A method for constructing an empirical model of the correlation between N and M based on large-scale test data and application thereof

Abstract

The application provides a method for constructing an empirical model of the correlation between N and M based on large batch test data, and relates to the technical field of structural engineering. The method for constructing the empirical model of the correlation between N and M based on large batch test data has a homogeneous expression form, can meet the proportional loading condition of plastic limit analysis, and has the hoop coefficient and the stability coefficient as explicit influence parameters, has clear physical meaning, and has a simple function form, so that engineering application is facilitated. The plastic development coefficient can accurately calculate the bending resistance of the component under different hoop coefficients after the hoop coefficient is introduced, and the compression-bending stability homogeneous generalized yield function can naturally degenerate into the strength HGYF after the stability coefficient is introduced, so that the strength and stability are uniformly expressed.

Description

Technical Field

[0001] This invention relates to the field of structural engineering technology, specifically to a method for constructing an empirical model of the correlation between N and M based on a large number of experimental data and its application. Background Technology

[0002] Concrete-filled steel tube (CFST) members, combining the advantages of both steel tubes and concrete, possess characteristics such as high load-bearing capacity, good ductility, and convenient construction, and are widely used in high-rise buildings and long-span bridge structures. In the design of CFST structures, accurately determining the correlation between axial force and bending moment (NM correlation) under compression and bending is a key issue in ensuring structural safety. However, existing technologies have significant shortcomings in constructing models of the internal force correlation of CFST members under compression and bending, mainly in the following aspects: (1) Defects in the compression-bending correlation model: Currently, the axial force-bending moment correlation of compression-bending members provided by domestic and international standards usually adopts piecewise non-homogeneous function expressions. For example, European standard EC4, American AISC, and relevant Chinese standards all describe the NM correlation curve in the form of piecewise functions. The defects of such expressions are: piecewise non-homogeneous functions cannot meet the proportional loading conditions required by plastic limit analysis, it is difficult to achieve monotonically stable numerical solutions in elastoplastic incremental analysis, and different calculation formulas need to be switched under different load combinations, which brings inconvenience to program design. In addition, in the existing NM correlation models, some model parameters are too numerous and their physical meanings are unclear, making it difficult to accurately reflect the comprehensive influence of material strength and geometric dimension changes on the correlation curve. Studies have shown that factors such as steel pipe yield strength, concrete strength, and section diameter-to-thickness ratio have a significant impact on the NM correlation curve, but there is no scheme in the existing models that uses a unified single parameter with clear physical meaning to comprehensively characterize the influence of the above factors.

[0003] (2) The influence of the confinement effect is not fully considered in the plastic development coefficient: In the calculation of flexural bearing capacity, the plastic development coefficient γm is a key parameter characterizing the plastic development capacity of the member section. However, some formulas in the current specifications take the plastic development coefficient as a fixed value and do not consider the influence of the confinement effect. For example, the plastic development coefficient of circular cross-section CFST members in my country's "Technical Specification for Concrete-Concrete Structural Structures" (GB50936-2014) is a fixed value of 1.2, which leads to poor rationality and applicability of the calculation results and makes it impossible to accurately calculate the flexural bearing capacity of members under different confinement coefficients. Some scholars have also proposed formulas for calculating the plastic development coefficient that consider the influence of the confinement coefficient, but there is a problem of curve distortion. For example, when the confinement coefficient is large, the curve shows an abnormal descent segment, which does not match the actual situation. Represented by the formula proposed by Professor Han Linhai, some scholars have introduced the influence of the confinement coefficient, but the formula is extremely complex, involves many parameters, and the physical meaning of some parameters is not clear. Furthermore, different scholars employ different approaches when considering the moment amplification factor, lacking a unified standard, which poses difficulties for engineering designers in practical applications. Summary of the Invention

[0004] The present invention aims to solve at least one of the problems mentioned in the background art above, and provides a method for constructing an empirical model of the correlation between N and M based on a large number of experimental data, with the hoop coefficient and stability coefficient as basic parameters, a concise and unified functional form, and clear physical meaning.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for constructing an empirical model of the correlation between N and M based on large-scale experimental data includes the following steps: S1, Determination of axial compressive strength bearing capacity, axial compressive stability bearing capacity, and flexural bearing capacity: The axial compressive strength bearing capacity N0 of the concrete-filled steel tube member is determined according to the formula... Calculate the axial compression stable bearing capacity. N u According to the formula Calculate the flexural bearing capacity M of the section. u According to the formula Calculate, where A sc f is the combined cross-sectional area of ​​the steel-concrete composite member. sc The combined axial compressive strength of the steel-concrete composite member. W is the stability coefficient. sc γ is the section modulus of flexural strength of a concrete-filled steel tube member. m The plastic development coefficient; S2, Establishment of the homogeneous generalized yield function for compressive-bending strength: Define the dimensionless axial force n = N / N u and dimensionless bending moment m=M / M uThe correlation data points between axial force N and bending moment M in concrete-filled steel tube members under different material strengths and geometric parameters were calculated using the fiber model method, with the confinement coefficient as the basis. ξ As a parameter influencing the homogeneous generalized yield function, a homogeneous generalized yield function for compressive-bending strength is established through regression analysis. S3, Establishment of the homogeneous generalized yield function for bending stability: Based on the aforementioned homogeneous generalized yield function for bending strength, a stability coefficient is introduced. To investigate the influence of bending stability, a homogeneous generalized yield function is established.

[0006] Furthermore, in step S2, the expression for the homogeneous generalized yield function of the compressive-bending strength is established as follows: ; In the formula, G Indicates the clamping coefficient ξ The highest power of a higher-order polynomial. k 0~ k G The coefficients are undetermined and obtained by least squares fitting; n = N / N u For dimensionless axial force, m = M / M u It is a dimensionless bending moment.

[0007] Furthermore, in step S3, the expression for the homogeneous generalized yield function for bending stability is established as follows: ; In the formula, It is the stability coefficient The function.

[0008] Furthermore, G When = 4, for a circular cross-section concrete-filled steel tube member, the expression for the homogeneous generalized yield function of the compressive-bending strength is: ; The corresponding homogeneous generalized yield function for bending stability is: ; Furthermore, G When = 4, for a dumbbell-shaped concrete-filled steel tube member, the expression for the homogeneous generalized yield function of the compressive-bending strength is: ; The expression for the corresponding homogeneous generalized yield function for bending stability is: ; Furthermore, G When = 4, for a rectangular cross-section concrete-filled steel tube member, the expression for the homogeneous generalized yield function of the compressive-bending strength is: ; The expression for the corresponding homogeneous generalized yield function for bending stability is: .

