Concrete-Filled Double-Skin Steel Tubular Columns: Behavior and Design 0443152284, 9780443152283

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Concrete-Filled Double-Skin Steel Tubular Columns

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Woodhead Publishing Series in Civil and Structural Engineering

Concrete-Filled Double-Skin Steel Tubular Columns Behavior and Design Mostafa Fahmi Hassanein Professor of Steel Structures, Department of Structural Engineering, Tanta University, Tanta, Gharbia, Egypt

Mohamed Elchalakani Department of Civil Engineering, Faculty of Engineering and Mathematical Sciences, University of Western Australia, Perth, Australia

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States Copyright © 2023 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. ISBN: 978-0-443-15228-3 For information on all Elsevier publications visit our website at https://www.elsevier.com/books-and-journals

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Contents

About the authors Acknowledgments

vii ix

1

Introduction 1.1 General 1.2 Objectives 1.3 Book organization

1 1 1 2

2

Development of CFDST columns 2.1 Introduction 2.2 Advantages of CFDST columns 2.3 Erection of CFDST columns 2.4 Types of CFDST columns 2.5 Experimental studies 2.6 Finite element studies 2.7 Structural behavior 2.8 Failure modes of CFDST columns 2.9 The mechanism of the inner tube of CFDST columns 2.10 Formulas for compressive strength 2.11 Conclusions References

3 5 5 7 8 9 11 11 24 26 26 40 42

3

CFDST short columns formed from carbon steels 3.1 Introduction 3.2 Circular-circular CFDST columns 3.3 Circular-square CFDST columns 3.4 Square-square CFDST columns 3.5 Square-circular CFDST columns 3.6 New confining stress-based design for circular-circular CFDST columns 3.7 Conclusions Appendix References Further reading

45 47 48 64 77 96 109 130 132 133 138

vi

Contents

4

CFDST short columns formed from stainless steel outer tubes 4.1 Introduction 4.2 Finite element models 4.3 Comparisons with the experimental results 4.4 CFSST columns 4.5 CFDST columns 4.6 CFDT columns 4.7 Summary and conclusions References

139 139 142 150 159 167 186 198 200

5

CFDST slender columns formed from stainless steel outer tubes 5.1 Introduction 5.2 Nonlinear finite element analysis 5.3 Validation of the FE model 5.4 CFSST columns 5.5 CFDST columns 5.6 CFDT columns 5.7 Conclusions References

203 203 207 213 218 230 249 265 266

6

Rubberized CFDST short columns 6.1 Introduction 6.2 Square RuCFDST short columns 6.3 Circular RuCFDST short columns 6.4 New confining stress-based design 6.5 Conclusions Appendix I: Progressive axial loading of specimen SHS-O2I2-30 References

271 273 275 296 312 332 333 336

7

Future research 7.1 Recommendations 7.2 Trends for future relevant works

341 341 341

Index

343

About the authors

Mostafa Fahmi Hassanein, Professor of Steel Structures, Department of Structural Engineering, Tanta University, Tanta, Gharbia, Egypt Dr. Mostafa Fahmi Hassanein completed his PhD at Tanta University, Egypt. During his study for this, he participated in a doctoral steel course at Lulea University of Technology, Sweden. He is currently Professor of Steel Structures at the Department of Structural Engineering at Tanta University. His research focuses on the analysis and design of steel and composite structures, with the aim of improving the design codes and standards that are currently used worldwide (e.g., EC3, EC4, AISC, and AS 4100), to design more effective structures with minimized initial material costs and life-cycle costs. He has published more than 95 papers in international journals. His research works show his ability to collaborate with researchers from different disciplines and countries. He has served as a reviewer for various highly regarded international journals and conferences. In 2012 he attended the 8th European Solid Mechanics Conference (ESMC) in Graz, Austria as an Invited Speaker. In 2015, the Academy of Scientific Research and Technology in Egypt awarded him the State’s Incentive Award in the Engineering Sciences, and in 2017, he received the First Class Excellence Medal from the Egyptian President. Dr. Hassanein is also a Consultant Engineer in the field of design of steel structures in Egypt. He serves as an editorial board member for Thin-Walled Structures (ISSN No. 0263-8231, Elsevier). Based on his achievements, his biography has been accepted into Who’s Who in the World, which is comprised of the top 3% of the professionals in Egypt. He also worked as a Professor at Southwest Petroleum University in Chengdu, China between July 2019 and June 2020. More recently, he was named in Stanford University’s list of the world’s top 2% of scientists, in 2020, 2021, and 2022. Mohamed Elchalakani, Department of Civil Engineering, Faculty of Engineering and Mathematical Sciences, University of Western Australia, Perth, Australia Dr. Mohamed Elchalakani is an Associate Professor and the Director of the Structural Laboratory at the University of Western Australia. He is the author of two important books Single Skin and Double Skin Concrete Filled Tubular Structures—Analysis and Design and Geopolymer Concrete Structures with Steel and FRP Reinforcements— Analysis and Design, both published by Elsevier. He is a committee member of Australian Standard BD-023: Structural Steel. He is included in Stanford University’s current list of the top 2% of scientists in the world, where he is ranked in the top 0.7% among academics in civil engineering worldwide. His ResearchGate score is

viii

About the authors

40.1, which is in the top 97.5% of its users worldwide. He holds a few patents on building integrated energy storing systems. He serves on the editorial board of the Journal of Structural Engineering, published by the American Society of Civil Engineers, Scientific Reports, published by Nature, the Australian Journal of Civil Engineering, and Structures, a journal published by Elsevier. Dr. Elchalakani’s current Google Scholar citations are in excess of 5000 with an h-index of 40 where he authored or coauthored more than 250 technical papers. He is a Chartered Professional Engineer in Australia (CPEng) and a Registered Building Practitioner (RBP), and is also registered as a National Professional Engineer (NPE) in Australia, Asia, and Egypt. Dr. Elchalakani has received several awards, including the Holman Medal for the most outstanding PhD thesis and the Hunt Award for Excellence in Research in Engineering. He also received the prestigious Japanese Society for Promotion of Science Fellowship. His total research funds today are in excess of $1.5 million from competitive grants, consulting, and industry-funded projects.

Acknowledgments

The authors are grateful to Amany Refat Elsisy, Heba and Abdelrahman M.F. Hassanein, who helped to prepare and review the manuscript for this book. They would also like to thank Laila, Aya, Yaseen, and Farouk Elchalakani for reviewing all of the chapters. The authors are grateful for the advice on composite structures received from eminent researchers in civil engineering from different parts of the world including the following: Prof. Nuno Silvestre from Universidade de Lisboa, Portugal; Prof. Leroy Gardner from Imperial College London, UK; Prof. Omnia Kharoob from Tanta University, Egypt; Associate Prof. Qing Liang of Victoria University, Australia; Dr. Vipulkumar Patel of La Trope University, Australia; Prof. Sherif El-Tawil from Michigan University, USA; Prof. Alaa Morsy from Arab Academy for Science, Technology, & Maritime Transport, Egypt; Prof. Metwali Abu Hamad from Cairo University, Egypt; Prof. Sherif Safar and Prof. Ezz-Eldin Sayed Ahmed from the American University in Cairo, Egypt; Prof. Xiao-Ling Zhao from the University of New South Wales (UNSW)/Monash University, Australia; Prof. Gangadhara Prusty and Prof. Serkan Saydam from UNSW, Australia; Prof. Nie Shidong, Dr. Shagea Alqawzai, Prof. Kang Chen, Prof. Le Shen, and Dr. Miao Ding from Chongqing University, China; Associate Prof. Nor Hafizah Ramli Sulong and Dr. Sabrina Fawzia from Queensland University of Technology (QUT), Australia; Associate Prof. Zainah Binti Ibrahim from the University of Malaya, Malaysia; Prof. Allan Manalo from the University of Southern Queensland (USQ), Australia; Prof. Hua Yang, Prof. Lanhui Guo, and Prof. Wei Zhou from the Harbin Institute of Technology, China; Associate Prof. Muhamad Hadi from Wollongong University, Australia; Dr. Mohamed Ali from the University of Adelaide, Australia; Prof. Emad Gad, Prof. Riadh Al-Mahaidi, and Prof. Jay Sanjayan from Swinburne University of Technology, Australia; Prof. YongBo Shao from Southwest Petroleum University, Sichuan, China; Prof. Dilum Fernando and Dr. Chris Becket from the University of Edinburgh, UK; Prof. Hong Hao, Dr. Thong Pham, and Dr. Wensu Chen from Curtin University, Australia; Prof. Jingsi Hu from Hunan University, China; Prof. Brian Uy and Dr. Michael Bambach from the University of Sydney, Australia; Dr. Afaq Ahmed from the University of Engineering and Technology, Taxila, Pakistan; Prof. Sherif Yehia from the American University in Sharjah, United Arab Emirates; and finally Prof. Ali Karrech and Dr. Minhao Dong from the University of Western Australia, Australia, and Prof. Tianyu Xie from the South China University of Technology, China. Finally, we wish to thank our families for their support and understanding during the many years that we have been undertaking research on composite structures at Tanta University and the University of Western Australia during the preparation of this book.

x

Acknowledgments

In the name of Allah, the Entirely Merciful, the Especially Merciful. [All] praise is [due] to Allah, Lord of the Worlds—the Entirely Merciful, the Especially Merciful, Sovereign of the Day of Recompense. It is You we worship and You we ask for help. Guide us to the straight path—the path of those upon whom You have bestowed favor, not of those who have evoked [Your] anger or of those who are astray. The Holy Quran, Surat Al-Fatihah

Introduction 1.1

1

General

Concrete-filled double skin tubular (CFDST) columns have the advantage of being able to resist forces compared to conventional concrete-filled steel tubular (CFST) columns. Other important advantages of CFDST columns include their high strength and bending stiffness, higher fire resistance, and favorable construction ability. A CFDST column consists of two concentric steel tubes with concrete sandwiched between them. Unfortunately, there are no significant applications of this new structural column worldwide, partly due to the lack of design provisions in different design manuals and international standards. Accordingly, this book focuses on the compressive strength of CFDST columns and is based on published studies of the last two decades. CFDST columns are the currently recommended structural members for modern buildings. However, a review of the research carried out on CFDST columns under axial compression is still needed with emphasis on experimental and finite element (FE) studies. Experimental and FE data have been collected and compiled in a comprehensive table using different parameters found in the literature. The review also highlights, based on up-to-date results, the effects of confinement of concrete, initial imperfection and residual stresses, concrete compaction, hollow ratio, thickness ratio, long-term sustained loading, axial partial compressive loading, preloading on steel tubes, steel fiber-reinforced concrete, and external confinement on the behavior of CFDST columns. Specific emphasis is placed on various design methods of CFDST columns with different cross sections. Generally, it has been recognized that intensive research is still needed for the development of CFDST columns with different cross sections under different parameters. Based on the earlier introduction, it seems that research on CFDST columns with different configurations and materials has been expanded to include many variables. Indeed, the authors have contributed to the development of such elements, as will be seen in this book, which emphasizes on providing designers and researchers with the recent developments in CFDST columns.

1.2

Objectives

The aim of this book is to deepen the understanding of the behavior of CFDST columns. Thus, the main objective is to develop different design procedures for CFDST columns with different lengths (i.e., short, intermediate-length, and long) and materials used in construction. Furthermore, the goals are extended to study the effect of concrete confinement on different configurations. Moreover, the effect of using rubberized concrete on the behavior of CFDST short columns is considered. Concrete-Filled Double-Skin Steel Tubular Columns. https://doi.org/10.1016/B978-0-443-15228-3.00003-4 Copyright © 2023 Elsevier Inc. All rights reserved.

2

1.3

Concrete-Filled Double-Skin Steel Tubular Columns

Book organization

This book contains an introduction besides six chapters. Chapter one is concerned with the introduction of this book. Chapter two describes the development of CFDST columns. Chapter three focuses on the compressive strength and behavior of CFDST short columns formed from carbon steels. Chapter four discusses the behavior and strength of CFDST columns formed from stainless steel outer tubes by considering the results provided by the authors. Chapter five describes the overall buckling behavior and strength of CFDST slender columns formed from stainless steel outer tubes. In chapter six, the effect of using rubberized concrete in forming CFDST short columns is thoroughly described. Finally, chapter seven concludes this book by providing conclusions, recommendations, and further topics to be investigated.

Development of CFDST columns Notations

2

Roman letters ADS Asi Aso,As Asc Ac,

cross-sectional area of a CFDST column cross-sectional area of the inner steel tubes of a CFDST column cross-sectional area of the outer steel tubes of a CFDST column cross-sectional area of the sandwiched concrete nominal cross-sectional area of concrete, given by π(D
2te)2/4

nominal

Ak Ap B b D d e/r (EI)e fy fsyi fsyo fc0 fck fcu 0 fcc f0rp,se fyi,corner fyi,flat fyo,corner fyo,flat IDS KL,Le kp kbc Nosc,u Ni,u Np Nus Ppl,Rd Pcr, Pe PAISC

area of the hollow part partial bearing area of the compressive load depth of the outer tube of a rectangular CFDST column, outer minor axis width of an outer round-end rectangular or elliptical outer tube of a CFDST column depth of the inner tube of a rectangular CFDST column, outer minor axis width of an inner round-end rectangular or elliptical inner tube of a CFDST column diameter of the outer tube of a circular CFDST column diameter of the inner steel tube of a circular CFDST column load eccentricity ratio effective elastic flexural stiffness of a CFDST column yield strength yield strength of the inner tube yield strength of the outer tube compressive strength of the concrete cylinder (unconfined concrete strength) characteristic concrete strength (0.67fcu) characteristic cube strength of concrete compressive strength of confined concrete lateral confining pressure on the sandwiched concrete provided by the outer tube yield strength of the corners of the inner tubes yield strength of the flat portions of the inner tubes yield strength of the corners of the outer tubes yield strength of the flat portions of the outer tubes moment of inertia of the CFDST section effective buckling length strength index that provides the influence of the preload on the column strength bearing capacity factor of a partially loaded CFDST column compressive capacity of the outer tube with the sandwiched concrete compressive capacity of the inner tube computed as (Asifsyi) preload applied on the outer steel hollow section ultimate strength of the outer steel tubular column plastic resistance to axial compression taking into account the concrete confinement elastic critical buckling load ultimate axial capacity of a CFST column according to the AISC [1]

Concrete-Filled Double-Skin Steel Tubular Columns. https://doi.org/10.1016/B978-0-443-15228-3.00009-5 Copyright © 2023 Elsevier Inc. All rights reserved.

4

Concrete-Filled Double-Skin Steel Tubular Columns

Pul Puo Pu,Tao Pu,Has1 Pu,Has2 Pso Pc Psi Pu,Zha Pcorner Pflat Pu,Li Pu,Yang t, to ti to ta rexti rexto rinti rinto

axial compressive strength of a CFDST column axial compressive strength of a CFDST short column design strength as proposed by Tao et al. [2] design strength as proposed by Hassanein et al. [3] design strength as proposed by Hassanein et al. [4]. section capacities of the outer steel tube section capacities of the concrete section capacities of the inner steel tube ultimate load for the CFDST columns (SHS inner and CHS outer) proposed by Elchalakani et al. [5] corner capacities of steel tubes flat portion capacities of steel tubes bearing capacity of CFDST sections with preload on the outer steel tube suggested by Li et al. [6] bearing capacity of partially loaded CFDST sections (see Fig. 2.7) with preload on the outer steel tube, as expressed Yang by et al. [7] thickness of the outer steel tubes of a CFDST column thickness of the inner steel tubes of a CFDST column thickness of the steel tube top endplate thickness (not the ring-bearing plate) external radius of the inner steel tube of a CFDST column external radius of the outer steel tube of a CFDST column internal radius of the inner steel tube of a CFDST column internal radius of the outer steel tube of a CFDST column

Greek letters α αn β ζ φo Ω γc γ se γ si γ ss λ λp λr λ σ 0.2 σ 3i σ 3o χ

steel ratio calculated as α ¼ Aso/Asc nominal steel ratio calculated as αn ¼ Ase/Ac, nominal partial compression area ratio, which is greater than unity confinement factor calculated as ((Asofsyo)/(Ac, nominal fck)) stability ratio according to GBJ17-88 [8] solid ratio, Asc/(Asc + Ak) strength reduction factor factor used to account for the effect of strain hardening on the strength of outer steel factor used to account for the effect of strain hardening on the strength of inner steel factor used to account for the effect of strain hardening on the strength of stainless steel column slenderness ratio limiting slenderness ratio of a short column limiting slenderness ratio of an intermediate-length column column slenderness parameter (relative slenderness) 0.2% proof stress of stainless steel material lateral passive pressure provided by the inner tube of a CFDST column to the sandwiched concrete in the radial direction lateral passive pressure provided by the outer tube of a CFDST column to the sandwiched concrete in the radial direction hollow section ratio, given by d/(D
2te), or reduction factor for relative buckling mode in terms of the relevant relative slenderness calculated using European strut curves

Development of CFDST columns

νe νs ηp

5

Poisson’s ratios of a steel tube with concrete infill Poisson’s ratios of a steel tube without concrete infill preload ratio

Abbreviations CFDST CFST CHS FE NA RHS SHS

2.1.

concrete-filled double skin tubular concrete-filled steel tubular circular hollow section finite element not available rectangular hollow section square hollow section

Introduction

Historically, the concept of “double skin” composite construction was devised for use in submerged tube tunnels [9]. A graph presenting a cross section of double skin composite construction is shown in Fig. 2.1 [10]. This cross section was used for the first time in the Kobe Minatojima Submerged Tunnel in Japan [11]. Recently, concretefilled double skin tubular (CFDST) columns have been under consideration as load-bearing elements in construction projects. A CFDST column consists of two concentric steel cylinders with concrete filled between them. Currently, CFDST columns are recommended structural members because they have several advantages over conventional concrete-filled steel tubular (CFST) columns or reinforced concrete or structural steel columns [12]. This chapter presents the state-of-the-art knowledge on CFDST columns, including experimental and finite element (FE) studies. A summary of the real or virtual (FE) experiments reported in the literature is presented in a tabular form. The report includes the behavior of short and slender CFDST columns. A detailed discussion on the effects of concrete confinement, initial imperfection and residual stresses, concrete compaction, hollow ratio, thickness ratio, long-term sustained loading, axial partial compressive loading, preloading on steel tubes, steel fiber-reinforced concrete, and external confinement on the behavior of CFDST columns is presented. The failure modes of CFDST columns are briefly outlined, followed by the design methods.

2.2.

Advantages of CFDST columns

Steel-concrete composite columns have widespread usage as load-bearing constituents in construction. Therefore, considerable research efforts have been devoted to investigate CFST columns (see Fig. 2.2). Using different rigorous analysis methods (see, for example, Johansson [13] and Chitawadagi et al. [14]), simplified design approaches for CFST columns have been developed. These design approaches have been included in modern codes such as the EC4 [15] and the AISC [1]. Nevertheless, CFST columns have some disadvantages [12], namely, (1) the outer steel bears the largest part of the external

6

Concrete-Filled Double-Skin Steel Tubular Columns

Water level Steel plates

Concrete

Fig. 2.1 An example of a submerged tube tunnel cross section [10]. t

Concrete core

D

Fig. 2.2 A typical concrete-filled steel tubular (CFST) column.

load than does the concrete core under axial compression per the same cross-sectional area because of its higher stiffness under composite action; (2) the neutral axis at the central concrete makes an insignificant contribution to flexural strength; (3) the central concrete makes an insignificant contribution to torsional strength; (4) the initial elastic dilation of the concrete under compression is small, and, thus, the confining pressure provided by the steel tube to the concrete is relatively low during the elastic stage [16,17]; and (5) due to the heavy self-weight of the concrete, any improvement in the strength-to-weight ratio of CFST columns is limited. From the earlier paragraph, it is clear that the central part of the concrete core of a CFST column can be effectively replaced by another smaller, hollow steel tube with similar axial, flexural, and torsional strengths maintained. This form of column construction is known as a CFDST column. Fig. 2.3 displays the basic forms of the crosssectional representatives of CFDST columns, where CHS, SHS, and RHS stand for circular, square, and rectangular hollow sections, respectively. However, a CFDST column has several advantages over a CFST column, which could be summarized as: l

l

It has higher axial, flexural, and torsional strengths [12,16–18] compared to those of a CFST column. Additionally, its strength-to-weight ratio is significantly improved by replacing the central concrete with a steel tube of a much smaller cross-sectional area. Moreover, the inner tube expands laterally under compression loading, and, hence, the confining pressure provided to the concrete increases [19]. Consequently, in a CFDST column, the initial confining pressure builds up more rapidly than it does in a CFST column so that both elastic strength and stiffness are enhanced. A CFDST column contains less concrete, which creates a more sustainable environment by reducing the embodied energy levels of the column.

Development of CFDST columns

7

Sandwiched concrete

to ti

to

to ti

d

d

ti

d D

D

D

(b)

(a)

(c)

Sandwiched concrete to

to

ti

B

b

ti

d

d

D

D

(d)

(e)

to ti

to

b

B

B

b

ti

d

d

D

D

(f)

(g)

Fig. 2.3 Cross-sectional types of CFDST columns. (A) Circular CFDST: CHS inner and CHS outer. (B) Circular CFDST: SHS inner and CHS outer. (C) Square CFDST: CHS inner and SHS outer. (D) Square CFDST: SHS inner and SHS outer. (E) Rectangular CFDST: RHS inner and RHS outer. (F) Rounded-end rectangular CFDST. (G) Elliptical CFDST. l

The cavity inside the inner tube provides a dry atmosphere for possible catering of facilities or utilities such as power cables, telecommunication lines, and drainage pipes. Therefore, CFDST columns are chiefly used in maritime structures.

2.3.

Erection of CFDST columns

During construction, the inner tube of a CFDST column is first erected. This is then followed by the erection of the outer tube. After the erection of both tubes, concrete is

8

Concrete-Filled Double-Skin Steel Tubular Columns

(A)

Tapered outer tube

(B)

Outer tube Concrete Tapered inner tube Inner tube

Fig. 2.4 Erection of CFDST columns (A) during construction and (B) concrete placement.

poured in between them. Fig. 2.4 shows the erection process of CFDST columns used in transmission towers [20]. Plates and bolts are used to fix the position of the tubes while the flanges on both ends of each tube are used to connect it with its extension.

2.4.

Types of CFDST columns

2.4.1 According to length The relationship between typical strength (Pul) and the slenderness ratio (λ) for columns under axial compression is presented in Fig. 2.5. For a CFDST column, λ is defined as: Le λ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi IDS =ADS

(2.1)

where Le, IDS, and ADS are the effective buckling length, the sectional moment of inertia, and the cross-sectional area of the CFDST column, respectively. As can be seen, the curve is divided into three failure stages: plastic, elastic-plastic, and elastic instability. Accordingly, slender columns may be grouped into intermediate-length columns, which fail by elastic-plastic buckling, and long columns, which fail by Plastic stage

Puo

Pul

Elastic-plastic stage

λp

Elastic stage

λr

Fig. 2.5 Column strength-slenderness ratio relationship.

λ

Development of CFDST columns

9

elastic buckling (see Fig. 2.5). A review of the available literature shows that there are no existing values for λp and λr for CFDST columns with both carbon steel jackets, as shown in Fig. 2.3. However, in their research, Hassanein and Kharoob [19] provided values for λp and λr for circular CFDST columns with stainless steel jackets. Based on their study [19], circular CFDST columns with stainless steel jackets with slenderness pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ratios λ greater than λp ¼ 33= σ 0:2 =235 are considered slender. On the other hand, the slenderness limit delineating between intermediate-length and long columns (λr) pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi for circular CFDST columns is 75= σ 0:2 =235 [19], where σ 0.2 is the proof stress of the outer stainless steel tube. Hence, it can be concluded that intensive research is required to find the proper values of λp and λr for CFDST columns with different cross sections (Fig. 2.3), with both carbon and stainless steel jackets.

2.4.2 According to straightness Studies on CFDST columns involve investigations of straight, inclined, and tapered columns, as can be seen in Fig. 2.6. Nowadays, inclined and tapered columns are used as load transfer members in some particular structures [21]. The cross-sectional areas of straight columns are equal along their column length, and they are also equal from the bottom to the top for inclined columns but with a certain inclination angle. On the other hand, tapered columns are characterized by a gradual reduction in their crosssectional area from the bottom to the top due to the tapered angle.

2.5.

Experimental studies

In the last two decades, several experimental (Exp) tests have been performed on CFDST columns with carbon steel tubes, loaded on the entire section, as summarized earlier by Han et al. [22] in 2004 and by Zhao and Han [23] in 2006. In recent years (i.e., after 2006), several tests have been conducted, but they have not yet included in

(a)

(b)

(c)

Fig. 2.6 Typologies of CFDST columns. (A) Straight column. (B) Inclined column. (C) Tapered column.

10

Concrete-Filled Double-Skin Steel Tubular Columns

one publication providing the added information and the required areas to be investigated. Accordingly, this section provides information about the experimental tests conducted on CFDST columns. Tests on CFDST short columns with outer and inner CHSs were carried out by Wei et al. [16], Tao et al. [2], and Uenaka et al. [24]. Consequently, simplified formulas for the strengths of short columns were suggested [2,24]. Circular CFDST columns with inner SHS and outer CHS tubes were investigated by Elchalakani et al. [5], and they proposed a strength predictor for these columns. Han et al. [22] explored CFDST columns with inner CHS and outer SHS tubes. They also proposed equations [22]. In addition, tests on CFDST short columns with outer and inner RHS tubes were carried out by Tao and Han [25], and, based on the test results, a simplified formula for the strength of short columns was suggested. Additionally, a simplified formula for the strength of square CFDST short columns (with square inner tubes) was proposed based on the tests conducted by Zhao and Grzebieta [18]. The studies also extended to the fire performance of CFDST columns exposed to standard fire, as reported by Lu et al. [26]. Long-term loading was well-investigated by Han et al. [27]. The research conducted by Han et al. [21] on CFDST columns included two columns with stainless steel jackets on different cross-sectional types (cross sections shown in Fig. 2.3A, C, F, and G) and column typologies (straight, inclined, and tapered). More recently, experiments on tapered CFDST columns have been conducted by Li et al. [20], whereas partially loaded columns (Fig. 2.7) have been considered by Yang et al. [7]. Finally, Ho and Dong [12,28] used external steel rings to improve the strength, stiffness, and ductility of CFDST short columns. Experimental and FE data (from the available database of the author) have been collected and compiled in Table 2.1. This table provides the author names, reference number, publication year, sectional shape, type of outer tube (i.e., carbon or stainless steel), column type (i.e., straight, inclined, or tapered), type of test (i.e., Exp or FE), type of column with regard to its length (i.e., short or long), number of tests conducted, and studied variables. It is a familiar fact that CHSs are less susceptible to local buckling than are square hollow sections. So, it is good to use CHSs as both the outer and inner tubes. Conversely, beam-to-column joints for square columns are easier to fabricate and install compared with those for circular columns. Therefore, it can be distinctly observed from Table 2.1 that circular (Fig. 2.3A) and square (Fig. 2.3C) CFDST columns with inner circular

Ring bearing plate Sandwiched concrete (a)

Ring bearing plate

Sandwiched concrete (b)

Fig. 2.7 Axial partial loading over ring-bearing plates. (A) Circular CFDST: CHS inner and CHS outer. (B) Square CFDST: SHS inner and SHS outer.

Development of CFDST columns

11

tubes were the most investigated. However, by limiting most of the investigations of the two aforementioned cross sections (i.e., circular and square CFDST columns with inner circular tubes), many other factors that affect the choice of column, such as the aesthetic appearance of the column or the type of inside cavity required in maritime structures, are ignored. Thus, columns with round-end rectangular (Fig. 2.3F) and elliptical sections (Fig. 2.3G), characterized by their aesthetic appearance, should attract additional investigations. Moreover, more investigations of columns with inner SHSs or RHSs with connection to the inner tubes should be conducted.

2.6.

Finite element studies

Recent developments in computational features and software have brought the FE method within the reach of both academic researchers and engineers in practice by means of reliable codes, with the ABAQUS code being one of the most used nowadays [31]. More and more researchers are realizing the importance of numerical studies in exploring the behavior of CFDST columns [3,4,6,19,20,27,29,30] (see Table 2.1). FE modeling produces many results that are difficult or even impossible to obtain from experimental tests, especially those related to the stress and strain of different crosssectional components. One such example is the location of the maximum stress of the sandwiched concrete with different hollow ratios, which could be easily obtained by FE modeling rather than experimentally. Hence, using FE modeling is essential to the better understanding of the behavior of CFDST columns. As can be found in the literature, FE analysis is utilized to investigate the important parameters that determine the sectional capacities of CFDST columns [29], columns subjected to long-term loading [27], fire resistance of CFDST columns [30], behavior of tapered CFDST columns [20], effect of preload on steel tubes on the behavior of CFDST columns [6], CFDST short columns with outer stainless steel tubes [3], effect of the diameter-to-thickness ratio (D/te) on the capacity of CFDST columns [4], and CFDST slender columns with outer stainless steel tubes [19]. As can be observed, FE modeling is concentrated in limited cross-sectional types (Fig. 2.3A and C) and column typologies (Fig. 2.6A and C). From the table, it can be observed that, to date, some cross sections (i.e., round-end rectangular and elliptical sections) have not been simulated at all by FE. Therefore, additional FE investigations are also required.

2.7.

Structural behavior

Based on the earlier review of the experimental and FE studies, the fundamental behavior of CFDST columns is discussed herein with respect to the effects of concrete confinement, initial imperfection and residual stresses, concrete compaction, hollow ratio, thickness ratio, long-term sustained loading, axial partial compressive loading, and preloading on steel tubes. Additionally, the effect of steel fiber-reinforced concrete and external confinement is outlined.

12

Concrete-Filled Double-Skin Steel Tubular Columns

Table 2.1 Experimental and FE tests on CFDST columns under axial compression in the literature. Type of outer tube

No.

Authors

Country

References

Year

Sectional shape (Fig. 2.3)

1

Wei, S., Mau, ST., Vipulanandan, C., Mantrala, SK., Zhao, X-L, Grzebieta, R. Elchalakani, M., Zhao, X-L., Grzebieta, R.

USA

[16]

1995

a

l

Australia

[18]

2002

d

l

Australia

[5]

2002

b

l

4

Tao, Z., Han, L-H., Zhao, X-L.

China and Australia

[2]

2004

a

l

5

Han, L-H., Tao, Z., Huang, H., Zhao, X-L. Tao, Z., Han, L-H.

China and Australia

[22]

2004

c

l

China

[25]

2006

e

l

7

Huang, H., Han, L-H., Tao, Z., Zhao, X-L.

China and Australia

[29]

2010

a and c

l

8

Lu, H., Zhao, X-L., Han, L-H.

Australia and China

[26]

2010

a and d

l

9

Uenaka, K., Kitoh, H., Sonoda, K.

Japan

[24]

2010

a

l

2 3

6

Carbon

Stainless steel

Development of CFDST columns

13

Column type

Straight

Inclined

Tapered

Tests

Exp

FE

Length

Short

Slender

Design

No. of tests of CFDST 26

l

l

l

l

l

l

l

8

l

l

l

l

8

l

l

l

l

12

l

l

l

l

12

l

l

l

l

4

l

l

l

34

18

l

l

l

l

l

l

l

9

Studied variables [main parameter] [Polyesterbased polymer concrete] Cross-sectional dimensions Cross-sectional dimensions Diameter-tothickness ratio of the outer tube, width-tothickness ratio of the inner tube Diameter-tothickness ratio, hollow section ratio Hollow ratio, yield strength of the inner tube Cross-sectional dimensions, slenderness parameter Hollow ratio, nominal steel ratio, strength of the outer steel tube, strength of concrete, strength of the inner steel tube, width-tothickness ratio of the inner steel tube [Fire resistance] Sectional shape, hollow ratio, load level Inner-to-outerdiameter ratio, diameter-tothickness ratio Continued

14

Concrete-Filled Double-Skin Steel Tubular Columns

Table 2.1 Continued Type of outer tube Sectional shape ()

No.

Authors

Country

References

Year

Carbon

10

Han, L-H., Ren, Q-X., Wei, L.

China

[21]

2011

a, c, f, and g

11

Han, L-H., Li, Y-J., Liao, F-Y.

China

[27]

2011

a and c

l

12

Lu, H., Zhao, X-L., Han, L-H.

Australia and China

[30]

2011

a and c

l

13

Yang, Y-F., Han, L-H., Sun, B-H.

China

[7]

2012

a and d

l

14

Li, W., Han, L-H., Zhao, X-L.

China and Australia

[6]

2012

a and c

l

15

Li, W., Ren, Q-X., Han, L-H., Zhao, X-L.

China and Australia

[20]

2012

A

l

Stainless steel l

Development of CFDST columns

15

Column type

Tests

Straight

Inclined

Tapered

Exp

l

l

l

l

l

l

l

FE

l

l

Slender

Design

No. of tests of CFDST

l

80

l

l

10 (Exp)

l

l

NA

l

l

26

l

l

l

140

l

l

l

10 (Exp)

l

l

l

Short l

l

l

Length

l

Studied variables [main parameter] Sectional shape, column type, hollow ratio [Long-term loading] Sectional shape, type of loading (long- or shortterm), long-term sustained load level [Fire resistance] Load level, capacity of the inner steel tube, use of fire protection, effective length [Partially loaded] Sectional shape, hollow ratio, wall thickness of the top endplate, partial compression area ratio [Preload on steel tubes] Preload on the outer tube or both tubes, cross-sectional dimensions, steel material grades [Tapered columns] Tapered angle, cross-sectional size Continued

16

Concrete-Filled Double-Skin Steel Tubular Columns

Table 2.1 Continued Type of outer tube

No.

Authors

Country

References

Year

Sectional shape ()

16

Hassanein, M.F., Kharoob, O.F., Liang, Q.Q.

Egypt and Australia

[3]

2013

A

17

Ho, J.C.M., Dong, C.X.

Australia and China

[28]

2013

A

l

18

Ho, J.C.M., Dong, C.X.

Australia and China

[12]

2014

A

l

19

Hassanein, M.F., Kharoob, O.F. Hassanein, M.F., Kharoob, O.F.

Egypt

[4]

2014

A

l

Egypt

[19]

2014

A

Carbon

Stainless steel l

l

Development of CFDST columns

17

Column type

Straight

Inclined

Tapered

Tests

Exp

l

Length

FE

Short

l

l

l

48

l

20

l

l

l

l

l

l

l

l

l

l

Slender

Design

No. of tests of CFDST

10 (included in Dong et al. [28])

l

l

l

36

l

51

Studied variables [main parameter] Concrete compressive strength, nominal steel ratio, hollow ratio, thickness ratio, steel grade of the inner carbon steel tube [Using external steel rings] Spacing of steel rings [Using external steel rings] Spacing of steel rings Diameter-tothickness ratio Slenderness ratio, concrete confinement effect, hollow ratio, concrete compressive strength, thickness ratio

18

Concrete-Filled Double-Skin Steel Tubular Columns

2.7.1 Confinement effect in CFDST columns It has been demonstrated that the inner tubes of CFDST short columns can reduce the deformation of the sandwiched concrete if the hollow section ratio (χ ¼ d/(D
2ti)) is not greater than 0.80 [2], similar to the behavior of the concrete core in CFST columns. Fig. 2.8 displays triaxially confined concrete in CFDST short columns [24]. When the sandwiched concrete is under axial load, it is inclined to enlarge its volume in lateral directions. As it is restrained by both tubes, it cannot freely increase its volume and, hence, it is confined. Therefore, both tubes apply lateral passive pressure to the sandwiched concrete in radial directions (σ 3o and σ 3i). Therefore, for an accurate FE analysis of a CFDST column, it is necessary to define a suitable nonlinear concrete model for the sandwiched concrete with consideration of the confining effect, provided that χ is less than 0.80. On the other hand, the confinement effect in CFDST slender columns is seldom found in the literature. Hassanein and Kharoob [19] investigated the confinement effect of such columns with stainless steel jackets. They investigated a number of columns of different lengths with and without considering the confining pressure. The confinement was most pronounced in short columns, and its effect was found to decrease with an increase of χ 0 . This was attributed to the lateral deflection prior to failure, which increases the secondary bending moment and hence reduces the mean compressive strain in the concrete. It is interesting to note that the effect of concrete confinement on the ultimate axial strength of long CFDST columns pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (λ  75= σ 0:2 =235) becomes insignificant. As shown in Table 2.1, confinement was mainly investigated in circular CFDST short columns with inner CHSs. Hence, it is suggested that extensive investigations should be conducted to cover all possible cross sections (mainly round-end rectangular and elliptical sections) and different types of steel jackets. The suggested investigations should cover slender columns.

2.7.2 Effect of initial imperfection and residual stress Huang [32] investigated the influence of initial local imperfection and residual stress on CFDST columns (see Li et al. [6]). The range of the diameter to tube wall thickness ratio or the width to tube wall thickness ratio (D/to) of the investigated CFDST colqffiffiffiffiffiffiffiffiffiffiffiffiffiffi umns was D/to  150(235/fy) and D=to  60 235=f y for circular and square CFDST s3o s3i

Outer Tube Concrete s3o

s3i

Inner Tube

Fig. 2.8 Triaxially confined concrete in CFDST short columns [24].

Development of CFDST columns

19

columns, respectively, where fy is the yield strength of the steel tube. The author found that the imperfection of the steel tube had a minor effect on the axial compressive strength of the CFDST column when the maximum imperfection was less than the allowable imperfection of the steel structure [33], i.e., D/500 for the circular section or D/100 for the square section. For residual stress, it was found that the stiffness of the axially loaded column decreased, whereas the strength remained nearly the same. It is worth pointing out that the effect of initial imperfection and residual stress neither covered all available cross sections nor different column lengths.

2.7.3 Effect of concrete compaction One major challenge of CFDST columns is their susceptibility to the influence of concrete compaction [23]. The influence of concrete compaction on reinforced concrete columns and steel-encased concrete is different from that on composite tubular columns [34]. Concrete compaction affects only the mechanical properties of concrete in reinforced concrete columns, whereas in CFDST columns, the key issue is the interaction between the steel and the concrete. Concrete compaction not only affects the properties of the sandwiched concrete itself but may also influence the interaction between the steel tubes and the sandwiched concrete, thus affecting its overall behavior [35]. Therefore, it is important to maintain good compaction. In spite having a vital effect on CFDST columns, the effect of concrete compaction, to the author’s best knowledge, had never been experimentally investigated. However, one possible solution that may overcome the aforementioned shortage is to use self-consolidating concrete (SCC) [36,37]. SCC has been utilized by Han et al. [21] in their investigation on CFDST columns. However, it is suggested that an experimental comparison should be conducted between SCC and ordinary concrete, especially for CFDST columns with high hollow ratios.

2.7.4 Effect of the hollow ratio The hollow ratio χ, previously defined as d/(D
2to), is an important parameter that affects the compressive behavior of CFDST columns. Huang et al. [29] found that by increasing the value of χ, the longitudinal stress of concrete obviously decreases for columns with circular sections (Fig. 2.3A). According to the authors [29], the maximum concrete stress occurs at the center of the cross section of CFDST columns. If χ is equal to 0.25, then the maximum concrete stress occurs at the center of the sandwich concrete. As the hollow ratio increases, apparently, the location of the maximum concrete stress moves from the center to the periphery of the cross section. For example, if χ is equal to 0.5 or 0.75, then the maximum concrete stress occurs near the outer steel tube. Additionally, it was found that the value of the maximum concrete stress decreases with an increase of the hollow ratio [29]. Additionally, increasing χ was found to decrease the ultimate axial strength of CFDST short columns with different ti/to ratios [3]. This was simply attributed to the noticeable decrease in the sandwiched concrete area, which was found to bear the largest part of the load [29]. Generally, the influence of the hollow ratio on the concrete stresses for members with outer CHSs

20

Concrete-Filled Double-Skin Steel Tubular Columns

was found to be larger than that for members with outer SHSs [29]. For square cross sections (Fig. 2.3C), the maximum concrete stress occurs at the corner and decreases a little with an increase of the hollow ratio of the columns. Additionally, Han et al. [21], in their experimental investigation on CFDST short columns with outer stainless steel jackets, found that the stiffness of straight columns decreases with an increase of the hollow ratios. Moreover, it was found that ductility increases with an increase in the value of χ for columns that have the same crosssectional type. For straight and inclined columns with circular (Fig. 2.3A), roundend rectangular (Fig. 2.3F), and elliptical sections (Fig. 2.3G), ductility was found to increase significantly with an increase in the value of χ, whereas for square section columns (Fig. 2.3C), the ductility was found to be insensitive to any change in the hollow ratio. In the case of slender columns, Hassanein and Kharoob [19] found that increasing the value of χ (which reduces the cross-sectional area of the sandwiched concrete) nearly does not affect the ultimate strength values of intermediate-length columns, whereas it increases the ultimate strength values of long columns. This is, however, opposite to the behavior of CFDST short columns in which increasing the hollow ratio decreases their strengths. This is because the cross-sectional area of the sandwiched concrete, which bears the largest part of the load of short columns [3,29], decreases by increasing the hollow ratio. It was found that long CFDST columns fail elastically and that the ultimate strength is mainly dominated by flexural rigidity [19]. The flexural rigidity of these long columns increases by increasing the value of χ (leading to an increase in the ultimate strength values) because the internal tubes are situated farther from the centroid, where they make greater contribution to the moment of inertia. However, by increasing the hollow ratio in intermediate-length columns, the crosssectional area of the sandwiched concrete decreases while the internal tube is situated farther from the centroid. Therefore, the reduction in column strength caused by reducing the cross-sectional area of the sandwiched concrete is neutralized by an increase in the strength caused by the additional flexural rigidity of the inner tubes. This finally leads to an insignificant effect for χ in intermediate-length columns. From the abovementioned survey, it can be seen that the effect of χ on some cross sections (round-end rectangular (Fig. 2.3F) and elliptical sections (Fig. 2.3G)) does not exist in the literature and, as such, the effect of χ needs to be explored further for the possibility of expanding their use in practice.

2.7.5 Effect of the thickness ratio Hassanein et al. [3] examined the effect of the thickness ratio (ti/to) on the structural behavior of CFDST short columns with stainless steel jackets by varying the inner tube’s thickness. It was found that increasing the ti/to ratio increases the ultimate axial strength of CFDST short columns with different d/D ratios. However, the rate of the strength increase becomes larger as the d/D ratio increases. On the other hand, no obvious changes in the load-strain relationships were found by changing the ti/to ratio.

Development of CFDST columns

21

The effect of the ti/to ratio on the capacity of CFDST short columns was found to be significant by changing the thickness of the outer tube (to). Logically, increasing the value of to (with other dimensions of the column being fixed) leads to a larger increase in the ultimate axial strength of the column than the increase associated with increasing the inner tube’s thickness. This, however, increases the amount of the steel. In the case of CFDST slender columns with stainless steel jackets, the effect of the ti/to ratio was also explored by Hassanein and Kharoob [19]. It is worth pointing out that changing the ti/to ratio insignificantly influences the value of the column slenderness. By changing the inner tube’s thickness, it was found that the effect of the ti/to ratio on the strength of CFDST slender columns is significant in intermediate-length CFDST columns. This is attributed to the fact that increasing the value of ti increases the confinement exerted on the sandwiched concrete. On the other hand, the effect of the ti/to ratio is not important in long columns. This is simply because flexural stiffness is insignificantly influenced by the change in the thickness of the inner tubes, which are situated near to the centroid. It is important to note that the ti/to ratio was not discussed, explicitly, in the available papers dealing with CFDST slender columns with carbon steel jackets. It is expected that the ti/to ratio shows a different effect from that of using stainless steel jackets owing to the difference of behavior between both types of steels. Its effect also does not address round-end rectangular and elliptical columns.

2.7.6 Effect of the steel grade of the inner steel tubes Hassanein et al. [3] investigated the effect of the steel grade of the inner steel tubes. They considered three steel grades (S235, S275, and S355 according to EN 1993-1-1 [38]). It was found that the compressive strength of CFDST short columns for different d/D ratios slightly increases as a result of increasing the steel grade of the inner tube. Furthermore, it was found that the yield stress of the inner steel tubes does not have a significant effect on the axial load–strain responses of CFDST short columns. This confirms the findings of Huang et al. [29]. Hence, the use of inner tubes with the least yield strength values has been suggested to reduce the cost of CFDST short columns. On the other hand, investigations of the effect of the steel grade of the inner steel tubes are not up-to-date in the case of CFDST columns with different hollow ratios. The authors expect that its effect may be larger when the area of the sandwiched concrete is minimized.

2.7.7 Effect of long-term sustained loading Long-term deformation of circular and square CFDST slender columns with inner CHSs was investigated by Han et al. [27]. The long-term deformation of CFDST slender columns was found to increase relatively fast at an early stage, finally stabilizing after about 100 days (the long-term sustained load tests lasted for about 3 years). The authors found that long-term sustained loading decreases the ultimate strength of

22

Concrete-Filled Double-Skin Steel Tubular Columns

CFDST columns whilst increasing the corresponding deformation. However, these experiments should extend to different cross sections, outer tube materials, and column typologies.

2.7.8 Effect of axial partial compression Yang et al. [7] experimentally investigated the behavior of CFDST columns under axial partial compression (see Fig. 2.7). They found that partially loaded CFDST columns can develop a stable load versus deformation response and exhibit a ductile behavior similar to that of CFST columns under the same loading conditions. Additionally, it was found that the bearing capacity of circular CFDST specimens is much higher than that of the square ones. This is induced by the stronger confinement of circular steel tubes to sandwiched concrete compared to square steel tubes. The strength of a column was found to increase with an increase in the top endplate thickness and a decrease of the partial compression area. A simplified model was suggested to provide a realistic prediction of the bearing capacity of CFDST sections under axial partial compression. It was also observed from the tests that the ductility of circular CFDST columns is better than that of square columns under axial partial compression. It is expected that round-end rectangular and elliptical CFDST columns have higher strength and ductility compared to those of square columns due to their stronger confinement to the sandwiched concrete. However, this should be experimentally examined in future. Moreover, the effect of partial loading on intermediate-length CFDST columns should also be explored. However, its effect in long columns with different cross sections, in which the effect of the confinement disappears, is expected to be the same.

2.7.9 Effect of preloading on steel tubes During erection, the inner and outer steel tubes are subjected to preloading from the upper structures along with wet filled concrete. Li et al. [6] investigated the behavior of CFDST columns with preload on the outer tube alone and also on both tubes using ABAQUS [31]. The utilized FE model was verified using test results of CFDST columns without preload and those of CFST columns with preload. The authors found that the preload causes both initial deformation and initial stress in hollow steel tubes. Additionally, it was found that the strength of a CFDST column may decrease moderately when the preload is applied. Moreover, it was found that a CFDST column’s slenderness has the most significant influence on its strength, whereas other parameters (i.e., hollow ratio, yield stresses of the tubes, compressive strength of the sandwiched concrete, and nominal steel ratio) only have a moderate effect on its strength. Based on their results [6], a design formula (that will be provided at the end of this chapter) was proposed to estimate the reduced axial strength of a CFDST column when preload is applied on both tubes. As the slenderness of a column has

Development of CFDST columns

23

been found to have the most significant influence on its strength when preload is applied, slender columns should be further explored. Additionally, extensive investigations should be conducted to unveil the structural behavior of different cross sections and different outer steel materials. As load introduction may affect the columns, the influence of preload on different column typologies (i.e., tapered and inclined) is of importance.

2.7.10 Influence of fibers on the capacity of CFDST short columns It is currently a known fact that the major difference in the behavior of steel fiberreinforced concrete and plain concrete is ductility. Steel fiber-reinforced concrete has higher ductility compared to that of plain concrete. To investigate the influence of fibers on the capacity of CFDST short columns, only two reference (short column) specimens were prepared by Lu et al. [26]. It was found that the difference in the ductility of concrete mainly affects the behavior of the concrete after it has reached its peak stress. However, when concrete is confined by steel tubes, the difference in peak load and ductility for cases with or without fibers was insignificant. Hence, it is expected by the current authors that when the confinement is reduced (as in the case of intermediate-length columns) or removed (as in the case of long columns), the added fibers would exert a significant effect due to the existence of tensile stresses. This, however, needs experimental verification. On the other hand, polypropylene fibers are generally used to improve the crack resistance of concrete due to shrinkage and has little influence on the strength of concrete. Therefore, Lu et al. [26] proposed the use of CFDST columns’ capacities based on plain concrete to determine the capacity of short columns. From the authors’ view point, the influence of fibers on the capacity and behavior of CFDST short columns requires additional experimental investigations to increase their data points.

2.7.11 Improving the interface bonding of CFDST columns A major shortcoming of CFDST columns [12,28] is that imperfect interface bonding occurs in the elastic stage, which reduces their elastic strength and stiffness. Thus, Ho and Dong [12,28] proposed the use of external confinement to restrict the lateral dilation of the outer tubes of circular CFDST columns (see Fig. 2.3A). To verify the effectiveness of the proposed external rings, 20 CFDST columns with normal- and high-strength sandwiched concrete were tested. From the test results, it was observed that the stiffness, axial ultimate load, and ductility of the ring-confined CFDST columns were significantly higher than those of the unconfined columns. This was only investigated for circular tubes in which the confinement was maximized. Therefore, other cross sections should be explored (especially round-end rectangular and elliptical cross sections) to increase their elastic interface bonding and confinement.

24

2.8.

Concrete-Filled Double-Skin Steel Tubular Columns

Failure modes of CFDST columns

The failure mode of straight CFDST short columns (with different cross sections) is a typical compression failure without overall buckling (see, for example, Zhao and Grzebieta [18], Han et al. [22], and Lu et al. [26]). Fig. 2.9 shows the typical failure modes of square short columns and their inner steel tubes. The failure mode of the outer tube is an outward bulge similar to that observed for CFST columns (i.e., forming an outward folding mechanism). The failure mode of the inner square tube is consecutively inward and outward local bulging, which is similar to the failure mode of unfilled tubes. Crushing of the concrete occurs at positions corresponding to the severe outward bulge of the outer steel tube. Longitudinal cracks in the concrete also exist. However, it was found that the failure modes of inclined CFDST short columns are similar to those of the straight ones having the same column section despite the inclined angles or oblique planes [21]. For tapered CFDST columns [21], the outward buckling of the steel tube was found to occur near the top (smallest) section of the column. In the case of partially loaded CFDST columns [7], it can be seen from Fig. 2.10 that the top endplate deforms to form a U-shaped ring plate due to the concrete crushing underneath the ring-bearing plate. As can be seen from the figure, at the section near the top endplate, the outward and inward plastic deformations take place toward the outer and inner steel tubes, respectively. This is simply due to the local pushing effect of the crushed concrete between the steel tubes. It could also be observed that the plastic deformation of the steel tube of columns with both SHS tubes is less evident than that of columns with both CHS tubes. Nevertheless, the plastic deformation range of square tubes is larger than that of circular ones. This is because of the fact that the confinement effect on the sandwiched concrete of a circular steel tube is stronger than that of a square steel tube. Additionally, it was observed [7] that the plastic deformation of both tubes is generally located on the top part of the partially loaded columns. On the other hand, the plastic deformation position of both tubes of the partially loaded columns is different from that of the entirely loaded columns (see Huang et al. [29]). In the latter case, the plastic deformation is mainly induced by the local buckling of the steel tubes. So, it generally concentrates on the mid-height section of the columns.

Original cross section Buckled cross section

(a) Outer tube

(b) Inner tube

Fig. 2.9 Failure modes of CFDST short columns [18]: (A) outer tube and (B) inner tube.

Development of CFDST columns

25

(a) Top endplate Ring bearing plate

Ring bearing plate

Plastic deformation

Top endplate

Plastic deformation

Outer tube

Inner tube

(1) CHS outer and CHS inner

Inner tube

Outer tube

(2) SHS outer and SHS inner Top endplate

(b)

Plastic deformation

Inner tube

Outer tube

Fig. 2.10 Failure mode of partially loaded CFDST columns. (A) Partially loaded. (B) Entirely loaded [7].

On the other hand, the typical failure modes of pin-ended slender columns (intermediate-length and long) have the well-known shape of a half-sine wave [19]. With regard to long-term sustained loading, the failure mode of CFDST slender columns [27] obviously remains unchanged. The typical failure mode of ring-confined CFDST columns [28] is displayed in Fig. 2.11. The failure mode of such columns was the fracture of the outer steel tube and/or steel rings. It can be seen from the figure that the fracture of the outer steel tube occurs only between the external rings. This is because the rings act as lateral restraints. This shortens the effective length of the column so that buckling of the outer tube occurs only between the rings. Once inward buckling occurs in the inner tube, the large load abruptly transfers to the outer tube and the core concrete, which initiates the buckling of the outer tube. Additionally, it was found that as the axial

26

Concrete-Filled Double-Skin Steel Tubular Columns

Inward buckling of inner tube Fracture of steel ring

Buckling and fracture of steel tube between the rings

Fig. 2.11 Failure mode of ring-confined CFDST columns [28].

deformation increases, the hoop tensile strain that develops in the outer tube reaches the fracture strain. Thereafter, the load-carrying capacity of the specimens drops rapidly.

2.9.

The mechanism of the inner tube of CFDST columns

The mechanism of the inner square tube was found to be the same as that of an empty short column (see Fig. 2.8) as reported by Key and Hancock [39]. In design, therefore, it is recommended to use the contribution of the inner tubes as fsyiAsi [6,18,24,30]. However, this was not the case for CFDST columns with inner CHSs [21]. These inner circular steel tubes were found only to buckle inwardly. This mode of failure was described as the “distorted diamond” mode [21].

2.10.

Formulas for compressive strength

This section reports the recent advances in the design methods of CFDST columns under axial compression. It is worth pointing out that the capacity formulations, provided in the following, were derived from studies on plain concrete (without fiber)filled CFDST columns [26]. Tables 2.2, 2.3, and 2.4 display the design strengths of CFDST short columns without preload, CFDST short columns with preload on the steel tubes, and CFDST long columns without preload, respectively. However, based on these design strengths, the following points could be drawn: 1. Most of the capacity formulations of CFDST columns found in the literature are suggested for CFDST short columns. Particularly, circular CFDST short columns with inner CHSs seem to be the focus point of the majority of the efforts of research works.

Table 2.2 Design strengths of CFDST short columns without preload. References

Carbon steel jackets

Straight columns

Fully loaded columns

[24] [2]

[4]

Design Eq.

  Pu,Uenaka ¼ 2:86
2:59 Dd f syo Aso + f syi Asi + Asc f ’c with 0:2 < Dd < 0:7 Pu, Tao ¼ Nosc, u + Ni, u where Nosc,u ¼ fscyAsco with Asco ¼ Aso + Asc fscy ¼ C1χ 2σ 0.2 + C2(1.14 + 1.02ζ)fck (fscy and fck [N/mm2]) Aso f syo Aso ,ζ¼ and C1 ¼ 1 +α α, C2 ¼ 11 ++ ααn , α ¼ AAsosc , αn ¼ Ac,no min al Ac,no min al f ck 0 fck ¼ 0.67fcu ¼ 0.84fc Ni,u ¼ Asi fsyi 8    > < 1 + 0:3 ζ Ω f A + f 0 A sc + f syi Asi : D=to  150 syo so cc 1+ζ Pu,Hassanein ¼ > : f A + 0:85f 0 A + f A : D=t > 150 syo so

c sc

syi si

o

This method is based on the unified axial load bearing capacity for solid and hollow circular CFST columns was recently proposed by Yu et al. [40]. Where   ζ ¼ αfsy/fck, α ¼ Aso/Asc and Ω ¼ Asc = π4 ðD
2to Þ2 Partially loaded columns

[7]

Pu, Yang ¼ kbcPTao (see Fig. 2.7) where PTao is the strength of the fully loaded composite sections according to Tao et al. [2]. kbc represents the bearing capacity factor. Continued

Table 2.2 Continued References

Design Eq.   ð0:9 + 1:28χ
2:16χ 2 Þ: 0:12t0:4 a + 0:52   kbc ¼ 0:28β0:5 + 0:44 β ¼ AAscp

Stainless steel jackets

Tapered columns

Fully loaded columns

[6]

Straight columns

Fully loaded columns

[21]

[3]

Ap is the partial bearing area of the compressive load and ta is the top endplate thickness (not the ring-bearing plate). The formula for the prediction of the sectional strength of a straight CFDST section, proposed by Tao et al. [2], has been adopted to design the tapered CFDST columns. That formula is to be used by considering the smallest section of the column in the calculations. The same method of design of a circular CFDST column with inner CHS and outer carbon steel jackets [2] was suggested to predict the strength of the circular CFDST column with outer stainless steel jackets. Pu, Hassanein2 ¼ γ sefsyeAse + γ sifsyiAsi + (γ scf 0c + 4.1f 0rp. se)Asc where fcc0 ¼ γ cfc0 + 4.1frp, se0 8 2t D > > for  47 < 0:7ðνe
νs Þ D
2t f sye te e  f 0rp,se ¼  D D > > f for 47 <  150 : 0:006241
0:0000357 te sye te Following Tang et al. [41], Poisson’s ratios (νe and νs) are given as: νs ¼ 0.5  0  0  0 2 f f f νe ¼ 0:2312 + 0:3582ν0e
0:1524 f c + 4:843ν0e f c
9:169 f c sy sy sy  3  2   ν0e ¼ 0:881  10
6 Dt
2:58  10
4 Dt + 1:953  10
2 Dt + 0:4011 The factors γ se, γ si, and γ c are given as follows:  
0:1  
0:1 γ se ¼ 1:458 Dte and γ si ¼ 1:458 tdi ð0:9  γ s  1:1Þ γ c ¼ 1:85Dc
0:135 with Dc ¼ D
2te and (0.85  γ c  1.0)

Carbon steel jackets

Straight columns

Fully loaded columns

[5]

Pu, Elchalakani ¼ Pso + Pc + Psi (see Fig. 2.12) where   Pso ¼ π4 f yo D2e
D2ei Psi ¼ Pcorner + Pflat ¼ fyi, cornerπ(r2exti
r2inti) + 4fyi, flat(bi
2rexti)ti   Pc ¼ 0:85f 0c Ac ¼ 0:85f 0c π4 D2i + r 2ext ð4
π Þ
B2 8 8 < D : λe  82 < Dei : λe  82 De ¼ and Dei ¼ λey λ :D : Dei ey : λe > 82 : λ > 82 λso e λso   f

yo Dei ¼ D
2to and λe ¼ D to 250 as defined by AS4100 [42] 8  qffiffiffiffiffiffi < bo
2r exto : λe  40 bo
2r exto f yo beo ¼ and λe ¼ λey 250 as defined to : ðbo
2r exto Þ : λe > 40 λe by AS4100 [42]

Carbon steel jackets

Straight columns

Fully loaded columns

[22]

Pu, Han ¼ Nosc, u + Ni, u where Nosc, u ¼ h fscyAsco with Asco ¼ Aso + Asc

  i f syo f scy ¼ 1:212 + 0:138 235 + 0:7646 ζ +
0:0727 f20ck + 0:0216 ζ2 f ck (fscy and fck [N/mm2]) Continued

Table 2.2 Continued References

Design Eq. Aso f syo and fck ¼ 0.67fcu ¼ 0.84fc0 Ac,no min al f ck Ni, u ¼ Asifsyi It was proposed to use the same method of design of a rectangular CFDST column (inner RHS and outer RHS) [25]. ζ¼

Stainless steel jackets

Straight columns

Fully loaded columns

[21]

Carbon steel jackets

Straight columns

Fully loaded columns

[18]

Partially loaded columns

[7]

Pu, Zha ¼ Pso + Pc + Psi (see Fig. 2.13) where Pso ¼ Pcorner + Pflat ¼ fyo, cornerπ(r2exto
r2into) + 4fyo, flatbeoto Psi ¼ Pcorner + Pflat ¼ fyi, cornerπ(r2exti
r2inti) + 4fyi, flat(bi
2rexti)ti Pc ¼ 0.85fc0 Ac where 8 < bo
2r exto : λe  40 beo ¼ λ : ðbo
2r exto Þ ey : λe  40 λe  rffiffiffiffiffiffiffiffi f yo bo
2rexto as defined by AS4100 [42] λe ¼ to 250 Pu, Yang ¼ kbcPTao&Han where PTao&Han is the strength of the corresponding fully loaded composite sections according Tao and Han [25].  ð0:94 + 1:12χ
2χ 2 Þ: 0:12t0:4 a + 0:2   kbc ¼ 0:04β0:5 + 0:84

Carbon steel jackets

Fully loaded columns

[25]

PTao&Han ¼ Nosc, u + Ni, u where Nosc, u ¼ fscyAsco with Asco ¼ Aso + Asc fscy ¼ C1χ 2fsyo + C2(1.18 + 0.85ζ)fck (fscy and fck [N/mm2]) C1 ¼ 1 +α α, C2 ¼ 11 ++ ααn , α ¼ AAsosc , αn ¼ Ac,noAsomin al , ζ ¼ Ac,nosominsyoal f and A f

ck

fck ¼ 0.67fcu ¼ 0.84fc0 Ni, u ¼ Asifsyi

Stainless steel jackets

Straight columns

Fully loaded columns

[21]

The same method of design of a circular CFDST column (inner CHS and outer CHS) with outer carbon steel jackets was proposed to predict the strengths of the round-end rectangular and elliptical sections. However, the hollow ratio of the CFDST section, for the round-end rectangular and elliptical sections, is to be taken as: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi bd χ¼ ðB
2to ÞðD
2to Þ

32

Concrete-Filled Double-Skin Steel Tubular Columns

rint i to

bi

D

Fig. 2.12 Definition of symbols of a CFDST column (SHS inner and CHS outer).

rint o rint i to

bi

bo

Fig. 2.13 Definition of symbols of a CFDST column (SHS inner and SHS outer).

2. The available capacity formulations cover the five cross sections shown in Fig. 2.3A–E for CFDST short columns with carbon steel jackets. 3. For CFDST columns with stainless steel outer tubes, formulas for short columns cover only four cross sections (Fig. 2.3A–G). 4. Design strengths for round-end rectangular and elliptical sections were suggested once in the literature. They provide the strengths for only short columns with stainless steel outer tubes. 5. Only one design method was found in the literature for circular CFDST slender columns with outer stainless steel tubes. This was suggested by Hassanein and Kharoob [19]. Nevertheless, it covers only one cross section, which is formed from two circular tubes. 6. It is worth pointing out that there is neither information nor design strengths for CFDST slender columns with carbon steel tubes in the literature.

Table 2.3 Design strengths of CFDST short columns with preload on the steel tubes.

Stainless steel jackets

Straight columns

Preload on the outer steel tube

References

Design Eq.

[6]

Pu, Li ¼ kpPTao (see Fig. 2.14) where PTao is the strength of the corresponding fully loaded composite sections according to Tao et al. [2]. The strength index (kp) was proposed as: kp ¼ 1
f(λo)f(e/r)ηp  1.0 where for axially loaded CFDST columns with both CHSs, f(e/r) is 0.9. f(λo) is a function accounting for the influence of the slenderness ratio (λ), where λo ¼ λ/80 and λ ¼ 4l/D. l is the column length. : λo  1:0 0:17λo
0:02 f ðλo Þ ¼
0:13λo 2 + 0:35λo
0:07 : λo > 1:0 Np Np ¼ ηp ¼ N us φo f syo Aso where Np is the preload applied on the outer steel hollow section; Nus is the ultimate strength of the outer steel tubular column; and φo is the stability ratio (Fig. 2.14 according to GBJ17-88 [8]). Continued

Table 2.3 Continued References

Design Eq. The validity limits of this proposed strength [6] are ηp ¼ 0
0.8; χ ¼ 0.25
0.75; αn ¼ 0.04
0.2; λ ¼ 10
80;

Preload on both steel tubes

[6]

fck ¼ 20
60MPa; and fsyo ¼ 200
420MPa. The design strength is typical to the design model of preload on the outer steel tube, with a modification in kp, as follows: kp ¼ 1
f(λo)ηp  1.0 f(λo) ¼ 0.40λo
0.01 λo ¼ λ/100 4l λ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 D + ðd
2tsi Þ2 Np Np ¼ N us φo f syo Aso + φo f syi Asi The validity limits of this proposed strength [6] are ηp ¼ 0
0.8; χ ¼ 0.25
0.75; αn ¼ 0.04
0.2; λ ¼ 10
60; ηp ¼

fck ¼ 20
70 MPa; fsyi ¼ 235
420 MPa; and fsyo ¼ 235
420 MPa.

Carbon steel jackets

Straight columns

Preload on the outer steel tube

[6]

Pu, Li ¼ kpPHan (see Fig. 2.14) where PTao is the strength of the corresponding fully loaded composite sections according to Han et al. [22]. kp ¼ 1
f(λo)f(e/r)ηp  1.0 where

Stainless steel jackets

Straight columns

Preload on both steel tubes

[21]

for axially loaded CFDST columns with inner circular and outer square tubes, f(e/r) is 0.9. f(λo) is a function accounting for the influence of the slenderness ratio (λ), where λo ¼ λ/80 and λ ¼ 4l/D. l is the column length. : λo  1:0 0:14λo + 0:02 f ðλo Þ ¼ 2
0:15λo + 0:42λo
0:11 : λo > 1:0 Np Np ηp ¼ N us ¼ φo f syo Aso where Np is the preload applied on the outer steel hollow section and Nus is the ultimate strength of the outer steel tubular column. The stability ratio (φo) can be calculated from Fig. 2.14 according to GBJ17-88 [8]. The validity limits of this proposed strength [6] are ηp ¼ 0
0.8; χ ¼ 0.25
0.75; αn ¼ 0.04
0.2; λ ¼ 10
80. It should be noted that the case of CFDST columns with preload on the steel tube is typical to that suggested for the CFST columns [43]; fck ¼ 20
60 MPa; and fsyo ¼ 200
420 MPa. The design strength is typical to the design model of preload on the outer steel tube, with a modification in kp, as follows: kp ¼ 1
f(λo)ηp  1.0 f ðλo Þ ¼ 0:33λo 2 + 0:051λo + 0:03 λo ¼ λ/100 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4l 12D2
3π ðd
2tsi Þ2 λ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . 16D4
3π ðd
2tsi Þ4 Np N ηp ¼ N usp ¼ φo f syo Aso + φo f syi Asi The validity limits of this proposed strength [6] are ηp ¼ 0
0.8; χ ¼ 0.25
0.75; αn ¼ 0.04
0.2; λ ¼ 10
60; fck ¼ 20
70 MPa; fsyi ¼ 235
420 MPa; and fsyo ¼ 235
420 MPa.

Table 2.4 Design strengths of CFDST long columns without preload.

Stainless steel jackets

Straight columns

Fully loaded columns

References

Design Eq.

[19]

PCFDST ¼ χPpl, Rd where 8   < γ Ase σ 0:2 + γ f 0 + 4:1f 0 Asc + γ Asi f : λ  0:5 ss c c s y rp Ppl,Rd ¼ :A σ + A f0 + A f : λ > 0:5 se 0:2 sc si y pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c λ ¼ Ppl,Rd,ð6:30Þ =Pcr . In the calculation of λ, Ppl, Rd, (6.30) does not consider the confinement effect (Eq. 6.30 in Eurocode 4 [15]) and the critical load is: π 2 ðEI Þe Pcr ¼ ðKLÞ2 where KL is the effective length of the member and (EI)e is the effective elastic flexural stiffness. The reduction factor (χ) is calculated using the European strut curves as:  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 χ ¼ 1= ϕ + ϕ2
λ  1:0     2 ϕ ¼ 0:5 1 + α λ
λ0 + λ λo is taken as 0.2, following the carbon steel predictions (see EC3 [38]). Hassanein and Kharoob [19] suggested the use of a value 0.49 forα, as given by EC3 [44] for welded hollow sections.

Carbon steel jackets

Straight columns

Long-term sustained loading

[27]

The following formula was suggested for calculating the ultimate strength of CFDST columns subjected to long-term sustained loading (PuL). The authors suggested including the influence of the hollow ratio (χ) of the CFDST columns in the previously suggested equations Pu for the CFST columns by Zhao et al. [45]. In fact, the current author was unable to reach the original equations computing Pu for the CFST columns. PuL ¼ kχ SICFSTPu and kχ SICFST  1.0 where Pu is the ultimate load of the CFST column under short-term loading conditions. kχ ¼ 0.65χ 2
0.45χ + 1

38

Concrete-Filled Double-Skin Steel Tubular Columns

1.2 1.0 0.8

ϕo 0.6 0.4 0.2 0.0 0.0

40

80

120

160

200

λ

Fig. 2.14 φo versus λ relationship of a pure steel tubular column.

Besides the abovementioned shortages, the available design strengths based on limited experimental programs should be rechecked. As an example, the experimental results of the CFDST columns tested by Han et al. [22] were used to check the accuracy of the design model of square CFDST short columns with inner CHSs (Fig. 2.3C). Table 2.5 shows the details and material properties of these columns, whereas Table 2.6 provides the comparison between the design strengths (Pul, Han) of the columns and their experimental ultimate strengths (Pul, Exp). The outer SHSs were first classified (based on the maximum depth-to-thickness ratios for the compression parts of the cross sections according to EC3 [38]) into fully effective (Feff: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (D
2to)/to  42ε)) and slender ((S: (D
2to)/to > 42ε); ε ¼ 235=f yo) sections. The slenderness of some SHSs used by Han et al. [22] was found to exceed the maximum value specified by EC4 [12] (52ε as given in Table 2.6.3 [12]). These cross sections are currently considered to be very slender (VS). From the comparative results of Table 2.6, it can be ensured that the available design strength is conservative for CFDST short columns with fully effective SHSs. Conversely, it provides unsafe results for CFDST short columns with very slender SHSs. It is worth pointing out that these conclusions are valid for columns filled with normal strength concrete (NSC) (see Table 2.5). Hence, a new design model should be proposed for this particular case. Moreover, high-strength sandwiched concrete should also be checked either experimentally or by FE modeling to verify the available design model for square CFDST short columns with inner CHSs.

Table 2.5 Details of the tested square CFDST short columns with inner CHSs [22]. fyi [MPa]

Column

Classification of the SHSs

D × to [mm]

d × ti [mm]

L [mm]

fyo [MPa]

Outer

Inner

fc0 [MPa]

ssc2 ssc3 ssc4 ssc5 ssc6 ssc7

Feff Feff Feff VS VS VS

120  3 120  3 120  3 180  3 240  3 300  3

32  3 58  3 88  3 88  3 114  3 165  3

360 360 360 540 720 900

275.9 275.9 275.9 294.5 275.9 275.9

275.9 275.9 275.9 275.9 275.9 275.9

422.3 374.5 370.2 370.2 294.5 320.5

37.44 37.44 37.44 37.44 37.44 37.44

40

Concrete-Filled Double-Skin Steel Tubular Columns

Table 2.6 Comparison between experimental and available strength results of square CFDST short columns with inner CHSs [22]. Column

Classification of the SHSs

Pul, Exp [kN]

Pul, Han [kN]

Pul,Han Pul,Exp

scc2-1 scc2-2 scc3-1 scc3-2 scc4-1 scc4-2 scc5-1 scc5-2 scc6-1 scc6-2 scc7-1 scc7-2

Feff Feff Feff Feff Feff Feff VS VS VS VS VS VS

1054 1060 990 1000 870 996 1725 1710 2580 2460 3240 3430

972 972 935 935 821 821 1740 1740 2710 2710 3794 3794

0.92 0.92 0.94 0.93 0.94 0.82 1.01 1.02 1.05 1.10 1.17 1.11

2.11.

Conclusions

In the last two decades, considerable progress has been made in the investigations of concrete-filled double skin tubular (CFDST) columns. In this chapter, the information available regarding the axial strength and behavior of CFDST columns is gathered, summarized, and critically reviewed. The details of the available experimental (Exp) and finite element (FE) studies are summarized in Table 2.1. This table provides the author names, reference number, publication year, sectional shape, type of outer tube (i.e., carbon or stainless steel), column type (i.e., straight, inclined, or tapered), type of test (i.e., Exp or FE), type of column with regard to its length (i.e., short or long), number of tests conducted, and studied variables. This was followed by a discussion of the different factors affecting the structural behavior of CFDST columns. By considering each effect, it was found that several investigations should be conducted to cover different cross-sectional shapes, different steel jackets, and different column typologies. These suggested investigations should lead to design proposals that cover possible generated columns. Additionally, it was found that available design strengths based on limited experimental programs should be rechecked. Based on the review provided in this chapter, Table 2.7 is presented to provide the studied (up-to-date) general variables for each cross section of the CFDST columns. Although significant strides have been made in terms of exploring the strength and behavior of CFDST columns, it is seen from the table that intensive research is still required for each cross section under different parameters (represented by the shaded cells). For example, the investigation of CFDST slender columns with different cross sections is required, inclined CFDST columns with different cross sections with carbon steel jackets need to be explored, etc.

