Statics and strength of materials for architecture and building construction

Statics and Strength

of Materials

for Architecture and

Building Construction

This page intentionally left blank

Statics and Strength

of Materials

for Architecture and

Building Construction

Fourth Edition

Barry Onouye

with Kevin Kane

Department of Architecture

College of Architecture and Urban Planning

University of Washington

Prentice Hall

Boston Columbus Indianapolis New York San Francisco Upper Saddle River

Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto

Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo

Editorial Director: Vernon R. Anthony

Acquisitions Editor: David Ploskonka

Editorial Assistant: Nancy Kesterson

Director of Marketing: David Gesell

Executive Marketing Manager: Derril Trakalo

Senior Marketing Coordinator: Alicia Wozniak

Marketing Assistant: Les Roberts

Project Manager: Maren L. Miller

Senior Managing Editor: JoEllen Gohr

Associate Managing Editor: Alexandrina

Benedicto Wolf

Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this

textbook appear on the appropriate page within the text. Unless otherwise stated, all artwork has been

provided by the author.

Copyright © 2012, 2007, 2002, 1999 Pearson Education, Inc., publishing as Prentice Hall, One Lake Street,

Upper Saddle River, New Jersey, 07458. All rights reserved. Manufactured in the United States of America.

This publication is protected by Copyright, and permission should be obtained from the publisher prior to

any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means,

electronic, mechanical, photocopying, recording, or likewise. To obtain permission(s) to use material from

this work, please submit a written request to Pearson Education, Inc., Permissions Department, One Lake

Street, Upper Saddle River, New Jersey, 07458.

Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks.

Where those designations appear in this book, and the publisher was aware of a trademark claim, the

designations have been printed in initial caps or all caps.

Library of Congress Cataloging-in-Publication Data

Onouye, Barry (Barry Shizuo)

Statics and Strength of Materials for Architecture and Building Construction / Barry Onouye with Kevin Kane,

Department of Architecture, College of Architecture and Urban Planning, University of Washington.—Fourth

Edition.

pages cm

Includes index.

ISBN 978-0-13-507925-6

1. Structural design. 2. Statics. 3. Strength of materials. 4. Strains and stresses. I. Kane, Kevin (John Kevin),

1954- II. Title.

TA658.O66 2012

624.1’771—dc22

2010053540

10 9 8 7 6 5 4 3 2 1

ISBN 10: 0-13-507925-X

ISBN 13: 978-0-13-507925-6

Senior Operations Supervisor: Pat Tonneman

Operations Specialist: Deidra Skahill

Art Director: Jayne Conte

Cover Designer: Suzanne Duda

Cover Image: Baloncici/Shutterstock

AV Project Manager: Janet Portisch

Full-Service Project Management and

Composition: PreMediaGlobal

Printer/Binder: Edwards Brothers

Cover Printer: Phoenix Color Corporation

Text Font: 10.5/12 Palatino

To our families . . .

This page intentionally left blank

Foreword

I have had the privilege of teaching with Barry Onouye in a design studio setting for 12 years.

From the outset, it was obvious that he had a sound knowledge of structures, but what also be￾came apparent over time was his profound understanding of architectural structures—the struc￾tural systems that play a critical role in the planning, design, and making of buildings. He is an

exceptional teacher, not only extremely knowledgeable but also able to explain principles and

concepts in an articulate manner and to relate his reasoning to the problems and opportunities in

architectural design and building construction. In the pages of this book, he has managed, along

with Kevin Kane, to convey this same extraordinary teaching ability.

Statics and Strength of Materials for Architecture and Building Construction is a refreshing treat￾ment of an enduring topic in architectural education. It combines in a single text the related

fields of statics—the external force systems acting on structural elements—and strength of

materials—the internal forces and deformations that result from external forces. Together, these

classic areas of inquiry give rise to the size and shape of structural elements and the configura￾tion of these elements into systems that unite and support the components and contents of a

building.

Such systems underlie all buildings, from the monuments of the past to the most humble

structures of the present. Whether visible to the eye or concealed by elements of enclosure, these

three-dimensional frameworks occupy space and establish the nature and composition of the

spaces within buildings. Even when obscured by the more discernible faces of floors, walls, and

ceilings, their presence can often be sensed by the mind’s eye. Thus, an understanding of struc￾tural theory and systems remains an essential component of architectural education.

Over the last century, numerous texts on building structures have been written for students

of architecture and building construction. What distinguishes this work is its effective weaving

of word and image. The problem for anyone teaching structures has always been to explain

structural theories and concepts to design students, for whom graphical material can be more

meaningful than numbers. The danger in a purely graphical approach, however, is the omission

of the mathematical models necessary for a realistic and rigorous treatment of the science of

structures. This text instead adopts the classical method for the teaching of building structures

and integrates visual information with the necessary mathematical models and essential struc￾tural principles and relates these concepts to real-world examples of architectural design in a

coherent and illuminating manner. This wise and balanced approach to the subject of statics and

strength of material should serve well both teachers and students of architectural structures.

