Spoke type cable truss structure with synergic stress of cable and membrane

The spoke-type cable truss structure, which utilizes cable-membrane synergy, solves the problem of insufficient adaptability of traditional spoke-type cable trusses in complex folded buildings. It achieves precise adaptation to the building's shape and optimization of stress, reduces material and construction costs, and improves structural stability and design flexibility.

CN120889347APending Publication Date: 2025-11-04SHANGHAI ARCHITECTURAL DESIGN & RES INST
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Patent Information

Application Number
CN202511265601.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-09-05
Publication Date
2025-11-04

AI Technical Summary

Technical Problem

Traditional spoke-type cable truss structures are difficult to adapt to the shape of buildings with complex folded surfaces, resulting in low structural efficiency, high material consumption, and high construction difficulty. In addition, the membrane material has a single function and cannot participate in stress optimization.

Method used

A spoke-type cable truss structure with cable-membrane synergy is designed. By setting cable-membrane units and cable truss units in the circumferential direction, the membrane ridge cable and membrane valley cable form a membrane skeleton, the folded membrane is laid on top, the radial cable and connecting rod form a triangle, and the suspension cable connects the membrane ridge cable and radial cable to form a tensioned cable-membrane structure, so as to realize the synergy of cable and membrane.

Benefits of technology

It achieves precise adaptation to complex building shapes, optimizes stress distribution, reduces the use of cables, lowers material costs and construction difficulty, while enhancing structural stability and design flexibility to meet more diverse building needs.

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Abstract

The invention provides a spoke type cable truss structure with a cable and a membrane cooperatively stressed. The spoke type cable truss structure comprises an upper inner pressing ring beam, a lower inner pressing ring beam, an outer pressing ring structure, a cable and membrane unit and a plurality of cable truss units distributed in the annular direction. Wherein each cable membrane unit comprises a plurality of folding surface membranes, a plurality of membrane ridge cables and a plurality of membrane valley cables, the membrane ridge cables and the membrane valley cables are alternately distributed, every two adjacent membrane ridge cables and the membrane valley cable located between every two adjacent membrane ridge cables are distributed in a V shape and form a membrane covering framework, and the folding surface membranes are laid on the membrane covering framework to form a tension cable membrane structure; each cable truss unit comprises a radial cable, a connecting rod and a plurality of suspension cables, the two ends of each radial cable are connected with the outer pressing ring structure and the lower inner pressing ring beam, the two ends of each connecting rod are connected with the upper inner pressing ring beam and the lower inner pressing ring beam, a triangle is defined by the membrane valley cables, the connecting rods and the radial cables, and the two ends of each suspension cable are connected with the membrane ridge cables and the radial cables. According to the invention, not only can complex folding surface geometric modeling be accurately adapted and the aesthetic property of the building be improved, but also the stress distribution is optimized through the synergistic effect of the cable and the film.
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Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of architectural structure design, and in particular to a spoke cable truss structure with cable membrane collaborative force. BACKGROUND

[0002] Traditional spoke cable truss structures are widely used in large-span buildings such as stadiums and exhibition centers due to their light weight, high efficiency and ability to span large spaces. The typical features are:

[0003] 1. Geometric modeling adaptability: through the collaborative action of the central radial cable truss and the ring cable, a regular circular, elliptical or saddle-shaped roof is formed, such as the Shenzhen Bao'an Stadium;

[0004] 2. Force system: the cable truss independently bears the roof load (self weight, wind load, snow load, etc.), and the building membrane above is used as an enclosure structure, with the membrane only transmitting wind pressure and not participating in the overall force;

[0005] 3. Technical advantages: the structure stiffness is improved through prestressed tensioning, and the construction is convenient.

