Editing Space frame

{{Short description|Rigid three-dimensional load-bearing truss structure}}
[[Image:ITP Zamudio.jpg|thumb|225px|The roof of this industrial building is supported by a space frame structure.]]
[[File:Articulacion malla.svg|thumb|225px|If a force is applied to the blue node and the red bar were {{em|not}} present, the resultant effect on the structure would depend entirely on the blue node's bending rigidity, {{em|i.e.}}{{tsp}}to its resistance (or lack thereof) to bending; however, with the red bar in place, then assuming negligible bending rigidity of the blue node as compared with the red bar's contributing rigidity, this 3-dimensional load-bearing truss structure could be solved using a rigidity matrix (neglecting angular factors).]]
In [[architecture]] and [[structural engineering]], a '''space frame''' or '''space structure''' ([[Three-dimensional space|3D]] [[truss]]) is a rigid, lightweight, truss-like structure constructed from interlocking [[strut]]s in a [[geometry|geometric]] [[pattern]]. Space frames can be used to span large areas with few interior supports. Like the truss, a space frame is strong because of the inherent rigidity of the triangle; flexing [[Structural load|load]]s (bending [[moment (physics)|moments]]) are transmitted as [[tension (mechanics)|tension]] and [[compression (physical)|compression]] loads along the length of each strut.

Chief applications include buildings and vehicles.

==History==
[[Alexander Graham Bell]] from 1898 to 1908 developed space frames based on tetrahedral geometry.<ref>{{cite web| title=Alexander Graham Bell| url=http://www.drachenarchiv.de/Seiten/b_bp_bell.html| url-status=dead| archive-date=2003-03-26| archive-url=https://web.archive.org/web/20030326123328/http://www.drachenarchiv.de/Seiten/b_bp_bell.html }}</ref><ref>{{cite journal |title=Tetrahedral Principle In Kite Structure | author=Alexander Graham Bell| journal=National Geographic Magazine| volume= XIV| issue=6 | date=June 1903| url=https://www.loc.gov/resource/magbell.37700202}}</ref> Bell's interest was primarily in using them to make rigid frames for nautical and aeronautical engineering, with the [[tetrahedral kite|tetrahedral truss]] being one of his inventions. 

[[Mero-Schmidlin|Max Mengeringhausen]] developed the space grid system called MERO (acronym of '''''ME'''ngeringhausen '''RO'''hrbauweise'') in 1943 in Germany, thus initiating the use of space trusses in architecture.<ref>{{cite web| url=http://tatproddel.tat.cloud.opentext.com/sites/constructionuk/default/en/reference/teaching-resources/architectural-teaching-resource/design/space-grid-structures/brief-history-and-development-of-systems| title=Modular space grids| url-status=dead| archive-url=https://web.archive.org/web/20160915031431/http://tatproddel.tat.cloud.opentext.com/sites/constructionuk/default/en/reference/teaching-resources/architectural-teaching-resource/design/space-grid-structures/brief-history-and-development-of-systems| archive-date=2016-09-15}}</ref> The commonly used method, still in use{{As of when|date=March 2025}}, has individual tubular members connected at node joints (ball shaped) and variations such as the space deck system, octet truss system, and cubic system. 

Stéphane de Chateau in France invented the Tridirectional SDC system (1957), Unibat system (1959), and Pyramitec (1960).<ref>{{cite web| url=http://www.setareh.arch.vt.edu/safas/010_system_05_unibat.html| title=Unibat system| date=4 August 2010}}</ref><ref>{{cite journal| title=The innovative structural conception in Stéphane du Château's work: from metallic trusses to the development of spatial frames| first=Cláudia Estrela| last=Porto| journal=Architectus| location=Poland| volume=4| issue=40| pages=51–64| date=2014| url=http://www.architectus.arch.pwr.wroc.pl/40/40_05.pdf| url-status=dead| archive-date=September 16, 2016| archive-url=https://web.archive.org/web/20160916221813/http://www.architectus.arch.pwr.wroc.pl/40/40_05.pdf }}</ref> A method of tree supports was developed to replace the individual columns.<ref>[http://citiesnow.in/blog/2015/07/09/evolution-of-space-frames/ Evolution of Space Frames] {{webarchive |url=https://web.archive.org/web/20151119115630/http://citiesnow.in/blog/2015/07/09/evolution-of-space-frames/ |date=November 19, 2015 }} Cities Now</ref> 

[[Buckminster Fuller]] patented the octet truss ({{US Patent|2,986,241}}) in 1961<ref>{{cite web| url=http://www.grunch.net/synergetics/docs/bellnote.html| title=Fuller on Bell| author=Dorothy Harley Eber, via telephone| date=June 29, 1978}}</ref> while focusing on [[architecture|architectural]] structures. 

