Nonlinear stability calculation method of arch bridge considering initial state of construction process structure

Abstract

The application relates to a kind of arch bridge nonlinear stability calculation methods considering the initial state of structure in construction process, including using Python computer program language programming, the finite element model of arch bridge construction process is established;Using OpenSeesPy open source library, the initial tangent displacement and actual displacement of arch rib segment cantilever assembly process are calculated;And the initial displacement and internal force state of structure after each arch rib segment cantilever assembly is completed are calculated;The initial displacement and internal force state of structure after each subsequent construction stage is completed are calculated;Based on the initial displacement and internal force state of structure in each construction stage, external load is applied;Load-displacement relationship of structure under external load in each construction stage is calculated respectively;According to the load-displacement relationship of the most unfavorable position of structure in each construction stage, the ultimate bearing capacity of structure in each construction stage is determined;And then the nonlinear stability safety factor of structure in each construction stage is calculated according to the ultimate bearing capacity.The method is simple, easy to operate, and good effect.

Description

Technical Field

[0001] This invention relates to the field of arch bridge construction technology, and in particular to a method for calculating the nonlinear stability of arch bridges that considers the initial state of the structure during the construction process. Background Technology

[0002] Most long-span steel-concrete composite arch bridges are constructed using cable-stayed installation. During the cantilever assembly of the arch rib segments, the arch rib structure is temporarily fixed by flexible cables and guy cables, highlighting structural stability issues, especially in the maximum cantilever state before closure, which is the most risky stage in the entire cantilever assembly process. Initial displacements and internal forces prematurely deplete the structure's load-bearing capacity, reducing its stability. For long-span arch bridges, the initial internal forces on the arch rib structure increase with the number of cantilever segments. At the maximum cantilever state, the accumulated initial internal forces significantly increase. Furthermore, as subsequent construction stages such as the removal of arch rib cables and guy cables, concrete pouring, installation of steel grating beams, and bridge deck paving progress until the bridge's completion, the initial state of the structure changes accordingly. If the accumulated structural state from previous construction processes is not considered, the initial state of the structure in stability analysis will deviate significantly from the actual stress conditions, leading to substantial discrepancies between the stability analysis results and reality.

[0003] Currently, the initial state of a structure in stability analysis is typically applied by multiplying the first-order instability mode obtained from linear stability analysis by a small coefficient to obtain the initial deformation, or by applying a small lateral disturbance force to the structure to obtain the initial stress state. However, these methods of applying the initial state are simplifications and differ significantly from the actual displacement and stress state of the structure during construction. Furthermore, current finite element analysis software, when performing stability analysis during the construction phase, may require extracting the current construction phase model separately for analysis, resulting in the model not including the accumulated structural state from previous construction phases; or it may fail to consider the initial tangential displacement during the cantilever assembly of the arch rib, leading to inaccurate displacement calculations for the arch rib segments; or it may fail to simultaneously consider the geometric and material nonlinearities of the structure, resulting in a significantly overestimated stability safety factor. Summary of the Invention

[0004] The purpose of this invention is to address the problem that existing technologies fail to consider the initial state of the structure during the construction process when calculating the stability of arch bridges, resulting in an overestimation of the calculated stability safety factor. This invention provides a method for calculating the nonlinear stability of arch bridges that considers the initial state of the structure during construction.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for calculating the nonlinear stability of an arch bridge considering the initial state of the structure during construction includes: Using Python computer programming language, a finite element model of the arch bridge construction process was established; using the OpenSeesPy open source library, the initial tangential displacement and actual displacement of the arch rib segment cantilever assembly process were calculated; and the initial displacement and internal force state of the structure after the cantilever assembly of each arch rib segment were calculated. Calculate the initial displacement and internal force state of the structure after each subsequent construction stage is completed; apply external loads based on the initial displacement and internal force state of the structure at each construction stage; calculate the load-displacement relationship of the structure under external loads at each construction stage. The ultimate bearing capacity of the structure at each construction stage is determined based on the load-displacement relationship at the most unfavorable position of the structure at each construction stage; then, the nonlinear stability safety factor of the structure at each construction stage is calculated based on the ultimate bearing capacity.

