Hancock G.J., Murray Th.M., Ellifritt D.S. Cold-Formed Steel Structures to the AISI Specification
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ISBN: 0-8247-9294-7
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Preface
This book describes the structural behavior and design of
cold-formed steel structural members, connections, and
systems. Cold-formed members are often more dif®cult to
design than conventional hot-rolled members because of
their thinness and the unusual shapes that can be roll-
formed. Design engineers familiar with hot-rolled design
can sometimes ®nd cold-formed design a daunting task.
The main objective of this book is to provide an easy
introduction to the behavior of cold-formed members and
connections with simple worked examples. Engineers
familiar with hot-rolled design should be able to make the
step to cold-formed design more easily using this text. The
book is in line with the latest edition of the American Iron
and Steel Institute (AISI) Speci®cation for the Design of
Cold-Formed Steel Structural Members (1996), including
the latest amendment (Supplement 1 1999) published in
July 2000.
iii
The book describes the main areas of cold-formed
members, connections, and systems in routine use today.
It presents the history and applications of cold-formed steel
design in Chapter 1, cold-formed steel materials in Chapter
2, and buckling modes of thin-walled members in Chapter
3. These three chapters provide a basic understanding of
how cold-formed steel design differs from hot-rolled steel
design. Chapters 4 to 9 follow the approach of a more
conventional text on structural steel design, with Chapter
4 on elements, Chapter 5 on ¯exural members, Chapter 6
on webs, Chapter 7 on compression members, Chapter 8 on
combined compression and bending, and Chapter 9 on
connections. Chapters 10 and 11 apply the member
design methods to common systems in which cold-formed
steel is used, roof and wall systems in Chapter 10 and steel
storage racks in Chapter 11. Chapter 12 gives a glimpse
into the future of cold-formed steel design where the direct
strength method is introduced. This method based on the
®nite strip method of structural analysis introduced in
Chapter 3 and currently under consideration by the AISI
Speci®cation Committee, gives a simpler and more direct
approach to design than the current effective width
approach. Residential framing is not covered in a separate
chapter since the design methods in Chapters 4 to 9 are
appropriate for members and connections used in wall
framing and roof trusses.
The book has been based on a similar one, Design of
Cold-Formed Steel Structures, written by the ®rst author
and published by the Australian Institute of Steel
Construction in 1988, 1994, and 1998 with design to the
Australian=New Zealand Standard AS=NZS 4600, which is
similar to the AISI Speci®cation. The Australian book is
completely in SI units to the Australian standard, whereas
this book is written in U.S. customary units to the AISI
speci®cation.
The worked examples in Chapters 4±8, 10 and 11 have
all been programmed as MATHCAD
TM
spreadsheets to
Preface
iv
ensure their accuracy. Hence, the numerical values quoted
in these chapters are taken directly from MATHCAD
TM
and have been rounded to the appropriate number of
signi®cant ®gures at each output. Rounding is therefore
not included in the computation as it would be if the values
were rounded progressively as is done in manual calcula-
tions. The ®nal values quoted in the book at the end of the
examples can therefore be compared directly with those
obtained using other computer software.
The book has involved substantial work to convert it
from the Australian version, with new Chapters 1 and 10
being written by the third and second authors, respectively.
The text was typed by Gwenda McJannet, and the draw-
ings were prepared by Mr. Ron Brew and Ms. Kim Pham,
all at the University of Sydney. We are grateful to these
people for their careful work. The ®rst author is grateful for
the advice on cold-formed steel design from Professor
Teoman Peko
È
z at Cornell University and Emeritus Profes-
sor Wei-Wen Yu at the University of Missouri±Rolla over
many years.
The assistance of Dr. Ben Schafer at Johns Hopkins
University with Chapter 12 is appreciated.
