Two-span continuous stiff overhanging large-span roof structure adopting direct tensioning technology

By adopting direct tensioning technology and fish belly plane main truss in large-span roof structures, combined with stable cable system and anchor head tensioning mechanism, the problems of roof structure adaptability and construction complexity in the existing technology are solved, and the effect of lightweight materials, simplified construction and reduced construction cost is achieved.

CN119956915APending Publication Date: 2025-05-09CHINA ARCHITECTURE DESIGN & RES GRP CO LTD
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Patent Information

Application Number
CN202510350315.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-03-24
Publication Date
2025-05-09

AI Technical Summary

Technical Problem

The existing large-span roof structure system using rigid overhanging components has limitations in adapting to a variety of roof shapes and architectural effects, and is complex in construction and high in construction.

Method used

A two-span continuous stiffness overhanging large-span roof structure is designed using direct tensioning technology, including a fish belly-shaped plane main truss, two-span continuous stiffness overhanging beams, end wall columns and conical columns. The chord on the main truss is directly tensioned through the anchor head tensioning mechanism, and a stable cable system is used to provide lateral constraints.

Benefits of technology

It realizes a roof structure suitable for a variety of flexible space layout methods, with a light appearance, material saving, simplifying construction processes, reducing process cost, and effectively controlling the off-surface stability of plane trusses caused by compressed areas and compressive stress.

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Abstract

The invention relates to a two-span continuous stiff overhanging large-span roof structure adopting a direct tensioning technology. The two-span continuous stiff overhanging large-span roof structure comprises a main truss, two-span continuous stiff overhanging beams, end wall columns, conical columns and anchor head tensioning mechanisms. The main truss is arranged in the middle of the two-span continuous overhanging beam; the two ends of the main truss in the length direction are connected to the tops of the end wall columns on the two sides, and the main truss is configured as a middle support of the two-span continuous stiff overhanging beam. The main truss is a fish-belly-shaped plane main truss and is provided with an upper chord member and a lower chord member; the conical columns are arranged at the two ends of the two-span continuous stiff suspension beam and are configured as supports on the two sides of the two-span continuous stiff suspension beam. And the anchor head tensioning mechanism is arranged at the end part of the upper chord of the main truss and is configured to directly and rigidly tension the upper chord, so that the upper chord is always kept in a preset tensioning state. The fish-belly-shaped plane truss is adopted in the main span direction, the direct tensioning technology and the structure stabilizing measure are supplemented, the structure stability is guaranteed, the appearance is light, and materials are saved.
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Description

Technical Field

[0001] The present application belongs to the technical field of large-span roof structures, and specifically relates to a two-span continuous rigid suspended large-span roof structure using direct tensioning technology. Background Art

[0002] The existing large-span roof structure systems using rigid suspension components usually include the following two approaches:

[0003] The first approach is to directly adopt a suspended structure system, the main structure of which includes rigid suspended components that simulate the stress of cable structures, lateral force-resistant components supported on both sides, and connecting components of each frame. This type of rigid suspended structure is the basic style of suspended roofs and has been successfully applied in some actual projects. The technical advantages of this type of roof are reasonable load-bearing mode, steel saving, and slender components; the corresponding main defect is that the roof layout is relatively single, mainly multi-frame parallel layout, which cannot be flexibly applied to various styles of building roof covering styles, and the application scope is relatively single.

[0004] The second approach is to use a two-way overhang structure roof system, including a main-direction space-structure overhang truss, a secondary-direction overhang, a supporting A-column, and special prestressed anti-tensioning technology. This type of overhang structure large-span roof system is equipped with a main and secondary two-way overhang structure, which can be effectively applied to specific space building roofs such as stadiums; at the same time, the main-direction overhang truss of this type of roof uses a space structure system for structural stability and safety requirements. Compared with the plane truss system, the appearance is relatively bloated and the structural material is relatively high; moreover, this type of roof needs to adopt a special prestressed anti-tensioning technology to solve the problem of tensile stress degradation under the conditions of the two-way overhang roof system. Although it achieves a higher work efficiency under the final state conditions, the overall construction process is relatively cumbersome and the process cost is relatively high.

