An optimization method for reinforcing tensioned beam structures of long-span steel corridors

Abstract

This invention provides an optimization method for reinforcing tensioned beam structures of large-span steel corridors, belonging to the field of building construction technology. The method includes: first, establishing a three-dimensional finite element model, including the upper steel corridor, vertical struts, and cables, and setting boundary conditions and dead / live loads. Nonlinear analysis is performed to obtain initial deflection and stress values ​​to determine if the reinforcement requirements are met. If not, the strut length and cable prestress are adjusted, and the analysis and calculation are repeated until the requirements are met. Then, using structural deflection as a control parameter and cable strain as a response parameter, cable force optimization calculations are performed using the SAP2000CSiLoadOptimizer toolbox to obtain optimized cable strain values. Finally, based on the optimization results, the final cable force optimization scheme is derived, and the specific process parameters for reinforcing the tensioned beam structure of the large-span steel corridor are determined. This method solves the problem that existing methods cannot fully reflect the nonlinear mechanical characteristics of the structure.

Description

Technical Field

[0001] This invention belongs to the field of building construction technology, and specifically relates to an optimization method for tensioned beam structures used to reinforce large-span steel connecting corridors. Background Technology

[0002] Long-span steel connecting corridors, as a new type of urban bridge, are widely used in urban landscape engineering and transportation hubs, featuring lightweight structure, beautiful design, and convenient construction. With the acceleration of urbanization, these structures are increasingly appearing in the public eye. However, limited by material properties and structural form, long-span steel connecting corridors commonly suffer from excessive deflection and stress concentration during service, seriously affecting their safety and reliability. Therefore, how to effectively improve the deformation resistance and damage resistance of long-span steel connecting corridors has become a key technical problem that urgently needs to be solved.

[0003] Currently, the main common methods for strengthening and optimizing the design of long-span steel connecting corridors are as follows:

[0004] 1) Rigid reinforcement method: Add stiffening ribs to the main beams or columns to increase the overall rigidity of the structure, thereby improving its resistance to deformation. However, this method increases the self-weight of the structure and also affects the aesthetics of the building.

[0005] 2) Tensioned Beam Optimization Method: Cables are added to both sides of the main beam to form a tensioned beam structure. The overall stress state is optimized by adjusting the prestress of the cables and the structural geometric parameters. This method is more economical and environmentally friendly than the rigid reinforcement method, but the optimization effect is more complex due to the coupling effect of many parameters.

[0006] 3) Dynamic vibration reduction method: Damping and vibration reduction devices are installed at key parts of the structure to absorb vibration energy and reduce the dynamic response of the structure. This method has high requirements for the dynamic characteristics of the structure and requires accurate identification of dynamic parameters and model establishment.

[0007] While the above methods have improved the deformation resistance of long-span steel connecting corridors to some extent, they still have the following shortcomings:

[0008] (1) The optimization method is too simple and cannot fully reflect the nonlinear mechanical characteristics of the structure, resulting in limited optimization effect.

[0009] (2) Parameter adjustment relies on experience judgment and lacks systematic analysis and optimization calculation methods, which cannot guarantee the optimal performance of the structure.

[0010] Therefore, there is an urgent need for a new optimization method that can comprehensively consider the nonlinear behavior of the structure, adopt a systematic parameter optimization algorithm, and take into account the feasibility of the construction process, so as to effectively improve the performance of long-span steel corridors. Summary of the Invention

[0011] In view of this, the present invention provides an optimization method for tensioned beam structures used to reinforce large-span steel connecting corridors, which can solve the technical problem that existing optimization methods cannot fully reflect the nonlinear mechanical characteristics of the structure, resulting in limited optimization effects.

[0012] This invention is implemented as follows:

[0013] This invention provides an optimization method for reinforcing a tensioned beam structure of a long-span steel connecting corridor, comprising the following steps:

[0014] S10. Establish a three-dimensional finite element model of a long-span steel connecting corridor, wherein the three-dimensional finite element model includes the upper steel connecting corridor, vertical struts and cables;

[0015] S20. Set the boundary conditions of the three-dimensional finite element model and determine the dead load and live load acting on the three-dimensional finite element model.

[0016] S30. Perform nonlinear analysis on the three-dimensional finite element model to obtain the initial deflection and stress values;

[0017] S40. Determine whether the initial deflection value and stress value meet the reinforcement requirements. If they do not meet the requirements, proceed to step S50. If they do meet the requirements, proceed to step S60.

[0018] S50. Adjust the length of the vertical strut and the prestress value of the cable, and return to step S30.

[0019] S60. Set the structural deflection value as the control parameter and the cable strain value as the response parameter.

[0020] S70. Use the SAP2000 CSiLoadOptimizer toolbox to perform cable stress optimization calculations and obtain the optimized cable strain values.

[0021] S80. The final cable force optimization result is obtained by back-calculating the optimized cable strain value.

[0022] S90. Determine the process parameters for reinforcing the tensioned beam structure of the large-span steel connecting corridor based on the final cable force optimization results.

[0023] Based on the above technical solution, the method for optimizing the tensioned beam structure for reinforcing large-span steel connecting corridors according to the present invention can be further improved as follows:

[0024] Specifically, step S10 includes:

[0025] Step 101: Collect the structural design drawings and material parameters of the long-span steel connecting corridor;

[0026] Step 102: Select finite element analysis software, including ANSYS or ABAQUS;

[0027] Step 103: Establish a three-dimensional finite element model in the finite element analysis software, including the upper structure of the steel connecting corridor, vertical struts and cables;

[0028] Step 104: Select the appropriate element type and mesh generation method based on the actual structural conditions;

[0029] Step 105: Model the connectors, including weld points and hinges, and apply the corresponding constraint relationships;

[0030] Step 106: Adjust and optimize the three-dimensional finite element model to ensure that it can accurately reflect the actual stress state and deformation of the long-span steel connecting corridor.

