A steel pipe arch rib installation support design method and system considering load combination

Abstract

The application discloses a steel pipe arch rib installation support design method and system considering load combination, and the method comprises the following steps: firstly, defining arch rib installation multi-source load and dividing standard combination and basic combination, establishing a support and arch rib collaborative stress integral analysis model, combining arch rib segments and bridge surface constraints to determine support topology, and configuring component parameters to form an initial scheme; secondly, extracting time-varying load effects at each construction stage, constructing a multi-objective optimization function model, and determining a global optimal objective function; then, establishing a coupling relationship between support deformation and arch rib linear, and solving optimal pre-camber through inverse analysis iteration to eliminate linear error; finally, carrying out multiple checking on the support, optimizing rod parameters and structure in combination with buckling analysis, establishing a collaborative mechanical model to complete whole-process checking, and determining final design parameters. The method realizes dual protection of arch rib installation precision and structural stability.

Description

Technical Field

[0001] This invention belongs to the field of steel pipe arch rib installation bracket design technology, and more specifically, relates to a design method and system for steel pipe arch rib installation bracket that considers load combinations. Background Technology

[0002] During the installation of steel pipe arch ribs, a reasonable support design is the core prerequisite for ensuring the installation accuracy and construction safety. Currently, the installation of steel pipe arch ribs largely relies on traditional support design methods. These methods do not fully consider the load variation characteristics during construction, simply selecting a single load for design without distinguishing the load differences at different construction stages, resulting in a mismatch between the support design and the actual construction conditions.

[0003] Traditional design methods fail to establish a strong correlation between support deformation and the installation alignment of the arch ribs, neglecting the dynamic changes in loads during construction and failing to properly control the uniformity of stress on the support. This can easily lead to problems such as insufficient support strength or uneven stress distribution. Furthermore, traditional designs do not fully consider the effects of initial defects and nonlinear forces, and lack sufficient quantification of the support stability safety factor, making it difficult to meet the safety requirements at different construction stages.

[0004] Furthermore, traditional designs do not establish an effective correlation between bracket deformation and arch rib installation alignment. Bracket deformation can easily lead to insufficient arch rib installation accuracy and result in alignment deviations. Moreover, the lack of a systematic collaborative verification process makes it difficult to fully consider structural stability and construction feasibility, and thus fails to meet the precision requirements for arch rib installation.

[0005] Based on the aforementioned practical problems, there is an urgent need for a scientific and reasonable design method. By clarifying the load combination and establishing a collaborative stress model, the design of the support structure and the installation accuracy of the arch rib can be optimized in a coordinated manner. This will solve the problems of poor adaptability, insufficient accuracy and instability in traditional designs, provide safe and reliable technical support for the installation of steel pipe arch ribs, and ensure construction safety and installation accuracy. Summary of the Invention

[0006] This invention aims to rationally define the multi-source loads during the installation stage of steel pipe arch ribs, classify load combination types, construct a collaborative force model of the support and arch ribs, and determine reasonable parameters of the support by combining iterative optimization and precise calculation, thereby offsetting the influence of deformation and error, ensuring the support's stress safety and construction feasibility, and achieving a dual guarantee of arch rib installation accuracy and structural stability.

[0007] To address the aforementioned deficiencies or improvement needs of existing technologies, as a first aspect of this invention, the present invention provides a design method for a steel pipe arch rib mounting bracket considering load combinations, comprising: S1. Define the multi-source loads during the arch rib installation stage and divide them into standard combinations and basic combinations. Establish an overall analysis model of the co-force between the support and the arch rib. Based on the segment division of the arch rib and the bridge deck constraints, determine the topology of the support. Configure the support component parameters according to the load distribution differences to form an initial scheme for the locally supported arch rib installation support. S2. Based on the overall stress model and the initial scheme of the local support bracket, the time-varying load effects of each construction stage of hoisting, splicing and closure are extracted. A multi-objective decision-making mathematical method is used to construct a function model with the stability safety factor, stress uniformity and deformation limit as optimization objectives. The stability safety factor of the bracket under each working condition is uniformly quantified and the global optimal objective function is determined. S3. Based on the overall stress model and the global optimal objective function, a strong coupling mapping relationship between the support deformation and the arch rib installation line is established. The optimal pre-camber of the support is solved by inverse analytical iterative method. The cumulative error and coupling deviation of the arch rib line caused by the support deformation are eliminated through multiple rounds of iterative correction. S4. Perform strength, stability, deformation and foundation reaction force verification on the support, and based on the verification results and buckling analysis conclusions, iteratively optimize the cross-section, spacing and connection structure of the support members; establish a collaborative mechanical model for the optimized support, conduct collaborative verification throughout the construction process and determine the final design parameters.

[0008] Furthermore, the standard combination and the basic combination in S1 are respectively: The standard combination is a linear combination of dead load, hoisting live load and wind load according to the principle of equivalent effect, and is used for the verification of support deformation and foundation reaction. The basic combination is composed of partial factors introduced from the constant load, hoisting live load and wind load, and the hoisting off-center load correction effect is considered. It is used for the strength and stability verification of the support.

[0009] Furthermore, the construction process of the overall analysis model in S1 is as follows: With the coordinated stress distribution between the support frame and the arch rib as the core objective, and based on the characteristics of multi-source loads, load vectors corresponding to the standard combination and the basic combination are constructed respectively. Combined with the finite element discretization method, the overall analysis model is constructed, and the core governing equations satisfy... ,in This represents the overall stiffness matrix of the support frame and arch ribs working together. This is the overall displacement vector of the structure. For the combined load vector, and Includes standard combined load vector With basic combined load vector Two categories, each corresponding to different verification scenarios; The support frame and arch ribs are discretized into elements to construct the element stiffness matrix. By unifying coordinate transformation, the stiffness matrices of each element are integrated into a global stiffness matrix. ,in For a single cell, the Gamcon matrix, The total number of units; The overall stiffness matrix Standard combined load vector Basic combined load vector Substituting each into the equilibrium equation, we obtain the equilibrium equation corresponding to the standard combination. The equilibrium equations corresponding to the basic combination ; Simultaneously, bridge deck constraint boundary conditions are applied, and two types of equilibrium equations are solved using numerical iteration methods to ensure that the solution results meet the structural mechanics equilibrium requirements, thus completing the force and deformation calculations under the standard combination and the basic combination.

