No edges and corners, design...a ball

Author: Yang Xiaotian

Among spatial geometries

The sphere without edges and corners

is the most perfect!

The surface potential energy of a sphere is minimal, which is why bubbles, balloons, inflatable structures, and even planetary bodies are spherical.

The space sail ball of the "BIT-1" satellite

Space sail ball: After the satellite enters orbit normally, it releases the flexible material and expands into a spherical shape, just like unfolding a "sail" , which can be used as a solar panel for a satellite or a large antenna for satellite communications.

In terms of mechanics, when the sphere is subjected to uniform tension or pressure, it only bears axial tension or pressure. The spherical shell is a very efficient structural form, just like it is difficult for us to break a thin egg shell with our hands.

United States Pavilion at the Montreal World Expo, Space Spherical Shell, 1967

Pressure tanks for storing gases and liquids are often designed to be spherical, because with the same surface area, the volume enclosed by a sphere is the largest. , at the same time, the spherical shell has the characteristics of light weight and high efficiency.

Spherical storage tank

Under the same diameter and working pressure, the plate thickness is only half that of the cylindrical storage tank

The sphere’s unique shape and efficient There are many excellent cases in architectural design as well as the charm of spatial characteristics. The Xiaoi team is currently designing a spherical structure. This article takes this opportunity to share with you the cases we have collected.

The grid form of the spherical shell

The grid forms of the spherical lattice shell are: Geodesic Dome, Ribbed Dome, Lamella Dome, Schwedler Dome , Kiewitt-shaped Kiewitt Dome, etc.

Ribbed Dome

Lamella Dome

Schwedler Dome (double oblique without weft)

Fuller With the Geodesic Dome

Around 1927, Fuller developed a new strategy for spherical surveying and projective mapping, called the Dymaxion map, which transformed the spherical terrain into a geometric series of planar triangles and squares. "By controlling the distortion produced when the projection is drawn, the size of the land on the map can be maintained in a more accurate proportion to reality. Because these geometric elements can be rearranged, we can "peel" the earth in countless different ways."

Fuller and the Dymaxion Map (1945)

Illustrations drawn by Kyle Vanhemert for Fuller

Fuller combined the idea of ??the Dymaxion map with energy geometry to invent The geodesic dome. Geodesic Line is a line connecting two points on a surface with the shortest line length.

Fuller-Geodesic Dome Patent

At the 1967 Montreal International Exposition, Fuller and Shoji Sadao designed a 3/4 spherical building with a diameter of 76m---the United States Pavilion. , the outer surface is covered with a transparent acrylic plate. This pavilion has become a symbol of American advanced technology and attracted the attention of the world.

Fuller and the U.S. Pavilion at the Montreal World Expo (1967)

In 1976, the dome suffered a fire during the renovation process

The exterior decoration was burned and the exposed The structure appears clearer.

In addition to the American Pavilion in Montreal, Fuller also designed many spherical structures, including Fly's Eye Dome and the tensegrity spherical structure.

Fly's Eye Dome designed and built by Fuller, 1965

Tensile ball structure (Icosahedron) based on geodesic dome structure

Fuller believed that "the existence of natural In order to provide a system with maximum strength with the minimum material, the basic units of the quadrilateral pyramid and the octahedron become the most efficient spatial structure after aggregation."

Coincidentally, in 1985, H.W. Kroto and R.E. Smalley discovered the third crystal form of carbon (the first two were diamond and graphite). In commemoration of Fuller's early conjecture, it was named "Fullerenes" - C60. Its molecular structure is a spherical 32-hedron, with carbon atoms connected by 20 six-membered rings and 12 five-membered rings, and has extremely strong molecular stability.

Fullerenes, footballs, and geodesic domes have similar structures

A sphere can be composed of regular hexagons and regular pentagons,

and pentagons The number must be 12.

Orlando Disney's Spaceship Earth, designed as a journey for passengers through a time machine, also uses a geodesic grid format.

Spaceship Earth

The difference is that Spaceship Earth is a complete sphere and uses a single-layer rather than a double-layer structure. It is 50m in diameter and is supported by three huge slanted columns. With. The surface of the sphere is covered with folded aluminum plates, making the appearance of the sphere more textured.

The surface of the sphere is covered with folded aluminum plates

***3840 nodes, 11324 aluminum plates

Amazon Spheres

Amazon in The Seattle headquarters spent a lot of money to build three glass spheres, called Amazon Spheres. Hundreds of lush plants are planted inside the spherical building, creating an indoor version of the "Amazon Rainforest" in the core area of ??the metropolis.

