Stress analysis method and system based on steel-concrete composite structure of small-and-medium-span bridge

Abstract

The invention relates to a stress analysis method and system based on a small and medium span bridge steel-concrete composite structure, and belongs to the technical field of stress analysis, and the method comprises the following steps: S1, building a finite element parameterized model of a steel-concrete composite bridge; s2, constructing a slippage effect model of a steel-concrete interface based on the constitutive relationship of the steel-concrete composite bridge; s3, applying a moving load working condition, and dividing a load position of the steel-concrete composite bridge through a dynamic grid; s4, solving and correcting the structural stress of the steel-concrete composite bridge; s5, key section stress distribution of the steel-concrete composite bridge is output so as to identify the maximum tension and compression stress area; the method has the beneficial effects that the dynamic change of the load action can be accurately reflected in the model so as to reflect the stress state of the bridge under the actual traffic load; and an accurate structural stress solution is gradually approximated, and a reliable stress analysis result is obtained by comprehensively considering material characteristics, structural geometrical shapes and load distribution factors.

Description

Technical Field

[0001] The present invention belongs to the technical field of stress analysis, and in particular relates to a stress analysis method and system based on a steel-concrete composite structure of a small and medium-span bridge. Background Art

[0002] Small and medium-span bridges occupy a vital position in transportation networks. Steel-concrete composite structures are widely used in their construction due to their high load-bearing capacity and rapid construction. 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 this stress state is crucial to ensuring the safety and durability of bridge structures.

[0003] Currently, common stress analysis methods for steel-concrete composite structures in small and medium-span bridges mainly include theoretical calculation methods and finite element analysis methods. Theoretical calculation methods usually perform mechanical analysis on the structure based on simplified mechanical models. However, due to their simplified treatment of the structure, they cannot accurately simulate the complex stress conditions of the actual structure, resulting in large errors in the stress analysis results. While finite element analysis methods can more accurately simulate the stress state of the structure, they require the establishment of a complex finite element model, which is computationally intensive, has low analysis efficiency, and requires a high level of professional expertise from the analyst. Therefore, there is an urgent need for a method that can efficiently perform stress analysis on steel-concrete composite structures in small and medium-span bridges. Summary of the Invention

[0004] The present invention provides a stress analysis method and system for steel-concrete composite structures of small and medium-span bridges, which are used to solve the technical problems of inaccurate analysis results and low efficiency in existing stress analysis methods. Through dynamic grid 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 effect can be accurately reflected in the model to reflect the stress state of the bridge under actual traffic loads. By solving the stress of the steel beam and the concrete slab, and continuously iteratively calculating and correcting, the accurate structural stress solution is gradually approached, and reliable stress analysis results are obtained by comprehensively considering material properties, structural geometry and load distribution factors.

[0005] In order to achieve the above object, the present invention is implemented by the following technical solutions:

[0006] The stress analysis method based on the steel-concrete composite structure of 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 relationship 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 of shear connectors.

[0009] S3. Apply a moving load case and use dynamic meshing to divide the load position of the steel-concrete composite bridge;

[0010] S4. Use a hierarchical iterative algorithm to solve and correct the structural stress of the steel-concrete composite bridge. The structural stress of the steel-concrete composite bridge includes the stress of the steel beam and the stress of the concrete slab.

[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 parameterized model of the steel-concrete composite bridge are:

[0013] Define geometric parameter variables of steel beams: Create geometric parameters of steel beams in finite element software;

[0014] Draw the steel beam cross section: I-beam is drawn by key point coordinates , Generate the cross-section profile and extrude it into a beam body. The box beam is formed by drawing a closed frame to define the thickness of the top plate, bottom plate and web. is the web height, is the flange width;

[0015] Draw concrete slab: Create rectangular or flanged slabs and couple them to the top surface of steel beams;

[0016] Generate shear connectors: Studs are placed on the top surface of the steel beams. The spacing pattern generates a cylinder with the top embedded in the concrete slab, where is the vertical spacing, is the horizontal spacing.

