Physical meaning of equilibrium and its application

Physical meaning of equilibrium

A body is in equilibrium when the forces and moments acting on it are balanced, ΣF = 0 and ΣM = 0. Physically, the body has no tendency to start moving, to speed up or to rotate. It stays at rest (static equilibrium) or moves at constant velocity. In an equilibrium state, every external action on the body is matched by an equal and opposite reaction.

Application in structural engineering

• Support reactions: the equilibrium equations give the reactions at the supports of beams, frames, arches and trusses from the applied loads.
• Internal forces: cutting a member and applying equilibrium to one part gives the axial force, shear force and bending moment at that section, which are needed to size the member.
• Truss analysis: the method of joints (ΣFx = 0, ΣFy = 0 at each joint) and the method of sections give member forces.
• Stability: a structure that cannot satisfy equilibrium under a load would move or collapse, so equilibrium is the basic condition of a safe design.
• Determinacy: counting the unknowns against the equations of equilibrium shows whether a structure is statically determinate or indeterminate.
• Foundations and retaining walls: equilibrium of forces and moments is checked against sliding and overturning.

Thus all structural design starts with the requirement that the structure and each of its parts are in equilibrium.