Frank Ching

vii

Preface

A primary aim of this book since its first publication in 1998 has been to develop and present basic

structural concepts in an easily understood manner using “building” examples and illustrations

to supplement the text. Much of this material has been “field tested,” revised, and modified over

the course of 40 years of teaching, and it will continue to be modified in the future. There was a

great temptation to add many new topical areas to this revision, but I decided to keep this book

focused primarily on statics and strength of materials. Instead, small tweaks and additions were

incorporated without trying to cover more material than is necessary in an introductory course.

Introducing structural theory without relying on a predominantly mathematical treatment has

been challenging, to say the least, and a noncalculus engineering alternative to the topic seemed to

be essential. Early on, it was decided that a heavily illustrated, visual approach was necessary in con￾necting and linking structural theory to real buildings and structural components. Using examples

and problems that are commonly found in buildings and structures around us appeared to be a log￾ical way of introducing mathematically based material in a nonthreatening way.

This text is organized along the lines of traditional textbooks on statics and strength of materials,

because it seems to be a very logical, time-tested approach. A sound understanding of statics and

strength of materials establishes a theoretical and scientific basis for understanding structural the￾ory. Numerical calculations are included as a way of explaining and testing one’s understanding of

the principles involved. Many fully worked example problems are also included, with additional

problems for student practice at the end of each chapter and on the companion website.

This text is intended as the next step following a basic introductory presentation of structural

principles and systems. Organizationally, the book consists of two parts: statics in Chapters 2

through 4, and strength of materials covered in Chapters 5 through 10.

A heavy emphasis is placed on the use of free-body diagrams in understanding the forces acting

on a structural member. All problems begin with a pictorial representation of a structural compo￾nent or assembly and are accompanied by a free-body diagram. Illustrations are used extensively to

ensure that the student sees the connection between the real object and its abstraction.

Chapter 1 introduces the student to the process of structural design. Loads and the basic func￾tional requirements of a building are introduced along with the larger architectural issues of build￾ing design. This revision has expanded the discussion on loads and, in particular, wind and

earthquake. Chapter 3 uses the principles discussed in Chapter 2 to solve an array of determinate

structural frameworks. Load tracing in Chapter 4 illustrates the interaction of one member with

other members and introduces the concept of load paths that develop in a building, with an attempt

to examine the overall structural condition regarding gravity and lateral loads. Although not cus￾tomarily covered in statics, load tracing was included to illustrate the power of the basic principle of

mechanics and the use of free-body diagrams as studied in Chapters 2 and 3. A general introduction

to lateral bracing strategies for multibay and multistory buildings is also included, but without any

accompanying force calculations due to its complexity.

Chapter 5 introduces the concepts of stress and strain and material properties as they relate to ma￾terials commonly used in the building industry. This text would be greatly complemented by stu￾dents taking a course on the methods and materials of construction either concurrently or before the

study of strength of materials. Cross-sectional properties are covered in Chapter 6, again with an em￾phasis on commonly used beam and column shapes. Chapters 7, 8, and 9 develop the basis for beam

and column analysis and design. Elastic theory has been utilized throughout, and the allowable

stress method has been employed for the design of beams and columns. Some simplifications have

been introduced to beam and column design equations to eliminate the complexity unwarranted for

preliminary design purposes. Sizing of beams and columns is well within the range of a final, closely

engineered element sized by the more complex formulas. It is assumed that students will take sub￾sequent courses in timber, steel, and concrete; therefore, building code equations and criteria have

not been incorporated in this text. This edition includes a new Section 8.7, which introduces the stu￾dent to the load resistance factor design (LRFD) method for designing steel members. No attempt

was made to do an extensive treatment of the topic, but it is recommended that an interested stu￾dent seek classes or other texts that deal exclusively with the subject of limit state design.

viii

Preface ix

Not included in this text is the study of indeterminate beams and frames, because it would

require substantial development beyond the purview of statics and strength of materials.

Indeterminate structure is probably one of the more important structural topics for building designers;

most of the commercial and institutional buildings of moderate or large size are of this type.

Indeterminate structural behavior, using one of the many available structural analysis/design soft￾ware packages, is emerging as a critical area of study for all future building designers.

This text is intended to be used for a one plus-semester (15+-weeks) class or two 10-week quar￾ters in architecture, building construction, and engineering technology programs. Chapters 4 and 11

might be of interest and use to the civil engineering student who wants to better understand build￾ing components in a larger context. Also, Chapters 8 and 9 might be useful for quick preliminary

methods of sizing beams and columns. Although this text might be used for self-study, its real bene￾fit is as a supplement to the instruction received in class.

Many of the topics covered in the text can be demonstrated in model form in class. The use of

slides of actual buildings representing the topic being covered will help to reinforce the concepts

through visual images. My previous teaching experience has convinced me of the need to use a vari￾ety of media and techniques to illustrate a concept.

The companion website, at www.pearsonhighered.com/onouye, features practice problems

found in the printed text. All problems on the companion website are accompanied by solutions to

enable the student to check their work during individual study sessions. Sufficient detail is provided

to assist students when they become “stuck” and need a nudge to continue in their work.

ACKNOWLEDGMENTS

I am indebted and grateful to a vast number of students over many years who have used the earlier

versions of this text and generously given suggestions for changes and improvements.

