Reticulated shell structure and hoisting and splicing method thereof

By determining the initial lifting point and adjusting it to meet the preset conditions in the construction of large mesh structure, the problem of poor deformed control in the construction was solved, and the improvement of precise docking and structural security was realized.

CN119378238APending Publication Date: 2025-01-28MCC (SHANGHAI) STEEL STRUCTURE TECHNOLOGY CORP LTD
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Patent Information

Application Number
CN202411452550.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-10-17
Publication Date
2025-01-28

AI Technical Summary

Technical Problem

In the construction of existing large grid shell structures, it is difficult to accurately control deformation during the docking process by section hoisting and air splicing, resulting in insufficient docking accuracy and uneven structural stress.

Method used

By determining the key parameters of the shell structure of the target mesh, determine the initial hanging point, and build a virtual mechanics model, calculate the theoretical deformed parameters, adjust the initial crane point until the preset conditions are met, determine the actual lifting point, and ensure the accuracy of the ceiling and stitching operations Essence

Benefits of technology

Realize the precise docking in the splicing process of the air, ensure the structural force to meet the design requirements, and improve the safety and stability of the overall structure.

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Abstract

The invention provides a reticulated shell structure and a hoisting and splicing method thereof. The method comprises the steps that target reticulated shell structures to be hoisted and key parameters of all the target reticulated shell structures are determined; determining an initial hoisting point of each target reticulated shell structure according to the key parameters; constructing a virtual mechanical model based on the initial hoisting points, and calculating theoretical deformation parameters of each target latticed shell structure in the hoisting process according to the virtual mechanical model; judging whether the theoretical deformation parameter meets a first preset condition or not, and if not, adjusting the position of the initial hoisting point until the theoretical deformation parameter meets the first preset condition so as to determine an actual hoisting point; and carrying out hoisting splicing operation on the to-be-hoisted target latticed shell structure according to the actual hoisting point. By means of the method, deformation of the latticed shell structures in the butt joint process can be accurately controlled, and the hoisting and splicing accuracy and efficiency are improved.
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Description

Technical Field

[0001] The present invention relates to the technical field of large-scale lattice shell structure construction, and more specifically, to a lattice shell structure and a hoisting and splicing method thereof. Background Art

[0002] In the construction process of large-scale lattice shell structures, segmented lifting and aerial splicing are key technologies. Traditional methods often rely on experience to judge the position of the lifting points, which makes it difficult to accurately control the deformation during the docking process, easily leading to problems such as insufficient docking accuracy and uneven structural force.

[0003] Therefore, there is an urgent need for a lifting point selection method to improve the accuracy, construction efficiency and structural safety of segmented lifting and aerial splicing. Summary of the invention

[0004] In view of the above problems, the purpose of the present invention is to provide a lattice shell structure and a method for hoisting and splicing the same, so as to solve the problems existing in the existing lattice shell structure hoisting and splicing method, such as difficulty in accurately controlling deformation during docking, easily leading to insufficient docking accuracy and uneven structural force.

[0005] The method for hoisting and splicing a lattice shell structure provided by the present invention comprises: determining a target lattice shell structure to be hoisted, and key parameters of each target lattice shell structure; determining an initial hoisting point of each target lattice shell structure according to the key parameters; constructing a virtual mechanical model based on the initial hoisting point, and calculating theoretical deformation parameters of each target lattice shell structure during the hoisting process according to the virtual mechanical model; judging whether the theoretical deformation parameters meet a first preset condition, and if not, adjusting the position of the initial hoisting point until the theoretical deformation parameters meet the first preset condition to determine an actual hoisting point; and performing hoisting and splicing operations on the target lattice shell structure to be hoisted according to the actual hoisting point.

[0006] In addition, an optional technical solution is that the target grid shell structure includes a first side span grid shell, a middle span grid shell and a second side span grid shell; one end of the first side span grid shell is movably fixed to the first support column through a first support, and one end of the second side span grid shell is movably fixed to the second support column through a second support; the middle span grid shell is hoisted between the first side span grid shell and the second side span grid shell.

