1
Theoretical Mechanics
2
3
Introduction
Statics is the branch of mechanics which studies the laws of
equilibria of bodies under the action of force systems,
It mainly studies simplifications and equilibrium conditions
of force systems and applications of the corresponding results,
4
静力学主要研究：力系的简化和力系的平衡条件及其应用。
引 言
静力学是研究物体在力系作用下平衡规律的科学。
5
Theoretical mechanics
6
7
§ 1–1 Fundamental concepts in statics
§ 1–2 Principles of statics
§ 1–3 Constraints and their reaction forces
§ 1–4 Force analysis and force diagrams
Chapter 1,Fundamental
principles of statics and force analysis
8
§ 1–1 静力学的基本概念
§ 1–2 静力学公理
§ 1–3 约束与约束反力
§ 1–4 物体的受力分析与受力图
第一章 静力学公理与物体的受力分析
9
Chapter 1,Fundamental
principles of statics and force analysis
§ 1-1 Fundamental concepts in statics
1,Force
1) Concept,the mechanical interaction of bodies is caused by
forces,This interaction can change the state of motion of a
body,
2) Effects of forces,① motion (external effect)
② deformation (internal effect),
3) The three elements,
magnitude,direction and
point of application,
A F
4) Unit of force,newton (N) (International System of Units)
kilonewton (kN)
10
力的单位,国际单位制：牛顿 (N)
千牛顿 (kN)
第一章 静力学基本公理和物体的受力分析
§ 1-1 静力学基本概念
一、力的概念
1．定义, 力是物体间的相互机械作用,这种作用可以改变物
体的运动状态。
2,力的效应,① 运动效应 (外效应 ) ② 变形效应 (内效应 )。
3,力的三要素,大小，方向，作用点 A F
11
Force system,a group of forces acting on a body,
Balanced force system,if a body subjected to a
force system is in equilibrium state,
we call the system to be a balanced,
A body is called to be in the state of equilibrium if it does not move
or if it moves with an uniform velocity,
2.Rigid body
A body which does not change its shape and dimension under
applied forces is called a rigid body
3.Equilibrium state
A
F
12
力系,是指作用在物体上的一群力。
平衡力系,物体在力系作用下处于平衡,
我们称这个力系为平衡力系。
是指物体相对于惯性参考系保持静止或作匀速直线运
动的状态。
二,刚体
就是在力的作用下，大小和形状都不变的物体。
三,平衡
A
F
13
§ 1-2 Principles of statics
Principles,conclusions obtained from longtime practice and from
many experiments,They are repeatedly proved by practice and now
are recognized without prove,
1st Principle,two force equilibrium
A rigid body subjected to the action of two forces can be in
equilibrium,the necessary and sufficient conditions are,
the two forces are equal in magnitude,| F1 | = | F2 |
the two forces are opposite in direction,F1 = –F2
the two forces are collinear,
the two forces act on the same body,
14
§ 1-2 静力学基本公理
公理,是人类经过长期实践和经验而得到的结论，它被反复的
实践所验证，是无须证明而为人们所公认的结论。
公理 1 二力平衡公理
作用于刚体上的两个力，使刚体平衡的必要与充分条件是,
这两个力 大小相等 | F1 | = | F2 |
方向相反 F1 = –F2
作用线共线,
作用于同一个物体上。
15
Explanation,
① As far as rigid bodies are concerned,the conditions above are
necessary and sufficient,
② As far as deformable bodies are concerned,the conditions
above are only necessary,
bodies (deformable body) string
二力杆
Double force
equivalent body
Double force
equivalent rod
③ double force equivalent body,is a rigid body subjected to
two forces must be in equilibrium,
16
说明, ①对刚体来说，上面的条件是充要的
③ 二力体,只在两个力作用下平衡的刚体叫二力体。
② 对变形体来说，上面的条件只是必要条件 (或多体中 )
二力杆
17
The action of a given force system on a rigid body remains unchanged
if another balanced force system is added to or subtracted from the
original system,
Corollary 1,transmissibility of a force
The point of application of a force acting on a rigid body can be
transferred to any other point on the line of action of the force without
altering its effect,
Therefore,as far as a rigid body is concerned,a force can be
characterized by three elements,magnitude,direction and line of
application,
2nd Principle,addition and subtraction of balanced force systems
18
在已知力系上加上或减去任意一个平衡力系，并不改变原
力系对刚体的作用。
推论 1：力的可传性。
作用于刚体上的力可沿其作用线移到同一刚体内的任一
点，而不改变该力对刚体的效应。
因此，对刚体来说，力作用三要素为,大小，方向，作用线
公理 2 加减平衡力系原理
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If a free rigid body remains in equilibrium