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

[0018] Establish a steel-concrete split model: For the steel part, use shell elements or solid elements to simulate the steel box girder / steel truss and assign the steel constitutive parameters; for the concrete part, use solid elements to simulate the concrete slab and assign the concrete constitutive parameters; meshing: increase the mesh density near the interface to ensure that the spring element nodes correspond one-to-one with the steel and concrete element nodes;

[0019] Arrange nonlinear spring units: Set spring units at the shear connector position of the steel-concrete interface; connection method: one end of the spring unit is connected to the steel unit node, and the other end is connected to the concrete unit node; for three-dimensional models, it is necessary to consider the coupling effect of the interface normal and tangential directions, and set normal springs and tangential springs.

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

[0021] Tangential Spring: Input Relationships: The Elastic Stage , reaching the ultimate load Then enter the softening stage: bilinear model or three-fold line model; is the nonlinear spring element force, is the nonlinear spring element displacement, is the elastic stiffness;

[0022] Normal Spring: Defines the normal stiffness, or nonlinearity in the pullout resistance of the connector.

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

[0024] Unit coordinate transformation:

[0025] The load position changes with time as ;in, To move the load at a constant speed, For any time;

[0026] It is based on uniform linear motion, moving the load at a constant speed Move on the structure at any time , can accurately determine the specific location of the load on the structure; Represents the moving load at time The location coordinates of The axis is established along the length of the bridge structure and is a time function.

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

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

[0029] in, is a vector representing the time The equivalent nodal force vector on the finite element node under the action of the moving load; shape function is about the local coordinates of the element The function used to describe the displacement in the unit is the local coordinate of the moving load in the unit , obtained by calculating the relative position of the load position in the unit; Over time The varying actual load function describes how the magnitude of the load acting on the structure changes with time.

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

[0031] Step 1: Initial parameter setting: input structural geometry, material properties and loading conditions;

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

[0033] Step 3: Correct the deformation difference using the interface coordination equation;

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

[0035] Step 5: Convergence judgment and iterative cycle;

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

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

[0038] According to the neutral axis position and section bending moment of the concrete slab and steel beam, the normal stress of the steel section of the concrete slab and steel beam is obtained: , ;in, is the normal stress of the steel section, is the normal stress in the concrete section; is the cross-sectional bending moment, and are the neutral axis positions of the steel section and the concrete section, respectively. is the elastic modulus ratio), is the moment of inertia of the converted section.

[0039] Optionally, the identification of the maximum tensile and compressive stress regions includes: regularly distributed normal stress, shear stress, and interface stress.

[0040] The stress analysis system based on steel-concrete composite structures of small and medium span bridges includes:

[0041] Parametric modeling module, used to establish finite element parametric models of steel-concrete composite bridges;

[0042] Slip effect modeling module, used to construct a slip effect model of the steel-concrete interface based on the constitutive relationship of steel-concrete composite bridges;

[0043] Load application module, used to apply moving load cases and divide the load positions of steel-concrete composite bridges through dynamic meshing;

[0044] Stress solution module, used to solve the structural stress of steel-concrete composite bridges and make corrections;

[0045] Result output module, used to output the stress distribution of key sections of steel-concrete composite bridges;

[0046] The parameterized 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.

[0047] Beneficial effects of the present invention:

[0048] This invention uses dynamic grid 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 effect can be accurately reflected in the model and truly reflect the stress state of the bridge under actual traffic loads;

[0049] By solving the stress of steel beams and concrete slabs, and through continuous iterative calculation and correction, we gradually approach the accurate structural stress solution, and comprehensively consider the material properties, structural geometry and load distribution factors to obtain reliable stress analysis results. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0051] Figure 1 Schematic diagram of the system structure of the present invention;

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

[0053] Figure 3 Schematic diagram of the hierarchical iterative algorithm workflow of the present invention. DETAILED DESCRIPTION

[0054] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0055] Example 1:

[0056] like Figure 1As shown, this embodiment provides a stress analysis system based on a steel-concrete composite structure of a small and medium span bridge, including:

[0057] Parametric modeling module, used to establish finite element parametric models of steel-concrete composite bridges;

[0058] Slip effect modeling module, used to construct a slip effect model of the steel-concrete interface based on the constitutive relationship of steel-concrete composite bridges;

[0059] Load application module, used to apply moving load cases and divide the load positions of steel-concrete composite bridges through dynamic meshing;

[0060] Stress solution module, used to solve the structural stress of steel-concrete composite bridges and make corrections;

[0061] Result output module, used to output the stress distribution of key sections of steel-concrete composite bridges;

[0062] The parameterized 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.

