Eq. 4.3.5.3 of this book): [

]2.4 ( ) ) 1 Mcd Ncd Vcd 2 + −c + Nc d Mcu Vcu ) ) ( ( 2 4 × 106 4 × 106 = 3.07 × − 1.24 × 2.32 × 107 2.32 × 107 ]2.4 ( )2 1 5 × 108 2 × 106 + · + 1.00 2.62 × 109 1.04 × 107 = 0.04 ≤ 1 (

Ncd −b Nc [

)2

(

Resistance in combined compression, bending and shear satisfies the requirements of the Standard. Similarly, the resistance of a single chord in combined compression, bending and shear in Example 2 satisfies the requirements of the Standard. (10) Verification of the resistance of a single CFST chord in combined compression, bending, torsion and shear (Sect. 4.3.6 of this book). Take the CFST chord of Example 1 as an example to verify: Ncd /Nc = 0.17 < 2ϕ 3 η0 [1 − ( TTcdcu )2 − ( VVcdcu )2 ]0.417 = 0.37, verify the resistance in combined compression, bending, torsion and shear in accordance with Eq. (6.2.9.43) of the Standard (Eq. 4.3.6.2in this book): [

]2.4 ( ) ) ( )2 1 Mcd Ncd Vcd 2 Tcd + −c + + Nc d Mcu Vcu Tcu ]2.4 )2 ) ( ( 1 5 × 108 4 × 106 4 × 106 + · = 1.30 × − 0.50 × 2.32 × 107 2.32 × 107 1.00 2.62 × 109 )2 ( )2 ( 2 × 106 109 + + 1.04 × 107 2.49 × 109 = 0.21 ≤ 1 (

Ncd −b Nc [

)2

(

The resistance in combined compression, bending, torsion and shear satisfies the requirements of the Standard. Similarly, the resistance in combined compression, bending, torsion and shear of a single chord of Example 2 satisfies the requirements of the Standard.

382

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

A.3.5 Calculation for Resistance of a Single Web In accordance with provisions in Sect. 6.2 of the Standard, the shear resistance, bending resistance and compressive resistance of a single web in three-chord trussed CFST hybrid structure without concrete slab are calculated. The calculation conditions are the same as Appendix Table A.1. In the verification of the bending resistance, the design value of axial force is N = 20,000 kN, and the initial deflection of the middle span of the structure is u0 = 100 mm. The distance of the center points of the sections at both ends of Examples 1 and 2 is 40,000 mm and 223,784 mm, respectively. (1) Verification of shear resistance of a single web (Eq. 5.2.1.39 of this book). Take the web of Example 1 as an example to verify: The design value of shear force on the web of the trussed CFST hybrid structure in axial compression: ∑ V =

Asc f sc = 817.24 kN 85

All the webs jointly bear the shear force. Suppose there are 39 horizontal webs, then the design value of shear force on each web is: Vw = 20.95 kN Second moment of cross-section of the web: Iw = 3.72 × 108 mm4 The moment of the total cross-section of the area above (or below) the neutralization axis of the web to the neutralization axis: S = 2.52 × 106 mm3 Maximum shear stress in cross-section of the web: τ=

Vw S = 7.9 N/mm2 < f v I w tw

Shear resistance of the web satisfies the requirements of the Standard. Similarly, shear resistance of a single web in Example 2 satisfies the requirements of the Standard. (2) Verification of bending resistance of a single web (Eqs. 5.2.1.40 and 5.2.1.41 of this book)

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

383

Take the web of Example 1 as an example to verify: Design value of bending moment and cross-sectional normal stresses of the web: N u0 l1 π · · m b L (1 − N /NE ) π 2 × 107 × 100 3000 · · = 4 3.58 4 × 10 [1 − (2 × 107 )/(7.62 × 107 )] = 178.49 kN m

M=

M γx W x 178.49 × 106 = 1.15 × (1.90 × 106 ) = 81.7 N/mm2 < f

σ =

Bending resistance of the web satisfies the requirements of the Standard. Similarly, the bending resistance of a single web of Example 2 satisfies the requirements of the Standard. (3) Verification of resistance of a single web in compression (Eqs. 5.2.1.40 and 5.2.1.42 of this book) Take the web of Example 1 as an example to verify: N u0 π · m sin θ L (1 − N /NE ) 2 × 107 × 100 π · = 2 × cos 0.46 × sin(π/2) × 40,000 1 − (2 × 107 )/(1.76 × 108 ) = 98.77 kN

Nwd =

Slenderness ratio of the web: √ λw = 0.8h i / Iw /Aw

√ = 0.8 × 2236.07/ (3.72 × 108 )/21,138.48 = 13.48 εk =

√

235/ f y = 0.83

λw /εk = 16.24 The stability factor can be obtained in accordance with the current national standard GB 50017 Standard for Design of Steel Structures, so ϕ = 0.986;

384

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

Nb = 0.019 < 1 ϕ Aw f w The resistance of the web in compression satisfies the requirements of the Standard. Similarly, the resistance of a single web in compression in Example 2 satisfies the requirements of the Standard.

A.3.6 Shear Resistance of the Structure Shear resistance of trussed CFST hybrid structure with horizontal webs and diagonal webs is calculated in accordance with Sect. 6.3 of the Standard. The calculation conditions of trussed CFST hybrid structure with horizontal webs are the same as those of trussed CFST hybrid structure without concrete slab in Appendix Table A.1 (Examples 1 and 2). The distance of the center points of the sections at both ends of Examples 1 and 2 is 40,000 mm and 223,784 mm, respectively. Calculation conditions for trussed CFST hybrid structure with diagonal webs: The angle between diagonal web and chord is θ = 60°, the initial deflection u0 = 150 mm, and the other dimensions are the same as that with the horizontal webs. Verify the resistance of diagonal cross-section of the structure when the two ends of the member bear the axial compression N = 20,000 kN. (1) Calculation for the shear resistance of trussed CFST hybrid structure with horizontal webs (Eq. 5.2.2.2 of this book) Take Example 1 as an example for calculation: Shear resistance of the structure: ∑ Vu = 0.9 Vcu = 0.9 × 3 × (1.04 × 107 ) = 2.81 × 104 kN Similarly, the shear resistance of Example 2 is 1.34 × 105 kN. (2) Verify the shear resistance of trussed CFST hybrid structure with diagonal webs (Eq. 5.2.1.42 of this book) N u0 π · m sin θ L (1 − N /NE ) π 2 × 107 × 150 = · 2 × cos 0.46 × sin(π/3) × 40,000 1 − (2 × 107 )/(1.76 × 108 ) = 171.39 kN

Vwd =

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

385

Calculate the shear resistance of diagonal web in compression: Slenderness ratio of the web: √ λw = (0.8h i / sin θ )/ Iw /Aw

√ = [0.8 × 2000/ sin(π/3)]/ (3.72 × 108 )/21,138.48 = 13.93

The stability factor of the web can be obtained in accordance with the current national standard GB 50017 Standard for Design of Steel Structures, so, ϕ = 0.987; Vu = ϕ f w Aw = 0.987 × 295 × 21,138.48 = 6.15 × 103 kN > Vwd The shear resistance of diagonal cross-section satisfies the requirements of the Standard. Similarly, the shear resistance of Example 2 satisfies the requirements of the Standard.

A.4 Design of Joints A.4.1 General Specifications for Joints In accordance with Sect. 8.1 of the Standard, the welding length of the intersecting joint plate inserted into the steel tube and the ratio of the length and thickness of the free edge of the joint plate are calculated. Calculation conditions: A plane gap K-joints joint in trussed CFST hybrid structure. The cross-sectional size of the steel tube in chord is 720 × 20 mm, the crosssectional size of the steel tube in web is 400 × 18 mm, the steel grade is Q355, and the strength class of concrete is C50. The angle between web and chord is 60°, and the distance between the centroids of chords is 2000 mm. The design value of tensile force of the web in tension is 1800 kN and the design value of compressive force of the web in compression is 3000 kN. In accordance with Provision 8.1.5 of the Standard, the welding length of the insert plate into the steel tube shall be determined by internal force calculation. There are 8 fillet welds in each connection, and the welding foot size is hf = 8 mm, f fw = 200 N/mm2 . In accordance with the current national standard GB 50017-2017 Standard for Design of Steel Structures, the effective length of welding seam for web in axial compression:

386

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

) ( lw ≥ N / 0.7h f f fw = 334.82 mm Welding length: l = lw + 2h f = 350.82 mm When web are subjected to axial tension, the effective length of the welding: ) ( lw ≥ N / 0.7h f f fw = 200.89 mm Welding length: l = lw + 2h f = 216.89 mm In accordance with Provision 8.1.6 of the Standard, when the ratio √ between the length and thickness of the free edge of the joint plate is greater than 60 235/ f y = 49.52, it is appropriate to roll the edge or set the longitudinal stiffening plate.

A.4.2 Regulations for Joints in Trussed CFST Hybrid Structure In accordance with Sect. 8.2 of the Standard, the eccentricity of joints between web and chord, and the overlap ratio of plane K-joints and N-joints are calculated under the same conditions as Sect. A.4.1. The gap length is 100 mm. Gap length a = 100 mm, so, the eccentricity of K-joint (Eq. 6.3.3.1) is 126.60 mm, −0.55 ≤ De = 0.18 ≤ 0.25, which satisfies the requirements of the Standard. The overlap ratio of plane K-joint is 25% ≤ ηov = qp · 100% = 32% ≤ 100%, which satisfies the requirements.

A.4.3 Resistance of Joints Verify the local bearing resistance in accordance with Sect. 8.2 of the Standard. Calculation conditions: The design value of tensile force of the web in tension is 1800 kN, and the design value of compressive force of the web in compression is 3000 kN. The design value of lateral local bearing force on chord is N LF = 20,000 kN and other dimensions are the same as Sect. A.4.1. (1) Verification of axial tensile resistance of web in tension (Eq. 6.3.3.3 of this book)

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

387

) ( 1 + sin θ , f Ntw = min f v tπ dw A w w 2 sin2 θ 1 + sin(π/3) , 295 × 21,590.64) = min(170 × 20 × π × 400 × 2 × sin2 (π/3) = min(5.32 × 106 , 6.37 × 106 ) = 5.32 × 103 kN > 1800 kN Axial tensile resistance of the web in tension satisfies the requirements of the Standard. (2) Verification of the axial compressive resistance of the web in compression Stability factor of the web ϕ = 0.987. The calculation method is the same as before; N 3.00 × 106 = 0.48 < 1 = ϕ Aw f w 0.987 × 21,590.64 × 295 The axial compressive resistance of the web in compression satisfies the requirements of the Standard. (3) Verification of resistance in lateral local bearing (Eqs. 6.3.3.4–6.3.3.8 of this book) The area of local bearing of CFST, dispersed bearing area when under lateral local bearing, coefficient of concrete strength when under lateral local bearing: Alc = π dw2 /4 = π × 4002 /4 = 1.26 × 105 mm2 Alc + 2dw D sin θ 1.26 × 105 + 2 × 400 × 720 = sin(π/3) = 7.21 × 105 mm2

Ab =

/ β1 = / =

Ab Alc 7.21 × 105 1.26 × 105

= 2.39

388

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

/ Alc f y · = 4.45 Ab f ck In accordance with Table 8.2.1 of Standard (Table 6.2 of this book), β c c = 2.00; Resistance of the chord in lateral local bearing: NuLF = βc β1 f c

Alc sin θ

= 2.00 × 2.39 × 23.1 ×

1.26 × 105 sin(π/3)

= 1.61 × 104 kN > NLF The resistance of the chord in lateral local bearing satisfies the requirements of the Standard.

