Determination method of plastic development degree and biaxial bending moment of steel member sections under biaxial compression and bending

Abstract

The present invention discloses a method for determining the degree of plastic development and biaxial bending moment of a steel member section under biaxial compression and bending, comprising: 1) selecting the cross-sectional form of the steel member to be analyzed and the constant axial pressure it is subjected to; 2) establishing key parameters x P and y Q The relationship between the displacement of the steel structure subjected to bidirectional loading; 3) Specify the loading displacement and iterate multiple times to solve the rotation angle of the dangerous section that satisfies the axial force equilibrium equation f ; 4) Analyze and calculate the cross-section plastic development coefficient under the specified loading displacement c 5) Based on the distribution of the normal stress in the critical section, perform integral moment calculations about the two principal axes to determine the biaxial bending moment of the component under the specified loading displacement. 6) Repeat the specified loading displacements with different magnitudes under the above loading conditions, using a specific incremental step as the displacement increment. This method can determine the normal strain distribution of the critical section and the bending moments about the two principal axes of the steel component under the specified deformation conditions within the analysis range.

Description

Technical Field

[0001] The present invention relates to a method for determining the degree of cross-sectional plastic development and biaxial bending moment of a steel member during the entire loading process under biaxial compression and bending. Specifically, the method predicts the position of the elastic-plastic neutral axis and the rotation angle of the dangerous cross-sectional area of the biaxial compression and bending steel member, determines the normal stress distribution form of the dangerous cross-sectional area, and establishes a theoretical relationship between the member's loading displacement, the normal stress distribution form, and the bending moments around different principal axes, thereby providing a design basis for the design of steel members taking into account specified plastic development. Background Art

[0002] Generally speaking, the cross-sectional normal stress distribution of biaxially compressed steel members has a certain degree of uncertainty, which further complicates the relationship between cross-sectional stress development and macroscopic bearing capacity. Furthermore, the elastic-plastic design method for steel members is an important foundation for the design of building steel structures. To fully and safely utilize the properties of steel and grasp the bearing capacity redundancy and rotational capacity range of the members, it is crucial to determine the normal stress development process of dangerous sections of steel members under complex stress conditions.

[0003] Currently, steel structure design codes primarily classify components based on cross-sectional grade, considering the bending capacity of components under strong axial compression and bending with full cross-sectional plasticity, partial plasticity, and no plasticity. However, they fail to consider the bidirectional effects of biaxial compression and bending. European and American steel structure design codes are overly simplistic and conservative in their design curves for biaxial bending moments, failing to fully reflect the degree of plasticity development in steel component sections and the macroscopic bearing capacity safety reserve.

[0004] The determination method proposed in the present invention provides a basis for determining the degree of cross-sectional plastic development and the two-principal-axis bending moments of steel components under bidirectional compression and bending loading. Summary of the Invention

[0005] The present invention aims to provide a method for determining the degree of cross-section plasticity development and biaxial bending moment of a steel member during the entire loading process under biaxial compression and bending. Based on the assumption of a flat cross section, the bending moments around different principal axes are calculated by rotating the plastic neutral axis when the full cross-section is plastic under axial compression and biaxial bending.

[0006] The basic principle of the present invention is based on the basic assumption of the flat section. According to the cross-sectional stress distribution form when the entire cross-section is plastic, the bending moment of the entire cross-section plastic around different principal axes is solved. Through the determination method proposed by the present invention, the degree of plastic development of steel components subjected to bidirectional compression and bending loads can be theoretically calculated and determined, and the corresponding bidirectional bending moment can be obtained; the safety and bearing capacity reserve of steel components in the actual stress process can be accurately grasped, providing a more accurate design basis for the actual design process. On this basis, the present invention can limit the degree of plastic development and bearing capacity of the structure to ensure that the structure has sufficient safety reserve, bearing capacity redundancy and rotation ability, providing a basis for the design of steel components and safety determination during use.

[0007] The present invention provides a method for determining the degree of cross-sectional plastic development and biaxial bending moment of a steel member during the entire loading process under biaxial compression and bending. The method is based on the results of parametric finite element analysis, combined with the assumption of a flat cross-section, and determines three key parameters through axial force balance. The method then establishes a theoretical connection between the loading displacement, cross-sectional normal stress distribution, and the bending moment around different principal axes. Ultimately, a quantitative evaluation can be made of the degree of plastic development and biaxial bending moment of the steel member under biaxial compression and bending, providing an important design basis for the design of steel members that consider partial plastic development.

