Stress Analysis Method and System for Steel-Concrete Composite Structures of Small-Span Bridges

Abstract

This invention relates to a stress analysis method and system for steel-concrete composite structures of small-to-medium span bridges, belonging to the field of stress analysis technology. The method includes the following steps: S1. Establishing a finite element parametric model of the steel-concrete composite bridge; S2. Constructing a slip effect model of the steel-concrete interface based on the constitutive relation of the steel-concrete composite bridge; S3. Applying a moving load condition and dividing the load location of the steel-concrete composite bridge using a dynamic mesh; S4. Solving for and correcting the structural stress of the steel-concrete composite bridge; S5. Outputting the stress distribution of key sections of the steel-concrete composite bridge to identify the maximum tensile and compressive stress areas. The beneficial effects of this invention are: ensuring that the dynamic changes of the load are accurately reflected in the model to reflect the stress state of the bridge under actual traffic loads; gradually approximating the accurate structural stress solution; and comprehensively considering material properties, structural geometry, and load distribution factors to obtain reliable stress analysis results.

Description

Technical Field

[0001] This invention belongs to the field of stress analysis technology, and specifically relates to a stress analysis method and system for steel-concrete composite structures of small and medium-span bridges. Background Technology

[0002] Small and medium-span bridges play a vital role in transportation networks, and steel-concrete composite structures are widely used in their construction due to their high load-bearing capacity and fast construction speed. However, steel-concrete composite structures are composed of steel and concrete, two materials with significantly different mechanical properties. Under load, the internal stress distribution of the structure is complex, and accurate analysis of its stress state is crucial to ensuring the safety and durability of the bridge structure.

[0003] Currently, common stress analysis methods for steel-concrete composite structures in small-to-medium span bridges mainly include theoretical calculation and finite element analysis. Theoretical calculation methods typically use simplified mechanical models for structural analysis, but due to this simplification, they struggle to accurately simulate the complex stress conditions of actual structures, leading to significant errors in stress analysis results. While finite element analysis can simulate the stress state of structures more accurately, it requires establishing complex finite element models, resulting in high computational costs, low analysis efficiency, and high skill requirements for analysts, thus limiting its practical engineering applications. Therefore, there is an urgent need for a more efficient method for stress analysis of steel-concrete composite structures in small-to-medium span bridges. Summary of the Invention

[0004] This invention provides a stress analysis method and system for steel-concrete composite structures of small-to-medium span bridges. It addresses the technical problems of inaccurate analysis results and low efficiency in existing stress analysis methods. Through dynamic mesh technology, the load positions on the bridge structure are divided in real time according to the load movement path, ensuring that the dynamic changes of the load are accurately reflected in the model to reflect the stress state of the bridge under actual traffic loads. By solving for the stress in the steel beams and concrete slabs, and through continuous iterative calculation and correction, the accurate structural stress solution is gradually approximated. Considering material properties, structural geometry, and load distribution factors, reliable stress analysis results are obtained.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0006] The stress analysis method based on steel-concrete composite structures for small and medium-span bridges includes the following steps:

[0007] S1. Establish a finite element parametric model of the steel-concrete composite bridge. The finite element parametric model includes: geometric parameters of the steel beams, geometric parameters of the concrete slabs, and distribution parameters of the shear connectors.

[0008] S2. Based on the constitutive relation of steel-concrete composite bridges, a slip effect model of the steel-concrete interface is constructed. The slip effect model uses nonlinear spring elements to simulate the mechanical behavior generated by shear connectors.

[0009] S3. Apply moving load conditions and divide the load locations of the steel-concrete composite bridge using dynamic grids;

[0010] S4. A hierarchical iterative algorithm is used to solve the structural stress of the steel-concrete composite bridge and then corrects it. The structural stress of the steel-concrete composite bridge includes: steel beam stress and concrete slab stress.

[0011] S5. Output the stress distribution of key sections of the steel-concrete composite bridge to identify the areas of maximum tensile and compressive stress.

[0012] Optionally, in step S1, the steps for constructing the finite element parametric model of the steel-concrete composite bridge are as follows:

[0013] Define the geometric parameters of the steel beam: Create the geometric parameters of the steel beam in the finite element software;

[0014] Drawing the cross-section of a steel beam: I-beams are drawn using the coordinates of key points. , Generate the cross-sectional profile, extrude it into a beam. For box beams, draw a closed frame to define the thickness of the top plate, bottom plate, and web. The web height, This refers to the wing width;

[0015] Draw the concrete slab: Create a rectangular or flanged slab that couples with the top surface of the steel beam;

[0016] Generate shear connection: Studs are installed on the top surface of the steel beam. A spacing array generates a cylinder, with the top embedded in a concrete slab. Vertical spacing This refers to the horizontal spacing.

