-
材料力学双语教学学习资料
1
第一章
绪
论
Chapter 1 Introduction
§
1-1
材料力学的任务
The Tasks
of Mechanics of Materials
1
＊
.
材料力学
: Mechanics of Materials
2.
构件
: Structural
Members
3.
变形
:
Deformation
4
＊
.
强度
: Strength
5
＊
.
刚度
: Rigidity
6
＊
.
稳定性
: Stability
§
1-2
变形固体的基本假设
Fundamental Assumptions of Solid
Deformation Bodies
1.
连续性假设
: Continuity
2.
均匀性假设
:
Homogeneity
3.
各向同性假设
: Isotropy
§
1.3
外力及其分类
External
Forces and Classification
1.
分布力
: Distributed Force
2.
集中力
: Point
Force
3.
静载荷
:
Static Load
4.
动载荷
: Dynamic Load
§
1.4
内力、截面法和应力的概念
Concepts of Internal
Forces
，
Method of
Section and Stress
1
＊
.
内力
: Internal Force
2
＊
.
截面法
: Method of Section
3.
截面法的三个步骤：截开，代替，平衡
Three steps of method of section: cut
off,
substitute , and equilibrium.
4
＊
.
应力
: Stress
5.
平均应力：
Average stress
6.
应力
（全应力）
：
Whole
stress
（
sum stress
）
7
＊
.
正应力
:
Normal Stress
8
＊
.
剪应
力
(
切应力
)
：
Shearing Stress
§
1.5
变形与应变
Deformation
and Strain
1
．
线应变
: Strain
2
．
剪应变
: Shearing Strain
§
1.6
杆件变形的基本形式
Basic
Types of Deformations of Rods
1
＊
.
拉伸或压缩
: Tension or
Compression
2
＊
.
剪切
: Shear
3
＊
.
扭转
: Torsion
4
＊
.
弯曲
: Bending
第二章
拉伸、压缩与剪切
Chapter
2 Tension
，
Compression and
Shear
§
2.1
轴向拉伸与压缩的概念和实例
The
Concept and Examples of Axial
Tension
and Compression
1.
拉杆
: Tensile Rod
2.
压杆
:
Compressive Rod
3.
受力特点：
外力合力的作用线与杆轴线重
合
Characteristic
of
the
External
Forces:
The
acting
line
of
the
resultant
of
external
forces is coincided
with the axis of the rod.
4.
变形特点：杆沿轴向伸长或缩短
Characteristic of Deformation: Rod will
elongate or contract along the axis of
the
rod.
§
2.2
轴向拉伸或压缩时横截面上的
内力和应力
Internal
Force and Stress of Axial Tension
or
Compression on the Cross Section
1
＊
.
横截面
: Cross Section
2
＊
.
轴力
: Normal Force
3
＊
.
轴力图
: Diagram of Normal Force
§
2.3
直杆轴向拉伸或压缩时斜截面上的
应力
Stress of Axial Tension or Compression
on the Skew
Section
1.
斜截面
: Skew Section
2.
?
?
?
?
cos
2
?
?
?
?
?
2
s
i
n
2
?
§
2.4
材料在拉伸时的力学性能
Mechanical Properties of Materials
with Tensile
Load
1.
标准试件
: Specimen
2.
低碳钢
(C
≤
0.3%): Low Carbon Steel
3.
弹性阶段
:Elastic Region
4.
屈服阶段
:Yielding
Stage
5.
强化阶段
:
Hardening
Stage
6.
颈缩阶段
:
Necking Stage
7
＊
.
σ
p
----
比例极限
:
Proportional Limit
8
＊
.
σ
e
----
弹性极限
:
Elastic Limit
9
＊<
/p>
.
σ
s
----
屈服极限
: Yielding
Stress
10
＊
.
σ
b
----
强度极限
: Ultimate Stress
11.
延伸率
: Percent
Elongation
12.
