Steps for free body diagram; equilibrium 2D/3D

Steps in drawing a free body diagram

1. Decide which body (or part of a structure, or a joint) is to be isolated and separate it completely from the surroundings.
2. Sketch the isolated body with its shape and main dimensions and angles.
3. Show the weight of the body at its centre of gravity, and all applied loads (point loads, distributed loads, couples) in their true position and direction.
4. Replace each support or connection by the reaction it develops:
   • roller or smooth surface: one force normal to the surface,
   • hinge or pin: two components (or one force of unknown direction),
   • fixed support: two force components and a moment,
   • cable: tension along the cable, away from the body,
   • smooth contact between bodies: normal force, equal and opposite on the two bodies (Newton's third law).
5. Label all forces, known ones with values and unknown ones with letters. Assume a sense for each unknown. A negative answer means the sense is opposite.
6. Choose a reference axis system and show the dimensions needed for moments.

Equilibrium of a particle

A particle is in equilibrium when the resultant force on it is zero. All forces on a particle are concurrent, so no moment equation is needed.

• 2D: ΣFx = 0, ΣFy = 0 (two equations, up to two unknowns).
• 3D: ΣFx = 0, ΣFy = 0, ΣFz = 0 (three equations, up to three unknowns).

Equilibrium of a rigid body

A rigid body is in equilibrium when the resultant force and the resultant moment about any point are both zero: ΣF = 0 and ΣM = 0.

• 2D: ΣFx = 0, ΣFy = 0, ΣM_O = 0 (three equations, up to three unknowns).
• 3D: ΣFx = ΣFy = ΣFz = 0 and ΣMx = ΣMy = ΣMz = 0 (six equations, up to six unknowns).

In 2D, force equations may be replaced by moment equations: either ΣFx = 0, ΣM_A = 0, ΣM_B = 0 (with line AB not perpendicular to the x axis), or ΣM_A = 0, ΣM_B = 0, ΣM_C = 0 (with A, B and C not on one straight line). Either way, there are never more than three independent equations.