A.4.4 Verification of the Fatigue Resistance (1) Constant amplitude fatigue The strength of the joint under constant amplitude fatigue is calculated in accordance with Provision 8.5.4 and Appendix D of the Standard. Calculation conditions: For a trussed CFST hybrid structure, the wall thickness t = 30 mm, the hot spot stress amplitude Δσhs = 100 N/mm2 , fatigue life N = 2 × 106 . Verify the fatigue resistance of the joint. As N < 5 × 106 , the allowable hot spot stress amplitude for constant amplitude fatigue is calculated in accordance with Provision 8.5.4 of the Standard; For gap K-joints, the calculation parameters of fatigue resistance can be obtained by referring to Table 8.5.4 of the Standard C = 4.345 × 1012 , β = 3. Allowable hot spot stress amplitude for constant amplitude fatigue [Δσhs ] = ( C )1/β = 129.51 N/mm2 ; N When the wall thickness of the steel tube t is greater than 25 mm, the influence of wall thickness of the steel tube on fatigue resistance should be considered, and the correction factor for wall thickness of the steel tube γt = (25/t)0.25 = 0.96. Δσhs < γt [Δσhs ]; The resistance of the joint under constant amplitude fatigue satisfies the requirements of the Standard. (2) Variable amplitude fatigue In accordance with Sect. 8.5.5 and Appendix D of the Standard, the resistance of the joint under variable amplitude fatigue is calculated.

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

389

Calculation conditions: for a trussed CFST hybrid structure, the wall thickness of the intersecting welded gap K-joint t = 30 mm, the hot spot stress amplitude (Δn) is 60, 80, 110 N/mm2 , and the corresponding frequency is 2 × 106 , 1 × 106 , 1 × 106 , respectively. Δσhs = 110 N/mm2 > γt [Δσhs,L ]1×108 = 49.68 N/mm2 , which shall be verified again in accordance with Clause 2 of Provision 8.5.5 of the Standard; [∑ Δσhs,e =

n i (Δσhs,i )β + ([Δσhs,c ]5×106 )−2 2 × 106

∑

n j (Δσhs,j )β+2

]1/β = 97.72 N/mm2 ;

Δσhs,e ≤ γt [Δσhs ]2×106 = 124.20 N/mm2 ; The resistance of the joint under variable amplitude fatigue satisfies the requirements of Standard.

A.5 Protective Design (1) Design of Corrosion Resistance In accordance with Sect. 9.2 of the Standard, the bending resistance of trussed CFST hybrid structure after corrosion is calculated. Calculation conditions: for a type trussed CFST hybrid structure with horizontal web and without concrete slab, the cross-sectional size is shown in Example 1 in Appendix Table A.1, the actual length of the structure L = 40,000 mm. The bending resistance of trussed CFST hybrid structure is calculated by assuming that the wall thickness of steel tube of CFST chord is uniformly corroded and the average damage is Δt = 2 mm. The bending resistance of trussed CFST hybrid structure is calculated. Take the structure of Example 1 as an example: The outside diameter of the steel tube after corrosion, the cross-sectional area of the steel tube, the nominal cross-sectional steel ratio of the cross-section, and the nominal confinement factor (Eqs. 7.2.2.1–7.2.2.5 of this book): De = D − 2Δt = 720 − 2 × 2 = 716 mm π 2 [D − (De − 2te )2 ] 4 e π = × [7162 − (716 − 2 × 18)2 ] 4 = 3.95 × 104 mm2

Ase =

390

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

Ase 3.95 × 104 = = 0.11 Ac 3.63 × 105

αe = ξe = αe

fy 345 = 0.11 × = 1.16 f ck 32.4

The characteristic value of axial compressive strength of CFST chord crosssection after corrosion (Eq. 3.3.2 of this book), and design value of axial compressive strength (Eq. 3.3.1 of this book): f scy = (1.14 + 1.02ξe ) f ck = (1.14 + 1.02 × 1.16) × 32.4 = 75.3 N/mm2 f sc = f scy /γsc = 75.3/1.40 = 53.8 N/mm2 where the γsc is taken in accordance with the structure of highway Bridges and culverts. The resistance of cross-section of single CFST chord to axial compression after corrosion (Eq. 4.2.1.3 of this book), and the resistance of cross-section to tension (Eq. 4.2.1.20 of this book): Nc = f sc Asc = 53.8 × (3.95 × 104 + 3.63 × 105 ) = 2.17 × 104 kN Nt = (1.1 − 0.4αs ) f As = (1.1 − 0.4 × 0.11) × 295 × (3.95 × 104 ) = 1.23 × 104 kN The stability factor of the structure after corrosion is ϕ = 0.822, which is calculated by the same method as in Sect. A.3.1; Bending resistance of trussed CFST hybrid structure after corrosion (Eq. 5.2.1.10 of this book): Mu = min{ϕ

∑

Nc ,

∑

Nt }h i

= min{0.822 × 3 × (2.16 × 107 ), 3 × (1.23 × 107 )} × 2000 = min{5.33 × 107 , 3.69 × 107 } × 2000

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

391

= 7.38 × 104 kN m Similarly, for highway bridge and culvert structures, the M u of Example 2 is 5.64 × 104 kN m. (2) Design of Fire Resistance The fire resistance ratings of trussed CFST hybrid structure is calculated in accordance with Sect. 9.3 of the Standard. Calculation conditions: for a three-chord trussed CFST hybrid structure without fire protection, the cross-sectional size of the steel tube of circular CFST chord is 500 × 12 mm, the strength class of the concrete is C50, the equivalent slenderness ratio λ is 25, and the fire load ratio nF is 0.5. Calculate the fire resistance ratings of trussed CFST hybrid structure. The fire resistance ratings of trussed CFST hybrid structure is calculated as follows (Eq. 7.3.3.1 of this book): tR = (0.7 f ck /20 + 6.3)(1.7D + 0.35)R (−1.577+0.021λ) = (0.7 × 32.4/20 + 6.3) × (1.7 × 0.5 + 0.35) × 0.5(−1.577+0.021×25) = 18.50 min (3) Verification of impact resistance The bending resistance of trussed CFST hybrid structure to impact is verified in accordance with Sect. 9.4 of the Standard. Calculation conditions: for a four-chord trussed CFST hybrid structure with horizontal webs, the outside diameter of the steel tube of the circular CFST chord is 360 mm, wall thickness is 20 mm, the steel grade is Q355, the strength class of concrete is C50 and the distance between the centroids of chords is 1000 × 1000 mm. The bending resistance of the trussed CFST hybrid structure when the velocity of the impactor is V 0 = 20 m/s and the dynamic bending moment M d = 500 kN m is verified. Cross-section steel ratio of CFST chord: αs =

As 21,352 = 0.27 = Ac 80,384

Static bending resistance of the single chord (Eq. 4.2.2.6 of this book): Mu = 689 kN m f 1 = −4.00 × 10−7 f y2 + 8.00 × 10−5 f y + 1.02 = −4.00 × 10−7 × 3452 + 8.00 × 10−5 × 345 + 1.02 = 1.00

392

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

f 2 = −3.66αs2 − 0.896αs + 1.13 = −3.66 × 0.272 − 0.896 × 0.27 + 1.13 = 0.62 f 3 = 7.00 × 10−7 D 2 − 1.30 × 10−3 D + 1.40 = 7.00 × 10−7 × 3602 − 1.30 × 10−3 × 360 + 1.40 = 1.02 f 4 = −1.00 × 10−3 V02 + 5.08 × 10−2 V0 + 0.385 = −1.00 × 10−3 × 202 + 5.08 × 10−2 × 20 + 0.385 = 1.00 Rd = 1.49 f 1 f 2 f 3 f 4 = 1.49 × 1.000 × 0.621 × 1.023 × 1.001 = 0.94 Mud = Rd Mu = 648 kN m > Md The bending resistance of trussed CFST hybrid structure under impact satisfies the requirements.

A.6 Construction and Acceptance (1) Calculation for resistance of member with void The resistance of member with void is calculated in accordance with Provision 10.3.10 and the specification of the Standard. Calculation conditions: Spheroidal void occurs in CFST chord of a trussed CFST hybrid structure. The cross-sectional size of the steel tube of the chord is 600 × 20 mm, the steel grade is Q355, the strength class of concrete is C50, and the height of void is 2 mm. The design value of resistance of a single chord in axial compression is calculated. Design values of resistance of cross-section of a single CFST chord to axial compression (Eq. 4.2.1.3 of this book): Nc = f sc Asc = 1.80 × 104 kN Spherical-cap void ratio of CFST members (Eq. 4.9.2 of this book):

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

χ=

393

ds = 0.34% < 0.6% D

The height of the spherical-cap void is not more than 5 mm, and there is no need to fill the void; Confinement factor of the CFST chord (Eq. 1.3.1 of this book): ξ = 1.58 > 1.24 f (ξ ) = 4.66 − 1.97ξ = 1.55 Reduction coefficient due to void (Eq. 4.9.4 of this book): K d = 1 − f (ξ )χ = 0.99 Design value of resistance of cross-section of single-chord CFST chord to axial compression considering the effect of void (Eq. 4.9.3 of this book): Nug = K d Nc = 1.78 × 104 kN (2) Calculation of ultimate shrinkage strain of core concrete The ultimate shrinkage strain of core concrete is calculated in accordance with the specification of Provision 10.3.7 of the Standard. In accordance with the structural design parameters and the material properties of conventional concrete, the crosssectional size of circular steel tube of CFST chord is 720 × 20 mm, and the strength class of core concrete in steel tube is C50. The time of wet curing is 28d, the chord length L was 40,000 mm, the concrete slump s is 100 mm, the percentage of fine aggregate to total aggregate ψ 50, the cement content c is 500 kg/m3 , and the air content in percent α v is 5. Volume-to-surface area ratio of the chord: (π × D 2 /4) × L (π × D 2 /4) × 2 + π × D × L (π × 7202 /4) × 40,000 = (π × 7202 /4) × 2 + π × 720 × 40,000 = 178.39 mm

V /S =

Correction factor for volume-to-surface ratio (Eq. 3.4.3 of this book): γvs = 1.2e−0.00472V /S = 1.2e−0.00472×178.39 = 0.52

394

Appendix A: Design Examples of Trussed Concrete-Filled Steel …

Correction factor for concrete slump (Eq. 3.4.4 of this book): γs = 0.89 + 0.00161s = 0.89 + 0.00161 × 100 = 1.05 If the percentage of fine aggregate to total aggregate ψ is 50, the correction factor for fine aggregate can be calculated in accordance with the following equation (Eq. 3.4.5 of this book): γψ = 0.30 + 0.014ψ = 0.30 + 0.014 × 50 = 1.00 Correction factor for cement content (Eq. 3.4.6 of this book): γc = 0.75 + 0.00061c = 0.75 + 0.00061 × 500 = 1.06 Correction factor for air content (Eq. 3.4.7 of this book): γα = 0.95 + 0.008αv = 0.95 + 0.008 × 5 = 0.99 Correction factor for restriction to the core concrete shrinkage due to the steel tube (Eq. 3.4.8 of this book): γu = 0.0002D + 0.63 = 0.0002 × 720 + 0.63 = 0.77 Ultimate value of shrinkage strain of core concrete (Eq. 3.4.2 of this book): (εsh )u = 780γcp γλ γvs γs γψ γc γα γu = 780 × 0.86 × 0.3 × 0.52 × 1.05 × 1 × 1.06 × 0.99 × 0.77 = 88.78 με

Appendix B

Design Examples of Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid Structures

In accordance with the structural dimensions and mechanical properties of materials of an practical engineering project, three concrete-encased CFST hybrid structure examples are designed as shown in Appendix Table B.1. Examples 1, 2, and 3 are single-chord, six-chord, and four-chord cross-sections, respectively. The grade of steel tube is Q355. HRB400 hot rolled ribbed reinforcement is used for longitudinal reinforcement and stirrups. The strength class of core concrete is C60, and the strength class of concrete encasement is C40. The thickness of the protective layer is 30 mm. The diameter and spacing of stirrup are 10 mm and 80 mm respectively, and the diameter of longitudinal reinforcement is 32 mm. Longitudinal reinforcements are uniformly arranged around the cross-section. The cross-section and number of reinforcements are shown in Appendix Figs. B.1 and B.2. For single-chord concreteencased CFST hybrid structure, the value of γ sc is taken in accordance with building structure, power tower structure and port engineering structure. For multiple-chord concrete-encased CFST hybrid structure, the value of γ sc is taken in accordance with highway bridge and culvert structure.