[0031] Furthermore, step S20 specifically includes:

[0032] Step 201: Based on the actual support conditions of the long-span steel connecting corridor, set boundary conditions in the finite element model;

[0033] Step 202: Set displacement constraints for the supports located on the piers or tension piles;

[0034] Step 203: Set different constraints for rolling or simply supported positions for other support locations;

[0035] Step 204: Determine the dead loads acting on the three-dimensional finite element model, including the self-weight of the steel connecting corridor and the permanent loads of the attached facilities;

[0036] Step 205: Determine the live loads acting on the three-dimensional finite element model, including temporary loads from personnel and vehicles;

[0037] Step 206: Determine the environmental loads acting on the three-dimensional finite element model, including wind load and snow load;

[0038] Step 207: According to the requirements of relevant design specifications, check and adjust the various loads that have been determined.

[0039] Furthermore, step S30 specifically includes:

[0040] Step 301: Establish a mathematical model for nonlinear analysis, including nonlinear stiffness matrix, displacement vector, external force vector, nonlinear internal force vector, strain-displacement matrix, nonlinear stress tensor, elasticity matrix, and nonlinear strain tensor.

[0041] Step 302: Construct nonlinear equilibrium equations, including considering the effects of material nonlinearity and geometric nonlinearity;

[0042] Step 303: Solve the nonlinear equilibrium equations using iterative algorithms, such as the Newton-Raphson method or the arc length method;

[0043] Step 304: Calculate the displacement field of the structure, including nodal displacements and component deformations;

[0044] Step 305: Calculate the stress field of the structure based on the displacement field, including the axial force, shear force and bending moment of each component;

[0045] Step 306: Extract the displacement values ​​of key nodes as initial deflection values;

[0046] Step 307: Extract the stress values ​​of key components as initial stress values.

[0047] Furthermore, nonlinear analysis can be performed using the following system of equations:

[0048]

[0049] In the formula, K(u) is the nonlinear stiffness matrix; u is the displacement vector; F is the external force vector; F nl (u) is the nonlinear internal force vector; B is the strain-displacement matrix; σ nl (u) is the nonlinear stress tensor; D is the elasticity matrix; ε nl (u) is the nonlinear strain tensor.

[0050] Displacement and stress calculation:

[0051]

[0052] In the formula, ε is the effective stiffness matrix; u For displacement calculation error; ε σ This represents the error in stress calculation.

[0053] Furthermore, step S40 specifically includes:

[0054] Step 401: Determine the maximum allowable deflection value of the long-span steel connecting corridor according to the structural design specifications;

[0055] Step 402: Determine the maximum allowable stress value of the long-span steel connecting corridor based on material properties and structural safety factor;

[0056] Step 403: Compare the initial deflection value obtained in step S30 with the maximum allowable deflection value;

[0057] Step 404: Compare the initial stress value obtained in step S30 with the maximum allowable stress value;

[0058] Step 405: When the initial deflection value is greater than the maximum allowable deflection value or the initial stress value is greater than the maximum allowable stress value, it is determined that the reinforcement requirements are not met.

[0059] Step 406: When the initial deflection value is less than or equal to the maximum allowable deflection value and the initial stress value is less than or equal to the maximum allowable stress value, it is determined that the reinforcement requirements are met.

[0060] Furthermore, step S50 specifically includes:

[0061] Step 501: Set the formula for calculating the adjustment amount of the vertical strut length, where the adjustment amount is proportional to the difference between the maximum deflection value and the maximum allowable deflection value;

[0062] Step 502: Set the formula for calculating the adjustment amount of the prestress value of the cable, where the adjustment amount is proportional to the difference between the maximum stress value and the maximum allowable stress value;

[0063] Step 503: Select an empirical adjustment coefficient to control the magnitude of each adjustment;

[0064] Step 504: Calculate the new length of the vertical strut, which is the previous length plus the adjustment amount;

[0065] Step 505: Calculate the new cable prestress value, which is the previous prestress value plus the adjustment amount;

[0066] Step 506: Apply the new vertical strut length and cable prestress value to the three-dimensional finite element model;

[0067] Step 507: Repeat the nonlinear analysis in step S30 until the reinforcement requirements are met.

[0068] Further adjustments were made to the length of the vertical struts and the prestress of the cables.

[0069]

[0070] In the formula, L i and P i These represent the vertical strut length and cable prestress after the i-th adjustment, respectively; ΔL i and ΔP i For adjustment amount; α L and α P For adjustment coefficients; u max and σ max These represent the maximum displacement and stress, respectively; u allow and σ allow These represent the maximum allowable displacement and stress, respectively.

[0071] Furthermore, step S60 specifically includes:

[0072] Step 601: Determine the target structural deflection value of the long-span steel connecting corridor according to the structural design requirements;

[0073] Step 602: Select key control points to monitor the actual deflection value of the structure;

[0074] Step 603: Set the target structure deflection value as a control parameter;

[0075] Step 604: Select the actual strain value of the cable as the response parameter;

[0076] Step 605: Establish a relationship model between control parameters and response parameters;

[0077] Step 606: Set an optimization target to make the actual deflection value as close as possible to the target deflection value;

[0078] Step 607: Set constraints to ensure that the strain values ​​of the cables meet the structural design requirements.

[0079] Furthermore, step S70 specifically includes:

[0080] Step 701: Construct a multi-objective optimization model, including the deflection objective function and the cable force uniformity objective function;

[0081] Step 702: Set optimization variables, including the cable tension values ​​of each cable;

[0082] Step 703: Determine the constraints, including the upper and lower limits of cable force, the maximum deflection limit, and the maximum stress limit;

[0083] Step 704: Set the optimization parameters in the SAP2000 CSiLoadOptimizer toolbox;

[0084] Step 705: Select a suitable multi-objective optimization algorithm, such as NSGA2 or MOEA / D;

[0085] Step 706: Run the optimization program to obtain a series of non-dominated solutions;

[0086] Step 707: Select the optimal cable strain value scheme from the non-dominated solutions.

[0087] Furthermore, the cable force optimization calculation employs a multi-objective optimization model:

[0088]

[0089] In the formula, f1(T) is the deflection objective function; f2(T) is the cable force uniformity objective function; T is the cable force vector; δ i and These are the actual and target deflections, respectively; T j and These represent the actual and target cable forces, respectively; n is the number of control points; m is the number of cables; T min and T max These are the lower and upper limits of the cable force, respectively; δ allow For the maximum allowable deflection; σ k The stress at the k-th critical point; σ allow The maximum allowable stress; p is the number of key points.

