Religion Cella

RELIGION CELLA SD4562 Capstone research (Individual stage)

2019-2020 16069192D, Kitty, Lee Yuen Yi Tutor: Dr. ir. Gerhard Bruyns

CONTENT

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Background

The aim of this research is to research the history, relationship, construction, aesthetic of flying buttress and rib vault.. The research documented in this report will serve as the basis for an ongoing capstone project.

Project Statement

How does rib vault have an effect on flying buttress and with what main architectural structure and user experience factor is important to cathedral atmosphere?

HISTORY OF CATHEDRAL

/ Flying buttress Research of flying buttress start from development of flying buttress structure, form, calculation, structure, data, and case studies which shows the function of flying buttress with rib vault.

2.1 Development of flying buttress 2.2 Advantage of flying buttress 2.3 Types 2.4 Case study 2.5 Calculation of flying buttress 2.6 Relationship to cathedral 2.7 Zoning 2.8 Conclusion

Aim

03 / Rib Vault

Research of flying buttress start from Construction, Overview of different vault, history and vault for different period, and zoom into geographical analysis, plan and vault in scale, case studies, and pattern on plan.

3.1 Background and history 3.2 User experience 3.3 Plan design of rib vault 3.4 Case study 3.5 Scale and dimension of vault 3.6 Litetural Review

The aim of this research is to research the history, relationship, construction, aesthetic of flying buttress and rib vault. The research documented in this report will serve as the basis for an ongoing capstone project.

Keywords

#Religion_cella #Religion_history #Element #Development #Evolution #Symbolism

Research questions Key question

How does rib vault have an effect on flying buttress and with what main architectural and user experience factor is important to cathedral atmosphere?

Sub question

What is the fuction of flying buttress in cahedral?

What is the elvolution of buttress?

What is the calucaltion of flying buttress?

How rib vault is spread throughout the world?

How can we identify different type of vaults?

How vault is designed on plan?

01 Evolution of Cathedral In the first stage,researches on the evolution of cathedral from different period and times.

In order to understand more about the spatial design and concept behind cathedral, the research will first have a macro view on the cathedral evolution, then focus on the interesting unique structure of flying buttress and rib vault.

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About cathedral

CATHEDRAL FEATURE Nave The majority of cathedrals and large churches of the Western European tradition have a high wide nave with a lower aisle separated by an arcade on either side. Occasionally the aisles are as high as the nave, forming a hall church. Many cathedrals have two aisles on either side. Notre Dame de Paris has two aisles and a row of chapels.

In the case of a centrally planned church, the major axis is that between the main door and the altar.

About cathedral

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CATHEDRAL FEATURE Facade Façade The façade or “west front” is the most ornate part of the exterior with the processional doors, often three in number, and often richly decorated with sculpture, marble or stone tracery. The façade often has a large window, sometimes a rose window or an impressive sculptural group as its central feature.

Transept The transept forms the arms of the church building. In English cathedrals of monastic foundation there are often two transepts. The intersection where the nave and transept meet is called the crossing and is often surmounted by a small spire called a flèche, a dome or, particularly in England, a large tower with or without a spire.

Vertical emphasis There is generally a prominent external feature that rises upwards. It may be a dome, a central tower, two western towers or towers at both ends as at Speyer Cathedral. The towers may be finished with pinnacles or spires or a small dome.

Three ancient cathedrals dominating townscapes which have retained medieval scale

Bamberg Cathedral, Germany, has a tower at each corner, topped by spires which rise from gables and are called “rhenish helms”.

Florence Cathedral, Italy, has a free-standing campanile and the largest dome built before the 19th century.

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Lincoln Cathedral, England, has two west towers and a huge crossing tower topped for 200 years by the world’s tallest spire.

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CATHEDRAL FEATURE East End

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CATHEDRAL FEATURE External decoration

East end Main article: Architectural development of the eastern end of cathedrals in England and France The east end is the part of the building which shows the greatest diversity of architectural form. At the eastern end, internally, lies the sanctuary where the altar of the cathedral is located.

Early Christian and Byzantine – A projecting semi-circular apse.

Romanesque – A rounded end. It may be a lower apse projecting from a higher square end, usual in Italy, Germany and Eastern Europe. In France and England the chancel terminated in a high eastern end of semi-circular form, surrounded by an ambulatory. While common in France, in England this form has only been retained without significant change at Norwich Cathedral.

The external decoration of a cathedral or large church building is often both architectural and pictorial. Decorative architectural devices include columns, pilasters, arcading, cornices, moldings, finials and tracery. The forms taken by these features is one of the clearest indications of the style and date of any particular building. Pictorial elements may include sculpture, painting and mosaic.

Sculpture is the predominant pictorial decorative element in most regions where buildings are of stone construction. In the great medieval churches of France, Spain, England and much of Germany, figurative sculpture is found adorning façades and portals.

Churches of brick, such as those of much of Italy, are often adorned with mosaics, inlays, inset marble friezes and free-standing statues at the roofline. Mosaics were a particular feature of Byzantine architecture and are the main form of adornment of many Orthodox churches, both externally and internally.

France, Spain, German and Eastern European Gothic – The eastern end is long and extends into a high vaulted apsidal end. The eastern aisles are continued around this apse, making a lower passage or ambulatory. There may be a group of projecting, radiating chapels called a chevet.

English Gothic – The eastern ends show enormous diversity. Canterbury Cathedral has an apsidal end with ambulatory and projecting chapels. No English Cathedral prior to the 19th century has a fully developed chevet. In the some, notably Lincoln Cathedral, the east end presents a square, cliff-like form while in most this severity is broken by a projecting Lady Chapel. There are also examples of the lower aisle continuing around the square east end.

three simple apses

has the cliff-like, buttressed east end usual in English Gothic churches

has an apse and wide ambulatory.

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The Gothic façade of Orvieto Cathedral is veneered with polychrome marble, and set, like a reliquary, with colorful mosaics and free-standing statues of marble and bronze.

The Russian Revival façade of the Church of the Savior on Blood is of red brick decorated with mosaics, glazed tiles and architectural ornament, particularly the ogee arches

The Baroque façade of the Cathedral of Cadiz contrasts dynamic architectural forms with precise Classical details and careful placement of free-standing sculpture.

