Hyperbolic paraboloid in construction

A hyperbolic paraboloid (sometimes referred to as ‘h/p’) is a doubly-curved surface that resembles the shape of a saddle, that is, it has a convex form along one axis, and a concave form on along the other. It is also a doubly-ruled surface, that is, every point on its surface lies on two straight lines across the surface. Horizontal sections taken through the surface are hyperbolic in format and vertical sections are parabolic.

The fact that hyperbolic paraboloids are doubly-ruled means that they are easy to construct using a series of straight structural members. As a consequence they are commonly used to construct thin ‘shell’ roofs. These can either be formed using timber or steel sections, that are then clad, or they can be constructed using concrete.

The use of hyperbolic paraboloids as a form of thin shell construction was pioneered in the post-war era, as a hybrid of modern architecture and structural engineering. By being both lightweight and efficient, the form was used as a means of minimising materials and increasing structural performance while also being capable of achieving impressive and seemingly complex designs.

Rather than derive their strength from mass, like many conventional roofs, thin shell roofs gain strength through their shape. The curvature of the shape reduces its tendency to buckle in compression (as a flat plane would) and means that they can achieve exceptional stiffness. By being braced in two directions they experience no bending and are able to withstand unequal loading, whether dead loads (such as equipment hung from the ceiling), or live loads (such as wind).

Hyperbolic paraboloid shell roofs can be constructed using reinforced concrete with a shell thickness of just 50 mm for diagonal spans up to 35 m. By using simple prestressing cables to resist tension forces, concrete hyperbolic paraboloid roofs can span over 24 feet, with thicknesses of less than 40 mm.

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[edit] External resources

• ‘Building Construction Handbook’ (6th ed.), CHUDLEY, R., GREENO, R., Butterworth-Heinemann (2007)