A method for predicting the bearing capacity of a shear span local corrosion high-performance steel beam

Abstract

The application provides a shear span local corrosion high-performance steel beam bearing capacity prediction method, and belongs to the technical field of computer-aided design. First, the material performance of the corroded high-performance steel is tested to obtain the change rule of the basic mechanical performance parameters of the corroded high-performance steel with the mass corrosion rate; according to different corrosion degrees, an equivalent thickness calculation formula based on strength equivalence is established, the equivalent thickness is corrected, and the corrected equivalent thickness is obtained; in combination with the proposed equivalent thickness, an equivalent constitutive model of the high-performance steel at different corrosion levels is established, and the model is used for describing the constitutive relationship of the high-performance steel after random corrosion; subsequently, the overall stability checking formula of the high-performance steel under the action of two-point symmetrical concentrated loads is derived; based on nonlinear iteration, the force-deformation state of the shear span corroded HPS beam full length is obtained, and the bearing capacity and deflection of the HPS beam are predicted. Compared with the experimental results, the method has good accuracy and can be used for evaluating the mechanical performance of the corroded HPS beam structure.

Description

Technical Field

[0001] This application relates to the field of computer-aided design technology, and in particular to a method for predicting the load-bearing capacity of high-performance steel beams with localized corrosion in shear span sections. Background Technology

[0002] Among the many new materials in the field of steel structure engineering, high performance steel (HPS) has gradually begun to attract the attention and importance of domestic engineering practitioners due to its excellent comprehensive properties such as high strength, high toughness, high corrosion resistance, easy weldability, and economic and environmental protection.

[0003] However, environmental factors such as humidity, temperature, and salt spray often trigger corrosion problems. This corrosion process is relatively slow and is often easily overlooked, but once an accident occurs, it can lead to huge casualties and property losses. Easily neglected engineering parts (such as the ends of steel structure bridges in coastal areas) are particularly prone to corrosion. Corrosion significantly impairs the structural performance of steel beams, leading to a decrease in toughness, fatigue performance, and load-bearing capacity, thereby affecting the overall structural safety and service life. The shear span, referring to the area between the concentrated load point on the steel beam and the support, exhibits stronger concealment of corrosion and greater potential risks in localized areas, making it a very typical corrosion condition in actual engineering projects.

[0004] For a long time, academic research has mainly focused on the design theories and methods of newly constructed high-performance steel structures, while research on the corrosion mechanism and load-bearing capacity degradation law of steel structures has been relatively scarce. Although many studies have focused on the safety and applicability of steel structures, the durability of corroded steel structures has not received enough attention, especially research on high-performance steel with localized corrosion in shear spans.

[0005] For example, existing literature such as "Experimental Study on the Influence of Corrosion on the Mechanical Properties of High-Performance Steel Q550E", Peng Jianxin et al., Highway Transportation Technology, 2018, and "Overall Stability Verification of High-Performance H-Shaped Steel Beams under Two-Point Symmetrical Loading", Peng Jianxin et al., Journal of Changsha University of Science and Technology (Natural Science Edition), 2022, have conducted preliminary studies on the constitutive model of corrosion and the bearing capacity and stability of steel beams. However, the above literature takes the steel beam as the whole as the research object and does not consider the characteristics of corrosion in the local area of ​​the shear span. On the other hand, the above literature also does not fully consider the influence of the randomness and complexity of corrosion on the constitutive model.

[0006] Therefore, there is a need to provide a technical solution to improve the accuracy and speed of constitutive models, as well as the prediction of the bearing capacity of shear span steel beams. Summary of the Invention

[0007] The purpose of this application is to provide a method for predicting the load-bearing capacity of high-performance steel beams with localized corrosion in shear spans. This method fully considers the randomness and complexity of corrosion, focuses on the equivalent constitutive model of randomly corroded HPS steel, and applies it to the prediction of the load-bearing capacity of steel beams in shear spans, thereby improving the accuracy and speed of the constitutive model and thus improving the prediction accuracy of the load-bearing capacity of steel beams in shear spans.

[0008] To achieve the above objectives, this application provides the following technical solution:

[0009] This application provides a method for predicting the load-bearing capacity of high-performance steel beams with localized corrosion in the shear span, including:

[0010] Step S1: Perform material performance testing on the corroded high-performance steel to obtain the variation law of the basic mechanical property parameters of the corroded high-performance steel with mass corrosion rate; establish an equivalent thickness calculation formula based on strength equivalence according to different corrosion degrees, and correct the equivalent thickness based on the three-dimensional size characteristics of rust pits and the probability statistics of rust pit types to obtain the corrected equivalent thickness; wherein, the basic mechanical property parameters include: yield strength, tensile strength, and elastic modulus;

[0011] Step S2: Based on the corrected equivalent thickness, establish an equivalent constitutive model for high-performance steel with different corrosion levels. This model is used to describe the constitutive relationship of high-performance steel after corrosion.

[0012] Step S3: Based on the principle of potential energy, derive the formula for verifying the overall stability of high-performance steel beams under symmetrical concentrated loads at any two points, and use the formula for verifying the overall stability of high-performance steel beams to determine whether there is instability or failure in the locally corroded steel beams of the shear span section.

[0013] Step S4: In the absence of instability failure, the locally corroded steel beam in the shear span is discretized and divided into elements. Based on the different corrosion levels of each element, the bearing capacity and deflection of the locally corroded steel beam in the shear span are obtained through nonlinear iteration according to the equivalent constitutive model of the high-performance steel and the pre-obtained moment-curvature relationship.

[0014] In some embodiments, material property tests are performed on the corroded high-performance steel to obtain the variation law of the basic mechanical property parameters of the corroded high-performance steel with the mass corrosion rate, including:

[0015] Accelerated corrosion tests were conducted on high-performance steel specimens to obtain data, and the mass corrosion rate of the specimens after corrosion was determined. ;

[0016] Static tensile tests were conducted on the corroded high-performance steel specimens to obtain test data for various basic mechanical property parameters;

[0017] The test data of various basic mechanical properties were analyzed and compared with the mass and corrosion rate of the specimen after corrosion. The basic mechanical properties and mass corrosion rate after rusting were obtained by fitting. The quantitative relationship.

[0018] In some embodiments, an equivalent thickness benchmark formula based on strength equivalence is established according to different degrees of corrosion, including:

[0019] Considering the pitting effect of rust damage, the pitting area loss degree (DOP) of high-performance steel specimens after rusting is calculated, and the pitting volume loss degree (DOPV) is introduced to describe the degree of pitting damage of high-performance steel specimens.

[0020] Numerical simulations were performed, and the simulation data were imported into MATLAB software. The relationship between ultimate load, elongation and DOPV was obtained by fitting, and then the equivalent thickness benchmark formula with equivalent strength was derived.

[0021] In some embodiments, the equivalent thickness is corrected based on the three-dimensional size features of the rust pit and the probability statistics of the rust pit type to obtain the corrected equivalent thickness, including: a first correction of the corrosion intensity DOC and a second correction of the probability statistics of the rust pit type.

[0022] The first correction of the corrosion intensity DOC includes: the corrosion intensity DOC is the ratio of pitting area loss degree DOP to pitting volume loss degree DPV, which is used to describe the three-dimensional size of the rust pit and the difference in pitting damage intensity caused by different types of rust pits.

[0023] The standard deviations of the rust pit diameter and depth were modified, and then random rust finite element numerical simulation was performed. The modified data was then imported into MATLAB software for analysis to obtain the variation law of rust intensity DOC with the standard deviation of rust pit diameter and the standard deviation of rust pit depth.

[0024] Based on the aforementioned variation pattern, the equivalent thickness is corrected once to obtain the corrected equivalent thickness.

[0025] The second-order correction of the probability statistics for the rust pit type includes:

[0026] Based on probability statistics of different rust pit types, the proportion of each type of rust pit under different corrosion rates was obtained;

[0027] Based on the proportion of various rust pits under different corrosion rates, the equivalent thickness is corrected a second time to obtain the corrected equivalent thickness.

[0028] In some embodiments, step S2: Based on the corrected equivalent thickness, establishing an equivalent constitutive model for high-performance steel with different corrosion levels includes:

[0029] Based on the aforementioned basic mechanical performance parameters, the least squares method was used to fit and obtain several key parameters of the constitutive model under different corrosion rates;

[0030] Based on the equivalent thickness, several key parameters of the constitutive model under different corrosion rates obtained from the fitting are modified to obtain the modified three-stage constitutive model, which is used as the equivalent constitutive model for high-performance steel. The expression is as follows:

[0031] ,

[0032] In the formula, For stress, For cross-sectional strain, For the equivalent elastic modulus, For equivalent yield strength, It is the equivalent ultimate strength; For equivalent yield strain, To effectively enhance strain, This is the equivalent limit strain.

