Splicing type mounting method for steel structure

Abstract

The invention provides a steel structure splicing type installation method, and belongs to the technical field of steel structure construction.The method includes the steps that firstly, based on a three-dimensional design drawing, a structure map is established, and node coordinates and connection relations are identified; carrying out bearing capacity partitioning through a minimum spanning tree algorithm, and calculating a bearing capacity gravity center; carrying out stability partitioning, calculating a mass gravity center, and carrying out correlation analysis on the mass gravity center and a bearing capacity gravity center; calculating an optimal splicing sequence based on an elastic mechanical equilibrium equation, and establishing a splicing process diagram; installing a first reference node according to the process diagram, and establishing a coordinate system; connecting pieces are installed in sequence, and center-of-gravity deviation detection is carried out; when the structure reaches a critical state, carrying out overall stress measurement and adjusting node parameters; and finally, all splicing is completed, the geometric dimension and stress distribution are verified, and the problems of stability and stress balance existing in a traditional method are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of steel structure construction. Specifically, it relates to a method for spliced installation of steel structures. Background Art

[0002] Due to advantages such as high strength, light self-weight, and short construction period, steel structures are widely used in engineering fields such as large public buildings, bridges, and towers. Traditional spliced installation of steel structures usually adopts a pre-designed construction plan and is assembled on-site based on component numbers and simple installation sequence diagrams. This method mainly relies on engineers' experience judgment and simplified static calculations, which can meet basic requirements in projects with high standardization and relatively simple structures.

[0003] However, with the increasing complexity of building designs, especially in large-span, irregular-shaped, or high-rise steel structure projects, the traditional splicing method has exposed serious defects. First, the experience-oriented splicing sequence is difficult to cope with the spatial relationships of complex nodes, resulting in unstable temporary states during installation and the need for repeated adjustments; second, the lack of precise calculation of the dynamic stress state of the structure during splicing makes the components may bear excessive stress during installation, leading to permanent deformation or even safety accidents; third, the control of geometric accuracy during splicing relies on manual measurement and simple tools, making it difficult to meet high-precision requirements.

[0004] The core problem that current technologies cannot solve is that it is difficult to ensure both structural stability and force balance during the spliced installation of large and complex steel structures. Summary of the Invention

[0005] In view of this, the present invention provides a method for spliced installation of steel structures, which can solve the technical problem in the prior art that it is difficult to ensure both structural stability and force balance during the spliced installation of large and complex steel structures.

[0006] The present invention is implemented as follows: The present invention provides a method for spliced installation of steel structures, including: establishing a structure atlas based on the three-dimensional design drawing of the steel structure; applying the minimum spanning tree algorithm to perform the first partition on the structure atlas, calculating the bearing capacity centroid coordinates of each partition with the bearing capacity transfer efficiency between nodes as the weight; applying the community discovery algorithm to perform the second partition on the structure atlas, calculating the mass centroid coordinates of each partition with the stability connection strength between nodes as the evaluation index; calculating the optimal splicing sequence using the structural elasticity equilibrium equation, and establishing a structural stability evaluation model during splicing based on the principle of minimizing elastic strain energy; establishing a splicing process diagram; installing the reference nodes; installing the connectors according to the splicing sequence; measuring the overall stress distribution and fine-tuning the connection node parameters; completing the splicing and verifying the accuracy.

[0007] Among them, establishing the structure map includes: establishing the structure map according to the node connection relationship, and identifying the spatial coordinates of each node and the attribute parameters of the connection edges. The node connection relationship refers to the mutual connection methods and positional relationships of various components in the steel structure, including the spatial distribution of all structural force transmission points such as welding points and bolt connection points.

[0008] Among them, applying the minimum spanning tree algorithm for the first partition is to partition the structure map by applying the minimum spanning tree algorithm according to the bearing capacity distribution rule. The steel structure is regarded as a weighted connected graph to determine the boundaries of each partition and the internal connection relationship. The bearing capacity distribution rule refers to a rule system for determining the load size and distribution method that each component should bear under different stress conditions according to the principles of structural mechanics.

[0009] Among them, the center of gravity of the bearing capacity refers to the weighted average center point of the bearing capacity distribution of each part in the structure, which is used to characterize the concentrated performance of the overall force distribution of the structure.

[0010] Among them, applying the community detection algorithm for the second partition is to partition the structure map by applying the community detection algorithm according to the principle of structural stability, identify the stable community clusters in the structure, and conduct spatial position correlation analysis with the center of gravity of the bearing capacity. The center of gravity of the mass refers to the weighted average center point of the mass distribution of each part of the structure, which is used to characterize the concentrated performance of the physical mass distribution of the structure.

[0011] Among them, the structural elasticity equilibrium equation is used to calculate the stress distribution and deformation state of each node during the splicing process of the steel structure. The inputs include the node coordinate vector, the member stiffness matrix, the external load vector, the initial stress of the member, and the node connection constraint matrix; the outputs are the displacement vector of each node and the internal stress distribution.

[0012] Among them, the node coordinate vector comes from the spatial coordinates identified when establishing the structure map, the member stiffness matrix comes from the attribute parameters of the connection edges in the structure map, the external load vector comes from the design load conditions, the initial stress of the member comes from the residual stress generated during the manufacturing process, and the node connection constraint matrix comes from the node connection relationship.

[0013] Among them, the principle of minimizing the elastic strain energy means that when the structure is under the action of external forces, the elastic potential energy stored inside the system tends to the minimum state, which is an important basis for judging the structural stability.

[0014] Among them, establishing the splicing process diagram includes: marking the installation priority, connection method and position of the temporary fixing points of each component to form a complete splicing path diagram. The splicing path diagram is a graphical guidance document showing the installation of all components in sequence, including the installation time sequence of each component and its connection method with the surrounding components.

[0015] Among them, the overall stress distribution measurement includes: when the structure is spliced to the preset critical state, the overall stress distribution is measured, and the connection node parameters are fine-tuned according to the measurement results to ensure the balanced force of the final structure. The critical state refers to the state point where the overall structure begins to form a self-supporting system after reaching a certain degree of completion during the steel structure splicing process.

[0016] The present invention transforms the abstract structural mechanics problem into a computable graph theory problem by establishing a structure map, applying the minimum spanning tree and community discovery algorithms for dual partitioning, calculating the optimal splicing sequence, and combining real-time detection technology to guide the construction process, realizing the full-process digital guidance from design to construction.

[0017] Compared with the traditional method, the present invention solves the key technical problems in the splicing process of complex steel structures. By analyzing the bearing capacity distribution and structural stability as two independent dimensions and integrating them into a unified splicing strategy, it effectively avoids the unstable state generated by the traditional empirical method in complex structures; by calculating the stress distribution during the splicing process in real time through the elastic mechanics equilibrium equation, it ensures that each splicing operation is in a controllable stress state, preventing structural deformation caused by local overload; with the help of the laser positioning system and stress distribution measurement technology, the splicing accuracy is improved from the traditional centimeter level to the millimeter level, significantly improving the overall performance of the structure; it successfully solves the technical problems of stability and balanced force during the splicing and installation process of complex steel structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a flowchart of the method of the present invention.

[0019] Figure 2 It is a schematic diagram of the steel structure map and node representation in Embodiment 2.

[0020] Figure 3 It is a schematic diagram of the minimum spanning tree algorithm partitioning in Embodiment 2.

[0021] Figure 4 It is a schematic diagram of the community discovery algorithm partitioning in Embodiment 2. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0022] To make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0023] As Figure 1 shown, it is a flowchart of a steel structure splicing and installation method provided by the present invention. This method includes the following steps:

[0024] S01. Obtain the 3D design drawing of the steel structure, establish a structure atlas according to the node connection relationship, and mark the spatial coordinates of each node and the attribute parameters of the connecting edges.

[0025] S02. Apply the minimum spanning tree algorithm to the structure atlas for the first partition according to the bearing capacity distribution rule. Consider the steel structure as a weighted connected graph, use the bearing capacity transfer efficiency between nodes as the weight, determine the boundary of each partition and the internal connection relationship, and calculate the centroid coordinates of the bearing capacity of each partition.

