Plastic Design and Second-Order Analysis of Steel Frames

519 Pages·2011·13.5 MB·English

Plastic Design and
Second-Order Analysis of
Steel Frames
W.F. Chen I. Sohal
Plastic Design and
Second-Order Analysis
of Steel Frames
With 312 illustrations
Includes two diskettes
Springer-Verlag
New York Berlin Heidelberg London Paris
Tokyo Hong Kong Barcelona Budapest
W.F.Chen I. Sohal
Department of Structural Engineering Department of Civil Engineering
Civil Engineering Bldg. Rutgers University
Purdue University Piscataway, NJ 08855
West Lafayette, IN 47907 USA
USA
Library of Congress Cataloging-in-Publication Data
Chen, Wai-Fah, 1936-
Plastic design and second-order analysis of steel frames / W.F.
Chen, 1. Sohal.
p. cm.
Includes bibliographical references and index.
ISBN-13:978-1-4613-8430-4
1. Structural frames--Design. 2. Plastic analysis (Engineering)
3. Steel, Structural. I. Sohal, I. II. Title.
TA660.F7C44 1994
624.1'S21--dc20 94-11614
Printed on acid-free paper.
© 1995 Springer-Verlag New York Inc.
Softcover reprint of the hardcover 1st edition 1995
All rights reserved. This work may not be translated or copied in whole or in part without the
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Production managed by Karen Phillips; manufacturing supervised by Gail Simon.
Typeset by Asco Trade Typesetting Ltd., Hong Kong.
9 S 7 6 543 2 1
ISBN -13:978-1-4613-8430-4 e-ISBN -13:978-1-4613-8428-1
DOl: 10.1007/978-1-4613-8428-1
To our families
Preface
This book grew out of lectures which the senior author gave for a number of
years to graduate students of structural engineering at Purdue University. Its
primary purpose is to present the basic concept and methods of analysis of
plastic theory, show how to use the theory in practical frame design, and
discuss how the practical design rules in the AISC-LRFD specifications are
related to theoretical considerations. These include the effect of axial load
and shear force on plastic moment capacity, frame, member and local insta
bility, and the significance of connection detailing in plastic design. Emphasis
upon these and other design problems commences in Chapter 2 ("Plastic
Hinges") and continues in Chapter 4 ("Equilibrium Method") and in Chapter
5 ("Work Method") where the design examples are given and calculations are
made as complete as possible. The methods described in the first six chapters
are suitable for hand calculations. Chapter 7 presents a computer-based
method for the first-order plastic hinge-by-hinge analysis for frame design.
The computer program FOPA developed and provided in this chapter can
be used by students to check their homework problems given at the end of
each chapter in a direct manner.
The advent of personal computers, particularly in the computing and
graphics performance of engineering workstations, has made more sophisti
cated methods of analysis feasible in design practice. While the use of first
order analysis for elastic or plastic design is still the norm of engineering
practice, a new generation of codes has emerged which recommends the
second-order theory as the preferred method of analysis (AISC-LRFD, 1993).
The advantage of using second-order theory for design practice is that the
effect of lateral deflections of a structure under loading upon the overall
geometry can be accounted for in a direct and more accurate manner. The
result is more realistic and economical design. For this reason, Chapter 8
provides a compact and convenient summary of the second-order plastic
hinge-by-hinge analysis methods suitable for computer application. This
chapter also attempts to take stock of where the structural engineering pro
fession stands with regard to direct analysis of inelastic strength and stability
for frame design, and where it might be going. Included with the text are
vii
viii Preface
two diskettes containing two computer programs: one for Chapter 7 (FOPA)
and the other for Chapter 8 (PHINGE). Both the menu-driven, user-friendly
programs capable of tracing every plastic hinge formation throughout the
entire range of loading up to plastic collapse (Chapter 7) or stability failure
(Chapter 8).
