Hyperbolic Paraboloids (also known as Hyparor h/p) resemble the shape of a saddle formed by the combination of concave and convex surfaces. They are doubly curved surfaces with negative Gaussian curvature. Along with being aesthetically dynamic, it has also been proven to be structurally efficient due to the capacity to cover long spans without intermediate supports. This amazing form is a result of the culmination of modern architecture and advanced structural engineering.

What are Hyperbolic Paraboloid shells?

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Hyperbolic paraboloid Source-©Stack exchange
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Standalone h/p shell structure Source-©


The shell structure is doubly ruled with the vertical ribs/ rules are parabolic and the horizontal ribs form the hyperbolic curvature. This unique shell structure can be as thin as 50 mm and is structurally stable to cover spans as large as 35m.H/p shells are characterized as anticlastic surfaces, i.e., it has negative Gaussian curvature. The cable and

arch mechanisms interact in two opposite directions. The forces and loads acting on the shell induce compression in the inner-built portion of the arches while it also causes tension in the internal cables or reinforcements. 

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Axes forming hyperbola and parabola Source- ©Engineering for a change

Hyperbolic-Paraboloids are lightweight shell structures which unlike standard structural members derive their stability from the form and not the mass. The curvilinear surfaces often act as the walls as well as the roof. Since the form is made up of curved surfaces; it has a reduced risk of buckling failure due to compression which is commonly observed in-plane structural members. The versatility of the form and the strength due to the rules along the two axes enables it to withstand the dead loads and the wind load. Hypars can be constructed with many construction materials based on usage, such as – Reinforced concrete, Steel members, Aluminum, Timber, Plywood, Bamboo, etc.

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Span and load distribution Source- ©


The hyperbolic paraboloid structures often are square or quadrilateral in the plan. However, the same characteristics are possible for planar triangular, pentagonal, hexagonal, and any other polygon surfaces.

The Hypar also features in a straight line form which is simpler to construct or prefabricate.

H/P roofs

Hyperbolic paraboloids have also been used as roofs called saddle roofs. This type of roof has been seen in various structures and is easy to assemble. During assembly or construction of such roofs, straight sections of lumber steel or some other material would be used. These skeleton structures could then be clad, sheathed, or left exposed as per utility and aesthetic appeal. H/p shells could also be tensile structures or tensegrity structures.

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Tensile saddle roof structure, City Hall Square Source-©G.L.M.S

History of Hyperbolic Paraboloids

Hypars were seen in parts of Europe or other countries, but the form was relatively unknown to the west until the 1950s. By 1962 it had gained widespread popularity amongst all practicing architects, structural engineers, civil engineers, and builders. It had gained a status symbolizing modernization and progress in the post-war era. It made appearances in all sorts of structures like churches, warehouses, residences, and gas stations. To date, hyperbolic paraboloids are seen in art installations, roofs of commercial structures, urban spaces, hardscapes, etc. in contemporary architecture.

Examples in architecture:

Philips Pavilion, Brussels 

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3D recreation of Philips Pavilion Source-©MaMaProductions

Le Corbusier and Iannis Xenakis were commissioned to design a pavilion by Phillips the electronics company. After World War II Phillips constructed the pavilion for the World Fair expo of 1958 held in Brussels. Corbusier promised to give Phillips a statement structure exhibiting the future of electronics and technology. The display in the installation was to be a multidisciplinary art spectacle showcasing the impact of the nuclear war and the post-war progress. Considering the acoustic requirements and the visual engagement of the audience a unique form was required. After extensive experimentation, Xenakis came up with a tent-like structure formed by a cluster of nine tangled hyperbolic-paraboloids.

The Church Army Chapel, London

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Church Army chapel Source-©Wikipedia

The Church Army Chapel in London was designed by Earnest Trevor Spashet. The Structure is known for its sectional aluminium spire being the tallest in the early 20th century. The spire was a tall, slim, and hollow cone. The structure has a saddle roof meaning its hyperbolic paraboloid in shape, having a curved form constructed with straight beams. The roof was designed by the architect after taking inspiration from Corbusier’s Modulor man proportions.

Los Mantieles, Mexico city

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Los Manteles flower structure Source-©Archdaily

Los Manteles is a restaurant designed by Felix Candela. Candela was known as a connoisseur of shell structures. After extensive experimentation with forms, he came up with a structure consisting of four intersecting Hypars. It had an extremely thin shell structure over the dynamic dining space. The roof is a circular array of four curved-edge Hyper Saddles that intersect at the center point, resulting in a symmetrical eight-sided groined vault. The vaults were arranged in a pattern of a flower and the openings on each petal light up the saddle roof and the continuous space beneath. 

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Four intersecting hypars- Detail Source-©beBee producer

Hypars or Hyperbolic Paraboloids are essentially a series of parabolas strung together. The structural form allows it to function like a tensile structure and the gentle sagging or curves result in a simplified yet dynamic three-dimensional shell structure. This curvilinear form has birthed several architectural marvels. 



Manasi is a young architect who never ceases to be amazed by the stories told by historical structures. She appreciates the power of words as they say what the pictures can’t show. She believes that any piece of art is a form of expression and should be used wisely to say something important.