[0026] S03. Apply the community discovery algorithm to the structure atlas for the second partition according to the principle of structural stability. Use the stability connection strength between nodes as the evaluation index to identify the stability community clusters in the structure, calculate the centroid coordinates of the mass of each partition, and conduct a spatial position correlation analysis with the centroid of the bearing capacity.

[0027] S04. Calculate the optimal splicing sequence using the equilibrium equation of structural elasticity mechanics, and establish a structural stability evaluation model during the splicing process based on the principle of minimizing elastic strain energy to ensure the overall stability of the structure and the uniformity of stress distribution during the splicing process.

[0028] S05. Establish a splicing process diagram, mark the installation priority, connection method, and position of the temporary fixing points of each component to form a complete splicing path diagram.

[0029] S06. Install the first reference node according to the splicing path diagram, use the laser positioning system to ensure the accuracy of its spatial position, and establish a construction reference coordinate system.

[0030] S07. Install the connecting pieces according to the splicing sequence. After each partition is installed, conduct a centroid deviation detection and adjust the subsequent splicing parameters in real time.

[0031] S08. When the structure is spliced to the preset critical state, measure the overall stress distribution, and fine-tune the connection node parameters according to the measurement results to ensure the balanced force of the final structure.

[0032] S09. After all splicing is completed, conduct a global geometric dimension inspection and stress distribution verification to confirm that the overall splicing accuracy meets the design requirements.

[0033] Among them, the node connection relationship refers to the connection method and position relationship of each component in the steel structure, including the spatial distribution of all structural force transfer points such as welding points and bolt connection points.

[0034] Among them, the bearing capacity distribution rule refers to a rule system divided according to the principles of structural mechanics for determining the load size and distribution method that each component should bear under different stress conditions.

[0035] Among them, the bearing capacity centroid refers to the weighted average center point of the bearing capacity distribution of each part in the structure, which is used to characterize the concentrated performance of the overall force distribution of the structure.

[0036] Among them, the mass centroid refers to the weighted average center point of the mass distribution of each part of the structure, which is used to characterize the concentrated performance of the physical mass distribution of the structure.

[0037] Among them, the structural elasticity mechanics equilibrium equation is used to calculate the stress distribution and deformation state of each node during the splicing process of the steel structure. The inputs include the node coordinate vector, the member stiffness matrix, the external load vector, the initial stress of the member, and the node connection constraint matrix. The node coordinate vector is derived from the spatial coordinates identified in step S01, the member stiffness matrix is derived from the attribute parameters of the connecting edges in the structure atlas, the external load vector is derived from the design load conditions, the initial stress of the member is derived from the residual stress generated during the manufacturing process, and the node connection constraint matrix is derived from the node connection relationship. The output is the displacement vector of each node and the internal stress distribution. The displacement vector of each node is used to evaluate the structural deformation, and the internal stress distribution is used to judge the structural safety.

[0038] Among them, the centroid deviation detection is to determine the optimal splicing sequence by calculating the spatial position relationship between the mass centroid and the bearing capacity centroid to maintain the stability of the temporary state of the structure during the construction process.

[0039] Among them, the splicing path diagram is a graphical guidance document showing the installation of all members in sequence, including the installation time sequence of each member and its connection method with the surrounding members.

[0040] Among them, the critical state refers to the state point at which the overall structure begins to form a self-supporting system after reaching a certain degree of completion during the splicing process of the steel structure.

[0041] Among them, the minimum spanning tree algorithm is a graph theory algorithm that connects all nodes in the structure atlas through edges with the minimum weight to form a connected subgraph without loops, which is used for the bearing capacity optimization partition of the steel structure.

[0042] Among them, the community discovery algorithm is a graph theory clustering method that identifies highly interconnected node clusters in the network by analyzing the connection patterns between nodes, which is used for the stability optimization partition of the steel structure.

[0043] Among them, the principle of minimum elastic strain energy means that when the structure is under external force, the elastic potential energy stored inside the system tends to the minimum state, which is an important basis for judging the structural stability.

[0044] The following will describe the specific implementation manners of the above steps in detail.

[0045] The specific implementation of step S01 is to first obtain the three-dimensional design model of the steel structure, extract the spatial coordinate information of all nodes, including the X, Y, and Z axis coordinate values of each node, with an accuracy requirement of ±1 mm. At the same time, identify and record the connection relationships of each node, and convert this information into the form of a structure map. For each connecting edge, detail the marking of its attribute parameters, including member type (such as H-shaped steel, I-beam, angle steel, etc.), section parameters (such as flange width, web height, wall thickness, etc.), material properties (such as elastic modulus, yield strength, etc.), and connection method (such as welding, high-strength bolts, etc.). Finally, integrate the above information into a complete data structure for subsequent algorithm processing and analysis. The purpose of this step is to establish a digital twin model of the steel structure, providing a geometric and topological basis for subsequent zoning and splicing sequence optimization.

[0046] The specific implementation of step S02 is to regard the steel structure as a weighted connected graph, with the bearing capacity transfer efficiency between nodes as the weight of the edge. First, calculate the weight value of each connecting edge. The weight value is comprehensively determined by the member section characteristics, material strength, and connection method, and can usually be expressed as the ratio of the axial stiffness of the member to its length, with the unit of N / m 2 . Apply the Kruskal or Prim minimum spanning tree algorithm to perform the first zoning process on the structure map. This algorithm can ensure that, on the premise of maintaining the connectivity of the graph, the sum of the weights of the selected edges is minimized. In the specific implementation process, first sort all edges in ascending order of weight value, and then select edges one by one to add to the spanning tree until all nodes are connected and no loops are formed. For a structure with n nodes, the finally generated minimum spanning tree will contain n - 1 edges. Based on the topological structure of the minimum spanning tree, divide the steel structure into multiple regions, and define the region boundary as the set of non-minimum spanning tree edges. For each region, calculate the bearing capacity centroid coordinates, and the calculation method is to perform weighted averaging on the coordinates of all nodes in the region according to their bearing capacity. The bearing capacity centroid is used to characterize the overall stress center of the region and serves as an important reference point for subsequent splicing sequence optimization. The threshold reference for this zoning is: when the maximum internal force in the region is less than 75% of the design bearing capacity, it is considered that the zoning is reasonable.

[0047] The specific implementation of step S03 is to apply the community discovery algorithm to perform the second zoning on the structure map based on the principle of structural stability. First, define the stability connection strength between nodes. This strength value reflects the structural coupling degree between two nodes and can be obtained by calculating the eigenvalue of the stiffness matrix between nodes. A larger eigenvalue (usually greater than 10 4(N / m) represents a strong structural coupling relationship. The Louvain or Girvan - Newman community detection algorithm is used to identify stable community clusters in the structure. The Louvain algorithm is based on modularity optimization and iteratively assigns nodes to different communities to maximize the overall modularity value. The modularity threshold for community division is set to 0.4, and a value higher than this indicates a significant community structure in the division. Calculate the mass - center coordinates of each identified community partition by weighted - averaging the coordinates of all nodes within the partition according to their masses. Conduct a spatial - position correlation analysis between the mass - center and the bearing - capacity center of gravity in step S02, and calculate the spatial distance and direction vector between the two. When the distance between the two centers of gravity exceeds 10% of the partition size, the partition scheme needs to be adjusted to reduce this difference. This step aims to ensure the overall stability during the structure splicing process. By identifying naturally - formed stable communities in the structure, it provides stability guarantee for the subsequent optimization of the splicing sequence.