The Gothic transept façade of Westminster Abbey (13th and 19th centuries) is decorated with layers of architectural details such as tracery, arcading and figurative carving.

has a high apse, ambulatory and chevet of radiating chapels with flying buttresses

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CATHEDRAL FEATURE Nave & Aisles

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CATHEDRAL FEATURE Ceiling, Crossing and Transept

The main body of the building, making the longer arm of the cross, where worshippers congregate, is called the nave. The term is from the Latin word for ship. A cathedral is symbolically a ship bearing the people of God through the storms of life. In addition, the high wooden roof of a large church is similarly constructed to the hull of a ship.

Crossing and transept

The nave is braced on either side by lower aisles, separated from the main space by a row of piers or columns. The aisles facilitate the movement of people, even when the nave is full of worshippers. They also strengthen the structure by buttressing the inner walls that carry the high roof, which in the case of many cathedrals and other large churches, is made of stone. Above the roof of the aisle are the clerestory windows which light the nave.

The crossing is the point in a large church at which the transept intersects the nave. This point is often marked externally by a tower or dome and internally by the piers and arches that are required to bear the weight of such a structure. The interior of the dome or tower may be one of the major architectural features of the interior of the church. In a centrally planned church such as Hagia Sophia, and typical of many Orthodox churches, the major interior space of the building is roofed by the dome.

In some large churches, particularly late Medieval churches, there are two aisles on either side of nave. Other churches have a single aisle and a row of chapels on either side. In some churches, particularly in Germany, the aisles are almost as high as the nave, forming a “hall church”. In this case, because there is no clerestory, the aisle windows are often very tall, to admit light to the nave.

The transept is symbolic of the arms of the Cross, but also provides space for congregation and for additional chapels.

Transept chapels are often dedicated to a particular saint, or to a particular aspect in the life and ministry of Christ, such as the Nativity or the Resurrection. In some English cathedrals there is often a second transept containing chapels, to facilitate the saying of the Divine Office by clergy each day.

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CATHEDRAL FEATURE Altar

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CATHEDRAL FEATURE Choir stalls and organ The term “choir” is used in three distinct ways in relation to cathedrals. As well as the architectural use, it pertains to the choir of “choristers”, often men and boys, that sing at the services. It is also the term used for that section of the church where the choir sits, and where choral services take place.

The altar in a church is a table on which is laid the Blessed Sacrament of bread and wine for consecration by a priest prior to use in the rite of Communion. The main altar in a church is located in a designated space called the “sanctuary” (“holy place”). The word has passed into modern English with an altered meaning because a criminal who could gain access to this area without capture was thereby given the sanctuary of the church[citation needed]. Many churches have an additional altar placed further forward in the church, as well as altars in chapels. The altar of a Catholic church may be made of marble. In most Protestant and Anglican churches altars are of wood, symbolic of the table of the Last Supper rather than of a sacrificial altar.

In a cathedral or large church, there may be fixed seating in this area, called “choir stalls” which also provided seating for the cathedral clergy and some congregation. The choir stalls are often richly carved and decorated. The bishop’s throne or cathedra is often located in this space. The choir may be separated from the nave by a highly decorated screen of wood or stone. The organ which provides music and accompanies the choir may be located on the screen, or may be in the gallery above the choir, or in a transept.

Some churches have an organ loft at the west end of the church.

The sanctuary is often separated from the body of the church by railings and screens, and, in the case of Orthodox and Byzantine Catholic churches, by an iconostasis which forms a complete visual as well as physical barrier. The sanctuary is usually the most ornately decorated part of a church, creating a visual focus towards the altar. This might be done in several ways. There might be a carved or painted altarpiece, a large carved screen called a reredos, or a structure called a ciborium which form a canopy over the altar. In English churches that have a square eastern end, a very large stained glass window often fills the wall behind the altar.

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CATHEDRAL FEATURE Font, Lectern, Pulpit

CATHEDRAL STYLE Early Christian

Font, lectern and pulpit Towards the western end of the nave stands the font, or water basin at which the rite of Baptism is performed. It is placed towards the door because the Baptism signifies entry into the community of the church. Standing to the front of the nave is a lectern from which the Holy Scripture is read. In many churches this takes the form of an eagle which supports the book on its outstretched wings and is the symbol of John the Evangelist.

The period of architecture termed Early or Paleo-Christian lasted from the first Christian Church buildings of the early 4th century until the development of a distinctly Byzantine style which emerged in the reign of Justinian I in the 6th century, rather than with the removal of the seat of the Roman Empire to Byzantium by Constantine in 330 CE. Some of the earliest Christian churches were constructed in Armenia where Christianity became the official religion in 301. The small aisless Basilica of the Holy Cross at Aparan is traditionally dated to the 4th century.

Large Early Christian churches generally took the form of aisled basilicas with an apse. Among the early larger churches in Rome the Basilica of Santa Maria Maggiore has retained much of its original internal arrangement, its vast basilical proportions, its simple apsidal end, its great colonnade supporting a straight cornice rather than arches and some very early mosaic decoration.

ROME

The third significant furnishing of the nave is the pulpit or rostrum from which the sermon is preached and the biblical readings are expounded. The pulpit might be made of marble or wood, and may be a simple structure or represent a highly elaborate carved sermon. It is often decorated with the winged figures of a man, a lion, a bull and an eagle, representing the Gospel writers, Matthew, Mark, Luke and John.

The Basilica of San Stefano Rotondo, Rome (circa 470)

Internally, Santa Sabina appears little changed since Early Christian times.

Ancient mosaics are incorporated into Baroque decorations.

INTERIOR

The Ancient Basilica of Santa Sabina, Rome ,has a typical basilical plan with a high semi-circular apse.

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The Mausoleum of Santa Costanza, Rome (circa 350)

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CATHEDRAL STYLE Byzantine

CATHEDRAL STYLE Romanesque

Ravenna, on the eastern coast of Italy, is home to several vast churches of basilica plan dating from the age of the Emperor Justinian (6th century CE). San Apollinare Nuovo is in plan similar to Santa Maria Maggiore, but the details of the carvings are no longer in the classical Roman style. The capitals are like fat lacy stone cushions. Many of the mosaics are intact.

After the decline of the Roman Empire, the building of large churches in Western Europe gradually gained momentum with the spread of organised monasticism under the rule of Saint Benedict and others. A huge monastery at Cluny, only a fraction of which still exists, was built using a simplified Roman style, stout columns, thick walls, small window openings and semi-circular arches. The style spread with monasticism throughout Europe. The technique of building high vaults in masonry was revived. A treatment of decoration evolved that had elements drawn from local Pre-Christian traditions and incorporated zig-zags, spirals and fierce animal heads. The typical wall decorations were painted fresco murals. Romanesque building techniques spread to England at about the time of the Norman conquest.