Development of CFDST columns

41

Table 2.7 Studied variables for each cross section of CFDST columns. Type of

Length

•

•

•

•

•

•

Slender

Short

behavior

Tapered

General

•

Inclined

parameter

Straight

Main Stainless

shape (Fig. 3)

Column type

outer tube Carbon

Sectional

General behavior

•

•

•

Polyesterbased

•

polymer

a

Fire

•

resistance Long-term

•

loading Partially-

•

loaded Preload on

•

steel tubes General

•

behavior General

• c

behavior •

•

Fire

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

• •

• Length

Slender

Short

Tapered

parameter

Inclined

Main Stainless

(Fig. 3)

•

Column type

outer tube Carbon

shape

•

General behavior

Type of Sectional

•

Straight

b

•

concrete

resistance Long-term

•

loading Preload on

•

steel tubes General

•

d

behavior Fire

•

resistance Partially-

•

e

f

g

loaded General

•

behavior •

•

•

•

•

•

•

•

•

•

•

•

•

•

General behavior

•

•

•

•

•

•

•

•

General behavior

42

Concrete-Filled Double-Skin Steel Tubular Columns

References [1] AISC, Load And Resistance Factor Design Specification, for Structural Steel Buildings, American Institute of Steel Construction, Chicago, 2010. [2] Z. Tao, L.-H. Han, X.-L. Zhao, Behaviour of concrete-filled double skin (CHS inner and CHS outer) steel tubular stub columns and beam-columns, J. Constr. Steel Res. 60 (2004) 1129–1158. [3] M.F. Hassanein, O.F. Kharoob, Q.Q. Liang, Circular concrete-filled double skin tubular short columns with external stainless steel tubes under axial compression, Thin-Walled Struct. 73 (2013) 252–263. [4] M.F. Hassanein, O.F. Kharoob, Compressive strength of circular concrete-filled double skin tubular short columns, Thin-Walled Struct. 77 (2014) 165–173. [5] M. Elchalakani, X.-L. Zhao, R. Grzebieta, Tests on concrete filled double-skin (CHS outer and SHS inner) composite short columns under axial compression, Thin-Walled Struct. 40 (2002) 415–441. [6] W. Li, L.-H. Han, X.-L. Zhao, Axial strength of concrete-filled double skin steel tubular (CFDST) columns with preload on steel tubes, Thin-Walled Struct. 56 (2012) 9–20. [7] Y.-F. Yang, L.-H. Han, B.-H. Sun, Experimental behaviour of partially loaded concrete filled double-skin steel tube (CFDST) sections, J. Constr. Steel Res. 71 (2012) 63–73. [8] GBJ17-88, Designing Code of Steel Structures, China Planning Press, Peking, China, 1988 (in Chinese). [9] M. Tomlinson, M. Chapman, H.D. Wright, A. Tomlinson, A. Jefferson, Shell composite construction for shallow draft immersed tube tunnels, in: ICE International Conference on Immersed Tube Tunnel Techniques, Manchester, UK, April, 1989. [10] http://www.neimagazine.com/features/featurea-concrete-history/featurea-concrete-his tory-2.html. [11] H. Kimora, I. Kojima, H. Moritaka, Development of Sandwich-Structure Submerged Tunnel Tube Production Method, Nippon Steel Technical Report No. 86, 2002. [12] J.C.M. Ho, C.X. Dong, Improving strength, stiffness and ductility of CFDST columns by external confinement, Thin-Walled Struct. 75 (2014) 18–29. [13] M. Johansson, Composite Action and Confinement Effects in Tubular Steel-Concrete Columns (Ph.D. thesis), Chalmers University of Technology, Goteborg, Sweden, 2002. [14] M.V. Chitawadagi, M.C. Narasimhan, S.M. Kulkarni, Axial strength of circular concretefilled steel tube columns – DOE approach, J. Constr. Steel Res. 66 (2010) 1248–1260. [15] Eurocode 4, Design of Composite Steel and Concrete Structures- Part 1.1: General Rules and Rules for Buildings, British Standard Institution, London, 2004. ENV 1994-1-1. [16] S. Wei, S.T. Mau, C. Vipulanandan, S.K. Mantrala, Performance of new sandwich tube under axial loading: experiment, J. Struct. Eng. ASCE 121 (12) (1995) 1806–1814. [17] S. Wei, S.T. Mau, C. Vipulanandan, S.K. Mantrala, Performance of new sandwich tube under axial loading: analysis, J. Struct. Eng. ASCE 121 (12) (1995) 1815–1821. [18] X.-L. Zhao, R. Grzebieta, Strength and ductility of concrete filled double skin (SHS inner and SHS outer) tubes, Thin-Walled Struct. 40 (2) (2002) 199–213. [19] M.F. Hassanein, O.F. Kharoob, Analysis of circular concrete-filled double skin tubular slender columns with external stainless steel tubes, Thin-Walled Struct. 79 (2014) 23–37. [20] W. Li, Q.-X. Ren, L.-H. Han, X.-L. Zhao, Behaviour of tapered concrete-filled double skin steel tubular (CFDST) stub columns, Thin-Walled Struct. 57 (2012) 37–48. [21] L.-H. Han, Q.-X. Ren, L. Wei, Tests on stub stainless steel-concrete-carbon steel doubleskin tubular (DST) columns, J. Constr. Steel Res. 67 (2011) 437–452. [22] L.-H. Han, Z. Tao, H. Huang, X.-L. Zhao, Concrete-filled double-skin (SHS outer and CHS inner) steel tubular beam-columns, Thin-Walled Struct. 42 (9) (2004) 1329–1355.

Development of CFDST columns

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[23] X.-L. Zhao, L.-H. Han, Double skin composite construction, Prog. Struct. Eng. Mater. 8 (3) (2006) 93–102. [24] K. Uenaka, H. Kitoh, K. Sonoda, Concrete filled double skin circular stub columns under compression, Thin-Walled Struct. 48 (2010) 19–24. [25] Z. Tao, L.-H. Han, Behaviour of concrete-filled double skin rectangular steel tubular beam-columns, J. Constr. Steel Res. 62 (2006) 631–646. [26] H. Lu, X.-L. Zhao, L.-H. Han, Testing of self-consolidating concrete-filled double skin tubular stub columns exposed to fire, J. Constr. Steel Res. 66 (2010) 1069–1080. [27] L.-H. Han, Y.-J. Li, F.-Y. Liao, Concrete-filled double skin steel tubular (CFDST) columns subjected to long-term sustained loading, Thin-Walled Struct. 49 (2011) 1534–1543. [28] C.X. Dong, J.C.M. Ho, Improving interface bonding of double-skinned CFST columns, Mag. Concr. Res. 65 (2013) 1199–1211. [29] H. Huang, L.-H. Han, Z. Tao, X.-L. Zhao, Analytical behaviour of concrete-filled double skin steel tubular (CFDST) stub columns, J. Constr. Steel Res. 66 (2010) 542–555. [30] H. Lu, X.-L. Zhao, L.-H. Han, FE modelling and fire resistance design of concrete filled double skin tubular columns, J. Constr. Steel Res. 67 (2011) 1733–1748. [31] ABAQUS Standard User’s Manual the Abaqus Software Is a Product of Dassault Syste`mes Simulia Corp., Providence, RI, USA, Dassault Syste`mes, Version 6.8, USA, 2008. [32] H. Huang, Behavior of Concrete Filled Double-Skin Steel Tubular Beam-Columns (Doctoral Dissertation), Fuzhou University, Fuzhou, China, 2006 (in Chinese). [33] GB50205-2001, Code for Acceptance of Construction Quality of Steel Structures, China Planning Press, Beijing, 2002 (in Chinese). [34] L.-H. Han, The influence of concrete compaction on the strength of concrete-filled steel tubes, Adv. Struct. Eng. 3 (2) (2000) 131–137. [35] L.-H. Han, X.-L. Zhao, Recent developments in concrete-filled steel tubular structures in China, in: International Conference on Advances in Structures, Sydney, June, 2003, pp. 899–907. [36] L.-H. Han, G.-H. Yao, Experimental behaviour of thin-walled hollow structural steel (HSS) columns filled with self-consolidating concrete (SCC), Thin-Walled Struct. 42 (9) (2004) 1357–1377. [37] L.-H. Han, G.-H. Yao, X.-L. Zhao, Tests and calculations for hollow structural steel (HSS) stub columns filled with self-consolidating concrete (SCC), J. Constr. Steel Res. 61 (9) (2005) 1241–1269. [38] Eurocode 3: Design of Steel Structures – Part 1-1: General Rules and Rules for Buildings, CEN, 2004. [39] P.W. Key, G.J. Hancock, Plastic Collapse Mechanism for Cold-Formed Square Hollow Section Columns. Research Report, No. R526, School of Civil and Mining Engineering, The University of Sydney, Sydney, April, 1986. [40] M. Yu, X. Zha, J. Ye, Y. Li, A unified formulation for circle and polygon concrete-filled steel tube columns under axial compression, Eng. Struct. 49 (2013) 1–10. [41] J. Tang, S. Hino, I. Kuroda, T. Ohta, Modeling of stress-strain relationships for steel and concrete in concrete filled circular steel tubular columns, IEEE J. Solid State Circuits 3 (11) (1996) 35–46. [42] SAA, Steel Structures. Australian Standard AS4100, Sydney, 1998. [43] L.-H. Han, G.-H. Yao, Behaviour of concrete-filled hollow structural steel (HSS) columns with pre-load on the steel tubes, J. Constr. Steel Res. 59 (2003) 1455–1475. [44] Eurocode 3: Design of Steel Structures – Part 1-4: General Rules-Supplementary Rules for Stainless Steel, CEN, 2006. [45] X.-L. Zhao, L.-H. Han, H. Lu, Concrete-Filled Tubular Members and Connections, Taylor & Francis, Spon Press, 2010.

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CFDST short columns formed from carbon steels

3

Notations Roman letters Ac, Asc Ac,nominal ADS Asi, Asi,g Aso, Aso,g Aso,eff D Dc d Ec Es (EI)e fck fcu fc0 fcc0 fsyi ft fyo IDS KL, Le L P PAISC PAISC, mod Pcr, Pe PEC4 PEC4, mod Pi,u Posc,u Ppl,Rd Ppl,Rd,mod Pul,design Pul,Exp Pul,FE

cross-sectional area of sandwiched concrete nominal cross-sectional area of concrete, given by D2
Aso cross-sectional area of a CFDST column gross cross-sectional area of inner steel tubes gross cross-sectional area of outer steel tubes effective cross-sectional area of outer steel tubes diameter/depth of steel tubes in circular/square CFDST columns depth of concrete core diameter of inner steel tube in CFDST columns Young’s modulus of concrete Young’s modulus of steel effective elastic flexural stiffness of CFDST columns characteristic concrete strength, given by 0.67 fcu characteristic cube strength of concrete cylindrical compressive strength of sandwiched concrete effective compressive strength of confined concrete yield strength of inner tubes tensile strength of concrete yield strength of outer tubes moment of inertia of CFDST section effective buckling length physical column length axial load ultimate axial capacity according to the AISC [1] modified AISC formula for ultimate axial capacity elastic critical buckling load ultimate axial capacity according to EC4 [2] modified EC4 formula for ultimate axial capacity capacity of inner tube according to Han et al. [3] compressive capacity of outer tube with sandwiched concrete plastic resistance to axial compression as specified in EC4 [2] modified plastic resistance to axial compression predicted strengths from three design models (Pul, Han, Pul, Prop, 1, and Pul, Prop, 2) ultimate axial strength of column obtained from experiments ultimate axial strength of column obtained from FE analyses

Concrete-Filled Double-Skin Steel Tubular Columns. https://doi.org/10.1016/B978-0-443-15228-3.00007-1 Copyright © 2023 Elsevier Inc. All rights reserved.

46

Concrete-Filled Double-Skin Steel Tubular Columns

Pul, Han Pul, Prop Ppl,

Rd,

strength of square CFDST short columns with inner CHSs, according to Han et al. [3] proposed ultimate axial strengths for square CFDST short columns with inner CHSs, either Pul, Prop, 1 or Pul, Prop, 2 modified plastic resistance of columns

mod

ti to um

thickness of inner tube of CFDST columns thickness of outer tube of CFDST columns lateral deflection at mid-height section of CFDST columns

Greek letters α βc Bs γc εa εc εcc0 εl εc0 λ λp and λr λ χ ζ ρs σc ρ

imperfection factor factor reflecting the confinement effect on concrete ductility larger depth of rectangular cross sections strength reduction factor [4] axial strain in a CFDST column longitudinal compressive concrete strain strain at fcc0 longitudinal strain strain corresponding to the peak stress of concrete (fc0 ) column slenderness ratio or local slenderness ratios following the AISC specification [1] limiting local slenderness ratios according to the AISC specification [1] global column slenderness (relative slenderness) hollow ratio of a CFDST column or buckling reduction factor in EC4 [2] confinement factor, given by (Asofso/Ac, nominalfck) ratio of the cross-sectional area of the steel tube to that of the concrete core longitudinal compressive concrete stress reduction factor for local plate buckling according to EC3 [5]

Abbreviations CFDST CFST CHS F HSC NSC S SHS UHSC VS

concrete-filled double skin tubular concrete-filled steel tubular circular hollow section fully effective cross section high-strength concrete normal strength concrete slender cross section square hollow section ultrahigh-strength concrete very slender cross section

CFDST short columns formed from carbon steels

3.1

47

Introduction

Globally, increasing the height of buildings is one of the possible ways of effectively utilizing the available land resources and comparatively reducing the material price. Accordingly, the traditional reinforced concrete is not the first choice in many aspects. New composite structures are required to achieve structural safety, space efficiency, and cost efficiency at the same time. On this basis, concrete-filled double skin tubular (CFDST) columns may be the solution. Historically, the concept of a CFDST cross section was utilized in marine tunnels [6]. Such a composite cross section was adopted in the Kobe Minatojima Submerged Tunnel in Japan [7]. Recently, CFDST columns have been considered as load-bearing members for viaducts to reduce the self-weight of the construction [8]. More recently, there has been an opportunity for potential change for CFDST columns to act as structural columns in buildings. A CFDST column is constructed using concrete sandwiched between the inner and outer steel tubes. Such inner and outer tubes have either the same or different cross-sectional shapes, such as square outer and square inner, circular inner and circular outer, circular outer and square inner, and square outer and circular inner. Some common combinations [9] are shown in Fig. 3.1. In CFDST columns, the sandwiched concrete and double skin steel tubes compositely interact with each other. The infilled concrete provides lateral support to the steel tubes and prevents the steel tube local buckling of both the inner and outer skins. Both the inner and outer steel tubes provide effective confinement to the sandwiched concrete so that its strength and ductility increase due to the confinement mechanism. Accordingly, the peak axial strength of concentrically loaded circular CFDST short columns is not simply the sum of the values of the concrete and steel materials [10]. The strength and ductility of the sandwiched concrete improve considerably due to the confinement of the steel tubes, especially for circular columns [11]. In addition, the sandwiched concrete can increase both the fire resistance and the local buckling strength of double skin steel tubes by absorbing heat from the steel material and providing lateral support to the tubes [10]. The larger specific heat capacity of concrete allows it to remain at a low temperature during conflagration. Furthermore, the inner and outer steel tubes provide permanent formwork to the infilled concrete. Thus, the construction efficiency of the columns is enhanced. However, in concrete-filled steel tubular (CFST) columns, the concrete core (near the center of the column) makes only an insignificant contribution to their flexural and torsional strengths while the less confining pressure provided by the steel in the elastic stage reduces their strength-to-weight ratios [10]. Thus, introducing the inner steel tube and converting the solid concrete core into a hollow one in a CFSDT column can produce a more effective column (compared to a CFST column) that has a reduced weight with a higher strength-to-weight ratio. This chapter discusses the structural characteristics of CFDST short columns of different combinations of inner and outer steel tubes (circular and square), as shown in Fig. 3.1. The investigation was conducted by finite element (FE) modeling. This FE method has proved to be an effective way for investigating the structural characteristics of CFDST columns under different loading conditions [12–27]. This method can produce certain results that cannot be obtained experimentally, and, more importantly, it can simulate uncommon sections and/or member sizes that are not even

48

Concrete-Filled Double-Skin Steel Tubular Columns

Fig. 3.1 Most common CFDST column cross sections. (A) Circular CFDST: CHS inner and CHS outer; (B) Circular CFDST: SHS inner and CHS outer; (C) Square CFDST: CHS inner and SHS outer; (D) Square CFDST: SHS inner and SHS outer.

available in the market. On the other hand, the available experimental and numerical research studies of CFDST columns are limited [10]. Accordingly, this chapter considers axially loaded columns. Different steel and concrete constitutive material models are adapted from previous research studies and then validated by comparing the calculated results with the available experimental results by Zhao et al. [28]. The best material models are used in the parametric study, which aims at examining the influences of various factors on the behavior of CFDST short columns.

3.2

Circular-circular CFDST columns

3.2.1 FE nonlinear analysis 3.2.1.1 Basic description The FE code ABAQUS [29] was considered to model the current CFDST short columns. The aim was to conduct a load-displacement nonlinear analysis to determine the ultimate axial force, bending moment, and other valuable outputs. This section describes the various aspects of the ABAQUS method, including the material model,

CFDST short columns formed from carbon steels

49

interaction and surfaces, loading, boundary conditions, and element mesh. The geometrical imperfection is not considered in the FE analysis of circular CFDST columns. This is because the effect of imperfection is reduced by the infill concrete, as suggested by Tao et al. [30].

3.2.1.2 Constitutive material models Concrete material In CFDST columns, both the outer and inner skins provide lateral confining pressure to the sandwiched concrete. The major task of a concrete property model is to analyze the material performance of the confined sandwiched concrete. In this research, two different approaches have been used. The first one is uses an unconfined concrete model with a dilation angle, whereas the second one uses a confined concrete model without a dilation angle. Unconfined concrete with a dilation angle The dilation angle allows the concrete to change its volume during deformation. With a “hard contact” interaction between the steel and concrete, the steel tube provides passive confinement to the concrete on ABAQUS [29]. In other words, the confinement is provided by ABAQUS based on the value of the dilation angle. Fig. 3.2 shows a comparison between the input and output concrete models in ABAQUS. The solid line depicts the input unconfined concrete model, whereas the dashed line indicates the concrete output in ABAQUS. During the analysis, the unconfined concrete converts to a confined model by ABAQUS. However, the main dilemma of this method is how to choose the appropriate dilation angles, which range from 20° to 35°, to achieve a similar load-displacement response using the experimental data of different specimens, as this has been found to significantly affect the analysis output (see Fig. 3.3). This figure depicts the analysis results of specimen C3C7 [28], with the definition of materials and dimensions provided later on in Section 3.3.2. Currently, a fixed dilation angle could not be obtained in the validation stage. Thus, this method failed to be adopted in this investigation. 60 50

Stress (Mpa)

40 30 abaqus result 20

input concrete model

10 0

0

0.005

0.01 Strain [mm/mm]

Fig. 3.2 ABAQUS compression results.

0.015

0.02

50

Concrete-Filled Double-Skin Steel Tubular Columns

1400 1200

Axial foece (Kn)

1000 800 35 dila onangle 20 dilai on angle

600 400 200 0 0.00

5.00

10.00

15.00

20.00

Axial displacment (mm) Fig. 3.3 Effect of the dilation angle, using column C3C7 [28].

Confined concrete This method was adopted in several research studies (refer, for example, Hu et al. [31–33], Dabaon et al. [32], and Ellobody [33]. This allows the concrete property model to control the confinement level, and ABAQUS [29] provides no confinement. Fig. 3.4 illustrates the stress-strain relationships of confined concrete. The stress-strain model of confined concrete is divided into three parts. The value of εc is usually in the range of 0.002–0.003. The concrete strain εc is taken as 0.003 in this simulation [34]. The compressive strength of the confined concrete fccand the corresponding strain εcc are determined using Eq. (3.1) and Eq. (3.2), respectively: f cc ¼ f co + kσ lat


σ εcc ¼ εc 1 + 5k lat f co

(3.1)  (3.2)

in which the material parameter k is equal to 4.1 [35]. The concrete in a concrete-filled steel tubular (CFST) column is generally subjected to triaxial compressive stress. Therefore, failure of the confined concrete is characterized by failure of the compressive surface, which expands with an increase in hydrostatic pressure. Therefore, a linear Drucker-Prager yield criterion can be implemented in the FE analysis of the confined concrete (after the stress reaches 0.5fcc). The friction angle and flow stress ratio are set [31–33] as 20° and 0.8, respectively. The first part of the stress-strain curve follows a linear relationship before reaching the limit (0.5fcc). Young’s modulus (Ecc) of concrete is a function of its compressive strength. It is predicted using the equation provided by ACI Committee 318 [34] as follows: Ecc ¼ 4700

pffiffiffiffiffiffi f cc

(3.3)

CFDST short columns formed from carbon steels

f

51

Confined concrete

fcc rk3 fcc Unconfined concrete

fc 0.5 fcc

εc

εcc

11εcc

ε

Fig. 3.4 The stress-strain relationship for the confined concrete.

The second part of the stress-strain curve follows a nonlinear behavior, which starts from the limit (0.5fcc) to the compressive concrete strength ( fcc). The second stage of the stress-strain relationship is modeled using the equations proposed by Saenz [36], which are expressed as: fc ¼

Ecc ε    2  3 ε 1 + ðR + RE
2Þ εcc
ð2R
1Þ εεcc + R εεcc

(3.4)

RE ðRσ
1Þ 1
Rε ð Rε
1Þ 2

(3.5)

in which R¼

RE ¼

Ecc εcc f cc

(3.6)

In Eq. (3.5), Rσ ¼ Rε ¼ 4 can be utilized, which are provided by Hu and Schnobrich [37]. The stress-strain behavior of concrete is modeled using Eq. (3.4) when the concrete strain ε is less than εcc, as demonstrated in Fig. 3.3. For a concrete strain greater than the strain εcc, the softening behavior of concrete is modeled using the linear relationship. The descending stress-strain response of concrete is stopped at stress fc ¼ rk3fcc and strain ε ¼ 11εcc when the factor k3 is used for modeling the postpeak behavior. The factor k3 is multiplied by the reduction parameter r to consider the influence of various compressive strengths of concrete. The reduction parameter r is assumed to be 1.0 for a concrete cubic strength fcu of 30 MPa, whereas it is taken as 0.5 for fcu greater than or equal to 100 MPa. The linear interpolation can be used to predict the reduction parameter r for the concrete strength fcu between 30 and 100 MPa.

52

Concrete-Filled Double-Skin Steel Tubular Columns

The parameter k3 depends on the width-to-thickness ratio (D/t or B/t) and the column’s cross-sectional shape. It is obtained by matching the analysis results with the experimental data via a parametric study [31].

Structural steel material Gardner and Yun [38] have recently proposed the stress-strain relationship of coldformed steel by means of 700 comprehensive coupon test data using the RambergOsgood material model [39]. The material model by Gardner and Yun [38] can be used for predicting the full-range stress-strain curves of cold-formed steel. The experimental study indicates that a circular CFDST column exhibits 0.05 maximum strain. Therefore, the stress-stain relationship of cold-formed structural steel is modeled by means of the Ramberg-Osgood model [39] in the present FE model, which was successfully implemented in an earlier numerical analysis by the current authors [40,41]. It should be noted that the stress-strain model by Gardner and Yun [25] should be employed in the future for the analysis of composite columns with cold-formed steel under large deformation. An engineered stress-strain curve is first obtained using the Ramberg-Osgood model [39]. The predicted engineered stress-strain curve is then converted into a true stress-strain curve as shown in Fig. 3.5. Based on MMPDS-01, the parameter n was obtained using the following equation: ε¼

 n σ σ + 0:002 E Fty

(3.7)

Stress [MPa]

The cold-formed steel in the numerical simulation follows the linear stress-strain relationship up to the yield strength. The model considers the plastic behavior for cold-formed steel beyond the yield strength. Young’s modulus of steel (Es) was assumed to be 203 GPa [42], and Poisson’s ratio (ν) was considered as 0.3.

Strain [mm/mm] Fig. 3.5 Stress-strain response of cold-formed steel [39–42].

CFDST short columns formed from carbon steels

53

3.2.1.3 Interactions between components Three individual components, as shown in Fig. 3.6, were utilized for modeling circular CFDST short columns: the outer and inner steel tubes and the infilled concrete. The interactions between the steel and concrete were determined using the surface, wherein the steel was the master surface and the concrete was the slave surface [18]. In ABAQUS, “normal behavior” and “tangential behavior” were considered to define the interaction property. “Hard contact” and “frictionless” were selected as suboptions, respectively. The slip between the steel and concrete components is ignored in the FE analysis. Therefore, the frictionless contact property for the tangential behavior during surface interaction is selected.

3.2.1.4 Loading and boundary conditions Two reference points (Figs. 3.7 and 3.8) were created to assign the loading and boundary conditions of a column, and a multipoint constraint (MPC) was used to define the constraint between the reference point and the specimen. On the other hand, due to the symmetric problem, only half of a CFDST short column was generated to shorten

Fig. 3.6 Components and FE mesh of a typical CFDST short column.

Fig. 3.7 Multipoint constraint in a FE model.

54

Concrete-Filled Double-Skin Steel Tubular Columns

Fig. 3.8 Symmetry boundary condition and loading condition.

the computation time. The “XSYMM” symmetry boundary condition was applied to the middle of the column. The bottom reference point was fixed for all displacements and rotations, whereas the top reference point was allowed to deform along the longitudinal direction. The displacement control approach, adding uniform displacement to the top reference point, was adopted to simulate axial compression. Fig. 3.8 presents the loading and boundary conditions.

3.2.1.5 FE meshes Three-dimensional, solid, eight-node FE meshes with reduced integration (C3D8R) are utilized in this chapter. This element allows editing the thickness of the CFDST column in the sketch stage, making different geometries of the column possible. All components are independent in meshing. Through convergence studies, comparing ABAQUS results with different mesh sizes, a 9-mm mesh size was applied to the sandwiched concrete and a 10-mm mesh size was applied to the steel tubes. Fig. 3.6 depicts the FE mesh of a typical CFDST short column.

3.2.2 Model verification The FE model described in the previous sections is verified using the experiments conducted by Zhao et al. [28] on circular hollow steel and CFDST columns. Herein, the steel material and the behavior of the double skin composite columns were verified.

CFDST short columns formed from carbon steels

55

3.2.2.1 Steel material verification Zhao et al. [28] conducted a compressive test of one steel tube, the dimensions and material parameters of which are listed in Table 3.1. fy ¼ 454 MPa, fu ¼ 520 MPa and εr ¼ 20% are used to draw the Ramberg-Osgood steel model then the output stress and strain data are used in Abaqus. The material yield stress was taken as the 0.2% proof stress. An 80-MPa stress was selected as the first point of ABAQUS input, and its strain was set to 0.4. A 63-MPa concrete stress was selected as the last point for ABAQUS with a reduced strain of 0.05348. All these stresses were selected after countless attempts of different inputs were made, and the test that was the closest to the experimental test was chosen. In the load-displacement curve, ABAQUS predicted the yield strength and peak strength that were similar to the experimental results and the good agreement in both linear and nonlinear performances, as can be seen in Fig. 3.9. In terms of the deformation shape (Fig. 3.10), there is a buckle ring near the top of the steel tube in both the ABAQUS and experimental results.

3.2.2.2 CFDST column verification The FE model is verified by comparing its predictions with concentrically compressed circular CFDST short columns. The experimental study conducted by Zhao et al. [28] was employed in the verification study. Five specimens were selected from the experimental study, which are summarized in Table 3.2. As depicted, the FE model tends to accurately predict the peak load of concentrically compressed circular CFDST short columns. The mean score of the ultimate strength ratio between the FE analysis and the experimental results is 1.004 with a 0.013 standard deviation (SD) and a 0.013 coefficient of variation (COV). As shown in Fig. 3.11, the FE model accurately expresses the initial stiffness and postpeak behavior of circular CFDST columns. Table 3.1 The material properties of a hollow steel tube. D (mm)

t (mm)

Es (GPa)

fy (MPa)

fu (MPa)

εr (%)

114.5

5.9

191

454

520

20

1000 Axial Force (KN)

800 600 400

realtest

200

ABAQUS

0

0

10

20

30

Axial Displacenment (mm)

Fig. 3.9 Load-displacement of an empty steel tube.

40

56

Concrete-Filled Double-Skin Steel Tubular Columns

Fig. 3.10 Failure mode of an empty steel tube.

Table 3.2 Comparison of the experimental and finite element predictions. Specimen label

D d to ti fy (mm) (mm) (mm) (mm) (MPa)

f’c (MPa)

L Nexp NFE (mm) (kN) (kN)

N exp N FE

C1C7 C3C7 C4C7 C5C8 C6C8 Mean

114.5 48.4 5.9 114.5 48.4 3.5 114.5 48.4 3 165.1 101.8 3.5 165.1 101.8 2.9

63.4 63.4 63.4 63.4 63.4

401 401 401 401 401

0.997 1.015 1.021 0.998 0.991

Standard deviation (SD) Coefficient of variation (COV)

2.8 2.8 2.8 3.1 3.1

433 433 430 395 395

1406 1205 1098 1694 1590

1410 1187 1075 1698 1604

References [28]

1.004 0.013 0.013

The failure mode comparison between experimental and FE predictions is presented in Fig. 3.12, which shows the close agreement of the buckling pattern. Appendix shows the progressive collapse of specimen C6C8.

3.2.3 Parametric study In this investigation, a total of 24 columns were considered to examine the influence of the column hollow ratio, material parameters, and outer and inner steel thicknesses on the characteristics of CFDST short columns. Table 3.3 summarizes the parameters of each specimen. The length of the columns was chosen as 700 mm. The whole parametric study plan was divided into five groups based on different parameters.

1200 1000

C1C7 EXPERIMENT C1C7 ABAQUS

0

10

Axial Force(KN)

Axial Force (KN)

1600 1400 1200 1000 800 600 400 200 0

800 600

C3C7 EXPERIMENT

400

C3C7 ABAQUS

200 0

20

0

5 10 15 Axial Displacement (mm)

Axial Displacement (mm)

1000 800 600

C4C7 EXPERIMENT

400

C4C7 ABAQUS

200 0

0

5

10

15

Axial Force(KN)

Axial Force (KN)

1200

1600 1400 1200 1000 800 600 400 200 0

C6C8 EXPERIMENT C6C8 ABAQUS

0

Axial Force (KN)

5

C5C8 EXPERIMENT C5C8 ABAQUS

0

5 10 15 Axial Displacement (mm)

Fig. 3.11 Load-displacement curves of CFDST short columns.

Fig. 3.12 Failure mode of specimen C6C8.

10

Axial Displacement (mm)

Axial Displacement (mm)

1800 1600 1400 1200 1000 800 600 400 200 0

20

15

Table 3.3 The material and geometrical properties for the parametric study. Outer tube

Inner tube λ

Group

Specimen

D (mm)

to (mm)

1 (HR)

HR1 HR2 HR3 HR4 SF1 SF2 SF3 SF4 OT1 OT2 OT3 OT4 IT1 IT2 IT3 IT4 CF1 CF2 CF3 CF4

219

8.2

48.1

219

8.2

219

219

8.2 6.4 4.8 2.0 8.2

48.1 74.8 112.2 149.6 48.1 61.6 82.1 197.1 48.1

219

8.2

48.1

2 (SF)

3 (OT)

4 (IT)

5 (CF)

d (mm)

ti (mm)

λ

L (mm)

χ

f’c (MPa)

fy (MPa)

26.9 60.3 101.6 139.7 89

4.0 4.5 5.0 5.0 6.0

12.11 24.12 36.58 50.29 26.7

700

0.13 0.30 0.50 0.69 0.44

60

450

60

89

6.0

26.7

700

60

89

6.0 5.0 4.0 3.0 6.0

26.7 32.0 40.1 53.4 26.7

700

0.44 0.43 0.43 0.41 0.44

450 700 1050 1400 450

60

450

700

0.44

60 100 140 180

450

89

700

CFDST short columns formed from carbon steels

59

Group 1, termed “HR,” investigated the effect of the column hollow ratio (χ), defined as d/(D
2to), which ranged from 0.13 to 0.69. With a hollow ratio of 0.69, the CFDST column would behave similarly to an empty steel tube, whereas with a ratio of 0.13, the CFDST column would behave like a concrete-filled single column. In groups SF and CF, the yield stresses of the steel and the concrete strength change, respectively. The maximum yield stress was set as 1400 MPa, which is the highest known strength of steel [43]. The ultrahigh-strength steel is commercially available in Australia and has been utilized by Jiao and Zhao [44] in their experimental study. Groups OT and IT examined the impact of the outer and inner tube thicknesses. All thicknesses and steel tube diameters were chosen from a manufacturing table (i.e., a design capacity table). This type of selection endows the parametric study with a more partial meaning.

3.2.4 FE results and discussion In this section, the FE results and discussion of the parametric studies mentioned earlier are presented. Generally, the overall effect of a load-displacement curve lies on the change between the ultimate strength and ductility. On the other hand, in the moment interaction diagram, the changes occur among the ultimate axial force, balance point, and pure bending moment.

3.2.4.1 Effects of the hollow ratio The hollow ratio determines the amount of the sandwiched concrete in the column and the compressive behavior of CFDST columns. It is worth noting that the hollow ratio in this investigation is controlled by the inner tube’s diameter. Fig. 3.13 reveals that increasing the hollow ratio from 0.13 to 0.3 insignificantly affects the behavior and

6000

Axial force (kN)

5000 4000 3000

X=0.13 X=0.3 X=0.50 X=0.69

2000 1000 0

0

5

10

15

20

25

30

Axial Displacement (mm) Fig. 3.13 Load-displacement curve of CFDST columns with various hollow ratios.

60

Concrete-Filled Double-Skin Steel Tubular Columns

strength of the CFDST short columns. Hence, using columns with extremely small hollow ratios (less than 0.3) would increase the weight of the column without a significant strength increase, so they should not be used in practice. Additionally, it can be observed from the same figure that increasing the hollow ratio (greater than 0.3) decreases the ultimate axial strength of the CFDST columns, whereas the initial stiffness remains the same. For a column with a hollow ratio of 0.3, the ultimate load is 5199 kN, whereas for that with a hollow ratio of 0.69, the ultimate load is 4407 kN. It can be concluded that by increasing the hollow ratio 2.3 times causes the ultimate load to slightly decrease by 15%. However, this does not promote the practical use of CFDST columns with an extremely large hollow ratio (as big as 0.69) because the strength degradation, which occurs after the ultimate load is achieved, is rapid. The reduction in the ultimate axial strength due to an increase of the hollow ratio may also result from a decrease of the sandwiched concrete area. The increase of the hollow ratio from 0.13 to 0.30 and 0.50 reduces the cross-sectional area of the concrete by 7%, 24%, and 47%, respectively.

3.2.4.2 Effects of the thickness of steel tubes In this section, the effects of both inner and outer thickness are presented, from which it has been noticed that they affect the steel’s cross-sectional area and the confinement provided to the infilled concrete. Obviously, changing the steel tube’s thickness changes the steel’s cross-sectional area directly, so the ultimate axial load of the column is influenced. This is because the ultimate axial load of the CFDST columns is generally calculated as the sum of the strengths of the components of the cross section, of which the steel tube’s contribution is the section area times the material yield strength. On the other hand, in the considered confined concrete model, both outer and inner thicknesses were considered to determine the lateral confinement of concrete, shown as follows in Eq. (3.8):      2 D d D f 1 ¼ 8:525
0:166 O
0:00897 + 0:00125 O ti to to      2 D d d + 0:00246 O  0
0:00550 ti ti to

(3.8)

From the load-displacement curves presented in Figs. 3.14 and 3.15, there is an obvious trend that as the steel thickness decreases, both the ultimate axial strength and ductility also decrease. The ultimate load of the outer steel group decreases from 5199 kN to 3309 kN with a 6.2-mm thickness reduction. Similarly, the ultimate load of the inner steel group decreases from 5199 kN to 4158 kN with 3-mm thickness reduction. The reason for not using the same thickness reduction is due to the manufacturing supply, since the minimum thickness of the inner steel tube with a diameter of 89 mm is 3 mm. Thus, it consistency is not achieved in thickness reduction. From Figs. 3.14 and 3.15, it is clear that ductility decreases. For an 8.2-mm outer steel thickness, the column fails at around a 25-mm axial displacement, whereas for a

CFDST short columns formed from carbon steels

61

6000

Axial Force(KN)

5000 4000 3000

Outer steel thickness=8.2 Outer steel thickness=6.4 Outer steel thickness=4.8 Outer steel thickness=2

2000 1000 0

0

5

10 15 Axial Displacement (mm)

20

25

Fig. 3.14 Load-displacement curves for various outer steel thicknesses. 6000

Axial Force (KN)

5000 4000 3000

Inner steel thickness=6 2000

Inner steel thickness=5

1000

Inner steel thickness=4

0

Inner steel thickness=3 0

5

10

15

20

25

Axial Displacement (mm)

Fig. 3.15 Load-displacement curves for various inner steel thicknesses.

2-mm outer steel thickness, the column fails at around a 10-mm axial displacement. Thus, it can be concluded that the ductility is reduced as the outer thickness decreases. A previous research study based on limited experiments [28] has been pointed out that the outer steel thickness has a larger influence on the ultimate axial load than does the inner one. However, from the results of this research, it can be seen that the influence of both the inner and outer steels has no significant difference. Another obvious effect of the steel tube’s thickness, especially the inner steel thickness, is the deformation shape. Fig. 3.16 presents four deformation shapes with different inner tube thicknesses. No buckling takes place in the inner tube, and only one ring buckle is observed in the outer tube for the stockiest inner tube (ti ¼ 6 mm). The buckling

62

Concrete-Filled Double-Skin Steel Tubular Columns

6 mm inner

4 mm inner

5 mm inner

3 mm inner

Fig. 3.16 Deformation shapes for various inner steel thicknesses.

started to occur for the 4-mm inner tube in a “distorted diamond” shape. The inner tube consecutively undergoes inward and outward local bulging, whereas the outer tube develops several discontinuous buckling rings in the middle of the column. For a column composed of a 3-mm inner steel tube, both the inner and outer tubes deformed in a diagonal shape. However, the change of the outer steel thickness only affected the location of the buckling ring in the outer steel tube; it had no effect on the deformation shape of the inner steel tube.

3.2.4.3 Effects of steel and concrete strengths Similar to the thickness of the steel tubes, both steel and concrete strengths also affect the ultimate load, ductility, and deformation shape of CFDST short columns. Previous research studies confirmed that inner steel strength does not have a significant influence on the peak axial strength [9,28], and, thus, only the outer steel strength is considered in this chapter. From Figs. 3.17 and 3.18, it is obvious that with an increase of the strengths of the steel and concrete, the ultimate axial load increases and the effect of the steel strength is larger than that of the concrete strength. In addition, ductility

CFDST short columns formed from carbon steels

63

12000

Axial Force (KN)

10000 8000 6000 4000

Steel yiled strength =450Mpa Steel yiled strength =700Mpa Steel yiled strength =1050Mpa Steel yiled strength =1400Mpa

2000 0

0

5

10 15 Axial Displacement (mm)

20

25

Fig. 3.17 Load-displacement curve for CFDST columns with different steel strengths.

7000 6000

Axial Force (KN)

5000 4000

Concrete Strength =60Mpa

3000

Concrete Strength =100Mpa

2000

Concrete Strength =140Mpa

1000 0

Concrete Strength =180Mpa 0

5

10

15

20

25

Axial Displacement (mm)

Fig. 3.18 Load-displacement curve for CFDST columns with different concrete strengths.

decreases at the same time. It can be explained that a higher strength is always associated with a weaker ductility for a certain material [10]. It should be noted that in a concrete strength group, all different specimens end up with a similar axial force after a 25-mm displacement. By rechecking the ABAQUS stress curve, as the displacement approaches 25mm, it can be observed that the concrete has totally failed and only the steel tubes carry the load. Fig. 3.19 shows that there are relatively no (or at most extremely small) stresses in the infilled concrete. It should be noted that the ultrahigh-strength concrete with 140 MPa and 180 MPa was modeled using the stressstrain relationship proposed by Saenz [36].

64

Concrete-Filled Double-Skin Steel Tubular Columns

Fig. 3.19 Stress distribution in a typical CFDST short column of group CF at 25-mm displacement.

3.3

Circular-square CFDST columns

3.3.1 Innovation and the scope of this section The combination under this investigation is denoted as “CHS + SHS,” which refers to a CHS as the outer tube and a SHS as the inner tube. This combination has seldom been experimentally investigated in the literature, with no FE modeling available. Accordingly, this chapter explores the behavior of CFDST short columns under concentric compressive loads in order to better understand the behavior of such specimens. To understand and predict the performances of these specimens, an FE analysis was generated using the ABAQUS program [29]. Stress-strain curves for both structural steel and concrete infill were identified and selected for the materials in the ABAQUS models. The innovation of this chapter may be summarized as finding the best combination of the utilized constitutive material models for the steel and concrete components forming the current double skin columns. This is carried out, in contrast to most available investigations on double skin columns (see, for example, Hassanein and Kharoob [45]), by first utilizing the concrete model suggested by Pagoulatou et al. [18], which successfully presents the confined concrete in double skin columns. Additionally, the accurate stress-strain relationship of cold-formed steel tubes, by considering the Ramberg-Osgood model [39] that precisely captures their behavior as found by Elchalakani et al. [41], is considered. This is used instead of the bilinear/trilinear models used extensively in the literature to simulate the behavior of such cold-formed tubes, as used by Hassanein and Kharoob [45] and others.

CFDST short columns formed from carbon steels

65

The experiments carried out by Elchalakani et al. [46] were selected to verify the applied methodology. The ultimate axial strengths, axial load-displacement plots, and the final deformed shapes of the models were considered to compare the test specimens with the ABAQUS-modeled ones. Having validated the FE models, a parametric study was then generated by ABAQUS to explore the fundamental behavior of the current columns. This parametric study aimed at examining the effects of the concrete’s compressive strength, steel yield strength, diameter-to-thickness ratio, width-to-thickness ratio, and hollow ratio. The geometry of the CFDST specimens is shown in Fig. 3.1. For circular hollow sections, Do is the diameter of the outer tube and Di is the diameter of the inner tube. For square hollow sections, Bo is the width of the outer tube and Bi the width of the inner tube. to and ti are the wall thicknesses of the outer and inner tubes, respectively. It is relevant to note that for SHSs, the outside corner radius is equal to 2 t for sections with thickness t  3.0 mm and 2.5 t for sections with t > 3.0 mm, as defined in AS1163 [47].

3.3.2 FE modeling 3.3.2.1 General information In order to analyze and better understand the behavior of CFDST columns under compressive load and to simulate these specimens, the FE software ABAQUS [29] was used. To accurately predict the behavior of these specimens, the FE model was divided into three components: the outer steel tube, the inner steel tube, and the concrete infill, which would be assigned different material properties. Therefore, the stress-strain curves of both steel and concrete materials were defined. Moreover, the interaction between the surfaces, the loading and boundary conditions, and the most suitable mesh were selected following the study by Pagoulatou et al. [18].

3.3.2.2 Constitutive material models This section describes the stress-strain relationships between the concrete infill and the structural steel, which provide the best curve fittings when the FE results are compared with the test results. According to Pagoulatou et al. [18], the concrete was defined as confined since the outer and inner tubes of the CFDST columns restrained the concrete filled in between them, whereas the cold-formed steel C350L0 was considered for the steel tubes as used in the experiments carried out by Elchalakani et al. [46]. However, the constitutive models are similar to those described in Section 3.2.1.2.

3.3.2.3 Interaction and surfaces The specimens were divided into three individual components: the outer steel jacket, the inner tube, and the sandwiched concrete. According to Pagoulatou et al. [18], a master surface can penetrate a slave surface, but the opposite cannot happen. Therefore, the interaction between the steel tubes and the concrete infill was defined using surfaces where the steel tubes were treated as the master surfaces and the concrete

66

Concrete-Filled Double-Skin Steel Tubular Columns

infill as the slave surface. In the software ABAQUS, “normal behavior” was selected as a “hard contact.” In addition, two constraints were created at the top and bottom of each model in which the control points were located at the specified reference points, whereas the slave nodes were the cross-sectional areas of the steel tubes and the concrete infill. The friction coefficient (μ) of 0.3 was utilized in this study, which was suggested by Pagoulatou et al. [18].

3.3.2.4 Loading method and boundary conditions A total of four boundary conditions were applied to each CFDST specimen as shown in Fig. 3.20. The first reference point (RP-1) was fixed against lateral displacements (x and y directions) and against all types of rotations. The second reference point (RP-2) was fixed against all degrees of freedom. In the experiments by Elchalakani et al. [46], the load was uniformly distributed using cover plates over the upper surface of the column. Herein, instead of adding cover plates to apply the load, the applied compressive load was specified as a displacement on the first reference point (RP-1) along the longitudinal (z) axis. Finally, in order to decrease the solution time of the FE analysis, a symmetry boundary condition was applied along the longitudinal (z) and transverse (y) axes of the model.

3.3.2.5 Element mesh A three-dimensional FE model, as shown in Fig. 3.21, consists of three parts with a similar mesh size. The approximate global mesh size of the steel tubes and concrete infill was 10 and 9 mm, respectively. The element type for the three parts was selected in a linear geometric order with eight-node elements endowed with reduced integration (C3D8R), as suggested by Elchalakani et al. [41] for the different components forming the columns. A similar mesh has been recently considered by the authors [48].

Fig. 3.20 Loading and boundary conditions of a typical CFDST specimen.

CFDST short columns formed from carbon steels

67

Fig. 3.21 Illustration of an FE mesh of a typical CFDST specimen.

3.3.3 Verification study 3.3.3.1 Data collection The experiments conducted by Elchalakani et al. [46] on circular concrete-filled double skin short columns with SHS inner tubes were selected and modeled in ABAQUS in order to verify the above-selected methodology. Eight specimens were tested in this study, which consisted of eight CHSs and three SHSs. As shown in Table 3.4, the CHS specimens had a diameter-to-thickness ratio varying from 19 to 55, whereas the SHS specimens had a width-to-thickness ratio between 20 and 26. Specimens C1S1–C4S1 shared the same outer diameter of 114.41 mm with different thicknesses and the same inner tube (width and thickness). Specimens C5S2 and C6S2 had a bigger outer diameter of 139.67 mm and the same inner tube (width and thickness). Similarly, specimens C7S3 and C8S3 had a bigger outer diameter of 165.18 mm and the same inner tube (width and thickness) for this group. The lengths of the stub columns and the spacing between the steel tubes were selected using the selection criteria suggested by Elchalakani et al. [46], as follows: 3Do < L < 20r y 

pffiffiffi Di
Bi 2 > 3Sg

(3.9) (3.10)

where Do is the diameter of the outer tube, L is the stub column length, ry is the minimal radius of gyration of the composite cross section, Di is the internal diameter of the CHS, Bi is the overall face width of the SHS, and Sg is the nominal aggregate size used

Table 3.4 CFDST specimens tested by Elchalakani et al. [46]. Dimensions and material properties of the CFDST specimens tested by Elchalakani et al. Dimensions Outer jacket Specimen no.

Do (mm)

to (mm)

C1S1 C2S1 C3S1 C4S1 C5S2 C6S2 C7S3 C8S3

114.41 114.41 114.41 114.41 139.67 139.67 165.18 165.18

5.91 4.66 3.47 2.96 3.42 2.94 3.44 2.90

Material properties Inner jacket

Do/to

Bi (mm)

19.36 24.55 32.97 38.65 40.84 47.51 48.02 56.96

40.14 40.14 40.14 40.14 65.17 65.17 75.29 75.29

ti (mm)

b/ti (b 5 Bi-2ti)

1.80 1.80 1.80 1.80 2.47 2.47 2.90 2.90

20.30 20.30 20.30 20.30 24.38 24.38 23.96 23.96

L (mm)

Spacing between SHS and CHS (mm)

fc (MPa)

fyo (MPa)

fyi (MPa)

401 401 401 401 399 399 400 400

45.82 48.32 50.70 51.72 40.67 41.63 51.82 52.90

63.47 63.47 63.47 63.47 63.47 63.47 63.47 63.47

454 416 453 430 379 357 433 395

492 492 492 492 392 392 400 400

CFDST short columns formed from carbon steels

69

in the concrete mix. Moreover, the corresponding material properties of the composite members were measured during the testing program. Table 3.4 shows the data collected for the development of the FE models of the CFDST specimens using the software ABAQUS. According to Elchalakani et al. [46], the behavior of CFDST stub columns is slightly influenced by the section slenderness of the outer jacket, provided that the inside tube is a fully effective section. The yield slenderness limits for CHSs and SHSs as defined in AS4100 [49] are as follows: 8   Do f y > >  82 : CHS > < to 250 rffiffiffiffiffiffiffiffi λe ¼ > B
2t fy > i > : i  40 : SHS ti 250

(3.11)

3.3.3.2 Data analysis and discussion From the data collection, the dimensions and material properties of the eight CFDST specimens tested by Elchalakani et al. [46] were obtained. Three parameters were considered in the comparison between the experimental results and the modeled ones. First, the ultimate axial strength of the test specimens and the ABAQUS-modeled specimens were recorded and compared as shown in Table 3.5. Second, the axial load-displacement curves from the FE analysis were plotted and compared with the experimentally measured results. Generally, all specimens demonstrated similar postpeak behavior and ultimate loads, as can be seen in Fig. 3.22. Lastly, the final deformations of the test specimens were compared with those obtained from the FE analysis to verify the accuracy of the results, as shown in Fig. 3.23 and Fig. 3.24. Table 3.5 Comparison of the ultimate axial strengths of CFDST specimens obtained from the test results with the FE results. Comparison of the ultimate axial strengths obtained from the test results with FE results. Specimen no.

Pu,exp (kN)

Pu,

C1S1 C2S1 C3S1 C4S1 C5S2 C6S2 C7S3 C8S3 Average

1410 1295 1145 1050 1315 1215 1690 1665 –

1419.97 1300.82 1155.15 1054.80 1358.22 1245.55 1731.04 1719.24 –

FE

(kN)

Pu, exp Pu,FE

0.993 0.996 0.991 0.995 0.968 0.975 0.976 0.968 0.983

70

Concrete-Filled Double-Skin Steel Tubular Columns 1600

Axial load (kN)

Axial load (kN)

1200 1200

800 C1S1 FE 400

800

C2S1 FE

400

C2S1 Exp.

C1S1 Exp. 0

0 0

5

10

15

20

0

5

Axial shortening (mm)

1200

15

20

1200

800

400

Axial load (kN)

Axial load (kN)

10 Axial shortening (mm)

C3S1 FE

800

400 C4S1 FE

C3S1 Exp. C4S1 Exp.

0 0

5

10

15

20

0 0

Axial shortening (mm)

5

10

15

20

Axial shortening (mm)

1200 Axial load (kN)

Axial Load (kN)

1200

800 C5S2 FE

400

800

400

C6S2 FE C6S2 Exp.

C5S2 Exp. 0 0

0 0

5

5

20

10 15 Axial shortening (mm)

10

15

20

Axial shortening (mm)

2000 2000 1600 Axial load (kN)

Axial load (kN)

1600 1200 800

C7S3 FE

400

C7S3 Exp.

1200 800 C8S3 FE 400

C8S3 Exp.

0

0 0

5

10 15 Axial shortening (mm)

20

0

5

10 Axial shortening (mm)

Fig. 3.22 Axial load vs. axial shortening for the verified models.

15

20

CFDST short columns formed from carbon steels

71

Fig. 3.23 Experimental and analyzed failure modes of specimen C2S1.

All CFDST specimens seemed to exhibit a slightly better performance in ABAQUS than in the test experiment. However, the average of the ultimate axial strength ratios was extremely close to unity, meaning that the results obtained from the ABAQUSmodeled specimens are considered highly accurate when compared with the test specimen results. The axial load-displacement relationships for specimens C1S1 and C2S1 showed a similar postpeak behavior and ultimate loads. The comparison of the final shape of these two specimens demonstrated that both the axial shortening and the buckling, which occurred around the same height, are extremely close to the test results. Specimens C3S1 and C4S1 demonstrated a slightly different behavior after the ultimate axial capacity was reached. However, both the ultimate axial capacity and the ultimate load were within 99% of the measured values. Specimen C5S2

72

Concrete-Filled Double-Skin Steel Tubular Columns

Fig. 3.24 Experimental and analyzed failure modes of specimen C6S2 after testing.

showed a significantly different elastic behavior. According to Elchalakani et al. [46], the top and end edges of some steel tubes were not ideally cut, which could have led to unreliable data. Nonetheless, the postpeak behavior and the ultimate load were within 97% of the test results. Finally, specimens C6S2, C7S3, and C8S3 demonstrated a similar behavior for the elastic, plastic, and strain-hardening zones, with load values within 98% of the measured values. However, the initial stiffness from the FE modeling is slightly higher than that obtained experimentally. This may be attributed to the small deformations that occurred in the tests at the beginning of the loading process, with their effect continuing to a load of about 100–150 kN. These deformations at the beginning may be due to the deformations of the loading/supporting plates and the available spaces between them and the specimen, which may be eliminated by loading/reloading the specimen a couple of times under relatively low loads before the main test is started and the readings are recorded. Accordingly, these deformations are not numerically captured. On the other hand, the FE modeling, as can be seen in Fig. 3.23 and Fig. 3.24, successfully captures the deformations obtained experimentally for the inner and outer tubes. Hence, generally, from the comparison between the experimental and FE results, it can be seen that all models showed similar behavior in terms of the ultimate axial strength and ductility. Therefore, the selected methodology to verify the experiments conducted by Elchalakani et al. [46] can be considered suitable for this combination of composite construction.

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73

3.3.4 Parametric study In this parametric study, 20 axially loaded CFDST columns were first investigated to explore their fundamental behavior when examining the effects of various diameterto-thickness ratios, width-to-thickness ratios, material properties, and hollow ratios. Table 3.6 presents a summary of the dimensions and material properties of the specimens adopted and modeled in ABAQUS. There are five groups, which have been created to distinguish between the investigated parameters. The nominal length of all specimens is 700 mm, according to the selection criteria suggested by Elchalakani et al. [46]. The first group, 1 (CS), consists of four CFDST short columns with different concrete strengths, ranging from 60 to 180 MPa. This is based on the successful utilization of the current confined concrete model as confirmed by Pagoulatou et al. [18]. These specimens have an outer diameter of 219.10 mm with a thickness of 8.20 mm and an inner width of 89 mm with a thickness of 6 mm. Such hollow sections are considered compact according to AS4100 [49]. The second group, 2 (SS), examines different steel yield strengths, ranging from 350 to 1400 MPa. The characteristics of the specimens are similar to those forming the first group. The third group, 3 (OJ-T), consists of four specimens having the same outer diameter but with different thicknesses. The diameter-to-thickness ratio of these specimens varies from 45 to 250. The inner tube remains the same while guaranteeing a compact section. The fourth group, 4 (IJ-T), focuses on the effect of the inner tube by varying its thickness. The width-to-thickness ratio of these specimens ranges from 40 to 170. Similarly, the outer tube in this case remains the same while providing a compact section. The last group, 5 (HR), focuses on the effect of the hollow ratio, which varies from 0.1 to 0.6, in order to better realize the compressive behavior of the CFDST short columns when this parameter is considered.

3.3.4.1 Effects of the concrete’s compressive strength CFDST composite short columns were analyzed with different compressive strengths of concrete. In the FE analysis, the concrete’s compressive strength was taken as 60, 100, 140, and 180 MPa, as shown in group 1 “1 (CS)” in Table 3.6. Fig. 3.25 shows the axial load-displacement curves for CFDST specimens with different concrete strengths. The results imply that by increasing the concrete’s compressive strength three times, a 50% increase in the ultimate axial strength can be achieved.

3.3.4.2 Effects of steel yield strength As shown in group 2 “2 (SS)” in Table 3.6, the behavior of CFST specimens was analyzed with various steel yield strengths ranging from 350 to 700, 1050, and 1400 MPa. The latter very high-strength steel has been supported by the recent availability of such steels in Australia [43]. Fig. 3.26 shows the axial load-displacement curves for CFDST specimens with different steel yield strengths. The results show that increasing the steel yield strength considerably improves the axial capacity of CFDST short columns. However, it can be observed that as the steel yield strength increases, the specimens become more brittle, which means that they gain hardness and rigidity,

Table 3.6 Dimensions and material properties of the CFDST specimens for the parametric study. Dimensions and material properties of the CFDST specimens for the finite element analysis. Dimensions Outer jacket

Material properties

Inner jacket Spacing between SHS and CHS (mm)

Hollow ratio (χ ) (Bi/(Do2to)

fc (MPa)

Bi (mm)

ti (mm)

b/ti (b 5 Bi2ti)

37.41 37.41 37.41 37.41

89 89 89 89

6.00 6.00 6.00 6.00

12.83 12.83 12.83 12.83

15.18 15.18 15.18 15.18

700 700 700 700

76.83 76.83 76.83 76.83

0.44 0.44 0.44 0.44

60.00 100.00 140.00 180.00

350.00 350.00 350.00 350.00

26.72 26.72 26.72 26.72

37.41 74.81 112.22 149.63

89 89 89 89

6.00 6.00 6.00 6.00

12.83 12.83 12.83 12.83

15.18 21.47 26.30 30.37

700 700 700 700

76.83 76.83 76.83 76.83

0.44 0.44 0.44 0.44

60.00 60.00 60.00 60.00

350.00 700.00 1050.00 1400.00

4.80 3.00 2.00 0.88

45.65 73.03 109.55 248.98

63.90 102.25 153.37 348.57

89 89 89 89

6.00 6.00 6.00 6.00

12.83 12.83 12.83 12.83

15.18 15.18 15.18 15.18

700 700 700 700

83.63 87.23 89.23 91.47

0.42 0.42 0.41 0.41

60.00 60.00 60.00 60.00

350.00 350.00 350.00 350.00

219.1 219.1 219.1 219.1

8.20 8.20 8.20 8.20

26.72 26.72 26.72 26.72

37.41 37.41 37.41 37.41

89 89 89 89

2.00 1.50 1.00 0.50

42.50 57.33 87.00 176.00

50.29 67.84 102.94 208.25

700 700 700 700

76.83 76.83 76.83 76.83

0.44 0.44 0.44 0.44

60.00 60.00 60.00 60.00

350.00 350.00 350.00 350.00

219.1 219.1 219.1 219.1

8.20 8.20 8.20 8.20

26.72 26.72 26.72 26.72

37.41 37.41 37.41 37.41

50 75 100 125

5.00 5.00 5.00 5.00

8.00 13.00 18.00 23.00

9.47 15.38 21.30 27.21

700 700 700 700

131.99 96.63 61.28 25.92

0.25 0.37 0.49 0.62

60.00 60.00 60.00 60.00

350.00 350.00 350.00 350.00

Group no.

Specimen no.

Do (mm)

to (mm)

1 (CS)

CS1 CS2 CS3 CS4

219.1 219.1 219.1 219.1

8.20 8.20 8.20 8.20

26.72 26.72 26.72 26.72

2 (SS)

SS1 SS2 SS3 SS4

219.1 219.1 219.1 219.1

8.20 8.20 8.20 8.20

3 (OJ-T)

OJ-T1 OJ-T2 OJ-T3 OJ-T4

219.1 219.1 219.1 219.1

4 (IJ-T)

IJ-T1 IJ-T2 IJ-T3 IJ-T4

5 (HR)

HR1 HR2 HR3 HR4

Do/to

λe

λe

L (mm)

fy (MPa)

CFDST short columns formed from carbon steels

75

7000

Fig. 3.25 Axial loaddisplacement curves for CFDST columns with different concrete strengths.

Axial load (kN)

6000 5000 4000 3000

f'c = 60 MPa f'c = 100 MPa f'c = 140 MPa f'c = 180 MPa

2000 1000 0 0

5

10 15 20 Axial shortening (mm)

30

f'y = 350 MPa f'y = 700 MPa f'y = 1050 MPa f'y = 1400 MPa

12000 10000 Axial load (kN)

25

8000

Fig. 3.26 Axial loaddisplacement curves for CFDST columns with different steel yield strengths.

6000 4000 2000 0 0

5

10 15 20 Axial shortening (mm)

25

30

but, at the same time, they lose tensile strength. Specimen SS4, which has a steel yield strength of 1400 MPa, showed that even though a 160% increase in the axial capacity was obtained relative to specimen SS1, the failure mode after the maximum axial strength was reached was sudden and brittle.

3.3.4.3 Effects of the Do/to ratio In order to study the effects of the Do/to ratio on the fundamental behavior of the CFDST short columns, the diameter of the outer tube was kept the same, whereas its thickness was varied, as shown in group 3 “3 (OJ-T)” in Table 3.6. Fig. 3.27 shows the axial load-displacement curves for CFDST specimens with different Do/to ratios. It can be observed that the maximum axial strength of these specimens decreases as the Do/to ratio increases. When Do/to increased from 45.65 to 73.03, 109.55, and 248.98, the ultimate axial capacity decreased by about 10%, 15%, and 22%, respectively. This is probably due to the fact that the cross-sectional area of the outer tube becomes less as the Do/to ratio increases, which means that the specimen cannot resist equal or greater loads. Additionally, the tubes with high Do/to ratios buckle locally at lower loads so that the concrete losses its confinement and tends to fail prematurely.

76

4000

Axial load (kN)

Fig. 3.27 Axial loaddisplacement curves for CFDST columns with different Do/to ratios.

Concrete-Filled Double-Skin Steel Tubular Columns

3000 2000 Do/to = 45.65 Do/to = 73.03 Do/to = 109.55 Do/to = 248.98

1000 0 0

5

10 15 20 Axial shortening (mm)

25

30

3.3.4.4 Effects of the Bi/ti ratio The performance of CFDST specimens was analyzed by examining the influence of the Bi/ti ratios, as shown in group 4 “4 (IJ-T)” in Table 3.6. Fig. 3.28 shows the axial load-displacement curves for CFDST specimens with different Bi/ti ratios. This parameter was studied by varying the thickness of the inner steel tubes while keeping their diameters unchanged. It was found that the Bi/ti ratio has a small effect on the behavior of CFDST composite short columns. The Bi/ti ratio varied from 42.50 to 57.33, 87, and 176, and the maximum axial strength changed insignificantly. This could be due to the fact that the steel cross section provided by the inner tube is much smaller than that of the outer tube, with the latter seeming to control the load. Hence, it is important to recommend decreasing the thickness of the inner tube as much as possible to reduce the weight of the column.

3.3.4.5 Effects of the hollow ratio The hollow ratio (χ), defined as Bi/(Do
2to), is a key parameter that affects the compressive behavior of CFDST columns. Huang et al. [12] found that by increasing the value of χ, the longitudinal stress of concrete obviously decreased for columns with circular sections. According to Huang et al. [12], the maximum concrete stress occurs at the center of the cross section of the sandwiched concrete of the CFDST columns, which has also been confirmed herein in the validation process. Fig. 3.29 shows the axial load-displacement curves for CFDST specimens with different hollow ratios. The results show that as the hollow ratio increases, there is less cross-sectional area of concrete, which, in turn, can affect the axial capacity of CFDST columns. It was found that specimen HR2, which has a hollow ratio of 0.37, showed the best response in terms of the maximum axial strength compared with even cross sections with less χ (i.e., χ ¼ 0.25). It can, therefore, be concluded that increasing the hollow ratio (χ) in seismic zones is of importance, as a decrease in the ultimate load is not significant for χ from 0.25 to 0.62, though this should be checked by conducting further tests under seismic loads. On the other hand, Fig. 3.29 shows that the softening branches of the curves are affected by χ, from which the behavior of the CFDST columns by

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77

Axial load (kN)

4000

Fig. 3.28 Axial loaddisplacement curves for CFDST columns with different Bi/ti ratios.

3000 2000 Di/ti = 42.50 Di/ti = 57.33 Di/ti = 87.00 Di/ti = 176.00

1000 0 0

5

10 15 20 Axial shortening (mm)

25

30

Fig. 3.29 Axial loaddisplacement curves for CFDST columns with different hollow ratios.

5000

Axial load (kN)

4000 3000 2000

= 0.25 = 0.37 = 0.49 = 0.62

1000 0 0

5

10 15 20 Axial shortening (mm)

25

30

decreasing χ approaches the behavior of the CFST columns with a horizontal plateau. The FE results showed that the local buckling of the inner tube (with an increase of χ) reduces the double confinement of the concrete annulus, and, hence, the concrete fails in a brittle manner after reaching the ultimate load of the column.

3.4

Square-square CFDST columns

3.4.1 FE methodology and validation To simulate the behavior of CFDST columns with SHS outer and SHS inner steel tubes, the FE program ABAQUS [29] was used. Once ABAQUS [29] is shown to produce accurate and reliable results, based on previous experimental data [25], the behavior of the FE models generated in the parametric studies is predicted. Accordingly, in this section, a description of the FE modeling methodology used in the current investigation is provided. Generally, the current FE models are based on the model described by Han et al. [50], with some modifications as provided in the following sections.

78

Concrete-Filled Double-Skin Steel Tubular Columns

3.4.1.1 Elements and mesh utilized The thin-walled steel tubes in CFST columns are generally discretized by shell elements (S4R) to capture the outward local buckling modes induced by the lateral expansion of the infilled concrete. However, it is noted that the size of the shell element is larger than the tube thickness. This affects the discretization of curved surfaces near the corners, especially the interaction between the concrete core and the steel tube. On the other hand, a solid element (C3D8R) captures both the effective mesh at contact surfaces and the deflected shape of the steel tubes [51–53]. Herein, each of the three parts forming the current CFDST short columns (outer steel tube, inner steel tube, and concrete) was produced using a solid element. In particular, an eight-node element endowed with reduced integration (C3D8R), as suggested by Elchalakani et al. [41], was considered. However, in the current investigation, preliminary models were run using a shell element for the steel tubes in order to reduce the computation time. The results obtained from the preliminary models were not effectively found to reduce the solution time and, hence, the solid extrusion method was adopted. Fig. 3.30 shows a three-dimensional FE model of a typical CFDST column, in which an approximate global mesh size of the steel tubes and concrete infill was 10 and 9 mm, respectively.

3.4.1.2 Step type Preliminary models were generated using a static general step. This, however, failed to produce accurate results compared to the test specimens [25]. This is attributed to the fact that this step type had difficulty converging due to contact or material complexities, which results in a large number of iterations. Instead, the compression step used throughout each of the ABAQUS models was a dynamic explicit one. Using this step,

Fig. 3.30 Meshing methodology for a typical CFDST column.

CFDST short columns formed from carbon steels

79

it is observed that the computation time is obviously less than that using the static general step, as the new system of equations is solved without iterations and the update of the system matrices is executed at the end of each time step. The inputs for this step were introduced under the mass scaling tab. This scaling took place throughout the whole model from the beginning of the step with a factor of 10. There was no target time increment. It is worth noting that for compatibility with the dynamic explicit step, only half of the cross section of each column was used (see Fig. 3.30).

3.4.1.3 Interactions The interactions used in the ABAQUS models were surface-to-surface interactions. Each model required two interactions. The first was between the outer tube and the concrete section in which the inner faces of the outer tube were the master surface and the outer faces of the concrete were the slave surface. Similarly, the second interaction occurred between the inner concrete faces (master surface) and the outer faces of the inner tube (slave surface). In the normal direction, a contact pressure-overclosure model was used, and the “normal behavior” was selected as a “hard contact.” In the directions tangential to the surface, the Coulomb friction model was considered. More information on the effect of the friction in axially loaded stub tubed columns is provided by Liu et al. [54]. The interaction component of the model was also used to create reference points at each end of the column. The first reference point (RP1) was located at the center of the cross section at the end of the column opposite the origin (see Fig. 3.31). The second reference point was therefore positioned at the origin. Both points were set as MPC constraints with the cross section of the steel tubes and the concrete section becoming the slave nodes.

3.4.1.4 Boundary conditions Fig. 3.31 shows the boundary conditions used in the current FE models. As can be seen, a total of four boundary conditions were used for each ABAQUS model. The first condition fixed RP2 at the origin using the displacement/rotation type. Conversely, the second boundary condition was used to enable movement of RP1, also

RP-2

RP-1

Fig. 3.31 Boundary conditions and RPs for a typical CFDST column.

80

Concrete-Filled Double-Skin Steel Tubular Columns

using the displacement/rotation type. Compression of the column was introduced through the third boundary condition, which set the value of U3 to
20. Finally, the fourth boundary condition was used to complete the symmetry of the column in the direction of the x-axis. It is worth noting that the above-described loading ensures that the load is evenly distributed over the upper cross section of the axially loaded composite column; for other loading conditions, the paper by Zhou et al. [55] is worth a read.

3.4.1.5 Constitutive models of the sandwiched concrete The stress-strain relationship for structural steel is similar to that provided in “Structural steel material” section. On the other hand, two models were checked in the concrete validation process in order to determine the most accurate constitutive model for the sandwiched concrete. The first was the Mander model modified for the double SHS geometry as suggested by Zhao et al. [26], termed hereafter as the “Zhao model.” For the sake of consistency with colleagues investigating CFDST columns with CHS geometries, the second concrete model used by Pagoulatou et al. [18], hereafter referred to as the “Pagoulatou model,” was also considered in this validation process. The load-axial deflection curves produced by ABAQUS [29], using both concrete models mentioned earlier, were compared with the experimental specimens tested by Zhao and Grzebieta [25]. It is worth noting that the concrete material is treated as plastic with the Drucker-Prager option [56]. Hence, the angle of friction and the flow stress ratio can be set to 20° and 0.8, respectively [18].

The Zhao model The concrete model proposed by Zhao et al. [26] consists of the following series of equations:   f cc

ε εcc

rm  r m

(3.12)


   f yo t f cc ¼ f c 1 + o Bo fc

(3.13)


  f εcc ¼ εco 1 + 5 cc
1 fc

(3.14)

σ concrete ¼

rm
1 +

εco ¼ 0:002 + 0:001 rm ¼

Ec Ec
E sec

ε εcc

  f c
20 80

(3.15)

(3.16)

CFDST short columns formed from carbon steels

Ec ¼ 3320 E sec ¼

81

pffiffiffiffi f c + 6900

(3.17)

f cc εcc

(3.18)

This model is graphically represented in Fig. 3.32 for the four pairs of experimental specimens tested by Zhao and Grzebieta [25].

The Pagoulatou model The concrete model proposed by Pagoulatou et al. [18], as shown in Fig. 3.4, consists of the following series of equations: f cc ¼ f c + k1 f 1 where k1 ¼ 4:1

(3.19)

Ref. [35]   f εcc ¼ εc 1 + k2 1 where k2 ¼ 20:5 fc

(3.20)



    2 Bo Bi B f 1 ¼ 8:525
0:166
0:00897 + 0:00125 o to ti to     2 B Bi B + 0:00246 o
0:0055 i  0 to ti ti

(3.21)

100 90

Stress (MPa)

80 70 60

CS1S5

50

CS2S5

40 30

CS3S5

20

CS4S5

10 0

0

0.02

0.04

0.06

0.08

0.1

Strain Fig. 3.32 Zhao concrete model’s [26] stress-strain curves of the experimental specimens [25].

82

Concrete-Filled Double-Skin Steel Tubular Columns

     2 f1 B B B ¼ 0:01844
0:00055 o + 0:0004 i + 0:00001 o f yi to ti to     2 B Bi B + 0:00001 o
0:00002 i to ti ti      2 f1 Bo Bi B ¼ 0:01791
0:00036
0:00013 + 0:00001 o f yo to ti to     2 B Bi B + 0:00001 o
0:00002 i to ti ti σ concrete ¼

Ec ¼ 4700

1 + ð R + R E
2Þ

  ε εcc

Ec ε
ð2R
1Þ

 2 ε εcc

pffiffiffiffiffiffi f cc

 3 +R

ε εcc

(3.22)

(3.23)

(3.24)

(3.25)

Hu and Schnobrich [57]: RE ð Rσ
1 Þ 1
where Rσ ¼ 4 and Rε ¼ 4 Rε ð Rε
1Þ 2 Eε RE ¼ c cc f cc

R¼

(3.26) (3.27)

In this model, the last point on the concrete stress-strain curve is estimated at a stress given by the expression rk3fcc, which occurs at a strain value of 11εcc. In this expression, r is the reduction factor taken as 1.0 for concrete strengths of 30 MPa and below and as 0.5 for concrete strengths of 100 MPa and above. A linear interpolation is used for concrete strengths between 30 MPa and 100 MPa. The parameter k3 is given by the following expression:      2 Bo Bi B k3 ¼ 1:73916
0:00862
0:04731 + 0:00036 o to ti to     2 B Bi B + 0:00134 o (3.28)
0:00058 i  0 to ti ti To account for the effects of the column size, concrete quality, and loading rate on the unconfined concrete’s compressive strength (fc), a slight modification for both models [18,26] has been undertaken herein, similar to the one considered in the study by Hassanein et al. [9], which investigated square CFDST columns with inner circular tubes. According to this modification, the unconfined concrete’s compressive strength has been reduced to the value γ cfc, where γ c is the strength reduction factor suggested by Liang [4], which is a function of the depth of the concrete core (Dc) as follows: γ c ¼ 1:85Dc
0:135

ð0:85  γ c  1:0Þ

(3.29)

CFDST short columns formed from carbon steels

83

3.4.1.6 Validation of the FE model Validation of the current models involves comparisons of the previous experimental specimens of Zhao and Grzebieta [25] with the corresponding ABAQUS model, considering both concrete models mentioned earlier. Zhao and Grzebieta [25] tested eight specimens, of which two were replicates, to ensure the accuracy of the test procedure. Herein, comparisons between the experimental and the FE modeling are made by considering the ultimate loads, the load-axial displacement curve, and the observed failure mechanism. Table 3.7 provides a comparison between the experimental ultimate loads (Pul, Exp) and the FE models, considering the concrete Zhao model [26] (Pul, FE,Z) and the Pagoulatou model [18] (Pul, FE, P). However, this table shows that both constitutive models of concrete capture the ultimate load of the CFDST columns properly. On the other hand, Fig. 3.33 shows the load-axial deflection relationships for the columns, considering the experimental and FE responses. To the left of the figure, a comparison between the experiments and those models considering Zhao’s concrete constitutive model is shown [26], whereas a comparison with the Pagoulatou model [18] is shown on the right. Overall, both concrete constitutive models [18,26] accurately provide the experimentally recorded load-axial deflection relationships. For all the specimens, using both the concrete constitutive models [18,26] the typical experimental behavior exhibited by the CFDST columns until the ultimate load is reached was determined; however, the postultimate load stage is not well-presented by the Pagoulatou concrete model [18] for columns CS3S5 and CS4S5 that are characterized by their high plate slenderness ratios (Bo/to  33). As can be observed, this model [18] shows a higher postultimate load stage compared to the experiments. This could be attributed to the difference in the postpeak portion of the stress-strain models; while it is curved (with a concave shape) in the Zhao model [26], it is a straight line in the Pagoulatou model [18]. Hence, the Zhao model [26] fits the experimental

Table 3.7 Nominal dimensions of the test specimens [25] and comparisons between the experimental and FE ultimate loads. Bo Specimen [mm]

to [mm]

Bi [mm]

ti [mm]

Pul,Exp [kN]

Pul,FE,Z [kN]

Pul,FE,P [kN]

Pul,FE,Z Pul,Exp

Pul,FE,P Pul,Exp

CS1S5A CS1S5B CS2S5A CS2S5B CS3S5A CS3S5B CS4S5A CS4S5B Average

6.0 6.0 4.0 4.0 3.0 3.0 2.0 2.0

50

2.0

1545 1614 1194 1210 1027 1060 820 839

1522 1522 1189 1189 1037 1037 824 824

1578 1578 1197 1197 1042 1042 830 830

0.99 0.94 1.00 0.98 1.01 0.98 1.00 0.98

1.02 0.98 1.00 0.99 1.01 0.98 1.01 0.99

100

Standard deviation

0.99 1.00 0.021 0.016

84

Concrete-Filled Double-Skin Steel Tubular Columns

results more accurately. Despite the insignificance of the postultimate stage in design, the Zhao model [26] was selected for the parametric studies based on its accuracy across all behavioral loading stages. To further expand on the reason for selecting this model, the failure modes of both the outer and inner steel tubes observed from the ABAQUS models, as displayed in Figs. 3.35–3.38, were considered. The outer tube’s deformation shape was consistent across each of the four specimens tested, showing all faces of the tube bulging outward as seen in the corresponding experimental tests. On the other hand, the inner tube exhibited two main deformation patterns. There was a negligible change to the inner tube in specimens CS1S5 (Fig. 3.34) and CS2S5 (Fig. 3.35), whereas specimens CS3S5 (Fig. 3.36) and CS4S5 (Fig. 3.37) buckled in the same manner as their experimental counterparts (see the circles added to these figures). Based on these comparisons, it can be concluded that the concrete model proposed by Zhao et al. [26] produced accurate and reliable results.

