A Timoshenko beam model equivalent method and system of a corrugated steel plate support structure

Abstract

The present disclosure provides a Timoshenko beam model equivalent method and system of a corrugated steel plate support structure, and relates to the technical field of stress analysis of a corrugated steel plate support structure, comprising: solving the stiffness coefficients of the corrugated steel plate in a local coordinate system, including tensile stiffness, bending stiffness and shear stiffness; solving the equivalent stiffness coefficients of the orthotropic corrugated steel plate in a global coordinate system, including equivalent tensile stiffness, equivalent bending stiffness and equivalent shear stiffness; solving the equivalent section bending stiffness of the corrugated steel support structure; solving the equivalent section shear stiffness of the corrugated steel support structure; and equivalent the corrugated steel support structure to a Timoshenko beam model. The present disclosure can realize the rapid equivalent of the corrugated steel plate support structure to a Timoshenko beam model.

Description

Technical Field

[0001] This disclosure relates to the field of stress analysis technology for corrugated steel plate support structures, specifically to an equivalent method and system for the Timoshenko beam model of corrugated steel plate support structures. Background Technology

[0002] The statements in this section are merely background information relating to this disclosure and do not necessarily constitute prior art.

[0003] Corrugated steel plate support structures have been widely used in the support structures of transportation infrastructure such as culverts, bridges, tunnels, and sheds due to their outstanding advantages such as lightweight, high strength, large deformation adaptability, and convenient construction. Their application prospects are also significant in complex geological conditions such as shallow-buried soft surrounding rock and fault crossings. However, due to the trapezoidal and sinusoidal corrugated structure of the corrugated steel plates, their mechanical properties exhibit significant anisotropy. The structure mainly achieves soil-structure interaction and bearing capacity with the surrounding soil through cross-sectional (lateral) deformation coordination. Therefore, existing research mostly focuses on the stress mechanism, bearing characteristics, and design methods of the cross-section, while systematic research on the longitudinal mechanical response of the structure is relatively lacking.

[0004] However, in practical engineering, shallow-buried corrugated steel plate support structures often face longitudinally uneven loads such as abrupt changes in geological conditions, tunnel excavation disturbances, fault displacement, and local overloading. These loads easily induce uneven longitudinal settlement and deformation of the structure. Corrugated steel plates have low longitudinal torsional stiffness and complex deformation modes. Their longitudinal stress includes not only bending deformation but also significant shear deformation. Excessive uneven deformation can lead to damage such as buckling and weld cracking in the structure itself, and may also trigger a chain reaction of instability in the support system, subsidence of surrounding roadbeds, and failure of traffic facilities, seriously threatening the operational safety of infrastructure and causing significant economic losses. Existing equivalent studies on corrugated steel plates mostly focus on lateral bearing capacity, which is insufficient to meet engineering design requirements.

[0005] Existing methods for studying the longitudinal stress behavior of linear structures such as tunnels, passages, and pipelines commonly employ the approach of equating the structure to an elastic beam model, including the Euler-Bernoulli beam model and the Timoshenko beam model. The Euler-Bernoulli beam model is suitable for slender beams, assuming that the cross-section remains planar before and after deformation and is always perpendicular to the neutral axis, neglecting shear deformation. The Timoshenko beam model, on the other hand, is suitable for scenarios where shear deformation is not negligible. It assumes that the cross-section remains planar after deformation but is no longer perpendicular to the neutral axis, and can simultaneously consider bending and shear deformation. Currently, the longitudinal stress of corrugated steel plate support structures is mainly calculated using numerical methods such as finite element analysis and finite difference analysis. However, these methods suffer from high resource consumption, low computational efficiency, and a lack of corresponding theoretical calculation methods. Therefore, it is urgent to clarify the equivalent longitudinal method for corrugated steel plate support structures to facilitate subsequent theoretical research and methodological innovation. Summary of the Invention

[0006] To address the aforementioned issues, this disclosure proposes an equivalent method and system for the Timoshenko beam model of corrugated steel plate support structures. By applying the Timoshenko beam model to the equivalent of corrugated steel plate support structures, the stress characteristics of longitudinal bending and shear coupling of corrugated steel plates are accurately matched, and the equivalent section bending stiffness and equivalent section shear stiffness of the corrugated steel plate support structure are clearly defined. This method can be directly adapted to the engineering design needs of various scenarios such as culverts, tunnels, and sheds.

