Chapter 7 Equilibrium of a Rigid Body (Statics静力学)

Engineering Mechanics STATICS
Keyong Wang Department of Engineering Mechanics School of Mechanical Engineering Shanghai University of Engineering Science
2
7.1 Conditions for Rigid-body 7.2 Free-Body Diagram 7.3 Equations of Equilibrium 7.4 Two- and Three-Force Members 7.5 Constraints and Statical Determinacy
If this resultant force and couple moment are both equal to zero, then the body is said to be in equilibrium.
Mathematically, the equilibrium of a body is expressed as
Fig. 7-1 It is important to be able to determine the forces in the cables used to support this submarine to insure that they do not fail. In this chapter we will study how to apply equilibrium methods to determine the forces acting on the supports of a rigid body such as this.
3
CHAPTER OBJECTIVES
■ To develop the equations of equilibrium for a rigid body.
■ To introduce the concept of the freebody diagram for a rigid body.
■ To show how to solve rigid-body equilibrium problems using the equations of equilibrium.
(b)
Fig. 7-2
6
(b)
(c)
Fig. 7-2
These two equatiium, they are also sufficient. To show this, consider summing moments about some other point, such as point A in Fig. 7-2c. We require
4
In this section, we will develop both the necessary and sufficient conditions for the
equilibrium of the rigid body in Fig. 7-2a. As shown, this body is subjected to an external force and couple moment system that is the result of the effects of gravitational, electrical, magnetic, or contact forces caused by adjacent bodies. The internal forces caused by interactions between particles within the body are not shown in this figure because these forces occur in equal but opposite collinear pairs and hence will cancel out, a consequence of Newton’s third law.
Fig. 7-2
5
The force and couple moment system acting on a body can be reduced to an equivalent resultant force and resultant couple moment at any arbitrary point O on or off the body, Fig. 7-2b.
This way the direction of the applied forces and their moment arms with respect to a fixed reference remain the same both before and after the body is loaded.
When applying the equations of equilibrium, we can generally assume that the body will remain
rigid and not deform under the applied load without introducing any significant error.
7
NOTES:
(b)
(c)
Fig. 7-2
When applying the equations of equilibrium, we will assume that the body remains rigid.
In reality, however, all bodies deform when subjected to loads. Although this is the case, most engineering materials such as steel and concrete are very rigid and so their deformation is usually very small.