[0063] Based on the design requirements of steel-concrete composite bridges, the parametric modeling module inputs key information on the geometric parameters of steel beams, concrete slabs, and shear connector distribution parameters to construct a finite element parametric model, providing a basic framework for subsequent analysis. This model can flexibly reflect the impact 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 slip between steel and concrete when subjected to stress. It uses nonlinear spring elements to simulate the mechanical behavior of shear connectors to construct a slip effect model. This accurately simulates the interaction between the steel-concrete interface under load, making the model closer to 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 in the load effect can be accurately reflected in the model and truly reflecting the stress state of the bridge under actual traffic loads.

[0066] The stress solution module uses a hierarchical iterative algorithm to solve the stress of steel beams and concrete slabs. Through continuous iterative calculation and correction, it gradually approaches the accurate structural stress solution, comprehensively considering material properties, structural geometry and load distribution factors to obtain reliable stress analysis results.

[0067] The result output module visualizes the calculated stress distribution of key sections of steel-concrete composite bridges. By analyzing this data, it is possible to quickly identify the areas of maximum tensile and compressive stress in the bridge structure, providing an important basis for bridge design optimization, safety assessment, and maintenance decision-making.

[0068] Example 2:

[0069] like Figure 2 As shown in Figure 2, the stress analysis method based on the steel-concrete composite structure of small and 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 relationship 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 of shear connectors.

[0072] S3. Apply a moving load case and use dynamic meshing to divide the load position of the steel-concrete composite bridge;

[0073] S4. Use a hierarchical iterative algorithm to solve and correct the structural stress of the steel-concrete composite bridge. The structural stress of the steel-concrete composite bridge includes the stress of the steel beam and the stress of the concrete slab.

[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 parameterized model of the steel-concrete composite bridge is established as follows:

[0077] Model parameter definition:

[0078] 1. Geometric parameters of steel beams;

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

[0080] Cross-sectional dimensions: web height and thickness ; Flange width and thickness ; The width of the top plate / bottom plate of the box beam is ,thickness ;Other parameters: chamfer radius , stiffener spacing , Liang Chang: (along the longitudinal direction of the bridge), material properties: elastic modulus , Poisson's ratio and density .

[0081] The steel beam adopts the elastic-plastic material model (such as bilinear kinematic hardening) and the element type is linear reduced integration shell element (S4R) or solid element (C3D8R).

[0082] 2. Concrete slab geometric parameters;

[0083] Sectional form: rectangular plate, plate with flange (common structure of composite beam). Sectional size: plate thickness Board width (transverse width, including flange); flange thickness ,width . Material Properties: Elastic Modulus , Poisson's ratio ,density and compressive strength .

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

[0085] 3. Shear connector distribution parameters;

[0086] Type: Stud, PBL key and channel connector. Dimensions: Stud diameter and height ;PBL key: hole diameter , steel bar diameter . Distribution method: Vertical spacing: (along the beam length); transverse spacing: (along the board width); layout area: starting position , end position . Material Properties: Shear Stiffness , Ultimate bearing capacity .

[0087] Shear connector: Solid element: assign steel properties; Spring element: define longitudinal shear stiffness , neglecting the lateral stiffness.

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

[0089] Define geometric parameter variables of steel beams: Create geometric parameters of steel beams in finite element software;

[0090] Draw the steel beam cross section: I-beam is drawn by key point coordinates , Generate cross-section profile and extrude it into beam body. Box beam is made by drawing closed frame to define the thickness of top plate, bottom plate and web.