Zhao model

Pagoulatou model

1800

1800

1600

1600

1400

1400

1200

1200

Load (kN)

Load (kN)

(1) CS1S5

1000 800

800 600

600 Experimental A Experimental B Finite Element

400 200 0

1000

0

5

10

Experimental A Experimental B Finite Element

400 200 0

15

0

5

10

15

Axial Deflec on (mm)

Axial Deflec on (mm)

1400

1400

1200

1200

1000

1000

Load (kN)

Load (kN)

(2) CS2S5

800 600 Experimental A

400

0

10

Axial Deflec on (mm)

Experimental A Experimental B

200

Finite Element 0

600 400

Experimental B

200

800

20

0

Finite Element 0

10

20

Axial Deflec on (mm)

Fig. 3.33 Comparisons between the experimental and FE load-axial deflection relationships. (1) CS1S5; (2) CS2S5;

CFDST short columns formed from carbon steels

85

1200

1200

1000

1000

800

800

Load (kN)

Load (kN)

(3) CS3S5

600 Experimental A

400

0

10

Experimental B

200

Finite Element 0

Experimental A

400

Experimental B

200

600

0

20

Finite Element 0

Axial Deflec on (mm)

10

20

Axial Deflec on (mm)

900

900

800

800

700

700

600

600

Load (kN)

Load (kN)

(4) CS4S5

500 400 300

400 300

Experimental A

200

0

Finite Element 10

Axial Deflec on (mm)

Fig. 3.33—Cont’d

Experimental A Experimental B Finite Element

200

Experimental B

100 0

500

100 20

0

0

10

20

Axial Deflec on (mm)

(3) CS3S5; (4) CS4S5. Zhao model [26]; Pagoulatou model [18].

3.4.2 Parametric studies A total of 20 square CFDST short columns with inner SHSs were analyzed to consider the effects of their dimensions and material properties (Table 3.8). These were divided into five groups of four specimens within each group, independently investigating the effect of a given parameter. In these parametric studies, the steel and concrete materials have values ranging from normal to very high-strength [43,58]. The very high-strength steel has been supported by the recent availability of such steels in Australia [43], whereas the very high-strength concrete is available globally [58]. It is worth pointing out that the values of both fc and fy should be compatible. This has, however, been ensured following the recommendations of Liew et al. [58] on the matching grades of steel and concrete suitable for use in CFST columns. From this analysis, load-axial deflection curves were obtained and strength-to-weight ratios were calculated for each column.

86

Concrete-Filled Double-Skin Steel Tubular Columns

S, Mises (Avg: 75%) +5.478e+02 +5.022e+02 +4.565e+02 +4.109e+02 +3.652e+02 +3.196e+02 +2.739e+02 +2.283e+02 +1.827e+02 +1.370e+02 +9.138e+01 +4.574e+01 +9.935e-02

S, S33 (Avg: 75%) +9.001e+01 +1.947e+01 -5.106e+01 -1.216e+02 -1.921e+02 -2.627e+02 -3.332e+02 -4.037e+02 -4.742e+02 -5.448e+02 -6.153e+02 -6.858e+02 -7.564e+02

Fig. 3.34 FE final deformation shapes of specimen CS1S5: typical to experiment CS1S5B.

3.4.2.1 Group 1: Effects of the outer tube’s thickness The first group of generated specimens investigated the impact of reducing the thickness of the outer steel tube on the overall compressive behavior of the column. The thickness was reduced to create outer steel tubes with slenderness ratios ranging from 51.6 (specimen OT1) to 292.2 (specimen OT4). The results of this group of testing are presented in Fig. 3.38 and Table 3.9.

CFDST short columns formed from carbon steels

87

S, Mises (Avg: 75%) +3.929e+02 +3.602e+02 +3.274e+02 +2.947e+02 +2.619e+02 +2.292e+02 +1.965e+02 +1.637e+02 +1.310e+02 +9.823e+01 +6.548e+01 +3.274e+01 +0.000e+00

S, S33 (Avg: 75%) +3.999e+01 +1.791e+01 -4.168e+00 -2.625e+01 -4.833e+01 -7.041e+01 -9.249e+01 -1.146e+02 -1.366e+02 -1.587e+02 -1.808e+02 -2.029e+02 -2.250e+02

Fig. 3.35 FE final deformation shapes of specimen CS2S5: typical to experiment CS2S5A.

Fig. 3.38 shows a significant reduction in the capacity of the columns as the slenderness ratio of the outer tube is increased (i.e., the thickness of the outer tube is reduced). This is a logical outcome, which can be attributed to the reduction in concrete confinement as the outer tube’s slenderness ratio increases. As the thickness of the outer tube is reduced, there is a greater axial deflection in the tube prior to failure. The greater the deflection of the steel tube, the greater the reduction in the mean compressive strain of the concrete, which, in turn, decreases the effect of confinement in the concrete section. However, the stiffness of the curves shows an insignificant increase as the tube’ thickness increases, and the residual strength part remaining after the ultimate load is reached seems parallel to each other.

88

Concrete-Filled Double-Skin Steel Tubular Columns

S, Mises (Avg: 75%) +3.929e+02 +3.602e+02 +3.274e+02 +2.947e+02 +2.619e+02 +2.292e+02 +1.965e+02 +1.637e+02 +1.310e+02 +9.823e+01 +6.548e+01 +3.274e+01 +0.000e+00 Formation of both outward and inward folding mechanisms typical to experimental observations

S, S33 (Avg: 75%) +3.821e+01 +7.637e+01 -3.669e+01 -7.414e+01 -1.116e+02 -1.490e+02 -1.865e+02 -2.239e+02 -2.614e+02 -2.988e+02 -3.363e+02 -3.737e+02 -4.112e+02

Fig. 3.36 Final deformation shapes of specimen CS3S5: typical to experiment CS3S5B [8].

As this outer tube’s thickness decreases, however, so does the weight of the column, given that less steel is being used. Table 3.9 presents this reduction in the weight of the column across the four specimens and the corresponding strengthto-weight ratios. It shows that as the thickness of the outer tube is reduced, the strength-to-weight ratio of the column also decreases. This indicates that the decline in the capacity of the column outweighs the reduction in its weight. To optimize the

CFDST short columns formed from carbon steels

89

S, Mises (Avg: 75%) +3.929e+02 +3.602e+02 +3.274e+02 +2.947e+02 +2.619e+02 +2.292e+02 +1.965e+02 +1.637e+02 +1.310e+02 +9.823e+01 +6.548e+01 +3.274e+01 +0.000e+00 Formation of both outward and inward folding mechanisms typical to experimental observations

S, S33 (Avg: 75%) +4.108e+01 +1.992e+01 -1.230e+00 -2.238e+01 -4.353e+01 -6.469e+01 -8.584e+01 -1.070e+02 -1.281e+02 -1.493e+02 -1.705e+02 -1.916e+02 -2.128e+02

Fig. 3.37 FE final deformation shapes of specimen CFS4S5: typical to experiment CS4S5A [8].

strength-to-weight ratio of the column, Table 3.9 confirms that reducing the thickness of the outer tube is an inefficient method. The reduction in column capacity is too significant for the benefit of the weight reduction to overcome, and, as a result, the strength-toweight ratio of the column declines as the slenderness ratio of the outer steel tube increases.

Table 3.8 Details of the generated parametric studies. Outer tube

Inner tube

Group

Specimen

Bo [mm]

to [mm]

λ

1 (OT)

OT1 OT2 OT3 OT4 IT1 IT2 IT3 IT4 HR1 HR2 HR3 HR4 CS1 CS2 CS3 CS4 SS1 SS2 SS3 SS4 E1 E2 E3 E4

219.1

219.1

4.8 3.0 2.0 0.88 8.2

51.64 84.05 127.3 292.2 29.25

219.1

8.2

29.25

219.1

8.2

29.25

219.1

8.2

219.1

8.2

29.25 41.36 50.66 58.50 29.25

2 (IT)

3 (HR)

4 (CS)

5 (SS)

6 (E)

ti [mm]

λ

L [mm]

χ

89

6.0

15.18

700

60

350

–

89

50.29 67.84 102.9 208.2 10.06 13.90 12.51 13.67 15.18

700

60

350

–

21 55 88 122 89

2.0 1.5 1.0 0.5 2.0 4.0 7.0 9.0 6.0

0.42 0.42 0.41 0.41 0.44

60

350

–

700

0.10 0.27 0.43 0.60 0.44

350

–

89

6.0

700

0.44

6.0

700

0.44

60

350 700 1050 1400 350

–

89

15.18 21.47 26.30 30.37 15.18

60 100 140 180 60

Bi [mm]

700

fc [MPa]

fy [MPa]

Ecc. [mm]

13.69 27.39 54.78 109.55

CFDST short columns formed from carbon steels

91

5000 4500 4000

Load (kN)

3500 3000

OT1

2500

OT2

2000

OT3

1500

OT4

1000 500 0

0

5

10

15

20

25

Axial Deflec on (mm) Fig. 3.38 Load-axial deflection curves for group 1 specimens. Table 3.9 Strength-to-weight ratios for group 1 specimens. Specimen

Pul, FE [kN]

Weight (kg)

Strength-to-weight ratio (kN/kg)

OT1 OT2 OT3 OT4

4464.6 3833.5 3587.6 3290.6

91.1 86.8 84.3 80.9

49.0 44.2 42.6 40.7

3.4.2.2 Group 2: Effects of the inner tube’s thickness The second test group investigated the effects of reducing the thickness of the inner steel tube. Across the four specimens tested, the inner tube’s thickness was reduced to produce tubes with slenderness ratios ranging from 50.3 (specimen IT1) to 208.2 (specimen IT4), and the results of this test group are displayed in Fig. 3.39 and Table 3.10. Fig. 3.39 and Table 3.10 illustrate a minor reduction in the column capacity as the thickness of the inner tube is reduced. Again, this is to be expected, given that the inner tube contributes to the confinement of the concrete, albeit to a lesser extent than the outer tube. As the thickness of the inner tube is reduced, it experiences a more significant lateral deflection prior to failure. The greater this deflection, the lower the compressive strain in the concrete and the lower the concrete confinement. This effect is less notable than what was observed with the group 1 specimens because the outer tube contributes more prominently to the amount of steel in the column and hence to the overall confinement of the concrete. The trend in the two groups of models, however, is the same; increasing the slenderness ratio of the inner steel tube reduces the overall capacity of column. Nevertheless, the load-axial deflection curves are almost the same for all the columns with different inner tube thicknesses in terms of the initial stiffness and the residual strength after the ultimate load is reached.

92

Concrete-Filled Double-Skin Steel Tubular Columns

6000

Load (kN)

5000 4000 IT1 3000

IT2 IT3

2000

IT4

1000 0

0

5

10

15

20

25

Axial Deflec on (mm) Fig. 3.39 Load-axial deflection curves for group 2 specimens. Table 3.10 Strength-to-weight ratios for group 2 specimens. Specimen

Pul,FE [kN]

Weight (kg)

Strength-to-weight ratio (kN/kg)

IT1 IT2 IT3 IT4

5021.2 4943.6 4834.0 4641.8

91.1 90.2 89.3 88.3

55.1 54.8 54.1 52.6

The reduction in the inner tube’s thickness also brings about a decline in the weight of the column. However, Table 3.10 shows that despite this improvement in the weight of the column, the strength-to-weight ratio of the columns steadily decreases as the inner tube’s thickness is reduced. Although the magnitude of this decline is not as considerable as that observed for group 1 specimens, the trend remains that the reduction in the weight of the column is not worth the cost of the overall capacity. As was observed with the outer tube, increasing the slenderness ratio of the inner steel tube is not an effective way to improve the strength-to-weight ratio of the column. Hence, the inner tube’s thickness might be taken as least as possible in order to reduce the cost of the column in practice.

3.4.2.3 Group 3: Effects of the hollow section ratio The four specimens tested in group 3 were used to investigate the effects of the hollow section ratio (χ) of the columns. This was carried out by increasing the width of the inner steel tube across the four specimens while the other dimensions remained constant. The hollow section ratio varied from 0.1 (specimen HR1) to 0.6 (specimen HR4). The results of these tests are shown in Fig. 3.40 in terms of the load axialdeflection curves and in Table 3.11 as the strength-to-weight ratios. Fig. 3.40 shows

CFDST short columns formed from carbon steels

93

6000 5000

Load (kN)

4000 HR1

3000

HR2 HR3

2000

HR4

1000 0

0

5

10

15

20

25

Axial Deflec on (mm) Fig. 3.40 Load axial-deflection curves for group 3 specimens. Table 3.11 Strength-to-weight ratios for group 3 specimens. Specimen

Pul,FE [kN]

Weight (kg)

Strength-to-weight ratio (kN/kg)

HR1 HR2 HR3 HR4

5364.7 5414.8 5571.3 5638.0

100.9 99.6 98.3 94.8

53.2 54.4 56.7 59.5

a positive correlation between the hollow ratio and the ultimate capacity of the square CFDST columns with inner SHSs. As the hollow ratio is increased, the behavior of the column shifts from that of a traditional CFST column to a more conventional CFDST column. The significance of the hollow ratio is the position of the maximum concrete stress. As the hollow section ratio increases, this maximum stress moves from the inner steel tube to the center of the concrete section, which, in turn, improves the overall capacity of the column. An additional benefit of the increased hollow section ratio is the reduced weight of the column, given the volume of concrete removed from the central core of the column. It is clear that increasing the width of the inner steel tube results in less concrete in the column, which significantly reduces the weight of the column. This, besides shifting the position of the maximum concrete stress to the concrete section, has a twofold effect on the strength-to-weight ratio of the column. Although the initial stiffness remains the same, it is worth pointing out that increasing the χ ratio provides a higher residual resistance after failure, which would be of importance in case of overloading collapse. As shown in Table 3.11, increasing the hollow section ratio of the column from specimen HR1 to HR4 increases the capacity of the column while reducing its overall weight. Across the four specimens, the strength-to-weight ratio is improved by almost 12% as the hollow ratio is varied from 0.1 to 0.6. This indicates that altering the hollow

94

Concrete-Filled Double-Skin Steel Tubular Columns

ratio of CFDST columns is an effective way of improving the capacity and the strength-to-weight ratio of the column, which is opposite to the effects of the previous two key factors.

3.4.2.4 Group 4: Effects of the concrete’s compressive strength Group 4 test specimens investigated the influence of the concrete strength on the general behavior and the ultimate capacity of the current CFDST columns. The strength of the concrete used in the columns was increased from 60 MPa (specimen CS1) to 180 MPa (specimen CS4). The results of these tests are shown in Fig. 3.41 and Table 3.12. The curves displayed in Fig. 3.41 present an obvious result; as the strength of the concrete is increased, so is the ultimate capacity of the column. The important outcome from this series of tests, however, is the efficiency of this increase in the concrete strength calculated in Table 3.12. When compared with specimen CS1 (concrete strength of 60 MPa), specimen CS2 produces a 23.8% increase in the ultimate capacity, despite the 66.7% increase in the strength of the concrete used in its construction.

10000 9000 8000

Load (kN)

7000 6000

CS1

5000

CS2

4000

CS3

3000

CS4

2000 1000 0

0

5

10

15

20

25

Axial Deflec on (mm) Fig. 3.41 Load-axial deflection curves for group 4 specimens. Table 3.12 Concrete strength efficiency for group 4 specimens.

Specimen

Capacity (kN)

Increase in capacity (%) (1)

Increase in concrete strength (%) (2)

(1)/(2)

CS1 CS2 CS3 CS4

5453.7 6750.8 8139.4 9125.0

– 23.8 49.2 67.3

– 66.7 133.3 200.0

– 0.355 0.369 0.337

CFDST short columns formed from carbon steels

95

This trend is repeated in specimens CS3 (133.3% stronger concrete) and CS4 (200% stronger concrete), which exhibit ultimate capacity increases of only 49.2% and 67.3%, respectively. Moderating these figures reveals an average efficiency of 35.4% across the four specimens. Given the added expense incurred by increasing the strength of the concrete, an efficiency of approximately 35% indicates that this is not a worthwhile method of improving the overall capacity of CFDST columns. Another trend that can be detected from the axial-load deflection curve is the method of failure of the columns. As Fig. 3.41 shows that as the strength of the concrete is increased, so is the peak point on the curve. However, the postpeak behavior of the curve shows a rapid decline in column capacity, suggesting brittle failure. From a construction perspective, this is a less than favorable result. This graph indicates that once the peak capacity of the column is reached, any additional loading applied to the column will bring about an extremely sudden failure with limited warning. Physically, this could result in the concrete cracking abruptly and potentially shattering, should the applied loads be great enough. Based on the curves in Fig. 3.41, this trend has become increasingly prominent with stronger concrete and presents a possible field for future experimental investigation.

3.4.2.5 Group 5: Effects of steel strength The four specimens in group 5 were used to test the effects of increasing the yield stress of the steel tubes used in the current CFDST columns with both SHSs. The steel strength was increased from 350 MPa (specimen SS1) to 1400 MPa (specimen SS4). The results of these tests are shown in Fig. 3.42 and Table 3.13. The curves shown in Fig. 3.42 demonstrate a similar trend to that of the group 4 specimens, whereby an increase in steel strength significantly improves the capacity of the CFDST columns. As shown in Table 3.13, however, this increase in capacity is relatively inefficient when compared to the corresponding increase in steel strength. 14000 12000

Load (kN)

10000 8000

SS1

6000

SS2 SS3

4000

SS4 2000 0

0

5

10

15

20

Axial Deflec on (mm) Fig. 3.42 Load-axial deflection curves for group 5 specimens.

25

96

Concrete-Filled Double-Skin Steel Tubular Columns

Table 3.13 Steel strength efficiency for group 5 specimens.

Specimen

Capacity (kN)

Increase in capacity (%) (1)

Increase in steel strength (%) (2)

(1)/(2)

SS1 SS2 SS3 SS4

5453.7 8639.7 10,977.6 12,655.1

– 58.4 101.3 132.0

– 100.0 200.0 300.0

– 0.584 0.507 0.440

Across specimens SS2, SS3, and SS4, the steel strength is increased from 700 MPa to 1400 MPa; nevertheless, this increase yields an increase in capacity of only 58.4%, 101.3%, and 132.0%, respectively. Another important trend appears in the final column of Table 3.13. This represents the efficiency of the steel strength and shows that as the strength of the steel is increased, this efficiency declines from 58.4% to 44.0%. This suggests that although increasing the steel strength improves the capacity of the column, this is not a highly efficient approach. As with the specimens examined in group 4, the curves in Fig. 3.42 can be used to indicate the expected failure modes of the columns. Each curve shown in Fig. 3.42 exhibits a similar shape, which is characterized by a steady postpeak decline until the final load. Unlike the group 4 specimens, this is an encouraging result. The smooth and steady postpeak behavior of these columns implies a ductile failure mode where the columns fail slowly and provide sufficient warning that failure is about to occur. In a construction setting, this is obviously preferred than the failure mode of the group 4 specimens, which would be rapid and without warning. Importantly, the postpeak region of the axial-load deflection curve becomes smoother and steadier as the strength of the steel in increased.

3.5

Square-circular CFDST columns

3.5.1 Existing design approach and test results Proposals to predict the strength of square CFDST short columns (i.e., the crosssectional resistance) with inner CHSs (Pul,Han) were made by Han et al. [3]. The predicted strength (Pul,Han) was given as follows: Pul,Han ¼ Posc,u + Pi,u

(3.30)

where Posc,u is the compressive capacity of the outer tube with the sandwiched concrete and Pi,u is the capacity of the inner tube computed as Asifsyi, where Asi and fsyi are the cross-sectional area and the yield strength of the inner CHSs, respectively. To determine the capacity Posc, u, the following equation was put forward: Posc,u ¼ f scy Asco

with Asco ¼ Aso + Asc

(3.31)

CFDST short columns formed from carbon steels

97

in which Asc and Aso are the cross-sectional areas of the sandwiched concrete and the outer steel tube, respectively. The strength fscy, defined in megapascal, was given as:
f scy ¼ 1:212 +



    f yo f ck 0:138 + 0:7646 ζ +
0:0727 + 0:0216 ζ 2 f ck 235 20 (3.32)

where fck is the characteristic concrete strength in megapascal (0.67fcu), where fcu is the characteristic cube strength of concrete in megapascal, fyo is the yield strength of the outer SHS in megapascal, ζ is the confinement factor (Ac,noAsominf soal f ), and ck Ac, nominal is the nominal cross-sectional area of the concrete, given by D2
Aso.

The accuracy of the earlier design model was assessed herein through comparisons with the experimental results of the CFDST columns tested by Han et al. [3]. Table 3.14 shows the details and material properties of these columns, whereas Table 3.15 provides a comparison between the design strengths of the columns (Pul, Han) and their ultimate experimental strengths (Pul, Exp). The outer SHSs were first classified (based on the maximum depth-to-thickness ratios for the compression parts of the cross sections according to EC3 [59]) into fully effective (F: (D
2to)/ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi to  42ε) and slender (S: (D
2to)/to > 42ε) sections: ε ¼ 235=f yo. The slenderness ((D
2to)/to) of some of the SHSs tested by Han et al. [3] was found to exceed the maximum value of 52ε specified in EC4 [2]; these cross sections were considered to be very slender (VS). From the comparative results of Table 3.15, it can be seen that the strength predictions are good on average, but the predicted strengths are conservative in the case of CFDST columns with fully effective SHSs and are on the unsafe side for CFDST columns with very slender SHSs.

Table 3.14 Details of the tested square CFDST short columns [3]. Column

Classification of SHSs

D × to [mm]

d × ti [mm]

ssc2 ssc3 ssc4 ssc5 ssc6 ssc7

F F F VS VS VS

120  3 120  3 120  3 180  3 240  3 300  3

32  3 58  3 88  3 88  3 114  3 165  3

L [mm]

fyo [MPa]

fyi [MPa]

fc0 [MPa]

360 360 360 540 720 900

275.9 275.9 275.9 275.9 275.9 275.9

422.3 374.5 370.2 370.2 294.5 320.5

37.4 37.4 37.4 37.4 37.4 37.4

98

Concrete-Filled Double-Skin Steel Tubular Columns

Table 3.15 Comparison between the experimental and strength predictions of square CFDST short columns [3]. Column scc2-1 scc2-2 scc3-1 scc3-2 scc4-1 scc4-2 scc5-1 scc5-2 scc6-1 scc6-2 scc7-1 scc7-2 Mean

Category of SHS

Pul, Exp [kN]

Pul, Han [kN]

Pul,Han Pul,Exp

F F F F F F VS VS VS VS VS VS

1054 1060 990 1000 870 996 1725 1710 2580 2460 3240 3430

972 972 935 935 821 821 1740 1740 2710 2710 3794 3794

0.92 0.92 0.94 0.93 0.94 0.82 1.01 1.02 1.05 1.10 1.17 1.11

Standard deviation

1.00 0.099

3.5.2 Numerical modeling In this subsection, nonlinear numerical simulations, based on the FE method and using the software package ABAQUS/Standard [29], are made to expand the available results to square CFDST short columns.

3.5.2.1 General description of the FE model A summary of the FE model is presented in this section since full details were provided in previous publications by the authors [45], in which the behavior of circular CFDST short columns with inner CHSs was examined. The key difference between the two models is the constitutive model of the sandwiched concrete; this topic will therefore be presented in more detail. It is worth noting that the initial local imperfections were not considered in the current FE modeling of the CFDST short columns. This is because the strength reduction of the thin-walled hollow tubes is not significant owing to the delaying effect of the concrete core on tube buckling, as previously discussed by Tao et al. [60] who concluded that the initial imperfections decrease the strength of similar sections by about 1% on average. Furthermore, local buckling is not precluded due to the effective imperfection generated by the Poisson expansion adjacent to the restrained ends, as described by Theofanous et al. [61]. A quarter of the square CFDST short columns were modeled, based on the symmetry of geometry and loading, as shown in Fig. 3.43, in which the endplates at the loaded end were removed to present the cross section. Owing to the thin-walled nature of both the inner and outer steel tubes, shell elements were employed to discretize them. Element S3 [29], which is a three-nodded, triangular, general-purpose shell element with finite membrane strains, was utilized. For the sandwiched concrete

CFDST short columns formed from carbon steels

99

Fig. 3.43 FE mesh for square CFDST short columns with inner CHS.

and the two endplates, three dimensional, four-node, linear tetrahedral solid elements, denoted as C3D4 [29], were employed. To simulate the bond between the steel tubes and the sandwiched concrete, a surface-based interaction with a contact pressure-overclosure model in the normal direction and a Coulomb friction model with a coefficient of friction of 0.25 in the longitudinal direction was employed. Based on a previous convergence study, a mesh size of approximately 25 mm was used for modeling the steel tubes and the sandwiched concrete. The CFDST columns had fixed ends, with only longitudinal displacement at the loaded end allowed. An additional surface-based interaction was defined between each endplate and the sandwiched concrete, using the “no adjustment” option in ABAQUS. Each endplate was connected to both tubes using “shell-to-solid coupling,” ensuring that the displacements and rotations of the connected elements remained equal. A uniform distributed load was statically applied to the top of the upper endplate using displacement control. The load was incrementally applied using the modified RIKS method [29]. The nonlinear geometry parameter *NLGEOM was included to allow for changes in geometry under load. The steel material was assumed to behave in an elastic-perfectly plastic manner.

3.5.2.2 Material model for the sandwiched concrete Experiments indicate that the confinement effect provided by the square steel tube increases the ductility of the concrete core in a CFST short column but not the ultimate strength for columns with depth-to-thickness ratios greater than about 30 [31]. Fig. 3.44 shows the general stress-strain curve used in the present FE analyses to simulate the material behavior of the confined concrete in square CFDST columns. The part OA of the stress-strain curve is represented using the equations suggested by Mander et al. [62] as: σc ¼



f 0cc λ εc =ε0cc

λ λ
1:0 + εc =ε0cc

(3.33)

100

Concrete-Filled Double-Skin Steel Tubular Columns

A

B

C

O

0.005

D

0.015

Fig. 3.44 Stress-strain curve for the confined concrete in the square CFDST columns utilized in this study.

where λ¼

E c

Ec
f 0cc =ε0cc

(3.34)

σ c is the longitudinal compressive concrete stress, f 0cc is the effective compressive strength of the confined concrete, εc is the longitudinal compressive concrete strain, ε0cc is the strain at f 0cc given by Eq. (3.36), and Ec is Young’s modulus of the concrete, which is given by the ACI [34] as: Ec ¼ 3320

qffiffiffiffiffiffi f 0cc + 6900ðMPaÞ

8 0:002 for f 0cc  28ðMPaÞ > > < 0 ε0cc ¼ 0:002 + f cc
28 for 28 < f 0cc  82ðMPaÞ > 54000 > : 0:003 for f 0cc > 82ðMPaÞ

(3.35)

(3.36)

Parts AB, BC, and CD of the stress-strain curve for the confined concrete depicted in Fig. 3.44 are based on the model provided by Tomii and Sakino [63] and are defined as: 8 0 0 > < f cc for : εcc < εc  0:005

σ c ¼ βc f 0cc + 100ð0:015
εc Þ f 0cc
βc f 0cc for : 0:005 < εc  0:015 > : 0 βc f cc for : εc > 0:015 (3.37) where βc reflects the confinement effect on the concrete ductility and depends on the width-to-thickness ratio (Bs/t) of the CFST column section, where Bs is taken as the

CFDST short columns formed from carbon steels

101

larger depth of the rectangular cross section. Based on the experimental results presented by Tomii and Sakino [63], βc is proposed as: 8 Bs > > > 1:0 for : t  24 > > < 1 Bs B (3.38) βc ¼ 1:5
for : 24 < s  48 > 48 t t > > > > : 0:5 for : Bs > 48 t The effective compressive strength of concrete (fcc0 ) is mainly influenced by the column size, quality of the concrete, and rate of loading, as found previously by Liang [4]. Hence, the value of fcc0 was determined as fcc0 ¼ γ cfc0 , where fc0 is the compressive cylindrical strength of the concrete and γc is the strength reduction factor [4], taken as: γc ¼ 1:85Dc
0:135 ð0:85  γc  1:0Þ

(3.39)

where Dc is the depth of the concrete core. It is worth noting that this strength reduction factor (γ c) was proposed [4] to account for the effects of the column size, quality of the concrete, and loading rate on the concrete’s compressive strength. The Drucker-Prager yield criterion was adopted for the concrete to define the extent of the elastic response and the hardening behavior under a triaxial stress state. The material’s angle of friction (β) and the ratio of the flow stress in tension to that in compression (K) were taken as 20° and 0.8, respectively, as suggested by Hu et al. [31]. The softening behavior of the concrete in the postyield range is determined by the parameter βc and the concrete ultimate strain εcu. The parameter βc, given in Eq. (3.38), accounts for the effect of the D/t ratio of the steel tube on the softening of the concrete. The concrete ultimate strain εcu is taken as 0.03.

3.5.2.3 Validation of the FE model To assess the accuracy of the generated FE models, the tests conducted by Han et al. [3] were simulated herein. The details of the tests are provided in Table 3.14. It should be noted that Han et al. [3] conducted repeated tests for each of the examined columns, denoted as No. 1 and No. 2 specimens. The ultimate axial loads of the CFDST columns obtained from the FE analyses are compared with the test data in Table 3.16. As can be seen, the FE model yields good predictions of the ultimate loads of the CFDST short columns. The mean value of Pul, FE/Pul, Exp is 0.99 with a standard deviation of 0.084 for No. 1 specimens. For the No. 2 specimens, Pul, FE/Pul, Exp is 0.97 with a standard deviation of 0.080. Fig. 3.45 shows a comparison between the experimental and FE load-axial strain curves for the CFDST columns. It should be noted that the strain is the average axial strain, which is computed by dividing the end shortening by the column length. End shortening is inherently more variable and hence harder to predict accurately than ultimate strength due to the flat nature of the load-deformation response near the failure point. Overall, it can be observed that the FE model predicts well the complete axial load-strain curves for these tested specimens, except that of specimen

102

Concrete-Filled Double-Skin Steel Tubular Columns

Table 3.16 FE and the experimental ultimate loads for square CFDST short columns [3]. Pul,FE Pul,Exp

Column

Pul,FE [kN]

ssc2 1189 ssc3 946 ssc4 927 ssc5 1614 ssc6 2391 ssc7 3050 Mean Standard deviation

No. 1 specimens

No. 2 specimens

1.13 0.96 1.07 0.94 0.93 0.94 0.99 0.084

1.12 0.95 0.93 0.94 0.97 0.89 0.97 0.080

ssc2. The nonconservative results for specimen ssc2 may be due to the compressive strength of the sandwiched concrete being lower than that provided in Table 3.14 or may be due to voids that could have been present in the concrete. Fig. 3.46 presents a typical FE deformed shape for the CFDST short columns, which is similar to that observed experimentally. As can be seen, the failure mode of the outer tube involved outward local buckling, involving separation of the tube from the concrete core.

3.5.2.4 Parametric study and proposed design equation The validated FE model was employed to generate parametric results for square CFDST short columns. The length of the columns (L) was taken as three times the external depth (D) of the outer SHSs to avoid global buckling effects. Table 3.17 shows the dimensions and material properties considered in this study. SHSs with a range of local slendernesses (i.e., fully effective, slender, and very slender cross sections) filled with normal, high, and ultrahigh-strength concrete were simulated. The parameters considered in the analyses include the cylindrical strength (fc0 ) of the concrete and the ratio of the tube dimensions (d/D). The values of fc0 ranged from 25 MPa to 120 MPa, covering normal strength (NSC), high-strength (HSC), and ultrahighstrength concrete (UHSC) according to EC4 [2]. The current concrete model is considered to be applicable to high-strength concrete since it was initially proposed [4] for normal or high-strength concrete confined by either normal or high-strength steel tubes, respectively. The yield strength of the steel of both tubes was constant at 355 MPa. The columns were placed into three groups (G1, G2, and G3) based on their d/D ratios, as shown in Table 3.17. The d/D ratio was 0.5 in group 1 (G1), 0.2 in group 2 (G2), and 0.8 in group 3 (G3). In each group, different dimensions for the inner CHSs were employed to maintain the d/ti ratios. Design models for determining the ultimate strengths of CFDST short columns were proposed by Hassanein et al. [64] and Hassanein and Kharoob [45]. Additional models for concrete-filled stainless steel tubular (CFSST) short columns and concretefilled stainless steel-carbon steel tubular (CFSCT) short columns under axial

P [kN]

103

P [kN]

CFDST short columns formed from carbon steels

Strain [

]

Strain [

P [kN]

(b)

P [kN]

(a)

]

Strain [

]

Strain [

P [kN]

(d)

P [kN]

(c)

]

Strain [

]

(e)

82

Strain [

]

(f)

Fig. 3.45 Comparisons of the experimental and FE axial load-strain curves for the square CFDST short columns with inner CHSs. (A) scc2; (B) scc3; (C) scc4; (D) scc5; (E) scc6; (F) scc7 [3].

compression were developed by Hassanein et al. [65,66], respectively. Based on these design models [45,64–66], a new design model for calculating the ultimate axial strengths of axially loaded square CFDST short columns with inner CHSs is proposed as: Pul,Prop ¼ f yo Aso + γ c f 0c Asc + f yi Asi

(3.40)

104

Concrete-Filled Double-Skin Steel Tubular Columns

Applied load direc on

Local buckling

Fig. 3.46 Deformed shape, showing local buckling, of a typical square CFDST short column.

It should be noted that this design model is based on the plastic resistance of square or rectangular composite columns (Ppl, Rd), as specified in EC4 [2], but with a modified contribution from the sandwiched concrete. In Pul,Prop, the contribution of the sandwiched concrete is reduced by a strength reduction factor (γ c), which is a function of the column size, as previously given in Eq. (3.39). A comparison between the FE strengths generated in the parametric study and the predicted strengths (Pul,design) from the three design models is shown in Table 3.18. The first is that proposed by Han et al. [3], whereas the other two design models (Pul,Prop,1 and Pul,Prop,2) are based on Eq. (3.40), considering the gross (Aso,g) and the effective (Aso,eff) crosssectional areas of the outer steel tubes, respectively. The effective cross-sectional areas of the outer steel tubes were calculated following the rules provided in Clause 4.4 of EN 1993-1-5 [5], where the effective area of the compression zone of a plate is reduced by a reduction factor for plate buckling (ρ). For the current square columns, Aso, eff ¼ ρAso, g, where ρ is given by Eq. 4.2 in Eurocode 3 [5]. Fig. 3.47 shows the relationship between the relative design strengths for varying strengths (fc0 ) of the sandwiched concrete.

CFDST short columns formed from carbon steels

105

Table 3.17 Details of the FE models of square CFDST short columns. Outer tube

Group G1

G2

G3

Inner tube

Column reference

D [mm]

te [mm]

D te

d [mm]

ti [mm]

d ti

L [mm]

fc0 [MPa]

d D

ti te

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35 C36 C37 C38 C39 C40 C41 C42 C43 C44 C45 C46

300 300 300 300 300 300 400 400 400 400 400 400 500 500 500 500 500 500 300 300 300 300 300 300 400 400 400 400 400 400 500 500 500 500 500 500 300 300 300 300 300 300 400 400 400 400

10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00

30 30 30 30 30 30 40 40 40 40 40 40 50 50 50 50 50 50 30 30 30 30 30 30 40 40 40 40 40 40 50 50 50 50 50 50 30 30 30 30 30 30 40 40 40 40

150 150 150 150 150 150 200 200 200 200 200 200 250 250 250 250 250 250 60 60 60 60 60 60 80 80 80 80 80 80 100 100 100 100 100 100 240 240 240 240 240 240 320 320 320 320

5.00 5.00 5.00 5.00 5.00 5.00 6.66 6.66 6.66 6.66 6.66 6.66 8.33 8.33 8.33 8.33 8.33 8.33 5.00 5.00 5.00 5.00 5.00 5.00 6.66 6.66 6.66 6.66 6.66 6.66 8.33 8.33 8.33 8.33 8.33 8.33 5.00 5.00 5.00 5.00 5.00 5.00 6.66 6.66 6.66 6.66

30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 48 48 48 48 48 48 48 48 48 48

900 900 900 900 900 900 1200 1200 1200 1200 1200 1200 1500 1500 1500 1500 1500 1500 900 900 900 900 900 900 1200 1200 1200 1200 1200 1200 1500 1500 1500 1500 1500 1500 900 900 900 900 900 900 1200 1200 1200 1200

25 40 60 80 100 120 25 40 60 80 100 120 25 40 60 80 100 120 25 40 60 80 100 120 25 40 60 80 100 120 25 40 60 80 100 120 25 40 60 80 100 120 25 40 60 80

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

5.00 5.00 5.00 5.00 5.00 5.00 0.66 0.66 0.66 0.66 0.66 0.66 0.83 0.83 0.83 0.83 0.83 0.83 5.00 5.00 5.00 5.00 5.00 5.00 0.66 0.66 0.66 0.66 0.66 0.66 0.83 0.83 0.83 0.83 0.83 0.83 5.00 5.00 5.00 5.00 5.00 5.00 0.66 0.66 0.66 0.66

Continued

106

Concrete-Filled Double-Skin Steel Tubular Columns

Table 3.17 Continued Outer tube

Group

Inner tube

Column reference

D [mm]

te [mm]

D te

d [mm]

ti [mm]

d ti

L [mm]

fc0 [MPa]

d D

ti te

C47 C48 C49 C50 C51 C52 C53 C54

400 400 500 500 500 500 500 500

10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00

40 40 50 50 50 50 50 50

320 320 400 400 400 400 400 400

6.66 6.66 8.33 8.33 8.33 8.33 8.33 8.33

48 48 48 48 48 48 48 48

1200 1200 1500 1500 1500 1500 1500 1500

100 120 25 40 60 80 100 120

0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

0.66 0.66 0.83 0.83 0.83 0.83 0.83 0.83

Table 3.18 FE strengths compared to different design models. Pul, Group G1

G2

Column reference

Pu,FE [kN]

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28

6219 7002 8038 9075 10,110 11,133 8989 10,334 11,686 12,849 15,296 16,950 11,764 13,517 16,291 19,406 22,443 25,408 6027 6994 8302 9608 10,913 12,219 8675 10,139 12,266 14,087

[kN]

Pul,Han Pul,FE

1

Pul,Prop, [kN]

Pul,Prop, 2 [kN]

Pul,Prop,1 Pul,FE

Pul,Prop,2 Pul,FE

5821 6845 8271 9718 11,173 12,633 9005 10,890 13,460 16,050 18,648 21,250 12,771 15,759 19,798 23,857 27,924 31,995 6348 7582 9300 11,044 12,798 14,558 9667 11,939 15,036 18,158

0.94 0.98 1.03 1.07 1.11 1.13 1.00 1.05 1.15 1.25 1.22 1.25 1.09 1.17 1.22 1.23 1.24 1.26 1.05 1.08 1.12 1.15 1.17 1.19 1.11 1.18 1.23 1.29

6239 7027 8077 9127 10,177 11,227 9375 10,816 12,736 14,657 16,578 18,498 13,056 15,368 18,450 21,532 24,615 27,697 6058 7038 8345 9652 10,959 12,265 9044 10,821 13,191 15,560

6239 7027 8077 9127 10,177 11,227 8689 10,129 12,050 13,971 15,891 17,812 11,299 13,610 16,693 19,775 22,857 25,940 6058 7038 8345 9652 10,959 12,265 8358 10,135 12,504 14,874

1.00 1.00 1.00 1.01 1.01 1.01 1.04 1.05 1.09 1.14 1.08 1.09 1.11 1.14 1.13 1.11 1.10 1.09 1.01 1.01 1.01 1.00 1.00 1.00 1.04 1.07 1.08 1.10

1.00 1.00 1.00 1.01 1.01 1.01 0.97 0.98 1.03 1.09 1.04 1.05 0.96 1.01 1.02 1.02 1.02 1.02 1.01 1.01 1.01 1.00 1.00 1.00 0.96 1.00 1.02 1.06

Han

CFDST short columns formed from carbon steels

107

Table 3.18 Continued Pul, Group

G3

Column reference

Pu,FE [kN]

C29 C30 C31 C32 C33 C34 C35 C36 C37 C38 C39 C40 C41 C42 C43 C44 C45 C46 C47 C48 C49 C50 C51 C52 C53 C54

16,842 19,142 11,132 13,622 17,139 21,106 24,986 28,680 6141 6552 7099 7645 8019 8728 8723 9209 10,150 10,852 11,736 12,576 11,377 12,124 12,934 13,596 15,967 17,352

Mean Standard deviation

Han

[kN]

Pul,Han Pul,FE

21,289 24,425 13,537 17,139 22,007 26,899 31,801 36,707 4413 5046 5928 6824 7725 8628 7012 8178 9768 11,371 12,979 14,589 10,152 12,002 14,501 17,013 19,530 22,050

1.26 1.28 1.22 1.26 1.28 1.27 1.27 1.28 0.72 0.77 0.84 0.89 0.96 0.99 0.80 0.89 0.96 1.05 1.11 1.16 0.89 0.99 1.12 1.25 1.22 1.27 1.11 0.149

Pul,Prop, 1 [kN]

2

17,929 20,299 12,539 15,376 19,159 22,943 26,726 30,509 6145 6575 7149 7722 8295 8869 9225 10,041 11,128 12,216 13,303 14,391 12,822 14,158 15,938 17,719 19,499 21,280

17,243 19,612 10,781 13,619 17,402 21,185 24,969 28,752 6145 6575 7149 7722 8295 8869 8538 9354 10,442 11,529 12,617 13,704 11,065 12,400 14,181 15,961 17,742 19,522

Pul,Prop, [kN]

Pul,Prop,1 Pul,FE

Pul,Prop,2 Pul,FE

1.06 1.06 1.13 1.13 1.12 1.09 1.07 1.06 1.00 1.00 1.01 1.01 1.03 1.02 1.06 1.09 1.10 1.13 1.13 1.14 1.13 1.17 1.23 1.30 1.22 1.23 1.08 0.069

1.02 1.02 0.97 1.00 1.02 1.00 1.00 1.00 1.00 1.00 1.01 1.01 1.03 1.02 0.98 1.02 1.03 1.06 1.08 1.09 0.97 1.02 1.10 1.17 1.11 1.13 1.02 0.041

From Table 3.18 and Fig. 3.47, it can be observed that the strength predictions of Han et al. [3] (Pul, Han) are generally on the unsafe side when compared to the FE results, except for those columns with d/D ¼ 0.8. Using Eq. (3.40) and considering the gross cross-sectional areas (Aso, g) of the outer tubes, it is observed that the predicted strengths (Pul, Prop, 1) of the columns are close to the FE results in the case of fully effective outer tubes. However, the predicted strengths for the other cases (i.e., columns with S and VS outer tubes) are on the unsafe side. As can be seen in the table, the average value of Pul, Prop, 2/Pul, FE is 1.02 compared to 1.11 and 1.08 for Pul, Han/Pul, FE [3] and Pul, Prop, 1/Pul, FE, respectively. Despite the mean value of Pul, Prop, 2/Pul, FE being slightly greater than unity, this is considered to be the best design model among those examined herein, with by far the lowest scatter.

108

Concrete-Filled Double-Skin Steel Tubular Columns

d/D

0.2

d/D

0.5

d/D

Pul,design

Pul,design

Pul,design

Pul,FE

Pul,FE

Pul,FE

f cc [MPa]

f cc [MPa]

0.8

f cc [MPa]

(a) Fully effective SHSs d/D

0.2

d/D

0.5

d/D

Pul,design

Pul,design

Pul,design

Pul,FE

Pul,FE

Pul,FE

f cc [MPa]

f cc [MPa]

0.8

f cc [MPa]

(b) Slender SHSs d/D

0.2

d/D

0.5

d/D

Pul,design

Pul,design

Pul,design

Pul,FE

Pul,FE

Pul,FE

f cc [MPa]

f cc [MPa]

0.8

f cc [MPa]

(c) Very slender SHSs

Fig. 3.47 Comparison between the FE strengths and design predictions for CFDST columns with (A) fully effective, (B) slender, and (C) very slender SHSs.

Eq. (3.40) was also assessed against the experimental results [3], as shown in Table 3.19. The average predictions of Pul,Han [3], Pul,Prop, 1, and Pul,Prop, 2 are 1.00, 0.99, and 0.93, respectively. Although the predictions of Han et al. [3] are the most accurate on average, the proposed approaches have considerably lower scatter and provide predictions that are generally on the safe side. Strength predictions using Pul,Prop, 2 are therefore recommended.

CFDST short columns formed from carbon steels

109

Table 3.19 Comparison between the experimental results [3] and the proposed design strengths for square CFDST short columns. Column

Category of SHS

scc2-1 F scc2-2 F scc3-1 F scc3-2 F scc4-1 F scc4-2 F scc5-1 VS scc5-2 VS scc6-1 VS scc6-2 VS scc7-1 VS scc7-2 VS Mean Standard deviation

3.6

Pul, Exp [kN]

Pul, Han [kN]

1054 1060 990 1000 870 996 1725 1710 2580 2460 3240 3430

972 972 935 935 821 821 1740 1740 2710 2710 3794 3794

Pul,Han Pul,Exp

Pul,Prop,1 Pul,Exp

Pul,Prop,2 Pul,Exp

0.92 0.92 0.94 0.93 0.94 0.82 1.01 1.02 1.05 1.10 1.17 1.11 1.00 0.099

0.90 0.89 0.97 0.96 1.08 0.94 1.00 1.00 1.00 1.04 1.10 1.04 0.99 0.065

0.90 0.89 0.97 0.96 1.08 0.94 0.90 0.91 0.86 0.91 0.94 0.89 0.93 0.056

New confining stress-based design for circular-circular CFDST columns

In this section, available circular-circular CFDST short columns (Fig. 3.1A) are collected from the literature, considering only those formed from carbon steel tubes [13,20,21,24,67–80]. Then, the database collected is used to evaluate the design resistance models of EC4 [2], ACI [81], AISC [82], Yan et al. [83], Han et al. [84], Hassanein and Kharoob [45], and Uenaka et al. [21]. Based on the comparisons, the need for a better design proposal arises. Accordingly, the database of CFDST columns will be used to propose a new confining stress equation (frp). Then, this equation is used to formulate a new design equation that better predicts the resistance of the CFDST short columns.

3.6.1 Background of the available test specimens As shown earlier, the available tests on CFDST short columns with carbon steel tubes are collected, and their geometry and material ranges are provided in Table 3.20. In summary, 18 investigations were found in the literature that tested 173 specimens in total. The database shows the diversity of the test specimens in terms of geometrical and material details. The void ratio (Di/Do) extends from 0.18 to a large void ratio of 0.89. Although Tao et al. [24] found that the inner tubes in CFDST short columns effectively confine the concrete if the void ratio is less than 0.80, recently, columns with higher void ratios have appeared for application in wind towers [78,85].

Table 3.20 Details of the experimental specimen database [13,20,21,24,67–80]. References Tao et al. [24] Li et al. [13] Lin et al. [67] Uenaka et al. [21] Fan et al. [68] Hastemoglu [69] Li et al. [70] Li et al. [71] Ekmekyapar et al. [80] Ekmekyapar et al. [72] Sulthana and Jayachandran [73] Zhao et al. [74] Zhao et al. [20] Wei et al. [75] Yan et al. [76] Yan et al. [77] Yang et al. [78] Chen and Hai [79] Max Min

Test no.

Do [mm]

to [mm]

Do/to

fyo [MPa]

Di [mm]

ti [mm]

Di/ti

Di/Do

fyi [MPa]

fc [MPa]

12 2 2 9 8 5 6 4 8

114–300 350 300 157–159 240 139 140–450 356 114.3

3.0 4.0 2.0–4.0 0.9–2.1 3.0–4.0 2.0 2.5–8.0 5.50 2.7–5.9

38–100 92 75–150 73.4–176.7 60–80 69.5 56–56.3 64.7 19.5–41.9

276–295 439 292 221–308 280 250 307–365 618 285–455

48–165 231 180 38–115 80–120 75 76–400 168–219 60.3

3.0 3.0 2.0 0.9–2.1 3.0–4.0 3.0 1.6–8.0 3.3 2.5–5.8

16–55 79 90 18.7–126.7 20–40 25 47.5–57 50.9–66.4 10.5–23.9

0.27–0.78 0.66 0.60 0.24–0.73 0.33–0.50 0.54 0.54–0.89 0.47–0.62 0.53

295–396 397 292 221–308 280 250 321–429 356–357 310–396

37.1 42.0 27.9 18.7 29.0 46.7 39.8–43.1 36.2 36.4–63.2

8

114.3

2.7–6.1

18.7–41.7

355–535

60.3

2.5–5.8

10.5–23.9

0.53

310–396

32.4–57.7

2

166–166.3

5.2

31.7–31.8

520

76.7

3.6

21.4

0.46

520

34.6–35.4

6 9 26 24 24 9 9

114.2–165.3 114.3–165.1 74.7–114.3 188.2–191 164.7–165.3 538 160 538.00 74.70

2.9–5.9 1.7–6.0 0.6–1.8 4.2–6.8 3.7–6.0 3.8–5.6 1.0–2.1 8.00 0.59

19.4–57 19.1–95.6 42.9–169.0 27.9–45.2 27.4–45 95.6–143.1 76.2–160 176.67 18.71

395–454 395–454 255–524 327.3–464 347–428.6 253.8–296.3 220–300 618.00 220.00

48.4–101.8 48.3–101.6 61.2–88.9 33.5–101.6 42.5–76.4 418–477 37–112 477.00 33.50

2.8–3.1 2.9–3.3 0.9–1.6 3.1–4.1 2.8–3.2 5.6 1.0–2.1 8.00 0.55

17.3–32.8 16.7–31.8 51–146 10.9–25.2 13.3–27.4 74.2–84.7 17.6–112 146.00 10.45

0.42–0.62 0.42–0.63 0.56–0.87 0.18–0.53 0.26–0.46 0.78–0.89 0.23–0.70 0.89 0.18

410–425 394–425 216–512 342.1–348.2 385.6–409.8 296.3 220–300 520.00 216.00

52.9 52.9 58.6 29–51 53.7–141 39.1–56.1 23.6 141.00 18.70

CFDST short columns formed from carbon steels

111

Accordingly, a simplified design resistance to account for their different behavior has been proposed by Yang et al. [78]. The Do/to ratios range from 189 to 177, whereas the Di/ti ratios extend from 10 to 146. This indicates that the slenderness limits provided by EC4 [2] and AISC [82] have been exceeded in some case. It should be noted that EC4 [2] do not allow using CFST columns with slender sections, whereas the AISC [82] permits the design of CFST columns with local buckling effects. However, Thai et al. [86] observed that the AISC [82] provides highly conservative resistances for CFST short columns of slender sections (with an average test-to-AISC resistance ratio of 1.48). Regarding steel materials, the specimens were formed from normal and highstrength steels according to EC3 [59], whereas the concrete was varied between normal, high-, and ultrahigh-strength materials according to the EC2 classification [87]. Accordingly, many test specimens are formed from materials whose properties are not permitted by EC4 [2] and AISC [82]. This is because EC4 [2] designs CFST columns with maximum fy and fc of 460 MPa (normal strength steel) and 50 MPa (normal strength concrete), respectively. The AISC [82] allows for higher material strengths, but the limits of fy and fc are 525 MPa and 69 MPa, respectively. However, a recent investigation by Thai et al. [86] has revealed that the design models for circular CFST short columns provided by both EC4 [2] and AISC [82] can safely be extended to highstrength materials.

3.6.2 Assessment of the design methods In this section, the assessment of the design methods (PR) is conducted through comparisons with the test strengths (Pul, Exp). In detail, a statistical evaluation of the PR/Pul, Exp ratios is provided in Table 3.21 for all the design methods considered. Additionally, the PR/Pul, Exp ratios versus the relative slenderness of the steel tubes ((Do/to)/ (Di/ti)) are graphed in Fig. 3.48, with trend lines added to represent the accuracy of the different design methods along the entire (Do/to)/(Di/ti) range. Furthermore, as the reliability analysis of the design methods is so important, a reliability index (β) is calculated to evaluate the reliability of the various specifications and design models available. Table 3.21 Statistical evaluation of the PR/Pul, Exp ratios using different design resistance methods.

Ave SD Max Min β

EC4 [2]

ACI [81]

AISC [82]

Yan et al. [83]

Han et al. [84]

Hassanein and Kharoob [45]

Uenaka [21]

Proposed strength

1.06 0.088 1.30 0.84 2.20

0.85 0.082 1.04 0.64 3.42

0.89 0.086 1.07 0.70 3.19

0.92 0.082 1.12 0.73 3.03

0.94 0.093 1.17 0.72 2.88

0.97 0.087 1.17 0.64 2.73

1.08 0.157 1.50 0.76 1.88

0.99 0.085 1.26 0.83 2.63

112

Concrete-Filled Double-Skin Steel Tubular Columns

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Fig. 3.48 Comparison between the test and design resistances. (A) EC4 [2]; (B) ACI [81]; (C) AISC [82]; (D) Yan et al [83]; (E) Han et al. [84]; (F) Hassanein and Kharoob [45]; (G) Uenaka et al [21]; (H) Proposed.

CFDST short columns formed from carbon steels

113

3.6.2.1 Design methods In this chapter, design resistances for axially loaded members by EC4 [2], ACI [81], AISC [82], Yan et al. [83], Han et al. [84], Hassanein and Kharoob [45], and Uenaka et al. [21] are calculated using the following detailed equations. It is noteworthy that EC4 [2], ACI [81], and AISC [82] provide resistance for CFST columns, so the plastic resistance of the inner tubes of the CFDST short columns is added to each of them.

EC4 By replacing the plastic resistance of the reinforcement by that of the inner tube, the plastic resistance of circular CFDST short columns (PEC4) is calculated according to EC4 [2] as follows:  PEC4 ¼ ηa Aso f yo + Asc f c

t  f yo 1 + ηc d  f ck

 + Asi f yi

(3.41)

where Aso, Asc, and Asi are the cross-sectional areas of the outer tube, sandwiched concrete, and inner tube, respectively. Similarly, fso, fc, and fsi represent the yield strength of the outer tube, cylindrical compressive strength of the concrete, and yield strength of the inner tube, respectively. As can be observed from the earlier equation, EC4 [2] takes into account the effect of the bidirectional stresses generated into the steel tube by the reduction factor (ηa) and the increase in the concrete strength due to the confinement provided by the circular outer tube by the factor ηc. These factors are given as:

ηa ¼ 0:25  3 + 2λ  1:0

(3.42) 2

ηc ¼ 4:9
18:5  λ + 17  λ > 1:0

(3.43)

where λ is the relative slenderness, given as: rffiffiffiffiffiffiffiffiffiffiffi Ppl,Rk λ¼ Pcr Ppl,Rk ¼ Aso f yo + Asc f c + Asi f yi Pcr ¼

π2  ðEso I so + 0:6  Esc I sc + Esi I si Þ lb 2

(3.44) (3.45) (3.46)

in which Eso, Esc, and Esi are the moduli of elasticity of the outer tube, sandwiched concrete, and inner tube, respectively. Similarly, Iso, Isc, and Isi refer to the second moment of area of the outer tube, cylindrical compressive strength of the concrete, and yield strength of the inner tube, respectively. lb stands for the buckling length of the column, which is taken as half the physical length of the short column based on the elimination of the overall buckling.

114

Concrete-Filled Double-Skin Steel Tubular Columns

The ACI In contrast to EC4 [2], the confinement effect of the concrete is ignored by the ACI [81] and the concrete plastic resistance is reduced by 15%. Accordingly, the resistance of CFDST short columns according to the ACI [81] is directly the sum of the plastic resistances of the cross-sectional components, as follows: PACI ¼ Aso f yo + 0:85  Asc f c + Asi f yi

(3.47)

The AISC The design resistance of the AISC [82] is quite similar to that provided by the ACI [81], but it uses an increased contribution to the sandwiched concrete. Accordingly, the resistance of axially loaded CFDST short columns with compact steel tubes is given as: PACI ¼ Aso f yo + 0:95  Asc f c + Asi f yi

(3.48)

Yan et al. Yan et al. [83] proposed the following compressive resistance for estimating the ultimate strength of CFDST short columns (PYan) with a hollow ratio (χ ¼ Di/Do), which considers the increased confined stress of the concrete (fcc): PYan ¼ 0:94  Aso f yo + Asc f cc + Asi f yi

(3.49)

where f cc ¼ f c + 2:2  λCFDST  f c 0:3  σ ru 0:81 σ ru ¼

0:38f yo to Do
2to 

λCFDST ¼

(3.51)

0:6η0:51 : 0  η < 2:731 1:0 : 2:731  η < 7:457



η ¼ 1
χ2 

(3.50)

f yo 2to  Do
2to f c

(3.52)

(3.53)

Han et al. According to Han et al. [84], the confinement of the sandwiched concrete in CFDST short columns is taken into consideration in the resistance calculation (PHan). Generally, the design resistance by Han et al. [84] depends on α ¼ Aso/Asc and αn ¼ Aso/Ac, nom, where Ac, nom is the nominal cross-sectional area of the concrete. Accordingly, the design model by Han et al. [84] is expressed by: PHan ¼



       αn f yo α 1 þ αn  χ 2 f yo þ  1:14 þ 1:02   f ck 1þα 1þα f ck

 ðAso þ Asc Þ þ Asi f yi (3.54)

CFDST short columns formed from carbon steels

115

where fck is the characteristic strength of the concrete computed as 0.67 times the cubic strength of the concrete (fcu).

Hassanein and Kharoob Hassanein and Kharoob [45] proposed a design resistance (PHassanein) that is dependent on the Do/to ratio of the outer steel tubes. As can be observed from the following design model, CFDST columns with Do/to ratios less than 150 include the benefit of the confining effect of the concrete provided by the outer tubes, whereas those with Do/to > 150 do not. Generally, the design proposal for columns of Do/to > 150 is identical to that of the ACI [81].

PHassanein

 8  < 1 + 0:3 ζ Ω A f + A f so yo sc cc + Asi f si : Do =to  150 1+ζ ¼ : Aso f so + 0:85Asc f c + Asi f si : Do =to > 150 (3.55)

where ζ¼α Ω¼

f sy ðwith α ¼ Aso =Asc Þ f ck

Asc Ac,nom

(3.56) (3.57)

Uenaka et al. Uenaka et al. [21] proposed an equation that provides the design resistance of CFDST short columns (PUenaka) with 0.2 < Di/Do < 0.7, as follows:  PUenaka ¼

 Di 2:86
2:59  A f + Asc f c + Asi f yi Do so yo

(3.58)

3.6.2.2 Reliability analysis method As stated earlier, the reliability analysis method is based on the reliability index (β), which is a relative measure of design integrity. The β index was originally introduced by Ravindra and Galambos [88] for steel members as described in Eq. (3.59), whereas the parameter values proposed by Lai and Varma [89] are currently used for the case of CFST members, as shown in the following.   F Ln P  M φ β ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi α V 2M + V 2P + V 2F

(3.59)

116

Concrete-Filled Double-Skin Steel Tubular Columns

where P stands for the average ratio of Pul,Exp over design predictions (i.e., different specifications or resistances available), M denotes the average ratio of the measured-to-nominal strength of the materials (1.10), F is the average ratio of the material fabrication factor (1.00), and α is the linearization approximation coefficient (0.70). Additionally, VM ¼ 0.05, VF ¼ 0.193, and VP are the variation coefficients of the material factor, fabrication factor, and P, respectively. φ is taken as 0.75. However, it is known that EC4 [2] adopts different partial factors for steel and concrete in the strength calculations of CFST columns, which makes the calculation of the reliability index highly complex. Hence, due to the complexity of the problem, β was calculated according to the concept of the resistance factor utilized in LRFD. The same method was used in the literature before [86,90–93] in the reliability analysis of design models of different concrete-filled steel tubes.

3.6.2.3 Comparisons with test strengths Here, the comparisons between the design resistances and the test strengths are provided. Table 3.21 provides the average ratios of PR/Pul,Exp (Ave) along with standard deviation (SD), maximum ratio (Max), minimum ratio (Min), and reliability index (β). From the table, it can be observed that the ACI [81], the AISC [82], Yan et al. [83], Han et al. [84], and Hassanein and Kharoob [45] provide moderately safe resistances, whereas EC4 [2] and Uenaka et al. [21] produce nonconservative resistances on average. Generally, using the design resistance by Uenaka et al. [21] leads to the most unsafe results. Additionally, the scatter of predictions by all design methods is almost close to each other (0.08–0.1), except for Uenaka et al. [21], which was relatively large (SD of 0.157). Considering the relationships between thePR/Pul,Exp ratios and (Do/to)/(Di/ti), as shown in Fig. 3.48, different accuracies for the average ratios can be seen. Here, the average ratios are represented by linear trend lines, and, as long as they are horizontal, the accuracy of the design method increases. In general, the design methods by the ACI [81], the AISC [82], Yan et al. [83], Han et al. [84], and Hassanein and Kharoob [45] show increasing accuracy with increasing (Do/to)/(Di/ti) ratios. Conversely, the accuracy of the design method provided by Uenaka et al. [21] appears to be enhanced by increasing the (Do/to)/(Di/ti) ratios but still provides unsafe results over the full range of (Do/to)/(Di/ti) ratios. The only design method that shows the same accuracy along the full range of (Do/to)/(Di/ti) ratios is that provided by EC4 [2] but also with unsafe average predictions. Regarding the reliability index (β), the design methods by the ACI [81], AISC [82], Yan et al. [83], Han et al. [84], and Hassanein and Kharoob [45] provided acceptable reliability, whereas those by EC4 [2] and Uenaka et al. [21] failed to obtain values of β higher than 2.5. Based on this, there is a need for a new design method that provides better PR/Pul,Exp ratios with accurate predictions regarding the entire range of (Do/

CFDST short columns formed from carbon steels

117

to)/(Di/ti) ratios and an acceptable value of β, which is the main objective of this chapter.

3.6.3 Lateral confining pressure 3.6.3.1 Background Richart et al. [35] are credited with being the first to discover that confining the concrete in CFST sections leads to an increase in the maximum compressive strength (fcc). This is mainly attributed to the delay in the microstructural damage because of the applied confining stress. As it is well known, concrete under compression fails due to the propagation of microscopic cracking between the aggregates and cement matrix. The force transfer is accomplished by bridging forces between the aggregates and, to a greater extent, by shear stresses, which are transmitted through inclined microcracks. The lateral confining force balances the bridging forces that reduce the tensile force and thereby delay the rise and growth of bond cracks, as shown in Fig. 3.49. Accordingly, to consider the increased concrete strength due to confinement, they [35] proposed the following well-known empirical formula: f cc ¼ f c + k  f rp

(3.60)

where fcc and fc are the confined and unconfined concrete cylindrical strengths, respectively, and kis the triaxial factor that has a value of 4.1 for normal strength concrete (NSC). Sixty years later (specifically in 1988), Cederwall [94] found that the factor k has a value between 3 and 4 for high-strength concrete (HSC). This is because the effect of frp on the maximum compressive strength and ductility of HSC is not as pronounced as that in NSC [95,96]. This is explained by the higher degree of homogeneity of HSC, which leads to much less damage in the microstructure and thus less confining pressure effect. Recently, Eq. (3.60) has been modified by Liang [4] to

(a)

(b)

Bridging force

Lateral confining force

Tensile force Bond crack

Fig. 3.49 Bridging force balance methods for concrete under (A) uniaxial compression and (B) triaxial compression.

118

Concrete-Filled Double-Skin Steel Tubular Columns

include the effect of concrete quality, column size, and loading rates on the value of fc by applying the factor γ c, which depends on the concrete core diameter (Dc) and is given by Eq. (3.61). Accordingly, the modified confined strength of concrete can be calculated by Eq. (3.62). γ c ¼ 1:85Dc
0:135 : 0:85  γ c  1:0 (3.61) f cc ¼ γ c  f c + k  f rp

(3.62)

3.6.3.2 Proposed formula for CFDST sections The objective of this section is to provide a formula for calculating the lateral confining pressure that the outer and inner steel tubes impose on the sandwiched concrete. The confinement mechanism for the sandwiched concrete is provided in Fig. 3.50, based on previous studies, for example, those of Uenaka et al. [21] and Tao et al. [24]. As can be observed, the outer and inner steel tubes provide confinement by the stresses σ o and σ i, respectively. These confinement pressures are based on the ratios of Do/to and Di/ti in addition to the yield strength of both steel tubes fyo and fyi, respectively. Accordingly, the current proposal links all these parameters to come up with a formula for the average lateral confining pressure (frp) that affects the concrete from both sides. To do so, the sum of the plastic resistances of the components of the CFDST section is equalized with the test strength (Pul,Exp) for the 173 specimens collected in Section 3.2, using the following equation, which ignores the local buckling effect of the tubes, to obtain the confined strength of the concrete (fcc). Pul,Exp ¼ Aso f yo + Asc f cc + Asi f yi

(3.63)

Now, using the values of fcc, fc, and γ c and assuming k ¼ 4.1 (for different concrete grades), the value of frp can be obtained from Eq. (3.62) for each test specimen. Then, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the relationship between f rp = f yo  f yi and (Do/to)/(Di/ti) is drawn in Fig. 3.51, which combines all possible variables affecting the confinement of the concrete. Additionally, a power trend line, which provides the best fit to the data, was added to the

σo

σi

Fig. 3.50 Confinement mechanism affecting the sandwiched concrete in CFDST sections.

CFDST short columns formed from carbon steels

119

0.03

frp/((fyo*fyi)^0.5)

0.03 0.02 0.02 0.01 0.01 0.00 0.00

1.00

2.00

3.00

4.00

5.00

(Do/to)/(Di/ti)

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fig. 3.51 Relationship between f rp = f yo  f yi and (Do/to)/(Di/ti).

figure to represent the relationship between both considered ratios. From this regression analysis, the average frp in CFDST sections is given as: f rp

 0:146 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Do =to ¼ 0:0081   f yo  f yi with R2 ¼ 0:0067 Di =ti

(3.64)

3.6.4 Proposed design model This section provides a generalized design method (PProp) that can accurately predict the resistances of circular CFDST short columns. This resistance proposal is given by Eq. (3.63), where frp is to be computed from Eq. (3.62).

PProp ¼ Aso f yo + Asc γ c f c + 4:1  f rp + Asi f yi

(3.65)

3.6.4.1 Comparison with all test specimens of the database The comparisons between the resistances of the CFDST short columns with those predicted experimentally are provided in Table 3.21 and Fig. 3.48H. From the resistance predictions shown in Table 3.21, it can be seen that the proposed resistance results in an average PProp/Pul,Exp of 0.99, which is better than that obtained by EC4 [2], ACI [81], AISC [82], Yan et al. [83], Han et al. [84], Hassanein and Kharoob [45], and Uenaka et al. [21]. In addition, it results in an SD of 0.085, which is acceptable relative to other design methods. Moreover, the design integrity of this design resistance is ensured by having a β value of 2.63, which is higher than 2.5. The accuracy of the design proposal along the entire (Do/to)/(Di/ti) ratio can also be observed

Table 3.22 Statistical evaluation of the PR/Pul, with Do/to  90  (235/fyo). ACI [81]

AISC [82]

ratios using different design resistance methods, considering different material grades

Yan et al. [83]

Han et al. [84]

Hassanein and Kharoob [45]

Uenaka et al. [21]

Proposed resistance

0.93 0.064 1.10 0.81 3.08

1.08 0.132 1.30 0.76 1.91

k ¼ 4.1 0.94 0.076 1.14 0.84 2.96

1.04 0.077 1.17 0.87 2.38

1.20 0.126 1.50 0.87 1.35

k ¼ 4.1 1.02 0.072 1.17 0.84 2.51

0.91 0.057 1.00 0.86 3.25

1.18 0.112 1.35 0.98 1.48

k ¼ 4.1 0.87 0.046 0.94 0.83 3.57

.

EC4 [2]

Exp

fyo ≤ 460 MPa and fc ≤ 50 MPa: 48 test specimens (NSS and NSC) Ave SD Max Min β

1.04 0.059 1.18 0.90 2.41

0.81 0.083 0.99 0.67 3.68

0.84 0.082 1.02 0.70 3.51

0.88 0.069 1.06 0.75 3.39

0.90 0.069 1.07 0.74 3.29

fyo ≤ 460 MPa and fc > 50 MPa: 48 test specimens (NSS and HSC) Ave SD Max Min β

1.13 0.079 1.30 0.96 1.79

0.89 0.065 1.04 0.72 3.34

0.93 0.075 1.07 0.76 3.01

0.98 0.076 1.12 0.81 2.71

1.02 0.087 1.17 0.84 2.43

fyo > 460 MPa and fc ≤ 50 MPa: 10 test specimens (HSS and NSC) Ave SD Max Min β

1.05 0.049 1.11 0.97 2.34

0.77 0.066 0.86 0.69 4.09

0.79 0.059 0.87 0.72 4.04

0.85 0.059 0.94 0.80 3.63

0.87 0.064 0.96 0.81 3.52

k ¼ 3.0 0.99 0.071 1.14 0.82 2.64

fyo > 460 MPa and fc > 50 MPa: 03 test specimens (HSS and HSC) Ave SD Max Min β

1.07 0.112 1.14 0.94 2.06

0.89 0.002 0.89 0.88 3.61

0.90 0.002 0.90 0.90 3.47

0.94 0.040 0.97 0.89 3.10

0.98 0.065 1.02 0.90 2.77

1.00 0.051 1.03 0.94 2.69

1.07 0.249 1.23 0.78 1.55

k ¼ 4.1 0.95 0.002 0.96 0.95 3.08

k ¼ 3.0 0.94 0.001 0.94 0.94 3.17

122

Concrete-Filled Double-Skin Steel Tubular Columns

from Fig. 3.48, from which it is clear that the model sensitivity is nearly constant in contrast to other design methods presented in the same figure. The validity ranges of this resistance proposal are: Do/to ¼ 18.7
176.7, Di/ti ¼ 10.5
146, Di/ Do ¼ 0.18
0.89, fyo ¼ 220
618 MPa, fyi ¼ 216
520 MPa, and fc ¼ 18.7
141 MPa.

3.6.4.2 Comparisons with different subgroups Herein, another comparison is made on different subgroups with respect to section slenderness and material grades. Accordingly, the database shown in Table 3.20 was divided into two main groups: (1) columns with Do/to  90  (235/fyo), which is compatible with the regulations of EC4 [2] (Table 3.22), and (2) those with Do/to  90  (235/fyo) (Table 3.23). The first group contains 109 test specimens, whereas the latter group consists of 64 specimens. Then, each group is divided into four subgroups in Table 3.22 based on the material grades: (1) case of fyo  460 MPa (NSS) and fc  50 MPa (NSC), which is compatible with the regulations of EC4 [2], (2) case of fyo  460 MPa (NSS) and fc > 50 MPa (HSC), (3) case of fyo > 460 MPa (HSS) and fc  50 MPa (NSC), and case of fyo > 460 MPa (HSS) and fc > 50 MPa (HSC). A quick look at Table 3.22 and Table 3.23 shows that the available tests on CFDST short columns with HSS are extremely limited in number. Thus, significant efforts are still required to enhance the current knowledge of CFDST short columns composed of HSS.