断面收缩率
: Percent Reduction of
Area
13.
塑性材料
:
Ductile Materials
14.
脆性材料
: Brittle Materials
15.
铸铁
:Cast iron
§
2.7
失效、安全系数和强度计算
Failure, Safety factor and Strength
calculation
1
＊
.
许用应力
: Allowable Stress
2.
安全系数
: Safety
Factor
3
＊
.
强度条件
: Strength Condition
?
N
max
?
F
A
?
[
?
]
4
＊
.
强度校核
: Check strength
?
max
?
[
?
]
5
＊
.
截面设计
: Section design
A
?
F
N
[
?
]
6
＊
.
确定许可载荷
:Determine allowable
load
F
N
?
A
[
?
]
§
2.8
轴向拉伸或压缩时的变形
Deformation in Axial Tension or
Compression
1.
弹性变形
: Elastic Deformation
2.
塑性变形
: Plastic Deformation
3.
纵
向
应
变
:
Longitudinal Strain
?
?
?
l
l
?
l
1
?
l
l
4.
横向应变
: Lateral Strain
?
'
?
?
d
d
'
?
d
d
?
d
5
．线弹性变形
:Linear
Elastic Deformation
6.
泊松比
:
Poisson’s
ratio
?
?
'
?
?
7
＊
.
弹性模量
-E
：表示材料抵抗拉压变形的
能力
E
-
modulus of elasticity
：
Indicates the capability of materials
for
resisting tension or compression
8
＊
.
抗拉刚度
-
EA
:
表示构件抵抗拉压变形的
能力
EA
-
the
axial
rigidity:
Indicates
the
capability
of
constructive
members
for
resisting tension or
compression
9
＊
.
胡克定律（
Hooke’s Law
）
:
当应力不超
过材料的比例极限时，应
力与应变成正
比
.
The stress is proportional to the
strain
within the elastic region.
?
?
E
?
?
L
?
F
N
L
EA
§
2.12
应力集中的概念
The
Concept of Stress Concentration
1.
由于截面尺寸的突然变化，
使截面上的应
力分布不再均匀，在某些部位出现远大
于平均值的应力，称应力集中。
Discontinuities of cross section may
result
in high localized or
concentrated stresses.
2.
理论应力集中系数
K
：
Theoretical
Stress-concentration Factor -
K
§
2.
13
剪切和挤压的实用计算
Practical Calculation of Shear and
Bearing
1
＊
.
剪切：
Shear
2.
剪切面：
Shearing Plane
3
＊
.
剪切
面上的内力
-
剪力：
Internal
Force in
Shearing Plane-Shearing Force
4.
剪切的实用计算：
Practical
Calculation of
Shear
?
?
F
S
A
< br>?
[
?
]
5.
挤压的实用计算：
Practical
Calculation
of
Bearing
?
bs
?
F
A
?
[
?
< br>bs
]
bs
6.
挤压强度条件：
工作中的挤压应力不应超
过许用挤压应力。
Strength condition of
bearing
：
Working
bearing stress should not exceed the
allowable bearing stress.
第三章
扭
转
Chapter Three Torsion
§
3.1
扭转的概念和实例
Concept
and Examples of Torsion
1.
电动机
: Generator
2.
涡轮
: Turbine
3
＊
.
扭转的受力特点：杆件的两端作用着大
小相等，方向相反，且作用面
垂直于杆
件轴线的力偶。
Characteristic of loads: Shaft is
loaded by
a torsional couple in planes
that are
perpendicular to the axis of
the shaft.
4
＊
.
变形特点：杆件的任意两个横截面发生
绕轴线的相对转动。
Characteristic
of
deformation:
any
two
cross sections will
twist along the axis.
5
＊
.
轴
: Shaft
§
3.2
外力偶矩的计算
扭矩和扭矩图
Calculation of the external
torque
Internal torque and
Its diagram
1
．扭转外力偶矩的计算：
Calculation of the
external
torque
2
＊
.