EXTERIOR

EXTERIOR INTERIOR

Representative of the period are Abbaye aux Hommes (the Abbey of the Men) in Caen, France; Worms Cathedral in Germany, the Cathedral of Pisa with its famous leaning campanile (bell tower), the Cathedral of Cefalù, Modena Cathedral and Parma Cathedral in Italy, and Durham Cathedral and Peterborough Cathedral in England.

INTERIOR

In the same town stands the uniquely structured, centrally planned, and domed church of San Vitale, of the same date. Its main internal space is 25 m across. The central dome is surrounded by eight apsidal semi-domes like the petals of a flower. There is a complex arrangement of curving arcades on several levels which gives a spatial effect only equalled by the Baroque church of Santa Maria della Salute built a thousand years later a few miles north in Venice. San Vitale was to be imitated in the 9th century in a simplified form by Charlemagne at Aachen, Germany.

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San Miniato al Monte, Florence, has basilical form, open timber roof and decoration of polychrome marble and mosaic.

Vézelay Abbey has clusters of vertical shafts rising to support transverse arches and a groin vault. The east end is Gothic.

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The nave of Peterborough Cathedral is in three stages supporting a rare wooden ceiling retaining its original decoration

The Church of St Philibert, Tournus, has tall circular piers and is roofed with transverse arches supporting a series of barrel vaults.

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CATHEDRAL STYLE Gothic

CATHEDRAL STYLE Renaissance

By the mid 12th century many large cathedrals and abbey churches had been constructed and the engineering skills required to build high arches, stone vaults, tall towers and the like, were well established. The style evolved to one that was less heavy, had larger windows, lighter-weight vaulting supported on stone ribs and above all, the pointed arch which is the defining characteristic of the style now known as Gothic. With thinner walls, larger windows and high pointed arched vaults, the distinctive flying buttresses developed as a means of support. The huge windows were ornamented with stone tracery and filled with stained glass illustrating stories from the Bible and the lives of the Saints.

In the early 15th century a competition was held in Florence for a plan to roof the central crossing of the huge, unfinished Gothic Cathedral. It was won by the artist Brunelleschi who, inspired by domes that he had seen on his travels, such as that of San Vitale in Ravenna and the enormous dome of the Roman period which roofed the Pantheon, designed a huge dome which is regarded as the first building of the Renaissance period. Its style, visually however, is ribbed and pointed and purely Gothic. It was Renaissance (a rebirth) in its audacity and the fact that it looked back to Roman structural techniques. Brunelleschi, and others like him, developed a passion for the highly refined style of Roman architecture, in which the forms and decorations followed rules of placement and proportion that had long been neglected. They sought to rediscover and apply these rules. It was a time of architectural theorising and experimentation. Brunelleschi built two large churches in Florence demonstrating how the new style could be applied, San Lorenzo’s and Santo Spirito. They are essays in the Classical, with rows of cylindrical columns, Corinthian capitals, entablatures, semi-circular arches and apsidal chapels.

INTERIOR

INTERIOR

EXTERIOR

EXTERIOR

Buildings representative of this period include Notre Dame, Paris; Chartres Cathedral, Reims Cathedral, Rouen Cathedral, Strasbourg Cathedral in France, Antwerp Cathedral in Belgium, Cologne Cathedral in Germany, St Stephen’s Cathedral Vienna in Austria, Florence Cathedral, Siena Cathedral, Milan Cathedral and San Lorenzo Maggiore, Naples in Italy, Burgos Cathedral, Toledo Cathedral and Leon Cathedral in Spain, Guarda Cathedral in Portugal, Salisbury Cathedral, Canterbury Cathedral and Lincoln Cathedral in England.

San Lorenzo, Florence

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Sant’Andrea, Mantua

St. Peter’s Basilica, Rome

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San Giorgio Maggiore, Venice

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CATHEDRAL STYLE Rococo

By the time that St Peter’s was completed, a style of architecture was developed by architects who knew all the rules that had been so carefully recovered, and chose to break them. The effect was a dynamic style of architecture in which the forms seem to take on life of their own, moving, swaying and undulating. The name Baroque means ‘mis-shapen pearl’.

The restored Frauenkirche, Dresden, Germany

Abbey of Saint Gall, St. Gallen, Switzerland

The Basilica of the Vierzehnheiligen, Germany

The Abbey Church at Birnau

St Anne’s Church, Kraków, Poland

The altar of the Seven Holy Helpers

Havana Cathedral, Cuba, (1748–77)

The Church of Saint Francis of Assisi 21 in Ouro Preto, Brazil (1766)

The Church of San Juan, Manila, Philippines (1774)

San Carlo alle Quattro Fontane, Rome (1634–47)

The chancel of the Basilica of Our Lady of Mercy, Barcelona.

Santa Maria della Salute, Venice (1631) 20

St Paul’s Cathedral, London

INTERNATIONAL

INTERIOR

INTERIOR

EXTERIOR

There are many large churches, abbeys, and basilicas built in this style, but few cathedrals in Western Europe, the most notable exception being St Paul’s Cathedral in London. St Paul’s is an unusual cathedral in that it was designed by a single individual and completed in a short time. The architect was Sir Christopher Wren and the building replaced the ancient cathedral which burnt down in the Great Fire of 1666. It is in the Baroque style, but it is a very controlled and English sort of Baroque in which Wren creates surprising and dramatic spatial effects, particularly in his use of the dome, which, like Brunelleschi’s dome in Florence, spans not only the nave but also the aisles, opening the whole centre of the church into a vast light space.

The Rococo style is a late evolution of Baroque architecture, first apparent in French domestic architecture and design. It is distinguished by the asymmetry found within its decoration, generally taking the form of ornate sculptured cartouches or borders. These decorations are loosely based on organic objects, particularly seashells and plant growth, but also on other natural forms that have an apparent “organised chaos” such as waves of clouds. The churches that are thus decorated may have strongly Baroque architectural form but a general lightness and delicacy of appearance, sometimes described as “playfulness”.

EXTERIOR

CATHEDRAL STYLE Baroque

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CATHEDRAL STYLE Modern

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CATHEDRAL FEATURE

In the 20th century, building in the Medieval style continued, but in a stripped-down, cleanly functional form, often in brick. A fine example is Guildford Cathedral in England. Another is Armidale Anglican Cathedral in Australia.

