1. Geodesic Domes
G. Mouna Reddy
060123

2. A geodesic dome is a spherical or partial-spherical shell structure or lattice shell based on a network of great circles (geodesics) lying on the surface of a sphere.
The geodesics intersect to form triangular elements that have local triangular rigidity and also distribute the stress across the entire structure.
When completed to form a complete sphere, it is known as a geodesic sphere.
The term "dome" refers to an enclosed structure and should not be confused with non-enclosed geodesic structures such as geodesic climbers found on playgrounds.
Spaceship Earth at Epcot, Walt Disney World, a geodesic sphere
Geodesic Domes

3. Principles of Geodesic Domes
Geodesic domes are further refinements of lamella domes and many features of their design have been patented by R. Buckminster Fuller.
Synergetics Inc., a Fuller’s company has built many such domes all over the world.
These domes are more amenable to prefabrication since the variation in length of their component members is quite small even for large spans and complicated types of bracing.
This results in a very regular network and leads to uniform stress distribution.
The framework of these domes consists of curved elements lying on the great arches of a true sphere.
Buckminster Fuller with one of his famed geodesic domes
Geodesic Domes

4. Principles of Geodesic Domes
  The intersecting elements form a three-way grid comprising of equilateral spherical triangles.
In Fuller’s original geodesic domes the grids were formed on the faces of spherical icosahedron, but now-a-days various other forms of polyhedral, e.g., dodecahedrons are also used.
It is known that an icosahedron exploded on to the surface of a sphere can be divided into 20 equilateral spherical triangles.
It is to be noted that this is the maximum number of equilateral triangles into which the sphere can be divided.
Buckminster Fuller’s patented drawing 1
Geodesic Domes

5. Principles of Geodesic Domes
  Each of these triangles can be subdivided into six triangles by drawing Medians and bisecting the sides of each triangle.
It will be found that these medians follow great circles which are the extensions of the sides of the equilateral triangles into which spherical icosahedron can be divided.
Using this method of construction it is possible to form fifteen complete great circles regularly arranged on the surface of the sphere.
In geodesic domes the members forming the framework are usually straight, being the chords of geodesic arcs.
Buckminster Fuller’s patented drawing 2
Geodesic Domes

6. Principles of Geodesic Domes
For larger span domes the primary type of bracing, which is truly geodesic, is not sufficient, since it leads to an excessive slenderness ratio of the bracing struts. Hence a secondary bracing is employed.
To obtain a regular network, the edges of the basic equilateral triangles are divided modularly.
The number of modules into which the edge of the spherical icosahedron is divided depends mainly on the span of the dome. This subdivision is usually termed as ‘frequency’.
It is to be noted that during such a subdivision the resulting triangles are no longer equilateral. Various types of subdivisions are used in practice.
Buckminster Fuller’s patented drawing 3
Geodesic Domes

7. DETAILS OF GEODESIC DOME GEOMETRIES
Icosahedron
Icosahedron exploded on a sphere
Spherical three way great circle griddling
GEODESIC CIRCLES
GEODESIC SUBDIVISION OF THE FACES OF ICOSAHEDRON
DETAILS OF GEODESIC DOME GEOMETRIES
VARIATION IN THE METHOD OF SUBDIVISION
GEODESIC SUBDIVISION INTO HEXAGONS & PENTAGONS

8. Principles of Geodesic Domes
Fuller prefers the one in which the members lie on the medians, which follow the great circles; this according to him results in a more uniform stress distribution.
The basic geodesic subdivision of a sphere results in a triangulated framework.
Six triangles interconnected at the same point produce a hexagon, a form which is very interesting from the architectural and structural point of view.
It must be noted, however, that no matter how distorted these hexagons are, a sphere cannot be covered with hexagons only.
Buckminster Fuller’s patented drawing 4
Geodesic Domes

9. Principles of Geodesic Domes
A minimum of twelve pentagons will have to be introduced. This follows from the fact that in an icosahedron exploded on a sphere there are 12 apices at which five triangles meet.
A spherical hexagonal unit, if consisting of pin-connected units is not stable. Hence, the joints have to be made rigid.
The whole unit may be stiffened by additional struts and cables also.
A hexagon may also be divided into three diamond units. This type of bracing is very popular for stressed skin domes.
Details of connections
Geodesic Domes

10. Advantages of Geodesic Domes
By virtue of its shape, geometry and structural system, Fuller’s geodesic dome has the following inherent advantages:
It is structurally simple once modular designs have been prepared for assembling into a specific plan.
It is industrially capable of mass production according to modular sizes of members and fittings.
Its components are light and easy to handle and transport and it is simple to erect the domes with these components.
It is inherently strong.
It can be adopted to very large diametrical domes.
The Montreal Biosphère, formerly the American Pavilion of Expo 67, by R. Buckminster Fuller, on Île Sainte-Hélène, Montreal, Canada
Geodesic Domes

11. Disadvantages of Geodesic Domes
The disadvantage of geodesic domes is due to the fact that, at the bottom of the structure, the perimeter units following the side of an icosahedron give an irregular and ragged line.
Also when other than hemispherical or plane truncated segments are used, the edges create architectural problems.
- These lie along segments of 5 great circles and are sometimes supported by several piers, all at different heights.
- They can also be supported by arches, making only five points of support for the whole dome.
- These piers or edge arches must be designed to carry the thrust of the dome, and the drag and the uplift due to wind loads.
The Climatron greenhouse at Missouri Botanical Gardens, built during 1960, inspired the domes in the science fiction movie Silent Running.
Geodesic Domes

12. Disadvantages of Geodesic Domes
- The connections of the dome to the piers are designed to permit a considerable amount of radial movement due to temperature changes.
- If the soil conditions are poor the piers should be held together by a tension ring of steel or prestressed concrete.
- If springing from ground level, it may be supported on a reinforced concrete peripheral thrust ring set on piles and with metal plate over the ring to which the struts and their bottom plates are welded.
Inside the Eden Project tropical biome.
Geodesic Domes

13. Erection of Geodesic Domes
The main advantage of the geodesic dome is the simplicity of its erection.
One method is to fasten sections of the dome together like a skirt around the central mast.
This portion is raised enough so that another zone of sections can be fastened to the first portion and so on.
Or, it can also be built like other domes from the bottom up. In this method the lowest zone is erected on piers, forming a complete circle. The next higher zone is erected on the lowest and so on.
Since any complete zone is stable by itself, this procedure can be followed with a minimum amount of scaffolding.
Construction details of a permanently installed tent-type geodesic dome by Buckminster Fuller
Geodesic Domes

14. Erection of Geodesic Domes
A good example of single layer geodesic steel dome is the structure designed by Synergetics Inc. for the Electro Minerals Division of the Carborundum Co., New York, which has a span of 90 m.
It consists of I-sections, bolted at each end with four bolts through small circular vertex plates provided above and below the joint.
Superior Dome – one of the largest geodesic domes of the world
Geodesic Domes

15. Analytical Hints Geodesic Domes
Similar to the lamella dome, the geodesic dome structure is highly indeterminate and cannot be analyzed with any high degree of accuracy except by resorting to a large number of simultaneous displacement equations.
As in lamella domes, the computation of geodesic triangles and different lengths and sizes of struts are tedious and time consuming.
Hence computer oriented matrix methods of analysis should be used for the analysis of these structures.
Tacoma Dome
Geodesic Domes