材料力学(双语)Bending弯曲

Chapter 4 Internal Forces in Bending
MECHANICS OF MATERIALS 材料力学（双语）

Content
§4.1 Concept of symmetrical 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 · the shearing-force and 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 §4.6 The internal-force diagrams of the planar rigid frames and curved rods
2

目录
§4.1 对称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 §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
3

4.1 Concept of symmetrical bending and calculation sketch of the beam
1. Concepts of Bending 1). BENDING(弯曲): 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（梁): The member of whose deformation is mainly bending is generally called beam.
4

3). Practical example in engineering about bending
5

6

4). Symmetric bending(平面弯曲) After deformation the curved axis of the beam is still in the same plane with the external forces. P1 q P2
M
The plane of symmetry
7

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.
8

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(简化) of the beams
In general case we take the place of the beam by its axis.
2). Simplification of the loads (荷载)
The loads (including the reaction) acting on the beam may be reduced into three types：concentrated force、concentrated force couple and distributed force.
3). Simplification of the supports (支座条件)
9

①Fixed hinged support
固定铰支座
2 constraints，1 degree of freedom. Such as the fixed hinged support under bridges.
②Movable hinged support
可动铰支座
1 constraint，2 degree of freedom. Such as the movable hinged support under the bridge.
10

θ

A B

D

B R R

A A A

B B B