A method for calculating internal forces in thin-walled structural members

Abstract

The present application relates to the technical fields of engineering structure mechanics, and discloses a kind of analytical calculation method of section internal force of thin-walled member, comprising the following steps, step S1: according to the basic composition of thin-walled member section stress, the member section stress σ is split into axial force normal stress σ N , bending normal stress σ M , constraint torsion normal stress σ T ;Step S2: according to the distribution law of various stresses on the thin-walled member section, the member section axial force N and axial force normal stress σ N ;Step S3: the member section stress σ is subtracted from axial force normal stress σ N ;Step S4: calculate bending normal stress σ M ;Step S5: according to the bending normal stress σ M solved by S4, solve the effective section characteristics of member;Step S6: solve section bending moment M.The present application compared with prior art, can be used for the thin-walled member internal force test in the fine plate shell or solid finite element model and actual structure, obtain internal force from stress result, suitable for open section and closed section thin-walled member simultaneously, solve the problem that thin-walled member section internal force is difficult to obtain.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of engineering structure mechanics, and particularly relates to a thin-walled member section internal force analytical calculation method. BACKGROUND

[0002] The thin-walled member generally refers to an equal cross-section straight rod with a thin cross-section, and the ratio of the wall thickness to the maximum width or height of the cross-section is less than 0.1. According to the cross-section type, the thin-walled member is divided into open cross-section and closed cross-section thin-walled members, and the cross-section is composed of a wing plate and a web. The frame, truss and other basic structures composed of a large number of thin-walled members have been widely applied to important engineering structures such as industrial plants, temporary facilities and long-span bridges. The internal force state of the key cross-section of the thin-walled member is the basis for the design of various complex structures and is also a key index for evaluating the reliability of the structure during service.

[0003] At the initial stage of structural design, different scale finite element models can be used to analyze the structure, and the internal force state of the thin-walled member can be directly obtained by using a simplified truss model, but the influence of local structure on the internal force distribution of the member cannot be considered. The refined plate shell or solid finite element model can fully consider various structural details, but only the cross-section stress of the member can be obtained, and the cross-section internal force cannot be obtained. During the service of the structure, the cross-section strain of the member is usually obtained by test, which cannot directly show the internal force distribution of the structure under various loads, and is not conducive to the judgment and targeted reinforcement of the overall stress condition of the structure.

[0004] Therefore, the present application is provided. SUMMARY

[0005] To solve the above technical problems, the basic idea of the technical solution of the present application is as follows:

[0006] A thin-walled member section internal force analytical calculation method comprises the following steps:

[0007] Step S1: According to the basic composition of the cross-section stress of the thin-walled member, the cross-section stress σ of the member is divided into axial normal stress σ N , bending normal stress σ M and constraint torsional normal stress σ T .

[0008] Step S2: According to the distribution law of various stresses on the cross-section of the thin-walled member (the axial normal stress σ N is equal at each place of the cross-section, the bending normal stress σ M and the constraint torsional normal stress σ T are self-balanced on the cross-section), the axial force N of the member cross-section and the axial normal stress σ N are calculated.

[0009] Step S3: subtract the axial normal stress σ N The bending normal stress σ M , the restrained torsion normal stress σ T , and the axial normal stress σ N are obtained.

[0010] Step S4: according to the distribution mode of the bending normal stress σ M , the restrained torsion normal stress σ T , and the axial normal stress σ N , the bending normal stress σ M is calculated.

[0011] Step S5: according to the bending normal stress σ M calculated in S4, the effective width W eff of the wing plate and the web and the corresponding equivalent bending normal stress σ M-eff are calculated, the effective section of the member is obtained, and the effective section bending moment Ieff is calculated.

[0012] Step S6: the section bending moment M is solved by using the effective section bending moment Ieff of the member and the equivalent bending normal stress σ M-eff .

[0013] As a preferred embodiment of the present application, according to the distribution law of each stress described in S1, the vertical bending normal stress σ My , the horizontal bending normal stress σ Mx , and the restrained torsion normal stress σ T , the integral of the stress on the section infinitesimal (plate thickness t x section infinitesimal length ds) is 0, and the integral is calculated as ∫σ My tds = ∫σ Mx tds + ∫σ T tds + ∫σ N tds = ∫σ N tds = N. N .

[0014] As a preferred embodiment of the present application, in the step S4, the vertical bending normal stress σ My and the horizontal bending normal stress σ Mx are calculated, which specifically includes:

[0015] 1) The vertical bending normal stress σ My-FB of the web of the section is equal to the vertical bending normal stress σ N of the web of the section excluding the axial normal stress σ 1-FB .

[0016] 2) The horizontal bending normal stress σ Mx of the wing plate on the two points symmetric about the vertical axis is equal in size and opposite in direction, and the restrained torsion normal stress σ T .T The same distribution rule is that the vertical bending normal stress σ of any two points m and n of the upper wing plate about the vertical axis is calculated by the formula My-U-m σ My-U-n . The same distribution rule is that the vertical bending normal stress σ of any two points o and p of the lower wing plate about the vertical axis is calculated by the formula My-B-o σ My-B-p .