[0006] However, with the development of complex folded surfaces (such as origami geometry, free-form surfaces) in architectural modeling, traditional spoke cable trusses face the following challenges:

[0007] 1. Insufficient geometric adaptability:

[0008] The radial grid of the traditional spoke cable truss is difficult to match the folded surface geometry (such as fold line turning, asymmetric curvature), resulting in the structure not being able to conform to the architectural shape. For example, the height difference between adjacent folds in the folded surface may force the cable truss to bend locally or concentrate stress, reducing the efficiency of the structure;

[0009] 2. Deterioration of force performance:

[0010] The introduction of complex load transmission paths in folded surface modeling makes it difficult for the ring cable and radial cable system of the traditional cable truss to evenly distribute the load. For example, the turning of the folded surface may cause the main cable tension to exceed the limit due to uneven cable force, requiring additional support members, increasing material consumption and construction difficulty;

[0011] 3. Single function of membrane:

[0012] The membrane only serves as an enclosure structure and cannot compensate for the structural deformation caused by the folded surface modeling through pretension adjustment, resulting in insufficient overall stiffness of the roof, which requires increasing the cable section or densifying the support nodes, reducing the economic efficiency.

[0013] Therefore, there is an urgent need for a spoke cable truss with cable membrane collaborative force, which enables the spoke cable truss structure to adapt to and fully utilize the folded surface modeling features of the building, achieving collaborative optimization of the structure and modeling, and improving overall performance and economic efficiency. SUMMARY

[0014] The present application aims to provide a spoke cable structure with membrane force to overcome the problem of poor adaptability of traditional spoke cable structures in complex folded surface modeling buildings.

[0015] In order to achieve the above-mentioned purpose, the present application provides a spoke cable structure with membrane force, comprising an upper internal pressure ring beam, a lower internal pressure ring beam, an external pressure ring structure, a membrane unit and a plurality of cable truss units distributed along the ring, the upper internal pressure ring beam is located above the lower internal pressure ring beam; wherein,

[0016] The membrane unit is arranged between the upper internal pressure ring beam and the external pressure ring structure along the ring, the membrane unit comprises a plurality of folded surface membranes and a plurality of membrane ridge cables and membrane valley cables alternately distributed along the ring, both ends of the membrane ridge cable and the membrane valley cable are connected with the external pressure ring structure and the upper internal pressure ring beam respectively, the membrane ridge cable is higher than the membrane valley cable, the adjacent two membrane ridge cables and the membrane valley cable located between the adjacent two membrane ridge cables are V-shapedly distributed and form a membrane covering framework, the folded surface membrane is laid on the membrane covering framework to form a tensioned cable membrane structure;

[0017] The cable truss unit comprises a radial cable, a connecting rod and a plurality of suspension cables, both ends of the radial cable are connected with the external pressure ring structure and the lower internal pressure ring beam respectively, both ends of the connecting rod are connected with the upper internal pressure ring beam and the lower internal pressure ring beam respectively, the membrane valley cable, the connecting rod and the radial cable enclose a triangle, both ends of the suspension cable are connected with the membrane ridge cable and the radial cable respectively.

[0018] Optionally, the suspension cable, the membrane valley cable, the connecting rod and the radial cable are located in the same plane.

[0019] Optionally, the suspension cables are uniformly distributed along the extension direction of the radial cable.

[0020] Optionally, the external pressure ring structure is spliced by a plurality of folded plate truss units along the ring, and the folded plate truss units are arranged obliquely or vertically.

[0021] Optionally, the folded plate truss unit comprises a main beam component, a structural outer column, two structural inner columns and a plurality of column web members, the main beam components of all the folded plate truss units are spliced along the ring to form an external pressure ring beam, the structural outer column and the two structural inner columns are parallel to each other, the structural outer column is located on the outer side of the external pressure ring beam and is connected with the external pressure ring beam through the column web members, the structural inner columns are connected with the external pressure ring beam perpendicularly; wherein,

[0022] Two ends of the membrane ridge cords are respectively connected to top ends of the two inner columns, and one end of the membrane valley cord and the radial cord is respectively connected to the outer compression ring beam.

[0023] Optionally, a plurality of connecting rods are arranged between the two inner columns.

[0024] Optionally, a plurality of membrane ridge cords, a plurality of membrane valley cords and the folded membrane are arranged between the two adjacent cable truss units.

[0025] Optionally, the membrane valley cords and the membrane ridge cords are arranged in a radial manner.

[0026] Optionally, the material of the folded membrane is PVC membrane, PTEF membrane or ETFE membrane.

[0027] Optionally, the upper inner compression ring beam and the lower inner compression ring beam are both ring cable structures.