B.1 Verification of Detailing B.1.1 Detailing for CFST Chord of CFST Hybrid Structure The diameter-to-thickness ratio, cross-sectional steel ratio, confinement factor, the outside diameter-to-sectional width ratio (D/B) are verified in accordance with Sect. 3.3 of the Standard. (1) Diameter-to-thickness ratio The ratio of diameter to thickness of the chord in Example 1 = 813/26 = 31.27.

© China Architecture & Building Press 2024 L. Han, Theory of Concrete-Filled Steel Tubular Structures, https://doi.org/10.1007/978-981-99-2170-6

395

396

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

Table B.1 Geometric dimensions of the structure Example Cross-sectional Cross-sectional Steel tube of the width B height H chord D × t (mm) (mm) (mm)

Example 1500 1

1800

Example 1500 2

1800

Example 1500 3

1800

813 × 26

Steel tube of the web dw × tw (mm)

Distance from hollow edge to outer surface of concrete t c (mm)

Distance between outer edge of steel tube and outer surface of concrete ac (mm)

–

–

–

273(219) × 10(8) 159 × 440 10 245 × 8

85

159 × 440 10

85

Note The dimensions in brackets are the dimensions of the CFST chord at the waist Fig. B.1 Cross-section of single-chord concrete-encased CFST hybrid structure. 1—CFST; 2—Concrete encasement; 3—Stirrups; 4—Longitudinal reinforcement

2 1 B

ac

tc

3

3

B (1) Four-chord

ac

tc

4

0.3H

0.3H

4

H

6 H

6

1

ac

2 5

tc

2 5

H

3

1 B

ac

tc

4

(2) Six-chord

Fig. B.2 Cross-section multiple-chord concrete-encased CFST hybrid structure. 1—CFST; 2— Concrete encasement; 3—Hollow part; 4—Web; 5—Stirrups; 6—Longitudinal reinforcement

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

397

Similarly, in Example 2, the diameter-to-thickness ratio of the corner chord is 27.30, and that of the chord in the middle position is 27.38. In Example 3, the diameter-to-thickness ratio of the chord is 30.63, which can meet the requirement. (2) Cross-sectional steel ratio In accordance with Eq. (3.3.1.1) of the Standard (Eq. 1.3.2 of this book): The cross-sectional steel ratio steel ratio of the chord in Example 1: ] [ π × (813/2)2 − (761/2)2 As αs = = = 0.14. Ac π × (761/2)2 Similarly, the cross-sectional steel ratio of the chord at the corner and the chord in the middle position in Example 2 are 0.16 and 0.16, respectively. In Example 3, the cross-sectional steel ratio of the chord is 0.14, which can satisfy the detailing requirements. (3) Confinement factor In accordance with Eq. (3.3.1.2) of the Standard (Eq. 1.3.1 of this book): Confinement factor of the chord in Example 1: ] [ π × (813/2)2 − (761/2)2 × 345 As f y = 1.27 ξ= = Ac f ck π × (761/2)2 × 38.5 Similarly, for Example 2, the confinement factor of the chord at the corner and chord in the middle position are 1.52 and 1.51, respectively, and the confinement factor of the chord in Example 3 is 1.33, which can satisfy the detailing requirements. (4) Outside diameter-to-sectional width ratio (D/B) The outside diameter-to-sectional width ratio (D/B) of the chord in Example 1 = 813/1500 = 0.54; Similarly, D/B of the chord at the corner in Example 2 is 0.18. The D/B of the chord in Example 3 is 0.16, which can satisfy detailing requirements.

B.1.2 Materials Match Verify the matching relationship between the strength of concrete and steel tube in accordance with Sect. 4.2 of the Standard. In each example, the grade of the steel tube is Q355, the strength class of the core concrete is C60, and the strength class of the concrete encasement is C40. The strength class of the core concrete is greater than that of the concrete encasement, and the strength class of the concrete encasement is greater than C30, which satisfies the requirements.

398

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

B.2 Calculation Indices (1) Strength calculation indices The design values of axial compressive strength and shear strength of CFST crosssection are calculated in accordance with Sect. 5.2 of the Standard. In accordance with Eqs. (5.2.1.1), (5.2.1.2), and (5.2.2) of the Standard (Eqs. 3.3.1–3.3.3 of this book): For CFST cross-section in Example 1, the design value of axial compressive strength (Eq. 3.3.1 of this book) and shear strength (Eq. 3.3.3 of this book): f scy γsc (1.14 + 1.02ξ ) f ck = γsc [ ( )] A f 1.14 + 1.02 Acs fcky f ck = γsc [ ( )] π ×[(813/2)2 −(761/2)2 ]×345 1.14 + 1.02 × × 38.5 2 π×(761/2) ×38.5 = γsc ) ( f sv = 0.422 + 0.313αs2.33 ξ 0.134 f sc [ ) ( )2.33 ]( As f y 0.134 As = 0.422 + 0.313 · f sc Ac Ac f ck { ]2.33 } [ π × (813/2)2 − π × (761/2)2 = 0.422 + 0.313 × π × (761/2)2 { }0.134 [ ] π × (813/2)2 − (761/2)2 × 345 × · f sc π × (761/2)2 × 38.5 f sc =

For building structure, power tower structure and port engineering structure, γ sc is taken as 1.20, which is substituted into the above equation, so, f sc = 78.02 N/mm2 , f sv = 34.25 N/mm2 . Similarly, for highway bridge and culverts, γ sc is taken as 1.40, and the f sc and f sv of cross-section of the CFST chord at the corner of Example 2 are 73.86 N/mm2 and 33.32 N/mm2 , respectively. The f sc and f sv of the cross-section of CFST chord in the middle position are 73.73 N/mm2 and 33.24 N/mm2 , respectively. In Example 3, the f sc and f sv of CFST chord cross-section are 68.75 N/mm2 and 30.40 N/mm2 , respectively. (2) Stiffness calculation indices

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

399

The elastic compression stiffness, elastic tension stiffness, elastic flexural stiffness and elastic shear stiffness of CFST cross-section and CFST hybrid structure crosssection are calculated in accordance with Sect. 5.2 of the Standard. In accordance with Table 4.4.8 in GB 50017 Standard for Design of Steel Structures, elastic modulus of steel E s = 2.06 × 105 N/mm2 , shear modulus Gs = 7.9 × 104 N/mm2 . In accordance with Provision 4.1.5 in GB 50010 Code for Design of Concrete Structures, for C60 concrete, E c,c = 3.60 × 104 N/mm2 , Gc = 0.4E c,c = 0.4 × 3.60 × 104 N/mm2 = 1.44 × 104 N/mm2 . In accordance with Table 4.2.5 in GB 50010 Code for Design of Concrete Structures, the elastic modulus E s,l of HRB400 longitudinal reinforcement is 2.00 × 105 N/mm2 . For Example 1, Elastic compression stiffness of CFST cross-section (Eq. 3.3.4 of this book): (E A)c = E s As + E c,c Ac ] [ = E s π (D/2)2 − (Di /2)2 + E c,c π (Di /2)2 ] [ = 2.06 × 105 × π × (813/2)2 − (761/2)2 + 3.60 × 104 × π × (761/2)2 = 2.96 × 107 kN Elastic compression stiffness of the cross-section of concrete-encased CFST hybrid structure (Eq. 3.3.8 of this book): (E A)c,h = ∑(E s As + E s,l Al + E c,c Ac ) + E c,oc Aoc ( ) π D2 π d 2 × 48 + E c,oc B H − = (E A)c + E s,l l 4 4 2 × 48 π × 32 = 2.96 × 1010 + 2.00 × 105 × 4 ) ( π × 8132 4 + 3.25 × 10 × 1500 × 1800 − 4 = 1.08 × 108 kN Elastic tension stiffness of CFST cross-section (Eq. 3.3.5 of this book): (E A)t = E s As ] [ = E s π (D/2)2 − (Di /2)2 ] [ = 206 × 103 × π × (813/2)2 − (761/2)2 = 1.32 × 107 kN Elastic tension stiffness of the cross-section of concrete-encased CFST hybrid structure (Eq. 3.3.7 of this book):

400

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

(E A)t,h = ∑(E s As + E s,l Al ) π × dl2 × 48 4 π × 322 × 48 10 5 = 1.32 × 10 + 2.00 × 10 × 4 = 2.10 × 107 kN

= 1.32 × 1010 + 2.00 × 105 ×

Elastic flexural stiffness of CFST cross-section (Eq. 3.3.8 of this book): E I = E s Is + E c,c Ic π(D 4 − Di4 ) π Di4 + E c,c 64 64 ] [ 4 − (761)4 π × (813) π × (761)4 3 + 3.60 × 104 × = 206 × 10 × 64 64 = 1.62 × 106 kN m2

= Es

Elastic flexural stiffness of the cross-section of concrete-encased CFST hybrid structure (Eq. 3.3.9 of this book): (E I )h = E s Is,h + E s,l Il,h + E c,c Ic,h + E c,oc Ioc,h = E I + E s,l Il,h + E c,oc Ioc,h = 1.62 × 1015 + 2.00 × 105 × 1.84 × 1010 ) ( π × 8134 1500 × 18003 − + 3.25 × 104 × 12 64 = 2.77 × 107 kN m2 Elastic shear stiffness of CFST cross-section (Eq. 3.3.10 of this book): G A = G s As + G c,c Ac ] [ = G s π (D/2)2 − (Di /2)2 + G c,c π(Di /2)2 ] [ = 7.9 × 104 × π × (813/2)2 − (761/2)2 + 1.44 × 104 × π × (761/2)2 = 1.16 × 107 kN Elastic shear stiffness of the cross-section of concrete-encased CFST hybrid structure (Eq. 3.3.11 of this book):

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

401

∑(

) G s As + G c,c Ac + G c,oc Aoc ( ) π × D2 = G A + G c,oc B H − 4

(G A)h =

= 1.16 × 1010 + 3.25 × 104 × 0.40 ( ) π × 8132 × 1500 × 1800 − 4 = 4.00 × 107 kN Calculation results for elastic stiffness of the cross-section of CFST and concreteencased CFST hybrid structure are shown in Appendix Table B.2.