EXTERIOR

After World War II traditionalist ideas were abandoned for the rebuilding of the bombed cathedral in Coventry. The old cathedral was actually a large parish church that had been elevated to cathedral status. Its glorious spire fortunately escaped severe damage. The new Coventry Cathedral, of alternating slabs of masonry and stained glass attempts to capture symbolically the sense of an old cathedral church, without attempting to reproduce it. Liverpool Metropolitan Cathedral is the 20th century’s answer to the centrally planned church, a vast circular structure with the sanctuary at the centre.

Cathedral of Brasília, Brazil

The Basilica of Our Lady of Altagracia, Dominican Republic

Tokyo Cathedral, Japan

Interior of the Christ Cathedral in Garden Grove, California

Interior of the Cathedral of Brasília, Brazil

Interior of the Cathedral of Chillán, Chile.

Interior of the Cathedral of Christ the Light, Oakland, California

INTERIOR

Liverpool Metropolitan Cathedral, by Sir Frederick Gibberd, 1967

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NORTH AISLE

Church architecture

Reason of the orientation set

Within church architecture, orientation is an arrangement by which the point of main interest in the interior is towards the east (Latin: oriens). The east end is where the altar is placed, often within an apse. The façade and main entrance are accordingly at the west end.

The first Christians faced east when praying, for which various explanations have been offered. In a tradition well established by the time of Christ, Jews in the diaspora would pray facing Jerusalem, which in most of the Roman Empire would have been to the east.

Another explanation is that Christ’s Second Coming would be on the clouds coming from the East: “For as the lightning cometh out of the east, and shineth even unto the west; so shall also the coming of the Son of man be.” (Matthew 24:27).

The opposite arrangement, in which the church is entered from the east and the sanctuary is at the other end, is called occidentation.

Since the eighth century most churches are oriented. Terms such as “east end”, “west door”, “north aisle” are commonly used as if the church were oriented, treating the altar end as the liturgical east.

At first, the orientation of the building in which Christians met was unimportant, but after the legalization of the religion in the fourth century, customs developed in this regard. These differed in eastern and western Christianity.

The Apostolic Constitutions, a work of eastern Christianity written between 375 and 380 AD, gave it as a rule that churches should have the sanctuary (with apse and sacristies) at the east end, to enable Christians to pray eastward in church as in private or in small groups. In the middle of the sanctuary was the altar, behind which was the bishop’s throne, flanked by the seats of the presbyters, while the laity were on the opposite side.

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EAST END ALTAR

WEST DOOR FACADE MAIN ENTRANCE

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CATHEDRAL Window

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CATHEDRAL Window Evidence of stained-glass windows in churches and monasteries in Britain can be found as early as the 7th century. The earliest known reference dates from 675 AD when Benedict Biscop imported workmen from France to glaze the windows of the monastery of St Peter which he was building at Monkwearmouth.

In the Middle East, the glass industry of Syria continued during the Islamic period with major centres of manufacture at Raqqa, Aleppo and Damascus and the most important products being highly transparent colourless glass and gilded glass, rather than coloured glass.

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CATHEDRAL Ceiling

Romanesque

Byzantine

Early Christian

CATHEDRAL Column

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CATHEDRAL Ceiling

Baroque

Modern

Renaissance

Gothic

Rococo

CATHEDRAL Ceiling

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CATHEDRAL Door

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CATHEDRAL Lighting Gothic style: the pointed arch, the ribbed vault, and the flying buttress. The pointed arch, a style that diffused to the West from the Arabic world, permitted the use of slender columns and high, large open archways. These stone arches were essential in the resultant stone bays that provided the basic support system for a Gothic cathedral freeing the area between arches from supporting the building. For the church’s interior, these “curtain walls” added to the delicacy, openness, light and verticality of the space. The curtain walls on the build-

Gothic

ing’s exterior were filled with glass, often stained or colored glass, conveying some Biblical or other sacred tales.

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Flying buttress

Flying buttress

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02 / Flying buttress Research of flying buttress start from development of flying buttress structure, form, calculation, structure, data, and case studies which shows the function of flying buttress with rib vault.

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Flying buttress

Flying buttress

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2.1 Development of Flying Buttress 2.2 Advantage of buttresss

The Physics and History Behind Buttresses The use of buttresses dates back to as early 3,000 B.C. when they were used in ancient temples in Mesopotamia, but buttresses weren’t fully utilized until the Roman era. A buttress is an architectural structure built against a counter-fort or projecting wall, which serves to protect or reinforce the wall. Years ago, buttresses were fairly features of common castles, domes, churches, and arches.

Since these structures were built primarily out of heavy stones, the weight of the arched or domed ceiling would buckle the walls outward. So, engineers began to pile large stacks of stones in intervals to buttress, or support the walls from pushing outward. These piles of stones became distinct features of Romanesque style churches and buttresses became part of their basic design.

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Romanesque style churches tended to be large, castle-like structures with thick walls and small openings for windows and doors. These churches were usually quite small, rarely scaling more than 5 stories, so the buttress design was not too complex. Its main goal was to solidify the foundation of the structure. However, as Europe moved into the Dark Ages, buildings began getting larger and gothic cathedrals became very prevalent.

These churches were built much higher than their predecessors, often reaching up to 200 ft. Since the stones to build them were considerably larger and heavier, buttresses were employed even more.

In order to negate the outward thrust of the walls caused by the weight of the ceiling and force of the wind, buttresses were built to absorb this thrust and then transfer it to the foundation below.

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Flying buttress

2.3 Types of buttresss Buttresses appear in at least five distinct types. Clasping buttresses support two walls as they meet at a corner by making some length of both walls at the corner thicker than the remainder of the wall. Angle buttresses, much like clasping, support walls at the corner by building each wall out beyond the corner, so that the corner resembles a cross shape. A flying buttress are thought of as half, or semi-arches. The upper end of the flying buttress supports the wall, while the lower end is attached to the structures foundation. Flying buttresses have played a vital role in medieval and gothic cathedral design.

The flying buttress is perhaps the most noteworthy buttress type, is because it allowed Gothic Cathedrals to develop into massive, airy structures. The flying buttress’ design provides for an equal and opposite force to applied to the base of domes and arches spanning interior spaces supporting the weight of the structure. Setback buttresses support walls located near a corner, but are set back from it. Finally, Diagonal buttresses also support walls near corners, but are built diagonally out of the corner of the wall, at a 135° angle with the wall.