[0033] In some embodiments, step S3: deriving the formula for verifying the overall stability of a high-performance steel beam under symmetrical concentrated loads at any two points based on the principle of potential energy, including:

[0034] The high-performance steel beam is a simply supported H-shaped steel beam with biaxial symmetry. Stability calculations are performed under two-point symmetrical loads.

[0035] By utilizing symmetry, we determine the expression for the bending moment from the left side of the beam to the mid-span.

[0036] Based on the principle of potential energy, the initial expression for the total potential energy is determined; combined with the boundary conditions at the ends of the simply supported beam, the initial expression for the total potential energy is rearranged and the parameters are replaced to obtain the replaced expression for the total potential energy.

[0037] By combining the stationary potential energy condition with the replaced total potential energy expression, the expression for the critical bending moment of the steel beam under two-point symmetrical load is obtained, and then the critical bending moment of elastic-plastic instability is calculated.

[0038] In some embodiments, step S4: In the absence of instability failure, the locally corroded steel beam in the shear span is discretized and element-divided. Based on the different corrosion levels of each element, according to the equivalent constitutive model of the high-performance steel and the pre-obtained moment-curvature relationship, the bearing capacity and deflection of the locally corroded steel beam in the shear span are obtained through nonlinear iteration, including:

[0039] Discretization and element partitioning: The local high-performance steel beam of the shear span is divided into n elements, each with specific cross-sectional properties; the value of the initial load P is defined, and the load increment value is set to a;

[0040] Elastic buckling stress calculation: Set the initial cross-sectional strain values, and based on the plane section assumption, the strain increment of the same cross-section is equal. Calculate the elastic buckling stress according to the equivalent constitutive model of high-performance steel.

[0041] Bending moment distribution analysis: Based on the calculated elastic buckling stress value and the section properties of each element, calculate the bending moment of each element;

[0042] Support reaction calculation: Considering the arrangement of lateral supports, calculate the support reaction force F based on the bending moment of each element, and check whether the support reaction force F meets the preset convergence condition. If the convergence condition is not met, then... Increase the load and iterate through the steps of calculating the elastic buckling stress until the termination condition is met.

[0043] The deflection is calculated using the bending moment and support reaction F of each unit, and then the bearing capacity of the corroded steel beam is calculated based on the moment-curvature relationship.

[0044] In some embodiments, the convergence condition satisfies: Alternatively, the convergence condition is that the slope of the load-displacement curve satisfies Furthermore, the termination condition is satisfied: ;

[0045] Where P is the load, F is the support reaction force, ε is the cross-sectional strain, and E is the cross-sectional strain. sc ΔF is the elastic modulus of the specimen after corrosion, ΔF is the change in support reaction force, Δε is the change in cross-sectional strain, Δω is the change in deflection, and ε uc This is the ultimate strain.

[0046] The technical solution of this application embodiment has the following beneficial effects:

[0047] In this embodiment, the technical solution first involves conducting material performance tests on the corroded high-performance steel to obtain its basic mechanical property parameters, providing verification for subsequent random simulation results. The variation law of the basic mechanical property parameters of the corroded high-performance steel with the mass corrosion rate is then obtained, establishing the relationship between damage parameters (such as mass corrosion rate) and mechanical property parameters. Based on different degrees of corrosion, an equivalent thickness benchmark formula with strength equivalence is established. The equivalent thickness is then corrected by fully considering the three-dimensional spatial distribution characteristics of rust pits and the randomness of rust pit types, resulting in the corrected equivalent thickness. Equivalent thickness; based on the corrected equivalent thickness, equivalent constitutive models of high-performance steel with different corrosion levels are established. This equivalent constitutive model is used for subsequent mechanical performance evaluation of components or structures. Subsequently, the overall stability verification formula of high-performance steel under two-point symmetrical concentrated loads is derived to ensure that the steel beam will not fail due to instability before reaching its bearing capacity. The locally corroded steel beam in the shear span is discretized and element-divided. Based on nonlinear iteration, the force-deformation state of the entire length of the locally corroded HPS beam in the shear span can be obtained, realizing the prediction of the bearing capacity and deflection of the locally corroded HPS beam in the shear span. Compared with experimental results, this method has good accuracy and can be used to evaluate the mechanical performance of corroded HPS beam structures. Furthermore, the proposed method helps to understand the specific impact of corrosion on structural performance and provides an evaluation tool for the maintenance and management of existing structures, helping to formulate maintenance plans and preventive measures. Specific technical effects include the following aspects:

[0048] 1. Improved the accuracy of the constitutive model of corroded high-performance steel beams: By conducting material property tests on corroded high-performance steel beams, the variation law of basic mechanical parameters such as yield strength, tensile strength and elastic modulus with mass corrosion rate was obtained; and the equivalent thickness was corrected based on the three-dimensional size characteristics of rust pits and the probability statistics of corrosion type, thereby more realistically reflecting the weakening effect of random corrosion on the geometric dimensions of steel beams and improving the reliability of the constitutive model of randomly corroded high-performance steel beams.

[0049] 2. Achieved refined modeling of locally corroded steel beams in shear spans: This application focuses on the shear span, a typical and high-risk corrosion area. By discretizing and dividing this area into elements, and combining the different corrosion levels of each element to establish corresponding mechanical models (i.e., high-performance steel equivalent constitutive models), the modeling accuracy and applicability are significantly improved. This effectively solves the shortcomings of traditional models in handling the non-uniformity and randomness of corrosion, and has good engineering promotion value.

[0050] 3. Achieved joint prediction of bearing capacity and deflection under nonlinear iteration: Combining the moment-curvature relationship with the nonlinear iterative algorithm, it can simultaneously predict the bearing capacity and deflection of locally corroded steel beams in shear spans, providing more comprehensive technical support for structural safety assessment, helping to identify potential safety hazards at an early stage and improve the safety management level of in-service structures. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the specimens used in corrosion and tensile tests under localized random corrosion, where t represents the thickness.

[0052] Figure 2 The diagram shows the mechanical property curves and their fitted curves of the Q550E rusted specimen, where (a) is the maximum load curve, (b) is the tensile strength curve, (c) is the elastic modulus curve, and (d) is the yield strength curve.

[0053] Figure 3 This is a schematic diagram illustrating the effect of different width-to-thickness ratios on the reduction factor.

[0054] Figure 4 This is a schematic diagram comparing the experimental curve and the equivalent constitutive model curve of specimen Q0-1.

[0055] Figure 5 This is a schematic diagram comparing the experimental curves with the equivalent constitutive model curves. Figure 2 Among them, (a) is a comparison between the experimental curve and the equivalent constitutive model curve of specimen Q5-1, and (b) is a comparison between the experimental curve and the equivalent constitutive model curve of specimen Q10-1.

[0056] Figure 6 This is a schematic diagram comparing the experimental curves with the equivalent constitutive model curves. Figure 3 Among them, (a) is a comparison between the experimental curve and the equivalent constitutive model curve of specimen Q15-1, and (b) is a comparison between the experimental curve and the equivalent constitutive model curve of specimen Q20-1.

[0057] Figure 7 The diagram shows a specimen for a tensile test under a two-point symmetrical concentrated load, where (a) is the front view and (b) is the cross-sectional view.

[0058] Figure 8 The diagram shows the bending-torsional buckling of a beam under two-point symmetrical concentrated loads, where (a) is the longitudinal elevation view and (b) is the cross-sectional view.

[0059] Figure 9 The figures show a comparison between the load-deflection curves and measured values ​​of different specimens at the mid-span section. (a) is the load-deflection curve of Q550-0, (b) is the load-deflection curve of Q550-1, (c) is the load-deflection curve of Q550-2, and (d) is the load-deflection curve of Q550-3. Detailed Implementation

[0060] To facilitate understanding of this technical solution, the relevant terms are explained by example below.

[0061] High-performance steel (HPS) structures are a type of structure made of high-performance steel. By improving the composition, production process and processing methods, HPS steel has high strength, good ductility and toughness, as well as excellent corrosion resistance and fatigue performance.

[0062] Constitutive models are mathematical models that describe the relationship between stress and strain in materials under external forces. Constitutive models can be used to predict how steel will respond to various load conditions in actual engineering projects.