[https://patentimages.storage.googleapis.com/1c/9a/7a/6aa02cf0efb93c/US4446666.pdf Gilman's Tetrahedral Truss] of 1980 was developed by [[John J. Gilman]], a material scientist known for his work on the molecular matrices of crystalline solids.  Gilman was an admirer of Buckminster Fuller's architectural trusses, and developed a stronger matrix, in part by rotating an alignment of tetrahedral nodes in relation to each other.

==Design methods==
Space frames are typically designed using a rigidity matrix. The special characteristic of the [[stiffness matrix]] in an architectural space frame is the independence of the angular factors.  If the joints are sufficiently rigid, then the angular deflections can be neglected, simplifying the calculations.

==Overview==
[[Image:SpaceFrame02.png|right|thumb|250px|Simplified space frame roof with the half-octahedron highlighted in blue]]
The simplest form of space frame is a horizontal slab of interlocking [[square pyramid]]s and [[tetrahedron|tetrahedra]] built from [[Aluminium]] or tubular [[steel]] struts. In many ways this looks like the horizontal jib of a tower crane repeated many times to make it wider.  A stronger form is composed of interlocking [[Tetrahedron|tetrahedra]] in which all the struts have unit length. More technically this is referred to as an isotropic vector matrix or, in a single unit width, an octet truss. More complex variations change the lengths of the struts to curve the overall structure or may incorporate other geometrical shapes.

==Types==
Within the meaning of space frame, we can find three systems clearly different between them:<ref name="ref1">Otero C. (1990). "Diseño geométrico de cúpulas no esféricas aproximadas por mallas triangulares, con un número mínimo de longitudes de barra". Tesis Doctoral. Universidad de Cantabria.</ref>

'''Curvature classification'''

* Space plane covers: These spatial structures are composed of planar substructures. Their behavior is similar to that of a plate in which the deflections in the plane are channeled through the horizontal bars and the shear forces are supported by the diagonals.<ref name="ref5">Cavia Sorret (1993).</ref>
[[Image:Tirumailai MRTS station Chennai (Madras).jpg|thumb|right|250px|This train station in India is supported by a barrel vault structure ]]

* Barrel vaults: This type of vault has a cross section of a simple arch. Usually this type of space frame does not need to use tetrahedral modules or pyramids as a part of its backing. 
* Spherical domes and other compound curves usually require the use of tetrahedral modules or pyramids and additional support from a skin.

'''Classification by the arrangement of its elements'''

* Single-layer grid: All elements are located on the surface to be approximated.
* Double-layer grid: Elements are organized in two layers parallel to each other at a certain distance apart. Each of the layers forms a lattice of triangles, squares, or hexagons in which the projection of the nodes in a layer may overlap or be displaced relative to each other. Diagonal bars connect the nodes of both layers in different directions in space. In this type of meshe, the elements are associated into three groups: upper cordon, cordon, and cordon lower diagonal.
* Triple-layer grid: Elements are placed in three parallel layers, linked by the diagonals. They are almost always flat.

Other examples classifiable as space frames are these:

* Pleated metallic structures: Emerged to try to solve the problems that formwork and pouring concrete had their counterparts. Typically run with welded joint, but may raise prefabricated joints, a fact which makes them space meshes.
* Hanging covers: Designs on the cable taut, spine, and the [[catenary arch]] ([[funicular curve|inverted funicular]]) show their ability to channel forces theoretically better than any alternative, and they have an infinite range of possibilities for composition and adaptability to any type of plant cover. However, imprecisions in shape risk having the loaded strand bend to unexpected stresses; mitigation of this problem requires pre-compression and pre-stressing elements. In most cases, they tend to be the cheapest solution that best fits the acoustics and ventilation of the covered enclosure.  They are vulnerable to vibration.
* Pneumatic structures: Closure membranes subjected to a pressurized state may be considered within this group.