[0028] The present application provides a spoke type cable truss structure with collaborative force of cable and membrane, which has at least one of the following beneficial effects:

[0029] 1) Compared with the traditional spoke type cable truss structure system, the present application can not only precisely adapt to complex folded surface geometric modeling and improve the building appearance, but also optimize the stress distribution through the collaborative action of cable and membrane, effectively reduce the use of cable material, and reduce the material cost and construction difficulty.

[0030] 2) In the design of the traditional spoke type cable truss structure, the main structure and the modeling of the membrane system are designed separately, the membrane structure is only used as a load, and does not provide stiffness to the structure itself, and the membrane structure does not directly participate in the stress of the main structure. The spoke type cable truss structure with collaborative force of cable and membrane designed by the present application breaks through the limitation of membrane material as a containment component in the traditional structure, realizes the high integration of structure and building shape, and optimizes the overall performance.

[0031] 3) The spoke type cable truss structure with collaborative force of cable and membrane ensures the stability and bearing capacity of the structure, enhances the flexibility of the design, and can be widely applied to the fields of large-span buildings, special-shaped space structures and the like, and has significant technical advantages and application prospect.

[0032] 4) Unlike the traditional folded plate truss which is mostly used to span large space and serve as horizontal member, the folded plate truss unit of the present application can provide support in vertical direction, adapting to more diversified architectural requirements. The folded plate truss unit can not only serve as the outer ring structure, but also jointly bear force with the inner ring of other structural types, balancing the radial cable force. Compared with the traditional outer pressure ring beam, the design of the closed ring of the folded plate truss unit greatly enhances the lateral resistance of the structure, improving the safety and stability under wind load and seismic action. In addition, the folded plate truss unit in the present application can better fit the architectural folded surface modeling, providing more flexible architectural form, with higher adaptability and plasticity. BRIEF DESCRIPTION OF DRAWINGS

[0033] Those skilled in the art will understand that the drawings provided for a better understanding of the present application, and do not constitute any limitation on the scope of the present application. Among them:

[0034] Figure 1 The three-dimensional schematic diagram of the spoke type cable truss structure of the cable membrane cooperative force provided by an embodiment of the present application is provided;

[0035] Figure 2 The perspective view of the spoke type cable truss structure of the cable membrane cooperative force provided by an embodiment of the present application is provided;

[0036] Figure 3 The cross-sectional view of the spoke type cable truss structure provided by an embodiment of the present application is provided;

[0037] Figure 4 The structural schematic diagram of the cable truss unit provided by an embodiment of the present application is provided;

[0038] Figure 5 The arrangement schematic diagram of the folded surface membrane provided by an embodiment of the present application is provided.

[0039] Among them:

[0040] 100-Upper inner pressure ring beam; 200-Lower inner pressure ring beam; 300-Outer pressure ring structure; 310-Folded plate truss unit; 311-Master beam member; 312-Structural outer column; 313-Structural inner column; 314-Column web member; 315-Connecting rod; 410-Radial cable; 420-Connecting rod; 430-Suspension cable; 500-Cable membrane unit; 510-Folded surface membrane; 520-Membrane ridge cable; 530-Membrane valley cable. DETAILED DESCRIPTION

[0041] In order to make the objects, advantages and features of the present application more clearly, the following further describes the present application in detail with reference to the accompanying drawings and specific embodiments. It should be noted that the drawings are very simplified and not drawn in proportion, and are only used to facilitate and clarify the purpose of describing the embodiments of the present application. In addition, the structures shown in the drawings are often part of the actual structures. In particular, different scales are sometimes used to show the different emphasis of each drawing.

[0042] As used in the present application, the singular forms "a," "an," and "the" include plural referents unless the content clearly dictates otherwise. As used in the present application, the term "or" is generally employed in its sense of "and / or" unless the content clearly dictates otherwise. As used in the present application, the term "several" is generally employed in its sense of "at least one" unless the content clearly dictates otherwise. As used in the present application, the term "at least two" is generally employed in its sense of "two or more" unless the content clearly dictates otherwise. In addition, the terms "first," "second," "third," are only used for the purpose of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, the features defined with "first," "second," "third" can explicitly or implicitly include one or at least two features.

