Fundamentals of Structural Analysis PDF

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lee01099_EP_front.qxp 8/10/10 1:26 PM Page b Table 1: Moment Diagrams and Equations for Maximum Deflection P 1 w 5 ⌬MAX ⌬MAX L a L wL wL Pa a wL2 L P1+ 2 2 L 8 M M –Pa 5wL4 Pa2 ⌬MAX = ⌬MAX = (L + a) 384EI 3EI 2 P 6 L w 2 ⌬MAX wL2 ⌬MAX wL2 12 L 12 L wL wL P PL P 2 wL2 2 2 4 2 24 M M wL2 wL2 – – PL3 ...

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Table 1: Moment Diagrams and Equations for Maximum Deflection 1

P

5

w

⌬MAX

⌬MAX wL 2

Pa L

wL 2

wL2 8 ⌬MAX =

M

5wL4 384EI

⌬MAX =

L

M

PL3

⌬MAX =

48EI

P

P

a

–

⌬MAX

wL2 12

L

384EI

P

⌬MAX

P 2

PL 8

P Pa M

–

Pa (3L2 – 4a2) 24EI

P

4

PL 8

8

⌬MAX P

PL

L

PL3 ⌬MAX = 3EI

PL 8

P 2

L

P

⌬MAX =

M wL2 – 12

wL4

⌬MAX = L 2

PL 8

wL 2

wL2 24

7

a

wL2 12

⌬MAX L wL 2

P 2

PL 4

–Pa

w

wL2 12

⌬MAX

3

Pa2 (L + a) 3EI

6

L 2

P 2

a L

P1+

M

P

2

a

L

L

⌬MAX =

M PL – 8

PL3 192EI

w ⌬MAX

wL2 2

wL L

M = – PL

wL4 ⌬MAX = 8EI

–

wL2 =M 2

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Table 2: Fixed-End Moments 1

–

PL 8

6

P

L 2

FEMAB

w

FEMBA

A

B

+

5wL2 96

–

PL 8

A

L

L 2

L 2

w

L 2

7

2 a –

Pb2a L2

P

b

A

B

+

Pba2 L2

–

11wL2 192

A

B

+

5wL2 96

B

+

5wL2 192

B

+

2EI␪ L

L

L

8

3 L 3 –

2PL 9

P

P

A

4EI␪ + L

L 3 B

+

␪

2PL 9

6EI␪ L2

L

9 w wL2 12

A

6EI␪ L2 L

4

–

␪B = 0

A

␪A = 0 –

B

+

wL2 12

6EI⌬ L2

⌬

A

␪B = 0 B

12EI⌬ L3

–

6EI⌬ L2

12EI⌬ L3

L L

5

10 +

w

–

wL2 20

A

B L

+

wL2 30

Mb (2a – b) L2 A

+

M B a

b L

Ma (2b – a) L2

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Fundamentals of Structural Analysis

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Fundamentals of Structural Analysis Fourth Edition

Kenneth M. Leet Professor Emeritus, Northeastern University

Chia-Ming Uang Professor, University of California, San Diego

Anne M. Gilbert Adjunct Assistant Professor, Yale University

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FUNDAMENTALS OF STRUCTURAL ANALYSIS, FOURTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. Previous editions © 2008, 2005, and 2002. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 DOC/DOC 1 0 9 8 7 6 5 4 3 2 1 0 ISBN 978-0-07-340109-6 MHID 0-07-340109-9 Vice President & Editor-in-Chief: Marty Lange Vice President EDP / Central Publishing Services: Kimberly Meriwether David Global Publisher: Raghothaman Srinivasan Senior Sponsoring Editor: Peter E. Massar Senior Marketing Manager: Curt Reynolds Developmental Editor: Lorraine K. Buczek Project Manager: Robin A. Reed Design Coordinator: Margarite Reynolds Senior Photo Research Coordinator: John C. Leland Cover Image: T.Y. Lin International China; lighting design: Tianjin Huadeng Design and Construction Company Buyer: Kara Kudronowicz Media Project Manager: Yeswini Devdutt Compositor: RPK Editorial Services Typeface: 10/12 Times Roman Printer: R. R. Donnelley All credits appearing on page or at the end of the book are considered to be an extension of the copyright page. Library of Congress Cataloging-in-Publication Data Leet, Kenneth. Fundamentals of structural analysis / Kenneth M. Leet, Chia-Ming Uang, Anne M. Gilbert. — 4th ed. p. cm. ISBN 0-07-340109-9 1. Structural analysis (Engineering) I. Uang, Chia-Ming. II. Gilbert, Anne. III. Title. TA645.L34 2011 624.1⬘71—dc22 www.mhhe.com