[0007] The present invention employs a nonlinear stability calculation method for arch bridges that considers the initial state of the structure during construction. Utilizing Python and the OpenSeesPy open-source library, it can model and solve for the initial tangential displacement and actual displacement of each arch rib segment. This allows for the determination of the initial displacement and internal force state of the structure after cantilever assembly of each arch rib segment under nonlinear conditions. This method considers the influence of the initial state of the structure during construction, enabling more accurate calculation of the nonlinear stability of the structure under different initial states. It provides technical support for the structural design of ultra-long span arch bridges, as well as the design of cable-stayed systems and the arrangement of wind-resistant measures such as cables during the construction phase. This method solves the problem that existing methods cannot consider the initial state of the structure during construction when calculating the stability of arch bridges. The method is simple, easy to operate, and effective.

[0008] Preferably, the ultimate wind load that the structure can withstand at each construction stage is determined based on the load-displacement relationship at the most unfavorable position of the structure at each construction stage; then, the critical instability wind speed of the structure at each construction stage is calculated based on the ultimate wind load.

[0009] Preferably, the finite element model includes a model for the steel pipe arch rib installation stage, a model for the concrete pouring stage inside the pipe, a model for the steel grating beam installation stage, a model for the bridge deck paving stage, and a model for the completed bridge stage.

[0010] More preferably, the steel pipe arch rib installation stage model includes the cantilever assembly process of the arch rib segments, the removal of the fastening cable construction process, and the removal of the wind cable construction process.

[0011] Preferably, in the finite element model, the elastic modulus of the cable is corrected using the Ernst formula, and the material properties of concrete and steel are defined respectively through the constitutive relations of concrete and steel.

[0012] Preferably, calculating the initial tangential displacement and actual displacement during the cantilever assembly of the arch rib segment includes the following steps: S1, Extract the first i ( i =1, 2, 3, …, N Coordinates of the segmental arch ribs; S2, Calculate the first i Displacement of the end point of the segmental arch rib cantilever under external load; S3, Extract the first i Coordinates of the +1 segment arch rib; S4, the first i The displacement of the segmental arch rib cantilever end point is applied at the first i +1 segment and the first i At the connection point of the segments; S5, the first i The cross section of the +1 segment arch rib is simplified to a 1×1 rectangular cross section; S6, Calculate the... i +1 segment initial tangential displacement of the cantilever end point under the action of the connection point displacement; S7, Update # i +1 Coordinates of the end point of the cantilevered arch rib segment; S8, Calculate the first i The actual displacement of the cantilever end node of segment +1 under external load; S9. Determine if the condition is met. ,in N This represents the total number of arch rib segments on one side; like ,make And will update i Input the value in step S2, and repeat steps S2 to S8; like ,Finish N Calculation of the actual displacement of each arch rib segment.

[0013] This method solves the problem that current general-purpose finite element software cannot simultaneously consider nonlinear effects and calculate initial tangential displacement. It can accurately calculate the initial tangential displacement of each arch rib segment, obtain the actual displacement of each arch rib segment, and then accurately calculate the initial displacement and internal force state of the structure after the cantilever assembly of each arch rib segment.

[0014] More preferably, when using a computer program to perform calculations, steps S4 to S7 involve parallel calculations by creating a new computer process.

[0015] Preferably, the external loads include dead loads and wind loads.

[0016] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for calculating the nonlinear stability of an arch bridge considering the initial state of the structure during construction, as described in any of the preceding claims.

[0017] The present invention also provides an electronic device, comprising: A memory on which computer programs are stored; A processor is configured to execute the program in the memory to implement the nonlinear stability calculation method for arch bridges that considers the initial state of the structure during construction, as described in any of the preceding embodiments.

