1
Mechanics of Materials
2
3
CHAPTER 0 INTRODUCTION
§ 0-1 THE RESEARCH OBJECT OF MECHANICS OF
MATERIALS
§ 0-2 THE TASKS OF MECHANICS OF MATERIALS
AND ITS RELATION WITH ENGINEERING
§ 0-3 THE PROPERTIES AND THE FUNDAMENTAL
ASSUMPTIONS OF THE SOLID DEFORMABLE BODIES
§ 0-4 BASIC TYPES OF THE DEFORMATION OF RODS
4
第零章 绪 论
材料力学：研究物体受力后的内在表现,
即，变形规律和破坏特征。
? § 0–1 材料力学的研究对象
? § 0–2 材料力学的任务及与工程的联系
§ 0–3可变形固体的性质及基本假设
? § 0–4 杆件变形的基本形式
5
? Leonardo Da Vinci said:, mechanics is a
mathematic paradise,because we acquired
mathematics's fruit here."
Le
on
ar
do
Da V
inc
i
Gali
leo
Gali
lei
He made a detailed study on the basic concepts of
movement including the center of gravity,speed and
acceleration and came up with the rigid mathematic
formulas,Especially the concept of acceleration is the
milestone in the history of mechanics,
Galileo (1564~1642) is a German
astronomer,mechanist and
philosopher.He was born in Pisa
onFeb15 1564 and died on Jan.8
1642 at the same place,
6
? 达芬奇说,
,力学是数学的乐园，
因为我们在这里获得了
数学的果实。,
达
芬
奇
伽
利
略
7
He once informally proposed law of inertia,which
established the foundation for Newton to propose
formally the first law and the second law, It can be
said that Galileo is the Pioneer of Newton in the
settlement of the classical mechanics, Galileo also
brought up with the law of resultant and the rule of
the parabolic motion and set up the principle of
relativity, He is the first scientist to make a tot of
achievements by the telescope,
He kept on fighting with the idealism and church
philosophy and suggested that we should study the
law of nature by specific experiments and thought
that experiences are the source of theory,
Gali
leo
Gali
lei
8
? 达芬奇说,
,力学是数学的乐园，
因为我们在这里获得了
数学的果实。,
达
芬
奇
伽
利
略
9
Here are his contributions to mechanics, he made a further study
on the basis of Galileo Galilei and other people and concluded
the three principles of objects’movement and made a firm
foundation for mechanics.He is the discoverer of the gravitation
law and set up the theoretical system of the classical mechanics,
He also made profound contributions to the field of
mathematics,optics and astronomy.<The math theory of natural
philosophy>is his most important work.He concluded many
important discoveries and study results in all his life in the book,
Isaac Newton (1642~1727) is a great
British physicist,mathematician and
astronomer,
He was born in a family of peasants in
Lincoln on Dec25 1624 and died of
Kidney stone in London on Mar20 1727,
10
11
He began his creative work between 1903 and 1906 and did
research in the University in Germany every year supervised by
famous scholars, He was a professor of colleges between 1907 and
1917.He came to America in 1922 and engaged in the study of
mechanics.In 1928,he found,the mechanics department of ASME”
and held,various kinds of mechanics seminars periodically,
He has many works on applied applying mechanics,
Especially since the year of late twenties he has written about 20
books applied such as <mechanics of Materials>,<Advanced
Mechanics of Materials> and <Mechanics of Structures> except
that he has done some work in teaching and training maters,
S.P is a Russian dynamicist with
American nationality, He was born
in Ukraine on Dec.23 1878 and died
in German on May.29 1972,
12
13
He makes great contributions to the research of local damage and
the engineering application of fracture dynamics,He has trained
some researchers in mechanics, He is active in academic activities
and takes some positions both at home and abroad,He is a
council member of the first session council conference,He council
chairperson of the second session council conference and the
executive manager of the third session council conference,He was
born in family in Shou city,Anhui province,Now he is the
professor of Southwest Jiao Tong University,
Sun Xunfang is an engineering mechanist
and mechanics educationist,He has
engaged in the research of fracture,
damage,fatigue and creep of solid
mechanics,He is the first to apply fracture
dynamics to practice and developed the
method of analysis in elasto-plastic
fracture dynamics with surface cracks and
assessment in integrity,
14
15
§ 0-1 THE RESEARCH OBJECTS OF MECHANICS OF
MATERIALS
? 1,Structure members
? 2,Classification of
