Last edited 08 Oct 2020

Conoid shell


A conoid is a special kind of warped ruled surface which, as a curved shell roof, can be used as an alternative to a barrel vault. The basic principle is that one edge of the shell is curved while the opposite edge is kept straight. In architecture, this is referred to as a ‘right conoid’.

Two basic geometrical forms are encountered:

  • A straight line is moved along a curved line at one end and a straight line at the other end, the resultant shape being cut to the required length.
  • A straight line is moved along a curved line at one end and a different curved line at the other end.

The end consists of a reinforced concrete or steel lattice, which serves as a stiffening beam to prevent shell deformation. Support is required at all corners.

Spans of up to 12 m with chord lengths of up to 24 m are possible. The typical chord-to-span ratio is 2:1.

When conoids are made of reinforced concrete they require formwork on which to set the reinforcing steel and pour the concrete. The initial cost of making the formwork is usually high, but it can be reduced by pouring many shells on the same form.

There can be a solid infill or glazed end diaphragm. Glass panes set between adjacent conoids at the curved front of each conoid can allow for illumination. If the conoids face north they get the best natural light, which can be important for space such as factories.

Conoid shells are an ideal shape for cantilevered roofs covering the stands of stadiums with either a curvature up or a curvature down.

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