[0005] Based on the above analysis, it can be seen that the two existing types of large-span roof structural systems mainly use rigid suspension components. Although the basic type is simple and efficient, the structural system cannot be applied to flexible and changeable roof shapes. Although the two-way suspension roof structural system can be applied to specific space buildings such as stadiums, the main truss is a space truss style, the architectural effect is poor, the material saving performance is poor, and based on the special prestressed reverse tension technology, its construction process is relatively complicated, which is not conducive to construction and installation. Summary of the invention

[0006] In view of the above analysis, an embodiment of the present invention aims to provide a two-span continuous rigid suspended large-span roof structure using direct tensioning technology to solve the above problems existing in the prior art.

[0007] The object of the present invention is achieved in that:

[0008] A two-span continuous rigid suspended long-span roof structure using direct tensioning technology, comprising:

[0009] Two-span continuous rigid cantilever beam;

[0010] End wall studs,

[0011] A main truss, the main truss is arranged in the middle of the two-span continuous suspension beam; the two ends of the main truss in the length direction are connected to the tops of the end wall columns on both sides, and is configured as a middle support of the two-span continuous rigid suspension beam; the main truss is a fish belly-shaped plane main truss, having an upper chord and a lower chord; the upper chord is a concave arc structure, and the lower chord is a horizontally arranged straight rod structure;

[0012] Cone columns, which are arranged at two ends of the two-span continuous rigid suspension beam and are configured as two side supports of the two-span continuous rigid suspension beam;

[0013] An anchor head tensioning mechanism is arranged at the end of the upper chord rod and is configured to directly and rigidly tension the upper chord rod so that the upper chord rod always maintains a predetermined tensioning state.

[0014] Furthermore, it also includes a stabilizing cable system, which is connected between the upper chord of the main truss and the continuous rigid suspension beams on both sides of the main truss, and is configured to provide lateral constraints to the main truss in the main direction plane.

[0015] Furthermore, the stabilizing cable system comprises a plurality of inverted V-shaped stabilizing cable units, and connection nodes between the inverted V-shaped stabilizing cable units and the upper chord are evenly spaced.

[0016] Furthermore, the inverted V-shaped stabilizing cable unit includes two stabilizing cables, the first ends of the two stabilizing cables are connected to the upper chord, the second ends of the two stabilizing cables are respectively connected to the continuous rigid cantilever beams on both sides of the main truss, and the plane where the inverted V-shaped stabilizing cable unit is located is perpendicular to the plane where the planar truss is located.

[0017] Furthermore, the fish-belly-shaped plane main truss also has vertical web members and diagonal web members, which are connected between the upper chord and the lower chord, and the upper chord, the lower chord, the vertical web members and the diagonal web members are located in the same vertical plane, and the vertical plane is the symmetry plane of the two-span continuous rigid cantilever beam.

[0018] Furthermore, the main truss and the end wall column are connected in a rigid connection manner.

[0019] Furthermore, the end wall column includes reinforced concrete and built-in steel sections arranged in the reinforced concrete. The built-in steel sections serve as the main load-bearing components of the end wall column, and the reinforced concrete provides load-bearing safety redundancy; the upper chord and the lower chord are directly and rigidly connected to the built-in steel sections of the end wall column.

[0020] Furthermore, the upper chord, the lower chord and the built-in steel section are welded.

[0021] Furthermore, the built-in steel section includes an end column, and a ground balancing cable is arranged inside the end column. The ground balancing cable is connected to the anchor head tensioning mechanism and is configured to provide an internal force balancing effect on the rigid tensioning anchor head.

[0022] Furthermore, the thickness of the reinforced concrete is 100-200 mm.

[0023] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0024] a) The present invention provides a two-span continuous rigid suspended large-span roof structure using direct tensioning technology, which is suitable for a variety of flexible space arrangements. Compared with the traditional main truss using a spatial truss style, the present application uses a fish-belly-shaped plane truss in the main span direction, which not only has a light appearance but also saves materials.

