Engineering Mechanics , livre ebook

Current Natural Sciences

Ping YI, Jun LIU and Feng JIANG

Engineering Mechanics

M E C H A N I C S

M E C H A N I C S

ISBN : 978-2-7598-2901-9

Current Natural Sciences

Engineering Mechanics

Ping YI, Jun LIU and Feng JIANG

Engineering mechanics provides the theories and methods of
describing and predicting the state of equilibrium or
accelerated motion of particles or rigid bodies under the action
of forces. It consists of three parts: statics (chapters 1–5),
kinematics (chapters 6 and 7) and kinetics (chapters 8–10)
and it is basically corresponding to the course of “theoretical
mechanics” in China. It is hoped that this book will help to develop
in engineering students the correct understanding of the principles
of mechanics and the ability to analyze and solve engineering
problems using the principles.

This book can be used as a teaching material for civil engineering,
hydraulic engineering, mechanical engineering, aerospace,
transportation and other engineering majors in colleges and
universities, and as a self-study book for relevant technical
personnel.

www.edpsciences.org

Current Natural Sciences

Ping YI, Jun LIU and Feng JIANG

Engineering Mechanics

Printed in France

EDP Sciences–ISBN(print): 978-2-7598-2901-9–ISBN(ebook): 978-2-7598-2902-6
DOI: 10.1051/978-2-7598-2901-9

All rights relative to translation, adaptation and reproduction by any means whatsoever
are reserved, worldwide. In accordance with the terms of paragraphs 2 and 3 of Article 41
of the French Act dated March 11, 1957,“copies or reproductions reserved strictly for
private use and not intended for collective use”and, on the other hand, analyses and
short quotations for example or illustrative purposes, are allowed. Otherwise,“any
representation or reproduction–whether in full or in part–without the consent of the
author or of his successors or assigns, is unlawful”(Article 40, paragraph 1). Any
representation or reproduction, by any means whatsoever, will therefore be deemed an
infringement of copyright punishable under Articles 425 and following of the French
Penal Code.

The printed edition is not for sale in Chinese mainland. Customers in Chinese mainland
please order the print book from Science Press. ISBN of the China edition: Science Press
978-7-03-073762-5

Science Press, EDP Sciences, 2022

Foreword

This book presents and illustrates the concepts, principles and analytical
problem-solving methodologies in engineering mechanics. It is divided into ten
chapters. Chapter1gives an introduction to engineering mechanics and its
fundamental concepts. Since the international system of units (SI units) receives
worldwide recognition, SI units are also introduced in chapter1and used
throughout the book. As a convenient tool, vector algebra is then presented in
chapter2. Chapter3discusses the simplification of a system of forces and couples or
a distributed loading. The conditions and equations of equilibrium for a particle and
a rigid body are developed and applied, especially to equilibrium problems of a
system of rigid bodies, such as frames, machines and trusses, in chapter4.
Applications to equilibrium problems involving frictional forces are discussed in
chapter5. The kinematics of particles is treated in chapter6, followed by a
discussion of planar kinematics of rigid bodies in chapter7. Kinetics are discussed in
chapter8(equations of motion), chapter9(work and energy), and chapter10
(impulse and momentum). In each of these three chapters, applications to only
particles’motion are considered first and then more difficult and practical
applications associated with the motion of rigid bodies are addressed.
Each chapter begins with theobjectives of the chapter. Then it consists of theory
sections, example problems and homework problems. The example problems serve
double purposes of amplifying the theories and demonstrating the neat work that
students should cultivate in their own solutions, and are presented in a logical and
orderly manner. Sometimes multiple solutions are provided for a problem, trying to
inspire students to broaden their thinking and better understand various principles
and methods. For some examples, there is a“RETHINK”section, where in-depth
discussions or enlightening questions are presented. Most of the problems are of
practical nature and should appeal to engineering students. They are meticulously
designed to help students master the principles of mechanics and their applications.

DOI: 10.1051/978-2-7598-2901-9.c901
Science Press, EDP Sciences, 2022

IV

Foreword

This book is financially supported by Dalian University of Technology and
DUT-BSU Joint Institute, which are gratefully acknowledged. During the
preparation of this book, many people have helped in its development. First, the authors are
particularly grateful to Dr. Dzianis Marmysh in Belarusian State University and
Dr. Ming Li in Dalian University of Technology for their specific help. Also, many
thanks to our graduate students who have taken the time to prepare and check the
solutions to some of the homework problems of the book. They are:

Baopei Cai
Xinyue Ma
Xiaoqian Wang
Na Li

Qingkang Wang
Dongchi Xie
Yuhan Zhang
Zhixuan Li

Linlang Feng
Weining Yang
Huiqing Liu
Juncheng Li

Yongke Li
Wenjian Nie
Xinshuai Guo
Yan Xing

Zuo Zhu
Hongzhi Wang
Shaopeng Bai
Chengcheng Fan

The authors also thank the staff at EDP Sciences and Science Press for their
great support anddedication during the preparation of this book.Lastly, the
authors wish to thank many of our colleagues and students for their helpful
comments and suggestions. Since this list is too long, it is hoped that they will
accept this anonymous recognition.
If you have any comments, problems, or suggestions related to the book, please
feel free to contact us. Your feedback will surely help us complement and improve it.

Ping Yi, Jun Liu, Feng Jiang
Dalian University of Technology
June, 2021

Contents

Foreword. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 1
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Mechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 FundamentalConcepts and Principles. . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 FundamentalConcepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Newton’s Laws of Motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 Newton’s Law of Gravitational Attraction. . . . . . . . . . . . . . . .
1.3 Unitsof Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Procedureof Problem Solving. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 2
Vectors and Vector Operations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Vectorsand the Parallelogram Law. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 CartesianVectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 CartesianVector Representation. . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Additionand Subtraction of Cartesian Vectors. . . . . . . . . . . . .
2.3 VectorDirected Along a Line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 DotProduct and Cross Product. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 CartesianVector Formulation of the Dot Product. . . . . . . . . .
2.4.2 Applicationsof the Dot Product. . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 CartesianVector Formulation of the Cross Product. . . . . . . . .

CHAPTER 3
Simplification of Force Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Momentof a Force about a Point. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 VectorFormulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Principleof Moments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 ScalarFormulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Momentof a Force about a Specified Axis. . . . . . . . . . . . . . . . . . . . .
3.3 Momentof a Couple. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 VectorFormulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 ScalarFormulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

III

1
1
2
2
3
3
4
6

11
11
14
16
19
21
24
25
26
29

37
37
38
43
43
47
52
52
54

VI

3.4

3.5

Contents

Simplification of a System of Forces and Couples. . . . . . . . . . . . . . . .
3.4.1 EquivalentSystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Reductionto One Force and One Couple. . . . . . . . . . . . . . . . .
3.4.3 FurtherSimplification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Application of Simplification of Parallel Forces. . . . . . . . . . . . . . . . . .
3.5.1 Centerof Gravity, Center of Mass, and Centroid of a Body. . .
3.5.2 Centerof Gravity, Center of Mass, and Centroid of Composite
Bodies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.3 Reductionin Distributed Loading. . . . . . . . . . . . . . . . . . . . . .

CHAPTER 4
Equilibrium of Rigid Bodies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Conditionsfor Rigid-Body Equilibrium. . . . . . . . . . . . . . . . . . . . . . . .
4.2 Free-BodyDiagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 SupportReactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Procedureof Drawing a Free-Body Diagram. . . . . . . . . . . . . . .
4.3 EquilibriumProblems of a Rigid Body. . . . . . . . . . . . . . . . . . . . . . . .
4.4 Two-an