[0091] Draw concrete slab: Create rectangular or flanged slabs and couple them to the top surface of steel beams;

[0092] Generate shear connectors: Studs are placed on the top surface of the steel beams. The spacing array generates a cylinder with the top end embedded in the 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 connector. Calculated from the characteristics of the connection, the spring stiffness The calculation method is:

[0094] ;

[0095] in, Indicates the ability of shear connectors to resist shear deformation. The compressive strength of concrete is an important indicator of the compressive performance of concrete, reflecting the compressive capacity of the concrete material itself. is the cross-sectional area of ​​the shear connector, It is the standard value of the yield strength of shear connector steel, reflecting 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 rate The shear stiffness of the shear connector is calculated by taking into account the compressive strength of the concrete, the cross-sectional area of ​​the shear connector, and the yield strength of the connector steel. This reflects the combined influence of the properties of both concrete and steel on the shear stiffness of the connector. Reflects the contribution of concrete compressive strength and connector cross-sectional area to shear stiffness, the denominator The results are corrected by taking into account the relative relationship between concrete strength and steel yield strength.

[0097] Finite element parametric models for steel-concrete composite bridges can rapidly change geometric parameters (such as steel beam cross-section dimensions, concrete slab thickness, and shear connector spacing), automatically generating models for different design options and performing calculations and analyses. Numerous alternatives can be compared in a short period of time to identify designs with optimal mechanical performance, significantly shortening the design cycle and reducing both human and material resources. For example, by varying the width and thickness of steel beam flanges, the effects on structural stress distribution and deformation can be observed to determine the optimal cross-sectional dimensions.

[0098] It is convenient to study the influence of various parameters on the mechanical properties of bridges. By systematically changing the parameters and analyzing the results, it is clear that the parameters play a key role in controlling the stress and deformation of the structure, providing a basis for refined design, analyzing the influence of the spacing of shear connectors on the slip of the steel-concrete interface and the overall stiffness of the composite beam, and guiding the reasonable arrangement of connectors.

[0099] Example 4:

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

[0101] Steel constitutive model: Ideal elastic-plastic model (elastic stage , after surrendering ) or consider nonlinear models of the reinforcement 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 consider the nonlinear model of damage evolution.

[0103] Interface slip constitutive model: Establish the load-slip relationship of the shear connector (e.g., the nonlinear curve fitted by the experiment is, ),in, is the interface shear stress, is the slip amount).

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

[0105] Define the nonlinear spring element force-displacement ( ) relationship, input nonlinear data through user-defined functions (USER subroutines) or tables;

[0106] Determine the spring unit parameters: Stiffness matrix: The spring unit only transmits axial force (corresponding to interface shear force), and the stiffness matrix is ​​a scalar , needs to be dynamically updated according to the interface slip constitutive relation.

[0107] Nonlinear parameter input: obtained through experimental data or theoretical formula fitting Discrete points of the curve (such as elastic stiffness , Ultimate load and the limit slip For stud connectors, the initial stiffness and ultimate bearing capacity can be calculated by referring to the test formulas in the Steel Structure Design Standard.

[0108] The construction of the slip effect model is:

[0109] Establish a steel-concrete split model: For the steel part, use shell elements (Shell) or solid elements (Solid) to simulate the steel box girder / steel truss and assign the steel constitutive parameters; for the concrete part, use solid elements to simulate the concrete slab and assign the concrete constitutive parameters; for meshing, encrypt the mesh near the interface to ensure a one-to-one correspondence between the spring element nodes and the steel and concrete element nodes.

[0110] Arrange nonlinear spring elements: Set up spring elements at the shear connector locations at the steel-concrete interface (e.g., at the center of the stud group). Connect one end of the spring element to the steel element node and the other end to the concrete element node. For 3D models, the coupling between the interface normal (uplift force) and tangential (shear force) needs to be considered. This may require the use of normal springs (to simulate interface friction or connector pullout stiffness) and tangential springs (to simulate shear force transmission).

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

[0112] Tangential spring (simulates shear force transfer): Input Relationship: e.g., elasticity stage , reaching the ultimate load Then enter the softening stage (stiffness degradation or constant friction). For example: bilinear model (elastic stage + ideal plastic stage) or three-fold line model (elastic stage + strengthening stage + softening stage). If the simulation results do not match the actual situation, the spring unit needs to be corrected. Curve parameters (e.g. initial stiffness, ultimate load).