2010025917 CIP

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ABOUT THE AUTHORS

Kenneth Leet is a Professor Emeritus of structural engineering at Northeastern University. He received his Ph.D. in structural engineering from the Massachusetts Institute of Technology. As a professor of civil engineering at Northeastern University, he taught graduate and undergraduate courses in reinforced concrete design, structural analysis, foundations, plates and shells, and capstone courses on comprehensive engineering projects for over thirty years. Professor Leet was given an Excellence in Teaching award at Northeastern University in 1992. He was also a faculty member for ten years at Drexel University in Philadelphia. In addition to being the author of the first edition of this book on structural analysis, originally published by Macmillan in 1988, he is the author of Fundamentals of Reinforced Concrete, published by McGraw-Hill in 1982 and now in its third edition. Before teaching, he was employed by the Corps of Army Engineers as a construction management engineer, by Catalytic Construction Company as a field engineer, and by several structural engineering firms as a structural designer. He has also served as a structural consultant to a number of government agencies and private firms, including the U.S. Department of Transportation, Procter & Gamble, Teledyne Engineering Services, and the City of Philadelphia and Boston Bridge Departments. As a member of the American Arbitration Association, the American Concrete Institute, the ASCE, and the Boston Society of Civil Engineers, Professor Leet actively participated in professional societies for many years. Chia-Ming Uang is a Professor of structural engineering at the University of California, San Diego (UCSD). He received a B.S. degree in civil engineering from National Taiwan University and M.S. and Ph.D. degrees in civil engineering from the University of California, Berkeley. His research areas include seismic analysis and design of steel, composite, and timber structures. Professor Uang also coauthored the text Ductile Design of Steel Structures for McGraw-Hill. He received the UCSD Academic Senate Distinguished Teaching Award in 2004. He is also the recipient of the ASCE Raymond C. Reese Research Prize in 2001, the ASCE Moisseiff Award in 2004, and the AISC Special Achievement Award in 2007. vii

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About the Authors

Anne M. Gilbert, PE, SECB, is an Adjunct Assistant Professor in the School of Architecture at Yale University. She is also a senior project engineer at Spiegel Zamecnik & Shah, Inc., and is a registered Structural Engineer in Connecticut and Washington, D.C. She received a B.A. in architecture at the University of North Carolina, a B.S. in civil engineering from Northeastern University, and a M.S. in civil engineering from the University of Connecticut. Gilbert specializes in structural design of hospitals, laboratories, university and residential buildings, as well as seismic evaluation and renovation of structures in high seismic areas. Her work includes preparation of construction documents and construction administration. Gilbert’s architectural design experience includes the design of commercial and residential buildings, and rehabilitation of urban brownstones.

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TA B L E O F C O N T E N T S

Preface

Chapter 1

xv

Introduction

3

1.1 1.2

3

Overview of the Text The Design Process: Relationship of Analysis to Design 1.3 Strength and Serviceability 1.4 Historical Development of Structural Systems 1.5 Basic Structural Elements 1.6 Assembling Basic Elements to Form a Stable Structural System 1.7 Analyzing by Computer 1.8 Preparation of Computations Summary

Chapter 2

Design Loads 2.1 Building and Design Code 2.2 Loads 2.3 Dead Loads 2.4 Live Loads 2.5 Snow Loads 2.6 Wind Loads 2.7 Earthquake Loads 2.8 Other Loads 2.9 Load Combinations Summary

Chapter 3

Statics of Structures—Reactions 3.1 3.2 3.3 3.4 3.5 3.6

Introduction Forces Supports Idealizing Structures Free-Body Diagrams Equations of Static Equilibrium

