Mechanics of Materials

Tenth Edition in SI Units

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This page intentionally left blank

MECHANICS

OF MATERIALS

This page intentionally left blank

MECHANICS

OF MATERIALS

TENTH EDITION IN sI uNITs

R. C. HIBBELER

SI Conversion by

Kai Beng Yap

Vice President and Editorial Director, ECS: Marcia J. Horton

Senior Editor: Norrin Dias

Editorial Assistant: Michelle Bayman

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and Associated Companies throughout the world

Visit us on the World Wide Web at:

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© 2018 by R. C. Hibbeler. Published by Pearson Education, Inc. or its affiliates.

The rights of R. C. Hibbeler to be identified as the author of this work have been asserted by him in

accordance with the Copyright, Designs and Patents Act 1988.

Authorized adaptation from the United States edition, entitled Mechanics of Materials, Tenth Edition, ISBN 978-0-13-431965-0,

by R. C. Hibbeler, published by Pearson Education, Inc., © 2017.

All rights reserved. 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 or otherwise, without either the prior written permission

of the publisher or a license permitting restricted copying in the United Kingdom issued by the Copyright Licensing

Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS.

Many of the designations by manufacturers and sellers 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.

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

the appropriate page within the text. Unless otherwise specified, all photos provided by R.C. Hibbeler.

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

10 9 8 7 6 5 4 3 2 1

ISBN 10: 1-292-17820-5

ISBN 13: 978-1-292-17820-2

Printed in Malaysia (CTP-VVP)

To the Student

With the hope that this work will stimulate

an interest in Mechanics of Materials

and provide an acceptable guide to its understanding.

This page intentionally left blank

PR E FA C E

It is intended that this book provide the student with a clear and thorough

presentation of the theory and application of the principles of mechanics

of materials. To achieve this objective, over the years this work has been

shaped by the comments and suggestions of hundreds of reviewers in the

teaching profession, as well as many of the author’s students. The tenth

edition has been significantly enhanced from the previous edition, and it

is hoped that both the instructor and student will benefit greatly from

these improvements.

New to this editioN

• Updated Material. Many topics in the book have been re-written in

order to further enhance clarity and to be more succinct. Also, some of

the artwork has been enlarged and improved throughout the book to

support these changes.

• New Layout Design. Additional design features have been added to this

edition to provide a better display of the material. Almost all the topics

are presented on a one or two page spread so that page turning is

minimized.

• Improved Preliminary and Fundamental Problems. These problems sets

are located just after each group of example problems. They offer students

basic applications of the concepts covered in each section, and they help

provide the chance to develop their problem-solving skills before

attempting to solve any of the standard problems that follow. The problems

sets may be considered as extended examples, since in this edition their

complete solutions are given in the back of the book. Additionally, when

assigned, these problems offer students an excellent means of preparing

for exams, and they can be used at a later time as a review when studying

for various engineering exams.

• New Photos. The relevance of knowing the subject matter is reflected

by the real-world application of the additional new or updated photos

placed throughout the book. These photos generally are used to explain

how the principles apply to real-world situations and how materials

behave under load.

8

P r e fa c e

• New Problems. New problems involving applications to many different

fields of engineering have been added in this edition.

• New Review Problems. Updated review problems have been placed at

the end of each chapter so that instructors can assign them as additional

preparation for exams.

hallmark elemeNts

Organization and Approach. The contents of each chapter are

organized into well-defined sections that contain an explanation of

specific topics, illustrative example problems, and a set of homework

problems. The topics within each section are placed into subgroups

defined by titles. The purpose of this is to present a structured method for

introducing each new definition or concept and to make the book

convenient for later reference and review.

Chapter Contents. Each chapter begins with a full-page illustration

that indicates a broad-range application of the material within the chapter.

The “Chapter Objectives” are then provided to give a general overview

of the material that will be covered.

