Analytic calculation method for internal force of section of thin-wall component

Abstract

The invention relates to the technical field of engineering structural mechanics, and discloses a thin-wall component section internal force analytical calculation method, which comprises the following steps: S1, according to the basic composition of the thin-wall component section stress, splitting the component section stress sigma into axial force normal stress sigma N, bending normal stress sigma M and constrained torsion normal stress sigma T; s2, according to the distribution rule of various stresses on the cross section of the thin-wall component, the axial force N and the axial force normal stress sigma N of the cross section of the component are calculated; s3, subtracting the normal stress sigma N of the axial force from the section stress sigma of the component; s4, calculating bending normal stress sigma M; s5, solving effective section characteristics of the component according to the bending normal stress sigma M solved in the step S4; and S6, solving the section bending moment M. Compared with the prior art, the method can be used for thin-wall component internal force testing in refined plate shells or solid finite element models and actual structures, internal force is obtained from stress results, meanwhile, the method is suitable for thin-wall components with open sections and closed sections, and the problem that the internal force of the sections of the thin-wall components is difficult to obtain is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of engineering structure mechanics, and in particular relates to a method for analyzing and calculating the internal forces of a thin-walled component cross section. Background Art

[0002] Thin-walled components generally refer to straight bars of equal cross-section with thinner cross-section thickness. The ratio of wall thickness to the maximum width or height of the cross-section is less than 0.1. According to the cross-section type, they are divided into open cross-section and closed cross-section thin-walled components. The cross-section consists of a wing plate and a web. Basic structures such as frames and trusses composed of a large number of thin-walled components have been widely used in important engineering structures such as industrial plants, large temporary facilities, and long-span bridges. Clarifying the internal force state of the key cross-section of thin-walled components is the basis for designing various complex structures, and is also a key indicator for evaluating the reliability of the structure during service.

[0003] In the early stage of structural design, finite element models of different scales can be used to analyze the structure. The simplified bar system model can directly obtain the internal force state of thin-walled components, but it cannot consider the influence of local structure on the internal force distribution of components; the refined plate and shell or solid finite element model can fully take into account various structural details, but it can only obtain the cross-sectional stress of the component, not the cross-sectional internal force. During the service life of the structure, the cross-sectional strain of the component is usually obtained by experimental testing, which cannot intuitively show the internal force distribution of the structure under various loads, which is not conducive to the judgment of the overall stress condition of the structure and targeted reinforcement.

[0004] In view of this, the present invention is proposed. Summary of the invention

[0005] In order to solve the above technical problems, the basic concept of the technical solution adopted by the present invention is:

[0006] A method for calculating the internal force of a thin-walled component cross section comprises the following steps:

[0007] Step S1: According to the basic composition of the cross-sectional stress of the thin-walled component, the cross-sectional stress σ of the component is split into the axial normal stress σ N , bending normal stress σ M , constrained torsional normal stress σ T ;

[0008] Step S2: According to the distribution law of various stresses on the cross section of the thin-walled component (axial normal stress σ N are equal, the bending normal stress σ M , constrained torsional normal stress σ T Maintain self-balance on the cross section), calculate the axial force N and the axial force normal stress σ of the component cross section N ;

[0009] Step S3: Subtract the axial normal stress σ from the component section stress σ N It can be concluded that only the bending normal stress σ M , constrained torsional normal stress σ T The composed cross-sectional normal stress σ1;

[0010] Step S4: According to the bending normal stress σ of the thin-walled component section M , constrained torsional normal stress σ T The distribution pattern of the bending normal stress σ M ;

[0011] Step S5: According to the bending normal stress σ solved in S4 M , calculate the effective width W of the section flange and web eff and the corresponding equivalent normal bending stress σ M-eff , obtain the effective section of the component and calculate the bending moment of inertia Ieff of the effective section;

[0012] Step S6: Use the effective section bending inertia moment Ieff of the component and the equivalent bending normal stress σ of the section M-eff Solve for the section bending moment M.

[0013] As a preferred embodiment of the present invention, according to the distribution law of each stress distribution on the cross section described in S1, the vertical bending normal stress σ My , transverse bending normal stress σ Mx , constrained torsional normal stress σ T The integral of the cross-sectional infinitesimal element (plate thickness t×cross-sectional infinitesimal element length ds) is 0, which can be obtained according to ∫σtds=∫σ My tds+∫σ Mx tds+∫σ T tds+∫σ N tds=∫σ N tds=NCalculate the axial force N and the axial force normal stress σ of one of the internal forces in the component section N .