[0009] Furthermore, Expressed as follows: .

[0010] Furthermore, G can be either 2 or 3.

[0011] Furthermore, the plastic development coefficient γ m The method for determining this is as follows: establish the plastic development coefficient γ m The functional relationship between the constriction coefficient ξ and the plastic development coefficient γ m The functional relationship between the clamping coefficient ξ and the clamping coefficient ξ can be expressed using a logarithmic function or a power function, wherein the logarithmic function is: ; The power function is: ; In the formula, a1, b1, c1, a1, b1, c1 and d are undetermined coefficients, which are determined through regression analysis.

[0012] This invention further provides an application of an empirical model construction method for the correlation between N and M based on large-scale experimental data in determining the compressive-bending bearing capacity of concrete-filled steel tube members, comprising the following steps: Based on the empirical model construction method for the correlation between N and M based on a large number of experimental data, a homogeneous generalized yield function for bending stability is established. For concrete-filled steel tube members subjected to eccentric compression, the eccentricity is... e Given the design conditions, the following relationship between bending moment and axial force is established: ; Substituting the relationship between bending moment and axial force into the definitions of dimensionless axial force and dimensionless bending moment, we obtain a linear expression for m with respect to n: ; Right now , where k= These are known constants; The obtained linear expression of m with respect to n Substituting into the established homogeneous generalized yield function for bending stability In the middle, and ordered =0, resulting in a univariate equation in n; solve this equation to obtain the values ​​of n, and substitute these values ​​into the formula n=N / N uThe compressive-bending capacity N of the concrete-filled steel tube member under the current yield state is calculated.

[0013] By adopting the above technical solution, the present invention has the following beneficial effects: The above-mentioned empirical model construction method for the correlation between N and M based on a large number of experimental data has a homogeneous expression in function form, which can satisfy the proportional loading condition for plastic limit analysis. At the same time, it uses the confinement coefficient and stability coefficient as explicit influence parameters with clear physical meaning and simple function form, which is convenient for engineering application. Among them, the plastic development coefficient can accurately calculate the bending bearing capacity of the component under different confinement coefficients after introducing the confinement coefficient. The homogeneous generalized yield function of compression-bending stability can naturally degenerate into strength HGYF after introducing the stability coefficient, realizing a unified expression of strength and stability.

[0014] Therefore, the homogeneous generalized yield function constructed by the empirical model of the correlation between N and M based on a large number of experimental data can not only accurately describe the yield trajectory of the section under the combined action of axial force and bending moment, but also meet the proportional loading conditions required by the plastic limit analysis, thus providing a unified theoretical basis for the analysis of the ultimate bearing capacity and stable bearing capacity of the structure. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating a preferred embodiment of the present invention for constructing an empirical model of the correlation between N and M based on a large batch of experimental data.

[0016] Figure 2 This is a graph showing the factors influencing the plasticity development coefficient, where... Figure 2 (a) is a graph showing the influence of steel pipe area on the plasticity development coefficient. Figure 2 b) is a graph showing the influence of concrete area on the plastic development coefficient.

[0017] Figure 3 This is a diagram showing the influence of the hoop coefficient on the plastic development coefficient.

[0018] Figure 4 The figure shows a comparison of the calculation results of the plasticity development coefficient established by the empirical model construction method based on the correlation between N and M of a large number of experimental data in the preferred embodiment of the present invention, namely, the calculation results of the newly established formula, the calculation formula of the plasticity development coefficient of the CFST national standard, the calculation formula of the plasticity development coefficient proposed by Zhong Shantong, the calculation formula of the plasticity development coefficient of the CFST local standard, and the calculation results of the fiber model method.

[0019] Figure 5 The flexural bearing capacity calculation result M is obtained by using the empirical model construction method based on the correlation between N and M of a large number of test data established by the preferred embodiment of the present invention. ucCompared with the flexural bearing capacity M obtained through test, ut A comparison chart of the results.

[0020] Figure 6 for nm Correlation curve influencing factor analysis chart, among which, Figure 6 (a) shows the diameter-to-thickness ratio of the steel pipe. nm Impact analysis diagram of the correlation curve, Figure 6 (b) represents the yield strength of the steel pipe. nm Impact analysis diagram of the correlation curve, Figure 6 (c) represents the concrete compressive strength relative to nm Impact analysis diagram of the correlation curve.

[0021] Figure 7 For the hoop coefficient nm Impact analysis diagram of the correlation curve.

[0022] Figure 8 (a)-(f) are the values ​​taken respectively ξ A comparison chart of the data points calculated by substituting 0.5, 1.0, 1.5, 2.0, 3.0, and 4.0 into the homogeneous generalized yield function constructed in the preferred embodiment of the present invention and the data points calculated by the fiber model method.

[0023] Figure 9 For different slenderness ratios obtained n - m The relevant curves, among which, Figure 9 (a) is ξ The results obtained at different slenderness ratios when =0.5 n - m Related curves Figure 9 (b) is ξ The results obtained at different slenderness ratios when =1.5 n - m Related curves.

[0024] Figure 10 Based on Figure 9 Dimensionless values ​​obtained under different slenderness ratios n - m The relevant curves, among which, Figure 10 (a) is ξ dimensionless at different slenderness ratios when =0.5 n - m Related curves Figure 10 (b) is ξ dimensionless at different slenderness ratios when =1.5 n - m Related curves.

[0025] Figure 11This is a comparison chart of the calculation results of the homogeneous generalized yield function for bending stability according to the embodiments of the present invention and the fiber model method, wherein, Figure 11 (a) is ξ Comparison of calculation results of homogeneous generalized yield function for bending stability at 0.5 and fiber model method. Figure 11 (b) is ξ Comparison of calculation results of homogeneous generalized yield function for bending stability at 1.5 and fiber model method.

[0026] Figure 12 This is a comparison chart of the calculated value of the flexural bearing capacity obtained from the homogeneous generalized yield function of the flexural stability according to an embodiment of the present invention and the experimental value of the flexural bearing capacity obtained through experimental measurement. Figure 12 The icon on the right indicates the source of the 330 sets of data. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0029] Please see Figure 1 A preferred embodiment of the present invention provides a method for constructing an empirical model of the correlation between N and M based on a large amount of experimental data, comprising the following steps: S1, Determination of axial compressive strength bearing capacity, axial compressive stability bearing capacity, and flexural bearing capacity: The axial compressive strength bearing capacity N0 of the concrete-filled steel tube member is determined according to the formula... Calculate the axial compression stable bearing capacity. N u According to the formula Calculate the flexural bearing capacity M of the section. u According to the formula Calculate, where A sc f is the combined cross-sectional area of ​​the steel-concrete composite member. sc The combined axial compressive strength of the steel-concrete composite member. W is the stability coefficient. sc γ is the section modulus of flexural strength of a concrete-filled steel tube member.m This is the plastic development coefficient.