[0090] Furthermore, step S80 specifically includes:

[0091] Step 801: Establish the nonlinear relationship equation between cable force and strain, taking into account the effects of material nonlinearity and geometric nonlinearity;

[0092] Step 802: Collect the initial state data of the cable, including the initial length, initial cable force, and endpoint coordinates;

[0093] Step 803: Obtain the elastic modulus, cross-sectional area, and temperature influence coefficient of the cable material;

[0094] Step 804: Determine the nonlinear coefficient of the cable, which can be obtained through material testing or empirical formulas;

[0095] Step 805: Construct a system of nonlinear equations that includes all cables;

[0096] Step 806: Select a suitable numerical solution method, such as Newton's iteration method or quasi-Newton method;

[0097] Step 807: Solve the nonlinear equations to obtain the optimized cable force values.

[0098] Furthermore, the cable force inverse calculation employs a system of nonlinear equations:

[0099]

[0100] In the formula, T j E is the tension in the j-th cable; j A is the elastic modulus; j ε is the cross-sectional area; j For strain; β j and γ j These are nonlinear coefficients; For cable force calculation error; L j and These represent the current and initial lengths, respectively; α T This is the temperature influence coefficient; The initial cable force; (x) j ,y j ,z j )and These are the coordinates of the current and initial endpoints, respectively.

[0101] Furthermore, step S90 specifically includes:

[0102] Step 901: Calculate the length adjustment amount for each cable based on the optimized cable force value;

[0103] Step 902: Considering the nonlinear characteristics of the cable material, correct the calculation results of the length adjustment amount;

[0104] Step 903: Calculate the height adjustment amount for each vertical strut, taking into account the coupling effect with the change in the length of adjacent cables;

[0105] Step 904: Calculate the angle adjustment of key nodes based on the geometric relationship between the vertical struts and cables;

[0106] Step 905: Evaluate the calculation errors of each adjustment amount and make necessary corrections;

[0107] Step 906: Compile a detailed process parameter table, including the tension of each cable, the lifting height of each vertical strut, and the angle adjustment value of each node;

[0108] Step 907: Develop construction procedures and quality control plans to ensure the accurate implementation of process parameters.

[0109] Furthermore, the process parameters are determined using the following set of equations:

[0110]

[0111] In the formula, ΔL j ΔH is the length adjustment amount for the j-th cable; k Δθ represents the height adjustment amount of the k-th vertical strut. l λ is the angle adjustment amount for the l-th node; k N is the coupling coefficient between the height of the vertical strut and the variation in the length of the adjacent cable; k H represents the set of cables connected to the k-th vertical strut; l and L l These represent the initial height and horizontal distance of the node, respectively. and These are the adjustment errors for length, height, and angle, respectively.

[0112] Methods for obtaining relevant parameters:

[0113] 1. K(u) and B: generated using finite element analysis software;

[0114] 2.F: Determined based on structural load analysis, taking into account dead load, live load, wind load, etc.

[0115] 3.D: Determined based on the mechanical properties of the material, taking into account the effects of temperature and stress level;

[0116] 4. and Determined based on structural design requirements and the principle of uniform stress distribution;

[0117] 5.T min and T max Determined based on cable material properties, fatigue life, and design specifications;

[0118] 6.δ allow and σ allow Determined according to structural design specifications and usage requirements;

[0119] 7.E j and A j The selection is based on the properties of the cable material and the design, taking into account the effect of temperature.

[0120] 8.β j and γ j : Obtained through nonlinear experiments on cable materials;

[0121] 9. and Obtained through on-site measurements;

[0122] 10.α T : Obtained through thermal property tests of cable materials;

[0123] 11.λ k Determined through structural analysis and numerical simulation;

[0124] 12. H l and L l : Obtained through on-site measurements and structural drawings.

[0125] The SAP2000 CSiLoadOptimizer is a toolkit developed by Computers and Structures, Inc. (CSI) for the SAP2000 structural analysis software. Its main functions are as follows:

[0126] Load Optimization: This tool helps users automatically generate suitable load combinations to optimize structural design. It can consider various load conditions, such as dead loads, live loads, wind loads, and seismic loads, and generate different load combinations according to relevant specifications.

[0127] Component Design: By analyzing the structural response under different load combinations, CSiLoadOptimizer can automatically select appropriate component sizes and reinforcement configurations to optimize the overall structural design.

[0128] Report generation: This tool can generate detailed design reports, including load analysis, component design and other information, which are convenient for users to view and archive.

[0129] Integration with SAP2000: CSiLoadOptimizer is directly integrated into SAP2000, allowing users to operate within the SAP2000 interface without switching between the two software programs.

[0130] Compared with existing technologies, the beneficial effects of the optimized method for reinforcing long-span steel connecting corridors provided by this invention are:

[0131] 1. A three-dimensional finite element model including the upper steel connecting corridor, vertical struts and cables was established, which fully considered the material nonlinearity and geometric nonlinearity of the structure, and can more accurately simulate the actual stress and deformation state of the large-span steel connecting corridor.

[0132] 2. A systematic parameter optimization algorithm was adopted, including steps such as structural parameter adjustment and cable force optimization calculation, which can effectively control structural deflection and stress and achieve the optimal design of structural performance.

[0133] 3. Taking into account the construction process factors of reinforcement and renovation, specific parameters such as the adjustment amount of cable length, the adjustment amount of vertical strut height, and the adjustment amount of node angle were determined, providing reliable guidance for on-site construction.

[0134] Compared with existing technologies, the method of this invention not only comprehensively considers the nonlinear characteristics of the structure, but also employs a systematic optimization algorithm to further optimize the overall stress state and deformation characteristics of the structure while meeting safety requirements. Simultaneously, construction process factors are incorporated into the optimization process, ensuring the operability of the optimization scheme. Therefore, this method can effectively improve the deformation resistance and reliability of long-span steel corridors, solving the technical problem that existing optimization methods cannot fully reflect the nonlinear mechanical characteristics of the structure, thus limiting the optimization effect. Attached Figure Description

[0135] Figure 1 This is a schematic diagram of the working principle of a tensioned beam structure.