[0043] Please refer to Figures 1-5 The embodiment provides a spoke cable-strut structure cooperatively stressed by cables and membranes, comprising an upper internal pressure ring beam 100, a lower internal pressure ring beam 200, an external pressure ring structure 300, a cable and membrane unit, and a plurality of cable-strut units distributed along the ring, the upper internal pressure ring beam 100 is located above the lower internal pressure ring beam 200; wherein

[0044] The cable and membrane unit 500 is arranged between the upper internal pressure ring beam 100 and the external pressure ring structure 300 along the ring, the cable and membrane unit 500 comprises a plurality of folded surface membranes 510 and a plurality of membrane ridge cables 520 and membrane valley cables 530 alternately distributed along the ring, the two ends of the membrane ridge cable 520 and the membrane valley cable 530 are connected with the external pressure ring structure 300 and the upper internal pressure ring beam 100 respectively, the membrane ridge cable 520 is higher than the membrane valley cable 530, the adjacent two membrane ridge cables 520 and the membrane valley cable 530 located between the adjacent two membrane ridge cables 520 are V-shapedly distributed and form a membrane covering framework, and the folded surface membrane 510 is laid on the membrane covering framework to form a tensioned cable and membrane structure.

[0045] The cable-strut unit comprises a radial cable 410, a connecting rod 420, and a plurality of suspension cables 430, the two ends of the radial cable 410 are connected with the external pressure ring structure 300 and the lower internal pressure ring beam 200 respectively, the membrane valley cable 530, the connecting rod 420, and the radial cable 410 enclose a triangle, and the two ends of the suspension cable 430 are connected with the membrane ridge cable 520 and the radial cable 410 respectively.

[0046] Compared with the traditional spoke cable-strut structure system, the present application can not only precisely adapt to complex folded surface geometric modeling and improve the building aesthetics, but also optimize the stress distribution through the synergy of cables and membranes, effectively reduce the use of cable materials, and reduce the material cost and construction difficulty. In addition, the spoke cable-strut structure system with cable-membrane synergistic stress not only ensures the stability and bearing capacity of the structure, but also enhances the flexibility of the design, which can be widely used in the fields of large-span buildings, special-shaped space structures and the like, and has significant technical advantages and application prospects.

[0047] Specifically, the membrane valley cable 530 and the membrane ridge cable 520 are arranged between the inner pressure ring beam and the outer pressure ring structure 300 to form a membrane covering framework, and the folded surface membrane 510 is laid on the membrane covering framework to form a tensioned cable membrane structure, directly outlining the building "paper folding" modeling, the stress form is the building shape, achieving a light and transparent building effect. In addition, after the folded surface membrane 510 is laid on the membrane covering framework, a V-shaped drainage ditch can be formed at the membrane valley cable 530, so that rainwater can be directly drained from the roof high area to the outer ring low area, without the need to set a drainage pipe below the roof range, which not only solves the problem of roof drainage, but also ensures better building effect.

[0048] In this embodiment, the spoke cable-strut structure with cable-membrane synergistic stress is similar to a saddle shape, and the cable-strut units are uniformly distributed along the ring direction.

[0049] In this embodiment, a plurality of membrane ridge cables 520 and a plurality of membrane valley cables 530 are separately arranged between the two adjacent cable-strut units. It should be noted that the two adjacent folded plate truss units 310 usually have a certain spacing, so that the area can be separately provided with a plurality of membrane ridge cables 520, a plurality of membrane valley cables 530 and a folded surface membrane 510 laid thereon. The adjacent membrane ridge cables 520 and the plurality of membrane valley cables 530 are distributed in a V shape and form a membrane covering framework to form a tensioned cable membrane structure with overall stress.

[0050] Preferably, the suspension cables 430 are uniformly distributed along the extension direction of the radial cables 410. In this embodiment, the suspension cables 430 are arranged vertically, and the two ends thereof are connected with the membrane ridge cables 520 and the radial cables 410, respectively. The suspension cables 430, the membrane valley cables 530, the connecting rods 420 and the radial cables 410 are located in the same plane.

[0051] In this embodiment, the membrane valley cables 530 and the membrane ridge cables 520 are arranged in a radial manner.

[0052] Preferably, the upper and lower inner compression ring beams 100 and 200 are both ring cable structures, and a double-layer ring cable + radial cable 410 is arranged on the inner side, so that the entire roof top stress is a full tension system, the overall stiffness is formed, the stress of the upper layer cable membrane system itself is fully utilized, and the stress of the upper layer main cable is reduced to the minimum. In addition, each tensioning member can be made of lighter and stronger material to realize large-span cantilever, thereby reducing material cost and construction difficulty.