==Applications==
Chief space frame applications include:

'''Buildings'''
* Industrial structures:
** [[Factory|Factories]]
** [[Warehouse]]s, 
* Commercial, entertainment, and service facilities: 
** [[Sports hall]]s
** Conference halls, pavilions, and [[exhibition center]]s
** [[Stadium]]s
** [[Museum]]s and fair houses
** [[Shopping mall]]s
** [[Airport]]s

'''[[#Vehicles|Vehicles]]''':
** Aircraft
** Automobiles
** Motorcycles
** Bicycles
** Spacecraft 

'''Architectural design elements''' 
** [[Atrium (architecture)|Atriums]]
** [[Geodesic]]s

===Construction===
Space frames are a common feature in modern building construction; they are often found in large roof spans in [[Modernism|modernist]] commercial and industrial buildings.

Examples of buildings based on space frames include:
* [[Stansted Airport]], by [[Foster + Partners]]
* [[Bank of China Tower, Hong Kong|Bank of China Tower]] and the [[Louvre Pyramid]], by [[I. M. Pei]]
* [[Rogers Centre]] by [[Rod Robbie]] and [[Michael Allen (architect)|Michael Allan]]
* [[McCormick Place]] East in [[Chicago]]
*[[Arena das Dunas]] in Natal, Brazil by [[Populous (company)|Populous]]
* [[Eden Project]] in Cornwall, England
* [[Ericsson Globe|Globen]], Sweden - Dome with diameter of 110 m, (1989)
* [[Biosphere 2]] by [[John P. Allen]], [[Phil Hawes]], [[Peter Jon Pearce]] in Oracle, Arizona
* [[Jacob K. Javits Convention Center]], [[New York City, New York]]
*[[Palau Sant Jordi]] in Barcelona, Spain by [[Arata Isozaki]]
* [[Sochi International Airport]] in [[Sochi]], [[Russia]]
* Entrance to [[Six Flags Magic Mountain]]
* [[Taoyuan International Airport|Taiwan Taoyuan International Airport]] airport terminal 2
* [[Harbin Grand Theatre|Harbin Opera House]] in China by [[Ma Yansong]]
* [[Heydar Aliyev Center|Hedyar Aliyev Centre]] in Azerbaijan by [[Zaha Hadid]] 

Large portable stages and lighting [[Crane (machine)#Gantry|gantries]] are also frequently built from space frames and octet trusses.

===Vehicles===
[[Image:Yeoman YA-1 vs CA-6 Wackett frame.jpg|thumb|Yeoman YA-1 vs CA-6 Wackett frames.]]

==== Aircraft ====
The [[CAC Wackett|CAC CA-6 Wackett]] and [[Yeoman Cropmaster|Yeoman YA-1 Cropmaster 250R]] aircraft were built using roughly the same welded steel-tube fuselage frame.

Many early "whirlybird"-style exposed-boom helicopters had tubular space-frame booms, such as the [[Bell 47]] series.

==== Cars ====
Space frames are sometimes used in the chassis designs of [[automobiles]] and [[motorcycles]]. In both a space-frame and a tube-frame chassis, the suspension, engine, and body panels are attached to a skeletal frame of tubes, and the body panels have little or no structural function. By contrast, in a [[unibody]] or [[monocoque]] design, the body serves as part of the structure.

Tube-frame chassis pre-date space frame chassis and are a development of the earlier [[ladder chassis]]. The advantage of using tubes rather than the previous open-channel sections is that they resist [[torsion (mechanics)|torsion]]al forces better. Some tube chassis were little more than a ladder chassis made with two large-diameter tubes, or even a single tube as a [[backbone chassis]]. Although many tubular chassis developed additional tubes and were even described as "space frames", their design was rarely correctly stressed as a space frame, and they behaved mechanically as a tube-ladder chassis, with additional brackets to support the attached components. The distinction of the true space frame is that all the forces in each strut are either tensile or compressive, never bending.<ref name="Ludvigsen, Colin Chapman, 153" /> Although these additional tubes did carry some extra load, they were rarely diagonalised into a rigid space frame.<ref name="Ludvigsen, Colin Chapman, 153" >{{harvnb|Ludvigsen|Colin Chapman|page=153–154}}</ref>

An earlier contender for the first true space-frame chassis is the one-off Chamberlain 8 race "special" built by brothers Bob and Bill Chamberlain in [[Melbourne]], Australia, in 1929.<ref>https://primotipo.com/2015/07/24/chamberlain-8-by-john-medley-and-mark-bisset/. ‘The Chamberlain An Australian Story’ John Hazelden </ref> Others attribute vehicles were produced in the 1930s by designers such as [[Buckminster Fuller]] and [[William Bushnell Stout]] (the [[Dymaxion car|Dymaxion]] and the [[Stout Scarab]]) who understood the theory of the true space frame from either architecture or aircraft design.<ref name="Ludvigsen, Colin Chapman, 150" >{{Cite book |title=Colin Chapman: Inside the Innovator |last=Ludvigsen |first=Karl |author-link=Karl Ludvigsen |publisher=Haynes Publishing |year=2010 |isbn=978-1-84425-413-2 |ref={{harvid|Ludvigsen|Colin Chapman}} |pages=150–164}}</ref>

