Félix Candela, The hyperbolic paraboloid (1958)

The Spanish-Mexican builder Félix Candela explained to architects why the hyperbolic paraboloid, a doubly curved surface made entirely of straight lines, was the ideal form for thin concrete shells that could be built cheaply on straight timber formwork.

Candela built several hundred shells in Mexico in the 1950s and 60s through his own firm, Cubiertas Ala. He preferred the hyperbolic paraboloid because its geometry is simple enough to calculate by hand, its double curvature makes a thin shell stiff, and its straight rulings allow the formwork to be made from straight boards. Umbrellas of four hypars on a single column roofed warehouses and markets; groined vaults of intersecting hypars spanned factories; and the restaurant Los Manantiales at Xochimilco (1958) was covered by eight hypar lobes only about four centimetres thick.

The book, part by part

I The hypar

A saddle generated by straight lines; strength from curvature; simple formwork.

Fig. 1The saddle and Candela’s combinations of it. Open in Models ↗

Rules: The hyperbolic paraboloid is made of straight lines · Strength from form

Rules drawn from The hyperbolic paraboloid

The hyperbolic paraboloid is made of straight lines

A saddle surface in which two opposite corners are raised and two lowered is a hyperbolic paraboloid; it contains two families of straight lines, so it can be formed with straight boards and yet has double curvature.

y = k·x·z (or any bilinear patch through four points not in one plane)

Strength from form

A thin curved shell carries load by the membrane forces in its surface, not by bending; so shape it to its loads and supports, and it can span great distances with a thickness of a few centimetres.

span ÷ thickness of a good shell ≈ 400–1000 (an egg: ≈ 100)