Concept

Three-pinned arch — where it appears

An arch with a hinge at each support and one at the crown, which makes it statically determinate. It is insensitive to settlement and temperature at the cost of a larger moment under an unsymmetrical load than a fixed arch would carry.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A three-pinned arch, rise 2.6 on span 9. A three-pinned arch under a uniform load. One moment equation about the crown hinge gives a horizontal thrust of 23.37, with no stiffness and no assumption about the section. The thrust line lands on the axis everywhere, so there is no bending anywhere in the arch.

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.

structures · Arch

A line of thrust, and the masonry it has to stay inside. An arch ring of 9% of the span in thickness, rising 28% of the span, under its own weight as a uniform load. Any horizontal thrust between 3.85 and 5.23 puts a line of compression entirely inside the masonry, so the arch stands — and which of them it actually takes is not decided by statics. The two extremes are drawn: the minimum-thrust line, which rides high at the crown and low at the haunches, and the maximum-thrust line, which does the opposite.

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.

structures · Arch

Named alongside it

The objects these essays reach for when they reach for this one.

Horizontal thrust Thrust line Bending moment Determinacy Funicular Geometrical factor of safety Hinge Lower-bound Safe theorem Support settlement

All concepts