[0136] Figure 2 A flowchart of the method provided by the present invention;

[0137] Figure 3 Partial design drawings of nodes for reinforcing large-span steel connecting corridors with tensioned beams;

[0138] Figure 4 Detailed design schematic diagram of the connection node for reinforcing the large-span steel connecting corridor with tensioned beams;

[0139] Figure 5A graph showing the deflection variation during the structural optimization process;

[0140] Figure 6 The optimized cable force distribution heatmap;

[0141] Figure 7 A diagram showing the stress comparison at key locations in the structure;

[0142] Figure 8 Box plot showing the statistical values ​​of process parameter adjustments. Detailed Implementation

[0143] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0144] like Figure 6 As shown, a tensioned beam is a self-balancing system formed by connecting bending and compression members and tension members with struts. The structural system includes an upper beam, intermediate struts, and lower cables. The prestress applied to the lower cables of the tensioned beam causes an upward component force in the intermediate struts, which in turn generates a negative bending moment in the upper beam, thereby changing the stress performance of the upper beam and improving its stiffness and load-bearing capacity. In the reinforcement of long-span steel corridors, the existing corridor serves as the upper beam structure. Vertical supports are installed at the bottom of the steel corridor, and cables connect the vertical supports to the upper steel corridor. Applying prestress to the cables causes the upper steel corridor to deform upward due to the action of the vertical struts, thus restoring the initial deflection and achieving the reinforcement purpose.

[0145] like Figure 1 The diagram shown is a flowchart of an optimization method for reinforcing a long-span steel connecting corridor using tensioned beams, provided by this invention. The method includes the following steps:

[0146] S10. Establish a three-dimensional finite element model of the long-span steel connecting corridor. The three-dimensional finite element model includes the upper steel connecting corridor, vertical struts and cables.

[0147] S20. Set the boundary conditions of the three-dimensional finite element model and determine the dead load and live load acting on the three-dimensional finite element model.

[0148] S30. Perform nonlinear analysis on the three-dimensional finite element model to obtain the initial deflection and stress values;

[0149] S40. Determine whether the initial deflection and stress values ​​meet the reinforcement requirements. If they do not meet the requirements, proceed to step S50. If they do meet the requirements, proceed to step S60.

[0150] S50. Adjust the length of the vertical strut and the prestress value of the cable, then return to step S30.

[0151] S60. Set the structural deflection value as the control parameter and the cable strain value as the response parameter.

[0152] S70. Use the SAP2000 CSiLoadOptimizer toolbox to perform cable stress optimization calculations and obtain the optimized cable strain values.

[0153] S80. The final cable force optimization result is obtained by back-calculating the optimized cable strain value.

[0154] S90. Determine the process parameters for reinforcing the tensioned beam structure of the large-span steel connecting corridor based on the final cable force optimization results.

[0155] The specific implementation methods of the above steps are described in detail below:

[0156] Step S10: Establish a three-dimensional finite element model of the long-span steel connecting corridor.

[0157] The specific implementation of step S10 is as follows: First, collect relevant data such as structural design drawings and material parameters of the large-span steel connecting corridor. Then, using finite element analysis software such as ANSYS or ABAQUS, establish a three-dimensional finite element model including the superstructure of the steel connecting corridor, vertical struts, and cables. During the modeling process, appropriate element types, mesh generation methods, and other parameters need to be selected according to the actual structural conditions. For connecting parts such as welds and hinges, corresponding constraint relationships should be used for modeling. The establishment of the entire three-dimensional finite element model aims to reflect the actual stress state and deformation of the large-span steel connecting corridor as accurately as possible.

[0158] Step S20: Set boundary conditions and determine the loads acting on the model

[0159] The specific implementation of step S20 is as follows: First, based on the actual support conditions of the long-span steel connecting corridor, reasonable boundary conditions are set in the finite element model. For example, for supports located on piers or tension piles, displacement constraints can be set; for other support locations, different constraint conditions such as rolling or simply supported can be set.

[0160] Secondly, determine the various loads acting on the three-dimensional finite element model. These mainly include:

[0161] 1) Dead load: such as the self-weight of the steel connecting corridor, attached facilities, and other permanent loads. It can be calculated based on the structural drawings and material parameters.

[0162] 2) Live load: such as temporary loads like personnel and vehicles. This can be determined based on the intended use and design specifications.

[0163] 3) Environmental loads: such as wind loads, snow loads, etc. These can be calculated based on meteorological data and design specifications.

[0164] The determination of the above-mentioned loads should comply with the requirements of relevant design specifications to ensure that the finite element model can accurately simulate the stress state of the long-span steel connecting corridor under actual use conditions.

[0165] Step S30: Perform nonlinear analysis on the three-dimensional finite element model.

[0166] The specific implementation of step S30 is as follows: For the established three-dimensional finite element model, a nonlinear analysis method is used to perform mechanical calculations. The main characteristic of nonlinear analysis is that it can consider the nonlinear effects of structural materials, geometry, etc., thereby more accurately reflecting the actual stress and deformation state of the structure.

[0167] Specifically, the nonlinear analysis process can employ the following set of mathematical equations:

[0168]

[0169] Where K(u) is the nonlinear stiffness matrix, u is the displacement vector, and F is the external force vector. nl (u) is the nonlinear internal force vector, B is the strain-displacement matrix, and σ nl (u) is the nonlinear stress tensor, D is the elasticity matrix, and ε nl (u) is the nonlinear strain tensor.

[0170] By solving this system of equations, the initial deflection and stress values ​​of the structure can be obtained, providing the necessary basic data for subsequent structural optimization steps.

[0171] Step S40: Determine whether the initial deflection and stress values ​​meet the reinforcement requirements.

[0172] The specific implementation method of step S40 is as follows: First, based on the structural design specifications and actual usage requirements, determine the maximum allowable deflection value u of the long-span steel connecting corridor. allow and the maximum allowable stress value σ allow .

[0173] Then, compare the initial deflection value u obtained in step S30. max and stress value σ max Compare with the above allowable values ​​to determine whether the reinforcement requirements are met:

[0174]

[0175] If the above requirements are not met, proceed to step S50 to adjust the structural parameters; if the requirements are met, proceed to step S60 to begin structural optimization calculations.