[0030] The formula for calculating axial compressive strength is the foundation for establishing the homogeneous generalized yield function. Major domestic and international standards and regulations, including the CFST national standard, CFST emblem, CFST local standard, American AISC, and European EC4, provide formulas for calculating CFST axial compressive strength and stability bearing capacity. The CFST emblem, AISC, EC4, AIJ, and the British Standards Institution's "Steel, concrete and composite bridges, Part 5: Code of practice for design of composite bridges" (BS 5400) all use the superposition principle, obtaining the axial compressive strength bearing capacity by superimposing the contributions of the steel pipe and concrete, thus neglecting to some extent the restraining effect of the steel pipe on the core concrete. In this embodiment, formulas for calculating axial compressive strength and stability bearing capacity are selected based on an experimental database.

[0031] (1.1) Calculation formula for axial compressive strength bearing capacity To avoid the influence of the specimen's compressive stability on the analysis results, this embodiment selects 150 short column members (in this embodiment, a short column of a circular cross-section CFST member is defined as having a slenderness ratio L / D ≤ ​​3.5) from 516 groups of members in the axial compression test database for analysis of axial compressive strength bearing capacity. These are not listed here. Because the analysis is to be compared with experimental results, the material strength of the members is calculated using standard values. Mathematical statistics are used to analyze the calculated axial compressive strength bearing capacity according to different specifications and regulations. N uc Test results of axial compressive strength bearing capacity N ut mean of ratios μ The coefficient of variation (COV) and the results are shown in Table 1.

[0032] Table 1 Comparison of Calculation Results from Various Regulations

[0033] Table 1 shows that EC4 overestimates the axial compressive strength bearing capacity, with the average value being 1.5% higher; the average values ​​of the calculation results from BS5400, AIJ, and AISC are lower, with errors exceeding 10%, indicating an underestimation of the axial compressive strength bearing capacity. In comparison, the axial compressive strength formula proposed by the CFST national standard and CFST local standard based on the unified CFST theory has higher accuracy in calculation results. Moreover, compared with the CFST local standard, the CFST national standard has better calculation accuracy and stability, with errors and coefficients of variation of 0.8% and 0.186, respectively. Based on the above analysis, this embodiment selects the CFST axial compressive strength bearing capacity calculation model provided by the CFST national standard for subsequent analysis and research. The CFST axial compressive strength bearing capacity calculation model provided by the CFST national standard is shown in the following formula: (1); In the formula, A sc The combined cross-sectional area of ​​the component. f sc The combined axial compressive strength of the component; f ck This refers to the standard value of the axial compressive strength of concrete. ξ Let be the clamping coefficient, and have . , A s This represents the cross-sectional area of ​​the steel pipe. f y For the yield strength of steel, A c This refers to the cross-sectional area of ​​the core concrete.

[0034] (1.2) Calculation formula for axial compression stability bearing capacity The following formula represents the axial compressive stability bearing capacity of a concrete-filled steel tube member. N u : (2); In the formula, This is the stability coefficient.

[0035] The stability coefficient of concrete-filled steel tubular members can be determined by national and local standards such as CFST, AISC, and EC4. The explicit expression, while the stability coefficient in Japanese AIJ and British BS5400 The expressions cannot be extracted separately, so these two specifications will not be listed here.

[0036] For the CFST national standard: (3); In the formula, It is the relative slenderness ratio of a concrete-filled steel tube member.

[0037] For CFST landmark (Fujian Provincial Engineering Construction Standard "Technical Specification for Steel Tube Concrete Structures" (DBJ / T13-51-2010)): (4); In the formula, It is the slenderness ratio of the concrete-filled steel tube component; 0, p These are the slenderness ratios that define the boundaries between elastic instability and elastoplastic instability; coefficients. a , b , c , d It needs to be based on the yield strength of the steel. f y Standard value of axial compressive strength of concrete f ck and steel content α s The parameters are calculated.

[0038] For AISC: (5); In the formula, N cr The critical force of the component.

[0039] For EC4: (6); In the formula, For calculating parameters, It is the relative slenderness ratio of a concrete-filled steel tube member.

[0040] This invention further compares and analyzes the calculation accuracy of the above stability coefficient expressions. For ease of separate analysis of the stability coefficient, equation (1) is uniformly adopted. The formula for calculating axial compressive strength bearing capacity is shown. From a database of 516 axial compression tests, 366 groups of steel-concrete composite members with medium to long columns (e.g., short columns in circular cross-section CFST members are defined as having a slenderness ratio L / D > 3.5) were selected, and the calculated values ​​from various specifications were analyzed. N uc Compared with test values N ut mean of ratios μ The coefficient of variation (COV) is used to characterize the influence of the stability coefficient in each specification, as shown in Table 2. It can be seen that the mean axial compression stability bearing capacity calculated by the CFST national standard and CFST local standard is too small, with an error exceeding 11%, indicating that their stability coefficient calculations are conservative. In contrast, AISC and EC4 achieve higher calculation accuracy, with EC4 showing the highest accuracy, with an error of less than 5%. Therefore, this embodiment uses the stability coefficient expression provided by EC4 to analyze and study the axial compression stability bearing capacity of CFST columns.

[0041] Table 2 Comparison of Calculation Results of Axial Compression Stability Bearing Capacity under the Code Stability Coefficient

[0042] Axial compressive strength bearing capacity in CFST national standard N Stability coefficients in 0 and EC4 The axial compression stability bearing capacity of the CFST member can be obtained from the calculation expression. N u The calculation formula is as follows: (7); In the formula, The stability coefficient; N 0 represents the axial compressive strength bearing capacity, and we have: (8); (9); In equations (7), (8), and (9), A s This represents the cross-sectional area of ​​the steel pipe; A c The cross-sectional area of ​​the core concrete; This is the clamping coefficient; f ck and f y These represent the standard value of the axial compressive strength of concrete and the yield strength of steel, respectively. It should be noted that the material strength can be taken as the design value or the standard value according to the calculation needs. For the calculation parameters, we have: (10); In the formula, For the relative slenderness ratio of concrete-filled steel tubular members, this embodiment uses the concise regularized slenderness ratio calculation expression from the CFST national standard. : (11); In the formula, E sc This represents the combined elastic modulus of the cross section of a concrete-filled steel tube member, where L is the length of the concrete-filled steel tube member and D is the diameter of the concrete-filled steel tube member.