扭矩：
Internal Torque
3.
符号规定：
Sign convention
4
＊
.
右手螺旋法则
: Right hand screw
rule
5
＊
.
扭矩图：
Diagram of Internal
Torque
§
3.3
纯剪切
Pure Shear
1.
薄壁圆筒的扭转实验：
Experiment of
thin-walled circular tube under torsion
2.
变形特点
: Characters of
deformations
：
截面间
的距离不变
;
所有横截面的位置
不变<
/p>
;
所有纵向线转过了一个角度
γ
。
Distances between
the sections remain
unchanged , All
cross sections remain
unchanged
,
All the generating lines
revolve through an angle
γ
.
3
＊
.
切应力互等定理：
Theorem of
complementary shearing stresses
4
＊
.
切应变：
Shearing strain
< br>5
＊
．剪切虎克定律：
Hook
e’s
law of shear
6
＊
.
剪切
弹性模量
G
：
Modulus of
elasticity of
shearing
第四节
圆轴扭转时的应力
Stresses
in a round shaft under torsion)
1
＊
.
Ip (
极惯性矩
) ---
polar moment of
inertia
2
＊
.
Wp
(
抗扭截面系数
)---- section modulus
in torsion
§
3.5
圆轴扭转时的变形
1.
扭转角
: The angle of twist
2
＊
.
抗扭刚度
G Ip
：
the torsional rigidity
3
＊
.
扭转的刚度条件
: Rigidity condition
in
torsion
4.
单位长度扭转角：
The angle of twist
per
unit length
Exercises
1. A
bracket
（支架）
is
shown in the figure
，
The
cross-section area of the steel bar
AB
is
A1=6cm
2
；
the cross-section
area of the
wooden bar
BC
is
A2=300cm
2
，
Knowing
the
allowable stress of steel
is[
σ
]=140MPa , the
allowable tensile stress of wood is
[
σ
]
L
=8MPa, and the allowable compressive
stress of wood is[
σ
]
Y
=4MPa. Try determine
the allowable load
P
of the bracket.
2.
A
wooden tenon(
榫
)
joint is shown in the
figure. Knowing
that the quantities are
a
=
b
=12cm
，
h
=35cm
，
< br>c
=4.5cm and
P
=40KN. Try
to
determine the shearing stress and bearing
stress for the joint.
h
h
P
c
P
a
P
b
A
3
．
Two boards are
bolted together as shown .
A
Each board has a thickness
(
P
P
δ
)
of 2 mm, and
a width
(
b
) of 15 mm . The diameter
d
of the
bolt is
4 mm .All the parts are made from the
same material and have the same
allowable
stresses
?
< br>?
?
?
160MPa,
?
?
?
?
=100MPa,
?
bs
?
?
300MPa. Try to design the
tensile
force
F
.
第四章
弯曲内力
Chapter Four
Internal Forces in
Bending
4.
A
tensile
bar
and
two
cover
boards
are
bolted
together
as
shown.
Each
cover
board
has
a
thickness
of
8
mm.
All
the
parts
are
made
from
the
same
material
?
and
have
the
same
allowable
stresses
?
?
?
80MPa,
?
?
?
=60MPa,
?
?
bs
?<
/p>
?
160MPa.
The
thickness
of
the
bar
?
=15mm,
the
tensile
force
F
=120KN. Try to design
(1)
the diameter
d
of the bolt .
(2)
the width
b
of the tensile bar.
5
．构件
在外力作用下抵抗破坏的能力称
为
；构件在外力作用下抵抗
变形的能力称为
；构件在外
力作用下保持原有平衡状态的能力称
为
。
(Please fill in the blanks
with proper words in English.)
< br>6
．杆件的基本变形一般
有
、
、
、
、四种。
(Please fill
in the blanks with proper words
in
English.)
