Architecturally, a catenary arch has the ability to withstand the weight of the material from which it is constructed, without collapsing. For an arch of uniform density and thickness, supporting only its own weight, the catenary is the ideal curve. 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. 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. In the 15th century
Brunelleschi designed the pointed, octagonal, Gothic dome on
Florence Cathedral in a manner that utilised the principle of the catenary arch. In the 17th century,
Christopher Wren designed the dome of
St Paul's Cathedral based directly on a catenary curve. The vaulted roof and buttresses of
Kings College Chapel, Cambridge, have been discovered to comply with the formula of the catenary arch. ,
Utah ==Examples==