CHSA Mexico City had many highlights, but one bucket-list item for many of us was seeing this adorable piece of concrete-shell construction on UNAM’s campus. I’ve used Felix Candela’s Cosmic Ray Pavilion to introduce students to shell principles for well over 20 years, so seeing it in person was a much-anticipated stop on our campus tour.
Candela was commissioned in 1951 to design and build the pavilion to house sensitive equipment used to detect incoming cosmic rays, high-energy particles that would have been absorbed by heavy building materials. For their experiments to work, the researchers required the pavilion roof to weigh less than 8 pounds per square foot. This would have been achievable in aluminum, but at a high cost, or in timber, which would not have been permanent enough. Traditional concrete would have been way too heavy, but Candela, by this point, understood how to use doubly-curved geometry to create shell structures—forms that, because of their shape, funneled stresses along their surfaces rather than relying on the depth and mass of girders or slabs to sustain loading.
The pavilion isn’t particularly big—just about 33’ square—but a traditional beam-and-slab system spanning that far would need to be about a foot deep—far too much material. From the outside, Candela’s basic structural solution is obvious. The parabolic shape in cross section is close enough to a true catenary that the dead weight of the roof is carried almost entirely through compression within the shell itself. Thin members in compression, though, risk buckling, so Candela also gently curved the shell in the lateral direction, giving it resistance to that force perpendicular to the parabola. You can just barely see this from the sides—the crown of the roof looks like it’s sagging—this secondary curvature tracks over the roof’s summit.
The double curvature creates a stiff shell structure—one that can only change shape if the material itself fails. Changing an eggshell’s shape requires crushing it, and for the Pavilion’s roof to change shape, it would have to crack. If the secondary curvature wasn’t there, the roof could simply unfold.[1] In Candela’s words:
“Any shape that can be formed by bending or folding a piece of paper cannot be considered a shell, because the shape is not really stable. You can bend a piece of paper, unbend it and it becomes flat again. Therefore, stability of form depends either on the flexural strength of the material or on some outside element of support. But, if one has a double chord surface, such as a dome, made of any unextensible material, it cannot be made flat again unless the material is completely destroyed.”[2]
So, ideal structural shape, but complex. Candela’s real genius was that he was a builder as well as an engineer, and he could translate another mathematical idea into concrete using widely available lumber and relatively unskilled labor. Ruled surfaces are generated by straight lines (generatrices) that connect points on two out-of-plane axes (directrices). The gradually changing three-dimensional angles of these lines produce surfaces that naturally have curvature in two directions, guaranteeing that they will be what Candela termed “lamina,” or shells. What Candela realized was that straight pieces of lumber could translate the “rulers” of these surfaces from abstract mathematics into, well, concrete construction.
By laying out grids of long, thin pieces of wood in gradually transforming angular forms, Candela created formwork onto which concrete could be placed and troweled, creating a doubly curved shape without the complex carpentry necessary to form, say, a perfectly hemispherical dome. Here, Candela used two layers of straight lumber—one of 2x4s providing structural support for another of tongue-in-groove, flat elements at a 60° angle to it. The few construction photographs of the result have their own geometrical beauty, but they also show how simple the woodwork was. Three arches stiffen the shell and are connected to crossbeams and arches that lift it off the ground. This provides a ‘front door’ beneath, reached by a stair cantilevered from a single central stalk. (Locked, despite our best efforts…)
So, a shape that is both structurally and constructionally efficient—but Candela brought the entire idea back around, noting that the mathematics of ruled surfaces allowed for “the feasibility of making accurate calculations quickly.” He wrote that his own engineering abilities were limited, and that he lacked the computing power and time necessary to analyze complex shells. This family of shapes—infinite in number but restricted by their reliance on straight-line generators and directors—reduced the mathematics involved to “a very simple equation of the second degree (one of the quadrics)….[with] only three co-ordinates and a single constant.”
Elsewhere, Candela emphasized that, as compelling as his doubly curved surfaces were, they relied on simple ideas. “’It is better to use simpler procedures which, in most cases, are sufficient when the designer is a constructor.”[3] But the discipline to achieve that simplicity also, in Candela’s mind, offered a ready-made source of beauty:
“A shell cannot be drawn by hand with a happy pencil. On the contrary, one must have a very close geometrical surface or form. This is a very good discipline because, if one is guided by geometry, it is probable that the structure will look attractive. It is one of the amazing properties of this surface that it is extremely difficult to do ugly things with it. A kind of automatic beauty is achieved . . . somewhat similar to design by computer. This is a very interesting proposition for architects.”[4]
Indeed.
[1] See Tyler S. Sprague, “Beauty, Versatility, Practicality”: The Rise of Hyperbolic Paraboloids in Post-war America.” Construction History, vol. 28, no. 1. 2013. 165-184
[2] Felix Candela, “Shell Structure Development.” The Canadian Architect, vol. 12, no. 1. Jan., 1967. 33.
[3] Quoted in Reyner Banham, “Concrete: Simplified Vaulting Practices.” The Architectural Review, vol. 114, no. 684. Sep 1, 1953. 199,
[4] “Shell Structure Development,” op. cit., 34.