[0113] Normal spring (to simulate the uplift effect): Define the normal stiffness (e.g., the interface stiffness between a concrete slab and a steel member), or consider the nonlinearity of the pullout resistance of a connector.

[0114] Applicable to: Interface mechanical performance 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, shrinkage) and the service phase (e.g. fatigue loads).

[0116] With further explanation, a simplified modeling process based on ANSYS:

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

[0118] Insert COMBIN39 elements between the interface node pairs and set them as tangential springs;

[0119] Define the nonlinearity of COMBIN39 through the TABLE array relation;

[0120] Apply loads and solve to extract interface slip and internal forces of connectors.

[0121] The slip effect model is mainly based on the following: slip (longitudinal relative displacement) and lifting (normal separation) of the steel-concrete interface are typical phenomena when the composite structure is subjected to stress, which are caused by the nonlinear deformation of the shear connector (such as stud bending and local crushing of concrete) and interface friction.

[0122] The slip effect model is constructed by constructing the interface shear stress-slip ( ), Normal force-separation ( ) constitutive relations, transforming complex physical processes into calculable mechanical parameters (such as initial stiffness, ultimate bearing capacity and softening characteristics), revealing the nonlinear nature of interface 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 causes the overall stiffness of the composite structure to be lower than that of the fully connected state. The model can calculate the stiffness reduction caused by slip. Internal force redistribution: The interface shear force distribution changes with the development of slip. The model can reveal the internal force transmission path and stress concentration between steel and concrete. The impact of different connector types (i.e., studs, PBL keys, and channels) on interface performance can be quantified. For example: Bearing capacity verification: The model calculates the load-slip curve of the connector to verify whether it meets the shear and pullout design requirements; parameter optimization: Analyze the inhibitory effect of connector spacing and layout on interface slip to reduce slip.

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

[0125] Nonlinear sources: Plastic deformation of connectors, local crushing of concrete and interface friction effects lead to nonlinear load-slip relationships.

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

[0127] Element selection: Studs use three-dimensional solid elements (such as C3D8) or beam elements (such as B31) to simulate bending deformation.

[0128] Concrete crushing and cracking are simulated using solid elements (C3D8R) with the damage plasticity model (CDP) activated.

[0129] The interface is simulated by nonlinear spring elements (such as COMBIN39) or contact elements (such as Surface-to-Surface) to simulate slip and separation.

[0130] Key settings: define the welding constraints between studs and steel beams (Tie constraints), contact between concrete and studs, apply displacement loads or force loads, track interface slip and connector stress;

[0131] Parametric analysis: By changing stud diameter, length, spacing, or concrete strength parameters, analyze the impact of parameters on connector stiffness, bearing capacity, and failure modes.

[0132] The mechanical behavior analysis of shear connectors is the core link of steel-concrete composite structures. It provides nonlinear mechanical characteristics through a closed-loop process of "theoretical modeling-numerical simulation-experimental verification".

[0133] Example 5:

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

[0135] in, Representation over time The variable load function describes the load magnitude acting on the structure at different times, emphasizes that the load is a function of time, and reflects the load changes caused by the position of the moving load on the bridge changing with time. is the load size, which is a constant. is the Dirac function (representing concentrated load). In moving load, the Dirac function is used to represent concentrated load, that is, the load acts on a "point". is the load moving speed, is the spatial position coordinate, For time. Describes a size of The concentrated moving load, the position of the moving load changes with time at a speed of The Dirac function is used to accurately represent the relationship between the load position on the structure and time.

[0136] Dynamic meshing and tracking load positions through coordinate transformations:

[0137] 1. Unit coordinate transformation;

[0138] The load position changes with time as ;in, To move the load at a constant speed, For any time;

[0139] It is based on the principle of uniform linear motion, moving the load at a constant speed Move on the structure at any time , can accurately determine the specific location of the load on the structure; Represents the moving load at time The location coordinates of The axis is established along the length of the bridge structure and is a time This means that the load position will change with time, reflecting the dynamic characteristics of the moving load.