[0053] In the embodiment, the material of the folded film 510 is glass fiber. Generally, the film material used in the building film structure can be roughly divided into PVC film, PTEF film and ETFE film according to different coating materials. The correct selection of the film material should consider the size, purpose, form, service life and budget of the building and other comprehensive factors. PVC film is cheaper than PTFE film in material and processing, and has the advantages of soft material and easy construction, but is poorer than PTFE film in strength, service life and fire resistance. PTFE film is a material coated with polytetrafluoroethylene resin on ultra-fine glass fiber fabric. The biggest feature of PTFE film is high durability, fire resistance and stain resistance. ETFE is the strongest fluoroplastic. It has greatly improved radiation resistance and mechanical properties while maintaining the good heat resistance, chemical resistance and electrical insulation properties of PTFE. The tensile strength can reach 50 MPa, which is nearly twice that of polytetrafluoroethylene.

[0054] Preferably, the outer compression ring structure 300 is spliced along the ring direction by a plurality of folded plate truss units 310, and the folded plate truss units 310 are arranged in an inclined or vertical manner. Unlike the traditional folded plate truss which is mainly used for spanning large spaces and serving as a horizontal component, the folded plate truss unit 310 of the present application can provide support in the vertical direction, adapting to more diversified building requirements. Specifically, in the embodiment, the folded plate truss unit 310 can not only serve as an outer ring structure, but also jointly bear stress with other structural types of inner rings to balance the radial cable force. Compared with the traditional outer compression ring beam, the design of the closed ring of the folded plate truss unit 310 greatly enhances the lateral resistance of the structure and improves the safety and stability under wind load and seismic action. In addition, the folded plate truss unit 310 can better fit the folded surface modeling of the building, provide more flexible building forms, and have higher adaptability and plasticity.

[0055] At the same time, the folded plate truss unit 310 adopts a factory unitized assembly method, which can greatly simplify the construction process, reduce the on-site construction difficulty, improve the construction efficiency and reduce the construction cost. The reasonable design of the folded plate truss can also use smaller cross-sectional size, thereby saving materials and reducing the self-weight of the structure, improving the utilization rate of materials and the overall structural efficiency.

[0056] Specifically, please refer to Figure 4 , and in combination with Figure 3The folded plate truss unit 310 comprises a main beam component 311, a structural outer column 312, two structural inner columns 313 and a plurality of column web members 314, the main beam components 311 of all the folded plate truss units 310 are spliced along the ring direction to form an outer pressure ring beam, the structural outer column 312 is parallel to the two structural inner columns 313, the structural outer column 312 is located on the outer side of the outer pressure ring beam and is connected to the outer pressure ring beam through the column web members 314, and the structural inner columns 313 are connected to the outer pressure ring beam perpendicularly.

[0057] One end of each of the two adjacent membrane ridge cords 520 is connected to the top end of the two structural inner columns 313, and one end of each of the membrane valley cords 530 and the radial cords 410 is connected to the outer pressure ring beam.

[0058] In the embodiment, the outer pressure ring beam can be pre-formed as an integral component by splicing the main beam components 311 along the ring direction, the structural inner columns 313 can be cut off at the joint with the outer pressure ring beam, and then welded to the outer pressure ring beam for connection and fixation.

[0059] In addition, the number and distribution of the column web members 314 are not limited in the embodiment and can be designed according to the construction requirements.

[0060] Preferably, a plurality of tie rods 315 are arranged between the two structural inner columns 313 for providing lateral restraint to the two structural inner columns 313 and enhancing the overall stability of the folded plate truss unit 310. The number and distribution of the tie rods 315 are not limited in the embodiment and can be designed according to the construction requirements.

[0061] In summary, the embodiment of the present application provides a spoke-type cable truss structure with collaborative force bearing of cable and membrane. Compared with the traditional spoke-type cable truss structure system, the present application can not only accurately adapt to complex folded surface geometric modeling and improve the architectural aesthetics, but also optimize the stress distribution through the collaborative action of cable and membrane, effectively reduce the use of cable material, and reduce the material cost and construction difficulty. In addition, the spoke-type cable truss structure system with collaborative force bearing of cable and membrane provided by the present application enhances the design flexibility under the premise of ensuring the structural stability and bearing capacity, and can be widely applied in the fields of large-span buildings, special-shaped space structures and the like, and has significant technical advantages and application prospects.

