Hyperbolic Paraboloid Roof (Hypar)

A hyperbolic paraboloid, often shortened to hypar, is a saddle-shaped surface that curves upward in one direction and downward in the direction at right angles. Mathematically it is a doubly ruled surface: although it is curved, it can be generated entirely by straight lines. This property makes hypar roofs practical to build, because the curved form can be produced with straight timber boards, straight formwork for concrete, or straight steel members.

Why it works structurally

The double curvature gives the surface great stiffness, so a hypar can span large areas with a very thin shell. Loads are carried largely by direct tension and compression within the surface rather than by bending. The edges typically need stiffening beams that collect forces and carry them to a small number of supports.

Notable designers and examples

• Félix Candela (1910-1997): the Spanish-born architect and engineer who worked in Mexico became the best-known builder of thin reinforced-concrete hypar shells. Examples include the Cosmic Rays Pavilion at the National Autonomous University of Mexico (1951) and the Los Manantiales restaurant in Xochimilco, Mexico City (1958), designed with Joaquín Álvarez Ordóñez.
• Warszawa Ochota railway station, Warsaw, Poland (1962), has a hypar saddle roof.
• Scotiabank Saddledome, Calgary, Canada (1983), uses a hypar saddle roof.
• Le Corbusier also used hypar surfaces.

Construction methods

• Concrete shells: cast on timber formwork made of straight boards set along the ruling lines.
• Timber: layered boards or glulam edge beams.
• Steel and cable nets: tensioned cables and membranes forming saddle surfaces.

Roofing considerations

Waterproofing a doubly curved surface is demanding: membranes, liquid-applied coatings, flexible metal or shingles that can follow the curve are used. Low points at the corners concentrate drainage, and the edges need robust flashing and gutters.