UNL ARCH231: Quiz 4

Gauged Arches:

- Precast Concrete Block Arches - Monolithic Concrete arches

Brick Arches:

- Rough Brick Arches - Axed Brick Arches - Gauged Brick Arches

Stone Arches:

- Rubble Arches - Ashlar Arches

4 reasons an arch could fail:

- crushing of the masonry. - sliding of voussoirs. - rotation of some joints about an edge. - uneven settlement of an abutment or pier.

Basilica Palladiana Vicenza, Italy (1614)

4 part groin vault. Palladio did the drawings, but the building was not completed until thirty years after his death.

Rampant Vault

A continuous barrel vault where one side is higher than the other. Usually used to support or form the ceiling of a stairway.

Cloister Vault

A domed shape and has a base that is square or shaped like a polygon. It has curved sections that rise from the square or polygon to a centered point.

A shell is a...

A shell is a thin, curved surface structure that transfers loads to supports by tension, compression, and shear only. Shells are distinguished from traditional vaults by their ability to resist tension.

Rib Vault

A vault reinforced by masonry ribs. When this type of vault has two masonry ribs dividing it into four sections, it is called a quadripartite rib vault. A vault divided by three masonry ribs that make six sections is called a sexpartite rib vault.

Hagia Sophia, Istanbul, Turkey

Alternative methods exist to balance the outward thrust at the base of a dome besides anchoring it by means of a tension ring; the large, relatively flat dome of Hagia Sophia, whose base is lifted high up into the air in order to make possible the incredible interior space, can be seen to be anchored by thick buttressing walls all around

Bus Station, Carceres, Spain by Justo Garcia Rubio Arquitecto, 2003

An architecture of two concrete shells appear to be formed from a single sheet of bent concrete. Where the shell geometry prevents forces being transferred into the foundations in pure compression, such as at the right-hand side of the larger shell, the shell thickness is greatly increased and the foundations strengthened.

Theatre of Marcellus Rome (13 BC)

Annular Vault

anticlastic surfaces

Anticlastic surfaces are doubly curved and have opposite curvature in each direction. Saddle shapes (including conoids, hyperbolic paraboloids, and hyperboloids) are anticlastic.

Segmental Arch

Arch that is less than a semi-circle.

Pantheon Rome, Italy

At the base of the dome, the outward thrusts resulting from the compression in all of the arched ribs needs to be resolved. To do so, a base ring can be provided that will be subject to a set of outward radial horizontal forces that put it into a state of tension. Such a tension ring can be thought of as the three-dimensional equivalent of the straight tie rod used to anchor the support points of a two-dimensional arch. Recently, steel reinforcing bars and especially post-tensioned pre-stressing wire strands encased in a concrete ring.

Kimmel Center for the Performing Arts Philadelphia, PA (2001)

Barrel Vault, Rafael Vinoly Architects Glazed vaulted form envelopes and unifies multiple smaller volumes and program elements; also is distinctive profile on skyline. Folding of surface is used to give stability to thin structural form.

Vault House

Barrel Vault, designed by Johnston Marklee Architects Johnston Marklee takes a curvaceous approach to reinventing the beach house paradigm. The vaults were formed out of wood framing and dropped from the floor plate.

Berlin Central Rail Station Berlin, Germany (2006)

Barrel Vault, von Gerkan, Marg und Partner Thin, criss-crossing, diagonal rod system stiffens gridded shell structure between intermittent arch ribs, allowing light to flood the station interior.

Types of developable surfaces

Barrel shapes (cones and cylinders). Continuous, Discontinuous, Transverse Folding, Free Form.

Taq-I Kisra Ctesiphon, Iraq (600-300 BC)

Built in 400 A.D. it is still the largest brick built arch in the world.

Factory of Vapor Aymeric, Catalonia

Catalan Vault

Church of Christ Obrero Atlanta, Uruguay (1952)

Catalan Vault. Eladio Dieste created a masonry ceramic through the use of thin layers of brick and fast drying mortar.