[0007] According to some embodiments, the present disclosure adopts the following technical solutions:

[0008] An equivalent method for the Timoshenko beam model of a corrugated steel plate support structure includes:

[0009] Obtain the equivalent corrugated steel plate support structure;

[0010] Calculate the stiffness coefficient of the corrugated steel plate in the local coordinate system;

[0011] The corrugated steel plate is treated as an orthotropic plate. The stress behavior of the corrugated steel plate element and the stress behavior of the corresponding element of the orthotropic plate are analyzed. The equivalent stiffness coefficient of the corrugated steel plate is calculated based on the stiffness coefficient.

[0012] Based on the equivalent stiffness coefficient, considering the influence of cross-sectional shape deformation on the bending stiffness coefficient and the shear stiffness coefficient, the equivalent cross-sectional bending stiffness and equivalent cross-sectional shear stiffness of the corrugated steel plate support structure are calculated.

[0013] Based on the equivalent section bending stiffness and equivalent section shear stiffness of the corrugated steel plate support structure, an equivalent Timoshenko beam model of the corrugated steel plate support structure is constructed according to the Timoshenko beam theory.

[0014] According to some embodiments, the present disclosure adopts the following technical solutions:

[0015] A Timoshenko beam model equivalent system for a corrugated steel plate support structure includes:

[0016] The parameter calculation module is used to obtain the equivalent corrugated steel plate support structure and calculate the stiffness coefficient of the corrugated steel plate in the local coordinate system.

[0017] The equivalent module treats the corrugated steel plate as an orthotropic plate, analyzes the stress behavior of the corrugated steel plate element and the corresponding element of the orthotropic plate, and calculates the equivalent stiffness coefficient of the corrugated steel plate based on the stiffness coefficient. Based on the equivalent stiffness coefficient, considering the influence of cross-sectional shape deformation on the bending stiffness coefficient and shear stiffness coefficient, the equivalent cross-sectional bending stiffness and equivalent cross-sectional shear stiffness of the corrugated steel plate support structure are calculated. Based on the equivalent cross-sectional bending stiffness and equivalent cross-sectional shear stiffness of the corrugated steel plate support structure, the Timoshenko beam equivalent model of the corrugated steel plate support structure is constructed based on the Timoshenko beam theory.

[0018] According to some embodiments, the present disclosure adopts the following technical solutions:

[0019] A computer program product includes a computer program that, when executed by a processor, implements the Timoshenko beam model equivalent method for a corrugated steel plate support structure.

[0020] According to some embodiments, the present disclosure adopts the following technical solutions:

[0021] A non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the Timoshenko beam model equivalent method for a corrugated steel plate support structure.

[0022] According to some embodiments, the present disclosure adopts the following technical solutions:

[0023] An electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute the Timoshenko beam model equivalent method for implementing a corrugated steel plate support structure.

[0024] Compared with the prior art, the beneficial effects of this disclosure are as follows:

[0025] This disclosure presents an equivalent method using the Timoshenko beam model for corrugated steel plate support structures, clarifying the equivalent flexural stiffness and shear stiffness of the structure. The Timoshenko beam model can accurately match the stress characteristics of longitudinal bending and shear coupling of corrugated steel plates. Applying it to the equivalent of corrugated steel plate support structures significantly improves the prediction accuracy of structural settlement and stress distribution under longitudinally uneven loads. It can be directly adapted to the engineering design needs of various scenarios such as culverts, tunnels, and sheds, and can also provide a scientific basis for the longitudinal stability design of structures, effectively avoiding risks such as buckling, weld cracking, and instability of the support system, reducing engineering hazards and subsequent maintenance costs.

[0026] This disclosure presents an equivalent method for the Timoshenko beam model of a corrugated steel plate support structure. It considers the influence of cross-sectional shape deformation on the bending stiffness coefficient and shear stiffness coefficient, and calculates the equivalent cross-sectional bending stiffness and equivalent cross-sectional shear stiffness of the corrugated steel plate support structure. Corrugated steel plate support structures possess a certain degree of flexibility, and their cross-sectional shape deforms during stress. By considering the influence of deformation on the bending stiffness coefficient and shear stiffness coefficient, the equivalent cross-sectional bending stiffness and equivalent cross-sectional shear stiffness of the corrugated steel plate support structure can be obtained with higher calculation accuracy.

