HYPAR

A hypar, or hyperbolic paraboloid, is a 3-dimensional, double-ruled surface which can be described using infinite planar, linear elements which form a smooth, continuous surface.

Felix Candela's use of the hypar geometry in his own design of structural concrete shells (up to 4cm thin) proved that the material economy in linear construction formwork had its advantages. While there are numerous projects implementing hyperbolic paraboloids as a premise for design, especially in the mid-20th century, straight members are usually used as formwork and reinforcing but are rarely left as a set of articulated lines across a continuous paraboloid surface.

Our experiments around the hypar retain this invisible line, repeating it so that the sum of many elements can be perceived as an exquisite whole. Even though these elements are unique, they can be efficiently nested onto a sheet of flat material for a more economical process of fabrication.

PROTOTYPING THE HYPAR, HYPER-THIN

Three separate experiments were carried out to test the use of flat profile aluminum members to compose the two directions of curvature in a self-supporting hyperbolic paraboloid. Each test also applies Candela’s position that design and construction are best coordinated between the efficient and effective use of materials and labor. But what happens when the material thickness is reduced to just a few millimeters? What new qualities does the hyper-thin hypar take on?

Our first prototype arrayed two layers of ultra-thin aluminum stripes in opposite directions and mechanically bonded them together using rivets. The system consists of a series of aluminum stripes that are not particularly strong when performing individually but achieve stiffness when put together.

While the performance of hyper-thin self-supported structures is generally achieved through the use of extensive or intensive double curvature, we discovered that the hypar largely lacks double curvature across its surface. The stiffness of the hypar at the saddle would not extend to the vertical sides and compromised the structural integrity of this first prototype. These quasi-planar regions do not withstand horizontal forces, such as wind loads, which typically drive the dimensioning of shell structures. Contrary to the common assumption, the geometry does not aid in the search for stiffness.

EXPERIMENTS IN SURFACE DEPTH

In our second and third phases of experimentation, we sought to increase the stiffness through the depth of the surface, adding thicker members and spacing elements that offset the two thin layers of aluminum.

 STRUCTURAL DEPTH THROUGH MEMBERS  The piped strategy was arrayed in two layers and implemented a coping system at its intersections to hold members rigidly in place. While assembly could be done quickly, the sheer amount of coping details escalated fabrication costs and prohibited further development of the prototype under strict budgeting.

 STRUCTURAL DEPTH IN LAYERS  The spaced cross-sectional model necessitated a transition from rivets to two-part screws, which not only complicated fabrication and assembly, but escalated the cost to a third of the total budget. Twisting at both ends of the stripes led to extreme levels of torsion, created alignment issues, and halted assembly of the prototype.

While achieving structural performance, these experiments failed on another count: economy.

HYPARBOLE was computationally conceived through the integration of pleating with the hypar’s curvature. This series of peaks and valleys introduced the structural depth to the surface without increasing thickness, adding hardware, or complicating the assembly process. Pleats were also proportioned to be easily divided into developable elements--further easing production and assembly.

Structural pleating, as developed by MARC FORNES / THEVERYMANY over a number of projects, poses a creative design solution to make the hypar hyper-thin. A combination of 582 1/8" body stripes, 1/4" anchor stripes, and 1/2" anchor plates were cut from flat sheets of aluminum and fastened to adjacent parts using 10,082 rivets. Compound curvature was achieved over the entirety of the 3,037 sq ft structure through overlapping aluminum elements that work together as a unified structural system.