A method for calculating the equivalent elastic modulus of reinforced concrete rectangular columns in flexural finite element modeling of the entire structure

Abstract

The present invention belongs to the field of civil engineering, and relates to a method for calculating the equivalent elastic modulus of bending of a reinforced concrete rectangular column during finite element modeling of the entire structure. It is characterized in that in the overall finite element simulation model of the reinforced concrete structure, the interaction between the steel bar and the concrete and the material properties thereof do not need to be reflected, so a homogeneous model is usually used to model the reinforced concrete components. The equivalent elastic modulus of bending of some components is obtained by finite element virtual simulation of some components, and the calculation formula of the equivalent elastic modulus of bending is obtained by using a multivariate regression model, thereby obtaining a general method for calculating the equivalent elastic modulus of bending of reinforced concrete rectangular columns. The present invention uses the calculation formula of the equivalent elastic modulus of bending to provide a calculation method for the elastic modulus parameter value of the column during the overall finite element modeling of the reinforced concrete structure, thereby simplifying the overall reinforced concrete structure modeling process and improving the efficiency of the structural finite element calculation.

Description

Technical Field

[0001] The invention belongs to the field of civil engineering and relates to a method for calculating the bending equivalent elastic modulus of a reinforced concrete rectangular column during overall structural finite element modeling. Background Art

[0002] In the overall finite element simulation model of reinforced concrete structure, the interaction between steel bars and concrete often does not need to be considered, and their respective material properties do not need to be reflected. Therefore, a homogeneous model is usually used to model reinforced concrete components. However, the influence of steel bars on the overall bending stiffness of the components cannot be ignored. The influence of steel bars on the stiffness of the components can be reflected by changing the elastic modulus parameters of the homogeneous material, that is, the equivalent bending elastic modulus is used to replace the elastic modulus of the original component. This not only ensures the accuracy of the finite element model, but also reduces the calculation cost of the finite element model.

[0003] In the finite element modeling of reinforced concrete rectangular columns, how to quickly and accurately calculate the equivalent flexural elastic modulus of the homogeneous model has always been a key and difficult problem in finite element modeling. Some literatures adopt the method of empirical value taking, but this will produce certain errors. There is still no mature and reliable calculation method for the equivalent flexural elastic modulus of reinforced concrete rectangular columns. Summary of the invention

[0004] The purpose of the invention is to provide a method for calculating the bending equivalent elastic modulus of a reinforced concrete rectangular column for an overall finite element model of a reinforced concrete structure.

[0005] The present invention is achieved through the following technical solutions:

[0006] Step 1: Establish a multivariate regression mathematical model of the equivalent elastic modulus of reinforced concrete rectangular columns:

[0007] The reinforcement ratio parameter x2 is:

[0008]

[0009] Where: A1 is the area of ​​the longitudinal reinforcement of the column cross section, A is the cross-sectional area of ​​the column;

[0010] The ratio of the moment of inertia provided by the steel bar to the moment of inertia of the section is x4:

[0011]

[0012] Where: n is the number of longitudinal reinforcements, y i is the distance from the i-th longitudinal reinforcement to the centroidal axis, A i is the cross-sectional area of ​​the i-th longitudinal reinforcement

[0013] Multiple regression mathematical model:

[0014]

[0015] Where: is the required equivalent elastic modulus of bending, b0 is the regression unknown constant, b1 is the influencing parameter of the elastic modulus of plain concrete, b2 is the influencing parameter of the reinforcement ratio, b3 is the influencing parameter of the cross-sectional size, b4 is the influencing parameter of the ratio of the moment of inertia, x1 is the elastic modulus of concrete, x2 is the reinforcement ratio, obtained by formula (1), x3 is the cross-sectional size of the column, x4 is the ratio of the moment of inertia provided by the steel bar to the moment of inertia of the cross-sectional area, obtained by formula (2);

[0016] Step 2: According to formula (3), the existing column model data is used for regression calculation to obtain the regression equation and calculate the equivalent elastic modulus of bending:

[0017] According to formulas (4), (5), (6), (7), and (8), the least squares method is used to estimate the regression parameters:

[0018]

[0019]

[0020]

[0021] Where: y n is the equivalent elastic modulus of bending of the existing model data, x in is the column section parameter of the existing model data;

[0022] List the normal equations according to the least squares method:

[0023]

[0024] It follows that:

[0025]

[0026] Solve The solved Substituting into the multivariate regression mathematical model (3), we can get the complete regression equation formula (3). Substituting x1, x2, x3, x4 in the first step into the regression equation formula (3), we can get the equivalent elastic modulus of the rectangular column against bending.

