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Cold-formed steel design
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H A I L E D B Y P R O F E S S I O N A L S A R O U N D T H E W O R L D as the definitive text
on the subject, Cold-Formed Steel Design is an indispensable resource for all who design for
and work with cold-formed steel. No other book provides such exhaustive coverage of both the
theory and practice of cold-formed steel construction. Updated and expanded to reflect all the
important developments that have occurred in the field over the past decade, this Fourth Edition
of the classic text provides you with more of the detailed, up-to-the-minute technical information
and expert guidance you need to make optimum use of this incredibly versatile material for
building construction.
Wei-Wen Yu and Roger LaBoube, respected authorities in the field, draw upon decades of
experience in cold-formed steel design, research, teaching, and development of design
specifications to provide guidance on all practical aspects of cold-formed steel design for
manufacturing, civil engineering, and building applications. Throughout the book, they describe
the structural behavior of cold-formed steel members and connections from both the theoretical
and experimental perspectives, and discuss the rationale behind the AISI and North American
design provisions. Cold-Formed Steel Design, Fourth Edition features:
• Thoroughly up-to-date 2007 North American (AISI S100) design specifications
• Both ASD and LRFD methods for USA and Mexico
• LSD (Limit States Design) method for Canada
• A new chapter on the Direct Strength Method
• Updates and revisions of all 14 existing chapters
• In-depth design examples and explanation of design provisions
Cold-Formed Steel Design, Fourth Edition is a necessary tool-of-the-trade for structural engineers,
manufacturers, construction managers, and architects. It is also an excellent advanced text
for college students and researchers in structural engineering, architectural engineering,
construction engineering, and related disciplines.
the definitive text in the field, thoroughly updated and expanded
WEI-WEN YU, PHD, PE, is Curators’ Professor Emeritus of Civil Engineering at Missouri University of Science and
Technology (formerly, University of Missouri–Rolla) and Founding Director of Wei-Wen Yu Center for Cold-Formed
Steel Structures. He was awarded the 2001 Shortridge Hardesty Award from the ASCE and the 2009 Lynn Beedle
Award from the Structural Stability Research Council.
ROGER A. LABOUBE, PHD, PE, is Curators’ Distinguished Teaching Professor of Civil Engineering at Missouri
University of Science and Technology (formerly, University of Missouri–Rolla) and Director of Wei-Wen Yu Center
for Cold-Formed Steel Structures. Dr. LaBoube is an active member of AISI Committee on Specification and
Committee on Framing Standards, and has an extensive industry and academic background related to the
design and behavior of cold-formed steel structures.
FOURTH EDITION
Cold-Formed
Steel Design
Wei-Wen Yu and Roger A. LaBoube
Yu
LaBoube Cold-Formed Steel Design
F O U R T H
Cover design: Holly Wittenberg EDITION
Cover photographs: Steel Deck Institute, Fox River Grove, IL
Technology/Engineering/Civil
Cold-Formed Steel Design
Cold-Formed Steel Design
Fourth Edition
Wei-Wen Yu
Roger A. LaBoube
Missouri University of Science and Technology
(Formerly University of Missouri-Rolla)
Rolla, Missouri
John Wiley & Sons, Inc.
This book is printed on acid-free paper.
Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical,
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Library of Congress Cataloging-in-Publication Data:
Yu, Wei-wen, 1924-
Cold-formed steel design / Wei-Wen Yu, Roger A. LaBoube. – 4th ed.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-46245-4 (cloth); ISBN 978-0-47074-3 (ebk); ISBN 978-0-47075-0 (ebk); ISBN 978-0-47076-7 (ebk)
1. Building, Iron and steel. 2. Sheet-steel. 3. Thin-walled structures. 4. Steel–Cold working. I. LaBoube, Roger A. II. Title.
