# Space frame

(Redirected from Structural geometry)
The roof of this industrial building is supported by a space frame structure.
If a force is applied to the blue node, and the red bar is not present, the behaviour of the structure depends completely on the bending rigidity of the blue node. If the red bar is present, and the bending rigidity of the blue node is negligible compared to the contributing rigidity of the red bar, the system can be calculated using a rigidity matrix, neglecting angular factors.

In architecture and structural engineering, a space frame or space structure is a rigid, lightweight, truss-like structure constructed from interlocking struts in a 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 loads (bending moments) are transmitted as tension and compression loads along the length of each strut. Steel space frames provide great freedom of expression and composition as well as the possibility to evenly distribute loads along each rod and external constraints. With these features, steel space frames can be used to achieve also complex geometries with a structural weight lower than any other solution. The inner highly hyper-static system provides an increased resistance to damages caused by fire, explosions, shocks and earthquakes. Space frames are modular and made of highly industrialized elements designed with a remarkable dimensional accuracy and precise surface finish.[1]

## History

Alexander Graham Bell from 1898 to 1908 developed space frames based on tetrahedral geometry.[2][3] Bell's interest was primarily in using them to make rigid frames for nautical and aeronautical engineering, with the tetrahedral truss being one of his inventions. Dr. Ing. Max Mengeringhausen developed the space grid system called MERO (acronym of MEngeringhausen ROhrbauweise) in 1943 in Germany, thus initiating the use of space trusses in architecture.[4] The commonly used method, still in use 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), Pyramitec (1960).[5][6] A method of tree supports was developed to replace the individual columns.[7] Buckminster Fuller patented the octet truss in 1961[8] while focusing on architectural structures.

## 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, the angular deflections can be neglected, simplifying the calculations.

## Overview

Simplified space frame roof with the half-octahedron highlighted in blue

The simplest form of space frame is a horizontal slab of interlocking square pyramids and 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 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:[9]

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.[10]
This train station is supported by a barrel vaults 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. The elements are organized in two layers parallel to each other at a certain distance apart. Each of the layers form 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 meshes, 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 we could attach with the definition of space frame 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 antifunicular show their ability to channel forces theoretically better than any other alternative, have an infinite range of possibilities for composition and adaptability to any type of plant cover or ensure vain. However, imprecisions in shape having the loaded strand (ideally adapts dynamically to the state of charge) and the risk of bending the arc to unexpected stresses are problems that require pre-compression and prestressing elements. Although in most cases tend to be the cheapest and the technical solution that best fits the acoustics and ventilation of the covered enclosure, are vulnerable to vibration.
The dome is a parashell concrete structure and is the only one in Scotland. It was constructed using a pioneering technique in which concrete was poured onto a special neoprene membrane and then pneumatically inflated.
• Pneumatic structures. Wherein the closure membrane is subjected to a pressurized state, may be considered within this group.

## Applications

### Construction

Space frames are a common feature in modern building construction; they are often found in large roof spans in modernist commercial and industrial buildings.

Examples of buildings based on space frames include:

Large portable stages and lighting gantries are also frequently built from space frames and octet trusses.

### Vehicles

Yeoman YA-1 vs CA-6 Wackett frames.

#### Aircraft

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

#### Cars

Spaceframes are sometimes used in the chassis designs of automobiles and motorcycles. In both a spaceframe 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 spaceframe 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 torsional 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 "spaceframes", their design was rarely correctly stressed as a spaceframe and they behaved mechanically as a tube ladder chassis, with additional brackets to support the attached components, suspension, engine etc. The distinction of the true spaceframe is that all the forces in each strut are either tensile or compression, never bending.[11] Although these additional tubes did carry some extra load, they were rarely diagonalised into a rigid spaceframe.[11]

The first true spaceframe chassis were produced in the 1930s by designers such as Buckminster Fuller and William Bushnell Stout (the Dymaxion and the Stout Scarab) who understood the theory of the true spaceframe from either architecture or aircraft design.[12]

The first racing car to attempt a spaceframe was the Cisitalia D46 of 1946.[12] 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 Type 360 for Cisitalia. As this included diagonal tubes, it can be considered the first true spaceframe.[12]

Jaguar C-Type frame

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

Colin Chapman of Lotus introduced his first 'production' car, the 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.[11] Although widely described as a spaceframe, Lotus did not build a true spaceframe chassis until the Mark VIII, with the influence of other designers, with experience from the aircraft industry.[11]

Other notable examples of space frame cars include the Audi R8, Ferrari 360, Lamborghini Gallardo, Mercedes-Benz SLS AMG, Pontiac Fiero and Saturn S-Series.

Chilean kitcar showing off its spaceframe structure (2013).

A large number of kit cars, possibly the majority made in the UK, use space frame construction, because manufacture in small quantity requires only simple and inexpensive jigs, and it is relatively easy for an amateur designer to achieve good stiffness with a space frame. Generally the space frames are MIG welded, although the more expensive kits often use TIG welding, a slower and more highly skilled process. Many of these resemble the Lotus Mark VII in general outline and mechanical layout, however others are close replicas of the AC Cobra or Italian supercars, but some are original designs resembling no other vehicle. Often, considerable effort has been made by the designers to produce true space frames, with all points of significant load braced in 3 dimensions, resulting in strength and stiffness comparable to, or better than, typical production cars. Others are tube frames but not true space frames because they use relatively large diameter tubes, often curved, which are carrying bending loads, but due to the large diameter remain adequately rigid. However some inferior designs are not true space frames, because the tubes are carrying considerable bending loads. This will result in considerable flexing due to dynamic loads, and ultimately fatigue fracture, a failure mechanism which is rare in a correctly designed true space frame. The reduced stiffness will also impair the handling.

A drawback of the spaceframe 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. Some spaceframes 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.[13] Although somewhat inconvenient, an advantage of the spaceframe is that the same lack of bending forces in the tubes that allow it to be modelled as a pin-jointed structure also means that such a removable section need not reduce the strength of the assembled frame.

2006 Ducati Monster S2R 1000.

#### Motorcycles and Bicycles

Italian motorbike manufacturer Ducati extensively uses tube frame chassis on its models.

Space frames have also been used in bicycles, such as those designed by Alex Moulton.

## References

1. ^ Tetrasteel. "Space frame structures".
2. ^
3. ^ Alexander Graham Bell (June 1903). "Tetrahedral Principle In Kite Structure". National Geographic Magazine. XIV (6).
4. ^
5. ^
6. ^ Cláudia Estrela Porto (2014). "Stéphane de Chateau's work" (PDF). Architectus. 4 (40): 51–64.
7. ^ Evolution of Space Frames Archived November 19, 2015, at the Wayback Machine. Cities Now
8. ^ Dorothy Harley Eber, via telephone (June 29, 1978). "Fuller on Bell".
9. ^ 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.
10. ^ Cavia Sorret (1993).
11. ^ a b c d Ludvigsen & Colin Chapman, p. 153–154
12. ^ a b c Ludvigsen, Karl (2010). Colin Chapman: Inside the Innovator. Haynes Publishing. pp. 150–164. ISBN 1-84425-413-5.
13. ^ Ludvigsen & Colin Chapman, p. 151