§
4-1
弯曲的概念和实例
§
4-1 The Concepts and
Examples in Bending
1
＊
．梁：
beam
2
．轴线：
axis
3
．纵向
对称面：
longitudinal plane of symmetry
4
＊
．平面弯曲：
pl
ane bending
5
＊
．弯曲
的受力特点：作用于杆件上的外力或
外力偶矩矢垂直于杆件轴线。
Characteristics of loads : external
forces or
external the couple vector
perpendicular
to the axis
of the rod.
6
＊
．弯曲
的变形特点：杆件的轴线由直线变为
曲线。
Characteristics of deformations :
the axis of
the
rod change into curve from original
straight lines.
7
＊
．弯曲变形：杆件在垂直于杆轴线的外力或
两个外力偶的作用
下，杆的轴线由直线变
为曲线，这种变形称为弯曲变形。
BENDING:
The
action of the external force
or
external the couple vector perpendicular
to the axis of the rod
makes the axis of the
rod change into
curve from original straight
lines,
this deformation is called bending.
§
4-2
受弯杆件的简化
§
4-2
Simplification of Bending Rods
1
．
集中力：
concentrated force
2
．
分布力：
distributed load
3
．
均布载荷：
uniform load
4
．
支座：
support
5
＊
.
简支粱：
simple supported beam
6
＊
.
外伸梁：
overhanging beam
7
＊
.
悬臂梁：
cantilever
beam
§
4-3
剪力和弯矩
§
4-3
Shearing Force and Bending Moment
1.
弯曲内力：
internal
forces in bending
2
＊
< br>.
剪力：
shearing force
3
＊
.
弯矩：
bending moment
4.
内力的正负规定：
sign conventions
for the internal forces
§
4-4
剪力方程和弯矩弯矩方程
剪力图和弯矩图
§
4-4
The Equations of Shearing Force and
Bending Moment
The Diagrams
of Shearing Force and Bending
Moment
1
＊
．剪力方程：
equation of shearing force
2
＊
．弯矩方程：
equation of bending moment
3
＊
．剪力图：
diagram of shearing force
4
＊
．弯矩图：
diagram of bending moment
<
/p>
§
4-5
载荷集度、剪力和弯矩间的关系
§
4-5
Relations among the Intensity of
Distributed Load , Shearing Force and
Bending Moment
1
＊
.
微分关系：
differentia
l relations
2
＊
.
规律法：
method of regulation
3
＊
.
控制截面法：
method of control
sections
4.
水平直线：
horizontal straight
line
5.
斜直线：
inclined straight line
6.
突变：
sudden change
7.
增函数：
increasing function
8.
减函数：
decreasing function
9.
盆状抛物线：
basin - like curve
10.
坟状抛物线：
tomb - like curve
11.
折向与
P
相反：
flexible opposite to
P
第五章
弯曲应力
Chapter Five
Stresses in Bending
§
5-1
纯弯曲
§
5-1 Pure Bending
1.
横力弯曲：
transverse bending
2
＊
.
纯弯曲：
pure bending
3.
平面假设：横截面变形后仍为平面，只是
绕中性轴发生转动，距中性轴等
高处，变
形相等。
Hypothesis
of
plane
section:
The
cross
sections
remain
still
planes,
and
only
rotate
through
some
angles
around
their
neutral
axes after deformation.
4
＊
.
中性层：
neutral layer
5
＊
.
中性轴：
neutral axis
6.
纵向对称轴：
longitudinal axis of
symmetry
§
5-2
纯弯曲时的正应力
§
5-2 Normal Stress in Pure
Bending
1
．
几何关系：
geometric relation
2
．
物理关系：
physics relation
3
．
静力关系：
static relation
4
＊
.
抗弯刚度
EIz
：
flexural rigidity
§
5-3
横力弯曲时的正应力
§
5-3 Normal Stress in
Transverse Bending
-
-
-
-
-
-
-
-
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