[0063] It should be noted that when localized corrosion occurs in the shear span section (i.e., the shear force zone of the beam) of high-performance steel beams, the overall stability verification and load-bearing capacity prediction are complex engineering problems. Corrosion leads to a reduction in the cross-section of the steel and a decrease in material properties, thereby affecting the overall stability and load-bearing capacity of the structure. Although some existing technologies provide constitutive models for steel under corrosion conditions—multi-segmented models—these are mainly for ordinary steel. The corrosion mechanism of high-performance steel is significantly different from that of ordinary steel, making existing constitutive models for ordinary steel under corrosion conditions unsuitable for the scenario faced in this embodiment. Some studies have also provided constitutive relationship models for high-performance steel under the influence of corrosion, considering the effect of corrosion rate. They introduce two parameters to describe the relationship between the yield plateau length and yield strain on the stress-strain curve of the uncorroded specimen, and between the ultimate strain and yield strain of the uncorroded specimen, thus constructing the constitutive model in two-segmented and three-segmented forms. However, the above methods generally treat corrosion as uniform corrosion and do not consider the influence of random corrosion on the constitutive model, lacking universality and being unsuitable for the scenario faced in this embodiment. Furthermore, considering the randomness and complexity of corrosion and conducting reasonable equivalent studies are highly significant for rapid assessment of mechanical properties, but such research has yet to be found. Since localized corrosion of the shear span is a very typical corrosion condition, research on high-performance steel with localized corrosion in the shear span is limited, and existing models directly describing the performance of steel beams after localized corrosion in the shear span have certain shortcomings. Therefore, how to assess the impact of localized corrosion on the performance of high-performance steel structures, especially in safety assessment, maintenance decisions, and reinforcement design, has become a core issue urgently needing to be addressed in the engineering field. It is necessary to conduct in-depth research on the impact of localized corrosion on high-performance steel beams to more accurately predict the remaining life and load-bearing capacity of the structure and to formulate scientific maintenance and reinforcement strategies.

[0064] In view of this, this embodiment discloses a method for predicting the load-bearing capacity of a locally corroded high-performance steel beam in a shear span section, belonging to the subfield of assessing the impact of steel corrosion performance on structural safety. The method involves 3D scanning of the corroded specimen to obtain its complex surface morphology. Material performance testing is used to obtain the basic mechanical property parameters of the corroded high-performance steel. Random corrosion simulation is used to obtain the relationship between the mechanical property parameters and corrosion damage parameters. Based on strength equivalence, considering the three-dimensional size characteristics and distribution of rust pit types, equivalent constitutive models of high-performance steel with different corrosion levels are established to describe the constitutive relationship of the locally corroded high-performance steel beam in the shear span section. Subsequently, the stability verification formula for the high-performance steel beam under two-point concentrated loads is derived. Based on this, a nonlinear iterative method is used to obtain the force-deformation state of the entire length of the corroded HPS beam, realizing the prediction of the load-bearing capacity and deflection of the HPS beam. The method proposed in this embodiment predicts the bending load-bearing capacity and deflection of locally corroded HPS steel beams. Comparison with experimental results shows good accuracy, and it can be used to evaluate the mechanical properties of corroded HPS beam structures. This not only helps to understand the specific impact of corrosion on structural performance, but also provides an assessment tool for the maintenance and management of existing structures, helping to develop maintenance plans and preventative measures.

[0065] The embodiments of this application will now be described with reference to the accompanying drawings.

[0066] This embodiment provides a method for predicting the load-bearing capacity of a high-performance steel beam with localized corrosion in the shear span, including the following steps:

[0067] Step S1: Perform material property tests on the corroded high-performance steel to obtain the variation law of the basic mechanical property parameters of the corroded high-performance steel with mass corrosion rate; establish an equivalent thickness benchmark formula based on strength equivalence according to different corrosion degrees, and correct the equivalent thickness based on the three-dimensional size characteristics of rust pits and the probability statistics of rust pit types to obtain the corrected equivalent thickness; wherein, the basic mechanical property parameters include: yield strength, tensile strength, and elastic modulus;

[0068] Step S2: Based on the corrected equivalent thickness, establish an equivalent constitutive model for high-performance steel with different corrosion levels. This model is used to describe the constitutive relationship of high-performance steel after corrosion.

[0069] Step S3: Based on the principle of potential energy, derive the formula for verifying the overall stability of high-performance steel under symmetrical concentrated loads at any two points, and use the formula for verifying the overall stability of high-performance steel beams to determine whether there is instability or failure in the locally corroded steel beams of the shear span section.

[0070] Step S4: In the absence of instability failure, the locally corroded steel beam in the shear span is discretized and divided into elements. Based on the different corrosion levels of each element, the bearing capacity and deflection of the locally corroded steel beam in the shear span are obtained through nonlinear iteration according to the equivalent constitutive model of the high-performance steel and the pre-obtained moment-curvature relationship.

[0071] In this embodiment, the purpose of step S1 is to perform material performance testing and equivalent thickness calculation. By directly measuring and experimenting to obtain the mechanical property parameters of the corroded steel, more accurate basic data can be provided for the subsequent construction of the constitutive model and structural analysis. The calculation of equivalent thickness not only considers the influence of corrosion on the steel beam surface, but also corrects for different types and distributions of rust pits, thereby more accurately reflecting the actual mechanical behavior of the corroded steel beam.

[0072] Specifically, step S1 includes two sub-steps:

[0073] (1) Obtain the basic mechanical properties of high-performance steel after corrosion: By testing high-performance steel after local corrosion, important material properties such as yield strength, tensile strength and elastic modulus can be obtained, providing a data basis for the load-bearing capacity analysis of high-performance steel beams and ensuring the accuracy of material properties.

[0074] (2) Establish an equivalent thickness benchmark formula: Based on different degrees of corrosion, an equivalent thickness benchmark formula with strength equivalence is derived to further correct the influence of rust pits. The corrected equivalent thickness can reflect the actual load-bearing capacity of the steel beam after corrosion, and avoid the reduction of structural strength due to the reduction of the thickness of the corrosion area. At the same time, by correcting the probability statistics of rust pit characteristics and types, the accuracy of equivalent thickness calculation is improved, and the influence of different corrosion forms on the mechanical properties of materials is considered.

[0075] In step S2, based on the corrected equivalent thickness, an equivalent constitutive model of high-performance steel is established for different corrosion levels. This model considers the influence of different degrees of local corrosion on the performance of high-performance steel and can accurately describe the stress-strain relationship of locally corroded high-performance steel in the shear span, providing a theoretical basis for subsequent load-bearing capacity prediction and stability analysis.

[0076] Based on the constitutive model accurately reflecting the mechanical behavior of the steel beam after corrosion, step S3 aims to derive the overall stability verification formula, enabling quantitative analysis of the impact of corrosion on the overall stability of the steel beam, and determining whether locally corroded steel beams in the shear span segment will experience instability. Specifically, the overall stability verification formula for high-performance steel beams under two-point symmetrical concentrated loads is derived using the potential energy principle. The potential energy principle is used to derive the equilibrium state or critical instability state of the structure under load. According to the potential energy principle, the stability of a system can be determined by analyzing the minimum potential energy of the system under different load conditions. For a structural object, potential energy mainly consists of its elastic potential energy, which is determined by the strain (deformation) of the material. If the deformation of the structure causes the system's potential energy to reach a local maximum or no longer decrease, the structure may become unstable. Therefore, the derived formula for verifying the overall stability of high-performance steel beams under two-point symmetrical concentrated loads can avoid oversimplification assumptions. Combined with the load action in engineering practice, it considers the impact of local corrosion on the reduction of bearing capacity under two-point symmetrical concentrated loads on the overall stability, and can quickly assess whether the high-performance steel beam can remain stable under local corrosion.

[0077] In summary, this embodiment provides a systematic and reliable method for predicting the stability and load-bearing capacity of high-performance steel beams with localized corrosion in shear span sections through the organic combination of the above four steps. Each step relies on the data and analysis results of the previous stage, gradually improving the accuracy of the calculation, and can better adapt to the performance of high-performance steel beams under different localized corrosion conditions in practice.

[0078] In some embodiments, material property tests are performed on the corroded high-performance steel to obtain the variation law of the basic mechanical property parameters of the corroded high-performance steel with the mass corrosion rate, including:

[0079] Accelerated corrosion tests were conducted on high-performance steel specimens to obtain data, and the mass corrosion rate of the specimens after corrosion was determined. ;

[0080] Static tensile tests were conducted on the corroded high-performance steel specimens to obtain test data for various basic mechanical property parameters;

[0081] The test data of various basic mechanical properties were analyzed and compared with the mass and corrosion rate of the specimen after corrosion. By performing fitting, the basic mechanical property parameters and mass corrosion rate after corrosion were obtained. The quantitative relationship.

[0082] In some embodiments, an equivalent thickness benchmark formula based on strength equivalence is established according to different degrees of corrosion, including:

[0083] Considering the pitting effect of rust damage, the pitting area loss degree (DOP) of high-performance steel specimens after rusting is calculated, and the pitting volume loss degree (DOPV) is introduced to describe the degree of pitting damage of high-performance steel specimens.