[0017] 3). The vertical bending normal stress σ My of any two points of the web about the horizontal axis is equal in size and opposite in direction, and the constraint torsional normal stress σ T has the same distribution rule, and the horizontal bending normal stress σ of any two points q and r of the outer web about the horizontal axis is calculated by the formula Mx-W-q σ Mx-W-r . The same distribution rule is that the horizontal bending normal stress σ of any two points s and t of the inner web about the horizontal axis is calculated by the formula Mx-N-s σ Mx-N-t .

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

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

[0020] When the present application is used to calculate the section internal force, the complex stress state of the thin-walled member section is decomposed into stresses generated by various single internal forces, and the required section internal force is solved according to the basic distribution mode of various stresses. Compared with the prior art, the present application can be used for the internal force test of thin-walled members in a refined plate-shell or solid finite element model and an actual structure, the internal force is obtained from the stress result, and the present application is suitable for open-section and closed-section thin-walled members, thereby avoiding the problem that it is difficult to obtain the section internal force of the thin-walled member in the prior art.

[0021] The specific embodiments of the present application will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0022] In the drawings:

[0023] Figure 1 Fig. 1 is a schematic diagram of a thin-walled member structure to be calculated in an embodiment of the present application.

[0024] Figure 2 A schematic diagram of a thin-walled member cross section to be calculated in the embodiment of the present application.

[0025] Figure 3 A schematic diagram of thin-walled member cross section stress decomposition to be calculated in the embodiment of the present application.

[0026] Figure 4 A schematic diagram of a thin-walled member effective cross section to be calculated in the embodiment of the present application.

[0027] Figure 5 A schematic diagram of a calculation flow in the embodiment of the present application.

[0028] In the figure: 1 - I-shaped thin-walled member; 2 - upper flange; 3 - web; 4 - lower flange; 5 - axial force normal stress; 6 - upper flange vertical bending normal stress; 7 - web vertical bending normal stress; 8 - lower flange vertical bending normal stress; 9 - transverse bending normal stress; 10 - restrained torsion normal stress; 11 - upper flange effective width; 12 - lower flange effective width. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical scheme and advantages of the embodiment of the present application more clear, the technical scheme in the embodiment will be clearly and completely described below in combination with the drawings in the embodiment of the present application, and the following embodiment is used to illustrate the present application.

[0030] As shown in Figures 1 to 3 , a thin-walled member cross section internal force analytical calculation method, comprising the following steps:

[0031] Step S1: According to the basic composition of the stress of the thin-walled member cross section, the member cross section stress σ is split into axial force normal stress σ N , bending normal stress σ M , and restrained torsion normal stress σ T ;

[0032] Step S2: According to the distribution law of various stresses on the thin-walled member cross section (the axial force normal stress σ N is equal everywhere on the cross section, the bending normal stress σ M and the restrained torsion normal stress σ T remain self-balanced on the cross section), the member cross section axial force N and the axial force normal stress σ N are calculated.

[0033] Step S3: The member cross section stress σ is subtracted by the axial force normal stress σ N , and the cross section normal stress σ1 composed of only the bending normal stress σ M and the restrained torsion normal stress σ T is obtained.

[0034] Step S4: According to the bending normal stress σM Constrained torsional normal stress σ T The distribution pattern is used to calculate the bending normal stress σ. M ;

[0035] Step S5: Solve for the bending normal stress σ based on S4 M Calculate the effective width W of the flange and web of the cross section. eff and the corresponding equivalent bending normal stress σ M-eff The effective cross section of the component is obtained, and the bending moment of inertia Ieff of the effective cross section is calculated.

[0036] Step S6: Utilize the bending moment of inertia I of the effective section of the member eff Equivalent bending normal stress σ of the cross section M-eff Solve for the bending moment M at the cross section.

[0037] Furthermore, according to the distribution law of each stress 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 integrals about the infinitesimal cross-section element (plate thickness t × cross-section element length ds) are all 0, which can be expressed as ∫σtds=∫σ My tds+∫σ Mx tds+∫σ T tds+∫σ N tds=∫σ N tds = N is used to calculate the axial force N and the axial normal stress σ, which are among the internal forces in the cross section of the member. N .

[0038] Furthermore, in step S4, the vertical bending normal stress σ is calculated. My With transverse bending normal stress σ Mx Specifically, it includes:

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

[0040] 2) Transverse bending normal stress σ at two points symmetrical about the vertical axis on the flange. Mx Equal in magnitude but opposite in direction, constrained torsional normal stress σ T It follows the same distribution pattern, through public... Calculate the vertical bending normal stress σ at any two points m and n that are symmetric about the vertical axis of the upper flange. My-Um σ My-Un Through formula Calculate the vertical bending normal stress σ at any two points o and p that are symmetric about the vertical axis of the lower flange. My-Boσ My-Bp ;

[0041] 3) Vertical bending normal stress σ at two points symmetrical about the transverse axis on the web. My Equal in magnitude but opposite in direction, constrained torsional normal stress σ T It follows the same distribution pattern, which can be expressed by the formula. Calculate the transverse bending normal stress σ at any two points q and r on the outer web that are symmetric about the transverse axis. Mx-Wq σ Mx-Wr Through formula Calculate the transverse bending normal stress σ at any two points s and t that are symmetric about the transverse axis on the inner web. Mx-N-s σ Mx-N-t .