[0043] The axial compression stability bearing capacity of 516 CFST axial compression members in the axial compression test database was calculated and analyzed using equation (7). The material strength was also calculated using standard values. The mean of the ratio of the calculated value to the experimental value was analyzed using mathematical statistics. μThe mean value of the coefficient of variation (COV) is 0.970, with an error of only 3% compared to the experimental value, and the coefficient of variation is 0.188, indicating that the calculation of the axial compression stability bearing capacity of the CFST component using formula (7) can achieve high calculation accuracy and good stability.

[0044] (1.3) Bending capacity of the section M u Calculation When the external load on a concrete-filled steel tube member exceeds the elastic range, a portion of the cross-section will enter a plastic state. As the external load increases, the plastic zone on the cross-section gradually expands until it reaches the ultimate limit state of bearing capacity. The bending moment at this point is called the flexural bearing capacity of the member. M u Typically greater than the elastic resistance of the cross section. M e The ratio of the flexural capacity to the elastic resistance of a structural member section. M u / M e This is called the plastic development coefficient. γ m This is used to characterize the plastic development capability of a component's cross-section, namely: (12); In this embodiment, a plastic development coefficient γ is established. m The functional relationship between the constriction coefficient ξ and the plastic development coefficient γ is specifically... m The functional relationship between the clamping coefficient ξ and the clamping coefficient ξ is expressed using a logarithmic function or a power function, wherein the logarithmic function is: (13); The power function is: (14); In the formula, a1, b1, c1, a2, b2, c2, and d are all undetermined coefficients, which are determined through regression analysis.

[0045] In this embodiment, a comprehensive experimental analysis of the model is conducted using the fiber model method to determine the influencing parameters of the plastic development coefficient. Finally, regression analysis is used to establish the cross-sectional plastic development coefficient γ of the CFST. m The calculation model is as follows: First, based on the material strength and geometric requirements of the components as determined by model tests and engineering practice, a batch of representative CFST bending members were designed within a certain range. In this embodiment, a circular cross-section CFST bending member is taken as an example, and the yield strength of the steel is taken as... f y =200~800MPa, standard value of compressive strength of concrete cube f cu,k=30~80MPa, outer diameter of steel pipe D =50~500mm, cross-sectional diameter to thickness ratio D / t CFST bending members with circular cross-sections of 20~120 mm. f y 100MPa interval f cu,k 10MPa interval D 150mm interval D / t By taking values ​​at intervals of 20, 1008 CFST bending member models can be established. To avoid extreme cases and fully utilize the deformation coordination performance between the steel tube and the core concrete, and based on engineering practice, members with a confinement coefficient ξ > 6.0 are removed. A total of 984 pure bending model specimens are established, as shown in Table 3.

[0046] Table 3. Parameter values ​​of pure bending specimens in numerical simulation.

[0047] Each selected value within the above range f y , f cu,k , D and t With a set of values ​​for (steel pipe wall thickness), a fiber model can be established for the flexural bearing capacity analysis of CFST members, and the section resistance can be obtained using the fiber model method. M uc Substituting into equation (12) yields a corresponding cross-sectional plastic development coefficient. γ m .because γ m The plasticity development coefficient is closely related to the cross-sectional material and geometric parameters of the component; therefore, it is necessary to analyze the main influencing factors and variation patterns of the coefficient. For each group... f y , f cu,k , D and t The values ​​that can be taken are specific A s , A c , f y , f ck and γ m Therefore, this section mainly analyzes... A s , A c , fy , f ck plasticity development coefficient γ m The influence pattern, such as Figure 2 As shown.

[0048] Geometric parameters of CFST members with circular cross-section D , t and material parameters f y , f cu,k The confinement coefficient varies depending on the value of . Furthermore, as shown in Table 3, the confinement coefficient... ξ The variation range is 0.12 to 5.55, covering the range commonly used in engineering. Because... f y , f cu,k , D and t Each set of values ​​can yield a specific hoop coefficient. ξ Meanwhile, the flexural bearing capacity of the section was obtained using the fiber model method. M uc Substituting these values ​​into equation (12) yields the corresponding plastic development coefficient. γ m Thus we obtain ξ and γ m The influence pattern, such as Figure 3 As shown.

[0049] from Figure 3 It can be seen from this that the plasticity development coefficient γ m With the clamp coefficient ξ There is a clear nonlinear relationship between them. The relationship between them can be established by using a logarithmic function or a power function, as shown in equation (13) and equation (14) respectively.

[0050] Flexural strength obtained by combining fiber model method M uc And equation (12), using regression analysis to calculate the undetermined coefficients in equations (13) and (14) respectively. a 1 = 1.163, b 1 = 0.63, c 1 = 0.176 and a 2 = -0.093, b 2 = 2.01, c 2 = 0.31, d=-0.656, and the fitting correlation coefficients of equations (13) and (14) are both 0.974, with residual mean square errors of 0.993 and 0.994 respectively. This indicates that the accuracy of the two function expressions is not significantly different. In this embodiment, the logarithmic function equation (13) is chosen more simply as the logarithmic function. γ m Substituting the calculation expression into the undetermined coefficients of the circular cross-section steel-concrete composite member obtained from the calculation, we get equation (15): Circular cross-section: (15); Similarly, by referring to the above steps, the plastic development coefficients of rectangular and dumbbell-shaped steel-concrete composite members can be obtained. γ m The calculation expression: Rectangular section: (16); Dumbbell-shaped cross-section: (17); The accuracy of the plastic development coefficient calculation model established in this embodiment is verified below. Taking a circular cross-section steel-concrete composite member as an example, the CFST national standard, CFST local standard, and Zhong Shantong [Zhong Shantong. Steel-concrete composite structures [M]. Beijing: Tsinghua University Press, 2003] also provide calculation models for the plastic development coefficient, as shown in equations (18), (19), and (20), respectively: (18); (19); (20); Further utilizing equations (18), (19), and (20), the plastic development coefficient calculated according to Table 3 and equation (15) (i.e., the newly created formula) established in the embodiments of the present invention is compared with the plastic development coefficient calculated by the fiber model method. The comparison results are as follows: Figure 4 As shown.

