1.1: Bodies
Bodies in Engineering Mechanics
A body , for the purposes of engineering mechanics, is a collection of matter that is analyzed as a single object. This can be something simple like a rubber ball, or it can be something made of many parts such as a car. What can count as a body and what cannot count as a body is dependent on the circumstances of the analysis. In some circumstances in engineering mechanics, it is useful to make certain assumptions about the bodies being analyzed. We will usually need to assume the body is either rigid or deformable, and we will also need to assume that the body is either a particle or an extended body.
Rigid versus Deformable Bodies
Rigid bodies do not deform (stretch, compress, or bend) when subjected to loads, while deformable bodies do deform. In actuality, no physical body is completely rigid, but most bodies deform so little that this deformation has a minimal impact on the analysis. For this reason, we usually assume in the statics and dynamics courses that the bodies discussed are rigid. In the strength of materials course we specifically remove this assumption and examine how bodies deform and eventually fail under loading.
There is no set boundary for determining if a body can be approximated as rigid, but there are two factors to look for that indicate that a rigid body assumption is not appropriate. First, if the body is being significantly stretched, compressed, or bent during the period of analysis, then the body should not be analyzed as a rigid body. Second, if the body has parts that are free to move relative to one another, then the body as a whole should not be analyzed as a rigid body; this is instead a machine, comprised of multiple connected bodies that will each need to be analyzed separately.
Particles versus Extended Bodies
Particles are bodies where all the mass is concentrated at a single point in space. Particle analysis will only have to take into account translational motion and the forces acting on the body, because rotation is not considered for particles. Extended bodies, on the other hand, have mass that is distributed throughout a finite volume. Often in engineering statics, we will take a shortcut and say rigid bodies to describe extended bodies that also happen to be rigid. This is because particles, as a single point, cannot deform. Extended body analysis is more complex and also has to take into account moments and rotational motions. In actuality, no bodies are truly particles, but some bodies can be approximated as particles to simplify analysis. Bodies are often assumed to be particles if the rotational motions are negligible when compared to the translational motions, or in systems where there is no moment exerted on the body, such as a concurrent force system.