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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Basket-handle arch | 1/3 | https://en.wikipedia.org/wiki/Basket-handle_arch | reference | science, encyclopedia | 2026-05-05T13:59:06.280548+00:00 | kb-cron |
A basket-handle arch (also depressed arch or chop arch) is characterized by an intrados profile formed by a sequence of circular arcs, each tangent to its neighbors, resulting in a smooth transition between arcs. The shape of a basket-handle arch resembles but is different than that of a semi-ellipse, with the latter featuring a continuous curvature that varies from the extremities of the long axis to the apex of the short axis. The simplest form, a three-centered arch, consists of three arc segments with distinct centers, while a five-centered arch is also commonly used. This type of arch is prevalent in architectural applications, particularly in bridge construction. Arches following curves with more than three centers are also used.
== History ==
Since Roman times, bridge vaults has been built with semicircular arches, forming a complete half-circumference. From the early Middle Ages onwards, the segmental arch, an incomplete half-circumference, was used to build vaults that were less than half the height of their opening. The pointed arch, which emphasizes height by rising above half the opening, did not see use in bridge construction until the Middle Ages. The basket-handle arch appeared at the beginning of the Renaissance, offering aesthetic advantages over segmental vaults, notably through its end arches being vertically tangential to the supports.
The earliest applications of basket-handle arches in France can be seen in the Pont-Neuf in Toulouse, constructed in the 16th century, and the Pont Royal in the following century. By the 18th century, the use of basket-handle arches became prevalent, particularly with three centers, as exemplified by the bridges at Vizille, Lavaur, Gignac, Blois (1716–1724), Orléans (1750–1760), Moulins (1756–1764), and Saumur (1756–1770). Notable architect Jean-Rodolphe Perronet designed bridges with eleven centers during the latter half of the 18th century, including those at Mantes (1757–1765), Nogent (1766–1769), and Neuilly (1766–1774). The Tours bridge (1764–1777) also featured eleven centers. Other arches were generally reduced to one-third or slightly more, except for Neuilly, which was reduced to one-fourth. In the 19th century, basket-handle arches were utilized in France's first major railroad bridges, including the Cinq-Mars bridge (1846–1847), Port-de-Piles bridge (1846–1848), Morandière bridges: Montlouis (1843–1845), and Plessis-les-Tours (1855–1857). In England, while the Gloucester Bridge (1826–1827) and the London Bridge (1824–1831) were elliptical, the Waterloo Bridge in London (1816–1818) retained the basket-handle arch form. Several basket-handle arches continued to be constructed into the late 19th and early 20th centuries. Notable examples include the Edmonson Avenue Bridge in Baltimore (1908–1909) with three centers, the Annibal Bridge (1868–1870) and Devil's Bridge (1870–1872) with five centers, the Emperor Francis Bridge in Prague (1898–1901) with seven centers, and the Signac Bridge (1871–1872) with nineteen centers. In the United States, the Thomas Viaduct, featuring a basket-handle arch, was built between 1833 and 1835. It is now owned and operated by CSX Transportation and remains one of the oldest railroad bridges still in service.
== Comparison between basket handle arch and ellipse ==
=== Aesthetics === Ancient architects placed considerable importance on the methods used to define the outline of the basket-handle arch. The flexibility inherent in these processes allowed for a wide variety of configurations, leading many architects to favor this type of curve over the ellipse, whose contour is rigidly determined by geometric principles. In the case of an ellipse, the opening of a vault and the height at the center—corresponding to the major and minor axes—result in fixed points along the intrados curve, leaving no room for architectural modification. Conversely, the multi-center curve offers greater design freedom, allowing architects to adjust the curve's base and apex according to their preferences, depending on the arrangement of the centers. This adaptability made the basket-handle arch an attractive option for those seeking aesthetic flexibility.
=== Advantages and disadvantages === The advantages of this layout approach were significant: the establishment of full-scale grooves was perceived as easier and more precise, allowing for immediate on-site layout of the normals and segment joints. The number of voussoir shapes was constrained by the number of distinct radii employed, whereas for elliptical arches, this number was typically equal to half the number of voussoirs plus one. However, the discontinuity of the layout led to the appearance of unsightly voussoirs, which could not always be removed during restoration work.
== Tracing curves with three centers ==
=== The ancient oval ===
Although the basket-handle arch was not utilized for bridge vaults in ancient times, it found application in the construction of other types of vaults. Heron of Alexandria, who authored mathematical treatises more than a century before the Common Era, outlined a straightforward method for tracing this arch. In Heron's method, if AB represents the width of the intended vault and the height (or rise) is undetermined, a half-circumference is described on AB. A vertical line OC is drawn through point C on this arc, and a tangent mn is constructed at point C. Lengths Cm and Cn are taken to be equal to half the radius of the arc. By connecting points mO and nO, points D and E are established. An isosceles triangle DOE is then traced, with its base equal to the height of the arch. Next, the line segment DA is divided into four equal parts, and parallels to DO are drawn through these division points (a, b, c). The intersections of these parallels with the horizontal axis AB and the extended vertical axis CO yield the necessary centers for tracing various curves with three centers along AB, often referred to as the ancient oval.