under the action of three nonparallel coplanar
forces,the lines of action of those forces
intersect at one point,Moreover,three forces are
coplanar,(under special circumstances,forces
intersect at infinite and become a
parallel force system),
3rd principle,the law of parallelogram
Corollary 2,three equivalent forces intersect
at one point
21 FFR ??
Two forces applied at one point of a body
have as their resultant a force applied at the
same point and represented by the diagonal
of a parallelogram constructed with two
given forces as its sides,
20
刚体受三力作用而平衡，若其中两力作
用线汇交于一点，则另一力的作用线必汇交
于同一点，且三力的作用线共面。（ 必共面，
在特殊情况下，力在无穷远处汇交 —— 平行
力系 。）
公理 3 力的平行四边形法则
作用于物体上同一点的两个力可合成
一个合力，此合力也作用于该点，合力的
大小和方向由以原两力矢为邻边所构成的
平行四边形的对角线来表示。
推论 2,三力平衡汇交定理
21 FFR ??
21
4th principle,the law of action force and reaction force
To any action of one material body on
another there is always an equal and
oppositely directed reaction,They are
equal in magnitude,opposite in
direction,collinear and exist together,
but act on different body,
Prove,∵ is a balanced force system,
∴ is a balanced force system too,
again∵ If two forces are in equilibrium,
they must be equal in magnitude,
opposite in direction and collinear,
∴ intersect at a point and are coplanar,
321,,FFF
321,,FFF
3,FR
Example
droplet
The force the droplet act
on the string
The force the string act
on the droplet
Gravitation
The reaction force of p
22
公理 4 作用力和反作用力定律
等值、反向、共线、异体、且同时存在。
[证 ] ∵ 为平衡力系,
∴ 也为平衡力系。
又 ∵ 二力平衡必等值、反向、共线,
∴ 三力 必汇交，且共面。
321,,FFF
321,,FFF
3,FR
[例 ] 吊灯
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5th principle,principle of solidification
If a deformable body subjected to the action of a force system is in
equilibrium,the state of equilibrium will not be disturbed if the
body solidifies(becomes rigid)
The 5th principle tells us
that the equilibrium of a
balanced deformable body
can be described by the
theory for a rigid body,
Soft string
draw
draw
Solidified rigid rod
draw
draw
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公理 5 刚化原理
变形体在某一力系作用下处于平衡，如将此变形体变成
刚体（刚化为刚体），则平衡状态保持不变。
公理 5告诉我们：处于平衡
状态的变形体，可用刚体静
力学的平衡理论。
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§ 1-3 constraints and their reaction forces
1,Concepts
Free body,A body not connected with other bodies and capable
of displacement in any direction is called a free body,
Constrained body,
A body whose displacement in space is restricted by
other bodies,either connected to or in contact with it,
is called a constrained body,
Constraint,Anything that restricts the displacement of a given
body in space.(here,constraint is a noun,not a verb),
Reaction force of a constraint,
The force by which a constraint acts on a body,thereby
restricting its displacements,is called the force of
reaction of the constraint,
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约束反力,约束给被约束物体的力叫约束反力。
§ 1-3 约束与约束反力
一、概念
自由体,位移不受限制的物体叫自由体。
非自由体,位移受限制的物体叫非自由体。
约束,对非自由体的某些位移预先施加的限制条件称为约束。
（这里，约束是名词，而不是动词的约束。）
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① their magnitude is usually unknown;
② their direction is always opposite to the direction in which
the given constraint prevents the displacement of the body;
③ the point of application is the contact point between the
body and the constraint,
The characteristics of reaction force of constraints,
G G
N1
N2
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① 大小常常是未知的；
②方向总是与约束限制的物体的位移方向相反；
③作用点在物体与约束相接触的那一点。
约束反力特点,
G G
N1
N2
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Strings can only be stretched,therefore the reaction force applies
at the point of contact and the direction of it is away from the
body,
2,Some common types of constraints and their reaction
force direction,
1) Constraints given by a string,
a chain or a strap
P P
T S1 S'1
S'2 S2
30
绳索类 只能受拉,所以它们的约束反力是 作用在接触点,方
向 沿绳索背离物体 。
二、约束类型和确定约束反力方向的方法,
1.由柔软的绳索、链条或皮带构成的约束
P P
T S1 S'1
S'2 S2
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the reaction force is applied at the point of contact and directed
normal to both surfaces,
2) Smooth contact plane (smooth,not taking friction into account )
P
N N
P
NA
NB
Common normal
Common
tangent
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约束反力 作用在接触点处,方向 沿公法线，指向受力物体