[0010] Furthermore, the method for generating the initial scheme of the partially supported arch rib mounting bracket in S1 is as follows: The ends of the arch rib segments and the linear inflection points are used as the reference for the layout of the support points, and coordinate transformation is used. The projected positions of each support point on the bridge deck are determined to define the planar layout and vertical height of the support columns; among which, Let be the coordinate vector of the support point in the global coordinate system. This is the coordinate transformation matrix. The coordinate vector of the arch rib segment in the local coordinate system; The scaffold is discretized into independent load-bearing elements based on its uprights using the finite element method. The element stiffness is then calculated using the formula... The stiffness of each element is obtained and integrated into the overall stiffness of the support. ;in, Here is the stiffness matrix of the support element. The element strain-displacement matrix, For the material constitutive matrix, For the unit computational domain, The overall stiffness matrix of the support; Standard combined load vector With basic combined load vector Substitute into the equilibrium equations respectively The internal force values ​​of each upright and horizontal bar are obtained by solving the problem. Then through the stress relationship Calculate the cross-sectional area of ​​the member that meets the stress requirements. ;in, The overall stiffness matrix of the support structure. The structural displacement vector. For load vectors, For the working stress of the component, The internal forces borne by the component. The cross-sectional area of ​​the component; Based on the cross-sectional parameters, steel members of corresponding specifications are selected. The uprights are arranged along the length of the arch rib segment according to the uneven distribution of force. Transverse and longitudinal connecting members are set between the uprights to form a spatial frame. The top of the support and the outer wall of the arch rib adopt a rigid fitting structure. Finally, the support points, member specifications, spatial frame form and top connection structure together constitute a complete initial scheme for the local support arch rib installation support.

[0011] Furthermore, the method for determining the stability safety factor of the support under each working condition in S2 is as follows: Based on the overall stress model and the initial scheme of the locally supported support, the time-varying load effects of each construction stage (hoisting, splicing, and closure) are extracted, and the geometric nonlinear equilibrium equations of the support are constructed. ,in To account for large geometric deformations and initial imperfections, the stiffness matrix is... The structural displacement vector. This represents the time-varying load vector that changes with the construction stage. Introducing initial defect modes As a vibration load, construct the vibration load vector. ,in The defect vibration coefficient is obtained by superimposing it on the time-varying load vector. ; The arc-length method is used to track the equilibrium path, and an iterative step-size control equation is constructed. ,in For the first Iteration step displacement increment, For the first Iteration step load scaling factor increment, The preset arc length step size is used; the corrected equilibrium equation is solved iteratively in each step. ,in For the first Tangent stiffness matrix For the first Step unbalanced force vector; By iteratively solving the equilibrium path of the support under the combined action of vibration and time-varying loads, the peak point of the load-displacement curve is identified as the ultimate bearing point, and the ultimate load considering initial imperfections and geometric nonlinearity is obtained. Establish the relationship for calculating the stability safety factor. ,in To ensure the stability and safety of the stent, For ultimate load, To determine the maximum load effect during the construction phase, the stability safety factor of the support under each working condition is determined.

[0012] Furthermore, the globally optimal objective function in S2 is specifically: in Design a variable vector for the support structure; The objective function for the stability safety factor is defined as follows: , To ensure a stable safety factor limit, Design variables The corresponding support stability safety factor; The objective function for stress uniformity is defined as follows: , This represents the total number of support components. For the first The stress of each component, The average stress of the component; The objective function for the deformation limit is defined as follows: , Design variables The corresponding maximum displacement of the support This is the displacement limit.

[0013] Furthermore, the process of solving for the optimal pre-camber of the support using the inverse analytical iterative method in S3 is as follows: Based on the overall stress model and the global optimal objective function, the equilibrium equations of the support under coupled loads at each construction stage are established based on the principle of mechanical equilibrium, and the vertical deformation of the support piers is obtained by solving the equations. By combining the spatial topological correspondence between the support and the arch rib, a geometric transfer relationship is constructed, and the deformation of the support pier point is mapped to the linear offset of the arch rib axis, thereby establishing a strong coupling mapping relationship between the deformation of the support and the installation line of the arch rib. Using the arch rib design line as the control benchmark, a line deviation model containing the pre-camber to be inverted is constructed. The inverse analytical iterative method is used to iteratively solve the pre-camber. By continuously updating the pre-camber and substituting it into the overall stress model, the support deformation and the actual line of the arch rib are recalculated. The convergence criterion is that the iterative difference of the line deviation vector approaches zero. The precamber obtained after iterative convergence is the optimal precamber of the support, which is used to offset the deformation of the support at each construction stage and eliminate the cumulative error and coupling deviation of the arch rib line caused by it.

[0014] Furthermore, the process of verifying the strength, stability, deformation, and foundation reaction force of the support in S4 is as follows: The strength verification adopts the fourth strength theory to control the equivalent stress of the support members to not exceed the allowable stress of the material; the stability verification combines eigenvalue buckling analysis and nonlinear buckling analysis to solve the critical load and ensure that the stability safety factor of the support meets the allowable requirements; the deformation verification controls the maximum deformation of the support to not exceed the preset allowable deformation value; the foundation reaction force verification controls the maximum foundation reaction force to not exceed the allowable bearing capacity of the foundation.

