• Review Points

Funicular Compression Structures

• By arranging material along the opposite profile of a sagging cable, it is possible to make a spanning structure that works in pure compression.

• It is common to use arches with pin supports and an internal hinge connection. This configuration is called a three-hinged arch. They were particularly popoular in the 19th and early 20th centuries because they are statically determinate.

Unbalanced Loading

• Unlike cables, which can reconfigure to a different stable profile when the load pattern changes, arches cannot.

• A loading that does not corrpespond to the arch's funicular profile will be called a non-funicular loading or unbalanced loading.

• There are two possible responses to unbalanced loading:

  1. The structure develops internal shear and moment to compensate for the difference between the funicular profile of the load and its own profile.

  2. The structure becomes unstable and collapses.

• Since the first option is preferred, it is generally necessary to design arch structures for shear and moment.

• Typically, the profile is based on the funicular profile corresponding to dead load acting alone, and the arch rib is designed to resist shear and bending moments resulting from unbalanced live loads.

• Arch structures sometimes vary from the dead-load funicular profile for architectural or functional reasons.

• Pier Luigi Nervi discussed this issue:

  A 160-foot arch is less limited than one of 330 feet, and, as a consequence, the latter is confined to a profile which corresponds exactly to the funicular curve of the permanent loads, but the profile of the former can vary considerably. But even the 160-foot arch will achieve maximum efficiency and best use of materials by following the funicular curve of the loads.

  Pier Luigi Nervi
  Aesthetics and Technology in Building
  Harvard Press, 1965, p. 187

• In addition to its insights concerning arch design, this statement also raises important issues concerning scale, which we will discuss soon.