[0027] This disclosure discloses an equivalent method for Timoshenko beam models of corrugated steel plate support structures. Based on the obtained equivalent section bending stiffness and equivalent section shear stiffness of the corrugated steel plate support structure, an equivalent Timoshenko beam model of the corrugated steel plate support structure is constructed. This transforms the originally complex mechanical problem of irregular structures into a mature mechanical problem of beam structures, reducing the difficulty and computational cost of subsequent analysis. Attached Figure Description

[0028] The accompanying drawings, which form part of this disclosure, are used to provide a further understanding of this disclosure. The illustrative embodiments of this disclosure and their descriptions are used to explain this disclosure and do not constitute an undue limitation of this disclosure.

[0029] Figure 1 This is a schematic diagram of the Timoshenko beam equivalent method for a corrugated steel plate support structure according to an embodiment of the present disclosure.

[0030] Figure 2 This defines the cross-sectional parameters of the corrugated steel plate according to embodiments of the present disclosure;

[0031] Figure 3 This is a schematic diagram illustrating the corrugated steel sheet as equivalent to an orthogonal irregular-shaped plate in an embodiment of this disclosure;

[0032] Figure 4 This is a schematic diagram of the equivalent stress on a corrugated steel plate unit according to an embodiment of this disclosure;

[0033] Figure 5This defines the dimensional parameters of the circular cross-section of the corrugated steel plate support structure according to embodiments of this disclosure;

[0034] Figure 6 This defines the shape and size parameters of the corrugated steel plate support structure pipe arch cross-section in this embodiment of the disclosure;

[0035] Figure 7 This is a schematic diagram of the equivalent stress on the longitudinal micro-element of the corrugated steel plate support structure according to an embodiment of the present disclosure. Detailed Implementation

[0036] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0037] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains.

[0038] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this disclosure. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0039] Example 1

[0040] One embodiment of this disclosure provides an equivalent method for the Timoshenko beam model of a corrugated steel plate support structure. The method steps are as follows:

[0041] Step 1: Obtain the equivalent corrugated steel plate support structure and calculate the stiffness coefficient of the corrugated steel plate in the local coordinate system;

[0042] Step 2: Treat the corrugated steel plate as an orthotropic plate, analyze the stress behavior of the corrugated steel plate element and the stress behavior of the corresponding element of the orthotropic plate, and calculate the equivalent stiffness coefficient of the corrugated steel plate based on the stiffness coefficient.

[0043] Step 3: Based on the equivalent stiffness coefficient, considering the influence of cross-sectional shape deformation on the bending stiffness coefficient and the shear stiffness coefficient, calculate the equivalent cross-sectional bending stiffness and equivalent cross-sectional shear stiffness of the corrugated steel plate support structure.

[0044] Step 4: Based on the equivalent section bending stiffness and equivalent section shear stiffness of the corrugated steel plate support structure, construct the Timoshenko beam equivalent model of the corrugated steel plate support structure according to the Timoshenko beam theory.

[0045] As one embodiment, this disclosure provides an equivalent method for the Timoshenko beam model of a corrugated steel plate support structure. This method addresses the longitudinal stress of the Timoshenko beam model in such structures, clarifying the calculation schemes for the equivalent section bending stiffness and equivalent section shear stiffness of the corrugated steel plate support structure, while also considering the coupled effects of bending and shear deformation. The specific implementation process is as follows:

[0046] Step S1: Solve for the stiffness coefficients of the corrugated steel plate in the local coordinate system, including tensile stiffness, bending stiffness and shear stiffness;

[0047] Specifically, the corrugated steel plate is composed of a combination of circular arc segments and straight segments, with the dividing point being the tangent point between the straight and circular arc segments. The parameters of the corrugated steel plate support structure are determined as follows:

[0048] like Figure 2 As shown, α The angle of inclination of the line segment; l t The length of the straight line segment; r Let be the inner radius of the arc segment; R The radius corresponding to the axis of the arc segment; c It is half the wavelength; f Half the wave height; l It is half the length of a single-cycle ripple, and the length of a single-cycle ripple is 2. l , t The thickness of the plate; the elastic modulus of the corrugated steel plate is E Poisson's ratio is ν ;

[0049] Furthermore, based on various parameters, the stiffness coefficients of the corrugated steel plate in the local coordinate system are determined using the basic formula of elasticity mechanics for flat steel plates. These coefficients include tensile stiffness coefficient, bending stiffness coefficient, and shear stiffness coefficient. The calculation process includes:

[0050] The stiffness coefficient of corrugated steel plate in the local coordinate system can be determined using the basic formula of elasticity mechanics for flat steel plate, where: the general physical equation of steel plate can be written in the following form:

[0051]

[0052] or,

[0053]

[0054] in, , , These represent the force vector, bending moment vector, and transverse shear force vector in the local coordinate system, respectively. , , These are the strain vector, curvature vector, and transverse shear strain vector of the corrugated plate in the local coordinate system, respectively. , , These are the tensile stiffness matrix, bending stiffness matrix, and shear stiffness matrix of the corrugated plate in the local coordinate system, respectively. k This is the shear correction factor, which is 5 / 6 for rectangular sections.

[0055] coefficients in , , , , These are collectively referred to as tensile stiffness coefficients;

[0056] coefficients in , , , , These are collectively referred to as bending stiffness coefficients;

[0057] coefficients in , These are collectively referred to as shear stiffness coefficients.

[0058] The calculation method for the above coefficients can be determined based on Kirchhoff's classical thin plate theory, and is determined by the thickness of the steel plate, the elastic modulus, and Poisson's ratio.

[0059] Furthermore, the stiffness coefficient of the corrugated steel plate can be obtained as follows:

[0060] (1) Tensile stiffness coefficient , , , , Obtained through the following calculations:

[0061]

[0062] (2) Bending stiffness coefficient , , , , Obtained through the following calculations:

[0063]

[0064] (3) Shear stiffness coefficient , Obtained through the following calculations:

[0065]

[0066] Step S2: Solve for the equivalent stiffness coefficients of the orthotropic corrugated steel plate in the global coordinate system, including the equivalent tensile stiffness, equivalent bending stiffness, and equivalent shear stiffness.

[0067] Specifically, the corrugated steel plate is treated as an orthotropic plate, and the stress behavior of the corrugated steel plate element is analyzed in relation to the stress behavior of the corresponding element in the orthotropic plate. The equivalent stiffness coefficient of the corrugated steel plate is then calculated based on the stiffness coefficient, including:

[0068] (1) Considering the corrugated steel plate as an orthogonal irregular plate, the corrugation extension direction of the corrugated steel plate is as follows: x The direction, perpendicular to the ripples, is y The direction of the corrugated steel sheet is outward. z direction;

[0069] (2) Based on the basic theory of elasticity, construct the corrugated steel plate in the global coordinate system. The constitutive equations are as follows:

[0070]

[0071] in, , , For force components, , , For bending moment components, , This represents the lateral shear force component. , , For strain components, , , For curvature components, , This represents the transverse shear strain component. , , , , This is the equivalent tensile stiffness coefficient. , , , , This is the equivalent bending stiffness coefficient. , This is the equivalent shear stiffness coefficient;

[0072] (3) such as Figure 4 As shown, take a corrugated steel plate unit ( x Take one cycle in the direction. y(Taking the direction per unit width), its stress behavior is compared with that of the corresponding element of the orthotropic plate, and the equivalent stiffness coefficient of the corrugated steel plate is solved using the principle of equivalent stress, the principle of equivalent strain energy, and the law of conservation of energy:

[0073]

[0074] Among them, the various stiffness coefficients , , , , , , , , , , , It has already been obtained in step S1.

[0075] Furthermore, the integral coefficients in the formula , , Obtained through the following methods:

[0076]

[0077]

[0078]

[0079] Furthermore, stiffness coefficient Obtained through the following methods:

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090] After solving the above integral formula, substitute the solutions into the above solutions for S11, S22, S33, S12, S13, S23, etc., and calculate these parameters to obtain K11.

[0091] Step S3: Solve for the equivalent section bending stiffness of the corrugated steel plate support structure;

[0092] Take a section of length along the longitudinal direction of the corrugated steel plate support structure as dx A pair of equal and opposite bending moments are applied at the neutral axes at both ends of a infinitesimal element. M The uncorrected equivalent section bending stiffness coefficient of the corrugated steel plate support structure was obtained through the basic theory of elasticity and the law of conservation of energy:

[0093]

[0094] Among them, the equivalent stiffness coefficient , , , The coefficients have already been obtained in step S2. and The calculation is performed using the following formula:

[0095]

[0096]

[0097] Integral term in the formula , The solution needs to be determined based on the cross-sectional shape.