[0084] A finite element numerical simulation of random corrosion was performed, and the simulation data was imported into MATLAB software. The relationship between ultimate load, elongation, and DOPV was obtained by fitting, and then the equivalent thickness formula based on equivalent strength was derived.

[0085] (1)

[0086] In the formula, Equivalent thickness; denoted as the percentage of pitting volume loss; t is the initial thickness. The relationship between DOPV and DOPV is a percentage; if the former is 100%, then the latter is 1.

[0087] In some embodiments, the rust pit characteristics and rust pit type probability statistical correction include: a first correction for corrosion intensity DOC and a second correction for rust pit type probability statistics;

[0088] The corrosion intensity DOC correction includes: the corrosion intensity DOC is the ratio of pitting area loss degree DOP to pitting volume loss degree DPV, which is used to describe the three-dimensional size of the rust pit and the difference in pitting damage intensity caused by different types of rust pits.

[0089] The standard deviations of the rust pit diameter and depth were modified, and then random rust finite element numerical simulation was performed. The modified data was then imported into MATLAB software for analysis to obtain the variation law of rust intensity DOC with the standard deviation of rust pit diameter and the standard deviation of rust pit depth.

[0090] Based on the aforementioned variation pattern, the equivalent thickness formula is modified once to obtain the modified equivalent thickness.

[0091] Secondary correction to the probability statistics of rust pit types, including:

[0092] Based on probability statistics of different rust pit types, the proportion of each type of rust pit under different corrosion rates was obtained;

[0093] Based on the proportion of various rust pits under different corrosion rates, the equivalent thickness is corrected a second time to obtain the corrected equivalent thickness.

[0094] In some embodiments, step S2 includes:

[0095] Based on the aforementioned basic mechanical performance parameters, the least squares method was used to fit and obtain several key parameters of the constitutive model under different corrosion rates.

[0096] Based on the equivalent thickness, several key parameters of the constitutive model under different corrosion rates obtained from the fitting are modified to obtain the modified three-stage constitutive model, which is used as the equivalent constitutive model for high-performance steel. The expression is as follows:

[0097] ,

[0098] In the formula, For stress, For cross-sectional strain, For the equivalent elastic modulus, For equivalent yield strength, It is the equivalent ultimate strength; For equivalent yield strain, To effectively enhance strain, This is the equivalent limit strain.

[0099] The above steps disclose a method for constructing an equivalent constitutive model to predict the corrosion of high-performance steel (HPS), which can be used for performance and safety assessment of high-performance steel structures. Material property tests are performed on the corroded HPS to obtain basic mechanical property parameters such as yield strength, tensile strength, and elastic modulus. Based on different degrees of corrosion, an equivalent thickness calculation formula based on strength equivalence is established, and after statistical correction based on rust pit characteristics and rust pit types, a more accurate equivalent thickness is obtained. A mathematical model based on the degree of corrosion (i.e., the equivalent constitutive model of high-performance steel) is established to describe the stress-strain relationship of the corroded HPS. This model can accurately predict the stress-strain relationship of steel under different degrees of corrosion and can be used for performance evaluation and safety analysis of corroded steel structures.

[0100] In some embodiments, step S3: deriving the formula for verifying the overall stability of high-performance steel under two-point symmetrical concentrated loads based on the potential energy principle, including:

[0101] The high-performance steel beam is a simply supported H-shaped steel beam with biaxial symmetry. Stability calculations are performed under two-point symmetrical loads.

[0102] First, using symmetry, determine the expression for the bending moment from the left side of the beam to the mid-span.

[0103] Then, based on the principle of potential energy, the initial expression for the total potential energy is determined; combined with the boundary conditions at the ends of the simply supported beam, the initial expression for the total potential energy is rearranged and the parameters are replaced to obtain the replaced expression for the total potential energy.

[0104] Finally, by combining the stationary potential energy condition with the replaced total potential energy expression, the expression for the critical bending moment of the steel beam under two-point symmetrical load is obtained, and the critical bending moment of elastic-plastic instability is calculated.

[0105] In some embodiments, step S4: In the absence of instability failure, the locally corroded steel beam in the shear span is discretized and element-divided. Based on the different corrosion levels of each element, according to the equivalent constitutive model of the high-performance steel and the pre-obtained moment-curvature relationship, the bearing capacity and deflection of the locally corroded steel beam in the shear span are obtained through nonlinear iteration, including:

[0106] Step S411: Discretization and element partitioning, specifically including the following steps: Divide the shear span local high-performance steel beam into n elements, each element having specific section properties; define the initial load as... kN, and set the load increment value to a kN;

[0107] Step S412: Elastic buckling stress calculation, as follows: Assume the initial cross-sectional strain Based on the assumption of a plane section, the strain increment of the same section is equal, and the elastic buckling stress is calculated according to the constitutive model;

[0108] Step S413: Bending moment distribution analysis, specifically as follows: Based on the calculated elastic buckling stress value and the section properties of each element, calculate the bending moment of each element;

[0109] Step S414: Calculate the support reaction force, as follows: Consider the arrangement of lateral supports, assuming only... The steel beam (where l is the beam span) is corroded. Based on the bending moment of each element, calculate the support reaction force F, and check whether the support reaction force F meets the preset convergence condition. If the convergence condition is not met, then proceed according to... Increase the load and return to step S412 for iteration until the termination condition is met;

[0110] Step S415: Calculate the deflection using the bending moment and support reaction F of each unit, and then calculate the bearing capacity of the corroded steel beam based on the bending moment-curvature relationship.

[0111] Furthermore, the convergence condition satisfies: Alternatively, the convergence condition is that the slope of the load-displacement curve satisfies Furthermore, the termination condition is satisfied: ;

[0112] Where P is the load, F is the support reaction force, ε is the cross-sectional strain, and E is the cross-sectional strain. sc ΔF is the elastic modulus of the specimen after corrosion, ΔF is the change in support reaction force, Δε is the change in cross-sectional strain, Δω is the change in deflection, and ε uc This is the ultimate strain.

[0113] To better understand the present invention, the following embodiments further illustrate the content of the present invention, but the present invention is not limited to the following embodiments. The method provided in this embodiment can be performed according to the following steps:

[0114] I. Experimental Preparation

[0115] 1. Corrosion Experiment

[0116] (1) Description of the rust specimen and design corrosion rate. The rust specimens were made of high-performance steel plate Q550E. Therefore, in the following text, the rust specimens are also referred to as high-performance steel specimens or rusted steel plate specimens, or simply specimens. The dimensions of the rust specimens were determined according to GB / T2975—2018 "Sampling Location and Specimen Preparation for Mechanical Properties Testing of Steel and Steel Products". The specific dimensions of the obtained rust specimens are as follows: Figure 1 As shown.

[0117] (2) Conduct electrochemical corrosion experiments. The corrosion rate is defined by the mass loss rate in the electrochemical accelerated corrosion test. Data are obtained by conducting accelerated corrosion tests on high-performance steel specimens. The mass corrosion rate of the specimen after corrosion can be calculated according to formula (3). Formula (3) is as follows:

[0118] (3)

[0119] in: The initial mass of the specimen; The quality of the specimen after corrosion.

[0120] 2. Conduct tensile tests to obtain basic mechanical property parameters such as yield strength, tensile strength, and elastic modulus.

[0121] The purpose of this step is to conduct static tensile tests on the corroded specimens, and to obtain stress-strain curves for HPS specimens with different corrosion rates by processing the stress and strain of 15 specimens after tensioning. These curves will be used to verify the constructed constitutive model in subsequent tests. Specifically, this includes:

[0122] (1) Based on the purpose of the tensile test, five target corrosion rates were designed, namely 0%, 5%, 10%, 15%, and 20%. The experimental results are shown in Table 1. Table 1 is as follows:

[0123] Table 1. Tensile test results of rusted Q550E steel specimens

[0124]

[0125] (2) The decrease in mechanical properties of the corroded Q550E high-performance steel specimens is directly related to the degree of corrosion of the tensile specimens. Based on the mechanical property curves plotted in Table 1, the mechanical property law of HPS steel was obtained from the curves. The yield strength and tensile strength decreased with the increase of mass corrosion rate, and the specimens did not have obvious yield plateaus. The yield strength ratio remained at about 0.91, so it can be considered that the yield strength ratio was 0.91.

[0126] The test data for various mechanical properties were analyzed, and the mechanical properties were fitted to the corrosion rate based on the mechanical property curves. The results are as follows: Figure 2 As shown. Figure 2 In the figure, (a) is the maximum load curve, (b) is the tensile strength curve, (c) is the elastic modulus curve, and (d) is the yield strength curve.