[0014] As a preferred embodiment of the present invention, in step S4, the vertical bending normal stress σ is calculated. My and the transverse bending normal stress σ Mx , including:

[0015] 1). Vertical bending normal stress of the web of the section σ My-FB Equal to the normal stress σ minus the axial force N The vertical bending normal stress σ of the cross-section web 1-FB ;

[0016] 2). Transverse bending normal stress σ at two points symmetrical about the vertical axis on the wing Mx Equal in magnitude and opposite in direction, constraining the torsion normal stress σT The same distribution law is used. Calculate the vertical bending normal stress σ at any two points m and n of the upper wing plate that are symmetrical about the vertical axis My-U-m , σ My-U-n , through the formula Calculate the vertical bending normal stress σ at any two points o and p of the lower wing plate that are symmetrical about the vertical axis My-B-o , σ My-B-p ;

[0017] 3). Vertical bending normal stress σ at two points symmetrical about the transverse axis on the web My Equal in magnitude and opposite in direction, constraining the torsion normal stress σ T The same distribution law can be obtained by the formula Calculate the transverse bending normal stress σ of any two points q and r of the outer web symmetric about the transverse axis Mx-W-q , σ Mx-W-r , through the formula Calculate the transverse bending normal stress σ of any two points s and t of the inner web symmetric about the transverse axis Mx-N-s , σ Mx-N-t .

[0018] As a preferred embodiment of the present invention, in step S6, after the effective cross section is solved according to S5, the equivalent bending normal stress σ of the upper wing plate and the lower wing plate is My-U-eff With σ My-B-eff is the peak stress σ of the upper and lower wing plates considering the shear lag effect My-U-Max With σ My-B-Max .

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] When using this method to calculate the cross-sectional internal forces, the present invention decomposes the cross-sectional stress state of a complex thin-walled component into stresses generated by various single internal forces, and solves the required cross-sectional internal forces according to the basic distribution patterns of various stresses. Compared with the prior art, this method can be used for refined plate and shell or solid finite element models and thin-walled component internal force tests in actual structures, and the internal forces are obtained from the stress results. It is also applicable to thin-walled components with open and closed cross-sections, and avoids the problem in the prior art that it is difficult to obtain the cross-sectional internal forces of thin-walled components.

[0021] The specific implementation modes of the present invention are further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In the attached picture:

[0023] Figure 1 Schematic diagram of the thin-walled component structure to be calculated in an embodiment of the present invention.

[0024] Figure 2 Schematic diagram of the cross section of a thin-walled component to be calculated in an embodiment of the present invention.

[0025] Figure 3 Schematic diagram of the cross-sectional stress decomposition of a thin-walled component to be calculated in an embodiment of the present invention.

[0026] Figure 4 Schematic diagram of the effective cross-section of a thin-walled component to be calculated in an embodiment of the present invention.

[0027] Figure 5 The figure is a schematic diagram of the calculation process of an embodiment of the present invention.

[0028] In the figure: 1—I-shaped thin-walled member; 2—upper wing plate; 3—web plate; 4—lower wing plate; 5—axial force positive stress; 6—vertical bending positive stress of upper wing plate; 7—vertical bending positive stress of web plate; 8—vertical bending positive stress of lower wing plate; 9—lateral bending positive stress; 10—constrained torsional positive stress; 11—effective width of upper wing plate; 12—effective width of lower wing plate. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The following embodiments are used to illustrate the present invention.