St. Paul's Cathedral, London, England

Christopher Wren. The large lantern load at the top is carried on an elongated masonry dome of conical shape (the three-dimensional equivalent of the funicular, compression-only profile of a top-loaded two-dimensional arch).

Maple Leaf Gardens Toronto (1946)

Cloister Vault

Air-Formed Concrete House

Completed in 1954 by Air-form, the Bubble Houses were designed by Eliot Noyes using the air-form monolithic dome system developed by Wallace Neff, which consists of reinforced concrete cast in place over an inflated balloon to establish the house's shape. The "balloon" form was inflated, covered with wire-mesh reinforcement, and sprayed with concrete. "both hurricane-proof and bugproof".

Anticlastic surface: Conoid

Conoids are generated by sweeping one end of a straight line along a curved path (usually a circular arc or a parabola) and the other end along a straight line (or a more shallow curve).

Granaries of Ramesseum Luxor, Egypt (approx. 1400 BC)

Constructed of mud bricks, they are the oldest examples still standing in Egypt. Their significance is that temple estates were economic powerhouses in ancient Egypt, responsible for feeding large numbers of workers and dependents.

Groin Vault

Created by two barrel vaults intersecting at right angles. The arches of groin vaults are round or pointed. Also known as a cross vault.

developable surfaces

Developable surfaces are singly curved; they are straight in one direction, curved in the other, and can be formed by bending a flat sheet. Cones and cylinders (or barrels).

MIT's Kresge Auditorium

Example of a synclastic surface. The explicitly radial-rib variety or of the masonry domes that effectively become ribbed because of the vertical cracking of their constituent material as the base splays apart, typically lie somewhere in the range of 1:50 to 1:100. the concrete of which it is made is reinforced with steel bars, giving the shell surface at once simultaneous compression and tension capability throughout and thereby preventing the splitting of the surface into the discrete arch-like segments.

King's College Chapel, Cambridge (1446)

Fan Vault. Late Gothic architecture. It was started in 1446 by Henry VI and took over a century to build. It has the largest fan vault in the world and some of the finest medieval stained glass.

free-form surfaces

Free-form surfaces are those which are not mathematically derived.

Roskilde Dome, Roskilde, Denmark Architect Kristoffer Tejlgaard

Geodesic dome. This structure allows for great strength and stability, construction of large-sized spaces using a minimum of building materials as well as reduced energy consumption used for heating because of the minimal surface and aerodynamic form of the dome.

Canary Wharf Underground Station London, England (1999)

Glass panels between arched ribs of entrance canopy at once draws daylight down into Underground station and people up to the ground surface.

Sea Folk Museum Toba, Japan (1992)

Glue-laminated arches mimic construction of ribs of the inverted hull of a wooden ship; stabilizing and partially enclosing solid surface made of wood planking is like that of its hull.

Fan Vault

Half cones that are fan-shaped. The cones meet in the center of the vault. Considered to be part of the rib vault family.

Anticlastic surface: Hyperbolic paraboloid

Hyperbolic paraboloids (hypars) are generated by sweeping a convex parabola along a concave parabola of the same curvature. The same surface can be generated by sweeping a straight line over a straight path at one end and another straight path (skewed relative to the first). Stresses in hypars relate to the direction of curvature. Compression stresses follow the convex curvature (arch action), while tension stresses follow the concave curvature (suspension action).

St. Peter's Basilica, Rome, Italy

Michelangelo Tension ring consists of iron chains. Windows around the base of the dome not only phenomenally lift it up into the air, but also may be a reflection of observations of radial cracking around base of such masonry structures. Used as a model for Saint Paul's in London (1675), Les Invalides in Paris (1680-1691) and the Capitol building in Washington (1794-1817).