[0176] This step ensures that the initial structure meets basic safety requirements, laying the foundation for subsequent optimization calculations.

[0177] Step S50: Adjust the length of the vertical strut and the prestress value of the cable.

[0178] The specific implementation method of step S50 is as follows: For the excessive deflection or stress found in step S40, it is necessary to adjust the length of the vertical struts and the prestress value of the cables to meet the reinforcement requirements. The specific implementation process is as follows:

[0179]

[0180] Where, L i and P i These represent the vertical strut length and cable prestress after the i-th adjustment, respectively; ΔL i and ΔP i For adjustment amount; α L and α P This is an empirical adjustment factor, which can be 0.1 to 0.3.

[0181] By successively adjusting the length of the vertical struts and the prestress of the cables, the maximum deflection and maximum stress of the structure are made to meet the reinforcement requirements, namely:

[0182]

[0183] After the adjustment is completed, return to step S30 to perform nonlinear analysis calculations again until the reinforcement requirements are met.

[0184] Step S60: Set the structural deflection value as the control parameter and the cable strain value as the response parameter.

[0185] The specific implementation of step S60 is as follows: After completing the structural adjustments in the aforementioned steps S40 and S50, the tensioned beam structure of the large-span steel connecting corridor is further optimized. Specifically, the structural deflection value is used as a control parameter, and the cable strain value is used as a response parameter for subsequent optimization calculations.

[0186] Specifically, the target structural deflection value is set to... The actual strain value of the cable is ε i Through optimized calculations, the actual deflection value δ was made more accurate. i Get as close as possible to the target value Simultaneously, the strain value ε of the cable i It can also meet the structural design requirements.

[0187] This step aims to ensure that the overall deformation of the structure meets the usage standards, while the cable stress is uniform and controllable, laying the foundation for subsequent cable stress optimization calculations.

[0188] Step S70: Perform cable stress optimization calculations using the SAP2000CSiLoadOptimizer toolbox.

[0189] The specific implementation of step S70 is as follows: a multi-objective optimization model is adopted, and the cable force is optimized and calculated using the SAP2000CSiLoadOptimizer toolbox to obtain the optimized cable strain value.

[0190] The specific optimization model is as follows:

[0191]

[0192] Where f1(T) is the deflection objective function, f2(T) is the cable force uniformity objective function, T is the cable force vector, and δ i and T represents the actual and target deflections, respectively. j and These represent the actual and target cable forces, respectively; n is the number of control points; m is the number of cables; and T is the total cable tension. min and T max These are the lower and upper limits of the cable force, δ allow To allow the maximum deflection, σ k For the stress at the k-th critical point, σ allow To determine the maximum allowable stress, p represents the number of key points.

[0193] By solving this multi-objective optimization problem, the optimal cable strain value that satisfies the requirements of structural deflection control and cable force uniformity can be obtained. This lays the foundation for subsequent cable force back-calculation.

[0194] Step S80: Based on the optimized cable strain values, the final cable force optimization result is derived.

[0195] The specific implementation of step S80 is as follows: the optimized cable force value is derived by using a set of nonlinear equations. The specific set of equations is as follows:

[0196]

[0197] Among them, T j Let E be the tension in the j-th cable. j Let A be the elastic modulus. j Let ε be the cross-sectional area. j For strain, β j and γ j For nonlinear coefficients, For cable force calculation error, L j and These represent the current and initial lengths, α. T The temperature influence coefficient, Let x be the initial cable force. j ,y j ,z j )and These are the coordinates of the current and initial endpoints, respectively.

[0198] By solving this set of nonlinear equations, the optimized cable force value T can be derived. j This provides the necessary data support for determining subsequent process parameters.

[0199] Step S90: Determine the process parameters for reinforcing large-span steel connecting corridors based on cable force optimization results.

[0200] The specific implementation method of step S90 is as follows: Based on the cable force optimization results obtained in step S80 above, and combined with on-site measurement data, determine the specific process parameters for the reinforcement of the large-span steel corridor, including the adjustment amount of cable length, the adjustment amount of vertical strut height, and the adjustment amount of node angle, etc. The specific calculation process is as follows:

[0201]

[0202] Where, ΔL j ΔH is the length adjustment amount for the j-th cable. k Let Δθ be the height adjustment amount of the k-th vertical strut. l λ is the angle adjustment amount for the l-th node. k N is the coupling coefficient between the height of the vertical strut and the change in the length of the adjacent cable. k H is the set of cables connected to the k-th vertical strut. l and L l These represent the initial height and horizontal distance of the node, respectively. and These are the adjustment errors for length, height, and angle, respectively.

[0203] Based on the above calculations, the specific process parameters for the reinforcement and renovation of the large-span steel corridor can be determined, providing guidance for subsequent on-site construction. To facilitate installation and ensure a reasonable stress state for the structure, the vertical struts and the upper steel corridor are connected by pins and lugs. The cables are connected to the vertical struts and the upper steel corridor via cable clamps and cable heads, with stiffening plates installed at the connection points. The stiffening plates of the vertical supports and the steel corridor are welded to the flange plates of the steel corridor, and corner braces are added. The node design for the tensioned beam reinforcement of the large-span steel corridor is as follows: Figure 7-8 As shown.

[0204] In summary, the present invention proposes an optimization method for the tensioned beam structure of a long-span steel corridor. Through steps such as establishing a three-dimensional finite element model, performing nonlinear analysis, adjusting structural parameters, and optimizing cable forces, the specific process parameters for reinforcement and renovation are finally determined.

[0205] Specifically, the principle of this invention is:

[0206] First, a three-dimensional finite element model including the upper steel connecting corridor, vertical struts, and cables was established, and nonlinear analysis was performed on it to obtain the initial structural deflection and stress state. Then, for cases where deflection or stress exceeded the standard, the structural parameters were optimized by adjusting the length of the vertical struts and the prestress of the cables to meet the reinforcement requirements.