[0042] 4) Further, in step S6, after solving for the effective cross-section based on S5, the equivalent bending normal stress σ of the upper and lower flanges is... My-U-eff With σ My-B-eff This refers to the peak stress σ of the upper and lower flanges, taking into account the effect of shear hysteresis. My-U-Max With σ My-B-Max Then follow M y =average(σ My-U-eff .I eff / y U ,σ My-B-eff .I eff / y B The vertical bending moment of the section can then be calculated, where y U y is the distance between the top plate and the centroid in the effective cross-section. B This is the distance between the base plate and the centroid in the effective cross-section.

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

[0044] The bending normal stress σ is obtained from S4. M Calculate the effective width W of the flange and web of the cross section. eff and the corresponding equivalent bending normal stress σ M-eff, the effective section of the member is obtained and the bending moment of inertia I of the effective section is calculated; in this embodiment, the bending normal stress of the upper and lower flanges on the section is affected by the shear lag effect, and bending normal stress peaks σ My-U-Max and σ My-B-Max and the stress distribution is symmetric about the vertical axis, W Ueff = ∫σ My-U tds / σ My-U-Max and W Beff = ∫σ My- B tds / σ My-B-Max The effective width of the upper and lower flanges is calculated, the effective section is obtained, and the bending moment of inertia I of the effective section is calculated eff , which is the equivalent bending normal stress of the section.

Claims

1. A method for analyzing internal forces in a thin-walled member cross section, characterized by, comprising the steps of: Step S1: According to the basic composition of the thin-walled member cross-section stress, the member cross-section stress σ is divided into axial force normal stress σ N , bending normal stress σ M , restrained torsion normal stress σ T ; Step S2: According to the distribution law of various stresses on the cross section of the thin-walled member, the axial force normal stress σ N of each part of the cross section is equal, the bending normal stress σ M , the constraint torsional normal stress σ T is self-balanced on the cross section, and the member cross section axial force N and the axial force normal stress σ N are calculated; Step S3: subtract the axial normal stress σ from the member cross-sectional stress σ N A cross-sectional normal stress σ1 consisting only of bending normal stress σ M , restrained torsional normal stress σ T may be obtained; Step S4: calculating the bending normal stress σ M of the thin-walled member in accordance with the distribution pattern of the bending normal stress σ T of the thin-walled member cross section M ; Step S5: the bending normal stress σ M , the effective width W eff of the cross section wing plate and web and the corresponding equivalent bending normal stress σ M-eff , the effective section of the component is obtained and the bending moment of inertia I eff of the effective section is calculated; Step S6: Utilize member effective cross-sectional bending resistance moment of inertia I eff With cross-sectional equivalent bending normal stress σ M-eff Solve cross-sectional bending moment M; According to the distribution law of each stress distribution described in S1 on the cross section, the vertical bending normal stress σ My , the transverse bending normal stress σ Mk , the constraint torsional normal stress σ T Regarding the cross section infinitesimal, the integral of the product of the plate thickness t and the cross section infinitesimal length ds is 0, which can be calculated according to ∫σ My tds=∫σ Mx tds+∫σ T tds+∫σ N tds=∫σ N tds=N The axial force N and the axial force normal stress σ N ; In the step S4, the vertical bending normal stress σ My and the transverse bending normal stress σ Mx , and specifically comprises: 1) the cross-sectional web vertical bending normal stress σ My-FB equal to the cross-sectional web vertical bending normal stress σ N 1-FB ;​ 2) The transverse bending normal stress σ of the wing plate about the vertical axis of symmetry of two points Mx The constraint torsional normal stress σ is equal in size and opposite in direction T The same distribution rule, through the formula The vertical bending normal stress of the upper wing plate about the vertical axis of symmetry of any two points m, n is calculated The vertical bending normal stress of the lower wing plate about the vertical axis of symmetry of any two points o, p is calculated The vertical bending normal stress of the lower wing plate about the vertical axis of symmetry of any two points o, p is calculated 3) Vertical bending normal stress σ at two points symmetrical about the transverse axis on the web. My Equal in magnitude but opposite in direction, constrained torsional normal stress σ T It follows the same distribution pattern, which can be expressed by the formula. Calculate the transverse bending normal stress σ at any two points q and r on the outer web that are symmetric about the transverse axis. Mx-W-q σ Mx-W-r Through formula Calculate the transverse bending normal stress σ at any two points s and t that are symmetric about the transverse axis on the inner web. Mx-N-s σ Mx-N-t。 2. The method of claim 1, wherein In step S6, after the effective cross section is solved according to S5, the equivalent bending normal stress σ My-U-eff With σ My-B-eff The stress peak σ My-U-Max With σ My-B-Max .

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