5 Types of buttress 1. Angle 2. Clasping 3. Flying 4. Set back 5. Diagonal

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Flying buttress

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About flying buttresss The flying buttress is often considered the quintessential element of Gothic architecture—the most visible sign of the startling developments in building technology that took place between 1130 and the end of the twelfth century in France. Generations of scholars have puzzled over the invention, deployment, and continuing modification of this remarkable engineering feature, which made possible the quest for extraordinary building height. Yet few historians or engineers have devoted attention to the precise structural function of the flying buttress.

While there is mention of the flying buttress by writers from the late Gothic period onwards, it is not until the mid-nineteenth century that its constructional, historical, and to a certain extent structural functions are addressed at length by French restoration architect and theorist Eugène-Emmanuel Viollet-le-Duc (1858). In the late-nineteenth century in Germany, Georg Ungewitter (1890) applied graphic static analysis techniques, which had been refined over the course of the nineteenth century in France, to the study of Gothic buildings, and devoted considerable attention to the flying buttress.

Other important contributions were made by Louis Barbier (1930), who used graphic analysis techniques to demonstrate that flying buttresses were structurally unnecessary in the churches of Saint-Germain-des-Prés in Paris and the Cathedral of Noyon, and by George Rosenberg (1936), who is perhaps the first to insist on the importance of the flying buttress for resisting wind, a point further developed by architect and historian John Fitchen (1955).

Jacques Heyman (1995) provided the clearest application of limit analysis to the structure of the flying buttress, and Robert Mark (1982), using photoelastic modeling, made important advances in our understanding of the role of the flying buttress in the context of Gothic building structure as a whole. Yet the great majority of studies has concerned the “mature” flying buttresses of the thirteenth century, while the critical experiments in early Gothic buttressing have been largely neglected. And though the art historical discussion of early flying buttresses1 has improved their classification and chronology, it has contributed little to our precise understanding of their structural role.

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Flying buttress

Flying buttress

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2.4 Case studies of buttresss Twenty French flying buttresses were analyzed to determine the range of their structural behavior.

These flyers, whose forms (the actual buttresses are in most cases either heavily restored or rebuilt) are assumed to date from the mid- to late- twelfth century, were chosen both for their importance in the discussion of early Gothic structure and also to represent the range of flyers found in typical twelfth- century churches. Flying buttress geometry was obtained photogrammetrically by the second author from the actual buildings or by tracing drawn sections in the cases where the flying buttress has either disappeared or been replaced. The structural analysis of these flying buttresses makes it possible to better understand their formal differences, and to address longstanding art-historical and structural assumptions.

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Flying buttress

Flying buttress

2.5 Calculation of Flying Buttress

Data of Flying Buttress

More realistic geometries are described by a variable thickness along the span and by a curved intrados.

Flying buttress length

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In such asymmetrical cases, the extrados hinge location moves away from the midpoint and depends on the flyer form and the distribution of its mass. As shown by figure 5, intrados arches described by circle segments with small radii, like those of the case study flying buttresses, exert lower minimum thrusts due

The structural function of the flying buttress is to transmit force from

to reduced weight; the flat parallelogram arch provides only an upper bound on the possible minimum

the upper walls and vaults of the main vessel of a church over the

thrust values for a given flying buttress geometry. In the following five sections, aspects of the structural

aisles to the culées and exterior pier buttresses. Some churches,

behavior of the flying buttress are studied in this new context.

such as Notre-Dame in Paris (nave section shown in figure 6), however, have more than one aisle over which the support must reach.

Art historians have in general tacitly assumed that a flying buttress long enough to make this leap—with perhaps a ten- to twelve-meter span—would have been technically impossible in the early- to mid-twelfth century, as noted by Murray (1998). It has been supposed, partly for this reason, that Notre-Dame was originally equipped with two short flying buttresses, each of which spanned a single aisle.7 Theresults of a parametric analysis in which the flying buttress lengthover-thickness ratio is varied against flyer inclination, presented in figure 6a, shed new light on this question.

Stated in the simplest terms, smaller flyers exert smaller forces than larger flyers—independent of flyer angle. This was noted by Heyman (1966), who showed furthermore that the passive thrust of a large flying buttress is much greater than that developed by a structural system composed of a series of two shorter ones linked together to span the same distance. Longer flyers require greater force to keep their stones together; stated in another way, they exert larger horizontal forces on their supporting elements. This might be of concern for long flying buttresses supported by tall culées, which must be sprung from a high enough point to clear the roofs of the aisles. Not only is a tall culée more susceptible to outward rotation, but long flying buttresses are more sensitive to such outward displacements of their supports (discussed in section 4.6 below). A longer flyer is thus more difficult to deploy because it depends to a greater extent on the immobility of its supports.

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2.5 Calculation of Flying Buttress

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Data of Flying Buttress

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2.6 Relationship of flying buttress and cathedral

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Case studies of Notre Dame de Paris

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Flying buttress Rib Vault and flying butress allow the wall to open a big window

Flying buttress with vault

Plan

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2.7 Zoning of flying buttress in case studies

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2.8 Conclusion of Flying Buttress 1. Thrust line analysis provides a simple but powerful tool for the minimum thrust calculation of any flyer shape and the correct determination of the extrados hinge location.

2. An upper bound for the minimum thrust of a flyer is given by the flat arch analytical solution as Hmin=WL/8t, where W is the weight of the flying buttress. This solution, however, cannot predict the location of the extrados hinge for non- parallelogram shapes.

3. For actual flyers with curved intrados, a good approximation of the minimum thrust is Hmin=WL/10t.

4. Short flyers can accommodate lower forces in minimum thrust conditions, but they are more vulnerable to sliding at the head region.

5. The inclination of a flyer has little effect on the minimum thrust value but affects the direction with which the thrust line enters the pier buttress. Steeper flyers contribute more to the stability of the buttress.

6. As the angle of the flyer increases, most of the vertical load is transferred to the culée support, relieving the clerestory wall.

Certain geometries may even result in a negative reaction at the head support.

7. All flyers studied transmit part of their weight to the clerestory wall under the conditions of minimum thrust.

8. Early Gothic flyers are relatively steep and cluster about a small range of low minimum horizontal thrusts.

9. Flyers that lean against the head wall and take no advantage of a wall buttress support are more likely to collapse due to sliding.