B.3 Calculation of Resistance B.3.1 Calculation of Resistance in Compression In accordance with Sects. 7.2–7.4 of the Standard (Sects. 5.3.2–5.3.4 of this book), the resistance of cross-section of single-chord and multi-chord concrete-encased CFST hybrid structures to axial compression are calculated. (1) For Example 1, Nrc = f c,oc Aoc + f l' Al [ ] d2 = f c,oc B H − π (D/2)2 + f 'l π l × 48 4 [ ] = 19.1 × 1500 × 1800 − π × (813/2)2 322 × 48 4 = 5.56 × 104 kN + 360 × π ×

Ncfst = f sc Asc f scy Asc = γsc (1.14 + 1.02ξ ) f ck Asc = γsc [ ( )] A f 1.14 + 1.02 Acs fcky f ck Asc = γsc

8.54 × 107

8.16 × 107

3.51 × 106 (2.26 × 106 )

2.71 × 106

2

3

1.26 × 107

1.67 × 107

2.10 × 107

Note The values in brackets are the data for the CFST chord in waist

1.23 × 106

1.70 × 106 (1.09 × 106 )

1.32 × 107

1.35 × 104

2.20 × 104 (9.09 × 103 )

1.62 × 106

1.08 × 108

2.96 × 107

1

2.66 × 107

2.77 × 107

2.77 × 107

Concrete-encased CFST hybrid structure

Single CFST

Concrete-encased CFST hybrid structure

Concrete-encased CFST hybrid structure

Single CFST

Single CFST

Elastic flexural stiffness (kN m2 )

Example

Elastic compression stiffness (kN) Elastic tensile stiffness (kN)

Table B.2 Cross-sectional stiffness

1.06 × 106

1.38 × 106 (8.85 × 105 )

1.16 × 107

Single CFST

2.95 × 107

3.09 × 107

4.00 × 107

Concrete-encased CFST hybrid structure

Elastic shear stiffness (kN)

402 Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

=

403

[ ( )] π ×[(813/2)2 −(761/2)2 ]×345 1.14 + 1.02 × × 38.5 × π × (813/2)2 π ×(761/2)2 ×38.5 γsc

For building structure, power tower structure and port engineering structure, γ sc is taken as 1.20, which is substituted into the above equation, N cfst = 4.05 × 104 kN. N0 = 0.9(Nrc + Ncfst ) ) ( = 0.9 × 5.56 × 104 + 4.05 × 104 = 8.65 × 104 kN (2) For Example 2, Nrc = f c,oc Aoc + f 'l Al [ = f c,oc B H − (B − 2tc )(H − 2tc ) −

2 π Dangle

4

2 π Dmiddle ×4− ×2 4

]

dl2 × 48 4 ⎡ ⎤ 1500 × 1800 − (1500 − 2 × 273) × (1800 − 2 × 273) ⎦ = 19.1 × ⎣ π × 2732 π · 2192 − ×4− ×2 4 4 322 × 48 + 360 × π × 4 = 4.87 × 104 kN + f 'l π

f scy γsc (1.14 + 1.02ξ ) f ck = γsc )] [ ( A f f ck 1.14 + 1.02 Acs fcky = γsc [ ( )] π ×[(273/2)2 −(253/2)2 ]×355 1.14 + 1.02 × × 38.5 π ×(253/2)2 ×38.5 = γsc

f sc-angle =

f scy γsc (1.14 + 1.02ξ ) f ck = γsc

f sc-middle =

404

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

= =

[ ( )] A f 1.14 + 1.02 Acs fcky f ck γsc )] [ ( π ×[(219/2)2 −(203/2)2 ]×355 × 38.5 1.14 + 1.02 × π×(203/2)2 ×38.5 γsc

where, f sc-angle f sc-middle Dangle Dmiddle

design value of cross-sectional axial compressive strength of CFST chord at the corner of structure (N/mm2 ); design value of cross-sectional axial compressive strength of CFST chord in the middle position of structure (N/mm2 ); outside diameter of steel tube of single CFST chord at the corner of structure (mm); outside diameter of steel tube of single CFST chord in the middle position of structure (mm).

In accordance with Eq. (7.3.1.4) of the Standard (Eq. 5.3.3.4 of this book), Ncfst =

∑

f sc,i Asc,i

= 4 f sc-angle Aangle + 2 f sc-middle Amiddle = 4 f sc-angle × π × (Dangle /2)2 + 2 f sc-middle × π × (Dmiddle /2)2 = 4 f sc-angle × π × (273/2)2 + 2 f sc-middle × π × (219/2)2 For highway bridge and culvert structure, γ sc is taken as 1.40, and then: Ncfst =

∑

f sc,i Asc,i

= 2.28 × 104 kN In accordance with Eq. (7.3.1.2) of the Standard (Eq. 5.3.3.2 of this book): N0 = 0.9(Nrc + Ncfst ) ) ( = 0.9 × 4.87 × 104 + 2.28 × 104 = 6.44 × 104 kN where, Aangle Amiddle

cross-sectional area of the single CFST chord at the corner of structure (mm2 ); cross-sectional area of the single CFST chord in the middle position of structure (mm2 ).

Similarly, N rc , N cfst , and N 0 of Example 3 are 5.10 × 104 , 1.30 × 104 and 5.76 × 104 kN respectively.

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

405

B.3.2 Calculation Resistance in Combined Compression and Bending In accordance with Sects. 7.2–7.5 of the Standard, the internal bending moment M of single-chord and multi-chord concrete-encased CFST hybrid structure are 8000 kN m and 5000 kN m, respectively. When the axial load ratio n = 0.2 and 0.6, and the effective length l 0 is 20 m and 30 m, respectively. Calculate the resistance in combined compression and bending of single-chord and multi-chord concrete-encased CFST hybrid structure considering the influence of slenderness ratio. Take Example 1 as an example: Step 1: In accordance with Provision 7.2.3 of the Standard, the resistance in axial compression and the corresponding bending resistance of the cross-section of the concrete encasement in the concrete-encased CFST hybrid structure are calculated. The strength class of concrete encasement is C40. Therefore, in accordance with Provision 7.2.3, α 1 and β 1 are taken as 1.0 and 0.80, respectively. For example, if the distance between the neutral axis and the compressive edge of the cross-section c = 600 mm, then β 1 · c = 480 mm. The area of the equivalent stress block of concrete encasement, that is, the area of the shaded part Ae,oc = 6.72 × 105 mm2 of the simplified cross-section of the concrete encasement in Fig. 7.2.3a of the Standard (Fig. 5.17 of this book). The distance between the compressive edge and the centroid of the equivalent stress block of the concrete encasement x e,oc = 240 mm. In accordance with Eqs. (7.2.3.3), (7.2.3.4) of the Standard (Eqs. 5.3.2.11 and 5.3.2.12 of this book), σ li is determined, specific as follows: When c = 600 mm, σ li is determined in accordance with the distance from the ith longitudinal reinforcement to the compression edge (x li ). As shown in Appendix Fig. B.1, the cross-section of concrete-encased CFST hybrid structure has 13 rows of longitudinal reinforcement. The first row and the 13th row have 13 longitudinal reinforcements, respectively. The other rows have 2 longitudinal reinforcements. The value of x li and σ li in the first row to 13th are given in Appendix Table B.3. The diameter of each longitudinal reinforcement is 32 mm, and the cross-sectional area of each longitudinal reinforcement is: 2 π dsteelbar 4 π × 322 = 4 = 804.25 mm2

Ali =

∑ So, when c = 600 mm, σli Ali = −2.49 × 103 kN. In accordance with Eqs. (7.2.3.1), (7.2.3.2) of the Standard, (Eqs. 5.3.2.9 and 5.3.2.10 of this book), the resistance of the cross-section of concrete encasement

406

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

Table B.3 The value of x li and σ li Row i

Distance from the ith longitudinal reinforcement to the compressed edge x li (mm)

Longitudinal reinforcement σ li (N/mm2 )

1

56.00

360.0

2

196.67

360.0

3

337.33

297.6

4

478.00

138.2

5

618.67

−21.1

6

759.33

−180.5

7

900.00

−339.9

8

1040.67

−360.0

9

1181.33

−360.0

10

1322.00

−360.0

11

1462.67

−360.0

12

1603.33

−360.0

13

1744.00

−360.0

of the single-chord concrete-encased CFST hybrid structure to compression Nrc' = 1.13 × 104 kN, and the corresponding bending resistance M rc = 1.74 × 104 kN m. Step 2: In accordance with Provision 7.2.4 (1) of the Standard, calculate the resistance of the cross-section of the core concrete cross-section in axial compression and the corresponding bending resistance. The uniaxial peak compressive stress σ o and uniaxial peak compressive strain εo of core concrete are determined by Tables 7.2.4.1 and 7.2.4.2 of the Standard (Tables 5.1 and 5.2 in the book). For Example 1, σ o = 47.3 N/mm2 and εo = 4306.59 με. At the same time, the ultimate compressive strain of the concrete compression edge is 0.0033 ε. When c = 600 mm, the area of the compression zone of the core concrete is Ac,c is 2.57 × 104 mm2 . By substituting the above data into Eqs. (7.2.4.3) and (7.2.4.4) of the Standard (Eqs. 5.3.2.15 and 5.3.2.16 in the book), the resistance of the core concrete in compression Nc' = 98.23 kN is obtained. Corresponding bending resistance of core concrete M c = 33.77 kN m. Step 3: In accordance with Clause 2 of Provision 7.2.4 of the Standard, calculate the resistance of cross-section of the steel tube to compression and the corresponding bending resistance. In accordance with Eqs. (7.2.4.11)–(7.2.4.15) of the Standard (Eqs. 5.3.2.23– 5.3.2.27 of this book), so, c = 600 mm, k 1 = 0.54, m1 = 3.25, m2 = 2.97, m3 = 0.53. Then, the resistance of cross-section of the steel tube to compression N ' s = −9.71 × 103 kN and the corresponding bending resistance Ms = 1.49 × 103 kN m are calculated by Eqs. (7.2.4.9) and (7.2.4.10) of the Standard (Eqs. 5.3.2.21 and

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

407

5.3.2.22 in the book). Step 4: In accordance with Eqs. (7.2.2.1) and (7.2.2.2) of the Standard (Eqs. 5.3.2.5 and 5.3.2.6 in the book). The design values of axial compressive force and bending moment of cross-section of concrete-encased CFST hybrid structure obtained by calculation shall satisfy the following requirements: N ≤ 1.65 × 103 kN, M ≤ 1.89 × 104 kN m. Step 5: Adjust the value of c and repeat step 1 to 4 to calculate the conditions that the design values of cross-sectional axial compressive force N and bending moment M of concrete-encased CFST hybrid structure should satisfy. The results are as follows: when c = 600 mm, N ≤ 1.65 × 103 kN, M ≤ 1.89 × 104 kN m; when c = 800 mm, N ≤ 1.45 × 104 kN, M ≤ 2.13 × 104 kN m; when c = 1000 mm, N ≤ 2.72 × 104 kN, M ≤ 2.21 × 104 kN m; when c = 1200 mm, N ≤ 3.89 × 104 kN, M ≤ 2.06 × 104 kN m; when c = 1400 mm, N ≤ 4.91 × 104 kN, M ≤ 1.79 × 104 kN m; when c = 1600 mm, N ≤ 5.77 × 104 kN, M ≤ 1.50 × 104 kN m. Step 6: Summarize the values of N and M in accordance with step 1 to 5. When M = 0, the values of N are derived from the data in Sect. B.3.1. Through repeated iterative calculation and trial, when N = 0, c = 574.89 mm and M = 1.84 × 104 kN m. Step 7: It has been known that the internal bending moment M of the concrete-encased CFST hybrid structure is 8000 kN m. In accordance with Provision 7.5.2 and 7.5.3 of the Standard (Sect. 5.3.5 (2) in the book), M 1 = M 2 = 8000 kN m. For building structure, power tower structure and port engineering structure, in accordance with Provision 7.5.3 of the Standard (Sect. 5.3.5 (3) in the book), when the axial load ratio is 0.2, the axial compressive force N = 1.73 × 104 kN and l0 = 20 m, ea = 60.00 mm, ei = 522.70 mm, h0 = 1744 mm, C m = 0.7 + 0.3 = 1.0, ξ c = 0.80, ηc = 1.25. The above data are substituted into Eq. (7.5.3.1) of the Standard (Eq. 5.3.5.4 of this book), and the design value of the bending moment of the control cross-section M = 1.00 × 104 kN m. The calculation results for the resistance of concrete-encased CFST hybrid structure in combined compression and bending are shown in Appendix Table B.4.

