STRUCTURAL STABILITY OF STEEL: CONCEPTS AND APPLICATIONS FOR STRUCTURAL ENGINEERS Structural Stability of Steel: Concepts and Applications for Structural Engineers Theodore V. Galambos Andrea E. Surovek Copyright 2008 John Wiley & Sons, Inc.
STRUCTURAL STABILITY OF STEEL: CONCEPTS AND APPLICATIONS FOR STRUCTURAL ENGINEERS THEODORE V. GALAMBOS ANDREA E. SUROVEK JOHN WILEY & SONS, INC.
This book is printed on acid-free paper. 1 Copyright # 2008 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, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the Web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at www.wiley.com/go/permissions. Limit of Liability/Disclaimer of Warranty: While the publisher and the author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor the author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information about our other products and services, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our Web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Galambos, T. V. (Theodore V.) Structural stability of steel : concepts and applications for structural engineers / Theodore Galambos, Andrea Surovek. p. cm. Includes bibliographical references and index. ISBN 978-0-470-03778-2 (cloth) 1. Building, Iron and steel Congresses. 2. Structural stability Congresses. I. Surovek, Andrea. II. Title. TA684.G26 2005 624.1 0 821 dc22 ISBN: 978-0-470-03778-2 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 2007035514
CONTENTS PREFACE ix CHAPTER 1 FUNDAMENTALS OF STABILITY THEORY 1 1.1 Introduction 1 1.2 Basics of Stability Behavior: The Spring-Bar System 3 1.3 Fundamentals of Post-Buckling Behavior 7 1.4 Snap-Through Buckling 18 1.5 Multi-Degree-of-Freedom Systems 20 1.6 Summary 23 Problems 24 CHAPTER 2 ELASTIC BUCKLING OF PLANAR COLUMNS 28 2.1 Introduction 28 2.2 Large-Deflection Solution of an Elastic Column 29 2.3 Differential Equation of Planar Flexure 32 2.4 The Basic Case: Pin-Ended Column 36 2.5 Five Fundamental Cases 39 2.6 The Effect of Imperfections 43 2.7 Stability of a Rigid Frame 52 2.8 End-Restrained Columns 55 2.9 Restrained Column Examples 62 2.10 Continuously Restrained Columns 74 2.11 Summary 80 Problems 80 Appendix 85 CHAPTER 3 INELASTIC COLUMN BUCKLING 87 3.1 Tangent and Reduced Modulus Concepts 87 3.2 Shanley s Contribution 93 3.3 Example Illustrating the Tangent Modulus and the Reduced Modulus Concepts 98 3.4 Buckling Strength of Steel Columns 101 3.5 Illustration of the Effect of Residual Stresses on the Buckling Strength of Steel Columns 103 v
vi CONTENTS 3.6 Effect of Initial Out-of-Straightness and Load Eccentricity 108 3.7 Design Formulas For Metal Columns 123 3.8 Summary 130 Problems 131 CHAPTER 4 BEAM-COLUMNS 134 4.1 Introduction 134 4.2 General Discussion of the Behavior of Beam-Columns 135 4.3 Elastic In-Plane Behavior of Beam-Columns 138 4.4 Elastic Limit Interaction Relationships 147 4.5 Example Problems of Beam-Column Strength 149 4.6 Systematic Methods of Analysis: Flexibility Method 159 4.7 Systematic Methods of Analysis: The Stiffness Method 170 4.8 Inelastic Strength of Beam-Columns 186 4.9 Design of Beam-Columns 197 Problems 199 CHAPTER 5 FRAME STABILITY 203 5.1 Introduction 203 5.2 Two-Bay Frame Examples 206 5.3 Summary 230 5.4 Selected References on Frames with Partially Restrained Joints 231 Problems 232 CHAPTER 6 LATERAL-TORSIONAL BUCKLING 236 6.1 Introduction 236 6.2 Basic Case: Beams Subjected to Uniform Moment 237 6.3 The Effect of Boundary Conditions 246 6.4 The Effect of Loading Conditions 249 6.5 Lateral-Torsional Buckling of Singly-Symmetric Cross-Sections 259 6.6 Beam-Columns and Columns 270 6.7 Inelastic Lateral-Torsional Buckling 278 6.8 Summary 288 Problems 289
CONTENTS vii CHAPTER 7 BRACING 290 7.1 Introduction 290 7.2 Discrete Bracing 292 7.3 Relative Bracing 297 7.4 Lean-on Bracing 299 7.5 Effects of Imperfections 300 7.6 Column Bracing Provisions 302 7.7 Beam Bracing 306 7.8 AISC Design Provisions for Beam Bracing 308 7.9 Summary 314 Suggested Reading 315 Problems 315 CHAPTER 8 SPECIFICATION-BASED APPLICATIONS OF STABILITY IN STEEL DESIGN 318 8.1 Introduction 318 8.2 Development of the Beam-Column Interaction Equations 319 8.3 Assessment of Column Strength 323 8.4 Assessment of Beam Strength 324 8.5 Specification-Based Approaches for Stability Assessment 330 8.6 Effective Length Factors, K-factors 344 8.7 Design Assessment by Two Approaches 354 8.8 Frame Design Requirements in Canada and Europe 359 8.9 Summary 361 Problems 361 REFERENCES 364 INDEX 369