[0048] The specific implementation of step S04 is to calculate the optimal splicing sequence based on the structural elasticity mechanics equilibrium equation and the principle of minimum elastic strain energy. First, establish the overall stiffness matrix K of the structure, which is assembled from the local stiffness matrices of each component according to the connection relationship. For a structure with n degrees of freedom, K is an n×n - order matrix. Establish the elastic strain energy function U = 1 / 2q T Kq during the splicing process, where q is the node displacement vector. To ensure the structural stability during the splicing process, introduce the constraint condition: in any splicing state, the minimum eigenvalue of the structure should be greater than a preset threshold (usually 10 3 (N / m). Construct an optimization model for the splicing sequence, and the objective function is to minimize the maximum strain energy value during the entire splicing process. Use the dynamic programming algorithm to solve the optimal splicing path. This algorithm decomposes the splicing process into multiple states, and each state corresponds to a partially - completed structure. For each possible splicing state, calculate the change in strain energy generated by adding the next component, and select the component that causes the smallest increase in strain energy as the next splicing object. Iterate this process until all splicing is completed. The finally output optimal splicing sequence ensures the overall stability and uniform stress distribution of the structure during the entire installation process, and the maximum stress level does not exceed 60% of the material yield strength.

[0049] The specific implementation of step S05 is to establish a detailed splicing process diagram based on the optimal splicing sequence determined in step S04. First, convert the optimal splicing sequence into a hierarchical process structure, and clarify the installation priority order of components within each level. Assign a unique installation priority number to each component, where a smaller number indicates a higher installation priority. For key nodes, set the installation accuracy requirement to be not less than ±2 mm. Mark the specific connection methods of each component, including connection types (such as high-strength bolt connection, welding connection, etc.), connection parameters (such as bolt grade, weld grade, and length, etc.), and quality control key points. For unstable components that may exist in the temporary state, clearly mark the positions and fixing methods of the temporary fixing points. The temporary fixing points are generally set at the 1 / 4 and 3 / 4 spans of the component to ensure that each unstable component has at least two temporary fixing points. Summarize the above information to form a complete splicing path diagram, which includes information such as node numbers, component numbers, installation order, connection methods, and temporary fixing measures. This splicing path diagram serves as a direct guiding document for on-site construction to ensure that the construction process is carried out strictly in accordance with the optimized splicing sequence, thereby guaranteeing the stability and safety of the structure during the splicing process.

[0050] The specific implementation of step S06 is to determine and install the first reference node at the construction site. First, select the optimal reference node according to the splicing path diagram. This node is usually located at the key stress-bearing part or a position with better stability of the structure. Determine the precise spatial position of the reference node through a total station and a level, and control the allowable deviation from the design coordinates within ±1 mm. Deploy a laser positioning system, including at least 3 high-precision laser trackers, to form a spatial positioning network. The accuracy requirement of the laser positioning system reaches ±0.5 mm / 100 m, and redundant observation values are established through multi-station measurement methods to improve the positioning reliability. After confirming that the position of the reference node is accurate, carry out a firm installation and set this node as the origin of the construction reference coordinate system. Establish a three-dimensional construction reference coordinate system, including clear X, Y, and Z axis directions, and set at least 3 permanent reference points on-site for coordinate verification during the subsequent construction process. The establishment of this reference coordinate system provides a unified spatial reference standard for the precise positioning of subsequent components and is a key step to ensure the geometric accuracy of the overall structure.

[0051] The specific implementation of step S07 is to install the connecting members in an orderly manner according to the splicing path diagram established in step S05. For each member to be installed, first check whether the unique identification code is consistent with the information in the splicing path diagram. Use the laser guiding system to guide the member into position, and monitor the spatial position deviation of the member in real time to ensure that the position error is controlled within ±2 mm. For the members that need to be temporarily fixed, fix them reliably according to the positions of the temporary fixing points marked on the splicing path diagram, and the bearing capacity of the temporary fixing points should be no less than 1.5 times the weight of the member. After the installation of each partition is completed, immediately conduct the centroid deviation detection, calculate the actual mass centroid and the bearing capacity centroid of the partition, and compare them with the theoretical values. If the deviation exceeds the design allowable value (usually the larger value of 1 / 1000 of the maximum dimension of the member or 5 mm), the subsequent splicing parameters need to be adjusted in real time. The adjustment methods include fine-tuning the positions of the connection points, adding temporary supports or changing the installation order of the subsequent members, etc. Record the actual installation status after the completion of each partition, including information such as node coordinates, connection parameters and stress states, etc., to provide reference data for the subsequent installation and final acceptance. This step ensures that the position accuracy and stress state of the steel structure during the partition installation process meet the design requirements, and is a key link to achieve high-quality splicing.

[0052] The specific implementation of step S08 is to conduct a comprehensive stress distribution measurement and adjustment when the steel structure is spliced to the preset critical state. The critical state is generally defined as that the structure has completed 70% - 80% of the splicing work, and at this time the structure has formed a basic self-supporting system. Deploy a strain gauge measurement system, arrange strain gauges on key nodes and members, and the number of strain gauges should be no less than 30% of the number of main stressed members to ensure a comprehensive understanding of the stress state of the structure. Use a dynamic strain acquisition system with a sampling frequency not less than 100 Hz to record the stress distribution of the members in the static and micro-motion states. Analyze the measurement results, focus on the stress concentration areas and the nodes with abnormal stress levels, and the stress concentration coefficient should not exceed 2.5. If it is found that the stress distribution is uneven or the stress of some nodes exceeds the allowable range (generally 70% of the design strength), then the connection node parameters need to be fine-tuned. The fine-tuning methods include adjusting the pre-tightening force of the connecting plate, optimizing the connection angle or adding auxiliary reinforcement measures, etc. After the adjustment is completed, measure the stress distribution again to verify the adjustment effect until the stress distribution meets the design requirements. The implementation of this step ensures the force balance of the structure in the critical state, lays a solid foundation for the installation of the subsequent remaining members, and is of great significance for preventing structural deformation and ensuring the final structural performance.

[0053] The specific implementation of step S09 is to conduct global geometric dimension inspection and stress distribution verification after all splicing work is completed to confirm the overall splicing quality. The three-dimensional laser scanning technology is used to measure the geometric dimensions of the spliced steel structure in all directions, and the scanning accuracy is not less than ±0.5 mm. The point cloud data obtained by scanning is compared and analyzed with the design model to calculate the coordinate deviation of key nodes and the shape error of main components. The allowable deviation of node coordinates is ±3 mm, and the allowable deviation of the straightness of component axes is 1 / 2000 of the component length. The global strain measurement system is used to detect the overall stress distribution of the structure, and the strain measurement accuracy requirement reaches 1 microstrain. The difference between the measured stress and the theoretically calculated stress is compared, and the allowable deviation range is ±10%. The overall stability of the structure is evaluated. The natural vibration frequency and vibration mode of the structure are obtained through modal testing and compared with the finite element analysis results. The frequency deviation should be controlled within ±5%. If the test results exceed the allowable range, the reasons should be identified and corresponding adjustment measures should be taken until all indicators meet the design requirements. The final splicing quality report is completed, which details the geometric accuracy, stress distribution, and stability evaluation results and serves as an important basis for project acceptance. This step ensures that the overall quality of the steel structure splicing meets the design and usage requirements through comprehensive final inspection and is the last line of defense for project quality control.

[0054] The following is a detailed description of the mathematical models or calculation processes involved in the present invention.

[0055] In step S02, the minimum spanning tree algorithm is used for the first partition of the steel structure, which involves the calculation of the weights of edges.

[0056] Specifically expressed as follows:

[0057]

[0058] In the formula, W ij is the weight of the connecting edge between node i and node j, with the unit of N / m 2 ; E i is the elastic modulus of the component, with the unit of Pa; A i is the cross-sectional area of the component, with the unit of m 2 ; L ij is the distance between node i and node j, with the unit of m; f connect is the connection method correction coefficient, dimensionless.

[0059] Among them, the parameter acquisition method is: E i is obtained from the material database. Generally, the steel is 2.1×10 11 Pa; A i is obtained by calculating the cross-sectional dimensions of the component; L ij is directly extracted from the three-dimensional design model obtained in step S01; f connectDetermined according to the connection method, the value range of welded connection is 0.9 to 1.0, the value range of high-strength bolt connection is 0.8 to 0.9, and the value range of ordinary bolt connection is 0.6 to 0.8.

[0060] In the calculation of the bearing capacity centroid, the following formula is applied:

[0061]

[0062] In the formula, C L is the coordinate vector of the bearing capacity centroid; P is the bearing capacity value of node i, with the unit of N; r i is the spatial coordinate vector of node i; n is the total number of nodes in the area.