[0008] The above determination method specifically includes the following steps:

[0009] 1) Select the cross-sectional form of the steel member to be analyzed (any cross-sectional form) and the constant axial pressure (in the actual stress process, the axial pressure on the member remains basically unchanged);

[0010] 2) Establish key parameter x P and y Q The relationship between the displacement of steel components subjected to bidirectional loading (x P and y Q The coordinates of the intersection of the elastic-plastic neutral axis and the two principal axes of the dangerous section are represented respectively); the actual stress process of the steel member under biaxial compression and bending can be regarded as the combined effect of the constant axial pressure at the loading end and the gradually increasing biaxial horizontal displacement. P and y Q Establish the relationship between component-level loading displacement and cross-section-level stress distribution.

[0011] 3) Specify the loading displacement, use the material properties of steel as the transition between cross-sectional strain and stress, and combine x P and y Q , assuming that the initial rotation angle of the dangerous section is Substitute the axial force balance equation and solve the dangerous section rotation angle that satisfies the axial force balance equation through multiple iterations.

[0012] 4) By analyzing steps 1) to 3), the distribution form of the normal stress at the dangerous section of the biaxial compression-bending steel member under the specified displacement loading is determined, and the tensile and compressive yielding area at the dangerous section of the member is obtained. Based on this analysis, the cross-section plastic development coefficient γ under the specified loading displacement is calculated;

[0013] 5) Based on the distribution of the normal stress of the dangerous section, the integral moment calculation of the two main axes is performed to obtain the bending moment M of the component around the two main axes under the specified loading displacement. x and M y ;

[0014] 6) Under the above loading conditions, repeatedly try different sizes of specified loading displacements, using a specific incremental step (η times the component edge yield displacement) as the displacement increment;

[0015] The specified loading displacement is the displacement increasing from 0 to 10 times the component's edge yield displacement. Repeat steps 4) through 5) to determine the degree of plastic development in the critical section of the steel component and the development of the biaxial bending moment under any biaxial compression-bending loading displacement. The value of η depends on the required calculation accuracy. Higher accuracy results in smaller η values, but the maximum value does not exceed 1.0. By varying the specified loading displacement and repeating steps 4) through 5), the degree of plastic development and biaxial bending moment of the component under the entire loading process are determined.

[0016] In the above method, the cross-section type of the steel member includes any cross-section steel member that does not produce local buckling failure. The constant axis pressure simulates the deadweight load of the member during the actual stress process.

[0017] In the above method, during the biaxial compression-bending loading process of the steel member before local buckling occurs, each cross section satisfies the plane section assumption at all times, and the position of the elastic-plastic neutral axis can be determined by the key parameter x P and y Q The position of the elastic-plastic neutral axis of the dangerous section of the steel member under the specified loading displacement can be determined by the key parameter x P and y Q The displacement determination method includes either of the following two methods: ① Establish a parametric finite element analysis model to extract two key parameters x under the normal strain distribution of the dangerous section P and y Q , establish the empirical formula of loading displacement and two key parameters through least square fitting; ② establish x through the development law of steel component elastic-plastic theory P and y Q Theoretical calculation formula.

[0018] In the above method, the curvature of the dangerous section rotation after the component is subjected to force is It is obtained by solving the axial force equilibrium equation and can truly reflect the stress and deformation of the cross section.

[0019] In the above method, the calculation method of the plastic development degree of the cross section is based on the distribution form of the cross section normal stress. The specific calculation formula is as follows:

[0020]

[0021] Where: γ represents the coefficient of plastic development degree of the section; A yc and A yt They represent the dangerous cross-sectional areas of the biaxial compression-bending steel member under compression and tension yield respectively, and are expressed by x P 、y Q and The geometric relationship can be used to find A yc and A yt ; A represents the area of the dangerous section;

[0022] The calculation formula for the two main axis bending moments of steel members subjected to bidirectional compression and bending is:

[0023] M x =∫σydA;M y =∫σxdA

[0024] Where M x and M y and represent the bidirectional bending moments of bidirectional compression-bending steel members respectively; σ is the normal stress distribution form of the dangerous section; x and y represent the coordinate values of the integration unit in the rectangular coordinate system respectively; dA represents the area of the integration unit.

[0025] In the above method, the prediction of the degree of plastic development and biaxial bending moment of biaxial compression-bending steel members can provide a reference for the partial plastic design of steel members. At the same time, after repeated analysis and calculation, the biaxial bending moment development curve and the plastic development degree curve of the member under the entire loading process can be obtained.