[0025] b) The present invention provides a two-span continuous rigid suspended large-span roof structure using direct tensioning technology. By adopting direct tensioning measures on the upper chord of the main truss, it can not only effectively reduce the compressive stress level in the middle part of the upper chord of the main truss and reduce the range of the compressed area, but also effectively control the out-of-plane stability problem of the plane truss caused by the compressed area and compressive stress, and also simplify the construction implementation process and save process costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the embodiments of this specification or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the embodiments of this specification. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0027] Figure 1 A schematic diagram of the first angle structure of a two-span continuous rigid suspension large-span roof structure using direct tensioning technology provided by the present invention;

[0028] Figure 2 A second angle structural schematic diagram of a two-span continuous rigid suspension large-span roof structure using direct tensioning technology provided by the present invention;

[0029] Figure 3 A schematic diagram of the elevation structure of a two-span continuous rigid suspension large-span roof structure using direct tensioning technology provided by the present invention;

[0030] Figure 4 A schematic diagram of the connection structure between the fish-belly-shaped plane main truss and the two-span continuous rigid cantilever beams provided by the present invention;

[0031] Figure 5 A schematic diagram of the structure in which the fish-belly-shaped plane main truss provided by the present invention is installed on the end wall columns on both sides;

[0032] Figure 6 A schematic diagram of the structure of the fish-belly-shaped plane main truss provided by the present invention;

[0033] Figure 7 for Figure 5 A magnified image of area A;

[0034] Figure 8 A schematic diagram of the local structure of the connection between the fish-belly-shaped plane main truss and the two-span continuous rigid cantilever beams provided by the present invention;

[0035] Fig. 9 This is a structural schematic diagram (top view) of a ground-mounted balancing cable and an anchor head tensioning mechanism provided in an end wall column provided by the present invention.

[0036] Reference numerals:

[0037] 1. Fish-belly-shaped plane main truss; 11. Upper chord; 12. Lower chord; 13. Vertical web member; 14. Diagonal web member; 2. Two-span continuous rigid suspension beam; 21. Cross beam; 3. End wall column; 4. Conical column; 5. Inverted V-shaped stabilizing cable unit; 6. Connecting lock; 7. Anchor head tensioning mechanism; 8. Ground balance cable. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be clearly and completely described in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. It should be noted that, in the absence of conflict, the embodiments in the present disclosure and the features in the embodiments can be combined, separated, interchanged and / or rearranged with each other. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0039] In the accompanying drawings, the size and relative size of components may be exaggerated for clarity and / or descriptive purposes. When the exemplary embodiments may be implemented differently, a specific process sequence may be performed in a different order than described. For example, two successively described processes may be performed substantially simultaneously or in an order opposite to the order described. In addition, the same reference numerals represent the same components.

[0040] The terms used here are for the purpose of describing specific embodiments, and are not intended to be restrictive. As used here, unless the context clearly indicates otherwise, the singular forms "one (kind, person)" and "said (the)" are also intended to include plural forms. In addition, when the terms "comprise" and / or "include" and their variations are used in this specification, it is explained that there are stated features, integral bodies, steps, operations, parts, assemblies and / or their groups, but it is not excluded that there are or add one or more other features, integral bodies, steps, operations, parts, assemblies and / or their groups. It should also be noted that, as used here, the terms "substantially", "approximately" and other similar terms are used as approximate terms and not as degree terms, so that they are used to explain the inherent deviations of the measured values, calculated values ​​and / or the values ​​provided that will be recognized by those of ordinary skill in the art.

[0041] Example 1

[0042] A specific embodiment of the present invention discloses a two-span continuous rigid suspension large-span roof structure using direct tensioning technology, which may be referred to as the "large-span roof structure" hereinafter. The main structure includes a fish-belly-shaped plane main truss, a two-span continuous rigid suspension beam, end wall columns, and tapered columns on both sides. The main truss and the end wall columns constitute a large-span main direction structural bearing system; the two-span continuous rigid suspension beams and the two-side tapered columns constitute a secondary direction bearing structure system, the middle support of the two-span continuous rigid suspension beams is a main direction fish-belly-shaped plane main truss, and the two side supports are tapered columns, forming a two-span continuous supporting structure; the two side tapered columns take into account both vertical bearing and horizontal force balance, effectively meeting the requirement that the suspension structure needs a horizontal force balancing mechanism; at the same time, a stabilizing cable system and an anchor head tensioning mechanism are used to directly tension the upper chord of the main truss to achieve the stability of the main direction plane truss.