structure members
plate
Or shell
bar or rod clump body
16
§ 0-1 材料力学的研究对象
?1、构件
?2、构件分类
杆
件
板
壳
块
体
? Beams and rods are the main research objects of
mechanics of materials
?材料力学以“梁、杆”为主要研究对
象
? Most structures are made up from the beams and rods
?工程中多为梁、杆结构
21
§ 0-2 THE TASKS OF MECHANICS OF MATERIALS
AND ITS RELATION WITH ENGINEERING
Strength,rigidity,stability
22
§ 0-2 材料力学的任务及与工程的联系
强度、刚度、稳定性
23
Streng th,
Capac ity to resist fail ure of a compo nent or a n el ement,
Rigidity,
Capac ity to resist defo rma tions of a co mponent or a n
eleme nt,
Sta bility,
Capac ity to rema in the origi nal state in equil ibrium of a
co mpon e nt or an el ement
24
强度,
杆 件 在 外 载 作 用 下, 抵 抗 断 裂 或 过 量 塑 性 变 形 的 能 力 。
刚度,
杆 件 在 外 载 作 用 下, 抵 抗 弹 性 变 形 的 能 力 。
稳定性,
杆 件 在 压 力 外 载 作 用 下, 保 持 其 原 有 平 衡 状 态 的 能 力 。
25
The tasks of mechanics of materials
Under the request that the strength,rigidity,stability
are satisfied,offer the necessary theoretical
foundation and calculation method for determining
reasonable shapes and dimensions,choosing proper
materials for the components at the most economic
price,
?,
26
材料力学的任务
?在满足强度、刚度、稳定性的要
求下，以最经济的代价，为构件
确定合理的形状和尺寸，选择适
宜的材料，而提供必要的理论基
础和计算方法。
27
? 1,Strength,
? Capacity to resist failure of a component or an element,
28
?1、强度,
构
件
的
抗
破
坏
能
力
31
32
33
34
35
? 2,Rigidity,
? Capacity to resist deformations of a component or an
element,
36
? 2、刚度：构件的抗变形能力。
37
38
39
40
41
Strength and rigidity
42
强
度
和
刚
度
43
Problems about the strength and rigidity of
engineering components
44
工程构件的强度、刚度问题
? 3 Stability,
? Capacity to remain the original state in equilibrium of a
component or an element
构
件
保
持
原
有
平
衡
状
态
的
能
力
? 3、
稳
定
性,
47
Problems about the strength,
rigidity and stability of
engineering structures
Problems
about stability
strength
rigidity
48
工程结构的强度,
刚度和稳定问题
稳
定
问
题
强
度
刚
度
49
There are problems about the strength,
rigidity and stability in a bicycle structure too
50
自行车结构也有强度,
刚度和稳定问题
51
The space station and space implements
52
空间站和航天器
53
Airplane
s and
guided
missiles
in the
weapon
industry
54
兵
器
工
业
、
飞
机
与
导
弹
55
56
57
58
59
60
61
? Problems about the
strength,rigidity and
stability in large bridges,
62
? 大型桥梁的强度,
刚度、稳定问题
63
Macao bridge
Nanpu bridge in Shanghai
Nanjing Yangtze
River bridge
64
澳 门 桥
上海南浦大桥
南京长江大桥
65
66
67
68
69
70
71
§ 0-3 THE PROPERTIES AND THE FUNDAMENTAL
ASSUMPTION OF THE SOLID DEFORMABLE BODIES
1,Continuity,The material of a solid deformable body is continuously
distributed over its volume so that there are not any cracks,defects or holes etc,
2,Homogeneity,The material of the solid deformable body is homogeneously
distributed over its volume so that the smallest element cut from the body possesses
the same specific mechanical properties as the body,
3,Isotropy,The mechanical properties are the same in all directions at a point,
material with this property is called isotropy material,Material that the mechanical
properties are different in all directions at a point is called anisotropy material,
4,Small deformations:The deformations for a solid deformable body caused
by external forces are very small compared with the dimensions of the body,Thus
when we study the equilibrium and motion of the solid deformable body,the
deformation of the body may be neglected,
72
§ 0-3 可变形固体的性质及其基本假设
一、连续性假设：物质密实地充满物体所在空间，毫无空隙。
（可用微积分数学工具）
二、均匀性假设：物体内，各处的力学性质完全相同。
三、各向同性假设：组成物体的材料沿各方向的力学性质完全
相同。（这样的材料称为各向同性材料；沿各方向的力学
性质不同的材料称为各向异性材料。）
四、小变形假设：材料力学所研究的构件在载荷作用下的变形
与原始尺寸相比甚小，故对构件进行受力分析时可忽略其
变形。
73
§ 0-4 BASIC TYPES OF DEFORMATIONS OF ROD
Combined Loading and deformation
Content
Types
Loading characteristics
Deformation characteristics
Axial Tension
Shear
Torsion
Bending
74
§ 0-4 杆件变形的基本形式
组合受力与变形
内容
种类
外力特点
变形特点
轴向拉伸 及
压缩
剪切
扭转
平面弯曲
75
76
Mechanics of Materials
2
3
CHAPTER 0 INTRODUCTION
§ 0-1 THE RESEARCH OBJECT OF MECHANICS OF
MATERIALS
§ 0-2 THE TASKS OF MECHANICS OF MATERIALS
AND ITS RELATION WITH ENGINEERING
§ 0-3 THE PROPERTIES AND THE FUNDAMENTAL
ASSUMPTIONS OF THE SOLID DEFORMABLE BODIES
§ 0-4 BASIC TYPES OF THE DEFORMATION OF RODS
4
第零章 绪 论
材料力学：研究物体受力后的内在表现,
即，变形规律和破坏特征。
? § 0–1 材料力学的研究对象
? § 0–2 材料力学的任务及与工程的联系
§ 0–3可变形固体的性质及基本假设
? § 0–4 杆件变形的基本形式
5
? Leonardo Da Vinci said:, mechanics is a
mathematic paradise,because we acquired
mathematics's fruit here."