[0018] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: This invention discloses a method for calculating the nonlinear stability of arch bridges that considers the initial state of the structure during construction. Utilizing Python and the OpenSeesPy open-source library, it can model and solve for the initial tangential displacement and actual displacement of each arch rib segment. This allows for the determination of the initial displacement and internal force state of the structure after cantilever assembly of each arch rib segment under nonlinear conditions. By considering the influence of the initial state of the structure during construction, it can more accurately calculate the nonlinear stability of the structure under different initial states. This provides technical support for the structural design of ultra-long span arch bridges, as well as the design of cable-stayed systems and the arrangement of wind-resistant measures such as cables during the construction phase. It solves the problem that existing methods cannot consider the initial state of the structure during construction when calculating the stability of arch bridges. This method is simple, easy to operate, and effective. Attached Figure Description

[0019] Figure 1 A schematic diagram of the nonlinear stability analysis process for an arch bridge considering the initial state of the structure during construction. Figure 2 A schematic diagram of the calculation process for the initial tangential displacement of the arch rib segment considering nonlinear effects. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings.

[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.

[0022] Example 1 like Figure 1 As shown, the nonlinear stability calculation method for an arch bridge considering the initial state of the structure during construction, as described in this invention, includes the following steps: Step 1: Use the Python computer programming language to program and establish a finite element model of the arch bridge construction process. The finite element model includes the steel pipe arch rib installation stage model, the concrete pouring stage model inside the pipe model, the bridge deck steel grid beam installation stage model, the bridge deck paving stage model, and the completed bridge stage model. Among them, the steel pipe arch rib installation stage model includes the cantilever assembly process of the arch rib segments, the removal of the cable fasteners, and the removal of the wind cables.

[0023] In the finite element model, the elastic modulus of the cable is corrected using the Ernst formula, and the material properties of concrete and steel are defined by the constitutive relations of concrete and steel, respectively.

[0024] Currently, Python programming software has many open-source function libraries to meet various computing needs. Among them, the OpenSees open-source library, namely OpenSeesPy, which is included in the Python development platform, can be used to call the relevant functions in the OpenSees open-source library to build finite element models using the Python language. Therefore, OpenSeesPy can be used to build finite element models to calculate the initial tangential displacement and actual displacement of the arch rib segment.

[0025] Step 2: Using the OpenSeesPy open-source library, calculate the initial tangential displacement and actual displacement of the arch rib segment during cantilever assembly, such as... Figure 2 As shown, it includes the following steps: 1. Extract the first i ( i =1, 2, 3, …, N The coordinates of the segmental arch rib.

[0026] 2. Calculate the first... i Displacement of the end point of the segmental arch rib cantilever under external load.

[0027] 3. Extract the first i The coordinates of the +1 segment arch rib.

[0028] 4. The first i The displacement of the segmental arch rib cantilever end point is applied at the first i +1 segment and the first i At the connection point of the segments.

[0029] 5. The first i The cross section of the +1 segment arch rib is simplified to a 1×1 rectangular cross section.

[0030] 6. Calculate the first... i The initial tangential displacement of the cantilever end point under the action of the connection point displacement of segment +1.

[0031] 7. Update the first i Coordinates of the end point of the +1 segment arch rib cantilever.

[0032] 8. Calculate the first... i The actual displacement of the +1 segment cantilever end node under external load.

[0033] 9. Determine if the condition is met. ,in N This represents the total number of arch rib segments on one side; like ,make And will update i Enter the value in step 2, and repeat steps 2 through 8; like ,Finish N Calculation of the actual displacement of each arch rib segment.

[0034] In the process of using a computer program for calculation, steps 4 to 7 can be performed in parallel by creating a new computer process.

[0035] Step 3: Calculate the initial displacement and internal force state of the structure after the cantilever assembly of each arch rib segment is completed.

[0036] Step 4: Calculate the initial displacement and internal force state of the structure after each subsequent construction stage is completed.

[0037] Step 5: Based on the initial displacement and internal force state of the structure at each construction stage calculated in Step 4, apply external loads, including dead loads and wind loads.

[0038] Step 6: Calculate the load-displacement relationship of the structure at each construction stage under the external loads applied in Step 5, including the total load-displacement relationship and the wind load-displacement relationship.

[0039] Step 7: Based on the load-displacement relationship at the most unfavorable position of the structure at each construction stage, determine the ultimate bearing capacity and the ultimate wind load that the structure can withstand at each construction stage.

