Introduction
The history of space structures may be divided into three stages: ancient space structures, premodern space structures and modern space structures [
1-
6], with the time divisions as 1925 and 1975. In 1925, the first reinforced concrete thin-shell structure with a diameter up to 40 m was built in Jena, Germany. In 1924, the first hemispherical single-layer latticed shell made of steel (pig iron) was built in Zeiss Planetarium, Germany. In 1975, the Pontiac Gymnasium (168 m × 220 m), the first representative air-supported membrane structure, was built in the US. Generally speaking, modern space structures are light and efficient structures developed starting in the 1970s and 1980s on the basis of new technologies and light-weight high-strength materials, such as membranes and steel cables. These structures include air-supported membrane structures, cable-membrane structures, cable truss structures, beam sting structures, suspen-dome structures, cable domes and so forth.
For premodern space structures widely built in the mid-twentieth century (such as thin shells, space trusses, lattice shells and ordinary cable structures), new space structures were developed by the combination of different structural forms and materials, the application of prestressing technology and the innovation of structural concepts and configurations are also ascribed to modern space structures. These modern space structures include composite space trusses, open-web grid structures, polyhedron space frame structures, partial double-layer latticed shells, cable-stayed grid structures, tree-type structures, prestressed segmental steel structures and so forth. Modern space structures are thus shown in two groups (part I and part II) in Fig. 1, covered with oblique lines. Figure 1 also indicates that premodern space structures are still being used.
Basic elements of space structures include rigid elements (such as plate/shell, beam and bar elements) and flexible elements (such as cable and membrane elements). Modern space structures can therefore be divided into modern rigid space structures, modern flexible space structures and modern rigid-flexible combined space structures. This paper provides a review of the structural shapes, characteristics and practical applications of modern long-span space structures in China.
Classification of modern space structures
New types of space structures are constantly emerging, so the traditional method of classification for space structures (Fig. 2) seems inconvenient and unable to cover all space structures. According to the practical space structures that have been constructed in the world, 38 types of space structures can be summarized, and all of these space structures are composed of one type of structural element, or two or three types of structural elements. The basic structural elements include plate/shell, beam, bar, cable and membrane elements. A new method for classification of space structures can therefore be proposed based on the basic structural elements composing the structure (Fig. 3). The advantages of the new method are its practicality and inclusiveness because this classification is related to the calculation method and computer analyses of space structures, and any new space structure can find its position in this classification framework. The framework can also enlighten people to create more and more new space structures.
Plate/shell, beam and bar are rigid elements, while cable and membrane are flexible elements. As shown in Fig. 3, all space structures can be divided into three parts: rigid space structures composed of rigid elements (encircled with solid wireframes in Fig. 3, including 17 types of rigid space structures in seven classes), flexible space structures composed of flexible elements (encircled with dotted wireframes in Fig. 3, including five types in three classes) and rigid-flexible combined space structures composed of flexible elements and rigid elements (encircled with combined solid and dotted wireframes in Fig. 3, including 16 types in seven classes).
Modern space structures have been developed since the 1970s and 1980s (shown with Part I and Part II in Fig. 1). These structures are light, efficient, creative and practical. All these structures can be classified into three groups (17 types in all): modern rigid space (five types), modern flexible space (two types) and modern rigid-flexible combined space structures (ten types). These groups are marked in Fig. 3 with shadow wireframe and will be discussed in this paper.
Application and development of modern rigid space structures
Modern rigid space structures include five types: open-web latticed shell, tree-type, polyhedron space frame, partial double-layer lattice shell and composite space truss structures.
Open-web latticed shell structures
An open-web latticed shell structure is usually composed of beam elements. The open-web latticed shell with a curved surface is a development of the open-web space truss, which evolved from the planar open-web truss [
8]. Most open-web latticed shells are two-way orthogonal or diagonal, and the joints in both upper and bottom chord planes are usually connected with five members. Open-web latticed shells are able not only to improve the structural behavior and reduce material consumption but also to provide enough space for a mechanical floor. Architects prefer the open-web latticed shell as roof structures because of the space for a mechanical floor.