[0098] For example Figure 5 The radius shown is For a circular cross-section, the integral term is calculated as follows:

[0099]

[0100]

[0101] For example Figure 6 The illustrated tubular arch cross-section shows that the arch axis is composed of three circular arcs of different radii, with the dividing point being the tangent point of two adjacent arcs. , , These are the radii of the arcs at the invert, axle, and crown positions, respectively. S , H These are the cross-sectional span and height, respectively. B The distance from the center of the arc at the axle position to the bottom of the structure is the height. The distance from the centerline of the cross-section to the bottom of the structure is [height / value]. and Let the heights of the two dividing points (tangent points) of the three circular arcs be respectively, and their distances be from the bottom of the structure. Then, the integral term is calculated as follows:

[0102] Considering the influence of cross-sectional shape deformation on the bending stiffness coefficient, the bending stiffness coefficient of the uncorrected equivalent cross-section is corrected, and the bending stiffness correction coefficient is taken as [value missing]. The equivalent section bending stiffness of the corrected corrugated steel plate support structure is:

[0103]

[0104] Step S4: Solve for the equivalent cross-sectional shear stiffness of the corrugated steel plate support structure;

[0105] Specifically, such as Figure 7 As shown, a section of length is taken along the longitudinal direction of the corrugated steel structure. dx A pair of equal and opposite shear forces are applied at the neutral axes at both ends of the infinitesimal element. The uncorrected equivalent section shear stiffness of the corrugated steel plate support structure was obtained through the basic theory of elasticity and the law of conservation of energy:

[0106]

[0107] stiffness coefficient in the formula , It has already been obtained in step S2.

[0108] Integral term in the formula , The solution needs to be determined based on the cross-sectional shape.

[0109] For example Figure 5 The integral term for the circular cross-section shown is calculated as follows:

[0110]

[0111]

[0112] For example Figure 6 The integral term for the arched cross-section shown is calculated as follows:

[0113]

[0114]

[0115] Furthermore, considering the influence of cross-sectional shape deformation on the shear stiffness coefficient, the shear stiffness coefficient of the uncorrected equivalent cross-section is corrected, and the shear stiffness correction coefficient is set to a value of [value missing]. The equivalent section shear stiffness of the corrected corrugated steel plate support structure is:

[0116]

[0117] Step S5: Equivalently model the corrugated steel plate support structure as a Timoshenko beam model;

[0118] Based on the equivalent section bending stiffness of the corrugated steel plate support structure obtained in steps S3 and S4 and equivalent section shear stiffness According to Timoshenko beam theory, the bending moment of a corrugated steel plate supported structure is equivalent to that of a Timoshenko beam. and shear force The expression is:

[0119]

[0120]

[0121] In the formula and These represent the vertical deformation and deflection angle of the Timoshenko beam under load.

[0122] Finally, the Timoshenko beam model equivalent of the corrugated steel plate support structure was completed using the above method.

[0123] The Timoshenko beam equivalent model disclosed herein can be used to conduct theoretical research on the longitudinal stress behavior of linear structures such as tunnels, passages, and pipelines. Corrugated steel plate support structures, as a type of underground support structure, can be used to conduct longitudinal characteristic theoretical analysis.

[0124] Example 2

[0125] One embodiment of this disclosure provides a Timoshenko beam model equivalent method for corrugated steel plate support structures, when the various parameters of the corrugated steel plate support structure are determined. α = 47.3°、 l t = 25.5mm r = 53mm 、R = 56.25mm 、c = 100mm 、f = 27.5mm l = 118.37mm 、t = At 6.5mm, the elastic modulus of the corrugated steel plate is E= 206000MPa, Poisson's ratio is ν= 0.3; The cross-sectional shape of the corrugated steel plate support structure is circular, and the dimensional parameters of the cross-sectional shape are defined as follows: Figure 5 As shown, the specific parameter values ​​for Example 2 are: = 5500mm, then the specific implementation process of the Timoshenko beam equivalent method for a corrugated steel plate support structure disclosed in this paper is as follows:

[0126] Step S1: Solve for the stiffness coefficient of the corrugated steel plate in the local coordinate system;

[0127] The calculation results of the tensile stiffness parameters of the flat steel plate are as follows:

[0128]

[0129]

[0130]