2.光滑接触面的约束 (光滑指摩擦不计 )
P
N N
P
NA
NB
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3) Smooth cylindrical pin
① cylindrical pin
Pin
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3.光滑圆柱铰链约束
① 圆柱铰链
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A XA
YA
A
A
Direction is uncertain
Magnified
picture
Pin
36
A
A
XA
YA
A
37
② fixed hinged support
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② 固定铰支座
39
fixed hinged support
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固定铰支座
41
runner and pin
(double surface
constraints)
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滑槽与销钉
（双面约束）
43
double force
equivalent rod
44
二 力 杆
45
Kinetic hinged support (step bearing)
The actual
direction of N can
be downward,
46
活动铰支座（辊轴支座）
N的实际方向也
可以向下
47
Kinetic hinged support (step bearing)
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活动铰支座（辊轴支座）
49
1,Force analysis
To solve a problem of statics,First select the body to be studied,
Secondly,in accordance with the given conditions and constraints,
analyze the forces which act on the bodies using the basic concepts
and principles,This process is called force analysis,
The forces acting on a body can be classified as,
1,active forces,such as the gravitational force,the force of wind
power,the pressure of gases,etc,
2,passive forces,such as reaction force of constraints,
§ 1-4 Force analysis and force diagrams
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一、受力分析
解决力学问题时，首先要选定需要进行研究的物体，即选
择研究对象；然后根据已知条件，约束类型并结合基本概念和
公理分析它的受力情况，这个过程称为物体的 受力分析 。
作用在物体上的力有：一类是,主动力,如重力,风力,气体
压力等。
二类是：被动力，即约束反力。
§ 1-4 物体的受力分析和受力图
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The main steps to draw the force diagrams,
① select the object under study;
② divide the object into several parts and
study the parts one by one;
③ draw the active forces;
④ draw the reaction force of the constraints,
2,Force diagrams
[Example 1]
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画物体受力图主要步骤为,①选研究对象；②取分离体；
③画上主动力；④画出约束反力。
二、受力图
[例 1]
53
[Example 2] Please,draw the force diagrams for
all components in the picture,
Q A
O
B
C
D
E
Rod
54
[例 2] 画出下列各构件的受力图
Q A
O
B
C
D
E
55
Q A
O
B
C
D
E
56
Q A
O
B
C
D
E
57
Q A
O
B
C
D
E
58
Q A
O
B
C
D
E
59
[Example 3] Please,draw the force diagrams for
all components in the picture,
Notice,three balanced forces
must intersect at a point,But
if they are parallel,they
intersect at infinity,This is a
special case,
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[例 3] 画出下列各构件的受力图
说明：三力平衡必汇交
当三力平行时，在无限
远处汇交，它是一种特
殊情况 。
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[Example 4] Sharp point contacts
Get rid of constraints Get rid of constraints
62
[例 4] 尖点问题
应去掉约束 应去掉约束
63
[Example 5] Please,draw the force diagrams for
all components in the picture,
64
[例 5] 画出下列各构件的受力图
65
3,Some problems which should be taken into account when
drawing a force diagram,
Mutual mechanical action forces exist,only if
bodies contact,except for gravitation and
electromagnetic force,So the bodies which are
in contact with the object under study should be
made clear,There must have force at the contact
point,the direction of the force depends on the
type of constraints,
Mind you,the force is the mutual mechanical
action between bodies,Thereby,every force the
body subjected,relatives to a body who applies
the force,We should make it clear,
1) Don’t leave
out any force
2) Don’t draw
redundant
force
66
三、画受力图应注意的问题
除重力、电磁力外，物体之间只有通过接触
才有相互机械作用力，要分清研究对象（受
力体）都与周围哪些物体（施力体）相接触，
接触处必有力，力的方向由约束类型而定。
2、不要多画力
要注意力是物体之间的相互机械作用。因此对
于受力体所受的每一个力，都应能明确地指出
它是哪一个施力体施加的。
1、不要漏画力
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The direction of constraint reaction force must be strictly
according to the type of constraint,never be simply supposed
by direct-view or the direction of the active force,When
analyzing the action forces and the reaction forces between
two bodies,please give attention to the direction of the forces,
If the direction of the action force has been determined,the
direction of the reaction force is opposite to the action force,
Don’t draw the direction of forces wrong,
3) Don’t draw the direction of force wrong