The roof of the National Grand Theater in Beijing (an ellipsoidal shell, with an overall plan size of 146 m × 212 m and a height of 46 m) is the longest span open-web latticed shell in the world. This roof is composed of 144 pieces of radial open-web arches and circumferential steel tubes. According to the calculations, the designer adopted our suggestion to add four groups of large cross bracings in both upper and bottom chord planes to improve the torsion resistance and stability of the structure.
Tree-type structures
Tree-type structures are a new type of pillar support structure composed of multi-level branches. Both the main members and branch members are beam elements, and the joints are rigid. Branch members connect with the roof structure so that the span of the roof and the internal forces of the structure can be effectively reduced.
The lobby of the Shenzhen Cultural Center has a type of three-level tree-type structure with trunks, branches and secondary branches (Fig. 5). In one of the structural schemes for the canopy roof of the Hangzhou Olympic Stadium, the supporting structure has a tree-type structure with two-level branches. The tree-type structure was also used in the Tainan Station of the high-speed railway from Taipei to Gaoxiong.
Polyhedron space frame structures [9]
The polyhedron space frame structure is a completely new structural system. A fundamental cell composition is composed of two 12-sided polyhedron cells and six 14-sided polyhedron cells. The intersecting lines of the polyhedrons over the cutting surfaces are the chord members of the roof and wall structures, while the remaining boundary lines of the polyhedrons are the interior web members (Fig. 7). Only four web members are connected at each interior joint so the polyhedron space frame is especially suited to fill plate structures with a certain height or three dimensional structures with the least members and least nodal joints. Each member in the polyhedron space frame must be a three-dimensional beam element to ensure that the member could bear and transfer the forces from all orientations.
The National Aquatics Center ‘Water Cube’ for the Beijing 2008 Olympic Games was the first polyhedron space frame structure in the world (plane 142 m × 212 m, height 30 m). To make it easy to fix the ETFE cushions, the surface members (chord members) adopt rectangular steel tubes joined with the drum-type welded hollow spherical joints, while the interior members (web members) use circular steel tubes for simplicity joined with normal welded hollow spherical joints. The Water Cube won the one and only Outstanding Structure Award 2010 presented by the International Association for Bridge and Structural Engineering (IABSE).
Partial double-layer lattice shells
Partial double-layer lattice shells are composed of a single-layer lattice shell and a double-layer lattice shell, as well as a combination structure with bar and beam elements. The parts of the structure that mainly resist bending forces are usually designed as double-layer lattice shells, while the parts that mainly resist membrane forces are usually designed as single-layer lattice shells. For a structure that needs to set up a skylight or an air vent, a double-layer lattice shell with a point- type single-layer shell can usually be designed. Spatial trusses may be set up to strengthen a single-layer lattice shell and to form a partial double-layer lattice shell with obvious partitions.
The Tashan Amusement Center in Yantai City (Fig. 9), built in 1992, is a partial double-layer lattice shell with point skylights. Guiping Gymnasium in Guangxi is a partial double-layer lattice shell with the top part as a single-layer lattice shell (Fig. 10). In a scheme for the canopy roof of Hangzhou Olympic Stadium, which looks like a flower with many petals, the petal parts are designed as double-layer lattice shells, while the parts among the petals are designed as single-layer lattice shells (Fig. 11).
Composite space truss structures
Replacing the top chord of a normal steel space truss with a reinforced concrete slab leads to a new type of space structure – the composite space truss, where the upper portion is a reinforced concrete slab and the lower portion is a steel truss. The composite space truss is a type of composite structure composed of bar, beam and plate elements. The composite space truss is suitable for both roofs and floors, as it combines the load bearing and the covering into one function.
In 1980, the first composite space truss was constructed as the canteen roof of Jiahe Coal Mine in Xuzhou (Fig. 12). To date, approximately 60 composite space trusses have been constructed as both roofs and floors of multi-story or high-rise buildings. The composite space truss structure is popular around the world for its various forms, large spans and widespread applications. The composite space truss with the longest span is the roof of Fuzhou Gymnasium in Jiangxi (45.5 m × 58 m). The largest composite space truss for a multi-story building is shown in the story floors of Xinxiang Department Store (Fig. 13, 35 m × 35 m), which is also the first application of the composite space truss in floor structures (four floors in total). The story floors of the Changsha Textile Building (24 m × 27 m) provide an example of the composite space truss used in high-rise buildings, with the size of the column grid up to 10 m × 12 m and 7 m × 12 m. The 6th and 7th floors of the Shanghai International Shopping Center (27 m × 27 m) were designed as prestressed composite space trusses.