Procedures for Analysis. Found after many of the sections of the

book, this unique feature provides the student with a logical and orderly

method to follow when applying the theory. The example problems are

solved using this outlined method in order to clarify its numerical

application. It is to be understood, however, that once the relevant

principles have been mastered and enough confidence and judgment have

been obtained, the student can then develop his or her own procedures

for solving problems.

Important Points. This feature provides a review or summary of the

most important concepts in a section and highlights the most significant

points that should be realized when applying the theory to solve problems.

Example Problems. All the example problems are presented in a

concise manner and in a style that is easy to understand.

Homework Problems. Apart from of the preliminary, fundamental,

and conceptual problems, there are numerous standard problems in the

book that depict realistic situations encountered in engineering practice.

It is hoped that this realism will both stimulate the student’s interest in

the subject and provide a means for developing the skill to reduce any

such problem from its physical description to a model or a symbolic

representation to which principles may be applied. Furthermore, in any

set, an attempt has been made to arrange the problems in order of

increasing difficulty. The answers to all but every fourth problem are

listed in the back of the book. To alert the user to a problem without a

P r e fa c e

reported answer, an asterisk (*) is placed before the problem number.

Answers are reported to three significant figures, even though the data

for material properties may be known with less accuracy. Although this

might appear to be a poor practice, it is done simply to be consistent,

and to allow the student a better chance to validate his or her solution.

Appendices. The appendices of the book provide a source for review

and a listing of tabular data. Appendix A provides information on the

centroid and the moment of inertia of an area. Appendices B and C list

tabular data for structural shapes, and the deflection and slopes of various

types of beams and shafts.

Accuracy Checking. The Tenth Edition has undergone a rigorous

Triple Accuracy Checking review. In addition to the author’s review of all

art pieces and pages, the text was checked by the following individuals:

• Scott Hendricks, Virginia Polytechnic University

• Karim Nohra, University of South Florida

• Kurt Norlin, Bittner Development Group

• Kai Beng Yap, Engineering Consultant

The SI edition was checked by three additional reviewers.

Realistic Diagrams and Photographs. Realistic diagrams with

vectors have been used to demonstrate real-world applications. In

addition, many photographs are used throughout the book to enhance

conceptual understanding and to explain how the principles of mechanics

of materials apply to real-world situations.

CHAPTER 8

▼

452

COMBINED LOADINGS

8–31. The drill is jammed in the wall and is subjected to the

torque and force shown. Determine the state of stress at

point A on the cross section of the drill bit at section a–a.

8–35. The block is subjected to the eccentric load shown.

Determine the normal stress developed at points A and B.

Neglect the weight of the block.

*8–32. The drill is jammed in the wall and is subjected to

the torque and force shown. Determine the state of stress at

point B on the cross section of the drill bit at section a–a.

*8–36. The block is subjected to the eccentric load shown.

Sketch the normal-stress distribution acting over the cross

section at section a–a. Neglect the weight of the block.

y

400 mm

150 kN

a 20 N ·m

100 mm

x

150 mm

a

a

C

125 mm

a

y

A

z

5 mm

3

A

B

5

4

150 N

B

Section a – a

Probs. 8–35/36

Probs. 8–31/32

8–33. Determine the state of stress at point A when the

beam is subjected to the cable force of 4 kN. Indicate the

result as a differential volume element.

8–37. If the 75-kg man stands in the position shown,

determine the state of stress at point A on the cross section

Illustrations with

Vectors

Most of the diagrams

throughout the book are in

full-color art, and many

photorealistic illustrations

with vectors have been added.

These provide a strong

connection to the 3-D nature of

engineering. This also helps the

student to visualize and be

aware of the concepts behind

the question.

9

P r e fa c e

Once the beam has

been selected, the shea

r formula can then

to be sure the allow

be used

able shear stress is

not exceeded, t

Often this requirem

allow Ú VQ> It.

ent will not present

a problem; however

is “short” and supp

, if the beam

orts large concentr

ated loads, the shea

limitation may dicta

r-stress

te the size of the beam

.