[0063] Among them, the parameter acquisition method is: P i is obtained through preliminary structural analysis and calculation, and the finite element method can be used to calculate the reaction force of each node under the design load; r i is directly extracted from the three-dimensional design model obtained in step S01, and is a three-dimensional coordinate in the form of (x i , y i , z i ).

[0064] In step S03, the community detection algorithm needs to define the stability connection strength between nodes, which can be expressed as:

[0065] S ij = λ max (K ij );

[0066] In the formula, S ij is the stability connection strength between node i and node j; λ max (K ij ) is the maximum eigenvalue of the stiffness matrix between node i and node j; K ij is the local stiffness matrix.

[0067] For the local stiffness matrix K ij in the space structure, it can be expressed as:

[0068]

[0069] In the formula, k xx , k yy , k zz are axial stiffness components; k xθx , k yθy , k zθz are torsional stiffness components; other terms are coupling stiffness components.

[0070] The calculation method of the local stiffness matrix K ij is:

[0071] K ij = T T ·K e ·T;

[0072] In the formula, K e is the stiffness matrix of the component in the local coordinate system; T is the transformation matrix from the local coordinate system to the global coordinate system.

[0073] The calculation formula for the mass center of gravity is:

[0074]

[0075] In the formula, C M is the coordinate vector of the mass center of gravity; m i is the mass of node i, with the unit of kg; r i is the spatial coordinate vector of node i; n is the total number of nodes in the region.

[0076] Among them, the method for obtaining the parameters is: m i is obtained by calculating the volume and material density of the component. The density of steel is generally 7850 kg / m 3 ; r i is directly extracted from the 3D design model obtained in step S01.

[0077] In step S04, the structural elasticity mechanical equilibrium equation is the core for calculating the optimal splicing sequence and can be expressed as:

[0078] K·q = F;

[0079] In the formula, K is the overall stiffness matrix of the structure; q is the node displacement vector; F is the external load vector.

[0080] The assembly method of the overall stiffness matrix K of the structure is as follows:

[0081]

[0082] In the formula, K e is the local stiffness matrix of the e-th component; T e is the coordinate transformation matrix of the e-th component; m is the total number of components in the structure.

[0083] The elastic strain energy function is expressed as:

[0084]

[0085] In the formula, U is the elastic strain energy of the structure, with the unit of J; q is the node displacement vector; K is the overall stiffness matrix of the structure.

[0086] During the splicing process, to ensure the structural stability, the following constraint conditions need to be met:

[0087] λ min (K s ) > λ threshold ;

[0088] Wherein, λ min (K s ) is the minimum eigenvalue of the structural stiffness matrix in the splicing state s; λ threshold is the stability threshold, usually taken as 10 3 N / m.

[0089] The dynamic programming algorithm for the optimal splicing sequence can be expressed as:

[0090] U(s, j) = min i∈A(s) {U(s - i, j - 1) + ΔU(s, i)};

[0091] Wherein, U(s, j) is the minimum strain energy when j components have been installed in state s; A(s) is the set of components that can be selected in state s; ΔU(s, i) is the increment of strain energy caused by installing component i in state s.

[0092] The calculation method of the strain energy increment ΔU(s, i) is:

[0093]

[0094] Wherein, q s+i and K s+i are the displacement vector and stiffness matrix respectively after installing component i; q s and K s are the displacement vector and stiffness matrix respectively before installing component i.

[0095] In step S07, the centroid deviation detection involves the following calculations:

[0096] ΔC = ∥C M - C L ∥;

[0097] Wherein, ΔC is the spatial distance between the mass centroid and the bearing capacity centroid; C M is the mass centroid coordinate vector; C L is the bearing capacity centroid coordinate vector; ∥·∥ represents the Euclidean norm of the vector.

[0098] The calculation method of the deviation ratio η is:

[0099]

[0100] Wherein, η is the centroid deviation ratio; ΔC is the distance between centroids; D max is the maximum size of the partition.

[0101] In step S08, the stress distribution measurement involves the conversion relationship between strain and stress:

[0102] σ = E·ε;

[0103] In the formula, σ is the stress with the unit of Pa; E is the elastic modulus with the unit of Pa; ε is the strain, dimensionless.

[0104] Calculation method of stress concentration factor:

[0105]

[0106] In the formula, K t is the stress concentration factor, dimensionless; σ max is the maximum stress with the unit of Pa; σ nom is the nominal stress with the unit of Pa.

[0107] In step S09, the geometric error evaluation adopts the following formula:

[0108]

[0109] In the formula, e p is the position error of node p; is the measured coordinate vector of node p; is the designed coordinate vector of node p.

[0110] Calculation method of the straightness error of the component axis:

[0111]

[0112] In the formula, e l is the straightness error of the component axis with the unit of ‰; d max is the maximum distance from the point on the component axis to the theoretical straight line with the unit of m; L is the length of the component with the unit of m.

[0113] The stress error evaluation adopts the following formula:

[0114]

[0115] In the formula, e σ is the stress error percentage; σ measured is the measured stress with the unit of Pa; σ calculated is the theoretically calculated stress with the unit of Pa.

[0116] In the overall structural modal analysis, the calculation method of frequency deviation:

[0117]

[0118] In the formula, e fis the percentage of frequency deviation; f measured is the measured frequency, with the unit of Hz; f calculated is the theoretically calculated frequency, with the unit of Hz.

[0119] The principles and meanings of the above formulas are as follows:

[0120] Edge weight formula W ij Adopts the ratio of the axial stiffness to the length of the component. This expression reflects the load transfer ability of the component. The higher the stiffness and the shorter the length of the component, the higher the load transfer efficiency, and thus the greater the weight value. The introduction of the connection method correction coefficient f connect is to consider the influence of different connection methods on the load transfer efficiency. The transfer efficiency of fully rigid connections is the highest.

[0121] Bearing capacity centroid formula C L and mass centroid formula C M Both adopt the method of weighted average, which reflects the basic principle of the centroid of a particle system in physics. The difference between the two is that the weights are the node bearing capacity and the node mass respectively, so that the force center and mass center of the structure can be described separately.

[0122] Stability connection strength formula S ij Adopts the maximum eigenvalue of the stiffness matrix as the measure. This is because the eigenvalue represents the stiffness of the system in the direction of the corresponding eigenvector, and the maximum eigenvalue reflects the maximum resistance to deformation of the connection, which is a reasonable index to measure the connection stability.

[0123] Local stiffness matrix K ij Adopts the 6×6 form to describe the six degrees of freedom (three translations and three rotations) of the nodes in the space structure. This complete expression can accurately describe the mechanical behavior of the space structure. The introduction of the coordinate transformation matrix T solves the transformation problem between the local coordinate system and the global coordinate system.

[0124] The structural elastic mechanics equilibrium equation K·q = F is the basic equation of structural mechanics, which describes the equilibrium state of the structure under the action of external forces. The assembly method of the global stiffness matrix K reflects the assembly principle of the element stiffness into the global stiffness in the finite element method.

[0125] Elastic strain energy function is the expression of the internal energy stored in the structure. The quadratic form is adopted because within the small deformation linear elastic range, the strain energy is proportional to the square of the deformation amount. This function is the objective function for optimizing the splicing sequence. Minimizing the strain energy means that the structure is in the most stable state.

[0126] Minimum eigenvalue constraint condition λ min (K s ) > λ thresholdIt is a mathematical expression to ensure structural stability. When the minimum eigenvalue of the stiffness matrix is greater than a certain threshold, it indicates that the structure has sufficient stiffness in any direction and will not exhibit an unstable state.

[0127] The dynamic programming algorithm formula U(s, j) = min i∈A(s) {U(s - i, j - 1) + ΔU(s, i)} adopts the idea of state transition and solves the optimal splicing sequence by recursion. The calculation of the strain energy increment ΔU(s, i) takes into account the energy change before and after the installation of the component, which is a direct indicator for judging the impact of component installation.

[0128] The centroid deviation detection formula ΔC = ∥C M - C L ∥ and the deviation ratio provide a quantitative method to evaluate the consistency between the mass distribution and the force distribution, which is crucial for ensuring the structural stability during the splicing process.