TA684.Y787 2010
624.1
821–dc22
2010005153
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
CONTENTS
Preface ix
CHAPTER 1 INTRODUCTION 1
1.1 General Remarks 1
1.2 Types of Cold-Formed Steel Sections and Their Applications 2
1.3 Standardized Metal Buildings and Industrialized Housing 8
1.4 Methods of Forming 12
1.5 Research and Design Specifications 17
1.6 General Design Considerations of Cold-Formed Steel Construction 20
1.7 Economic Design and Optimum Properties 26
CHAPTER 2 MATERIALS USED IN COLD-FORMED STEEL CONSTRUCTION 27
2.1 General Remarks 27
2.2 Yield Stress, Tensile Strength, and Stress–Strain Curve 33
2.3 Modulus of Elasticity, Tangent Modulus, and Shear Modulus 34
2.4 Ductility 34
2.5 Weldability 36
2.6 Fatigue Strength and Toughness 37
2.7 Influence of Cold Work on Mechanical Properties of Steel 37
2.8 Utilization of Cold Work of Forming 40
2.9 Effect of Temperature on Mechanical Properties of Steel 42
2.10 Testing of Full Sections and Flat Elements 43
2.11 Residual Stresses Due to Cold Forming 44
2.12 Effect of Strain Rate on Mechanical Properties 46
CHAPTER 3 STRENGTH OF THIN ELEMENTS AND DESIGN CRITERIA 47
3.1 General Remarks 47
3.2 Definitions of Terms 47
3.3 Design Basis 50
3.4 Serviceability 59
v
vi CONTENTS
3.5 Structural Behavior of Compression Elements and Design Criteria 59
3.6 Perforated Elements and Members 91
3.7 Plate Buckling of Structural Shapes 95
3.8 Additional Information 95
CHAPTER 4 FLEXURAL MEMBERS 97
4.1 General Remarks 97
4.2 Bending Strength and Deflection 97
4.3 Design of Beam Webs 156
4.4 Bracing Requirements of Beams 182
4.5 Torsional Analysis of Beams and Combined Bending and
Torsional Loading 190
4.6 Additional Information on Beams 190
CHAPTER 5 COMPRESSION MEMBERS 191
5.1 General Remarks 191
5.2 Yielding 191
5.3 Flexural Column Buckling 192
5.4 Torsional Buckling and Flexural–Torsional Buckling 194
5.5 Effect of Local Buckling on Column Strength 200
5.6 Distortional Buckling Strength of Compression Members 201
5.7 Effect of Cold Work on Column Buckling 202
5.8 North American Design Formulas for Concentrically Loaded
Compression Members 203
5.9 Effective Length Factor K 207
5.10 Built-Up Compression Members 209
5.11 Bracing of Axially Loaded Compression Members 209
5.12 Design Examples 210
5.13 Compression Members Having One Flange Fastened to Decks or Panels 218
5.14 Wall Studs 220
5.15 Additional Information on Compression Members 221
CHAPTER 6 COMBINED AXIAL LOAD AND BENDING 223
6.1 General Remarks 223
6.2 Combined Tensile Axial Load and Bending 224
6.3 Combined Compressive Axial Load and Bending (Beam–Columns) 225
6.4 North American Design Criteria 232
6.5 Design Examples 235
6.6 Second-Order Analysis 248
6.7 Additional Information on Beam–Columns 249
CHAPTER 7 CLOSED CYLINDRICAL TUBULAR MEMBERS 251
7.1 General Remarks 251
7.2 Types of Closed Cylindrical Tubes 251
7.3 Flexural Column Buckling 251
7.4 Local Buckling 252
7.5 North American Design Criteria 255
7.6 Design Examples 259
CONTENTS vii
CHAPTER 8 CONNECTIONS 263
8.1 General Remarks 263
8.2 Types of Connectors 263
8.3 Welded Connections 263
8.4 Bolted Connections 281
8.5 Screw Connections 292
8.6 Other Fasteners 296
8.7 Rupture Failure of Connections 299
8.8 I- or Box-Shaped Compression Members Made by Connecting
Two C-Sections 299
8.9 I-Beams Made by Connecting Two C-Sections 301
8.10 Spacing of Connections in Compression Elements 304
CHAPTER 9 SHEAR DIAPHRAGMS AND ROOF STRUCTURES 307
9.1 General Remarks 307
9.2 Steel Shear Diaphragms 307
9.3 Structural Members Braced by Diaphragms 319
9.4 Shell Roof Structures 329
9.5 Metal Roof Systems 340
CHAPTER 10 CORRUGATED SHEETS 343
10.1 General Remarks 343
10.2 Applications 343
10.3 Sectional Properties and Design of Arc- and Tangent-Type
Corrugated Sheets 343
10.4 Sectional Properties and Design of Trapezoidal-Type Corrugated Sheets 348
CHAPTER 11 COMPOSITE DESIGN 349
11.1 General Remarks 349
11.2 Steel-Deck-Reinforced Composite Slabs 349
11.3 Composite Beams or Girders with Cold-Formed Steel Deck 350
CHAPTER 12 INTRODUCTION TO STAINLESS STEEL DESIGN 353
12.1 General Remarks 353
12.2 Differences between Specifications for Carbon Steels and Stainless Steels 355
CHAPTER 13 LIGHT-FRAME CONSTRUCTION 359
13.1 General Remarks 359
13.2 Framing Standards 359
13.3 Design Guides 367
CHAPTER 14 COMPUTER-AIDED DESIGN 369
14.1 General Remarks 369
14.2 Computer Programs for Design of Cold-Formed Steel Structures 369
viii CONTENTS
CHAPTER 15 DIRECT-STRENGTH METHOD 371
15.1 General Remarks 371
15.2 North American DSM Provisions 371
15.3 Commentary on Appendix 1 (DSM) 373
15.4 Direct-Strength Method Design Guide 376
15.5 Design Examples 376
APPENDIX A THICKNESS OF BASE METAL 381
APPENDIX B TORSION 383
B.1 Introduction 383
B.2 Shear Center 383
B.3 Torsional Stresses 384
B.4 Design Criteria for Combined Bending and Torsional Loading 393
APPENDIX C FORMULAS FOR COMPUTING CROSS-SECTIONAL PROPERTY βy 395