Steel Section

s. Most manufacture

d steel beams are prod

rolling a hot ingot

uced by

of steel until the desi

red shape is formed.

so-called rolled shap

These

es have properties

that are tabulated

American Institute

in the

of Steel Constru

ction (AISC) man

representative listin

ual. A

g of different cross sect

ions taken from this

given in Appendix

manual is

B.

their depth and mas

s per unit length; for

example, W460 * 68

indicates

unit length of 68 kg>m

, Fig. 11–4. For any

given selection, the

unit length, dimensi

mass per

ons, cross-sectional

area

, moment of inertia,

section modulus are

reported. Also inclu

and

ded is the radius of

which is a geometric

gyration, r,

property related to

the section’s buckling

This will be discusse

g strength.

d in Chapter 13.

Typical profile view

of a steel

wide-flange beam

15.4 mm

9.14 mm

459 mm

FOR

ENTER

A

154 mm

C

HEAR

7.5 S

OPEN T

HIN-W

ALLED

419

RS

MEMBE

The large shear force

that occu

ribution

curs

rs at the

W460 68

support of this steel

flow dist

beam can cause

e shear- distribution is

localized buckling of

with th

the beam

m’s

s to do

hen this t forces of Ff

’s flanges

ha

W

ts

or web. To avoid this,

b.

is

24

ltan

ts

a “stiffener” A is

ber tw

11–4 eb, Fig. 7–

emFig.

placed along the web

momen

give resu

on the m flanges and w

to maintain

s, it will g. 7–24c. If the couple

in stability.

yThe reas

ed

nel’s

web area

, Fi

Photographs

Many photographs are used

throughout the book to enhance

conceptual understanding and

explain how the principles of

mechanics of materials apply to

real-world situations.

▼

10

7

nc

e and

e chan

e web

r

unbala

along th over the flang of V = P in th

sible fo

A, the

respon

e

ed

e

t point

integrat nge and a forc

ed abou is seen to be ewed from th

m

m

su

fla

are

rces

rnal

hen vi

fo

te

es

w

in

rc

e

e

in each

is

fo

e

ng

activ

ockw

e fla

cl

re

th

is

e three

is

e

th

es

t

by

us

t

is

th

of

ted

beca

even

al tw

ue crea

7–24a,

he actu

r to pr

to

or torq e member. T

in Fig. ting. In orde is necessary

th

shown

is

as

t, it

,

en

eb

w

om

twisting the beam, as cause the tw

m

the

lanced

e from

front of m” forces Ff ncel the unba

distance

briu

e ca

centric

or

or

ec

e,

ef

P

“equili

er

an

Ff d =

cated

and th

int O lo quire π MA =

twisting

at a po

re

apply P Fig. 7–24d. We

Ff d

in

nter .

n

ow

=

sh

e

xural ce

P

er or fle ut twisting,

ear cent

ho

d the sh will bend wit shear center

lle

ca

is

am

the

ed

located

t, the be e location of

only us

int O so

is poin

t th

e comm

The po applied at th

often lis ctions that ar

books

P is

s se

nd

ays

os

w

ha

cr

al

n

l

When

wil

Desig

led beam

r center area. For

7–24e.

thin-wal

the shea

nal

riety of

no

ted that s cross-sectio

a,

25

no

for a va .

7–

be

ld

, Fig.

ber’

tice

is, it shou

a mem is applied at A nges for this

in prac

is analys

etry of

P

fla

ents

From th axis of symm tated 90° and the web and

em

el

e

in

is ro

an

in thes

has

lie on if the channel the shear flow e resultants

ember

e

e,

e

forc

ly, if a m

exampl ill occur sinc

ore the 25b. Obvious of a wide-flang

w

d theref

es

ax

e

es

twisting mmetrical, an about A, Fig. 7– , as in the case

of th

on

ry

ts

sy

ti

et

is

en

ec

m

case

sym

mom

inters

te zero

axes of

ith the

will crea ction with two ill coincide w

se

er w

a cross

ear cent

sh

e

th

beam,

ntroid).