[0007] In addition, an optional technical solution is that the first side span lattice shell and the second side span lattice shell are respectively provided with at least two initial hoisting points, and the middle span lattice shell is provided with at least four initial hoisting points.

[0008] In addition, an optional technical solution is that the theoretical deformation parameters of each target grid shell structure during the lifting process include: the deformation of the first side span grid shell at the docking node away from the first support, the deformation of the second side span grid shell at the docking node away from the second support, and the deformation of the docking nodes at both ends of the middle span grid shell.

[0009] In addition, an optional technical solution is that the first preset condition includes:

[0010] |f1-f21|≤h, and |f3-f23|≤h

[0011] Among them, f1 represents the deformation of the first side span lattice shell at the docking node away from the first support, f21 represents the deformation of the middle span lattice shell at the docking node close to the first side span lattice shell end, f3 represents the deformation of the second side span lattice shell at the docking node away from the second support, f23 represents the deformation of the middle span lattice shell at the docking node close to the second side span lattice shell end, and h represents the preset error allowable value.

[0012] In addition, an optional technical solution is that the preset error allowable value is no more than 10 mm.

[0013] In addition, an optional technical solution is that when the theoretical deformation parameter does not meet the first preset condition, it also includes: adjusting the number of the initial lifting points, and adding auxiliary support devices in the target lattice shell structure until the theoretical deformation parameter meets the first preset condition.

[0014] In addition, an optional technical solution is that the target lattice shell structure includes an upper chord, a lower chord, and an inclined web member arranged between the upper chord and the lower chord; the upper chords and one end of the upper chord and the inclined web member are connected by an upper chord bolt ball node; the lower chords and the other end of the lower chord and the inclined web member are connected by a lower chord bolt ball node.

[0015] In addition, an optional technical solution is to perform hoisting and splicing operations on the target lattice shell structure to be hoisted according to the actual hoisting point, including: installing deformation detection equipment on each target lattice shell structure, and monitoring the actual deformation parameters in the hoisting process in real time through the deformation detection equipment; comparing and analyzing the actual deformation parameters with the theoretical deformation parameters, and resetting the hoisting point position according to the comparison and analysis results until the actual deformation parameters and the theoretical deformation parameters meet a second preset condition; and performing hoisting and splicing operations on the target lattice shell structure to be hoisted according to the reset hoisting point position that meets the second preset condition.

[0016] On the other hand, the present invention further provides a lattice shell structure, which is formed by hoisting using the above-mentioned lattice shell structure hoisting and splicing method.

[0017] By utilizing the above-mentioned lattice shell structure and its hoisting and splicing method, the corresponding initial hoisting point is determined according to the key parameters of the target lattice shell structure to be hoisted, and then a virtual mechanical model is constructed based on this to calculate the theoretical deformation parameters of each target lattice shell structure during the hoisting process. By adjusting the position of the initial hoisting point until the theoretical deformation parameter meets the first preset condition, the actual hoisting point information is determined, and the target lattice shell structure is hoisted and spliced ​​according to the actual hoisting point. This can ensure that the deformation of the nodes on the docking side of each section of the lattice shell structure tends to be consistent when docking in the air, thereby achieving precise docking, ensuring that the structural force meets the design requirements, and improving the safety and stability of the overall structure.

[0018] In order to achieve the above and related purposes, one or more aspects of the present invention include the features that will be described in detail later. The following description and the accompanying drawings describe some exemplary aspects of the present invention in detail. However, these aspects indicate only some of the various ways in which the principles of the present invention can be used. In addition, the present invention is intended to include all these aspects and their equivalents. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] By referring to the following description in conjunction with the accompanying drawings, and with a more comprehensive understanding of the present invention, other objects and results of the present invention will become more apparent and easy to understand. In the accompanying drawings:

[0020] Figure 1 It is a flow chart of a method for hoisting and splicing a lattice shell structure according to an embodiment of the present invention;

[0021] Figure 2 is a top view of a lattice shell structure according to an embodiment of the present invention;

[0022] Figure 3 is a side view of a lattice shell structure according to an embodiment of the present invention;

[0023] Figure 4 It is a side view of the lattice shell structure after the hoisting is completed according to an embodiment of the present invention.