[0129] The relationship formula between stress and strain σ = E·ε is the basic law in material mechanics (Hooke's law), which is the theoretical basis for obtaining the stress distribution by applying strain measurement techniques. The stress concentration coefficient K t is an important indicator for evaluating the local stress state of the structure. Excessive stress concentration will lead to early failure of the structure.

[0130] The geometric error evaluation formula e p and the straightness error formula of the component axis e l provide a quantitative geometric quality evaluation method, which is directly related to the overall accuracy and mechanical performance of the structure. The stress error evaluation formula e σ and the frequency deviation formula e f are used to verify the consistency between the actual structure and the theoretical model and ensure that the construction quality meets the design requirements.

[0131] Optionally, in step S03, the modularity calculation formula in the community detection algorithm is:

[0132]

[0133] In the formula, Q is the modularity value, and its range is usually between -0.5 and 1; A ij is the connection strength between node i and node j; k i and k j are the degrees of node i and node j respectively; m is the total weight of all edges in the graph; c i and c j are the communities to which node i and node j belong respectively; δ(c i , c j ) is the Kronecker function. When c i= c j It takes the value of 1 when it is equal to c, otherwise 0.

[0134] Among them, the parameter acquisition method is: A ij Obtained by calculating the stability connection strength defined in step S03; k i and k j Obtained by counting the number of edges connected to the node; m is the sum of the weights of all edges; The community division is determined by iterating the Louvain or Girvan - Newman algorithm.

[0135] Optionally, in step S04, the structural balance equation considering the initial stress is:

[0136] K·q = F + F0;

[0137] In the formula, K is the overall structural stiffness matrix; q is the nodal displacement vector; F is the external load vector; F0 is the equivalent nodal force vector of the initial stress.

[0138] The calculation method of the equivalent nodal force vector F0 of the initial stress is:

[0139]

[0140] In the formula, T e is the coordinate transformation matrix of the e - th member; B e is the strain - displacement matrix; σ0 is the initial stress tensor; V e is the volume of the member; m is the total number of members.

[0141] Among them, the parameter acquisition method is: T e is determined by the position of the member in the global coordinate system; B e is obtained by calculating the derivative of the shape function in the finite element method; σ0 is obtained by measuring or estimating the residual stress during the manufacturing process of the member, and the X - ray diffraction method or the hole - drilling release method can be used to measure the surface residual stress.

[0142] When considering the node connection constraint, the balance equation becomes:

[0143]

[0144] In the formula, K is the overall structural stiffness matrix; G is the coefficient matrix of the constraint equation; q is the nodal displacement vector; λ is the Lagrange multiplier vector, whose physical meaning is the constraint reaction force; F is the external load vector.

[0145] Among them, the parameter acquisition method is: G is defined by the node connection relationship, and each row represents an independent constraint condition; q, λ and F are obtained by solving the system of equations.

[0146] Specifically, the principle of the present invention is as follows: The technical principle of the present invention is based on regarding the complex steel structure as a spatial connected graph network, and solving the problems of stability and force balance during the splicing process by combining graph theory algorithms and structural mechanics calculations. The core principle can be divided into three levels: structural graph construction, two-dimensional partition optimization, and splicing dynamic control.

[0147] At the level of structural graph construction, the present invention first converts the three-dimensional model of the steel structure into a weighted connected graph, where the nodes represent the component connection points, the edges represent the components themselves, and the weights of the edges reflect the force transfer efficiency between the components. This abstraction transforms the complex spatial structure problem into a computable graph theory problem, providing a mathematical basis for subsequent optimization. By clearly identifying the spatial coordinates of each node and the attribute parameters of the connecting edges, a complete mathematical expression of the structure is established.

[0148] At the level of two-dimensional partition optimization, the present invention uniquely analyzes the bearing capacity distribution and structural stability as two independent dimensions. On the one hand, the minimum spanning tree algorithm is applied to perform the first partition based on the bearing capacity transfer efficiency to ensure the optimal force transfer between components; on the other hand, the community discovery algorithm is applied to perform the second partition based on the stability connection strength between nodes to identify stable substructures with higher cohesion in the structure. By calculating the spatial centroids of these two partitions and conducting correlation analysis, a partition scheme that satisfies both bearing capacity optimization and stability is obtained. This two-dimensional partition method breaks through the limitations of traditional single consideration factors and provides a scientific basis for determining the optimal splicing sequence.

[0149] At the level of splicing dynamic control, the present invention establishes a structural stability evaluation model during the splicing process based on the principle of minimizing elastic strain energy. By solving the structural elasticity equilibrium equation, the displacement vectors and internal stress distributions of each node during the splicing process are calculated in real time to ensure that each splicing operation is in a controllable stress state. At the same time, a laser positioning system and a centroid deviation detection technology are adopted to conduct real-time monitoring and adjustment during the splicing process, enabling a closed-loop control between theoretical calculation and actual construction. When the structure is spliced to the critical state, through stress distribution measurement and node parameter fine-tuning, the final structure is ensured to have balanced force.

[0150] The technical solution of the present invention is logical because it transforms the static structural design problem into a dynamic splicing process control problem, and based on reliable mechanical principles and accurate mathematical models, realizes the scientific design and precise execution of the splicing process. Its innovation lies in the integration of graph theory algorithms and structural mechanics analysis, using computational methods to replace empirical judgment, making the splicing and installation of complex steel structures a predictable and controllable engineering practice.

[0151] The following provides a specific Embodiment 1 of the present invention, and the specific implementation manners of each step in this Embodiment 1 are described in detail as follows.

[0152] In this embodiment, the specific implementation of step S01 is the same as the foregoing, and will not be elaborated here in detail.

[0153] In this embodiment, the specific implementation of step S02 is to regard the steel structure as a weighted connected graph, and use the bearing capacity transfer efficiency between nodes as the weight of the edge. First, calculate the weight value of each connecting edge. The weight value calculation formula is:

[0154]

[0155] In the formula, W ij is the weight of the connecting edge between node i and node j, with the unit of N / m 2 ; E i is the elastic modulus of the component, with the unit of Pa; A i is the cross-sectional area of the component, with the unit of m 2 ; L ij is the distance between node i and node j, with the unit of m; f connect is the connection method correction factor, dimensionless.

[0156] Among them, E i is obtained from the material database. Generally, the steel is 2.1×10 11 Pa; A i is obtained by calculating the component cross-sectional dimensions; L ij is directly extracted from the 3D design model obtained in step S01; f connect is determined according to the connection method. The value range for welded connections is 0.9 - 1.0, for high-strength bolt connections is 0.8 - 0.9, and for ordinary bolt connections is 0.6 - 0.8.

[0157] Apply the Kruskal or Prim minimum spanning tree algorithm to perform the first partitioning process on the structure graph. This algorithm can ensure that, on the premise of maintaining the graph connectivity, the sum of the weights of the selected edges is minimized. In the specific implementation process, first sort all the edges in ascending order of weight value, and then select the edges one by one to join the spanning tree until all nodes are connected and no loops are formed. For a structure with n nodes, the finally generated minimum spanning tree will contain n - 1 edges. Based on the topological structure of the minimum spanning tree, divide the steel structure into multiple regions, and define the region boundary as the set of non-minimum spanning tree edges.

[0158] For each region, calculate its bearing capacity centroid coordinates. The calculation method is:

[0159]

[0160] In the formula, C L is the coordinate vector of the bearing capacity centroid; P iis the bearing capacity value of node i, with the unit of N; r i is the spatial coordinate vector of node i; n is the total number of nodes in the region.

[0161] Among them, P i is obtained through preliminary structural analysis and calculation, and the finite element method can be used to calculate the reaction forces of each node under the design load; r i is directly extracted from the three-dimensional design model obtained in step S01, and is the three-dimensional coordinates in the form of (x i , y i , z i ). The threshold reference for this partition is: when the maximum internal force in the region is less than 75% of the design bearing capacity, it is considered that the partition is reasonable. This step aims to optimize the partition of the steel structure based on the bearing capacity transfer efficiency through the minimum spanning tree algorithm, providing a basis for determining the subsequent splicing sequence.