(the ce

flects

beam de bove)

ilever

roid (a

is cant

how th ugh the cent ow).

el

ro

Notice

th

(b

er

ed

ad

cent

when lo h the shear

ug

and thro

P

P

Ff

Ff

A

A

V

P

2

A

V

P

2

(b)

(a)

25

Fig. 7–

P r e fa c e

Video Solutions. An invaluable resource in and out of the classroom,

▼

Reduces lecturers’ time spent

on repetitive explanation of

concepts and applications.

Flexible resource for students,

offering learning at a

comfortable pace

▼

Independent video replays

of a lecturer’s explanation

reinforces students’

understanding

▼

these complete solution walkthroughs of representative problems and

applications from each chapter offer fully worked solutions, self-paced

instruction, and 24/7 accessibility via the companion Website. Lecturers

and students can harness this resource to gain independent exposure to a

wide range of examples by applying formulae to actual structures.

11

12

P r e fa c e

CoNteNts

The subject matter is organized into 14 chapters. Chapter 1 begins with a

review of the important concepts of statics, followed by a formal definition

of both normal and shear stress, and a discussion of normal stress in axially

loaded members and average shear stress caused by direct shear.

In Chapter 2 normal and shear strain are defined, and in Chapter 3 a

discussion of some of the important mechanical properties of materials is

given. Separate treatments of axial load, torsion, and bending are presented

in Chapters 4, 5, and 6, respectively. In each of these chapters, both linearelastic and plastic behavior of the material covered in the previous chapters,

where the state of stress results from combined loadings. In Chapter 9 the

concepts for transforming multiaxial states of stress are presented. In a

similar manner, Chapter 10 discusses the methods for strain transformation,

including the application of various theories of failure. Chapter 11 provides

a means for a further summary and review of previous material by covering

design applications of beams and shafts. In Chapter 12 various methods for

computing deflections of beams and shafts are covered. Also included is a

discussion for finding the reactions on these members if they are statically

indeterminate. Chapter 13 provides a discussion of column buckling, and

lastly, in Chapter 14 the problem of impact and the application of various

energy methods for computing deflections are considered.

Sections of the book that contain more advanced material are indicated

by a star (*). Time permitting, some of these topics may be included in

the course. Furthermore, this material provides a suitable reference for

basic principles when it is covered in other courses, and it can be used as

a basis for assigning special projects.

Alternative Method of Coverage. Some instructors prefer to cover

stress and strain transformations first, before discussing specific applications

of axial load, torsion, bending, and shear. One possible method for doing this

would be first to cover stress and its transformation, Chapter 1 and Chapter 9,

followed by strain and its transformation, Chapter 2 and the first part of

Chapter 10. The discussion and example problems in these later chapters have

been styled so that this is possible. Also, the problem sets have been subdivided

so that this material can be covered without prior knowledge of the intervening

chapters. Chapters 3 through 8 can then be covered with no loss in continuity.

aCkNowledgmeNts

Over the years, this text has been shaped by the suggestions and comments

of many of my colleagues in the teaching profession. Their encouragement

and willingness to provide constructive criticism are very much appreciated

and it is hoped that they will accept this anonymous recognition. A note

of thanks is given to the reviewers.

S. Apple, Arkansas Tech University

A. Bazar, University of California, Fullerton

P r e fa c e

M. Hughes, Auburn University

R. Jackson, Auburn University

E. Tezak, Alfred State College

H. Zhao, Clemson University

There are a few people that I feel deserve particular recognition. A longtime friend and associate, Kai Beng Yap, was of great help to me in

preparing the problem solutions. A special note of thanks also goes to

Kurt Norlin in this regard. During the production process I am thankful

for the assistance of Rose Kernan, my production editor for many years,

and to my wife, Conny, for her help in proofreading and typing, that was

needed to prepare the manuscript for publication.

