静力学第一章静力学公理

Chapter 1 Principles of statics
1.1 Force
1. Definition
Force is the name assigned to the mutual interaction between two bodies that produces the deformation of the bodies and/or affects the motion of the bodies. Contact forces arise from the direct contact between bodies are frequently referred to simply as "pushes" or "pulls." Field forces do not result from the direct contact of two bodies but are applied remotely; examples of field forces are gravitational and electromagnetic forces. As discussed in Introduction, the unit of force in SI units is the Newton (N).
2. All applied forces are drawn and labeled on the sketch. The weight of the body is considered to be an applied force acting at the center of gravity.
Two-force Principle: 二力平衡公理 Two forces can be in equilibrium only if the case where they are equal in magnitude, opposite in direction, and collinear in action.
如棘爪.不计自重时为二力构 件．
b. Three-force bodies 推 论 2 Three-force Principle: Three nonparallel,
coplanar forces that hold a body in equilibrium must be
concurrent.
工程力学是研究工程结构和构件在一定的载荷作 用下的破坏情况 , 以及构件形式、尺寸、材料的设计
的科学。
Statics
Introduction
1.Statics: 研究物体在平衡（Equilibrium）状态下的
科学。即研究物体在力的作用下处于平衡状态的规律 及其应用。
任务:(1) FBD物体的受力分析。
a. Two-force bodies(二力构件)
If a body is held in equilibrium by two forces, the forces must be equal in magnitude and oppositely directed along the same line of action.
另外，提醒大家的是：注意充分利用牛顿第三定律（作用与 反作用）．
The Parallelogram Law for the Addition of Forces Two forces acting on a particle may be replaced by a single force, called their resultant, obtained by drawing the diagonal of the parallelogram which has sides equal to the given forces.
b. The general procedure
1. A sketch of the body is drawn assuming that all supports (surfaces of contact, supporting cables, etc.) have been removed.
(2) Reducting of (Resultants of) Force systems力系的简化----即用一简单力系代替原有力系
而不改变其对物体的作用效果。
(3)Equilibrium Equations力系的平衡条件。
2.Inertial reference frames
An inertial reference frame is defined to be any rigid co-ordinate system in which Newton’s laws of particle motion relative to that frame are valid with an acceptable degree of accuracy. In most design applications used on the surface of the earth, an inertial frame can be approximated with sufficient accuracy by attaching the coordinate system to the earth.
a. FBD
The Free-body diagram (FBD) of a body is a sketch of the body showing all forces that act on it. The term free implies that all supports have been removed and replaced by the forces (reactions) that they exert on the body.
2. Sliding vector: a vector that has a unique line of action.
3. Free vector: a vector whose point of application and line of action are not unique. (Thus. a free vector is described completely by its magnitude and direction.)
Reaction forces(reactions): Forces that is exerted on a body by the supports to which it is attached.
Applied forces: Forces acting on a body that is not provided by supports.
(2)directiorn; F
(3)point
of
application.
tension load
compressing load
1.2 Principles of Statics
Newton’s Third Law The forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense.
F1 = -F2
此公理揭示了最简单的力系平衡条件。
加减平衡力系公理 The action of a given system of forces will in no way be changed if the add to, or subtract from, these forces any other system of forces is equilibrium.
3. The reactions due to each support are drawn and labeled on the sketch. (If the sense of a reaction is unknown, it should be assumed. The solution will determine the correct sense: A positive result indicates that the assumed sense is correct, whereas a negative result means that the correct sense is opposite to the assumed sense.
2.Rigid Body
A body is called as rigid body that its deformation is negligible when subjected to any load.
3.The three characteristics
(1)magnitude;
E书x写pr:eFsrsiபைடு நூலகம்no:r F
4. All relevant angles and dimensions are shown on the sketch.
c. Reactions of Supports
Special Cases: Two-Force Bodies and Three-Force Bodies
FR = F1 + F2
此公理给出了力系简化的基本方法. 合力的大小和方向也 可通过图(b)和(c)所示的力三角形法得到. 平行四边形法则是 力的合成法则, 也是力的分解法则. 例如, 拉力作用在螺钉A上 (图1-5), 此力与水平方向的夹角为α，按此法则可将其沿水平及 铅垂方向分解为两个分力F1和F2 。
故:当只考虑刚体受力时,作用力矢可看作滑移矢量