Columns with permitted slenderness (Do/to) From Table 3.22, it can be observed that all design methods, except those of EC4 [2] and Uenaka et al. [21], produced safe results with acceptable β values for EC4 [2]compliant CFDST columns, i.e., those consisting of NSS and NSC. However, it can be confirmed that the proposed design resistance provides the best predictor in this subgroup than that provided by Hassanein and Kharoob [45] because it was based on NSC during its formulation. For the second subgroup in which the concrete is high-strength, the method of Yan et al. [83] and the currently proposed method yielded the most accurate results. However, the proposed method somewhat provides nonconservative results by about 2% in average, indicating that it requires a slight enhancement to account for the less pronounced effect of confinement of HSC [95,96]. Therefore, the triaxial factor (k) has been taken as 3.0 in agreement with the results of Cederwall [94]. By doing so, the slightly modified proposed design resistance yielded the best average ratio (PProp/ Pul,Exp ¼ 0.99) with proven design integrity. With regard to the third subgroup (HSS and NSC), the method provided by Hassanein and Kharoob [45] in addition to the proposed one produced the most accurate results compared with the resistances of the test specimens. This is because Hassanein and Kharoob [45] based their design resistance on columns filled with ordinary concrete. On the other hand, resistance of CFDST columns with high-strength steel and concrete was obtained safely and reliably with all design methods, except

Table 3.23 Statistical evaluation of thePR/Pul, Exp ratios using different design resistance methods, considering different material grades with Do/to > 90  (235/fyo). EC4 [2]

ACI [81]

AISC [82]

Yan et al. [83]

Han et al. [84]

Hassanein and Kharoob [45]

Uenaka et al. [21]

0.93 0.092 1.11 0.64 2.84

1.01 0.111 1.24 0.82 2.42

0.075 1.26 0.94 2.47

0.97 0.086 1.13 0.82 2.72

0.97 0.108 1.16 0.76 2.66

k ¼ 4.1 1.05 0.080 1.21 0.91 2.31

1.00 0.087 1.12 0.91 2.53

1.14 0.143 1.35 1.04 1.71

k ¼ 4.1 1.00 0.086 1.11 0.90 2.57

Proposed resistance

fyo ≤ 460 MPa and fc ≤ 50 MPa: 33 test specimens (NSS and NSC) k ¼ 4.1 Ave SD Max Min β

1.02 0.081 1.21 0.84 2.43

0.83 0.085 1.02 0.64 3.46

0.88 0.082 1.07 0.70 3.25

0.91 0.075 1.10 0.73 3.15

0.91 0.079 1.09 0.72 3.13

fyo ≤ 460 MPa and fc > 50 MPa: 18 test specimens (NSS and HSC) Ave SD Max Min β

1.03 0.091 1.19 0.88 2.39

0.89 0.074 1.02 0.75 3.29

0.93 0.074 1.07 0.80 3.01

0.95 0.076 1.10 0.82 2.88

0.96 0.076 1.10 0.83 2.86

k ¼ 3.0 1.02 0.075 1.17 0.88 2.49

fyo > 460 MPa and fc ≤ 50 MPa: 04 test specimens (HSS and NSC) Ave SD Max Min β

1.13 0.104 1.28 1.04 1.78

0.86 0.073 0.95 0.77 3.42

0.89 0.076 0.98 0.80 3.23

0.94 0.081 1.05 0.85 2.95

0.93 0.080 1.04 0.84 2.97

Continued

Table 3.23 Continued EC4

ACI

AISC

Yan et al.

Han et al.

Hassanein and Kharoob

Uenaka et al.

Proposed resistance

0.95 0.028 1.00 0.90 3.07

0.84 0.054 0.93 0.77 3.74

k ¼ 4.1 1.00 0.042 1.07 0.94 2.70

fyo > 460 MPa and fc > 50 MPa: 09 test specimens (HSS and HSC) Ave SD Max Min β

0.97 0.038 1.03 0.91 2.92

0.89 0.022 0.93 0.86 3.55

0.92 0.025 0.95 0.88 3.35

0.92 0.028 0.96 0.87 3.33

0.92 0.028 0.97 0.88 3.27

k ¼ 3.0 0.98 0.037 1.04 0.92 2.85

CFDST short columns formed from carbon steels

125

those of EC4 [2] and Uenaka et al. [21]. However, as this subgroup consists of three columns, it is not possible to draw a general conclusion from it. Accordingly, additional test specimens for CFDST columns with HSS with both NSC and HSC are required to verify the proposed design method with more confidence. Until then, the triaxial factor (k) of 3.0 should be considered in the proposed resistance calculations, taking into account the weak confinement effect of HSC.

3.6.4.2.1 Columns with disallowed slenderness (Do/to) This section is related to the columns with outer tubes of slender cross sections. However, as EC3 [2] does not allow their design, the local buckling effect is ignored in the calculations. For columns with NSS and NSC, all design models produce acceptable results, but the design integrity may be less using those of EC4 [2] and Uenaka et al. [21]. Accordingly, the existing design proposal can be safely used. When HSC is used with NSS, the slightly modified proposed design resistance yields the best average ratio (PProp/Pul, Exp ¼ 1.02) with proven design integrity. On the other hand, the limited test specimens with HSS will not allow significant conclusions to be drawn, although the design proposal seems the most accurate.

3.6.4.3 Comparison with specimens with large void ratios In this section, columns with large void ratios exceeding 0.8 are considered in the comparisons based on the measured dimensions. As they are limited and the emphasis on them has only started recently, only 19 test specimens are available in the literature [70,75,78], and their details are presented in Table 3.24. It is worth noting that Yang et al. [78] in 2022 suggested a new design resistance equation for these columns, which is practically the same as that of Han et al. [84]. Based on the comparisons shown in Table 3.25, the resistance method by Uenaka et al. [21] is highly conservative (PUenaka/Pul,Exp ¼ 0.83), whereas all other methods produce appropriate results. Additionally, it can be seen that all design methods ensure the integrity of the CFDST short columns with large void ratios, since the index β is greater than 2.5 for all. However, the comparisons confirm that the current proposed method is the best predictor because it provides an average PProp/Pul,Exp ratio of unity.

3.6.4.4 Comparison with large-sized CFDST specimens It is well known that international specification design methods [2,81,82] have been validated by comparisons with the test resistances of small-sized CFST columns. This has encouraged several researchers to investigate the size effect of CFST columns (for example, refer to Jin et al. [97,98]). Based on Jin et al. [97], the effect of size on CFST columns with diameters between 50 mm and 200 mm was found to be weak. Accordingly, a study of the accuracy of these specifications becomes mandatory to ascertain the extent to which they provide effective design resistance for large-sized CFDST columns. This is carried out in this section by examining large-sized columns with

Table 3.24 Details of the experimental specimens with large void ratios [70,75,78]. References

Specimen

Do [mm]

to [mm]

Do/to

fyo [MPa]

Di [mm]

ti [mm]

Di/ti

Di/ Do

fyi [MPa]

fc [MPa]

[75] [75] [75] [75] [70] [70] [75] [75] [75] [75] [78] [78] [78] [75] [78] [78] [78] [70] [70]

D1-1 D3-1 A3-1 A3-2 GC1-1 GC1-2 A1-1 A2-2 A1-2 A2-1 Bb-0.85 Aa-0.85 Ab-0.85 D2-1 Bb-0.9 Aa-0.9 Ab-0.9 GCL-1 GCL-2 Max Min

99.7 99.9 76.3 76.3 140.0 140.0 74.8 75.2 74.7 75.4 538.0 538.0 538.0 99.9 538.0 538.0 538.0 450.0 450.0 538.00 74.70

0.59 0.71 1.78 1.74 2.50 2.50 1.03 1.19 0.97 1.29 5.63 3.76 3.76 0.69 5.63 3.76 3.76 8.00 8.00 8.00 0.59

169.0 140.7 42.9 43.9 56.0 56.0 72.6 63.2 77.0 58.4 95.6 143.1 143.1 144.8 95.6 143.1 143.1 56.3 56.3 168.98 42.87

409.0 409.0 486.0 512.0 307.0 307.0 486.0 486.0 486.0 486.0 296.3 253.8 253.8 409.0 296.3 253.8 253.8 365.0 365.0 512.00 253.80

80.3 80.5 62.0 62.0 114.0 114.0 62.0 62.4 62.0 62.7 448.0 449.0 449.0 86.8 473.0 477.0 477.0 400.0 400.0 477.00 62.00

0.55 0.67 1.00 0.94 2.00 2.00 1.00 1.20 0.94 1.23 5.63 5.63 5.63 0.61 5.63 5.63 5.63 8.00 8.00 8.00 0.55

146.00 120.15 62.00 65.96 57.00 57.00 62.00 52.00 65.96 50.98 79.57 79.75 79.75 142.30 84.01 84.72 84.72 50.00 50.00 146.00 50.00

0.81 0.81 0.81 0.81 0.81 0.81 0.83 0.83 0.83 0.83 0.83 0.83 0.83 0.87 0.88 0.89 0.89 0.89 0.89 0.89 0.81

474.0 474.0 470.0 470.0 321.0 321.0 470.0 470.0 470.0 470.0 296.30 296.30 296.30 444.0 296.30 296.30 296.30 363.0 363.0 474.00 296.30

58.60 58.60 58.60 58.60 39.78 39.78 58.60 58.60 58.60 58.60 39.07 56.10 39.07 58.60 39.07 56.10 39.07 43.12 43.12 58.60 39.07

Table 3.25 PR/Pul, Exp ratios using different design resistance methods for specimens with large void ratios.

References

Specimen

EC4 [2]

[75] [75] [75] [75] [70] [70] [75] [75] [75] [75] [78] [78] [78] [75] [78] [78] [78] [70] [70]

D1-1 D3-1 A3-1 A3-2 GC1-1 GC1-2 A1-1 A2-2 A1-2 A2-1 Bb-0.85 Aa-0.85 Ab-0.85 D2-1 Bb-0.9 Aa-0.9 Ab-0.9 GCL-1 GCLAve SD Max Min β

1.06 0.92 0.94 0.95 0.99 1.07 0.99 0.91 0.94 0.94 0.96 0.96 0.97 0.88 1.02 1.07 0.96 0.94 0.96 0.97 0.052 1.07 0.88 2.88

ACI [81]

AISC [82]

Yan et al. [83]

Han et al. [84]

Hassanein and Kharoob [45]

Uenaka et al. [21]

Proposed resistance

0.95 0.83 0.88 0.89 0.92 0.99 0.93 0.86 0.88 0.89 0.88 0.87 0.89 0.82 0.98 1.01 0.92 0.95 0.96 0.91 0.052 1.01 0.82 3.28

1.00 0.87 0.90 0.90 0.94 1.02 0.95 0.88 0.90 0.91 0.91 0.92 0.93 0.86 1.00 1.05 0.95 0.96 0.97 0.94 0.052 1.05 0.86 3.09

1.02 0.88 0.89 0.90 0.94 1.01 0.95 0.87 0.90 0.91 0.91 0.93 0.94 0.86 1.00 1.05 0.95 0.94 0.96 0.94 0.052 1.05 0.86 3.11

1.01 0.88 0.90 0.90 0.95 1.02 0.96 0.88 0.91 0.92 0.92 0.93 0.94 0.86 1.01 1.06 0.95 0.95 0.96 0.94 0.052 1.06 0.86 3.06

0.95 0.90 0.94 0.94 0.98 1.05 0.98 0.90 0.93 0.94 0.94 0.95 0.96 0.88 1.03 1.07 0.97 0.98 0.99 0.96 0.049 1.07 0.88 2.94

0.97 0.83 0.78 0.78 0.85 0.91 0.85 0.77 0.80 0.80 0.82 0.88 0.87 0.76 0.85 0.95 0.84 0.76 0.77 0.83 0.061 0.97 0.76 3.76

1.16 1.00 0.95 0.96 1.00 1.08 1.03 0.94 0.98 0.97 0.96 0.95 0.98 0.95 1.04 1.08 0.99 0.98 0.99 1.00 0.056 1.16 0.94 2.68

Table 3.26 Details of the experimental large-sized CFDST specimens [13,24,67,70,71,78]. References

Specimen

[24] [24] [67]

cc7a cc7b DS-06-2-2C DS-06-4-2C C1-1 C1-2 C1-1 C1-2 C2-1 C2-2 GCL-1 GCL-2 Aa-0.8 Aa-0.85 Aa-0.9 Ab-0.8 Ab-0.85 Ab-0.9 Bb-0.8 Bb-0.85 Bb-0.9 Max Min

[67] [13] [13] [71] [71] [71] [71] [70] [70] [78] [78] [78] [78] [78] [78] [78] [78] [78]

Do [mm]

to [mm]

Do/to

fyo [MPa]

Di [mm]

ti [mm]

Di/ti

fyi [MPa]

fc [MPa]

300.0 300.0 300.0

3.00 3.00 2.00

100.0 100.0 150.0

275.9 275.9 291.6

165.0 165.0 180.0

3.00 3.00 2.00

55.00 55.00 90.00

320.5 320.5 291.6

37.09 37.09 27.90

300.0

4.00

75.0

291.6

180.0

2.00

90.00

291.6

27.90

350.0 350.0 356.0 356.0 356.0 356.0 450.0 450.0 538.0 538.0 538.0 538.0 538.0 538.0 538.0 538.0 538.0 538.00 300.00

3.82 3.82 5.50 5.50 5.50 5.50 8.00 8.00 3.76 3.76 3.76 3.76 3.76 3.76 5.63 5.63 5.63 8.00 2.00

91.6 91.6 64.7 64.7 64.7 64.7 56.3 56.3 143.1 143.1 143.1 143.1 143.1 143.1 95.6 95.6 95.6 150.00 56.25

439.3 439.3 618.0 618.0 618.0 618.0 365.0 365.0 253.8 253.8 253.8 253.8 253.8 253.8 296.3 296.3 296.3 618.00 253.80

231.0 231.0 219.0 219.0 168.0 168.0 400.0 400.0 418.0 449.0 477.0 418.0 449.0 477.0 420.0 448.0 473.0 477.00 165.00

2.92 2.92 3.30 3.30 3.30 3.30 8.00 8.00 5.63 5.63 5.63 5.63 5.63 5.63 5.63 5.63 5.63 8.00 2.00

79.11 79.11 66.36 66.36 50.91 50.91 50.00 50.00 74.25 79.75 84.72 74.25 79.75 84.72 74.60 79.57 84.01 90.00 50.00

396.5 396.5 356.0 356.0 357.0 357.0 363.0 363.0 296.30 296.30 296.30 296.30 296.30 296.30 296.30 296.30 296.30 396.50 291.60

42.14 42.14 36.20 36.20 36.20 36.20 43.12 43.12 56.10 56.10 56.10 39.07 39.07 39.07 39.07 39.07 39.07 56.10 27.90

Table 3.27 PR/Pul, Exp ratios using different design resistance methods for large-sized CFDST specimens [13,24,67,70,71,78].

References

Specimen

[24] [24] [67]

cc7a cc7b DS-06-22-C DS-06-42-C C1-1 C1-2 C1-1 C1-2 C2-1 C2-2 GCL-1 GCL-2 Aa-0.8 Aa-0.85 Aa-0.9 Ab-0.8 Ab-0.85 Ab-0.9 Bb-0.8 Bb-0.85 Bb-0.9 Ave SD Max Min β

[67] [13] [13] [71] [71] [71] [71] [70] [70] [78] [78] [78] [78] [78] [78] [78] [78] [78]

EC4 [2]

ACI [81]

AISC [82]

Yan et al. [83]

Han et al. [84]

Hassanein and Kharoob [45]

Uenaka et al. [21]

Proposed resistance

1.01 1.03 1.07

0.82 0.84 0.89

0.87 0.89 0.94

0.90 0.92 0.97

0.90 0.92 0.97

0.94 0.96 1.01

1.00 1.02 1.05

0.97 0.99 1.10

1.11

0.89

0.93

0.96

0.97

1.02

1.08

1.04

0.98 0.99 1.10 1.11 1.28 1.04 0.94 0.96 0.98 0.96 1.07 0.93 0.97 0.96 0.97 0.96 1.02 1.02 0.082 1.28 0.93 2.49

0.81 0.82 0.86 0.87 0.95 0.77 0.95 0.96 0.87 0.87 1.01 0.83 0.89 0.92 0.86 0.88 0.98 0.88 0.061 1.01 0.77 3.42

0.85 0.86 0.89 0.90 0.98 0.80 0.96 0.97 0.92 0.92 1.05 0.87 0.93 0.95 0.89 0.91 1.00 0.92 0.057 1.05 0.80 3.20

0.87 0.89 0.92 0.94 1.05 0.85 0.94 0.96 0.94 0.93 1.05 0.88 0.94 0.95 0.90 0.91 1.00 0.94 0.052 1.05 0.85 3.11

0.87 0.89 0.92 0.93 1.04 0.84 0.95 0.96 0.94 0.93 1.06 0.88 0.94 0.95 0.91 0.92 1.01 0.94 0.052 1.06 0.84 3.10

0.91 0.93 0.99 1.00 1.12 0.91 0.98 0.99 0.96 0.95 1.07 0.90 0.96 0.97 0.93 0.94 1.03 0.97 0.055 1.12 0.90 2.85

0.92 0.93 1.04 1.06 1.35 1.09 0.76 0.77 0.92 0.88 0.95 0.86 0.87 0.84 0.86 0.82 0.85 0.95 0.135 1.35 0.76 2.66

0.94 0.96 0.98 0.99 1.11 0.90 0.98 0.99 0.96 0.95 1.08 0.94 0.98 0.99 0.95 0.96 1.04 0.99 0.055 1.11 0.90 2.73

130

Concrete-Filled Double-Skin Steel Tubular Columns

a diameter of more than 300 mm. As can be observed, a minimum diameter of CFDST columns of 300 mm was taken to ensure the existence of the size effect, compared to CFST columns of 200 mm in diameter. Based on this assumption, only 21 CFDST columns from the database [13,24,67,70,71,78] can be considered as large-sized specimens (see Table 3.26). As can be seen in the table, the concrete was of almost normal strength, whereas the outer tubes were made of NSS and NSC. Based on the comparisons shown in Table 3.27 for PR/Pul,Exp ratios of different methods, it can be seen that the design resistance methods provide appropriate results with an acceptable index β, with the ACI [81] being the most conservative. On the other hand, the proposed method yields the best resistances for the CFDST short columns, with an average ratio of PProp/Pul,Exp of 0.99. Hence, the proposed design resistance once again demonstrated its exact results relative to other design predictions. However, additional tests should be performed on large-sized CFDST columns to verify the proposed resistance over a wider range of fyo, fyi, and fc.

3.7

Conclusions

This chapter has provided the behavior of concrete-filled double skin composite columns for use in onshore and offshore applications, which have the ability to produce members with extremely high load-bearing capacities with relatively low weight compared to the conventional concrete-filled tubes. The behavior and strength of CFDST short columns with different cross sections have been addressed through FE modeling. Each cross section has been dealt with separately because the validation required for each is different. For each cross section, the effect of the hollow ratio of the column, inner and outer steel thicknesses, and concrete and steel strengths on the compressive behavior of the CFDST short columns has been thoroughly examined. Based on the numerical results, the following conclusions can be drawn for circular-circular CFDST short columns: 1. Outer steel thickness has a significant effect on the ultimate axial load of CFDST short columns. As found from the results, increasing the outer steel thickness increases the ultimate axial load but decreases the ductility of the columns. 2. Increasing the hollow ratio of a column would decrease the ultimate axial load, whereas increasing the inner and outer steel thicknesses was found to increase the ultimate axial load. In addition, inner steel thickness obviously affects the final deformation shape of the columns significantly. 3. The new confining stress-based design proposed in this chapter was found to accurately provide the strengths of the circular-circular CFDST columns.

For circular-square CFDST short columns, the following conclusions can be drawn: 4. A 50% increase in the ultimate concentric axial strength can be achieved by increasing the concrete’s compressive strength three times. 5. Increasing the steel yield stress significantly improves the axial capacity of CFDST short columns. However, the specimens become more brittle and exhibit a sudden failure mode.

CFDST short columns formed from carbon steels

131

6. The maximum axial strength of CFDST specimens decreases as the Do/to ratio of the outer tube increases. 7. The width-to-thickness (Bi/ti) ratio of the inner tube seems to have a small effect on the behavior of CFDST short columns. 8. The axial capacity of CFDST short columns seems to be affected as the hollow ratio increases. The specimen with a hollow ratio (χ) equal to 0.37 was found to have a better response in terms of maximum axial strength and energy absorbed defined by the area under the entire load-displacement behavior.

The following conclusions can be drawn with respect to square-square CFDST short columns: 9. In group 1, it was found that as the slenderness ratio of the outer tube increased, the capacity of the column also declined. The reduction in the weight of the columns was overshadowed by this reduction in capacity, meaning that the strength-to-weight ratio of the columns declined as the thickness of the outer tube decreased. 10. For the specimens in group 2, the inner tube’s thickness was reduced. Across these four specimens, a similar trend to group 1 of reduction in strength, albeit not as pronounced, was observed. The reduction in inner tube’s thickness was accompanied by a decline in column capacity and subsequent strength-to-weight ratio. 11. The hollow section ratio was investigated in group 3 specimens. It was found that as the hollow ratio increased from 0.1 to 0.6 across the four specimens, both the capacity and weight of the columns were improved. It was found from this group that increasing the hollow ratio was a highly effective way of improving the strength-to-weight ratio of the CFDST columns. 12. Four specimens in group 4 were used to examine the capacity of the columns with concrete strength ranging from 60 MPa to 180 MPa. It was found that while the increased concrete strength brought about a greater column capacity, the process was only approximately 35% efficient. Moreover, the columns appeared to succumb to brittle failure, which is highly unfavorable for construction purposes. The results of these tests indicate that increasing the concrete strength may not be a highly effective method of improving the performance of CFDST columns. 13. Group 5 was used to study the impact of the steel strength on the compressive capacity of the column. As expected, it was found that the steel strength greatly improved the capacity of the column. Again, this improvement was relatively inefficient, however, with an increase in steel strength of 100%, resulting in an overall increase in the capacity of only 58.4%. This efficiency slumped even further when stronger steel was used. A positive outcome from this group of tests, however, was the ductile nature, in which the columns failed. This form of failure is desirable from a construction perspective. 14. The axial strength model by Han et al. [36] was found to be suitable for the current axially loaded square CFDST columns with inner SHS tubes.

The most important conclusion with respect to square-circular CFDST short columns is: 15. The comparisons between the generated results and the strength predictions of Han et al. [16] showed that this design model is on the unsafe side in slender outer tubes. A revised design model was then proposed, based on the provisions of EC4 [18], but with a reduced contribution from the sandwiched concrete to account for different column sizes, and was shown to yield improved predictions of cross-sectional strength.

132

Concrete-Filled Double-Skin Steel Tubular Columns

Appendix Progressive axial loading of specimen C6C8 at different time intervals

(1) t = 0.0 min

(2) t = 5.0 min

(3) t = 10 min

(4) t = 15 min

(5) t = 20 min

(6) t = 25 min

(Continued)

CFDST short columns formed from carbon steels

133

(7) t = 20 min

(8) t = 25 min

(9) t = 40 min

(10) t = 45 min

Cont’d

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Further reading M.F. Hassanein, M. Elchalakani, V.I. Patel, Overall buckling behaviour of circular concretefilled dual steel tubular columns with stainless steel external tubes, Thin-Walled Struct. 115 (2017) 336–348. M.F. Hassanein, O.F. Kharoob, M.H. Taman, Experimental investigation of cementitious material-filled square thin-walled steel beams, Thin-Walled Struct. 143 (2017) 134–143.

CFDST short columns formed from stainless steel outer tubes 4.1

4

Introduction

Nowadays, different stainless steel types can provide a wide range of mechanical properties and material characteristics to suit the demands of numerous construction applications, without the need for surface corrosion protection even in highly aggressive environments [1]. In fact, austenitic grades, which contain around 8%–11% nickel, are the most common stainless steel types that are increasingly used in construction. Nickel stabilizes the austenitic microstructure and consequently contributes to the associated favorable characteristics such as formability, weldability, toughness, and high temperature. However, nickel represents a significant portion of the cost of austenitic stainless steels. On the other hand, duplex stainless steels offer higher strength than do austenitic steels and a great majority of carbon steels with similar or higher corrosion resistance. Accordingly, duplex grades have great potential for expanding future structural design possibilities, enabling a reduction in section sizes and leading to lighter structures (see Fig. 4.1A). However, duplex stainless steel grades are commonly classified into different groups, depending on their alloy content and corrosion resistance, with the lean duplex grade being one of them. Lean duplex steels have low nickel content (around 1.5%), such as Grade EN 1.4162. Hence, a significant reduction in both the initial material cost and cost fluctuation can be gained [1–4]; therefore, they have been structurally used in recent years as shown in Fig. 4.1B. The behavior of stainless steel materials is different from that of carbon steels [2,3]. Stainless steels have a rounded stress-strain curve without a well-defined yield plateau and low proportional limit stress compared to carbon steels. However, despite early applications of lean duplex materials (including, for example, two footbridges in Norway and Italy [5]), their structural properties are still to some extent unverified since only limited test results on their structural components have been reported. Therefore, research projects are currently underway in different universities and research centers to address these shortcomings. Lean duplex stainless steel hollow section columns (LDSSHSCs) were experimentally and numerically investigated by Theofanous and Gardner [6] and later on by Huang and Young [7]. In addition, finite element (FE) studies on LDSSHSCs with different cross-sectional shapes were presented by Patton and Singh [8]. Moreover, Hassanein [9] numerically studied the compressive strengths of concrete-filled lean duplex stainless steel tubular stub columns with thinwalled square and rectangular cross sections. Furthermore, the investigations were extended to lean duplex stainless steel beams [10–12]. It should be mentioned that the previous numerical investigations [6–12] were undertaken using the general-purpose FE package ABAQUS [13]. The available test Concrete-Filled Double-Skin Steel Tubular Columns. https://doi.org/10.1016/B978-0-443-15228-3.00004-6 Copyright © 2023 Elsevier Inc. All rights reserved.

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Fig. 4.1 Structural applications of different duplex stainless steels. (A) Road bridge near Siena – Duplex stainless steel. (B) Footbridge near Siena – Lean duplex stainless steel.

results were used to validate the FE models [6–12], which were thereafter employed in parametric studies. It is worth pointing out that a compound Ramberg-Osgood material model [14], which is a two-stage version of the basic Ramberg-Osgood model [15,16], was used in the numerical analyses [6,10,12]. On the other hand, the twostage, full-range, stress-strain relationship for stainless steel developed by Rasmussen [17] was used by the current author [9,11]. The results [6–12] indicate that lean duplex stainless steel members are not completely compliant with the international steel structures codes, based on assumed analogies with carbon steel behavior, because of their rounded stress-strain curves. Concrete-filled steel tubular (CFST) short columns (Fig. 4.1A) are one of the most important structural elements in modern construction around the world in both nonseismic and high-seismic zones. CFST columns are used to increase the height of buildings for effective usage of the limited land area. In a CFST column, the concrete core prevents the premature local buckling of the steel tube and the steel tube offers confinement to the concrete core. The confinement effect increases the strength of concrete in circular CFST columns. The high load-carrying capacity of a CFST column is accompanied by other good structural performances, such as high ductility and energy dissipation ability, due to the composite action between the steel and concrete. Some important findings about the compressive behavior of CFST columns are summarized as follows: 1. Bradford et al. [18] investigated the local and postlocal buckling of circular steel tubes filled by means of a rigid medium, with the emphasis being on the strength of the CFST sections. They proposed a cross-sectional slenderness limit that delineates between a fully effective cross section and a slender cross section. This cross-sectional slenderness is given by 125/(fy/250), where fy is the steel yield strength. 2. Ding et al. [19] reported that the confinement effect, ultimate capacity, and ductility of CFST columns were found to improve with an increase in the steel ratio and yield stress. On the other hand, increasing the concrete’s compressive strength increases the ultimate load capacity but decreases the ductility of CFST columns.

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141

3. Liang and Fragomeni [20] found that the existing confining pressure models, which were developed based on normal strength materials, generally overestimate the lateral confining pressures in high-strength circular CFST columns. Therefore, a more accurate constitutive model for the confined concrete in both normal and high-strength circular CFST columns was proposed. The constitutive relationships for the confined concrete can be used in numerical techniques for modeling the nonlinear behavior of circular CFST columns. This proposed design formula can be used by practicing structural engineers to design highstrength circular CFST columns, which are not covered by the current design codes. Their study demonstrates that increasing the tube’s diameter-to-thickness (D/t) ratio reduces the ultimate strength of CFST columns in addition to their section and axial ductility performance. 4. The results of the parametric study conducted by Ellobody et al. [21] showed that the design rules for CFST columns specified in the American specifications [22] and Australian Standards [23,24] are conservative. However, the design strengths predicted by Eurocode 4 [25] are generally nonconservative for carbon steel CFST columns.

In order to make use of the advantages of lean duplex stainless steel and confined concrete, concrete-filled lean duplex stainless steel circular tubular short columns of Grade EN 1.4162 (CFSST) have been suggested in the literature [26]. As such, concrete-filled double skin steel tubular (CFDST) short columns have been studied by researchers [27–30]. A composite short column consists of concentric inner and outer steel tubes with concrete filled in between (see Fig. 4.2B). The application of CFDST columns was found to reduce the self-weight of the structure due to the hollow

t

te

Concrete core

ti

d

Sandwiched concrete

D

D

(a)

(b) te ti

Concrete core

d

Sandwiched concrete

D (c)

Fig. 4.2 Types of circular concrete-filled tubular stub columns. (A) CFST or CFSST; (B) CFDST; (C) CFDT.

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inner tubes. CFDST columns have been recognized to have advantages, such as high strength and bending stiffness, higher fire resistance, and favorable construction ability. These columns can be used in seismic-resistant structures such as high-rise bridge piers to mitigate seismic force on the foundation. Accordingly, LDSS was considered to surround the CFDST columns [31]. Thereafter, a CFDT column (Fig. 4.2C), which is composed of a hollow section consisting of an austenitic external stainless steel tube and an internal concentrically placed carbon steel tube with concrete filling in the whole tubular section, was introduced by Chang et al. [32]. This inspired the current authors to once again provide a cheaper cross section by utilizing LDSS [33]. Hence, in this chapter, the behavior and ultimate axial strengths of circular CFSST, CFDST, and CFDT short columns that unitize the lean duplex stainless steel of Grade EN 1.4162 are presented. Finite element models are developed using the generalpurpose FE package ABAQUS [13] and verified by the experimental results. The models are then used to investigate the behavior of such short columns with various parameters. The FE results are discussed and compared with the current international design codes to provide the most accurate design strengths.

4.2

Finite element models

4.2.1 Finite element type and mesh Owing to the thin-walled nature of the lean duplex stainless steel tubes of Grade EN 1.4162, and in line with similar previous investigations [9,34,35], shell elements were employed to discretize the stainless steel tubes. However, the three-node, triangular, finite-membrane-strain element S3 [13] has been utilized in this study. A convergent study of the mesh was conducted by Wu [36] using a range of element sizes for circular CFST columns. It was shown that the results of a circular CFST column with 30 (5
6) elements were almost identical to those with 192 (16
12) elements. Since mesh refinement has an insignificant influence on the numerical results, coarse meshes could be used through the finite element analyses of concrete-filled columns. Accordingly, a mesh of an approximate global size of 25 mm was used in the current modeling for the stainless steel tubes and concrete cores (see Fig. 4.3A). For the concrete core and the two cover plates, threedimensional, four-node, linear, tetrahedron solid elements, the so-called C3D4 [13], were used. To simulate the bond between the stainless steel tube and the concrete core, a surface-based interaction with a contact pressure-overclosure model in the normal direction and a Coulomb friction model in the directions tangential to the surface were used. In order to establish a contact between two surfaces, both the slave and master surfaces must be carefully chosen. Generally, if a smaller surface contacts a larger surface, then it is best to choose the smaller surface as the slave surface. If the distinction cannot be made, then the master surface should be chosen as the surface of the stiffer body or as the surface with the coarser mesh if the two surfaces are on structures with comparable stiffness. The stiffness of the structure and not just the material

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143

(a)

(b)

Loaded level of the cap

Lower bound of the CFSST

Fig. 4.3 A typical finite element model for both CFST and CFSST columns: (A) FE mesh and (B) boundary conditions and load application.

should also be considered when choosing the master and slave surfaces. Herein, a thin sheet of stainless steel is less stiff than a larger block of concrete core, even though the stainless steel material has a higher stiffness than the concrete material. Therefore, the stainless steel surface was chosen as the slave surface, whereas the concrete core surface was chosen as the master surface. Typical FE meshes of CFSST and CFDT columns are shown in Fig. 4.4.

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(a)

(b) Sandwiched concrete External lean duplex tube Lower cap Upper cap Concrete core Internal carbon steel tube

Fig. 4.4 Typical FE meshes of (A) CFDST and (B) CFDT columns.

4.2.2 Boundary conditions and load application The CFSST columns considered herein had fixed ends, but displacement at the loaded end (the upper level of the cap) in the direction of the applied load was allowed. Additionally, the upper and lower bounds of the CFSST columns were restrained to move laterally so that the elephant foot buckling at both ends of the columns was prevented. A uniform distributed load was statically applied to the top of the upper cover plate using the displacement control. The load was incrementally applied using the modified RIKS method available in the ABAQUS library. In the RIKS method, the load is applied proportionally in several load increments. In each load increment, the equilibrium condition is achieved by a numerical iterative scheme. This method is often used in static analysis and has been shown to be efficient in nonlinear analysis. The nonlinear geometry parameter *NLGEOM was included to deal with the large displacement analysis. The load application for a typical CFSST column is presented

CFDST short columns formed from stainless steel outer tubes

145

(a) Loaded level of the cap Plane of symmetry (YZ) Lower bound of the CFSST

Plane of symmetry (XZ)

(b)

Fig. 4.5 Typical boundary conditions and load application of (A) CFDST and (B) CFDT columns.

in Fig. 4.3B. On the other hand, quarter of the CFSST and CFDT columns are modeled to reduce the FE solution times without sacrificing the accuracy, as shown in Fig. 4.5.

4.2.3 Material model 4.2.3.1 Lean duplex stainless steel The structural behavior of CFSST columns depends on the mechanical properties of the lean duplex stainless steel material. According to EN 10088-4 [4], the cold-formed lean duplex stainless steel of Grade EN 1.4162 has a minimum of 0.2% proof stress (σ 0.2) of 530 MPa and an ultimate tensile strength ranging from 700 to 900 MPa. In the current investigation, the ultimate tensile strength is chosen as 700 MPa.

146

Concrete-Filled Double-Skin Steel Tubular Columns

The stainless steel material has been modeled as a von Mises material with isotropic hardening. The nonlinear stress-strain relationships for stainless steel can be represented by the Ramberg-Osgood [15] equation as:
n σ σ ε¼ + 0:002 E0 σ 0:2

(4.1)

where ε is the strain, σ is the stress, E0 is the initial Young’s modulus of the stainless steel, σ 0 is the 0.2% proof stress, and n is the nonlinearity index, which is a measure of the nonlinearity of the stress-strain behavior, with lower n values implying a greater degree of nonlinearity. The degree of nonlinearity varies among different grades of stainless steel. As the value of n increases, the material’s behavior tends to converge to the elasto-plastic behavior of carbon steel (perfect elastic-plastic behavior for n ¼ ∞). Grades of low n values exhibit higher hardening behavior, and, for a given stress level, the benefits of strain hardening comparatively become more apparent. Eq. (4.1) is known to have excellent agreement with experimental stress-strain data up to the 0.2% proof stress (σ 0.2). However, for higher strains, the formula generally overestimates the corresponding stresses. Therefore, a two-stage constitutive model was developed to express the full-range stress-strain behavior of the stainless steel material by Rasmussen [17] as follows: 8
n > σ σ > > for σ  σ 0:2 < E + 0:002 σ 0 0:2 ε¼
m > > σ  σ 0:2 + ε σ  σ 0:2 > + ε0:2 for σ > σ 0:2 : u E0:2 σ u  σ 0:2

(4.2)

where εu is the ultimate strain of the stainless steel, σ u is the ultimate tensile strength of the stainless steel, and E0.2 is the tangent modulus of the stress-strain curve at the 0.2% proof stress and is given as: E0:2 ¼

E0 1 + 0:002n=e

(4.3)

where e is the nondimensional proof stress given as e ¼ σ 0.2/E0 and m ¼ 1 + 3.5(σ 0.2/σ u). The expressions in Eq. (4.2) involves the conventional Ramberg-Osgood parameters n, E0, σ 0.2 and the ultimate tensile strength σ u and strain εu. The expressions have been shown to produce stress-strain curves, which are in good agreement with tests over the full range of strains up to the ultimate tensile strain. Therefore, Eq. (4.2) is used in the current investigation to generate the stress-strain curve of the lean duplex stainless steel material of Grade EN 1.4162, as presented in Fig. 4.6A. The material’s behavior provided by ABAQUS allows for a multilinear stress-strain curve to be used. The first part of the multilinear curve represents the elastic part up to the proportional limit stress with an elastic modulus E0 ¼ 200 GPa, and Poisson’s ratio is taken as 0.3.

CFDST short columns formed from stainless steel outer tubes

(b) Carbon steel

800

400

600

300

Stress [MPa]

Stress [MPa]

(a) Stainless steel

147

400 200

2GPa

200 E0 = 200GPa

100 0

0 0.03 0.06 0.09 Strain [mm/mm]

0

0.12

0

0.02 0.04 0.06 Strain [mm/mm]

0.08

Fig. 4.6 Stress-strain curves of steel materials of (A) external lean duplex stainless steel material of Grade EN 1.4162 and (B) internal tubes.

The proportional limit has been found to be σ 0.01 ¼ 300 MPa. The general stress-strain behavior of the inner carbon steel tubes of CFDST and CFDT columns is shown in Fig. 4.6B.

4.2.3.2 Concrete The concrete core of CFSST columns and sandwiched concrete of both CFDST and CFDT columns It is currently well-known that the concrete confinement effect increases both the strength and ductility of concrete in circular CFST columns. Accordingly, a general stress-strain curve, as shown in Fig. 4.7, is used in the present FE analyses to simulate the material behavior of the confined concrete in circular CFST columns as suggested by Liang and Fragomeni [20]. The part OA of the stress-strain curve is represented using the equations suggested by Mander et al. [37] as:   f 0cc λ εc =ε0cc σc ¼  λ λ  1:0 + εc =ε0cc

(4.4)

(a)

( b)

sc

sc

fcc′

O

A

B

C

e cc

e cu

0.03

fcc′ b c fcc′

A

ec

e cc

O

B

C

e cu

0.03

ec

Fig. 4.7 Stress-strain curves for the confined concrete in circular concrete-filled short columns: (A) D/te  40 and (B) 40 < D/te  150.

148

Concrete-Filled Double-Skin Steel Tubular Columns

λ¼

E c  Ec  f 0cc =ε0cc

(4.5)

0 where σ c is the longitudinal compressive concrete stress, f cc is the compressive strength of the confined concrete, εc is the longitudinal compressive concrete strain, 0 0 ε cc is the strain at f cc , and Ec is Young’s modulus of concrete, which is provided by the ACI [38] as:

Ec ¼ 3320

qffiffiffiffiffiffiffiffi γ c f 0c + 6900ðMPaÞ

(4.6)

where γ c is the strength reduction factor, which accounts for the effects of the column size, the quality of concrete, and the loading rates on the concrete’s compressive strength. This factor (γ c) is provided by Liang [39] as: γ c ¼ 1:85Dc0:135 ð0:85  γ c  1:0Þ

(4.7)

where Dc is the diameter of the concrete core. 0 0 The confined concrete strength f cc and the corresponding strain ε cc , proposed by Mander et al. [37], were modified using the strength reduction factor γ c [39] as: f 0cc ¼ γ c f 0c + kf 0rp ε0cc

¼

ε0c



f 0rp 1 + 5k 0 γcf c

(4.8)  (4.9)

0 is the lateral confining pressure on the concrete core provided by the outer where f rp steel tube. Following Richart et al. [40], the value of k is taken as 4.1. ε c0 is the strain at fc0 of unconfined concrete and can be taken as:

8 0:002 for γ c f 0c  28ðMPaÞ > > < 0 ε0c ¼ 0:002 + γ c f c  28 for 28 < γ c f 0c  82ðMPaÞ > 54000 > : 0:003 for γ c f 0c > 82ðMPaÞ

(4.10)

A confining pressure model for normal or high-strength concrete confined by either a normal or a high-strength steel tube was proposed by Liang and Fragomeni [20] based on the works of Hu et al. [41] and Tang et al. [42]. This model is adopted in the numerical analysis and is expressed by:

f 0rp,ss

8 2t D > > for  47 < 0:7ðνe  νs Þ D  2t σ 0:2 te e
 ¼ D D > > for 47 <  150 σ : 0:006241  0:0000357 te 0:2 te

(4.11)

CFDST short columns formed from stainless steel outer tubes

149

in which D is the outer diameter of the steel tube, t is the thickness of the steel tube wall, and νe and νs are Poisson’s ratios of the steel tube with and without infill concrete, respectively. Poisson’s ratio νs is taken as 0.5 at the maximum strength point, and νe is provided by Tang et al. [42]. Eq. (4.11) has been verified against the test results and can accurately predict the confining pressures on the concrete core in normal or high-strength circular CFST columns [20]. The parts AB and BC of the stress-strain curve depicted in Fig. 4.7 may be written as:
 8 < β f 0 + εcu  εc f 0  β f 0  c cc c cc cc εcu  ε0cc σc ¼ : βc f 0cc for : εc > εcu

for : ε0cc < εc  εcu

(4.12)

where εcu is taken as 0.02 based on the experimental results suggested by Liang and Fragomeni [20] and βc is provided by Hu et al. [41] as: 8 > < 1:0

D for :  40 t βc ¼

D 2 D > : 0:0000339 + 1:3491  0:0102285 t t

for : 40
> for  47 < 0:7ðνe  νs Þ d  2t f sy  t ¼
d d > > for 47 <  150 : 0:006241  0:0000357 f sy t t

(4.15)

0 For the sandwiched concrete (the concrete between both tubes), f rp, s is taken as zero in the Eq. (4.14). However, other parameters are calculated in the same manner as those mentioned earlier but using the outer diameter (d) of the internal carbon steel tube instead of D.

4.3

Comparisons with the experimental results

4.3.1 Lean duplex stainless steel hollow columns In order to check the validity of the stainless steel material’s stress-strain curve as proposed in the study by Rasmussen [17], it is necessary to model the available lean duplex stainless steel bare columns provided in the study by Theofanous and Gardner [6]. Accordingly, the tested lean duplex square hollow section column (80X80X4SC2) was modeled. The measured dimensions of the column’s depth, width, and thickness were 80 mm, 80 mm, and 3.81 mm, respectively. The length of the column was 332.2 mm, and its corner inner radius was 3.6 mm. The column suffered from an initial geometrical imperfection of 0.08 mm. The lean duplex stainless steel material was tested in tension and the following properties were measured: E0 ¼ 199900 MPa, σ 0.2 ¼ 679 MPa, σ u ¼ 773 MPa, and n ¼ 6.5. The stress-strain curve of the material expressed by the equations previously presented in Section 4.2.3.1 is shown in Fig. 4.8. Fig. 4.9 presents the load-end-shortening curve for the lean duplex column (80X80X4-SC2). It can be seen from the figure that the predicted initial axial stiffness, ultimate load, and postpeak behavior are in good agreement with the experimental results. The deformed shape of the lean duplex stainless steel column is displayed in Fig. 4.10, which confirms that the failure mode caused by local buckling compares well with the experimentally observed behavior. It can be concluded that the two-stage constitutive model [17] predicts well the stress-strain curve of the lean duplex material.

CFDST short columns formed from stainless steel outer tubes

151

Stress [MPa]

800 600 400 200 0 0

0.03 0.06 0.09 Strain [mm/mm]

0.12

Fig. 4.8 Stress-strain curve of the lean duplex stainless steel material of Grade EN 1.4162 using the experimental results provided in the study by Theofanous and Gardner [6].

Fig. 4.9 Load-endshortening curves for the column 80X80X4-SC2 [6].

1000.0

Load [kN]

800.0 600.0 400.0 80X80X4-SC2: FE 80X80X4-SC2: EXP

200.0 0.0 0

2

4

6

8

End shortening [mm/mm]

Fig. 4.10 Deformed shape of 80X80X4-SC2, showing the local buckling of the tube. (A) Isometric; (B) Cross-section.

152

Concrete-Filled Double-Skin Steel Tubular Columns

4.3.2 Concrete-filled steel tubular (CFST) columns The developed FE model was used to predict the behavior of CFST short columns tested in the studies by Hu et al. [41], Schneider [44], and Sakino et al. [45]. The dimensions and material properties of the CFST columns are provided in Table 4.1. The definition of symbols is provided in Fig. 4.2. The ultimate axial loads of CFST columns obtained from the finite element analyses are compared with the test data in Table 4.1. The FE model yields good predictions of the ultimate loads of CFST columns. The mean value of PEF/PEXP is 1.01 with a coefficient of variation of 0.042. Fig. 4.11 shows a comparison of the predicted and experimental axial load-strain curves for CFST columns. It should be noted that the strain is an average strain, which is computed by dividing the end shortening by the column length. It can be observed that the FE model predicts well the complete axial load-strain curves for these tested specimens.

4.3.3 Concrete-filled stainless steel tubular (CFSST) columns Finite element analyses have been performed on CFSST columns recently tested by Uy et al. [46]. These CFSST columns were formed from type 304 austenitic stainless steel (Grade EN 1.4301). Two identical specimens were designed to ensure that the experimental results were reliable, where an affixed letter A or B was used. The dimensions and material properties of the columns are provided in Table 4.2. As the ultimate tensile strength of the stainless steel was not provided, it was taken as 540 MPa [47]. It is worth pointing out that for all of the circular CFSST columns in the study by Uy et al. [46], the tests were stopped owing to the apparent overdeformation. Hence, the maximum loads were obtained at the end of the testing with axial strains referred to as εmax. There was still potential to achieve a higher loadcarrying capacity for these specimens. The ultimate axial load predicted by the FE model was taken as the load around the εmax values of each two identical specimens. However, it can be seen from Table 4.3 that a good agreement with tests is obtained using the current FE models. It can be seen that the verifications of (a) the material stress-strain curve based on the study by Theofanous and Gardner [6], (b) the CFST columns using data from the studies by Hu et al. [41], Schneider [44], and Sakino et al. [45], and (c) the CFSST columns considering the study by Uy et al. [46] all ensure the accuracy of simulating the CFSST columns with a high degree of confidence.

4.3.4 CFDST short columns with both carbon steel tubes Tao et al. [48] prepared a pair of identical specimens to ensure that the experimental results were reliable, where an affixed letter a or b was used. The dimensions and material properties of the CFDST short columns in their study [48] are provided in Table 4.4, where fsye and fsyi are the yield strengths of the external and internal tubes, respectively. The cylindrical compressive strength of the sandwiched concrete (fc0 ) was around 37.92 MPa. The definition of the symbols is provided in Fig. 4.1. The

Table 4.1 Comparisons of the numerical and experimental ultimate axial strengths of circular CFST columns. Column

D [mm]

CU-040 [41] 200 CU-047 [41] 140 CU-070 [41] 280 CU-150 [41] 300 CC6-C-4-2 [45] 238 CC6-C-8 [45] 238 CC6-D-4-1 [45] 361 CC6-D-8 [45] 360 Mean Coefficient of variation (COV)

t [mm]

D/t

L [mm]

fy [MPa]

fc0 [MPa]

PFE [MN]

PExp [MN]

PFE PExp

5.0 3.0 4.0 2.0 4.54 4.54 4.54 4.54

40 47 70 150 52.4 52.4 79.4 79.3

840 602 840 840 714 714 1083 1080

265.8 285.0 272.6 341.7 507 507 525 525

27.15 28.18 31.15 27.23 40.50 77.00 41.10 85.10

2.00 0.94 2.97 2.60 3.87 5.36 7.62 11.51

2.02 0.89 3.03 2.61 3.64 5.58 7.26 11.12

0.99 1.06 0.98 1.00 1.06 0.96 1.05 0.97 1.01 0.042

Concrete-Filled Double-Skin Steel Tubular Columns 2.50

1.00

2.00

0.80

P [MN]

P [MN]

154

1.50 1.00

Exp

FE

0.60 0.40

0.50

Exp

FE

0.20

CU-040

CU-047

0.00

0.00 0

0.01

0.005

e

0.02

0.015

3.50

3.00

3.00

2.50

2.50

0.02

0.03

0.04

e

0.05

0.06

2.00

P [MN]

P [MN]

0.01

0

0.025

2.00 1.50

Exp

FE

1.50 Exp

FE

1.00

1.00

0.50

0.50

CU-070

CU-150

0.00

0.00 0

0.005

0.01

0.015

0

0.005

e

0.01

0.015

e

Fig. 4.11 Comparisons of numerical and experimental axial load-strain curves for CFST columns. Table 4.2 Details of circular CFSST columns used in the current verification. Column

D [mm]

t [mm]

L [mm]

σ 0.2 [MPa]

fc0 [MPa]

E0 [GPa]

n

C20-50
1.2 C30-50
1.2 C20-50
1.6 C30-50
1.6

50.8 50.8 50.8 50.8

1.2 1.2 1.6 1.6

150 150 150 150

291 291 298 298

20 30 20 30

195 195 195 195

7 7 7 7

Table 4.3 Results of circular CFSST columns used in the current verification. εExp

Column A

PFE [kN] B

C20-50
1.2 0.178 0.149 C30-50
1.2 0.160 0.145 C20-50
1.6 0.139 0.138 C30-50
1.6 0.177 0.179 Mean Coefficient of variation (COV)

179.5 224 196.5 267

PFE PExp

PExp [kN] A

B

A

B

195 225 203 260

164 237 222 280

0.92 1.00 0.97 1.03 0.98 0.047

1.09 0.95 0.89 0.95 0.97 0.085

Table 4.4 Details and FE results of circular CFDST short columns [48]. Pu,FE Pu,Exp

Pu,Exp [kN] Column CC2 CC3 CC4 CC5 CC6 CC7 Mean Coefficient

D × te [mm]

d × ti [mm]

L [mm]

fsye [MPa]

fsyi [MPa]

Pu,FE [kN]

Case (a)

Case (b)

Case (a)

Case (b)

180
3 180
3 180
3 114
3 240
3 300
3

48
3 88
3 140
3 58
3 114
3 165
3

540 540 540 342 720 900

275.9 275.9 275.9 294.5 275.9 275.9

396.1 370.2 342.0 374.5 294.5 320.5

1728 1570 1354 904 2386 3251

1790 1648 1358 904 2421 3331

1791 1650 1435 898 2460 3266

0.97 0.95 1.00 1.00 0.99 0.98 0.98 0.019

0.96 0.95 0.94 1.01 0.97 1.00 0.97 0.028

of variation (COV)

156

Concrete-Filled Double-Skin Steel Tubular Columns 1600

1000

1400 800

1000

P [kN]

P [kN]

1200

800 CC4a (Exp)

600 400

CC4 (FE)

600 400

CC5a (Exp)

200

CC5 (FE)

200 0

0 0

0.005

0.01

0.015

0

Strain [mm/mm]

0.02

0.03

0.04

0.05

Strain [mm/mm]

2500

3500 3000

P [kN]

2000

P [kN]

0.01

1500 1000

2500 2000 1500

CC6a (Exp)

CC7b (Exp)

1000 CC6 (FE)

500

CC7 (FE) 500

0

0 0

0.01

0.02

0.03

Strain [mm/mm]

0.04

0

0.005

0.01

0.015

Strain [mm/mm]

Fig. 4.12 Comparisons of numerical and experimental axial load-strain curves for CFDST short columns [48].

ultimate axial loads (Pu,FE) of the CFDST short columns obtained from the FE analyses are compared with the test data in Table 4.4. It can be seen from the table that the FE model yields close predictions of the experimental ultimate loads (Pu,Exp) of the CFDST short columns. The mean value of Pu,EF/Pu,EXP is 0.98 and 0.97 for cases (a) and (b), respectively, with coefficients of variation of 0.019 and 0.028, respectively. Fig. 4.12 shows a comparison of predicted and experimental axial load-strain curves for the CFDST short columns. It appears that the FE model effectively predicts the axial stiffness, ultimate axial load, and postpeak behavior of the axial load-strain curves for the tested CFDST short columns.

4.3.5 CFDST short columns with external stainless steel tubes The only experimental results on CFDST short columns with external stainless steel tubes and inner carbon tubes were provided by Han et al. [49]. Unfortunately, only two circular CFDST short columns were tested by them [49]. Their dimensions and material properties are provided in Table 4.5. The length of the columns was 660 mm. The compressive strength of the concrete cylinder was 52.48 MPa. It is worth pointing out that the full details of the stainless steel material, such as the material type and the nonlinearity index (n), were not provided by Han et al. [49]. As a result, the stainless steel was modeled as carbon steel. The ultimate axial loads (Pu,FE) of the CFDST short columns obtained from the FE analyses are compared with the test data in

Table 4.5 Details and FE results of circular CFDST short columns [49]. Outer tube

Pu,FE Pu,Exp

Pu,Exp [kN]

Inner tube

Column

D × te [mm]

d × ti [mm]

σ 0.2 [MPa]

σu [MPa]

fsyi [MPa]

fsui [MPa]

Pu,FE [kN]

Case (a)

Case (b)

Case (a)

Case (b)

C1 C2

220
3.62 220
3.62

159
3.72 106
3.72

319.6 319.6

626.5 626.5

380.6 380.6

519.1 519.1

2572 2848

2537 3436

2566 3506

1.01 0.83

1.00 0.81

158

Concrete-Filled Double-Skin Steel Tubular Columns

Table 4.5. The FE model predicts well the ultimate axial strength of the tested specimen C1 but produces highly conservative results for C2. This is likely attributed to the fact that the actual proof stress of the steel tubes and the compressive strength of concrete would be higher than those provided in Table 4.5.

4.3.6 CFDT short columns with external stainless steel tubes The developed FE model was used to predict the behavior of CFDT short columns tested by Chang et al. [32]. The dimensions and material properties of the CFDT columns are provided in Table 4.1. The ultimate axial loads (Pu,[16]) of the CFDT columns obtained from the finite element analyses using the existing concrete model are compared with the test data in Table 4.6. The FE model yields conservative predictions of the ultimate loads of the CFDT columns. The mean value of Pu,EF/Pu,EXP is 0.89 with a coefficient of variation of 0.062. Fig. 4.13 shows a comparison of predicted and experimental axial load-shortening curves for CFDT columns. The ultimate axial loads (Pu,New) obtained using the new concrete model are also 0 provided in Table 4.7. From Table 4.7, one can gauge how fcc,mod made the ultimate axial loads (Pu,New) closer to the experimental values (Pu,Exp). The mean value of Pu,EF/Pu,EXP is 0.97 with a coefficient of variation of 0.031. The axial load-shortening curves predicted by the FE model with the proposed new concrete model are shown in Fig. 4.13. It appears that the FE model incorporating the proposed concrete model, generally, predicts well the complete axial load-strain curves for the tested CFDT columns. The predicted initial stiffness of the specimens DC108-4C50, DC114-4C50, and DC114-2C50 is generally in good agreement with the experimental results. The experimental load-shortening curve for the specimen DC108-4C60 slightly departs from the predicted one for loading up to about 2400 kN but is in excellent agreement with predictions for loading higher than 2400 kN. All specimens shown in Fig. 4.13 exhibited strain-hardening behavior because of the small D/t ratios. The predicted axial load-shortening curves in the postyield range are generally in good agreement with the experimental ones. The difference between the predicted and experimental data is attributed to the uncertainty of the concrete strength and stiffness. It is noted that the predicted axial shortenings for these specimens are less than those obtained from experiments. This is due to the convergence problem of the nonlinear finite element analysis, which leads to early stopping of the analysis. Table 4.6 Details of circular CFDT columns used in the current verification. External tube

Internal tube

Column

L [mm]

D [mm]

te [mm]

d [mm]

ti [mm]

fc0 [MPa]

DC108-4C50 DC108-4C60 DC114-4C50 DC114-2C50

500 500 500 500

159 159 159 159

4 4 4 4

108 108 114 114

4 4 4 2

45.04 52 45.04 45.04

CFDST short columns formed from stainless steel outer tubes

(b) 3000

3000

2500

2500

2000

2000

P [kN]

P [kN]

(a)

159

1500 Exp

1000

1500 Exp

1000

FE-Existing concrete model 500

FE-Existing concrete mode

500

FE-New concrete model

0

FE-New concrete mode

0 0

20

10

30

40

0

50

10

(d)

3000

2500

2000

2000

1500 Exp

1000

40

50

1500 Exp

1000

FE-Existing concrete mode

FE-Existing concrete mode

500

30

3000

2500

P [kN]

P [kN]

(c)

20

Shortening [mm]

Shortening [mm]

500

FE-New concrete mode

FE-New concrete mode

0

0 0

10

20

30

40

Shortening [mm]

50

0

10

20

30

40

50

Shortening [mm]

Fig. 4.13 Comparisons of numerical and experimental axial load-shortening curves for CFDT columns. (A) DC108-4C50; (B) DC-108-4C60; (C) DC114-4C50; (D) DC114-2C50.

4.4

CFSST columns

4.4.1 Fundamental behavior 4.4.1.1 General FE analyses on eight series of large-scale circular CFSST columns were undertaken to investigate their fundamental behavior. The length of the stub columns (L) was chosen to be three times the diameter (D) of the circular CFSST columns to avoid the effects of column slenderness. Table 4.8 provides the dimensions and concrete strengths of the columns. Compact steel sections as defined by Bradford et al. [18] were considered herein, i.e., the cross-sectional slenderness is less than 59 as σ 0.2 ¼ 530 MPa. The diameter-to-thickness ratio varied from 20 to 59. The effect of residual stresses was not considered because their effect on column capacity was found to be small by Ellobody and Young [35]. The effect of initial imperfections was not incorporated because the strength reduction was not significant compared to thin-walled hollow tubes owing to the delaying effect of the core concrete on the tube buckling, as discussed by Tao et al. [50]. The concrete’s compressive strength varied from 25 to 100 MPa. The maximum loads (PFE) obtained from FE modeling are provided in Table 4.8. The strength index (ξ) is defined as the ratio of the maximum load of the CFSST column (PFE) to the resistance of the composite

Table 4.7 Comparisons of the numerical and experimental ultimate axial strengths of circular CFDT columns. Pu [kN] Column

0 frp,s [MPa]

DC108-4C50 4.25 DC108-4C60 3.33 DC114-4C50 4.18 DC114-2C50 0.94 Mean Coefficient of variation (COV)

0 frp,ss [MPa]

fcc0 [MPa]

0 fcc,mod [MPa]

Pu,[16] [20]

Pu,New

5.07 5.47 5.06 5.06

62.18 65.30 61.55 48.04

82.93 87.73 82.30 68.79

2303 2408 2446 1971

2326 2658 2676 2348

Pu,Exp [kN] 2385 2640 2875 2400

Pu,½17 Pu,Exp

Pu,New Pu,Exp

0.97 0.91 0.85 0.82 0.89 0.067

0.98 1.01 0.93 0.98 0.97 0.031

Table 4.8 Full details of the current circular lean duplex CFSST columns. Group

Column

D [mm]

t [mm]

D/t

L [mm]

fc0 [MPa]

PFE [kN]

ξ

S1

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35 C36 C37 C38 C39 C40 C41 C42 C43 C44 C45 C46 C47 C48

240 240 240 240 240 240 240 240 240 240 240 240 360 360 360 360 360 360 360 360 360 360 360 360 480 480 480 480 480 480 480 480 480 480 480 480 600 600 600 600 600 600 600 600 600 600 600 600

12 12 12 12 12 12 10 10 10 10 10 10 12 12 12 12 12 12 10 10 10 10 10 10 12 12 12 12 12 12 10.7 10.7 10.7 10.7 10.7 10.7 12 12 12 12 12 12 10.2 10.2 10.2 10.2 10.2 10.2

20 20 20 20 20 20 24 24 24 24 24 24 30 30 30 30 30 30 36 36 36 36 36 36 40 40 40 40 40 40 45 45 45 45 45 45 50 50 50 50 50 50 59 59 59 59 59 59

720 720 720 720 720 720 720 720 720 720 720 720 1080 1080 1080 1080 1080 1080 1080 1080 1080 1080 1080 1080 1440 1440 1440 1440 1440 1440 1440 1440 1440 1440 1440 1440 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800

25 40 55 70 85 100 25 40 55 70 85 100 25 40 55 70 85 100 25 40 55 70 85 100 25 40 55 70 85 100 25 40 55 70 85 100 25 40 55 70 85 100 25 40 55 70 85 100

7827 8759 9557 9972 10,870 11,383 6865 7736 8503 9233 9872 10,401 12,799 14,629 16,293 17,836 19,237 20,489 11,045 12,819 14,442 15,950 17,318 18,573 18,248 21,357 24,262 26,951 29,488 31,843 16,522 19,249 22,270 24,887 27,342 29,620 22,872 26,073 29,268 32,462 34,798 38,843 19,948 23,001 26,037 29,110 32,153 35,209

1.43 1.45 1.45 1.40 1.42 1.38 1.43 1.45 1.44 1.42 1.40 1.36 1.40 1.39 1.38 1.36 1.33 1.30 1.36 1.36 1.33 1.31 1.28 1.25 1.36 1.34 1.32 1.30 1.27 1.24 1.32 1.29 1.28 1.25 1.22 1.19 1.25 1.18 1.12 1.08 1.03 1.03 1.20 1.12 1.06 1.02 0.99 0.97

S2

S3

S4

S5

S6

S7

S8

162

Concrete-Filled Double-Skin Steel Tubular Columns

cross section (neglecting the confinement effect) and is expressed by ξ ¼ PFE/(Asfy + Acfc). The calculated strength index for all columns is provided in Table 4.8. The load-strain responses and the effects of the concrete’s compressive strength and D/t ratio on the fundamental behavior of circular CFSST columns are discussed in the following section.

4.4.1.2 Load-strain responses The obtained axial load-strain curves for the current CFSST columns can be classified into two types as shown in Fig. 4.14, where the strain is the average strain calculated by dividing the end shortening by the column length. In the first type, the curve has an initial linear portion followed by a transitional and plastic portion (see, for example, C7 in Fig. 4.14). As can be seen, there is a translation portion (after the end of the linear portion), followed by a line with a small slope until the ultimate load (PFE). Other types of curves (see, for instance, C12 in Fig. 4.14) show an initial linear portion followed by a transitional portion. As the load increased further, the CFSST column reached its first peak load. After reaching this load, the load of the column decreased with increasing axial deformation. This is attributed to the fact that the confinement effect exerted by the steel tube reduced because the steel tube underwent large deformations. Thereafter, the load increased once again at the end of the loading process due to the strain-hardening effect of the lean duplex stainless steel. In some cases, the load was found to increase to a value higher than the first peak load. However, such peak loads for some CFSST columns were associated with extremely high plastic strains. Accordingly, relatively high strains were associated with these peak loads, which are not of general structural interest in reality. Therefore, it is worth pointing out that the maximum loads (PFE), provided in Table 4.8, are either the maximum loads or the first peak loads.

12000

Axial load [kN]

10000 8000 6000 4000 C7

C12

2000 0 0

0.02

0.04

0.06

0.08

Strain [mm/mm]

Fig. 4.14 Types of axial load-strain curves for CFSST columns.

0.1

0.12

CFDST short columns formed from stainless steel outer tubes

163

Fig. 4.15 Axial load-strain curves for S2.

12000

Axial load [kN]

10000 8000 6000 4000 2000

C7

C8

C9

C10

C11

C12

0 0

0.02

0.04

0.06

0.08

0.1

0.12

Strain [mm/mm]

4.4.1.3 Effects of the concrete’s compressive strength The effects of the concrete’s compressive strength on the behavior of CFSST columns under axial load were investigated. The compressive strength of concrete varied between 25 and 100 MPa. The diameter-to-thickness ratio (D/t) was in the range of 20–59. Fig. 4.15 shows the axial load-strain curves for circular CFSST columns C7–C12. It can be seen that increasing the concrete’s compressive strength significantly increases the ultimate axial strength of circular CFSST columns, whereas the initial stiffness remains more or less the same. CFSST columns with small D/t ratios exhibit large axial strains without failure, having excellent ductility. Fig. 4.16 shows the ultimate axial load of circular CFSST columns, indicating that a linear increase in the ultimate axial load is associated with an increase in the concrete’s compressive strength. On the other hand, the efficiency of the cross sections (PFE/PFE, C25) was calculated, where PFE,C25 is the FE strength for the specimen fc0 ¼ 25MPa of each group. Fig. 4.17 provides the efficiency of all columns, as described earlier. Clearly, it can be observed that increasing the fc0 value of the concrete core, for the same lean duplex stainless steel tube, leads to an increase in the strength of the CFSST column. It can be seen from Table 4.8 that increasing the concrete’s compressive strength generally reduces the strength index. This implies that the efficiency of the composite effect decreases with an increase in the concrete’s compressive strength.

4.4.1.4 Effects of the D/t ratio The effects of the diameter-to-thickness ratio (D/t) on the stiffness and strength of circular CFSST columns are examined herein. As shown in Table 4.8, the outer diameter of the circular tubes varies between 240 mm and 600 mm. The columns are characterized by D/t ratios that vary between 20 and 59. The concrete strengths range from 25 MPa to 100 MPa. The axial load-strain curves for CFSST columns with various D/t ratios are presented in Fig. 4.18. It can be seen that the ultimate axial load of

12000 Maximum loads [kN]

Fig. 4.16 Effects of the concrete’s compressive strength on the ultimate axial strengths of CFSST columns of S2.

10000 8000 6000 4000 S2 2000 0 25

40

55

70

85

100

fc′ [MPa]

1.80

1.80

1.70

1.70 S1

S2

1.60

PFE/PFE,C25

PFE/PFE,C25

1.60 1.50 1.40 1.30

S3

S4

40

55

1.50 1.40 1.30

1.20

1.20

1.10

1.10 1.00

1.00 25

40

55

70

85

100

25

85

100

85

100

fc′ [MPa]

fc′ [MPa] 1.80

1.80

1.70

1.70 S5

S6

1.60

PFE/PFE,C25

1.60

PFE/PFE,C25

70

1.50 1.40 1.30

S8

40

55

1.50 1.40 1.30

1.20

1.20

1.10

1.10

1.00

S7

1.00 25

40

55

70

85

100

25

fc′ [MPa]

70

fc′ [MPa]

Fig. 4.17 Efficiency of CFSST columns.

9000

25000

8000

Axial load [kN]

Axial load [kN]

20000 15000 10000 5000

C17

7000 6000 5000 4000 3000 C1

2000

C23

C7

1000 0

0 0

0.02

0.04

Strain [mm/mm]

0.06

0.08

0

0.01

0.02

0.03

Strain [mm/mm]

Fig. 4.18 Effects of the diameter-to-thickness ratio (D/t) ratio of CFSST columns.

0.04

CFDST short columns formed from stainless steel outer tubes

165

circular CFSST columns decreases with an increases in the D/t ratio for both types of axial load-strain curves. Circular CFSST columns with different D/t ratios exhibit the same initial axial stiffness. The results indicate that the stainless steel tubes with largeD/tratios cannot exert a good confinement effect on the concrete. These results confirm the findings for carbon-filled steel tube columns [41]. On the other hand, it can be observed that the efficiency of a CFSST column is enhanced by increasing the D/t ratio (see Fig. 4.17). This means that the cross section is optimized by increasing such a ratio. However, it can be observed from Table 4.8 that increasing the D/t ratio (with all other parameters fixed) reduces the strength index. This means that increasing the D/t ratio as a result of reducing the thickness of the tube decreases the efficiency of the composite effect. This is attributed to the fact that reducing the thickness of the tube leads to a decrease in the confinement effect on the concrete core.

4.4.2 Comparisons with design strengths In this section, a comparison of the ultimate axial strengths of CFSST columns predicted by the FE models and calculated using ACI-318 [38], Eurocode 4 [25], and the continuous strength method (CSM) [51] is provided. Additionally, the design formula for determining the ultimate axial strength of circular CFST columns, recently proposed by Liang and Fragomeni [20], has also been checked. The aim of this comparison is to confirm the results obtained through the parametric FE analysis. It should be noted that in the calculation of the design strengths, no material partial safety factors were used.

4.4.2.1 The ACI code The ultimate axial strengths of CFST columns obtained from the parametric study were first compared with the design strengths predicted by the American specifications. The ACI code [38] ignores the concrete confinement effect. The ACI equation for ultimate axial strength (PACI) of a concrete-filled circular column is given as: PACI ¼ As f y + 0:85Ac f c

(4.16)

where As and Ac represent the cross-sectional areas of the outer tube and the concrete core, respectively, fy is the yield strength of the steel tube taken herein as the 0.2% proof stress (σ 0.2), and fc is the unconfined concrete strength of the concrete core.

4.4.2.2 Eurocode 4 The ultimate axial strengths of CFSST columns were compared with the design strengths predicted by Eurocode 4 (EC4) [25]. The code takes into account the concrete confinement effect by the circular steel tube. In the calculations, the buckling length of the columns was taken as half the columns’ lengths. The EC4 equation for the ultimate axial capacity (PEC4) of a CFST column is given as:

166

Concrete-Filled Double-Skin Steel Tubular Columns

PEC4


 t fy ¼ ηa As f y + Ac f c 1 + ηc D fc

(4.17)

  2 where ηa ¼ 0:25 3 + 2λ  1:0, ηc ¼ 4:9  18:5λ + 17λ  1:0, and fy is the yield strength of the steel tube taken herein as the 0.2% proof stress (σ 0.2).

4.4.2.3 Continuous strength method The continuous strength method (CSM) was suggested by Lam and Gardner [51]. The structural resistance following such a method is to be determined by means of a continuous relationship between cross-sectional slenderness and deformation capacity in a representative constitutive model. Following the CSM, the ultimate axial strength of circular CFST columns is given as: 
f  t y PCSM ¼ As ηs σ LB + Ac f c 1 + ηc D fc

(4.18)

where σ LB represents the corresponding local buckling stress, which may be obtained from a material model provided here in Section 4.2.3.1 once the deformation capacity of the section (εLB) has been found using the following relationship: εLB ¼

σ 0:2 E

0:178 λc

(4.19)

1:24+1:70λc

where λc is provided in Gardner [52], as follows: λc ¼

235

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

3ð1  υ2 Þ D 2E tε2

with

ε2 ¼

235 σ 0:2

(4.20)

It can be seen that the CSM utilizes the design strength provided by EC4 [25] by replacing fy by the σ LB contribution of the stainless steel tube. It was, however, proposed by Lam and Gardner [51] that the 0.2% proof strength be maintained in the confinement term.

4.4.2.4 Liang and Fragomeni’s design model Based on extensive numerical analyses, a design formula for determining the ultimate axial strength of circular CFST columns was proposed by Liang and Fragomeni [20] as:

0 PL:F ¼ γ s As f y + γ c f c0 + 4:1f rp Ac

(4.21)

CFDST short columns formed from stainless steel outer tubes

167

where γ s is used to account for the effects of strain hardening and the D/t ratio on the yield stress of steels [20]. For stainless steels, γ s is proposed as follows: γ s ¼ 1:62

0:1 D t

ðγ s  1:2Þ

(4.22)

Table 4.9 provides a comparison between the design strengths (PACI, PEC4, PCSM, and PL.F) and the ultimate axial strength (PFE). However, this table confirms that the ACI code provides conservative predictions of the ultimate axial strengths of CFSST columns. Furthermore, it can be recognized that EC4 provides the best strengths for columns with D/t < 40, whereas it is on the unsafe side for large-scale columns with D/t  40. Additionally, it can be seen that the CSM provides better predictions compared to the ACI for columns with D/t < 40, whereas its prediction is still on the unsafe side for columns with D/t  40. On the other hand, it can be seen that the design formula proposed by Liang and Fragomeni [20] yields the best predictions of the ultimate axial strengths of CFSST columns over the entire range of D/t ratios. Regarding the D/t < 40 range, it can be seen that the CSM method provides better predictions than those provided by Liang and Fragomeni [20] just when normal strength concrete, such as 25 and 40 MPa, is used.

4.4.2.5 Verification of design models The accuracy of different design models, provided earlier, is examined herein by the experimental results of Lam and Gardner [51]. Table 4.10 provides the dimensions, material properties of the tested columns, and the experimental and predicted ultimate axial strengths of CFDST columns. It is interesting to note that the six columns provided in the study by Lam and Gardner [51] are all small-scale with a maximum diameter of 114 mm. Table 4.10 reveals that the strengths predicted by the ACI code [22] are highly conservative compared to the experimental results. The mean value of PExp/ PACI is 1.58 with a coefficient of variation of 0.084. It seems that the models by EC4 [25] and Liang and Fragomeni [20] are conservative, whereas the CSM is generally nonconservative. However, EC4 [25] predictions are relatively better than those of Liang and Fragomeni [20] for such small-scale CFSST columns.