[0015] As a second aspect of the present invention, a steel pipe arch rib mounting bracket design system considering load combinations is also provided, comprising: The initial scheme construction unit is used to define the multi-source loads in the arch rib installation stage and divide the standard combination and basic combination, and establish an overall analysis model of the co-force of the support and the arch rib. Based on the segment division of the arch rib and the bridge deck constraints, the topology of the support is determined, and the support component parameters are configured according to the load distribution differences to form the initial scheme of the locally supported arch rib installation support. The support optimization function construction unit is used to extract the time-varying load effects of each construction stage, such as hoisting, splicing, and closure, based on the overall stress model and the initial scheme of the local support support. It uses a multi-objective decision-making mathematical method to construct a function model with the stability safety factor, stress uniformity, and deformation limit as optimization objectives, uniformly quantifies the support stability safety factor under each working condition, and determines the global optimal objective function. The support pre-camber solution unit is used to establish a strong coupling mapping relationship between support deformation and arch rib installation line shape based on the overall force model and the global optimal objective function. It uses the inverse analytical iterative method to solve for the optimal pre-camber of the support and eliminates the cumulative error and coupling deviation of the arch rib line shape caused by support deformation through multiple rounds of iterative correction. The support parameter optimization unit is used to verify the strength, stability, deformation and foundation reaction of the support, and to iteratively optimize the cross-section, spacing and connection structure of the support members based on the verification results and buckling analysis conclusions. A collaborative mechanical model is established for the optimized support, and collaborative verification is carried out throughout the construction process to determine the final design parameters.

[0016] As a third aspect of the invention, a computer-readable storage medium is also provided, on which a computer program is stored, which is executed by a processor, according to any one of the claims, a design method for a steel pipe arch rib mounting bracket considering load combinations.

[0017] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: 1. The present invention provides a design method for steel pipe arch rib installation supports considering load combinations. This method defines multi-source loads during the arch rib installation stage and divides them into standard and basic combinations. An overall analytical model of the support and arch rib working together under stress is established. Based on the segment division of the arch rib and bridge deck constraints, the support topology is determined. Support component parameters are configured according to load distribution differences, forming an initial scheme for a locally supported arch rib installation support. The standard combination is used for support deformation and foundation reaction calculations, while the basic combination is used for support strength and stability calculations. The overall analytical model is constructed using the finite element discretization method, integrating the stiffness characteristics of the support and arch rib and applying bridge deck constraints to complete the stress and deformation calculations under different load combinations. This technical feature ensures accurate matching between load combinations and calculation scenarios. The overall analytical model can realistically reflect the collaborative stress state of the support and arch rib. The initial scheme is constructed in accordance with actual construction conditions, providing an accurate and reliable foundation for subsequent optimization design and avoiding design risks caused by unreasonable load combination division or model construction deviations.

[0018] 2. The steel pipe arch rib installation support design method of the present invention, considering load combinations, extracts the time-varying load effects at each construction stage based on the overall stress model and the initial scheme of the locally supported support. A multi-objective decision-making mathematical method is used to construct a globally optimal objective function with stability safety factor, stress uniformity, and deformation limit as optimization objectives, uniformly quantifying the support stability safety factor under various working conditions. By considering the influence of geometric nonlinearity and initial defects, the ultimate load of the support is solved and the stability safety factor is determined. The constructed multi-objective function achieves coordinated control of support stability, stress, and deformation. This technical feature enables refined analysis of the support's stress state at each construction stage. The globally optimal objective function provides a unified criterion for subsequent optimization work, effectively solving the problem of support performance imbalance caused by single-objective optimization, and ensuring that the support has reasonable safety reserves and stress performance under various working conditions.

[0019] 3. The steel pipe arch rib installation support design method of this invention, considering load combinations, establishes a strong coupling mapping relationship between support deformation and arch rib installation alignment based on an overall stress model and a global optimal objective function. It employs an inverse analytical iterative method to solve for the optimal pre-camber of the support, performs strength, stability, deformation, and foundation reaction force verification and iterative optimization, establishes a collaborative mechanical model for collaborative verification throughout the construction process, and finally determines the support design parameters and forms the final scheme. The optimal pre-camber can offset the arch rib alignment deviation caused by support deformation, iterative optimization ensures that all support indicators meet requirements, and collaborative verification eliminates process interference problems. This technical feature achieves collaborative optimization of support design and arch rib alignment control, effectively eliminates cumulative alignment errors, ensures support stress safety and construction feasibility, and provides a guarantee for arch rib installation accuracy and construction safety. Attached Figure Description

[0020] Figure 1This is a flowchart illustrating the design method of a steel pipe arch rib mounting bracket considering load combinations according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the overall model of the steel pipe arch rib and the mounting bracket working together under stress according to an embodiment of the present invention. Figure 3 Embodiments of the present invention Figure 4 This is a schematic diagram of the system units in an embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0022] Example 1 Please refer to Figure 1 This embodiment 1 provides a design method for a steel pipe arch rib mounting bracket considering load combinations, including: S1. Define the multi-source loads during the arch rib installation stage and divide them into standard combinations and basic combinations. Establish an overall analysis model of the co-force between the support and the arch rib. Based on the segment division of the arch rib and the bridge deck constraints, determine the topology of the support. Configure the support component parameters according to the load distribution differences to form an initial scheme for the locally supported arch rib installation support. S2. Based on the overall stress model and the initial scheme of the local support bracket, the time-varying load effects of each construction stage of hoisting, splicing and closure are extracted. A multi-objective decision-making mathematical method is used to construct a function model with the stability safety factor, stress uniformity and deformation limit as optimization objectives. The stability safety factor of the bracket under each working condition is uniformly quantified and the global optimal objective function is determined. S3. Based on the overall stress model and the global optimal objective function, a strong coupling mapping relationship between the support deformation and the arch rib installation line is established. The optimal pre-camber of the support is solved by inverse analytical iterative method. The cumulative error and coupling deviation of the arch rib line caused by the support deformation are eliminated through multiple rounds of iterative correction. S4. Perform strength, stability, deformation and foundation reaction force verification on the support, and based on the verification results and buckling analysis conclusions, iteratively optimize the cross-section, spacing and connection structure of the support members; establish a collaborative mechanical model for the optimized support, conduct collaborative verification throughout the construction process and determine the final design parameters.