[0017] Optionally, in step S2, the slip effect model is:

[0018] Establish a steel-concrete split model: Steel part: Use shell elements or solid elements to simulate steel box girders / steel trusses and assign constitutive parameters to the steel; Concrete part: Use solid elements to simulate concrete slabs and assign constitutive parameters to the concrete; Mesh generation: Densify the mesh near the interface to ensure that spring element nodes correspond one-to-one with steel and concrete element nodes;

[0019] Arrange nonlinear spring elements: Set spring elements at the shear connection positions of the steel-concrete interface; Connection method: Connect one end of the spring element to the steel element node and the other end to the concrete element node; For the three-dimensional model, the coupling effect of the interface normal and tangential needs to be considered, and normal springs and tangential springs should be set.

[0020] Optionally, define the nonlinear behavior of the spring element:

[0021] Tangential spring: Input Relationship: Elastic Phase Reaching the ultimate load Then comes the softening phase: a bilinear model or a tri-segmented line model; among which, For nonlinear spring element force, For nonlinear spring element displacement, Elastic stiffness;

[0022] Normal spring: Defines normal stiffness, or the nonlinearity of the pull-out bearing capacity of a connector.

[0023] Optionally, in step S3, the dynamic mesh is divided and the load position is tracked through coordinate transformation:

[0024] Element coordinate transformation:

[0025] The load location changes over time as follows ;in, For moving loads at a constant speed, For any time;

[0026] It is based on uniform linear motion, with the moving load moving at a constant speed. Structurally movable, at any given moment These methods can accurately determine the specific location of the load on the structure. Represents the moving load at time [time]. Location coordinates, The axis is established along the length of the bridge structure and is related to time. The function.

[0027] Optionally, in step S3, the load location is tracked:

[0028] The equivalent nodal forces of the moving load on the element nodes can be calculated using shape function interpolation: ;

[0029] in, It is a vector representing time. The equivalent nodal force vector on the nodes of the finite element under the action of a moving load; shape function It concerns the local coordinates of the unit. The function is used to describe the displacement within an element, which is the local coordinate of the moving load within the element. This is obtained by calculating the relative position of the load within the element; For time The changing actual load function describes how the magnitude of the load acting on the structure changes over time.

[0030] Optionally, in step S4, the steps of the hierarchical iterative algorithm are as follows:

[0031] Step 1: Initial parameter setting; input structural geometric parameters, material properties, and load conditions;

[0032] Step 2: Calculate stress independently for each layer;

[0033] Step 3: Correct deformation difference using interface compatibility equations;

[0034] Step 4: Iteratively calculate the stress correction value;

[0035] Step 5: Convergence assessment and iterative loop;

[0036] Step 6: Output the final stress results.

[0037] Optionally, in step S5, the stress distribution of key sections of the steel-concrete composite bridge is determined using the equivalent section method:

[0038] Based on the neutral axis position and bending moment of each section of the concrete slab and steel beam, the normal stress of each steel section is obtained: , ;in, The normal stress in the steel section is... The normal stress is the stress in the concrete section. The bending moment of the section, and These represent the neutral axis positions of the steel section and the concrete section, respectively. The ratio of elastic modulus, The elastic modulus of steel, The elastic modulus of concrete. The moment of inertia of the converted section.

[0039] Optionally, the regions of maximum tensile and compressive stress can be identified by: the distribution patterns of normal stress, shear stress, and interfacial stress.

[0040] A stress analysis system based on steel-concrete composite structures for small-to-medium span bridges includes:

[0041] The parametric modeling module is used to create finite element parametric models of steel-concrete composite bridges.

[0042] The slip effect modeling module is used to construct a slip effect model of the steel-concrete interface based on the constitutive relation of steel-concrete composite bridges.

[0043] The load application module is used to apply moving load conditions and divide the load locations of steel-concrete composite bridges through dynamic mesh.

[0044] The stress solving module is used to solve and correct the structural stress of steel-concrete composite bridges.

[0045] The results output module is used to output the stress distribution of key sections of steel-concrete composite bridges.

[0046] The parametric modeling module is connected to the slip effect modeling module, which in turn is connected to the load application module. The load application module is connected to the stress solution module, and the stress solution module is connected to the result output module.

[0047] The beneficial effects of this invention are:

[0048] This invention uses dynamic mesh technology to divide the load position on the bridge structure in real time according to the load movement path, ensuring that the dynamic changes of the load can be accurately reflected in the model and truly reflect the stress state of the bridge under actual traffic load.

[0049] By solving for the stress in the steel beams and concrete slabs, and through continuous iterative calculations and corrections, the accurate structural stress solution is gradually approximated. Taking into account material properties, structural geometry, and load distribution factors, reliable stress analysis results are obtained. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This is a schematic diagram of the system structure of the present invention;

[0052] Figure 2 This is a schematic diagram of the workflow of the present invention;

[0053] Figure 3 This is a schematic diagram of the workflow of the hierarchical iterative algorithm of the present invention. Detailed Implementation

[0054] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0055] Example 1:

[0056] like Figure 1 As shown, this embodiment provides a stress analysis system based on steel-concrete composite structures for small-to-medium span bridges, including:

[0057] The parametric modeling module is used to create finite element parametric models of steel-concrete composite bridges.

[0058] The slip effect modeling module is used to construct a slip effect model of the steel-concrete interface based on the constitutive relation of steel-concrete composite bridges.