B.3.3 Calculation of Resistance Under Long-Term Load In accordance with Provision 7.6 of the Standard (Sect. 5.3.6 in the book) and Appendix C (Tables 5.3–5.5 in the book), the resistance of concrete-encased CFST hybrid structure to axial compression under long-term load is calculated under the following conditions: The effective length l0 is 20 m and 30 m. The resistance of concrete-encased CFST hybrid structure to combined compression and bending under long-term load is calculated under the following calculation conditions: Axial load ratio n = 0.2 and 0.6, the effective lengths l0 are 20 m and

408

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

Table B.4 Resistance of concrete-encased CFST hybrid structure in combined compression and bending Example

l 0 = 20 m n = 0.2

Type

l 0 = 20 m n = 0.6

l 0 = 30 m n = 0.2

l 0 = 30 m n = 0.6

Example 1 M (kN m) M = 1.00 × 104 M = 1.16 × 104 M = 1.24 × 104 M = 1.68 × 104 N = 1.73 × 104 N = 5.19 × 104 N = 1.72 × 104 N = 5.19 × 104

N (kN)

Example 2 M (kN m) M = 6.33 × 103 M = 7.78 × 103 M = 8.09 × 103 M = 1.17 × 104 N = 1.29 × 104 N = 3.86 × 104 N = 1.29 × 104 N = 3.86 × 104

N (kN)

Example 3 M (kN m) M = 6.21 × 103 M = 7.52 × 103 M = 7.75 × 103 M = 1.11 × 104 N = 1.15 × 104 N = 3.45 × 104 N = 1.15 × 104 N = 3.45 × 104

N (kN)

Note In Example 1, the value of γ sc is determined by building structure, power tower structure and port engineering structure. In Examples 2 and 3, the value of γ sc is determined according to the structure of highway bridge and culvert. The resistance in combined compression and bending of each example satisfy the requirements of the Standard

30 m, and the design values of bending moment M 2 subjected by single-chord and multi-chord concrete-encased CFST hybrid structure are 8000 kN m and 5000 kN m, respectively. (1) For Example 1, In accordance with Eq. (7.3.1.2) of the Standard (Eq. 5.3.3.2 in the book), For building structure, power tower structure and port engineering structure, N0 = 0.9(Nrc + Ncfst ) = 8.65 × 104 kN In accordance with Provision 7.5.1 of the Standard, the stability factor ϕ (Sect. 5.3.5 (1) in this book) of concrete-encased CFST hybrid structure shall be determined by the slenderness ratio of the structure in accordance with GB 50010 Code for Design of concrete Structures. Calculate the slenderness ratio of the structure l0 /i: in accordance with GB 50010 Code for Design of Concrete Structures, i is the minimum radius of gyration of the cross-section. l0 l0 =√ i I /A = /(

l0

) B H 3 /12 /(B H )

l0 = /( ) 1500 × 18003 /12 /(1500 × 1800)

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

409

When the effective length l0 is 20 m, l 0 /i = 38.49. When the effective length l0 is 30 m, l0 /i = 57.74. In accordance with Table 6.2.15 in GB 50010 Code for Design of Concrete Structures, the linear interpolation method is adopted. When l0 /i = 38.49, the stability factor ϕ is 0.97. When l0 /i = 57.74, the stability factor ϕ is 0.85. In accordance with Eq. (7.5.1) of the Standard (Eq. 5.3.5.1 in the book), the resistance of normal cross-section to axial compression considering the influence of slenderness ratio is calculated as follows: When l 0 = 20 m, Nu = 0.9ϕ(Nrc + Ncfst ) = ϕ · N0 = 0.97 × 8.65 × 104 = 8.39 × 104 kN When l 0 = 30 m, Nu = 0.9ϕ(Nrc + Ncfst ) = ϕ · N0 = 0.85 × 8.65 × 104 = 7.35 × 104 kN Refer to Appendix C (Tables 5.3–5.5 of this book), and obtain the long-term load coefficient k cr of concrete-encased CFST hybrid structure as shown in Appendix Table B.5 by linear interpolation. Table B.5 Resistance of concrete-encased CFST hybrid structure in axial compression Example

Type

l 0 = 20 m

l 0 = 30 m

ϕ

k cr

Resistance in axial compression (kN)

ϕ

k cr

Resistance in axial compression (kN)

1

Building structure, power tower structure, port engineering structure

0.97

0.82

6.88 × 104

0.85

0.59

4.34 × 104

2

Highway bridge and culvert structure

0.98

0.83

5.24 × 104

0.89

0.75

4.30 × 104

3

Highway bridge and culvert structure

0.98

0.88

4.96 × 104

0.89

0.75

3.85 × 104

410

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

For Example 1, When l0 = 20 m, kcr = 0.82, In accordance with Eq. (7.6.1) of the Standard (Eq. 5.3.6 in the book): NuL = kcr Nu = 0.82 × 8.39 × 104 = 6.88 × 104 kN When l 0 = 30 m, k cr = 0.59, In accordance with Eq. (7.6.1) of the Standard (Eq. 5.3.6 in the book): NuL = kcr Nu = 0.59 × 7.35 × 104 = 4.34 × 104 kN (2) For Example 2, For the structure of highway Bridges and culverts, in accordance with Eq. (7.3.1.2) of the Standard (Eq. 5.3.3.2 in the book), N0 = 0.9(Nrc + Ncfst ) = 6.44 × 104 kN Calculate the slenderness ratio of the structural l0 /i: in accordance with GB 50010 Code for Design of Concrete Structures, i is the minimum radius of gyration of the cross-section. l0 l0 =√ i I /A = /[

l0 ] (B H 3 )−(B−2tc )(H −2tc )3 /[B H − (B − 2tc )(H − 2tc )] 12

= /[

l0 1500 × 18003 − (1500 − 2 × 440) × (1800 − 2 × 440)3 12

]

/[1500 × 1800 − (1500 − 2 × 440) × (1800 − 2 × 440)] When the effective length l0 is 20 m, l 0 /i = 35.17. When the effective length l0 is 30 m, l0 /i = 52.75. In accordance with Table 6.2.15 in GB 50010 Code for Design of Concrete Structures, linear interpolation method is adopted. When l0 /i = 35.17, the stability factor ϕ is 0.98. When l0 /i = 52.75, the stability factor ϕ is 0.89.

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

411

In accordance with Eq. (7.5.1) of the Standard (Eq. 5.3.5.1 in the book), the resistance of normal cross-section to axial compression considering the influence of slenderness ratio is calculated as follows: When l 0 = 20 m, Nu = 0.9ϕ(Nrc + Ncfst ) = ϕ · N0 = 0.98 × 6.44 × 104 = 6.31 × 104 kN When l 0 = 30 m, Nu = 0.9ϕ(Nrc + Ncfst ) = ϕ · N0 = 0.89 × 6.44 × 104 = 5.73 × 104 kN Refer to Table C.0.2 in Appendix C of the Standard (Tables 5.3–5.5 in the book), when l0 = 20 m, k cr = 0.83, In accordance with Eq. (7.6.1) of the Standard (Eq. 5.3.6 in the book): NuL = kcr Nu = 0.83 × 6.31 × 104 = 5.24 × 104 kN Refer to Table C.0.2 in Appendix C of the Standard (Tables 5.3–5.5 in the book), when l0 = 30 m, k cr = 0.75, In accordance with Standard Eq. (7.6.1) of the Standard (Eq. 5.3.6 in the book): NuL = kcr Nu = 0.75 × 5.73 × 104 = 4.30 × 104 kN The resistance in axial compression of each example under long-term load is shown in Appendix Table B.5. Taking Example 1 as an example, it is known that M 1 = M 2 = 8000 kN m, N = n × N 0 × k cr , where n is the axial load ratio, N 0 is determined in accordance with Sect. B.3.1, and k cr is determined in accordance with Appendix Table B.5. For building structure, power tower structure and port engineering structure, ea = 60.00 mm, ei = 522.70 mm, h0 = 1744 mm, C m = 0.7 + 0.3 = 1.0, ξ c = 0.78 and ηc = 1.25, in accordance with Provision 7.5.3 (Sect. 5.3.5 (3) in the book). Plug the

412

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

Table B.6 Resistance in combined compression and bending of concrete-encased CFST hybrid structure under long-term load Example

Type

l 0 = 20 m, n = 0.2

l 0 = 20 m, n = 0.6

l 0 = 30 m, n = 0.2

l 0 = 30 m, n = 0.6

Example 1

M (kN m)

M = 9.80 × 103

M = 1.12 × 104

M = 1.08 × 104

M = 1.33 × 104

N (kN)

N = 1.42 × 104 N = 4.25 × 104 N = 1.02 × 104 N = 3.06 × 104

M (kN m)

M = 6.16 × 103

N (kN)

N = 1.07 × 104 N = 3.21 × 104 N = 9.65 × 103 N = 2.90 × 104

M (kN m)

M = 6.11 × 103

N (kN)

N = 1.01 × 104 N = 3.04 × 104 N = 8.63 × 103 N = 2.59 × 104

Example 2

Example 3

M = 7.43 × 103 M = 7.32 × 103

M = 7.23 × 103 M = 7.03 × 103

M = 9.92 × 103 M = 9.50 × 103

Note The value of γ sc in Example 1 is determined by building structure, power tower structure and port engineering structure. In Examples 2 and 3, γ sc is determined according to the structure of highway bridge and culvert

above data into Eq. (7.5.3.1) of the standard (Eq. 5.3.5.4 in the book), then M = 9.80 × 103 kN m. The calculation results of resistance in combined compression and bending of each example under long-term load are shown in Appendix Table B.6.

B.3.4 Shear Resistance of Cross-Section In accordance with Sect. 7.7 of the Standard (Sect. 5.3.7 of the book), shear resistance of cross-section of single-chord and multi-chord concrete-encased CFST hybrid structures are calculated. (1) For Example 1, in accordance with Provision 7.7.2 of the Standard (Eqs. 5.3.7.1– 5.3.7.4 of this book), ρsv =

Asv sB d2

π · 4s · 2 sB 2 π × 104 × 2 = 80 × 1500 = 1.31 × 10−3 =

ρ=

Al Aoc

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

= =

π

dl2 4

413

× 48 2

B H − π D4 π×

322 4

× 48

1500 × 1800 − π ×

8132 4

= 1.77% In accordance with Table 4.2.3.1 in GB 50010 Code for Design of Concrete Structures, the design value of tensile strength of HRB400 steel reinforcement is 360 N/mm2 , so, f v = 360 N/mm2 . In accordance with Provision 7.7.2 of the Standard, the shear resistance of the concrete encasement is calculated as follows (Eq. 5.3.7.2 of this book): / √ Vrc = 0.45Aoc (2 + 60ρ) f cu,oc ρsv f v )/ ( √ Asv π D2 fv = 0.45 × B H − (2 + 60ρ) f cu,oc 4 sB ] [ π × 8132 = 0.45 × 1500 × 1800 − 4 / √ × (2 + 60 × 1.77%) × 40 × 1.31 × 10−3 × 360 = 2.97 × 103 kN In accordance with Provision 7.7.3 of the Standard, the shear resistance of the encased CFST is calculated as follows (Eq. 5.3.7.4 of this book): Vcfst =

∑

0.9(0.97 + 0.2 ln ξi )Asc,i f sv,i

= 0.9(0.97 + 0.2lnξ )Asc f sv π D2 · f sv 4 π × 8132 × f sv = 0.9 × (0.97 + 0.2 × ln 1.27) × 4 = 0.9 × (0.97 + 0.2 ln ξ ) ·