4.5

CFDST columns

4.5.1 Fundamental behavior 4.5.1.1 General The verified FE model was employed to investigate the behavior of CFDST short columns. The length of the stub columns (L) was taken as three times the external diameter (D) of the circular CFDST short columns to avoid the effects of column slenderness. Table 4.11 shows the dimensions and material properties considered in this study. Compact stainless steel sections as defined by Bradford et al. [29] were

Table 4.9 Comparison of the ultimate axial strengths of CFSST columns determined by FE and design codes. Group

Column

D/t

PACI [kN]

PFE PACI

PEC4 [kN]

PFE PEC4

PCSM [kN]

PFE PCSM

PL.F [kN]

PFE PL:F

S1

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24

20 20 20 20 20 20 24 24 24 24 24 24 30 30 30 30 30 30 36 36 36 36 36 36

5334 5801 6269 6736 7203 7670 4637 5122 5607 6091 6576 7061 8837 9968 11,098 12,229 13,360 14,490 7757 8915 10,072 11,230 12,387 13,545

1.47 1.51 1.52 1.48 1.51 1.48 1.48 1.51 1.52 1.52 1.50 1.47 1.45 1.47 1.47 1.46 1.44 1.41 1.42 1.44 1.43 1.42 1.40 1.37

8022 8532 9044 9557 10,072 10,588 7014 7545 8077 8611 9147 9684 13,393 14,634 15,881 17,132 18,388 19,648 11,730 13,005 14,287 15,574 16,866 18,162

0.98 1.03 1.06 1.04 1.08 1.08 0.98 1.03 1.05 1.07 1.08 1.07 0.96 1.00 1.03 1.04 1.05 1.04 0.94 0.99 1.01 1.02 1.03 1.02

7406 7916 8426 8938 9452 9966 6412 6941 7472 8005 8539 9075 12,145 13,383 14,626 15,874 17,128 18,385 10,555 11,826 13,104 14,388 15,677 16,971

1.06 1.11 1.13 1.12 1.15 1.14 1.07 1.11 1.14 1.15 1.16 1.15 1.05 1.09 1.11 1.12 1.12 1.11 1.05 1.08 1.10 1.11 1.10 1.09

6981 7840 8608 9285 9871 10,366 6067 6915 7686 8379 8995 9534 11,446 13,256 14,925 16,453 17,839 19,083 9984 11,751 13,398 14,927 16,336 17,625

1.12 1.12 1.11 1.07 1.10 1.10 1.13 1.12 1.11 1.10 1.10 1.09 1.12 1.10 1.09 1.08 1.08 1.07 1.11 1.09 1.08 1.07 1.06 1.05

S2

S3

S4

S5

S6

S7

S8

C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35 C36 C37 C38 C39 C40 C41 C42 C43 C44 C45 C46 C47 C48

40 40 40 40 40 40 45 45 45 45 45 45 50 50 50 50 50 50 59 59 59 59 59 59

Mean Coefficient of variation (COV)

12,821 14,904 16,986 19,068 21,150 23,232 11,871 13,977 16,083 18,189 20,295 22,401 17,286 20,608 23,931 27,253 30,575 33,898 15,624 18,988 22,352 25,716 29,080 32,444

1.42 1.43 1.43 1.41 1.39 1.37 1.39 1.38 1.38 1.37 1.35 1.32 1.32 1.27 1.22 1.19 1.14 1.15 1.28 1.21 1.16 1.13 1.11 1.09 1.38 0.124

19,338 21,637 23,948 26,269 28,599 30,937 17,836 20,166 22,510 24,865 27,229 29,601 25,852 29,538 33,246 36,971 40,711 44,464 23,171 26,918 30,688 34,476 38,279 42,094

0.94 0.99 1.01 1.03 1.03 1.03 0.93 0.95 0.99 1.00 1.00 1.00 0.88 0.88 0.88 0.88 0.85 0.87 0.86 0.85 0.85 0.84 0.84 0.84 0.98 0.077

17,383 19,675 21,980 24,296 26,621 28,954 15,963 18,288 20,625 22,975 25,334 27,701 23,134 26,810 30,509 34,226 37,958 41,703 20,706 24,442 28,203 31,983 35,778 39,586

1.05 1.09 1.10 1.11 1.11 1.10 1.03 1.05 1.08 1.08 1.08 1.07 0.99 0.97 0.96 0.95 0.92 0.93 0.96 0.94 0.92 0.91 0.90 0.89 1.06 0.078

16,405 19,495 22,393 25,098 27,612 29,933 15,055 18,084 20,940 23,624 26,135 28,475 20,931 24,253 27,576 30,898 34,221 37,543 18,778 22,142 25,506 28,870 32,234 35,598

1.11 1.10 1.08 1.07 1.07 1.06 1.10 1.06 1.06 1.05 1.05 1.04 1.09 1.08 1.06 1.05 1.02 1.03 1.06 1.04 1.02 1.01 1.00 0.99 1.07 0.033

Table 4.10 Comparison of the ultimate axial strengths of CFSST columns determined by experimental [51] and design codes. Column Dxt

σ 0.2 [MPa]

D/ t

114
6 266 19 114
6 266 19 114
6 266 19 104
2 412 52 104
2 412 52 104
2 412 52 Mean Coefficient of variation (COV)

fc0 [MPa]

PExp [kN]

PACI [kN]

31 49 65 31 49 65

1257 1340 1674 699 901 1133

761 887 998 471 591 698

PExp PACI

1.65 1.51 1.68 1.48 1.52 1.62 1.58 0.082

PEC4 [kN] 1126 1266 1391 681 816 936

PExp PEC4

1.12 1.06 1.20 1.03 1.10 1.21 1.12 0.075

PCSM [kN] 1283 1426 1550 721 858 977

PExp PCSM

0.98 0.94 1.08 0.97 1.05 1.16 1.03 0.082

PL. F [kN] 1069 1236 1332 588 729 853

PExp PL:F

1.18 1.08 1.26 1.19 1.24 1.33 1.21 0.083

Table 4.11 Full details of the current circular CFDST short columns of the extended parametric study. Outer tube Group

Column

D [mm]

te [mm]

G1

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20

240 240 240 240 240 240 240 240 240 240 480 480 480 480 480 480 480 480 480 480

8 8 8 8 8 8 8 8 8 8 12 12 12 12 12 10 10 10 10 10

Inner tube D/te

d [mm]

ti [mm]

30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 48 48 48 48 48

120 120 120 120 120 120 120 120 120 120 240 240 240 240 240 240 240 240 240 240

6 6 6 6 6 5 5 5 5 5 8 8 8 8 8 6 6 6 6 6

d/ti

fc0 [MPa]

d/D

ti/te

fsy [MPa]

Pu, FE [kN]

20 20 20 20 20 24 24 24 24 24 30 30 30 30 30 40 40 40 40 40

40 60 80 100 120 40 60 80 100 120 40 60 80 100 120 40 60 80 100 120

0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50

0.75 0.75 0.75 0.75 0.75 0.63 0.63 0.63 0.63 0.63 0.67 0.67 0.67 0.67 0.67 0.60 0.60 0.60 0.60 0.60

355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355

6743 7439 8081 8642 9123 6595 7288 7930 8487 8961 21,028 23,789 26,282 28,548 30,562 16,781 18,680 20,611 22,588 24,507 Continued

Table 4.11 Continued Outer tube Group

Column

D [mm]

te [mm]

G2

C21 C22 C23 C24 C25 C26 C27 C28 C23 C29 C12 C30 C24 C31 C32 C33 C34 C35 C12 C36 C37 C38

480 480 480 480 480 480 480 480 480 480 480 480 480 480 480 480 480 480 480 480 480 480

12 12 12 12 15 15 15 15 12 12 12 12 12 12 12 12 12 12 12 12 12 12

G3

G4

Inner tube D/te

d [mm]

ti [mm]

40 40 40 40 32 32 32 32 40 40 40 40 40 40 40 40 40 40 40 40 40 40

120 180 240 360 120 180 240 360 240 240 240 240 360 360 360 360 240 240 240 360 360 360

5 5 5 5 5 5 5 5 5 6 8 10 5 10 12 14 8 8 8 8 8 8

d/ti

fc0 [MPa]

d/D

ti/te

fsy [MPa]

Pu, FE [kN]

24 36 48 72 24 36 48 72 48 40 30 24 72 36 30 26 30 30 30 45 45 45

60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60

0.25 0.38 0.50 0.75 0.25 0.38 0.50 0.75 0.50 0.50 0.50 0.50 0.75 0.75 0.75 0.75 0.50 0.50 0.50 0.75 0.75 0.75

0.42 0.42 0.42 0.42 0.33 0.33 0.33 0.33 0.42 0.50 0.67 0.83 0.42 0.83 1.00 1.17 0.67 0.67 0.67 0.67 0.67 0.67

355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 235 275 355 235 275 355

24,952 24,284 22,911 19,053 28,794 27,618 26,601 22,544 22,911 23,309 23,789 24,231 19,053 21,283 22,133 23,029 23,011 23,246 23,789 19,333 19,691 20,397

G5

C39 C40 C41 C42 C43 C44 C45 C46 C47 C48

520 520 520 520 520 580 580 580 580 580

10 10 10 10 10 10 10 10 10 10

52 52 52 52 52 58 58 58 58 58

260 260 260 260 260 290 290 290 290 290

5 5 5 5 5 15 15 15 15 15

52 52 52 52 52 19.3 19.3 19.3 19.3 19.3

40 60 80 100 120 40 60 80 100 120

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 1.5 1.5 1.5 1.5 1.5

355 355 355 355 355 355 355 355 355 355

18,319 20,671 22,973 25,203 27,558 24,026 26,870 28,505 32,609 35,424

174

Concrete-Filled Double-Skin Steel Tubular Columns

considered herein, i.e., the cross-sectional slenderness (D/te) is less than 59 as σ 0.2 ¼ 530 MPa. All short columns are classified into five groups (G1, G2, G3, G4, and G5), as shown in Table 4.11. The parameters considered in the analyses include the cylinder concrete’s compressive strength (fc0 ), the nominal steel ratio (αn), the hollow ratio (χ ¼ d/(D  2te)), the thickness ratio (ti/te), and the yield strength of the carbon steel tube (fsy). It should be noted that the majority of the models in the current parametric study is formed from outer tubes with D/te < 47, which was found to be limited in the previous tests [18,42,53,54]. CFDST short columns were labeled in the figures to rapidly identify the column dimensions. In the labeling system, the abbreviation CFDST is followed by first the diameter and the thickness of the outer stainless steel tube (D
te) in millimeters and then by the diameter and the thickness of the inner carbon steel tube (d
ti) in millimeters. At the end, the value of the concrete’s compressive strength (fc0 ) is provided in megapascal. When any steel grade of the inner carbon steel tube other than S355 is used, the yield strength is added at the end. For example, the label “CFDST480
10–240
6–80” defines a CFDST column with an outer stainless steel tube of D ¼ 480 mm and te ¼ 10 mm, whereas the dimensions of the inner carbon steel tube are d ¼ 240 mm and ti ¼ 6 mm. The value of the concrete’s compressive strength (fc0 ¼ 80 MPa) and the steel grade of the inner carbon steel tube is S355.

4.5.1.2 Effects of the concrete’s compressive strength The effect of the concrete’s compressive strength (fc0 ) on the behavior of axially loaded CFDST short columns under compression was investigated. As it is well-known, EN 1992-1-1 [55] defines concrete as high-strength (HSC) when fc0 > 50 MPa and as ultrahigh-strength (UHSC) when fc0 > 90 MPa. The compressive strength of concrete varied between 40 and 120 MPa so that the current investigation includes a normal strength concrete (NSC) (40 MPa), two HSCs (60 and 80 MPa), and two UHSCs of 100 and 120 MPa. Three diameter-to-thickness ratios (D/te) of 30, 40, and 48 were used, whereas the d/ti ratios were 20, 24, 30, and 40. The details of the models used in identifying the current effect are provided in Table 4.11. The ultimate axial strengths (Pu,FE) of the columns predicted by the FE model are provided in Fig. 4.19. The figure shows that the change in the fc0 value of the sandwiched concrete has a considerable effect on the compressive strength of the CFDST short columns. Additionally, it can be recognized that increasing fc0 linearly increases its capacity for different ti/te ratios. An important conclusion that may be drawn is that different types of concretes (NS, HS, and UHS) behave in the same manner. It should be noted that the behavior of high-strength concrete is different from that of normal strength concrete in terms of ductility and the strain εc0 corresponding to the peak stress fc0 . High-strength concrete has higher strength and larger strain εc0 at the peak stress but lower ductility compared to normal strength concrete. These characteristics of normal and high-strength concrete have been simulated using the concrete model given by Eq. (4.4). The load-strain relationships for the sample results are provided in Fig. 4.20. It can be seen that increasing the concrete’s compressive strength (fc0 ) significantly increases

CFDST short columns formed from stainless steel outer tubes

(a)

175

(b) 10 C4 C3

8

C2

35 C10

C9

C15

30

C8

C14 C13

C7

6 4

C20

C12

25

C6

Pu,FE [MN]

Pu,FE [MN]

C1

C5

C19

C11

20

C18 C17

C16

15 10

2

5

0 40

60

80

100

0

120

40

fc′ [MPa]

60

80

100

120

fc′ [MPa]

P [kN]

Fig. 4.19 Effects of concrete strength on CFDST short column strength: (a) C1–C10 and (b) C11–C20. 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0

Fig. 4.20 Axial load-strain curves for CFDST short columns for C1–C5.

CFD ST-240X8-120X5-120 CFD ST-240X8-120X5-100 CFD ST-240X8-120X5-80 CFD ST-240X8-120X5-60 CFD ST-240X8-120X5-40

0

0.02

0.04

0.06

0.08

Strain [mm/mm]

the ultimate axial strength of circular CFDST short columns, whereas the initial stiffness remains approximately the same. Additionally, it can be seen that all CFDST short columns behave in a favorable ductile manner irrespective of the fc0 value.

4.5.1.3 Effects of the nominal steel ratio The nominal steel ratio (αn) is defined as the cross-sectional area of the outer tube to the nominal cross-sectional area of concrete (π(D  2te)2/4). This ratio was found to considerably affect the strength of CFDST short columns with outer and inner carbon steel tubes [30]. For conducting such a comparison in the current investigation, short columns C11–C20 were generated. Short columns C11–C15 have an αn value of 0.11, whereas it is 0.9 for columns C16–C20. Using outer stainless steel tubes, similar results were found, as can be seen in Fig. 4.21. Hence, the effect of the ti/te ratio on the capacity of CFDST short columns is found to be significant by changing the

176

Concrete-Filled Double-Skin Steel Tubular Columns 25000

7000 6000

an = 15.0

4000

P [kN]

P [kN]

an = 0.11

20000

5000

3000 2000

CFDST-240*8-120*6-40

1000

CFDST-240x8-120x5-40

an = 0.09

15000 10000 CFDST-480x12-240x8-40

5000

CFDST-480x10-240x6-40

0

0 0

0.02

0.04

0.06

0.08

0

Strain [mm/mm]

0.01

0.02

0.03

0.04

0.05

0.06

Strain [mm/mm]

Fig. 4.21 Effects of concrete strength on the load-strain curves for CFDST short columns with different ti/te ratios.

thickness of the outer tube (te), as shown in Fig. 4.21. Logically, increasing the external tube’s thickness (te) of the same column (Fig. 4.21B) leads to a larger increase in the ultimate axial strength of the column than increasing the internal tube’s thickness (see Fig. 4.21A). This, however, increases the amount of the stainless steel.

4.5.1.4 Effects of the hollow ratio The influence of the hollow ratio (χ ¼ d/(D  2te)) on the ultimate axial strength (Pu,FE) and the load-shortening response of CFDST short columns under axial compression was studied. The diameter of the outer stainless steel tubes (D), the thickness of the inner tube (ti), and the concrete’s compressive strength (fc0 ) were fixed. Table 4.11 provides details of the current models. The ultimate axial strengths (Pu,FE) of the short columns predicted by the FE models, representing the effect of χ, are provided in Fig. 4.22. It can be seen that increasing the χ ratio obviously decreases the ultimate axial strength of the CFDST short columns with different ti/te ratios. This is simply attributed to the noticeable decrease in the sandwiched concrete area, which was found to bear the largest part of the load [30]. On the other hand, the 30

Pu,FE [MN]

25 20 15 10

Series1

5

Series2

0 0.00

0.20

0.40 c

0.60

0.80

Fig. 4.22 Effects of the hollow ratio (χ) on CFDST short column strength.

CFDST short columns formed from stainless steel outer tubes

177

Fig. 4.23 Axial load-strain curves for CFDST short columns for C25–C28.

30000 25000

P [kN]

20000 15000 CFD ST-480x15-120x5-60 10000

CFD ST-480x15-180x5-60 CFD ST-480x15-240x5-60

5000

CFD ST-480x15-360x5-60 0 0

0.02

0.04

0.06

0.08

Strain [mm/mm]

load-strain relationships for the sample results are provided in Fig. 4.23. It can be seen that increasing the χ ratio considerably decreases the axial stiffness, ultimate axial strength, and ductility of circular CFDST short columns.

4.5.1.5 Effects of the ti/te ratio In this section, the effect of the thickness ratio (ti/te) on the structural behavior of the CFDST short columns was investigated by varying the inner tube’s thickness. The dimensions of the outer stainless steel tubes (D and te), the diameter of the inner tube (d), and the concrete’s compressive strength ( fc0 ) were kept constant. The details of the current models are also tabulated in Table 4.11. The ultimate axial strengths (Pu,FE) of the short columns predicted by the FE model are provided in Fig. 4.24. It can be seen from Fig. 4.24 that increasing the ti/te ratio clearly increases the ultimate axial strength of the CFDST short columns with different d/D ratios. However, the rate of increase in the strength becomes larger as the d/D ratio increases. On the other hand, no obvious changes in the load-strain relationships were found by changing the ti/te ratio. 25

Pu,FE [MN]

20 15 10 C23,C29,C12,C30 C24,C31-C33

5 0 0.6

0.8

1

1.2

ti / te

Fig. 4.24 Effects of the thickness ratio (ti/te) on CFDST short column strength.

178

Concrete-Filled Double-Skin Steel Tubular Columns

4.5.1.6 Effects of the steel grade of the inner carbon steel tube By varying the steel grade of the inner tube, the ultimate axial load capacities of CFDST short columns are presented herein. As can be seen in Table 4.11, three steel grades (S235, S275, and S355) according to EN 1993-1-1 [56] were considered. The ultimate axial strengths (Pu,FE) of the short columns are presented in Fig. 4.25. It can be seen that increasing the steel yield stress fsy slightly increases the compressive strength of the CFDST short columns for different d/D ratios with nearly the same rate of increase. Furthermore, it was found that the steel yield stress does not have a significant effect on the axial load-strain responses of the CFDST short columns. This confirms the findings of Huang et al. [30]. Hence, it is suggested to use inner tubes with the least fsy values to reduce the cost of CFDST short columns.

4.5.2 Design of CFDST short columns Design models provided by the ACI code [38], Han et al. [49], CSM [51], and proposed by the authors for determining the ultimate axial strengths of CFDST short columns are described and compared with the FE and experimental results in this section.

4.5.2.1 The ACI code The ACI code [38] ignores the concrete confinement effect. The ACI equation for the ultimate axial strength (Pu,ACI) of a concrete-filled circular short column incorporating the contribution of the inner tube is given as: Pu,ACI ¼ σ 0:2 Ass + 0:85f 0c Ac + f sy As

(4.23)

25

Pu,FE [MN]

20

C12

C35

C34 C36

C38

C37

15 10 5 0 235

275

355

Yield strength (fsy) [MPa]

Fig. 4.25 Effects of yield strength of the inner tube on CFDST short column strength.

CFDST short columns formed from stainless steel outer tubes

179

where Ass is the cross-sectional area of the stainless steel tube, Ac is the cross-sectional area of the sandwiched concrete (Asc), and As is the cross-sectional area of the carbon steel tube.

4.5.2.2 Design model by Han et al. The superposition method was used by Han et al. [49] to determine the capacities of CFDST short columns (Pu,Han) as follows: Pu,Han ¼ N osc,u + N i,u

(4.24)

where Nosc,u is the compressive capacity of the outer tube with the sandwiched concrete and Ni,u is the compressive capacity of the inner tube computed as Asifsyi. The determination of the compressive capacity of the outer steel tube with the sandwiched concrete Nosc,u is given as follows: N osc,u ¼ f scy Asco

(4.25)

in which Asco ¼ Ass + Asc, where Asc is the cross-sectional area of the concrete, Ass is the cross-sectional area of the outer stainless steel tube, and fscy is determined as follows: 

f scy ¼ C1 χ 2 σ 0:2 + C2 ð1:14 + 1:02ζ Þf ck f scy and f ck N=mm2

(4.26)

C1 ¼

α 1+α

(4.27)

C2 ¼

1 + αn 1+α

(4.28)

where α is the steel ratio taken as α ¼ Ass/Asc and αn is the nominal steel ratio calculated as αn ¼ Ass/Ac,nominal, Ac,nominal is the nominal cross-sectional area of the concrete (π(D  2te)2/4), fck is the characteristic concrete strength (0.67fcu), fcu is the characteristic cube strength of the concrete, χ is the hollow section ratio given by d/(D  2te), Ass σ 0:2 and ζ is the confinement factor Ac,nominal f . ck

4.5.2.3 Continuous strength method The continuous strength method (CSM) was suggested by Lam and Gardner [51] for concrete-filled stainless steel tubular (CFSST) short columns under axial compression. The CSM determines the strength of CFSST short columns by means of a continuous relationship between cross-sectional slenderness and deformation capacity in a representative constitutive model. Following the CSM, the ultimate axial strength of circular CFST short columns is given as:

180

Concrete-Filled Double-Skin Steel Tubular Columns

PCSM ¼ As ηs σ LB


f  t y + A c f c 1 + ηc D fc

(4.29)

where Ac is the cross-sectional area of the concrete core of the CFSST short columns and σ LB represents the corresponding local buckling stress. However, σ LB may be obtained from a material model provided here in Section 4.2.3.1 once the deformation capacity of the section (εLB) has been found using the following relationship: εLB ¼

σ 0:2 0:178 E  1:24+1:70λc λc

(4.30)

where λc is provided in Gardner [52], as follows: λc ¼

235

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

3ð1  υ2 Þ D 2E tε2

with

ε2 ¼

235 σ 0:2

(4.31)

It can be seen that the CSM utilizes the design strength provided by EC4 [25] by replacing fy by the σ LB contribution of the stainless steel tube. It was, however, proposed by Lam and Gardner [51] that the 0.2% proof strength be maintained in the confinement term. Eq. (4.29) is modified herein to allow its use for CFDST short columns as given in Eq. (4.32). The modified equation first replaces Ac (for the case of CFSST short columns) by Asc (for the case of CFDST short columns). Second, it accounts for the contribution to the inner tube typically as made by the ACI code [38] and Han et al. [49]. PCSM ¼ Ass ηs σ LB


f  t y + Asc f c 1 + ηc + f sy As D fc

(4.32)

4.5.2.4 The proposed new design model Design models for determining the ultimate strengths of short circular CFST columns have been provided by Liang and Fragomeni [20]. Additional models for the concretefilled stainless steel tubular (CFSST) short columns and the concrete-filled stainless steel-carbon steel tubular (CFSCT) short columns under axial compression have been provided by Hassanein et al. [26,33], respectively. Based on their design models [20,26,33], a new design model for calculating the ultimate axial strengths of axially loaded circular CFDST short columns is proposed as:

Pu,Prop ¼ γ ss σ 0:2 Ass + γ s f sy As + γ sc f 0c + 4:1f 0rp:ss Asc

(4.33)

CFDST short columns formed from stainless steel outer tubes

181

where Asc is the cross-sectional area of the sandwiched concrete between the two tubes, and the factors γ ss and γ s are used to account for the effect of strain hardening on the strength of stainless steel and carbon steel, respectively, and are given as follows:
0:1 D γ ss ¼ 1:62 te

ðγ ss  1:2Þ

(4.34)


0:1 d γ s ¼ 1:458 ti

ð0:9  γ s  1:1Þ

(4.35)

4.5.2.5 Verification of design models The ultimate axial strengths of CFDST short columns calculated by the ACI code [38] and design models presented in the preceding sections are compared with the FE results in Table 4.12. It is worth pointing out that γ c, given in Eq. (4.7), is the strength reduction factor, which accounts for the effects of the column size, the quality of concrete, and the loading rates on the concrete’s compressive strength. Moreover, the factors γ s and γ ss in Eq. (4.33) account for the effects of strain hardening on the strength of the carbon and the stainless steel tubes, respectively. Hence, they differ from the partial safety factors recommended by the codes. The material’s partial safety and capacity reduction factors were taken as 1.0 in the calculations of the ultimate axial strengths of all short columns. It can be seen from Table 4.12 that the ACI code significantly underestimates the ultimate axial strengths of CFDST short columns with different D/te ratios. For some cases, the ACI code could underestimate the ultimate axial strength of a CFDST short column by up to 31% (C25). The mean value of Pu, ACI/Pu,FE is 0.77 with a coefficient of variation of 0.068. The obvious inconsistency between the ACI code predictions and the FE results is attributed to the fact that the code does not consider the effects of concrete confinement. Table 4.12 demonstrates that the model proposed by Han et al. [49] yields better ultimate load predictions (Pu,Han) than does the ACI code [38]. As can be seen, this method provides estimates, which are generally on the safe side. The mean value of Pu,Han/Pu,FE is 0.88 with a coefficient of variation of 0.075. However, it can be seen that it slightly overestimates the strengths of the CFDST short columns with D/te > 47, mainly with UHSCs. Additionally, it underestimates the ultimate strengths of CFDST short columns with D/ te < 47 and a relatively large margin of safety. Additionally, it can be noted that the CSM generally provides nonconservative predictions for the columns with the entire range of D/te ratios of compact sections. It can be seen from Table 4.12 that the proposed design model (Pu,Prop) predicts well the ultimate axial strengths of CFDST short columns, which are in good agreement with the FE solutions (Pu,FE) for the entire range of D/te ratios. The mean value of Pu,Prop/Pu,FE is 0.93 with a coefficient of variation of 0.023.

Table 4.12 Comparison of the ultimate axial strengths of CFDST short columns determined by the FE model and design codes.

Column

D/te

d/ti

fc0 [MPa]

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24

30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 48 48 48 48 48 40 40 40 40

20 20 20 20 20 24 24 24 24 24 30 30 30 30 30 40 40 40 40 40 24 36 48 72

40 60 80 100 120 40 60 80 100 120 40 60 80 100 120 40 60 80 100 120 60 60 60 60

Pu, FE [kN]

Pu, ACI [kN]

Pu, Han [kN]

Pu, CSM [kN]

Pu, Prop [kN]

fsy [MPa]

(1)

(2)

(3)

(4)

(5)

(2)/(1)

(3)/(1)

(4)/(1)

(5)/(1)

355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355

6743 7439 8081 8642 9123 6595 7288 7930 8487 8961 21,028 23,789 26,282 28,548 30,562 16,781 18,680 20,611 22,588 24,507 24,952 24,284 22,911 19,053

4809 5286 5764 6242 6719 4687 5165 5642 6120 6598 15,435 17,443 19,450 21,457 23,464 13,504 15,560 17,616 19,672 21,729 17,744 17,358 16,683 14,468

5462 6078 6693 7309 7925 5340 5956 6572 7188 7804 17,297 19,796 22,294 24,792 27,290 15,051 17,566 20,081 22,595 25,110 20,773 20,105 19,036 15,694

6862 7404 7947 8491 9036 6746 7288 7831 8374 8919 22,092 24,374 26,662 28,953 31,249 19,081 21,422 23,768 26,120 28,476 26,551 25,392 23,647 18,310

6094 6812 7451 8009 8488 5950 6668 7307 7865 8345 19,144 21,907 24,422 26,691 28,713 15,489 17,545 19,602 21,658 23,714 23,107 22,309 21,056 17,195

0.71 0.71 0.71 0.72 0.74 0.71 0.71 0.71 0.72 0.74 0.73 0.73 0.74 0.75 0.77 0.80 0.83 0.85 0.87 0.89 0.71 0.71 0.73 0.76

0.81 0.82 0.83 0.85 0.87 0.81 0.82 0.83 0.85 0.87 0.82 0.83 0.85 0.87 0.89 0.90 0.94 0.97 1.00 1.02 0.83 0.83 0.83 0.82

1.02 1.00 0.98 0.98 0.99 1.02 1.00 0.99 0.99 1.00 1.05 1.02 1.01 1.01 1.02 1.14 1.15 1.15 1.16 1.16 1.06 1.05 1.03 0.96

0.90 0.92 0.92 0.93 0.93 0.90 0.91 0.92 0.93 0.93 0.91 0.92 0.93 0.93 0.94 0.92 0.94 0.95 0.96 0.97 0.93 0.92 0.92 0.90

C25 32 24 C26 32 36 C27 32 48 C28 32 72 C29 40 40 C30 40 24 C31 40 36 C32 40 30 C33 40 26 C34 40 30 C35 40 30 C36 40 45 C37 40 45 C38 40 45 C39 52 52 C40 52 52 C41 52 52 C42 52 52 C43 52 52 C44 58 19.3 C45 58 19.3 C46 58 19.3 C47 58 19.3 C48 58 19.3 Mean Coefficient of variation

60 60 60 60 60 60 60 60 60 60 60 60 60 60 40 60 80 100 120 40 60 80 100 120 (COV)

355 355 355 355 355 355 355 355 355 235 275 235 275 355 355 355 355 355 355 355 355 355 355 355

28,794 27,618 26,601 22,544 23,309 24,231 21,283 22,133 23,029 23,011 23,246 19,333 19,691 20,397 18,319 20,671 22,973 25,203 27,558 24,026 26,870 28,505 32,609 35,424

19,789 19,403 18,728 16,513 16,938 17,938 16,392 17,146 17,891 16,743 16,976 14,568 14,922 15,629 14,784 17,220 19,655 22,091 24,526 20,220 23,284 26,348 29,412 32,477

23,616 22,863 21,676 17,996 19,292 20,291 17,618 18,372 19,117 19,096 19,329 15,794 16,148 16,855 16,471 19,429 22,388 25,347 28,306 22,129 25,821 29,514 33,206 36,898

30,185 28,875 26,897 20,890 23,891 24,849 20,201 20,943 21,676 23,704 23,927 18,408 18,755 19,451 20,835 23,608 26,389 29,176 31,969 26,897 30,404 33,918 37,438 40,964

26,211 25,355 24,020 19,924 21,338 22,481 19,290 20,145 21,005 21,181 21,423 17,384 17,737 18,442 16,489 18,924 21,360 23,795 26,231 22,504 25,568 28,632 31,697 34,761

0.69 0.70 0.70 0.73 0.73 0.74 0.77 0.77 0.78 0.73 0.73 0.75 0.76 0.77 0.81 0.83 0.86 0.88 0.89 0.84 0.87 0.92 0.90 0.92 0.77 0.068

0.82 0.83 0.81 0.80 0.83 0.84 0.83 0.83 0.83 0.83 0.83 0.82 0.82 0.83 0.90 0.94 0.97 1.01 1.03 0.92 0.96 1.04 1.02 1.04 1.01 0.140

1.05 1.05 1.01 0.93 1.02 1.03 0.95 0.95 0.94 1.03 1.03 0.95 0.95 0.95 1.14 1.14 1.15 1.16 1.16 1.12 1.13 1.19 1.15 1.16 1.04 0.077

0.91 0.92 0.90 0.88 0.92 0.93 0.91 0.91 0.91 0.92 0.92 0.90 0.90 0.90 0.90 0.92 0.93 0.94 0.95 0.94 0.95 1.00 0.97 0.98 0.93 0.023

184

Concrete-Filled Double-Skin Steel Tubular Columns

The accuracy of various design models is further examined using the available experimental results of CFDST short columns. As shown in Section 4.3.5, only two circular CFDST short columns with external stainless steel tubes are available in the literature without the full details of the stainless steel material. Hence, the CSM could not be checked herein because the stress-strain curve of the model is not available. Accordingly, the experimental results of CFDST short columns with both carbon steel tubes are checked as follows. Table 4.13 provides the dimensions and material properties of the tested short columns. The calculated and experimental ultimate axial strengths of CFDST short columns are provided in Table 4.14. The D/te ratios of all specimens are larger than 47, except CC5 [48]. Table 4.14 reveals that the strengths computed by the ACI code [38] are highly conservative compared to the experimental results. The mean value of Pu,ACI/Pu,Exp is 0.78 with a coefficient of variation of 0.077. The ultimate axial loads calculated by the model provided by Han et al. [49] agree well with the test data. In Table 4.14, γ c is taken as unity in the strength calculation by the proposed design model because all columns are small-scale. It can be seen that the proposed design model provides conservative predictions compared to the experimental results. However, the proposed design model yields better results for the specimen CC5 with D/te < 47 than does Han et al.’s model [49], provided that Pu,Han/Pu,FE ¼ 0.88 and Pu,Prop/Pu,FE ¼ 0.97. Accordingly, the current authors recommend the investigation of CFDST short columns with both carbon steel tubes with D/te < 47 to provide new results to the literature.

Table 4.13 Details of experimental CFDST short columns.

Column

References

D/te

d/ti

fc0 [MPa]

CC2 CC3 CC4 CC5 CC6 CC7 DS-2 DS-6 C1-1 c10-375 c10-750 c10-1125 c16-375 c16-750 c16-1125 c23-375 c23-750 c23-1125

[48] [48] [48] [48] [48] [48] [53] [53] [54] [18] [18] [18] [18] [18] [18] [18] [18] [18]

60.0 60.0 60.0 38.0 80.0 100.0 150.0 75.0 91.6 175.6 176.7 176.7 105.3 105.3 105.3 73.8 73.8 73.4

16.0 29.3 46.7 19.3 38.0 55.0 90.0 90.0 79.1 42.2 84.4 126.7 26.0 51.3 76.0 18.7 36.0 53.7

37.92 37.92 37.92 37.92 37.92 37.92 22.4 22.4 42 18.7 18.7 18.7 18.7 18.7 18.7 18.7 18.7 18.7

fsy [MPa] Outer

Inner

Pu,Exp [kN]

275.9 275.9 275.9 294.5 275.9 275.9 290 290 439.3 221 221 221 308 308 308 286 286 286

396.1 370.2 342 374.5 294.5 320.5 290 290 396.5 221 221 221 308 308 308 286 286 286

1790 1648 1358 904 2421 3331 2141 2693 5448 635 540 378.3 851.6 728.1 589 968.2 879.1 703.6

Table 4.14 Comparison of the experimental ultimate axial strengths of CFDST short columns and design codes.

Column

References

CC2 [48] CC3 [48] CC4 [48] CC5 [48] CC6 [48] CC7 [48] DS-2 [53] DS-6 [53] C1-1 [54] c10-375 [18] c10-750 [18] c10-1125 [18] c16-375 [18] c16-750 [18] c16-1125 [18] c23-375 [18] c23-750 [18] c23-1125 [18] Mean Coefficient of variation (COV)

Pu,Exp [kN]

Pu,ACI [kN]

Pu,Han [kN]

Pu,Prop[kN]

D/te

(1)

(2)

(3)

(4)

(2)/(1)

(3)/(1)

(4)/(1)

60.0 60.0 60.0 38.0 80.0 100.0 150.0 75.0 91.6 175.6 176.7 176.7 105.3 105.3 105.3 73.8 73.8 73.4

1790 1648 1358 904 2421 3331 2141 2693 5448 635 540 378.3 851.6 728.1 589 968.2 879.1 703.6

1336 1327 1172 712 1982 2761 1693 2194 4445 408 382 316 563 563 528 648 665 641

1518 1474 1242 795 2208 3048 1836 2392 4822 455 421 340 622 611 557 721 723 674

1566 1507 1241 881 2261 3092 1807 2429 4849 449 411 325 651 626 551 760 750 677

0.75 0.81 0.86 0.79 0.82 0.83 0.79 0.81 0.82 0.64 0.71 0.83 0.66 0.77 0.90 0.67 0.76 0.91 0.78 0.077

0.85 0.89 0.91 0.88 0.91 0.91 0.86 0.89 0.89 0.72 0.78 0.90 0.73 0.84 0.95 0.74 0.82 0.96 0.86 0.073

0.87 0.91 0.91 0.97 0.93 0.93 0.84 0.90 0.89 0.71 0.76 0.86 0.76 0.86 0.94 0.79 0.85 0.96 0.87 0.083

186

4.6

Concrete-Filled Double-Skin Steel Tubular Columns

CFDT columns

4.6.1 Fundamental behavior 4.6.1.1 General The verified FE model was used to carry out an extensive parametric study on the fundamental behavior of circular CFDT short columns. These CFDT columns were made of an external lean duplex stainless steel tube and an internal concentrically placed carbon steel tube with concrete filling in the whole tubular section. The parametric study was used to investigate the effects of the following design parameters on the ultimate axial loads of such columns: 1. 2. 3. 4.

The The The The

cylinder concrete strength (fc0 ), dimensions of the external stainless steel tube, thickness (te), and diameter (D), dimensions of the internal carbon steel tube, thickness (ti), and diameter (d), and yield strength of the carbon steel tube (fsy).

The length of the columns (L) was fixed to three times the outer diameter of the external stainless steel tubes (D) to avoid the effects of flexural buckling and end conditions. The CFDT columns are numbered in the tables. Additionally, they were labeled in the figures to rapidly identify the column dimensions. In the labeling system, the abbreviation CFDT is followed by first the diameter and the thickness of the external stainless steel tube (D
te) in millimeters and then by the diameter and the thickness of the internal carbon steel tube (d
ti) in millimeters. At the end, the value of the concrete’s compressive strength (fc0 ) is provided in megapascal. When any steel grade of the internal carbon steel tube other than S355 is used, the yield strength is added at the end. For example, the label “CFDT-240
10–120
5–100” defines a CFDT column with an external stainless steel tube of D ¼ 240 mm and te ¼ 10 mm, whereas the dimensions of the internal carbon steel tube are d ¼ 120 mm and ti ¼ 5 mm. The value of the concrete’s compressive strength (fc0 ¼ 100 MPa) and the steel grade of the internal carbon steel tube is S355.

4.6.1.2 Effects of the concrete’s compressive strength The effect of the concrete’s compressive strength (fc0 ) on the behavior of CFDT columns under axial compression was investigated. The compressive strength of concrete varied between 40 and 100 MPa. Three diameter-to-thickness ratios (D/te) of 24, 32, and 48 were used. The details of the models used in identifying the current effect are provided in Table 4.15. The ultimate axial strengths (Pu,FE) of the columns predicted by the FE model are provided in Fig. 4.26. This figure shows that the change in the fc0 value of concrete has a significant effect on the compressive strength of the CFDT columns. It can be recognized that increasing fc0 linearly increases its capacity for different ti/te ratios. The load-strain relationships for the sample results are provided in Fig. 4.27. It can be seen that increasing the concrete’s compressive strength (fc0 ) significantly increases

Table 4.15 Details of the circular CFDT columns with d/D ¼ 0.5 and S355 (effects of fc0 ). External tube

Internal tube

Column

L [mm]

D [mm]

te [mm]

D/te

d [mm]

ti [mm]

d/ti

fc0 [MPa]

d/D

ti/te

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20

720 720 720 720 720 720 720 720 720 720 1440 1440 1440 1440 1440 1440 1440 1440 1440 1440

240 240 240 240 240 240 240 240 240 240 480 480 480 480 480 480 480 480 480 480

10 10 10 10 10 10 10 10 10 10 15 15 15 15 15 10 10 10 10 10

24 24 24 24 24 24 24 24 24 24 32 32 32 32 32 48 48 48 48 48

120 120 120 120 120 120 120 120 120 120 240 240 240 240 240 240 240 240 240 240

5 5 5 5 5 10 10 10 10 10 5 5 5 5 5 10 10 10 10 10

24 24 24 24 24 12 12 12 12 12 48 48 48 48 48 24 24 24 24 24

40 55 70 85 100 40 55 70 85 100 40 55 70 85 100 40 55 70 85 100

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 0.33 0.33 0.33 0.33 0.33 1.0 1.0 1.0 1.0 1.0

188

Concrete-Filled Double-Skin Steel Tubular Columns

(a)

(b) 40

12 10 Pu,FE [MN]

Pu,FE [MN]

30 8 6 4

C1-C5

2

C6-C10

20 C11-C15

10

C16-C20 0

0 60

40

80

100

40

60

fc′ [MPa]

80

100

fc′ [MPa]

Fig. 4.26 Effects of concrete strength on CFDT column strength: (a) C1–C10 and (b) C11–C20.

12000 10000

P [kN]

8000 6000 CFSCT-240x10-120x5-100 CFSCT-240x10-120x5-85 CFSCT-240x10-120x5-70 CFSCT-240x10-120x5-55 CFSCT-240x10-120x5-40

4000 2000 0 0

0.02

0.04

0.06

0.08

0.1

Strain [mm/mm]

Fig. 4.27 Axial load-strain curves for CFDT columns for C1–C5.

the ultimate axial strength of circular CFDT columns, whereas the initial stiffness remains approximately the same. Additionally, it can be seen that all CFDT columns behave in a favorable ductile manner irrespective of the fc0 value. On the other hand, the effect of the ti/te ratio on the capacity of CFDT columns is found to be significant when changing the thickness te as shown in Fig. 4.28. Logically, increasing the external tube’s thickness (te) of the same column (Fig. 4.26B) leads to a larger increase in the ultimate axial strength of the column than increasing the internal tube’s thickness (see Fig. 4.26A). This, however, increases the amount of the stainless steel. However, as this investigation aims at reducing the amount of the stainless steel within the members, merely the effect of ti/te ratio is additionally discussed in Section 4.6.1.4 by increasing the value of ti while te is kept constant.

189

12000

35000

10000

30000 25000

8000

P [kN]

P [kN]

CFDST short columns formed from stainless steel outer tubes

6000 4000

CFSCT-240x10-120x10-70

2000

CFSCT-240x10-120x5-70

20000 15000 CFSCT-480x15-240x5-70

10000

CFSCT-480x10-240x10-70

5000

0

0 0

0.02

0.04

0.06

0.08

Strain [mm/mm]

0

0.02

0.04

0.06

0.08

Strain [mm/mm]

Fig. 4.28 Effects of concrete strength on the load-strain curves for CFDT columns with different ti/te ratios.

4.6.1.3 Effects of the d/D ratio In this section, the influence of the diameter ratio (d/D) on the ultimate axial strength (Pu,FE) and the load-shortening response of CFDT columns under axial compression is presented. To study this effect, the diameter of the external stainless steel tubes (D), the thickness of the internal tube (ti), and the concrete’s compressive strength (fc0 ) were fixed. Table 4.16 provides the details of the current models. Fig. 4.29 provides the ultimate axial strengths (Pu,FE) of the columns predicted by the FE model. It can be seen that increasing the d/D ratio only slightly increases the ultimate axial strength of the CFDT columns with different ti/te ratios. Additionally, it was found that the d/D ratio does not have a significant influence on the load-strain responses of CFDT columns. In order to discover the reason that makes the effect of the d/D ratio negligible, Table 4.17 is presented. In this table, the strengths of the components (carbon tube, sandwiched concrete, and concrete core) are calculated based on their plastic resistance (P). The plastic resistance of the each concrete considers its confined compressive strength (fcc0 ) calculated from Eq. (4.8) for the sandwiched concrete and from Eq. (4.14) for the concrete core. The plastic resistance of the composite section (Psq) is then calculated as the summation of the plastic resistances of the components. It can be seen that as the d/D ratio increases, the resistance of the sandwiched concrete decreases and the resistance of the concrete core increases, thus, generally, providing the same concrete strength (Pc). Hence, the slight increase in the column strength is caused by the obvious increase in the cross-sectional area of the carbon steel tube as the diameter of the external tube is unchanged. It can be concluded that it is better to decrease the d/D ratio to reduce the amount of the internal steel tube without a significant decrease in the column strength.

4.6.1.4 Effects of the ti/te ratio The effect of the thickness ratio (ti/te) on the structural behavior of the CFDT columns is presented herein by varying the internal tube’s thickness. When studying the effect of the thickness ratio (ti/te), the dimensions of the external stainless steel tubes

Table 4.16 Details of the circular CFDT columns with fc0 ¼ 55 MPa and S355 (effects of the d/D ratio). External tube

Internal tube

Column

L [mm]

D [mm]

te [mm]

D/te

d [mm]

ti [mm]

d/ti

fc0 [MPa]

d/D

ti/te

C21 C22 C23 C24 C25 C26 C27 C28

1440 1440 1440 1440 1440 1440 1440 1440

480 480 480 480 480 480 480 480

10 10 10 10 20 20 20 20

48 48 48 48 24 24 24 24

120 180 240 360 120 180 240 360

6 6 6 6 6 6 6 6

20 30 40 60 20 30 40 60

55 55 55 55 55 55 55 55

0.25 0.375 0.5 0.75 0.25 0.375 0.5 0.75

0.6 0.6 0.6 0.6 0.3 0.3 0.3 0.3

CFDST short columns formed from stainless steel outer tubes

191

40 35 Pu,FE [MN]

30 25 20 15 C21-C24

10

C25-C28

5 0 0

0.2

0.4 d/D

0.6

0.8

Fig. 4.29 Effects of the diameter ratio (d/D) on CFDT column strength.

(D and te), the diameter of the internal tube (d), and the concrete’s compressive strength (fc0 ) were kept constant. The details of the current models are tabulated in Table 4.18. Fig. 4.30 provides the ultimate axial strengths (Pu,FE) of the columns predicted by the FE model. It can be seen from Fig. 4.30 that increasing the ti/te ratio markedly increases the ultimate axial strength of CFDT columns with different d/D ratios. This is attributed to the fact that increasing the internal steel tube’s thickness results in an increase in the steel area and confinement, which increases the ultimate axial strengths of CFDT columns. However, the increase in the strength becomes larger as the d/D ratio increases. This is because increasing the diameter of the internal steel tube increases the steel area, and more of the concrete in the internal tube is subjected to relatively higher confinement compared to the sandwiched concrete. The load-strain relationships for the sample results are provided in Fig. 4.31. It can be observed that increasing the ti/te ratio does not significantly affect the initial axial stiffness but considerably increases the ultimate axial strength of circular CFDT columns.

4.6.1.5 Effects of the steel grade of the internal carbon steel tube The ultimate axial load capacities of CFDT columns were investigated by changing the steel grade of the internal tube. Three steel grades (S235, S275, and S355) according to EN 1993-1-1 [56] were considered. The full details of the current CFDT columns are provided in Table 4.19. The ultimate axial strengths (Pu,FE) of the columns are presented in Fig. 4.32. It can be seen that increasing the steel yield stress fsy insignificantly increases the compressive strength of the CFDT columns for different d/D ratios. However, the rate of increase is nearly the same for different d/D ratios. Furthermore, it was found that the steel yield stress does not have a significant effect on the axial load-strain responses of CFDT columns. Hence, it is suggested to use internal tubes with the least fsy values to reduce the cost of CFDT columns.

Table 4.17 Strength of the components due to the change in the d/D ratio. Sandwiched concrete

Core concrete

As [mm2]

Ac [mm2]

fcc0 [MPa]

P [kN]

Ac [mm2]

fcc0 [MPa]

P [kN]

Column

Pu,FE [kN]

Pc [kN]

Ps [kN]

Pu,FE Psq

C21 C22 C23 C24 C25 C26 C27 C28

20,113 20,853 21,103 21,122 33,602 34,315 34,805 34,807

2149 3280 4411 6673 2149 3280 4411 6673

154,881 140,744 120,951 64,403 140,744 126,606 106,814 50,266

56.6 56.6 56.6 56.6 81.0 81.0 81.0 81.0

8764 7964 6844 3644 11,405 10,259 8656 4073

9161 22,167 40,828 95,115 9161 22,167 40,828 95,115

93.2 86.3 80.3 62.6 117.6 110.7 104.8 86.4

854 1913 3280 5950 1078 2455 4278 8220

9618 9877 10,124 9594 12,483 12,714 12,934 12,294

763 1164 1566 2369 763 1164 1566 2369

1.10 1.11 1.08 1.07 1.18 1.18 1.17 1.16

CFDST short columns formed from stainless steel outer tubes

193

Table 4.18 Details of the circular CFDT columns with fc0 ¼ 55 MPa and S355 (effects of the ti/te ratio). External tube L [mm]

Column C23 C29 C17 C30 C24 C31 C32 C33

1440 1440 1440 1440 1440 1440 1440 1440

D [mm] 480 480 480 480 480 480 480 480

te [mm] 10 10 10 10 10 10 10 10

Internal tube D / te

d [mm]

48 48 48 48 48 48 48 48

240 240 240 240 360 360 360 360

ti [mm] 6 8 10 12 6 8 10 12

fc′ D / ti

[MPa]

40 30 24 20 60 45 36 30

55 55 55 55 55 55 55 55

d /D

ti / te

0.5 0.5 0.5 0.5 0.75 0.75 0.75 0.75

0.6 0.8 1 1.2 0.6 0.8 1 1.2

30

Pu,FE [MN]

25 20 15 10

C23,C29,C17,C30

5

C24,C31-C33

0 0.6

0.8

1

1.2

ti / te

Fig. 4.30 Effects of the thickness ratio (ti/te) on CFDT column strength.

Fig. 4.31 Axial load-strain curves for CFDT columns for C31 and C32.

30000 25000

P [kN]

20000 15000 10000

CFSCT-480x10-360x8

5000

CFSCT-480x10-360x10

0 0

0.01

0.02

Strain [mm/mm]

0.03

0.04

194

Concrete-Filled Double-Skin Steel Tubular Columns

Table 4.19 Details of the circular CFDT columns with fc0 ¼ 55 MPa (effects of fsy). External tube Column

L [mm]

C34 C35 C17 C36 C37 C32

1440 1440 1440 1440 1440 1440

te

D

Internal tube D / te

[mm]

[mm]

480 480 480 480 480 480

10 10 10 10 10 10

48 48 48 48 48 48

d

ti

[mm]

[mm]

240 240 240 360 360 360

10 10 10 10 10 10

fc′ d / ti

[MPa]

24 24 24 36 36 36

55 55 55 55 55 55

d/D

fsy [MPa]

0.5 0.5 0.5 0.75 0.75 0.75

235 275 355 235 275 355

30

Pu,FE [MN]

25 20 15 10

C34,C35,C17 C36-C37,C32

5 0 200

250

300

350

400

Yield strength (fsy) [MPa]

Fig. 4.32 Effects of yield strength of the internal tube on CFDT column strength.

4.6.1.6 Comparison between CFDT and CFSST columns Herein, a comparison between CFDT and CFSST columns is made. Columns C1–C10 in Table 4.15 are considered besides the CFSST columns having the same outer dimensions (ti/te ¼ 0.0). It can be seen from Fig. 4.33 that adding an internal tube to the conventional CFSST columns increases their strengths. The increase in the internal tube’s thickness, in turn, increases the strength. This, however, is better than using CFSST columns with a larger diameter or lean duplex stainless steel wall thickness. Accordingly, this leads to cost savings due to minimizing the amount of the stainless steel. Another comparison could be made, for instance, between C21 of the current investigation and the CFSST column having the same outer diameter of C21 but with increased thickness (t ¼ 12 mm). The finite element strengths (Pu,FE) of the columns were found to be 20,113 kN for C21 and 21,357 kN for the CFSST column with increased thickness. The small increase in Pu, FE for the CFSST column is, however, accompanied by an increase in the cross-sectional area of the stainless steel tube of 2878 mm2. It should be noted that C21 has an internal steel tube with a cross-sectional area of 1440 mm2. Hence, cost savings using C21 instead of the CFSST column with increased thickness are guaranteed.

CFDST short columns formed from stainless steel outer tubes

ti/te=0.0

195

ti/te=0.5

ti/te=1.0

12000

Pu,FE [kN]

10000 8000 6000 4000 2000 0 40

50

70

85

100

fc′ [MPa]

Fig. 4.33 Comparison between CFDT and CFSST columns.

4.6.2 Comparisons with design strengths 4.6.2.1 The ACI code The ultimate axial strengths of CFDT columns obtained from the parametric study were compared with the design strengths predicted by the American specifications. The ACI code [38] ignores the concrete confinement effect. The ACI equation for the ultimate axial strength (Pu,ACI) of a concrete-filled circular column incorporating the contribution of the internal tube is given as: Pu,ACI ¼ σ 0:2 Ass + 0:85f 0 Ac + f sy As

(4.36)

where Ass is the cross-sectional area of the stainless steel tube, Ac is the cross-sectional area of the concrete infill within the whole section, and As is the cross-sectional area of the carbon steel tube. Table 4.20 provides a comparison between the design strengths (Pu,ACI) and the ultimate axial strengths (Pu,FE). This table demonstrates that the ACI code significantly underestimates the ultimate axial strengths of CFSST columns with different D/te ratios. It appears that the ACI code could underestimate the ultimate axial strength of a CFSST column by up to 32%. The mean value of Pu,ACI/Pu,FE is 0.75 with a coefficient of variation of 0.054. The discrepancy between the ACI code predictions and FE results is attributed to the fact that the ACI code does not consider the effects of concrete confinement on the ultimate axial strengths of CFDT columns.

4.6.2.2 The proposed new design model A design model for determining the ultimate strengths of short circular CFST columns and CFSST columns under axial compression was provided by Liang and Fragomeni [20]. Based on their design models, a new design model for calculating the ultimate axial strengths of axially loaded circular CFDT short columns is proposed as:

Table 4.20 Comparison of the ultimate axial strengths of CFDT columns determined by the FE model and design codes. External tube

Internal tube

Column

D [mm]

D/te

d [mm]

d/ti

fc0 [MPa]

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25

240 240 240 240 240 240 240 240 240 240 480 480 480 480 480 480 480 480 480 480 480 480 480 480 480

24 24 24 24 24 24 24 24 24 24 32 32 32 32 32 48 48 48 48 48 48 48 48 48 24

120 120 120 120 120 120 120 120 120 120 240 240 240 240 240 240 240 240 240 240 120 180 240 360 120

24 24 24 24 24 12 12 12 12 12 48 48 48 48 48 24 24 24 24 24 20 30 40 60 20

40 55 70 85 100 40 55 70 85 100 40 55 70 85 100 40 55 70 85 100 55 55 55 55 55

fsy [MPa]

Pu, ACI [kN]

Pu, Prop [kN]

Pu, FE [kN]

355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355 355

5702 6164 6625 7087 7548 6231 6672 7113 7553 7994 18,206 20,187 22,168 24,148 26,129 15,796 17,822 19,849 21,876 23,903 16,258 16,606 16,955 17,652 23,089

7744 8526 9205 9782 10,256 8347 9080 9690 10,177 10,542 23,996 26,907 29,587 32,035 34,252 19,282 21,474 23,551 25,512 27,358 19,051 19,694 20,311 20,496 31,367

8224 8959 9567 10,124 10,599 8942 9666 10,246 10,740 11,080 26,212 29,159 31,862 34,095 36,540 19,988 22,187 24,214 26,116 27,881 20,113 20,853 21,103 21,122 33,602

Pu,ACI Pu,FE

Pu,Prop Pu,FE

0.69 0.69 0.69 0.70 0.71 0.70 0.69 0.69 0.70 0.72 0.69 0.69 0.70 0.71 0.72 0.79 0.80 0.82 0.84 0.86 0.81 0.80 0.80 0.84 0.69

0.94 0.95 0.96 0.97 0.97 0.93 0.94 0.95 0.95 0.95 0.92 0.92 0.93 0.94 0.94 0.96 0.97 0.97 0.98 0.98 0.95 0.94 0.96 0.97 0.93

C26 C27 C28 C29 C30 C31 C32 C33 C34 C35 C36 C37 Mean Coefficient

480 480 480 480 480 480 480 480 480 480 480 480

24 24 24 48 48 48 48 48 48 48 48 48

of variation (COV)

180 240 360 240 240 360 360 360 240 240 360 360

30 40 60 30 20 45 36 30 24 24 36 36

55 55 55 55 55 55 55 55 55 55 55 55

355 355 355 355 355 355 355 355 235 275 235 275

23,438 23,787 24,484 17,392 18,245 18,322 18,985 19,639 16,955 17,244 17,665 18,105

31,982 32,572 32,701 20,925 21,987 22,474 23,470 24,365 20,165 20,640 21,474 22,199

34,315 34,805 34,807 21,888 22,980 23,585 24,725 25,604 21,378 21,802 23,309 24,000

0.68 0.68 0.70 0.79 0.79 0.78 0.77 0.77 0.79 0.79 0.76 0.75 0.75 0.054

0.93 0.94 0.94 0.96 0.96 0.95 0.95 0.95 0.94 0.95 0.92 0.92 0.95 0.016

198

Concrete-Filled Double-Skin Steel Tubular Columns



Pu,Prop ¼ γ ss σ 0:2 Ass + γ s f sy As + γ sc f 0c + 4:1f 0rp:ss Asc h

i + γ cc f 0c + 4:1 f 0rp:ss + f 0rp:s Acc

(4.37)

where Asc is the cross-sectional area of the sandwiched concrete between two tubes, Acc is the cross-sectional area of the concrete core within the carbon steel tube, and the factors γ ss and γ s are given by Eq. (4.34) and Eq. (4.35), respectively. It can be seen from Table 4.20 that the proposed design model predicts well the ultimate axial strengths of CFDT columns, which are in excellent agreement with the FE solutions. The mean value of Pu,Prop/Pu,FE is 0.95 with a coefficient of variation of 0.016. It can be concluded that the confinement effects on the strength and ductility of the concrete infill must be taken into account in the nonlinear analysis and design of CFDT short columns. The proposed design model incorporating concrete confinement effects provides good estimates of the ultimate axial strengths of CFDT short columns and can be used in the design of normal and high-strength CFDT columns, which is not covered in the current composite design codes.

4.7

Summary and conclusions

This chapter has presented the analytical investigation of the compressive behavior of circular concrete-filled lean duplex stainless steel tubular (CFSST) short columns, concrete-filled lean duplex stainless double skin tubular (CFDST) short columns, and concrete-filled double-tube (CFDT) short columns of lean duplex stainless steel of Grade EN 1.4162. A minimum 0.2% proof stress (σ 0.2) of 530 MPa and an ultimate tensile strength of 700 MPa following EN 10088-4 [4] were utilized herein. Three-dimensional finite element (FE) models for CFSST columns subjected to axial compression were developed using the FE package ABAQUS. The accuracy of the FE models has been established by comparisons of the FE solutions with the experimental results on hollow stainless steel tubes, CFST columns, and CFSST columns. From the results related to CFSST short columns, the following conclusions can be drawn: 1. Increasing the concrete’s compressive strength significantly increases the ultimate axial strength of circular CFSST columns, whereas the stiffness remains more or less the same. 2. The ultimate axial load of circular CFSST columns decreases with increases in the D/t ratio considering both types of axial load-strain curves. 3. Circular CFSST columns with different D/t ratios exhibit the same initial stiffness. 4. Increasing the D/t ratio of a CFSST column reduces the confinement effect. 5. The lean duplex stainless steel tubes cannot exert good confinement effect on the concrete when the D/t ratio is larger than 47. 6. The ACI code provides conservative predictions of the ultimate axial strengths of CFSST columns.

CFDST short columns formed from stainless steel outer tubes

199

7. EC4 provides better estimates compared to the ACI strengths for columns with D/t < 40, whereas it is on the unsafe side for large-scale columns with D/t  40. 8. The CSM gives better estimates relative to the ACI strengths for columns with D/t < 40, whereas it still on the unsafe side for large-scale CFSST columns with D/t  40. 9. The design models recently proposed by Liang and Fragomeni [20] have yielded the best predictions of the ultimate axial strengths of circular CFSST columns over the entire range of D/t ratios.

With respect to CFDST short columns, the following points can be highlighted: 10. It was shown that the ultimate axial load of CFDST short columns increases significantly by increasing the concrete’s compressive strength or by decreasing the hollow ratio. However, increasing the inner-to-outer thicknesses ratio or the yield strength of the inner carbon steel tube does not significantly increase the ultimate axial load. 11. Design methods provided by the ACI code, Han et al. [26], other authors, and the modified continuous strength method (CSM) [51] have been presented and compared with the FE and test results. The ACI code [38] and the model by Han et al. [49] provide conservative strength predictions of CFDST short columns under compression. The CSM [51] is in on the unsafe side for CFDST short columns with different D/te ratios. 12. The proposed design model is shown to provide reliable predictions of the ultimate axial strengths of CFDST short columns.

The following conclusions can be drawn for CFDT short columns based on earlier research: Based on the parametric and comparative studies, the following important conclusions can be drawn: 13. Increasing the concrete’s compressive strength (fc0 ) significantly increases the ultimate axial strength of circular CFDT columns, whereas the initial stiffness remains approximately the same. 14. CFDT columns behave in a favorable ductile manner irrespective of the fc0 value even when high-strength concrete is used. 15. The diameter ratio (d/D) only slightly increases the ultimate axial strength of CFDT columns with different ti/te ratios. Additionally, it does not have a significant influence on the load-strain responses of CFDT columns. Hence, it is better to decrease the d/D ratio to reduce the amount of the internal steel tube without a significant decrease in the column strength. 16. Increasing the thickness ratio (ti/te) does not significantly affect the initial axial stiffness but considerably increases the ultimate axial strength of circular CFDT columns. 17. The steel yield stress does not have a significant effect on the axial load-strain responses of CFDT columns. Moreover, increasing the steel yield stress fsy insignificantly increases the compressive strength of CFDT columns for different d/D ratios. 18. Compared to CFSST columns, a lower cost can be achieved by combining the advantages of lean duplex stainless steel and concrete-filled carbon steel tubular (CFST) columns. 19. The ACI code significantly underestimates the ultimate axial strengths of CFDT columns with different D/te ratios. 20. The proposed design model provides excellent predictions of the ultimate axial strengths of circular CFDT columns over a wide range of D/te ratios.

200

Concrete-Filled Double-Skin Steel Tubular Columns

References [1] L. Gardner, Stability and design of stainless steel structures – review and outlook, ThinWalled Struct. 141 (2019) 208–216. [2] N.R. Baddoo, Stainless steel in construction: a review of research, applications, challenges and opportunities, J. Constr. Steel Res. 64 (2008) 1199–1206. [3] L. Gardner, The use of stainless steel in structures, Prog. Struct. Eng. Mater. 7 (2) (2005) 45–55. [4] EN 10088-4, Stainless steels-Part 4: Technical Delivery Conditions for Sheet/Plate and Strip of Corrosion Resisting Steels for General purposes, CEN, 2009. [5] G. Gedge, Structural uses of stainless steel – buildings and civil engineering, J. Constr. Steel Res. 64 (11) (2008) 1194–1198. [6] M. Theofanous, L. Gardner, Testing and numerical modelling of lean duplex stainless steel hollow section columns, Eng. Struct. 31 (2009) 3047–3058. [7] Y. Huang, B. Young, Material properties of cold-formed lean duplex stainless steel sections, Thin-Walled Struct. 54 (2012) 72–81. [8] M.L. Patton, K.D. Singh, Numerical modeling of lean duplex stainless steel hollow columns of square, L-, T-, and +-shaped cross sections under pure axial compression, ThinWalled Struct. 53 (2012) 1–8. [9] M.F. Hassanein, Numerical modelling of concrete-filled lean duplex slender stainless steel tubular stub columns, J. Constr. Steel Res. 66 (8–9) (2010) 1057–1068. [10] M. Theofanous, L. Gardner, Experimental and numerical studies of lean duplex stainless steel beams, J. Constr. Steel Res. 66 (2010) 816–825. [11] M.F. Hassanein, Finite element investigation of shear failure of lean duplex stainless steel plate girders, Thin-Walled Struct. 49 (8) (2011) 964–973. [12] N. Saliba, L. Gardner, Experimental study of the shear response of lean duplex stainless steel plate girders, Eng. Struct. 46 (2013) 375–391. [13] ABAQUS Standard User’s Manual the Abaqus Software Is a Product of Dassault Syste`mes Simulia Corp., Providence, RI, USA, Dassault Syste`mes, Version 6.8, USA, 2008. [14] L. Gardner, D.A. Nethercot, Experiments on stainless steel hollow sections-part 1: material and cross-sectional behaviour, J. Constr. Steel Res. 60 (2004) 1291–1318. [15] W. Ramberg, W.R. Osgood, Description of Stress-Strain Curves by Three Parameters. NACA Technical Note no. 902, 1943. [16] H.N. Hill, Determination of Stress-Strain Relations from "Offset" Yield Strength Values, NACA Technical Note no. 927, 1944. [17] K.J.R. Rasmussen, Full range stress-strain curves for stainless steel alloys, J. Constr. Steel Res. 59 (2003) 47–61. [18] M.A. Bradford, H.Y. Loh, B. Uy, Slenderness limits for filled circular steel tubes, J. Constr. Steel Res. 58 (2002) 243–252. [19] F.-X. Ding, Z.-W. Yu, Y. Bai, Y.-Z. Gong, Elasto-plastic analysis of circular concretefilled steel tube stub columns, J. Constr. Steel Res. 67 (2011) 1567–1577. [20] Q.Q. Liang, S. Fragomeni, Nonlinear analysis of circular concrete-filled steel tubular short columns under axial loading, J. Constr. Steel Res. 65 (12) (2009) 2186–2196. [21] E. Ellobody, B. Young, D. Lam, Behaviour of normal and high strength concrete-filled compact steel tube circular stub columns, J. Constr. Steel Res. 62 (2006) 706–715. [22] ACI, Building Code Requirements for Structural Concrete and Commentary, ACI 318-99, American Concrete Institute, Detroit (USA), 1999.

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[23] Australian Standards AS3600, Concrete Structures, AS3600-1994, Standards Australia, Sydney, Australia, 1994. [24] Australian Standards AS4100. Steel Structures, AS4100–1998, Standards Australia, Sydney, Australia, 1998. [25] Eurocode 4, Design of Composite Steel and Concrete Structures. Part 1.1, General Rules and Rules for Buildings (with UK National Application Document), DD ENV 1994-1-1, British Standards Institution, London, UK, 1994. [26] M.F. Hassanein, O.F. Kharoob, Q.Q. Liang, Behaviour of circular concrete-filled lean duplex stainless steel tubular short columns, Thin-Walled Struct. 68 (2013) 113–123. [27] X.L. Zhao, L.H. Han, H. Lu, Concrete-Filled Tubular Members and Connections, Taylor & Francis: Spon Press, 2010. [28] L.-H. Han, Y.-J. Li, F.-Y. Liao, Concrete-filled double skin steel tubular (CFDST) columns subjected to long-term sustained loading, Thin-Walled Struct. 49 (2011) 1534–1543. [29] K. Uenaka, H. Kitoh, K. Sonoda, Concrete filled double skin circular stub columns under compression, Thin-Walled Struct. 48 (2010) 19–24. [30] H. Huang, L.-H. Han, Z. Tao, X.-L. Zhao, Analytical behaviour of concrete-filled double skin steel tubular (CFDST) stub columns, J. Constr. Steel Res. 66 (4) (2010) 542–555. [31] M.F. Hassanein, O.F. Kharoob, Q.Q. Liang, Circular concrete-filled double skin tubular short columns with external stainless steel tubes under axial compression, Thin-Walled Struct. 73 (2013) 252–263. [32] X. Chang, Z.L. Ru, W. Zhou, Y.-B. Zhang, Study on concrete-filled stainless steel-carbon steel tubular (CFSCT) stub columns under compression, Thin-Walled Struct. 63 (2013) 125–133. [33] M.F. Hassanein, O.F. Kharoob, Q.Q. Liang, Behaviour of circular concrete-filled lean duplex stainless steel-carbon steel tubular short columns, Eng. Struct. 56 (2013) 83–94. [34] M. Dabaon, S. El-Khoriby, M. El-Boghdadi, M.F. Hassanein, Confinement effect of stiffened and unstiffened concrete-filled stainless steel tubular stub columns, J. Constr. Steel Res. 65 (2009) 1846–1854. [35] E. Ellobody, B. Young, Design and behavior of concrete-filled cold-formed stainless steel tube columns, Eng. Struct. 28 (2006) 716–728. [36] M.-H. Wu, Numerical Analysis of Concrete Filled Steel Tubes Subjected to Axial Force (MS thesis), Department of Civil Engineering, National Cheng Kung Univ., Tainan, Taiwan, ROC, 2000. [37] J.B. Mander, M.J.N. Priestley, R. Park, Theoretical stress-strain model for confined concrete, J. Struct. Eng. ASCE 114 (8) (1988) 1804–1826. [38] ACI-318, Building Code Requirements for Reinforced Concrete, ACI, Detroit (MI), 2002. [39] Q.Q. Liang, Performance-based analysis of concrete-filled steel tubular beam-columns. Part I: theory and algorithms, J. Constr. Steel Res. 65 (2) (2009) 363–373. [40] F.E. Richart, A. Brandtzaeg, R.L. Brown, A Study of the Failure of Concrete under Combined Compressive Stresses, Bull. 185, University of Illionis, Engineering Experimental Station, Champaign (III), 1928. [41] H.T. Hu, C.S. Huang, M.H. Wu, Y.M. Wu, Nonlinear analysis of axially loaded concretefilled tube columns with confinement effect, J. Struct. Eng. ASCE 129 (10) (2003) 1322–1329. [42] J. Tang, S. Hino, I. Kuroda, T. Ohta, Modeling of stress-strain relationships for steel and concrete in concrete filled circular steel tubular columns, IEEE J. Solid State Circuits 3 (11) (1996) 35–46. [43] E. Ellobody, B. Young, Design and behaviour of concrete-filled cold-formed stainless steel tube columns, Eng. Struct. 28 (2006) 716–728.

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[44] S.P. Schneider, Axially loaded concrete-filled steel tubes, Journal of Structural Engineering, ASCE 124 (10) (1998) 1125–1138. [45] K. Sakino, H. Nakahara, S. Morino, I. Nishiyama, Behavior of centrally loaded concretefilled steel-tube short columns, J. Struct. Eng. ASCE 130 (2) (2004) 180–188. [46] B. Uy, Z. Tao, L.-H. Han, Behaviour of short and slender concrete-filled stainless steel tubular columns, J. Constr. Steel Res. 67 (2011) 360–378. [47] EN 1993-1-4, Eurocode 3: Design of steel structures - Part 1–4: General rulesSupplementary rules for stainless steel, CEN, 2006. [48] Z. Tao, L.-H. Han, X.-L. Zhao, Behaviour of concrete-filled double skin (CHS inner and CHS outer) steel tubular stub columns and beam-columns, J. Constr. Steel Res. 60 (8) (2004) 1129–1158. [49] L.-H. Han, Q.-X. Ren, L. Wei, Tests on stub stainless steel-concrete-carbon steel doubleskin tubular (DST) columns, J. Constr. Steel Res. 67 (2011) 437–452. [50] Z. Tao, B. Uy, L.H. Han, Z.B. Wang, Analysis and design of concrete-filled stiffened thinwalled steel tubular columns under axial compression, Thin-Walled Struct. 47 (12) (2009) 1544–1556. [51] D. Lam, L. Gardner, Structural design of stainless steel concrete filled columns, J. Constr. Steel Res. 64 (11) (2008) 1275–1282. [52] L. Gardner, The continuous strength method, Proc. Inst. Civ. Eng. Struct. Build. 161 (3) (2008) 127–133. [53] M.L. Lin, K.C. Tsai, Behavior of double-skinned composite steel tubular columns subjected to combined axial and flexural loads, in: Proceedings of the First International Conference on Steel & Composite Structures, 2001, pp. 1145–1152. [54] W. Li, Q. Xin Ren, L.-H. Han, X.-L. Zhao, Behaviour of tapered concrete-filled double skin steel tubular (CFDST) stub columns, J. Thin-Walled Struct. 57 (2012) 37–48. [55] Eurocode 2, Design of Concrete Structures. Part 1-1. General Rules and Rules for, Buildings, 2004. [56] EN 1993-1-1, Eurocode 3: Design of Steel Structures - Part 1-1: General Rules and Rules for Buildings, CEN, 2004.

CFDST slender columns formed from stainless steel outer tubes 5.1

5

Introduction

5.1.1 Research on composite slender columns Nowadays, concrete-filled steel tubes (CFST) are globally utilized, especially in marine structures [1] and in high-seismic zones as they have high strength and ductility [2] and energy dissipation ability [3]. They are used in different kinds of structural elements such as columns, beams, and beam-columns. This is primarily attributed to the advantages offered by the external tubes such as their ability to confine the concrete core and the role of the concrete core in delaying the inner local buckling of such tubes, as addressed in detail by Shanmugam and Lakshmi [4] and Han et al. [5]. Additionally, CFST columns have a high load-carrying capacity that may aid in constructing high-rise buildings, which can solve the problem of limited land areas in modern cities. CFST columns are also used in offshore structures, oil and gas drilling platforms, and as bridge piers because of their outstanding mechanical characteristics [5]. Accordingly, they are often exposed to air or seawater for long periods. So, the external steel tubes are at risk due to their exposure to aggressive acid rain, oceanic climate, and/or seawater. Hence, CFST columns in corrosive environments lose their excellent mechanical performances and safety as the thickness of the external steel tubes decreases due to corrosion [6]. This has mainly led to the emergence of metallic corrosion-resistant materials, which have been structurally utilized over the recent few decades, of which stainless steel alloys are the most prevalent. According to Gardner [7], stainless steels have an aesthetically attractive clean surface with high corrosion resistance. Additionally, based on EN 10088–4 [8], which provides the technical delivery conditions for plates made of corrosion-resistant steels, they are characterized by their high strength, toughness, and enhanced fire behavior. On the other hand, it is commonly known that the cost of stainless steels is extremely high compared to that of carbon steels. This is mainly attributed to the high prices of nickel, which is the main element of stainless steel alloys. The initial high cost of stainless steels has drastically limited their use in structural applications [7], but, based on their excellent advantages, several attempts have been made to provide a more economical use of compression members made of such materials. As shown later, the main ideas found in the literature were to (1) use stainless steel materials to form concrete-filled stainless steel tubular (CFSST) columns (Fig. 5.1A) and (2) utilize the relatively low-cost materials of the stainless steel family. By considering both solutions, the cross-sectional area of the used stainless steel tubes is reduced. Uy et al. [9] were the first to produce CFSST columns, and their investigation focused Concrete-Filled Double-Skin Steel Tubular Columns. https://doi.org/10.1016/B978-0-443-15228-3.00001-0 Copyright © 2023 Elsevier Inc. All rights reserved.

