nisee.berkeley.edu http://nisee.berkeley.edu/elibrary/getpkg?id=GoddenE45-65

Shells: Hyperbolic paraboloids (hypar)

Image-GoddenE45 Hypar roof, Court House Square. Designed to

house a shop, this large concrete shell covers an area of 112 ft X

113.5 ft without interior supports and rises 32.5 ft above ground.

The shell thickness is 3 in. increasing to 6 in. at the ridges.

(Denver, Colorado)

Image-GoddenE46 Detail of one of the supporting buttresses in

the hypar shell roof. Each buttress is oriented in the diagonal of

the shell as viewed in plan. This is the direction of the resultant

force exerted by the two edge beams at the corner. (Denver,

Colorado)

Image-GoddenE47 Side view of steel buttress. Note that the

buttress is inclined at an angle to the vertical in line with the edge

beams, to be in line with the resultant boundary force. (Denver,

Colorado)

Image-GoddenE48 Hinged joint at the top of the buttress. The

complete shell is supported on four stainless steel pins. (Denver,

Colorado)

Image-GoddenE49 Office building. Consisting of a series of hypar

shells designed in such a way that half a shell is cantilevered

above the main windows. (Near San Francisco, California)

Image-GoddenE50 Cantilevered shell. The concrete edge beam

tapers from minimum at the unsupported end to maximum at the

support point. (San Francisco Bay Area)

Image-GoddenE51 Marine Stadium. This structure facing the

waterfront for water sports is roofed with a series of hypar shells.

The geometry of the shells and the structural system at the back

of the stadium can be seen in GoddenE52. (Miami, Florida)

Image-GoddenE52 Marine Stadium. Close-up of two bays of the

stadium taken from the back. The diagonal members act as ties

for the long cantilever roof as well as providing in-plane stability to

the structure. (Miami, Florida)

Image-GoddenE53 Hypar roof, University of California, Berkeley.

Each column supports an umbrella roof consisting of four small

hypar shells. The column spacing is 20 ft. (Berkeley, California)

Image-GoddenE54 Hypar roof, University of California, Berkeley.

Each column supports an umbrella roof consisting of four small

hypar shells. The column spacing is 20 ft. (Berkeley, California)

Image-GoddenE55 Hypar roof, University of California, Berkeley.

This roof system is also used as a restaurant roof. Note the

interesting geometry and high window opening caused by

staggering the alternate rows of shells. (Berkeley, California)

Image-GoddenE56 Oakland International Airport. This central

tower-terminal building uses hypar umbrella shells over the main

hall, and cantilevered barrel shells at the entrance. (Oakland,

California)

Image-GoddenE57 Umbrella hypar shells in the Oakland Airport

tower-terminal building. Each set of four hypar shells is

independently supported on a long central column. The column

spacing is 35 ft. (Oakland, California)

Image-GoddenE58 Interior view of Oakland Airport tower/terminal

building showing the arrangement of the hypar shells. (Oakland,

California)

Image-GoddenE59 St. Mary's Cathedral. An interesting structure

consisting of eight hypar shells on end forming a total roof

structure. The form of the building is difficult to visualize, hence

views from different angles, both inside and outside the cathedral,

are shown in GoddenE60-E63. (San Francisco, California)

Image-GoddenE60 Oblique external view of St. Mary's Cathedral,

showing the ridge between the shell pairs at the corners of the

building in plan. The line extends from the center of the cross at

the apex of the building and descends in a straight line to the

support point shown in GoddenE63. (San Francisco, California)

Image-GoddenE61 St. Mary's Cathedral. Interior view looking

upwards and showing the mid-point at the apex. The form of the

roof can be deduced from GoddenE60-E61. (San Francisco,

California)

Image-GoddenE62 St. Mary's Cathedral. Interior view, floor level

looking towards the altar. Note that the shells are terminated at

the bottom in an arch form between the supports (two of the

supports are just out of view to the left and right, but a close-up of

one of the supports is given in GoddenE63) giving an outside view

from the cathedral floor. (San Francisco, California)

Image-GoddenE63 St. Mary's Cathedral. Interior View, showing

one of the four corner shell supports. (San Francisco, California)

Image-GoddenE64 American Airlines Hangar, SFO. This double

cantilever roof structure consists of a series of hypar shells made

of this steel decking. Cantilevers are 230 ft. long, 56 ft. wide, and

have a depth that tapers from 40 ft. maximum to 4 ft. at the tip.

The bottom of the roof is 80 ft. above the floor. Built on a module

design, the roof currently has eight pairs of balanced hypars. (San

Francisco International Airport)

Image-GoddenE65 American Airlines Hangar, SFO. Interior view.

The point of support of the hypars is seen in the background, and

the flattening angle between plates can be seen by comparing the

background and foreground geometry. The roof includes a set of

cables that can be tightened to counteract vertical displacements.

The top of the cantilever (over the hangar doors) is off the top of

the slide. (San Francisco International Airport)

Set E: Domes and Shells