[0026] Beneficial effects of the present invention:

[0027] The present invention provides a method for determining the degree of cross-sectional plastic development and biaxial bending moment of steel members subjected to bidirectional compression and bending during the entire loading process of the steel members under bidirectional compression and bending. For cross-sections where partial plastic development is considered in the actual design process, the present invention can use any specified degree of cross-sectional plastic development as the design standard, and can fully consider the safety reserve of the member's macroscopic bearing capacity, providing a design basis for the plastic design of steel members considering partial plastic development under complex stress states. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 The diagram below is a bidirectional compression-bending stress diagram of a rectangular steel member.

[0029] Figure 2The deformation diagram of the dangerous section of the steel member under bidirectional compression and bending;

[0030] Figure 3 Schematic diagram of normal stress distribution in dangerous sections of steel components;

[0031] Figure 4 The definition of the cross-sectional dimensions of the H-shaped steel member in the embodiment;

[0032] Figure 5 This is a deformation diagram of the H-section steel member in the embodiment;

[0033] Figure 6 is the steel material model in the embodiment;

[0034] Figure 7 A bidirectional bending moment-loading level curve is calculated for the embodiment;

[0035] Figure 8 Schematic diagram of plastic development degree calculated for the embodiment (in u / u e =5 as an example). DETAILED DESCRIPTION

[0036] The specific implementation manner of the present invention is described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of this specific implementation manner. Those skilled in the art can still modify the technical solutions described in the following embodiments or replace some of the technical features therein. These modifications or replacements will not cause the essence of the corresponding technical solutions to deviate from the technical scope of the present invention.

[0037] Example:

[0038] The present invention provides a method for determining the degree of cross-sectional plastic development and biaxial bending moment of a steel member during the entire loading process under biaxial compression and bending, comprising the following steps:

[0039] 1) Select the cross-sectional form of the steel member to be analyzed (any cross-sectional form) and the constant axial pressure (in the actual stress process, the axial pressure on the member remains basically unchanged);

[0040] 2) Establish key parameter x P and y Q The relationship between the bidirectional loading displacement of steel components and the actual stress process of bidirectional bending of steel components can be regarded as the combined effect of the constant axial pressure at the loading end and the gradually increasing bidirectional horizontal displacement. P and y Q Establish the relationship between component-level loading displacement and cross-section-level stress distribution.

[0041] 3) Specify the loading displacement, use the material properties of steel as the transition between cross-sectional strain and stress, and combine xP and y Q , assuming that the initial rotation angle of the dangerous section is Substitute the axial force balance equation and solve the dangerous section rotation angle that satisfies the axial force balance equation through multiple iterations.

[0042] 4) Through the analysis of steps 1) to 3), the distribution of normal stress in the dangerous section of the biaxial compression-bending steel member under the specified displacement loading is determined, and the tensile and compressive yielding areas at the dangerous section of the member are obtained. Based on this analysis, the cross-sectional plastic development coefficient γ under the specified loading displacement is calculated; the formula derivation process mainly obtains the plastic compression and tensile cross-sectional areas through geometric relationships, and then divides the obtained coefficient by the total area, which is defined as the cross-sectional plastic development coefficient;

[0043] 5) Furthermore, based on the distribution of the normal stress of the dangerous section, the integral moment calculation of the two main axes is performed to obtain the bending moment M of the component around the two main axes under the specified loading displacement. x and M y ;

[0044] 6) Under the above loading conditions, repeatedly attempt different loading displacements, using a specific incremental step (η times the component edge yield displacement) as the displacement increment. Repeat steps 4) through 5) above with the loading displacement increasing from 0 to 10 times the component edge yield displacement to determine the degree of plastic development in the critical section of the steel member and the development of the biaxial bending moment under any biaxial compression-bending loading displacement.

[0045] In the above method, the cross-sectional type of the steel member includes any steel member that does not produce local buckling failure.

[0046] In the above method, during the biaxial compression-bending loading process of the steel member before local buckling occurs, each cross section satisfies the plane section assumption at all times, and the position of the elastic-plastic neutral axis can be determined by the key parameter x P and y Q The only certainty.

[0047] In the above method, the rotation angle of the dangerous section after the component is subjected to force is It is obtained by solving the axial force equilibrium equation and can truly reflect the stress and deformation of the cross section.

[0048] In the above method, the prediction of the degree of plastic development and biaxial bending moment of biaxial compression-bending steel members can provide a reference for the partial plastic design of steel members. At the same time, after repeated analysis and calculation, the biaxial bending moment development curve and the plastic development degree curve of the member under the entire loading process can be obtained.