4) There are no constraints on the force diagrams
The force diagrams can be draw only on a part of the object,
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约束反力的方向必须严格地按照约束的类型来画，不
能单凭直观或根据主动力的方向来简单推想。在分析
两物体之间的作用力与反作用力时，要注意，作用力
的方向一旦确定，反作用力的方向一定要与之相反，
不要把箭头方向画错。
3、不要画错力的方向
4、受力图上不能再带约束。
即受力图一定要画在分离体上。
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Whether a force is an external force or an internal one depend
on the special objects,When a body system is divided into
several parts,some internal forces of old system may turn into
the external forces of the new object under study,
If the direction of the reaction force of a constraint is defined,it
should be kept to the same in the analysis of the whole body as
in the analysis of the components,
5) no internal forces but only external forces can be drawn on
a force diagram
6) The force diagram for the whole object should be in
accordance with the force diagrams for any part,they
should assort with each other,but not conflict,
7) Make a exact judge for the double forces components,
70
一个力，属于外力还是内力，因研究对象的不同，有
可能不同。当物体系统拆开来分析时，原系统的部分
内力，就成为新研究对象的外力。
对于某一处的约束反力的方向一旦设定，在整体、局
部或单个物体的受力图上要与之保持一致。
5、受力图上只画外力，不画内力。
6,同一系统各研究对象的受力图必须整体与局部一致，相
互协调，不能相互矛盾。
7,正确判断二力构件。
71
72
Theoretical Mechanics
2
3
Introduction
Statics is the branch of mechanics which studies the laws of
equilibria of bodies under the action of force systems,
It mainly studies simplifications and equilibrium conditions
of force systems and applications of the corresponding results,
4
静力学主要研究：力系的简化和力系的平衡条件及其应用。
引 言
静力学是研究物体在力系作用下平衡规律的科学。
5
Theoretical mechanics
6
7
§ 1–1 Fundamental concepts in statics
§ 1–2 Principles of statics
§ 1–3 Constraints and their reaction forces
§ 1–4 Force analysis and force diagrams
Chapter 1,Fundamental
principles of statics and force analysis
8
§ 1–1 静力学的基本概念
§ 1–2 静力学公理
§ 1–3 约束与约束反力
§ 1–4 物体的受力分析与受力图
第一章 静力学公理与物体的受力分析
9
Chapter 1,Fundamental
principles of statics and force analysis
§ 1-1 Fundamental concepts in statics
1,Force
1) Concept,the mechanical interaction of bodies is caused by
forces,This interaction can change the state of motion of a
body,
2) Effects of forces,① motion (external effect)
② deformation (internal effect),
3) The three elements,
magnitude,direction and
point of application,
A F
4) Unit of force,newton (N) (International System of Units)
kilonewton (kN)
10
力的单位,国际单位制：牛顿 (N)
千牛顿 (kN)
第一章 静力学基本公理和物体的受力分析
§ 1-1 静力学基本概念
一、力的概念
1．定义, 力是物体间的相互机械作用,这种作用可以改变物
体的运动状态。
2,力的效应,① 运动效应 (外效应 ) ② 变形效应 (内效应 )。
3,力的三要素,大小，方向，作用点 A F
11
Force system,a group of forces acting on a body,
Balanced force system,if a body subjected to a
force system is in equilibrium state,
we call the system to be a balanced,
A body is called to be in the state of equilibrium if it does not move
or if it moves with an uniform velocity,
2.Rigid body
A body which does not change its shape and dimension under
applied forces is called a rigid body
3.Equilibrium state
A
F
12
力系,是指作用在物体上的一群力。
平衡力系,物体在力系作用下处于平衡,
我们称这个力系为平衡力系。
是指物体相对于惯性参考系保持静止或作匀速直线运
动的状态。
二,刚体
就是在力的作用下，大小和形状都不变的物体。
三,平衡
A
F
13
§ 1-2 Principles of statics
Principles,conclusions obtained from longtime practice and from
many experiments,They are repeatedly proved by practice and now
are recognized without prove,
1st Principle,two force equilibrium
A rigid body subjected to the action of two forces can be in
equilibrium,the necessary and sufficient conditions are,
the two forces are equal in magnitude,| F1 | = | F2 |
the two forces are opposite in direction,F1 = –F2
the two forces are collinear,
the two forces act on the same body,
14
§ 1-2 静力学基本公理
公理,是人类经过长期实践和经验而得到的结论，它被反复的
实践所验证，是无须证明而为人们所公认的结论。
公理 1 二力平衡公理
作用于刚体上的两个力，使刚体平衡的必要与充分条件是,
这两个力 大小相等 | F1 | = | F2 |
方向相反 F1 = –F2
作用线共线,
作用于同一个物体上。
15
Explanation,
① As far as rigid bodies are concerned,the conditions above are
necessary and sufficient,
② As far as deformable bodies are concerned,the conditions
above are only necessary,
bodies (deformable body) string
二力杆
Double force
equivalent body
Double force
equivalent rod
③ double force equivalent body,is a rigid body subjected to
two forces must be in equilibrium,
16
说明, ①对刚体来说，上面的条件是充要的
③ 二力体,只在两个力作用下平衡的刚体叫二力体。
② 对变形体来说，上面的条件只是必要条件 (或多体中 )
