Rigid vs deformable bodies; free body diagram

Rigid body

A rigid body is an ideal body in which the distance between any two points never changes under load. It does not deform. Statics treats bodies as rigid, which allows the equilibrium equations to be written for the original geometry, and the principle of transmissibility to be used.

Deformable body

A deformable body changes its size and shape when loaded. The change depends on the load and the material. The study of stresses, strains and deflections of such bodies belongs to strength of materials.

Free body diagram (FBD)

A free body diagram is a sketch of a body or part of a structure, separated from its surroundings, in which all external forces and moments acting on it (applied loads, weight, support reactions and contact forces) are shown.

Why it is used in structural analysis

• It turns a physical structure into a clear force system to which ΣFx = 0, ΣFy = 0 and ΣM = 0 can be applied.
• It shows which forces are known and which reactions are unknown, so no force is missed or counted twice.
• Cutting a structure at a section and drawing the FBD of one part gives internal forces: axial force, shear force and bending moment, or member forces in a truss.
• It helps in checking whether the problem is statically determinate.
• A correct FBD is the first step of every statics problem. Most errors come from a wrong or incomplete FBD.