10. The structural behavior of the studied flyers agrees very well with the theoretical results of the parametric analyses.

11. The intrados of all cases studied can be described by a single circle, but not all intrados are quarter-circles. An intrados closer to a quarter circle can accommodate lower horizontal force values and therefore can withstand greater displacements.

12. Most early flyers studied have an intrados defined by a center located in the vicinity of the head wall. Construction consid-

Acknowledgements I would like to thank M. A. Nikolinakou , A. J. Tallon J. A. Ochsendorf , Philippe Block and Thierry Ciblac for their assistance in developing the interactive flying buttress computer models. Jacques Heyman and Stephen Murray read early versions of the paper and offered helpful comments. Financial support for this research was provided by the MIT France program, the Mellon Foundation, and the Georges Lurcy Educational Trust.

erations may justify this practice, since this places the center on or in front of the head wall, which may have been useful for constructing the timber falsework to support the flying buttress during construction.

13. Offset centers improve the structural efficacy of the flying buttress since they direct the flyer thrust to the pier buttress at a steeper angle, providing a stabilizing action to the supporting buttress. As the center of the intrados moves inside the building, less of the flyer vertical load is transferred to the clerestory wall. Flyers with offset intrados centers also tend to render the thrust more horizontal at the head, which reduces the threat of sliding failure.

14. Offset intrados centers do not necessarily imply steeper flyer angles; both geometrical parameters, however, have similar effects on the interaction of the flyer with its neighboring elements.

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03 / Rib Vault Research of flying buttress start from Construction, Overview of different vault, history and vault for different period, and zoom into geographical analysis, plan and vault in scale, case studies, and pattern on plan.

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3.1 Background and history

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Geograhical Analysis

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Glossary of keywords

A total of 59 vaults in Western Europe have been studied (Maira, 2016a), which are: Notre Dame de Paris, Bourges, Laon, Sens, and Lyon Cathedrals and the Churches of Notre Dame de Dijon, Sainte Madeleine in Troyes and Saint Julien le Pauvre (France); Canterbury, Rochester, and Lincoln Cathedrals (England); Limburg an der Lahn and Bremen Cathedrals and Maulbronn Monastery (Germany); Lausanne Cathedral (Switzerland); Piacenza Cathedral, Basilica of San Antonino in Piacenza, and Certosa di Pavia Monastery (Italy). Ávila, Cuenca and Sigüenza Cathedrals, the Monasteries of Santa María de Huerta in Soria, Las Huelgas Reales in Burgos, Roncesvalles, and Santa María de Piedra in Zaragoza, the Churches of San Saturnino in Pamplona, Santa Magdalena in the Ancient Priory and Hospital of Valdefuentes in Burgos, Santa María la Real of Gamonal in Burgos, La Asunción de Nuestra Señora of Salmerón in Guadalajara and NuestraSeñora de la Asunción of Utiel in Valencia, and the Hermitage of San Bartolomé in Navarre (Spain).

France Germany Italy

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Development about rib vaule 1144

1132

1132

Basilica of Saint-Denis (completed 1144)

Vezelay Abbey 1132

Vézelay Abbey 1132

Disambulatory of the Basilica of Saint-Denis (completed 1144)

Vezelay Abbey illustrates the transition from Romanesque architecture to Gothic architecture; the nave is covered with romanesque groin vaults, while the choir (background) has the new Gothic rib vaults, inaugurated in 1132

Six-part rib vaults in the narthex of Vézelay Abbey (1132)

1190

Notre -Dame de Paris (1102-1190)

1386

1836

Old Louisiana State Capitol

Late Gothic Vault of the Monastery of Batalha, Portugal (1386)

Architects: James H. Dakin, William Alfred Freret

Six-part rib vaults of ceiling of nave of Notre-Dame de Paris (1102-1190)

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The Sexpartite Vault

Islamic and Moorish architecture

In the 12th century, the momentum of the development of the rib vault shifted to France, particularly to Paris and the Ile-de-France. The sexpartite vault, with six compartments divided by thin ribs and a crossing arch, appeared, almost simultaneously in England and France.

[13] Early examples of sexpartite rib vaults are found at the Abbaye-aux-Hommes (begun 1066) and Abbaye-aux-Dames at Caen. Most notably, it then appeared in Noyon Cathedral (begun 1131); the square Gothic porch of the Romanesque church of Vézelay Abbey in France (1132); Sens Cathedral (begun 1135); The Choir of the Basilica of Saint-Denis (begun 1140); Notre Dame de Paris (begun 1160); Bourges Cathedral, and Laon Cathedral, It soon appeared in England, where it was used by William of Sens at Canterbury Cathedral, and in St Faith’s Chapel in Westminster Abbey (1180)[14][15][16]

An early form of rib vault was used in Moorish architecture in the Mosque-Cathedral of Cordoba, begun in the 8th century, to decorate the two smaller domes of the Mosque. Unlike the later Gothic rib vaults, the ribs were thick, and did not extend outside the edges of the vault. The ribs intersect one another off-center, forming an eight-pointed star in the center which is topped by a pendentive dome.[5] The pendentive dome was adapted from Byzantine architecture; The dome itself was supported not by the ribs but by the pendentives.

The massive dome of Hagia Sophia (6th century) was a prominent example of a pendentive dome.

In the early sexpartite vault, like those Sens Cathedral and Notre-Dame Cathedral, the thrust of the weight was transferred via the ribs to alternating columns and pillars. A new innovation appeared during the High Gothic: the four-part rib vault, which was used in Chartres Cathedral, Amiens Cathedral and Reims Cathedral. The ribs of this vault distributed the weight more equally to the four supporting pillars below, and established a closer connection between the nave and the lower portions of the church walls, and between the arcades below and the windows above. This allowed for greater height and thinner walls, and contributed to the strong impression of verticality given by the newer Cathedrals.[17]

The ribbed vaults of the mosque-cathedral of Córdoba served as models for later mosque buildings in the Islamic West of al-Andaluz and the Maghreb. At around 1000 AD, the Mezquita de Bab al Mardum (today: Mosque of Cristo de la Luz) in Toledo was constructed with a similar, eight-ribbed dome. Similar domes are also seen in the mosque building of the Aljafería of Zaragoza. The architectural form of the ribbed dome was further developed in the Maghreb: The central dome of the Great Mosque of Tlemcen, a masterpiece of the Almoravids built in 1082, has twelve slender ribs, the shell between the ribs is filled with filigree stucco work.

