Thrust line — where it appears
The shape that carries itself, and the arch that is its reflection
Hang a chain and it takes the one shape that carries its load in pure tension. Turn the shape upside down and it carries the same load in pure compression. That is what an arch is.
The polygon that finds the shape
A hanging string under five loads has no smooth curve in it — it has five vertices and six straight segments, and every slope in it is a running sum divided by one number.
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.
The line that must stay inside
A masonry arch does not stand because its shape is right. It stands because some line of compression can be drawn inside the stonework — any one will do, and there are infinitely many to choose from.
The middle third
A material that cannot be pulled imposes a condition on where the load may land, and the condition is a region rather than a point. For a rectangle it is the famous middle third; for every other section it is a shape nobody quotes, and one ordinary section's is nearly twice as generous as the rule allows.
Named alongside it
The objects these essays reach for when they reach for this one.
Horizontal thrustFunicularForm findingSag ratioThree pinned archBearing pressureBending momentCatenaryDeterminacyEccentricityFunicular polygonGeometrical factor of safety