The Art and Design of the Hypar Roof

For tens of thousands of drivers that pass it each day, the roof of the iconic former Birkenstock campus warehouse in Novato, California, evokes snow-strewn mountains or a terrain of tent canopies. While looking from beneath, jagged triangles—jutting out unsupported over the building’s perimeter—suggest a royal crown.

The soaring geometric roof, originally built for the McGraw-Hill Company and the future home of the Eames Institute’s museum, is the structure’s most distinctive, and remarkable feature; a motif that will be integral to the museum’s identity.

In the early 1960s, California architect John Savage Bolles (1905–1983), and Jan Lubicz-Nycz (1925–2011) designed one of the Bay Area’s most sculptural, geometric roofs in close collaboration with structural engineer Raj Desai (1928–2022). Their pioneering experiment in thin-shell concrete, completed in 1964, capitalized on technological advances developed by architects and engineers in the post–World War II era, as they sought to build longer spans with less material.

By the 1960s, such spans—the term describing the distance between structural supports—could cover immense distances with astonishingly small thicknesses of only three inches of concrete, proportionally much thinner than an eggshell. Over time, architects and engineers kept innovating thin-shell concrete designs, and the movement culminated in 1976 with the record-breaking, 660-foot span of the Seattle Kingdome’s roof. These remarkable designers fulfilled their aesthetic vision informed by the possibilities of structural technology.

The Birkenstock roof is made by repeating a very particular mathematical surface: the hyperbolic paraboloid, also known as a hypar, or saddle-shaped surface. In selecting this design, Bolles, Lubicz-Nycz, and Desai were likely inspired by Mexican architect-engineer Felix Candela, perhaps the greatest designer of reinforced concrete hypar shells. Candela, who constructed hypar-roofed factories across Mexico in the 1950s and rose to global fame in the early 1960s, once said about the geometry, “Of all the shapes we can give to a shell, the easiest and the most practical to build is the hyperbolic paraboloid.”

Candela delivered the keynote lecture at the 1962 World Conference on Shell Structures, held in San Francisco. At the conference, Candela showcased the hypar-shelled factories and warehouses he had successfully constructed in Mexico, which would have made a strong impression on Desai, a UC Berkeley engineering alum who attended the event.

The geometric theme continued throughout the forum, where a considerable percentage of the presented papers discussed hypar shells. Curiously, the expansive roof in Novato was the only major hypar concrete roof built by Bolles and Desai, so it is an anomaly in their long and distinguished careers in California.

The key to the strength and efficiency of such structures is their geometry: the curved surfaces carry loads through a combination of tension and compression. Theoretically, a shell might be in pure compression under its dead load (self-weight). However, in real practice, variable loads like snow, wind, or live loads can introduce bending and tension. The regions of compression are carried by the thin concrete, while the regions of tension are carried by steel reinforcing bars inside the concrete.

Mathematically, a hypar is a ruled surface that can be generated from a repetition of straight lines or curved lines. To understand how the surface can be formed through straight lines, imagine four wooden planks that make the four sides of a square frame. When the two opposite corners are tilted upward, the square becomes twisted. The hypar surface is then generated by placing other straight planks extending from one side of the twisted square to its parallel side.

The process of building hypar architectural structures from curved lines—specifically, curved supports—requires a complex formwork involving parabolic arches. Candela, on the other hand, built hypar concrete shells with straight wooden planks as his formwork, establishing an easy and cost-effective construction method. The evocative curved roofs and other forms were architecturally expressive and structurally efficient.

The hyperbolic paraboloid belongs to what is known as the anticlastic family of double curved surfaces. Spheres and domes are synclastic surfaces; in contrast to them, where the curves are all in the same direction, the anticlastic surfaces have two main curvatures running in opposite directions, and its surface is ruled, meaning it can be formed using straight lines. Examples of anticlastic geometries include the conoid, the hyperboloid, and the hyperbolic paraboloid.

While the 1960s were the heyday for thin-shell concrete structures, architects and artists had long explored the peculiar characteristics of hypar surfaces. Catalan architect Antoni Gaudí used hypar geometries in many of his projects and throughout his Sagrada Familia in Barcelona. During the late 1930s and early 1940s, Russian-born artist Antoine Pevsner used the hyperbolic paraboloid as a motif in his sculptures. The work Pevsner developed alongside his brother Naum Gabo had a seminal influence in consolidating the constructivist movement. Throughout the 1930s and 1940s in Great Britain, abstract artists like Henry Moore and Barbara Hepworth took inspiration from the mathematical models displayed at Oxford University and the Science Museum. Hepworth subsequently developed string sculptures using the hyperbolic paraboloid geometry.

While several other hypar shells were built in the United States during the 1950s, the Novato roof is one of the most significant projects that still survives today from that period. It is a dramatic experiment in mid-century architecture and engineering, and it embodies the exploration of geometry and form that is central for all designers. ❤

—Marisela Mendoza Ramos is an architectural educator and associate professor at Nottingham Trent University, with a research focus on circular economy–driven creative practices, adaptive architecture, and the cultural significance of historic spatial structures.

—John Ochsendorf is an engineer, educator, and designer on the MIT faculty since 2002, and a Curious 100 honoree. Trained at Cornell, Princeton, and the University of Cambridge, he is known for creative research at the intersection of structural engineering and architecture to further sustainability in the built environment.

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