[0024] Markings in the accompanying drawings: first side span lattice shell W1, middle span lattice shell W2, second side span lattice shell W3, upper chord 11, lower chord 12, inclined web member 13, upper chord bolt ball node 14, lower chord bolt ball node 15, first support column 16, first bearing 2, embedded rod 3, ground 4.

[0025] The same reference numerals throughout the drawings indicate similar or corresponding features or functions. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0027] In the following description, for the purpose of illustration, in order to provide a comprehensive understanding of one or more embodiments, many specific details are set forth. However, it is apparent that these embodiments may also be implemented without these specific details. In other examples, for ease of describing one or more embodiments, known structures and devices are shown in the form of block diagrams.

[0028] In the description of the present invention, it is to be understood that the orientations or positional relationships indicated by the following terms “center”, “longitudinal”, “lateral”, “length”, “width”, “thickness”, “up”, “down”, “front”, “back”, “left”, “right”, “vertical”, “horizontal”, “top”, “bottom”, “inside”, “outside”, “clockwise”, “counterclockwise”, “axial”, “radial”, “circumferential”, etc. are based on the orientations or positional relationships shown in the accompanying drawings and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the content or structure of the present invention.

[0029] In order to solve the problems existing in the existing hoisting and splicing methods of lattice shell structures, such as difficulty in accurately controlling deformation during the docking process, which easily leads to insufficient docking accuracy and uneven structural force, the present invention provides a lattice shell structure and a hoisting and splicing method thereof, which can determine the corresponding initial hoisting point according to the key parameters of the target lattice shell structure to be hoisted, and construct a virtual mechanical model based on this, and determine the theoretical deformation parameters of each target lattice shell structure during the hoisting process through the virtual mechanical model, and then adjust the relevant information of the initial hoisting point so that the theoretical deformation parameters meet the first preset condition to determine the actual hoisting point, so as to ensure the accurate docking and structural safety of the shell lattice structure during the aerial splicing process.

[0030] In order to describe the structure of the lattice shell structure and the hoisting and splicing method thereof in detail, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0031] Figure 1 The schematic flow chart of the method for hoisting and splicing a lattice shell structure according to an embodiment of the present invention is shown; Figures 2 to 4 The schematic structures of the lattice shell structure according to the embodiments of the present invention are respectively shown.

[0032] like Figures 1 to 4 As shown together, the method for hoisting and splicing a lattice shell structure according to an embodiment of the present invention comprises:

[0033] S100: Determine the target lattice shell structure to be hoisted and key parameters of each target lattice shell structure.

[0034] Among them, before the splicing and hoisting of the grid shell structure, it is necessary to first determine the target grid shell structure to be hoisted, such as a two-segment cylindrical shell grid shell structure, a three-segment cylindrical shell grid shell structure or more segments, and then determine the key parameters of each target grid structure, which may include specific dimensions, material properties, connection methods and connection point locations, etc.

[0035] S200: Determine the initial hoisting point of each target lattice shell structure according to the key parameters.

[0036] In this process, the lifting point positions of each target lattice shell structure can be preliminarily set as the initial lifting point positions based on the structural characteristics and construction experience.

[0037] As a specific example, for an embodiment of a three-section cylindrical shell lattice structure, the target lattice structure includes a first side span lattice, a middle span lattice and a second side span lattice; one end (left end) of the first side span lattice is movably fixed to the first support column 16 via a first support 2, and one end (right end) of the second side span lattice is movably fixed to the second support column via a second support; the middle span lattice is hoisted between the first side span lattice and the second side span lattice. Therefore, two-point hoisting can be selected for the first side span lattice and the second side span lattice, and four-point hoisting can be selected for the middle span lattice according to its size, that is, at least two initial hoisting points are respectively provided for the first side span lattice and the second side span lattice, and at least four initial hoisting points are provided for the middle span lattice.

[0038] Specifically, two lifting points (initial lifting points) D1 are set for the first side span grid shell, and the two lifting points D1 are symmetrically distributed along the width direction of the first side span grid shell. Similarly, two lifting points D1 are set for the first side span grid shell, and the two lifting points D3 are symmetrically distributed along the width direction of the second side span grid shell. The four lifting points of the middle span grid shell include two lifting points D21 close to the side of the first side span grid shell, and two lifting points D23 close to the side of the second side span grid shell. Specifically, the positions and numbers of the lifting points can be flexibly adjusted according to the size, shape and lifting requirements of the grid shell.

