双语版材料力学第四章

9
3. 工程实例
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
4).Planar bending：After deformation the curved axis of the beam is still in the same plane with the external forces.
the shearing-force and the bending-moment diagrams
§4–4 Relations among the shearing force、the bending moment and the density of the distributed load and their applications §4–5 Plot the bending-moment diagram by the theorem of superposition
§4–4 剪力、弯矩与分布荷载集度间的关系及应用
§4–5 按叠加原理作弯矩图 §4–6 平面刚架和曲杆的内力图 弯曲内力习题课
6
§4–1
CONCEPTS OF PLANAR BENDING AND CALCULATION SKETCH OF THE BEAM
1、CONCEPTS OF BENDING
诚实是力量的一种 象征，它显示着一个人 的高度自重和内心的 安全感与尊严感。
——艾琳· 卡瑟
1
走正直诚实的生 活道路，定会有一个 问心无愧的归宿。 ——高尔基
2
Mechanics of Materials
3
第四章
弯曲内力
4
CHAPTER 4
INTERNAL FORCES IN BENDING
非对称弯曲—— 若梁不具有纵对称面，或者，梁虽具有纵 对称面但外力并不作用在对称面内，这种
弯曲则统称为非对称弯曲。
下面几章中，将以对称弯曲为主，讨论梁的应力和变 形计算。
30
2、Calculation sketch of the beam In general supports and external forces of the beam are very complex. We should do some necessary simplification for them for our convenient calculation and obtain the calculation sketch. 1). Simplification of the beams
Symmetric bending（as shown in the following figure） — a special example of the planar bending. P1 q
P2
M
The plane of symmetry
27
4. 平面弯曲：杆发生弯曲变形后，轴线仍然和外力在同一 平面内。
1). BENDING: The action of the external force or the external 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. 2).BEAM：The member of which the deformation is mainly bending is generally called beam.
§4–1 Concepts of planaFra Baidu bibliotek bending and calculation sketch of the beam
§4–2 The shearing force and bending moment of the beam §4–3 The shearing-force and bending-moment equations
In general case we take the place of the beam by its axis.
2). Simplification of the loads The loads (including the reaction) acting on the beam may be reduced into three types：
7
§4–1 平面弯曲的概念及梁的计算简图
一、弯曲的概念 1. 弯曲: 杆受垂直于轴线的外力或外力偶矩矢的作用时,轴 线变成了曲线，这种变形称为弯曲。 2. 梁：以弯曲变形为主的 构件通常称为梁。
8
3).Practical examples in engineering about bending
对称弯曲（如下图）—— 平面弯曲的特例。
P1 q P2
M
纵向对称面
28
Unsymmetrical bending— if a beam does not possess any plane of symmetry, or the external forces do not act in a plane of symmetry of the beam with symmetric planes, this kind of bending is called unsymmetrical bending. In later chapters we will mainly discuss the bending stresses and deformations of the beam under symmetric bending. 29
§4–6 The internal-force diagrams of the planar rigid theorem
for frames and curved rods Exercise lessons about the internal force of bending
5
第四章
弯曲内力
§4–1 平面弯曲的概念及梁的计算简图 §4–2 梁的剪力和弯矩 §4–3 剪力方程和弯矩方程 · 剪力图和弯矩图