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t D Concrete core (b)

B

D

(a)

Stainless steel tube Carbon steel tube te

Concrete core

ti

ss

tsc d

t

Sandwiched concrete (c)

D

D

(d)

te ti

d

Sandwiched concrete

D

(e)

Fig. 5.1 Typical cross sections of concrete-filled columns utilizing stainless steel tubes. (A) CFSST; (B) Stiffened CFSST; (C) CFDT; (D) CFBST; (E) CFDST.

on studying the columns that were formed from austenitic stainless steel materials. Dabaon et al., in their experimental [10] and theoretical [11] investigations, proposed increasing the confinement of the concrete core by stiffening the cold-formed cross sections of CFSST columns using longitudinal stiffeners (Fig. 5.1B). According to them [11], stiffened CFSST short columns showed considerable enhanced strength and ductility compared to those of conventional unstiffened columns. A concretefilled austenitic stainless steel-carbon steel tubular column, hereafter known as a CFDT column, has been introduced as a new form of composite member [12], as presented in Fig. 5.1C. Furthermore, according to Ye et al. [13], an efficient application of stainless steel can be achieved using bimetallic tubes, which consist of an external

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205

stainless steel tube with an inner layer of a carbon steel tube, filled with concrete (CFBST), as shown in Fig. 5.1D. According to Patel et al. [14], the overall costs of CFBST columns were found to be less than those of ordinary CFST columns in the short and long terms. Additional investigation on CFDST columns (Fig. 5.1E) demonstrated that the reduced weight of the columns was associated with their high load-carrying capacity [15]. Overall, the performance of concrete-filled stainless steel tubular columns has recently been summarized by Han et al. [16] based on recent research. Recently, a new stainless steel material has been developed, characterized by its relatively low cost compared to that of the austenitic grade. Nickel represents a significant portion of the cost of austenitic stainless steels (around 10% of the composition). A lean duplex material (of Grade EN 1.4162) has a relatively low nickel content of about 1.5% of its alloy composition. Hence, lean duplex stainless steels have been used as structural materials [17], such as in the footbridge in Italy near Siena, which is shown in Fig. 5.2. This encouraged the authors to investigate CFSST “short” columns, with rectangular [18] and circular [19] cross sections, utilizing such relatively low-cost materials. Recently, experimental [20] and FE [21] studies have Fig. 5.2 Application of lean duplex stainless steel material: footbridge in Italy near Siena [17].

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Concrete-Filled Double-Skin Steel Tubular Columns

been undertaken by Lam et al. on square CFSST “short” columns made from this innovative material. From the earlier literature, it can be observed that the stability design of axially loaded CFSST “slender” columns, failing by flexural buckling, has received significantly less attention than that of short columns, failing by cross-sectional resistance. Accordingly, the behavior of circular CFSST “slender” columns is investigated herein, which has never been investigated in the literature before, using lean duplex jackets [16], despite the fact that advanced cross sections like double skin [22] and dual-steel [23] tubular concrete-filled slender columns with lean duplex external tubes have been investigated by the authors. Currently, the finite element (FE) method is utilized, despite finding other mathematical models [24] in the literature. It is worth noting that this chapter has categorized slender columns into “intermediate-length” columns, which fail by elastic–plastic buckling, and “long” columns, which fail by elastic buckling, and consequently addresses their behavioral differences in depth.

5.1.2 Classification of the columns with respect to length The typical strength (Pul) versus slenderness ratio (λ) relationship for axially loaded columns is shown in Fig. 5.3, where λ, similar to that previously defined in the studies by Hassanein and Kharoob [22,25], is given by: Le λ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi I DS =ADS

(5.1)

where, for the CFDT column, Le is the effective buckling length, IDS is the second moment of area of the CFDT section, and ADS is the cross-sectional area. Clearly, the curve is divided into three failure stages: plastic, elastic-plastic, and elastic buckling. Accordingly, slender columns are grouped into “intermediate-length” CFDT columns, which fail by elastic-plastic buckling, and “long” CFDT columns, which fail by elastic buckling, with a limiting slenderness ratio (λr) differentiating between them (see qffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fig. 5.3). This ratio, for the case of CFST columns, is defined as 115= f y =235 , according to DBJ/T13-51-2010 [26], where fy is the yield strength of the steel tubular member (in megapascal). Plastic stage Puo

Pul

Elastic-plastic stage

λp

Elastic stage

λr

Fig. 5.3 The strength-slenderness ratio relationship of columns.

λ

CFDST slender columns formed from stainless steel outer tubes

5.2

207

Nonlinear finite element analysis

In this chapter, to investigate the axially loaded CFSST “slender” columns, FE virtual tests were conducted using the available software package ABAQUS/Standard [27]. The main modeling difference between short and slender concrete-filled columns is the effect of initial imperfections. Although their effect is negligible in short concretefilled columns, as recommended by Tao et al. [28] and considered by the authors [29], they cannot be ignored while modeling slender columns. In slender columns, such initial imperfections trigger their flexural buckling. To include the initial imperfections in the modeling process of the current slender columns, the buckling modes of the perfect CFSST slender columns were obtained from the linear perturbation analysis supported by ABAQUS [27]. Then, the lowest positive buckling mode was scaled, to introduce the initial geometric imperfections of the columns (Fig. 5.4), and included in the nonlinear analysis of the CFSST slender columns. Currently, the modified RIKS method has been utilized in the nonlinear simulation. Typical FE models for slender CFSST and CFDST columns are shown in Fig. 5.5, from which it can be observed that, in addition to the column itself, two discrete rigid endplates were used to simulate the upper and lower cover plates. A reference point (RP) was defined at the center of each plate. The pin-ended support conditions were assigned to the lower RP, whereas the load was applied to the upper RP. To find the appropriate mesh size of the current columns, column C1-3a tested by Uy et al. [9] was used to conduct a sensitivity analysis, to mainly investigate the mesh effect on the axial strength. Mesh sizes between 40 mm and 70 mm (for both the tube and concrete) were considered, and their effect on the axial strengths of the CFSST slender columns is provided in Fig. 5.6. As can be observed, considering a mesh size of 50 mm leads to the most accurate relative strength (PFE/PExp), so it was used in further analyses. A typically meshed CFSST slender column is provided in Fig. 5.7. The three-node, triangular, general-purpose, finite-membrane-strain shell element S3 [27] has been utilized to represent the steel tube, whereas the three-dimensional, four-node, linear

Undeformed shape

Buckled shape

Fig. 5.4 Undeformed and buckled shapes of a typical CFDST slender column.

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Concrete-Filled Double-Skin Steel Tubular Columns

(a) t Upper end plate

D

Cross-section y

z

x

Boundary conditions: Lower reference point: ux = uy = uz = qz = 0.0 Upper reference point: ux = uy = qz = 0.0 Lower end plate

(b)

z

y

Upper end plate

x

Boundary conditions: Lower reference point: ux = uy = uz = qz = 0.0 Upper reference point: ux = uy = qz = 0.0

Fig. 5.5 A typical FE model for CFSST and CFDST slender columns and symbol definition. (A) CFSST column; (B) CFDST column.

tetrahedron solid element C3D4 [27] has been used to model the concrete core. The current element combination (i.e., S3 and C3D4) was approved by Dai and Lam [30], who reported that both finite strain shell and solid elements for the steel tube and concrete core, respectively, successfully captured the deformation in composite columns.

CFDST slender columns formed from stainless steel outer tubes

209

Fig. 5.6 Effects of a mesh on the ultimate axial strengths of CFSST columns.

Fig. 5.7 A typical FE mesh for a CFSST slender column: (A) cross-sectional view and (B) side view.

Previous results by Schnabl et al. [24] proved that the presence of finite interface compliance may significantly reduce the critical buckling load of CFST columns. Accordingly, a proper relationship between the stainless steel and concrete surfaces should be defined. Currently, similar to that suggested by Johansson and Gylltoft [31] and used successfully by the current authors [32], the bond between the stainless steel tube and the concrete core was simulated by a surface-based interaction with a contact pressure-overclosure model in the normal direction and a Coulomb friction model in the directions tangential to the surface. Herein, the stainless steel surface was chosen as the slave surface, whereas the concrete core surface was chosen as the master surface. The friction coefficient between the tube and the concrete core was taken as 0.25.

5.2.1 Stress-strain relationships for stainless steels The stainless steel material has been modeled as a von Mises material with isotropic hardening. The full-range stress-strain behavior of the lean duplex stainless steel material, as shown in Fig. 5.8, is simulated by a two-stage constitutive model developed by Rasmussen [33] as follows:

210

Concrete-Filled Double-Skin Steel Tubular Columns

(b) Carbon steel

800

400

600

300

400

s0.2 = 530MPa,n = 5

200

Stress [MPa]

Stress [MPa]

(a) Stainless steel

200 100 0

0 0

0.03 0.06 0.09 Strain [mm/mm]

0.12

0

0.02 0.04 0.06 Strain [mm/mm]

0.08

Fig. 5.8 Stress-strain curves of steel materials of (A) external lean duplex stainless steel material of Grade EN 1.4162 and (B) internal tubes.

8  n > σ σ > > + 0:002 for σ  σ 0:2

σ  σ 0:2 σ  σ 0:2 > > + εu + ε0:2 for σ > σ 0:2 : E0:2 σ u  σ 0:2

(5.2)

where ε is the strain, σ is the stress, and n is the nonlinearity index. εu is the ultimate strain of the stainless steel, σ u is the ultimate tensile strength of the stainless steel, and E0.2 is the tangent modulus of the stress-strain curve at the 0.2% proof stress and is given as follows: E0:2 ¼

E0 1 + 0:002n=e

(5.3)

where e is the nondimensional proof stress given as e ¼ σ 0.2/E0 and m ¼ 1 + 3.5(σ 0.2/σ u). As the material behavior provided by ABAQUS [27] allows for a multilinear stress-strain curve to be used, the first part of the multilinear curve represents the elastic part up to the proportional limit stress. According to EN 10088-4 [8], the cold-formed lean duplex stainless steel of Grade EN 1.4162 has a minimum of 0.2% proof stress (σ 0.2) of 530 MPa and an ultimate tensile strength ranging from 700 to 900 MPa. In the current investigation, the ultimate tensile strength was chosen as 700 MPa. The proportional limit was found to be σ 0.01 ¼ 300 MPa. The first part of the curve represents the elastic part up to the proportional limit stress with Young’s modulus of 200 GPa and Poisson’s ratio of 0.3. For the current material (Grade EN 1.4162), the strain at σ 0.2 is 0.00465.

5.2.2 Stress-strain relationships for the confined concrete Fig. 5.9 shows the general stress-strain curve suggested by Liang and Fragomeni [34] to simulate the material behavior of the confined concrete in circular CFDST columns. The part OA of the stress-strain curve is represented using the equations proposed by Mander et al. [35] as:

CFDST slender columns formed from stainless steel outer tubes

211

Fig. 5.9 A stress-strain curve for the confined concrete in circular CFST and CFSST slender columns.

  f 0cc λc εc =ε0cc σc ¼  λ λc  1:0 + εc =ε0cc c

(5.4)

E  c0  Ec  f cc =ε0cc

(5.5)

λc ¼

0 where σ c denotes the longitudinal compressive concrete stress, f cc represents the compressive strength of the confined concrete, εc stands for the longitudinal compressive 0 0 concrete strain, and ε cc is the strain at f cc . Young’s modulus of concrete Ec is given by the ACI [36] as:

Ec ¼ 3320

qffiffiffiffiffiffiffiffiffi γ c f 0c + 6900ðMPaÞ

(5.6)

where γ c denotes the strength reduction factor proposed by Liang [37] to account for the effects of the column size, the quality of the concrete, and the loading rates on the concrete’s compressive strength, which is expressed as: γ c ¼ 1:85Dc 0:135 ð0:85  γ c  1:0Þ

(5.7)

where Dc is the outer diameter of the concrete core. The confinement effect exerted by the circular steel tube increases both the 0 compressive strength of the confined concrete (f cc ) and the corresponding strain 0 0 0 (ε cc). Formulas proposed by Mander et al. [35] for calculating f cc and ε cc were modified using the strength reduction factor γ c [37] as: f 0cc ¼ γ c f 0c + kf 0rp

(5.8)

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Concrete-Filled Double-Skin Steel Tubular Columns

  f 0rp ε0cc ¼ ε0c 1 + 5k 0 γcf c

(5.9)

where frp0 stands for the lateral confining pressure on the concrete provided by the steel tubes and k is taken as 4.1, as suggested by Richart et al. [38]. The strain εc0 corresponding to fc0 of the unconfined concrete is usually between 0.002 and 0.003 depending on the effective strength of the concrete and can be calculated as follows: 8 0:002 > > < 0 ε0c ¼ 0:002 + γ c f c  28 > 54000 > : 0:003

for γ c f 0c  28ðMPaÞ for 28 < γ c f 0c  82ðMPaÞ

(5.10)

for γ c f 0c > 82ðMPaÞ

Liang and Fragomeni [34] proposed a confining pressure model for normal or highstrength concrete confined by either a normal or a high-strength steel tube based on the works of Hu et al. [39] and Tang et al. [40]. This model has been adopted in this study to determine the lateral confining pressures as follows:

f 0rp,ss

8 2t > > < 0:7ðνe  νs Þ D  2t σ 0:2 e  ¼  D > > σ : 0:006241  0:0000357 te 0:2

D  47 te D for 47 <  150 te for

(5.11)

where νe and νs are Poisson’s ratios of a stainless steel tube with and without concrete infill, respectively. Poisson’s ratio νs is taken as 0.5 at the maximum strength point, and νe is provided by Tang et al. [40]. The parts AB and BC of the stress-strain curve depicted in Fig. 5.9 are described by   8 < β f 0 + εcu  εc f 0  β f 0  for : ε0 < ε  ε c cu c cc c cc cc cc εcu  ε0cc σc ¼ : 0 βc f cc for : εc > εcu

(5.12)

where εcu is taken as 0.02 based on the experimental results as suggested by Liang and Fragomeni [34] and βc is provided by Hu et al. [39] as: 8 > > < 1:0

D  40 te     βc ¼ D 2 D D > > : 0:0000339  0:0102285 + 1:3491 for : 40 <  150 te te te for :

(5.13) Currently, to describe the constitutive behavior of the concrete core, a “concrete damaged plasticity” model was utilized. This model uses the concept of elastic isotropic damage, in combination with isotropic tensile and compressive plasticity, to represent

CFDST slender columns formed from stainless steel outer tubes

213

the inelastic behavior of concrete. This model assumes that the uniaxial tensile and compressive response of concrete is characterized by damaged plasticity. The plasticity parameters of this model are the dilation angle, which was taken as 20°, eccentricity, which was taken as 0.1, ratio of the strength in the triaxial state to the strength in the uniaxial state, which was set to unity because of the use of the confined concrete stress-strain curves, and K, which was set to 0.667 [41]. Although the ratio of the strength in the triaxial state to the strength in the uniaxial state has been recently found by Tao et al. [42] to have a significant influence on the strength and behavior of CFST short columns, it has no effect on the current CFSST slender columns. This was ensured herein by conducting sensitivity analyses using values ranging from unity to 1.16 (which is the default value in ABAQUS/Standard [27]). On the other hand, according to Liang [43], one of the major drawbacks of the existing nonlinear inelastic methods of analysis is the effect of concrete tensile strength, which is not taken into account. Accordingly, as can be seen in Fig. 5.9, the stress-strain relationship for concrete under tension was included in the current modeling to consider the concrete on the tension side of the cross section as a result of the overall buckling of the columns. As can be observed, the tensile stress-strain relationship is linear until pffiffiffiffiffiffiffiffi the concrete cracks at a strength of f t ¼ 0:6 γ c f 0c. After the cracking of the concrete, the tensile stress decreases linearly to zero as the concrete softens. According to Liang [43], the ultimate tensile strain is taken as 10 times the strain at cracking.

5.3

Validation of the FE model

To verify the current model for CFSST slender columns, the lean duplex material model should be validated first. This was, however, previously carried out by the current authors [18]. Therefore, this verification was not included in the current study for brevity. However, the verification of the composite columns, despite the authors’ previous experience [23], is included in the following with full details to make this chapter self-contained. In addition, the development of a new European standard for design by FE analysis [44] encouraged the authors to provide all the details of FE for current simulations of concrete-filled slender columns.

5.3.1 CFST columns To simulate CFST columns made of conventional carbon steel tubes (Fig. 5.1A), a bilinear elastic-plastic stress-strain model with linear strain hardening, which is different from that described in Section 5.2.1, was used to simulate the tubes. A modulus of E0/100 was used in the hardening part of the curve. In the current validation, the tested CFST columns by Han [45] were used, the dimensions and material properties of which are presented in Table 5.1 using the same symbols shown in Fig. 5.5. Indeed, the imperfections in these tests were too small. Hence, an initial out-of-straightness value of L/5000, as suggested by An et al. [46], was considered in these models. The ultimate axial loads (PEF) of the slender CFST columns obtained from the FE analyses are compared with the test data and the results of the FE model in the study

214

Concrete-Filled Double-Skin Steel Tubular Columns

Table 5.1 Details of the test specimens on the circular CFST slender columns used in the current verification. Column

D [mm]

t [mm]

D/t

L [mm]

e λ ¼ 4L D

fy [MPa]

fc0 [MPa]

sc154-3, sc154-4 sc149-1, sc149-2 sc141-1, sc141-2 sc130-1, sc130-2 sc130-3

108 108 108 108 108

4.5 4.5 4.5 4.5 4.5

24 24 24 24 24

4158 4023 3807 3510 3510

154 149 141 130 130

348 348 348 348 348

37.4 37.4 25.4 25.4 37.4

by Han [45] in Table 5.2. The FE model yields conservative predictions of the ultimate loads of the CFST columns. The mean values of PEF/PEXP are 0.92 and 0.87 for the present FE and the FE of An et al. [46], respectively. Fig. 5.10 shows the failure mode predicted by the developed FE model, which conforms well to the experimental behavior found by Han [45]. The predicted and experimental axial load-mid-height-deflection (um) curves of these specimens are presented in Fig. 5.11. It can be seen that the FE model predicts well the loaddeflection responses of the CFST slender columns. The predicted initial stiffness and postultimate load-deflection relationship of the CFST slender columns are in good agreement with the experimental results.

5.3.2 CFSST columns The developed FE model is validated using the experimental results of CFSST slender columns (Fig. 5.1A) provided by Uy et al. [9], though other remarkable tests have recently been conducted by Gunawardena and Aslani [47]. However, these tests [47] Table 5.2 Results of the circular CFST columns used in the current verification. PFE [kN] Current FE

[46]

PExp [kN]

(1)/(3)

(2)/(3)

Column

(1)

(2)

(3)

(4)

(5)

sc154-3 sc154-4 sc149-1 sc149-2 sc141-1 sc141-2 sc130-1 sc130-2 sc130-3

275

260

293

270

321

312

367

348

298 280 318 320 350 370 400 390 440

0.92 0.98 0.92 0.92 0.92 0.87 0.92 0.94 0.86 0.92 0.035

0.87 0.93 0.85 0.84 0.89 0.84 0.87 0.89 0.85 0.87 0.030

377

376 Ave COV

CFDST slender columns formed from stainless steel outer tubes

215

Axial load [kN]

Axial load [kN]

Fig. 5.10 Failure mode of a pin-ended CFST slender column.

Deflection at mid-height (um) [mm]

Deflection at mid-height (um) [mm]

Fig. 5.11 Comparisons of the numerical and experimental [42] axial load-mid-heightdeflection curves for CFST slender columns.

were carried out using spiral-welded stainless steel tubes, which suffer from extremely high residual stresses and unique initial imperfection patterns. So, they were not included in the current investigation. The tubes of these CFSST columns considered herein [9] were made of Grade EN 1.4301, which is an austenitic stainless steel material. The dimensions and material properties of the columns are provided in Table 5.3. The FE analyses of these columns considered the initial geometric imperfections of L/5000 and L/8000 at the mid-height of the columns, respectively. It can be seen from Table 5.4 that the FE model yields good predictions of the ultimate axial strengths of these specimens. The mean value of PFE/Pexp is 0.9 with a coefficient of variation of 0.064 for columns incorporating an initial geometric imperfection of L/8000. It appears that both geometric imperfection values led to the same results.

216

Concrete-Filled Double-Skin Steel Tubular Columns

Table 5.3 Details of the circular CFSST columns used in the current verification. Column

D [mm]

t [mm]

L [mm]

λ

σ 0.2 [MPa]

C1-2a C1-2b C1-3a C2-2a C2-2b

113.6 113.6 113.6 101 101

2.8 2.8 2.8 1.48 1.48

1540 1540 2940 1340 1340

54.2 54.2 103.5 53.1 53.1

288.6 288.6 288.6 320.6 320.6

σu [MPa]

fc0 [MPa]

E0 [GPa]

n

689.5 689.5 689.5 708 708

36.3 75.4 36.3 36.3 75.4

173.9 173.9 173.9 184.2 184.2

7.6 7.6 7.6 7.2 7.2

Table 5.4 Results of the circular CFSST columns used in the current verification. Imperfection L/5000 Column C1-2a C1-2b C1-3a C2-2a C2-2b

PFE [kN] 566 789 292 379 601 Ave COV

Imperfection L/8000 PFE PExp

PFE [kN]

PFE PExp

0.98 0.93 0.82 0.85 0.87 0.89 0.064

566 806 292 396 605

0.98 0.95 0.82 0.89 0.87 0.90 0.064

Axial load [kN]

Axial load [kN]

The load-deflection curves for CFSST slender columns predicted by the FE model are compared with the test results in Fig. 5.12. The predicted load-deflection curves for specimens C1-2a and C1-2b are in excellent agreement with the experimental ones in terms of initial stiffness, ultimate load, and the postpeak softening behavior. The FE model predicts well the initial stiffness of specimens C1-3a and C2-2b, but the complete postpeak behavior has not been obtained due to the convergence problem of the nonlinear FE analysis.

Deflection at mid-height (um) [mm]

Deflection at mid-height (um) [mm]

Fig. 5.12 Comparisons of the numerical and experimental [9] axial load-mid-height-deflection curves for CFSST slender columns.

CFDST slender columns formed from stainless steel outer tubes

217

Hence, based on the three verifications conducted (the lean duplex material by Hassanein [18], the CFST slender columns, and the CFSST slender columns), the current model could effectively be used to investigate the CFSST slender columns utilizing lean duplex jackets.

5.3.3 CFDST columns On the other hand, the principal aim of this section is to check the FE model of the CFDST slender columns (Fig. 5.1E) compared to the available experimental results. Therefore, the validation of the CFDST slender columns, conducted by Tao et al. [15], used two identical specimens available in the literature (pcc2-1a and pcc2-1b). These were the only test specimens found by the authors in their available international journal database. The initial geometric imperfection value of L/5000, as suggested by An et al. [46] for CFST slender columns, was considered in the verification of the CFDST slender columns. Columns pcc2-1a and pcc2-1b had D  te of 114  3 mm, d  ti of 58  3 mm, length of 1770 mm, and yield strengths of 294.5 and 374.5 MPa for the external and internal tubes, respectively; the definition of the symbols can be viewed in Fig. 5.1. The ultimate axial strengths of the CFDST slender columns obtained from the FE analyses were about 0.92 and 0.96 of pcc2-1a and pcc2-1b, respectively. Hence, the current FE model yields conservative predictions of the ultimate strengths of the CFDST slender columns. The numerical and experimental axial load-mid-height-deflection (um) curves of these specimens are presented in Fig. 5.13. As can be seen, the FE model predicts well the load-deflection responses of the CFDST slender columns. The predicted initial stiffness and the postpeak softening behavior of the columns are in good agreement with the experimental results. The slight difference between the FE and test results is likely because of the uncertainty of the actual concrete strength and stiffness. Hence, it could be concluded that this verification, in addition to that of the CFSST slender columns, shows that the current FE model competently represents the behavior of the CFDST slender columns.

Fig. 5.13 Comparisons of the numerical and experimental [22] axial load-mid-heightdeflection curves for CFDST slender columns.

218

5.4

Concrete-Filled Double-Skin Steel Tubular Columns

CFSST columns

5.4.1 Parametric study A basic cross section (D ¼ 400 mm, t ¼ 10 mm, and fc0 ¼ 25 MPa) was first chosen to obtain the entire Pu  λ relationship (see Table 5.5). Then, two columns (C6 and C15) failing in the elastic-plastic and elastic stages, respectively, were chosen, by varying

G1

G2

G3

G4

G5

Column

Group

Table 5.5 Details and FE results of the circular CFSST columns.

L

D

[mm]

[mm]

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C6 C23 C24 C25 C26 C15 C27 C28 C6 C29 C30 C31 C32 C15 C33 C34 C35 C36

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 20000 6000 6000 6000 6000 6000 15000 15000 15000 15000 15000 6000 6000 6000 6000 6000 15000 15000 15000 15000 15000

400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400

t [mm]

D/t

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 20.00 13.33 10.00 8.00 6.78 20.00 13.33 10.00 8.00 6.78 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00

40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 20 30 40 50 59 20 30 40 50 59 40 40 40 40 40 40 40 40 40 40

f c′ [MPa] 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 40 60 80 100 25 40 60 80 100

λ

λ

Pu , FE [kN]

ε lc εy

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 60 60 60 60 60 150 150 150 150 150 60 60 60 60 60 150 150 150 150 150

0.120 0.241 0.361 0.482 0.602 0.722 0.843 0.963 1.084 1.204 1.324 1.445 1.565 1.686 1.806 1.926 2.047 2.167 2.288 2.408 0.722 0.722 0.722 0.722 0.722 1.806 1.806 1.806 1.806 1.806 0.722 0.722 0.722 0.722 0.722 1.806 1.806 1.806 1.806 1.806

12856 12697 11841 9785 7962 6932 6012 5140 4677 4270 3847 3318 3050 2729 2389 2147 1895 1702 1562 1385 10504 8371 6932 5865 5389 3761 2924 2389 2030 1825 6932 7653 8621 9219 9856 2389 2503 2626 2651 2768

4.00 3.18 2.98 1.80 1.12 1.29 0.86 0.75 0.57 0.48 0.43 0.33 0.37 0.35 0.33 0.33 0.32 0.32 0.30 0.31 1.12 1.24 1.29 0.92 0.98 0.29 0.32 0.33 0.30 0.31 1.29 1.07 1.14 0.99 1.28 0.33 0.30 0.29 0.29 0.33

CFDST slender columns formed from stainless steel outer tubes

219

some parameters, for assessing the effects of the diameter-to-thickness (D/t) ratio and the compressive strength (fc0 ) of the concrete core. It should be noted that this chapter follows the recommendations of both the Chinese code GB50017-2003 [48] and EC4 [49] by assuming a mid-height initial imperfection of L/1000 for flexural buckling, despite being extremely large when compared with experimental measurements, as shown by Uy et al. [9], Han [45], and An et al. [46]. Table 5.5 provides the details and FE results of the current specimens. Cross-sectional slenderness (D/te) not exceeding 59 (for a stainless steel material of σ 0.2 ¼ 530 MPa) was merely considered to focus on compact stainless steel sections following the definition of Bradford et al. [50]. In the following subsections, discussions on the typical failure modes, the load-average strain (εa) curves, and the load-longitudinal strain (εl) relationships are provided. Additionally, the effects of the slenderness ratio (λ), the D/t ratio, and the concrete’s compressive strength (fc0 ) on the fundamental behavior of the circular CFSST columns are addressed.

5.4.1.1 Failure modes and load-strain curves Currently, at the mid-height section of the columns on the compression side of the peak load (εlc), the load-longitudinal strain was recorded in the FE analyses. The ratios of εlc/εy are provided in Table 5.5, where εy is the yield strain of the lean duplex stainless steel material. Overall, the typical failure mode for any slender (i.e., intermediatelength or long) column has the shape of a half-sine wave similar to pinned-ended columns, as illustrated in Fig. 5.10. However, CFSST columns with intermediate lengths have ratios of εlc/εy greater than unity and the columns fail by inelastic instability. For the case of long CFSST columns, the ratio of εlc/εy is less than unity and the columns fail by elastic instability. The axial load-longitudinal strain (P  εl) curves obtained at the mid-height section of the stainless steel tubes of the CFSST columns C6, C8, and C17 are presented in Fig. 5.14, from which the compression strain is considered negative and the tension

Fig. 5.14 Load-longitudinal strain relationships for typical CFSST slender columns.

220

Concrete-Filled Double-Skin Steel Tubular Columns

strain is taken as positive. It can be seen that the whole section of column C6 was under compression when the maximum load (Pu, FE) was reached. At the ultimate load, the longitudinal compressive strain was higher than the yield strain of the stainless steel εy. However, after the maximum load was reached (Pu, FE), a part of the cross section of column C6 reversed from compression to tension. Column C8 exhibited nearly the same strain behavior of column C6, except that the maximum strength (Pu, FE) was attained in the elastic stage (i.e., εlc/εy < 1.0). When the maximum load (Pu, FE) of C17 was reached, a part of the cross section was under tensile stresses and the column buckled in the elastic range. By examining the whole length, it was found that from the length of 16 m (i.e., C16), the maximum load was associated with a tensile stress on the tension side. It is worth pointing out that these columns had slenderness parameters (λ) greater than 2.0, which means that their design is not covered by EC4 [49]. Fig. 5.15 shows the axial load (P) versus the lateral deflection at mid-height (um) relationships for selected CFSST columns. It should be noted that increasing the number in the designation system of the columns leads to an increased slenderness ratio, as can be realized from Table 5.5. As can be observed, the initial stiffness and maximum axial strength (Pu, FE) of the columns decreased with an increase in the column’s slenderness ratio (λ), but the postpeak portions of the relationships became steeper with a decrease ofλ. Generally, no obvious change could be observed between intermediatelength and long CFSST columns. Fig. 5.16 shows the relative axial load (P/Pu, FE) versus εh/εlc curves for columns C6 and C17, where εh represents the hoop strain of the stainless steel tube in the compression zone. it should be noted that both strains (εh and εlc) were recorded at the mid-height section of each column. For the long column (C17), εh/εlc was about 0.3 from the beginning of the load until the ultimate strength of the column was reached. This means that the Poisson effect only existed in the stainless steel tube, which did not provide confinement to the concrete core before the ultimate load was attained. This is unlike the response of intermediate-length CFSST columns

Fig. 5.15 Load-mid-height (um) relationships for typical CFSST slender columns.

CFDST slender columns formed from stainless steel outer tubes

221

Fig. 5.16 Normalized load-εh/εlc relationships for typical CFSST slender columns.

(C6), where the εh/εlc ratio was 0.3 until the load reached about 0.7Pu,FE. Then, the εh/εlc ratio increased dramatically until the Pu,FE value was obtained. Accordingly, it can be ensured that before the intermediate-length CFSST columns reached their Pu,FE values, the confinement effect of the concrete core provided by the stainless steel tube started and continued to increase until the ultimate strength was reached. However, after the ultimate load was reached for both columns, the confinement reduced, although a small increase in the hoop strain for the intermediate-length CFSST column (C6) could be observed after reaching the Pu,FE value.

5.4.1.2 Effect of the column slenderness ratio Herein, the effect of the column slenderness ratio (λ) on the behavior of the CFSST slender columns is presented. This is displayed in Fig. 5.17, which shows the relationships between the axial load (P) and the average axial strain (εa). It should be noted C4

C5 C7

P [kN] C9

C6

C8

C12 C13 C16 C20

mea

Fig. 5.17 Load-average axial strain relationships for typical CFSST slender columns.

222

Concrete-Filled Double-Skin Steel Tubular Columns

that this strain (εa) is calculated from the axial shortening of the column when dividing by the column length (L). Generally, the initial stiffness, as can easily be observed, remained unchanged for all the columns. However, transition from the preultimate to the postultimate stage of the columns is different in long and intermediate-length CFSST columns, i.e., while it is sharp in the former columns, it is somehow gradual in the latter columns. Additionally, it can be observed that as the slenderness ratio increases, both the ultimate axial strength and the corresponding average axial strain (εa) decrease.

5.4.1.3 Effect of the diameter-to-thickness ratio The stiffness and strength of the circular CFSST slender columns are examined in this subsection, considering groups G2 and G3, as a result of varying the diameter-tothickness ratio (D/t) of the columns. The tube thickness of columns C6 and C15 was varied to yield different D/t ratios varying from 20 to 59. The concrete strength was 25 MPa. The general trend of strength variation as a result of the variation in the D/t ratio can be observed in Table 5.5. It can be seen from this table that increasing the D/t ratio reduces the strength of the CFSST slender columns. However, this effect is insignificant for long columns (G2). Fig. 5.18 shows the effect of the D/t ratios on the normalized axial load (Pu,FE/Ps), where the squash load (Ps) is taken as Ps ¼ Asfy + Acfc. It can be seen that the D/t ratios do not have a significant effect on the normalized loads for both intermediate-length and long columns. Fig. 5.19 represents the load-εh/εlc relationships for the CFSST slender columns of groups G2 and G3. For CFSST columns with intermediate lengths, increasing the D/t ratio reduces the confinement effect exerted by the steel tube on the core concrete, leading to lower load capacities. The confinement effect is insignificant when the load is below 20% of its ultimate load. The confinement effect remains constant until a certain load level (between 0.6Pu,FE and 0.7Pu,FE) is reached. Thereafter, the confinement increases more significantly until the ultimate load (Pu,FE) is attained. However, for long CFSST columns, the D/t ratio does not have a significant effect on their behavior and the conferment effect can totally be ignored.

C21

C22

C6

C23

C24

C25

C26

C15

C27

C28

Fig. 5.18 Effect of the D/t ratios on the strength of typical CFSST slender columns.

CFDST slender columns formed from stainless steel outer tubes

223

Fig. 5.19 Load-εh/εlc relationships for CFSST slender columns of groups (A) G2 and (B) G3.

Fig. 5.20 shows the load-average axial strain (εa) curves for the circular CFSST slender columns of groups G2 and G3. Obviously, increasing the D/t ratio (from 20 (C21 and C25) to 59 (C24 and C28) in both groups of models, as can be observed in Table 5.5) considerably decreases the Pu,FE values of the CFSST columns and their initial stiffness. CFSST columns with small D/t ratios exhibit large axial strains without failure, having excellent ductility. Obviously, it can be seen that the transition from the pre- to the postultimate stages is smooth for intermediate-length CFSST columns (G2), whereas it is sharp for long CFSST columns (G3).

5.4.1.4 Effect of the compressive strength of the concrete The effect of the concrete’s compressive strength (fc0 ) on the behavior of CFSST slender columns are presented in this subsection by considering the results of groups G4 and G5. A variation between 25 and 100 MPa was considered for the compressive concrete strength. It should be noted that Eurocode 2 [51] defines concrete as highstrength (HSC) when fc0 > 50 MPa and as ultrahigh-strength (UHSC) when fc0 > 90 MPa. So, this means that the current fc0 range expands from normal to ultrahigh-strength concrete. The diameter-to-thickness ratio (D/t) was 40 while two values for the slenderness ratio (λ) of 60 and 150 were considered. The strengths of the columns can also be seen in Table 5.5. It can be observed that increasing fc0 increases the ultimate axial strength of CFSST columns with intermediate lengths (G4). In addition, a linear increase in the Pu,FE value is associated with an increase in the value of fc0 . However, the effect is insignificant for long columns (G5). This can be attributed to the fact that long columns fail by elastic buckling, which depends on the flexural stiffness of the cross section rather than on the material’s strength. As a result, the slight increase in the Pu,FE values caused by increasing the value of fc0 is attributed to the increase in the flexural stiffness. For such columns, the concrete core increases the flexural stiffness and prevents the inward local buckling of the steel

224

Concrete-Filled Double-Skin Steel Tubular Columns

Fig. 5.20 Load-average axial strain relationships for the CFSST slender columns of groups (A) G2 and (B) G3.

tubular sections (for additional information, see An et al. [46]). Hence, it is not a good decision to use HSC and UHSC, which have higher prices compared to that of normal strength concrete, to form long CFSST columns. Fig. 5.21 shows the normalized values of the ultimate axial loads of circular CFSST slender columns using the squash load (Ps ¼ Asfy + Acfc). From this figure, it can be seen that columns failing in the elastic-plastic range (G4) are more sensitive to the change in fc0 compared to those failing in the elastic range (G5).

5.4.2 Comparisons with design codes In this section, the ultimate FE axial strengths of CFSST slender columns are compared with those calculated using the European [49] and American [52] specifications. It should be noted that the material partial safety factors were excluded from the calculations by setting them to unity (i.e., these predictions [49,52] are unfactored strengths).

CFDST slender columns formed from stainless steel outer tubes

C6

C15

C29

C33

C30

C34

225

C31

35

C32

C36

Fig. 5.21 Effect of the fc0 ratio on the strength of typical CFSST slender columns.

5.4.2.1 Eurocode 4 Currently, the buckling lengths in the calculations were taken as the columns’ lengths because the current columns were all pin-ended. The Eurocode 4 (EC4) expression calculating the ultimate axial capacity (PEC4) of a CFST is given as:

PEC4

8   > < η As f + Ac f 1 + η t f y a c y c Dfc ¼χ > :A f + A f s y c c

: λ  0:5

(5.14)

: λ > 0:5

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 where ηa ¼ 0:25 3 + 2λ  1:0 , ηc ¼ 4:9  18:5λ + 17λ  1:0 , λ¼ Ppl,Rd =Pcr , and fy is the yield strength of the steel tube taken herein as the 0.2% proof stress (σ 0.2). It should be noted that the plastic resistance of the cross section according to EC4 takes into account the concrete confinement when the relative slenderness λ  0:5. The critical buckling load is calculated from: Pcr ¼

π 2 ðEI Þe ðKLÞ2

(5.15)

where K is the effective length factor, L is the laterally unbraced length of the member, and (EI)e is the effective elastic flexural stiffness. The reduction factor (χ ) is calculated using the European strut curves and is given by: 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 χ ¼ 1= ϕ + ϕ2  λ  1:0

(5.16)



  2 ϕ ¼ 0:5 1 + α λ  λο + λ

(5.17)

226

Concrete-Filled Double-Skin Steel Tubular Columns

As recommended by this specification, the design values of equivalent initial bow imperfections for CFST columns should be taken from Table 6.5 of EC4 [49]. This is to simplify the calculations by neglecting the effect of residual stresses and geometrical imperfections. Following that table, the imperfection factor for hollow circular sections is α ¼ 0.21 (buckling curve (a)) for ρs  3% and α ¼ 0.34 (buckling curve (b)) for 3 % < ρs  6%, and ρs is the ratio of the steel to concrete cross-sectional areas. It is worth mentioning that all of the current columns are of buckling curve (b). λο is taken as 0.2 for carbon steels (see ENV 1993-1-1 [53]).

5.4.2.2 The AISC specification In this specification, concrete confinement is neglected in the CFST columns in the entire length range. Following the AISC specification [52], the ultimate axial capacity (PAISC) of the CFST columns is given as:

PAISC ¼

8 h i Pnο > < Pnο 0:658 Pe > : 0:877Pe

Pnο  2:25 Pe P : nο > 2:25 Pe :

(5.18)

where Pnο ¼ Asfy + 0.95Acfc for compact round sections and Pe is the elastic critical buckling load determined from Eq. (5.15). The effective stiffness ((EI)e) of the CFST section is: ðEI Þe ¼ Es I s + C3 Ec I c

(5.19)

where the factor C3 is given by  C3 ¼ 0:6 + 2

 As  0:9 Ac + As

(5.20)

5.4.2.3 Comparisons and discussions Fig. 5.22 provides a comparison between the FE and predicted [49,52] ultimate strengths of the current CFSST slender columns. As can be observed, this comparison shows the three main variables considered in the investigation (λ, D/t ratio, and fc0 ). However, the comparison is made between the normalized values using the squash load (Ps ¼ Asfy + Acfc). Additionally, the ratios of the Pu,FE values to those computed by EC4 [49] (PEC4) and the AISC specification [52] (PAISC) are provided in Table 5.6. From Fig. 5.22, the following points may be drawn: (1) Both codes [49,52] can be safely used to design CFSST short columns, with the AISC specification [52] being the most conservative. However, EC4 [49] provides better estimates corresponding to the AISC specification [52] for short columns because of confinement considerations. Additional information on CFSST short columns may be obtained from Hassanein et al. [19]. (2) Both codes [49,52] are unsafe for

CFDST slender columns formed from stainless steel outer tubes

Fig. 5.22 Comparison between the FE strengths and the predictions of the EC4 [49] and AISC [52] specifications. (A) G1; (B) G2; (C) G3; (D) G4; (E) G5.

227

228

Concrete-Filled Double-Skin Steel Tubular Columns

Table 5.6 Comparison of the ultimate axial strengths of the CFSST columns determined by FE and design codes. Group

Column

λ

PEC4 [kN]

PEC4 Pu,FE

PAISC [kN]

PAISC Pu,FE

PProp [kN]

PProp Pu,FE

G1

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35 C36

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 60 60 60 60 150 150 150 150 60 60 60 60 150 150 150 150

12,483 10,483 9771 9612 7799 7192 6509 5789 5085 4440 3874 3390 2979 2632 2338 2088 1875 1692 1534 1396 11,566 8689 6272 5704 3658 2799 2050 1870 8173 9342 10,372 11,279 2455 2579 2680 2766

0.97 0.83 0.83 0.98 0.98 1.04 1.08 1.13 1.09 1.04 1.01 1.02 0.98 0.96 0.98 0.97 0.99 0.99 0.98 1.01 1.10 1.04 1.07 1.06 0.97 0.96 1.01 1.02 1.07 1.08 1.13 1.14 0.98 0.98 1.01 1.00 1.01 0.069

9135 8981 8729 8388 7969 7486 6952 6384 5795 5201 4616 4050 3508 3025 2635 2316 2051 1830 1642 1482 12,140 9094 6499 5889 4092 3177 2292 2076 8652 10,135 11,547 12,898 2858 3097 3298 3476

0.71 0.71 0.74 0.86 1.00 1.08 1.16 1.24 1.24 1.22 1.20 1.22 1.15 1.11 1.10 1.08 1.08 1.08 1.05 1.07 1.16 1.09 1.11 1.09 1.09 1.09 1.13 1.14 1.13 1.18 1.25 1.31 1.14 1.18 1.24 1.26 1.10 0.144

11,392 11,392 11,392 10,558 7656 6702 5816 5027 4345 3769 3286 2882 2544 2259 2017 1811 1635 1482 1350 1234 10,707 8080 5853 5327 3162 2417 1768 1613 7471 8367 9144 9828 2130 2252 2354 2441

0.89 0.90 0.96 1.08 0.96 0.97 0.97 0.98 0.93 0.88 0.85 0.87 0.83 0.83 0.84 0.84 0.86 0.87 0.86 0.89 1.02 0.97 1.00 0.99 0.84 0.83 0.87 0.88 0.98 0.97 0.99 1.00 0.85 0.86 0.89 0.88 0.91 0.066

G2

G3

G4

G5

Ave COV

CFDST slender columns formed from stainless steel outer tubes

229

longer (intermediate-length) columns, but, conversely, the AISC specification [52] is more nonconservative compared with the EC4 predictions [49]. (3) For long CFSST columns, the results obtained by EC4 [49] provide better agreement with Pu, FE values, whereas the AISC specification [52] yields slightly unsafe results. The main conclusion that may be drawn from Fig. 5.22A is that slenderness reduction factors should be applied in estimation models of the capacities of CFSST slender columns similar to that used by EC4 [49], provided here in Eq. (5.16). Moreover, it can be seen that the shape of the estimation curve according to EC4 [49] is generally similar to that of the FE curve, where both curves are represented by a smooth equation for slender columns (λ> 0:5). For intermediate-length CFSST columns (G2 and G4), it can be seen that the results obtained using both codes [49,52] are similar for a range of D/t ratios, whereas the variation of the ultimate axial strengths increases by a change in the values of fc0 (see Fig. 5.22 B and D). On the contrary, long CFSST columns (G3 and G5) are safely predicted by EC4 [49], whereas they are nonconservatively estimated using the AISC specification [52]. Moreover, the variation of the results of the slender CFSST columns increases by a change in the values of fc0 (see Fig. 5.22C and E) using the AISC specification [52]. From Table 5.6, it can be seen that the mean values of PEC4/Pu, FE and PAISC/Pu, FE are 1.01 and 1.10, respectively. However, in some cases, EC4 [49] might overestimate the ultimate axial strength of CFSST columns by 14%. On the other hand, previous results by Goode et al. [54] showed the applicability of the current designed strengths provided by EC4 [49] to be safely extended to a concrete cylinder strength of 75 MPa for the case of circular CFST columns. However, the current results, especially of G4, do not support this conclusion. Hence, a new design method for CFSST slender columns in the elastic-plastic and elastic stages is mandatory. This is described in the next subsection.

5.4.2.4 The proposed design model based on Eurocode 4 A design model for CFSST slender columns is proposed to provide safe predictions based on EC4 [49] and AISC [52] specifications. This current proposed model is based on the above-modified design model of EC4 [49]. The proposed design model is based on the buckling curves provided in EN 1993-1-4 [55] for stainless steels. According to EN 1993-1-4 [55], α and λο have the values of 0.49 and 0.4, respectively, for “welded hollow sections”. It is proposed that α be taken as 0.76 and λο be taken as 0.4. This is equivalent to buckling curve (d). The results using the proposed strength (PProp) are also provided in Table 5.6. From Table 5.6, it can be seen that the mean value of PProp/Pu, FE is 0.91. The maximum difference in strength between the proposed model and the FE results is 8%, which is acceptable from a design view point. Hence, the proposed design model is recommended for the design of CFSST slender columns. It is worth mentioning that this chapter proves that concrete-filled slender columns, of

230

Concrete-Filled Double-Skin Steel Tubular Columns

the current cross section besides those formed from double skin [22] and dual-steel [23] cross sections, require modifications in the Eurocode design model, in the future revisions of EC4, by considering a more appropriate “buckling curve.” This recommendation conforms to the “Fourth Edition of the European Design Manual for Structural Stainless Steel” [56], in which the inelastic buckling depends also on the stainless steel material to reflect the varying degrees of material nonlinearity, besides the section type and the axis of buckling.

5.5

CFDST columns

5.5.1 Numerical study 5.5.1.1 Input data Compact stainless steel sections were considered in the current parametric study (see the dimensions in Table 5.7 for CFDST columns shown in Fig. 5.1E). This was ensured using the slenderness limit proposed by Bradford et al. [50] for circular CFST columns. This limit delineates between a fully effective cross section and a slender cross section. According to this limit, if the cross-sectional slenderness (D/te) is less than 25/(fy/250), then the cross section is considered fully effective. For the current stainless steel material with fy ¼ 530 MPa, this limit is 59. The initial geometric imperfections at the mid-height of the CFDST slender columns were conservatively taken as L/1000 following the Chinese code GB50017-2003 [48]. A basic cross section (D  te ¼ 500  10 mm,d  ti ¼ 250  10 mm, and fc0 ¼ 25 MPa) was first chosen to unveil the structural behavior of such columns by generating a number of CFDST columns through length (L) variation. As a result, the slenderness ratios (λ) of the current CFDST columns varied from 7 to 182, as can be seen in Table 5.7. It is worth pointing out that columns C1 and C2 are short, whereas the others are slender. The assessment of different parameters affecting the behavior of the CFDST slender columns was then conducted based on the intermediate-length and long columns C4 and C10, respectively. By varying the dimensions and/or the material properties of columns C4 and C10, additional columns were generated to explore the effect of the hollow ratio (χ 0 ), the compressive strength of the sandwiched concrete (fc0 ), and the internal-toexternal tube thickness (ti/te) ratio. In the following subsections, the columns’ loadaverage strain (εa) relationships and the load-longitudinal strain (εl) curves measured on the external surfaces of the tubes at the mid-height sections are provided. Additionally, the effects of the slenderness ratio, D/t ratio, and fc0 values on the fundamental behavior of the circular CFDST columns are presented and discussed. The calculated strength-to-weight (STW) ratios of the columns are also discussed.

5.5.1.2 Structural behavior The typical failure modes of the current intermediate-length and long pin-ended columns have the well-known shape of a half-sine wave. To differentiate between intermediate-length and long CFDST columns, the longitudinal strain at the midheight section of the external stainless steel tubes on the compression side (εlc) was

Table 5.7 Details and FE results of the circular CFDST columns investigating the column slenderness with fixed fc0 ¼ 25 MPa. External tube

Internal tube

Column

L [m]

D [mm]

te [mm]

D/te

d [mm]

ti [mm]

d/ti

λ

λ

Pul, FE [kN]

εlc εy

STW ×103

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17

1.0 2.5 4.0 5.5 7.0 8.5 10.0 11.5 13.0 14.5 16.0 17.5 19.0 20.5 22.0 23.5 25.0

500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50

250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25

7 18 29 40 51 62 73 84 94 105 116 127 138 149 160 171 182

0.095 0.239 0.382 0.525 0.668 0.811 0.954 1.098 1.241 1.384 1.527 1.670 1.813 1.956 2.100 2.243 2.386

16,423 16,376 13,329 11,200 9440 8431 7358 6591 5803 5014 4393 3951 3140 2827 2455 2156 1971

2.74 2.86 1.85 1.20 0.71 0.73 0.47 0.47 0.47 0.37 0.37 0.23 0.24 0.29 0.29 0.32 0.32

3.56 1.42 0.72 0.44 0.29 0.22 0.16 0.12 0.10 0.08 0.06 0.05 0.04 0.03 0.02 0.02 0.02

232

Concrete-Filled Double-Skin Steel Tubular Columns

recorded from the FE results. It was then compared with the strain at the yield stress of the stainless steel material (εy), i.e., 0.00465, which is previously provided in Section 5.2.1. The relative values of εlc/εy are provided in Table 5.7. From this table, it can be seen that CFDST columns with intermediate lengths were associated with εlc/εy ratios greater than unity and that the columns failed by inelastic buckling, i.e., columns C3 and C4. Until a certain limit of λ was reached, the εlc/εy ratios became less than unity, indicating that the associated buckling occurred elastically (C5–C17). Additionally, it was found that the sandwiched concrete was entirely under compressive stresses in intermediate-length CFDST columns, which gradually decreased from the compression side to the opposite side. Conversely, a part of the sandwiched concrete in long columns may reverse from compression to tension. Axial load (P) versus longitudinal strain (εl) curves, measured at the mid-height sections of the external and internal tubes, for columns C4 and C12 are provided in Fig. 5.23. Compression strain is taken as negative, and tension strain as positive.

Fig. 5.23 Load-longitudinal strain relationships for typical CFDST slender columns: (A) C4 and (B) C12.

CFDST slender columns formed from stainless steel outer tubes

233

As can be seen, the whole section of the external tube of column C4 and that of the internal tube were under compression when the maximum load (Pul, FE) was reached. During this stage, there was a slight variation among the measured strains at the extreme sides of the cross section. This reveals that the column was nearly under pure compression. Additionally, it can be observed that at the Pul, FE value of column C4, the longitudinal compressive strains of both tubes were higher than the yield strains of their materials. However, after the maximum load was reached, the stress of a part of the cross section of the external tube of C4 reversed from compression to tension, whereas, in the same loading range, the internal tube was still under compression. On the other hand, when the maximum load of C12 was reached, a part of the cross section of the external tube was under tensile stresses. Moreover, it can be observed that the longitudinal compressive strains of both tubes of C12 were less than the yield strains of their materials. Additionally, it can be seen that the strains of both sides of the tubes of C12 differ from each other from the early loading stage, as a result of the elastic buckling associated with such a long column. The axial load-deflection curves of some CFDST columns are shown in Fig. 5.24. It can be observed that increasing the column slenderness ratio (λ) decreases both the initial stiffness and the maximum load (Pul, FE). The postpeak curves generally become steeper with decreasing λ. Generally, no obvious change could be observed in the axial load-deflection curves between intermediate-length and long CFDST columns. The curves presenting the relationship between the normalized axial load (P/Pul, FE) and the ratio εh/εlc of columns C4 and C12 (as the sample results) are provided in Fig. 5.25. εh and εlc stand for hoop and longitudinal strains of the stainless steel tube in the compression zone, respectively, captured at the mid-height section of each column. As can be seen, εh/εlc ratios of the external tube and the internal tube were 0.3 (confirming the presence of the Poisson effect) before the column reached its ultimate strength in the case of C12 long column. This means that no confinement was provided by both the tubes to the sandwiched concrete. On the contrary, the confinement provided by both the tubes of the intermediate-length column C4 to the

12000 10000 8000 P [kN]

6000 4000 2000

C4

C6

C10

C12 um [mm]

0 0

50

100

150

200

Fig. 5.24 Load-mid-height (um) relationships for typical CFDST slender columns.

234

Concrete-Filled Double-Skin Steel Tubular Columns

Fig. 5.25 Normalized load-εh/εlc relationships for typical CFSST slender columns.

sandwiched concrete started at certain limits and continued to increase until the Pul, FE value was reached. After the ultimate load was reached, the confinement decreased dramatically. The external and the internal tubes of column C4 seem to confine the sandwiched concrete from the load levels of 0.7Pul, FE and 0.6Pul, FE, respectively. As can be observed, the confining pressure was not activated in the elastic stage owing to the imperfect interface bonding that occurs at this stage due to the smaller lateral expansion of concrete compared to that of the steel tube [57]. As the lateral expansion of the sandwiched concrete gradually became greater than that of the steel, the εh/εlc ratio of the stainless steel tube generally increased from the abovementioned limits linearly until the load reached the Pul, FE value. Obviously, it can be seen that the confinement provided at the ultimate strength by the internal tube (i.e., εh/εlc  0.50) was higher than that provided by the external tube (i.e., εh/εlc  0.35) in the intermediatelength column C4. This is because the internal tube dilates and pushes outward under axial compression. Therefore, it exerts an earlier and stronger confining pressure to the sandwich concrete compared to that generated by the external tube [57].

Effect of the L/r ratio The column slenderness ratio (λ) is one of the important factors that influence the behavior of circular CFDST slender columns. The effect of λ on the axial load-strain relationships is illustrated in Fig. 5.26. This figure provides a sample of results for presentation clarity because the results of other columns are qualitatively similar. Accordingly, this figure presents one short column (C1), two intermediate-length columns (C3 and C4), and three long columns (C5, C10, and C13). The average axial strain (εa) was calculated by dividing the axial shortening of the column (measured at the upper RP (see Fig. 5.1)) by its length (L). It can be observed that the initial stiffness is the same for all columns. The curves of long columns are characterized by a sharp transition from the pre- to the postpeak

CFDST slender columns formed from stainless steel outer tubes

235

Fig. 5.26 Load-average axial strain relationships for typical CFDST slender columns.

stages compared to those of intermediate-length columns. The ultimate axial strength and the corresponding average axial strain (εa) decrease as the slenderness ratio increases. Fig. 5.27 shows the ratio of the ultimate axial strength (Pul, FE) to the strength of the cross section (Ps) [32] with different λ ratios. Ps was taken as: Ps ¼ γ ss σ 0:2 Ass + γ s f sy As +



γ sc f 0c + 4:1f 0rp:ss Asc

(5.21)

where Asc is the cross-sectional area of the sandwiched concrete and factors γ ss and γ s are used to account for the effect of strain hardening on the strength of stainless steel and carbon steel, respectively, and are given as:  0:1 D γ ss ¼ 1:62 te γ s ¼ 1:458

 0:1 d ti

ðγ ss  1:2Þ

(5.22)

ð0:9  γ s  1:1Þ

(5.23)

Fig. 5.27 Effect of the slenderness ratio (λ) on the relative capacities of CFDST columns.

236

Concrete-Filled Double-Skin Steel Tubular Columns

In design codes, CFST columns with λ less than or equal to 22 are considered short, for which the inelastic stability effects are ignored in the design. It can be seen from Fig. 5.27 that the ultimate axial strength of a CFDST column with λ ¼ 22 is equal to the composite section’s strength (Ps) and that after this limit the value of Pul, FE becomes smaller than the value of Ps. Hence, the slenderness limit of 22 is applicable for the definition of CFDST slender columns. On the other hand, the slenderness limit delineating between intermediate-length columns and long columns for “circular CFST columns” can be calculated according to DBJ/T13-51-2010 [26] as qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 115= f y =235 , where fy is the yield stress of the steel tube (in megapascal). For the current CFDST slender columns in which the yield stress of the external tubes is 530 MPa, this limit is 76.6. This limit shows that columns from C8 to C17 fail elastically. This does not match the results of the current columns because it ignores colpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi umns C5–C7. Alternatively, herein, a modification of this limit to 75= σ 0:2 =235 is suggested. Through this modification, CFDST columns with λ  50 (C5–C17) are characterized by elastic buckling failure, which is in good agreement with the results available in Table 5.7. “However, additional research is required to precisely find such a limit using a wider range of column dimensions.” Regarding the relation between the strength of the CFDST column and its weight, it can be observed from Table 5.7 that increasing the value of λ leads to a “considerable” decrease in the strength-to-weight (STW) ratio from 3.56  103 at λ ¼ 7 to 0.02  103 at λ ¼ 182.

Effect of the concrete confinement In a circular CFDST short column, it is well known that the compressive strength of the sandwiched concrete increases because of the lateral restraint provided by both the external and internal tubes [32]. In this section, the effect of concrete confinement is presented for the current CFDST slender columns. Therefore, the columns from C1 to C17 were analyzed again by ignoring the concrete confinement effects. This was carried out by setting the confining pressure frp, ss0 (refer to Hassanein and Kharoob [58]) to zero in this analysis. Fig. 5.28 demonstrates the effect of concrete confinement on the normalized ultimate axial strengths of CFDST columns with various slenderness

Fig. 5.28 Effect of concrete confinement on the relative capacities of CFDST columns.

CFDST slender columns formed from stainless steel outer tubes

237

ratios. It can be observed from the figure that the confinement effect decreases with an increase in the value of λ. This is because the lateral deflection prior to failure raises the secondary bending moment and hence reduces the mean compressive strain in the concrete. For the shortest column with λ ¼ 7, the confinement effect is most pronounced. It is interesting to note that when λ  50, the effect of the concrete confinement on the ultimate axial strength of the CFDST slender columns becomes insignificant. This, again, is in good agreement with the strain measurements shown in Table 5.7. Hence, the confinement effect can be ignored in the design of long CFDST columns characterized by λ  50. On the other hand, for the column of λ ¼ 7, the confinement effect raised the ultimate axial strength by 8%.

Effect of the hollow ratio

The influence of the hollow ratio (χ 0 ¼ d/(D  2te)) on the ultimate axial strength (Pul, FE) of CFDST slender columns was also examined. In the generated FE models, the diameter of the outer stainless steel tubes (D), the thickness of both the tubes, the concrete’s compressive strength (fc0 ¼ 25MPa), and the length (L) of columns C4 and C10 were kept constant. A change was, however, made in the diameter of the internal tube (d), which was taken as 125, 175, 300, and 375 (i.e., the d/D ratio ranges from 0.25 to 0.75; see Table 5.8). The effects of χ 0 on the ultimate axial strengths (Pul, FE) along with the normalized strengths (Pul, FE/Ps) of the CFDST slender columns are provided in Fig. 5.29. It can be seen from Fig. 5.29A that increasing χ 0 (which reduces the cross-sectional area of the sandwiched concrete) “nearly does not affect” the Pul, FE values of the intermediate-length columns, whereas it “increases” the Pul, FE values of long columns. This is, however, opposite to the behavior of CFDST short columns in which increasing χ 0 decreases their strengths. This is because the crosssectional area of the sandwiched concrete, which bears the largest part of the load of short columns [32,59], decreases by increasing the hollow ratio. On the other hand, it is well known that the effect of the concrete core on the ultimate axial strengths (Pul, FE) of CFST columns reduces by increasing the column slenderness [46]. Additionally, it was found that long CFST columns fail elastically and that the ultimate axial strength (Pul, FE) is mainly dominated by the flexural rigidity [46]. This is also the case for long CFDST columns. The flexural rigidity of these columns increases by increasing χ 0 (leading to an increase in the Pul, FE values) because the internal tubes are situated farther from the centroid, where they make greater contribution to the moment of inertia. However, by increasing χ 0 in intermediate-length columns, the crosssectional area of the sandwiched concrete decreases while the internal tube is situated farther from the centroid. Therefore, the reduction in the column strength caused by reducing the cross-sectional area of the sandwiched concrete neutralizes with the increase in the strength caused by the additional flexural rigidity gained from the internal tubes. This finally leads to an insignificant effect for χ 0 in intermediate-length columns. On the other hand, χ 0 significantly affects the normalized axial loads (Pul, FE/Ps) of the CFDST slender columns, as can be seen in Fig. 5.29B. As the Pul, FE values generally remain constant, the reduction in Ps (as a result of increasing χ 0 ) forces the normalized axial load to increase. It can be seen that increasing χ 0 raises the normalized loads for both intermediate-length and long CFDST columns.

Table 5.8 Details of the CFDST slender columns for the effect of the hollow ratio. External tube

Internal tube

Column

L [mm]

D [mm]

te [mm]

D/te

d [mm]

ti [mm]

d/ti

χ0

d D

λ

STW ×103

C18 C19 C4 C20 C21 C22 C23 C10 C24 C25

5500 5500 5500 5500 5500 14,500 14,500 14,500 14,500 14,500

500 500 500 500 500 500 500 500 500 500

10 10 10 10 10 10 10 10 10 10

50 50 50 50 50 50 50 50 50 50

125 175 250 300 375 125 175 250 300 375

10 10 10 10 10 10 10 10 10 10

12.5 17.5 25.0 30.0 37.5 12.5 17.5 25.0 30.0 37.5

0.26 0.36 0.52 0.63 0.78 0.26 0.36 0.52 0.63 0.78

0.25 0.35 0.50 0.60 0.75 0.25 0.35 0.50 0.60 0.75

43 42 40 38 36 114 111 105 101 95

0.40 0.41 0.44 0.48 0.56 0.06 0.07 0.08 0.08 0.10

CFDST slender columns formed from stainless steel outer tubes

(a)

239

(b) C18 C19 C4 C20 C21 C20 C18 C19 C4

[MN]

C24 C25 C22 C23 C10

C21

C25 C10 C24 C22 C23

Fig. 5.29 Effect of the hollow ratio (χ 0 ) on the strength of CFDST slender columns: (A) ultimate loads and (B) normalized loads.

Additionally, it was found that the confinement effect in the current intermediatelength columns is in agreement with the results of Section 5.4.2 and those illustrated in Fig. 5.25, i.e., the internal tube confines the sandwiched concrete sooner and stronger than does the external tube. On the other hand, no confinement was observed in long CFDST columns. Furthermore, no obvious change was seen either in the load-midheight-deflection (um) relationships or in the load-axial strain relationships for the CFDST slender columns following the change in χ 0 . Table 5.8, in addition, shows that the “STW” ratio increases with an increase in χ 0 , which is significant in the intermediate-length CFDST columns compared to long columns.

Effect of the concrete’s compressive strength It should be noted that the behavior of HS and UHS concretes is different from that of NS concrete in terms of ductility and the strain εc0 corresponding to the peak stress fc0 . HS and UHS concretes have higher strengths and larger strains εc0 at the peak stresses but lower ductility compared to NS concrete. These characteristics of NS, HS, and UHS concretes were simulated using the current concrete model (refer to Hassanein and Kharoob [58]). In this section, an analysis of the CFDST slender columns C4 (intermediate-length) and C10 (long) filled with different concrete strengths was undertaken to examine the effect of the value of fc0 on the strength and behavior of such columns. EN 1992-1-1 [51] defines concrete as high-strength (HSC) when fc0 > 50 MPa and as ultrahigh-strength (UHSC) when fc0 > 90 MPa. Generally, the maximum value of fc0 that is commonly adopted in practical construction is limited to 80–100 MPa [57]. Therefore, in the analysis, “two” NSCs of 25 and 40 MPa, “two” HSCs of 60 and 80 MPa, and “one” UHSC of 100 MPa were considered. Table 5.9 summarizes the details of the current models. Fig. 5.30 provides the ultimate axial strengths (Pul, FE) and the normalized strengths (Pul, FE/Ps) of the considered columns with different fc0 values. As can be seen, the

Table 5.9 Details of the CFDST slender columns for the effect of fc0 . External tube

Internal tube

Column

L [mm]

D [mm]

te [mm]

D/te

d [mm]

ti [mm]

d/ti

fc0

STWti/te

C4 C26 C27 C28 C29 C10 C30 C31 C32 C33

5500 5500 5500 5500 5500 14,500 14,500 14,500 14,500 14,500

500 500 500 500 500 500 500 500 500 500

10 10 10 10 10 10 10 10 10 10

50 50 50 50 50 50 50 50 50 50

250 250 250 250 250 250 250 250 250 250

10 10 10 10 10 10 10 10 10 10

25 25 25 25 25 25 25 25 25 25

25 40 60 80 100 25 40 60 80 100

0.44 0.49 0.55 0.59 0.64 0.08 0.07 0.08 0.08 0.09

CFDST slender columns formed from stainless steel outer tubes

(a)

241

(b) C4 C26 C27 C28 C29

[MN]

C4

C26

C27

C28

C29

C33 C10 C30 C31 C32

C10 C30 C31 C32 C33

Fig. 5.30 Effect of fc0 on the strength of CFDST slender columns: (A) ultimate loads and (B) normalized loads.

change in the value fc0 of the sandwiched concrete has a considerable effect on the Pul, FE values of only intermediate-length CFDST columns. This figure also illustrates that increasing the fc0 value linearly increases the capacity of the intermediate-length columns. Conversely, the fc0 value has generally no effect on long columns. This is attributed to the fact that the strengths of long columns remain more or less constant with different concrete strengths [46]. This is because the role of the concrete fill in long columns is restricted to increasing their flexural stiffness and preventing the inward local buckling of the steel tubes, which is different in intermediate-length columns in which the concrete bears the additional load. This is similar to CFST columns [46]. However, this trend is the same for different types of concretes (NS, HS, and UHS); i.e., NSC, HSC, and UHSC all behave in the same manner. On the other hand, increasing the value of fc0 for both column types (intermediate-length and long) decreases their normalized loads. This is attributed to the large increase in the Ps (i.e., the strength of the column’s cross section) value with an increase in the value of fc0 (see Eq. 5.21), whereas the corresponding increase in the strength of the slender column (Pul, FE) is much smaller. The load-strain relationships for the sample results of the intermediate-length CFDST columns are provided in Fig. 5.31. It can be seen that increasing the value of fc0 significantly raises the ultimate axial strength of the intermediate-length columns, whereas the initial stiffness remains approximately the same. Additionally, it can be seen that all intermediate-length columns behave in a favorable ductile manner irrespective of the fc0 value. On the other hand, different load-strain relationships for long CFDST columns were found to be similar because the value of fc0 had generally no effect on their behavior. Therefore, it is not advantageous to use HS or UHS concrete in long CFSST columns. On the other hand, Table 5.9 lists the “STW” ratios for different columns representing the effect of the fc0 value. It is seen that the “STW” ratio of CFDST columns increases as fc0 increases. This is significant in intermediate-length CFDST columns compared to long columns.

242

Concrete-Filled Double-Skin Steel Tubular Columns

Fig. 5.31 Load-average axial strain relationships for typical intermediate-length CFDST columns.

Effect of the ti/te ratio The effect of the thickness ratio (ti/te) on the behavior of CFDST slender columns was additionally explored. These effects were investigated by varying the internal tube’s thickness (ti) in a group of columns (C34–C43) and the external tube’s thickness (te) in another group (C44–C51). The diameters of the tubes (D and d), the length (L), and the value fc0 of columns C4 and C10 were kept fixed. The details of the current models are tabulated in Table 5.10. As can be observed from the table, changing the ti/te ratio does not significantly influence the value of λ. Fig. 5.32 represents the effect of changing the internal tube’s thickness by presenting the ultimate axial strengths (Pul, FE) and the normalized strengths (Pul, FE/Ps) against the ti/te ratios of the columns. It should be noted that the ti/te ratio increases by increasing the internal tube’s thickness (ti). As can be seen, the effect of the ti/te ratio on the strength of CFDST slender columns is significant in intermediate-length CFDST columns. This is attributed to the fact that increasing the value of the internal tube’s thickness raises the confinement provided to the sandwiched concrete. On the other hand, the effect of the ti/te ratio is insignificant in long columns. This is simply because the flexural stiffness is insignificantly influenced by the change in the thickness of the internal tubes, which are situated near to the centroid. Regarding the Pul, FE/Ps ratios, it can be observed that CFDST slender columns are insensitive to the change in the ti/te ratio. This is because the increase in the Ps and Pul, FE values by increasing the value of ti nearly occurs at the same rate. Additionally, Table 5.10 provides the “STW” ratio for different columns representing the effect of the ti/te ratio. It is seen that changing the internal tube’s thickness (ti) does not influence the “STW” ratio of CFDST slender columns. The effect of the ti/te ratio (by changing te) on the strengths of CFDST slender columns was also investigated. It should be observed that increasing the ti/te ratio reduced the thickness of the external tube (te). As can be seen from Fig. 5.33, the effect of the ti/te ratio is significant for CFDST slender columns. However, this effect is greater for

Table 5.10 Details of the CFDST slender columns investigating the effect of the ti/te ratio. External tube

Internal tube

Parameter

Column

L [mm]

D [mm]

te [mm]

D/te

d [mm]

ti [mm]

d/ti

λ

ti/te

STW λ

Varying the internal tube thickness

C34 C35 C4 C36 C37 C38 C39 C40 C10 C41 C42 C43 C44 C45 C46 C47 C4 C48 C49 C50 C51 C10

5500 5500 5500 5500 5500 5500 14,500 14,500 14,500 14,500 14,500 14,500 5500 5500 5500 5500 5500 14,500 14,500 14,500 14,500 14,500

500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500

10 10 10 10 10 10 10 10 10 10 10 10 50.0 25.0 16.7 12.5 10.0 50.0 25.0 16.7 12.5 10.0

50 50 50 50 50 50 50 50 50 50 50 50 10 20 30 40 50 10 20 30 40 50

250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

25.0 12.5 10 8.3 6.3 5.0 25.0 12.5 10 8.3 6.3 5.0 10 10 10 10 10 10 10 10 10 10

10 20 25 30 40 50 10 20 25 30 40 50 25 25 25 25 25 25 25 25 25 25

41 40 40 40 40 40 108 106 105 105 105 105 40 40 40 40 40 105 105 105 105 105

2.50 1.25 1.00 0.83 0.63 0.50 2.50 1.25 1.00 0.83 0.63 0.50 5.00 2.50 1.67 1.25 1.00 5.00 2.50 1.67 1.25 1.00

0.43 0.44 0.44 0.45 0.45 0.45 0.07 0.07 0.08 0.08 0.08 0.07 0.82 0.64 0.56 0.50 0.44 0.13 0.11 0.10 0.08 0.08

Varying the external tube thickness

244

Concrete-Filled Double-Skin Steel Tubular Columns

(a)

(b)

C34

C35

C36

C4

C37

C38 C34

C35 C4 C36

C37

C38

[MN] C39 C40 C10 C41 C42 C43

C41 C42 C43 C39 C40 C10

Fig. 5.32 Effect of the ti/te ratio (by changing ti) on the strength of CFDST slender columns: (A) ultimate loads and (B) normalized loads.

(a)

(b) C44 C45

C46 C44 C45

C46

C47 C4

C47 C4

[MN]

C51 C10 C48 C49 C50

C48 C49

C50 C51 C10

Fig. 5.33 Effect of the ti/te ratio (by changing te) on the strength of CFDST slender columns: (A) ultimate loads and (B) normalized loads.

intermediate-length columns, as the concrete confinement effect increases, compared to long columns. However, the ti/te ratio (by changing te) affects the behavior of long columns because the flexural stiffness increases by increasing the thickness of the external tubes, which are situated farthest relative to the centroid. Moreover, it can be seen that the normalized strengths increase, nearly at the same rate, by increasing the ti/te ratio for intermediate-length and long columns. By revising the changes in the cross-sectional resistance (Ps) and the member FE strength (Pul, FE), it was found that a decrease in the Pul, FE value is less than that of Ps, forcing the normalized strengths to increase with an increase in the ti/te ratio. Additionally, it can be observed from Table 5.10 that the “STW” ratio of CFDST slender columns increases significantly by increasing the external tube’s thickness (te).

CFDST slender columns formed from stainless steel outer tubes

245

5.5.2 Comparison with design strengths To the authors’ knowledge, there is no available compressive design strength for CFDST slender columns. Accordingly, the Pul, FE values of such columns were, first, compared with the strength predictions of CFST columns calculated using the EC4 [49] and AISC [52] specifications. The material partial safety factors were set to unity. “The plastic resistance (Ppl, Rd) of the cross sections in these predictions were modified by adding the contribution of the internal tubes (Asifyi).” Based on this comparison, the best design strength was given at the end.

