A stability calculation method for composite corrugated steel pipe culvert

Abstract

The invention discloses a stability calculation method for a composite corrugated steel pipe culvert, which relates to the technical field of pipeline and culvert engineering, and comprises the following steps: determining the relevant material parameters of the corrugated steel and the composite layer, including: the thickness of the corrugated steel t 1 , composite layer thickness t 2 , elastic modulus E of corrugated steel 1 , elastic modulus E of the composite layer 2 , Poisson's ratio of corrugated steel μ 1 , Poisson's ratio of composite layer μ 2 The corrugated section cutting angle θ, the plane section length a, the plane section width b, the rotation constraint stiffness ξ of the combined structure of corrugated steel and composite layer, and the combination coefficient λ of corrugated steel and composite layer; assuming that the loaded edge of the plane section is simply supported, and the unloading edge of the plane section is subject to elastic rotation constraint of the rotation constraint stiffness ξ. The present invention can accurately evaluate the local stability of the plane section of the combined structure of corrugated steel and composite layer under compression, taking into account the unique corrugated shape of the corrugated steel, the material properties of the composite layer, and the degree of integration of the combined structure, thereby providing a comprehensive and accurate stability calculation method.

Description

Technical Field

[0001] The invention relates to the technical field of pipeline and culvert engineering, and in particular to a stability calculation method for a composite corrugated steel pipe culvert. Background Art

[0002] Corrugated steel has been widely used in pipelines, culverts and other projects because of its unique corrugated shape and excellent mechanical properties, which can significantly improve the bending stiffness of the structure. However, when the overburden load is large, the corrugated steel pipe may cause structural damage due to insufficient stability. Composite corrugated steel pipe is a composite structure composed of steel structure and other materials, such as concrete. It has the advantages of light weight, high stiffness and high stability, and therefore has broad application prospects. However, the local instability of the plane section of the composite corrugated steel pipe under pressure may cause local damage to the structure and cause overall instability. Therefore, the local stability calculation of the composite corrugated steel pipe culvert is still a key issue in the design.

[0003] The existing theoretical calculation methods lack consideration of the local stability of the plane section of the double-layer composite corrugated steel pipe, including the corrugation shape, the material properties of the composite layer, and the influence of the interaction between the two materials after the combination on the structural stability. In addition, although the numerical simulation method can be used to calculate the stability of the composite corrugated steel pipe culvert, there are problems such as complex modeling process and composite material interface simulation and poor calculation convergence. Therefore, it is necessary to propose an analytical calculation method for the local stability of the double-layer composite corrugated steel pipe culvert. Summary of the invention

[0004] The purpose of the present invention is to provide a stability calculation method for the plane section of a composite corrugated steel pipe culvert, which solves the problem that the traditional calculation method cannot accurately predict the local stability of the combined structure of corrugated steel and composite layer under load.

[0005] The present invention solves the above technical problems through the following technical solutions, and the present invention comprises the following steps:

[0006] Step 1: Determine the relevant material parameters of the corrugated steel and the composite layer, including: corrugated steel thickness t 1 , composite layer thickness t 2 , elastic modulus E of corrugated steel 1 , elastic modulus E of the composite layer 2 , Poisson's ratio of corrugated steel μ 1 , Poisson's ratio of composite layer μ 2 , the corrugated section cutting angle θ, the plane section length a, the plane section width b, the rotational constraint stiffness ξ of the combined structure of the corrugated steel and the composite layer, and the combination coefficient λ of the corrugated steel and the composite layer;

[0007] Assume that the loaded edge of the plane segment is simply supported, the unloaded edge of the plane segment is subject to elastic rotation constraint of rotation constraint stiffness ξ, the plane segment of the combined structure of corrugated steel and composite layer is regarded as a rectangular composite plate constrained by the corrugated segment, and assume that the deformation of the combined structure of corrugated steel and composite layer is bending with small deflection, and the cross section and material are isotropic;

[0008] Step 2: Calculate the total stiffness D of the combined structure of corrugated steel and composite layer;

[0009] Step 3: Assume that in the y direction, the deformation function of the plane segment is a quartic polynomial function, and in the x direction, the deformation function of the plane segment is a sine series. The deformation function of the plane segment is:

[0010]

[0011] In the formula, C m is a constant, M is the total unstable wave number, m is the half unstable wave number, δ is the rotation constraint coefficient, a is the length of the plane segment, b is the width of the plane segment, x is the coordinate along the length a direction, and y is the coordinate along the width b direction;

[0012] The plane segment boundary conditions of the combined structure of corrugated steel and composite layer are:

[0013]

[0014] Step 4: Since the soil can only withstand compression, when the corrugated steel and composite layer structure are in contact with the soil, the soil constraint takes effect. When the corrugated steel and composite layer structure are not in contact with the soil, the soil constraint fails. The local buckling load is calculated by the minimum potential energy principle. The local buckling load Substitution The critical instability wave number m can be obtained cr , the critical instability wave number m cr Substitute the local buckling load The local critical buckling instability load P is obtained x_cr .