For building structure, power tower structure and port engineering structure, γ sc is taken as 1.20, f sv = 34.25 N/mm2 , and then V cfst = 1.63 × 104 kN. In accordance with Provision 7.7.1 of the Standard (Eq. 5.3.7.1 of this book), V ≤ Vrc + Vcfst = 2.97 × 103 + 1.63 × 104 = 1.93 × 104 kN (2) For Example 2, in accordance with Provision 7.7.2 of the Standard (Eqs. 5.3.7.1– 5.3.7.4 of this book),

414

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

ρsv =

Asv sB π

ds2 4

×4 sB 2 π × 104 × 4 = 80 × 1500 = 2.62 × 10−3 =

d2

π 4l × 48 Al ρ= =[ π D2 Aoc B H − (B − 2tc )(H − 2tc ) − 4angle × 4 − =⎡ ⎣

π×

322 4

2 π Dmiddle 4

× 48

1500 × 1800 − (1500 − 2 × 440) × (1800 − 2 × 440)

π × 2732 π × 2192 ×4− ×2 4 4 = 2.12% −

×2

]

⎤ ⎦

In accordance with Provision 7.7.2 of the Standard, the shear resistance of the concrete encasement is calculated as follows (Eq. 5.3.7.2 of this book): / √ Vrc = 0.45Aoc (2 + 60ρ) f cu,oc ρsv f v [ = 0.45 × B H − (B − 2tc )(H − 2tc ) − /

2 π Dangle

4

2 π Dmiddle ×4− ×2 4

]

√ Asv fv (2 + 60ρ) f cu,oc sB ⎤ ⎡ 1500 × 1800 − (1500 − 2 × 440) × (1800 − 2 × 440) ⎦ = 0.45 × ⎣ π × 2732 π × 2192 − ×4− ×2 4 4 / √ × (2 + 60 × 2.12%) × 40 × 2.62 × 10−3 × 360 ×

= 3.62 × 103 kN In accordance with Provision 7.7.3 of the Standard, the shear resistance of the CFST part is calculated as follows (Eq. 5.3.7.4 of this book): Vcfst =

∑

0.9(0.97 + 0.2 ln ξi )Asc,i f sv,i

= 0.9 × (0.97 + 0.2 ln ξ ) ·

2 π Dangle

4

· f sv × 4 + 0.9

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

415

Table B.7 Shear resistance of cross-section of the concrete-encased CFST hybrid structure Example

Type

V rc (kN)

V cfst (kN)

Example 1

Building structure, power tower structure, port engineering structure

2.97 × 103

1.63 × 104 1.93 × 104

V (kN)

Example 2

Highway bridge and culvert structure

3.62 × 103

9.77 × 103 1.34 × 104

2 π · Dmiddle · f sv × 2 4 π × 2732 = 0.9 × (0.97 + 0.2 × ln 1.52) × 4

× (0.97 + 0.2 ln ξ ) ×

× f sv × 4 + 0.9 × (0.97 + 0.2 × ln 1.51) ×

π × 2192 × f sv × 2 4

For highway bridge and culverts, γ sc is taken as 1.40, the f sv of single CFST components at the corner and in the middle position are 33.32 N/mm2 and 33.24 N/mm2 , respectively. Then V cfst = 9.77 × 103 kN is obtained. In accordance with Provision 7.7.1 of the Standard (Eq. 5.3.7.1 of the book), V ≤ Vrc + Vcfst = 3.62 × 103 + 9.77 × 103 = 1.34 × 104 kN The calculation results of shear resistance of cross-section of each example are shown in Appendix Table B.7.

B.3.5 Calculation for Resistance of Arch Structure In accordance with Sect. 7.8 of the Standard, the resistance of concrete-encased CFST hybrid arch structure is calculated. Calculation conditions: The main arch structure is a fixed arch with 300 m span, the arch axis is catenary, and the rise-to-span ratio is 1/5. The cross-section is the same as that of the above concrete-encased CFST hybrid structure, and the crosssection is uniform along the length. Calculate its resistance when the axial load ratio (n) of equivalent beam-column is n = 0.4. For Example 2, when n is 0.4, for highway bridge and culverts, the axial load N borne by concrete-encased CFST hybrid structure is 2.57 × 104 kN. Based on Provision 7.3.2–7.3.4 of the Standard, [(2)–(4) in Sect. 5.3.3 of this book], by calculation, when N = 2.57 × 104 kN, distance between the neutral axis and the compressive edge of the cross-section c = 1,137.55 mm, M = 2.21 × 104 kN m. Calculation results of bending resistance of concrete-encased CFST hybrid arch structure are shown in Appendix Table B.8.

416

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

Table B.8 Bending resistance of concrete-encased CFST hybrid arch structure Example

Neutral axis c when n = 0.4 (mm)

Bending resistance when n = 0.4 (kN m)

Example 2

1137.55

2.21 × 104

Example 3

1047.40

2.21 × 104

Note The data in the table are calculated according to the coefficient γ sc corresponding to the highway bridge and culvert structure

B.4 Protective Design B.4.1 Design of Fire Resistance In accordance with the provisions of Sect. 9.3 (Sect. 7.3 in this book) and Appendix E of the Standard (Tables 7.1–7.3 of this book), the fire resistance ratings of single-chord concrete-encased CFST hybrid structures are calculated. Calculation condition: load ratio during fire R = 0.2. In accordance with Appendix E of the Standard (Tables 7.1–7.3 of the book), the fire resistance ratings t R of single-chord concrete-encased CFST hybrid structure is related to load ratio R, cross-sectional width B, slenderness ratio λ and other factors, among which, the resistance coefficient (ncfst ) of the encased CFST member is determined in accordance with the specification in Provision 9.3.6 of the Standard (Eq. 7.3.3.2 of this book). In accordance with known conditions, load ratio during fire R = 0.2. In accordance with Appendix E of the Standard, when l0 is 20 m and 30 m, the fire resistance ratings of each single-chord concrete-encased CFST hybrid structure is greater than 3.00 h.

B.4.2 Verification of Impact Resistance The bending resistance of CFST hybrid structure under impact is calculated in accordance with Sect. 9.4 of the Standard. Calculation conditions: velocity of the impactor (V 0 ) is 10 m/s, axial load ratios (n) is 0.2 or 0.6. (1) For Example 1, Step 1: Through calculation, when N = 0, c = 574.89 mm and M = 1.84 × 104 kN-m, M is denoted as M u at this time. Step 2: In accordance with Eqs. (9.4.3.3)–(9.4.3.12) of the Standard (Eqs. 7.4.2.9– 7.4.2.18 of this book): 2 m 1 = 1.27 × 10−4 f cu,oc − 1.39 × 10−2 f cu,oc + 1.36

= 1.27 × 10−4 × 402 − 1.39 × 10−2 × 40 + 1.36

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

= 1.01 2 m 2 = −7.24 × 10−6 f cu,c + 1.69 × 10−3 f cu,c + 0.925

= −7.24 × 10−6 × 602 + 1.69 × 10−3 × 60 + 0.925 = 1.00 m 3 = −2.31 × 10−4 f yl + 1.07 = −2.31 × 10−4 × 400 + 1.07 = 0.98 m 4 = 3.37 × 10−4 f y + 0.883 = 3.37 × 10−4 × 345 + 0.883 = 1.00 g1 = −5.92ρ + 1.06 = −5.92 × 1.8% + 1.06 = 0.95 g2 = 0.235αs + 0.978 = 0.235 × 0.14 + 0.978 = 1.01 ( )2 D D g3 = −0.238 + 7.70 × 10−2 + 1.02 B B = −0.238 × 0.542 + 7.70 × 10−2 × 0.54 + 1.02 = 0.99 γv = −7.50 × 10−3 V02 + 0.136V0 + 0.354 = −7.50 × 10−3 × 102 + 0.136 × 10 + 0.354 = 0.96 γn = 3.08n 2 − 1.47n + 1.16 = 3.08 × 0.22 − 1.47 × 0.2 + 1.16 = 0.99 where, n is 0.2.

417

418

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

Step 3: In accordance with Eqs. (9.4.3.2) and (9.4.3.7) of the Standard (Eqs. 7.4.2.8 and 7.4.2.13 of this book): γg = g1 g2 g3 = 0.95 × 1.01 × 0.99 = 0.95 γm = m 1 m 2 m 3 m 4 = 1.01 × 1.00 × 0.98 × 1.00 = 0.99 Step 4: In accordance with Eq. (9.4.3.1) of the Standard (Eq. 7.4.2.7 of this book), it can be calculated as follows: Rd = 1.52γm γg γv γn = 1.52 × 0.99 × 0.95 × 0.96 × 0.99 = 1.36 Step 5: In accordance with Eq. (9.4.1) of the Standard (Eq. 7.4.2.1 of this book), M d = Rd M u = 1.36 × 1.84 × 104 = 2.50 × 104 kN m. Step 6: Repeat the above steps and calculate that when n is 0.6, Rd = 1.89. In accordance with Eq. (9.4.1) of the Standard (Eq. 7.4.2.1 of this book), M d = Rd M u = 1.92 × 1.84 × 104 = 3.53 × 104 kN m. (2) For Example 3, Step 1: Through iterative calculation and trial, when N = 0, c = 348.03 mm and M = 1.55 × 104 kN m. M at this time is denoted as M u . Step 2: In accordance with Eqs. (9.4.3.15)–(9.4.3.24) of the Standard (Eqs. 7.4.2.21– 7.4.2.30 of this book): 2 m 1 = 5.78 × 10−5 f cu,oc − 4.64 × 10−3 f cu,oc + 1.10

= 5.78 × 10−5 × 402 − 4.64 × 10−3 × 40 + 1.10 = 1.01 2 m 2 = −4.89 × 10−5 f cu,c + 4.51 × 10−3 f cu,c + 0.905

= −4.89 × 10−5 × 602 + 4.51 × 10−3 × 60 + 0.905 = 1.00

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

419

m 3 = −1.33 × 10−6 f yl2 + 7.44 × 10−4 f yl + 0.898 = −1.33 × 10−6 × 4002 + 7.44 × 10−4 × 400 + 0.898 = 0.98 m 4 = −7.26 × 10−4 f y + 1.25 = −7.26 × 10−4 × 355 + 1.25 = 0.99 g1 = 566ρ 2 − 12.6ρ + 1.07 = 566 × 2.0%2 − 12.6 × 2.0%+1.07 = 1.04 g2 = −2.33αs + 1.23 = −2.33 × 0.14 + 1.23 = 0.90 D + 1.54 B = −2.74 × 0.16 + 1.54

g3 = −2.74 = 1.10

γv = −7.00 × 10−3 V02 + 0.105V0 + 0.673 = −7.00 × 10−3 × 102 + 0.105 × 10 + 0.673 = 1.02 γn = 6.43n 2 − 4.22n + 1.71 = 6.43 × 0.22 − 4.22 × 0.2 + 1.71 = 1.12 where, n is 0.2. Step 3: In accordance with Eqs. (9.4.3.14) and (9.4.3.19) of the Standard (Eqs. 7.4.2.13 and 7.4.2.20 of this book): γg = g1 g2 g3 = 1.04 × 0.90 × 1.10 = 1.03

420

Appendix B: Design Examples of Concrete-Encased Concrete-Filled …

Table B.9 Bending resistance of concrete-encased CFST hybrid structure under impact load Example

c (mm)

Mu (kN m)

Rd (n = 0.2)

Rd (n = 0.6)

Md (kN m) (n = 0.2)

Md (kN m) (n = 0.6)

Example 1

574.89

1.84 × 104

1.36

1.92

2.50 × 104

3.53 × 104

Example 3

348.03

1.55 × 104

0.70

0.93

1.09 × 104

1.44 × 104

γm = m 1 m 2 m 3 m 4 = 1.01 × 1.00 × 0.98 × 0.99 = 0.98 Step 4: In accordance with Eq. (9.4.3.13) of the Standard (Eq. 7.4.2.7 of this book): Rd = 0.61γm γg γv γn = 0.61 × 0.98 × 1.03 × 1.02 × 1.12 = 0.70 Step 5: In accordance with Eq. (9.4.1) of the Standard (Eq. 7.4.2.1 of this book), M d = Rd M u = 0.70 × 1.55 × 104 = 1.09 × 104 kN m. Step 6: Repeat the above steps and calculate: when n is 0.6, Rd = 0.93. In accordance with Eq. (9.4.1) of the Standard (Eq. 7.4.2.1 of this book), M d = Rd M u = 0.93 × 1.55 × 104 = 1.44 × 104 kN m. The bending resistance of concrete-encased CFST hybrid structure under impact load is calculated as shown in Appendix Table B.9.

