A parabolic arch is an arch in the shape of a parabola. [1] In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
A parabolic arch is an arch in the shape of a parabola. [1] In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
While a parabolic arch may resemble a catenary arch, a parabola is a quadratic function while a catenary is the hyperbolic cosine, cosh(x), a sum of two exponential functions. One parabola is f(x) = x2 + 3x− 1, and hyperbolic cosine is cosh(x) = ex + e−x/2. The curves are unrelated.
Unlike a catenary arch, the parabolic arch employs the principle that when weight is uniformly applied above, the internal compression (see line of thrust) resulting from that weight will follow a parabolic curve. Of all arch types, the parabolic arch produces the most thrust at the base. Also, it can span the widest area. It is commonly used in bridge design, where long spans are needed. [2] [3]
When an arch carries a uniformly distributed vertical load, the correct shape is a parabola. When an arch carries only its own weight, the best shape is a catenary. [3]
A hen's egg can be fairly well described as two different paraboloids connected by part of an ellipse. [4] [5]
Self-supporting catenary arches appeared occasionally in ancient architecture, for examples in the main arch of the partially ruined Sassanian palace Taq Kasra (now in Iraq), the largest single-span vault of unreinforced brickwork in the world, and the beehive huts of southwestern Ireland. In the modern period, parabolic arches were first used extensively from the 1880s by the Catalan architect Antoni Gaudí, [6] deriving them from catenary arched shapes, constructed of brick or stone, and culminating in the catenary based design of the famous Sagrada Familia. Other Catalan architects then used them into the 1920s, and they appeared occasionally in German expressionist architecture of the 1920s-30s. From the 1940s they gained a new popularity in reinforced concrete, including in shell concrete forms often as hyperbolic parabloids, especially by Felix Candela in Mexico and Oscar Niemeyer in Brazil, but they could be found around the world, especially for churches, in the 1950s and 60s. Since the 1990s Spanish designer Santiago Calatrava has frequently used parabolas for his signature roof structures and bridges. Structures that are self-supporting arches like the Sheffield Winter Garden are often closer to true catenaries.
Bridges have used a variety of arches since ancient times, sometimes in very flat segmental arched forms but rarely in the form of a parabola. A simple hanging rope bridge describes a catenary, but if they were in the form of a suspension bridges they usually describe a parabola in shape, with the roadway hanging from the inverted arch. Modern suspension bridges were built from the early 19th century, beginning with chains and progressing to more and more elegant steel rope examples, and are still in use today. Parabolic arches that support the roadway from below (or in the form of a through arch) first appeared in the 1870s, and have been used occasionally ever since; examples include:
In physics and geometry, a catenary 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 suspension bridge is a type of bridge in which the deck is hung below suspension cables on vertical suspenders. The first modern examples of this type of bridge were built in the early 1800s. Simple suspension bridges, which lack vertical suspenders, have a long history in many mountainous parts of the world.
An arch is a curved vertical structure spanning an open space underneath it. Arches may support the load above them, or they may perform a purely decorative role. As a decorative element, the arch dates back to the 4th millennium BC, but structural load-bearing arches became popular only after their adoption by the Ancient Romans in the 4th century BC.
Santiago Calatrava Valls is a Spanish-Swiss architect, structural engineer, sculptor and painter, particularly known for his bridges supported by single leaning pylons, and his railway stations, stadiums, and museums, whose sculptural forms often resemble living organisms. His best-known works include the Olympic Sports Complex of Athens, the Milwaukee Art Museum, the Turning Torso tower in Malmö, Sweden, the World Trade Center Transportation Hub in New York City, the Auditorio de Tenerife in Santa Cruz de Tenerife, the Margaret Hunt Hill Bridge in Dallas, Texas, and his largest project, the City of Arts and Sciences and Opera House in his birthplace, Valencia. His architectural firm has offices in New York City, Doha, and Zurich.
An arch bridge is a bridge with abutments at each end shaped as a curved arch. Arch bridges work by transferring the weight of the bridge and its loads partially into a horizontal thrust restrained by the abutments at either side, and partially into a vertical load on the arch supports. A viaduct may be made from a series of arches, although other more economical structures are typically used today.