[0030] like Figures 1 to 3 As shown, a method for analyzing and calculating the internal force of a thin-walled component section includes the following steps:

[0031] Step S1: According to the basic composition of the cross-sectional stress of the thin-walled component, the cross-sectional stress σ of the component is split into the axial normal stress σ N , bending normal stress σ M , constrained torsional normal stress σ T ;

[0032] Step S2: According to the distribution law of various stresses on the cross section of the thin-walled component (axial normal stress σ N are equal, the bending normal stress σ M , constrained torsional normal stress σ T Maintain self-balance on the cross section), calculate the axial force N and the axial force normal stress σ of the component cross section N ;

[0033] Step S3: Subtract the axial normal stress σ from the component section stress σ N It can be concluded that only the bending normal stress σ M , constrained torsional normal stress σ T The normal stress of the composed section is σ1;

[0034] Step S4: According to the bending normal stress σ of the thin-walled component sectionM , constrained torsional normal stress σ T The distribution pattern of the bending normal stress σ M ;

[0035] Step S5: According to the bending normal stress σ solved in S4 M , calculate the effective width W of the section flange and web eff and the corresponding equivalent bending normal stress σ M-eff , obtain the effective section of the component and calculate the bending moment of inertia Ieff of the effective section;

[0036] Step S6: Use the effective section bending inertia moment I eff Equivalent bending normal stress σ M-eff Solve for the section bending moment M.

[0037] Furthermore, according to the distribution law of each stress distribution on the cross section described in S1, the vertical bending normal stress σ My , transverse bending normal stress σ Mx , constrained torsional normal stress σ T The integral of the cross-sectional infinitesimal element (plate thickness t×cross-sectional infinitesimal element length ds) is 0, which can be obtained according to ∫σtds=∫σ My tds+∫σ Mx tds+∫σ T tds+∫σ N tds=∫σ N tds=NCalculate the axial force N and the axial force normal stress σ of one of the internal forces in the component section N .

[0038] Furthermore, in step S4, the vertical bending normal stress σ is calculated My and the transverse bending normal stress σ Mx , including:

[0039] 1). Vertical bending normal stress of the web of the section σ My-FB Equal to the normal stress σ minus the axial force N The vertical bending normal stress σ of the cross-section web 1-FB ;

[0040] 2). Transverse bending normal stress σ at two points symmetrical about the vertical axis on the wing Mx Equal in magnitude and opposite in direction, constraining the torsion normal stress σ T The same distribution law is also used. Calculate the vertical bending normal stress σ at any two points m and n of the upper wing plate that are symmetrical about the vertical axis My-Um , σ My-Un , through the formula Calculate the vertical bending normal stress σ at any two points o and p of the lower wing plate that are symmetrical about the vertical axis My-Bo, σ My-Bp ;

[0041] 3). Vertical bending normal stress σ at two points symmetrical about the transverse axis on the web My Equal in magnitude and opposite in direction, constraining the torsion normal stress σ T The same distribution law can be obtained by the formula Calculate the transverse bending normal stress σ of any two points q and r of the outer web symmetric about the transverse axis Mx-Wq , σ Mx-Wr , through the formula Calculate the transverse bending normal stress σ of any two points s and t of the inner web symmetric about the transverse axis Mx-N-s , σ Mx-N-t .

[0042] 4) Further, in step S6, after solving the effective cross section according to S5, the equivalent bending normal stress σ of the upper wing plate and the lower wing plate is My-U-eff With σ My-B-eff is the peak stress σ of the upper and lower wing plates considering the shear lag effect My-U-Max With σ My-B-Max , and then follow M y =average(σ My-U-eff .I eff / y U ,σ My-B-eff .I eff / y B ) can be used to solve the vertical bending moment of the section, where y U is the distance between the top plate and the centroid in the effective section, y B is the distance between the base plate and the centroid in the effective section.

[0043] Specifically, the cross-sectional normal stress σ generated by the I-shaped thin-walled member (1) under various loads can be decomposed into the following: Figure 3 The four types of cross-sectional normal stresses are shown, among which the axial normal stress of the cross-sectional web and flange is (5)σ N are the same; the vertical bending normal stress of the upper wing plate (6)σ My-U 、Vertical bending normal stress of web (7)σ My-F 、Vertical bending normal stress of lower wing plate (8)σ My-B Self-balanced about the transverse neutral axis on the cross section; transverse bending normal stress (9)σ Mx Self-balanced about the vertical neutral axis; constrained torsional normal stress (10)σ T About shear center self-balancing.