[0140] 2. Tracking load positions, i.e. dynamic distribution of load vectors;

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

[0142] in, is a vector representing the time The equivalent nodal force vector on the finite element unit node under the action of the moving load. In the finite element model, the structure is composed of multiple units and nodes. The actual load needs to be equivalently distributed to each node before it can be used to solve the structural response (such as displacement and stress); shape function is about the local coordinates of the element A function used to describe the distribution of displacement or other physical quantities within the unit. Its value range is between 0 and 1, and it has specific values ​​at different nodes of the unit (for example, the shape function value is 1 at a certain node and 0 at other nodes). is the local coordinate of the moving load within the element, obtained by calculating the relative position of the load position in the element; Over time The varying actual load function, in a moving load problem, describes how the magnitude of the load acting on the structure varies with time.

[0143] In finite element analysis, the structure is discretized into elements and nodes. Acting on the structure, it cannot be used directly to solve the structural response, through the shape function , the actual moving load Converted into equivalent nodal force vectors on the finite element nodes , the complex actual load effect is integrated into the finite element equation solution system in the form of nodal force, laying the foundation for the subsequent calculation of the displacement and stress response of the structure.

[0144] Shape Function Depends on the local coordinates of the load within the element , which can accurately consider the specific location of the moving load within the unit. Loads at different locations contribute differently to the forces at each node of the unit. Through the interpolation calculation of the shape function, the load is reasonably distributed to the corresponding nodes, accurately reflecting the impact of the load position and distribution on the structural force.

[0145] A moving load moves on the structure over time, and at each time step, the load is moved according to its actual position (via embodied), dynamically update the equivalent node force vector , combined with the structural dynamics equation, the simulation analysis of the dynamic response of the structure under the full action of moving loads can effectively solve the key problems of structural mechanical behavior analysis under moving load conditions.

[0146] Coupling of load position and mesh update: Mesh update based on time step, each time step The load moving distance is , Represents the distance that a moving load moves in one time step, indicating the length of distance that a load travels on a structure (e.g., a bridge) along its direction of movement within a specific time interval. To move the load at a constant speed, it reflects how fast the load moves per unit time; The time step refers to the length of time. In numerical calculations for structural dynamics analysis, the entire time process is divided into a series of small time intervals, known as time steps, to discretize time for a step-by-step solution. By continuously updating the mesh information and accurately capturing changes in load position, the finite element model can more accurately reflect the structure's true stress state under moving loads, avoiding calculation errors caused by inaccurate load position determination. This provides accurate load input for solving the structure's displacement, stress, and strain responses at different times, which is crucial for analyzing the mechanical behavior of bridges under moving loads.

[0147] Example 6:

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

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

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

[0151] Step 2.1: Calculate concrete slab stress: Consider the concrete slab as an independent component, subject to the loads acting directly on it (e.g., bridge deck loads and partial dead loads). Calculate the initial stress of the concrete slab using elastic theory or finite element method. and deformation ;

[0152] Step 2.2: Calculate the stress of the steel beam; treat the steel beam as an independent component, bearing the load directly acting on the beam (such as: deadweight, transferred load), and calculate the initial stress of the steel beam according to elastic theory or finite element method and deformation .

[0153] Step 3: Correct the deformation difference using the interface coordination equation;

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

[0155] According to the interface connection conditions (such as shear key stiffness ), establish the interface coordination equation and solve the interlayer shear force : ;

[0156] The interlayer shear force Applied as additional load in opposite directions to both layers of the structure:

[0157] Apply upward shear force to the concrete slab , exerting downward shear force on the steel beam ;

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

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

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

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

[0162] Analyze the shear force between layers of steel beams Additional stress under action and additional deformation .

[0163] Update stresses and deformations: .

[0164] Step 5: Convergence judgment and iterative cycle;

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

[0166] like ≤ Allowable deformation error (eg: 10 -3 m), terminate the iteration; otherwise, return to step 3 and use the updated deformation and Recalculate interlayer shear , repeat the iteration until convergence. Representatives in the The displacement (or deformation) of the steel beam at the interface during the iteration is the longitudinal displacement of the steel beam at the interface with the concrete slab after taking into account various loads and interface factors in the current iteration step. Representatives in the In the first iteration, the displacement (or deformation) of the concrete slab at the interface is the longitudinal displacement of the concrete slab at the interface connected to the steel beam after considering various factors.