[0015] Preferably, in step 2, the total stiffness D of the combined structure of the corrugated steel and the composite layer includes the stiffness D of the corrugated steel 1 , composite layer stiffness D 2 And the combined stiffness D during the transition from the free sliding state to the fully combined state of the combined structure 3 , that is, the total stiffness D of the combined structure of corrugated steel and composite layer is:

[0016] D=D 1 +D 2 +D 3 ;

[0017] and:

[0018]

[0019] Among them, E 1 is the elastic modulus of corrugated steel, μ 1 is the Poisson's ratio of corrugated steel, t 1 is the thickness of the corrugated steel;

[0020]

[0021] Among them, E 2 is the elastic modulus of the composite layer, μ 2 is the Poisson's ratio of the composite layer, t 2 is the composite layer thickness;

[0022]

[0023] Among them, t 0 =t 1 +t 2 is the total thickness of the combined structure of corrugated steel and composite layer, is the relative compressive stiffness of the cross-section of the combined structure of corrugated steel and composite layer, λ is the combination coefficient of the combined structure of corrugated steel and composite layer;

[0024] D 1 , D 2 With D 3 Substituting into the total stiffness D formula of the combined structure of corrugated steel and composite layer, we get:

[0025]

[0026] Preferably, in step three, the rotation constraint coefficient δ of the unloading edge of the plane segment is:

[0027]

[0028] Where ξ is the rotational constraint stiffness of the combined structure of corrugated steel and composite layer.

[0029] Preferably, in step 4, when the semi-instability wave number m is an even number, based on the Rayleigh-Ritz calculation method, the total potential energy Λ is expressed as the strain energy U of the combined structure of the corrugated steel and the composite layer e , the external force potential energy V of the combined structure of corrugated steel and composite layer, and the elastic potential energy U of the rotation constraint boundary ξ and the elastic potential energy U of the elastic foundation k The sum of the potential energy Λ is:

[0030]

[0031] The strain energy U of the combined structure of corrugated steel and composite layere , the external force potential energy V of the combined structure of corrugated steel and composite layer, and the elastic potential energy U of the rotation constraint boundary ξ and the elastic potential energy U of the elastic foundation k Substituting the total potential energy Λ, we get:

[0032]

[0033] Among them, P x is the axial force per unit length in the x-axis direction of the plane segment, M is the total instability wave number, k is the soil compression stiffness, μ is the Poisson's ratio of the corrugated steel and the composite layer, T 1 、T 2 、T 3 、T 4 、T 5 and T 6 The expression is:

[0034]

[0035] According to the principle of minimum potential energy, T 1 、T 2 、T 3 、T 4 、T 5 and T 6 Expression Substitution The local buckling load for the case of an even half-instability wave number can be obtained as for:

[0036]

[0037] Where η is the aspect ratio of the straight portion, defined as η = a / b;

[0038] when When The minimum value of the local critical buckling load P x_cr , the local buckling load Substitution The calculation formula for the even critical instability wave number can be obtained:

[0039]

[0040] Substituting the even critical instability wave number into the local buckling load Obtain the local critical buckling instability load P x_cr .

[0041] Preferably, the strain energy U of the combined structure of the corrugated steel and the composite layer is e for:

[0042]

[0043] Preferably, the external force potential energy V of the combined structure of the corrugated steel and the composite layer is:

[0044]

[0045] Among them, w is the deformation function, P x is the axial force per unit length in the x-axis direction of the plane segment, P y is the axial force per unit length in the y-axis direction of the plane segment, P xy is the shear force per unit length on the cross section.

[0046] Preferably, the elastic potential energy U of the rotation constraint boundary ξ for:

[0047]

[0048] Preferably, the elastic potential energy U of the elastic foundation k for:

[0049]

[0050] Where k is the soil compression stiffness.

[0051] Preferably, in step 4, when the semi-instability wave number m is an odd number, the total potential energy Λ is:

[0052] Λ=γU k +U e +U ξ +V;

[0053] Among them, the support effect γ of the soil can be expressed as:

[0054]

[0055] or

[0056]

[0057] According to the principle of minimum potential energy, T 1 、T 2 、T 3 、T 4 、T 5 and T 6 Expression Substitution The local buckling load under the case of odd half unstable waves can be obtained

[0058]

[0059] when When The minimum value of the local critical buckling load P x_cr , the local buckling load Substitution The calculation formula of odd critical instability wave number can be obtained;

[0060] When γ=(m-1) / 2m, the odd critical instability wave number calculation formula is:

[0061]

[0062] When γ=(m+1) / 2m, the odd critical instability wave number calculation formula is:

[0063]

[0064] Then, substitute any odd critical instability wave number mentioned above into the local buckling load Obtain the local critical buckling instability load P x_cr .