4 6 7 10 19 21 23 24

27 27 28 29 36 42 43 58 62 63 64

73 73 74 81 85 86 88 ix

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Contents

3.7 3.8

Equations of Condition Influence of Reactions on Stability and Determinacy of Structures 3.9 Classifying Structures 3.10 Comparison between Determinate and Indeterminate Structures Summary

Chapter 4

Trusses 4.1 Introduction 4.2 Types of Trusses 4.3 Analysis of Trusses 4.4 Method of Joints 4.5 Zero Bars 4.6 Method of Sections 4.7 Determinacy and Stability 4.8 Computer Analysis of Trusses Summary

Chapter 5

Beams and Frames 5.1 5.2 5.3 5.4 5.5 5.6

Introduction Scope of Chapter Equations for Shear and Moment Shear and Moment Curves Principle of Superposition Sketching the Deflected Shape of a Beam or Frame 5.7 Degree of Indeterminacy Summary

Chapter 6

Cables 6.1 6.2 6.3 6.4

Introduction Characteristics of Cables Variation of Cable Force Analysis of a Cable Supporting Gravity (Vertical) Loads 6.5 General Cable Theorem 6.6 Establishing the Funicular Shape of an Arch Summary

Chapter 7

Arches 7.1 7.2

Introduction Types of Arches

94 97 105 108 111

123 123 126 127 128 132 134 142 148 151

167 167 172 173 180 198 202 207 211

227 227 228 229 230 232 234 237

243 243 244

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Contents

7.3 7.4

Three-Hinged Arches Funicular Shape for an Arch That Supports a Uniformly Distributed Load Summary

Chapter 8

Live Load Forces: Influence Lines for Determinate Structures 8.1 8.2 8.3

Introduction Influence Lines Construction of an Influence Line 8.4 The Müller–Breslau Principle 8.5 Use of Influence Lines 8.6 Influence Lines for Girders Supporting Floor Systems 8.7 Influence Lines for Trusses 8.8 Live Loads for Highway and Railroad Bridges 8.9 Increase–Decrease Method 8.10 Absolute Maximum Live Load Moment 8.11 Maximum Shear Summary

Chapter 9

Deflections of Beams and Frames 9.1 Introduction 9.2 Double Integration Method 9.3 Moment-Area Method 9.4 Elastic Load Method 9.5 Conjugate Beam Method 9.6 Design Aids for Beams Summary

Chapter 10

Work-Energy Methods for Computing Deflections 10.1 10.2 10.3 10.4 10.5 10.6

Introduction Work Strain Energy Deflections by the Work-Energy Method (Real Work) Virtual Work: Trusses Virtual Work: Beams and Frames

246 247 252

259 259 259 260 268 271 274 280 285 288 292 296 297

309 309 310 317 335 339 347 350

363 363 364 366 369 370 387

xi

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Contents

10.7 10.8

Finite Summation Bernoulli’s Principle of Virtual Displacements 10.9 Maxwell-Betti Law of Reciprocal Deflections Summary

Chapter 11

Analysis of Indeterminate Structures by the Flexibility Method 11.1 11.2 11.3

Introduction Concept of a Redundant Fundamentals of the Flexibility Method 11.4 Alternative View of the Flexibility Method (Closing a Gap) 11.5 Analysis Using Internal Releases 11.6 Support Settlements, Temperature Change, and Fabrication Errors 11.7 Analysis of Structures with Several Degrees of Indeterminacy 11.8 Beam on Elastic Supports Summary

Chapter 12

Analysis of Indeterminate Beams and Frames by the Slope-Deflection Method 12.1 12.2

Introduction Illustration of the Slope-Deflection Method 12.3 Derivation of the Slope-Deflection Equation 12.4 Analysis of Structures by the Slope-Deflection Method 12.5 Analysis of Structures That Are Free to Sidesway 12.6 Kinematic Indeterminacy Summary

Chapter 13

Moment Distribution 13.1 13.2

Introduction Development of the Moment Distribution Method

399 401 404 408

421 421 422 423 426 436 443 448 455 458

467 467 468 469 476 492 502 503

513 513 514

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Contents

13.3

Summary of the Moment Distribution Method with No Joint Translation 13.4 Analysis of Beams by Moment Distribution 13.5 Modification of Member Stiffness 13.6 Analysis of Frames That Are Free to Sidesway 13.7 Analysis of an Unbraced Frame for General Loading 13.8 Analysis of Multistory Frames 13.9 Nonprismatic Members Summary