PREFACE In order to truly understand the behavior and design of metal structures, an engineer needs to have a fundamental understanding of structural stability. More so than structures designed using other construction materials, steel structures are governed to a great extent on stability limit states. All major international design specifications include provisions based on stability theory. The purpose of this book is to provide students and practicing engineers with both the theory governing stability of steel structures and a practical look at how that theory translates into design methodologies currently implemented in steel design specifications. The topics presented in the text pertain to various aspects of elastic buckling and inelastic instability. An understanding of stability limits is very important in the design of structures: Catastrophic failures can, and tragically have, resulted from violating fundamental principles of stability in design. Maintaining stability is particularly important during the erection phase of construction, when the structural skeleton is exposed prior to the installation of the final stabilizing features, such as slabs, walls and/or cladding. The book contains a detailed treatment of the elastic and inelastic stability analysis of columns, beams, beam-columns, and frames. In addition, it provides numerous worked examples. Practice problems are included at the end of each chapter. The first six chapters of this book are based on lecture notes of the first author, used in his teaching of structural engineering graduate courses since 1960, first at Lehigh University in Bethlehem, Pennsylvania, (1960 1965), then at Washington University in St. Louis, Missouri, (1966 1981), and finally at the University of Minnesota in Minneapolis, Minnesota. The genesis of the course material was in lectures at Lehigh University given by Professors Bruce Johnston, Russell Johnson, and Bruno Thurlimann in the 1950s. The material in the last two chapters is concerned with the application of stability theory in the practical design of steel structures, with special emphasis on examples based on the 2005 Specification for Structural Steel Buildings of the American Institute of Steel Construction (AISC). Chapter 7 is based heavily on the work performed by Professors Joe Yura and Todd Helwig of the University of Texas in developing Appendix 6 of the 2005 AISC Specification. A portion of the material in Chapter 8 is based on the work of the second author and Professor Don White of Georgia Tech, as well as verification studies and design examples developed by members of AISC TC 10, chaired by Dr. Shankar Nair. The material in the book is suitable for structural engineering students at the graduate level. It is also useful for design engineers who wish to ix
x PREFACE understand the background of the stability design criteria in structural specifications, or for those who may have a need to investigate special stability problems. Since the fundamental mechanics governing the behavior of beams, columns, beam-columns, and frames is discussed in the book, it is also useful for an international structural engineering constituency. A background in both structural analysis approaches and differential equations is essential in understanding the derivations included in the first six chapters. Chapter 1 is an introduction to the principles of stability theory. The various aspects of behavior at the limits of instability are defined on hand of simple spring-bar examples. Chapter 2 deals with the stability of axially loaded planar elastic systems. Individual columns, simple frames, and subassemblies of members are analyzed. The background for the effective length concept of designing metal structures is also presented. Chapter 3 expands the analysis to the nonlinear material behavior. Tangent modulus, reduced modulus, and maximum strength theories are introduced. Derivations are presented that lead to an understanding of modern column design formulas in structural codes. The subject of Chapter 4 is the elastic and inelastic stability limit of planar beam-columns. Various aspects of the interaction between axial force and bending moment are presented, and the interaction formulas in design specifications are evaluated. Chapter 5 illustrates many features of elastic and inelastic instability of planar frames using as example a one-story two-bay structure. In Chapter 6 the out-of-plane lateral-torsional buckling of beams, columns, and beam-columns is presented. Since stability of the structure is vitally dependent on the strength and stiffness of the bracing systems that are provided during erection and in the final stage of construction, Chapter 7 is devoted entirely to this subject. Modern design standards for structural steel design require an analysis procedure that provides stability through the direct inclusion of the destabilizing effects of structural imperfections, such as residual stresses and unavoidable out-of-plumb geometry. The topic of Chapter 8 is the analysis and design of steel frames according to the 2005 Specification of the AISC.