Appendix C

Finite Element Analysis Examples of Concrete-Encased Concrete-Filled Steel Tubular (CFST) Hybrid Structures

The main arch structure of deck arch bridge is a concrete-encased CFST hybrid structure. The effective span of the bridge is 600 m, the total width of the bridge deck is 24.5 m, two-way four-lane bridge with a design speed of 100 km/h, and the vehicle load grade is highway Class I. The safety grade of the bridge structure is level I, the design reference period is 100 years, the design basic wind speed is 27.6 m/s, and the navigation standard is Class III channel. The seismic basic intensity in the bridge area is 7 degree, the earthquake peak ground acceleration is 0.1 g, and the characteristic period of seismic response spectrum is 0.35 s. The anti-seismic measures of the bridge detailing should be considered in accordance with 8 degree. The seismic fortification of the bridge is classified as Class A. The design environment category is I. The overall layout of the arch columns is shown in Appendix Fig. C.1.

3

Column

4

5

6

7

8

9

10

11 12

2

13

1

12,500

6,000 4,000 4,0004,000 4,000 4,000 4,000 4,000 4,000 4,000 4,000 4,0004,000 6,000 60,000

Fig. C.1 Overall layout of the main arch structure (unit: cm)

© China Architecture & Building Press 2024 L. Han, Theory of Concrete-Filled Steel Tubular Structures, https://doi.org/10.1007/978-981-99-2170-6

421

422

Appendix C: Finite Element Analysis Examples of Concrete-Encased …

C.1 Condition of Calculation (1) Arch structure The main arch is a double-ribbed variable cross-section catenary fixed arch, which adopts the concrete-encased CFST hybrid structure, and the single ribs of arch box adopt single-box and single-chamber cross-section. The span is 600 m, the rise-tospan ratio is 5/24, and the arch axis coefficient is 1.9. The radial height of the arch cross-section at the top is 8 m, and the radial height of the base of the arch crosssection is 12 m. The radial height of the cross-section varies linearly from 8 to 12 m between the arch and the base of the arch, and the width of the rib is 6.5 m. The thickness of the concrete slab is 0.65 m. Between the base of the arch of the arch circle and the column 1: the thickness of the bottom concrete is 1.3 m. Between column 1 and column 4: the thickness of the bottom concrete slab is 0.80 m. Between column 4 and arch at the top: the thickness of the bottom concrete slab is 0.65 m. Between the base of the arch and arch column 1: the thickness of the concrete web changes gradually from 0.95 to 0.75 m. Between column 1 and column 2: the thickness of the concrete web gradually changes from 0.55 to 0.45 m. Between column 2 and the arch at the top: the thickness of the concrete web is 0.45 m. In the concrete-encased CFST hybrid arch structure, the cross-sectional dimensions of the upper and lower CFST chord are ϕ900 × 35 mm and ϕ900 × 30 mm, respectively. C80 concrete is adopted for core concrete. The chords is connected by 4L110 × 110 × 10 mm, 4L200 × 125 × 18 mm or 4L160 × 100 × 16 mm steel profiles to form a trussed CFST hybrid structure, with temporary cross bracing at the corresponding position of the cross partition. The detailing of the arch rib crosssection is shown in Appendix Fig. C.2. The cross-section form, strength grade of material, cross-section size, thickness of the slab, width of the beam, etc. of each component of the main arch are shown in Appendix Table C.1. (2) Action of load During the construction stage of the main arch, only the gravity of each component of the main arch is considered, including the self-weight of steel tube, profile steel, the dry concrete, unformed concrete, and reinforcement. The density of the steel is 7850 kg/m3 . The density of the concrete is 2500 kg/m3 . Loads during the service stage mainly come from the column on the arch and the bridge deck, including the self-weight of the column and the bridge deck. Vehicle loads are corresponded to Appendix Fig. C.1. The loads acting on the each column are shown in Appendix Table C.2. (3) Construction procedure The placement concrete for arch ring is divided into three rings and eight working platforms are placed symmetrically at the same time. There are 6 sections for each working platform for the top and bottom slab, and 7 sections for each working platforms for the web. Appendix Fig. C.3 shows placement scheme of concrete for

Appendix C: Finite Element Analysis Examples of Concrete-Encased …

423

Table C.1 Cross-sectional form, material and size of each component Component

Cross-section form

Material

Cross-sectional size, thickness of the slab, width of the beam (mm)

Steel tube of the chord

Circular tube cross-section

Q420D steel

ϕ900 × 35

Vertical connecting system

L-shaped steel

Q420D steel

4L200 × 125 × 18 4L160 × 100 × 16

Transverse connection system

L-shaped steel

Q420D steel

4L110 × 110 × 10

Top slab

Plate cross-section

C60 concrete

650

Bottom slab

Plate cross-section

C60 concrete

650, 800, 1300

Web

Plate cross-section

C60 concrete

450, 550, 750, 850, 950

Cross tie beam Plate cross-section

C60 concrete

450

Fig. C.2 Detailing of the cross-section of the arch rib

Encased CFST

Concrete encasement Encased CFST

Table C.2 The loads acting on the column Construction Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7 stage (13) (12) (11) (10) (9) (8) Load during construction (kN)

18,054

18,751

13,866

14,100

9891

12,764

4751

Load during the service stage (kN)

18,762

19,711

14,648

15,051

10,550

13,737

5473

half-span arch ring. Appendix Table C.3 shows the construction sequence of the components of the main arch. After the placement of arch ring, carry out column construction, beam construction, rigid structure closing, phase II dead load, combined with the layout of the construction surface, which can be divided into 57 procedures.

424

Appendix C: Finite Element Analysis Examples of Concrete-Encased …

Table C.3 Construction sequence of each component of the main arch Number

Schematic diagram

Procedure

1

Form steel tube skeleton

2

Place the core concrete

3

Place the concrete for bottom slab

4

Place the concrete for web

5

Place the concrete for top slab

Appendix C: Finite Element Analysis Examples of Concrete-Encased …

425

Top and bottom slab Working platform 4 Top and bottom slab Working platform 3 Top and bottom slab Working platform 2

Top and bottom slab Working platform 1

Web Working platform 4 Web Working platform 3

The center line of the bridge spans

Web Working platform 2

Web Working platform 1

Fig. C.3 Concrete placement scheme of main arch structure

C.2 Establishment of Finite Element Analysis Model In accordance with the stipulation of “Analysis method” in Sect. 5.3 of the Standard, a three-dimensional finite element analysis model of the main arch structure is established in ABAQUS. In accordance with the designed form of arch axis, the main arch structure is divided into three cross-sections: base of the arch to No. 1 column is the first cross-section, No. 1 column to No. 2 column is the second cross-section, and No. 2 column to the arch at the top is the third cross-section. The top slabs, bottom slabs and webs of the three cross-sections are different, and the height of the cross-section increases linearly from the top of arch to the base of arch. In accordance with Appendix A.1 and Appendix A.2 of the Standard (Sects. 3.5 and 3.6 of this book), the constitutive models of core concrete, confined concrete, unconfined concrete outside stirrups, steel tube and reinforcement are determined.

C.3 Structural Safety Analysis During the Construction and Service Stages (1) Stress analysis during the construction stage Corresponding to Appendix Table C.3, the construction stage includes five stages: forming the steel tube skeleton, placing the core concrete, placing the concrete for the bottom slab, placing the concrete for web, and placing the concrete for the top slab. The obtained minimum principal stress cloud of concrete arch cross-section during the construction and bridge formation stages are given in Appendix Fig. C.4.

426

Appendix C: Finite Element Analysis Examples of Concrete-Encased …

1) Steel tube skeleton formation stage: the maximum stress of the skeleton is located at the steel tube of the upper chord in the base of the arch of, the value is 72.3 N/ mm2 . 2) Core concrete placement stage: the maximum stress of the skeleton is also located at the steel tube of the upper chord in the base of the arch, which is 191.5 N/mm2 . The maximum principal stress and minimum principal stress of core concrete of the upper chord in the base of the arch are −1.8 N/mm2 and −23.6 N/mm2 , respectively. The stress of core concrete that is placed first is higher, while the stress of core concrete that is placed last is lower. 3) Concrete of the bottom slab placement stage: the maximum stress of the skeleton is located in the steel tube of the upper chord of the arch at the top, which is 244.9 N/mm2 . The minimum principal stress of the core concrete is located at the lower chord in the base of the arch, which is −32.3 N/mm2 , and its maximum principal stress is 1.4 N/mm2 . The minimum principal stress of slab concrete is located at the base of the arch, which is −12.7 N/mm2 , and the maximum principal stress is located at the interface between column 2 and the bottom slab, which is 3.8 N/mm2 . 4) Concrete of web placement stage: the maximum stress of skeleton is located in the steel tube of the lower chord of the second section skeleton and its value is 248.1 N/mm2 . The minimum principal stress of the core concrete in the steel tube is located at the lower chord in the base of the arch, whose value is −37.4 N/ mm2 , and its maximum principal stress is 1.3 N/mm2 . The minimum principal stress of the concrete encasement is located at the slab concrete of the base of the arch with a value of −22.2 N/mm2 , and the maximum principal stress is located at the interface between column 3 and the bottom slab with a value of 3.0 N/ mm2 . 5) Concrete of the top slab placement stage, the maximum stress of the skeleton is located at the lower chord of the second section skeleton, and its value is 269.4 N/ mm2 . The minimum principal stress of the concrete in the steel tube is located at the lower chord at the base of the arch, whose value is −40.4 N/mm2 , and its maximum principal stress is 1.5 N/mm2 . The minimum principal stress of the concrete encasement is located at the bottom slab of the base of the arch with a value of −24.2 N/mm2 . The maximum principal stress is located at the interface between column 3 and the bottom slab with a value of 3.2 N/mm2 . (2) Strain analysis during the construction stage During the entire construction process, the maximum strain of steel tube appears at the steel tube of the 0/14 position (the base of the arch) during the bridge finished stage, and its value is −1405 με, which is not up to the maximum elastic strain of steel (−1631 με) defined in the material constitutive model, indicating that the steel tube is always in the linear elastic stage. The stress of core concrete in steel tube at the base of the arch, the top of arch, and 11 interfaces in the middle of main arch structure during construction is analyzed.