[0127] Based on the fitting results, the quantitative relationship between the decrease in various mechanical properties after corrosion and the mass corrosion rate is obtained, and the corresponding formula is as follows:

[0128] (4)

[0129] (5)

[0130] (6)

[0131] (7)

[0132] (8)

[0133] In the formula: This represents the maximum load on the specimen after corrosion. For ultimate load, The tensile strength of the specimen after corrosion. The tensile strength before corrosion. The elastic modulus of the specimen after corrosion is given. The elastic modulus of the uncorroded specimen. The yield strength of the specimen after corrosion. The yield strength of the uncorroded specimen. Elongation For quality corrosion rate, This represents the initial elongation.

[0134] II. Derivation of Equivalent Thickness

[0135] The purpose of this step is to establish an equivalent thickness benchmark formula based on strength equivalence according to different degrees of corrosion, and to obtain a more accurate equivalent thickness after statistical correction based on rust pit characteristics and rust pit types. Specifically, it includes the following sub-steps:

[0136] First, a 3D scan of the complex morphology of the corroded specimen was performed to obtain the variation patterns of key elements such as the proportion of rust pit types and morphological feature parameters (i.e., the three-dimensional dimensions of rust pits) with the corrosion rate. Specifically, a 3D scan of the corroded specimen was performed to obtain a point cloud, which was then reverse-engineered. Key steps included data processing operations such as deletion, compression, and denoising on the acquired point cloud model. After the point cloud model was converted into a polygonal model, mesh processing, plane fitting, and repair operations were performed to convert the polygonal model into a precise curved surface model. The processed scanned model was then used to obtain the variation patterns of the shape proportion of rust pits with the corrosion rate, as well as the statistical characteristics of the three-dimensional dimensions of the rust pits.

[0137] Then, the finite element method was used to perform a numerical simulation of the randomly corroded steel plate. The simulation process is as follows:

[0138] Step 1: Read the scan data: Read the 3D scan data of the rusted specimen;

[0139] Step 2: Probability and statistical analysis to obtain distribution parameters: Perform probability and statistical analysis on the size of the rust pits to extract key distribution parameters. These distribution parameters include the number, depth, length, width, and probability distribution type of different types of rust pits, and calculate the mean, standard deviation, etc.

[0140] Step 3: Assuming the number of rust pits is N0, calculate the volume loss rate based on the average value obtained in Step 2: The volume of different types of rust pits can be calculated based on the average value, and then the volumes of all types of rust pits can be summed to obtain the total volume loss. Then, the total volume loss can be divided by the total volume of the uncorroded specimen to obtain the volume loss rate (total volume loss of rust pits).

[0141] Step 4: Determine if the total volume loss of the rust pits is equal to the rust level (e.g., the difference between the two is less than the preset first error threshold): where the rust level is the target rust rate. If they are equal, proceed to Step 5; if they are not equal, return to Step 3 and adjust the number of rust pits N0 according to the difference between the total volume loss of the rust pits and the rust level until the requirements are met.

[0142] Step 5: Generate random rust pits by combining distribution parameters: Based on the distribution parameters in Step 1, modify the standard deviation of the rust pit diameter and depth, and randomly generate the three-dimensional dimensions of each rust pit;

[0143] Step 6: Using randomly generated rust pits, determine whether the total volume loss of the rust pits is equal to the level of corrosion (e.g., the difference between the two is less than the preset second error threshold). If they are equal, proceed to step 7; otherwise, return to step 5 to regenerate the random rust pit size until the error requirement is met.

[0144] Step 7: Randomly distribute the number of rust pits on each surface: Randomly distribute the rust pits with random three-dimensional dimensions to each surface of the rusted specimen, such as the top surface and the side surface, so that their spatial distribution is also random.

[0145] Step 8: Combine boundary and distribution parameters to obtain the rust pit parameter array: for example, record the spatial coordinates and three-dimensional dimensions (depth, length, width) of each rust pit.

[0146] Step 9, Numerical Simulation: Parametric simulation is performed using finite element software, including: inputting the rust pit parameter array, automatically generating randomly distributed rust pit entities on the surface of the specimen through programming, and performing finite element analysis on the specimen containing random rust to obtain simulation results.

[0147] Furthermore, the numerical simulation model contains different types of rust pits (such as ellipsoids, cones, and hemispheres). The model was imported into the finite element analysis software Workbench for numerical simulations at different corrosion rates (i.e., target corrosion rates, such as 0%, 5%, 10%, 15%, and 20%). The simulation results are shown in Table 2.

[0148] Table 2 Statistical Table of Simulation Results

[0149]

[0150] Considering the pitting effect of rust damage, the rust damage is initially simplified to uniform rust for treatment. Therefore, the residual pitting damage intensity DOP of the specimen after rusting can be obtained by formula (9), which is as follows:

[0151] (9)

[0152] In the formula: and Let L be the diameter and area of ​​the i-th rust pit, respectively; n be the total number of rust pits; L, W, and H be the length, width, and height of the specimen, respectively; and A be the total area.

[0153] Considering that the load-bearing capacity of the corroded specimen is not only related to DOP, but also closely related to the pitting depth, the pitting volume loss (DOPV) is introduced to describe the degree of pitting damage over time. The DOPV of the specimen can be calculated by formula (10), which is as follows:

[0154] (10)

[0155] In the formula: and Let V be the volume and depth of the i-th rust pit, respectively, and V be the total volume.

[0156] The data obtained from the finite element simulation were imported into MATLAB software, and the relationship between the ultimate load and DOPV was fitted to obtain the calculation formula (11):

[0157] (11)

[0158] In the formula: For ultimate load, This represents the percentage of pitting volumetric damage intensity.

[0159] Finite element models with different uniform loss thicknesses were established using ANSYS software. The tensile stress was simulated and the relationship between the strengthening degradation rate and the uniform thickness was obtained by fitting.

[0160] Combining the above formulas, we derive the equivalent thickness benchmark formula based on equivalent strength:

[0161] (12)

[0162] In the formula: For equivalent thickness, t represents the percentage of pitting volumetric damage intensity; t represents the initial thickness.

[0163] Under the same pitting volume damage intensity (i.e. the same DOPV), the three-dimensional dimensions, pit type, and minimum cross section of the rust pit of the rust specimen will cause slight deviations in the ultimate strength. Therefore, the above equivalent thickness formula needs to be modified.

[0164] (1) Corrosion intensity DOC first correction

[0165] For the same pitting volumetric damage intensity, the pitting damage intensity varies due to differences in the three-dimensional size and type of rust pit. Here, we introduce the corrosion intensity DOC to describe the relationship between the two:

[0166] (13)

[0167] Rust pits formed on the surface of high-performance steel are mostly random rust pits. During the formation of random rust pits, the standard deviations of both the pit depth and radius affect the corrosion intensity. Different simulation data were obtained by modifying the standard deviations of the pit diameter and depth (as shown in Table 2). Then, random rust finite element numerical simulations were performed, and the obtained data were imported into MATLAB software for analysis. The variation of corrosion intensity with the standard deviations of pit depth and radius was obtained:

[0168] (14)

[0169] In the formula, The standard deviation of the rust pit diameter is... The standard deviation of the rust pit depth. The diameter of the rust pit. This represents the depth of the rust pit.

[0170] Based on this, and combined with the random simulation results in Table 2 above, the equivalent thickness is fitted again using formula (14) to obtain the corrected equivalent thickness formula:

[0171] (15)

[0172] In the formula: For equivalent thickness, This represents the percentage of pitting volume loss. for The percentage.

[0173] The deviation between the initial equivalent thickness ultimate strength and the equivalent thickness ultimate strength after one correction is calculated and compared to verify the effect of the one correction.

[0174] (2) Secondary correction of the probability statistics of rust pit types

[0175] Since the above finite element simulation only considers a single type of rust pit, while steel structures have various types of rust pits during the corrosion process, the equivalent thickness is modified twice by combining the proportion of various types of rust pits under different corrosion rates to obtain formula (16):

[0176] (16)

[0177] In the formula: b represents a hemispherical rust pit, y represents a conical rust pit, and e represents an ellipsoidal rust pit. , , The percentages of hemispherical, conical, and ellipsoidal rust pits, respectively. , , The equivalent thicknesses are for hemispherical, conical, and ellipsoidal rust pits, respectively.

[0178] After two corrections, the deviation in ultimate strength became smaller and smaller, indicating that the equivalent strength calculation after two corrections was more accurate and could better predict the performance of high-performance steel after corrosion.

[0179] To investigate the applicability of the conclusions obtained from the above secondary correction to steel plates with different width-to-thickness ratios, the width-to-thickness ratio was... Set to 60, 80, and 140, and set the reduction factor corresponding to different aspect ratios. With quality loss rate Plot a curve based on the distribution, such as Figure 3 As shown in the figure. From the figure, we can derive the reduction coefficients corresponding to different width-to-thickness ratios b / t. With quality loss rate The variation pattern is the same. Therefore, the conclusion can be applied to steel plates with different width-to-thickness ratios, and thus we can conclude that:

[0180] (17)

[0181] In the formula: This represents the ultimate stress of the uncorroded specimen.