In writing this book, we have endeavored to present the plastic methods in
as simple a manner as possible. It also serves as an introduction to the
second-order theory for inelastic frame design. Attention is directed to both
analysis and design, and emphasis is placed on the physical significance of the
various calculations involved. The book is aimed squarely for students of
structural engineering who are familiar with the processes of elastic analysis
and design of building frames. The first six chapters present the fundamental
concepts, theorems, and the plastic methods of analysis and design; numer
ous examples suitable for hand calculation are included for illustration, and
suitable problems provided at the end of each chapter for the student. The
last two chapters are concerned specifically with the computer-based analysis
methods for frame design. Here, for second-order inelastic analysis (Chapter
8) only an introduction to this quite difficult subject is given. It combines the
structural stability theory with the plastic theory described in this book. The
AISC-LRFD provisions for the use of plastic theory in practical design are
the basis for the solution of various practical building frame design problems
developed in the book.
The two computer programs were developed by Dr. M. Abdel-Ghaffar
(Chapter 7) and Dr. R.J.Y. Liew (Chapter 8) as a part of their Ph.D. thesis
work in the School of Civil Engineering at Purdue University for the research
project entitled "Second-Order Inelastic Analysis for Frame Design" spon
sored by the National Science Foundation (Dr. Ken Chong, Program
Director).
Dr. Sohal wishes to thank his Department Chairman Yong S. Chae, for
reducing the teaching load for a few semesters; Dean Ellis H. Dill, for his
encouragement; and his teachers, students, colleagues, friends, computer and
administrative staff, laboratory technicians, AAUP, research and sponsored
programs personnel, secretaries, neighbors and the family, for their technical
and personal support. Particularly, he is indebted to Dr. Pritam and Rupinder
Dhillon, Dr. Rakesh and Madhu Kapania, Ms. Jessica K. Dembski, Drs. J.
Wiesenfeld, L.S. Beedle, M. Shinozuka, T.Y. Galambos, D.R. Sherman, R.
Bjorhovde, S.c. Goel, S. Sridharan, S.T. Mau, J.T.P. Yao, J.T. Gaunt, V.J.
Meyers, A.F. Grandt, Jr., T.Y. Yang, R.H. Lee, Donald White, K.c. Sinha,
K.L. Bhanot, M.S. Ghuman, A.F. Saleeb, Eric M. Lui, Y. Ohtani, W.O.
McCarron, Susan Pritchard, M. Taheri, Andrew J. Hinkle, Bernard Stahl,
Nipen Saha, Ers. Robinder S. Sandhu, Gopal Gupta, Harjinder Singh,
Gursharan Wason, Pushpinder Singh, Bhagwan D. Garg, Ajay Garg, Tarsem
Lal Dhall, Daljit Mand and Dr. Harjit Bhatia, for their informal academic
and personal support. Special thanks are due to Drs. Eiki Yamaguchi, Lian
Duan, W.S. King, Mrs. Liping Cai, Messrs, John Sayler, Rajesh Mankani,
Preface
IX
Edward Gray and Seeth Ramakrishnan, who contributed to the examples
and solution of the problems in this book, through their home works. He will
also like to thank Messrs. Ashish Patel, Ghassan Habib, Peter Tardy, Jae
Chung, Gwo-Gong Huang, Shay Burrows, Mohammed EI-Hawwat, Young
Cho, David Brill, Nadeem Syed, Satvinder Singh, Mark Palus, Michael
Steiner, David Stanger, Drs. Anil Khajuria, James Stewart, Ahmed Ezeldin,
Zheng Zang, Benxian Chen, Luis Aguiar, Ms. Kristi Latimer, Ms. Gargi
Shah and several others; who participated in useful discussions on the text,
during their structural analysis and design classes at Rutgers University.