[0059] The load application module is used to apply moving load conditions and divide the load locations of steel-concrete composite bridges through dynamic mesh.

[0060] The stress solving module is used to solve and correct the structural stress of steel-concrete composite bridges.

[0061] The results output module is used to output the stress distribution of key sections of steel-concrete composite bridges.

[0062] The parametric modeling module is connected to the slip effect modeling module, which in turn is connected to the load application module. The load application module is connected to the stress solution module, and the stress solution module is connected to the result output module.

[0063] Based on the design requirements of steel-concrete composite bridges, the parametric modeling module inputs key information such as the geometric parameters of the steel beams, the geometric parameters of the concrete slabs, and the distribution parameters of the shear connectors to construct a finite element parametric model, which provides a basic framework for subsequent analysis. This model can flexibly reflect the influence of different parameters on the bridge structure.

[0064] The slip effect modeling module, based on the constitutive relationship of steel-concrete composite bridges, takes into account the relative slippage that occurs between steel and concrete under stress. It uses nonlinear spring elements to simulate the mechanical behavior of shear connectors, thereby constructing a slip effect model that accurately simulates the interaction between the steel-concrete interface under load, making the model closer to the actual structural performance.

[0065] The load application module simulates moving load conditions. Through dynamic mesh technology, the load positions on the bridge structure are divided in real time according to the load movement path, ensuring that the dynamic changes of the load can be accurately reflected in the model and truly reflect the stress state of the bridge under actual traffic loads.

[0066] The stress solution module uses a hierarchical iterative algorithm to solve for the stress in steel beams and concrete slabs. Through continuous iterative calculation and correction, it gradually approximates the accurate structural stress solution. Taking into account material properties, structural geometry and load distribution factors, it obtains reliable stress analysis results.

[0067] The results output module visualizes the calculated stress distribution of key sections of steel-concrete composite bridges. By analyzing this data, the maximum tensile and compressive stress areas in the bridge structure can be quickly identified, providing an important basis for bridge design optimization, safety assessment, and maintenance decisions.

[0068] Example 2:

[0069] like Figure 2 As shown, the stress analysis method for steel-concrete composite structures of small-to-medium span bridges includes the following steps:

[0070] S1. Establish a finite element parametric model of the steel-concrete composite bridge. The finite element parametric model includes: geometric parameters of the steel beams, geometric parameters of the concrete slabs, and distribution parameters of the shear connectors.

[0071] S2. Based on the constitutive relation of steel-concrete composite bridges, a slip effect model of the steel-concrete interface is constructed. The slip effect model uses nonlinear spring elements to simulate the mechanical behavior generated by shear connectors.

[0072] S3. Apply moving load conditions and divide the load locations of the steel-concrete composite bridge using dynamic grids;

[0073] S4. A hierarchical iterative algorithm is used to solve the structural stress of the steel-concrete composite bridge and then corrects it. The structural stress of the steel-concrete composite bridge includes: steel beam stress and concrete slab stress.

[0074] S5. Output the stress distribution of key sections of the steel-concrete composite bridge to identify the areas of maximum tensile and compressive stress.

[0075] Example 3:

[0076] Based on Example 2, in step S1, the finite element parametric model of the steel-concrete composite bridge is established as follows:

[0077] Model parameter definition:

[0078] 1. Geometric parameters of the steel beam;

[0079] Section type: I-beam or box girder.

[0080] Cross-sectional dimensions: Web height and thickness ; flange width and thickness The widths of the top and bottom plates of the box girder are respectively ,thickness Other parameters: chamfer radius Stiffening rib spacing Liang Chang: (Along the bridge longitudinal direction), material properties: elastic modulus Poisson's ratio and density .

[0081] The steel beams are modeled using elastoplastic materials (e.g., bilinear kinematic hardening), with element types of linear reduced integral shell elements (S4R) or solid elements (C3D8R).

[0082] 2. Geometric parameters of the concrete slab;

[0083] Cross-sectional shape: rectangular plate, flanged plate (a common structure in composite beams). Cross-sectional dimensions: plate thickness. ; board width (Lateral width, including flange); flange thickness ,width Material properties: Elastic modulus Poisson's ratio ,density and compressive strength .

[0084] The concrete slab is modeled using a plastic damage model (CDP), considering cracking and crushing, with the element type being solid element (C3D8R).

[0085] 3. Shear connection component distribution parameters;

[0086] Types: Studs, PBL keys, and channel steel connectors. Geometric dimensions: Stud diameter. and height PBL key: Hole diameter , diameter of reinforcing bars Distribution pattern: Vertical spacing: (Along the beam length); Lateral spacing: (Along the width of the board); Layout area: starting point Finish line Material properties: shear stiffness Ultimate bearing capacity .

[0087] Shear connector: Solid element: assigns properties to steel; Spring element: defines longitudinal shear stiffness. Ignore lateral stiffness.

[0088] Steps for constructing a finite element parametric model of a steel-concrete composite bridge:

[0089] Define the geometric parameters of the steel beam: Create the geometric parameters of the steel beam in the finite element software;

[0090] Drawing the cross-section of a steel beam: I-beams are drawn using the coordinates of key points. , Generate the cross-sectional profile and extrude it into a beam. For box beams, draw a closed frame to define the thickness of the top plate, bottom plate, and web.