[0182] Since the equivalent thickness is determined based on different degrees of corrosion, the ultimate stress of the steel plate based on the corrected equivalent thickness is equal to the ultimate stress of the randomly corroded steel plate. Assume the thickness of the uncorroded steel plate is... The ultimate stress of a corroded steel plate can be denoted as... He should be equal to The corresponding ultimate stress.

[0183] (18)

[0184] In the formula, The ultimate stress of the uncorroded specimen corresponds to the thickness of the uncorroded plate. ; It is the equivalent thickness The corresponding ultimate stress, This is the reduction factor.

[0185] III. Establishing a Mathematical Model

[0186] Here, the mathematical model refers to the equivalent constitutive model of high-performance steel with different corrosion levels.

[0187] 1. Determination of constitutive model parameters

[0188] The yield strength of the corroded specimen was fitted using the least squares method. Tensile strength of specimens after corrosion Elongation and the elastic modulus of the specimen after corrosion Corrosion rate The relationship is used to obtain the stress-strain model (constitutive model) under different corrosion rates:

[0189] (19)

[0190] 2. Establish an equivalent constitutive model

[0191] Considering the impact of random corrosion on mechanical property degradation and the convenience of replacing randomly corroded steel with uncorroded steel plates using the equivalent thickness method, an equivalent constitutive model is established. The constitutive parameters are then adjusted based on the modified equivalent thickness. , , , , , After making corresponding modifications, the degenerate equivalent constitutive model (i.e., the modified three-stage constitutive model) is obtained, as shown in the following expression:

[0192] (20)

[0193] In the formula, For stress, In response, For the equivalent elastic modulus, For equivalent yield strength, It is the equivalent ultimate strength; For equivalent yield strain, To effectively enhance strain, This is the equivalent limit strain.

[0194] , The expression for the parameter correction result of the constitutive model is as follows:

[0195] (twenty one)

[0196] Equivalent bulk modulus of materials containing surface rust pit damage:

[0197] (twenty two)

[0198] According to mechanics of materials:

[0199] (twenty three)

[0200] By rearranging equations (22) and (23), the equivalent elastic modulus of the material containing surface rust pit damage is obtained:

[0201] (twenty four)

[0202] In the formula For quality corrosion rate, This is the initial bulk modulus of the material. The initial shear modulus of the material. It is Poisson's ratio.

[0203] The physical parameters of the uncorroded Q550E ( It is 0.3. The Pa is 175 GPa. Substituting 81 GPa into equation (24), we obtain the equivalent elastic modulus expression for Q550E steel with rust pits on the surface:

[0204] (25)

[0205] Equivalent yield strain :

[0206] (26)

[0207] Analysis of the experimental results shows that the critical mass corrosion rate at which the yield plateau disappears in the Q550E corrosion specimen is 20%. For corrosion rates less than the critical rate, assuming the yield plateau length decreases linearly with increasing corrosion rate, and considering the mass corrosion rate, the equivalent strengthening strain can be determined using the following formula:

[0208] (27)

[0209] In the formula: λ1 is a preset parameter. The critical mass corrosion rate.

[0210] Considering that the strain change and elongation change follow the same pattern during the tensile test, the equivalent ultimate strain is calculated using the elongation degradation regression formula as follows:

[0211] (28)

[0212] In the formula, λ2 is another preset parameter, for example, Its value signifies that on the stress-strain curve of the uncorroded specimen, the yield plateau length is the yield strain. times.

[0213] IV. Validation of the modified equivalent constitutive model using experimental data.

[0214] The measured values ​​of the equivalent constitutive model parameters of the corroded specimens are shown in Table 3:

[0215] Table 3 Calculated values ​​of parameters for the equivalent constitutive model

[0216]

[0217] Experimental curves were plotted based on measured values, and curves were also plotted based on calculated values ​​from the equivalent constitutive model. The two were then compared. Figure 4 , Figure 5 , Figure 6 As shown, where Figure 4 Comparison of experimental curves and equivalent constitutive model curves for specimen Q0-1; Figure 5 (a) shows a comparison between the experimental curve and the equivalent constitutive model curve of specimen Q5-1, and (b) shows a comparison between the experimental curve and the equivalent constitutive model curve of specimen Q10-1. Figure 6(a) shows a comparison between the experimental curve and the equivalent constitutive model curve of specimen Q15-1, and (b) shows a comparison between the experimental curve and the equivalent constitutive model curve of specimen Q20-1. The results show that the calculated values ​​in the nonlinear curves are in high agreement with the measured values ​​in the experimental curves, indicating that the modified three-stage constitutive model curves can well describe the stress-strain curves of high-performance steel after corrosion. This model can accurately predict the constitutive relationship of high-performance steel after corrosion and can be used for performance evaluation and safety analysis of corroded steel structures.

[0218] The established mathematical model is validated using experimental data to ensure its accuracy and reliability.

[0219] It is important to note that constitutive models are crucial tools in materials science for researching and developing new materials. By constructing and validating constitutive models, researchers can gain a deeper understanding of the nature and behavioral characteristics of materials, thereby guiding the development and optimized design of new materials. Constitutive models are also widely used in engineering. Engineers can use them to predict and evaluate the performance of materials or structures under specific working conditions, such as strength, stiffness, and wear resistance. Currently, relatively mature constitutive models exist for uncorroded HPS, which can predict its mechanical behavior under different stress states quite well. However, for corroded HPS, due to the changes in microstructure and degradation of mechanical properties caused by corrosion, existing constitutive models often cannot accurately predict its mechanical behavior. Many scholars and engineers have dedicated themselves to studying the impact of corrosion on the mechanical properties of HPS and have proposed some empirical formulas and models to predict the mechanical properties after corrosion. However, most of these methods do not take into account the complexity and randomness of the corrosion process, nor do they provide equivalent treatment for such problems to improve the efficiency of the evaluation. In addition, the mechanical properties of HPS vary greatly under different corrosion conditions, which poses a great challenge to establishing a universal constitutive model.

[0220] To alleviate the aforementioned problems, this embodiment proposes a method for accurately predicting HPS constitutive models after corrosion, thereby predicting and describing material behavior, supporting materials science research and development, and guiding engineering design and analysis. For random corrosion, the proposed method is more efficient, convenient, and has a wider range of applications.

[0221] After constructing a three-stage nonlinear constitutive model, the overall stability of the high-performance steel beam with localized corrosion in the shear span is verified, and its load-bearing capacity is predicted. For example, this can be performed as follows:

[0222] V. Stability Calculation of Uncorroded High-Performance Steel Beams

[0223] To simplify the derivation of the critical bending moment formula, the following basic assumptions need to be established for analysis:

[0224] 1) The research object is an ideal elastic material;

[0225] 2) When the beam is subjected to lateral bending and torsion, the geometry of the member section remains unchanged; since the local corrosion of the shear span has little impact on the overall stability, the impact of local corrosion of the shear span on the overall stability is ignored, that is, in the stability verification, the uncorroded high-performance steel beam is taken as the research object.

[0226] 3) The beam has a large bending stiffness, and the deformation in the bending plane before the overall instability is very small. The bending strain energy in the plane is negligible, and the influence of the bending deformation in the plane on the lateral bending and torsion is negligible.

[0227] 4) Ignore welding residual stress and initial geometric defects.

[0228] Figure 7 A schematic diagram of a specimen for a tensile test under two-point symmetrical concentrated load is shown, where (a) is a front view and (b) is a cross-sectional view; Figure 8 This is a schematic diagram of flexural-torsional buckling of a beam under two-point symmetrical concentrated loads, where (a) is the longitudinal elevation view and (b) is the cross-sectional view. Figure 7 , Figure 8 As shown, the stability of a doubly symmetric H-shaped simply supported steel beam under two-point symmetric loads is checked. The bending moment from the left side of the beam to the mid-span is expressed as follows:

[0229] (29)

[0230] In the formula: l is the beam span, and z is the distance from the load application point to the coordinate origin O. y represents the vertical direction, and r is the ratio of the distance from the concentrated load point to the center of the support to the span of the beam.

[0231] According to the principle of potential energy, the expression for the total potential energy is as follows:

[0232] (30)

[0233] In the formula: It is the moment of inertia of the cross section; It represents the warping moment of inertia; G represents the shear modulus. It represents the torsional moment of inertia; u represents the lateral displacement of the beam after it undergoes out-of-plane bending and torsional deformation. is the second derivative of u; q represents the distance from the point of application of the load to the shear center; Indicates the torsion angle of the cross section. , They are respectively The first and second derivatives. The boundary conditions at the ends of the simply supported beam are:

[0234] (31)

[0235] Assume the deformation function that satisfies the boundary conditions is:

[0236] (32)

[0237] In the formula: , These are the displacement constants.