[0027] The beneficial effects of the present invention are as follows: in view of the problem of determining the elastic modulus of the homogeneous model of reinforced concrete rectangular columns when the overall finite element modeling of reinforced concrete monolithic structures is carried out, a reasonable method for calculating the bending equivalent elastic modulus of reinforced concrete rectangular columns when the overall finite element modeling of the structure is proposed, which provides theoretical guidance and data support for the problem of determining the elastic modulus of the homogeneous model of reinforced concrete rectangular columns when the overall finite element modeling of reinforced concrete monolithic structures is carried out, thereby simplifying the modeling process of the overall reinforced concrete structure and improving the efficiency of the structural finite element modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a reinforcement diagram of an embodiment of the present invention;

[0029] Figure 2 It is the column model data table of the present invention. DETAILED DESCRIPTION

[0030] The present invention will be further described below with reference to the accompanying drawings and by way of embodiments.

[0031] Example

[0032] A method for calculating the equivalent elastic modulus of bending of reinforced concrete rectangular columns in the overall finite element modeling of the structure. It is characterized in that in the overall finite element simulation model of reinforced concrete structure, the interaction between steel and concrete and their own material properties do not need to be reflected, so a homogeneous model is usually used to model reinforced concrete components. A reinforced concrete frame structure uses ABAQUS software to establish a finite element simulation model. In the structure, a frame column is 6 meters high, with a cross-sectional size of 0.5 meters * 0.5 meters, and concrete is C40. The specific reinforcement form is shown in Figure 1 .

[0033] A method for calculating the equivalent elastic modulus of bending of a reinforced concrete rectangular column in overall structural finite element modeling comprises the following steps:

[0034] Step 1: Establish a multivariate regression mathematical model of the equivalent elastic modulus of reinforced concrete rectangular columns:

[0035] The reinforcement ratio parameter x2 is:

[0036]

[0037] The ratio of the moment of inertia provided by the punching steel bar to the moment of inertia of the section is x4:

[0038]

[0039] Multiple regression mathematical model:

[0040]

[0041] Step 2: According to formula (3), use Figure 2 The existing column model data provided in the attached table are used for regression calculation to obtain the regression equation and the equivalent bending elastic modulus is calculated:

[0042] According to formulas (4), (5), (6), (7), and (8), the least squares method is used to estimate the regression parameters:

[0043]

[0044]

[0045]

[0046] List the normal equations according to the least squares method:

[0047]

[0048] It follows that:

[0049]

[0050] Solve That is, the regression equation formula (5)

[0051]

[0052] Substitute x1, x2, x3, and x4 from the first step into formula (3)

[0053] It can be concluded that the equivalent elastic modulus of the rectangular column is: 3.610×10 10 N / m 2

[0054] Although the specific calculation method of the present invention is described above in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Technical personnel in the relevant field should understand that various modifications or variations that can be made by technical personnel in the field without creative work on the basis of the design of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for calculating the equivalent elastic modulus of bending of reinforced concrete rectangular columns in finite element modeling of the entire structure, characterized in that: In the overall finite element modeling of the structure, the bending equivalent elastic modulus of the rectangular column homogeneous model is calculated by the following steps: Step 1: Establish a multivariate regression mathematical model for the equivalent elastic modulus of reinforced concrete rectangular columns in bending: The reinforcement ratio parameter x2 is: Where: A1 is the area of ​​the longitudinal reinforcement of the column cross section, A is the cross-sectional area of ​​the column; The ratio of the moment of inertia provided by the steel bar to the moment of inertia of the section x4 is: Where: n is the number of longitudinal reinforcements, y i is the distance from the i-th longitudinal reinforcement to the centroidal axis, A i is the cross-sectional area of ​​the i-th longitudinal reinforcement: Multiple regression mathematical model: Where: is the required equivalent elastic modulus of bending, b0 is the regression unknown constant, b1 is the influencing parameter of concrete elastic modulus, b2 is the influencing parameter of reinforcement ratio, b3 is the influencing parameter of section size, b4 is the influencing parameter of moment of inertia ratio, x1 is the elastic modulus of concrete, x2 is the reinforcement ratio, obtained by formula (1), x3 is the column section size, x4 is the ratio of the moment of inertia provided by the steel bar to the moment of inertia of the section, obtained by formula (2); Step 2: According to formula (3), the existing column model data is used for regression calculation to obtain the regression equation and calculate the equivalent elastic modulus of bending: According to formulas (4), (5), (6), (7), and (8), the least squares method is used to estimate the regression parameters: Where: y n is the equivalent elastic modulus of bending of the existing model data, x in is the column section parameter of the existing model data; List the normal equations according to the least squares method: It follows that: Solve The solved Substituting into the multivariate regression mathematical model (3), we can get the complete regression equation formula (3). Substituting x1, x2, x3, x4 in the first step into the regression equation formula (3), we can get the equivalent elastic modulus of the rectangular column against bending.

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