A post-WW2 attempt to build a racing car space frame was the [[Cisitalia D46]] of 1946.<ref name="Ludvigsen, Colin Chapman, 150" /> This used two small-diameter tubes along each side, but they were spaced apart by vertical smaller tubes, and so were not diagonalised in any plane. A year later, [[Porsche]] designed their [[Porsche 360|Type 360]] for [[Cisitalia]]. As this included diagonal tubes, it can be considered a true space frame and arguably the first mid-rear engined design.<ref name="Ludvigsen, Colin Chapman, 150" />

[[File:Jaguar C-Type Frame.JPG|thumb|right|[[Jaguar C-Type]] frame]]

The [[Maserati Tipo 61]] of 1959 (Birdcage) is often thought of as the first, but in 1949, [[Robert Eberan von Eberhorst]] designed the [[Jowett Jupiter]] exhibited at that year's [[London Motor Show]]; the Jowett went on to take a class win at the 1950 Le Mans 24hr. Later, [[TVR]], the small British car manufacturers, developed the concept and produced an alloy-bodied two-seater on a multi-tubular chassis, which appeared in 1949.

[[Colin Chapman]] of [[Lotus Cars|Lotus]] introduced his first "production" car, the [[Lotus Mark VI|Mark VI]], in 1952. This was influenced by the [[Jaguar C-Type]] chassis, another with four tubes of two different diameters, separated by narrower tubes. Chapman reduced the main tube diameter for the lighter Lotus, but did not reduce the minor tubes any further, possibly because he considered that this would appear flimsy to buyers.<ref name="Ludvigsen, Colin Chapman, 153" /> Although widely described as a space frame, Lotus did not build a true space-frame chassis until the [[Lotus Mark VIII|Mark VIII]], with the influence of other designers, with experience from the aircraft industry.<ref name="Ludvigsen, Colin Chapman, 153" />

[[Image:Kitcar (8906407466).jpg|thumb|Chilean kitcar showing off its space frame structure (2013).]]
A large number of [[kit car]]s use space frame construction, because manufacturing them in small quantity requires only simple and inexpensive [[jig (tool)|jig]]s, and it is relatively easy for an amateur designer to achieve good stiffness with a space frame.

A drawback of the space-frame chassis is that it encloses much of the working volume of the car and can make access for both the driver and to the engine difficult. The [[Mercedes-Benz 300 SL]] "Gullwing" received its iconic upward-opening doors when its tubular space frame made using regular doors impossible.

Some space frames have been designed with removable sections, joined by bolted pin joints. Such a structure had already been used around the engine of the [[Lotus Mark III]].<ref name="Ludvigsen, Colin Chapman, 151" >{{harvnb|Ludvigsen|Colin Chapman|page=151}}</ref>  Although somewhat inconvenient, an advantage of the space frame is that the same lack of bending forces in the tubes that allow it to be modeled as a [[pin-jointed truss|pin-jointed structure]] also means that creating such a removable section need not reduce the strength of the assembled frame.
{{Multiple image
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| image1 = Moulton @ the MoMA.jpg
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| caption1 = [[Moulton Bicycle]] at the [[Museum of Modern Art]]
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| caption2 = 2006 [[Ducati]] Monster S2R 1000
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==== Motorcycles and bicycles ====
Italian motorbike manufacturer [[Ducati]] extensively uses tube-frame chassis on its models.

Space frames have also been used in [[bicycle]]s, which readily favor stressed triangular sectioning.

==See also==
* [[Backbone chassis]]
* [[Body-on-frame]]
* [[Exoskeleton car]]
* [[Framing (construction)]]
* [[Monocoque]]
* [[Modular construction system]]
* [[Platonic solid]]
* [[Stressed skin]]
* [[Superleggera]]
* [[Tensegrity]]
* [[Tessellated roof]]
* [[Tetrahedral-octahedral honeycomb]]

==References==
{{reflist}}

{{Commons category|Space frames}}

{{Buckminster Fuller}}

[[Category:Structural system]]
[[Category:Structural engineering]]