[0039] S300: constructing a virtual mechanical model based on the initial lifting point, and calculating theoretical deformation parameters of each target lattice shell structure during the lifting process according to the virtual mechanical model.

[0040] Among them, after determining the initial lifting point of each target lattice shell structure, the virtual mechanical model of each target lattice shell structure can be established respectively through finite element analysis software or structural mechanics model, and then the lifting force and constraint conditions are set in the virtual mechanical model to calculate the theoretical deformation of each target lattice shell structure during the lifting process, among which the vertical deformation of the docking side node can be focused on, that is, the deformation f1 of the docking side node F1 of W1, the deformation f3 of the docking side node F3 of W3, and the deformation f21 and f23 of the docking side nodes F21 and F23 of W2 and W1, W3. The specific distribution of the docking side nodes can be referred to Figure 2 shown.

[0041] In other words, the theoretical deformation parameters of each target lattice shell structure during the lifting process include at least: the deformation f1 of the first side span lattice shell at the docking node away from the first support, the deformation f3 of the second side span lattice shell at the docking node away from the second support, and the deformation f21 and f23 of the docking nodes at both ends of the middle span lattice shell. Deformation parameters of other key positions may also be added according to the lattice shell structure.

[0042] S400: Determine whether the theoretical deformation parameter satisfies a first preset condition. If not, adjust the position of the initial hoisting point until the theoretical deformation parameter satisfies the first preset condition to determine the actual hoisting point.

[0043] Among them, after determining the theoretical deformation parameters of each docking side node, they can be theoretically optimized. According to the engineering requirements and structural characteristics, a reasonable error allowable value h is set as the judgment standard for deformation coordination. Then, the deformations f1, f21, f3, and f23 obtained in the previous step are compared with each other to determine whether they meet the requirements of deformation coordination, that is, the first preset condition.

[0044] Specifically, the first preset condition includes: |f1-f21|≤h, and |f3-f23|≤h; wherein f1 represents the deformation of the first side span grid shell at the docking node away from the first support, f21 represents the deformation of the middle span grid shell at the docking node close to the first side span grid shell end, f3 represents the deformation of the second side span grid shell at the docking node away from the second support, f23 represents the deformation of the middle span grid shell at the docking node close to the second side span grid shell end, and h represents the preset error allowable value.

[0045] It can be seen that if the above first preset conditions are met, it means that the current initial lifting point position is reasonable and no adjustment is required; otherwise, the lifting point position of W1, W2 or W3 should be adjusted according to the structural characteristics and deformation. When adjusting, you can consider changing the position and number of the lifting points or adding auxiliary supports. After each adjustment of the lifting point position, you need to re-construct and calculate the new theoretical deformation parameters until the theoretical deformation parameters meet the first preset conditions.

[0046] Among them, the preset error allowable value can be set to no more than 10mm, so as to meet the mechanical strength requirements of the lattice shell structure, and can be set specifically according to the application scenario and lifting requirements.

[0047] S500: performing hoisting and splicing operations on the target lattice shell structure to be hoisted according to the actual hoisting points.

[0048] Among them, due to the complexity and changeability of the actual lifting process, it is not possible to directly rely on the actual lifting points obtained in theory for lifting. It is also necessary to ensure the accuracy of the lifting and splicing through trial lifting and real-time data analysis. Among them, deformation detection equipment, such as displacement sensors and strain gauges, can be installed on each target lattice shell structure. The actual deformation parameters of the lifting process can be monitored in real time through the deformation detection equipment, and the lifting adjustment can be made by comparing the actual deformation parameters with the theoretical deformation parameters. At the same time, it is also necessary to conduct a comprehensive inspection of the lifting equipment, rigging, connectors, etc. before the trial lifting to ensure the safety and reliability of the lifting.