[0091] Draw the concrete slab: Create a rectangular or flanged slab that couples with the top surface of the steel beam;

[0092] Generate shear connection: Studs are installed on the top surface of the steel beam. A spacing array generates cylinders, with the top of which is embedded in a concrete slab;

[0093] Simplified modeling: If detailed simulation is not required, nonlinear spring elements can be used to simulate the shear stiffness of the shear connection. Calculated based on the characteristics of the connecting parts, the spring stiffness The calculation method is as follows:

[0094] ;

[0095] in, This indicates the ability of a shear connector to resist shear deformation. Concrete compressive strength is an important indicator characterizing the compressive performance of concrete, reflecting the compressive capacity of the concrete material itself. Let be the cross-sectional area of ​​the shear connector. The yield strength standard value of shear connector steel reflects the stress level when the connector steel begins to enter the plastic deformation stage. It is an important mechanical property indicator of steel and is related to the material and production process of the steel.

[0096] Spring stiffness This study comprehensively considers the compressive strength of concrete, the cross-sectional area of ​​the shear connector, and the yield strength of the steel used in the connector, calculating the shear stiffness of the shear connector through a specific combination method. It demonstrates the combined influence of the properties of both concrete and steel on the shear stiffness of the connector. This reflects the contribution of concrete compressive strength and connector cross-sectional area to shear stiffness, denominator This involves correcting the results by considering the relative relationship between concrete strength and steel yield strength.

[0097] For finite element parametric models of steel-concrete composite bridges, geometric parameters (such as steel beam cross-sectional dimensions, concrete slab thickness, and shear connector spacing) can be quickly changed to automatically generate models of different design schemes and perform calculations and analyses. A large number of schemes can be compared in a short time to identify designs with good mechanical performance, significantly shortening the design cycle and reducing manpower and material resources. For example, changing the flange width and thickness of the steel beam can observe the impact on structural stress distribution and deformation, thus determining the optimal cross-sectional dimensions.

[0098] This method facilitates the study of the influence of various parameters on the mechanical performance of bridges. By systematically changing the parameters and analyzing the results, it clarifies the key control role of the parameters on the structural stress and deformation, providing a basis for refined design. It also analyzes the influence of the spacing of shear connectors on the slippage of the steel-concrete interface and the overall stiffness of the composite beam, guiding the rational arrangement of connectors.

[0099] Example 4:

[0100] Based on Example 2, in step S2, the constitutive relation of the steel-concrete composite bridge is:

[0101] Constitutive model of steel: adopting an ideal elastic-plastic model (elastic stage) After surrendering Alternatively, consider a nonlinear model for the strengthening segment.

[0102] Concrete constitutive model: Select the stress-strain curve recommended by the code (such as the parabolic ascending segment + linear descending segment in the "Code for Design of Concrete Structures"), or a nonlinear model that considers damage evolution.

[0103] Interface slip constitutive model: Establish the load-slip relationship of shear connection (e.g., the experimentally fitted nonlinear curve is...). ),in, For interfacial shear stress, (This refers to the slip).

[0104] The element type for the slip effect model is finite element software (such as ANSYS, ABAQUS, and MIDAS), and nonlinear spring elements (such as COMBIN39 in ANSYS and SpringA / SpringB in ABAQUS) are selected.

[0105] Define nonlinear spring element force-displacement ( The relationship is established by inputting non-linear data through a user-defined function (USER subroutine) or a table;

[0106] Determine the spring element parameters: Stiffness matrix: The spring element only transmits axial force (corresponding to interface shear force), and the stiffness matrix is ​​a scalar. It needs to be dynamically updated based on the constitutive relationship of the interface sliding.

[0107] Nonlinear parameter input: obtained by fitting experimental data or theoretical formulas. Discrete points of the curve (e.g., elastic stiffness) Ultimate load and limit slip For studded connections, the initial stiffness and ultimate bearing capacity can be calculated using the experimental formulas in the "Steel Structure Design Standard".

[0108] The slip effect model is constructed as follows:

[0109] Establish a steel-concrete split model: Steel part: Use shell elements or solid elements to simulate steel box girders / steel trusses and assign constitutive parameters to the steel; Concrete part: Use solid elements to simulate concrete slabs and assign constitutive parameters to the concrete; Mesh generation: Densify the mesh near the interface to ensure that spring element nodes correspond one-to-one with steel and concrete element nodes.

[0110] Arrange nonlinear spring elements: Place spring elements at the shear connection locations of the steel-concrete interface (e.g., at the center of the stud group). Connection method: Connect one end of the spring element to the steel element node and the other end to the concrete element node; for the 3D model, the coupling effect of the interface normal (lifting force) and tangential (shear force) needs to be considered, which may require setting normal springs (to simulate interface friction or pull-out stiffness of the connector) and tangential springs (to simulate shear force transmission).

