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A chain hanging from points forms a catenary. The silk on a spider's web forming multiple elastic catenaries.. In physics and geometry, a catenary (US: / ˈ k æ t ən ɛr i / KAT-ən-err-ee, UK: / k ə ˈ t iː n ər i / kə-TEE-nər-ee) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field.
A mudbrick catenary arch A catenary curve (left) and a catenary arch, also a catenary curve (right). One points up, and one points down, but the curves are the same. A catenary arch is a type of architectural arch that follows an inverted catenary curve. The catenary curve has been employed in buildings since ancient times.
Catenary: An arched roof in the form of a catenary curve. Arched roof, bow roof, [11] Gothic, Gothic arch, and ship's bottom roof. Historically also called a compass roof. [12] [13] Circular Bell roof (bell-shaped, ogee, Philibert de l'Orme roof): A bell-shaped roof. Compare with bell-cast eaves. Domed; Onion dome or rather an imperial roof ...
The envelope of the normals of the tractrix (that is, the evolute of the tractrix) is the catenary (or chain curve) given by y = a cosh x / a . The surface of revolution created by revolving a tractrix about its asymptote is a pseudosphere. The tractrix is a transcendental curve; it cannot be defined by a polynomial equation.
The practical designs for bridges are somewhere in between, and thus use the curves that represent a compromise that combines both the catenary and the funicular curve for particular non-uniform distribution of load. [83] The practical free-standing arches are stronger and thus heavier at the bottom, so a weighted catenary curve is utilized for ...
In a simple suspension bridge the deck lies on the main cables In a suspended deck bridge the deck is carried below the main cables by vertical "suspenders" Comparison of a catenary (black dotted curve) and a parabola (red solid curve) with the same span and sag. The catenary represents the profile of a simple suspension bridge, or the cable of ...
The Gateway Arch is a weighted catenary: thick at the bottom, thin at the top.. A weighted catenary (also flattened catenary, was defined by William Rankine as transformed catenary [1] and thus sometimes called Rankine curve [2]) is a catenary curve, but of a special form: if a catenary is the curve formed by a chain under its own weight, a weighted catenary is the curve formed if the chain's ...
A catenoid A catenoid obtained from the rotation of a catenary. In geometry, a catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). [1] It is a minimal surface, meaning that it occupies the least area when bounded by a closed space. [2]