[0044] The bending normal stress σ solved by S4 M , calculate the effective width W of the section flange and web eff and the corresponding equivalent normal bending stress σ M-eff, the effective cross section of the component is obtained and the bending moment of inertia I of the effective cross section is calculated; in this embodiment, the bending normal stress of the upper wing plate and the lower wing plate of the cross section is affected by the shear lag, and the bending normal stress peak σ appears at the position of the wing plate and the web My-U-Max With σ My-B-Max And the stress distribution is symmetrical about the vertical axis, which can be calculated according to W Ueff =∫σ My-U tds / σ My-U-Max With W Beff =∫σ My- B tds / σ My-B-Max Calculate the effective width of the upper and lower wing plates, and after obtaining the effective cross section, calculate the bending moment of inertia I of the effective cross section eff , at this time the equivalent bending normal stress of the section.

Claims

1. A method for calculating the internal forces of a thin-walled component cross section, characterized in that: The steps include: Step S1: According to the basic composition of the cross-sectional stress of the thin-walled component, the cross-sectional stress σ of the component is split into the axial normal stress σ N , bending normal stress σ M , constrained torsional normal stress σ T ; Step S2: According to the distribution law of various stresses on the cross section of the thin-walled component (axial normal stress σ N are equal, the bending normal stress σ M , constrained torsional normal stress σ T Maintain self-balance on the cross section), calculate the axial force N and the axial force normal stress σ of the component cross section N ; Step S3: Subtract the axial normal stress σ from the component section stress σ N It can be concluded that only the bending normal stress σ M , constrained torsional normal stress σ T The composed cross-sectional normal stress σ1; Step S4: According to the bending normal stress σ of the thin-walled component section M , constrained torsional normal stress σ T The distribution pattern of the bending normal stress σ M ; Step S5: According to the bending normal stress σ solved in S4 M , calculate the effective width W of the section flange and web eff and the corresponding equivalent bending normal stress σ M-eff , obtain the effective section of the component and calculate the bending moment of inertia Ieff of the effective section; Step S6: Use the effective section bending inertia moment Ieff of the component and the equivalent bending normal stress σ of the section M-eff Solve for the section bending moment M.

2. A method for calculating the internal forces of a thin-walled component cross section according to claim 1, characterized in that: According to the distribution law of each stress distribution on the cross section described in S1, the vertical bending normal stress σ My , transverse bending normal stress σ Mk , constrained torsional normal stress σ T For the cross-sectional infinitesimal element, the integral of the plate thickness t×cross-sectional infinitesimal element length ds is 0, which can be obtained according to ∫σtds=∫σ My tds+∫σ Mx tds+∫σ T tds+∫σ N tds=∫σ N tds=NCalculate the axial force N and the axial force normal stress σ of one of the internal forces in the component section N .

3. A method for calculating the internal forces of a thin-walled component cross section according to claim 1, characterized in that: In step S4, the vertical bending normal stress σ is calculated. My and the transverse bending normal stress σ Mx , specifically including: 1). Vertical bending normal stress of the web of the section σ My-FB Equal to the normal stress σ minus the axial force N The vertical bending normal stress σ of the cross-section web 1-FB ; 2). Transverse bending normal stress σ at two points symmetrical about the vertical axis on the wing Mx Equal in magnitude and opposite in direction, constraining the torsion normal stress σ T The same distribution law is used. Calculate the vertical bending normal stress σ at any two points m and n of the upper wing plate that are symmetrical about the vertical axis My-U-m , σ My-U-n , through the formula Calculate the vertical bending normal stress σ at any two points o and p of the lower wing plate that are symmetrical about the vertical axis My-B-o , σ My-B-p ; 3). Vertical bending normal stress σ at two points symmetrical about the transverse axis on the web My Equal in magnitude and opposite in direction, constraining the torsion normal stress σ T The same distribution law can be obtained by the formula Calculate the transverse bending normal stress σ of any two points q and r of the outer web symmetric about the transverse axis Mx-W-q , σ Mx-W-r , through the formula Calculate the transverse bending normal stress σ of any two points s and t of the inner web symmetric about the transverse axis Mx-N-s , σ Mx-N-t .

4. A method for calculating the internal forces of a thin-walled component cross section according to claim 1, characterized in that: In step S6, after the effective cross section is solved according to step S5, the equivalent bending normal stress σ of the upper wing plate and the lower wing plate is My-U-eff With σ My-B-eff is the peak stress σ of the upper and lower wing plates considering the shear lag effect My-U-Max With σ My-B-Max .

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