[0023] This embodiment 1 further elaborates on the above steps.

[0024] (1) Initial scheme construction During the installation of steel pipe arch ribs, the support structure must simultaneously withstand multiple loads, including dead loads, construction live loads, and wind loads. Different stress calculation scenarios have clear requirements for distinguishing between load combinations and structural stress analysis. Reasonably classifying load combination types and establishing accurate collaborative stress models are fundamental to ensuring the safety and reliability of the support design and matching the arch rib installation alignment with construction needs. Based on this engineering background, we first systematically define the various loads during the arch rib installation stage and, according to the different purposes of structural verification, classify the loads into two forms: standard combinations and basic combinations.

[0025] The standard combination consists of dead load, hoisting live load and wind load, which are linearly superimposed according to the principle of equivalent load effect. This combination is mainly used in the deformation verification of support structure and the foundation reaction force verification scenario, focusing on reflecting the stress and deformation characteristics of the structure under normal use.

[0026] The basic combination also consists of dead load, hoisting live load and wind load. During the combination process, corresponding load partial factors are introduced, and adjustments are made in combination with the eccentric load effect that may occur during hoisting construction. This combination is mainly used for strength verification and stability verification of the support structure, which is more in line with the design requirements of the ultimate limit state of the structure's bearing capacity.

[0027] Please refer to Figure 2 as well as Figure 3 After completing the load combination division, with the coordinated force distribution between the support frame and the arch rib as the core objective, and based on the characteristics of multi-source loads, load vectors corresponding to the standard combination and the basic combination were constructed respectively. Combined with the finite element discretization method, the overall analysis model was constructed, and the core governing equations satisfy... ,in This represents the overall stiffness matrix of the support frame and arch ribs working together. This is the overall displacement vector of the structure. For the combined load vector, and Includes standard combined load vector With basic combined load vector Two categories, each corresponding to different verification scenarios; The support frame and arch ribs are discretized into elements to construct the element stiffness matrix. By unifying coordinate transformation, the stiffness matrices of each element are integrated into a global stiffness matrix. ,in For a single cell, the Gamcon matrix, The total number of units; The overall stiffness matrix Standard combined load vector Basic combined load vector Substituting each into the equilibrium equation, we obtain the equilibrium equation corresponding to the standard combination. The equilibrium equations corresponding to the basic combination ; Simultaneously, bridge deck constraint boundary conditions are applied, and two types of equilibrium equations are solved using numerical iteration methods to ensure that the solution results meet the structural mechanics equilibrium requirements, thus completing the force and deformation calculations under the standard combination and the basic combination.

[0028] Based on the calculation results of the overall analysis model, the initial design of the locally supported arch rib installation bracket was further carried out. The ends of the arch rib segments and the linear inflection points were used as the reference points for the bracket support locations, and coordinate transformation was employed. The projected positions of each support point on the bridge deck are determined to define the planar layout and vertical height of the support columns; among which, Let be the coordinate vector of the support point in the global coordinate system. This is the coordinate transformation matrix. The coordinate vector of the arch rib segment in the local coordinate system; The scaffold is discretized into independent load-bearing elements based on its uprights using the finite element method. The element stiffness is then calculated using the formula... The stiffness of each element is obtained and integrated into the overall stiffness of the support. ;in, Here is the stiffness matrix of the support element. The element strain-displacement matrix, For the material constitutive matrix, For the unit computational domain, The overall stiffness matrix of the support; Standard combined load vector With basic combined load vector Substitute into the equilibrium equations respectively The internal force values ​​of each upright and horizontal bar are obtained by solving the problem. Then through the stress relationship Calculate the cross-sectional area of ​​the member that meets the stress requirements. ;in, The overall stiffness matrix of the support structure. The structural displacement vector. For load vectors, For the working stress of the component, The internal forces borne by the component. The cross-sectional area of ​​the component; Based on the calculated cross-sectional parameters, steel members of suitable specifications were selected. Considering the uneven load distribution along the arch rib, the uprights were arranged differentially along the length of the arch rib segments, and transverse and longitudinal connecting members were installed between the uprights to form a stable spatial frame structure. The top of the support adopts a structure that is rigidly fitted to the outer wall of the arch rib to ensure effective support and force transfer for the arch rib. Finally, combining the layout of support points, selection of member specifications, spatial frame arrangement, and top connection structure, a complete initial scheme for a locally supported steel pipe arch rib installation support was formed.

[0029] (2) Construction of scaffold optimization function Throughout the segmental installation of the steel pipe arch ribs, the structural stress is not constant but exhibits significant time-varying characteristics as the arch rib segments are hoisted, positioned, and joined. The magnitude, location, and stress form of the loads borne by the support differ significantly at different construction stages. Relying solely on the initial design is insufficient to guarantee that the support possesses reasonable stability reserves, uniform stress distribution, and controllable deformation amplitude under all working conditions. Therefore, a refined analysis of the structural response at different construction stages is necessary, along with function construction and optimization guided by multi-objective synergistic optimization.