Gregory J. Hancock
Thomas M. Murray
Duane S. Ellifritt
Preface
v
Contents
Preface v
1. Introduction 1
1.1 De®nition 1
1.2 Brief History of Cold-Formed Steel Usage 1
1.3 The Development of a Design Standard 2
1.4 History of Cold-Formed Standards 3
1.5 Common Section Pro®les and Applications of
Cold-Formed Steel 5
1.6 Manufacturing Processes 13
1.6.1 Roll Forming 13
1.6.2 Brake Forming 14
1.7 General Approach to the Design of Cold-Formed Sections 16
1.7.1 Special Problems 16
1.7.2 Local Buckling and Post-Local Buckling of Thin
Plate Elements 16
1.7.3 Effective Width Concept 17
1.7.4 Propensity for Twisting 20
vii
1.7.5 Distortional Buckling 20
1.7.6 Cold Work of Forming 22
1.7.7 Web Crippling Under Bearing 23
1.7.8 Connections 24
1.7.9 Corrosion Protection 26
1.7.10 Inelastic Reserve Capacity 27
1.8 Two Design Methods 27
1.8.1 Allowable Stress Design 28
1.8.2 Load and Resistance Factor Design 28
1.9 Load Combinations 29
References 30
2. Materials and Cold Work of Forming 33
2.1 Steel Standards 33
2.2 Typical Stress±Strain Curves 37
2.3 Ductility 41
2.4 Effects of Cold Work on Structural Steels 46
2.5 Corner Properties of Cold-Formed Sections 49
2.6 Fracture Toughness 52
References 54
3. Buckling Modes of Thin-Walled Members in Compression
and Bending 57
3.1 Introduction to the Finite Strip Method 57
3.2 Singly-Symmetric Column Study 60
3.2.1 Unlipped Channel 60
3.2.2 Lipped Channel 64
3.2.3 Lipped Channel (Fixed Ended) 69
3.3 Purlin Section Study 71
3.3.1 Channel Section 71
3.3.2 Z-Section 73
3.4 Hollow Flange Beam in Bending 74
References 76
4. Stiffened and Unstiffened Compression Elements 79
4.1 Local Buckling 79
4.2 Postbuckling of Plate Elements in Compression 81
Contents
viii
4.3 Effective Width Formulae for Imperfect Elements
in Pure Compression 84
4.4 Effective Width Formulae for Imperfect Elements Under
Stress Gradient 89
4.4.1 Stiffened Elements 89
4.4.2 Unstiffened Elements 90
4.5 Effective Width Formulae for Elements with Stiffeners 90
4.5.1 Edge-Stiffened Elements 90
4.5.2 Intermediate Stiffened Elements with One
Intermediate Stiffener 93
4.5.3 Intermediate Stiffeners for Edge-Stiffened Elements
with an Intermediate Stiffener, and Stiffened
Elements with More than One Intermediate
Stiffener 93
4.6 Examples 95
4.6.1 Hat Section in Bending 95
4.6.2 Hat Section in Bending with Intermediate Stiffener
in Compression Flange 100
4.6.3 C-Section Purlin in Bending 106
4.6.4 Z-Section Purlin in Bending 115
References 124
5. Flexural Members 127
5.1 General 127
5.2 Torsional-Flexural (Lateral) Buckling 129
5.2.1 Elastic Buckling of Unbraced Simply Supported
Beams 129
5.2.2 Continuous Beams and Braced Simply Supported
Beams 134
5.2.3 Bending Strength Design Equations 141
5.3 Basic Behavior of C- and Z-Section Flexural Members 142
5.3.1 Linear Response of C- and Z-Sections 142
5.3.1.1 General 142
5.3.1.2 Sections with Lateral Restraint Only 143
5.3.1.3 Sections with Lateral and Torsional
Restraint 145
5.3.2 Stability Considerations 148
5.4 Bracing 153
5.5 Inelastic Reserve Capacity 155
Contents
ix
5.5.1 Sections with Flat Elements 155
5.5.2 Cylindrical Tubular Members 157
5.6 Example: Simply Supported C-Section Beam 158
References 163
6. Webs 167
6.1 General 167
6.2 Webs in Shear 168
6.2.1 Shear Buckling 168
6.2.2 Shear Yielding 170
6.3 Webs in Bending 172
6.4 Webs in Combined Bending and Shear 174
6.5 Web Stiffeners 176
6.6 Web Crippling 176
6.6.1 Edge Loading Alone 176
6.6.2 Combined Bending and Web Crippling 179
6.7 Webs with Holes 182
6.8 Example: Combined Bending with Web Crippling
of Hat Section 184
References 186
7. Compression Members 189
7.1 General 189
7.2 Elastic Member Buckling 190
7.3 Stub Column Axial Strength 194
7.4 Long Column Axial Strength 195
7.5 Effect of Local Buckling of Singly-Symmetric Sections 198
7.6 Examples 202
7.6.1 Square Hollow Section Column 202
7.6.2 Unlipped Channel Column 205
7.6.3 Lipped Channel Column 210
References 220
8. Members in Combined Axial Load and Bending 221
8.1 Combined Axial Compressive Load and Bending:
General 221
8.2 Interaction Equations for Combined Axial Compressive
Load and Bending 223
Contents
x