[0049] Then, according to the actual lifting points initially determined, each target lattice shell structure is trial-lifted, and during the lifting process, the deformation data of each detection point is recorded in real time, especially the vertical deformation of the docking side node. The actual deformation parameters can be recorded as f1', f21', f3', f23', and then the actual deformation parameters are compared and analyzed with the theoretical deformation parameters to judge the coordination of the deformation, and the lifting point position is reset according to the comparison and analysis results until the actual deformation parameters and the theoretical deformation parameters meet the second preset condition; according to the reset lifting point position that meets the second preset condition, the target lattice shell structure to be lifted is lifted and spliced.

[0050] Among them, the second preset condition includes: |f1'-f21'|≤h and |f3'-f23'|≤h, wherein f1' represents the real-time deformation of the first side span grid shell at the docking node away from the first support, f21' represents the real-time deformation of the middle span grid shell at the docking node close to the first side span grid shell end, f3' represents the real-time deformation of the second side span grid shell at the docking node away from the second support, f23' represents the real-time deformation of the middle span grid shell at the docking node close to the second side span grid shell end, and h represents the preset error allowable value.

[0051] If any of the above second preset conditions is not met, the position of the lifting point that needs to be adjusted is determined based on the trial lifting results and the deformation difference. It may be necessary to adjust the lifting point of the side span gridshell W1 or W3, or the lifting point of the middle span gridshell W2, or both. Then, according to the adjustment plan, the new lifting point position is reset, and the lifting equipment and deformation detection equipment are reinstalled, and the trial lifting operation is repeated until the lifting point position that meets the second preset condition is found. Finally, each target gridshell structure is actually lifted and spliced ​​according to the lifting point position that meets the second preset condition.

[0052] In a specific embodiment of the present invention, the target lattice shell structure further includes an upper chord 11, a lower chord 12, and an inclined web member disposed between the upper chord 11 and the lower chord 12; the upper chord 11 and one end of the upper chord 11 and the inclined web member 13 are connected by an upper chord bolt ball node 14; the lower chord 12 and the other end of the lower chord 12 and the inclined web member 13 are connected by a lower chord bolt ball node 15. When the target lattice shell structures are actually hoisted, the embedded rods 3 can be installed between the target lattice shell structures, and the target lattice shell structures are spliced ​​and fixed by the embedded rods 3.

[0053] In addition, in the method for hoisting and splicing the lattice shell structure of the present invention, the data such as the position of the hanging points and the deformation amount that finally meet the deformation coordination requirements during the theoretical verification and trial hoisting process can be recorded as a basis for subsequent construction, and a detailed construction verification and trial hoisting report can be compiled, including the virtual mechanical model establishment process, deformation calculation results, hanging point adjustment records, analysis results and other contents. The problems encountered in the construction verification and trial hoisting process, solutions and successful experiences are summarized to provide a reference for similar projects.

[0054] Corresponding to the above-mentioned net shell structure hoisting and splicing method, the present invention also provides a net shell structure, which is hoisted and formed using the above-mentioned net shell structure hoisting and splicing method. It should be noted that the embodiments of the above-mentioned net shell structure can refer to the description in the embodiment of the net shell structure hoisting and splicing method, and will not be repeated here one by one.

[0055] According to the above-mentioned grid shell structure and its hoisting and splicing method, the corresponding initial hoisting point is determined according to the key parameters of the target grid shell structure to be hoisted, and then a virtual mechanical model is constructed based on this to calculate the theoretical deformation parameters of each target grid shell structure during the hoisting process, and the actual hoisting point information is determined by adjusting the position of the initial hoisting point until the theoretical deformation parameter meets the first preset condition, and then during the actual hoisting process, the deformation data is monitored in real time through trial hoisting, and finally the target grid shell structure to be hoisted is hoisted and spliced ​​according to the reset hoisting point position that meets the second preset condition, which can ensure that the deformation of the docking side nodes of each section of the target grid shell structure tends to be consistent when docking in the air, ensuring the accurate docking and structural safety of the grid shell structure during the aerial splicing process.

[0056] As described above, the lattice shell structure and the hoisting and splicing method thereof according to the present invention are described by way of example with reference to the accompanying drawings. However, those skilled in the art should understand that various improvements can be made to the lattice shell structure and the hoisting and splicing method thereof proposed by the present invention without departing from the content of the present invention. Therefore, the protection scope of the present invention should be determined by the content of the attached claims.