In particular, this book would not be possible without the shared authorship of Kevin Kane and

his skill and insightfulness illustrating the structural concepts. Kevin’s major contributions, along

with drawing and coordinating all of the illustrations, are evident in Chapters 4 and 10. Additional

thanks to Cynthia Esselman, Murray Hutchins, and Gail Wong for drawing assistance that helped

us meet deadlines.

Special acknowledgment and appreciation is given to Tim Williams and Loren Brandford for

scanning and typing assistance, Robert Albrecht for reviewing the earlier manuscript; Ed Lebert for

some of the practice problems, Chris Countryman for proofreading the problems and solutions, Bert

Gregory and Jay Taylor for providing information pertinent to Chapter 10, and Elga Gemst, a teach￾ing assistant from long ago, for helping me prepare the original strength of materials sections and

the biographies of famous thinkers of the past. Thanks also go to the reviewers of this edition: Allen

C. Estes, Cal Poly San Luis Obispo; Deborah Oakley, University of Las Vegas; Dennis O’Lenick,

Valencia Community College; and Kerry Slattery, Southern Illinois University, Edwardsville. Finally,

thanks to a friend and colleague, Frank Ching, who encouraged us to pursue this project. He has

served as a mentor and role model for many of us who teach here at the University of Washington.

A warm and sincere thanks to our families for their support and sacrifice throughout this process.

Thank you Yvonne, Jacob, Qingyu, Jake, Amia, and Aidan.

Barry Onouye

This page intentionally left blank

Definition of Terms

Measurement U.S. Units Metric (S.I.)

a measure of length inch (in. or ′′) millimeter (mm)

feet (ft. or ′) meter (m)

a measure of area square inches (in.2

) square millimeters (mm2

)

square feet (ft.2

) square meters (m2

)

a measure of mass pound mass (lbm) kilogram (kg)

a measure of force pound (lb. or #) newton (N)

kilopound = 1,000 lb. (k) kilonewton = 1,000 N (kN)

a measure of stress (force/area) psi (lb./in.2 or #/in.2

) pascal (N/m2

)

ksi (k/in.2

)

a measure of pressure psf (lb./ft.2 or #/ft.2

) kilopascal = 1,000 Pa

moment (force × distance) pound-feet (lb.-ft. or #-ft.) newton-meter (N-m)

kip-feet (k-ft.) kilonewton-meter (kN-m)

a load distributed over length ω (lb./ft., #/ft., or plf) ω (kN/m)

density (weight/volume) γ (lb./ft.3 or #/ft.3

) γ (kN/m3

)

force = (mass) × (acceleration); acceleration due to gravity: 32.17 ft./sec.2 = 9.807 m/sec.2

1 m = 39.37 in. 1 ft. = 0.3048 m

1 m2 = 10.76 ft.2 1 ft.2 = 92.9 × 10-3 m2

1 kg = 2.205 lb.-mass 1 lbm = 0.4536 kg

1 kN = 224.8 lb.-force 1 lb. = 4.448 N

1 kPa = 20.89 lb./ft.2 1 lb./ft.2 = 47.88 Pa

1 MPa = 145 lb./in.2 1 lb./in.2 = 6.895 kPa

1 kg/m = 0.672 lbm/ft. 1 lbm/ft. = 1.488 kg/m

1 kN/m = 68.52 lb./ft. 1 lb./ft = 14.59 N/m

Prefix Symbol Factor

giga- G 109 or 1,000,000,000

mega- M 106 or 1,000,000

kilo- k 103 or 1,000

milli- m 10-3 or 0.001

Conversions

Also, refer to Appendix Table A-7.

xi

This page intentionally left blank

Contents

CHAPTER 1 INTRODUCTION 1

1.1 Definition of Structure 1

1.2 Structural Design 2

1.3 Parallels in Nature 3

1.4 Loads on Structures 5

1.5 Basic Functional Requirements 9

1.6 Architectural Issues 11

CHAPTER 2 STATICS 15

2.1 Characteristics of a Force 15

2.2 Vector Addition 23

2.3 Force Systems 29

2.4 Equilibrium Equations: Two-Dimensional 61

2.5 Free-Body Diagrams of Rigid Bodies 74

2.6 Statical Indeterminacy and Improper Constraints 86

CHAPTER 3 ANALYSIS OF SELECTED DETERMINATE STRUCTURAL SYSTEMS 96

3.1 Equilibrium of a Particle 96

3.2 Equilibrium of Rigid Bodies 111

3.3 Plane Trusses 119

3.4 Pinned Frames (Multiforce Members) 153

3.5 Three-Hinged Arches 164

3.6 Retaining Walls 175

CHAPTER 4 LOAD TRACING 195

4.1 Load Tracing 195

4.2 Lateral Stability Load Tracing 231

CHAPTER 5 STRENGTH OF MATERIALS 251

5.1 Stress and Strain 251

5.2 Elasticity, Strength, and Deformation 267

5.3 Other Material Properties 274

5.4 Thermal Effects 289

5.5 Statically Indeterminate Members (Axially Loaded) 294

xiii