Determinacy
Counting the unknowns, and finding out whether statics can answer
Two equations per joint, one unknown per member, one per restraint. Subtract, and the sign of the answer says whether the structure is a mechanism, solvable, or beyond what equilibrium alone can settle.
The equation that is not new, and the three that are
A plane free body yields exactly three independent equations. Most attempts at a fourth are one of the first three wearing different clothes — and on a beam under vertical load, one of the three is already saying nothing.
The hinge put in on purpose
An arch with two pinned feet cannot be solved by statics. Add a third hinge at the crown — deliberately weakening it — and the whole structure falls out of one moment equation.
Named alongside it
The objects these essays reach for when they reach for this one.
Bending momentCompatibilityForce equilibriumFree body diagramHorizontal thrustIndependent equationsIndeterminacyLine of actionMechanismMoment centreMoment equilibriumRedundancy