Annunciation Greek Orthodox Church

Milwaukee; Frank Lloyd Wright The thin shell, reinforced concrete dome is quite shallow. The edge is reinforced to act as a tension ring to resist the considerable outward thrust. The spheres are solid glass, cast into the concrete drum wall; because the spheres nearly touch each other, they contribute substantially to the support of the weight of the drum. The drum wall is supported on the perimeter of a second, inverted dome which also forms the floor of the balcony. This is reinforced at the perimeter and behaves as a tension ring. This inverted dome rests on the four concave-curved bearing walls and pilasters which enclose the ground-level sanctuary and the stairways to the balcony; these extend down to the foundations.

Reichstag, Berlin, Germany

Norman Foster + Partners. The large glass dome at the very top of the Reichstag has a 360-degree view of the surrounding Berlin cityscape. Bending capacity comes from ribs made of triangular hollow steel sections. Built as symbol for the reunification of Germany, and open parliamentary government.

Palazzetto Dello Sport, Rome, Italy

Pier Luigi Nervi as structural engineer, Annibale Vitellozzi as architect Built for the 1960 Olympics, the palazzetto is a modest sports stadium in an innovative concrete dome. Designed by Pier Luigi Nervi it hosted boxing among other sports during the Olympic Games. The innovative dome is made of ribbed reinforced concrete. The lower half of the dome has continuous ribbon of window the whole way around the circular stadium, beneath the elegantly ribbed, white-painted concrete ceiling. Angled props around the perimeter are yet another way to resist a dome's outward thrusts, in a manner reminiscent of Gothic flying buttresses.

Catalan Vault

Plain bricks that form a low arch. Also known as the Catalan turn, timbrel vault. Widely used in Catalonia from which it derives its name. Also known as "masonry vault", "tiled vault", "laminated vault", "flat vault" and "layered vault."

Winter Garden Sheffield, England (2002)

Pringle Richards Sharratt Architects Vault's glulam arched ribs stabilized by diagonal cross-bracing maximizing light penetration for greenhouse plant growth.

Auroville Earth Institute and Woodchester Mansion, Gloucestershire

Rampant Vault

Cathedral St Julien du Mans Le Mans, France (1254)

Rib Vault. The ten bays of the aisled nave are gathered into five double bays with an alternating system of supports and square domed-up quadripartite vaults over the main vessel (the aisles are groin vaulted).

United States Capitol Building, Washington DC

Rib depth is provided by means of cast iron trusswork. Single elongated, curving, cast iron structural ribs - 36 around the perimeter.

Montreal Biosphere Geodesic Dome 1967, Buckminster Fuller

Richard Buckminster Fuller developed the geodesic dome—the only large dome that can be set directly on the ground as a complete structure and the only practical kind of building that has no limiting dimensions (i.e., beyond which the structural strength must be insufficient).

Abbaye aux Dames Caen, France (1050 AD)

Six-Part Groin Vault

Gateway Arch St Louis, Missouri

Stainless steel, in the form of an inverted catenary, which is a very stable structure that is often used in bridges, domes, and arches. A catenary is the shape that a chain or necklace forms when held by the two ends. The Dutch mathematician Christiaan Huygens named this curve from the Latin word catenarius, which means "related to a chain."

Dome stress directions

Stresses in a domed shell can be understood as acting in two directions; along arch lines and along hoop lines. Under uniform loading, a dome is in compression along arch lines everywhere.

synclastic surfaces

Synclastic surfaces are doubly-curved and have similar curvature in each direction.

Duomo, Florence, Italy

Tension ring consists of sawn timber members linked by metal dowels.

Cloisters of Gloucester Cathedral, England (1360)

The 14th century cloisters are a major highlight of Gloucester Cathedral. The fan-vaulted roof is the finest in Europe, and the cloisters enclose a peaceful garden. This was used in the filming of Harry Potter and the Sorcerer's Stone.

extrados

The exterior curve, surface, or boundary of the visible face of an arch.

haunch

The haunch, where the thrust of the arch is usually greatest, is at a point located about one-third the distance between the springer and keystone.

rise

The height from the springing line to under side of the arch at the keystone.

crown

The highest point of the arch.

span

The horizontal distance from springing to springing of the arch.

intrados

The inner curve or surface of an arch forming the concave underside.