[0065] Compared with the prior art, the beneficial effects of the present invention are:

[0066] 1. The present invention can accurately evaluate the local stability of the plane section of the combined structure of corrugated steel and composite layer under compression, taking into account the unique corrugated shape of the corrugated steel, the material properties of the composite layer and the degree of integration of the combined structure, thereby providing a comprehensive and accurate stability analysis method.

[0067] 2. The local stability calculation method of the present invention combines the mechanical properties of corrugated steel and the strength characteristics of the composite layer material, providing a more comprehensive and accurate analysis method; it can accurately predict the stability of the structure in the design stage and effectively avoid potential safety risks. It not only improves the reliability of the design, but also helps to optimize the use of materials, thereby maximizing cost-effectiveness. It can significantly improve the quality of the design of the combined structure of corrugated steel and composite layers, ensuring the safety, reliability and economic benefits of the project. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a flowchart of the steps of the present invention;

[0069] Figure 2 It is a schematic diagram of the combined structure of corrugated steel and composite layer;

[0070] Figure 3 for Figure 1 A partial schematic diagram of the plane section of the middle A area;

[0071] Figure 4 It is a diagrammatic illustration of a plan section of a combined structure of corrugated steel and composite layers;

[0072] Figure 5It is a schematic diagram of the mechanical model of the plane segment;

[0073] Figure 6 for Figure 4 Simplified schematic diagram of the middle BB section;

[0074] Figure 7 This is a graph showing the influence of the combination coefficient on the local stability in Example 2;

[0075] Among them, (a) is the relationship diagram of the influence of the elastic modulus of corrugated steel on the critical instability wave number, (b) is the relationship diagram of the influence of the elastic modulus of corrugated steel on the critical instability load, and (c) is the comparison image of the finite element simulation and analytical calculation results;

[0076] Figure 8 This is a relationship diagram of the influence of elastic modulus on local stability in Example 3;

[0077] Among them, (a) is the relationship diagram of the influence of the combination coefficient on the critical instability wave number, and (b) is the relationship diagram of the influence of the combination coefficient on the critical instability load;

[0078] Fig. 9 This is a graph showing the effect of material thickness on local stability in Example 4;

[0079] Among them, (a) is the relationship diagram of the influence of the thickness of the composite layer material on the critical instability wave number, and (b) is the relationship diagram of the influence of the thickness of the composite layer material on the critical instability load.

[0080] In the figure: 1-corrugated section; 2-flat section; 21-corrugated steel; 22-composite layer. DETAILED DESCRIPTION

[0081] The above and other technical features and advantages of the present invention are described in more detail below in conjunction with the accompanying drawings.

[0082] Embodiment 1

[0083] This embodiment proposes a solution: a stability calculation method for a composite corrugated steel pipe culvert, such as Figure 1-6 As shown, the following steps are included:

[0084] The fixed pitch corrugated steel 21 can be divided into two parts: corrugated section 1 and flat section 2. The relevant material parameters of the corrugated steel 21 and the composite layer 22 are measured, including: the thickness of the corrugated steel 21 t 1 , the thickness of the composite layer 22 is t 2 , elastic modulus E of corrugated steel 21 1 , elastic modulus E of the composite layer 22 2 , corrugated steel 21 Poisson's ratio μ 1 、Poisson's ratio of composite layer 22μ 2 , the cutting angle θ of the corrugated section 1, the length a of the plane section 2, and the width b of the plane section 2.

[0085] The corrugated steel 21 and the composite layer 22 are combined into an integral component by technical means. The rotational constraint stiffness ξ of the combined structure of the corrugated steel 21 and the composite layer 22 (hereinafter referred to as the combined structure) is measured under experimental conditions, and the combination coefficient λ of the corrugated steel 21 and the composite layer 22 is given according to the degree of bonding between the corrugated steel 21 and the composite layer 22.

[0086] When the combined structure is in a completely combined state (no relative sliding displacement between layers in the horizontal direction), the corrugated steel 21 and the composite layer 22 have the same neutral plane, and the distances between this neutral plane and the neutral planes of the corrugated steel 21 and the composite layer 22 are t s With t d .

[0087] When the interlayer contact condition of the composite structure transitions from the free smooth state to the fully bonded state, the neutral layers of the two layers of material will change from the free smooth state to the fully bonded state. 1 、x 2 The x value of the fully coupled axial state 0 axis transitions, they are related to x 1 、x 2 The distances are λt s and λt d , λ∈[0,1], that is, when λ=0, the layers are in a free and smooth state; when λ=1, the layers are in a completely bonded state; 0<λ<1 is a semi-bonded state.