[0049] Taking H-section steel members as an example, the following gives a specific method for determining the degree of plastic development and biaxial bending moment of the cross-section of biaxially compressed and bent steel members.

[0050] Step 1: Select an H-shaped cross-section steel member as an embodiment of the present invention, such as Figure 4 As shown;

[0051] Step 2: Based on Figure 4 The H-shaped cross-section steel member dimensional parameter diagram shown in the figure is used to establish a batch finite element analysis model. The width-to-thickness ratio of the steel member is changed by changing the thickness while keeping the cross-section height (h=300mm) and width (b=200mm) fixed. Set to 5 to 9, with a step of 2; web width-to-thickness ratio The model is set to 15 to 35 with a step size of 5, for a total of 15 component models with different cross-sectional sizes. The loading condition is bidirectional horizontal displacement loading of the column top under constant axial pressure, and the axial compression ratio (n = N / Af y ) is set to 0~0.4 with a step of 0.1; the displacement loading direction angle (α is the loading between the displacements of the two main axis directions) is set to 0°~90° with a step of 15°, for a total of 35 different loading conditions. In summary, a total of 525 finite element models were established for analysis, such as Figure 5 As shown;

[0052] Based on the finite element analysis results, the key parameters x are fitted by the least squares method. P and y Q ,

[0053]

[0054]

[0055] Where A w represents the area of the web of the H-section steel member; u represents the loading displacement; u e Characterizing edge yield displacement L is the length of the steel member, f y is the yield strength of steel, and the material model of steel is as follows Figure 6 As shown, E is the elastic modulus of steel; u / u e Characterizes the displacement loading level, with a value of 1≤u / u e ≤10.

[0056] Step 3: Under the specified loading displacement u0, assume the initial rotation angle of the dangerous section Solve the rotation angle of the dangerous section that satisfies the axial force equilibrium equation like Figure 3 As shown;

[0057]

[0058] Step 4: The three key parameters x calculated from steps 2 and 3 P ,y Q and The theoretical value of is used to establish the normal stress distribution form of the dangerous section of the steel component at this moment, and the cross-section plastic development coefficient γ is calculated, as follows: Figure 8 As shown;

[0059]

[0060] Where: γ represents the coefficient of plastic development degree of the section; A yc and A yt They represent the dangerous cross-sectional areas of biaxial compression-bending steel members under compressive yielding and tensile yielding, respectively, and are expressed by x P 、y Q and The geometric relationship can be used to find A yc and A yt ; A represents the area of the dangerous section.

[0061] Step 5: Based on the normal stress distribution form of the dangerous section of the component under the specified loading displacement, perform integral moment calculation on the two main axes to obtain the bending moment M of the component around the two main axes under the specified loading displacement. x and M y ,like Figure 8 As shown;

[0062] M x =∫σydA;M y =∫σxdA

[0063] Step 6: Reselect the specified displacement (0 to the member basically reaches full cross-section plasticity) and axial compression ratio, repeat the above steps 4 to 5, and establish the cross-section plastic development and biaxial bending moment development of the biaxial compression steel member during the entire loading process, such as Figure 7 As shown;

[0064] Through the above steps, the degree of cross-sectional plasticity development and the development of biaxial bending moment of a steel member with a cross-sectional size of H300×200×10×16 (unit: mm) and steel material properties of Q355 were predicted during the entire loading process under the loading conditions of an axial compression ratio of 0.2 and a loading direction angle of 30°. The results are shown in Table 1.

[0065] Table 1

[0066]

[0067] Through the above examples, the degree of plastic development and biaxial bending moment can be determined under any loading displacement, such as in u / u e =7, x P、y Q and They are -63.0mm, -109.1mm and 17.2×10 -4 °, and at this time γ=70.3%, M x =266.3kN·m,M y =64.7kN·m, and the following x P and y Q Basically, no longer changes. Although it continues to increase, the impact on γ and M x and M y Basically, there is no effect. Similarly, the method for determining the degree of plastic development and bidirectional bending moment of H-section steel members proposed in this example can be used to determine the above indicators under any loading displacement.