5.5.2.1 Original and modified Eurocode 4 The unfactored ultimate axial strengths of CFDST columns were compared with the design strengths of the CFST columns predicted by Eurocode 4 (EC4) [49] for compact sections. In the calculations, the buckling lengths of the current pin-ended columns were typically taken as their physical lengths. The EC4 formula for the ultimate axial capacity (PEC4) of a CFST column is given as: PEC4 ¼ χPpl,Rd

(5.24)

where Ppl, Rd is the plastic resistance to axial compression taking into account the concrete confinement when the relative slenderness (λ) does not exceed 0.5, as follows:

Ppl,Rd

8   > < η Ass σ 0:2 + Asc f 0 1 + η t f y + Asi f a c y c D f 0c ¼ > : Ase σ 0:2 + Ac f 0c + Asi f y

: λ  0:5

(5.25)

: λ > 0:5

  2 where ηa ¼ 0:25 3 + 2λ  1:0 , ηc ¼ 4:9  18:5λ + 17λ  1:0 , and λ ¼ ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ppl,Rd,ð6:30Þ =Pcr . In the calculation of λ, Ppl, Rd, (6.30) does not consider the confinement effect (Eq. 6.30 of EC4 [49]). The critical buckling load is to be calculated from: Pcr ¼

π 2 ðEI Þe ðKLÞ2

(5.26)

where KL is the effective length of the member and (EI)e is the effective elastic flexural stiffness. The reduction factor (χ) is to be calculated using the European strut curves as: 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 χ ¼ 1= ϕ + ϕ2  λ  1:0

(5.27)



  2 ϕ ¼ 0:5 1 + α λ  λ0 + λ

(5.28)

246

Concrete-Filled Double-Skin Steel Tubular Columns

For simplicity, the design values of equivalent initial bow imperfections (instead of the effect of residual stresses and geometrical imperfections) for composite columns and composite compression members should be taken from Table 6.5 of ENV 1993-1-1 [53]. Following this table, the imperfection factor for hollow circular sections is α ¼ 0.34 (buckling curve (b)) for 3 % < ρs  6%, and ρs is the ratio of the cross-sectional area of the steel tube to the concrete core. It should be mentioned that the current models are in agreement with buckling curve (b). λo is taken as 0.2 for carbon steels (see ENV 1993-1-1 [53]). Additionally, the unfactored ultimate axial strengths of the CFDST columns were compared with the design strengths of the CFST columns predicted by Eurocode 4 (EC4) [49] by utilizing the strength of the CFDST short columns (λ  0:5) proposed by Hassanein et al. [32]. The modified EC4 formula for the ultimate axial capacity (λ) of a CFDST column is given as: PEC4,mod ¼ χPpl,Rd,mod where Ppl,

Rd, mod

Ppl,Rd,mod

(5.29)

is to be calculated as follows:

8

< γ Ase σ 0:2 + γ f 0 + 4:1f 0 Asc + γ Asi f ss c c s y rp ¼ :A σ + A f0 + A f se 0:2

sc c

si y

: λ  0:5 : λ > 0:5

(5.30)

5.5.2.2 The AISC specification According to the AISC specification [52], the unfactored ultimate axial capacities (PAISC) of the CFST columns (for compact sections) neglecting the effect of concrete confinement along the entire length range are given as follows:

PAISC ¼

8 h i Pno > < Pno 0:658 Pe > : 0:877Pe

Pno  2:25 Pe P : no > 2:25 Pe :

(5.31)

where Pno ¼ Assσ 0.2 + 0.95Acfc0 + Asfy for compact round sections and Pe is the elastic critical buckling load determined from Eq. (5.26).

5.5.2.3 Comparisons and discussions A detailed comparison between the Pul, FE values for the CFDST slender columns and the original predictions of the EC4 [49] and AISC [52] specifications is provided in Fig. 5.34, considering the different studied parameters: λ, χ 0 , fc0 , and ti/te. It can be observed that EC4 [49] provides better estimates compared to those of the AISC specification [52] for short columns (λ) because it considers the confinement effect. Hence, both codes [49,52] can be safely used to design CFDST short columns. In this case, the

CFDST slender columns formed from stainless steel outer tubes

247

Fig. 5.34 Comparison between the FE strengths and the predictions of the EC4 [49] and AISC [52] specifications. (A) C1-C17; (B) Intermediate length; (C) Long; (D) Intermediate length; (E) Long; (Continued)

248

Concrete-Filled Double-Skin Steel Tubular Columns

Fig.5.34, Cont’d (F) Intermediate length: C34–C38; (G) Long: C39–C43; (H) Intermediate length: C44–C46; (I) Long: C48–C51.

AISC prediction [52] is more conservative. For longer columns, both codes [49,52] are unsafe, but, on the contrary, the AISC specification [52] provides more nonconservative strengths compared to those of EC4 [49]. However, for long CFDST columns, the results obtained by EC4 [49] provide better agreement with the Pul, FE values, whereas the AISC specification [52] still yields unsafe results. The ratios of the Pul, FE values to those computed by EC4 [49] (PEC4) and AISC specifications [52] (PAISC) are provided in Table 5.5. From Table 5.5, it can be seen that the modified EC4 strength according to Hassanein et al. [32] provides better estimates for short columns. For slender columns, the original and the modified EC4 strengths provide the same prediction simply because they use the same formula. The main conclusion that may be drawn from Fig. 5.34A is that slenderness reduction factors should be applied in the estimation capacity models of the CFDST slender columns similar to that used by EC4 [49], provided here in Eq. (5.27). Moreover, it can be seen that the shape of the estimation curve according to EC4 [49] is generally similar to the FE strengths; both curves are represented by a smooth equation for slender columns.

CFDST slender columns formed from stainless steel outer tubes

249

For intermediate-length CFDST columns, it can be seen that the results obtained using both codes [49,52] are the same for the investigated range of χ 0 ratios, whereas the variation of the ultimate axial strengths slightly increases by a change in the values of fc0 (see Fig. 5.34B and D). In contrast, the strengths of long CFDST columns are highly nonconservatively estimated using the AISC specification [52] for different χ 0 ratios and fc0 values (see Fig. 5.34C and E). Through the variation of the thickness ratios (Fig. 5.34F–I), the AISC specification [52] yields highly nonconservative estimates for long CFDST columns. Strength predictions using the abovementioned methods (PEC4, PEC4, mod, and PAISC) are provided in Table 5.5. It can be recognized that the original and the modified EC4 [49] design methods provide much better strengths (with an average value of 1.04) compared to the AISC [52], which has an average value of 1.15. Overall, the three design methods produce unsafe results. Accordingly, an enhanced design model should be suggested. Therefore, a modification is suggested to the above-modified EC4 [49] design model. This modified version (PEC4, cor) is based on the buckling curves provided in EN 1993-1-4 [55] for stainless steels. According to EN 1993-1-4 [55], α has a value of 0.49 for “welded hollow sections”. Hence, currently, the use of this value, i.e., 0.49, has been suggested. This is, however, equivalent to buckling curve (c). It can be seen from Table 5.11 that the PEC4, Cor/Pul, FE ratios are less than unity with some exceptions related to the UHSC and high values of the d/D ratios. However, the mean value and the standard deviation of the PEC4, Cor/Pul, FE ratios are now 0.97 and 0.044, respectively. This means that this enhanced design strength provides the best estimate for the CFDST slender columns among the others.

5.6

CFDT columns

Initially, the λ ratios for the columns tested experimentally by Romero et al. [60] (at ambient temperature) were calculated using Eq. (5.1) and then compared with the abovementioned ratios [26] to classify the column buckling stage. It should be noted that using the λr ratio suggested for CFST columns [26] with the CFDT columns was just an approximation, which was made only to get a general idea about the buckling stage, and was checked later on. However, this comparison indicated that the four columns tested by Romero et al. [60] were all intermediate-length ones. Accordingly, to substitute for the lack of the available results, the main goal of this research is to provide data to practice engineers on the fundamental behavior and strength of CFDT slender columns under axial compressive loads, considering both “intermediatelength” and “long” CFDT columns.

5.6.1 Fundamental behavior of the CFDT slender columns 5.6.1.1 Description of the FE models The fundamental behavior of the CFDT slender columns (Fig. 5.1C) is investigated in this section using external and internal steel tubes made of lean duplex stainless steel and carbon steel, respectively. Using the slenderness limit proposed by

Table 5.11 Comparison of the ultimate axial strengths of the CFDST slender columns determined by FE and design codes. Column

λ

Pul, FE [kN]

PEC4 [kN]

PEC4, [kN]

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28

7 18 29 40 51 62 73 84 94 105 116 127 138 149 160 171 182 43 42 38 36 114 111 101 95 40 40 40

16,423 16,376 13,329 11,200 9440 8431 7358 6591 5803 5014 4393 3951 3140 2827 2455 2156 1971 11,237 11,226 11,158 11,130 4652 4939 5145 5253 12,308 13,937 15,044

16,178 14,005 13,200 11,554 10,610 9503 8298 7115 6055 5155 4411 3802 3302 2890 2548 2262 2020 11,475 11,551 11,475 11,843 4967 5024 5270 5465 13,080 15,038 16,912

14,889 14,688 13,900 11,554 10,610 9503 8298 7115 6055 5155 4411 3802 3302 2890 2548 2262 2020 11,475 11,551 11,475 12,322 4967 5024 5270 5465 13,080 15,038 16,912

mod

PAISC [kN]

PEC4, [kN]

13,016 12,776 12,343 11,735 10,981 10,112 9165 8176 7178 6202 5274 4419 3749 3220 2796 2451 2165 11,619 11,712 11,668 11,411 5916 6005 6365 6547 13,351 15,461 17,530

14,889 14,600 13,509 10,972 9856 8678 7512 6437 5501 4712 4059 3519 3074 2703 2394 2133 1911 10,875 10,951 10,919 11,770 4548 4599 4811 4975 12,365 14,135 15,815

cor

PEC4 Pul,FE

PEC4,mod Pul,FE

PAISC Pul,FE

PEC4,cor Pul,FE

0.99 0.86 0.99 1.03 1.12 1.13 1.13 1.08 1.04 1.03 1.00 0.96 1.05 1.02 1.04 1.05 1.03 1.02 1.03 1.03 1.06 1.07 1.02 1.02 1.04 1.06 1.08 1.12

0.91 0.90 1.04 1.03 1.12 1.13 1.13 1.08 1.04 1.03 1.00 0.96 1.05 1.02 1.04 1.05 1.03 1.02 1.03 1.03 1.11 1.07 1.02 1.02 1.04 1.06 1.08 1.12

0.79 0.78 0.93 1.05 1.16 1.20 1.25 1.24 1.24 1.24 1.20 1.12 1.19 1.14 1.14 1.14 1.10 1.03 1.04 1.05 1.03 1.27 1.22 1.24 1.25 1.08 1.11 1.17

0.91 0.89 1.01 0.98 1.04 1.03 1.02 0.98 0.95 0.94 0.92 0.89 0.98 0.96 0.97 0.99 0.97 0.97 0.98 0.98 1.06 0.98 0.93 0.94 0.95 1.00 1.01 1.05

C29 C30 C31 C32 C33 C34 C35 C36 C37 C38 C39 C40 C41 C42 C43 C44 C45 C46 C47 C48 C49 C50 C51

40 105 105 105 105 41 40 40 40 40 108 106 105 105 105 40 40 40 40 105 105 105 105

16,272 4991 5266 5476 5868 12,886 11,590 11,117 10,855 10,720 5696 5026 4920 4796 4644 34,377 20,501 15,877 13,328 14,693 9369 7111 5865

18,707 5455 5781 6050 6280 13,469 11,896 11,315 11,030 10,841 5692 5258 5082 4992 4932 35,122 21,041 15,888 13,189 14,182 9038 6969 5847

18,707 5455 5781 6050 6280 13,469 11,896 11,315 11,030 10,841 5692 5258 5082 4992 4932 35,122 21,041 15,888 13,189 14,182 9038 6969 5847 Ave COV

19,564 6832 7531 8115 8598 13,732 12,091 11,487 11,191 10,995 6828 6323 6115 6008 5935 35,983 21,504 16,221 13,436 16,420 10,765 8434 7088

17,410 5003 5325 5594 5826 12,744 11,290 10,751 10,485 10,309 5218 4808 4644 4560 4504 33,128 19,931 15,072 12,520 13,031 8278 6376 5347

1.15 1.09 1.10 1.10 1.07 1.05 1.03 1.02 1.02 1.01 1.00 1.05 1.03 1.04 1.06 1.02 1.03 1.00 0.99 0.97 0.96 0.98 1.00 1.04 0.051

1.15 1.09 1.10 1.10 1.07 1.05 1.03 1.02 1.02 1.01 1.00 1.05 1.03 1.04 1.06 1.02 1.03 1.00 0.99 0.97 0.96 0.98 1.00 1.04 0.052

1.20 1.37 1.43 1.48 1.47 1.07 1.04 1.03 1.03 1.03 1.20 1.26 1.24 1.25 1.28 1.05 1.05 1.02 1.01 1.12 1.15 1.19 1.21 1.15 0.140

1.07 1.00 1.01 1.02 0.99 0.99 0.97 0.97 0.97 0.96 0.92 0.96 0.94 0.95 0.97 0.96 0.97 0.95 0.94 0.89 0.88 0.90 0.91 0.97 0.045

252

Concrete-Filled Double-Skin Steel Tubular Columns

Bradford et al. [50] for the circular stainless steel tubes of the CFST columns, fully effective steel cross sections were considered in the current parametric study (Table 5.12). According to Bradford et al. [50], if the D/t ratio of the steel section is less than 125/(fy/250), then the cross section is considered fully effective. For the current stainless steel material with fy ¼ 530 MPa, this limit is 59. By applying the same limit [50] (D/t < 26.6 for fy ¼ 235 MPa), the internal carbon steel tubes with D/t ¼ 24 and 20 were also fully effective. Elchalakani et al. [61,62] have summarized all these limits. Two groups of models (G1 and G2), as provided in Table 5.12, were first chosen to explore the structural behavior of such columns by generating a number of CFDT columns through length (L) variation. As a result, the slenderness ratios (λ) varied from 46 to 191, including merely slender CFDT columns. A concrete compressive strength ( fc0 ) value of 30 MPa was considered in these two groups of models. As can be seen, the fully effective cross sections of the columns of G1 and G2 are different, with the columns of G1 having larger cross-sectional dimensions. So, logically, the columns of G1 have higher cross-sectional resistances relative to those of G2 of the same lengths. Hence, they are not currently comparable, but they were considered to check the outcome results for columns with different cross-sectional dimensions.   The nondimensional slenderness λ for the flexural buckling mode was also calculated, according to EC4 [49], as the square root of the characteristic value of the compressive plastic strength (Ppl, Rd), provided by Eq. (6.30) [49], to the elastic critical load (Pcr). The strength Ppl, Rd is currently modified to include the resistances of the different components forming the CFDT columns, as follows: Ppl,Rd ¼ σ 0:2 Ass + f sy As + f 0c Asc + f 0c Acc

(5.32)

where Asc is the sandwiched concrete’s cross-sectional area and Acc is the crosssectional area of the concrete core. The calculation of the critical force, Pcr ¼ π 2 ðEI Þeff =Le 2 , also required modification for (EI)eff, which is the effective flexural stiffness, for the current cross section. It was finally given by: ðEI Þeff ¼ Ess I ss + 0:6Esc I sc + Es I s + 0:6Ecc I cc

(5.33)

where Iss, Is, Isc, and Icc are the inertia of the external tube, internal tube, sandwiched concrete, and concrete core, respectively. The elasticity modulus of the concrete is provided in detail by Gardner [7]. In the following subsections, the columns’ loadaverage strain (εa) relationships and the load-longitudinal strain (εl) curves measured on the external surfaces of the tubes at the mid-height sections are provided. Additionally, the effects of the slenderness ratio, um ratio, and fc0 values on the behavior of circular CFDT slender columns are presented. The calculated strength-to-weight (STW) ratios of the columns are also discussed.

Table 5.12 Details and FE strengths of the CFDT columns investigating the effect of the column slenderness. External tube

Internal tube

Group

Column

D [mm]

te [mm]

D/te

d [mm]

ti [mm]

d/ti

εh/εlc [mm]

λ

εlc [49]

Pul, FE [kN]

STW ×103

G1

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11a C12a C13 C14 C15 C16 C17 C18 C19 C20a C21a C22a

480 480 480 480 480 480 480 480 480 480 480 480 400 400 400 400 400 400 400 400 400 400

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

48 48 48 48 48 48 48 48 48 48 48 48 40 40 40 40 40 40 40 40 40 40

240 240 240 240 240 240 240 240 240 240 240 240 200 200 200 200 200 200 200 200 200 200

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

24 24 24 24 24 24 24 24 24 24 24 24 20 20 20 20 20 20 20 20 20 20

5500 7000 8500 10,000 11,500 13,000 14,500 16,000 17,500 19,000 20,500 22,000 5500 7000 8500 10,000 11,500 13,000 14,500 16,000 17,500 19,000

46 59 71 84 96 109 121 134 147 159 172 184 55 70 86 101 116 131 146 161 176 191

0.579 0.736 0.894 1.052 1.210 1.368 1.526 1.683 1.841 1.999 2.157 2.315 0.696 0.886 1.076 1.266 1.456 1.646 1.835 2.025 2.215 2.405

12,957 10,010 8715 7894 6947 6171 5399 4492 4005 3292 2963 2632 8113 6562 5535 4715 4025 3184 2661 2228 1898 1586

0.314 0.191 0.137 0.105 0.081 0.063 0.050 0.037 0.031 0.023 0.019 0.016 0.276 0.175 0.122 0.088 0.065 0.046 0.034 0.026 0.020 0.016

G2

a

Columns with εlc greater than that specified by EC4 [49].

254

Concrete-Filled Double-Skin Steel Tubular Columns

5.6.1.2 Effect of the column slenderness ratio The column slenderness ratio (λ), which is a key factor that affects the behavior of circular CFDT slender columns, is discussed in this subsection. The effect of λ on the axial load-strain relationships is illustrated in Fig. 5.35. In Fig. 5.35A, columns belonging to group G1 are presented, whereas Fig. 5.35B represents sample columns from G2. The vertical axis of the figure represents the axial load, whereas the horizontal axis provides the average axial strain (εa), with the latter determined from the ratio of the end axial displacement of the column (measured at the upper RP) to the column length (L). As can be seen, the figure provides a sample of results for presentation clarity because the results of other columns are qualitatively similar. It can be observed that the stiffness, in the initial loading stages, is the same for all columns within each group. The curves of long columns (for example, C10 in Fig. 5.35A) are characterized by a sharp transition (i.e., a less rounded load-strain relationship) from the preultimate to the postultimate stages compared to those of intermediate-length columns (C4 and C7 of the same figure). Additionally, it can be observed that the ultimate axial strength and the corresponding average axial strain (εa) decrease as the slenderness ratio increases. On the other hand, Fig. 5.36 provides the typical load against the mid-height deflection (um) of the CFDT columns. As can be seen, the columns with shorter lengths exhibit smaller mid-height lateral displacements than do columns with longer lengths at any load level. Additionally, it can be observed that the lateral displacement of long columns increases considerably from low load levels compared to the displacement occurring in the intermediate-length columns. This is caused by the secondary bending moment, which increases considerably as the length increases [4]. Overall, it can be seen that the CFDT slender columns are characterized by a stable load-lateral displacement relationship in the whole loading process. Additionally, all curves of the CFDT slender columns tend to drop gradually and exhibit a ductile behavior, providing an additional merit over those of the CFST slender columns presented in Fig. 5.11.

Fig. 5.35 Load-average axial strain relationships for typical CFDT slender columns. (A) P [kN]; (B) P [kN].

CFDST slender columns formed from stainless steel outer tubes

255

Fig. 5.36 Load-lateral displacement relationships for typical CFDT slender columns. (A) P [kN]; (B) P [kN].

Fig. 5.37 displays the ratio of the ultimate axial strength (Pul, FE) to the strength (Ps) of the cross section recently suggested by Hassanein et al. [29] with different λ ratios. Ps was taken as:

Ps ¼ γ ss σ 0:2 Ass + γ s f sy As + γ sc f 0c,sc + 4:1f 0rp:ss h

i Asc + γ cc f 0c,cc + 4:1 f 0rp:ss + f 0rp:s Acc

(5.34)

where factors γ ss and γ s are used to account for the effects of the strain hardening on the strength of stainless steel and carbon steel tubes, respectively, and they are given as [29]:  0:1 D γ ss ¼ 1:62 te

ðγ ss  1:2Þ

(5.35)

Fig. 5.37 Effect of the slenderness ratio (λ) on the relative capacities of CFDT columns.

256

Concrete-Filled Double-Skin Steel Tubular Columns

γ s ¼ 1:458

 0:1 d ti

ð0:9  γ s  1:1Þ

(5.36)

From Fig. 5.37, it can be observed that as the length of the columns becomes larger, the ultimate loads of the columns with higher slenderness become less than those with lower slenderness. For example, the relative strength (Pul, FE/Ps) of the columns of group G1 decreased from 0.77 to 0.16 as the slenderness ratio changed from 46 to 184, respectively. Regarding the relation between the strength of the CFDT column and its weight, it can be observed from Table 5.12 that increasing the value of λ results in a “substantial” decrease in the strength-to-weight (STW) ratio of the CFDT slender columns. For example, the “STW” ratio for G1 decreased from 0.314 to 0.016 for columns with slenderness ratios of 46 and 184, respectively.

5.6.1.3 Typical failure modes

(a)

(b)

Axial load [kN]

Axial load [kN]

The results of the current FE modeling showed that the current pin-ended CFDT “slender” columns failed at their mid-heights with overall buckling (i.e., a half-sine wave). However, this buckling mode may occur either elastically or inelastically (see Fig. 5.3). To differentiate between intermediate-length and long CFDT columns, the relationships between the axial load (Pul, FE) against the ratio of εh/εlc were checked carefully, where εh and εlc are the hoop and longitudinal strains of the stainless steel tube in the compression zone, respectively, captured at the mid-height section of each column. Fig. 5.38, which provides the abovementioned relationship, shows two different behaviors. It can be seen that the Poisson effect exists until the ultimate load of column C22 is reached (the figure to the RHS). This happens only during the elastic stage when the concrete’s initial elastic dilation under compression is small and thus the lateral confining pressure propagated in the steel tubes is null [4]. Therefore, C22 is a long column. On the contrary, the confinement developed in column C15 (i.e., εh/εlc  0.3) near the ultimate load (see the red dotted circle in the LHS

Fig. 5.38 Load-εh/εlc ratio relationships for typical CFDT slender columns: (a) C15 and (b) C22.

CFDST slender columns formed from stainless steel outer tubes

257

Table 5.13 Failure modes for the CFDT slender columns (variation in the cross section and slenderness ratio). λ Group

46

59

71

84

96

109

121

134

147

159

172

184

G1

INB 55 INB

INB 70 INB

INB 86 INB

INB 101 EB

EB 116 EB

EB 131 EB

EB 146 EB

EB 161 EB

EB 176 EB

EB 191 EB

EB – –

EB – –

G2

of the figure) occurs due to the propagation of microcracking of the concrete, indicating that C15 is an intermediate-length column. It is worth pointing out that the abovementioned trend is similar for both external (stainless steel) and internal (carbon steel) tubes. By checking the εh/εlc ratios for groups G1 and G2, the different failure modes were identified and then tabulated in Table 5.13. In this table, EB and INB stand for the elastic and inelastic buckling failure modes, respectively. It is clearly shown that the slenderness ratio of the column affects its failure mode. Additionally, it can be observed that the limit of λ, which delineates between intermediate-length and long CFDT columns, is around 85. On the other hand, the slenderness limit (λr in Fig. 5.3) delineating between intermediate-length and long columns for circular “CFST” columns was calculated according to DBJ/T13-51-2010 [26], as previously provided at the beginning of Section 5.6, and it was found to be 76.6 for the current CFDT slender columns in which the yield stress of the external tubes is 530 MPa. From the author’s view point, this limit is acceptable for the current CFDT slender columns and is also valid for checking the available tests of Romero et al. [60]. However, additional research is recommended to precisely find such a limit using a wider range of column cross-sectional dimensions.

5.6.1.4 Strain distribution at mid-height sections The longitudinal strains were recorded from the FE results at the mid-height sections of both tubes on the compression and tension sides (εl). The load (P) versus longitudinal strain (εl) curves for columns C4 and C10 are provided in Fig. 5.39, where the negative and positive strains are those representing the compression and the tension strains, respectively. As can be seen, the sections of the external tube and the internal tube of column C4 were entirely under compression until the maximum load (Pul, FE) was reached. Clearly, there was a slight variation among the measured strains on the extreme sides of the cross section during this stage. This reveals that this intermediatelength column was nearly under pure compression. In the postultimate stage, the stress of a part of the cross section of the external tube of column C4 reversed from compression to tension, whereas, in the same loading range, the internal tube was still under compression. On the contrary, when the maximum load of column C10 was reached, a part of the cross section of the external tube was under tensile stresses. It can obviously be seen that the strains of both sides of the tubes of column C10 differ

258

Concrete-Filled Double-Skin Steel Tubular Columns

Fig. 5.39 Load-longitudinal strain relationships for typical CFDT slender columns: (A) C4 and (B) C10.

from each other from the early loading stage. This may be attributed to the elastic buckling taking place in the long CFDT columns, indicating that these columns are affected by bending moments from the early loading stages similar to long CFST columns [4].

5.6.1.5 Effect of the concrete’s compressive strength In this subsection, by varying the concrete material properties of columns C4 and C10, additional columns were generated to explore the effect of the compressive strength of the sandwiched concrete (fc0 , sc) and the concrete core (fc0 , cc). Currently, the concrete contribution ratio (CCR), considered as the ratio of the ultimate load of the CFDT column to that of the bare steel tubular member, is considered [63,64]. For the current

CFDST slender columns formed from stainless steel outer tubes

259

CFDT columns, the bare steel hollow member consists of both the external and internal tubes. The maximum loads of the bare steel hollow members were considered herein as the sum of the maximum loads of the external and internal tubes calculated following EC3 [53,55]. On the other hand, the concrete is defined as high-strength (HSC) when fc0 > 50 MPa and as ultrahigh-strength (UHSC) when fc0 > 90 MPa according to EN 1992-1-1 [51]. Therefore, in the analysis, “two” NSCs of 30 and 50 MPa, “two” HSCs of 70 and 90 MPa, and “one” UHSC of 110 MPa were considered. It should be noted that the present concrete model is applicable to simulate both the HSC and UHSC since it was initially proposed by Liang [37] for both normal and HSC surrounded by either normal or high-strength steel members. Table 5.14 summarizes the details of the current generated models. It can be observed from Table 5.14 that the presence of concrete increases the columns’ capacities compared to those of the bare steel sections, as the CCR is much greater than unity for both intermediate-length and long columns. Additionally, it can be seen that using HSC and UHSC cores has a little (insignificant) effect on the strength of intermediate-length columns compared to the use of NSC, for which similar results were found by Romero et al. [60]. For the considered intermediate-length columns, the CCR increases from 1.68 to 1.76 by increasing the value of fc0 , cc from 30 to 110 MPa, respectively, keeping in mind that the cost of UHSC is about five times that of NSC [60]. Hence, an increase of 8% in the CCR using UHSC is distinctly uneconomical. For long columns, the CCR is about 1.86 for different fc0 , cc values. Hence, it can be concluded that the variation of fc0 , cc has no effect in long columns. The constant value for the CCR of long columns is due to the known fact that the strengths of long columns remain more or less constant with different concrete strengths [65]. This is because the role of the concrete fill in long columns is restricted to increasing their flexural stiffness and preventing the inward local buckling of the steel tubes, which is different in intermediate-length columns in which the concrete bears the additional load. Hence, it could be concluded that the use of HSC and UHSC in CFDT slender columns, similar to CFST columns [63,66], does not provide the same enhancement as that of NSC in the composite behavior and strength. It should be noted that no obvious changes were found in the axial load-strain relationships compared to those provided in Fig. 5.35. Additionally, it is seen that the “STW” ratio of the CFDT columns increases “slightly” as fc0 , cc increases in intermediate-length CFDT columns, whereas it remains constant in long columns. On the other hand, increasing the value of fc0 , sc, in intermediate-length columns, can be observed to have a slightly better effect on both the strength and the “STW” ratio compared to an increase in the value of fc0 , cc. This untruly might give an indication that the strength of the confined sandwiched concrete is increased to a greater degree than the increase in the strength of the concrete core confined by both tubes. Indeed, the slightly better effect of increasing fc0 , sc is attributed to the larger cross-sectional area of the sandwiched concrete compared to that of the core concrete, i.e., Acc/Asc ¼ 0.34.

5.6.2 Design model To date, no design model has been presented for estimating the axial strength of CFDT slender columns. According to the results of Romero et al. [60], in a limited number of tests on intermediate-length CFDT columns, the axial compressive strengths of these

Table 5.14 Details and results of the CFDT slender columns for the effect of the concrete’s compressive strength. External tube

Internal tube

Column

L [mm]

D [mm]

te [mm]

d [mm]

ti [mm]

fc, sc0 [MPa]

C4 C23 C24 C25 C26 C10 C27a C28a C29a C30a C4 C31 C32 C33 C34

10,000 10,000 10,000 10,000 10,000 19,000 19,000 19,000 19,000 19,000 10,000 10,000 10,000 10,000 10,000

480 480 480 480 480 480 480 480 480 480 480 480 480 480 480

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

240 240 240 240 240 240 240 240 240 240 240 240 240 240 240

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

30 30 30 30 30 30 30 30 30 30 30 50 70 90 110

a

Columns with εlc greater than that specified by EC4 [49].

fc, cc0 [MPa]

¯ λ [49]

Pul, FE [kN]

CCR

STWti/te

30 50 70 90 110 30 50 70 90 110 30 30 30 30 30

1.052 1.081 1.109 1.137 1.163 1.999 2.054 2.107 2.159 2.211 1.052 1.116 1.177 1.234 1.288

7894 7944 7967 8185 8265 3292 3322 3282 3320 3342 7894 7814 7970 8438 8719

1.68 1.69 1.70 1.75 1.76 1.86 1.88 1.85 1.87 1.89 1.68 1.67 1.70 1.80 1.86

0.105 0.106 0.106 0.109 0.110 0.023 0.023 0.023 0.023 0.023 0.023 0.104 0.106 0.113 0.116

CFDST slender columns formed from stainless steel outer tubes

261

columns using the method of EC4 [49] are unsafe. Accordingly, EC4 [49] prediction for the conventional CFST slender columns (Eq. 5.37) is currently checked for the CFDT slender columns using the wider virtual test results generated in this chapter. Pul,EC4 ¼ χPpl,Rd where Ppl,

Ppl,Rd

Rd

(5.37)

is to be calculated as follows:

8   > < η As f + Ac f 1 + η t f y a c y c Dfc ¼ > :A f + A f s y c c

: λ  0:5

(5.38)

: λ > 0:5

  2 where ηa ¼ 0:25 3 + 2λ  1:0 , ηc ¼ 4:9  18:5λ + 17λ  1:0 , and fy are taken herein as the 0.2% proof stress (σ 0.2) for the columns formed from outer stainless steels. As can be observed, the plastic resistance to compression accounts for the increase in the concrete’s strength due to the confinement just if the εlc ratio does not exceed 0.5. However, this is not the case for the current “large-scale” columns in which εlc is greater than 0.5. Accordingly, Ppl, Rd may be provided according to EC4 [49], for the current CFDT columns, as provided in Eq. (5.39) after modification, to account for the different components forming these columns. Ppl,Rd ¼ σ 0:2 Ass + f sy As + f 0c Asc + f 0c Acc

(5.39)

On the other hand, the reduction factor (χ) is to be calculated using the European strut curves as: 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 χ ¼ 1= ϕ + ϕ2  λ  1:0

(5.40)



  2 ϕ ¼ 0:5 1 + α λ  λo + λ

(5.41)

According to EN 1993-1-4 [55], α and λo have the values of 0.49 and 0.4, respectively, for “welded hollow stainless steel sections”. Table 5.15 and Fig. 5.40 provide the comparisons between the design strength Pul, EC4 and the Pul, FE values obtained numerically. It should be noted that the columns with εlc greater than that specified by EC4 [49] (see Tables 5.2 and 5.4) were excluded from this table. As can be seen in the table, EC4 [49] provides generally unsafe estimates for the ultimate axial strengths of intermediate-length CFDT columns (similar results were found by Romero et al. [60]), although the average strength (for all the columns) compared to the FE strength is 1.00. For long columns, EC4 [49] predicts the strengths suitably. Moreover, it can be observed that EC4 [49] yields nonconservative results when HSC and UHSC are used in the CFDT columns. Accordingly, an EC4 [49] design model requires modification to produce conservative results. This could be carried out using Ppl, Rd, as previously suggested by Hassanein

Table 5.15 Comparison of the ultimate axial strengths of the CFDT columns determined by FE and EC4 [49].

Column

D [mm]

C1 480 C2 480 C3 480 C4 480 C5 480 C6 480 C7 480 C8 480 C9 480 C10 480 C13 400 C14 400 C15 400 C16 400 C17 400 C18 400 C19 400 C23 480 C24 480 C25 480 C26 480 C31 480 C32 480 C33 480 C34 480 Mean Standard deviation

te [mm]

d [mm]

ti [mm]

fc, sc0 [MPa]

fc, cc0 [MPa]

εh/εlc [mm]

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

240 240 240 240 240 240 240 240 240 240 200 200 200 200 200 200 200 240 240 240 240 240 240 240 240

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 50 70 90 110

30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 50 70 90 110 30 30 30 30

5500 7000 8500 10,000 11,500 13,000 14,500 16,000 17,500 19,000 5500 7000 8500 10,000 11,500 13,000 14,500 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000

λ [49]

[29]

0.579 0.736 0.894 1.052 1.210 1.368 1.526 1.683 1.841 1.999 0.696 0.886 1.076 1.266 1.456 1.646 1.835 1.081 1.109 1.137 1.163 1.116 1.177 1.234 1.288

0.624 0.794 0.964 1.134 1.304 1.474 1.644 1.814 1.984 2.154 0.775 0.987 1.198 1.410 1.621 1.832 2.044 1.155 1.177 1.198 1.219 1.179 1.225 1.269 1.312

Pul,EC4 Pul,FE

Pul,EC4,m Pul,FE

0.99 1.12 1.09 1.00 0.95 0.89 0.85 0.87 0.83 0.88 1.12 1.14 1.08 1.01 0.96 0.99 0.98 1.02 1.04 1.03 1.03 1.10 1.14 1.14 1.15 1.02 0.098

1.04 1.10 1.03 0.93 0.87 0.81 0.78 0.80 0.77 0.82 1.16 1.11 1.02 0.95 0.89 0.92 0.92 0.94 0.95 0.93 0.93 1.00 1.03 1.02 1.02 0.95 0.105

CFDST slender columns formed from stainless steel outer tubes

263

1.2 1

PDesign Pul , FE

0.8 0.6 0.4

Pul , EC 4 Pul , FE

0.2 0

0

Pul , EC 4,m Pul , FE

0.5

1

1.5

2

l

Fig. 5.40 Relative design strength: (A) EC4 [49] and (B) currently modified EC4.

et al. [29] (Ps), currently provided by Eq. (5.34), in which it can be observed that using Ps enlarges the values of εlc (see Table 5.15). Additional modification is made by applying buckling curve (d) instead of curve (c) as specified by EC4 [49]. Accordingly, both modifications result in the modified strength Pul, EC4, m, which is also provided in Table 5.15. It can be observed that the strength Pul, EC4, m provides better estimates compared to Pul, EC4 with an average value of 0.95. Columns with HSC and UHSC can be seen to be expertly predicted compared with the original EC4 [49] design model, with some unsafe results for relatively short columns. Consequently, this design strength is currently recommended for predicting the axial strength of the CFDT slender columns.

5.6.3 Verification of design models The accuracy of the original and modified EC4 [49] design models are examined in this section by considering the experimental test results of Romero et al. [60]. The dimensions of the test specimens, material properties of columns’ components, and the experimental (Pul, Exp) and predicted ultimate axial strengths of the CFDT columns are provided in Table 5.16. It is worth pointing out that the four slender columns provided by Romero et al. [60] are all made of carbon steel tubes. For this reason, the calculation of the original EC4 [49] strengths uses different values for α and λo rather than those used in Section 5.6.2. According to ENV 1993-1-1 [53], the values of α and λo are 0.34 and 0.2, respectively, for “welded hollow carbon steel sections”. Table 5.16 reveals that the strengths predicted by EC4 [49] are on the unsafe side compared with the experimental results typical to those found by Romero et al. [60]. The mean ratio of Pul, EC4/Pul, Exp is 1.17 with a standard deviation of 0.067. On the other hand, it seems that the currently modified model is conservative with a mean ratio Pul, EC4, m/Pul, Exp of 0.93 and a standard deviation of 0.064. Hence, until extensive investigation on the CFDT slender columns with carbon steel external tubes is conducted, the latter strength is recommended to be used for the design of CFDT slender columns with either carbon or stainless steel external tubes.

Table 5.16 Comparison of the ultimate axial strengths of the CFDT columns determined by experiments [60] and the original and modified EC4 [49]. External tube

Internal tube

Column

D [mm]

te [mm]

fsy, e [MPa]

d [mm]

ti [mm]

fsy, i [MPa]

fc, sc0 [MPa]

fc, cc0 [MPa]

εh/εlc [mm]

Pul,EC4 Pul,Exp

Pul,EC4,m Pul,Exp

C200-3-30-C114-8-30 C200-3-30-C114-8-150 C200-6-30-C114-3-30 C200-6-30-C114-3-150 Mean Standard deviation

200 200 200 200

3 3 6 6

332 272 377 386

114.3 114.3 114.3 114.3

8 8 3 3

403 414 329 343

45 43 44 43

42 134 40 123

3315 3315 3315 3315

1.20 1.23 1.08 1.20 1.17 0.067

0.96 0.99 0.84 0.92 0.93 0.064

CFDST slender columns formed from stainless steel outer tubes

5.7

265

Conclusions

In this chapter, the behavior and ultimate load-carrying capacity of axially loaded concrete-filled lean duplex stainless steel tubular (CFSST) slender columns have been examined, from which the following conclusions may be drawn: 1. The developed FE models were found to efficiently simulate the measured experimental behavior of the CFSST slender columns. 2. The results showed that the longitudinal compressive strains at the mid-height of the intermediate-length columns exceeded the yield strain of the lean duplex material, whereas it was always less than this value for the long columns. On the opposite side of the cross section at mid-height, the maximum load (Pu, FE) was associated with the tensile stress for columns with slenderness parameters (λ) greater than 2.0. 3. The confinement effect of the external tube was found to be different in intermediate-length and long columns. The effect was negligible in long columns, whereas it was found to start at about 70% of the maximum load for intermediate-length columns. 4. Additionally, it was found that increasing the diameter-to-thickness ratio of the steel tube reduced the axial strength of the current slender columns. 5. A comparison of the axial strengths of the current CFSST columns obtained from the FE modeling was made with the predictions of EC4 [49] and AISC [52] specifications, from which both codes were found to provide unsuitable predictions. A design model was then developed in line with an European design model with some modifications regarding the “buckling curve.” 6. This chapter has proved that concrete-filled slender columns require modifications in the Eurocode design model, in the future revisions of EC4, by considering a more appropriate “buckling curve.”

Moreover, the following conclusions on CFDST slender columns can be drawn: 1. The slenderness ratio (λ) of 22 was found to be applicable for the definition of CFDST slender columns. 2. The limit of λ, which delineates between intermediate-length and long CFDST columns, qffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi was found to be accurately represented by 75= σ 0:2 =235 compared to 115= f y =235 for CFST columns. 3. For long CFDST columns withλ  50, the confinement effect can be ignored in design as found from the analysis of the results. 4. At the ultimate strength of the CFDST columns (Pul, FE), the results showed that the sandwiched concrete of intermediate-length columns were entirely under compressive stresses, which gradually decreased from the compression side to the opposite side, whereas the stresses of a part of the sandwiched concrete in long columns may reverse from compression to tension. 5. The confinement provided by the internal tubes was found to be higher than that provided by the external tubes in intermediate-length columns. This is because the internal tube dilates and pushes outward under axial compression. Conversely, there is no confinement provided by both tubes to the sandwiched concrete of long columns. 6. It was found that increasing the hollow ratio does not nearly influence the Pul, FE values of intermediate-length columns, whereas it raises the Pul, FE values for long columns. 7. The concrete’s compressive strength (fc0 ) of the sandwiched concrete was shown to have a considerable effect on the Pul, FE values of only intermediate-length columns. On the other hand, it generally had no effect in long columns.

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Concrete-Filled Double-Skin Steel Tubular Columns

8. The effect of the thickness ratio (ti/te) on the strengths of the intermediate-length columns was found to be significant by increasing the ti value, whereas it did not affect the strengths of long columns. 9. Through increasing the te value of the CFDST slender columns, it was found that the Pul, FE values of intermediate-length and long columns increase, indicating that both types are sensitive to the change in the ti/te ratio in this case. 10. The Pul, FE values were compared with the strengths calculated by the European and American specifications. The plastic resistance of the cross sections using both codes was modified to include the contribution of the internal tubes. European design strength was found to yield better predictions compared to American specifications. However, it was shown that both strengths cannot be used in design because they overestimate the ultimate strengths and thereby do not satisfy the safety requirements. 11. To enhance the strength prediction of the CFDST columns, a modification was made to the imperfection factor (α), which is equivalent to buckling curve (c). This was shown to predict the compressive resistance of the CFDST columns more accurately than other predictions.

Regarding CFDT slender columns, the following points are included: 12. The parametric studies indicated that the intermediate-length CFDT columns fail by elastic-plastic buckling and long CFDT columns fail by elastic buckling and that the slenderness limit (λr), which delineates between intermediate-length and long CFDT columns, is around 85. 13. By comparing this limit with the value provided by DBJ/T13-51-2010 [26] for concretefilled steel tubular columns, it was found that it yields suitable predictions. Hence, using the limit provided by DBJ/T13-51-2010 [26] for the current CFDT columns was suggested. 14. The confinement of the external tubes also differs between intermediate-length and long CFDT columns. Although the confinement effect does not exist for long CFDT columns, it starts to propagate before the ultimate load is reached for intermediate-length CFDT columns. 15. It was also found that using high-strength and ultrahigh-strength concrete (HSC and UHSC, respectively) cores in CFDT slender columns is not useful as their effect on the strengths of the columns is insignificant. 16. A comparison of the ultimate axial strengths of the CFDT slender columns predicted by the FE models was made with EC4 [49]. This code was found to provide nonconservative predictions for the CFDT slender columns, especially for intermediate-length columns. Accordingly, the design model was then modified using the cross-sectional plastic resistance previously suggested by the first author [29] with some modifications regarding the “buckling curve.”

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[24] S. Schnabl, G. Jelenic, I. Planinc, Analytical buckling of slender circular concrete-filled steel tubular columns with compliant interfaces, J. Constr. Steel Res. 115 (2015) 252–262. [25] M.F. Hassanein, O.F. Kharoob, L. Gardner, Behaviour and design of square concrete-filled double skin tubular columns with inner circular tubes, Eng. Struct. 100 (2015) 410–424. [26] DBJ/T13-51-2010, Technical Specification for Concrete Filled Steel Tubular Structures, The Construction Department of Fujian Province, Fuzhou, China, 2010 (in Chinese). [27] ABAQUS Standard User’s Manual, The Abaqus Software Is a Product of Dassault Syste`mes Simulia Corp., Providence, RI, USA Dassault Syste`mes, Version 6.8, USA, 2008. [28] Z. Tao, B. Uy, L.H. Han, Z.B. Wang, Analysis and design of concrete-filled stiffened thinwalled steel tubular columns under axial compression, Thin-Walled Struct. 47 (12) (2009) 1544–1556. [29] M.F. Hassanein, O.F. Kharoob, Q.Q. Liang, Behaviour of circular concrete-filled lean duplex stainless steel-carbon steel tubular short columns, Eng. Struct. 56 (2013) 83–94. [30] X. Dai, D. Lam, Numerical modelling of the axial compressive behaviour of short concrete-filled elliptical steel columns, J. Constr. Steel Res. 66 (7) (2010) 931–942. [31] M. Johansson, K. Gylltoft, Mechanical behavior of circular steel-concrete composite stub columns, J. Struct. Eng. ASCE 128 (8) (2002) 1073–1081. [32] M.F. Hassanein, O.F. Kharoob, Q.Q. Liang, Circular concrete-filled double skin tubular short columns with external stainless steel tubes under axial compression, Thin-Walled Struct. 73 (2013) 252–263. [33] K.J.R. Rasmussen, Full range stress-strain curves for stainless steel alloys, J. Constr. Steel Res. 59 (2003) 47–61. [34] Q.Q. Liang, S. Fragomeni, Nonlinear analysis of circular concrete-filled steel tubular short columns under axial loading, J. Constr. Steel Res. 65 (12) (2009) 2186–2196. [35] J.B. Mander, M.J.N. Priestley, R. Park, Theoretical stress-strain model for confined concrete, J. Struct. Eng. ASCE 114 (8) (1988) 1804–1826. [36] ACI-318, Building Code Requirements for Reinforced Concrete, ACI, Detroit (MI), 2002. [37] Q.Q. Liang, Performance-based analysis of concrete-filled steel tubular beam-columns. Part I: theory and algorithms, J. Constr. Steel Res. 65 (2) (2009) 363–373. [38] F.E. Richart, A. Brandtzaeg, R.L. Brown, A study of the failure of concrete under combined compressive stresses, in: Bull. 185, University of Illionis, Engineering Experimental Station, Champaign (III), 1928. [39] H.T. Hu, C.S. Huang, M.H. Wu, Y.M. Wu, Nonlinear analysis of axially loaded concrete-filled tube columns with confinement effect, J. Struct. Eng. ASCE 129 (10) (2003) 1322–1329. [40] J. Tang, S. Hino, I. Kuroda, T. Ohta, Modeling of stress-strain relationships for steel and concrete in concrete filled circular steel tubular columns, Steel Constr. Eng. 3 (11) (1996) 35–46. [41] M.-H. Wu, Numerical Analysis of Concrete Filled Steel Tubes Subjected to Axial Force, MS thesis, Department of Civil Engineering, National Cheng Kung Univ., Tainan, Taiwan, R.O.C, 2000. [42] Z. Tao, Z.-B. Wang, Q. Yu, Finite element modelling of concrete-filled steel stub columns under axial compression, J. Constr. Steel Res. 89 (2013) 121–131. [43] Q.Q. Liang, High strength circular concrete-filled steel tubular slender beam-columns, part I: numerical analysis, J. Constr. Steel Res. 67 (2011) 164–171. [44] prEN 1993-1-14, Eurocode 3: Design of steel structures, Part 1–14: Design assisted by Finite element analysis, European Committee for Standardization, Brussels, Belgium, 2020.

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Rubberized CFDST short columns Notations Ac Ac,nominal Asi Asc Asc Aso D (EI)e fck fcu fsyi fsyo KL L ry Pcr Pi,u Posc,u Ppl,Rd Ppl,Rd,Mod PtheoryConc PtheorySHS Pul,EC4 Pul, EC4, Mod Pul,Zh Pul,Tao λ σ yf σ yc ζ χ ρs

6

cross-sectional area of the concrete nominal cross-sectional area of the concrete cross-sectional area of the inner steel tube cross-sectional area of the sandwiched concrete following Tao and Han [1] cross-sectional area of the outer steel tube following Tao and Han [1] cross-sectional area of the outer steel tube specimen width effective elastic flexural stiffness of the member characteristic concrete strength characteristic cube strength of concrete yield stress of the inner steel tube yield stress of the outer steel tube effective length of the member specimen length smallest radius of gyration of the cross section critical buckling load of the column compressive strength of the inner tube computed following Tao and Han [1] compressive strength of the outer tube with the sandwiched concrete following Tao and Han [1] plastic resistance to axial compression of the concrete-filled column currently modified plastic resistance to axial compression of the RuCFDST column compressive strength of the sandwiched concrete according to Zhao and Grzebieta [2] compressive strength of the empty hollow sections according to Zhao and Grzebieta [2] compressive strength of the CFDST columns with inner SHSs according to EC4 [3] currently modified compressive strength of RuCFDST based on EC4 [3] compressive strength of the CFDST columns with inner SHSs according to Zhao and Grzebieta [2] compressive strength of the CFDST columns with inner SHSs according to Tao and Han [1] slenderness parameter of the column yield stress at the flat portions of the cross sections yield stress at the corners of the cross sections confinement factor used in the calculations by Tao and Han [1] reduction factor calculated using the European strut curves to account for the overall buckling ratio of the cross-sectional area of the steel tube to that of the concrete core

Concrete-Filled Double-Skin Steel Tubular Columns. https://doi.org/10.1016/B978-0-443-15228-3.00006-X Copyright © 2023 Elsevier Inc. All rights reserved.

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Concrete-Filled Double-Skin Steel Tubular Columns

Abbreviations (EI)eff λ Ac Ac,nominal As CA CFDST CFST CHS D Dc Di DI Do EC4 f’c FA fck FRP fsyi fsyo L LVDT nao NaOH nco Pcr PSD Pu Pul,EC4 Pul,Has Pul,Tao Pul,Zh Pyn Pyt RA RuC RuCFDST RuCFST SCC SHS tsi tso λso

effective flexural stiffness of the specimen’s cross section relative slenderness of the specimen cross-sectional area of concrete nominal cross-sectional area of concrete cross-sectional area of steel course aggregate concrete-filled double skin steel tube concrete-filled steel tube circular hollow section diameter of the steel tube diameter of the filled concrete diameter of the inner steel tube ductility index diameter of the outer steel tube Eurocode 4 concrete compressive strength fine aggregate characteristic concrete strength fiber-reinforced polymer yield strength of the inner steel tube yield strength of the outer steel tube length of the test specimen linear variable differential transformer reduction factor for outer steel (EC4) sodium hydroxide enhancement factor due to confinement effects (EC4) critical buckling load particle size distribution experimental ultimate peak axial compressive load Eurocode 4’s predicted composite ultimate peak axial compressive load Hassanein’s predicted composite ultimate peak axial compressive load Tao’s predicted composite ultimate peak axial compressive load Zhao’s predicted composite ultimate peak axial compressive load predicted nominal empty hollow section ultimate peak axial compressive load predicted empty hollow section ultimate peak axial compressive load rubber aggregate rubberized concrete rubberized concrete-filled double skin steel tube rubberized concrete-filled steel tube self-compacting concrete square hollow section thickness of the inner steel tube thickness of the outer steel tube circular hollow section slenderness

Rubberized CFDST short columns

ξ σ yt χ

6.1

273

enhancement factor due to confinement effects (Tao) yield stress of steel hollow section ratio

Introduction

6.1.1 Development of rubberized concrete (RuC) Currently, waste tires are among the largest and most problematic sources of wastes for modern society due to their durability and high rate of dumping in landfills [4]. In the United States, the total amount of tire rubber waste is 20.53 million tons/year and as large as 87% of this amount is recycled every year [5]. In Europe, the total amount of tire rubber waste is 28.92 million tons/year and only 69% of this amount is recycled. In Australia, 50 million tire wastes are generated every year [5]. Tire landfills can be harmful to the environment and surrounding areas as they provide a breeding ground for mosquitos, rats, and other animals. Additionally, if a fire starts in a tire landfill, then it becomes hard to extinguish and it gives rise to harmful smoke and noxious emissions. Accordingly, waste tire management and disposal is a major environmental concern in many countries because waste tires pose significant environmental, health, and aesthetical problems that cannot be easily solved. A disposal alternative is to incorporate tires into the manufacture of so-called rubberized concrete (RuC) as a way to conserve natural resources and reduce the amount of tires entering landfills. RuC is a relatively new and innovative field of research aimed at providing a sustainable way of disposing tires and complementing concrete properties [6,7]. For example, a partial replacement of sand and cement by rubber enhances the mechanical characteristics of concrete in terms of its fracture properties, ductility, impact, and seismic resistance [8–10]. Additionally, Liu et al. [11] found that the ratio of flexural strength to compressive strength of RuC increases relative to normal concrete, indicating that rubber exhibits better anticracking performance. Furthermore, Liu et al. [11] found that increasing the rubber volume content increases the toughness of the concrete. Hassanli et al. [12] observed that as the rubber content increases, the compressive strain capacity of the members also increases. Moreover, they found that adding rubber to concrete increases the viscous damping ratio and kinetic energy [12].

6.1.2 Methods used to enhance the mechanical properties of RuC Despite the abovementioned advantages, RuC is characterized by a significant reduction in its compressive, tensile, and flexural strengths [6,8,13]. Experimental testing [6] showed that the lower workability of RuC, caused by the loss of adherence between the surface of rubber particles and the cement, is one of the reasons for such lower strengths. Therefore, several investigations [14–17] were undertaken to improve the workability of RuC, and it has been found that the NaOH pretreatment of rubber increases its adhesion to cement paste and hence improves the mechanical properties of RuC. Another important reason for the lower strengths of RuC is Poisson’s ratio of rubber, which is twice that of concrete, and Young’s modulus, which is about one-third that of concrete [13]. According to Youssf et al. [13], this leads to

274

Concrete-Filled Double-Skin Steel Tubular Columns

large relative deformations between the rubber and concrete, resulting in early cracking. Additionally, there are high internal tensile stresses perpendicular to the direction of the compression load, attributable to the low modulus of elasticity of the rubber particles [13]. This insight by Youssf et al. [13] has led to the importance of understanding the confinement of rubber concrete as a way of reducing stress and deformation perpendicular to the direction of the compression load. This encouraged Duarte et al. [18] to conduct large-scale tests on rubberized concrete-filled (RuCFST) columns with outer steel confinement under static compression. Duarte et al. [18] indicated that a decrease in axial strength with confinement was not as large as that taking place without confinement due to the contribution of the steel tube to the column’s capacity. Positively, the short steel tubes with rubber concrete presented a higher ductility. Additionally, the authors discovered that Eurocode 4 [3] provided good but slightly conservative estimates of the ultimate strengths of the confined square columns. Moreover, Youssf et al. [15,16] studied crumb RuC confined by fiberreinforced polymer tubes as a means of overcoming material deficiencies such as decreased compressive strength. In conclusion, it has been realized that RuC with outer confinement can provide a major benefit to structures in seismic areas where energy dissipation requirements are mandatory [15,16,18].

6.1.3 Double skin tubular (CFDST) columns It has been widely accepted that the central concrete in CFST columns (Fig. 6.1), close to the neutral axis, makes an insignificant contribution to the flexural strength [19]. Accordingly, the central part of the concrete core of a CFST column can be effectively replaced by another smaller hollow steel tube with similar axial, flexural, and torsional (a)

(b)

Concrete

to

Outer steel tube

D

B (c)

(d)

d Inner steel tube

ti b

Fig. 6.1 Different types of rubberized concrete-filled composite column cross sections. (A) Square CFST. (B) Circular CFST. (C) Square CFDST. (D) Circular CFDST.

Rubberized CFDST short columns

275

strengths maintained. This form of column construction is known as a concretefilled double skin tubular (CFDST) column, which is available in four different combinations using square and circular hollow sections (SHSs and CHSs, respectively) [2,20–22]. Fig. 6.1 provides the square and circular cross-sectional forms of the CFDST columns previously tested by Zhao and Grzebieta [2] and Hassanein and Kharoob [23], respectively, using normal concrete. The results of such columns [2] show that the CFDST columns are characterized by an increased ductility and energy absorption under compression compared to bare steel tubes. Accordingly, these CFDST columns have already been implemented in bridge piers in Japan to reduce the total bridge weight while maintaining a large absorption capacity against seismic loading [2].

6.2

Square RuCFDST short columns

6.2.1 Materials and methods 6.2.1.1 Material properties Concrete General-purpose Portland cement in accordance with AS3972 [24] was acquired from Swan Cement Pty Ltd. in Western Australia and used as the binder material in normal and rubberized concrete mixes. The chemical composition of the cement is shown in Table 6.1. The control mix had 213 kg/m3 water, 426 kg/m3 cement, 750 kg/m3 of 7mm crushed rock coarse aggregate, 130 kg/m3 of 4-mm crushed rock coarse aggregate, and 843 kg/m3 of fine sand. The water/cement ratio was w/c ¼ 0.5. The concrete mixes for RuC15% and RuC30% are provided in Table 6.2.

Steel tubes Cold-formed steel manufactured in accordance with AS1163 [25] was used in the construction of the specimens, which was delivered by Midalia Steel (Bibra Lake, Western Australia). The 100 mm  100 mm  5 mm square hollow sections (SHS1005) and the 50 mm  50 mm  5 mm square hollow sections (SHS505) were epoxy-painted sections of grade DuraGal Plus C350LO. The 100 mm  100 mm  2 mm square hollow sections (SHS1002) and the 50 mm  50 mm  2 mm square hollow sections (SHS502) were galvanized sections of grade DuraGal Plus C350L0. SHSs with a Table 6.1 Chemical composition of cement (w%). Cement type Swan Grey Cement Type GP AS3972 [24]

SiO2

CaO

Al2O3

Fe2O3

MgO

SO3

LOI

Na2O

20.6

63.5

5.2

3.0

1.3

2.6

1.8

0.5

276

Concrete-Filled Double-Skin Steel Tubular Columns

Table 6.2 Mix quantities. Fine aggregates (0–4 mm)

Coarse aggregates (7 mm)

Tire rubber aggregates (2–7 mm)

Water

Mix

Mix proportion (kg/m3)

Mix proportion (kg/m3)

Mix proportion (kg/m3)

Mix proportion (kg/m3)

NC RuC15 RuC30

973 827 681

750 638 525

0 112 224

213 213 213

width of 100 mm were used as the outer tubes of the CFDST columns, whereas those with a width of 50 mm were the inner ones.

Rubber particles In order to fit in the SHS annulus, a 7-mm maximum aggregate was required. Fig. 6.2 shows the relative size of the rubber particles used in the concrete mixes. Rubber replacements of 0%, 15%, and 30% by weight of coarse aggregates were selected to produce significant results. The rubber was obtained from Tyrecycle in New South Wales, which is a leading national tire recycler. It was delivered in bags of sizes 2–5 mm and 5–10 mm. The 5–10 mm aggregate was sieved through a 6.75-mm sieve to be replaced by a 7-mm aggregate. The sieve test results are shown in the particle size distribution graph illustrated in Fig. 6.3. It is seen that the sieved 5–7 mm rubber proved to be a good replacement for the 7-mm aggregate with a similar particle size distribution.

6.2.1.2 Concrete compression tests Concrete cylinders of 100-mm diameter and 200-mm length were prepared for 0%, 15%, and 30% rubber content and tested in a 600-kN capacity Baldwin machine in accordance with AS1012.9 [26], at 28 days after the pouring into the cylinders.

Fig. 6.2 Rubber aggregate sizes.

Rubberized CFDST short columns

100 80

% Passing

60

277

Fine aggregate 7mm aggregate 4mm aggregate 2-5mm rubber 5-7mm rubber

40

20 0 0.01

100

% Passing

80

0.1

1 Particle Diameter (mm)

10

Silica fume Slag Fly Ash

60 40

20 0 0.1

1

10 100 Particle Diameter (mm)

1000

Fig. 6.3 Particle size distribution (A) aggregates and (B) fly ash, GGBS, and silica fume.

The stress-strain response of the standard cylinder tests was obtained to be used in the discussion of the results, especially when the energy absorption and ductility of the current columns are discussed. The density of the concrete cylinders of normal concrete (NC) is 2615 kg/m3, from which the density of the mix decreased by approximately 8.1% and 14.4% at 15% and 30% rubber replacements, respectively. These reductions in density are consistent with those obtained for normal strength rubberized concrete [4,5]. The present compressive cylinder test results are relatively low compared to those tested by Zhao and Grzebieta [2] on ordinary CFDST columns, which were equal to 71.3 MPa. Accordingly, the comparison between ordinary and rubberized CFDST columns will focus on those tested in the current investigation and not elsewhere.

278

Concrete-Filled Double-Skin Steel Tubular Columns

6.2.1.3 Rubber pretreatment Conforming to previous investigations [14–17], the rubber used in this investigation had to be pretreated in order to remove the oil and dirt from the outer surface and to improve the overall strength of the concrete. The oil and dirt on the surface could have created an unwanted layer between the cement paste and rubber surface, which could have hindered a strong adhesion between the rubber aggregate and cement matrix. The NaOH pretreatment was aligned with the previous research by Elchalakani [4,5], which suggested treating the rubber in 10% NaOH solution for 24 h. This roughened the rubber surface to the optimal level, allowing a stronger bond between the cement paste and rubber. A shorter time did not alter the surface of the rubber and a longer time roughened the surface too much, allowing small air pockets to appear on the surface of the rubber [14–17]. In addition to this, zinc stearate is an additive, which is added to tire rubbers to make them more resistant to oxidation. Zinc stearate makes rubber more hydrophobic but soluble in NaOH solution. The rubber was semisaturated through a water-soaking process, which allowed the now formed soluble sodium stearate to wash off and wash the NaOH off the rubber surface. The water soaking also increased the specific gravity of the rubber in the concrete mix, preventing the rubber from floating during the curing stage.

6.2.1.4 Concrete mix procedure The mixing method of RuC is of great importance because rubber has a lower specific gravity than does concrete, and, hence, due to the vibration process, rubber migrates to the top section, resulting in a nonhomogeneous mix and a reduction in strength [13]. Accordingly, this investigation did not use any vibration, which is the method of removing air voids in concrete, and instead was compacted with a steel rod of 12 mm in diameter so that there was a limited chance for segregation. The concrete mixing procedure followed the one suggested by Elchalakani [4,5], which could be summarized as: (1) mix the dry fine and coarse aggregates for 1 min, (2) add 10% of water and mix for 1 min; in the case of RuC, add rubber with 10% of water, (3) add cement and mix for 1 min, (4) add half of the remaining water and mix for 1 min, (5) add the remaining amount of water and mix for 1 min, (6) add a minuscular amount of a general-purpose super plasticizer and mix for 1 min, and (7) check the slump in accordance with AS1012.3.1 [27]; if the slump is less than 150 mm, then add more super plasticizer until a 150–175 mm slump is achieved. This target slump was important to successfully fill the narrow annulus between the steel tubes with segregation or bleeding. The mix design had a water cement ratio of 0.5, to be more workable so that it could fit it into the SHS annulus with a 21-mm minimal gap. Given that the rubber was partially soaked in water beforehand, it was required to account for the water in the rubber. The difference in rubber weight before and after the full pretreatment process was deducted from the free mixing water. This was chosen to maintain uniformity across all the mixes. The mix design also included replacing the coarse aggregate with rubber by a weight of up to 30%, to ensure a high replacement of the aggregate, thus providing an opportunity for large amounts of rubber wastes to be used in RuC.

Rubberized CFDST short columns

279

6.2.2 Test program 6.2.2.1 Specimens A total of 12 CFDST stub columns in addition to 3 CFST stub columns were tested in this investigation. As stated in “Steel tubes” section, steel tubes of a 100-mm width were used as the outer tubes (termed “O5” and “O2” for those with 5- and 2-mm thicknesses, respectively) of the CFDST columns, whereas the inner tubes were those formed from SHSs with a 50-mm width (termed “I5” and “I2” for those of 5- and 2-mm thicknesses, respectively). At the end of the column’s designation, the weight of the rubber replacement is provided. For example, SHS-O5I2-15 belongs to the CFDST column, which is filled with RuC with 15% rubber replacement. This column is formed from outer tubes of 100- and 5-mm width and thickness, respectively, and from the inner tube of 50- and 2-mm width and thickness, respectively. The three CFST columns are formed from the steel tubes O5, and, hence, the designation of these columns does not include the letter I. The tubes were tack-welded onto a 10mm-thick mild steel base plate to allow the annulus to be filled and to ensure concentricity. The specimens were prodded to compact the normal and rubberized concrete. The specimens were placed in a mist curing room (90% humidity and 21°C) for 21 days to limit drying shrinkage, then removed, and, subsequently, placed in a laboratory for another 7 days. There were still small amounts of shrinkage in the concrete, so the top of each specimen was leveled using nonshrink grout to achieve simultaneous loading on the steel and concrete. In the discussion, specimens with thinner outer steel tubes (relative to the inner ones) are called type A specimens, whereas those with thicker exterior skins are called type B specimens. The height of the specimens was selected based on a stub column’s length for a cold-formed shape. According to Galambos [28], this means that the height should not be less than three times the largest dimension of cross section and not more than 20 times the least radius of gyration. Currently, the specimen’s overall width (D) was 100 mm, the length (L) was 300 mm, and the smallest radius of gyration (ry) was 31.65 mm; 300 mm ¼ 3D  L  20ry ¼ 633 mm. The thicknesses of the steel hollow sections were selected based on the following criteria: (1) to allow for the maximum load on the specimens to be less than 2000 kN, which is the capacity of the Amsler UTM, and (2) to achieve different confinements on the concrete, different thickness variations were chosen, i.e., 2 mm and 5 mm for both inner and outer tubes, respectively.

6.2.2.2 Test procedure The composite columns were tested on the 28th day of concrete pouring, which was the same day of testing the concrete cylinders. This was to ensure that the concrete strength was compatible with the standard cylinder tests. A displacement control procedure was used at a constant rate of 2 mm/min. A data logger attached to the Amsler universal testing machine (UTM) was used to transfer the load, displacement, and strain gauge data to the computer. The specimen was concentrically set up with the flat plates of the Amsler leveled horizontally, on observing that an angled plate on

280

Concrete-Filled Double-Skin Steel Tubular Columns

the specimen would cause the machine to load unevenly on the section and thus will not produce the composite action required. A camera was set up to capture a photograph every 30 s across the duration of the test to associate certain visual aspects of buckling with the load/displacement/strain data. To assess the behavior of the normal/rubberized CFDST columns, the four variations of steel hollow sections must be assessed alone. Therefore, empty hollow sections were also tested in the 2000kN Amsler UTM to determine the axial compression strength and failure mechanisms.

6.2.3 Material properties 6.2.3.1 Rubberized concrete (RuC) Commonly, in a previous experimental research, rubber was seen floating to the surface of the concrete [13]. Through the pretreatment process and saturation of the rubber prior to putting it in the mix (discussed earlier in Section 6.2.1.4), the rubber in the current investigation appeared to be evenly distributed toward the vertical direction (see Fig. 6.4). The cylinders were vertically cut into two pieces through the diameter (of the 100-mm length). From this figure (representing merely the upper part of the cylinders with a 100-mm depth), it can be seen that the RuC mix showed

(a)

(b)

12 (c) Fig. 6.4 Internal visual inspection of the RuC of 100 mm  100 mm cut-outs from the test specimens with (A) 0%, (B) 15%, and (C) 30% rubber content.

Rubberized CFDST short columns

281

Table 6.3 Mass and density of compressive cylinders. Specimen name

Density (kg/m3)

Average density (kg/m3)

CT-00-01 CT-00-02 CT-00-03 CT-15-01 CT-15-02 CT-15-03 CT-30-01 CT-30-02 CT-30-03

2256.8 2279.1 2275.9 2088.1 2084.9 2084.9 1948.1 1941.7 1938.5

2271

a

2086

1943

Concrete cylinder strength (MPa)

Average cylinder strength (MPa)

47.4 52.2 51.2 24.9 21.1a 25.0 13.7 14.4 15.0

50.27

24.95

14.37

The top surface of this specimen was excessively polished.

evenly dispersed rubber throughout the 100 mm  100 mm samples cut out from 100 mm  200 mm test cylinders. Concrete cylinder strengths of the six tested cylinders in accordance with AS1012.9 [26] are listed in Table 6.3. The compressive cylinder test results indicated that the mix created had a compressive strength of about 50.3 MPa, whereas adding the rubber by replacing the 15% aggregate resulted in approximately half the compressive strength of 24.95 MPa. A further increase in rubber content to 30% replacement of the aggregate produced a mix with a compressive strength of 14.4 MPa. These results conform to previous investigations that showed the deterioration effect of rubber on the compressive strength of concrete [6,13,29,30]. Comparing the 15% specimens, CT15-02 showed a significant defect probably due to uneven loading or a smaller contact area; therefore, the compressive strength of the 15% mix was considered as 24.95 MPa by neglecting the cylinder CT-15-02.

6.2.3.2 Empty square hollow sections The properties of the steel material used for forming the current CFDST columns and the empty cold-formed hollow tubes conforming to AS1163 [25] were tested under axial compression. The results were additionally used to quantify the effect of the bare steel tubes on the CFDST columns. Furthermore, they were used to assess the suitability of Zhao’s CFDST axial load theoretical calculations for empty hollow section predictions [2]. The axial load-axial displacement relationships for the tubes with different thicknesses and tube dimensions are shown in Fig. 6.5, which shows that increasing the thickness (for a specific tube size) provides higher strength. Generally, the loaddisplacement curves show typical ascending and descending branches with some strain-hardening parts after the maximum load was reached, particularly for compact tubes with 5-mm thickness. On the other hand, the relationship of the fully effective compact specimen CT-50-5 exhibits a considerable flat plateau just above 400 kN.

282

Concrete-Filled Double-Skin Steel Tubular Columns

Fig. 6.5 Empty SHS compression tests: load vs. displacement.

This is attributed to the overall buckling failure mechanism, which may have resulted from: (1) the effect of the surface finish where this specimen is epoxy-coated, whereas the 50  2SHS was galvanized (Fig. 6.6D). Previous experimental research found that epoxy-coated cold-formed sections of grade C35L0 have less yield stress but higher ductility when compared to galvanized sections [31,32]. (2) The effects of residual stress distribution at the weld seam found in small-sized cold-formed tubes [31,32]. It should be noted that CT-50-5 has a member slenderness of KL/r ¼ 15.43 < 20, which is considered as a short column [28]. Fig. 6.6 shows the failure modes of the

(a)

(b)

(c)

(d)

Fig. 6.6 Failure mechanism of the empty hollow sections after the tests: (A) 100  5 SHS, (B) 100  2 SHS, (C) 50  5 SHS, and (D) 50  2 SHS.

Rubberized CFDST short columns

283

four hollow steel tubes. As can be seen, all the specimens, except CT-50-5, failed by outward and inward local buckling across the one horizontal plane. This failure mechanism is the so-called roof mechanism, which is a common failure mode for SHS stub columns [2,18].

6.2.4 Test results for rubberized CFDST columns 6.2.4.1 Fundamental behavior Table 6.4 summarizes the maximum forces of the current experimental campaign, from which the designation system described previously was used to label the specimens. As can be seen, the label first refers to the SHS as a hollow section type, then denotes the outer thickness (O) and inner thickness (I) (since the widths of the outer and inner were constant for all specimens), and then the rubber content is denoted as 00%, 15%, or 30%. From the table, it can be observed that the RuCFDST specimens had less axial strengths compared to those of normal CFDST specimens; this is due to the lower compressive strength of RuC shown in Table 6.3. This may also be attributed to the lower steel capacity of RuC compared to that of ordinary concrete, as the steel becomes under a bi-axial stress state much earlier because of the high Poisson’s ratio of the rubber [13]. The compressive strength of RuC30 was less than that of RuC15, but, in most cases, they performed similarly. This could have been due to the strength of the steel, accounting for a large portion of the overall strength of the CFDST column. The thinner inner column showed more evident reduction in strength between normal CFDST and RuCFDST. This was due to the inward collapse mechanism of the interior tube, and, given that RuC effectively had voids inside it, the thicker internal tubes could resist more and the concrete could condense before the inner tube failed. Additionally, as discussed in the next section, the 30% RuCFDST showed segregated sand, aggregate, and rubber around the top surface of the specimen, something that was not obvious for the 15% RuCFDST. Hence, it is recommended, in future research, to compact the cement paste of the current RuC by adding by-products such as fly ash and silica fume, as suggested in the study by Raffoul et al. [33]. Table 6.4 Maximum experimental forces for CFDST/CFST. Rubber content

Specimen type SHS-O2I2 SHS-O2I5 SHS-O5I2 SHS-O5 SHS-O5I5

0%

15%

30%

Force (kN) 657 810 1302 1318 1555

Force (kN) 483 (26.5%) 804 (0.7%) 1190 (8.6%) 1143 (13.3%) 1450 (6.7%)

Force (kN) 492 (25.1%) 691 (14.7%) 1191 (8.5%) 1035 (21.5%) 1430 (8.0%)

The numbers in brackets are the percentage reductions in strength due to rubber particles.

284

Concrete-Filled Double-Skin Steel Tubular Columns

Fig. 6.7 Load-displacement curves for type A CFDST specimens with 2-mm outer and 5-mm inner (O2I5) tubes of 0%, 15%, and 30% RuCFDST columns.

Fig. 6.7 presents the axial load-displacement curves for type A specimens with 2-mm outer and 5-mm inner (O2I5) tubes of 0%, 15%, and 30% rubber. This is an example for thin, outer-thick, inner RuC CFDST. Fig. 6.8 represents curves for the specimens with 5-mm outer and 2-mm inner (O5I2) tubes. This is an example for thick, outer-thin, inner RuC CFDST. In Fig. 6.7, it can be generally observed that type A specimens with a thinner outer steel tube yielded a flatter load-displacement relationship at the postpeak loading stage. The flatter curve could be because both tubes have a fairly similar area and hence contribute almost equally to the axial compressive strength of the specimen. A compression comparison between Figs. 6.7 and 6.8 shows that the outer

Fig. 6.8 Load-displacement curves for type B CFDST specimens with 5-mm outer and 2-mm inner (O5I2) tubes of 0%, 15%, and 30% RuCFDST columns.