[0207] Furthermore, this invention employs a multi-objective optimization algorithm, using the structural deflection value as a control parameter and the cable strain value as a response parameter to optimize the cable force of the structure. This step aims to ensure that the overall deformation of the structure is controlled within the allowable range, while the cable force can also reach a uniform and controllable state.

[0208] After completing the above parameter optimization calculations, this invention also derives the final cable force value from the optimization results, and determines the specific process parameters for reinforcement and modification based on this, such as the adjustment amount of cable length, the adjustment amount of vertical strut height, and the adjustment amount of node angle. This not only meets the optimization requirements of structural performance, but also ensures the operability of the optimized scheme in actual construction.

[0209] The above optimization effects are mainly due to the following key technologies:

[0210] 1. A three-dimensional finite element model is used to comprehensively describe the structural morphology and stress characteristics. Compared with simplified two-dimensional models or one-dimensional beam elements, the three-dimensional model can more accurately reflect the actual stress state of long-span steel connecting corridors, laying the foundation for subsequent nonlinear analysis and parameter optimization.

[0211] 2. Nonlinear analysis methods are used to consider the coupling effects of materials and geometry. By solving nonlinear equations involving strain-stress and displacement-strain relationships, the initial deflection and stress state of the structure can be obtained, providing a basis for determining reinforcement requirements.

[0212] 3. A systematic parameter optimization algorithm is employed to achieve optimal structural performance. The multi-objective optimization model involved in this invention can simultaneously meet the objective requirements of structural deflection control and cable strain uniformity, and determines specific process parameters through cable force back-calculation. Compared with empirical parameter tuning, this systematic optimization method can better improve structural performance.

[0213] 4. Integrating construction process factors into the optimization process. In addition to meeting structural requirements, this invention also derives actual process parameters such as cable length adjustment, vertical strut height adjustment, and node angle adjustment based on the optimization results, ensuring the operability of the optimized solution in on-site construction.

[0214] In summary, the proposed method for strengthening and optimizing long-span steel corridors fully considers the nonlinear characteristics of the structure, employs a systematic parameter optimization algorithm, and takes into account construction process requirements, thereby effectively improving the structure's deformation resistance and reliability.

[0215] To better understand and implement this invention, a specific application scenario is provided below: A large-span steel corridor with a span of 120 meters has been built in a certain area. As an important urban transportation hub, this steel corridor bears a large flow of people and vehicles. During long-term use, it has developed serious problems such as excessive deflection and local stress concentration, and urgently needs to be reinforced and renovated.

[0216] According to the optimization method proposed in this invention, a detailed analysis and optimization design of the large-span steel connecting corridor were carried out. The specific process is as follows:

[0217] 1. Establish a three-dimensional finite element model

[0218] First, design drawings and material parameters of the large-span steel connecting corridor were collected, and a three-dimensional finite element model including the upper steel connecting corridor, vertical struts, and cables was established using ANSYS software. During the modeling process, appropriate element types and meshing methods were selected based on the actual structural conditions, and corresponding constraints were applied to connecting components such as welds and pins. The entire three-dimensional model aims to reflect the actual stress and deformation state of the large-span steel connecting corridor as accurately as possible.

[0219] Table 1. Parameters of the 3D Finite Element Model of the Large-Span Steel Connecting Corridor

[0220] Parameter name Parameter value Total number of nodes 23456 Total number of units 18345 Elastic modulus of steel 210GPa Poisson's ratio of steel 0.3 steel yield strength 345MPa tensile strength of steel 490MPa

[0221] 2. Determine the applied load.

[0222] After establishing the three-dimensional finite element model, based on the requirements of the site survey and design specifications, the various loads acting on the large-span steel connecting corridor were determined, mainly including:

[0223] (1) Dead load: It consists of the self-weight of the steel connecting corridor and permanent loads such as ancillary facilities. The total dead load is calculated to be 35.6 kN / m.

[0224] (2) Live load: including personnel load and vehicle load. The total live load is calculated to be 45.2 kN / m according to the usage function and relevant specifications.

[0225] (3) Environmental load: Based on local meteorological data, the wind load is taken as 0.65 kN / m. 2 The snow load is taken as 0.35 kN / m. 2 .

[0226] The determination of the above-mentioned loads complies with the requirements of relevant design specifications, providing accurate external load inputs for subsequent nonlinear analysis.

[0227] 3. Nonlinear analysis and calculation

[0228] After establishing the finite element model and determining the loads, nonlinear analysis calculations were performed on the long-span steel connecting corridor. The specific set of mathematical equations used is as follows:

[0229]

[0230] By solving the above set of nonlinear equations, the initial deflection and stress values ​​of the large-span steel connecting corridor under the current load were obtained. Specific results are shown in Table 2.

[0231] Table 2 Initial Analysis Results of Large-Span Steel Connecting Corridors

[0232]

[0233]

[0234] As shown in Table 2, the maximum deflection of this long-span steel connecting corridor exceeds the allowable value, and the local stress is also close to the material's yield strength, posing a certain safety hazard. Therefore, further optimization and adjustment of the structural parameters are needed to meet the reinforcement requirements.

[0235] 4. Structural parameter adjustment

[0236] To address the issues of excessive deflection and stress identified in step 3, adjustments and optimizations were first made to the length of the vertical struts and the prestress of the cables. The specific adjustment process is as follows:

[0237]

[0238] Where, α L =0.2,α P =0.15. Through three iterations of calculation, the length of the vertical strut was adjusted from 12m to 15.12m, and the prestress of the cable was adjusted from 45kN to 41.55kN. After the adjustment, the maximum deflection of the large-span steel corridor was reduced to 116.8mm, and the maximum stress was reduced to 301MPa, both of which meet the reinforcement requirements.

[0239] 5. Cable Stress Optimization Calculation

[0240] After initial adjustments to the structural parameters, a multi-objective optimization model was further employed to optimize the cable forces, aiming to achieve coordinated control of structural deflection and cable strain. The specific optimization model is as follows:

[0241]

[0242] Where, δ i and The actual and target deflections (100mm) are respectively, T j and These represent the actual and target cable forces, respectively; n = 25 represents the number of deflection control points; m = 32 represents the number of cables; T min =30kN,T max =120kN is the cable force limit, δ allow =120mm is the maximum allowable deflection, σ k For the stress at the k-th critical point, σ allow =310MPa is the maximum allowable stress, p=45 is the number of critical stress points.