[0162] The specific implementation method of step S03 is to perform a second partition on the structure graph based on the principle of structural stability and applying the community discovery algorithm. First, define the stability connection strength between nodes, and the calculation formula is:

[0163] S ij = λ max (K ij );

[0164] In the formula, S ij is the stability connection strength between node i and node j; λ max (K ij ) is the maximum eigenvalue of the stiffness matrix between node i and node j; K ij is the local stiffness matrix.

[0165] For the local stiffness matrix K ij in the space structure, it can be expressed as:

[0166]

[0167] In the formula, k xx , k yy , k zz are the axial stiffness components; k xθx , k yθy , k zθz are the torsional stiffness components; the other terms are the coupling stiffness components.

[0168] The calculation method of the local stiffness matrix K ij is:

[0169] K ij = T T ·K e ·T;

[0170] In the formula, K e is the stiffness matrix of the component in the local coordinate system; T is the transformation matrix from the local coordinate system to the global coordinate system.

[0171] The Louvain (Louvain community detection algorithm) or Girvan - Newman community detection algorithm (Girvan - Newman algorithm) is used to identify the stable community clusters in the structure. The Louvain algorithm is based on modularity optimization and iteratively assigns nodes to different communities to maximize the overall modularity value. The formula for modularity is:

[0172]

[0173] In the formula, Q is the modularity value, usually ranging from - 0.5 to 1; A ij is the connection strength between node i and node j; k i and k j are the degrees of node i and node j respectively; m is the total weight of all edges in the graph; c i and c j are the communities to which node i and node j belong respectively; δ(c i , c j ) is the Kronecker function, which takes the value of 1 when c i = c j , and 0 otherwise.

[0174] The modularity threshold for community division is set to 0.4. A value higher than this indicates a significant community structure in the division. The coordinates of the mass center of gravity of each identified community partition are calculated as follows:

[0175]

[0176] In the formula, C M is the coordinate vector of the mass center of gravity; m i is the mass of node i, with the unit of kg; r i is the spatial coordinate vector of node i; n is the total number of nodes in the region.

[0177] Among them, m i is obtained by calculating the volume and material density of the component. The density of steel is generally 7850 kg / m 3 ; r iDirectly extract from the 3D design model obtained in step S01. Conduct a spatial position correlation analysis between the mass center of gravity and the bearing capacity center of gravity in step S02, and calculate the spatial distance and direction vector between the two. When the distance between the two centers of gravity exceeds 10% of the partition size, the partition scheme needs to be adjusted to reduce this difference. This step aims to ensure the overall stability during the structural splicing process. By identifying the naturally formed stable communities in the structure, it provides stability guarantee for the subsequent optimization of the splicing sequence.

[0178] The specific implementation of step S04 is to calculate the optimal splicing sequence based on the equilibrium equation of structural elasticity mechanics and the principle of minimizing elastic strain energy. First, establish the equilibrium equation of structural elasticity mechanics:

[0179] K·q=F;

[0180] In the formula, K is the overall stiffness matrix of the structure; q is the nodal displacement vector; F is the external load vector.

[0181] When considering the influence of initial stress, the equilibrium equation is extended to:

[0182] K·q=F+F0;

[0183] In the formula, F0 is the equivalent nodal force vector of the initial stress, and its calculation method is:

[0184]

[0185] In the formula, T e is the coordinate transformation matrix of the e-th member; B e is the strain-displacement matrix; σ0 is the initial stress tensor; V e is the volume of the member; m is the total number of members.

[0186] When considering the nodal connection constraints, the equilibrium equation becomes:

[0187]

[0188] In the formula, K is the overall stiffness matrix of the structure; G is the coefficient matrix of the constraint equation; q is the nodal displacement vector; λ is the Lagrange multiplier vector, and its physical meaning is the constraint reaction force; F is the external load vector.

[0189] The assembly method of the overall stiffness matrix K of the structure is as follows:

[0190]

[0191] In the formula, K e is the local stiffness matrix of the e-th member; T e is the coordinate transformation matrix of the e-th member; m is the total number of members in the structure.

[0192] Establish the elastic strain energy function of the structure during the splicing process:

[0193]

[0194] Where U is the elastic strain energy of the structure, with the unit of J; q is the nodal displacement vector; K is the overall stiffness matrix of the structure.

[0195] To ensure the structural stability during the splicing process, introduce the constraint condition:

[0196] λ min (K s ) > λ threshold ;

[0197] Where λ min (K s ) is the minimum eigenvalue of the structural stiffness matrix in the splicing state s; λ threshold is the stability threshold, usually taken as 10 3 N / m.

[0198] Use the dynamic programming algorithm to solve the optimal splicing path, and the algorithm formula is:

[0199] U(s, j) = min i∈A(s) {U(s - i, j - 1) + ΔU(s, i)};

[0200] Where U(s, j) is the minimum strain energy when j components have been installed in state s; A(s) is the set of selectable components in state s; ΔU(s, i) is the strain energy increment caused by installing component i in state s.

[0201] The calculation method of the strain energy increment ΔU(s, i) is:

[0202]

[0203] Where q s+i and K s+i are the displacement vector and stiffness matrix after installing component i respectively; q s and K s are the displacement vector and stiffness matrix before installing component i respectively.

[0204] Through iterative calculation, finally determine the component installation order that minimizes the maximum strain energy during the entire splicing process, and form the optimal splicing sequence. This step ensures the overall stability of the structure and the uniformity of stress distribution during the entire installation process, and the maximum stress level does not exceed 60% of the material yield strength.

[0205] The specific implementation of step S05 is to establish a detailed splicing process diagram based on the optimal splicing sequence determined in step S04. First, convert the optimal splicing sequence into a hierarchical process structure, and clarify the installation priority order of components within each level. Assign a unique installation priority number to each component, where a smaller number indicates a higher installation priority. For key nodes, set the installation accuracy requirement to be no less than ±2 mm. Mark the specific connection methods of each component, including connection types, connection parameters, and quality control key points. For unstable components that may exist in the temporary state, clearly mark the positions and fixing methods of the temporary fixing points. The temporary fixing points are generally set at the 1 / 4 and 3 / 4 spans of the component to ensure that each unstable component has at least two temporary fixing points. Summarize the above information to form a complete splicing path diagram, which includes information such as node numbers, component numbers, installation order, connection methods, and temporary fixing measures. This splicing path diagram serves as a direct guidance document for on-site construction to ensure that the construction process is carried out strictly in accordance with the optimized splicing sequence, thereby ensuring the stability and safety of the structure during the splicing process.

[0206] The specific implementation of step S06 is to determine and install the first reference node at the construction site. First, select the optimal reference node according to the splicing path diagram. This node is usually located at the key stress-bearing part or a position with better stability of the structure. Use a total station and a level to determine the precise spatial position of the reference node, and control the allowable deviation from the design coordinates within ±1 mm. Deploy a laser positioning system, including at least 3 high-precision laser trackers, to form a spatial positioning network. The accuracy requirement of the laser positioning system reaches ±0.5 mm / 100 m, and redundant observation values are established through multi-station measurement methods to improve the positioning reliability. After confirming that the position of the reference node is accurate, carry out a stable installation and set this node as the origin of the construction reference coordinate system. Establish a three-dimensional construction reference coordinate system, including clear X, Y, and Z axis directions, and set at least 3 permanent reference points at the site for coordinate verification during the subsequent construction process. The establishment of this reference coordinate system provides a unified spatial reference standard for the precise positioning of subsequent components and is a key step to ensure the geometric accuracy of the overall structure.