[0040] Step 8: Calculate the nonlinear stability safety factor of the structure at each construction stage based on the ultimate bearing capacity, and calculate the critical instability wind speed of the structure at each construction stage based on the ultimate wind load.

[0041] In particular, for arch bridges constructed using the cable-stayed method, the method of this invention can accurately calculate the initial tangential displacement of the arch rib segment during the cantilever assembly process under nonlinear conditions. This allows for the accurate determination of the initial displacement and internal force state of the structure during different construction processes. Furthermore, it enables the calculation of the ultimate bearing capacity, nonlinear stability safety factor, and critical instability wind speed of the structure during the cantilever assembly process of each arch rib segment. This provides technical support for the design of the cable-stayed system, the analysis of wind load warning limits during structural construction, and the optimization of wind-resistant measures such as cable wind cables.

[0042] This embodiment describes a nonlinear stability calculation method for arch bridges that considers the initial state of the structure during construction. Utilizing Python and the OpenSeesPy open-source library, it solves the problem that current general-purpose finite element software cannot simultaneously consider nonlinear effects and calculate initial tangential displacement. It can accurately calculate the initial tangential displacement of each arch rib segment, obtaining the actual displacement of each segment. Furthermore, it accurately calculates the initial displacement and internal force state of the structure after the cantilever assembly of each arch rib segment. This method can be used for construction stages such as the removal of cable-stayed cables and guy cables, concrete pouring within pipes, installation of steel grating beams on the bridge deck, and bridge deck paving, as well as for the initial state calculation and nonlinear stability analysis of the structure in the completed bridge state. It more accurately calculates the nonlinear stability of the structure under different initial states, thus providing technical support for the structural design of ultra-long span arch bridges and the design of cable-stayed systems and the arrangement of wind-resistant measures such as guy cables during the construction stage. It solves the problem that existing methods cannot consider the initial state of the structure during the construction process when calculating the stability of arch bridges. This method is simple, easy to operate, and has good results.

[0043] Example 2 The present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for calculating the nonlinear stability of an arch bridge considering the initial state of the structure during construction, as described in Example 1.

[0044] Computer-readable storage media are used to store various types of data to support the operation of the electronic device. This data may include, for example, instructions for any application or method used to operate on the electronic device, as well as application-related data. The computer-readable storage medium may be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0045] Example 3 An electronic device according to the present invention includes: A memory on which computer programs are stored; A processor is configured to execute the program in the memory to implement the method for calculating the nonlinear stability of an arch bridge considering the initial state of the structure during construction, as described in Embodiment 1.

[0046] As a preferred embodiment of this invention, the electronic device may include a processor, a memory, and may also include one or more of a multimedia component, an input / output (I / O) interface, and a communication component.

[0047] The processor controls the overall operation of the electronic device to complete all or part of the steps in the above-mentioned method for calculating the nonlinear stability of arch bridges that considers the initial state of the structure during construction.

[0048] Memory is used to store various types of data to support the operation of the electronic device. This data may include, for example, instructions for any application or method used to operate on the electronic device, as well as application-related data. Memory can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0049] The multimedia component may include a screen and an audio component, wherein the screen may be, for example, a touch screen, and the audio component is used to output and / or input audio signals; for example, the audio component may include a microphone for receiving external audio signals, the received audio signals may be further stored in memory or transmitted via a communication component; the audio component may also include at least one speaker for outputting audio signals.

[0050] I / O interfaces provide interfaces between the processor and other interface modules, such as keyboards, mice, buttons, etc.; these buttons can be virtual buttons or physical buttons.

[0051] The communication component is used for wired or wireless communication between the electronic device and other devices; wireless communication, such as Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G, 4G or 5G, or one or more combinations thereof, and the corresponding communication component may include: Wi-Fi module, Bluetooth module, NFC module, mobile communication module.

[0052] As a preferred embodiment, the electronic device may be implemented by one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components to perform the above-described method for calculating the nonlinear stability of arch bridges that considers the initial state of the structure during the construction process.

[0053] In addition, the computer-readable storage medium provided in this embodiment can be the memory including program instructions, which can be executed by the processor of an electronic device to complete the above-mentioned method for calculating the nonlinear stability of an arch bridge considering the initial state of the structure during the construction process.