Amazon Spheres*** has 2,643 glass curtain walls. The 4 layers of ultra-white glass are used to reduce solar heat radiation and ensure the light necessary for plant photosynthesis.

The total length of the building is about 40 meters, and the diameter of the sphere is about 24-29m. It looks like three interfering bubbles. The structural material is a combination of glass and steel. The design team used a unique grid method to divide the sphere.

Futuristic and organic structural skeleton

You can still vaguely see traces of regular pentagons and hexagons

The grid shape looks like Very complex, but its generation logic is derived from regular fullerene or football grids. The process of grid generation is to divide the pentagon into 5 equal parts and merge it with the hexagon next to it to form a basic unit; then divide the basic unit into 5 parts based on the center point and merge the boundaries of adjacent basic units. , that is, the structural grid of Amazon Spheres is obtained.

Structural grid generation logic of Amazon Spheres

Although Amazon Spheres has become a new internet celebrity in Seattle, it has to complain about its curtain wall panel design. As you can see from the picture above, the steel structure grid has both the organic feel of dynamic curves and the clear logic of the design. However, after being roughly covered with a triangular glass curtain wall, the architectural effect is greatly reduced.

The steel structure skeleton has smooth lines

The main frames are connected by steel plates to enhance the structural integrity

Steel structure skeleton module details

The suspended Bird's Nest Conference Room

There is a seating area on the top floor where the lighting is best. Bask in the sun, take a nap, and wake up to work full of energy.

Ribbed Dome

The ribbed dome has a simple form and simple structure. There are many cases of this type of spherical building.

Ericsson Globe

Ericsson Globe, 1989

The Ericsson Globe in Stockholm, Sweden, designed by Svante Berg and Lars Vretblad, may be the world's largest The largest spherical structure. It has a diameter of 110 meters, an internal height of 85 meters, a volume of 600,000 square meters, and can accommodate 16,000 spectators for performances.

Building structure section

The performance venue and stands in the lower part of the building are reinforced concrete structures, and the upper hemispherical roof is a double-layer grid in the form of a rib ring. The surface is uniformly covered with white metal plates, like a golf ball.

In 2010, the peripheral cable car was opened and called Skyview.

New Reichstag Building

The Reichstag Building designed by Norman Foster also used a ribbed ring-shaped dome for its renovation. It is like a beacon on the city skyline and has become a symbol of Berlin. Important city landmark.

The renovation draws inspiration from the original building. On the one hand, it retains the marks of the old masons and the slogans left by the Soviet Red Army in 1945 as a "museum of its own history"; on the other hand, the thick shell Below is the light and transparent interior. The 360-degree perspective reveals the beauty of Berlin, forming a strong contrast with the old buildings. The public area of ??the building extends all the way to the roof to the terrace restaurant and dome, and the spiral passage leads people to the dome and observation platform.

The dome steel lattice shell structure is as transparent as possible, and the expression of components and detailed nodes is also very delicate. Although the structure itself is not very difficult or innovative, the exquisite expression of the exposed steel structure itself still achieves good results in the end.

Lamella Dome, a duplex spherical shell

In the early stages of the Amazon Spheres project introduced earlier, the design plan also considered using the duplex spherical shell Lamella Dome, but the expressiveness was not as good as the later plan. And give up.

Amazon Spheres’ initial spherical shell plan

Among the spherical buildings that have been built, there are not many cases of using the rectangular shape. The main reason is that the size difference of the connected square grid is relatively large. The top rods of the ball are densely converged together, while the middle part of the ball body is sparse and the lengths of the rods are different. The differentiated grid makes it difficult to use components of uniform specifications for the structure and curtain wall, which increases the construction cost.

Concept plan for a technology ball in Dubai

Due to space limitations, the following case will not be elaborated. In short, spherical architecture is an architectural form with unlimited design potential.

La Géode is a spherical cinema designed by architect Adrien Fainsilber and engineer Gérard Chamayou. The mirrored stainless steel reflects the beautiful urban scenery of Paris on the building surface.

LaGéode mirrored stainless steel spherical building

China Science and Technology Museum’s mirrored stainless steel spherical building

Two spherical buildings at the Shanghai International Convention Center

Together with the adjacent Oriental Pearl Tower, it forms a scene of large and small beads falling on a jade plate

Various dome theater structures

Various radomes

Innovative spherical shell grid

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