[0088] Obtain relevant material parameters of the supporting layer (soil), including: elastic modulus E s and Poisson's ratio μ s Since the cohesion, internal friction angle and expansion angle of the soil have little effect on the stability of the soil-composite structure system, their effects are ignored in this calculation method, and only the influence of the stiffness k of the soil is considered.

[0089] In order to obtain a general formula applicable to all corrugations and thicknesses, a local buckling stability analysis was performed on the plane segment 2 in the composite structure. In the calculation method, it is assumed that the loaded edge of the plane segment 2 is simply supported, and the unloading edge of the plane segment is subject to an elastic rotation constraint of the rotation constraint stiffness ξ. The plane segment 2 is regarded as a rectangular composite structure constrained by the corrugated segment 1; the soil support is simplified to a spring to simulate an elastic foundation that only bears compression; and it is assumed that the deformation of the rectangular composite structure is a small deflection bending, that is, the vertical tension and compression and horizontal shear deformation of the material section can be ignored; the layers are vertically continuous and there is no voiding phenomenon; the cross section and material are isotropic. The above parameters are substituted into the calculation method for stability calculation.

[0090] Based on the parameters obtained above, the stiffness of the combined structure is first calculated, including the stiffness of the corrugated steel D 1 , composite layer stiffness D 2And the combined stiffness D during the transition from the free sliding state to the fully combined state of the combined structure 3 , that is, the total stiffness D of the combined structure of corrugated steel and composite layer is: D = D 1 +D 2 +D 3 ,and:

[0091]

[0092] Among them, E 1 is the elastic modulus of the corrugated steel 21, μ 1 Poisson's ratio of corrugated steel, t 1 The thickness of the corrugated steel is 21;

[0093]

[0094] Among them, E 2 is the elastic modulus of the composite layer 22, μ 2 is the Poisson's ratio of the composite layer 22, t 2 is the thickness of the composite layer 22;

[0095]

[0096] Among them, t 0 =t 1 +t 2 is the total thickness of the combined structure, is the relative compressive stiffness of the composite structure section, λ is the combination coefficient of the composite structure;

[0097] D 1 , D 2 With D 3 Substituting into the total stiffness D formula of the composite structure, we get:

[0098]

[0099] Since the Poisson's ratios of the upper and lower plate materials (i.e., the corrugated steel 21 and the composite layer 22) are generally close, in order to simplify the calculation, the difference between the two materials is ignored in the embodiment, and the Poisson's ratio of the corrugated steel 21 and the composite layer 22 is uniformly denoted as μ in the following text.

[0100] The strain energy U of the combined structure e for:

[0101]

[0102] The external force potential energy V of the combined structure is:

[0103]

[0104] Among them, w is the deformation function, Px is the axial force per unit length in the x-axis direction of the plane segment, P y is the axial force per unit length in the y-axis direction of the plane segment, P xy is the shear force per unit length on the cross section.

[0105] Assume that in the y direction (short side direction), the deformation function of plane segment 2 is a quartic polynomial function; in the x direction (long side direction), the deformation function of plane segment 2 is a sine series. Therefore, according to the deformation coordination condition, the deformation function of plane segment 2 is:

[0106]

[0107] Where m is the semi-instability wave number and δ is the rotation constraint coefficient.

[0108] The boundary conditions of the plane segment 2 of the composite structure are:

[0109]

[0110] Substituting the boundary conditions in formula (8) into formula (7), the expression of the rotation constraint coefficient δ on the unloading edge of the plane segment is obtained by formula (9):

[0111]

[0112] Where ξ is the rotational constraint stiffness of the combined structure of corrugated steel and composite layer.

[0113] Substituting formula (9) into formula (7), formula (7) can be further rewritten as formula (10):

[0114]

[0115] Since m in formula (7) is the semi-instability wave number of plane segment 2 in the x direction, only integer values ​​of m are considered in the calculation process. Therefore, considering the characteristics that the supporting layer (soil) can only bear compression force, when the composite structure contacts the supporting layer (soil), the constraint of the supporting layer (soil) exists; when the composite structure is not in contact with the supporting layer (soil), the constraint of the supporting layer (soil) fails. Therefore, when m is an odd number or an even number, the local instability of the plane segment 2 of the composite structure needs to be calculated separately and the corresponding derivation is performed respectively.

[0116] When the semi-instability wave number m is an even number, based on the Rayleigh-Ritz calculation method, the total potential energy Λ is expressed as the strain energy U of the combined structure of corrugated steel and composite layer e , the external force potential energy V of the combined structure of corrugated steel and composite layer, and the elastic potential energy U of the rotation constraint boundary k and the elastic potential energy U of the elastic foundation kThe sum of the potential energy Λ is:

[0117]

[0118] Among them, the strain energy U e , potential energy V are obtained by formula (5) and (6) respectively, and the elastic potential energy U of the rotation constraint boundary is ξ and the elastic potential energy U of the elastic foundation k They are:

[0119]

[0120]

[0121] Among them, ξ is the rotational constraint stiffness of the plane segment, and k is the soil compression stiffness.