[0030] Based on the established overall stress model and the initial scheme of the locally supported scaffold, the time-varying load effects of each construction stage (hoisting, splicing, and closure) are extracted, and the geometric nonlinear equilibrium equations of the scaffold are constructed. ,in To account for large geometric deformations and initial imperfections, the stiffness matrix is... The structural displacement vector. This represents the time-varying load vector that changes with the construction stage. Introducing initial defect modes As a vibration load, construct the vibration load vector. ,in The defect vibration coefficient is obtained by superimposing it on the time-varying load vector. ; The arc-length method is used to track the equilibrium path, and an iterative step-size control equation is constructed. ,in For the first Iteration step displacement increment, For the first Iteration step load scaling factor increment, The preset arc length step size is used; the corrected equilibrium equation is solved iteratively in each step. ,in For the first Tangent stiffness matrix For the first Step unbalanced force vector; By iteratively solving the equilibrium path of the support under the combined action of vibration and time-varying loads, the peak point of the load-displacement curve is identified as the ultimate bearing point, and the ultimate load considering initial imperfections and geometric nonlinearity is obtained. Establish the calculation relationship of the stability safety factor. ,in To ensure the stability and safety of the stent, For ultimate load, To determine the maximum load effect during the construction phase, the stability safety factor of the support under each working condition is determined.

[0031] Under the premise of quantifying the stability and safety factors for each working condition, a globally optimal objective function containing three core control objectives is constructed using the support design parameters as optimization variables. The first objective revolves around the stability and safety factor, using its limit as the control benchmark to ensure the actual stability and safety factor of the structure meets and approaches the set requirements. The second objective focuses on stress uniformity, calculating the dispersion of stress in each component from the average stress to control the overall stress distribution of the support towards equilibrium, avoiding premature failure due to stress concentration in local components. The third objective uses deformation limits as constraints, comparing the actual maximum displacement of the support with the allowable displacement limit to ensure that structural deformation remains within a controllable range. Specifically, the globally optimal objective function is: in Design a variable vector for the support structure; The objective function for the stability safety factor is defined as follows: , To ensure a stable safety factor limit, Design variables The corresponding support stability safety factor; The objective function for stress uniformity is defined as follows: , This represents the total number of support components. For the first The stress of each component, The average stress of the component; The objective function for the deformation limit is defined as follows: , Design variables The corresponding maximum displacement of the support This is the displacement limit.

[0032] By synergistically optimizing the above three objectives, a globally optimal objective function that balances structural stability, uniform stress distribution, and controllable deformation is ultimately formed, providing a unified optimization criterion for subsequent setting of the support pre-camber and optimization of structural parameters.

[0033] (3) Solution of pre-camber of support The installation alignment of the steel pipe arch rib directly determines the bridge's alignment accuracy and load-bearing performance after completion. Deformation of the support structure under load at each construction stage is transmitted to the arch rib structure through the support points, leading to axial offset and alignment deviation. If these errors are not controlled, they can easily accumulate throughout the hoisting, splicing, and closure processes, ultimately affecting the arch rib installation quality and the overall structural safety. To fundamentally counteract the alignment effects of support deformation and achieve coordinated control of the support's load-bearing performance and the arch rib installation alignment, a correlation mechanism between deformation and alignment needs to be established based on existing analysis, and reasonable pre-camber parameters need to be determined through iterative calculations.

[0034] Based on the overall stress model and the global optimal objective function, the optimal precamber of the support structure is determined through inversion. The established overall stress model and the solved global optimal objective function serve as the basis for the solution. The overall stress model fully encompasses the geometric parameters, material properties, time-varying load effects at each construction stage, and the influence of initial defects of the support structure. The global optimal objective function, through multi-objective optimization, yields the optimal stiffness distribution of the support structure, i.e., the overall tangential stiffness matrix of the support structure corresponding to the global optimal solution. Uniform stress state of each component and stability safety factor that meets design requirements; Based on this, a strong coupling mapping relationship between the deformation of the support and the installation line of the arch rib is established. The specific establishment process is as follows: Based on the mechanical equilibrium principle in the overall force model, the equilibrium equations of the support under coupled loads at each construction stage are established. ,in This is the overall tangential stiffness matrix of the support structure, determined after the global optimal objective function has converged. This refers to the coupled load vector for the entire construction process, which is already determined in the overall stress model. It includes time-varying loads at each stage of hoisting, splicing, and closure, as well as the structural self-weight and additional loads caused by initial defects. The actual vertical deformation vector of the support pier point can be obtained directly from the equilibrium equations. ; Based on the spatial topological relationship between the support frame and the arch rib, the support frame piers directly support the arch rib nodes, and there is a one-to-one correspondence between their spatial coordinates. Therefore, a geometric transfer matrix is ​​constructed. , The elements are uniquely determined by the coordinate difference and spatial angle between the support pier point and the corresponding node of the arch rib, through... Deformation of the support points Linear offset mapped to the arch rib axis That is, to establish geometric transitive relationships The mechanical equilibrium equations obtained by solving Substituting the geometric transfer relations, we obtain a strong coupled mapping relationship between the support deformation and the arch rib installation line shape. ; With arch rib design line To establish a control reference, a linear deviation vector is constructed. ,in Let be the precamber vector of the support structure to be inverted and solved. Each component corresponds to the pre-camber value of each support frame support point, used to offset the deviation in the arch rib alignment caused by support deformation. The actual shape of the arch rib under the action of pre-camber, pre-camber The initial geometry of the support can be altered, thereby affecting its deformation. And ultimately change the arch rib profile through coupling mapping relationship. ; To obtain the optimal precamber through inversion The solution is obtained by inverse analytical iterative method, the core of which is to gradually reduce the linear deviation by iteratively correcting the pre-camber. Until the deviation is eliminated, the specific iterative process is as follows: Set the initial value of the pre-camber. The initial value is taken as the initial deformation compensation value of the support without pre-arching, which is obtained based on the initial deformation calculation of the overall stress model mentioned above, and then substituted into the coupling mapping relationship. The actual shape of the arch rib under the initial pre-camber was calculated. Thus, the initial linear deviation is obtained. Constructing an inverse analytical iterative format ,in The first-order sensitivity matrix of linear deviation to precamber is obtained by differentiating the coupling mapping relationship with respect to precamber. The inverse of the sensitivity matrix is ​​obtained by directly solving the LU decomposition method. For the first The precamber vector of the round iteration, For the first Linear deviation in round iteration; After each iteration, the updated pre-camber will be... Substitute the overall stress model from the previous text and solve the deformation of the support again. Then, the actual shape of the new arch rib is obtained through the coupling mapping relationship. And calculate the new linear deviation. During the iteration process, the continuous iterative difference of the linear deviation vector naturally tends to zero, that is... As a convergence criterion, this convergence criterion is naturally determined by the structural mechanical equilibrium characteristics, which can guarantee the rationality of the solution results.