What is an arches weakness?

The keystone, and the other voussoirs at the crown, press out against the voussoirs at the haunches, which may buckle and allow the crown to fall if they are not properly buttressed. The lateral thrust at the haunches can be counteracted by the thrust of arches placed to either side, as in an arcade, but, unless the arcade is circular, the lateral thrust of the arches at the end must finally be counteracted by the sheer mass of an abutment.

the dome's three-dimensional equivalent of an arch:

The ocular ring can be thought of as the dome's three-dimensional equivalent of an arch's famous keystone - without it, the rest of the structure simply does not function as intended.

SHELL.TER, Cerveira, Portugal by LIKEarchitects

The pergola tunnel resembles the most advanced parametric design.

depth of arch

The perpendicular distance between the intrados of arch to the extrados of arch.

Padre Pio Church San Giovanni Rotondo, Italy (2004)

The plan arrangement follows that of a spiral, consisting of an overlapping array of stone arches radiating out from the central altar. The shapes of the arches to follow those of tilted parabolas.

Barrel Vault

The simplest of the vaults and is the base design for many vaults that have a more intricate design. It consists of an ongoing series of semicircular arches. One is directly behind another, causing it to look like a half of a barrel.

skewback

The upper surface of an abutment or pier from which an arch springs; its face is on a line radiating from the center of the arch.

Segovia Aqueduct

The visible part of the great structure consists of 800 meters of granite blocks, 166 arches, 120 pillars. And not a bit of mortar or cement was used to hold it all together. Instead, the stones were precisely cut to transmit and bear the load in a perfect equilibrium.

T/F: Deeper spherical domes are in hoop compression above 45 degrees and in hoop tension below.

True

T/F: Shallow domes are in hoop compression only.

True

T/F: Shell domes resist tension.

True

Annular Vault

Uses the barrel vault as its base. Instead of a straight line, the barrel vault has a ring shape and springs out from two walls that are concentric.

Catalan vault construction process:

Wood being constructed as a structure before bricks are laid. Bricks are arranged using mortar. Bricks with mortar are arranged from the edge of the vault until it reaches the thrust of the vault. Mortar is laid over the surface in order to withstand more pressure and create more stability.

an arch is...

a pure compression form that can span a large area by creating compressive stresses and eliminating tensile stresses.

abutment

a structure built to support the lateral pressure of an arch or span.

springing line

a theoretical horizontal line from which the curvature of an arch begins.

spandrel

a triangular space enclosed by the curves of arches

pier

a vertical support that holds up an arch or a vault.

Upward buckling in shell domes is located...

along the hoop lines below about 45 degrees above the horizontal.

Relieving Arch

an arch occurring above another or a lintel used to distribute loads laterally away from an opening.

Types of Shells

synclastic surfaces, developable surfaces, anticlastic surfaces, free-form surfaces.

Kimball Museum by Louis I. Kahn, Fort Worth, Texas

barrel shell. The roof structure consists of 14 barrel shells. The shells are cycloids in section. (similar in shape to a semi-ellipse, a cycloid is a curve generated by a point on a circle rolling over a straight line). Compressive forces between each side of the shell are transferred across the slit by 11 concrete spacers which serve to hold the two sides apart.

A dome is similar to a rotated arch except that...

circumferential forces are developed, which are compressive near the crown and tensile in the lower portion.

Meridional forces are always...

compressive under full vertical loading.

Hoop forces are ___________ in the upper zone and _______ in the lower zone.

compressive; tensile

Sundome Yakima,WA, Loofburrow Architects

concave in the hoop direction, convex in the arch direction, resulting in an umbrella-like ribbed appearance. Six reusable forms were used to cast the dome. These were built using straight wood joists angled to give the desired saddle shape and sheathed with plywood.