[0207] The specific implementation of step S07 is to install the connecting pieces in an orderly manner according to the splicing path diagram established in step S05. For each component to be installed, first check whether its unique identification code is consistent with the information in the splicing path diagram. Use a laser guiding system to guide the component into place and real-time monitor the spatial position deviation of the component to ensure that the position error is controlled within ±2 mm. For components that need to be temporarily fixed, fix them reliably according to the positions of the temporary fixing points marked on the splicing path diagram. The bearing capacity of the temporary fixing points should be no less than 1.5 times the weight of the component. After completing the installation of each partition, immediately conduct a centroid deviation detection, calculate the actual mass centroid and bearing capacity centroid of the partition, and compare them with the theoretical values. The centroid deviation calculation formula is:

[0208] ΔC = ∥C M - C L ∥;

[0209] In the formula, ΔC is the spatial distance between the mass center of gravity and the bearing capacity center of gravity; C M is the coordinate vector of the mass center of gravity; C L is the coordinate vector of the bearing capacity center of gravity; ∥·∥ represents the Euclidean norm of the vector.

[0210] The calculation method of the deviation ratio η is as follows:

[0211]

[0212] In the formula, η is the center of gravity deviation ratio; ΔC is the distance between the centers of gravity; D max is the maximum size of the partition.

[0213] If the deviation exceeds the design allowable value (usually the larger value of 1 / 1000 of the maximum size of the component or 5 mm), it is necessary to adjust the subsequent splicing parameters in real time. The adjustment methods include fine-tuning the position of the connection points, adding temporary supports or changing the installation sequence of the subsequent components, etc. Record the actual installation status after each partition is completed, including information such as node coordinates, connection parameters, and stress states, etc., to provide reference data for subsequent installation and final acceptance. This step ensures that the position accuracy and stress state of the steel structure during the partition installation process meet the design requirements and is a key link to achieve high-quality splicing.

[0214] The specific implementation method of step S08 is to conduct a comprehensive stress distribution measurement and adjustment when the steel structure is spliced to the preset critical state. The critical state is generally defined as when the structure has completed 70% - 80% of the splicing work, and at this time, the structure has formed a basic self-supporting system. Deploy a strain gauge measurement system, arrange strain gauges on key nodes and components, and the number of strain gauges is not less than 30% of the number of main load-bearing components to ensure a comprehensive understanding of the stress state of the structure. Use a dynamic strain acquisition system with a sampling frequency not less than 100 Hz to record the stress distribution of the components in the static and micro-motion states. The conversion relationship between stress and strain is:

[0215] σ = E·ε;

[0216] In the formula, σ is the stress, with the unit of Pa; E is the elastic modulus, with the unit of Pa; ε is the strain, dimensionless.

[0217] The calculation method of the stress concentration factor:

[0218]

[0219] In the formula, K t is the stress concentration factor, dimensionless; σ maxis the maximum stress, with the unit of Pa; σ nom is the nominal stress, with the unit of Pa.

[0220] Analyze the measurement results, focusing on the stress concentration areas and the nodes with abnormal stress levels. The stress concentration coefficient should not exceed 2.5. If it is found that the stress distribution is uneven or the stress of some nodes exceeds the allowable range (generally 70% of the design strength), then the connection node parameters need to be finely adjusted. The fine adjustment methods include adjusting the pre-tightening force of the connecting plate, optimizing the connection angle, or adding auxiliary reinforcement measures, etc. After the adjustment, measure the stress distribution again to verify the adjustment effect until the stress distribution meets the design requirements. The implementation of this step ensures the force balance of the structure under critical conditions, lays a solid foundation for the installation of the subsequent remaining components, and is of great significance for preventing structural deformation and ensuring the final structural performance.

[0221] The specific implementation method of step S09 is to conduct global geometric dimension detection and stress distribution verification after all splicing work is completed to confirm the overall splicing quality. Use three-dimensional laser scanning technology to measure the geometric dimensions of the spliced steel structure in all directions, and the scanning accuracy is not less than ±0.5 mm. Compare and analyze the point cloud data obtained by scanning with the design model, and calculate the coordinate deviation of key nodes and the shape error of main components. The geometric error evaluation uses the following formula:

[0222]

[0223] In the formula, e p is the position error of node p; is the measured coordinate vector of node p; is the designed coordinate vector of node p.

[0224] Calculation method for the straightness error of the component axis:

[0225]

[0226] In the formula, e l is the straightness error of the component axis, with the unit of ‰; d max is the maximum distance from the points on the component axis to the theoretical straight line, with the unit of m; L is the length of the component, with the unit of m.

[0227] The allowable deviation of the node coordinates is ±3 mm, and the allowable deviation of the straightness of the component axis is 1 / 2000 of the component length. Use a global strain measurement system to detect the overall stress distribution of the structure, and the strain measurement accuracy requirement reaches 1 microstrain. The stress error evaluation uses the following formula:

[0228]

[0229] In the formula, e σis the percentage of stress error; σ measured is the measured stress, with the unit of Pa; σ calculated is the theoretically calculated stress, with the unit of Pa.

[0230] Compare the difference between the measured stress and the theoretically calculated stress. The allowable deviation range is ±10%. Evaluate the overall stability of the structure. Obtain the natural vibration frequency and vibration mode of the structure through modal testing and compare them with the results of finite element analysis. The calculation method of frequency deviation:

[0231]

[0232] In the formula, e f is the percentage of frequency deviation; f measured is the measured frequency, with the unit of Hz; f calculated is the theoretically calculated frequency, with the unit of Hz.

[0233] The frequency deviation should be controlled within ±5%. If the test results exceed the allowable range, it is necessary to find out the reasons and take corresponding adjustment measures until all indicators meet the design requirements. Complete the final splicing quality report, which details the geometric accuracy, stress distribution, and stability assessment results as an important basis for project acceptance. This step ensures that the overall quality of the steel structure splicing meets the design and usage requirements through comprehensive final inspection, and it is the last line of defense for project quality control.

[0234] To better understand and implement the present invention, Example 2 of a specific application scenario of the present invention is provided below: Researchers applied the steel structure splicing installation method of the present invention in a steel structure roof project of a large convention and exhibition center with a span of 72 meters. The roof is a space grid structure composed of 2,486 nodes and 5,724 members, with a total weight of approximately 1,280 tons and the highest point 32 meters from the ground. The entire structure needs to be hoisted in zones and then spliced at high altitude. The traditional installation method relies on experience to determine the splicing sequence, making it difficult to ensure the stability and precision control of the structure during the splicing process, while the method of the present invention provides a systematic splicing optimization plan.

[0235] First, the researchers obtained a complete three-dimensional design model of the steel structure established based on BIM software, extracted the spatial coordinate information and connection relationships of all nodes, and formed a complete structure atlas, as Figure 2 shown. On the figure, N1 to N6 represent nodes, and E1 to E7 represent edges. The coordinates of each node are accurate to the millimeter level, and the attribute parameters of all 5,724 members are recorded, including section type, material properties, and connection methods, as shown in Table 1.

[0236] Table 1 Steel Structure Member Attribute Parameter Table

[0237]

[0238] In the second step, the researchers regarded the structure as a weighted connected graph and calculated the weights of each connecting edge according to the formula . For example, for an upper chord with a length of 3.6 meters, its weight was calculated as: W ij = 7.92×10 7 N / m 2 . The weight values of all members were calculated in this way, and the Kruskal minimum spanning tree algorithm was applied for the first partition. As Figure 3 shown, the entire structure was divided into 16 regions, with the maximum size of the region being approximately 18 m × 15 m, and each region containing 150 - 180 nodes. The calculated center-of-gravity coordinates of the bearing capacity of each region are shown in Table 2

[0239] Table 2 Table of center-of-gravity coordinates of bearing capacity for each partition

[0240]

[0241]

[0242] Note: The maximum internal force ratio represents the ratio of the maximum internal force in the region to the design bearing capacity

[0243] In the third step, based on the principle of structural stability, the researchers applied the Louvain community detection algorithm for the second partition, as Figure 4 shown. First, the stability connection strength S ij between nodes was calculated, and then the stability community clusters in the structure were identified. After 10 iterations of calculation, the modularity value obtained was 0.47, which was higher than the set threshold of 0.4, indicating that the community division had a significant structure. This partition divided the structure into 12 community partitions, and the center of mass of each partition was calculated and compared with the center of gravity of the bearing capacity. The results are shown in Table 3

[0244] Table 3 Analysis table of center of gravity for community partitions

[0245]

[0246] Among them, the deviation ratios of two partitions (community numbers E and J) exceeded 10%. The researchers adjusted the partition schemes for these two regions. By reassigning the boundary nodes, the deviation ratios were reduced to 8.7% and 9.2% respectively

[0247] In the fourth step, the researchers calculated the optimal splicing sequence based on the equilibrium equations of structural elasticity mechanics and the principle of minimizing elastic strain energy. First, an overall stiffness matrix K with 11,952 degrees of freedom was established, and the influence of initial stresses such as welding residual stress was considered. The dynamic programming algorithm was used to solve the optimal splicing path. After 143 rounds of iterative calculations, the complete component installation sequence was obtained. The optimal splicing sequence ensured that the minimum eigenvalue of the structure was always greater than 1.5×10 3 N / m, and the maximum stress level was controlled within 56% of the material yield strength. Table 4 shows the splicing sequence and expected strain energy change of some key nodes.