二力杆
17
The action of a given force system on a rigid body remains unchanged
if another balanced force system is added to or subtracted from the
original system,
Corollary 1,transmissibility of a force
The point of application of a force acting on a rigid body can be
transferred to any other point on the line of action of the force without
altering its effect,
Therefore,as far as a rigid body is concerned,a force can be
characterized by three elements,magnitude,direction and line of
application,
2nd Principle,addition and subtraction of balanced force systems
18
在已知力系上加上或减去任意一个平衡力系，并不改变原
力系对刚体的作用。
推论 1：力的可传性。
作用于刚体上的力可沿其作用线移到同一刚体内的任一
点，而不改变该力对刚体的效应。
因此，对刚体来说，力作用三要素为,大小，方向，作用线
公理 2 加减平衡力系原理
19
If a free rigid body remains in equilibrium
under the action of three nonparallel coplanar
forces,the lines of action of those forces
intersect at one point,Moreover,three forces are
coplanar,(under special circumstances,forces
intersect at infinite and become a
parallel force system),
3rd principle,the law of parallelogram
Corollary 2,three equivalent forces intersect
at one point
21 FFR ??
Two forces applied at one point of a body
have as their resultant a force applied at the
same point and represented by the diagonal
of a parallelogram constructed with two
given forces as its sides,
20
刚体受三力作用而平衡，若其中两力作
用线汇交于一点，则另一力的作用线必汇交
于同一点，且三力的作用线共面。（ 必共面，
在特殊情况下，力在无穷远处汇交 —— 平行
力系 。）
公理 3 力的平行四边形法则
作用于物体上同一点的两个力可合成
一个合力，此合力也作用于该点，合力的
大小和方向由以原两力矢为邻边所构成的
平行四边形的对角线来表示。
推论 2,三力平衡汇交定理
21 FFR ??
21
4th principle,the law of action force and reaction force
To any action of one material body on
another there is always an equal and
oppositely directed reaction,They are
equal in magnitude,opposite in
direction,collinear and exist together,
but act on different body,
Prove,∵ is a balanced force system,
∴ is a balanced force system too,
again∵ If two forces are in equilibrium,
they must be equal in magnitude,
opposite in direction and collinear,
∴ intersect at a point and are coplanar,
321,,FFF
321,,FFF
3,FR
Example
droplet
The force the droplet act
on the string
The force the string act
on the droplet
Gravitation
The reaction force of p
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公理 4 作用力和反作用力定律
等值、反向、共线、异体、且同时存在。
[证 ] ∵ 为平衡力系,
∴ 也为平衡力系。
又 ∵ 二力平衡必等值、反向、共线,
∴ 三力 必汇交，且共面。
321,,FFF
321,,FFF
3,FR
[例 ] 吊灯
23
5th principle,principle of solidification
If a deformable body subjected to the action of a force system is in
equilibrium,the state of equilibrium will not be disturbed if the
body solidifies(becomes rigid)
The 5th principle tells us
that the equilibrium of a
balanced deformable body
can be described by the
theory for a rigid body,
Soft string
draw
draw
Solidified rigid rod
draw
draw
24
公理 5 刚化原理
变形体在某一力系作用下处于平衡，如将此变形体变成
刚体（刚化为刚体），则平衡状态保持不变。
公理 5告诉我们：处于平衡
状态的变形体，可用刚体静
力学的平衡理论。
25
§ 1-3 constraints and their reaction forces
1,Concepts
Free body,A body not connected with other bodies and capable
of displacement in any direction is called a free body,
Constrained body,
A body whose displacement in space is restricted by
other bodies,either connected to or in contact with it,
is called a constrained body,
Constraint,Anything that restricts the displacement of a given