[0122] Therefore, substituting formulas (5), (6), (12) and (13) into formula (11) yields:

[0123]

[0124] Among them, T 1 、T 2 、T 3 、T 4 、T 5 and T 6 The expression is:

[0125]

[0126] According to the minimum potential energy principle, substitute formula (15) into Local buckling load for:

[0127]

[0128] Here, η is the aspect ratio of the straight portion, defined as η = a / b.

[0129] when The local buckling load can be obtained when The minimum value of the local critical buckling load P x_cr ), substitute formula (16) into The calculation formula for the even critical instability wave number can be obtained:

[0130]

[0131] The even critical buckling wave number is calculated by formula (17), and then the even critical buckling wave number is substituted into formula (16) to obtain the local critical buckling load P x_cr .

[0132] Similarly, when the semi-instability wave number m is an odd number, the total potential energy A is:

[0133] Λ=γU k +U e +U ξ +V (18)

[0134] Among them, the support effect γ of the soil can be expressed as:

[0135]

[0136] or

[0137]

[0138] According to the minimum potential energy principle, substitute formula (15) into The local buckling load under the odd half-instability wave condition can be obtained

[0139]

[0140] when When The minimum value of the local critical buckling load P x_cr ), substitute formula (21) into The calculation formula of odd critical instability wave number can be obtained.

[0141] Therefore, when γ=(m-1) / 2m, the odd critical instability wave number is:

[0142]

[0143] When γ=(m+1) / 2m, the odd critical instability wave number is:

[0144]

[0145] The odd critical buckling wave number is calculated by formula (22) or formula (23), and then the odd critical buckling wave number is substituted into formula (21) to obtain the local critical buckling instability load P x_cr .

[0146] In order to simplify the calculation, the present invention performs dimensionless processing on the calculation formula obtained in the above steps during the calculation process, and uses the program to perform the calculation. First, the following dimensionless parameters are defined:

[0147] in, is the dimensionless length of the short side of plane segment 2, is the dimensionless corrugated steel thickness, is the dimensionless thickness of the composite layer, is the dimensionless elastic modulus of the corrugated steel 21, is the dimensionless elastic modulus of the composite layer 22, is the dimensionless rotational constraint stiffness, is the dimensionless stiffness of the corrugated steel 21, is the dimensionless stiffness of the rear composite layer 22, is the dimensionless interlayer composite stiffness.

[0148] Since the semi-instability wave number m is a positive integer, in order to avoid ambiguity and simplify the calculation, an even or odd semi-instability wave number is selected and substituted into the formula for calculation. Substitute the dimensionless related parameters into formula (4), (9), (15), (19) or (20), calculate the related intermediate quantities, and then substitute the calculated intermediate quantities into formula (16) or formula (21) to obtain the local critical buckling instability load. At the same time, the corresponding dimensionless post-critical instability wave number is obtained

[0149] Embodiment 2

[0150] In this embodiment, two layers of the same corrugated steel material after welding are used, that is, the corrugated steel 21 and the composite layer 22 are both a combination structure of the same corrugated steel material. The combined structure after welding is in a completely combined state, and its combination coefficient λ=1. And through experiments and consulting relevant data, the relevant material parameter range is obtained: corrugated steel elastic modulus E 1 :2.0×10 5 ~2.1×10 5 MPa, corrugated steel thickness t 1 : 1~3mm, composite layer thickness t 2 : 1~3mm, the long side length a of the corrugated steel plane section: 5×10 2 ~30×10 2 mm, short side width b of the corrugated steel plane section: 30-60 mm, Poisson's ratio μ of the corrugated steel 21 and the composite layer 22: 0-0.5, soil stiffness k: 30-60 MPa, rotational constraint stiffness ξ: 1.5×10 10 ~3×10 10 N·m / rad.

[0151] During the calculation process, the given dimensionless parameters include: the length of the short side of the dimensionless plane segment Elastic modulus of the composite layer after dimensionlessness Dimensionless corrugated steel thickness Dimensionless composite layer thickness The combination coefficient λ = 1, the Poisson's ratio μ of the corrugated steel 21 and the composite layer 22 = 0.3, and the rotational constraint stiffness

[0152] Figure 7 This is a graph showing the influence of the elastic modulus of corrugated steel on local stability in Example 2, where Figure 7 (a) The relationship between the elastic modulus of corrugated steel and the critical instability wave number. Figure 7 (b) The relationship between the elastic modulus of corrugated steel and the critical instability load. Figure 7 (c) Comparison image of finite element simulation and analytical calculation results. Figure 7 The elastic modulus of corrugated steel can be obtained from The influence on the critical stability of the composite structure. At a certain critical point, the critical instability wave number changes with the dimensionless elastic modulus of the corrugated steel. The reason for the sudden decrease is that the increase of elastic modulus makes the combined structure have a greater total stiffness, and the wavelength at the time of instability increases accordingly, resulting in a decrease in wave number.

