Structural Engineering & Statics
where the load goes
Generator

The three-force generator

Rendered here at the parameters it defaults to, with every essay that calls it — which is the same list as the blast radius of changing it.
Three forces must meet at a pointA body held by two supports and one load. The reaction at the roller is vertical and the load's direction is given, so their lines of action fix a meeting point — and the pin reaction has to point at it.the loadroller: vertical onlypin: any directionall three lines meet here

3 essays call three-force. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

the loadroller: vertical onlypin: any directionall three lines meet here Equilibrium

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.

 1289.510.5ΣM = 0about AΣM = 0about BΣM = 0about CΣM about one support gives the other reaction; ΣF then gives the first Equilibrium

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.

 crown hinge — no moment here, by constructionH = 23.4H = 23.427.027.0thrust line and axis coincide — the definition of funicular Structural form

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.

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