Rigid and deformable body; FBD principles

Rigid body

A rigid body is an ideal body that does not deform under load: the distance between any two of its points is constant. Statics treats solid bodies as rigid.

Deformable body

A deformable body changes shape and size under load (stretching, bending, twisting). This is the real behaviour of bodies and is studied in strength of materials.

Principles of the free body diagram

1. Isolate the body or joint completely from its surroundings.
2. Show every external force on it: applied loads, weight (at the centre of gravity) and reactions.
3. Replace each support by its reaction: roller, one normal force; hinge, two components; fixed, two components and a moment; cable, a tension along the cable; smooth contact, a normal force.
4. Show only external forces. Internal forces cancel in pairs (Newton's third law).
5. Mark known values, label unknowns, and show dimensions and angles.

Principle of static equilibrium

A body at rest stays at rest when the resultant force and moment on it are both zero:

• Particle: ΣFx = 0, ΣFy = 0 (and ΣFz = 0 in 3D).
• Rigid body (2D): ΣFx = 0, ΣFy = 0, ΣM = 0.

Example

A ladder AB of length L and weight W rests on a smooth wall at A and on rough ground at B. It makes angle θ with the ground, and A is at height h above the ground. FBD: W at the middle, N_A horizontal at A, N_B vertical and friction F horizontal at B. Then ΣFx = 0 gives F = N_A; ΣFy = 0 gives N_B = W; and ΣM_B = 0 gives N_A × h = W × (L/2) cos θ. These give all the unknowns.