body in space.(here,constraint is a noun,not a verb),
Reaction force of a constraint,
The force by which a constraint acts on a body,thereby
restricting its displacements,is called the force of
reaction of the constraint,
26
约束反力,约束给被约束物体的力叫约束反力。
§ 1-3 约束与约束反力
一、概念
自由体,位移不受限制的物体叫自由体。
非自由体,位移受限制的物体叫非自由体。
约束,对非自由体的某些位移预先施加的限制条件称为约束。
（这里，约束是名词，而不是动词的约束。）
27
① their magnitude is usually unknown;
② their direction is always opposite to the direction in which
the given constraint prevents the displacement of the body;
③ the point of application is the contact point between the
body and the constraint,
The characteristics of reaction force of constraints,
G G
N1
N2
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① 大小常常是未知的；
②方向总是与约束限制的物体的位移方向相反；
③作用点在物体与约束相接触的那一点。
约束反力特点,
G G
N1
N2
29
Strings can only be stretched,therefore the reaction force applies
at the point of contact and the direction of it is away from the
body,
2,Some common types of constraints and their reaction
force direction,
1) Constraints given by a string,
a chain or a strap
P P
T S1 S'1
S'2 S2
30
绳索类 只能受拉,所以它们的约束反力是 作用在接触点,方
向 沿绳索背离物体 。
二、约束类型和确定约束反力方向的方法,
1.由柔软的绳索、链条或皮带构成的约束
P P
T S1 S'1
S'2 S2
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the reaction force is applied at the point of contact and directed
normal to both surfaces,
2) Smooth contact plane (smooth,not taking friction into account )
P
N N
P
NA
NB
Common normal
Common
tangent
32
约束反力 作用在接触点处,方向 沿公法线，指向受力物体
2.光滑接触面的约束 (光滑指摩擦不计 )
P
N N
P
NA
NB
33
3) Smooth cylindrical pin
① cylindrical pin
Pin
34
3.光滑圆柱铰链约束
① 圆柱铰链
35
A XA
YA
A
A
Direction is uncertain
Magnified
picture
Pin
36
A
A
XA
YA
A
37
② fixed hinged support
38
② 固定铰支座
39
fixed hinged support
40
固定铰支座
41
runner and pin
(double surface
constraints)
42
滑槽与销钉
（双面约束）
43
double force
equivalent rod
44
二 力 杆
45
Kinetic hinged support (step bearing)
The actual
direction of N can
be downward,
46
活动铰支座（辊轴支座）
N的实际方向也
可以向下
47
Kinetic hinged support (step bearing)
48
活动铰支座（辊轴支座）
49
1,Force analysis
To solve a problem of statics,First select the body to be studied,
Secondly,in accordance with the given conditions and constraints,
analyze the forces which act on the bodies using the basic concepts
and principles,This process is called force analysis,
The forces acting on a body can be classified as,
1,active forces,such as the gravitational force,the force of wind
power,the pressure of gases,etc,
2,passive forces,such as reaction force of constraints,
§ 1-4 Force analysis and force diagrams
50
一、受力分析
解决力学问题时，首先要选定需要进行研究的物体，即选
择研究对象；然后根据已知条件，约束类型并结合基本概念和
公理分析它的受力情况，这个过程称为物体的 受力分析 。
作用在物体上的力有：一类是,主动力,如重力,风力,气体
压力等。
二类是：被动力，即约束反力。
§ 1-4 物体的受力分析和受力图
51
The main steps to draw the force diagrams,
① select the object under study;
② divide the object into several parts and
study the parts one by one;
③ draw the active forces;
④ draw the reaction force of the constraints,
2,Force diagrams
[Example 1]
52
画物体受力图主要步骤为,①选研究对象；②取分离体；
③画上主动力；④画出约束反力。
二、受力图
[例 1]
53
[Example 2] Please,draw the force diagrams for
all components in the picture,
Q A
O
B
C
D
E
Rod
54
[例 2] 画出下列各构件的受力图
Q A
O
B
C
D
E
55
Q A
O
B
C
D
E
56
Q A
O
B
C
D
E
57
Q A
O
B
C
D
E
58
Q A