Appendix C: Finite Element Analysis Examples of Concrete-Encased …

(1) Place the core concrete

427

(2) Place the concrete of the bottom slab

(3) Place the concrete of the web (4) Place the concrete of the top plate

(5) Finish

Fig. C.4 Minimum principal stress cloud of concrete in the cross-section arch at the top during the construction and formation stages (kPa)

During the whole construction, the concrete-encased CFST hybrid structure framework is constructed first and then the core concrete in the steel tube is placed. The results show that the strain of core concrete in the steel tube is less than that of the steel tube, its maximum strain appears at the upper chord of the arch at the top during the bridge formation stage, and its value is −1172 με, which is higher than the maximum elastic strain of −1011 με defined in the core concrete constitutive model, indicating that the some areas of the core concrete in steel tube has entered the elasto-plastic stage. The stress of external concrete at base of the arch, arch, and 11 interfaces in the middle of main arch structure during construction is analyzed. During the final construction stage, namely the construction of concrete encasement, the CFST has produced a large deformation, and the strain of concrete encasement is less than the CFST strain. At the same time, the construction is divided into ring placement, placement of the concrete for bottom slab, placement of the concrete in the web and placement of the concrete for top slab. The concrete in bottom slab is the first to participate in the structural loading and the strain is large. The concrete in top slab is the last to participate in the structural loading, the strain is minimum. The maximum strain of the concrete encasement appears at the chord of the base of the arch during the bridge formation stage, and the value is −646 με, which is lower than the maximum elastic strain of −1007 με defined in the material constitutive model, indicating that the concrete encasement is in the linear elastic stage and the material strength satisfies the requirements. (3) Stress analysis during the service stage

428

Appendix C: Finite Element Analysis Examples of Concrete-Encased …

When the main arch structure is subjected to the load during the service stage, the maximum stress of the steel tube of 0/14 span (namely the base of the arch) is 303.9 N/mm2 , indicating that the steel tube can maintain the linear elasticity under the working condition. At the failure stage, the 7/14 span steel tube (namely the top of the arch) has the maximum stress of 420.6 N/mm2 and the steel tube yields. Due to the influence of the construction process, the core concrete in the steel tube has generated construction stress during the construction stage. During the service stage, the principal compressive stress of the core concrete at the base of the arch is 46.3 N/mm2 . The strength class of the core concrete is C80, and the peak stress of the concrete stress–strain model in the finite element is defined as 70.0 N/mm2 , indicating that the stress of the core concrete in the steel tube during the service stage is 66% of the peak stress, and the concrete strength can satisfy the requirements. During the failure stage, the principal compressive stress of the core concrete can reach 77.5 N/ mm2 , which is higher than the peak stress of C80 concrete defined in the material constitutive model (70.0 N/mm2 ), indicating that the strength of the core concrete in the steel tube is improved due to the confinement effect of the steel tube. At the same time, due to the influence of the construction process, the concrete encasement has generated construction stress during the construction stage. During the service stage, the maximum compressive stress of the concrete encasement at the interface 1 is 21.3 N/mm2 . The strength class of the concrete encasement is C60, and the peak stress of its constitutive model is 51.0 N/mm2 , indicating that the stress of the concrete in the steel tube during construction is 42% of its peak stress, and the strength of the concrete can satisfy the requirements. As shown in Appendix Fig. C.5a, the maximum stress of concrete-encased CFST hybrid structure during the bridge formation stage is located at the steel tube of the lower chord in the second section skeleton, with a value of 308.3 N/mm2 . The minimum principal stress of the core concrete is located at the lower chord in the base of the arch, and its value is −47.6 N/mm2 , and its maximum principal stress is 1.0 N/mm2 . The minimum principal stress of concrete encasement is located at the base of the arch, with a value of −24.1 N/mm2 , and its maximum principal stress is located at the interface between column 1 and bottom slab, with a value of 3.0 N/mm2 . As shown in Appendix Fig. C.5b, during the stage of application of vehicle load, the maximum stress of the skeleton is located at the steel tube of the lower chord in the base of the arch, with a value of 312.2 N/mm2 . The minimum principal stress of core concrete is located at the lower chord in the base of the arch chord, which is −47.6 N/mm2 , and its maximum principal stress is 0.9 N/mm2 . The minimum principal stress of concrete encasement is located at the base of the arch, with a value of −24.7 N/ mm2 , and its maximum principal stress is located at the interface between column 6 and bottom slab, with a value of 3.1 N/mm2 . (4) Strain analysis during the service stage During the bridge formation stage, the maximum strain of the steel tube is located at the position of the steel tube of the lower chord in the base of the arch, and its value is −1405 με. This strain has not reached the maximum elastic strain defined in the

Appendix C: Finite Element Analysis Examples of Concrete-Encased …

Base of the arch

1/4 span of the arch

429

Top of the arch

(a) Stress distribution at the bridge formation stage

(b) Stress distribution during the application of vehicle load stage

Fig. C.5 Minimum principal stress cloud during the service stage (kPa)

material constitutive model (−1631 με), indicating that the material is in the linear elastic stage. During the ultimate failure state, the maximum strain of the steel tube is located at the upper chord of the arch, and the value is −3676 με, indicating that the steel tube at this position has yielded. During the bridge formation stage, the maximum strain of concrete in steel tube appears at the lower chord in the base of the arch and its value is −1172 με. During the ultimate failure state, the concrete strain at the upper chord in the top of the arch is the largest, which is −3009 με, indicating that it is crushed. When the structure is in the ultimate failure state, the maximum strain of the concrete encasement appears at the top slab in the top of the arch, and its value is −3792 με, which exceeds the ultimate compressive strain of the concrete, so it is crushed. (5) Displacement analysis during the service stage Calculation results of displacement during the each stage are given in Appendix Table C.4. It can be seen that within the span of the main arch structure, the vertical deformation of the arch is the largest. After the load applied on the main arch structure reaches the construction load, the vertical displacement of the arch reaches 882.7 mm. Stress concentration usually occurs where the structure geometry changes dramatically, such as gaps, holes, grooves, and rigid constraints. The stress concentration phenomenon of arch rib model mainly occurs at the joint of column and arch rib, the joint of diaphragm and cross, and the joint of steel tube and chord. The stress

430

Appendix C: Finite Element Analysis Examples of Concrete-Encased …

Table C.4 Displacement of the top of arch during each stage Load condition

Additional deflection (mm)

Cumulative deflection (mm)

Formed bridge load

104.8

861.2

21.5

882.7

Vehicle load

(a) With long-term load

(b) Without long-term load

Fig. C.6 Influence of long-term load on vertical displacement of main arch structure (m)

concentration phenomenon at these locations may the local stress of the structure to be too large and yield, which affects the safety of the structure. (6) Analysis of the effect of long-term load During the service of the main arch structure, both the core concrete and concrete encasement will shrink and creep, which may affect its mechanical performance under long-term load. Due to the closed environment of the steel tube, the shrinkage and creep of the core concrete are small, while the shrinkage and creep values of the concrete encasement are relatively large because it is directly exposed to the external environment and has no confinement effect of the steel tube. In accordance with the construction process of the bridge, environmental conditions and engineering design basis, considering that the relative humidity of the local environment is 80%, the relative humidity of the concrete encasement during the long-term loading process is 80%, and the relative humidity of the core concrete is 90%. The methods for determining concrete shrinkage and creep are described in Sect. 3.4 of this book. During the long-term loading stage, the structure continually deforms. Taking the displacement of the top of the arch as an example, the deformation of the main arch structure during the 100-year service period is calculated considering the long-term load of the main arch structure from the construction stage, and is compared with the deformation of the structure without long-term load, as shown in Appendix Fig. C.6. The vertical deformation increases gradually from the base of the arch to the top of the arch, and the vertical deformation at the top of the arch is the largest. Appendix Fig. C.7 shows the variation rule of the displacement for the top of the arch over time. The deformation of the main arch structure increases slowly during the service stage, and with the increase of load holding time, the deformation growth rate slows down gradually. After the completion of the construction stage, the displacement for the top of the arch is 1.308 m. The vertical displacement for

Appendix C: Finite Element Analysis Examples of Concrete-Encased …

431

Δ (m) 2.0

Increment of deformation is 0.042 m

1.5

Initial vertical displacement is 1.308 m

Increment of deformation is 0.079 m

1.0

0.5 0

20

40

60

80

100

t (year)

Fig. C.7 Displacement of the top of the arch (Δ)-load holding time (t) relationship

the top of the arch increases by 0.042 m after 3 years load holding. After the end of long-term load (service 100 years), the vertical displacement for the top of the arch of the structure increases by 0.079 m.

C.4 Calculation and Analysis of Resistance Through finite element analysis, whether there is a long-term load has an impact on load (F)-displacement of the top of the arch (Δ) relationship, as shown in Appendix Fig. C.8, both of which take into account the influence of construction stage. (1) Resistance under monotonic short-term loading Load–displacement of the top of the arch relationship considering the influence of the construction stage is given in Appendix Fig. C.8. In the figure, the vertical coordinate is the load applied within the half-span range, and the horizontal coordinate is the displacement of the top of the arch. The total of constant load and live load during the service stage is 313,753 kN. After entering the failure stage, when the load reaches 2.10 times of the load in the service stage, the stiffness of the curve decreases obviously, and the load–displacement curve enters the elasto-plastic stage. When loaded to point B' in this figure, the load is 824,897 kN, which is 2.63 times the load during the service stage. (2) Resistance under long-term loading

432

Appendix C: Finite Element Analysis Examples of Concrete-Encased …

F (×105kN)

With long-term load Without long-term load

Δ (m) Fig. C.8 Influence of long-term loading on load (F)-displacement of the top of the arch (Δ) relationship

Under long-term loading, when the structure deforms, the internal force redistribution may occur. The influence of long-term loading on load–displacement of the top of the arch relationship is shown in Appendix Fig. C.8. Both curves take the influence of construction process into consideration. When the load during normal service stage is applied to point A and point A' , the displacements of the top of the arch of point A and point A' are 0.826 m and 1.308 m, respectively. During the loading process from point A' to point A'' , that is, under the action of long-term load (the value of long-term load remains constant and the load is held for 100 years), the concrete is continually deformed, the displacement of the top of the arch relationship increases from 1.308 to 1.387 m, and the top of the arch drops 0.079 m. After that, all the loads on the main arch structure continue to increase until the structure lost its bearing capacity and is not suitable for further loading. Due to the continuous large deformation of the structure during the failure stage, the load borne by the structure when the tangent stiffness of the structure is reduced to 5% of the initial stiffness during the failure stage is taken as the resistance. B and B' in Appendix Fig. C.8 are respectively the limit points of load–displacement of the top of the arch relationship without long-term load and with long-term load. The ultimate load without long-term load is 824,897 kN, which is 2.63 times of the load during the service stage, and the ultimate load with long-term load is 840,373 kN, which is 2.70 times of the load during the service stage. It can be seen that the long-term load has little influence on the resistance of the main arch structure. When the resistance at point B'' is reached, the failure mode, strain and stress distribution of the main arch structure are shown in Appendix Fig. C.9.

Appendix C: Finite Element Analysis Examples of Concrete-Encased …

433

Plastic strain concentration

Plastic strain concentration

(a) Plastic strain distribution of concrete encasement Plastic strain concentration

Plastic strain concentration

(b) Mises stress distribution of the steel tubes (kPa) Plastic strain concentration

Equivalent plastic strain cloud of the base of arch

Equivalent plastic strain cloud at Equivalent plastic strain cloud of the 1/4 span of arch the top of arch

(c) Plastic strain of the cross-section

Fig. C.9 Strain and stress distribution of main arch structure

434

Appendix C: Finite Element Analysis Examples of Concrete-Encased …

It can be seen from the failure modes of steel tube and concrete encasement that the equivalent plastic strain of concrete encasement is mainly concentrated in the top slab zone of the arch at the top and the bottom slab zone of 1/4 span and extends outward for a certain distance. The maximum stress of the steel tube is located in the upper chord zone of the arch at the top, where buckling occurs, and the value of stress is 421.7 N/mm2 .

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