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

[0168] After the iteration converges, the stress of the steel beam , concrete slab stress , including the initial stress and the correction amount of all iterative steps, to further verify the rationality of stress distribution and structural safety performance.

[0169] It is suitable for elastic stage analysis, takes into account the nonlinear effect of concrete, and needs to be combined with the material constitutive expansion iterative process.

[0170] Hierarchical iterative algorithm in the analysis of steel-concrete composite bridge structures:

[0171] Steel-concrete composite structures are composed of steel and concrete, two materials with significantly different mechanical properties. Iterative optimization approximates the true stress state. During the loading process, nonlinear iterations of steel-concrete composite structures introduce material nonlinearity (concrete cracking, steel yielding) and geometric nonlinearity (large deformation effects). Traditional linear analysis struggles to accurately reflect the structural limit state. The layered iterative algorithm incrementally updates the stress-strain state of each layer through iterative corrections until convergence to an equilibrium solution, thereby capturing the full stress evolution of the structure.

[0172] Example 7:

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

[0174] According to the neutral axis position and section bending moment of the concrete slab and steel beam, the normal stress of the steel section of the concrete slab and steel beam is obtained: , ;in, is the normal stress of the steel section, is the normal stress in the concrete section; is the cross-sectional bending moment, and are the neutral axis positions of the steel section and the concrete section, respectively. is the elastic modulus ratio), is the moment of inertia of the converted section (reflecting the ability of the section to resist bending deformation).

[0175] Normal stress is the concentration of internal force distributed on the cross section when a component is deformed by axial tension, compression or bending, reflecting the stress conditions per unit area inside the material.

[0176] Identify the areas of maximum tensile and compressive stresses as:

[0177] Normal stress with regular distribution:

[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 can 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 cross-section: The top surface of the concrete slab is in compression, and the bottom surface is in tension (negative bending moment). The upper edge of the steel beam is in tension, and the lower edge is in 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 bottom edge of the steel beam.

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

[0182] Areas of maximum tensile and compressive stress are the structural "weak links," and their identification and analysis are a continuous process throughout the entire project lifecycle (design → construction → monitoring → maintenance). By precisely locating these areas, we achieve the goals of "safety and controllability, optimized design, and efficient maintenance," ensuring that 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 modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope of 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 based on the scope of protection of the claims.

Claims

1. A stress analysis method based on steel-concrete composite structures of small and medium span bridges, characterized by: The steps include: 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 relationship 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 of shear connectors. S3. Apply a moving load case and use dynamic meshing to divide the load position of the steel-concrete composite bridge; S4. Use a hierarchical iterative algorithm to solve and correct the structural stress of the steel-concrete composite bridge. The structural stress of the steel-concrete composite bridge includes the stress of the steel beam and the stress of the concrete slab. 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 the steel-concrete composite structure of small and medium span bridges according to claim 1 is characterized in that: In step S1, the steps for constructing the finite element parameterized model of the steel-concrete composite bridge are: Define geometric parameter variables of steel beams: Create geometric parameters of steel beams in finite element software; Draw the steel beam cross section: I-beam is drawn by key point coordinates , Generate the cross-section profile and extrude it into a beam body. The box beam is formed by drawing a closed frame to define the thickness of the top plate, bottom plate and web. is the web height, is the flange width; Draw concrete slab: Create rectangular or flanged slabs and couple them to the top surface of steel beams; Generate shear connectors: Studs are placed on the top surface of the steel beams. The spacing pattern generates a cylinder with the top embedded in the concrete slab, where is the vertical spacing, is the horizontal spacing.