Chapter 14

Indeterminate Structures: Influence Lines 14.1 14.2

Introduction Construction of Influence Lines Using Moment Distribution 14.3 Müller–Breslau Principle 14.4 Qualitative Influence Lines for Beams 14.5 Live Load Patterns to Maximize Forces in Multistory Buildings Summary

Chapter 15

Approximate Analysis of Indeterminate Structures 15.1 15.2

Introduction Approximate Analysis of a Continuous Beam for Gravity Load 15.3 Approximate Analysis of a Rigid Frame for Vertical Load 15.4 Approximate Analysis of a Continuous Truss 15.5 Estimating Deflections of Trusses 15.6 Trusses with Double Diagonals 15.7 Approximate Analysis of a Multistory Rigid Frame for Gravity Load 15.8 Analysis of Unbraced Frames for Lateral Load 15.9 Portal Method 15.10 Cantilever Method Summary

519 520 528 543 549 554 555 566

575 575 576 580 581 588 598

603 603 605 611 615 621 623 626 635 638 646 651

xiii

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Contents

Chapter 16

Introduction to the General Stiffness Method 16.1 16.2

Introduction Comparison between Flexibility and Stiffness Methods 16.3 Analysis of an Indeterminate Structure by the General Stiffness Method Summary

Chapter 17

Matrix Analysis of Trusses by the Direct Stiffness Method 17.1 17.2

Introduction Member and Structure Stiffness Matrices 17.3 Construction of a Member Stiffness Matrix for an Individual Truss Bar 17.4 Assembly of the Structure Stiffness Matrix 17.5 Solution of the Direct Stiffness Method 17.6 Member Stiffness Matrix of an Inclined Truss Bar 17.7 Coordinate Transformation of a Member Stiffness Matrix Summary

Chapter 18

Matrix Analysis of Beams and Frames by the Direct Stiffness Method 18.1 18.2 18.3

Introduction Structure Stiffness Matrix The 2 ⫻ 2 Rotational Stiffness Matrix for a Flexural Member 18.4 The 4 ⫻ 4 Member Stiffness Matrix in Local Coordinates 18.5 The 6 ⫻ 6 Member Stiffness Matrix in Local Coordinates 18.6 The 6 ⫻ 6 Member Stiffness Matrix in Global Coordinates 18.7 Assembly of a Structure Stiffness Matrix—Direct Stiffness Method Summary Glossary Answers to Odd-Numbered Problems Photo Credits Index

659 659 660 664 677

683 683 688 689 690 693 697 709 710

715 715 717 718 729 739 748 750 753 757 761 768 769

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P R E FA C E

This text introduces engineering and architectural students to the basic techniques required for analyzing the majority of structures and the elements of which most structures are composed, including beams, frames, arches, trusses, and cables. Although the authors assume that readers have completed basic courses in statics and strength of materials, we briefly review the basic techniques from these courses the first time we mention them. To clarify the discussion, we use many carefully chosen examples to illustrate the various analytic techniques introduced, and whenever possible, we select examples confronting engineers in real-life professional practice.

Features of This Text 1. Historical Notes. New to this edition are historical notes that have been added to various chapters providing points in the history of accomplishments and developments in structural analysis methods. 2. Expanded treatment of design loads. Chapter 2 is devoted to a comprehensive discussion of loads that include dead and live loads, snow, earthquake, and wind loads Based on the ANSI/ASCE 7 Standard. The presentation aims to provide students with a basic understanding of how design loads are determined for practical design of multistory buildings, bridges, and other structures. 3. New homework problems. A substantial number of the problems are new or revised for this edition (in both metric and U.S. Customary System units), and many are typical of analysis problems encountered in practice. The many choices enable the instructor to select problems suited for a particular class or for a particular emphasis. 4. Computer problems and applications. Computer problems, some new to this edition, provide readers with a deeper understanding of the structural behavior of trusses, frames, arches, and other structural systems. These carefully tailored problems illustrate significant aspects of structural behavior that, in the past, experienced designers needed many years of practice to understand and to analyze correctly. The computer problems are identified wit...