[0238] For u and in the deformation function Find the first and second derivatives respectively, then substitute them into the total potential energy expression, and simplify to get:

[0239] (33)

[0240] Let the integral be: , , .

[0241] After replacing the integral expression, equation (33) can be rewritten as follows:

[0242] (34)

[0243] By the condition of stationary potential energy , have to:

[0244] (35)

[0245] (36)

[0246] Finally, the critical bending moment of the steel beam under two-point symmetrical loads is obtained:

[0247] (37)

[0248] In the formula: Let be the critical bending moment of the steel beam, r be the ratio of the distance from the concentrated load point to the support center to the beam span, l be the beam span, A, B, and D be integral substitution symbols, E be the modulus of elasticity, and I be the modulus of elasticity. y Let I be the moment of inertia of the cross section, q be the distance from the point of application of the load to the shear center, and I be the moment of inertia of the cross section. w Let G be the warping moment of inertia, and I be the shear modulus. t For torsional moment of inertia.

[0249] The critical bending moment for elastic-plastic instability can be calculated from the above formula. When the critical bending moment is less than the ultimate bending moment At that time, that is When a steel beam is subjected to static loading without lateral support, it will experience overall instability during the elastoplastic stage. In this case, lateral supports should be added on both sides of the load point to ensure the overall stability of the beam without increasing the bending load capacity of the steel beam.

[0250] Taking a steel beam made of Q550E material as an example, a rusted specimen for a tensile test under two-point symmetrical concentrated loads was re-fabricated, such as... Figure 7 As shown, a tensile test was performed on the rusted specimen, and the test results were obtained.

[0251] Assuming that the H-beam undergoes flexural-torsional buckling in the elastic stage, formula (37) is used for calculation, with elastic modulus E = 20300 kN / cm2 and shear elastic modulus G = 7900 kN / cm2. The geometric properties of the calculated section are shown in Table 4.

[0252] Table 4 Geometric properties of the cross section

[0253]

[0254] when hour, , , In the above formula, z is the distance from the point of application of the load to the origin of the coordinate system.

[0255] Substituting the calculation formulas for the above parameters into formula (37), we get:

[0256]

[0257] (38)

[0258] In the formula: The critical instability stress, It is the section modulus for bending resistance.

[0259] Under assumed elastic stage flexural-torsional buckling conditions, the critical stress for overall instability of the Q550E welded H-beam exceeds the steel proportional limit. However, the beam experiences overall instability in the elastoplastic stage, while the overall instability coefficient in the elastic stage is lower. for:

[0260] (39)

[0261] When calculated When the value is greater than 0.6, the stability coefficient of the elastoplastic stage is calculated using the following formula. replace value:

[0262] (40)

[0263] The critical bending moment for elastoplastic instability is:

[0264] (41)

[0265] The critical bending moment for elastoplastic instability of the experimental reference beam B0 was calculated. and ultimate bending moment The values ​​were 128.7 kN•m and 173.5 kN•m, respectively. The results indicate that without lateral support, the ultimate bending moment exceeds the critical moment for instability, and the steel beam will lose overall stability in the elastoplastic stage. Therefore, it is necessary to add stiffening ribs on both sides of the loading point as lateral supports to ensure the overall stability of the beam during the test loading process without increasing the bending capacity of the steel beam.

[0266] VI. Bearing Capacity Prediction

[0267] The test beam parameters for predicting the load-bearing capacity of high-performance steel beams with localized corrosion in the shear span are shown in Table 5 below:

[0268] Table 5 Corrosion parameters of the test beams

[0269]

[0270] 1. Discretization and Element Partitioning:

[0271] The HPS beam is divided into n (e.g., n=180) elements, each element having an equal length of 10mm, and each element having specific cross-sectional properties.

[0272] Define the initial load, such as kN, and set the load increment value to a (e.g., a=1) kN, and the load increment in the calculation process is also 1kN, that is .

[0273] 2. Calculation of elastic buckling stress

[0274] Assuming initial cross-sectional strain Based on the assumption of a planar section, the strain increments of the same section are equal, and the elastic buckling stress is calculated according to the equations of the three-stage nonlinear constitutive model (equivalent constitutive model for high-performance steel) provided in the aforementioned embodiments. .

[0275] 3. Bending moment distribution analysis

[0276] Based on the calculated elastic buckling stress Based on the section properties, the bending moment of each element is calculated using the following equation. :

[0277] (42)

[0278] in: It is the plastic development coefficient of beams in the standard GB50017-2017, with a value of 1.05; It is the moment of inertia (cm) 4 ); y c It is the maximum distance (cm) from the elastic neutral axis to the top flange.

[0279] 4. Calculation of Support Reaction Force

[0280] Consider arranging lateral supports, assuming only The steel beams are corroded; the support reaction force can be calculated using the following formula. :

[0281] (43)

[0282] in, It is the distance from any element section i to the corroded end. It is the coefficient of increase in the load-bearing capacity of the beam due to the stiffening ribs.

[0283] Check the support reaction force Does it meet the convergence condition? ,in: The elastic modulus of the specimen after corrosion is given. , The elongation of the material.

[0284] If it does not converge, then according to Increase the load, return to the elastic buckling stress calculation, and increase the strain. Continue iterating until the termination condition is met.

[0285] 5. Deflection Analysis

[0286] Calculate deflection using bending moment and support reaction force F:

[0287] (44)

[0288] The formula for calculating curvature is:

[0289] (45)

[0290] If F satisfies the above convergence condition, then the support reaction force F obtained in step 5 is substituted into the deflection calculation formula combined with the curvature calculation formula:

[0291] (46)

[0292] In the formula: For deflection, E scLet β be the elastic modulus of the corroded specimen, and β be the deflection value of section i under the action of F. β depends on the bending moment diagram obtained by applying a unit force to section i of any element. The graphical product between the bending moment diagram obtained by the force F applied to the beam at any time and the bending moment diagram is defined as:

[0293] (47)

[0294] In the formula, M P The bending moment caused by F.

[0295] Assuming only The steel beam is corroded, and the change in the corrosion rate affects both the elastic modulus E and the moment of inertia I of the centroid section. Therefore, β needs to be calculated in two different sections:

[0296] (48)

[0297] (49)

[0298] (50)

[0299] In the formula: and Let represent the elastic modulus and moment of inertia of the corroded section, respectively. and These represent the elastic modulus and moment of inertia of the uncorroded section, respectively.

[0300] 6. Nonlinear Iterative Calculation

[0301] Output the corresponding support reaction force F, cross-sectional strain ε, and deflection ω, then return to the discretization and element generation steps. Perform iterations; if the slope of the load-displacement curve does not satisfy... Then return and redetermine the load increment 'a', when the assumed cross-sectional strain is greater than the ultimate strain, i.e. The calculation ends when the time is right.

[0302] The force-deformation state of the entire length of the locally corroded HPS beam in the shear span section was obtained through the above nonlinear iterative calculation.

[0303] 7. Comparison of calculated and experimental values ​​of support reaction force and deflection

[0304] Through the above calculation steps, the load-deflection curve of the mid-span section was obtained, and it was compared and analyzed with the experimental results, as shown in Table 6.

[0305] Table 6 Calculated and experimental values ​​of the ultimate flexural bearing capacity of the test beams

[0306]

[0307] Based on this, a load-deflection curve was plotted and compared with the measured values. The results are as follows: Figure 9 As shown in Table 6. Figure 9 It can be seen that the deflection curve of the uncorroded beam exhibits a typical three-stage characteristic, while the yield plateau of the deflection curve after corrosion disappears, showing a two-stage characteristic. The experimental and calculated values ​​for the elastic and strengthening stages are in good agreement, while the experimental yield strength is slightly lower than the calculated value, mainly due to differences in the constitutive model at the yield stage. This indicates that the constitutive model proposed in this embodiment is suitable for predicting the load-bearing capacity of locally corroded high-performance steel beams, and the calculation method has high accuracy in calculating the flexural bearing capacity of locally corroded high-performance steel beams.

[0308] In summary, the method for predicting the load-bearing capacity of locally corroded high-performance steel beams in this invention shows a high degree of agreement between theoretical calculations and experimental simulations. It can be effectively used for overall stability verification and load-bearing capacity prediction of locally corroded high-performance steel beams. This not only helps in understanding the specific impact of corrosion on structural performance but also provides an assessment tool for the maintenance and management of existing structures, aiding in the development of maintenance plans and preventative measures.