TWA Terminal New York, by Eero Saarinen and Associates

consists of four concrete shells resting on four Y-shaped columns. Aesthetic, rather than structural, considerations. Therefore, the thickness of the shells and the depth of the edge beams are relatively large compared with those of other shell structures.

Crest, London, England by Zaha Hadid Architects

construction technique involving the assembly of aluminum panels into a pre-stressed flat plate which is then lifted into a self-supporting structure.

With an arch, as the height _________, the outward thrust _________.

decreases; increases.

A tension ring encircles...

encircles the base of a dome to contain the outward components of the meridional forces.

Warm Mineral Springs Motel Venice, FL, by Lundy

forest of hypar umbrella shells for the roof structure. The umbrellas appear to float as freestanding forms. The shell was site cast and consists of four adjacent hypars. They are supported only in the center by a square precast column.

Los Manantiales Restaurant

four intersecting hypars. The structure behaves by arch-action compressive forces following the convex curvature and accumulating in the groins (valleys) where they are transferred by arch action to the supports. The shell is extraordinarily thin.

Bolshoy Ice Dome, Sochi, Russia by Botta Management

geometric ellipsoid shape and in a system of exterior built in LEDs that may color the building into Fabrgee-like patterns or any other patterns, or leave it blank and pure.

Coyoacan (Mexico) Market and High-Life Textile Factory, by Felix Candela

hypar umbrella. Economical choice due to relatively lower labor costs (and relatively higher costs of alternative steel construction).

Zarzuela Hippodrome 1935 Madrid, Torroja Architect

hyperboloid umbrella shell. The cantilevered configuration allowed positioning of the main support columns behind the spectators allowing an unobstructed view of the racecourse. A total of 30 shells, arranged in three groups (12, 6, 12) sheltered the grandstands. A slender vertical member in the rear of each umbrella provided the tension necessary to prevent the shell from tipping toward the front.

What does a thrust need to be restrained with?

internal ties or external bracing (abutments).

Shell, Nagano Prefecture, Japan byARTechnic

large shell shaped structure. a shape, made at a completely different place for a completely different purpose. Within this shell shaped structure will one find floors constructed, wall separating spaces, and rooms furnished.

Where is lateral thrust strongest in an arch?

lateral thrust is strongest at the haunches of the arch (the part midways between the crown and the springing).

Ellipsoids produce ____ hoop tension and paraboloids produce ____ hoop tension.

more; less.

Because arch lines are semicircular in a hemispherical dome, there is a tendency for them to be stable __ ___ but to buckle ______ in the lower portion (like arches and vaults).

on top; upward.

As the forces are carried to the ground, the arch will push _______ at the base, which is called the ______.

outward; thrust.

McDonnell Planetarium St. Louis, Hellmuth, by Obata & Kassabaum

reinforced concrete hyperboloid shell, a saddle shape commonly used for the large cooling towers for nuclear plants. Its shape is unrelated to the 60' diameter hemisphere dome inside used to enclose the planetarium. Tension rings at the top and bottom to resist the outward thrust at both locations. 12 columns support the entire shell perimeter.

Hoop forces restrain...

restrain the out-of-plane movement of the meridional strips in the shell of a dome.

springing stone

stone at the springing line.

Dome

surfaces of revolution, usually generated by rotating an arc of a circle around a vertical axis. A spherical surface structure having a circular plan and constructed of a continuous rigid material or of short, linear elements.

Wyss Garden Center Heinz Isler, engineer, 1961, Solo Thurn, Switzerland

unicular model consisting of a suspended membrane which is then stiffened and inverted to determine the optimum shape for a thin-shell dome. His earliest experiments (in 1955) involved hanging wet fabrics in catenary shapes outside in the winter, allowing it to freeze, then inverting it and studying the resulting shape. As a result, his extremely thin shells remain in pure compression under most loading conditions, developing none of the tension cracks found in most shells.

Voussoirs

wedge shaped blocks holding the curve of the arch.