[0153] At the same time, as the dimensionless elastic modulus of the corrugated steel The dimensionless local critical buckling load It gradually increases, also because the combined structure obtains greater rigidity, and its strength is also improved accordingly, so a higher load is required to reach the critical instability state. Since the two layers of material are composed of the same corrugated steel material, their material properties are almost the same. In this embodiment, only the change of elastic modulus is considered to affect the stability of the combined structure.

[0154] Figure 7 (c) shows the comparison image of the finite element simulation and analytical calculation results. It can be seen from the figure that the numerical curve calculated by the formula is in good agreement with the finite element simulation curve, which verifies the reliability of the stability calculation method of the composite corrugated steel pipe culvert of the present invention.

[0155] Therefore, the dimensionless elastic modulus of the corrugated steel can be obtained: The change of can affect the instability behavior of the combined structure. A larger elastic modulus makes the combined structure have a larger rigidity, which means that the combined structure has better stability. Therefore, in actual engineering applications, the corrugated steel 21 and the composite layer 22 materials with a larger elastic modulus can be appropriately selected to improve the stability of the structure.

[0156] Embodiment 3

[0157] In this embodiment, different types of corrugated steel materials are used to form a composite structure, that is, different types of corrugated steel materials are used for the corrugated steel 21 and the composite layer 22. By using different combinations, the stability under different combination levels is considered. And through experiments and consulting relevant materials, the relevant material parameter range is obtained: the elastic modulus E of the corrugated steel 1 :2.0×105 ~2.1×10 5 MPa, corrugated steel thickness t 1 : 1~3mm, composite layer thickness t 2 : 1~3mm, the long side length a of the corrugated steel plane section: 5×10 2 ~30×10 2 mm, short side width b of the corrugated steel plane section: 30-60 mm, Poisson's ratio μ of the corrugated steel 21 and the composite layer 22: 0-0.5, soil stiffness k: 30-60 MPa, rotational constraint stiffness ξ: 1.5×10 10 ~3×10 10 N·m / rad.

[0158] During the calculation process, the given dimensionless parameters include: the length of the short side of the dimensionless plane segment Dimensionless elastic modulus of corrugated steel Elastic modulus of the composite layer after dimensionlessness Dimensionless corrugated steel thickness Dimensionless composite layer thickness Poisson's ratio μ of the corrugated steel 21 and the composite layer 22 is 0.3 and the rotational constraint stiffness is

[0159] Figure 8 This is a graph showing the influence of the combination coefficient on local stability in Example 3. Figure 8 (a) The relationship between the combination coefficient and the critical instability wave number. Figure 8 (b) The relationship between the combination coefficient and the critical instability load. Figure 8 The influence of the combination coefficient on the critical stability of the composite structure can be obtained from the equation. When the combination coefficient λ varies from 0 to 1, the critical instability wave number after dimensionless calculation is As the combination coefficient λ increases, it decreases; while the dimensionless local critical buckling instability load As the combination coefficient λ increases, it shows a linear increasing trend.

[0160] In summary, when the combination coefficient λ changes in the range of 0 to 1, the combined structure gradually transitions from a free sliding state to a fully combined state, which can increase the thickness, stiffness and other material parameters of the combined structure, while improving the stability of the structure. Therefore, the load required for instability is greater, resulting in the critical buckling instability load after local dimensionlessness. The improvement of stability makes the wavelength of the structure unstable gradually increase, and its wave number will decrease abruptly.

[0161] Therefore, in actual engineering, the appropriate stability effect can be obtained by appropriately changing the combination degree of the combined structure.

[0162] Embodiment 4

[0163] In this embodiment, a composite structure is formed by combining corrugated steel material and concrete material, that is, the corrugated steel 21 is made of corrugated steel material, and the composite layer 22 is made of concrete material. Through experiments and consulting relevant materials, the relevant material parameter range is obtained: the elastic modulus E of the corrugated steel 1 :2.0×10 5 ~2.1×10 5 MPa, corrugated steel thickness t 1 : 1~3mm, the long side length a of the corrugated steel plane section: 5×10 2 ~30×10 2 mm, short side width b of corrugated steel plane section: 30~60mm, Poisson's ratio μ of corrugated steel 21 and concrete: 0~0.5, elastic modulus E of concrete 2 :2.0×10 4 ~4.0×10 4 MPa, concrete thickness t 2 :1~3mm,soil stiffness k:30~60MPa,rotational constraint stiffness ξ:1.5×10 10 ~3×10 10 N·m / rad.