[0051] from Figure 4 As can be seen, the plastic development coefficient in the CFST national standard uses a fixed value and does not consider the influence of material strength and geometric dimensions, making it impossible to accurately calculate the plastic development coefficient of components under different hoop coefficients; the calculation results of the CFST local standard are generally too small; and the calculation formula proposed by Zhong Shantong is generally overestimated. ξ The results at smaller times are underestimated. ξ The result when it is larger, and ξ Beyond a certain range, the curve shows a downward segment, which is inconsistent with the actual situation. In contrast, the curve obtained by the plastic development coefficient calculation formula established in the embodiment of the present invention passes through most of the experimental data points, and the overall result is in good agreement with the calculation result of the fiber model method.

[0052] After obtaining the expression of the calculation model for the plastic development coefficient, i.e., formulas (15)-(17), the flexural bearing capacity M of the steel-concrete composite member can be established according to the unified theory. u The expression is shown in equation (21) below: .

[0053] Based on the experimental database, the calculation formula for the flexural bearing capacity of the cross section established in this embodiment is compared with the calculation formulas provided by the CFST national standard, CFST local standard, American steel structure design code AISC, Japanese standard AIJ, European standard EC4, and British standard BS5400, thereby verifying the applicability and accuracy of the calculation formula for the flexural bearing capacity of the cross section established in this embodiment.

[0054] Formulas (18) and (19) respectively give the calculation models of the plastic development coefficient of the CFST national standard and the CFST local standard. Substituting the calculated plastic development coefficient into the above formula (12) will give the surface flexural bearing capacity M. u The calculation formula can be used to calculate the flexural capacity, which will not be elaborated here. International standards and codes such as AISC, EC4, BS5400, and AIJ are based on limit equilibrium theory, solving for the flexural capacity through the internal force equilibrium conditions of the section. Except for EC4, AISC, AIJ, and BS5400 do not consider the contribution of concrete to the flexural capacity. The calculation formula for the flexural capacity of EC4 is as follows: (twenty two); AISC uses different formulas for calculating flexural capacity depending on the range of the generalized width-to-thickness ratio. The section is divided into compact (limiting slenderness ratio) sections. λ p Non-compact and slender (boundary length-to-slenderness ratio) λ r Three types of cross-sections: (twenty three); The formula for calculating flexural bearing capacity recorded in AIJ is as follows: (twenty four); In the formula, D represents the diameter of the circular CFST section, and t represents the wall thickness of the steel pipe.

[0055] The formula for calculating flexural bearing capacity is described in BS5400: (25); Subsequently, based on the collected data from 121 sets of flexural bearing capacity tests, the accuracy and applicability of different flexural bearing capacity calculation formulas were compared, and the calculation results of different formulas were statistically analyzed according to the principles of mathematical statistics.M uc With test results M ut mean of ratios μ The coefficient of variation (COV) is shown in Table 4.

[0056] Table 4 Calculation results of flexural bearing capacity under different specifications

[0057] As can be seen from the table, the calculation results of BS5400, AIJ, and AISC are all much smaller than the experimental results, indicating that ignoring the contribution of concrete to the flexural bearing capacity will lead to overly conservative calculation results. The average value of the calculation results of the CFST national standard is too large, and the plastic development coefficient of the circular CFST section is a fixed value of 1.2, which cannot be applied to circular CFST pure bending members with different material strengths and geometric dimensions. Its rationality and applicability are poor, resulting in unstable calculation results. In contrast, the calculation results of the CFST standard and EC4 are closer to the experimental results, but the calculation error is still greater than 11.3%. The calculation results of the formula in this embodiment have an error of less than 8.1% compared with the experimental results, and can achieve higher calculation accuracy than other formulas. This shows that the flexural bearing capacity formula established in this embodiment can more accurately predict the flexural bearing capacity of the member, and the coefficient of variation is 0.135, indicating good calculation stability.

[0058] To more intuitively illustrate the accuracy of the flexural bearing capacity calculation formula established in this embodiment, the flexural bearing capacity of 121 circular CFST members in the pure bending test database was calculated using the formula, and the distribution of these values ​​was compared with the test results. Figure 5 As shown in the figure, the calculation results of the formula in this embodiment are compactly distributed on both sides of the contour lines, indicating that the calculation results are in good agreement with the experimental results. The flexural bearing capacity established in this embodiment has good calculation accuracy and stability.

[0059] S2, Establishment of the homogeneous generalized yield function for compressive-bending strength: Define the dimensionless axial force n = N / N u and dimensionless bending moment m=M / M u The correlation data points between axial force N and bending moment M in concrete-filled steel tube members under different material strengths and geometric parameters were calculated using the fiber model method, with the confinement coefficient as the basis. ξ As a parameter influencing the homogeneous generalized yield function, a homogeneous generalized yield function for compressive-bending strength is established through regression analysis.

[0060] In this embodiment, the homogeneous generalized yield function of compressive-bending strength is established. The expression is: (26); In the formula, GIndicates the clamping coefficient ξ The highest power of a higher-order polynomial. k 0~ k G The coefficients are undetermined and obtained by least squares fitting; n = N / N u For dimensionless axial force, m = M / M u The bending moment is dimensionless; N and M represent the axial force and bending moment of the member under the current yield state, respectively.

[0061] The relationship between axial force and bending moment when a component section reaches the yield state can be fully reflected by the homogeneous generalized yield function (HGYF) of compressive-bending strength. Currently, the cross-sectional internal force relationships provided by domestic and international standards are often expressed as piecewise non-homogeneous functions, which cannot satisfy the proportional loading conditions required for plastic limit analysis. Therefore, this embodiment of the invention utilizes the fiber model method and combines it with the previously determined formulas for calculating axial compression and bending bearing capacity to establish a homogeneous generalized yield function for CFST component strength. Furthermore, considering the influence of the stability coefficient, a homogeneous generalized yield function for compressive-bending stability is established. This embodiment utilizes... L / D This invention analyzes and establishes the compressive-bending strength HGYF of a short steel-concrete tubular (CFST) member with a strength of 3. To reasonably analyze and determine the compressive-bending strength HGYF of the CFST member, this invention involves extensive theoretical calculations. During the application of axial force, the eccentricity is continuously changed by adjusting the position of the pressure loading point to calculate the strength. n - m Correlation, among which n and m This represents dimensionless axial force and bending moment. For CFST members with circular cross-sections, variations in material strength and geometric dimensions are considered within a certain range. Specifically, the yield strength of the steel pipe... f y =200~800MPa, standard value of compressive strength of concrete cube f cu,k =30~80MPa, cross-sectional diameter to thickness ratio D / t =20~120, to facilitate parameter control, the outer diameter of the steel pipe is fixed. D =200mm. When f y 100MPa interval f cu,k 10MPa interval D / t By using values ​​at intervals of 20, 252 CFST compression-bending member models can be created. To avoid extreme cases and fully utilize the deformation coordination performance between the steel tube and the core concrete, the confinement coefficient is removed here based on engineering practice. ξFor components with a strength greater than 6.0, a total of 246 compression-bending component models were established, and the model parameters are shown in Table 5.