Claims

1. A method for determining the degree of plastic development and biaxial bending moment of a steel member section under biaxial compression and bending, characterized in that The following steps are involved: 1) Select the cross-sectional form of the steel member to be analyzed and the constant axial pressure it is subjected to; during the actual stress process, the axial pressure on the member remains basically unchanged; 2) Establish key parameter x P and y Q The relationship between the displacement of the steel member under biaxial loading, x P and y Q Respectively represent the intersection coordinates of the elastic-plastic neutral axis of the dangerous section and the two principal axes; The actual stress process of biaxial compression and bending of steel members can be regarded as the combined effect of the constant axial pressure at the loading end and the gradually increasing biaxial horizontal displacement. P and y Q Establish the relationship between component-level loading displacement and cross-section-level stress distribution; 3) Specify the loading displacement, use the material properties of steel as the transition between cross-sectional strain and stress, and combine x P and y Q , assuming that the initial rotation angle of the dangerous section is Substitute the axial force balance equation and solve the dangerous section rotation angle that satisfies the axial force balance equation through multiple iterations. 4) By analyzing steps 1) to 3), the distribution form of the normal stress at the dangerous section of the biaxial compression-bending steel member under the specified displacement loading is determined, and the tensile and compressive yielding area at the dangerous section of the member is obtained. Based on this analysis, the cross-section plastic development coefficient γ under the specified loading displacement is calculated; 5) Based on the distribution of the normal stress of the dangerous section, the integral moment calculation of the two main axes is performed to obtain the bending moment M of the component around the two main axes under the specified loading displacement. x and M y ; 6) Under the above loading conditions, try different loading displacements repeatedly, with a specific incremental step as the displacement increment; The specific incremental step refers to η times the component edge yield displacement, and the specified loading displacement refers to increasing from 0 to 10 times the component edge yield displacement. Repeat the above steps 4) to 5) to determine the degree of plastic development of the dangerous section of the steel component under any biaxial compression-bending loading displacement and the development of the biaxial bending moment.

2. The method for determining the degree of plastic development and biaxial bending moment of a steel member cross section under biaxial compression and bending according to claim 1 is characterized in that: In step 1), the cross-sectional type of the steel member includes any cross-sectional type steel member that does not produce local buckling failure; the constant axial pressure simulates the deadweight load of the member during the actual stress process.

3. The method for determining the degree of plastic development and biaxial bending moment of a steel member cross section under biaxial compression and bending according to claim 1 is characterized in that: In step 2), the position of the elastic-plastic neutral axis of the dangerous section of the steel member under the specified loading displacement is determined by the key parameter x P and y Q The displacement determination method includes either of the following two methods: ① Establish a parametric finite element analysis model to extract two key parameters x under the normal strain distribution of the dangerous section P and y Q , establish the empirical formula of loading displacement and two key parameters through least square fitting; ② establish x through the development law of steel component elastic-plastic theory P and y Q Theoretical calculation formula.

4. The method for determining the degree of plastic development and biaxial bending moment of a steel member cross section under biaxial compression and bending according to claim 1 is characterized in that: In step 3), the rotation angle of the dangerous section after the component is subjected to force It is obtained by solving the axial force equilibrium equation and combining it with the different material properties of the steel structure to truly reflect the stress and deformation of the cross section.

5. The method for determining the degree of plastic development and biaxial bending moment of a steel member cross section under biaxial compression and bending according to claim 1 is characterized in that: In step 4), the calculation method of the cross-section plastic development coefficient is based on the distribution of the cross-section normal stress. The specific calculation formula is as follows: Where: γ represents the coefficient of plastic development degree of the section; A yc and A yt They represent the dangerous cross-sectional areas of biaxial compression-bending steel members under compressive yielding and tensile yielding, respectively, and are expressed by x P 、y Q and The geometric relationship can be used to find A yc and A yt ; A represents the area of the dangerous section.

6. The method for determining the degree of plastic development and biaxial bending moment of a steel member cross section under biaxial compression and bending according to claim 1 is characterized in that: In step 5), the calculation formula for the two-axis bending moment of the steel member subjected to bidirectional compression and bending is: M x =∫σydA;M y =∫σxdA Where M x and M y They represent the bidirectional bending moment of the bidirectional compression-bending steel member respectively; σ is the normal stress distribution form of the dangerous section; x and y represent the coordinate values of the integration unit in the rectangular coordinate system respectively; dA represents the area of the integration unit.

7. The method for determining the degree of plastic development and biaxial bending moment of a steel member cross section under biaxial compression and bending according to claim 1 is characterized in that: In step 6), the value of η depends on the calculation accuracy requirement. The higher the calculation accuracy, the smaller the η value, but the maximum value does not exceed 1.

0. By changing the specified loading displacement, repeating steps 4) to 5), the degree of plastic development and the two-axis bending moment of the component under the entire loading process are determined.

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