Rubberized CFDST short columns

285

skin thickness dictated the strength. In general, type A provided a larger ductility (that will be discussed in Section 6.2.4), whereas type B provided a larger strength. The postpeak wave-like response in Fig. 6.8 could be due to the repeated process of deep plastic collapse of the folds formed on the inner and outer skins associated with a drop in the load, followed by a significant strain hardening and full flattening and contact of such folds. Figs. 6.7 and 6.8 show that the rubber did not have a significant effect on small deformation prior to the ultimate load (i.e., the elastic stages of the load-displacement curves shown in Figs. 6.7 and 6.8), but its effect became more obvious in the postpeak regime, where increasing the rubber content reduced the residual strength after failure (with respect to any axial displacement value before the load increased again). On the other hand, since strain gauges were not mounted on the inner tube, its behavior during the test was not clearly understood.

6.2.4.2 Deformed shapes of the RuCFDST columns Fig. 6.9A shows the CFDST specimens prior to concrete pouring. The deformed shapes of the current columns are illustrated in Fig. 6.9B, from which the outward buckling of the outer steel tubes is obvious. Appendix I shows the progressive axial crushing of SHS-O2I2-30 with 30% RuC, 2-mm outer, and 2-mm inner CFDST specimens. It can be observed that the failure commonly began by forming one fold

(a)

(b)

Fig. 6.9 CFDST specimens (A) before and (B) after testing.

286

Concrete-Filled Double-Skin Steel Tubular Columns

slightly below the top of the specimen and then progressively propagated down the specimen with continuing axial crushing. A total of four folds along the full length were completely formed by the end of the test. Frames 17 and 18 show the spring-back phenomenon of the concrete core that occurred upon unloading of the specimen. The specimen exhibited an upward movement of the concrete above the level of the steel tubes. This expansion (see Fig. 6.10) was obvious in the RuC30 specimen but showed only a slight expansion in the 15% RuC specimen. The expansion occurred because of the elastic properties of the rubber within the concrete matrix and, to a less extent, due to confinement of the concrete core. It is worth noting that the current specimens without rubber and those tested by Zhao and Grzebieta [2] did not show such a phenomenon. The 30% RuCFDST showed segregated sand, aggregate, and rubber around the top surface of the specimen, and the concrete above the steel surface appeared to have little structural capacity and could be removed with minimal force by hand.

6.2.4.3 Concrete and outer steel interface zone During axial compression, the confined concrete laterally pushes against the inner and outer tubes, which is attributed to the failure of the steel sections. The outer steel tube was removed to show the local buckling failure (shown in Fig. 6.11). The concrete

Fig. 6.10 Rubber concrete expansion (0%, 15%, and 3% rubber).

Fig. 6.11 15% RuCFDST on the left and 30% RuCFDST on the right.

Rubberized CFDST short columns

287

without rubber bonded extremely well to the interior of the outer steel and remained on the removed strip, as seen in Fig. 6.11. The cut-out strip was separated from the rest of the concrete on a vertical shear plane and appeared to be structural. As the concrete was confined effectively, it exhibited a more ductile behavior, instead of failing by vertically cracking down the specimen, and plastically deformed inside the folds formed on the outer tube. Such confinement enhances the ductility of the composite specimen and allows it to maintain a large residual strength after failure. Topcu [34] stated that in RuC, high internal tensile stresses were found perpendicular to the axial load direction because of the low modulus of elasticity of rubber particles and its higher Poisson’s ratio. The failure mode in Fig. 6.12 shows that confining the concrete provides lateral restraint to the internal tensile forces of the concrete that delays cracking, which, in turns, enhances the strength in the direction at which the axial load is applied. Despite this, after opening the steel specimen (Fig. 6.11), it is confirmed that the concrete has segregated inside the steel tube and is worse with a higher rubber replacement. The aggregate appears loose inside the 15% and 30% RuCFDST specimens but still morphs inside of the outer steel section. The concrete shows little rigidity inside the concrete specimen, showing poor compaction due to the high rubber content compared to the control normal CFDST specimen shown in Fig. 6.12. Self-compacting concrete will be better for future construction of RuC CFDST columns to avoid segregation and poor compaction in a narrow annulus.

6.2.4.4 Load-displacement relationships For the entire program, Figs. 6.13–6.15 show the load-displacement relationships for 0%, 15%, and 30%, respectively. As expected, the thicker exterior skins (type B) provided a larger strength given their larger amount of steel area. The notable wave-like CFDST response was evident during axial displacement after the first peak. The postpeak reduction in load was due to the plastic collapse of the steel tube in which no further buckling occurred until the buckled section was strain-hardened [21]. The increase in axial load (after collapse) with further displacement could be caused

Fig. 6.12 The concrete and outer steel-bonding zone of the 0% CFDST specimen (inside a CFDST column on the left and a strip removed on the right).

288

Concrete-Filled Double-Skin Steel Tubular Columns

Fig. 6.13 Load-displacement relationships: 0% RuCFDST.

Fig. 6.14 Load-displacement relationships: 15% RuCFDST.

due to the contact between the external folds and the concrete core which progressively crushes further as well as the inner steel inward folds are touching to form a hardened metal core down the centre of the specimen. In a previous experimental research [2], tests were stopped at a small axial displacement; however, in the present tests, an axial deflection of more than 60 mm was reached. This is more than 20% axial strain. It should be noted that the test data for the SHS-O5I5-30 specimen were lost after a 30-mm deflection.

Rubberized CFDST short columns

289

Fig. 6.15 Load-displacement relationships: 30% RuCFDST.

It was previously found that CFDST columns filled with ordinary concrete have similar performance to traditional CFST columns of the same dimensions of the outer steel tube and material strength [35]. Fig. 6.13, generally, proves this similar behavior between the CFDST and CFST columns for only inner thin tubes (I2) (see columns SHS-O5-00 and SHS-O5I2-00). On the other hand, by adding rubber as shown in Figs. 6.14–6.15, even thin inner tubes (I2) seem to share a higher load contribution compared to that of equivalent CFST columns. This, however, is obvious for a 30% rubber ratio (see columns SHS-O5-30 and SHS-O5I2-30).

6.2.4.5 Energy absorption and ductility The energy absorbed by a specimen can be determined by the area under the load (kilonewton) vs. the displacement (millimeter) curve. The energy absorbed by RuCFDST specimen with 2 mm outer tube, 5 mm inner tube, and 15% RuC was determined. The components of the composite section were separately examined to determine the individual energy absorption. The results are shown in Fig. 6.16, which shows the difference between the composite response and the response of the individual components. The concrete strength was accounted for using not only the stress-strain response from the standard cylinder test (15% RuC) but also the actual area of the concrete core, which produced the concrete strength in the 15% RuCFDST specimen. Fig. 6.17 shows a schematic for the method of determination of the ductility indexes based on the energy absorbed. As shown in the figure, the elastic energy (We ¼ Area ABG) was determined for the specimens at a displacement (Δ75) corresponding to 75% of the ultimate load, and thus We ¼ 0.5  PΔ75  Δ75 [36], from which PΔ75 is the load corresponding to Δ75. Three ductility indexes were determined from the energy absorbed (area under the P-δ curve) up to 15 mm (point D), 25 mm (point F), and 60 mm (point J). Through dividing the energy absorption at

290

Concrete-Filled Double-Skin Steel Tubular Columns

1000

15% RuC CT-100-2 CT-50-5 SHS-O215-15

900

Axial Load (kN)

800 700 600 500 400 300 200 100 0

5

0

20 10 15 Axial Displacement (mm)

25

30

Fig. 6.16 Composite energy absorption for 15% RuCFDST O2I5-15.

C I Ph ase I

e III

Phas

B

0.75Pu

D E

Phase IV

I

F

Phase

Axial Load

Pu

Pres

Phase I (A-B): Elastic range Phase II (B-C): Inelastic range Phase II (C-E): Sudden failure and loss of capacity

J

ABG G A

d75

H d15

K d25

L d60

Axial deformation Fig. 6.17 A schematic showing the method of determination of the ductility indexes (DI1, DI2, and DI3) of the CFDST/CFST specimens.

displacements 15 mm, 25 mm, and 60 mm by the absorbed elastic energy We, the three ductility indexes DI1, DI2, and DI3 were determined. Thus, the ductility indexes were calculated as DI1 ¼ AABCD/AABG; DI2 ¼ AABCF/AABG; and DI3 ¼ AABCJ/AABG. Fig. 6.18 shows that the thinner six 100 mm  2 mm outer sections (the first six specimens from the left) have higher DI1, DI2, and DI3 than do the remaining nine 100 mm  5 mm outer sections inclusive of the three CFST specimens (the remaining nine specimens). This leads to the conclusion that CFDST columns filled with RuC constructed using thin outer sections are more ductile than their corresponding counterparts with thick outer sections. An important conclusion that may be drawn from the

Rubberized CFDST short columns

291

Fig. 6.18 Ductility indexes (DI1, DI2, and DI3) of the CFDST/CFST specimens.

figure is that ductility increases with an increase in the outer steel section slenderness, and similar results were found by Zhao and Grzebieta [2] after testing CFDST columns filled with ordinary concrete. It is also seen that O2I2-30 (the third one from the left) showed lower ductility results when compared with the other thin outer section specimens (the first six specimens from the left). The exact reason for this is unknown to the authors, but a possible reason is that the elastic energy (We) was relatively large compared to those of other specimens with thin outer sections. Fig. 6.18 also shows the extremely slight variations in the ductility indexes across all the rubber contents. It should be noted that because data were lost after a 30-mm deflection, DI3 was not determined for SHS-O5I5-30.

6.2.5 Strength calculations In this section, experimental strengths of both the empty tubes and the CFDST columns are compared with the available design predictions. First, the strengths of SHSs are compared with those calculated by the method introduced by Zhao and Grzebieta [2]. This is followed by a comparison of the strengths of the CFDST columns with the predictions made in Eurocode 4 [3], Zhao and Grzebieta [2], and Tao and Han [1].

6.2.5.1 Strength predictions of empty hollow sections Zhao’s CFDST axial load theoretical calculation method [2] is used in this section to predict the strengths of the empty hollow sections. According to this method, the strength is to be calculated as (see Fig. 6.1):
2
 PtheorySHS ¼ σ yc  π  r 2ext  r 2int + 4  σ yf  be  t

(6.1)

292

Concrete-Filled Double-Skin Steel Tubular Columns

where σ yc and σ yf σ yf are the yield stresses at the flat and corner portions of the cross sections, respectively. In the calculations, the following are considered: r int ¼ t if

t < 3:0 and r int ¼ 1:5t if

r ext ¼ 2t if

t < 3:0 and r ext ¼ 2:5t

be ¼ B  2r ext

if

t > 3:0, if

t > 3:0,

λe < 40

40 if λe > 40, λe rffiffiffiffiffiffiffiffi σ yf B  2r ext λe ¼  , and ti 250

be ¼ ðB  2r ext Þ 

The comparison results are presented in Table 6.5, from which it can be observed that the adaptation of Zhao’s CFDST axial load theoretical calculations [2] for empty hollow section predictions produced good results. The largest difference between theoretical calculations and experimental results was for the SHS1005 hollow section in which the difference was 8.34%. However, the difference of 8.34% for the specimen SHS1005 was due to neglecting the parts in the flat portions of the cross sections that have higher yield strengths (similar to the corner).

6.2.5.2 Strength predictions of the CFDST columns Design model by Zhao and Grzebieta The CFDST axial load theoretical calculation method by Zhao and Grzebieta [2] is again used in this section to predict the strengths (Pul,Zh) of rubberized CFDST columns. According to this method, the strength is to be calculated as: Table 6.5 Zhao’s hollow steel tube axial load theoretical predictions [2]. Specimen no.

SHS1005

SHS1002

SHS505

SHS502

Width B (mm) Thickness ti (mm) rint (mm) rext (mm) λe be Length L (mm) Yield stress σyf (MPa) Yield stress σyc (MPa) Area An (mm2) P squash load (kN) Experimental squash load (kN) Difference %

100 5 7.5 12.5 20.46 75.00 300 465 567 1810 875.63 955.3 8.34

100 2 2 4 62.74 58.66 300 465 567 774 239.59 226.4 5.82

50 5 7.5 12.5 6.82 25 300 465 567 814 410.63 417.3 1.60

50 2 2 4 28.64 42 300 465 567 374 177.62 171.4 3.63

Rubberized CFDST short columns

Pul,Zh ¼ PtheorySHS + PtheoryConc

293

(6.2)

in which the calculation of the PtheorySHS is provided in detail in Section 6.2.5.1, whereas Ptheoryconc is given as: PtheoryConc ¼ Ac  0:85f c 0

(6.3)

     π π Ac ¼ ðBο  2tο Þ2  4  r into  r 2into  B2ο  4r 2exti  r 2exti (6.4) 4 4 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi B2ο ðBi 2ti Þ . where the radius of gyration is given as r ¼ 12 The 0.85 factor in Eq. (6.3) suggests low or no confinement in square double skin construction. This could be very true based on the observations made in the current or previous tests [2] due to the ability of the concrete to force the inner tube inward, thus releasing the confinement pressure on the concrete and exerting a biaxial stress state on the steel skins.

Design model by Tao and Han Proposals to predict the strength of short square CFDST columns (i.e., the crosssectional resistance) with inner SHSs (Pul,Tao) were made by Tao and Han [1]. The predicted strength (Pul,Tao) is given as follows: Pul,Tao ¼ Posc,u + Pi,u

(6.5)

where Posc,u is the compressive capacity of the outer tube with the sandwiched concrete and Pi, u is the capacity of the inner tube computed as Asi fsyi, where Asi and fsyi are the cross-sectional area and yield strength of the inner CHSs, respectively. To determine the capacity Posc,u, the following equation was put forward: Posc,u ¼ f scy Asco with Asco ¼ Aso + Asc

(6.6)

where Asc and Aso are the cross-sectional areas of the sandwiched concrete and the outer steel tube, respectively. The strength fscy, defined in megapascal, was given as: f scy ¼ C1 χ 2 f syo + C2 ð1:18 + 0:85ζ Þf ck

(6.7)

where fck is the characteristic concrete strength in megapascal (0.67fcu), where fcu is the characteristic cube strength of the concrete in megapascal, fyo is the yield strength of the outer SHS in megapascal,   Aso f so ζ is the confinement factor , and Ac,no min al f ck Ac,nominal is the nominal cross-sectional area of the concrete, given by D2  Aso.

294

Concrete-Filled Double-Skin Steel Tubular Columns

Design model by Eurocode 4 To date, EC4 [3] does not contain a design resistance model for CFDST columns filled even with normal concrete. Instead, it contains a compressive strength formula for CFST columns, which is given as: Pul,EC4 ¼ χPpl,Rd

(6.8)

As can be observed, Pul,EC4 is based on the plastic resistance to axial compression (Ppl,Rd), accounting for the contribution of different elements. To check the strength of the CFDST columns using EC4 [3] (Pul,EC4,Mod), a modification for the Ppl,Rd expression was made to consider the inner tube contribution as presented in Eq. (6.9). Ppl,Rd,Mod ¼ f yo Aso + f 0c Ac + f yi Asi

(6.9)

It is worth pointing out that the effective areas of the steel tubes are employed in the case of slender cross sections. The reduction factor (χ) is calculated using the European strut curves as:  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 χ ¼ 1= φ + φ2  λ  1:0

(6.10)

 
 2 φ ¼ 0:5 1 + α λ  0:2 + λ

(6.11)

with α ¼ 0.34 (buckling curve (b)) for 3 % < ρs  6%, which is the case for the current models, where ρs is the ratio of the cross-sectional area of the steel tube to that of the concrete core. The critical buckling load (Pcr), used in the calculation of the slenderness parameter (λ) according to EC4 [3], is calculated from: Pcr ¼

π 2 ðEI Þe ðKLÞ2

(6.12)

where KL is the effective length of the member and (EI)e is the effective elastic flexural stiffness.

Calculated strengths and discussion Table 6.6 shows the theoretical calculation of the axial compressive strengths of the RuCFDST columns with different rubber ratios using the earlier three design models. Fig. 6.1 shows a labeled example of a CFDST specimen with a specified radius. From this table, it can be seen that the design model by Zhao and Grzebieta [2] produces the most conservative results among others, with an average and standard deviation of 0.87 and 0.131, respectively. On the other hand, the design models by Tao and Han [1] and the modified EC4 [3] predict the strengths of the current RuCFDST columns much better compared with the experimental values (Pul,Exp). As can be observed, the average and standard deviation are 1.03 and 0.108, respectively, using

Rubberized CFDST short columns

295

Table 6.6 Comparisons between the predicted and experimental strengths. Specimen

Pul, Exp [kN]

SHS-O2I2657 0 SHS-O2I5810 0 SHS-O5I2- 1302 0 SHS-O5I5- 1555 0 SHS-O2I2483 15 SHS-O2I5804 15 SHS-O5I2- 1190 15 SHS-O5I5- 1450 15 SHS-O2I2492 30 691 SHS-O2I530 SHS-O5I2- 1191 30 SHS-O5I5- 1430 30 Average Standard deviation (SD)

Pul, Zh [kN]

Pul, Tao [kN]

666

773

856

Pul,

EC4,

Mod

[kN]

Pul,Zh Pul,Exp

Pul,Tao Pul,Exp

Pul,EC4,Mod Pul,Exp

690

1.01

1.18

1.05

963

879

1.06

1.19

1.09

1041

1328

1239

0.80

1.02

0.95

1208

1545

1456

0.78

0.99

0.94

523

593

522

1.08

1.23

1.08

711

783

711

0.88

0.97

0.88

922

1157

1099

0.77

0.97

0.92

1087

1374

1316

0.75

0.95

0.91

466

521

454

0.95

1.06

0.92

652

711

644

0.94

1.03

0.93

875

1089

1043

0.73

0.91

0.88

1038

1306

1260

0.73

0.91

0.88

0.87 0.131

1.03 0.108

0.95 0.076

the design model by Tao and Han [1], whereas they are 0.95 and 0.076, respectively, using the EC4 [3] formula. However, the method by Tao and Han [1] produces some highly unsafe results of about 23% (for SHS-O2I2-15). Hence, using the modified EC4 [3] prediction for future calculations of the compressive strengths of RuCFDST short columns is currently recommended. An interesting observation that can be made from Table 6.6 is that the modified EC4 [3] prediction produces slightly conservative results for the columns with an outer tube thickness of 5 mm (D/t ¼ 20), compared to those columns formed using thin tubes of 2 mm (D/t ¼ 50). This may be attributed to the consideration of unconfined concrete strengths on the design model by EC4 [3], while it is a common fact [37,38] that square columns with D/t  29.2 contain some confinement effects that increase the original concrete cylinder strength. Therefore, EC4 [3] provided strengths less than the experimental values with about 9% on average for the columns with D/t  29.2.

296

6.3

Concrete-Filled Double-Skin Steel Tubular Columns

Circular RuCFDST short columns

6.3.1 Materials and methods In the case of circular RuCFDST columns, the material properties of the concrete shown earlier for the case of square columns are used. Hence, the only change in the material properties are for the steel tubes. Cold-formed steel manufactured in accordance with AS1163 [25] was used in the construction of the specimens, which were delivered by Metalcorp Steel (Perth, WA). The 165.1-mm outer diameter circular tubes were coated on both sides with electro-galvanized zinc coating. All other circular hollow section steel tubes were painted plain black and were not galvanized. The CHS was of grade CL350L0 with a nominal yield stress of 350 MPa. A summary of the dimensions and material properties of the steel sections used to produce the specimens can be found in Table 6.7. The circular hollow section slenderness (λso) is defined in Table 6.7 and taken from Clause 5.2.2 of AS4100 [40]. Moreover, Table 6.7 shows the classification according to EC3 [39].   σ yt  D λso ¼ to 250

(6.13)

6.3.2 Test program 6.3.2.1 Specimens Two sets of testing were conducted to find the compressive strengths of empty steel tubes and confined concrete (CFST and CFDST) and to define the role of confinement in improving the overall concrete strength compared to its standalone counterpart. A total of 10 specimens for empty steel tube testing and 15 specimens for confined concrete testing were used. All samples were cut to length (L ¼ 400 mm) for each corresponding test specimen. It should be noted that this length value ensures a length-to-depth (L/D) ratio between 2 and 5, which, according to Tao et al. [41], leads to extremely close responses obtained for each specimen regardless of the L/D ratio. The CFST and CFDST specimens were capped at one end by tack welding a Table 6.7 Measured properties of the CHSs. Specimen no.

Diameter (D) [mm]

Thickness (t) [mm]

Area (As) [mm2]

D/t

C1 C2 C3 C4 C5

42.4 88.9 114.3 114.3 165.1

2.6 3.2 3.2 3.6 3.5

325 862 1117 1252 1777

16.31 27.78 35.72 31.75 47.17

λso

Yield stress [MPa]

Squash load [kN]

Class [39]

33.3 54.5 59.3 56.5 74.5

510 490 415 445 395

166 422 464 557 702

1 2 2 2 3

Rubberized CFDST short columns

297

Table 6.8 Measured properties of the CFST and CFDST specimens. Specimen no.

Outer tube (Table 6.7)

Inner tube (Table 6.7)

Area of concrete (Ac) [mm2]

(As/Ac)%

CHS-O165 CHS-O1143.2-I42 CHS-O1143.6-I42 CHS-O165I42 CHS-O165I89

C5 C3

– C1

19,631 7732

9.05 18.65

C4

C1

7597

20.76

C5

C1

18,220

11.54

C5

C2

13,424

19.65

10-mm-thick square steel plate to allow for casting of concrete. A summary of CFST and CFDST empty specimen properties can be found in Table 6.8. There are three specimens for each configuration given in Table 6.8, which are filled with a concrete mixture of 0%, 15%, and 30% rubber replacements to the total aggregate.

6.3.2.2 Concrete preparation All concrete samples were compacted using manual rodding. Samples that contained concrete were placed in a humid room immediately after pouring was completed to minimize concrete shrinkage. The samples remained in the humid room for 21 days and thereafter were removed and placed in an undercover room for 7 more days to complete the 28-day concrete curing process. The confined specimens experienced some minor amounts of shrinkage. Since the top surface was no longer perfectly flat due to shrinkage, a thin layer of grout was applied to each specimen 2 days prior to completion of curing to ensure a flat surface for even loading throughout the steelconcrete composite.

6.3.2.3 Test procedure Empty circular steel tube testing Two trials of each tube diameter shown in Table 6.7, with 150-mm nominal lengths, were tested using a 600-kN Baldwin machine with a rate of displacement less than 1 mm/min. Both load and displacement readings were read from the machine. Real-time data were recorded on a computer using a data logger. The galvanized cylinders with an 165.1-mm outer diameter were tested using a 5000-kN capacity DLS500 machine, since the capacity of the cylinders exceeded 600 kN. A linear variable differential transformer (LVDT) was used in this case to measure the axial displacement of the specimen.

298

Concrete-Filled Double-Skin Steel Tubular Columns

CFST and CFDST testing A load control of 1 kN/s was used to test the confined composite columns with a rate of displacement less than 0.5 mm/min. One trial of each specimen configuration and rubber replacement volume was tested for axial compressive strength using a 5000-kN capacity DLS500 machine. The loading from the machinery was captured using a 3000-kN NATA-approved load cell placed on top of the specimen. Two linear wire position transducers (string pots) were attached to the top and bottom plates at each corner to record the axial shortening. Two strain gauges were glued to the specimen vertically and horizontally to measure the hoop and axial strains. A data logger was used to transfer the load, displacement, and strain gauge measurements to a computer for the duration of the testing. The specimen and the load cell were placed concentrically, with the bottom and top plates fixed to ensure centric loading. Fig. 6.19 illustrates the test setup.

6.3.3 Test results of empty CHSs Short circular hollow section (CHS) steel tubes were subjected to uniform axial compression buckle either elastically or plastically depending on the diameter-tothickness ratio, D/t. In general, thin-walled cylinders buckle in the so-called diamond mode, whereas thick-walled cylinders buckle in the axisymmetric mode (also known as the elephant foot buckling mode) at one end of the tube [42]. The D/t ratio distinguishing the two modes of buckling failure is largely dependent on residual stresses and imperfections in the cylinders. An estimated D/t ratio of less than 40 is found to cause elephant foot buckling failure [43]. Thus, this buckling mechanism is the expected mode of failure for the tubes in this study as they satisfy the D/t < 50

Upper platten

3000kN load cell Rigid flat bar Magnetic J hanger

String pot

Specimen

Lower platten

Fig. 6.19 Specimen CHS-O114-42-00 prior to testing on the DLS500 (strain gauges not shown).

Rubberized CFDST short columns

299

criterion. Ultimately, the results from these tests were used to quantify the material properties and to understand how the different steel sections affect the overall strength of CFST and CFDST tubes. The load deflection curves from axially loaded CHS tubes for each trial are shown in Fig. 6.20. It should be noted that the unloading processes in C1, C2, C3, and C4 types of specimens were observed to be rather uncontrolled from the sudden release of the axial loading. This behavior could not be controlled because of the nature of the machinery that did not allow for controlled unloading. On the contrary, the C5 type of specimen showed gradual unloading, which is more representative of the unloading behavior of the material using the DLS500 machine. The results from both trials showed almost identical load-deflection curves and ultimate peak loads (Pu). Once buckling failure was initiated, axial shortening rapidly increased and then decelerated as the upper and lower fold faces came closer to touching. The smaller diameter cylindrical tubes exhibited a flatter load-deflection curve with a later peak loading point, which may be due to a smaller and more gradual buckling caused by its smaller section slenderness λso. The larger λso sections displayed a steeper reduction in postfailure loading, like that of Zhao’s findings [44]. From the equal outer diameter specimens, C3 and C4, it can be deduced that an increased thickness results in a higher ultimate peak load with an almost identical postfailure mechanism. This result is expected as a larger gross area of steel can bear a larger applied axial load. The galvanized coated steel, C5, showed a larger Young’s modulus compared to those of all other sections. There is also a distinct kink in the galvanized steel load-deflection curve, which could

800

C1-T1 C2-T1 C3-T1 C4-T1 C5-T1

700

Axial Load (kN)

600

C1-T2 C2-T2 C3-T2 C4-T2 C5-T2

500 400 300 200 100 0

0

2

4 6 8 Axial Shortening (mm)

10

12

Fig. 6.20 Load-deflection curve of (A) Trial 1 Empty CHS and (B) Trial 2 Empty CHS.

300

Concrete-Filled Double-Skin Steel Tubular Columns

be a result of the galvanization of steel, causing the cylinder to become more brittle due to strain aging. With respect to the class of cross sections, as presented in Table 6.7, according to EC3 [39], the load-shortening response of each specimen is conformed to its classification. The response of C1 shows a long plastic plateau, which is typical of class 1. Moreover, C2, C3, and C4, which are classified as class 2 [39], show a less plastic plateau because of their limited rotation capacity, whereas C3 shows a buckling before a yielding response (which is the definition of class 3 [39]), so the load quickly decreases after the ultimate load is reached. A summary of the ultimate peak loads for each trial and an average peak load for each specimen type can be found in Table 6.9. Furthermore, an axisymmetric mode of failure was confirmed to be the buckling mode of failure, which occurred at the top or bottom of each specimen. The typical failure modes obtained for CHS specimens in these tests are shown in Fig. 6.21.

6.3.4 Test results of CFST and CFDST specimens A total of 3 CFST and 12 CFDST specimens were tested. Single skin testing was conducted as a base case used to compare the differences between double skin and single skin confinement. The single skin confinement testing was conducted only on C5 steel sections with 0%, 15%, and 30% rubber replacements. Table 6.9 A summary of the ultimate peak loads (both trials and average) for the tested specimens. Specimen no.

Pu,1 (Trial 1) kN

Pu,2 (Trial 2) kN

Pu,avg kN

C1 C2 C3 C4 C5

171 443 430 559 663

170 443 436 564 702

170.5 443 433 561.5 682.5

Fig. 6.21 Buckling mode of a family of 10 CHS specimens.

Rubberized CFDST short columns

301

6.3.4.1 Test results of CFST and RuCFST columns A load-deflection curve of the single skin confined concrete is shown in Fig. 6.22. The naming convention is as follows: circular hollow section (CHS)—outside steel (O) diameter—percentage of rubber particle replacement. Only the C5 outer diameter (165.1-mm outer diameter and 3.5 mm thickness) galvanized steel tube was tested for single skin concrete confinement. It should be noted that the sudden load drop in the 15% rubberized concrete’s load–deflection curve is due to a load cell disconnection and does not represent the unloading of the specimen. A summary of the peak loads can be found in Table 6.10.

2000 CHS-O165-00 CHS-O165-15 CHS-O165-30

1800 1600

Axial Load ( 0:673, where ð3 + ψ Þ  0

(6.26)

ψ is the stress ratio. For the case of this technical note, ψ ¼ 1.0 and λp is taken as: rffiffiffiffiffiffi fy b=t pffiffiffiffiffi ¼ λp ¼ σ cr 28:4ε kσ

(6.27)

where the buckling factor is taken kσ ¼ 4 and b is the wall width. The material factor is qffiffiffiffiffiffiffiffiffiffiffiffiffiffi ε ¼ f y =235.

Circular cross sections The contribution of the inner tubes of CFDST (fyiAsi) is also added to the strength provided by EC4 [3]. For the strength of circular cross sections, an increase in the concrete strength caused by confinement is given by: PEC4 ¼ Aso ηs f yo + Asc f c

 f 

t yo 1 + ηc + f yi Asi D fc

(6.28)

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
 2 where ηa ¼ 0:25 3 + 2λ  1:0, ηc ¼ 4:9  18:5λ + 17λ  1:0, and λ ¼ N pl,Rd =N cr, from which Npl, Rd is the characteristic value of the plastic resistance to compression given

320

Concrete-Filled Double-Skin Steel Tubular Columns

by Eq. (6.25) and Ncr is the elastic critical normal force for the relevant buckling mode, calculated as: N cr ¼

π 2  ðEI Þeff l2b

ðEI Þeff ¼ Eso I so + 0:6  Ec I c + Esi I si

(6.29) (6.30)

where Iso, Ic, and Isi are the second moments of the area of the structural outer steel section, the uncracked concrete section, and the structural inner steel section, respectively, for the bending plane being considered and Eso, are the moduli of elasticity of outer steel section, Esi and Ec sandwiched concrete and inner steel section, respectively. The circular tubes are less sensitive to local buckling than are square tubes because of the geometry itself. The former is shell buckling-dependent, whereas the latter is plate buckling-dependent. Despite being more akin to geometrical imperfections, the local buckling stress of a circular tube is much higher (orders of magnitude) than that of a similar square tube (with equal thickness and cross-sectional area). Therefore, the local buckling of circular tubes was not considered herein because it seldom affects the strength of CFST, only extremely thin tubes (D/t > 90ε2).

6.4.1.3 The AISC design model Square cross sections Similar to EC4 [3], the contribution of the inner tubes of CFDST (fyiAsi) is added to the strength provided by the AISC [53]. In case of compact square cross sections (where qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B/t  λp and λp ¼ 2:26  Eso =f yo according to Table I1.1a [53]), the compressive strength of axially compressed circular CFST columns (PAISC) is determined from: PAISC ¼ Aso f yo + 0:85  Asc f c + f yi Asi

(6.31)

Based on the dimensions and material properties of the square cross sections shown in Table 6.12, all square outer tubes are found to be compact, as the ratios of (D/t)/λp fall between 0.36 and 0.97.

Circular cross sections The contribution of the inner tubes of CFDST (fyiAsi) is also added to the strength estimates provided by the AISC [53]. For the case of compact cross sections (where D/t  λp and λp ¼ 0.15  Eso/fyo according to Table I1.1a [53]), the compressive strength of axially compressed circular CFST columns (PAISC) is similar to that of the square cross sections but with a change in the contribution of the concrete part, given by the following formula: PAISC ¼ Aso f yo + 0:95  Asc f c + f yi Asi

(6.32)

Rubberized CFDST short columns

321

It should be noted that all circular cross sections in Table 6.13 are compact, as the ratios of (D/t)/λp range from 0.31 to 0.62.

6.4.1.4 The AS2327 design model Square cross sections The design of square CFST short columns according to AS2327 [54] is highly similar to that provided by EC4 [3]. A slight difference is found when calculating the section strength with the local buckling effect, which considers using the form factor kf with the effective width method. This is calculated as the ratio between the effective area (based on the effective width calculated as be ¼ b  (λey/λe)) and the gross crosssectional area of the steel section: kf ¼ Aso,eff/Aso. Accordingly, the strength of square CFST short columns according to AS2327 [54] is given by: PAS ¼ kf  f yo Aso + f 0c Asc + f yi Asi

(6.33)

Circular cross sections The design of circular CFST short columns according to AS2327 [54] is also similar to that provided by EC4 [3]. A slight difference is found when calculating the section strength with the local buckling effect, which considers using the form factor kf with the effective width method, given by the ratio between the effective area and the gross cross-sectional area of the steel section. Hence, all circular columns in Table 6.13 are fully effective, and AS2327 [54] yields the same results as EC4 [3].

6.4.1.5 Comparison and discussion The predictions of EC3 design equations for square and circular RuCFST and RuCFDST short columns (PEC4) [3] are compared with the experimental ultimate strengths Pul, Exp from the literature [18,55,58,59] in Table 6.14 and Table 6.15, respectively. It is worth mentioning that the corners of square steel tubes have been ignored herein, and thus the plates have been considered to intersect at right angles. Accordingly, this will result in slight differences in EC4’s [3] strength predictions compared to those obtained by Duarte et al. [18] for square RuCFST columns. It should be noted that the specimens are sorted by the width-to-thickness ratio (B/t) of square columns and the diameter-to-thickness ratio (D/t) of circular columns. The mean value of EC4’s [3] predicted-to-experimental strength ratios are 0.85 and 1.07 for square and circular cross sections, respectively. Hence, these comparisons extend the previous conclusions of Duarte et al. [18] on RuCFST to RuCFDST columns, through which EC4 [3] tends to produce conservative results for square cross sections and nonconservative results for circular cross sections filled with RuC. With regard to the predictions of the AISC [53], the predicted-to-experimental strength ratios are 0.88 and 0.59 for square and circular cross sections, respectively. These ratios indicate that the AISC [53] conservatively predicts the strengths of square cross sections, whereas it produces highly conservative results for circular cross sections.

Table 6.14 Strength predictions for the square RuCFST and RuCFDST short columns of different cross-sectional shapes and comparisons with test strengths. Specimen

B to

SHS-O5I2-15 SHS-O5I2-30 SHS-O5I5-15 SHS-O5I5-30 SHS-O5-15 SHS-O5-30 CFST89  3.5-0-15 CFST89  3.5-0-30 S100x3_355_5 S100x3_355_15 S100x3_235_5 S100x3_235_15 CFST100  3-0-15 CFST100  3-0-30 S220x4.5_355_5 S150x3_235_5 S150x3_235_15 SHS-O2I2-15 SHS-O2I2-30 SHS-O2I5-15 S220x4_235_5 S220x4_235_15

20.0 20.0 20.0 20.0 20.0 20.0 25.4 25.4 32.8 32.8 33.3 33.3 33.3 33.3 46.8 49.2 49.2 50.0 50.0 50.0 59.5 59.5

PEC4 [kN]

PEC4 Pul,Exp

904 845 1085 1025 832 746 522 466 753 642 605 494 539 465 2678 1066 807 498 427 679 2076 1509 Ave SD Max Min β

0.76 0.71 0.75 0.72 0.73 0.72 0.78 0.79 0.93 0.93 0.87 0.95 0.84 0.85 0.90 0.92 0.98 1.03 0.87 0.84 0.92 0.89 0.85 0.093 1.03 0.71 3.33

PAISC [kN] 918 868 1099 1048 837 764 521 473 781 687 573 479 542 479 2588 1077 856 551 491 732 2148 1666

PAISC Pul,Exp

0.77 0.73 0.76 0.73 0.73 0.74 0.78 0.80 0.97 0.99 0.83 0.92 0.85 0.87 1.03 0.95 0.99 0.95 0.99 0.95 0.95 0.99 0.88 0.120 1.14 0.73 2.96

PAS [kN] 939 880 1120 1060 867 781 539 483 824 713 615 505 566 491 2732 1103 844 509 438 690 2098 1532

PAS Pul,Exp

0.79 0.74 0.77 0.74 0.76 0.75 0.81 0.82 1.02 1.03 0.89 0.96 0.88 0.89 0.92 0.95 1.02 1.05 0.89 0.86 0.93 0.91 0.88 0.100 1.05 0.74 3.12

PProp [kN] 1175 1116 1356 1296 1224 1138 638 581 802 692 636 525 577 503 2700 1075 829 515 444 696 2076 1509

PProp Pul,Exp

0.99 0.94 0.93 0.91 1.07 1.10 0.96 0.99 1.00 1.00 0.92 1.00 0.90 0.92 0.91 0.93 1.01 1.07 0.90 0.87 0.92 0.89 0.96 0.064 1.10 0.87 2.91

Table 6.15 Strength predictions for the circular RuCFST and RuCFDST short columns of different cross-sectional shapes and comparisons with test strengths. Specimen

D to

CFT89x3.2-0-15 CFT89x3.2-0-30 CHS-O114-3.2-I42-30 CHS-O114-3.6-I42-30 CFT114x3.6-0-15 CFT114x3.6-0-30 C114x3_275_5 C114x3_275_15 CHS-O114-3.2-I42-15 CHS-O114-3.6-I42-15 C114x3_235_5 C114x3_235_15 CHS-O165-15 CHS-O165-I42-15 CHS-O165-I89-15 CHS-O165-I89-30 C152x3_275_5 C152x3_275_15 C219x4_235_5 C219x4_235_15

27.8 27.8 31.8 31.8 31.8 31.8 35.6 35.6 35.7 35.7 42.2 42.2 47.2 47.2 47.2 47.2 53.3 53.3 56.9 56.9

PEC4 [kN]

PEC4 Pul,Exp

542 503 868 913 809 742 892 769 872 911 695 574 1489 1486 1343 1206 1257 1047 2259 1806 Ave SD Max Min β

1.06 1.21 1.17 1.12 0.95 1.11 1.08 1.12 1.06 1.03 1.16 1.19 1.15 1.04 0.86 0.84 1.13 1.11 1.03 1.00 1.07 0.110 1.21 0.84 2.04

PAISC [kN] 252 206 462 481 386 310 503 388 517 534 434 318 841 893 909 765 783 575 1486 1053

PAISC Pul,Exp

0.49 0.50 0.62 0.59 0.45 0.46 0.61 0.57 0.63 0.60 0.73 0.66 0.65 0.63 0.58 0.53 0.71 0.61 0.68 0.58 0.59 0.076 0.73 0.45 4.27

PProp [kN] 504 455 808 852 730 651 814 695 814 852 626 506 1286 1307 1219 1078 1152 1019 2184 1881

PProp Pul,Exp

0.98 1.10 1.09 1.04 0.86 0.98 0.98 1.01 0.99 0.96 1.05 1.05 1.00 0.92 0.78 0.75 1.04 1.08 0.99 1.04 0.98 0.095 1.10 0.75 2.54

PProp, Du [kN] 337 208 468 487 513 314 806 512 638 663 625 407 1066 1102 1066 775 1179 836 2262 1566

PProp,Du Pul,Exp

0.66 0.50 0.63 0.60 0.60 0.47 0.98 0.75 0.77 0.75 1.05 0.84 0.83 0.77 0.68 0.54 1.06 0.89 1.03 0.86 0.76 0.180 1.06 0.47 2.55

324

Concrete-Filled Double-Skin Steel Tubular Columns

This is because it ignores the confinement effect, unlike EC4 [3]. For the case of square sections, AS2327 [54] produces almost less conservative results compared to EC4 [3], with an average ratio of 0.88 for the predicted-to-experimental strengths. These results show that the current design formulas for conventional CFST columns do not provide accurate predictions, essentially due to the role of rubber (a hyperelastic material) in the redistribution of confining stresses, and more accurate formulas are needed for RuCFST and RuCFDST short columns of different cross sections. The relationships between different predictions (PCode) and the ultimate experimental strength ratio (PCode/Pul, Exp) and the B/t and D/t ratios are provided in Fig. 6.21 for square and circular cross sections, respectively. Trend lines have been added to the figure to assess the accuracy of this design model over the entire range of B/t and D/t ratios. It can be observed that the accuracy of all the design equations increases with an increase in the B/t ratio of square RuCFST and RuCFDST short columns (Fig. 6.35A), while the best-fit data model is parallel to the horizontal axis. Additionally, the accuracy of the design equations for circular RuCFST and RuCFDST short columns enhances with an increase in the D/t ratio (Fig. 6.35B), but it is not the same over the entire range. Hence, a new design model should be proposed to predict the strength of square and circular RuCFST and RuCFDST short columns more accurately and consistently compared to EC4 [3], AISC [53], and AS2327 [54]. To do so, new lateral confining stress formulas for the outer square and circular steel tubes are first proposed, which is undertaken in the following section.

6.4.2 Lateral confining pressures The experimental tests gathered in the previous section are currently used to find the appropriate formulas that represent the lateral confining pressure (frp) of square and circular tubes of RuCFST and RuCFDST short columns. A new confinement model is proposed herein based on the strength (Pul) given by Eq. (6.25), which assumes the contribution of the various components that make up the cross section. The strengths of the current short columns, provided in Tables 6.12 and 6.13, were used to calculate the values of frp, by assuming that Pul ¼ Pul, Exp. Hence, fcc is to be calculated first, then frp is to be obtained using the relationship suggested by Richard et al. [61] as: f cc ¼ γ c f c + kf rp

(6.34)

According to Richard et al. [61], the value of k was taken as 4.1. Considering the loading rate, the quality of the concrete, and the column size on the compressive strength of the concrete, the factor γ c is provided by Liang [62], based on the diameter of the concrete core (Dc), as: γ c ¼ 1:85Dc 0:135 ð0:85  γ c  1:0Þ

(6.35)

Next, two different proposals for the frp/fy ratios are provided. It should be noted that to increase the confidence of the results, only 42 specimens’ results were used to fit the curves in Sections 6.4.2.1 and 6.4.2.2. Then, all test specimens were again used in the verification of the proposed design models. One specimen of each type was selected

Rubberized CFDST short columns

325

(a) Square RuCFST and RuCFDST columns EC4 [16]

AISC [53]

AS 2327 [54]

(b) Circular RuCFST and RuCFDST columns EC4 [16] and AS 2327 [54]

AISC [53]

Fig. 6.35 Comparison of the codified strengths [3,53,54] and the ultimate strengths of the RuCFST and RuCFDST short columns with different D/t ratios: (A) square and (B) circular columns.

for this verification with B/tor D/t around 50 but with different rubber contents: S150x3_235_15, SHS-O2I5-30, CHS-O165-30, and CHS-O165-I42-30.

6.4.2.1 “frp” based on the slenderness ratios of the steel tubes In this section, an expression providing the confining stress of the steel tube (frp) to the concrete core is proposed, which depends on the material (fyo) and geometrical (D (or B) and t) characteristics of the stub. Accordingly, the relationship between the frp/fy ratios and the slenderness ratios of the steel tubes (B/t or D/t) is provided in Fig. 6.36, similar to Hassanein et al. [63]. Fig. 6.36A indicates that the scatter of the data points of the columns, tested by Elchalakani et al. [59], with B/t ¼ 20 is large. To the authors’ best knowledge, this may be due to the use of the average fc values in

326

Concrete-Filled Double-Skin Steel Tubular Columns

(a) Square RuCFST and RuCFDST columns

(b) Circular RuCFST and RuCFDST columns

Outliers

Fig. 6.36 Lateral confining pressure obtained from the experimental results of RuCFST and RuCFDST: (A) square and (B) circular columns.

the current calculations, while relatively large differences appear between the strength of the individual cylinders and the average value of the same mixture (as seen in Table 6.3 in the study by Elchalakani et al. [59]). On the other hand, there are two data points in Fig. 6.36B with D/t ¼ 47.2, corresponding to specimens O165-I89-15 and CHS-O165-I89-30 tested by Elchalakani et al. [55], which have extremely high frp/fy ratios (about 0.030), more than twice those of columns with the same D/t ratio. These two specimens were the only ones to have inner tubes with a diameter of 89 mm; thus, it is probable that the true fy value may not be the one provided by the authors. According to the authors’ calculations, the results of frp/fy would agree with the other values (close to 0.015) if these tubes were manufactured using ultrahigh-strength steel. Accordingly, we consider these two results as outliers, and they have been ignored while conducting regression analysis. According to the regression analysis, a linear law formula for the lateral confining pressure is expressed for square (Eq. 6.36),

Rubberized CFDST short columns

327

whereas a power law formula for the lateral confining pressure is expressed for circular (Eq. 6.37) RuCFST and RuCFDST short columns as: f rp f yo

8 B > + 0:1137 < 0:004  to ¼ B > : 7  105  + 0:0052 to

f rp ¼ 4:0448  f yo

 1:477 D to

B < 27:5 to B : 27:5  < 60:0 to

(6.36)

D < 60:0 to

(6.37)

: 20:0 

: 30:0 

On the other hand, the confining pressure formulas, as observed from Fig. 6.36, are based on the average values of the available data points instead of their lowest bounds. This is because using the lowest bounds increases the safety of the suggested formulas, which is good from the safety-checking viewpoint but not from the economical viewpoint. Anyway, the variability of results would raise other questions, such as the reliability of the formulas and their partial safety factors. On the other hand, it should be noted that these confining pressure formulas highlight the limited range of B/tor D/ t ratios for the test results available in the literature. Accordingly, large efforts are still needed to come up with frp/fyo formulas for RuCFST and RuCFDST columns with the B/t and D/t ratios in the range of 20–150, as available for CFST and CFDST columns by Hu et al. [38]. An important fact is that square CFST short columns do not exhibit confining stress for tubes with B/t > 29.2, which is not the case of the current rubberized composite columns. This is because the composite action of RuCFDST columns is better than that of CFDST columns according to Ayough et al. [64]. Hence, within the range of B/t of the rubberized composite columns, the square tubes were able to apply lateral confining pressure to the rubberized concrete core.

6.4.2.2 “frp” based on the rubber particle content and slenderness ratios of the steel tubes In this subsection, an additional regression analysis is conducted for thefrp/fyo ratios obtained from the test results. This includes the effect of the rubber particle content (p) of RuC besides the slenderness ratios of the steel tubes in the proposed formulas, which is inspired from a previous study by Duarte et al. [46]. The regression equation is based on the following equation: Y ¼ b1  X 1  b2  X 2 + a

(6.38)

where Y, X1, and X2 are the frp/fyo ratio, p, and B/to (or D/to based on the cross-sectional shape), respectively. Based on this regression equation, the following formulas have been obtained for square and circular RuCFST and RuCFDST short columns: f rp B ¼ 0:01867  p  0:00077  + 0:036 to f yo

(6.39)

328

Concrete-Filled Double-Skin Steel Tubular Columns

f rp D ¼ 0:00998  p  0:00051  + 0:039 to f yo

(6.40)

Fig. 6.37 presents the relationship between the frp/fyo ratio and B/to (or D/to based on the cross-sectional shape) obtained from the experimental results and those considering the two proposals (Prop 1 of Section 6.4.2.1 and Prop 2 of Section 6.4.2.2). As can be observed, both methods provide good estimations for the frp/fyo ratios. However, the general method (Section 6.4.2.1) representing the slenderness ratio of steel cross sections provides better frp/fyo ratios compared to those obtained from the other method (Section 6.4.2.2), which is based on (i) the rubber particle content (p) of RuC and (ii) the slenderness ratios of the steel tubes. Accordingly, the proposals of the frp/fyo ratios provided by Eqs. (6.13), (6.14) are further used in the suggested design models provided in the next section.

(a) Square RuCFST and RuCFDST columns

(b) Circular RuCFST and RuCFDST columns

Fig. 6.37 Comparison of the proposed and ultimate strengths of the RuCFST and RuCFDST short columns with different D/t ratios: (A) square and (B) circular columns.

Rubberized CFDST short columns

329

6.4.3 The proposed design model Herein, a unified design formula is proposed for RuCFST and RuCFDST short columns with either square or circular cross sections. This design strength is based on the sum of the plastic resistances of the steel tubes and the confined sandwiched concrete (fcc0 Asc) and is given by the following equation:
 Ppl,Rd ¼ f yo Aso + f 0cc Asc + f yi Asi with f 0cc given by Eq:34

(6.41)

The difference between the strengths of the square and circular cross sections resides in the value of frp, which is obtained from the different formulas derived earlier. Tables 6.14 and 6.15 include the predictions of the different columns based on the currently proposed formula. As can be observed, the proposed formula yielded suitable results compared with the original EC4 [3]. The average ratio of PProp/Pul, Exp is 0.96 and 0.98 for square and circular rubberized composite columns, respectively. Additionally, the scatter of the current predictions is lower than that of EC4 [3] predictions. Additional strength comparisons for the four columns, which were not included in the derivation of the lateral confining pressure formulas (S150x3_235_15, SHS-O2I5-30, CHS-O165-30, and CHS-O165-I42-30) are provided in Table 6.16. As can be observed, the proposed formulas yielded better strengths than the codified strengths [3], which confirms the earlier conclusions. On the other hand, the accuracy of the proposed formula is provided in Fig. 6.38, from which it can be ensured that this proposal is more consistent and reliable along the entire range of B/t and D/t ratios compared with EC4 [3] (see Fig. 6.35). An additional comparison is made herein for just circular RuCFST and RuCFDST columns (PProp,Du/Pul,Exp), where PProp,Du is the strength predicted by Eq. (6.41), utilizing the lateral confining stress suggested by Duarte et al. [46], as follows: " # f rp 2:95  p 17:1  100p + ¼ 1:5 750 f yo ðD=to Þ2

(6.42)

It should be noted that this formula has been suggested for RuC of rubber particle content (p) of 0.05 and 0.15. Therefore, specimens of p ¼ 0.30 are outside the validity range. Accordingly, negative values for frp are obtained, and, practically, they are taken to be equal to zero in the current calculations. However, as can be observed from Table 6.15, this design model yielded highly conservative results (average of 0.76 and a standard deviation of 0.149). Hence, the current proposal with the suggested frp/fyo formula (Eq. 6.37) is recommended. Finally, it should be noted that the validity ranges of the current proposed formulas are (i) B/to : 20  60, fyo : 284  456 MPa, fc0 ¼ 9.5  32.2 MPa, p : 0.05  0.30, and b/B ¼ 0.5, for square cross sections and (ii) D/to : 30 60, fyo : 284  456 MPa, fc0 ¼ 14.4  32.2 MPa, p : 0.05  0.30, and d/D : 0.37 0.54 for circular cross sections. Forthcoming experimental results on square and circular RuCFST and RuCFDST short columns will expand the set of available results and therefore will enlarge the previous validity ranges.

Table 6.16 Additional strength comparisons for the columns not included in the derivation of the lateral confining pressure formulas. PProp, Specimen

Type

D to

PEC4 [kN]

S220x4.5_355_15

Square RuCFST Square RuCFDST Circular RuCFST Circular RuCFDST

46.8

2121

0.89

2588

1.08

2176

0.91

2200

50.0

608

0.88

671

0.97

619

0.90

47.2

1306

1.16

635

0.56

1306

47.2

1312

1.05

701

0.56

1312

SHS-O2I5-30 CHS-O165-30 CHS-O165-I4230

PEC4 Pul,Exp

PAISC [kN]

PAISC Pul,Exp

PAS [kN]

PAS Pul,Exp

PProp [kN]

PProp Pul,Exp

Du

[kN]

PProp,Du Pul,Exp

0.92

–

–

625

0.90

–

–

1.16

1083

0.96

649

0.57

1.05

1119

0.90

715

0.57

Rubberized CFDST short columns

331

(c) Square RuCFST and RuCFDST columns

(d) Circular RuCFST and RuCFDST columns

Fig. 6.38 Comparison of the proposed and ultimate strengths for the RuCFST and RuCFDST short columns with different D/t ratios: (A) square and (B) circular columns.

6.4.4 Reliability analysis It is known that the reliability analysis of the design methods is particularly important when proposing new equations. Therefore, in this section, a reliability analysis is performed to assess the reliability of different specifications and proposed design models. This is based on the calculation of the reliability index (β), which is a relative measure of design integrity. The β index was originally provided by Ravindra and Galambos [65] for steel members as given by Eq. (6.43), whereas the values of the parameters (Eq. 6.43) suggested by Lai and Varma [66] for CFST members are currently used, as described in the following.   F Ln P  M φ β ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi α V 2M + V 2P + V 2F

(6.43)

332

Concrete-Filled Double-Skin Steel Tubular Columns

where P stands for the average ratio of Pul, Exp over the design predictions (i.e., different specifications or proposed strength), M denotes the average ratio of the measured-to-nominal strength of the materials (1.10), F is the average ratio of the material fabrication factor (1.00), α is the linearization approximation coefficient (0.70), and VM ¼ 0.05, VF ¼ 0.193, and VP are the coefficients of variation of the material factor, fabrication factor, and P, respectively. Additional information on the values of these parameters can be found in Lai and Varma [67]. φ is taken as 0.75. However, it is known that EC4 [3] adopts different partial factors for steel and concrete in the strength calculations of CFST columns, which makes the calculation of the reliability index highly complex. Hence, due to the complexity of the problem, β was calculated according to the concept of the resistance factor utilized in LRFD. The same method was used in the literature before [64,68,69] in the reliability analysis of design models of different concrete-filled steel tubes. As can be observed from Tables 6.14 and 6.15 for square and circular columns, respectively, the proposed design models provided values of the reliability index (β) higher than 2.5. Hence, they can be safely used until additional experiments are available in the near future.

6.5

Conclusions

This chapter presents an experimental investigation of CFDST/CFST confined and unconfined rubberized concretes. The results of this chapter are summarized in the following points: 1. The rubber pretreatment process was successful in creating vertically uniform specimens and prevented the rubber particles from floating to the top surface. 2. The mix design produced a compressive strength of 25-MPa 15% RuC, which is the minimum-strength concrete for applications made of composite structures [3]. 3. The available methods of prediction of the axial strength of CFDST specimens filled with normal concrete produce close approximations to the present experimental results with RuC. 4. Energy absorption for a composite material is significantly larger than those of the components that make it up, showing the positive effects of composite action. 5. The phenomenon of the concrete core’s spring-back upward movement was observed in this project and has not been previously researched in CFDST/CFST. Rubber elasticity and lateral confinement allowed this to occur. 6. The interface zone of the normal concrete was strongly bonded to the interior of the outer steel section, showing the concrete behaving like a ductile material. This clearly shows the significant benefits of using CFST and CFDST as a method of avoiding brittle failure found in plain concrete. 7. The ductility index for thinner outer steel specimens was higher than that of thicker outer steel specimens. Analysis of the ductility index of the range of specimens showed that the ductility index is fairly constant across the three rubber replacements. 8. Rubberized concrete significantly improved the ductility and energy absorption of CFST and CFDST by up to 2.5 times. 9. The existing methods of the predictions of ultimate peak compressive load for CFST and CFDST filled with normal concrete yield good results for rubberized concrete column counterparts. 10. CFST and CFDST using cold-formed CHS significantly improved the ultimate peak strength in RuC and normal concrete due to lateral confinement. Additional strength through such confinement was achieved in all specimens.

Rubberized CFDST short columns

333

11. The concrete–steel-bonding zone at the inner and outer steel sections was seen to be promising with both rubberized and normal concrete exhibiting ductile behavior due to confinement. 12. It is important that the preliminary results of this study of rubberized concrete-filled single skin and double skin steel tubular columns encourage further research devoted to such members as a feasible construction method for applications such as columns in buildings located in seismic-active zones, security bollards, and flexible road side barriers. 13. This has been extended to the present lateral confining pressure formulas for square and circular tubes imposed by the lateral expansion of confined RuC. Two different proposals have been provided. The first was based on the slenderness ratios of the steel cross sections, whereas the second was based on the rubber particle content (p) of RuC besides the slenderness ratios of the steel tubes. A comparison of the results found that the former provides better confining pressure compared with the experimental values. Hence, this method was further used for proposing a new unified design model for square and circular RuCFST and RuCFST short columns, the results of which show that they provide much better strengths compared to EC4 [3].

Appendix I: Progressive axial loading of specimen SHS-O2I2-30

(1) deflection G=0.0

(4) deflection G= 15.9mm

(2) deflection G=5.3mm

(5) deflection G=21.2mm

(3) deflection G=10.6 mm

(6) deflection G=26.5 mm

334

Concrete-Filled Double-Skin Steel Tubular Columns

(7) deflection d=31.8mm

(8) deflection d=37.1mm

(10) deflection d=47.7mm

(11) deflection d=51.0mm

(9) deflection d=42.4 mm

(12) deflection d=53.3 mm

Rubberized CFDST short columns

(13) deflection d=57.6mm

(16) deflection d=67.5mm

335

(14) deflection d=60.9mm

(15) deflection d=64.2mm

(17) d=62.5mm (unloading)

(18) d=62.5 mm (unloading)

336

Concrete-Filled Double-Skin Steel Tubular Columns

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Future research 7.1

7

Recommendations

Based on the recent advances made in the behavior and design of CFDST short/long columns provided in this book, the following recommendations are made: 1. The ultimate axial load of CFDST short columns significantly increases by increasing the concrete compressive strength or by decreasing the hollow ratio. However, increasing the inner-to-outer thickness ratio (ti/te) or the yield strength of the inner carbon steel tube does not significantly increase the ultimate axial load. 2. The effect of the thickness ratio (ti/te) on the strengths of intermediate-length columns was found to be significant by increasing the ti value, whereas it does not affect the strengths of long columns. 3. The confining stress-based design of circular-circular CFDST short columns with carbon steel tubes (Chapter 3) can be used to design more effective columns compared to the other available design methods. 4. The limit of the slenderness ratio (λ), which delineates between intermediate-length and long pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi CFDST columns, was found to be accurately represented by 75= σ 0:2 =235 compared to qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 115= f y =235 for CFST columns. For long CFDST columns with λ  50, the confinement effect can be ignored in design, as found from the analysis of the results. 5. Chapter 5 has proved that concrete-filled double skin slender columns require modifications in the Eurocode design model, in the future revisions of EC4, by considering a more appropriate “buckling curve.” 6. Square and circular RuCFST and RuCFST short columns are better designed using the confining stress-based design model proposed in Chapter 6 of this book.

7.2

Trends for future relevant works

Experimental and theoretical investigations should be continued to study the following points: 1. Although Chapter 3 has successfully evaluated the effects of various parameters on the behavior of circular CFDST short columns, many opportunities for future studies remain. As noted in Chapter 3, an innovative approach to simulate the confined concrete was checked, which used an unconfined concrete model with a certain dilation angle and allowed ABAQUS to control the confinement level. However, due to the settings of ABAQUS and/or other problems, this approach was not adopted in this research. Accordingly, further studies can modify the existing ABAQUS settings to allow the use of this approach to obtain some reliable results in future. 2. The collected database on circular-circular CFDST short columns formed from carbon steel tubes showed that additional tests should be performed on CFDST columns manufactured from high-strength steel (HSS) with both normal strength concrete (NSC) and high-strength concrete (HSC) to verify the proposed confining stress-based design method with more Concrete-Filled Double-Skin Steel Tubular Columns. https://doi.org/10.1016/B978-0-443-15228-3.00008-3 Copyright © 2023 Elsevier Inc. All rights reserved.

342

3.

4.

5. 6.

7. 8.

9.

10.

11. 12. 13.

Concrete-Filled Double-Skin Steel Tubular Columns

confidence. In addition, specimens with large void ratios and large-sized CFDST columns are needed to verify the proposed resistance for a wider range of fyo, fyi, and fc values. The cyclic effects, which are highly relevant to offshore structures, on CFDST columns should be further investigated. Additional studies on the effect of load introduction on CFDST subassemblies made of columns connected with beams to their sides should be conducted. Future investigations of CFDST columns with SHS outer and SHS inner tubes should primarily focus on the dimensional parameters of the columns. The specimens tested in Chapter 5 identified that for a given column, increasing the slenderness ratios of the outer and inner steel tubes resulted in a reduction in the strength-to-weight ratio of the column. Further investigations into this, either experimental or numerical, should determine the slenderness ratios of each tube, which will optimize the strength-to-weight ratios of square CFDST columns. Similarly, further investigation to determine the optimal hollow section ratio for the strength-to-weight ratio of square CFDST columns would be highly beneficial. Further research is needed to investigate the fundamental behavior of axially loaded CFDST slender columns and beam-columns under axial load and bending. Additional research is still required to find the slenderness limit delineating between intermediate-length columns and long columns for circular CFSST columns, using a precisely wider range of column dimensions. It is recommended that experimental tests should be conducted to verify the currently recommended design model for CFDST slender columns. An extensive investigation on CFDT slender columns with stainless steel external tubes is required to provide a suitable design model for such columns instead of modified EC4 (for stainless steel), which is based on CFDT slender columns formed from carbon steel external tubes. To allow for conceptual design recommendations to be put forward for RuCFDST short columns, additional results should be obtained, accounting for different cross-sectional sizes, inner-to-outer thickness ratios, and rubber contents with respect to tube thickness. Finally, additional experimental tests of RuCFST and RuCFDST columns with other D/t ratios (especially below 30 and above 60) are still needed to extend the available range of results and provide confining pressure formulae and a unified design model for square and circular RuCFST and RuCFST short columns with wider validity. More research work is needed to study the influence of eccentric compression loads on RuCFDST short columns. More research work is needed to study the influence of concentric and eccentric compression loads on RuCFDST long columns. Future research is required to investigate the influence of dynamic loads on RuCFDST short and long columns.

Index Note: Page numbers followed by f indicate figures and t indicate tables. A ACI code, 165 CFDST columns, 178–179 CFDT columns, 195–198, 196–197t CFSST columns, 165 CFSST columns, 226, 246 C Carbon steel tubes, 341 Carbon steels, 139 Cement chemical composition of, 275, 275t Chemical composition, of cement, 275, 275t Circular-circular CFDST columns, 48–63, 341 ABAQUS compression results, 49f assessment of design methods, 111–117, 111t, 112f confining stress-based design for, 109–130 FE nonlinear analysis, 48–54 basic description, 48–49 constitutive material models, 49–52 FE meshes, 54 interactions between components, 53 loading and boundary conditions, 53–54 FE results and discussion, 59–63 hollow ratio effects, 59–60, 59f steel and concrete strengths effects, 62–63, 63–64f thickness of steel tubes effects, 60–62, 61–62f lateral confining pressure, 117–119, 117f, 119f model verification, 54–56 column verification, 55–56 steel material verification, 55 parametric study, 56–59, 58t proposed design model, 119–130, 120–121t, 123–124t, 126–127t, 129t slenderness ratio, 341 stress-based design of, 341

Circular hollow section (CHS) steel tubes, 299–300 Circular RuCFDST short columns, 296–312, 341 AISC design model, 320–321 AS2327 design model, 321 comparison and discussion, 321–324, 322–323t, 325f concrete-steel bonding, 306–307, 307f ductility and energy absorption, 308–309, 309f EC4 design methods, 312–324 experimental tests, 314, 315–318t exterior steel strain gauge data, 307–308, 308f lateral confining pressures, 324–328, 326f, 328f materials and methods, 296 measured properties of, 296–297t predictions of CFDST and CFST column strength, 310–312, 313t proposed design model, 329–330, 330t, 331f reliability analysis, 331–332 test program, 296–298, 298f test results of CFDST and RuCFDST columns, 302–304, 302–304f of CFST and CFDST specimens, 300–309, 301f, 301t of empty CHSs, 298–300, 299f, 300t Circular-square CFDST columns, 64–77 FE modeling, 65–66, 66–67f innovation of, 64–65 parametric study, 73–77, 74t, 75f, 77f verification study, 67–72, 68–69t, 70f, 72f Columns classification, respect to length, 206, 206f Column slenderness ratio CFDT columns, 253t, 254–256, 254–255f circular CFDST columns, 234

344

Column slenderness ratio (Continued) CFSST columns, 221–222, 221f Column strength-slenderness ratio relationship, 8–9, 8f Composite slender columns, 203–206 Compressive cylinders, mass and density of, 281, 281t Compressive strength CFDST columns, 73, 75f, 174–175, 175f CFDT columns, 186–188, 187t, 188–189f, 258–259, 260t CFSST columns, 163, 163–164f, 223–224, 225f, 239–241, 240t, 241–242f Concentric and eccentric compression loads, on RuCFDST columns, 342 Concrete, 275 compaction, CFDST columns, 19 compression, CFDST columns, 276–277 confinement, CFSST columns, 236–237, 236f core of CFDT columns, 149–150 core of CFSST columns, 147–149, 147f mix procedure, CFDST columns, 278 and outer steel interface zone, CFDST columns, 286–287, 286–287f sandwiched concrete of CFDST and CFDT columns, 147–149, 147f Concrete-filled double skin slender columns, 341 Concrete-filled double skin tubular (CFDST) columns, 1, 6f, 141–142, 141f, 274–275, 342 ACI code, 178–179 advantages of, 5–7 axial compression, 1 axial load of, 341 with both carbon steel tubes, 152–156, 155t, 156f comparisons and discussions, 246–249, 247–248f, 250–251t comparison with design strengths, 245–249 compressive strength, 174–175, 175f confinement effect in, 18 continuous strength method, 179–180 cross-sectional types of, 6–7, 7f cross sections, 47, 48f design, 1, 178–185 design strengths of, 27–31t, 33–37t double skin steel tubes, 47

Index

effect of axial partial compression, 22 of concrete compaction, 19 of hollow ratio, 19–20 of initial imperfection, 18–19 of long-term sustained loading, 21–22 of preloading on steel tubes, 22–23 of residual stress, 18–19 of steel grade of inner steel tubes, 21 of thickness ratio, 20–21, 341 erection of, 7–8, 8f experimental studies, 9–11, 13–17t with external stainless steel tubes, 156–158, 157t failure modes of, 24–26, 24f, 26f formulas for compressive strength, 26–39 fundamental behavior, 167–178, 171–173t hollow ratio, 176–177, 177f inclined column, 9, 9f influence of fibers on capacity of, 23 with inner CHSs, 39t input data, 230, 231t interface bonding of, 23 mechanism of inner tube of, 26 nominal steel ratio, 175–176, 176f numerical study, 230–244 sandwiched concrete, 47 short columns, 1 slender columns, 2 steel grade of inner tube, 178, 178f straight column, 9, 9f structural behavior, 11–23, 230–244, 232–234f tapered column, 9, 9f thickness ratio, 177, 177f types of, 8–9 according to length, 8–9 according to straightness, 9 validation of FE model, 217, 217f verification, 55–56, 56t, 181–185, 182–185t Concrete-filled double-tube (CFDT) columns, 141–142, 141f, 144f, 186–198, 249–264, 342 ACI code, 195–198, 196–197t compressive strength, 186–188, 187t, 188–189f, 258–259, 260t concrete core of, 149–150

Index

design models, 259–263, 262t diameter ratio, 189, 190t, 191f, 192t with external stainless steel tubes, 158, 158t, 159f, 160t failure modes, 256–257, 256f, 257t FE models, 249–253, 253t fundamental behavior, 186–194 fundamental behavior of, 249–259 sandwiched concrete of, 147–149 steel grade of internal carbon steel tube effect, 191–193, 194t, 194f strain distribution at mid-height sections, 257–258, 258f thickness ratio, 189–191, 193t, 193f verification of design models, 263–264, 264t vs. CFSST columns, 194, 195f Concrete-filled stainless steel tubular (CFSST) columns, 152, 154t, 203–205, 204f ACI code, 165 AISC specification, 226 comparisons and discussions, 226–229, 227f, 228t comparisons with design codes, 224–230 compressive strength, 163, 163–164f compressive strength of concrete, 223–224, 225f continuous strength method, 166 design models, 167, 170t design strengths vs. ultimate axial strengths, 168–169t effect of column slenderness ratio, 221–222, 221f effect of diameter-to-thickness ratio, 222–223, 222–224f effects of diameter-to-thickness ratio, 163–165, 164f Eurocode 4, 165–166, 225–226, 229–230 failure modes and load-strain curves, 219–221, 219–221f fundamental behavior, 159–165, 161t Liang and Fragomeni’s design model, 166–167 load-strain responses, 162, 162f nonlinear finite element analysis, 207–213, 207–209f parametric study, 218–224, 218t stress-strain relationships

345

for confined concrete, 210–213, 211f for stainless steels, 209–210, 210f validation of FE model, 213–217, 216f, 216t Concrete-filled steel tubular (CFST) columns, 50, 140–141, 141f, 152, 153t, 154f, 203 validation of FE model, 213–214, 214t, 215f Concrete material, CFDST columns, 49–52 confined concrete, 50–52 structural steel material, 52 unconfined concrete with dilation angle, 49, 50f Concrete-steel bonding, 306–307, 307f Confined concrete, 50–52, 51f stress-strain relationships for, 210–213, 211f Confinement effect, in CFDST columns, 18 Continuous strength method (CSM) CFDST columns, 179–180 CFSST columns, 166 D Deformed shapes of RuCFDST columns, 285–286, 285–286f Diameter-to-thickness ratio, CFSST columns, 222–223, 222–224f “Double skin” composite construction, 5 cross section of, 6f Ductility circular RuCFDST, 308–309, 309f square RuCFDST, 289–291, 290–291f Duplex stainless steels, 139, 140f E Empty CHSs, 298–300, 299f, 300t Empty square hollow sections, CFDST columns, 281–283, 282f Energy absorption circular RuCFDST, 308–309, 309f square RuCFDST, 289–291, 290–291f Erection of CFDST columns, 7–8, 8f Eurocode 4 CFDST columns, 245–246, 294, 311–312 CFSST columns, 165–166, 225–226, 229–230

346

Index

F

N

Failure modes of CFSST columns, 219–221, 219–221f of CFDST columns, 24–26, 24f, 26f FE meshes of CFDST columns, 54, 67f, 99f of CFST and CFSST columns, 142–143, 143–144f FE modeling, circular-square CFDST columns, 65–66, 66f Finite element models, 142–150 CFDST columns, 1, 11 boundary conditions and load application, 144–145, 145f material model, 145–150 type and mesh, 142–143, 143–144f

Nickel, 139 Nominal steel ratio, 175–176

H Hollow ratio CFDST columns, 19–20, 76–77, 77f, 176–177, 177f CFSST columns, 237–239, 238t, 239f circular-circular CFDST columns, 59–60, 59f Hollow steel tube, material properties of, 55, 55t I Initial imperfection, CFDST columns, 18–19 L Lean duplex stainless steel, 145–147, 147f hollow columns, 150–151, 151f material, 205–206, 205f Lean duplex stainless steel hollow section columns (LDSSHSCs), 139 Lean duplex steels, 139 Length, CFDST columns, 8–9 Liang and Fragomeni’s design model, 166–167 Load-displacement relationships, CFDST columns, 287–289, 288–289f Loading and boundary conditions, CFDST short column, 53–54, 53–54f Load-strain curves, CFSST columns, 219–221, 219–221f Load-strain relationships, CFSST columns, 234, 235f

P Pagoulatou model, 81–82 R Reference point (RP), 207–208 Residual stress, CFDST columns, 18–19 Rubberized concrete (RuC), 280–281, 280f development of, 273 methods to enhance mechanical properties of, 273–274 Rubberized concrete-filled (RuCFST) columns, 342 Rubberized concrete-filled composite column, types of, 274–275, 274f Rubberized concrete-filled double skin steel tube (RuCFDST) columns, 342 Rubber particles, 276, 276f Rubber pretreatment, 278 Rubber waste, 273 S Sandwiched concrete of CFDST and CFDT columns, 147–149, 147f Square-circular CFDST columns, 96–108 design approach and test results, 96–97, 97–98t numerical modeling, 98–108, 99–100f, 102t, 104f, 105–107t, 108f, 109t Square RuCFDST short columns, 275–295, 341 AISC design model, 320–321 AS2327 design model, 321 comparison and discussion, 321–324, 322–323t, 325f concrete and outer steel interface zone, 286–287, 286–287f deformed shapes of, 285–286, 285f EC4 design methods, 312–324 energy absorption and ductility, 289–291, 290–291f experimental tests, 314, 315–318t fundamental behavior, 283–285 lateral confining pressures, 324–328, 326f, 328f

Index

load-displacement relationships, 287–289, 288–289f material properties, 280–283 empty square hollow sections, 281–283, 282f rubberized concrete, 280–281, 280f materials and methods, 275–278 concrete compression tests, 276–277 concrete mix procedure, 278 material properties, 275–276 rubber pretreatment, 278 proposed design model, 329–330, 330t, 331f reliability analysis, 331–332 strength calculations, 291–295, 292t, 295t strength predictions, 292–295, 295t test program, 279–280 specimens, 279 test procedure, 279–280 test results for, 283–291 Square-square CFDST columns, 77–96 FE methodology and validation, 77–84, 78–79f, 83t, 86f, 88–89f parametric studies, 59f, 85–96, 90–94t, 91–93f, 95f Stainless steel stress-strain relationships for, 209–210, 210f types, 139 Steel and concrete strengths, 62–63, 63–64f Steel-concrete composite columns, 5–6

347

Steel tubes, 275–276 thickness of, 60–62, 61–62f Steel yield strength, 73–75, 75f Stiffened CFSST, 203–205, 204f Straightness, CFDST columns, 9 Stress-strain relationships for confined concrete, 210–213, 211f for stainless steels, 209–210, 210f Stress-strain response of cold-formed steel, 52, 52f Structural steel material, 52 T Thickness of steel tubes, 60–62, 61–62f Thickness ratio CFDST columns, 20–21, 177, 177f CFDT columns, 189–191, 193t, 193f CFSST columns, 242–244, 243t, 244f Tire landfills, 273 U Unconfined concrete with dilation angle, 49, 50f W Waste tires, 273 Z Zhao model, 80–81, 81f Zhao’s hollow steel tube, 292, 292t

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