[0243] Optimization calculations were performed using the SAP2000CSiLoadOptimizer toolbox, and optimized results that meet the requirements of structural deflection control and cable force uniformity were obtained. Key parameters are shown in Table 3.

[0244] Table 3 Results of Cable Stress Optimization Calculation

[0245] parameter value Maximum deflection 99.6mm Average cable force 74.2kN Standard deviation of slack 8.6kN

[0246] As can be seen from Table 3, after cable force optimization calculation, the maximum deflection of the large-span steel corridor is controlled within 100mm, and the cable force is also in a relatively uniform state, which meets the design requirements.

[0247] 6. Cable force reverse calculation and process parameter determination

[0248] Based on the above optimized calculation results, a reverse calculation was finally performed on the cable force, and the specific process parameters for reinforcement and modification were determined, including the adjustment amount of cable length, the adjustment amount of vertical strut height, and the adjustment amount of node angle, as detailed below:

[0249]

[0250] Based on the above calculations, the specific process parameters for the reinforcement and renovation of this large-span steel connecting corridor were determined:

[0251] 1) Cable length adjustment ΔL j Between 0.12 and 0.48 m;

[0252] 2) Vertical strut height adjustment ΔH k Between 0.15 and 0.42 m;

[0253] 3) Node angle adjustment amount Δθ l Between 0.4 and 1.2 degrees.

[0254] These specific process parameters provide reliable guidance for subsequent on-site construction. The following charts and graphs visually demonstrate the optimization effect of this invention in this embodiment:

[0255] Figure 2 The curve depicting the deflection variation during the structural optimization process is shown. The horizontal axis represents the number of optimization iterations, and the vertical axis represents the maximum deflection value (unit: mm). As can be seen from the figure, the initial deflection was 135.6 mm, and through multiple iterations of optimization, the deflection was eventually reduced to 99.6 mm, which is far below the allowable value of 120 mm shown by the red dashed line.

[0256] Figure 3 This is an optimized heatmap of cable force distribution. The map uses different shades of color to represent the magnitude of the cable force in each cable, and labels the specific values ​​in each grid. The map shows the cable force distribution of 32 cables across 4 layers, with an average cable force of 74.2 kN and a standard deviation of 8.6 kN. This heatmap provides a visual assessment of the uniformity of cable force distribution, serving as a reference for cable adjustment during construction.

[0257] Figure 4 The figure shows a comparison of stress at key structural locations. It includes stress values ​​at four key locations: mid-span, quarter-span, supports, and connection nodes. Different colored bars represent the initial stress, optimized stress, and allowable stress, respectively. The figure shows that although the optimized stress is slightly higher, it remains within the allowable stress range, ensuring the structural safety.

[0258] Figure 5 This is a box plot showing the statistical range of process parameter adjustments. The plot statistically analyzes the adjustment ranges of three key process parameters: cable length adjustment, vertical strut height adjustment, and node angle adjustment. The box plot clearly shows the median, quartile range, and extreme values ​​of each parameter's adjustment, providing specific reference data for on-site construction.

[0259] In summary, the optimization method proposed in this invention was used to conduct a detailed reinforcement design for a 120-meter span steel connecting corridor. First, a three-dimensional finite element model was established, and nonlinear analysis was used to determine the initial deflection and stress state. Then, by adjusting the length of the vertical struts and the prestress of the cables, the structural performance met the reinforcement requirements. Furthermore, a multi-objective optimization algorithm was used to optimize the cable force, achieving coordinated control of structural deflection and cable strain. Finally, specific process parameters were derived from the optimization results, ensuring the operability of the optimized scheme in on-site construction. The entire optimization design process fully considered the nonlinear characteristics of the structure, adopted a systematic parameter optimization algorithm, and took into account construction process factors, providing a scientific and effective solution for the reinforcement and renovation of this large-span steel connecting corridor.

[0260] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the structure of tensioned beams used to reinforce large-span steel connecting corridors, characterized in that... This includes the following steps: S10. Establish a three-dimensional finite element model of a long-span steel connecting corridor, wherein the three-dimensional finite element model includes the upper steel connecting corridor, vertical struts and cables; S20. Set the boundary conditions of the three-dimensional finite element model and determine the dead load and live load acting on the three-dimensional finite element model. S30. Perform nonlinear analysis on the three-dimensional finite element model to obtain the initial deflection and stress values; S40. Determine whether the initial deflection value and stress value meet the reinforcement requirements. If they do not meet the requirements, proceed to step S50. If they do meet the requirements, proceed to step S60. S50. Adjust the length of the vertical strut and the prestress value of the cable, and return to step S30. S60. Set the structural deflection value as the control parameter and the cable strain value as the response parameter. S70. Use the SAP2000 CSiLoadOptimizer toolbox to perform cable stress optimization calculations and obtain the optimized cable strain values. S80. The final cable force optimization result is obtained by back-calculating the optimized cable strain value. S90. Determine the process parameters for reinforcing the tensioned beam structure of the large-span steel connecting corridor based on the final cable force optimization results; Step S40 specifically includes: Step 401: Determine the maximum allowable deflection value of the long-span steel connecting corridor according to the structural design specifications; Step 402: Determine the maximum allowable stress value of the long-span steel connecting corridor based on material properties and structural safety factor; Step 403: Compare the initial deflection value obtained in step S30 with the maximum allowable deflection value; Step 404: Compare the initial stress value obtained in step S30 with the maximum allowable stress value; Step 405: When the initial deflection value is greater than the maximum allowable deflection value or the initial stress value is greater than the maximum allowable stress value, it is determined that the reinforcement requirements are not met. Step 406: When the initial deflection value is less than or equal to the maximum allowable deflection value and the initial stress value is less than or equal to the maximum allowable stress value, it is determined that the reinforcement requirements are met. Step S80 specifically includes: Step 801: Establish the nonlinear relationship equation between cable force and strain, taking into account the effects of material nonlinearity and geometric nonlinearity; Step 802: Collect the initial state data of the cable, including the initial length, initial cable force, and endpoint coordinates; Step 803: Obtain the elastic modulus, cross-sectional area, and temperature influence coefficient of the cable material; Step 804: Determine the nonlinear coefficient of the cable, which can be obtained through material testing or empirical formulas; Step 805: Construct a system of nonlinear equations that includes all cables; Step 806: Select either the Newton iteration method or the quasi-Newton method as the numerical solution method; Step 807: Solve the nonlinear equations to obtain the optimized cable force values; Step S90 specifically includes: Step 901: Calculate the length adjustment amount for each cable based on the optimized cable force value; Step 902: Considering the nonlinear characteristics of the cable material, correct the calculation results of the length adjustment amount; Step 903: Calculate the height adjustment amount for each vertical strut, taking into account the coupling effect with the change in the length of adjacent cables; Step 904: Calculate the angle adjustment of key nodes based on the geometric relationship between the vertical struts and cables; Step 905: Evaluate the calculation errors of each adjustment amount and make necessary corrections; Step 906: Compile a detailed process parameter table, including the tension of each cable, the lifting height of each vertical strut, and the angle adjustment value of each node; Step 907: Develop construction procedures and quality control plans to ensure the accurate implementation of process parameters.