Application and development of modern flexible space structures
Modern flexible space structures include air-supported membrane structures and membrane structures with flexible supports.
Air-supported membrane structures
Pneumatic membrane structures include air-inflated membrane structures and air-supported membrane structures. Only the latter is discussed in this paper. The pressure inside the air-supported membrane structure is relatively low (only 1.003 standard atmospheres), so that people can live inside the structure. The types of membrane material (composed of fabric substrate and coating) include mainly PVC and PTFE. The membrane material suitable for use as an air cushion is a type of polymeric material that does not include a fabric substrate such as ETFE (ethylene tetrafluoroethylene). The basic requirements for membrane materials are strength, light transmission, self-cleaning capacity and firing resistance.
During the 1970s and 1980s, over ten large air-supported membrane structures with the span exceeding 100 m were built as the roof of gymnasiums roof in America, Canada and Japan, such as the Pontiac Gymnasium mentioned above and the Tokyo Dome (ellipse 180 m × 180 m) in Japan (1988). In China, an air-supported membrane structure with the overall planned size of 28 m × 36 m was built in the 1970s as a temporary exhibition room north of the Shanghai Exhibition Hall. Another air-supported membrane structure (ellipse, 95 m × 105 m) was built in 2010 as the sand sculpture exhibition hall in the Resonant Sand Gorge of Inner Mongolia (Fig. 14).
Membrane structures with flexible supports
Skeleton-supported membrane structures can be classified into two types: membrane structures with rigid supports and membrane structures with flexible supports. For the latter, the supporting members are mainly steel cables. Membrane structures with flexible supports are flexible space structures composed of cable and membrane elements and are also referred to as tensile membrane structures. The interaction between the membrane and the supporting cables is very obvious, so this effect must be accounted for in the design and analysis of tensile membrane structures. In practical design, membrane structures with flexible supports are usually adopted combined with membrane structures with rigid supports such as beams and arches.
The canopy roof for Weihai Stadium (Fig. 15) is composed of 24 umbrella-like tensile membrane elements, with the overall size of 209 m × 236 m and an inner ring of 143 m × 205 m. The roofing system for the project Expo Axis for Expo Shanghai 2010 is composed of six steel structures named Sun Valley and multi-span continuous tensile cable-membrane structures. The Expo Axis roofing system is the largest tensile membrane structure in the world to date, with a total length of 840 m, the largest span of 97 m and the total covering area of 64000 m2. The supporting system for the membrane involves ridge, valley, edge, suspension, wind suction, and back stay cables and so forth, as well as 19 inner masts, 31 outer masts and 18 supporting points on the sun valleys.
Application and development of rigid-flexible combined space structures
Rigid-flexible combined space structures in abundant variety have become the mainstream of application and development of modern space structures, including ten types: beam string, suspen-dome, composite structures of cable dome and single-layer lattice shell, Tensairity structures, prestressed grid, cable-stayed grid, truss string, prestressed segmental steel, and cable truss structures, as well as cable domes.
Beam string structures
Beam string structures (BSSs) are a type of rigid-flexible combined space structure composed of bottom chord cables, upper chord beams and vertical compressive bars. BSSs were proposed in Japan in the 1990s. A BSS is a type of self-balance structure in which the design state is achieved by tensioning of bottom chord cables. The bracing system should be installed in the roofing system to ensure the out-of-plane stability. The principle of multi-stage tensioning and loading and the principle of multi-stage design should be adopted to obtain the best state of internal forces in the structure under service loading. The nonlinear effect of the structure should be taken into account in the analysis of BSSs. Spatial beam string structures (for example, two-way orthogonal beam string structures) have been developed from planar beam string structures.