APPENDIX D DEFINITIONS OF TERMS 397
NOMENCLATURE 401
ACRONYMS AND ABBREVIATIONS 413
CONVERSION TABLE 415
REFERENCES 417
INDEX 483
PREFACE
This fourth edition of the book has been prepared to provide
readers with a better understanding of the analysis and
design of the thin-walled, cold-formed steel structures that
have been so widely used in building construction and other
areas in recent years. It is a revised version of the first
author’s book, Cold-Formed Steel Design, third edition,
published by John Wiley & Sons, Inc. in 2000. All the revisions are based on the 2007 edition of the North American
Specification with Supplement No.1, which combines the
allowable strength design (ASD), the load and resistance
factor design (LRFD), and the limit states design (LSD)
methods.
The material was originally developed for graduate
courses and short courses in the analysis and design of
cold-formed steel structures and is based on experience
in design, research, and development of the American
Iron and Steel Institute (AISI) and North American design
criteria.
Throughout the book, descriptions of the structural
behavior of cold-formed steel members and connections
are given from both theoretical and experimental points
of view. The reasons and justification for the various
design provisions of the North American specification are
discussed at length. Consequently the text not only will be
instructive for students but also can serve as a major source
of reference for structural engineers and researchers.
Of the published book’s 15 chapters, Chapters 1–9
and 13 have been completely revised according to the
combined ASD/LRFD/LSD North American specification
and framing standards. Other chapters have been updated
on the basis of available information. Chapter 15 is a new
chapter on the direct-strength method.
Chapter 1 includes a general discussion of the application
of cold-formed steel structures and a review of previous and
recent research. It also discusses the development of design
specifications and the major differences between the design
of cold-formed and hot-rolled steel structural members.
Because of the many research projects in the field that
have been conducted worldwide during the past 35 years,
numerous papers have been presented at various conferences and published in a number of conference proceedings
and engineering journals. At the same time, new design
criteria have been developed in various countries. These
new developments are reviewed in this chapter.
Since material properties play an important role in the
performance of structural members, the types of steels and
their most important mechanical properties are described
in Chapter 2. In addition to the revision of Table 2.1, new
information on the use of low-ductility steel for concentrically loaded compression members has been included in
Section 2.4. Section 2.6 includes additional information on
fatigue strength.
In Chapter 3, the strength of thin elements and design
criteria are discussed to acquaint the reader with the fundamentals of local buckling and postbuckling strength of thin
plates and with the basic concepts used in design. This
chapter has been completely revised to include detailed
information on design bases for ASD, LRFD, and LSD
with a revised Table 3.1, the unstiffened elements with
stress gradient, the uniformly compressed elements with
intermediate stiffeners, and noncircular holes.
Chapter 4 deals with the design of flexural members.
Because the design provisions were revised extensively
during 2001–2007, this chapter has been completely
rewritten to cover the design of beams using ASD, LRFD,
and LSD methods. It includes new and revised design
information on inelastic reserve capacity of beams with
unstiffened elements, distortional buckling strength, shear
strength of webs, web crippling strength and combination
with bending, bearing stiffeners in C-section beams,
bracing requirements, and beams having one flange
fastened to a standing seam roof system.
ix
x PREFACE
The design procedures for compression members are
discussed in Chapter 5. This chapter has been brought up
to date by including new design information on distortional
buckling strength, built-up members, bracing requirements,
and Z-section members having one flange fastened to a
standing seam roof.
In 2007, the North American specification introduced the
second-order analysis approach as an optional method for
stability analysis. A new Section 6.6 has been added in
Chapter 6 to deal with this alternative method. In addition, revisions have also been made on the design of
beam–columns using ASD, LRFD, and LSD methods.
Chapter 7 covers the design of closed cylindrical tubes.
This revised chapter reflects the rearrangement of design
provisions in the North American specification and minor
changes made in the 2007 edition of the specification.