[0111] Define the nonlinear behavior of the spring element:

[0112] Tangential spring (simulating shear force transmission): Input Relationship: e.g., elastic phase Reaching the ultimate load Then it enters the softening phase (stiffness degradation or maintaining constant friction). Examples include: a bilinear model (elastic phase + ideal plastic phase) or a tri-linear model (elastic phase + strengthening phase + softening phase). If the simulation results do not match reality, the spring element needs to be corrected. Curve parameters (e.g., initial stiffness, ultimate load).

[0113] Normal spring (simulating the lift-up effect): Defines normal stiffness (e.g., the interface contact stiffness between a concrete slab and a steel member), or considers the nonlinearity of the pull-out bearing capacity of the connector.

[0114] Applicable to: interfacial mechanical property analysis of steel-concrete composite beams, composite arch bridges and steel-concrete composite slab structures.

[0115] Simulation of slip effects during the construction phase (e.g., concrete creep and shrinkage) and the service phase (e.g., fatigue load).

[0116] Further explanation of the simplified modeling process based on ANSYS:

[0117] Create steel elements (Shell63) and concrete elements (Solid65), mesh them, and define the material constitutive model;

[0118] Insert a COMBIN39 unit between the interface node pairs and set it as a tangential spring;

[0119] The non-linearity of COMBIN39 is defined using a TABLE array. relation;

[0120] Apply loads and solve for the interface slip and internal forces of the connectors.

[0121] The slip effect model mainly states that slip (longitudinal relative displacement) and uplift (normal separation) at the steel-concrete interface are typical phenomena when composite structures are under stress, caused by the nonlinear deformation of shear connectors (such as stud bending and local crushing of concrete) and interface friction.

[0122] The slip effect model is constructed by interfacial shear stress-slip ( ), normal force-separation ( The constitutive relations of interfaces transform complex physical processes into calculable mechanical parameters (such as initial stiffness, ultimate bearing capacity, and softening properties), revealing the nonlinear nature of interfacial mechanical behavior.

[0123] The performance of composite structures depends on the coordinated deformation capacity of steel and concrete. The slip effect model can quantitatively analyze the contribution to stiffness: interface slip leads to a lower overall stiffness of the composite structure compared to the fully connected state; the model can calculate the stiffness reduction caused by slip. Internal force redistribution: the distribution of interfacial shear force changes with slip development; the model can reveal the internal force transmission path and stress concentration phenomena between steel and concrete. The influence of different connector types (i.e., studs, PBL keys, and channel steel) on interface performance can be quantified, for example: load-bearing capacity verification: by calculating the load-slip curves of the connectors using the model, it verifies whether the shear and pull-out design requirements are met; parameter optimization: analyzing the effect of connector spacing and arrangement on suppressing interface slip to reduce the amount of slip.

[0124] Mechanical behavior analysis of shear connectors: Stress characteristics: Shear connectors (such as studs and PBL keys) mainly transmit longitudinal shear force at the steel-concrete interface and resist uplift force.

[0125] Nonlinearity originates from plastic deformation of the connectors, localized crushing of concrete, and interfacial friction effects, which cause the load-slip relationship to be nonlinear.

[0126] The specific method for analyzing the mechanical behavior of shear connectors is as follows:

[0127] Element selection: The studs are simulated by three-dimensional solid elements (e.g., C3D8) or beam elements (e.g., B31).

[0128] Concrete is simulated using solid elements (C3D8R) and the damage-plasticity model (CDP) is activated to simulate crushing and cracking.

[0129] The interface simulates sliding and separation using nonlinear spring elements (e.g., COMBIN39) or contact elements (e.g., Surface-to-Surface).

[0130] Key settings: Define the welding constraints (Tie constraints) between the studs and the steel beam, the contact between the concrete and the studs, apply displacement or force loads, and track interface slippage and connection stress;

[0131] Parametric analysis: By changing the diameter, length, spacing or concrete strength parameters of the studs, the influence of these parameters on the stiffness, bearing capacity and failure mode of the connector is analyzed.

[0132] The mechanical behavior analysis of shear connectors is a core aspect of steel-concrete composite structures. Through a closed-loop process of "theoretical modeling - numerical simulation - experimental verification", nonlinear mechanical properties are provided.

[0133] Example 5:

[0134] Based on Example 2, in step S3, the moving load is represented as a load function that varies with time or location, specifically: ;

[0135] in, Represents the passage of time The varying load function describes the magnitude of the load acting on the structure at different times, emphasizing that the load is a function of time, and reflecting the change in load effect caused by the changing position of the moving load on the bridge over time. The load magnitude is a constant. The Dirac function (representing concentrated loads) is used in moving loads to represent concentrated loads, i.e., loads acting on a single "point". For the speed at which the load moves, Spatial location coordinates, For time. Describes a size of A concentrated moving load, the position of the moving load changes with time at a velocity The changes are accurately represented by the Dirac function, which describes the relationship between the location of the load on the structure and time.