[0043] Specifically, if Figures 1 to 9 As shown, the long-span roof structure includes a main truss, two-span continuous rigid suspension beams 2, end wall columns 3, tapered columns 4 and an anchor head tensioning mechanism 7; the main truss is arranged in the middle of the two-span continuous suspension beams; the two ends of the main truss in the length direction are connected to the tops of the end wall columns 3 on both sides, and are configured as the middle support of the two-span continuous rigid suspension beams 2; the main truss is a fish belly-shaped plane main truss 1, having an upper chord 11 and a lower chord 12; the upper chord 11 is a concave arc structure, and the lower chord 12 is a horizontally arranged straight rod structure; the tapered columns 4 are arranged at the two ends of the two-span continuous rigid suspension beams 2, and are configured as the two side supports of the two-span continuous rigid suspension beams 2; the anchor head tensioning mechanism 7 is arranged at the end of the upper chord 11, and is configured to directly and rigidly tension the upper chord 11, so that the upper chord 11 always maintains a predetermined tensioning state.

[0044] In this embodiment, the large-span roof structure further includes a stabilizing cable system, which is connected between the upper chord 11 of the main truss and the continuous rigid suspension beams on both sides of the main truss, and is configured to provide lateral constraints to the main truss in the main direction plane. The stabilizing cable system includes a plurality of inverted V-shaped stabilizing cable units 5, which provide lateral constraints to the main truss in the main direction plane by using an inverted V-shaped stabilizing cable structure and a low prestressed tensioning method, thereby ensuring the lateral stability of its compression zone.

[0045] Optionally, the connection nodes between the inverted V-shaped stabilizing cable unit 5 and the upper chord 11 of the main truss in the main direction plane are arranged at intervals, that is, a connection point is arranged between two truss nodes, and the inverted V-shaped stabilizing cable unit 5 is connected to the upper chord 11 of the plane truss, and the connection nodes are evenly spaced on the upper chord 11; on the one hand, the number of cable structures is reduced and the mechanism is simplified; on the other hand, the interval arrangement scheme can meet the out-of-plane stability requirements of the main direction plane truss.

[0046] Specifically, the inverted V-shaped stabilizing cable unit 5 includes two stabilizing cables, the first ends of the two stabilizing cables are connected to the upper chord 11, and the second ends of the two stabilizing cables are respectively connected to the continuous rigid suspension beams on both sides of the main truss. The plane where the inverted V-shaped stabilizing cable unit 5 is located is perpendicular to the plane where the plane truss is located. The inverted V-shaped stabilizing cable unit 5 is used to provide lateral constraints on both sides of the main direction plane truss to ensure its out-of-plane stability. Furthermore, the inverted V-shaped cable unit adopts a low prestress setting scheme to reduce the prestress level to avoid excessive initial reaction force; at the same time, the appropriate prestress level ensures that there is no relaxation under various structural load conditions.

[0047] Optionally, two ends of the stabilizing cable are respectively connected to the upper chord 11 and the suspension beam via a pin, and the lower end of the stabilizing cable is connected to the crossbeam 21 of the suspension beam.

[0048] Optionally, the two-span continuous rigid suspension beam 2 is further provided with a horizontally arranged connecting lock 6, the connecting lock 6 is perpendicular to the plane where the fish belly plane main truss 1 is located, and the connecting lock 6 and the two stabilizing cables of the inverted V-shaped stabilizing cable unit 5 form a triangular structure. This structural setting can further improve the stability of the roof structure.

[0049] In this embodiment, the fish-belly plane main truss 1 further has a vertical web member 13 and a diagonal web member 14, which are connected between the upper chord 11 and the lower chord 12, and the upper chord 11, the lower chord 12, the vertical web member 13, and the diagonal web member 14 are located in the same vertical plane, which is the symmetry plane of the two-span continuous rigid suspension beam 2. The main truss adopts a fish-belly plane structure, and only rigid components in the plane are set, which has a light appearance and saves materials.

