Beer
Johnston
Ninth Edition
Ninth Edition
ISBN 978-0-07-352940-0
MHID 0-07-352940-0
Part of
ISBN 978-0-07-727555-6
MHID 0-...
NINTH EDITION
VECTOR MECHANICS
FOR ENGINEERS
Statics and Dynamics
Ferdinand P. Beer
Late of Lehigh University
E. Russell J...
VECTOR MECHANICS FOR ENGINEERS: STATICS & DYNAMICS, NINTH EDITION
Published by McGraw-Hill, a business unit of The McGraw-...
About the Authors
iii
As publishers of the books by Ferd Beer and Russ Johnston we are
often asked how they happened to wr...
the early part of World War II and taught for four years at Williams
College in the Williams-MIT joint arts and engineerin...
Contents
v
Preface xv
List of Symbols xxiii
1 Introduction 1
1.1 What Is Mechanics? 2
1.2 Fundamental Concepts and Princip...
3 Rigid Bodies: Equivalent
Systems of Forces 72
3.1 Introduction 74
3.2 External and Internal Forces 74
3.3 Principle of T...
viiEquilibrium in Three Dimensions 189
4.8 Equilibrium of a Rigid Body in Three Dimensions 189
4.9 Reactions at Supports a...
Frames and Machines 316
6.9 Structures Containing Multiforce Members 316
6.10 Analysis of a Frame 316
6.11 Frames Which Ce...
ix
9 Distributed Forces:
Moments of Inertia 470
9.1 Introduction 472
Moments of Inertia of Areas 473
9.2 Second Moment, or...
11 Kinematics of Particles 600
11.1 Introduction to Dynamics 602
Rectilinear Motion of Particles 603
11.2 Position, Veloci...
xiContents
13 Kinetics of Particles: Energy and
Momentum Methods 754
13.1 Introduction 756
13.2 Work of a Force 756
13.3 K...
15 Kinematics of Rigid Bodies 914
15.1 Introduction 916
15.2 Translation 918
15.3 Rotation about a Fixed Axis 919
15.4 Equ...
xiii
17 Plane Motion of Rigid Bodies: Energy
and Momentum Methods 1080
17.1 Introduction 1082
17.2 Principle of Work and E...
19 Mechanical Vibrations 1212
19.1 Introduction 1214
Vibrations without Damping 1214
19.2 Free Vibrations of Particles. Si...
Preface
OBJECTIVES
The main objective of a first course in mechanics should be to
develop in the engineering student the a...
• In Dynamics, the same division is observed. The basic concepts of
force, mass, and acceleration, of work and energy, and...
xviisum of their moments to the rates of change of the linear and angular
momentum of the particle. This makes possible an...
are in U.S. customary units. The authors believe that this approach
will best serve the need of students, who, as engineer...
xixnecessary to the understanding of the text are carefully presented in
Chaps. 2 and 3. However, special problems are inc...
text and to help students understand the principles of mechanics.
The problems are grouped according to the portions of ma...
xxiMcGRAW-HILL CONNECT ENGINEERING
McGraw-Hill Connect Engineering is a web-based assignment and
assessment platform that ...
xxii Preface The authors gratefully acknowledge the many helpful com-
ments and suggestions offered by users of the previo...
xxiii
List of Symbols
a Constant; radius; distance
A, B, C, . . . Reactions at supports and connections
A, B, C, . . . Poi...
V Vector product; shearing force
V Volume; potential energy; shear
w Load per unit length
W, W Weight; load
x, y, z Rectan...
a Introduction
In the latter part of the seventeenth
century, Sir Isaac Newton stated the
fundamental principles of mechan...
1H1
C H A P T E R
1
Introduction
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Chapter 1 Introduction
1.1 What Is Mechanics?
1.2 Fundamental Concepts and
Principles
1.3 Systems of Units
1.4 Conversion ...
3To define an event, it is not sufficient to indicate its position in
space. The time of the event should also be given.
T...
4 Introduction SECOND LAW. If the resultant force acting on a particle is not zero,
the particle will have an acceleration...
5The principles we have just listed will be introduced in the course
of our study of mechanics as they are needed. The stu...
6 Introduction which was originally chosen to represent 1/86 400 of the mean solar
day, is now defined as the duration of ...
7
Using scientific notation, one may also write
3.82 km 5 3.82 3 103
m
47.2 mm 5 47.2 3 1023
m
The multiples of the unit o...
8 Introduction the submultiples of the unit of area are
1 dm2
5 (1 dm)2
5 (1021
m)2
5 1022
m2
1 cm2
5 (1 cm)2
5 (1022
m)2
...
9U.S. Customary Units. Most practicing American engineers still
commonly use a system in which the base units are the unit...
10 Introduction requires greater attention than the corresponding operation in SI
units. If, for example, the magnitude of...
11W 5 mg
1 lb 5 (0.4536 kg)(9.807 m/s2
) 5 4.448 kg ? m/s2
or, recalling Eq. (1.5),
1 lb 5 4.448 N (1.11)
Units of Mass. T...
12 Introduction
no place in its solution for your particular fancy. The solution must be
based on the six fundamental prin...
13The fundamental principles of mechanics listed in Sec. 1.2 will
be used to write equations expressing the conditions of ...
14
Many engineering problems can be
solved by considering the equilibrium of
a “particle.” In the case of this
excavator, ...
2C H A P T E R
15
Statics of Particles
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16
2.1 INTRODUCTION
In this chapter you will study the effect of forces acting on particles.
First you will learn how to r...
17that line; through the use of an appropriate scale, the length of this
segment may be chosen to represent the magnitude ...
18 Statics of Particles vectors are called free vectors. Still other physical quantities, such
as forces acting on a rigid...
19From the parallelogram law, we can derive an alternative
method for determining the sum of two vectors. This method, kno...
20 Statics of Particles If the given vectors are coplanar, i.e., if they are contained in
the same plane, their sum can be...
21
the particle A as the given forces. As indicated above, the order in
which the vectors P, Q, and S representing the giv...
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