The roof for the terminal building of Shanghai Pudong International Airport (Fig. 17) is the first representative beam string structure in China (the longest span is 82.6 m and the longitudinal spacing between string beams is 9 m). The roof for the T2 terminal building of Pudong Airport (Fig. 18, plan size (48+ 89+ 48) × 414 m, longitudinal spacing 9 m) adopts a three-span continuous beam string structure supported by the spatial double-layer Y-shaped columns (column spacing 18 m), which are also the simplest tree-type structure. The roof of the library hall on the Zijingang Campus of Zhejiang University is a type of two-way orthogonal beam string structure. The no-column canopy of Tianjin Railway Station is a five-span beam (coupled beam) string structure (48.5 m × 2+ 41 m+ 42 m+ 39.5 m).
Suspen-dome structures
Suspen-domes are a type of rigid-flexible combined space structure composed of horizontal hoop cables, diagonal cables (cable elements), vertical compressive members (bar elements) and single-layer lattice shell (beam element). The suspen-dome combines the advantages of both lattice shells and cable-domes. Through a reasonable arrangement of prestressing cables, horizontal reactions could be reduced and the stiffness of the structure could be improved. The planform of a suspen-dome is usually round and could sometimes be an ellipse, polygon and rectangle.
Hikarigaoka Dome in Japan, built in 1993, is the first suspen-dome in the world. The hall of the service business center in the Baoshui district of Tianjin is a representative early suspen-dome in China. Changzhou Gymnasium (ellipse 80 m × 120 m) and Beijing Polytechnic University Gymnasium (round 93 m) were built in 2007 and 2008, respectively. Jinan Olympic Gymnasium (round 122 m), built in 2009, adopted a suspen-dome with the longest span in the world (Fig. 19). The no-column canopy for Shenzhen North Railway Station built in 2010 adopted a two-way multi-span continuous cylindrical lattice shell with a column grid of 28 m × 43 m and covering area of 68000 m2, the first suspended cylindrical lattice shell with rectangular planform in the world.
Composite structures of a cable dome and a single-layer lattice shell
Composite structures of a cable dome and a single-layer lattice shell (Fig. 21), a new space structure proposed by Chinese scholars, are rigid-flexible combined space structures composed of bar, beam and cable elements. The single-layer lattice shell could be installed on the self-balance system without the full scaffolding system. The rigid roofing material could be employed on the single-layer lattice shell instead of the membrane on the cable domes, so this new structure has wider application than cable domes.
A model test of the composite structure of a cable dome and a single-layer lattice shell (diameter 5 m) was carried out in Zhejiang University (Fig. 22) [
15], and this new structure system has also been studied in Ref. [
16]. A composite structure of a cable dome and a single-layer lattice shell was one of the design schemes of the Jinan Olympic Gymnasium for the National Games, but the suspen-dome scheme was finally adopted.
Tensairity
Tensairity (Tension+ air+ integrity) is a new space structure created by replacing the vertical bar in the beam string structure with the air-rib. Tensairity is composed of three types of elements: beam, cable and membrane elements. Tensairity was first reported at the IASS France Symposium in 2004. The garage of Montreux Station in Switzerland was the first practical use of a Tensairity structure (Fig. 24) [
18]. A Tensairity structure was also adopted for a bridge in France. A Tensairity structure has not been built in China to date, and research is being carried out on its design theory, analysis method, construction measures and application prospects.
Prestressed grid structures
Combining prestressing technology with space grid structures (including space trusses and lattice shells) leads to prestressed grid structures, composed of bar and cable elements. Prestressing cables are usually installed on or below the bottom chord plane of space trusses or at the perimeter of lattice shells. The application of prestressing technology can improve the structural behavior of space grids and reduce the material consumption. In general, the steel consumption in prestressed grid structures could be reduced by approximately 25%.
Qingyuan Gymnasium, with a hexagon planform (length of diagonal up to 93.6 m), was built in 1994. The roof is a combination of six unisymmetrical double-layer twist lattice shells supported on six columns, and six prestressing cables are installed along the perimeter of the lattice shell (Fig. 25). The roof of Panzhihua Gymnasium (octagonal planform 74.8 m × 74.8 m) is a double-layer spherical lattice shell, where eight trusses are designed between adjacent supports and the bottom chords of the trusses adopt prestressing cables instead of steel bars (Fig. 26). The floor structures of the 6th and 7th floor of the Shanghai International Shopping Center adopt prestressed composite space trusses, with four prestressing cables installed at a plane 20 cm below the bottom chord plane. The roof of Gaoyao Gymnasium (54.9 m × 69.3 m) is a combination of four double-layer twist lattice shells supported on four columns (at the middle of each edge), and four prestressing cables are installed between the columns.