[0136] Dynamic mesh generation and load location tracking via coordinate transformation:

[0137] 1. Element coordinate transformation;

[0138] The load location changes over time as follows ;in, For moving loads at a constant speed, For any time;

[0139] It is based on the principle of uniform linear motion, where the moving load moves at a constant speed. Structurally movable, at any given moment These methods can accurately determine the specific location of the load on the structure. Represents the moving load at time [time]. Location coordinates, The axis is established along the length of the bridge structure and is related to time. The function implies that the load position changes over time, reflecting the dynamic characteristics of moving loads.

[0140] 2. Track the load location, i.e., the dynamic distribution of the load vector;

[0141] The equivalent nodal forces of the moving load on the element nodes can be calculated using shape function interpolation: ;

[0142] in, It is a vector representing time. The equivalent nodal force vector on the nodes of a finite element under moving load. In the finite element model, the structure is composed of multiple elements and nodes. The actual load needs to be equivalently distributed to each node in order to solve for the structural response (e.g., displacement and stress); shape functions It concerns the local coordinates of the unit. The shape function is used to describe the distribution of displacement or other physical quantities within an element. Its value ranges from 0 to 1, and it has specific values ​​at different nodes of the element (e.g., the shape function value is 1 at a certain node and 0 at other nodes). These are the local coordinates of the moving load within the element, obtained by calculating the relative position of the load within the element. For time The changing actual load function, in the case of moving load problems, describes how the magnitude of the load acting on the structure changes over time.

[0143] In finite element analysis, the structure is discretized into elements and nodes. Actual moving loads... Acting on the structure, it cannot be directly used to solve the structural response; it must be solved through shape functions. The actual moving load Transformed into equivalent nodal force vectors on finite element nodes This approach integrates complex actual loads into the finite element equation solution system in the form of nodal forces, laying the foundation for subsequent calculations of the structure's displacement and stress response.

[0144] Shape function Depends on the local coordinates of the load within the element It can accurately consider the specific location of moving loads within the element. Loads at different locations contribute differently to the forces at each node of the element. Through shape function interpolation calculations, loads are rationally distributed to the corresponding nodes, accurately reflecting the influence of the load's location and distribution on the structural stress.

[0145] The moving load moves across the structure over time, and at each time step, the load's position is determined based on its real-time location (via...). (Reflection), dynamically updating the equivalent nodal force vector By combining structural dynamics equations, the dynamic response of the structure under the action of moving loads throughout the entire process is simulated and analyzed, effectively solving the key problem of analyzing the mechanical behavior of structures under moving load conditions.

[0146] Coupling of load location and mesh update: Time-step based mesh update, each time step Inside, the load travels a distance of... , It represents the distance a moving load travels within a time step, indicating the length of the path the load travels along its direction of movement on a structure (such as a bridge) within a specific time interval. For moving loads at a constant speed, it reflects how fast the load moves per unit time; The time step, in numerical calculations for structural dynamics analysis, is a series of small time intervals divided into discrete time steps to discretize the time for stepwise solutions. By continuously updating the mesh information, it accurately captures changes in load position, enabling the finite element model to more precisely reflect the true stress state of the structure under moving loads. This avoids calculation errors caused by inaccurate load position determination and provides accurate load inputs for solving the displacement, stress, and strain responses of the structure at different times. It is crucial for analyzing the mechanical behavior of bridges under moving load conditions.

[0147] Example 6:

[0148] Based on Example 2, such as Figure 3 As shown, in step S4, the calculation steps of the hierarchical iterative algorithm are as follows:

[0149] Step 1: Initial parameter setting; input structural geometric parameters (e.g., beam height, plate thickness, and cross-sectional dimensions) and material properties (elastic modulus of steel). , elastic modulus of concrete Poisson's ratio and load conditions (dead load, live load and temperature load).

[0150] Step 2: Calculate stress independently for each layer;

[0151] Step 2.1: Calculate the stress in the concrete slab: Treat the concrete slab as an independent component, bearing loads directly acting on it (such as bridge deck loads and some dead loads); calculate the initial stress of the concrete slab using elastic theory or the finite element method. and deformation ;

[0152] Step 2.2: Calculate the stress in the steel beam; treat the steel beam as an independent component, bearing loads directly acting on the beam (such as its own weight and transmitted loads), and calculate the initial stress of the steel beam using elastic theory or the finite element method. and deformation .

[0153] Step 3: Correct deformation difference using interface compatibility equations;

[0154] Calculate the initial deformation difference between the steel beam and the concrete slab at the interface: ;

[0155] Based on interface connection conditions (e.g., shear key stiffness) Establish interface compatibility equations and solve for inter-story shear forces. : ;

[0156] Inter-story shear As an additional load, it is applied in the opposite direction to the two-layer members:

[0157] Applying an upward shear force to the concrete slab Applying downward shear force to the steel beam ;

[0158] Step 4: Iteratively calculate the stress correction value;

[0159] Step 4.1: Calculate the stress correction for the concrete slab;

[0160] Analysis of interstory shear force in concrete slabs Additional stress under action and additional deformation .

[0161] Step 4.2: Calculate the stress correction for the steel beam;

[0162] Analysis of interstory shear force in steel beams Additional stress under action and additional deformation .

[0163] Update stress and deformation: .