[0054] The above description is only 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 protection scope of the present invention.

Claims

1. A method for calculating the nonlinear stability of an arch bridge considering the initial state of the structure during construction, characterized in that, include: Using Python computer programming language, a finite element model of the arch bridge construction process was established; using the OpenSeesPy open source library, the initial tangential displacement and actual displacement of the arch rib segment cantilever assembly process were calculated; and the initial displacement and internal force state of the structure after the cantilever assembly of each arch rib segment were calculated. Calculate the initial displacement and internal force state of the structure after each subsequent construction stage is completed; apply external loads based on the initial displacement and internal force state of the structure at each construction stage; calculate the load-displacement relationship of the structure under external loads at each construction stage. The ultimate bearing capacity of the structure at each construction stage is determined based on the load-displacement relationship at the most unfavorable position of the structure at each construction stage; then, the nonlinear stability safety factor of the structure at each construction stage is calculated based on the ultimate bearing capacity.

2. The arch bridge nonlinear stability calculation method considering the initial state of the construction process structure according to claim 1, wherein, Based on the load-displacement relationship at the most unfavorable location of the structure at each construction stage, the ultimate wind load that the structure can withstand at each construction stage is determined; then, the critical instability wind speed of the structure at each construction stage is calculated based on the ultimate wind load.

3. The method according to claim 1, wherein, The finite element model includes the steel pipe arch rib installation stage model, the concrete pouring stage model inside the pipe model, the bridge deck steel grating beam installation stage model, the bridge deck paving stage model, and the completed bridge stage model.

4. The method according to claim 3, wherein, The model for the installation stage of the steel pipe arch rib includes the cantilever assembly process of the arch rib segments, the removal of the cable fasteners, and the removal of the wind cables.

5. The method for calculating the nonlinear stability of an arch bridge considering the initial state of the structure during construction, as described in claim 1, is characterized in that... In the finite element model, the elastic modulus of the cable is corrected using the Ernst formula, and the material properties of concrete and steel are defined by the constitutive relations of concrete and steel, respectively.

6. The method for calculating the nonlinear stability of an arch bridge considering the initial state of the structure during construction, as described in claim 1, is characterized in that... The calculation of the initial tangential displacement and actual displacement during the cantilever assembly of the arch rib segment includes the following steps: S1, Extract the first i ( i The coordinates of the arch rib segments (=1, 2, 3, …, N) are given. S2, Calculate the first i Displacement of the end point of the segmental arch rib cantilever under external load; S3, Extract the first i Coordinates of the +1 segment arch rib; S4, the first i The displacement of the segmental arch rib cantilever end point is applied at the first i +1 segment and the first i At the connection point of the segments; S5, the first i The cross section of the +1 segment arch rib is simplified to a 1×1 rectangular cross section; S6, Calculate the... i +1 segment initial tangential displacement of the cantilever end point under the action of the connection point displacement; S7, Update # i +1 Coordinates of the end point of the cantilevered arch rib segment; S8, Calculate the first i The actual displacement of the cantilever end node of segment +1 under external load; S9. Determine if the condition is met. ,in N This represents the total number of single-sided arch rib segments; like ,make And will update i Input the value in step S2, and repeat steps S2 to S8; like ,Finish N Calculation of the actual displacement of each arch rib segment.

7. The method for calculating the nonlinear stability of an arch bridge considering the initial state of the structure during construction, as described in claim 6, is characterized in that... When using a computer program to perform calculations, steps S4 to S7 involve parallel calculations by creating a new computer process.

8. The method for calculating the nonlinear stability of an arch bridge considering the initial state of the structure during construction, as described in any one of claims 1-7, is characterized in that... External loads include dead loads and wind loads.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the method for calculating the nonlinear stability of an arch bridge considering the initial state of the structure during construction, as described in any one of claims 1-7.

10. An electronic device, characterized in that, include: A memory on which computer programs are stored; A processor is configured to execute the program in the memory to implement the method for calculating the nonlinear stability of an arch bridge considering the initial state of the structure during construction, as described in any one of claims 1-7.

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