The construction of shells and hyper parabolic paraboloids are simplistic in their origin. To understand how forces flow through the transverses and down to the ground you must first understand the arch. Like all curved forms the arch through a series of segmented lines transfers the compressive loads to the ground, the more segmented lines the greater the fluidity of the curve on the arch. The arch in its most efficient form is parabolic by nature.

 


St. Mary's Cathedral

Hyper Parabolic Paraboloids in Architecture

Kimbell Art Museum
The hyper parabolic paraboloid is a series of these parabolas strung together. This series however is a non-developable surface so the construction of it has to be precise. The two axial parabolas generate a surface curve that is both in compression and in tension. The use of reinforcing steel in the upward curvature of the parabola allows for the tensile forces to flow into first the neutral sag, or catenary then the thrust of the forces flow into the compression on the downward parabola.
Shells and Hyper Parabolic Paraboloids

St. Louis Planetarium

Barrel Shells are a curved structure that are similar to a barrel vault deriving its structural integrity from the arch. The barrel shell however is much thinner so therefore can not handel concentrated loads.

Hyperbolic Paraboloids are formed by a series of parabolas that are interconnected creating a series of transversal axis through which they remain in compression and tension.

Hyperboloids are created by a series of strait lines that flow from the top ring to the bottom ring. These strait lines however have been rotated creating a series of hyperbolas.

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