The City of Arts and Sciences is a cultural and architectural complex in the city of Valencia, Spain. It is the most important modern tourist destination in the city of Valencia and one of the 12 Treasures of Spain.
The Victoria Falls Bridge crosses the Zambezi River just below the Victoria Falls and is built over the Second Gorge of the falls. As the river forms the border between Zimbabwe and Zambia, the bridge links the two countries and has border posts on the approaches to both ends, at the towns of Victoria Falls, Zimbabwe, and Livingstone, Zambia.
Hannskarl Bandel, was a German-American structural engineer.
Eladio Dieste was a Uruguayan engineer who made his reputation by building a range of structures from grain silos, factory sheds, markets and churches, most of them in Uruguay and all of exceptional elegance.
The Zubizuri, also called the Campo Volantin Bridge or Puente del Campo Volantin, is a tied arch footbridge across the Nervion River in Bilbao, Spain. Designed by architect Santiago Calatrava, the bridge links the Campo Volantin right bank and Uribitarte left bank of the river.
Contemporary architecture is the architecture of the 21st century. No single style is dominant. Contemporary architects work in several different styles, from postmodernism, high-tech architecture and new references and interpretations of traditional architecture to highly conceptual forms and designs, resembling sculpture on an enormous scale. Some of these styles and approaches make use of very advanced technology and modern building materials, such as tube structures which allow construction of buildings that are taller, lighter and stronger than those in the 20th century, while others prioritize the use of natural and ecological materials like stone, wood and lime. One technology that is common to all forms of contemporary architecture is the use of new techniques of computer-aided design, which allow buildings to be designed and modeled on computers in three dimensions, and constructed with more precision and speed.
Félix Candela Outeriño was a Spanish and Mexican architect who was born in Madrid and at the age of 26, emigrated to Mexico, acquiring double nationality.
The Chords Bridge, also called the Bridge of Strings or Jerusalem Light Rail Bridge, is a side-spar cable-stayed bridge in Jerusalem. The structure was designed by the Spanish architect and engineer Santiago Calatrava and is used by Jerusalem Light Rail's Red Line, which began service on August 19, 2011. Incorporated in the bridge is a glass-sided pedestrian bridge enabling pedestrians to cross from Kiryat Moshe to the Jerusalem Central Bus Station. The bridge, which cost about $70 million, was inaugurated on June 25, 2008.
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. It forms an underlying principle to the overall system of vaults and buttresses in stone vaulted Gothic cathedrals and in Renaissance domes. It is not a parabolic arch, although the non-circumferential curves used in arch designs look similar, and match at shallow profiles, so a catenary is often misclassified as a parabola.
Antoni Gaudí i Cornet was a Catalan architect and designer, known as the greatest exponent of Catalan Modernisme. Gaudí's works have a sui generis style. Most are located in Barcelona, including his main work, the Sagrada Família church.
Parametric design is a design method in which features, such as building elements and engineering components, are shaped based on algorithmic processes rather than direct manipulation. In this approach, parameters and rules establish the relationship between design intent and design response. The term parametric refers to the input parameters that are fed into the algorithms.
St Paul's Anglican Church is a heritage-listed church at 8 Main Street, Proserpine, Whitsunday Region, Queensland, Australia. It was designed by Eddie Oribin and built from 1958 to 1959 by Les Tinsley & Co. It is also known as St Paul's Anglican Memorial Church and Proserpine Church of England. It was added to the Queensland Heritage Register on 11 October 2013.
A weighted catenary 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 weight is not consistent along its length. Formally, a "regular" catenary has the equation
The College of Saint Teresa-Ganduxer is a school on the Carrer de Ganduxer in the old town of Sant Gervasi de Cassoles, currently part of the Tres Torres neighborhood of the Sarrià—Sant Gervasi district of Barcelona. The school offers all the courses of the regular education curriculum from the second cycle of infantile education to the baccalaureate. It used to be a girls-only school, but by the end of the twentieth century it was a mixed school. It has an agreement with the Generalitat de Catalunya to teach the compulsory education curriculum. The building, designed by noted Catalan Modernisme architect Antoni Gaudí, has been declared a Spanish Cultural Asset of National Interest.
