Field
Equilibrium
Nothing moves, so everything adds to nothing — and the free body decides what everything means.
Everything adds to nothing, and that is the whole of statics
A structure that stays put obeys two statements — the forces on it sum to zero, and so do the moments. Every number in the subject comes out of those two sentences.
The free body is a choice, and choosing it well is the whole skill
Cutting a structure open is not a step in the method. It is the method — and where the cut is made decides whether the answer takes one line or twenty.
Three forces must meet at a point, and a drawing can find it
A body held by exactly three forces has their lines of action concurrent. That is a theorem, it is enough to solve for direction and magnitude, and for a century it was done with a straightedge.
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.