3.2.5—Rigid body equilibrium

A rigid body is in equilibrium when the vector sum of all forces is zero and the sum of moments about any point is zero. Translational balance alone does not prevent rotation.

Draw all external forces, resolve components, then take moments about a point that removes unknown reactions. Use the force equations afterwards to determine the remaining reactions.

A horizontal beam supported at its ends carries a central load. Equal upward reactions satisfy force balance; taking moments about either support confirms the reactions and prevents a net turn.

A pair of equal opposite forces can form a couple with zero resultant force but non-zero moment, so the body can still rotate.