Free body diagram
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.
Answering one question without solving the rest
A truss of fifty members can be interrogated about one of them. Cut through three, take moments about the point where two of them meet, and the third falls out in a single line.
The load that is spread out, and the force that replaces it
A distributed load can be swapped for a single force at its centroid. The reactions come out identical and the bending moment does not, and knowing which side of the cut the swap is legitimate on is most of the skill.
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.
What a cut reveals, and why it was there all along
Cut a beam anywhere and two quantities appear on the face — a shear force and a bending moment. Nothing was applied there. They are what the material was already doing.
Named alongside it
The objects these essays reach for when they reach for this one.
Moment equilibriumForce equilibriumIdealisationLine of actionLoad pathMethod of sectionsMoment centreReactionsResultantRigid bodyBending momentBoundary