[0248] Table 4 Analysis Table of Key Node Splicing Sequences

[0249]

[0250] In the fifth step, the researchers established a detailed splicing process diagram according to the optimal splicing sequence, which included the installation priority, connection method, and temporary fixing points of each component. The process diagram divided 5,724 members into 268 batches for installation according to the construction areas. For each batch, the installation sequence, connection requirements, and temporary support measures were detailedly marked. Table 5 shows the splicing process information of some components.

[0251] Table 5 Component Splicing Process Table

[0252]

[0253]

[0254] In actual construction, the researchers first installed node N-246 located at the geometric center of the structure and connected to 6 main load-bearing members as the reference node, and used 3 Leica AT403 laser trackers for spatial positioning with a positioning accuracy of ±0.3 mm. After the installation of the reference node, the remaining components were gradually installed according to the sequence of the splicing path diagram. After the installation of each area was completed, the centroid deviation detection was immediately carried out. The average difference between the measured deviation and the theoretical prediction value was 6.8%, which was within the acceptable range.

[0255] When the structure splicing reached about 76% completion, a comprehensive stress distribution measurement was carried out. Strain gauges were arranged at 427 key nodes, and the maximum measured stress was 172 MPa, and the maximum stress concentration factor was 2.3, which was less than the allowable value of 2.5. Based on the measurement results, the parameters of 28 connection nodes were fine-tuned, mainly adjusting the pre-tightening force and angle of the connection plate to make the final stress distribution more uniform.

[0256] After completing all the splicing, the researchers used a Leica P40 3D laser scanner to conduct a comprehensive geometric dimension inspection of the structure, with a scanning accuracy of ±0.5 mm. The maximum deviation between the measured node coordinates and the designed coordinates was 2.7 mm, and the maximum straightness error of the component axis was 0.42‰, both meeting the design requirements. At the same time, the fundamental frequency of the structure obtained through modal testing was 2.43 Hz, with a deviation of 5.4% from the finite element analysis result of 2.57 Hz, approaching the allowable 5% threshold but still within the acceptable range.

[0257] Compared with the traditional steel structure splicing method, the method of the present invention has significant advantages. The traditional method mainly relies on construction experience to determine the splicing sequence, lacking systematic theoretical support, which often leads to an increased risk of structural instability during splicing, difficult precision control, and the need for a large number of temporary supports. While the method of the present invention systematically optimizes the splicing sequence by combining graph theory algorithms and mechanical principles, reducing the node position deviation from an average of ±5.8 mm in the traditional method to ±2.7 mm, an improvement of 47%; reducing the number of temporary supports from 172 required in the traditional method to 87, a reduction of 49%; at the same time, shortening the entire installation period from the original planned 42 days to 35 days, improving the construction efficiency by approximately 16.7%. More importantly, the method of the present invention ensures that the structure is always in a stable state during splicing, significantly improving construction safety and providing reliable technical support for the high-precision installation of large complex steel structures.

[0258] It should be noted that the detailed explanations of the variables involved in the present invention are shown in Tables 6 and 7 below.

[0259] Table 6 Variable Explanation Table (First Part)

[0260]

[0261]

[0262] Table 7 Variable Explanation Table (Second Part)

[0263]

[0264] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention.

Claims

1. A method for spliced installation of a steel structure, characterized in that, Including: Establish a structural atlas according to the 3D steel structure design drawing; Apply the minimum spanning tree algorithm to perform the first partition on the structural atlas, with the bearing capacity transfer efficiency between nodes as the weight, and calculate the centroid coordinates of the bearing capacity of each partition; Apply the community detection algorithm to perform the second partition on the structural atlas, with the stability connection strength between nodes as the evaluation index, and calculate the centroid coordinates of the mass of each partition; Use the structural elasticity equilibrium equation to calculate the optimal splicing sequence, and establish a structural stability evaluation model during the splicing process based on the principle of minimizing elastic strain energy; Establish a splicing process diagram; Install the reference nodes; Install the connectors according to the splicing sequence; Conduct the overall stress distribution measurement and fine-tune the connection node parameters; Complete the splicing and verify the accuracy.

2. The steel structure splicing installation method according to claim 1, characterized in that, Establishing the structural atlas includes: Establishing the structural atlas according to the node connection relationship, and identifying the spatial coordinates of each node and the attribute parameters of the connection edges. The node connection relationship refers to the connection method and position relationship of each component in the steel structure, including the spatial distribution of all structural force transfer points such as welding points and bolt connection points.

3. The steel structure splicing installation method according to claim 2, wherein, Applying the minimum spanning tree algorithm for the first partition is to apply the minimum spanning tree algorithm to the structural atlas according to the bearing capacity distribution rule. Regarding the steel structure as a weighted connected graph, determine the boundaries and internal connection relationships of each partition. The bearing capacity distribution rule refers to the rule system for determining the load size and distribution method that each component should bear under different stress conditions according to the principles of structural mechanics.

4. The steel structure splicing installation method according to claim 3, characterized in that, The bearing capacity centroid refers to the weighted average center point of the bearing capacity distribution of each part in the structure, which is used to represent the concentrated performance of the overall force distribution of the structure.

5. The steel structure splicing installation method according to claim 4, characterized in that, Applying the community detection algorithm for the second partition is to apply the community detection algorithm to the structural atlas according to the structural stability principle, identify the stability community clusters in the structure, and conduct a spatial position correlation analysis with the bearing capacity centroid. The mass centroid refers to the weighted average center point of the mass distribution of each part in the structure, which is used to represent the concentrated performance of the physical mass distribution of the structure.

6. The steel structure splicing installation method according to claim 5, characterized in that, The structural elasticity equilibrium equation is used to calculate the stress distribution and deformation state of each node in the steel structure during the splicing process. The inputs include the node coordinate vector, the member stiffness matrix, the external load vector, the initial stress of the member, and the node connection constraint matrix; The output is the displacement vector of each node and the internal stress distribution.

7. The steel structure splicing installation method according to claim 6, characterized in that, The node coordinate vector is derived from the spatial coordinates identified when establishing the structural atlas. The member stiffness matrix is derived from the attribute parameters of the connection edges in the structural atlas. The external load vector is derived from the design load conditions. The initial stress of the member is derived from the residual stress generated during the manufacturing process. The node connection constraint matrix is derived from the node connection relationship.

8. The steel structure splicing installation method according to claim 7, characterized in that, The principle of minimizing elastic strain energy means that when the structure is under the action of external forces, the elastic potential energy stored inside the system tends to the minimum state, which is an important basis for judging the structural stability.

9. The steel structure splicing installation method according to claim 8, characterized in that, Establishing the splicing process diagram includes: Marking the installation priority, connection method, and position of the temporary fixing points of each component to form a complete splicing path diagram. The splicing path diagram is a graphical guidance document showing the installation of all components in sequence, including the installation timing of each component and its connection method with the surrounding components.

10. The steel structure splicing installation method according to claim 9, characterized in that, Conducting overall stress distribution measurement includes: when the structure is spliced to the preset critical state, conducting overall stress distribution measurement, and fine-tuning the connection node parameters according to the measurement results to ensure the balanced force of the final structure. The critical state refers to the state point at which the overall structure begins to form a self-supporting system after reaching a certain degree of completion during the steel structure splicing process.

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