[0035] Precamber corresponding to iterative convergence This is the optimal pre-camber of the support. This optimal pre-camber can offset the deformation of the support under load at each construction stage in the overall stress model. Through multiple rounds of iterative correction, the cumulative error and coupling deviation of the arch rib shape caused by the deformation of the support are completely eliminated. At the same time, it meets the requirements of the global optimal objective function for the support stiffness, stress uniformity and stability safety factor, and realizes the coordinated optimization of support design and arch rib installation line control.

[0036] (4) Optimization of stent parameters As the core support structure for the installation of steel pipe arch ribs, the support structure's stress safety and deformation controllability are directly related to the safety of the entire construction process and the installation accuracy of the arch ribs. After the initial pre-camber optimization, it is still necessary to verify whether the support structure performance meets the design and construction requirements through systematic mechanical calculations. At the same time, weak links are optimized and adjusted, and the compatibility between the support structure and the construction process is verified. Finally, reasonable design parameters are determined to form a complete support structure design scheme.

[0037] First, in accordance with the design specifications and the specific requirements of each construction condition, a suitable load combination is selected. This load combination covers various loads during the construction process, including the self-weight of the support and arch ribs, the live load generated by hoisting operations, wind loads, loads caused by temperature changes, and additional loads caused by initial defects. At the same time, corresponding partial factors are introduced according to different load types to ensure that the load combination can truly reflect the actual stress state of the support at each construction stage, providing a reliable load basis for subsequent verification calculations.

[0038] Based on the selected load combination, four core calculations were performed sequentially: support strength, stability, deformation, and foundation reaction. The strength calculation employed the fourth strength theory, satisfying... ,in , These are the normal stresses on the cross-section of the support member. For shear stress, The allowable stress of the support material; stability verification combines eigenvalue buckling analysis and nonlinear buckling analysis, with eigenvalue buckling analysis solving for the critical load. ( It is the smallest eigenvalue. The overall stiffness matrix of the support structure. (Eigenvectors), nonlinear buckling analysis considers geometric nonlinearity and material nonlinearity, and solves for the actual critical load. To ensure the stability and safety factor of the stent ( (To allow for a stability safety factor); deformation verification meets the requirements. ,in This represents the maximum deformation of the support. The allowable deformation value of the support; the foundation reaction calculation meets the requirements. ,in The maximum reaction force of the foundation Here is the foundation stiffness matrix. This refers to the allowable bearing capacity of the foundation.

[0039] After completing all verification calculations, and combining the buckling analysis results, the weak points and possible instability modes of the support structure are accurately identified. Based on this, iterative optimization of the support structure is carried out. The optimization mainly includes the cross-sectional dimensions of the support members, the spacing between the uprights and horizontal members, and the connection structure of each component. By adjusting these parameters, the load-bearing capacity of the weak points and the overall stability of the support are enhanced. After each round of optimization, the optimized support parameters must be re-substituted into the above verification process for verification. This iterative adjustment continues until the strength, stability, deformation, and foundation reaction of the support all meet the corresponding allowable limits, ensuring that the performance of the support structure meets the design standards.

[0040] After the support structure is optimized, a collaborative verification of the entire construction process is required to ensure the compatibility and coordination between the support and each stage of the arch rib installation. By establishing a collaborative mechanical model of the support and each construction process, the stress and deformation state of the support during each stage of arch rib segment hoisting, alignment, splicing, temporary consolidation, and system transformation is simulated. The focus is on verifying the spatial matching, temporal adaptability, and stress coordination between the support and each construction process, promptly identifying and eliminating interference problems and potential sudden stress changes between processes, and avoiding safety accidents or alignment deviations caused by incompatibility between the support and the process during construction.

[0041] Finally, based on the comprehensive mechanical calculation results, buckling analysis conclusions, and collaborative verification throughout the construction process, the final design parameters of the support system were determined, including the selection of member specifications, arrangement, connection structure, support point layout, and foundation treatment methods. By integrating the results of various analyses and verifications, a final design scheme for the support system was formed that balances load-bearing safety, construction feasibility, and alignment control requirements. This provides scientific and reliable technical support for the installation of steel pipe arch ribs, ensuring the accuracy of arch rib installation and construction safety.

[0042] Example 2 Please refer to Figure 4 This embodiment 2 provides a steel pipe arch rib mounting bracket design system that considers load combinations, including: The initial scheme construction unit is used to define the multi-source loads in the arch rib installation stage and divide the standard combination and basic combination, and establish an overall analysis model of the co-force of the support and the arch rib. Based on the segment division of the arch rib and the bridge deck constraints, the topology of the support is determined, and the support component parameters are configured according to the load distribution differences to form the initial scheme of the locally supported arch rib installation support. The support optimization function construction unit is used to extract the time-varying load effects of each construction stage, such as hoisting, splicing, and closure, based on the overall stress model and the initial scheme of the local support support. It uses a multi-objective decision-making mathematical method to construct a function model with the stability safety factor, stress uniformity, and deformation limit as optimization objectives, uniformly quantifies the support stability safety factor under each working condition, and determines the global optimal objective function. The support pre-camber solution unit is used to establish a strong coupling mapping relationship between support deformation and arch rib installation line shape based on the overall force model and the global optimal objective function. It uses the inverse analytical iterative method to solve for the optimal pre-camber of the support and eliminates the cumulative error and coupling deviation of the arch rib line shape caused by support deformation through multiple rounds of iterative correction. The support parameter optimization unit is used to verify the strength, stability, deformation and foundation reaction of the support, and to iteratively optimize the cross-section, spacing and connection structure of the support members based on the verification results and buckling analysis conclusions. A collaborative mechanical model is established for the optimized support, and collaborative verification is carried out throughout the construction process to determine the final design parameters.