Cable-stayed grid structures
Introducing the concept of stay cables in cable-stayed bridges into space grid structures (including space trusses and lattice shells) leads to a new rigid-flexible combined space structure – a cable-stayed grid structure composed of bar and cable elements. By installing several stay cables on space trusses or lattice shells, the span of the structure is reduced, and the stiffness is improved. Stay cables could also be pre-tensioned to optimize the member stresses and to reduce the material consumption. Cables should be arranged in multiple directions, and cables should not be relaxed under arbitrary conditions of loading.
Six pieces of cable-stayed space trusses were built for the warehouse of the Port of Singapore Authority (PAS) in 1993 (Fig. 27). Four belonged to type A with plan dimensions of 120 m × 96 m and six towers, and the other two belonged to type B with plan dimensions of 96 m × 70 m and four towers. Jiuguan Tollhouse of the Taijiu express highway in Shanxi province adopted a cable-stayed double-layer latticed shell (14 m × 65 m) with a single tower (Fig. 28). The roof for the main stadium of Gragon Sports Center in Hangzhou is a cable-stayed double-layer lattice shell with two towers (Fig. 29), and 18 stability cables were installed on the upper chord plane of the lattice shell to resist the upward wind loading. The roof for the sports center of Zhejiang University (Zijingang campus) is a single-layer lattice shell suspended by a cable-stayed cable net (Fig. 30).
Truss string structures
Substituting upper chord beams in beam string structures (BSSs) with trusses leads to truss string structures (TSSs). A TSS is composed of bar and cable elements. The truss in a TSS may be designed as planar or spatial, and, for both types, the bracing system should be installed to ensure the out-of-plane stability of the TSS.
The representative projects of TSSs include the following: the spatial truss string structure for the roof of Guangzhou International Convention and Exhibition center (Fig. 31, span 126.6 m, 2002), spatial truss string structure for the canopy of Beijing North Railway Station (span 107 m, longitudinal spacing 20 m, covering area 70,000 m2, 2007), two-way orthogonal truss (planar truss) string structure for the roof of National Gymnasium for the Beijing Olympic Games (Fig. 32, 2008), the two-way TSS with the longest span in the world.
Prestressed segmental steel structures
A prestressed segmental steel structure, a patented technology developed by Chinese engineers and researchers, is composed of prefabricated arch sheets, horizontal tie members, joint bodies as diaphragms with crossing tie rods, and a panel of lattice arch composed of two pieces of arch sheets, horizontal tie members at upper and lower chord planes and two pieces of joint bodies (Fig. 33). Arch sheets and joint bodies are usually prefabricated off-site and then assembled with segments on the ground on-site. Crossing tie rods are used as connecting bars between nearby panels during installation, and the prestress is also introduced into the structure through these tie rods. Long-span structures can be assembled from small (light) components without the use of large hoisting facilities, so the construction of prestressed segmental steel structures is easy and fast. A prestressed segmental steel structure is also a type of rigid-flexible combined space structure composed of bar and cable elements.
Prestressed segmental steel structures were used to build small hangars in the early stages. The roof for the indoor tennis court at Diaoyutai State Guesthouse built in 1994 has a prestressed segmental steel structure composed of three pieces of cylindrical lattice shells, where the middle piece can be opened (Fig. 34). The water paradise for Beijing Hot Spring Leisure City built in 2005 has a similar structure with a retractable roof. Generally speaking, prestressed segmental steel structures (with maximum span approximately 130 m) can be used widely in either permanent buildings or temporary buildings, as they can be built or disassembled easily.
