Félix Candela

The Hyperbolic Paraboloid

The hyperbolic-paraboloid shell is doubly curved which means that, with proper support, the stresses in the concrete will be low and only a mesh of small reinforcing steel is necessary. This reinforcement is strong in tension and can carry any tensile forces and protect against cracks caused by creep, shrinkage, and temperature effects in the concrete.

Hyperbolic parabolid with curved edges. Hyperbolic parabolid with straight edges.


Prototypical “umbrella” structure showing foundation, which is also an umbrella form.

Candela posited that “of all the shapes we can give to the shell, the easiest and most practical to build is the hyperbolic paraboloid.” This shape is best understood as a saddle in which there are a set of arches in one direction and a set of cables, or inverted arches, in the other. The arches lead to an efficient structure, but that is not what Candela meant by stating that the hyperbolic paraboloid is practical to build. The shape also has the property of being defined by straight lines. The boundaries, or edges, of the hypar can be straight or curved. The edges in the second case are defined by planes “cutting through” the hypar surface.