The [[Gateway Arch]] in the American city of [[St. Louis]] ([[Missouri]]) is an inverted catenary arch.<ref name="Modern Steel Construction">{{cite web|url=http://msc.aisc.org/globalassets/modern-steel/archives/1961-1995/1963v04.pdf|title=Modern Steel Construction|author=|date=|website=|accessdate=}}</ref>
The [[Gateway Arch]] in the American city of [[St. Louis]] ([[Missouri]]) is a catenary arch.<ref name="Modern Steel Construction">{{cite web|url=http://msc.aisc.org/globalassets/modern-steel/archives/1961-1995/1963v04.pdf|title=Modern Steel Construction|author=|date=|website=|accessdate=}}</ref>
Due to [[aspect ratio]], the top being thinner than the bottom, its actual shape is technically a "[[weighted catenary]]".<ref name="How the Gateway arch got its Shape">{{cite web|url=http://www.msri.org/people/staff/osserman/papers/NNJ_v12n2_Osserman_pp167-189.pdf|title=How the Gateway arch got its Shape|author=Robert Osserman |date=|website=|accessdate=}}</ref>
Due to [[aspect ratio]], the top being thinner than the bottom, its actual shape is technically a "[[weighted catenary]]".<ref name="How the Gateway arch got its Shape">{{cite web|url=http://www.msri.org/people/staff/osserman/papers/NNJ_v12n2_Osserman_pp167-189.pdf|title=How the Gateway arch got its Shape|author=Robert Osserman |date=|website=|accessdate=}}</ref>
Revisionasof07:34,19December2023
A catenary arch is an architectural pointed arch that follows an inverted catenary curve
Amudbrick catenary archAcatenary curve (left) and a catenary arch, also a catenary curve (right). One points up, and one points down, but the curves are the same.
The 17th-century scientist Robert Hooke wrote: "Ut pendet continuum flexile, sic stabit contiguum rigidum inversum", or, "As hangs a flexible cable so, inverted, stand the touching pieces of an arch."[2]
A note written by Thomas Jefferson in 1788 reads, "I have lately received from Italy a treatise on the equilibrium of arches, by the Abbé Mascheroni. It appears to be a very scientific work. I have not yet had time to engage in it; but I find that the conclusions of his demonstrations are, that every part of the catenary is in perfect equilibrium".[3]
Structural properties
Architecturally, a catenary arch has the ability to withstand the weight of the material from which it is constructed, without collapsing.[4][5] For an arch of uniform density and thickness, supporting only its own weight, the catenary is the ideal curve.[6]
Catenary arches are strong because they redirect the vertical force of gravity into compression forces pressing along the arch's curve. In a uniformly loaded catenary arch, the line of thrust runs through its center.[7][8]
This principle has been employed architecturally to create arched structures that follow exactly, and in a visibly apparent way, the form of an inverted catenary. A significant early example of this is the arch of Taq Kasra. The catenary, spun 180 degrees, forms the structure of simple domed building such as the beehive homes of the Dingle Peninsula, Ireland.
The principle of the catenary is also the underlying factor in the much more complex architectural systems of the Medieval and Renaissance architecture. Buildings that have heavy roofs that are arched in shape and deliver a strong outward thrust must comply with the form of the catenary curve in order not to collapse. This does not imply that the arches themselves are catenary in form, but that the total system of walls or buttresses that support the roof or dome contain a catenary curve, which delivers the downward thrust.
Igloos are designed with a catenary arch cross-section.[27][18] This shape offers an optimal balance between height and diameter, avoiding the risk of collapsing under the weight of compacted snow.[18]