[0309] Based on tensile test results of corroded components, this paper analyzes the degradation and failure characteristics of the ultimate flexural bearing capacity of locally corroded steel beams, establishes a constitutive model considering the influence of corrosion, and proposes a method for predicting the bearing capacity of locally corroded high-performance steel beams in shear span sections. This method can more accurately describe the mechanical behavior of locally corroded HPS steel beams and proposes a method for calculating flexural bearing capacity, providing a scientific basis for the durability assessment of high-performance steel structures. Furthermore, this simulation method can accurately predict the mechanical properties of high-performance steel beams, significantly saving experimental time and costs.

[0310] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for predicting the load-bearing capacity of a high-performance steel beam with localized corrosion in a shear span, characterized in that, Includes the following steps: Step S1: Perform material property tests on the corroded high-performance steel to obtain the variation law of the basic mechanical property parameters of the corroded high-performance steel with mass corrosion rate; establish an equivalent thickness benchmark formula based on strength equivalence according to different corrosion degrees, and correct the equivalent thickness based on the three-dimensional size characteristics of rust pits and the probability statistics of rust pit types to obtain the corrected equivalent thickness; wherein, the basic mechanical property parameters include: yield strength, tensile strength, and elastic modulus; Step S2: Based on the corrected equivalent thickness, establish equivalent constitutive models of high-performance steel with different corrosion levels; Step S3: Based on the principle of potential energy, derive the formula for verifying the overall stability of high-performance steel beams under symmetrical concentrated loads at any two points, and use the formula for verifying the overall stability of high-performance steel beams to determine whether there is instability or failure in the locally corroded steel beams of the shear span section. Step S4: In the absence of instability failure, the locally corroded steel beam in the shear span is discretized and divided into elements. Based on the different corrosion levels of each element, the bearing capacity and deflection of the locally corroded steel beam in the shear span are obtained through nonlinear iteration according to the equivalent constitutive model of the high-performance steel and the pre-obtained moment-curvature relationship. Based on different degrees of corrosion, an equivalent thickness benchmark formula with strength equivalence is established, including: Considering the pitting effect of rust damage, the pitting area loss (DOP) of the high-performance steel specimen after rusting is calculated using the following formula: ， In the formula: and Let L be the diameter and area of ​​the i-th rust pit, respectively; n be the total number of rust pits; L, W, and H be the length, width, and height of the specimen, respectively; and A be the total area. Meanwhile, the pitting volume loss (DOPV) is introduced to describe the degree of pitting damage in high-performance steel specimens, as shown in the following formula: ， In the formula: and Let V be the volume and depth of the i-th rust pit, respectively, and V be the total volume. A finite element numerical simulation of random corrosion was performed, and the simulation data was imported into MATLAB software. The relationship between ultimate load, elongation, and DOPV was obtained by fitting, and then the equivalent thickness benchmark formula with strength equivalence was derived. ， In the formula, Equivalent thickness; The percentage of pitting volumetric damage intensity; t is the initial thickness; The equivalent thickness is corrected based on the three-dimensional size characteristics of rust pits and the probability statistics of rust pit types, resulting in a corrected equivalent thickness, including: a first correction of corrosion intensity DOC and a second correction of rust pit type probability statistics; The first correction of the corrosion intensity DOC includes: the corrosion intensity DOC is the ratio of the pitting volume loss (DOPV) to the pitting area loss (DOP), used to describe the three-dimensional dimensions of the rust pit and the differences in pitting damage intensity caused by different rust pit types; the formula is as follows: ， The standard deviations of the rust pit diameter and depth were modified, and then random rust finite element numerical simulation was performed. The simulation data was then imported into MATLAB software for analysis to obtain the variation law of rust intensity DOC with the diameter of the rust pit, the depth of the rust pit, the standard deviation of the rust pit diameter, and the standard deviation of the rust pit depth. Based on the results of the random simulation, the equivalent thickness is refitted using the aforementioned variation pattern to obtain a corrected equivalent thickness: ， In the formula: For equivalent thickness, This represents the percentage of pitting volume loss. for percentage; The second-order correction of the probability statistics for the rust pit type includes: Based on probability statistics of different rust pit types, the proportion of each type of rust pit under different corrosion rates was obtained; Based on the proportion of various rust pits under different corrosion rates, the equivalent thickness is corrected a second time to obtain the corrected equivalent thickness: ， In the formula: b represents a hemispherical rust pit, y represents a conical rust pit, and e represents an ellipsoidal rust pit. , , The percentages of hemispherical, conical, and ellipsoidal rust pits, respectively. , , The equivalent thicknesses are for hemispherical, conical, and ellipsoidal rust pits, respectively.

2. The method according to claim 1, characterized in that, Material property tests were conducted on the corroded high-performance steel to obtain the variation law of the basic mechanical property parameters of the corroded high-performance steel with mass corrosion rate, including: Accelerated corrosion tests were conducted on high-performance steel specimens to obtain data, and the mass corrosion rate of the specimens after corrosion was determined. ; Static tensile tests were conducted on the corroded high-performance steel specimens to obtain test data for various basic mechanical property parameters; The test data of various basic mechanical properties were analyzed and compared with the mass and corrosion rate of the specimen after corrosion. By performing fitting, the basic mechanical property parameters and mass corrosion rate after corrosion were obtained. The quantitative relationship.

3. The method according to claim 1, characterized in that, Step S2: Based on the corrected equivalent thickness, establish equivalent constitutive models for high-performance steel with different corrosion levels, including: Based on the aforementioned basic mechanical performance parameters, the least squares method was used to fit and obtain several key parameters of the constitutive model under different corrosion rates. Based on the equivalent thickness, several key parameters of the constitutive model under different corrosion rates obtained from the fitting are corrected, resulting in a corrected three-stage constitutive model, which is used as the equivalent constitutive model for high-performance steel. The expression is as follows: ， In the formula, For stress, For cross-sectional strain, For the equivalent elastic modulus, For equivalent yield strength, It is the equivalent ultimate strength; For equivalent yield strain, To effectively enhance strain, This is the equivalent limit strain.

4. The method according to claim 1, characterized in that, Step S3: Derive the formula for verifying the overall stability of a high-performance steel beam under symmetrical concentrated loads at any two points based on the principle of potential energy, including: The high-performance steel beam is a simply supported H-shaped steel beam with biaxial symmetry. Stability calculations are performed under two-point symmetrical loads. By utilizing symmetry, we determine the expression for the bending moment from the left side of the beam to the mid-span. Based on the principle of potential energy, the initial expression for the total potential energy is determined; combined with the boundary conditions at the ends of the simply supported beam, the initial expression for the total potential energy is rearranged and the parameters are replaced to obtain the replaced expression for the total potential energy. By combining the stationary potential energy condition with the replaced total potential energy expression, the expression for the critical bending moment of the steel beam under two-point symmetrical load is obtained, and then the critical bending moment of elastic-plastic instability is calculated.

5. The method according to claim 1, characterized in that, Step S4: In the absence of instability failure, the locally corroded steel beam in the shear span is discretized and element-divided. Based on the different corrosion levels of each element, and according to the equivalent constitutive model of the high-performance steel and the pre-obtained moment-curvature relationship, the bearing capacity and deflection of the locally corroded steel beam in the shear span are obtained through nonlinear iteration, including: Discretization and element partitioning: The local high-performance steel beam of the shear span is divided into n elements, each with specific cross-sectional properties; the value of the initial load P is defined, and the load increment value is set to a; Elastic buckling stress calculation: Set the initial cross-sectional strain values, and based on the plane section assumption, the strain increment of the same cross-section is equal. Calculate the elastic buckling stress according to the equivalent constitutive model of high-performance steel. Bending moment distribution analysis: Based on the calculated elastic buckling stress value and the section properties of each element, calculate the bending moment of each element; Support reaction calculation: Considering the arrangement of lateral supports, calculate the support reaction force F based on the bending moment of each element, and check whether the support reaction force F meets the preset convergence condition. If the convergence condition is not met, then... Increase the load and iterate through the steps of calculating the elastic buckling stress until the termination condition is met. The deflection is calculated using the bending moment and support reaction F of each unit, and then the bearing capacity of the corroded steel beam is calculated based on the moment-curvature relationship.

6. The method according to claim 5, characterized in that, The convergence condition is satisfied as follows: Alternatively, the convergence condition is that the slope of the load-displacement curve satisfies Furthermore, the termination condition is satisfied: ; Where P is the load, F is the support reaction force, ε is the cross-sectional strain, and E is the cross-sectional strain. sc ΔF is the elastic modulus of the specimen after corrosion, ΔF is the change in support reaction force, Δε is the change in cross-sectional strain, Δω is the change in deflection, and ε uc This is the ultimate strain.

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