I would also like to thank all my students who have used the previous

edition and have made comments to improve its contents; including all

those in the teaching profession who have taken the time to e-mail me

their comments, but in particular G. H. Nazari.

I would greatly appreciate hearing from you if at any time you have

any comments or suggestions regarding the contents of this edition.

Russell Charles Hibbeler

hibbeler@bellsouth.net

global editioN

The publishers would like to thank the following for their contribution to

the Global Edition:

Contributor for the Tenth Edition in SI Units

Kai Beng Yap is currently a registered professional engineer who works

in Malaysia. He has BS and MS degrees in civil engineering from the

University of Louisiana, Lafayette, Louisiana; and has done further

graduate work at Virginia Tech in Blacksburg, Virginia. He has taught at

the University of Louisiana and worked as an engineering consultant in

the areas of structural analysis and design, and the associated infrastructure.

Reviewers for the Tenth Edition in SI Units

Imad Abou-Hayt, Aalborg University of Copenhagen

Weena Lokuge, University of Southern Queensland

Samit Ray Chaudhuri, Indian Institute of Technology Kanpur

Contributors for Earlier SI Editions

Pearson would like to thank S. C. Fan, who has retired from Nanyang

Technological University, Singapore, and K. S. Vijay Sekar, who teaches

in SSN College of Engineering, India, for their work on the 8th and 9th

SI editions of this title, respectively.

13

your work...

your

youranswer

answer

feedback

feedback

0.000844

0.000844mm3 3

®®

16

P r e fa c e

resourCes for iNstruCtors

• MasteringEngineering. This online Tutorial Homework program allows

you to integrate dynamic homework with automatic grading and adaptive

tutoring. MasteringEngineering allows you to easily track the performance

of your entire class on an assignment-by-assignment basis, or the detailed

work of an individual student.

• Instructor’s Solutions Manual. An instructor’s solutions manual was

prepared by the author. The manual includes homework assignment lists

and was also checked as part of the accuracy checking program. The

Instructor Solutions Manual is available at www.pearsonglobaleditions.com.

• Presentation Resources. All art from the text is available in PowerPoint

slide and JPEG format. These files are available for download at www

.pearsonglobaleditions.com. If you are in need of a login and password for

this site, please contact your local Pearson representative.

• Video Solutions. Developed primarily by Professor Edward Berger,

Purdue University, video solutions located on the companion Website

offer step-by-step solution walkthroughs of representative homework

problems from each section of the text. Make efficient use of class time

and office hours by showing students the complete and concise problem

solving approaches that they can access anytime and view at their own

pace. The videos are designed to be a flexible resource to be used however

each instructor and student prefers. A valuable tutorial resource, the

videos are also helpful for student self-evaluation as students can pause

the videos to check their understanding and work alongside the video.

resourCes for studeNts

• Mastering Engineering. Tutorial homework problems emulate the

instructor’s office-hour environment, guiding students through engineering

concepts with self-paced individualized coaching. These in-depth tutorial

homework problems are designed to coach students with feedback specific

to their errors and optional hints that break problems down into simpler steps.

• Companion Website—The companion Website, located at

www.pearsonglobaleditions.com/hibbeler, includes opportunities for

practice and review, including access to video solutions offering complete,

step-by-step solution walkthroughs of representative homework problems

from various sections of the text.