Like the member design, the design of connections has
been updated in Chapter 8 using the ASD, LRFD, and
LSD methods with additional and revised design provisions for bearing strength between bolts and connected
parts, combined shear and tension in bolts, block shear
strength, revised design information on screw connections,
and power-actuated fasteners.
Because various types of structural systems, such as
shear diaphragms and shell roof structures, have become
increasingly popular in building construction, Chapter 9
contains design information on these types of structural
systems. It includes the new standard for the cantilever
test method for shear diaphragms and the revised design
procedure for wall studs. A new Section 9.5 has been added
for metal roof systems.
The sectional properties of standard corrugated sheets
are discussed in Chapter 10 because they have long been
used in buildings for roofing, siding, and other applications.
Minor revisions have been made in Section 10.4.
Steel decks are widely used in building construction.
Consequently the updated information in Chapter 11 on
their use in steel-deck-reinforced composite slabs and
composite beams is timely.
Chapter 12 contains an introduction to the design of coldformed stainless steel structural members supplementing the
information on cold-formed carbon steel structural members
in other chapters. This chapter has been updated on the basis
of the revised Structural Engineering Institute/American
Society of Civil Engineers (SEI/ASCE) Standard 8-02 and
recent research findings for the design of cold-formed
stainless steel structural members.
During recent years, cold-formed steel members have
been used increasingly for residential and commercial
construction. The previous Chapter 14 has been completely
rewritten based on new and revised framing standards. This
chapter has been changed to Chapter 13 using the new title
of Light-Frame Construction.
The increasing use of computers for design work
warrants the brief introduction that is given in the revised
Chapter 14 for the computer-aided design of cold-formed
steel structures.
In 2004, a new Appendix 1 was added in the North American specification for the use of the direct-strength method
to determine the nominal axial strength for columns and
flexural strength for beams. These alternative design procedures are discussed in the new Chapter 15. Also discussed
in this chapter are the Commentary on Appendix 1,
the Direct Strength Method Design Guide, and design
examples.
It is obvious that a book of this nature would not have
been possible without the cooperation and assistance of
many individuals, organizations, and institutions. It is based
primarily on the results of continuing research programs on
cold-formed steel structures that have been sponsored by
the American Iron and Steel Institute (AISI), the ASCE,
the Canadian Sheet Steel Building Institute (CSSBI), the
Cold-Formed Steel Engineers Institute (CFSEI) of the Steel
Framing Alliance (SFA), the Metal Building Manufacturers
Association (MBMA), the Metal Construction Association
(MCA), the National Science Foundation (NSF), the Rack
Manufacturers Institute (RMI), the Steel Deck Institute
(SDI), the Steel Stud Manufacturers Association (SSMA),
and other organizations located in the United States and
abroad. The publications related to cold-formed steel structures issued by AISI and other institutions have been very
helpful for the preparation of this book.
The first author is especially indebted to his teacher,
the late Professor George Winter of Cornell University,
who made contributions of pronounced significance to the
building profession in his outstanding research on coldformed steel structures and in the development of AISI
design criteria. A considerable amount of material used in
this book is based on Dr. Winter’s publications.
Our sincere thanks go to Mr. Robert J. Wills, Vice
President, Construction Market Development, Steel Market
Development Institute (a business unit of the American Iron
and Steel Institute), for permission to quote freely from
the North American Specification, Commentary, Design
Manual, Framing Standards, Design Guides, and other AISI
publications. An expression of appreciation is also due to
the many organizations and individuals that granted permission for the reproduction of quotations, graphs, tables, and
photographs. Credits for the use of such materials are given
in the text.
We wish to express our sincere thanks to Mr. Don Allen,
Mr. Roger L. Brockenbrough, Dr. Helen Chen, Mr. Jay W.
Larson, Professor Teoman B. Pekoz, Professor Benjamin
PREFACE xi
W. Schafer, Professor Reinhold M. Schuster and Professor
Cheng Yu for their individual reviews of various parts of
the manuscript. Their suggestions and encouragement have
been of great value to the improvement of this book.
We are very grateful to Mrs. Christina Stratman for her
kind assistance in the preparation of this book. Thanks are
also due to Miss Domenica Cambio and Miss Mingyan
Deng for their careful typing and preparation of drawings. The financial assistance provided by the Missouri
University of Science and Technology through the first
author’s Curators’ Professorship and the sponsors for the
Wei-Wen Yu Center for Cold-Formed Steel Structures is
appreciated.
This book could not have been completed without the
help and encouragement of the authors’ wives, Yuh-Hsin
Yu and Karen LaBoube, as well as for their patience,
understanding, and assistance.
Wei-Wen Yu
Roger A. LaBoube
Rolla, Missouri
March 2010
Cold-Formed Steel Design