[0164] During the calculation process, the given dimensionless parameters include: the length of the short side of the dimensionless plane segment Dimensionless elastic modulus of corrugated steel Elastic modulus of the composite layer after dimensionlessness Dimensionless corrugated steel thickness The Poisson's ratio of corrugated steel 21 to concrete is μ = 0.2, the interlayer bonding coefficient is λ = 1, and the rotational constraint stiffness is

[0165] Since the thickness of concrete is controllable during the grouting process, this embodiment considers the critical stability situation based on the change of concrete thickness.

[0166] Fig. 9 This is a graph showing the effect of the thickness of the composite layer material on the local stability of Example 4. Fig. 9 (a) Relationship between the thickness of the composite material and the critical instability wave number. Fig. 9 (b) The relationship between the thickness of the composite material and the critical instability load. Fig. 9 It can be seen that within the given dimensionless parameter range, as the dimensionless concrete thickness As the value of Produces a jump-like descent.

[0167] Local critical buckling load after dimensionless calculation With the dimensionless concrete thickness Because the increase in concrete thickness increases the total thickness of the composite structure, resulting in an increase in the stiffness of the composite structure, a higher load is required to make the composite structure reach a critical instability state, so the dimensionless local critical buckling instability load is Gradually increase.

[0168] However, the improvement of stability will gradually increase the wavelength when the structure is unstable, and its wave number will decrease suddenly. The change is to increase the total thickness of the composite structure, thereby increasing the total stiffness of the composite structure. Its effect is similar to the dimensionless composite layer concrete thickness. Similarly, it will not be discussed here. Therefore, it can be concluded that the change in material thickness has a greater impact on the instability behavior of the composite structure. The increase in thickness makes the composite structure have greater rigidity, which means that the composite structure has better stability. Therefore, in actual engineering applications, if conditions permit, the thickness of the composite layer 22 or the corrugated steel 21 can be appropriately increased to improve the stability of the structure.

[0169] The above description is only a preferred embodiment of the present invention, which is only illustrative and not restrictive of the present invention. Those skilled in the art understand that many changes, modifications, and even equivalences may be made to the present invention within the spirit and scope defined by the claims of the present invention, but all of them will fall within the scope of protection of the present invention.

Claims

1. A stability calculation method for a composite corrugated steel pipe culvert, characterized in that: The following steps are involved: Step 1: Determine the relevant material parameters of the corrugated steel and the composite layer, including: corrugated steel thickness t1, composite layer thickness t2, elastic modulus E1 of the corrugated steel, elastic modulus E2 of the composite layer, Poisson's ratio μ1 of the corrugated steel, Poisson's ratio μ2 of the composite layer, corrugated section cutting angle θ, plane section length a, plane section width b, rotational constraint stiffness ξ of the combined structure of the corrugated steel and the composite layer, and combination coefficient λ of the corrugated steel and the composite layer; When the composite structure is in a fully combined state and there is no relative sliding displacement between the layers in the horizontal direction, the corrugated steel and the composite layer have the same neutral plane, and the distances between this neutral plane and the neutral planes of the corrugated steel and the composite layer are t s With t d , When the interlayer contact condition of the composite structure transitions from the free smooth state to the fully bonded state, the neutral layers of the two layers of material will transition from the x1 and x2 axes of the free smooth state to the x0 axis of the fully bonded state, and their distances from x1 and x2 are λt s and λt d ,λ∈[0,1], that is, whenλ=0, the interlayer is in a free and smooth state, whenλ=1, the interlayer is in a completely bonded state; 0<λ<1 is a semi-bonded state; Assume that the loaded edge of the plane segment is simply supported, the unloaded edge of the plane segment is subject to elastic rotation constraint of rotation constraint stiffness ξ, the plane segment of the combined structure of corrugated steel and composite layer is regarded as a rectangular composite plate constrained by the corrugated segment, and assume that the deformation of the combined structure of corrugated steel and composite layer is bending with small deflection, and the cross section and material are isotropic; Step 2: Calculate the total stiffness D of the combined structure of corrugated steel and composite layer; In step 2, the total stiffness D of the combined structure of corrugated steel and composite layer includes the stiffness D1 of corrugated steel, the stiffness D2 of composite layer and the combined stiffness D3 during the transition process from free sliding state to fully combined state of the combined structure, that is, the total stiffness D of the combined structure of corrugated steel and composite layer is: D = D1 + D2 + D3; and: Among them, E1 is the elastic modulus of the corrugated steel, μ1 is the Poisson's ratio of the corrugated steel, and t1 is the thickness of the corrugated steel; Among them, E2 is the elastic modulus of the composite layer, μ2 is the Poisson's ratio of the composite layer, and t2 is the thickness of the composite layer; Among them, t0=t1+t2 is the total thickness of the combined structure of corrugated steel and composite layer, is the relative compressive stiffness of the cross-section of the combined structure of corrugated steel and composite layer, λ is the combination coefficient of the combined structure of corrugated steel and composite layer; Substituting D1, D2 and D3 into the total stiffness D formula of the combined structure of corrugated steel and composite layer, we get: Step 3: Assume that in the y direction, the deformation function of the plane segment is a quartic polynomial function, and in the x direction, the deformation function of the plane segment is a sine series. The deformation function of the plane segment is: In the formula, C m is a constant, M is the total unstable wave number, m is the half unstable wave number, δ is the rotation constraint coefficient, a is the length of the plane segment, b is the width of the plane segment, x is the coordinate along the length a direction, and y is the coordinate along the width b direction; The plane segment boundary conditions of the combined structure of corrugated steel and composite layer are: Step 4: Since the soil can only withstand compression, when the corrugated steel and composite layer structure are in contact with the soil, the soil constraint takes effect. When the corrugated steel and composite layer structure are not in contact with the soil, the soil constraint fails. The local buckling load is calculated by the minimum potential energy principle. The local buckling load Substitution The critical instability wave number m can be obtained cr , the critical instability wave number m cr Substitute the local buckling load The local critical buckling instability load P is obtained x_cr .