[0062] The above is only the preferred embodiment of the present application, and does not limit the present application in any way. Any person skilled in the art can make any form of equivalent replacement, modification or change to the technical solutions and technical contents disclosed in the present application without departing from the scope of the technical solutions of the present application, which still falls within the protection scope of the present application.

Claims

1. A spoke-type cable truss structure with cable-membrane co-supporting force, characterized in that, It includes an upper inner pressure ring beam, a lower inner pressure ring beam, an outer pressure ring structure, a cable membrane unit, and several cable truss units distributed along the circumferential direction, wherein the upper inner pressure ring beam is located above the lower inner pressure ring beam; wherein, The cable-membrane unit is arranged circumferentially between the upper inner tension ring beam and the outer pressure ring structure. The cable-membrane unit includes several folded membranes and several membrane ridge cables and membrane valley cables that are alternately distributed circumferentially. The two ends of the membrane ridge cables and the membrane valley cables are respectively connected to the outer pressure ring structure and the upper inner pressure ring beam. The membrane ridge cables are higher than the membrane valley cables. Two adjacent membrane ridge cables and the membrane valley cables located between the two adjacent membrane ridge cables are distributed in a V-shape and form a membrane frame. The folded membranes are laid on the membrane frame to form a tension cable membrane structure. The cable truss unit includes radial cables, connecting rods, and several suspension cables. The two ends of the radial cables are connected to the outer pressure ring structure and the lower inner pressure ring beam, respectively. The two ends of the connecting rods are connected to the upper inner pressure ring beam and the lower inner pressure ring beam, respectively. The membrane valley cable, the connecting rods, and the radial cables form a triangle. The two ends of the suspension cables are connected to the membrane ridge cable and the radial cables, respectively.

2. The spoke-type cable truss structure with cable-membrane cooperative stress as described in claim 1, characterized in that, The suspension cable, the membrane valley cable, the connecting rod, and the radial cable are located in the same plane.

3. The spoke-type cable truss structure with cable-membrane cooperative stress as described in claim 2, characterized in that, The suspension cables are evenly distributed along the extension direction of the radial cables.

4. The spoke-type cable truss structure with cable-membrane cooperative stress as described in claim 1, characterized in that, The outer pressure ring structure is composed of several folded plate truss units spliced ​​together along the circumferential direction, and the folded plate truss units are arranged at an angle or vertically.

5. The spoke-type cable truss structure with cable-membrane cooperative stress as described in claim 4, characterized in that, The folded plate truss unit includes main beam members, external structural columns, two internal structural columns, and several column web members. All the main beam members of the folded plate truss unit are spliced ​​circumferentially to form an external pressure ring beam. The external structural columns are parallel to the two internal structural columns, located outside the external pressure ring beam and connected to it via the column web members. The internal structural columns are perpendicularly connected to the external pressure ring beam. One end of each of the two adjacent membrane spine cables is connected to the top of the two inner columns of the structure, and one end of the membrane valley cable and the radial cable are connected to the outer pressure ring beam.

6. The spoke-type cable truss structure with cable-membrane cooperative stress as described in claim 5, characterized in that, Several connecting rods are also installed between the two structural internal columns.

7. The spoke-type cable truss structure with cable-membrane cooperative stress as described in claim 1, characterized in that, Several membrane ridge cables, several membrane valley cables, and a folded membrane are separately provided between two adjacent cable truss units.

8. The spoke-type cable truss structure with cable-membrane cooperative stress as described in claim 1, characterized in that, Both the membrane valley cord and the membrane ridge cord are arranged radially.

9. The spoke-type cable truss structure with cable-membrane cooperative stress as described in claim 1, characterized in that, The folding mask is made of PVC film, PTEF film or ETFE film.

10. The spoke-type cable truss structure with cable-membrane cooperative stress as described in claim 1, characterized in that, Both the upper inner pressure ring beam and the lower inner pressure ring beam are ring cable structures.