[0050] Optionally, the lower chord 12 of the fish-belly-shaped plane main truss 1 adopts a parallel double-rod structure, and a plurality of supporting vertical rods are provided between the upper and lower parallel double rods.

[0051] In this embodiment, the end wall column 3 adopts a steel-concrete structure, and the end wall column 3 includes reinforced concrete and built-in steel arranged in the reinforced concrete. The built-in steel serves as the main load-bearing component of the end wall column 3, and the outer reinforced concrete part provides load-bearing safety redundancy, and serves as an integrated implementation method of the building appearance; the upper chord 11 and the lower chord 12 are directly rigidly connected to the built-in steel of the end wall column 3. Furthermore, the thickness of the reinforced concrete is 100 to 200 mm, and a reinforced concrete solution is adopted. The end wall column 3 adopts an external reinforced concrete structure, which, on the one hand, works in coordination with the built-in steel, and the structure has load-bearing safety redundancy; on the other hand, the building outer cladding is omitted, and the surface of the exposed concrete is adopted, which directly serves as an integrated implementation method of the building appearance.

[0052] In this embodiment, the upper chord 11 of the main truss is directly and rigidly tensioned by using direct tensioning technology, so that the upper chord 11 always maintains a predetermined tensioning state. Fig. 9 As shown, an anchor tensioning mechanism 7 is provided at the end of the upper chord 11 of the main truss, and the upper chord 11 is directly and rigidly tensioned by the anchor tensioning mechanism 7. The direct tensioning level is determined according to the setting conditions of the end wall column 3 and the ground balance cable 8, and can be set according to the principle that the compressive stress level of the upper chord 11 of the main plane truss is reduced by half and the distribution range of the compression area is reduced by half when the anchor tensioning mechanism is not provided.

[0053] In this embodiment, the main truss and the end wall column 3 are connected in a rigid connection manner, and the upper chord 11 and the lower chord 12 are directly connected to the built-in steel of the end wall column 3 to ensure the rigid connection effect and realize the limited transmission of axial force (upper chord tension, lower chord pressure). Optionally, the upper chord 11 and the lower chord 12 are welded to the built-in steel.

[0054] In one optional embodiment, referring to Fig. 9 The built-in steel section of the end wall column 3 includes an end column, and a ground-type balancing cable 8 is arranged inside the end column. The ground-type balancing cable 8 is connected to the anchor head tensioning mechanism 7 and is configured to provide an internal force balancing effect for the rigid tension anchor head. Two ground-type balancing cables 8 are symmetrically arranged inside each end wall column 3, and the two ground-type balancing cables 8 are symmetrically connected to the anchor head tensioning mechanism 7. By arranging the ground-type balancing cable in the built-in steel section of the end wall column 3, the ground-type balancing cable is connected to the direct tensioning anchor head, and an internal force balancing effect is provided for the rigid tensioning anchor head, effectively alleviating the horizontal force effect transmitted to the end wall column 3 by the direct tensioning anchor head, and reducing its local bending load.

[0055] In this embodiment, the cone column 4 is an inverted V-shaped structure, which is more beautiful while ensuring the supporting function. Optionally, the top end of the cone column 4 is hingedly connected to the suspension beam.

[0056] Compared with the prior art, the two-span continuous rigid suspension large-span roof structure provided in this embodiment using direct tensioning technology can achieve the following beneficial effects:

[0057] 1. It is suitable for a variety of flexible space arrangements. Compared with the traditional main truss in the form of a space truss, this application uses a fish-belly-shaped plane truss in the main span direction, which is not only light in appearance but also saves materials.

[0058] 2. By directly tensioning the upper chord of the main truss, the compressive stress level in the middle of the upper chord of the main truss can be effectively reduced, the range of the compression zone can be reduced, and the out-of-plane stability problem of the plane truss caused by the compression zone and compressive stress can be effectively controlled.