[0062] Table 5. Parameter values ​​for the compression-bending member model.

[0063] Furthermore, the data in Table 5 were used to conduct... n - m Analysis of influencing factors of correlation. In this embodiment, the fiber model method is used to calculate and analyze the influence of the material strength and geometric dimensions of the component on the strength of the circular cross-section CFST component. n - m The influence of the correlation curve, such as Figure 6 As shown, Figure 6 The effects of three parameters—yield strength of steel pipe, compressive strength of concrete, and diameter-to-thickness ratio—on the strength of circular cross-section CFST members were discussed. n - m The impact of the correlation curve.

[0064] Under otherwise identical conditions, by Figure 6 (a) It can be seen that when f y =400MPa f cu,k At a pressure of 50 MPa, the diameter-to-thickness ratio of a circular cross-section CFST member is compared to... n - m The curve has a significant impact, and as the diameter-to-thickness ratio increases, the curve expands outwards, and in... D / t >After 40, it will appear m >1.0, the more similar it is to reinforced concrete components; by Figure 6 (b) Yes, when f cu,k =50MPa D / t When the yield strength of the steel pipe is 80, f y right n - m The curve also has a significant impact, as... f y As the value increases, the curve approaches the origin, indicating that the steel pipe contributes more to the stress process; Figure 6 (c) Yes, when f y =400MPa D / t When the concrete cube compressive strength is 80, f cu,k right n - m The curve also has an impact, asf cu,k As the value increases, the curve expands outward, indicating that concrete contributes more during the stress process. At this point, the mechanical properties of CFST members are similar to those of reinforced concrete members.

[0065] In summary, the cross-sectional geometry and material strength of circular cross-section CFST members have a significant impact on... n - m The correlations all have a significant impact, and it can be seen that when the steel pipe plays a dominant role, the curve approaches the origin; conversely, when the concrete plays a dominant role, the curve expands outward, showing... m For cases where the value is greater than 1.0, it can be seen that the influence of the diameter-to-thickness ratio, steel pipe, and concrete strength is somewhat correlated, while the confinement coefficient... ξ=f y A s / f ck A c It can comprehensively reflect the balance between steel pipe and concrete, therefore, further comparison of the confinement coefficient is necessary. n - m To facilitate comparative analysis, the influence of correlation patterns is explained. Figure 7 The material strength of the components is uniformly set as follows: f y =400MPa f cu,k =50MPa, the influence pattern is as follows Figure 7 As shown. It can be seen from this that the clamping coefficient affects... n - m The correlation has a significant impact and comprehensively reflects... Figure 6 The pattern (a~c) shows that as the clamping coefficient increases, the mechanical properties of the steel pipe become more prominent, and the curve approaches the origin more closely, comprehensively reflecting the influence of material strength and cross-sectional geometry.

[0066] Therefore, in this embodiment of the invention, the hoop coefficient is used as the influence parameter of the homogeneous generalized yield function of the compressive bending strength, and the axial force and bending moment bearing capacity of the model component in Table 5 are calculated by using the fiber model method. The homogeneous generalized yield function (HGYF) of the compressive bending strength of the circular cross section CFST component is established by regression analysis, as shown in Equation (26).

[0067] Data points were obtained using the fiber model method. , N g To fit the number of collocation points, the undetermined coefficients in the above formula can be obtained according to the principle of least squares. k 0~ k G The value of is defined by the sum of squared residuals as shown in equation (27). with mean squared deviation The fitting accuracy was verified, and the calculation results are shown in Table 6.

[0068] (27); Table 6 Sum of Squares and Root Mean Square of Residuals

[0069] As shown in Table 6, when G As the value of increases gradually from 1 to 5, the sum of squared residuals of the fitting results with mean squared deviation As the yield strength decreases, the fitting accuracy of the homogeneous generalized yield function (HGYF) for bending strength also improves. G When =4 and 5, All are within 0.5, and the standard deviation is... The stability of 3.4% indicates that the HGYF expression for the compressive bending strength has high fitting accuracy at this point, and from a computational efficiency perspective, G When =4, the number of iterations is 27, which is relatively... G =5 has higher computational efficiency. Therefore, this embodiment selects =5. G =4. Establish the homogeneous generalized yield function for the compressive-bending strength of the CFST member: (28); In this embodiment of the invention, respectively take ξ =0.5, 1.0, 1.5, 2.0, 3.0, 4.0, and substitute them into equation (28) for calculation. Compare the calculation results of equation (28) with the data points calculated by the fiber model method. The results are as follows: Figure 8 As shown, the calculated curve of the bending strength HGYF can pass through the data points of the fiber model method uniformly and accurately, and the two results are in good agreement, proving that the calculation accuracy of the bending strength HGYF established in this embodiment is high.

[0070] Similarly, a homogeneous generalized yield function for the compressive-bending strength can be established for the axial force and bending moment relationship model of CFST members with rectangular and dumbbell-shaped cross sections, without considering stability effects, and when... G When = 4, for a dumbbell-shaped concrete-filled steel tube member, the expression for the homogeneous generalized yield function of the compressive-bending strength is: (29); For a steel-concrete composite member with a rectangular cross-section, the expression for the homogeneous generalized yield function of the compressive-bending strength is as follows: (30)

[0071] S3, Establishment of the homogeneous generalized yield function for bending stability: Based on the aforementioned homogeneous generalized yield function for bending strength, a stability coefficient is introduced. To investigate the influence of bending stability, a homogeneous generalized yield function is established.

[0072] Specifically, the expression for the homogeneous generalized yield function for bending stability is as follows: (31); when G When = 4, the established homogeneous generalized yield function for bending stability is: (32); In the formula, It is the stability coefficient The function, considering the stability coefficient When =1, =1, which allows it to revert to the axial compression state, therefore Expressed as follows: (33); In the formula, G For higher-order polynomials The highest power, k 1~ k G These are coefficients to be determined.