[0164] Step 5: Convergence assessment and iterative loop;

[0165] Set the deformation difference convergence index for the current iteration. ;

[0166] like ≤ Permissible deformation error (e.g., 10) -3 If m), terminate the iteration; otherwise, return to step 3 and use the updated deformation. and Recalculate inter-story shear force Repeat the iteration until convergence. Representative at the In the next iteration, the displacement (or deformation) of the steel beam at the interface is the longitudinal displacement of the steel beam at the interface with the concrete slab after considering various loads and interface effects in the current iteration step. Representative at the In the next iteration, the displacement (or deformation) of the concrete slab at the interface is the longitudinal displacement of the concrete slab at the interface with the steel beam after considering various factors.

[0167] Step 6: Output the final stress results;

[0168] After iterative convergence, the stress in the steel beam stress in concrete slabs It includes the initial stress and corrections for all iteration steps, to further verify the rationality of the stress distribution and the structural safety performance.

[0169] It is suitable for elastic stage analysis. Considering the nonlinear effects of concrete, it needs to be combined with the material constitutive extension iterative process.

[0170] Layered iterative algorithm in the structural analysis of steel-concrete composite bridges:

[0171] Steel-concrete composite structures are composed of two materials with significantly different mechanical properties: steel and concrete. While iterative optimization approximates the actual stress state, nonlinear iterative analysis of steel-concrete composite structures exhibits material nonlinearity (concrete cracking, steel yielding) and geometric nonlinearity (large deformation effects) during loading. Traditional linear analysis struggles to accurately reflect the structure's limit state. A layered iterative algorithm, through iterative correction, gradually updates the stress-strain state of each layer of material until it converges to an equilibrium solution, thus realizing the stress evolution throughout the entire structural process.

[0172] Example 7:

[0173] Based on Example 2, in step S5, the stress distribution of the key sections of the steel-concrete composite bridge is determined using the equivalent section method:

[0174] Based on the neutral axis position and bending moment of each section of the concrete slab and steel beam, the normal stress of each steel section is obtained: , ;in, The normal stress in the steel section is... The normal stress is the stress in the concrete section. The bending moment of the section, and These represent the neutral axis positions of the steel section and the concrete section, respectively. The ratio of elastic modulus, This is used to calculate the moment of inertia of the cross section (which reflects the cross section's ability to resist bending deformation).

[0175] Normal stress is the intensity of internal forces distributed on a cross section when a component is subjected to axial tension, compression, or bending deformation, reflecting the stress situation per unit area inside the material.

[0176] The region of maximum tensile and compressive stress is identified as follows:

[0177] Normal stress with a regular distribution pattern:

[0178] Mid-span section: The top surface of the concrete slab is under tension, and the bottom surface is under compression; the lower edge of the steel beam (which may be a composite beam) is under tension, and the upper edge is under compression.

[0179] The maximum tensile stress may occur on the top surface of the concrete slab or the lower edge of the steel beam; the maximum compressive stress may occur on the bottom surface of the concrete slab or the upper edge of the steel beam.

[0180] Support section: The top surface of the concrete slab is under compression, and the bottom surface is under tension (negative bending moment); the upper edge of the steel beam is under tension, and the lower edge is under compression. The maximum tensile stress may occur at the upper edge of the steel beam or the bottom surface of the concrete slab; the maximum compressive stress may occur at the top surface of the concrete slab or the lower edge of the steel beam.

[0181] It should also be noted that shear stress is concentrated in the web of the steel beam or near the steel-concrete interface, and the peak region needs to be identified through finite element analysis; interface stress is local tensile and compressive stress around the shear connector, which may lead to concrete cracking or steel fatigue, and needs to be analyzed in detail.

[0182] The areas of maximum tensile and compressive stress are the "weak links" in a structure's stress distribution, and their identification and analysis are crucial throughout the entire project lifecycle (design → construction → monitoring → maintenance). By accurately locating these areas, the goals of "safety and controllability, optimized design, and efficient maintenance" can be achieved, ensuring the structure operates reliably under various loads.