2. The stability calculation method of the composite corrugated steel pipe culvert according to claim 1 is characterized in that: In step 3, the rotation constraint coefficient δ of the unloading edge of the plane segment is: Where ξ is the rotational constraint stiffness of the combined structure of corrugated steel and composite layer.

3. The stability calculation method of the composite corrugated steel pipe culvert according to claim 1 is characterized in that: In step 3, when the semi-instability wave number m is an even number, based on the Rayleigh-Ritz calculation method, the total potential energy Λ is expressed as the strain energy U of the combined structure of the corrugated steel and the composite layer e , the external force potential energy V of the combined structure of corrugated steel and composite layer, and the elastic potential energy U of the rotation constraint boundary ξ and the elastic potential energy U of the elastic foundation k The sum of the potential energy Λ is: The strain energy U of the combined structure of corrugated steel and composite layer e , the external force potential energy V of the combined structure of corrugated steel and composite layer, and the elastic potential energy U of the rotation constraint boundary ξ and the elastic potential energy U of the elastic foundation k Substituting the total potential energy Λ, we get: Among them, P x is the axial force per unit length in the x-axis direction of the plane segment, M is the total instability wave number, k is the soil compression stiffness, μ is the Poisson's ratio of the corrugated steel and the composite layer, and the expressions of T1, T2, T3, T4, T5 and T6 are: According to the principle of minimum potential energy, substitute the expressions of T1, T2, T3, T4, T5 and T6 into The local buckling load for the case of an even half-instability wave number can be obtained as for: Where η is the aspect ratio of the straight portion, defined as η = a / b; when When The minimum value of the local critical buckling load P x_cr , the local buckling load Substitution The calculation formula for the even critical instability wave number can be obtained: Substituting the even critical instability wave number into the local buckling load Obtain the local critical buckling instability load P x_cr .

4. The stability calculation method of the composite corrugated steel pipe culvert according to claim 3 is characterized in that: The strain energy U of the combined structure of corrugated steel and composite layer e for:

5. The stability calculation method of composite corrugated steel pipe culvert according to claim 3 is characterized in that: The external force potential energy V of the combined structure of the corrugated steel and the composite layer is: Among them, w is the deformation function, P x is the axial force per unit length in the x-axis direction of the plane segment, P y is the axial force per unit length in the y-axis direction of the plane segment, P xy is the shear force per unit length on the cross section.

6. The stability calculation method of composite corrugated steel pipe culvert according to claim 3 is characterized in that: The elastic potential energy U of the rotation constraint boundary ξ for:

7. The stability calculation method of composite corrugated steel pipe culvert according to claim 3 is characterized in that: The elastic potential energy U of the elastic foundation k for: Where k is the soil compression stiffness.

8. The stability calculation method of composite corrugated steel pipe culvert according to claim 3 is characterized in that: In step 3, when the semi-instability wave number m is an odd number, the total potential energy Λ is: Λ=γU k +U e +U ξ +V; Among them, the support effect γ of the soil is expressed as: or According to the principle of minimum potential energy, substitute the expressions of T1, T2, T3, T4, T5 and T6 into The local buckling load under the case of odd half unstable waves can be obtained when When The minimum value of the local critical buckling load R x_cr , the local buckling load Substitution The calculation formula of odd critical instability wave number can be obtained; When γ=(m-1) / 2m, the odd critical instability wave number calculation formula is: When γ=(m+1) / 2m, the odd critical instability wave number calculation formula is: Then, substitute any odd critical instability wave number mentioned above into the local buckling load Obtain the local critical buckling instability load P x_cr .

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