[0073] For a dumbbell-shaped concrete-filled steel tube member, the expression for the homogeneous generalized yield function for compressive-bending stability is as follows: (34).

[0074] For a steel-concrete composite member with a rectangular cross-section, the expression for the homogeneous generalized yield function for compressive-bending stability is as follows: (35)

[0075] The stability problem in CFST arch bridge structures is significant, and the homogeneous generalized yield function (HGYF) for compressive-bending stability is fundamental to studying the stable bearing capacity of CFST arch bridges. Therefore, this invention uses the compressive-bending strength HGYF of a circular cross-section CFST bridge as a basis to study the influence of stability factors on HGYF, and then establishes a homogeneous generalized yield function HGYF for compressive-bending stability considering stability effects. Specifically, taking... Figure 7 Component parameters f y =400MPa f cu,k =50MPa ξ Members with a slenderness ratio of 0.5 to 4.0 in increments of 0.5 are used as the sample basis for studying the homogeneous generalized yield function of compressive-bending stability. The slenderness ratio of the members is controlled by changing the member length. =4 L / DThe changes were analyzed, and the improved dimensional model method was used to calculate the differences. In the case of components n - m The relationship curve is used to analyze the slenderness ratio of the components. right n - m The influence of the relationship curve.

[0076] This embodiment uses the hoop coefficient ξ We will analyze the slenderness ratio of components with values ​​of 0.5 and 1.5 as representatives. right n - m The influence of the curve, such as Figure 9 As shown. It can be seen that, n - m Relationship curve is affected The impact is significant, with The increase, n - m The relationship curve gradually approaches the origin. Further analysis is needed. Figure 9 It was discovered that when When the value of ... The effect on the axial compressive stability bearing capacity of the circular cross-section CFST member is significant, while the effect on the flexural bearing capacity is very small and can be ignored.

[0077] Furthermore, by utilizing the search... Figure 9 In N / N u and M / M u , thus obtaining dimensionless n - m Correlation curves, such as Figure 10 As shown in the figure. It can be seen from the figure that, with... The increase, n - m As the curve gradually moves towards the origin, the area between it and the coordinate axes gradually decreases, indicating... right n - m The influence of the correlation curve is significant, and the impact of stability on the correlation of internal forces needs to be considered.

[0078] Therefore, the embodiments of the present invention consider the influence of stability, and in order to maintain a consistent expression with the bending strength HGYF, a stability coefficient is added to the bending strength HGYF of the CFST member, and a bending stability homogeneous generalized yield function HGYF as shown in equation (31) is established.

[0079] Substituting equation (33) into equation (32), the data points are calculated using the fiber model method. , N g To fit the number of collocation points, the undetermined coefficients in the above formula can be obtained according to the principle of least squares. k 0~ k G The value of is defined by the sum of squared residuals in equation (27). with mean squared deviation The fitting accuracy was verified, and the calculation results are shown in Table 7.

[0080] Table 7 Sum of Squares and Root Mean Square of Residuals

[0081] As shown in Table 7, with the highest power... G As the sum of squared residuals of the fitting results increases, with mean squared deviation As the value gradually decreases, the fitting accuracy of HGYF also increases. G When ≥2, the sum of squared residuals and the root mean square error gradually stabilize, and when G When the value is 2 or 3, the number of iterations is 16, which is the most efficient. To make the calculation expression more concise, this embodiment selects... G =2 Create an expression : (36); At this point, the calculated sum of squared residuals The mean square error is 0.705. The value is 0.030, indicating a high fitting accuracy.

[0082] In this embodiment, the homogeneous generalized yield function for bending stability is compared with the calculation results of the fiber model method. The clamping coefficient is used as the reference. ξ Taking components with values ​​of 0.5 and 1.5 as examples for analysis, such as... Figure 11 As shown in the figure, the solid line represents the result of the fiber model method, and the dashed line represents the calculation result of the homogeneous generalized yield function for compression-bending stability established in this embodiment. It can be seen that the two curves are in good agreement overall, indicating that the homogeneous generalized yield function for compression-bending stability established in this embodiment can accurately reflect the internal force correlation of CFST members.

[0083] The accuracy and applicability of the homogeneous generalized yield function for compressive-bending stability established in this embodiment were verified using the CFST component eccentric compression test database. The axial compressive stability and flexural capacity of 365 circular cross-section CFST components in the eccentric compression test database were calculated using equations (2) and (21), respectively. These values ​​were then substituted into the HGYF defined in equation (32) to calculate the compressive-bending capacity of the 365 circular cross-section CFST components in the eccentric compression test database. It should be noted that the numerical simulation component for establishing the homogeneous generalized yield function for compressive-bending stability... ξ The value ranges from 0.3 to 4.0. Therefore, after filtering 365 sets of test data in the bias test database, ξ A total of 330 groups of components with a strength ranging from 0.3 to 4.0 were identified. The calculation results of HGYF were compared with the experimental results, such as... Figure 12 As shown, the calculated data points of the homogeneous generalized yield function for bending stability are evenly distributed near the contour lines, indicating that the calculated results of the homogeneous generalized yield function for bending stability established in this embodiment are in good agreement with the experimental results.

[0084] Furthermore, quantitative analysis was conducted using mathematical statistics methods. Figure 12 The mean and coefficient of variation of the ratio of calculated to experimental values ​​of the bending capacity under medium pressure are shown. The calculated mean is 1.026, and the coefficient of variation is 0.168, indicating that the calculation accuracy of the homogeneous generalized yield function for bending stability established in this embodiment is high. It should be noted that the database used in this invention comes from different research groups, and the specimen preparation, testing equipment, and operating methods are different. It also includes a large number of components with different geometric dimensions and material parameters, proving that the homogeneous generalized yield function for bending stability established in this embodiment has wide applicability.

[0085] The above-mentioned empirical model construction method for the correlation between N and M based on a large number of experimental data has a homogeneous expression in function form, which can satisfy the proportional loading condition for plastic limit analysis. At the same time, it uses the confinement coefficient and stability coefficient as explicit influence parameters with clear physical meaning and simple function form, which is convenient for engineering application. Among them, the plastic development coefficient can accurately calculate the bending bearing capacity of the component under different confinement coefficients after introducing the confinement coefficient. The homogeneous generalized yield function of compression-bending stability can naturally degenerate into strength HGYF after introducing the stability coefficient, realizing a unified expression of strength and stability.