[0059] The specific implementation methods described above further illustrate the purpose, technical solutions and beneficial effects of the present application in detail. It should be understood that the above description is only the specific implementation method of the present application and is not intended to limit the scope of protection of the present application. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A two-span continuous rigid suspension long-span roof structure using direct tensioning technology, characterized in that: include: Two-span continuous rigid cantilever beam (2); End wall studs (3), A main truss, wherein the main truss is arranged in the middle of the two-span continuous suspension beam; the two ends of the main truss in the length direction are connected to the tops of the end wall columns (3) on both sides, and are configured as the middle support of the two-span continuous rigid suspension beam (2); the main truss is a fish belly-shaped plane main truss (1), having an upper chord (11) and a lower chord (12); the upper chord (11) is a concave arc structure, and the lower chord (12) is a horizontally arranged straight rod structure; Cone columns (4), the cone columns (4) being arranged at the two end portions of the two-span continuous rigid suspension beam (2) and configured as two side supports of the two-span continuous rigid suspension beam (2); An anchor head tensioning mechanism (7) is arranged at the end of the upper chord (11) and is configured to directly and rigidly tension the upper chord (11) so that the upper chord (11) always maintains a predetermined tensioned state.

2. The two-span continuous rigid suspension large-span roof structure using direct tensioning technology according to claim 1 is characterized in that: It also includes a stabilizing cable system, which is connected between the upper chord (11) of the main truss and the continuous rigid suspension beams on both sides of the main truss, and is configured to provide lateral constraints to the main truss in the main direction plane.

3. The two-span continuous rigid suspension large-span roof structure using direct tensioning technology according to claim 2 is characterized in that: The stabilizing cable system comprises a plurality of inverted V-shaped stabilizing cable units (5), wherein the connection nodes between the inverted V-shaped stabilizing cable units (5) and the upper chord (11) are evenly spaced.

4. The two-span continuous rigid suspension large-span roof structure using direct tensioning technology according to claim 3 is characterized in that: The inverted V-shaped stabilizing cable unit (5) comprises two stabilizing cables, the first ends of the two stabilizing cables are connected to the upper chord (11), the second ends of the two stabilizing cables are respectively connected to the continuous rigid suspension beams on both sides of the main truss, and the plane where the inverted V-shaped stabilizing cable unit (5) is located is perpendicular to the plane where the planar truss is located.

5. The two-span continuous rigid suspension large-span roof structure using direct tensioning technology according to claim 1 is characterized in that: The fish-belly-shaped plane main truss (1) further comprises a vertical web member (13) and a diagonal web member (14), wherein the vertical web member (13) and the diagonal web member (14) are connected between the upper chord member (11) and the lower chord member (12), and the upper chord member (11), the lower chord member (12), the vertical web member (13) and the diagonal web member (14) are located in the same vertical plane, and the vertical plane is a symmetric plane of the two-span continuous rigid suspension beam (2).

6. The two-span continuous rigid suspension large-span roof structure using direct tensioning technology according to claim 1 is characterized in that: The main truss and the end wall column (3) are connected in a rigid connection manner.

7. The two-span continuous rigid suspension large-span roof structure using direct tensioning technology according to claim 6 is characterized in that: The end wall column (3) comprises reinforced concrete and built-in steel sections arranged in the reinforced concrete, wherein the built-in steel sections serve as the main load-bearing components of the end wall column (3), and the reinforced concrete provides load-bearing safety redundancy; The upper chord (11) and the lower chord (12) are directly and rigidly connected to the built-in steel sections of the end wall column (3).

8. The two-span continuous rigid suspension large-span roof structure using direct tensioning technology according to claim 7 is characterized in that: The upper chord (11) and the lower chord (12) are welded to the built-in steel section.

9. The two-span continuous rigid suspension large-span roof structure using direct tensioning technology according to claim 8, characterized in that: The built-in steel section comprises an end column, and a ground balancing cable (8) is arranged inside the end column. The ground balancing cable (8) is connected to the anchor head tensioning mechanism (7) and is configured to provide an internal force balancing effect for the rigid tensioning anchor head.

10. The two-span continuous rigid suspension large-span roof structure using direct tensioning technology according to claim 7, characterized in that: The thickness of the reinforced concrete is 100-200 mm.

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