Rigid body and perfectly rigid assumption

Rigid body

A rigid body is an idealised body in which the distance between any two particles always remains constant, however large the forces acting on it are. It does not change its shape or size under load, so there is no deformation.

Why 'perfectly rigid' is assumed

• Every real body deforms a little under load. In statics the deformations are very small compared with the size of the body, so the geometry (the lengths and angles that fix the lines of action and moment arms) is practically unchanged.
• With this assumption the equations of equilibrium (ΣF = 0, ΣM = 0) can be written using the original, undeformed dimensions. There is no need to know how the body deforms.
• The principle of transmissibility holds only for a rigid body. A force can then be slid along its line of action, which makes finding resultants and moments simple.
• Material properties such as the modulus of elasticity are not needed, so the problem reduces to pure geometry and force balance.
• Deformation and stress are studied separately in strength of materials, where the body is treated as deformable.

So the assumption simplifies the analysis a great deal, while the error it introduces is negligible for the bodies met in statics.