3. The stress analysis method based on the steel-concrete composite structure of small and medium span bridges according to claim 1 is characterized in that: In step S2, the slip effect model is: Establish a steel-concrete split model: For the steel part, use shell elements or solid elements to simulate the steel box girder / steel truss and assign the steel constitutive parameters; for the concrete part, use solid elements to simulate the concrete slab and assign the concrete constitutive parameters; Meshing: Encrypt the mesh near the interface to ensure that the spring unit nodes correspond one-to-one with the steel and concrete unit nodes; Arrange nonlinear spring units: Set spring units at the shear connector position of the steel-concrete interface; connection method: one end of the spring unit is connected to the steel unit node, and the other end is connected to the concrete unit node; for three-dimensional models, it is necessary to consider the coupling effect of the interface normal and tangential directions, and set normal springs and tangential springs.

4. The stress analysis method based on the steel-concrete composite structure of small and medium span bridges according to claim 3 is characterized in that: Define the nonlinear behavior of the spring element: Tangential Spring: Input Relationships: The Elastic Stage , reaching the ultimate load Then enter the softening stage: bilinear model or three-fold line model; is the nonlinear spring element force, is the nonlinear spring element displacement, is the elastic stiffness; Normal Spring: Defines the normal stiffness, or nonlinearity in the pullout resistance of the connector.

5. The stress analysis method based on the steel-concrete composite structure of small and medium span bridges according to claim 1 is characterized in that: In step S3, the dynamic grid is divided and the load position is tracked by coordinate transformation: Unit coordinate transformation: The load position changes with time as ;in, To move the load at a constant speed, For any time; It is based on uniform linear motion, moving the load at a constant speed Move on the structure at any time , can accurately determine the specific location of the load on the structure; Represents the moving load at time The location coordinates of The axis is established along the length of the bridge structure and is a time function.

6. The stress analysis method based on the steel-concrete composite structure of small and medium span bridges according to claim 5 is characterized in that: In step S3, the tracking load position is: The equivalent nodal forces of moving loads on element nodes can be calculated by shape function interpolation: ; in, is a vector representing the time The equivalent nodal force vector on the finite element node under the action of the moving load; shape function is about the local coordinates of the element The function used to describe the displacement in the unit is the local coordinate of the moving load in the unit , obtained by calculating the relative position of the load position in the unit; Over time The varying actual load function describes how the magnitude of the load acting on the structure changes with time.

7. The stress analysis method based on the steel-concrete composite structure of small and medium span bridges according to claim 1 is characterized in that: In step S4, the steps of the hierarchical iterative algorithm are: Step 1: Initial parameter setting: input structural geometry, material properties and loading conditions; Step 2: Calculate stress independently for each layer; Step 3: Correct the deformation difference using the interface coordination equation; Step 4: Iteratively calculate the stress correction value; Step 5: Convergence judgment and iterative cycle; Step 6: Output the final stress results.

8. The stress analysis method based on the steel-concrete composite structure of small and medium span bridges according to claim 1 is characterized in that: In step S5, the stress distribution of the key sections of the steel-concrete composite bridge is calculated using the converted section method: According to the neutral axis position and section bending moment of the concrete slab and steel beam, the normal stress of the steel section of the concrete slab and steel beam is obtained: , ;in, is the normal stress of the steel section, is the normal stress in the concrete section; is the cross-sectional bending moment, and are the neutral axis positions of the steel section and the concrete section, respectively. is the elastic modulus ratio), is the moment of inertia of the converted section.

9. The stress analysis method based on the steel-concrete composite structure of small and medium span bridges according to claim 8 is characterized in that: The identification of the maximum tensile and compressive stress areas includes: regular distribution of normal stress, shear stress and interface stress.

10. A stress analysis system based on a steel-concrete composite structure of a small- to medium-span bridge, for executing a stress analysis method based on a steel-concrete composite structure of a small- to medium-span bridge according to any one of claims 1 to 9, characterized in that: include: Parametric modeling module, used to establish finite element parametric models of steel-concrete composite bridges; Slip effect modeling module, used to construct a slip effect model of the steel-concrete interface based on the constitutive relationship of steel-concrete composite bridges; Load application module, used to apply moving load cases and divide the load positions of steel-concrete composite bridges through dynamic meshing; Stress solution module, used to solve the structural stress of steel-concrete composite bridges and make corrections; Result output module, used to output the stress distribution of key sections of steel-concrete composite bridges; The parameterized 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 solving module, and the stress solving module is connected to the result output module.

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