2. The method for optimizing a tensioned beam structure for reinforcing a large-span steel connecting corridor according to claim 1, characterized in that, Step S10 specifically includes: Step 101: Collect the structural design drawings and material parameters of the long-span steel connecting corridor; Step 102: Select finite element analysis software, including ANSYS or ABAQUS; Step 103: Establish a three-dimensional finite element model in the finite element analysis software, including the upper structure of the steel connecting corridor, vertical struts and cables; Step 104: Select the appropriate element type and mesh generation method based on the actual structural conditions; Step 105: Model the connectors, including weld points and hinges, and apply the corresponding constraint relationships; Step 106: Adjust and optimize the three-dimensional finite element model to ensure that it can accurately reflect the actual stress state and deformation of the long-span steel connecting corridor.

3. The method for optimizing a tensioned beam structure for reinforcing a large-span steel connecting corridor according to claim 2, characterized in that, Step S20 specifically includes: Step 201: Based on the actual support conditions of the long-span steel connecting corridor, set boundary conditions in the finite element model; Step 202: Set displacement constraints for the supports located on the piers or tension piles; Step 203: Set different constraints for rolling or simply supported positions for other support locations; Step 204: Determine the dead loads acting on the three-dimensional finite element model, including the self-weight of the steel connecting corridor and the permanent loads of the attached facilities; Step 205: Determine the live loads acting on the three-dimensional finite element model, including temporary loads from personnel and vehicles; Step 206: Determine the environmental loads acting on the three-dimensional finite element model, including wind load and snow load; Step 207: According to the requirements of relevant design specifications, check and adjust the various loads that have been determined.

4. The method for optimizing a tensioned beam structure for reinforcing a large-span steel connecting corridor according to claim 3, characterized in that, Step S30 specifically includes: Step 301: Establish a mathematical model for nonlinear analysis, including nonlinear stiffness matrix, displacement vector, external force vector, nonlinear internal force vector, strain-displacement matrix, nonlinear stress tensor, elasticity matrix, and nonlinear strain tensor. Step 302: Construct nonlinear equilibrium equations, including considering the effects of material nonlinearity and geometric nonlinearity; Step 303: Solve the nonlinear equilibrium equation using an iterative algorithm, choosing either the Newton-Raphson method or the arc-length method; Step 304: Calculate the displacement field of the structure, including nodal displacements and component deformations; Step 305: Calculate the stress field of the structure based on the displacement field, including the axial force, shear force and bending moment of each component; Step 306: Extract the displacement values ​​of key nodes as initial deflection values; Step 307: Extract the stress values ​​of key components as initial stress values.

5. The method for optimizing a tensioned beam structure for reinforcing a large-span steel connecting corridor according to claim 4, characterized in that, Step S50 specifically includes: Step 501: Set the formula for calculating the adjustment amount of the vertical strut length, where the adjustment amount is proportional to the difference between the maximum deflection value and the maximum allowable deflection value; Step 502: Set the formula for calculating the adjustment amount of the prestress value of the cable, where the adjustment amount is proportional to the difference between the maximum stress value and the maximum allowable stress value; Step 503: Select an empirical adjustment coefficient to control the magnitude of each adjustment; Step 504: Calculate the new length of the vertical strut, which is the previous length plus the adjustment amount; Step 505: Calculate the new cable prestress value, which is the previous prestress value plus the adjustment amount; Step 506: Apply the new vertical strut length and cable prestress value to the three-dimensional finite element model; Step 507: Repeat the nonlinear analysis in step S30 until the reinforcement requirements are met.

6. The method for optimizing a tensioned beam structure for reinforcing a large-span steel connecting corridor according to claim 5, characterized in that, Step S60 specifically includes: Step 601: Determine the target structural deflection value of the long-span steel connecting corridor according to the structural design requirements; Step 602: Select key control points to monitor the actual deflection value of the structure; Step 603: Set the target structure deflection value as a control parameter; Step 604: Select the actual strain value of the cable as the response parameter; Step 605: Establish a relationship model between control parameters and response parameters; Step 606: Set an optimization target to make the actual deflection value as close as possible to the target deflection value; Step 607: Set constraints to ensure that the strain values ​​of the cables meet the structural design requirements.

7. The method for optimizing a tensioned beam structure for reinforcing a large-span steel connecting corridor according to claim 6, characterized in that, Step S70 specifically includes: Step 701: Construct a multi-objective optimization model, including the deflection objective function and the cable force uniformity objective function; Step 702: Set optimization variables, including the cable tension values ​​of each cable; Step 703: Determine the constraints, including the upper and lower limits of cable force, the maximum deflection limit, and the maximum stress limit; Step 704: Set the optimization parameters in the SAP2000 CSiLoadOptimizer toolbox; Step 705: Select NSGA2 or MOEA / D as the multi-objective optimization algorithm; Step 706: Run the optimization program to obtain a series of non-dominated solutions; Step 707: Select the optimal cable strain value scheme from the non-dominated solutions.

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