[0043] Example 3 This embodiment 3 also provides a computer-readable storage medium storing a computer program that, when executed by a processor, can implement any step of a design method for a steel pipe arch rib mounting bracket that considers load combinations.

[0044] The computer-readable storage medium may include various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0045] For a description of the computer-readable storage medium provided in this application, please refer to the above method embodiments; further details will not be repeated here.

[0046] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A design method for a steel pipe arch rib mounting bracket considering load combinations, characterized in that, include: S1. Define the multi-source loads during the arch rib installation stage and divide them into standard combinations and basic combinations. Establish an overall analysis model of the co-force between the support and the arch rib. Based on the segment division of the arch rib and the bridge deck constraints, determine the topology of the support. Configure the support component parameters according to the load distribution differences to form an initial scheme for the locally supported arch rib installation support. S2. Based on the overall stress model and the initial scheme of the local support bracket, the time-varying load effects of each construction stage of hoisting, splicing and closure are extracted. A multi-objective decision-making mathematical method is used to construct a function model with the stability safety factor, stress uniformity and deformation limit as optimization objectives. The stability safety factor of the bracket under each working condition is uniformly quantified and the global optimal objective function is determined. S3. Based on the overall stress model and the global optimal objective function, a strong coupling mapping relationship between the support deformation and the arch rib installation line is established. The optimal pre-camber of the support is solved by inverse analytical iterative method. The cumulative error and coupling deviation of the arch rib line caused by the support deformation are eliminated through multiple rounds of iterative correction. S4. Perform strength, stability, deformation and foundation reaction force verification on the support, and based on the verification results and buckling analysis conclusions, iteratively optimize the cross-section, spacing and connection structure of the support members; establish a collaborative mechanical model for the optimized support, conduct collaborative verification throughout the construction process and determine the final design parameters.

2. The design method for a steel pipe arch rib mounting bracket considering load combinations according to claim 1, characterized in that, The standard combination and the basic combination in S1 are respectively: The standard combination is a linear combination of dead load, hoisting live load and wind load according to the principle of equivalent effect, and is used for the verification of support deformation and foundation reaction. The basic combination is composed of partial factors introduced from the constant load, hoisting live load and wind load, and the hoisting off-center load correction effect is considered. It is used for the strength and stability verification of the support.

3. The design method for a steel pipe arch rib mounting bracket considering load combinations according to claim 1, characterized in that, The construction process of the overall analysis model in S1 is as follows: With the coordinated stress distribution between the support frame and the arch rib as the core objective, and based on the characteristics of multi-source loads, load vectors corresponding to the standard combination and the basic combination are constructed respectively. Combined with the finite element discretization method, the overall analysis model is constructed, and the core governing equations satisfy... ,in This represents the overall stiffness matrix of the support frame and arch ribs working together. This is the overall displacement vector of the structure. For the combined load vector, and Includes standard combined load vector With basic combined load vector Two categories, each corresponding to different verification scenarios; The support frame and arch ribs are discretized into elements to construct the element stiffness matrix. By unifying coordinate transformation, the stiffness matrices of each element are integrated into a global stiffness matrix. ,in For a single cell, the Gamcon matrix, The total number of units; The overall stiffness matrix Standard combined load vector Basic combined load vector Substituting each into the equilibrium equation, we obtain the equilibrium equation corresponding to the standard combination. The equilibrium equations corresponding to the basic combination ; Simultaneously, bridge deck constraint boundary conditions are applied, and two types of equilibrium equations are solved using numerical iteration methods to ensure that the solution results meet the structural mechanics equilibrium requirements, thus completing the force and deformation calculations under the standard combination and the basic combination.

4. The design method for a steel pipe arch rib mounting bracket considering load combinations according to claim 1, characterized in that, The method for generating the initial scheme of the partially supported arch rib mounting bracket in S1 is as follows: The ends of the arch rib segments and the linear inflection points are used as the reference for the layout of the support points, and coordinate transformation is used. The projected positions of each support point on the bridge deck are determined to define the planar layout and vertical height of the support columns; among which, Let be the coordinate vector of the support point in the global coordinate system. This is the coordinate transformation matrix. The coordinate vector of the arch rib segment in the local coordinate system; The scaffold is discretized into independent load-bearing elements based on its uprights using the finite element method. The element stiffness is then calculated using the formula... The stiffness of each element is obtained and integrated into the overall stiffness of the support. ;in, Here is the stiffness matrix of the support element. The element strain-displacement matrix, For the material constitutive matrix, For the unit computational domain, The overall stiffness matrix of the support; Standard combined load vector With basic combined load vector Substitute into the equilibrium equations respectively The internal force values ​​of each upright and horizontal bar are obtained by solving the problem. Then through the stress relationship Calculate the cross-sectional area of ​​the member that meets the stress requirements. ;in, The overall stiffness matrix of the support structure. The structural displacement vector. For load vectors, For the working stress of the component, The internal forces borne by the component. The cross-sectional area of ​​the component; Based on the cross-sectional parameters, steel members of corresponding specifications are selected. The uprights are arranged along the length of the arch rib segment according to the uneven distribution of force. Transverse and longitudinal connecting members are set between the uprights to form a spatial frame. The top of the support and the outer wall of the arch rib adopt a rigid fitting structure. Finally, the support points, member specifications, spatial frame form and top connection structure together constitute a complete initial scheme for the local support arch rib installation support.