Ribs decorating the dome of the Aljafería of Zaragoza, Spain (11th century)

Columns and arches supporting the dome of the Mosque of Cristo de la Luz ((11th century)

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Ribs of the left dome of the Mosque-Cathedral of Cordoba (8th century)

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From Norman and Romanesque to the Gothic A new variation of rib vault began to appear in England and in Normandy in the late 11th century. Romanesque churches traditionally covered the nave with a barrel vault, with round arches, or a groin vault, formed when two barrel vaults met at right angles. The newer churches and cathedrals used a Gothic rib vault, with a network of thin ribs that divided the vault into compartments. The ribs reached downward and outward to supporting columns and pillars, and later, outwards to buttress outside the walls. These vaults had an additional feature; they met in a pointed, or broken arch, rather than a rounded arch, which gave them greater strength and spread the thrust both outwards and downwards, like an open ladder.[9] Since these vaults were essentially supported by the columns and buttresses, not the walls, the walls themselves could be higher and thinner, and could be filled with stained glass. The combination of the three elements; the broken, or pointed arch, which carried the directed the thrust outwards as well as downwards; the ribs, which carried the thrust downward to the pillars and outward to the buttresses; and the flying buttress which counterbalanced the thrust against the walls, were together the three crucial elements of Gothic architecture. The earliest of the Gothic rib vaults are generally considered to be in the nave of Durham Cathedral, built between 1093 and 1104.]

The domed ceiling of the Romanesque Round Church, Cambridge in England, begun in 1130, has a similar system of ribs. The Norman-Romanesque Cefalu Cathedral in Sicily, begun in 1131, built after Sicily was conquered by the Normans, featured a similar kind rib vault, as did the Romanesque Lessay Abbey (11th century), in Normandy (destroyed in World War II but rebuilt.[

Nave of Durham Cathedral (1093-1135)

Norman-Romanesque ribbed vault in Cefalu Cathedral in Sicily. (12th century)

Vaults of the choir of the Romanesque Lessay Abbey, Normandy (11th century)

Vault of the Tribune - of Serrab one Priory inv v, Spain (12th century)

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The Quadripartite Vault The use of four-part vaults allowed cathedrals to be built much taller. The 11th century Durham Cathedral (1093–1135), with the earlier six-part rib vaults, is 73 feet (22 meters) high. The 12th-century nave of Notre Dame de Paris, also with six-part rib vaults, is 115 feet, or 35 meters high. The later Amiens Cathedral (built 1220–1266), with the new four-part rib vaults, has a nave that is 138.8 feet (42.30 meters) high. The tallest nave of all the Gothic Cathedrals is Beauvais Cathedral, though only a single bay was completed. It is 47.5 m (156 ft) in height, taller than the nave of St. Peter’s Basilica in Rome.

Romanesque ribbed groin vault of the Basilica of Sant'Ambrogio, Milan (end of 11th century)

The choir of Beauvais Cathedral (1225-1272) the tallest of Gothic church interiors.

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Four-part rib vaults at Amiens Cathedral (1220-1270) allowed greater height and larger windows

Hall of the guards of the Conciergerie, part of the earlier royal palace, in Paris (13th century)

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Nave of Cologne Cathedral (1248–1322)

Stronger four-part rib vaults at Rouen Cathedral (13th c.)

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Decorated Gothic, Perpendicular Gothic and the fan vault In the last period of Gothic architecture, beginning in about 1350, particularly in England, the rib vaults lost their simple functional appearance and were loaded with decorative elements, to match the rest of the extremely ornate interiors. This style was called Perpendicular Gothic. The vaults retained their function, but they were covered with stonework resembling ivy, vegetation, arrangements of fans, or starlike patterns.

Another type of rib vault particular to England is the Lierne. It features a tertiary rib, called a lierne, connecting one rib to another. The resulting construction is called a lierne vault or stellar vault (named after the star shape generated by connecting liernes). This type of rib vault appeared during the 14th century in the Decorated period. Examples are Gloucester Cathedral in England, and the Church of Saint-Pierre in Caen in France. The fan vault was a type of rib vault particular to England. The ribs are all of the same curve and spaced equidistantly, in a manner resembling a fan. The ceiling of King’s College Chapel, Cambridge, has the world’s largest fan-vaulted ceiling.

Fan vault in the chapel of King's College, Cambridge (1446–1554)

Vaulting of Canterbury Cathedral (late 14th century)

Church of Saint-Pierre, Caen (15th century)

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3.2 User experience of various type of vault

Examples

Fan vault in Bath Abbey (mostly 19th century

The Lady Chapel, Ely Cathedral (begun 1321)

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The Quadripartite Vault examples

Fan vault Examples

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Modern example

Famous Examples

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3.3 Plan design of Rib Vault

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Cathedral of Condom

Here are the plan of applying decorative vault inside cathedral.

Cathedral of Condom

Star Vault St Jean au Marché church

Star Vault Albrechtsburg Castle of meissen

Decorated Vault St. Anne’s Church, Annaberg-BuchholzV V

Star Vault St. Mary’s Church in Gdansk

Decorated Vault Willibrordi-Dom

Vault Church of the Assumption of the Virgin

Reticulate Vault Church of St. George

Star Vault Our Lady of Consolation Collegiate

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Star Vault St Jean au Marché church

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Decorated Vault St. Anne’s Church, Annaberg-Buchholz

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Star Vault Albrechtsburg Castle of meissen

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Plan and pattern of valut

Star Vault St. Mary’s Church in Gdansk

As we can see from above research. The decorative vault usually apply many pattern and froms in their plans. I have organised some pattern that we always see as follow.

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Plan and pattern of valut

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DESIGNING YANHUITLÁN’S VAULT ON THE HORIZONTAL PROJECTION

http://www.mixtec-stonecutting.com/yanhuitlan

THE CHURCH OF YANHUITLAN The plan of Santo Domingo Yanhuitlán’s church shows four squares of 14m each and a semicircular apse. This single-nave church draws a rectangular shape formed by square modules repeated four times. Each of the squares hosts one vault. The interior walls of this church are completely flat, projecting the buttresses towards the outside. Since this church was built under the single-nave scheme, the complexity of construction resided in the vaulting systems that would make up the roof.