O
B
C
D
E
59
[Example 3] Please,draw the force diagrams for
all components in the picture,
Notice,three balanced forces
must intersect at a point,But
if they are parallel,they
intersect at infinity,This is a
special case,
60
[例 3] 画出下列各构件的受力图
说明：三力平衡必汇交
当三力平行时，在无限
远处汇交，它是一种特
殊情况 。
61
[Example 4] Sharp point contacts
Get rid of constraints Get rid of constraints
62
[例 4] 尖点问题
应去掉约束 应去掉约束
63
[Example 5] Please,draw the force diagrams for
all components in the picture,
64
[例 5] 画出下列各构件的受力图
65
3,Some problems which should be taken into account when
drawing a force diagram,
Mutual mechanical action forces exist,only if
bodies contact,except for gravitation and
electromagnetic force,So the bodies which are
in contact with the object under study should be
made clear,There must have force at the contact
point,the direction of the force depends on the
type of constraints,
Mind you,the force is the mutual mechanical
action between bodies,Thereby,every force the
body subjected,relatives to a body who applies
the force,We should make it clear,
1) Don’t leave
out any force
2) Don’t draw
redundant
force
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三、画受力图应注意的问题
除重力、电磁力外，物体之间只有通过接触
才有相互机械作用力，要分清研究对象（受
力体）都与周围哪些物体（施力体）相接触，
接触处必有力，力的方向由约束类型而定。
2、不要多画力
要注意力是物体之间的相互机械作用。因此对
于受力体所受的每一个力，都应能明确地指出
它是哪一个施力体施加的。
1、不要漏画力
67
The direction of constraint reaction force must be strictly
according to the type of constraint,never be simply supposed
by direct-view or the direction of the active force,When
analyzing the action forces and the reaction forces between
two bodies,please give attention to the direction of the forces,
If the direction of the action force has been determined,the
direction of the reaction force is opposite to the action force,
Don’t draw the direction of forces wrong,
3) Don’t draw the direction of force wrong
4) There are no constraints on the force diagrams
The force diagrams can be draw only on a part of the object,
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约束反力的方向必须严格地按照约束的类型来画，不
能单凭直观或根据主动力的方向来简单推想。在分析
两物体之间的作用力与反作用力时，要注意，作用力
的方向一旦确定，反作用力的方向一定要与之相反，
不要把箭头方向画错。
3、不要画错力的方向
4、受力图上不能再带约束。
即受力图一定要画在分离体上。
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Whether a force is an external force or an internal one depend
on the special objects,When a body system is divided into
several parts,some internal forces of old system may turn into
the external forces of the new object under study,
If the direction of the reaction force of a constraint is defined,it
should be kept to the same in the analysis of the whole body as
in the analysis of the components,
5) no internal forces but only external forces can be drawn on
a force diagram
6) The force diagram for the whole object should be in
accordance with the force diagrams for any part,they
should assort with each other,but not conflict,
7) Make a exact judge for the double forces components,
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一个力，属于外力还是内力，因研究对象的不同，有
可能不同。当物体系统拆开来分析时，原系统的部分
内力，就成为新研究对象的外力。
对于某一处的约束反力的方向一旦设定，在整体、局
部或单个物体的受力图上要与之保持一致。
5、受力图上只画外力，不画内力。
6,同一系统各研究对象的受力图必须整体与局部一致，相
互协调，不能相互矛盾。
7,正确判断二力构件。
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