C O NTE NTS

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

2

2.1

2.2

21

Stress

Chapter Objectives 21

Introduction 21

Equilibrium of a Deformable Body 22

Stress 40

Average Normal Stress in an Axially

Loaded Bar 42

Average Shear Stress 50

Allowable Stress Design 64

Limit State Design 66

4

4.1

4.2

4.3

4.4

4.5

4.6

4.7

*4.8

*4.9

3.1

3.2

3.3

3.4

3.5

3.6

*3.7

Mechanical Properties

of Materials

Chapter Objectives 141

Saint-Venant’s Principle 141

Elastic Deformation of an Axially Loaded

Member 143

Principle of Superposition 158

Statically Indeterminate Axially Loaded

Members 158

The Force Method of Analysis for Axially

Loaded Members 165

Thermal Stress 173

Stress Concentrations 180

Inelastic Axial Deformation 183

Residual Stress 185

87

5

3

141

87

Strain

Chapter Objectives

Deformation 87

Strain 88

Axial Load

Chapter Objectives 103

The Tension and Compression Test 103

The Stress–Strain Diagram 105

Stress–Strain Behavior of Ductile and

Brittle Materials 109

Strain Energy 113

Poisson’s Ratio 124

The Shear Stress–Strain Diagram 126

Failure of Materials Due to Creep

and Fatigue 129

201

Chapter Objectives 201

Torsional Deformation of a Circular

Shaft 201

5.2 The Torsion Formula 204

5.3 Power Transmission 212

5.4 Angle of Twist 224

5.5 Statically Indeterminate Torque-Loaded

Members 240

*5.6 Solid Noncircular Shafts 247

*5.7 Thin-Walled Tubes Having Closed Cross

Sections 250

5.8 Stress Concentration 260

*5.9 Inelastic Torsion 263

*5.10 Residual Stress 265

5.1

103

Torsion

18

contents

6

Bending

281

Chapter Objectives 281

Shear and Moment Diagrams 281

Graphical Method for Constructing Shear

and Moment Diagrams 288

6.3 Bending Deformation of a Straight

Member 307

6.4 The Flexure Formula 311

6.5 Unsymmetric Bending 328

*6.6 Composite Beams 338

*6.7 Reinforced Concrete Beams 341

*6.8 Curved Beams 345

6.9 Stress Concentrations 352

*6.10 Inelastic Bending 362

6.1

6.2

9

9.1

9.2

9.3

9.4

9.5

10

7

7.1

7.2

7.3

7.4

*7.5

8

8.1

8.2

Transverse Shear

385

Chapter Objectives 385

Shear in Straight Members 385

The Shear Formula 386

Shear Flow in Built-Up Members 404

Shear Flow in Thin-Walled Members 413

Shear Center for Open Thin-Walled

Members 418

Combined Loadings

Chapter Objectives 431

Thin-Walled Pressure Vessels 431

State of Stress Caused by Combined

Loadings 438

431

10.1

10.2

*10.3

*10.4

10.5

10.6

*10.7

11

Stress Transformation

463

Chapter Objectives 463

Plane-Stress Transformation 463

General Equations of Plane-Stress

Transformation 468

Principal Stresses and Maximum In-Plane

Shear Stress 471

Mohr’s Circle—Plane Stress 487

Absolute Maximum Shear Stress 499

Strain Transformation

511

Chapter Objectives 511

Plane Strain 511

General Equations of Plane-Strain

Transformation 512

Mohr’s Circle—Plane Strain 520

Absolute Maximum Shear Strain 528

Strain Rosettes 530

Material Property Relationships 534

Theories of Failure 546

Design of Beams and

Shafts

Chapter Objectives 563

11.1 Basis for Beam Design 563

11.2 Prismatic Beam Design 566

*11.3 Fully Stressed Beams 580

*11.4 Shaft Design 584

563

19

contents

12

12.1

12.2

*12.3

*12.4

12.5

12.6

12.7

*12.8

12.9

13

13.1

13.2

13.3

*13.4

*13.5

*13.6

*13.7

Deflection of Beams

and Shafts

595

Chapter Objectives 595

The Elastic Curve 595

Slope and Displacement by

Integration 599

Discontinuity Functions 617

Slope and Displacement by the

Moment-Area Method 629

Method of Superposition 644

Statically Indeterminate Beams

and Shafts 652

Statically Indeterminate Beams and

Shafts—Method of Integration 653

Statically Indeterminate Beams and

Shafts—Moment-Area Method 658

Statically Indeterminate Beams and

Shafts—Method of Superposition 664

Buckling of Columns

Chapter Objectives 683

Critical Load 683

Ideal Column with Pin Supports 686

Columns Having Various Types of