West Lafayette, IN W.F.Chen
I.S. Sohal
Contents
Preface vii
Chapter 1 Basic Concepts 1
1.1 Plastic Design vs. Elastic Design 1
1.2 The Ductility of Steel 3
1.3 Moment-Curvature Relationship 7
1.4 Flexure of a Fixed-Ended Beam with Uniformly
Distributed Load 15
1.5 Margin of Safety in Plastic Design with Load
Factor 18
1.6 A Brief Historical Account of Plastic Design 21
1.7 Current and Future Design Philosophies 22
1.8 Examples 27
1.9 Summary 34
References 36
Problems 37
Chapter 2 The Plastic Hinge 42
2.1 Introduction 42
2.2 Moment-Curvature Relationship and Plastic Hinge
Length 42
2.3 The Full Plastic Moment 51
2.4 Design of Cross Section 54
2.5 Effect of Axial Load 58
2.6 Effect of Shear Force 65
2.7 Effect of Combined Axial and Shear Force 71
2.8 Compactness 71
2.9 Connections 77
2.10 Examples 93
2.11 Summary 114
References 115
Problems 116
xi
Contents
Xli
Chapter 3 The Tools Used in Plastic Analysis and Design 120
3.1 Introduction 120
3.2 The Assumption of Ductility of Steel 120
3.3 The Assumption on Small Changes in Geometry of
Structures 124
3.4 The Equation of Virtual Work 125
3.5 The Fundamental Theorems 133
3.6 Upper- and Lower-Bound Solutions Based on the Limit
Theorem 140
3.7 Illustrative Examples 144
3.8 Summary 151
References 153
Problems 154
Chapter 4 Equilibrium Method 157
4.1 Introduction 157
4.2 Basis of the Method 158
4.3 Moment Equilibrium Equations 159
4.4 Mechanism Check 160
4.5 Design of Simple Beams 164
4.6 Design of Portal Frames 177
4.7 Practical Procedure for Large Structures 188
4.8 Examples of Portal and Gable Frames 206
4.9 Summary 217
References 218
Problems 218
Chapter 5 Work Method 223
5.1 Introduction 223
5.2 Basis of the Method 224
5.3 Work Equation 224
5.4 Moment Check 231
5.5 Design of Rectangular Portal Frame 237
5.6 Calculation of Geometrical Relations 241
5.7 Gable Frames 247
5.8 The Combination of Mechanisms 258
5.9 Multi-Story and Multi-Bay Frames 267
5.10 Distributed Loads 292
5.11 Examples For Distributed Loads 299
5.12 Summary 321
References 323
Problems 323
Chapter 6 Estimate of Deflections 331
6.1 Introduction 331
6.2 Deflections at Collapse and Working Loads 331
6.3 Slope Deflection Method 332
Contents xiii
6.4 Dummy Load Method 337
6.5 The Deflection Theorem 341
6.6 Simple Beams 342
6.7 Simple Frames 346
6.8 Multi-Story and Multi-Bay Frames 359
6.9 Rotational Capacity Requirement 364
6.10 Examples 368
6.11 Summary 378
References 379
Problems 380
Chapter 7 First-Order Hinge-by-Hinge Analysis 381
7.1 Introduction 381
7.2 Stiffness Matrix of Elastic Beam-Element 382
7.3 Stiffness Matrix for a Beam Element with Plastic Hinge at
End A 385
7.4 Stiffness Matrix for a Beam Element with Plastic Hinge at
End B 386
7.5 Plastic Hinges at Both Ends A and B 387
7.6 Stiffness Matrix for a Beam with an Intermediate Plastic
Hinge 387
7.7 Numerical Procedure for First-Order Plastic Analysis 391
7.8 Numerical Examples 392
7.9 Summary and Conclusions 414
References 415
Appendix 416
M. Abdel-GhafJar
Chapter 8 Second-Order Plastic Hinge Analysis 425
J. Y. Richard Liew and W.F. Chen 425
8.1 Introduction
8.2 Modeling of Elastic Beam-Column Element 428
8.3 Modeling of Truss Elements 435
8.4 Modeling of Plastic Hinges 437
8.5 Limitations of Elastic-Plastic Hinge Models for Advanced
Analysis 441
8.6 Desirable Attributes for Plastic-Hinge-Based Advanced
Analysis 446
8.7 Approximate Effects of Distributed Yielding 448
8.8 Modeling of Semirigid Frames 458
8.9 Computer Program-PHINGE 467
8.10 Analysis of a One-Story Portal Frame 482
8.11 Analysis of a Semirigid Braced Frame 490
References 494
Problems 496
Index 503