Cable truss structures
Cable truss structures are a type of space structure composed of double-layer cables and vertical bars (Fig. 35). The concave (bending-down) cables and the convex (bending-up) cables are referred to as load-bearing cables and stability cables, respectively, while the vertical bars between the cables are compressive web members. When load-bearing cables (or stability cables) are prestressed, the structure becomes self-balancing. Cable truss structures can generally be used to build long span structures with rectangular, round or toroidal planforms.
Cable truss structures have been widely used in China. The roof for Jilin Skating Hall (span 59 m) adopted cable trusses in which the upper cable and the lower cable are offset (1986, Fig. 36) [
19]. Foshan Century Lotus Stadium (outer and inner diameters 310 m and 125 m) has a folded-plate-type cable truss structure with a toroidal plan supported on a toroidal truss (Fig. 37). Baoan Stadium for Shenzhen Universiade (2010) has a cable truss structure with an elliptic plan (230 m × 237 m). A box-section ringbeam and tubular flying columns are arranged at the outer and inner rings of the roof, respectively, and the roofing has membrane material supported on small arch beams. Yueqing Stadium in Zhejiang province has a cable truss structure with a crescent plan (229 m × 221 m, Fig. 39). The model test has been finished, and the installation started in 2011.
Cable domes
Cable domes, a type of rigid-flexible combined space structure that is more flexible, are composed mainly of cable, as well as bar and membrane elements. A cable dome fully realizes Fuller’s idea that islands of compression reside in a sea of tension. A cable dome is a structure with high efficiency and is usually regarded as the climax of modern space structures. The Comprehensive Gymnasium of the Seoul Olympic Games, designed by American engineer Geiger in 1986, is the first cable dome in the world (Fig. 40). The Geiger dome is composed of ridge cables, valley cables, stay cables, bottom chord ring cables (hoop cables), vertical struts (masts), outer ringbeams, inner rings and membrane roofing (Fig. 41).
Many studies have been carried out on cable domes in China. Some new types of cable domes have been proposed, including a Kiewitt cable dome, type I composite cable dome (composite structure of Geiger and Levy domes), type II composite cable dome (composite structure of Kiewitt and Levy domes), and bird-nest cable dome. A quick calculation method for Geiger and Levy domes, as well as a double singular value decomposition method, has been established. Using this quick calculation method, self-stress modes of cable domes can be obtained. These studies enhance the analysis method of prestress design of cable domes. The practical application of cable domes in China is just beginning. The atrium of the factory building of the Jinhua Shengyuan Group built in 2009 adopted the first cable dome in China (Fig. 42). Another cable dome with a diameter of 72 m was built in 2010 as the roof of Yijinhuoluo Gymnasium in Ordos (Fig. 43).
Conclusions
(1) Modern space structures have been developed since the 1970s and 1980s, both in China and internationally. After approximately 30 years of rapid development, modern space structures have become widely used in China in sports buildings, convention and exhibition halls, theaters, terminal buildings, railway stations, industrial buildings, warehouses and so forth.
(2) Modern long-span space structures have two groups. The first part consists of structures developed based on light-weight high-strength materials such as membranes and steel cables, including air-supported membrane, cable-membrane, cable truss, and beam string structures, suspend-domes, cable domes and so forth. The other part consists of structures developed by the combination of different structural forms and materials, the application of prestressing technology and the innovation of structural concepts and configurations, including composite space trusses, cable-stayed grid structures, prestressed grid structures, polyhedron space frame structures and so forth.
(3) According to the classification of space structures according to the basic elements (including three types of rigid elements (plate/shell, beam and bar elements)) and two types of flexible elements (cable and membrane elements), modern space structures can be divided into modern rigid space structures, modern flexible space structures and modern rigid-flexible combined space structures. This paper provides a review of their application and development in China.
(4) The modern long-span space structures discussed in this paper are structures with promotional value and application prospects. Further development is still needed to improve the design and construction technology of these structures. Seventeen types of modern space structures now exist. More and more new types of modern space structures will be developed in the future.
(5) China has won several ‘first in the world’ awards for long-span structures, such as the earliest application of new space structures, the longest span of space structures, the largest quantity of space structures, the largest covering area of space structures and so forth. China has become a country with many large space structures. Continued efforts should be paid to make China develop into a country that leads the field in innovative modern space structures.
Higher Education Press and Springer-Verlag Berlin Heidelberg
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