Le
on
ar
do
Da V
inc
i
Gali
leo
Gali
lei
He made a detailed study on the basic concepts of
movement including the center of gravity,speed and
acceleration and came up with the rigid mathematic
formulas,Especially the concept of acceleration is the
milestone in the history of mechanics,
Galileo (1564~1642) is a German
astronomer,mechanist and
philosopher.He was born in Pisa
onFeb15 1564 and died on Jan.8
1642 at the same place,
6
? 达芬奇说,
,力学是数学的乐园，
因为我们在这里获得了
数学的果实。,
达
芬
奇
伽
利
略
7
He once informally proposed law of inertia,which
established the foundation for Newton to propose
formally the first law and the second law, It can be
said that Galileo is the Pioneer of Newton in the
settlement of the classical mechanics, Galileo also
brought up with the law of resultant and the rule of
the parabolic motion and set up the principle of
relativity, He is the first scientist to make a tot of
achievements by the telescope,
He kept on fighting with the idealism and church
philosophy and suggested that we should study the
law of nature by specific experiments and thought
that experiences are the source of theory,
Gali
leo
Gali
lei
8
? 达芬奇说,
,力学是数学的乐园，
因为我们在这里获得了
数学的果实。,
达
芬
奇
伽
利
略
9
Here are his contributions to mechanics, he made a further study
on the basis of Galileo Galilei and other people and concluded
the three principles of objects’movement and made a firm
foundation for mechanics.He is the discoverer of the gravitation
law and set up the theoretical system of the classical mechanics,
He also made profound contributions to the field of
mathematics,optics and astronomy.<The math theory of natural
philosophy>is his most important work.He concluded many
important discoveries and study results in all his life in the book,
Isaac Newton (1642~1727) is a great
British physicist,mathematician and
astronomer,
He was born in a family of peasants in
Lincoln on Dec25 1624 and died of
Kidney stone in London on Mar20 1727,
10
11
He began his creative work between 1903 and 1906 and did
research in the University in Germany every year supervised by
famous scholars, He was a professor of colleges between 1907 and
1917.He came to America in 1922 and engaged in the study of
mechanics.In 1928,he found,the mechanics department of ASME”
and held,various kinds of mechanics seminars periodically,
He has many works on applied applying mechanics,
Especially since the year of late twenties he has written about 20
books applied such as <mechanics of Materials>,<Advanced
Mechanics of Materials> and <Mechanics of Structures> except
that he has done some work in teaching and training maters,
S.P is a Russian dynamicist with
American nationality, He was born
in Ukraine on Dec.23 1878 and died
in German on May.29 1972,
12
13
He makes great contributions to the research of local damage and
the engineering application of fracture dynamics,He has trained
some researchers in mechanics, He is active in academic activities
and takes some positions both at home and abroad,He is a
council member of the first session council conference,He council
chairperson of the second session council conference and the
executive manager of the third session council conference,He was
born in family in Shou city,Anhui province,Now he is the
professor of Southwest Jiao Tong University,
Sun Xunfang is an engineering mechanist
and mechanics educationist,He has
engaged in the research of fracture,
damage,fatigue and creep of solid
mechanics,He is the first to apply fracture
dynamics to practice and developed the
method of analysis in elasto-plastic
fracture dynamics with surface cracks and
assessment in integrity,
14
15
§ 0-1 THE RESEARCH OBJECTS OF MECHANICS OF
MATERIALS
? 1,Structure members
? 2,Classification of