[0183] 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 variations or substitutions that can be easily conceived by those skilled in the art within the technical scope described in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A stress analysis method for steel-concrete composite structures of small-to-medium span bridges, characterized in that, Includes the following steps: S1. Establish a finite element parametric model of the steel-concrete composite bridge. The finite element parametric model includes: geometric parameters of the steel beams, geometric parameters of the concrete slabs, and distribution parameters of the shear connectors. S2. Based on the constitutive relation of steel-concrete composite bridges, a slip effect model of the steel-concrete interface is constructed. The slip effect model uses nonlinear spring elements to simulate the mechanical behavior generated by shear connectors. S3. Apply moving load conditions and divide the load locations of the steel-concrete composite bridge using dynamic grids; In step S3, the dynamic mesh is divided and the load position is tracked through coordinate transformation: Element coordinate transformation: The load location changes over time as follows ;in, For moving loads at a constant speed, For any time; It is based on uniform linear motion, with the moving load moving at a constant speed. Structurally movable, at any given moment These methods can accurately determine the specific location of the load on the structure. Represents the moving load at time [time]. Location coordinates, The axis is established along the length of the bridge structure and is related to time. The function; In step S3, the tracking load location is: The equivalent nodal forces of the moving load on the element nodes can be calculated using shape function interpolation: ; in, It is a vector representing time. The equivalent nodal force vector on the nodes of the finite element under the action of a moving load; shape function It concerns the local coordinates of the element. The function is used to describe the displacement within an element, which is the local coordinate of the moving load within the element. This is obtained by calculating the relative position of the load within the element; For time The changing actual load function describes how the magnitude of the load acting on the structure changes over time; S4. A hierarchical iterative algorithm is used to solve the structural stress of the steel-concrete composite bridge and then corrects it. The structural stress of the steel-concrete composite bridge includes: steel beam stress and concrete slab stress. In step S4, the steps of the hierarchical iterative algorithm are as follows: Step 1: Initial parameter setting; input structural geometric parameters, material properties, and load conditions; Step 2: Calculate stress independently for each layer; Step 3: Correct deformation difference using interface compatibility equations; Step 4: Iteratively calculate the stress correction value; Step 5: Convergence assessment and iterative loop; Step 6: Output the final stress results; S5. Output the stress distribution of key sections of the steel-concrete composite bridge to identify the areas of maximum tensile and compressive stress.

2. The stress analysis method based on steel-concrete composite structures for small-to-medium span bridges according to claim 1, characterized in that, In step S1, the steps for constructing the finite element parametric model of the steel-concrete composite bridge are as follows: Define the geometric parameters of the steel beam: Create the geometric parameters of the steel beam in the finite element software; Drawing the cross-section of a steel beam: I-beams are drawn using the coordinates of key points. , Generate the cross-sectional profile, extrude it into a beam. For box beams, draw a closed frame to define the thickness of the top plate, bottom plate, and web. The web height, This refers to the wing width; Draw the concrete slab: Create a rectangular or flanged slab that couples with the top surface of the steel beam; Generate shear connection: Studs are installed on the top surface of the steel beam. A spacing array generates a cylinder, with the top embedded in a concrete slab. Vertical spacing This refers to the horizontal spacing.

3. The stress analysis method based on steel-concrete composite structures for small-to-medium span bridges according to claim 1, characterized in that, In step S2, the slip effect model is: Establish a steel-concrete composite model: Steel part: Use shell elements or solid elements to simulate steel box girders / steel trusses and assign constitutive parameters to the steel; Concrete part: Use solid elements to simulate concrete slabs and assign constitutive parameters to the concrete. Mesh generation: Densify the mesh near the interface to ensure a one-to-one correspondence between spring element nodes and steel and concrete element nodes; Arrange nonlinear spring elements: Set spring elements at the shear connection positions of the steel-concrete interface; Connection method: Connect one end of the spring element to the steel element node and the other end to the concrete element node; For the three-dimensional model, the coupling effect of the interface normal and tangential needs to be considered, and normal springs and tangential springs should be set.

4. The stress analysis method based on steel-concrete composite structures for small-to-medium span bridges according to claim 3, characterized in that, Define the nonlinear behavior of the spring element: Tangential spring: Input Relationship: Elastic Phase Reaching the ultimate load Then comes the softening phase: a bilinear model or a tri-segmented model; among which, For nonlinear spring element force, For nonlinear spring element displacement, Elastic stiffness; Normal spring: Defines normal stiffness, or the nonlinearity of the pull-out bearing capacity of a connector.

5. The stress analysis method based on steel-concrete composite structures for small-to-medium span bridges according to claim 1, characterized in that, In step S5, the stress distribution of the critical sections of the steel-concrete composite bridge is determined using the equivalent section method: Based on the neutral axis position and bending moment of each section of the concrete slab and steel beam, the normal stress of each steel section is obtained: , ;in, The normal stress in the steel section is... The normal stress is the stress in the concrete section. The bending moment of the section, and These represent the neutral axis positions of the steel section and the concrete section, respectively. The ratio of elastic modulus, The elastic modulus of steel, The elastic modulus of concrete. The moment of inertia of the converted section.

6. The stress analysis method based on steel-concrete composite structures for small-to-medium span bridges according to claim 5, characterized in that, The identification of the maximum tensile and compressive stress regions includes: normal stress, shear stress, and interface stress with regular distribution patterns.

7. A stress analysis system for steel-concrete composite structures of small-to-medium span bridges, used to execute the stress analysis method for steel-concrete composite structures of small-to-medium span bridges according to any one of claims 1-6, characterized in that, include: The parametric modeling module is used to create finite element parametric models of steel-concrete composite bridges. The slip effect modeling module is used to construct a slip effect model of the steel-concrete interface based on the constitutive relation of steel-concrete composite bridges. The load application module is used to apply moving load conditions and divide the load locations of steel-concrete composite bridges through dynamic mesh. The stress solving module is used to solve and correct the structural stress of steel-concrete composite bridges. The results output module is used to output the stress distribution of key sections of steel-concrete composite bridges. The parametric modeling module is connected to the slip effect modeling module, the slip effect modeling module is connected to the load application module, the load application module is connected to the stress solution module, and the stress solution module is connected to the result output module.

Images