A peculiar feature of the square vaults of Yanhuitlán is the presence of two tiercerons in each web panel. The origins of this layout are found in the late-Gothic vaults of southern Europe. Looking at the horizontal projection (plan) each one is placed on a square. Later one can notice that the set of tiercerons running near the diagonal arches, called in this study “high tiercerons”, are drawn with an equilateral triangle whose sides are equal to the initial square’s sides. Once this equilateral triangle is drawn one can locate its vertex intersecting with the ridge rib (tip of the triangle) defining the position of the boss connecting the low tiercerons on each web panel. These vaults do not present warped ribs; instead, the high tiercerons continue until they intersect the diagonals, forming a ring with straight sections around the keystone. The double tierceron is not common in squared-plan vaults. Double tiercerons are typically used in rectangular-plan vaults as the second tierceron is used to divide the longer web panel in order to add structural rigidity. v

In the monastic order of the Dominicans the churches were a very important part of their ambitious projects, especially in the Mixteca where the church is much more elaborate than the rest of the monastic complex buildings. We should remember that ribbed vaults were used only when ostentatious construction was desired in colonial Mexico.

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STEREOTOMY

DESIGNING YANHUITLÁN’S VAULT ON THE VERTICAL PROJECTION

A Renaissance vault differs from a Gothic vault because the geometry of the first followed preconceived forms while the geometry of the second is the result of the construction process.

The Renaissance architect already knew in advance how the dome was going to be and this preconceived shape aimed to be spherical. The sphere in this period of time was a representation of the universe and all creation. The Yanhuitlán vault is one spherical. They can be linked to the Toledo school because their ribs and straight bonds find a precedent in the vaults of St. Juan de los Reyes in Toledo, built in the late fifteenth century. In this

Once the lines were delineated on the horizontal projection, the common task of the designer was to draw each one of the arches of the vault on the vertical projection or section.

Curiously, one can notice that the diagonals and tiercerons arches of Yanhuitlán’s vaults respond to the geometry of a sphere. The overall shape of this vault was predetermined and the arches respond to that geometry. This is a very peculiar vault solution, originated in Renaissance vault design practices. In addition to the spherical nature of this vault, this study has found that transverse and former arches reveal a particular solution. The design of these transverse and former arches followed a method known in Spain as “a la vuelta de la diagonal”, which was commonly used in Gothic vaults and also applied in some of the late-Gothic Spanish solutions.

This form of defining arches is performed by transferring an arc already used in the vault to another arch of shorter span.

The method is commonly visualized as rotating an arch to a different plane where the smaller arch develops. In these vaults the lower tiercerons are rotated to the plane where the transversal/former arches are situated. Arches are pointed as a result of this procedure, similar to those pointed arches found in Gothic European cathedrals.

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Spanish building one also notices that the vaults have double tierceron and straight bonds on the higher tierceron. Another precedent may be the vault in the church of the Dominican convent of Santa Cruz de Segovia, which was also designed in the late fifteenth century on square plan, double tercelete and straight bonds. http://www.mixtec-stonecutting.com/yanhuitlan

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Yanhuitlán bosses vary depending on the intersection. The intersection between the low tierceron and the ridge rib and the intersection between the diagonal and high tierceron extension are by means of a boss whose axis is directed towards the center of the dome. The rest of the bosses have a vertical axis. The layout of Yanhuitlán’s voussoirs within the web panels follows the “French style”. The voussoirs’ stones are arranged similarly to a groin vault which is based on two equal cylinders intersecting perpendicularly with each other. http://www.mixtec-stonecutting.com/yanhuitlan

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3.5 Scale and dimension of Vault Group 1

Group 3

Semicircular diagonal ribs with their centers of curvature on the impost line.

The diagonal ribs are pointed arches with their centers of curvature on the impost line.

Transverse ribs are pointed and the central rib is semicircular and stilted approximately 2.5 m above the impost line.

The transverse ribs and the central rib are pointed with their centers on the impost or stilted slightly above it.

The wall ribs are either pointed or semicircular, and are noticeably stilted above the impost line.

The wall ribs are either semicircular or pointed, sometimes they are lancet arches and at other times they are very stilted above the impost.

These vaults cover square or slightly rectangular sections and are always partially standardized, the standard elements being their transverse and diagonal ribs.

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English

Spanish

Germany + Switzerland+Italy

All their ribs are standardized based on the curvature of the diagonal ribs, with the exception of the wall ribs which only very occa- sionally have the same curvature, applying the French system of standardization.

Group 2

Group 4

Semi- circular diagonal ribs with their centers of cur- vature on the impost line.

Other rib vault examples.

The transverse and cross ribs are pointed, with their centers of cur- vature on, or slightly stilted above, the impost line.

The wall ribs can be either semicircular or pointed and are always stilted above the impost.

These vaults usually cover square or slightly rectangular spaces, although there are some rare examples covering markedly rectangular spaces.

All the ribs are the same and are based on the curvature of the diagonals with the exception of the wall ribs.

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Conclusion Ribbed Vault. The ribbed vault was used by Gothic architects to give the buildings flexibility in roof and wall engineering. These vaults were easier to construct when comparing them to the barrel vault, and they were also stronger and more flexible.

I will use the reseaarch to further develope my next project.

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Idea 1

Idea 2

Multi-culture hub for young generation

Travel addicted - Travel as a believe to design an airport

In these days and age, young generation especially 90s in Hong Kong is facing a living problem that they can not affort buying an apartment. In this case, their choice is limited to small apartment or share house. Their living qualitiy is declining due to the high property price. Thus, the project is aim to reverse the thinking of small space equal to low living standard.

These years, the transportation become very convenience. People loves to travel around the world as a citizen. This also become a trend and most popular things to do in holiday.

Let us assume if travel become a kind of believe that everyone would love to travel and airport become their holy place, because they must go to airport if they need a flight.

Even though the young generation cannot afford to have a regular apartment, it is not necessary to decrease the living quality. To tackle the situation, this project suggest to have a multi-culture hub for young generation to move in. The hub is suggested to provide public space, leisure space, living space and retails etc.

As airport become a holy place for them and I will interprete the space and structural as a cathedral and intergrated with more elements from my previous research. It will become a new form of long space with great lighting quality that extended by flying buttress as a specific language.

Keyword: #multi-culture #hub #lighting #small_space #reverse #weightless

Keyword: #Travel #holyplace #cathedral #flying_buttress #lighting #globalization

Methodology: Section drawing, space planing, axonometric, modeling

Methodology: Section drawing, space planing, axonometric, college, modeling

Reference

Reference

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