structure members
plate
Or shell
bar or rod clump body
16
§ 0-1 材料力学的研究对象
?1、构件
?2、构件分类
杆
件
板
壳
块
体
? Beams and rods are the main research objects of
mechanics of materials
?材料力学以“梁、杆”为主要研究对
象
? Most structures are made up from the beams and rods
?工程中多为梁、杆结构
21
§ 0-2 THE TASKS OF MECHANICS OF MATERIALS
AND ITS RELATION WITH ENGINEERING
Strength,rigidity,stability
22
§ 0-2 材料力学的任务及与工程的联系
强度、刚度、稳定性
23
Streng th,
Capac ity to resist fail ure of a compo nent or a n el ement,
Rigidity,
Capac ity to resist defo rma tions of a co mponent or a n
eleme nt,
Sta bility,
Capac ity to rema in the origi nal state in equil ibrium of a
co mpon e nt or an el ement
24
强度,
杆 件 在 外 载 作 用 下, 抵 抗 断 裂 或 过 量 塑 性 变 形 的 能 力 。
刚度,
杆 件 在 外 载 作 用 下, 抵 抗 弹 性 变 形 的 能 力 。
稳定性,
杆 件 在 压 力 外 载 作 用 下, 保 持 其 原 有 平 衡 状 态 的 能 力 。
25
The tasks of mechanics of materials
Under the request that the strength,rigidity,stability
are satisfied,offer the necessary theoretical
foundation and calculation method for determining
reasonable shapes and dimensions,choosing proper
materials for the components at the most economic
price,
?,
26
材料力学的任务
?在满足强度、刚度、稳定性的要
求下，以最经济的代价，为构件
确定合理的形状和尺寸，选择适
宜的材料，而提供必要的理论基
础和计算方法。
27
? 1,Strength,
? Capacity to resist failure of a component or an element,
28
?1、强度,
构
件
的
抗
破
坏
能
力
31
32
33
34
35
? 2,Rigidity,
? Capacity to resist deformations of a component or an
element,
36
? 2、刚度：构件的抗变形能力。
37
38
39
40
41
Strength and rigidity
42
强
度
和
刚
度
43
Problems about the strength and rigidity of
engineering components
44
工程构件的强度、刚度问题
? 3 Stability,
? Capacity to remain the original state in equilibrium of a
component or an element
构
件
保
持
原
有
平
衡
状
态
的
能
力
? 3、
稳
定
性,
47
Problems about the strength,
rigidity and stability of
engineering structures
Problems
about stability
strength
rigidity
48
工程结构的强度,
刚度和稳定问题
稳
定
问
题
强
度
刚
度
49
There are problems about the strength,
rigidity and stability in a bicycle structure too
50
自行车结构也有强度,
刚度和稳定问题
51
The space station and space implements
52
空间站和航天器
53
Airplane
s and
guided
missiles
in the
weapon
industry
54
兵
器
工
业
、
飞
机
与
导
弹
55
56
57
58
59
60
61
? Problems about the
strength,rigidity and
stability in large bridges,
62
? 大型桥梁的强度,
刚度、稳定问题
63
Macao bridge
Nanpu bridge in Shanghai
Nanjing Yangtze
River bridge
64
澳 门 桥
上海南浦大桥
南京长江大桥
65
66
67
68
69
70
71
§ 0-3 THE PROPERTIES AND THE FUNDAMENTAL
ASSUMPTION OF THE SOLID DEFORMABLE BODIES
1,Continuity,The material of a solid deformable body is continuously
distributed over its volume so that there are not any cracks,defects or holes etc,
2,Homogeneity,The material of the solid deformable body is homogeneously
distributed over its volume so that the smallest element cut from the body possesses
the same specific mechanical properties as the body,
3,Isotropy,The mechanical properties are the same in all directions at a point,
material with this property is called isotropy material,Material that the mechanical
properties are different in all directions at a point is called anisotropy material,
4,Small deformations:The deformations for a solid deformable body caused
by external forces are very small compared with the dimensions of the body,Thus
when we study the equilibrium and motion of the solid deformable body,the
deformation of the body may be neglected,
72
§ 0-3 可变形固体的性质及其基本假设
一、连续性假设：物质密实地充满物体所在空间，毫无空隙。
（可用微积分数学工具）
二、均匀性假设：物体内，各处的力学性质完全相同。
三、各向同性假设：组成物体的材料沿各方向的力学性质完全
相同。（这样的材料称为各向同性材料；沿各方向的力学
性质不同的材料称为各向异性材料。）
四、小变形假设：材料力学所研究的构件在载荷作用下的变形
与原始尺寸相比甚小，故对构件进行受力分析时可忽略其
变形。
73
§ 0-4 BASIC TYPES OF DEFORMATIONS OF ROD
Combined Loading and deformation
Content
Types
Loading characteristics
Deformation characteristics
Axial Tension
Shear
Torsion
Bending
74
§ 0-4 杆件变形的基本形式
组合受力与变形
内容
种类
外力特点
变形特点
轴向拉伸 及
压缩
剪切
扭转
平面弯曲
75
76