[0086] Therefore, the homogeneous generalized yield function constructed by the above-mentioned empirical model of the correlation between N and M based on a large number of experimental data can not only accurately describe the yield trajectory of the section under the combined action of axial force and bending moment, but also meet the proportional loading conditions required by the plastic limit analysis, thus providing a unified theoretical basis for the analysis of the ultimate bearing capacity and stable bearing capacity of the structure.

[0087] This invention further provides an application of an empirical model construction method for the correlation between N and M based on large-scale experimental data in determining the compressive-bending bearing capacity of concrete-filled steel tube members, comprising the following steps: Based on the empirical model construction method for the correlation between N and M based on a large number of experimental data, a homogeneous generalized yield function for bending stability is established. For concrete-filled steel tube members subjected to eccentric compression, the eccentricity is... e Given the design conditions, the following relationship between bending moment and axial force is established: ; Substituting the relationship between bending moment and axial force into the definitions of dimensionless axial force and dimensionless bending moment, we obtain a linear expression for m with respect to n: ; Right now , where k= These are known constants; The obtained linear expression of m with respect to n Substituting into the established homogeneous generalized yield function for bending stability In the middle, and ordered =0, resulting in a univariate equation in n; solve this equation to obtain the values ​​of n, and substitute these values ​​into the formula n=N / N u The compressive-bending capacity N of the concrete-filled steel tube member under the current yield state is calculated.

[0088] The above description is a detailed description of the preferred embodiments of the present invention. However, the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modifications made under the technical spirit of the present invention should fall within the patent scope covered by the present invention.

Claims

1. A method for constructing an empirical model of the correlation between N and M based on large-scale experimental data, characterized in that, Includes the following steps: S1, Determination of axial compressive strength bearing capacity, axial compressive stability bearing capacity, and flexural bearing capacity: The axial compressive strength bearing capacity N0 of the concrete-filled steel tube member is determined according to the formula... Calculate the axial compression stable bearing capacity. According to the formula Calculate the flexural bearing capacity M of the section. u According to the formula Calculate, where A sc f is the combined cross-sectional area of ​​the steel-concrete composite member. sc The combined axial compressive strength of the steel-concrete composite member. W is the stability coefficient. sc γ is the section modulus of flexural strength of a concrete-filled steel tube member. m The plastic development coefficient; S2, Establishment of the homogeneous generalized yield function for compressive-bending strength: Define the dimensionless axial force n = N / N u and dimensionless bending moment m=M / M u The correlation data points between axial force N and bending moment M in concrete-filled steel tube members under different material strengths and geometric parameters were calculated using the fiber model method, with the confinement coefficient as the basis. ξ As a parameter influencing the homogeneous generalized yield function, a homogeneous generalized yield function for compressive-bending strength is established through regression analysis. S3, Establishment of the homogeneous generalized yield function for bending stability: Based on the aforementioned homogeneous generalized yield function for bending strength, a stability coefficient is introduced. To investigate the influence of bending stability, a homogeneous generalized yield function is established.

2. The method for constructing an empirical model of the correlation between N and M based on large-scale experimental data as described in claim 1, characterized in that, In step S2, the expression for the homogeneous generalized yield function of the compressive-bending strength is established as follows: ； In the formula, G Indicates the clamping coefficient ξ The highest power of a higher-order polynomial. k 0~ k G The coefficients are undetermined and obtained by least squares fitting; n = N / N u For dimensionless axial force, m = M / M u It is a dimensionless bending moment.

3. The method for constructing an empirical model of the correlation between N and M based on large-scale experimental data as described in claim 2, characterized in that, In step S3, the expression for the homogeneous generalized yield function for bending stability is established as follows: ； In the formula, It is the stability coefficient The function.

4. The method for constructing an empirical model of the correlation between N and M based on large-scale experimental data as described in claim 3, characterized in that, G When = 4, for a circular cross-section concrete-filled steel tube member, the expression for the homogeneous generalized yield function of the compressive-bending strength is: ； The corresponding homogeneous generalized yield function for bending stability is: 。 5. The method for constructing an empirical model of the correlation between N and M based on large-scale experimental data as described in claim 3, characterized in that, G When = 4, for a dumbbell-shaped concrete-filled steel tube member, the expression for the homogeneous generalized yield function of the compressive-bending strength is: ； The expression for the corresponding homogeneous generalized yield function for bending stability is: 。 6. The method for constructing an empirical model of the correlation between N and M based on large-scale experimental data as described in claim 3, characterized in that, G When = 4, for a rectangular cross-section concrete-filled steel tube member, the expression for the homogeneous generalized yield function of the compressive-bending strength is: ； The expression for the corresponding homogeneous generalized yield function for bending stability is: 。 7. The method for constructing an empirical model of the correlation between N and M based on large-scale experimental data as described in claim 3, characterized in that, Expressed as follows: 。 8. The method for constructing an empirical model of the correlation between N and M based on large-scale experimental data as described in claim 7, characterized in that, G can be either 2 or 3.

9. The method for constructing an empirical model of the correlation between N and M based on large-scale experimental data as described in claim 1, characterized in that, Plasticity development coefficient γ m The method for determining this is as follows: establish the plastic development coefficient γ m The functional relationship between the constriction coefficient ξ and the plastic development coefficient γ m The functional relationship between the clamping coefficient ξ and the clamping coefficient ξ can be expressed using a logarithmic function or a power function, wherein the logarithmic function is: ； The power function is: ； In the formula, a1, b1, c1, a1, b1, c1 and d are undetermined coefficients, which are determined through regression analysis.

10. An application of an empirical model construction method for the correlation between N and M based on large-scale experimental data in determining the compressive-bending bearing capacity of concrete-filled steel tube members, characterized in that... Includes the following steps: According to claim 1, the empirical model construction method for the correlation between N and M based on a large number of experimental data establishes a homogeneous generalized yield function for bending stability. For concrete-filled steel tube members subjected to eccentric compression, the eccentricity is... e Given the design conditions, the following relationship between bending moment and axial force is established: ； Substituting the relationship between bending moment and axial force into the definitions of dimensionless axial force and dimensionless bending moment, we obtain a linear expression for m with respect to n: ； Right now , where k= These are known constants; The obtained linear expression of m with respect to n Substituting into the established homogeneous generalized yield function for bending stability In the middle, and ordered =0, resulting in a univariate equation in n; solve this equation to obtain the values ​​of n, and substitute these values ​​into the formula n=N / N u The compressive-bending capacity N of the steel-concrete composite member under the current yield state is calculated.

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