Claims

1. A method for hoisting and splicing a lattice shell structure, characterized in that: include: Determine the target lattice shell structure to be hoisted and the key parameters of each target lattice shell structure; Determining the initial hoisting point of each target lattice shell structure according to the key parameters; Building a virtual mechanical model based on the initial lifting point, and calculating theoretical deformation parameters of each target lattice shell structure during the lifting process according to the virtual mechanical model; Determine whether the theoretical deformation parameter satisfies a first preset condition, and if not, adjust the position of the initial hoisting point until the theoretical deformation parameter satisfies the first preset condition to determine the actual hoisting point; The target lattice shell structure to be hoisted is hoisted and spliced ​​according to the actual hoisting point.

2. The method for hoisting and splicing a lattice shell structure according to claim 1, characterized in that: The target lattice shell structure includes a first side span lattice shell, a middle span lattice shell and a second side span lattice shell; One end of the first side span lattice shell is movably fixed to the first support column through a first support, and one end of the second side span lattice shell is movably fixed to the second support column through a second support; The middle span lattice shell is hoisted between the first side span lattice shell and the second side span lattice shell.

3. The method for hoisting and splicing a lattice shell structure according to claim 2, characterized in that: The first side span lattice shell and the second side span lattice shell are respectively provided with at least two initial hoisting points, and the middle span lattice shell is provided with at least four initial hoisting points.

4. The method for hoisting and splicing a lattice shell structure according to claim 2, characterized in that: The theoretical deformation parameters of each target lattice shell structure during the hoisting process include: The deformation of the first side span lattice shell at the docking node away from the first support, the deformation of the second side span lattice shell at the docking node away from the second support, and the deformation of the docking nodes at both ends of the middle span lattice shell.

5. The method for hoisting and splicing a lattice shell structure according to claim 4, characterized in that: The first preset condition includes: |f1-f21|≤h, and |f3-f23|≤h Among them, f1 represents the deformation of the first side span lattice shell at the docking node away from the first support, f21 represents the deformation of the middle span lattice shell at the docking node close to the first side span lattice shell end, f3 represents the deformation of the second side span lattice shell at the docking node away from the second support, f23 represents the deformation of the middle span lattice shell at the docking node close to the second side span lattice shell end, and h represents the preset error allowable value.

6. The method for hoisting and splicing a lattice shell structure according to claim 5, characterized in that: The preset error allowable value is no greater than 10 mm.

7. The method for hoisting and splicing a lattice shell structure according to claim 1, characterized in that: When the theoretical deformation parameter does not meet the first preset condition, the method further includes: The number of the initial lifting points is adjusted, and auxiliary support devices are added to the target lattice shell structure until the theoretical deformation parameter meets the first preset condition.

8. The method for hoisting and splicing a lattice shell structure according to claim 1, characterized in that: The target lattice shell structure comprises an upper chord, a lower chord and an inclined web member arranged between the upper chord and the lower chord; The upper chord members are connected to each other and one end of the upper chord member and the inclined web member are connected via an upper chord bolt ball node; The lower chord members are connected to each other and the other end of the lower chord member and the inclined web member are connected through a lower chord bolt ball node.

9. The method for hoisting and splicing a lattice shell structure according to claim 1, characterized in that: Performing hoisting and splicing operations on the target lattice shell structure to be hoisted according to the actual hoisting point includes: Installing deformation detection equipment on each target lattice shell structure, and monitoring actual deformation parameters in real time during the test hoisting process through the deformation detection equipment; Comparing and analyzing the actual deformation parameter with the theoretical deformation parameter, and resetting the suspension point position according to the comparison and analysis result, until the actual deformation parameter and the theoretical deformation parameter meet a second preset condition; The target lattice shell structure to be hoisted is hoisted and spliced ​​according to the reset hoisting point position that meets the second preset condition.

10. A lattice shell structure, characterized in that: The lattice shell structure is hoisted and formed by the hoisting and splicing method according to any one of claims 1 to 9.

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