5. The design method for a steel pipe arch rib mounting bracket considering load combinations according to claim 1, characterized in that, The method for determining the stability safety factor of the support under each working condition in S2 is as follows: Based on the overall stress model and the initial scheme of the locally supported support, the time-varying load effects of each construction stage (hoisting, splicing, and closure) are extracted, and the geometric nonlinear equilibrium equations of the support are constructed. ,in To account for large geometric deformations and initial imperfections, the stiffness matrix is... The structural displacement vector. This represents the time-varying load vector that changes with the construction stage. Introducing initial defect modes As a vibration load, construct the vibration load vector. ,in The defect vibration coefficient is obtained by superimposing it on the time-varying load vector. ; The arc-length method is used to track the equilibrium path, and an iterative step-size control equation is constructed. ,in For the first Iteration step displacement increment, For the first Iteration step load scaling factor increment, The preset arc length step size is used; the corrected equilibrium equation is solved iteratively in each step. ,in For the first Tangent stiffness matrix For the first Step unbalanced force vector; By iteratively solving the equilibrium path of the support under the combined action of vibration and time-varying loads, the peak point of the load-displacement curve is identified as the ultimate bearing point, and the ultimate load considering initial imperfections and geometric nonlinearity is obtained. ; Establish the relationship for calculating the stability safety factor ,in To ensure the stability and safety of the stent, For ultimate load, To determine the maximum load effect during the construction phase, the stability safety factor of the support under each working condition is determined.

6. The design method for a steel pipe arch rib mounting bracket considering load combinations according to claim 1, characterized in that, The globally optimal objective function in S2 is specifically: in Design a variable vector for the support structure; The objective function for the stability safety factor is defined as follows: , To ensure a stable safety factor limit, Design variables The corresponding support stability safety factor; The objective function for stress uniformity is defined as follows: , This represents the total number of support components. For the first The stress of each component, The average stress of the component; The objective function for the deformation limit is defined as follows: , Design variables The corresponding maximum displacement of the support This is the displacement limit.

7. The design method for a steel pipe arch rib mounting bracket considering load combinations according to claim 1, characterized in that, The process of solving the optimal pre-camber of the support using the inverse analytical iterative method in S3 is as follows: Based on the overall stress model and the global optimal objective function, the equilibrium equations of the support under coupled loads at each construction stage are established based on the principle of mechanical equilibrium, and the vertical deformation of the support piers is obtained by solving the equations. By combining the spatial topological correspondence between the support and the arch rib, a geometric transfer relationship is constructed, and the deformation of the support pier point is mapped to the linear offset of the arch rib axis, thereby establishing a strong coupling mapping relationship between the deformation of the support and the installation line of the arch rib. Using the arch rib design line as the control benchmark, a line deviation model containing the pre-camber to be inverted is constructed. The inverse analytical iterative method is used to iteratively solve the pre-camber. By continuously updating the pre-camber and substituting it into the overall stress model, the support deformation and the actual line of the arch rib are recalculated. The convergence criterion is that the iterative difference of the line deviation vector approaches zero. The precamber obtained after iterative convergence is the optimal precamber of the support, which is used to offset the deformation of the support at each construction stage and eliminate the cumulative error and coupling deviation of the arch rib line caused by it.

8. The design method for a steel pipe arch rib mounting bracket considering load combinations according to claim 1, characterized in that, The process of verifying the strength, stability, deformation, and foundation reaction of the support in S4 is as follows: The strength verification adopts the fourth strength theory to control the equivalent stress of the support members to not exceed the allowable stress of the material; the stability verification combines eigenvalue buckling analysis and nonlinear buckling analysis to solve the critical load and ensure that the stability safety factor of the support meets the allowable requirements. Deformation verification controls the maximum deformation of the support to not exceed the preset allowable deformation value; foundation reaction verification controls the maximum foundation reaction to not exceed the foundation's allowable bearing capacity.

9. A design system for a steel pipe arch rib mounting bracket considering load combinations, characterized in that, include: The initial scheme construction unit is used to define the multi-source loads in the arch rib installation stage and divide the standard combination and basic combination, and establish an overall analysis model of the co-force of the support and the arch rib. Based on the segment division of the arch rib and the bridge deck constraints, the topology of the support is determined, and the support component parameters are configured according to the load distribution differences to form the initial scheme of the locally supported arch rib installation support. The support optimization function construction unit is used to extract the time-varying load effects of each construction stage, such as hoisting, splicing, and closure, based on the overall stress model and the initial scheme of the local support support. It uses a multi-objective decision-making mathematical method to construct a function model with the stability safety factor, stress uniformity, and deformation limit as optimization objectives, uniformly quantifies the support stability safety factor under each working condition, and determines the global optimal objective function. The support pre-camber solution unit is used to establish a strong coupling mapping relationship between support deformation and arch rib installation line shape based on the overall force model and the global optimal objective function. It uses the inverse analytical iterative method to solve for the optimal pre-camber of the support and eliminates the cumulative error and coupling deviation of the arch rib line shape caused by support deformation through multiple rounds of iterative correction. The support parameter optimization unit is used to verify the strength, stability, deformation and foundation reaction of the support, and to iteratively optimize the cross-section, spacing and connection structure of the support members based on the verification results and buckling analysis conclusions. A collaborative mechanical model is established for the optimized support, and collaborative verification is carried out throughout the construction process to determine the final design parameters.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, The computer program is executed by a processor as described in any one of claims 1-8: a design method for a steel pipe arch rib mounting bracket that takes into account load combinations.

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