Supports 692

The Secant Formula 704

Inelastic Buckling 710

Design of Columns for Concentric

Loading 718

Design of Columns for Eccentric

Loading 728

683

14

Energy Methods

741

Chapter Objectives 741

External Work and Strain Energy 741

Elastic Strain Energy for Various Types

of Loading 746

14.3

Conservation of Energy 759

14.4

Impact Loading 766

*14.5

Principle of Virtual Work 777

*14.6

Method of Virtual Forces Applied

to Trusses 780

*14.7

Method of Virtual Forces Applied

to Beams 788

*14.8

Castigliano’s Theorem 797

*14.9

Castigliano’s Theorem Applied

to Trusses 799

*14.10 Castigliano’s Theorem Applied

to Beams 802

14.1

14.2

Appendix

A

B

C

Geometric Properties of an Area 810

Geometric Properties of Structural

Shapes 824

Slopes and Deflections of Beams 829

Solutions and Answers for

Preliminary Problems 831

Fundamental Problems Partial

Solutions and Answers 841

Selected Answers

Index

883

863

Chapter

1

(© alexskopje/Fotolia)

The bolts used for the connections of this steel framework are subjected to stress.

In this chapter we will discuss how engineers design these connections and their

fasteners.

StReSS

Chapter OBJeCtIVeS

n

In this chapter we will review some of the important principles of

statics and show how they are used to determine the internal

resultant loadings in a body. Afterwards the concepts of normal and

shear stress will be introduced, and specific applications of the

analysis and design of members subjected to an axial load or direct

shear will be discussed.

1.1

IntroductIon

Mechanics of materials is a branch of mechanics that studies the internal

effects of stress and strain in a solid body. Stress is associated with the

strength of the material from which the body is made, while strain is a

measure of the deformation of the body. A thorough understanding of

the fundamentals of this subject is of vital importance for the design of

any machine or structure, because many of the formulas and rules

of design cited in engineering codes are based upon the principles of

this subject.

21

22

Chapter 1

StreSS

Historical Development.

1

The origin of mechanics of materials

dates back to the beginning of the seventeenth century, when Galileo

Galilei performed experiments to study the effects of loads on rods and

beams made of various materials. However, it was not until the beginning

of the nineteenth century when experimental methods for testing

materials were vastly improved. At that time many experimental and

theoretical studies in this subject were undertaken, primarily in France,

by such notables as Saint-Venant, Poisson, Lamé, and Navier.

Through the years, after many fundamental problems had been solved,

it became necessary to use advanced mathematical and computer

techniques to solve more complex problems. As a result, mechanics of

materials has expanded into other areas of mechanics, such as the theory

of elasticity and the theory of plasticity.

1.2

EquIlIbrIum of a dEformablE

body

Since statics plays an important role in both the development and

application of mechanics of materials, it is very important to have a good

grasp of its fundamentals. For this reason we will now review some of the

main principles of statics that will be used throughout the text.

Loads. A body can be subjected to both surface loads and body

forces. Surface loads that act on a small area of contact are reported by

concentrated forces, while distributed loadings act over a larger surface

area of the body. When the loading is coplanar, as in Fig. 1–1a, then a

resultant force FR of a distributed loading is equal to the area under the

distributed loading diagram, and this resultant acts through the geometric

center or centroid of this area.

700 N

FR 400 N

200 N/m

B

A

1m

1m

1m

(a)

Fig. 1–1

1.5 m

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