[0131] The calculation results of the bending stiffness parameters of the flat steel plate are as follows:

[0132]

[0133]

[0134]

[0135] The calculation results of the bending stiffness parameters of the flat steel plate are as follows:

[0136]

[0137] Step S2: Solve for the equivalent stiffness coefficient of the orthotropic corrugated steel plate in the global coordinate system;

[0138] Integral coefficient , , The calculation result is:

[0139]

[0140]

[0141]

[0142] stiffness coefficient The calculation result is:

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152] Therefore, the equivalent stiffness coefficient of the corrugated steel plate is:

[0153] Equivalent tensile stiffness:

[0154]

[0155]

[0156]

[0157]

[0158] Equivalent bending stiffness:

[0159]

[0160]

[0161]

[0162]

[0163] Equivalent shear stiffness:

[0164]

[0165]

[0166] Step S3: Solve for the equivalent section bending stiffness of the corrugated steel support structure;

[0167] stiffness coefficient , , , The coefficients have been obtained in step S1. and The calculation is performed using the following formula:

[0168]

[0169]

[0170] Example 2: The corrugated steel plate support structure has a circular cross-section, and the integral term... , The result is:

[0171]

[0172]

[0173] Therefore, the equivalent sectional bending stiffness of the corrugated steel plate support structure is:

[0174]

[0175] Step S4: Solve for the equivalent cross-sectional shear stiffness of the corrugated steel support structure;

[0176] stiffness coefficient , It has already been obtained in step S2.

[0177] Example 2: The corrugated steel plate support structure has a circular cross-section, and the integral term... , The result is:

[0178]

[0179]

[0180] Therefore, the equivalent cross-sectional shear stiffness of the corrugated steel plate support structure is:

[0181]

[0182] Step S5: Equivalently model the corrugated steel support structure as a Timoshenko beam.

[0183] Steps S3 and S4 have yielded the equivalent section bending stiffness of the corrugated steel plate support structure. and equivalent section shear stiffness According to Timoshenko beam theory, the bending moment of a corrugated steel plate supported structure is equivalent to that of a Timoshenko beam. and shear force The expression is:

[0184]

[0185]

[0186] In the formula, and These represent the vertical deformation and deflection angle of the Timoshenko beam under load.

[0187] Thus, the equivalent Timoshenko beam model of the corrugated steel plate support structure was completed using the above method.

[0188] To verify the accuracy of the calculation results, ABAQUS finite element software was used to perform a detailed simulation calculation on Example 2, employing methods such as... Figure 7 Simulation calculations were performed on the stress loading mode shown, and the equivalent flexural stiffness and equivalent shear stiffness of the corrugated steel plate support structure were calculated. The calculation results are as follows:

[0189]

[0190]

[0191] The ratio of the calculation results in this publication to the simulation calculation results is:

[0192] ,

[0193] As can be seen, the ratios of the calculation results in Example 2 to the simulation results are all above 0.9, indicating a high degree of agreement and verifying the accuracy of the calculation method disclosed herein.

[0194] Example 3

[0195] One embodiment of this disclosure provides a Timoshenko beam model equivalent method for corrugated steel plate support structures, when the various parameters of the corrugated steel plate support structure are determined. α = 51.1°、 l t = 102.07mm r = 76.2mm 、R = 81.2mm 、 c = 190.5mm 、f = 70mm l = 246.91mm 、t = 10mm; the elastic modulus of the corrugated steel plate is E= 206000MPa, Poisson's ratio is ν= At 0.3, the cross-sectional shape of the corrugated steel plate support structure is a tubular arch, and the dimensional parameters of the cross-sectional shape are defined as follows: Figure 6 As shown, the specific parameter values ​​for Example 3 are: = 9650mm = 1660mm = 5140mm, S = 10277.56mm, H = 7505mm, B = 2457.07mm, = 3503.55mm = 962.67mm = 2500.99mm. The specific implementation process of the Timoshenko beam model equivalent method for a corrugated steel plate support structure disclosed in this paper is as follows:

[0196] Step S1: Solve for the stiffness coefficient of the corrugated steel plate in the local coordinate system;

[0197] The calculation results of the tensile stiffness parameters of the flat steel plate are as follows:

[0198]

[0199]

[0200]

[0201] The calculation results of the bending stiffness parameters of the flat steel plate are as follows:

[0202]

[0203]

[0204]

[0205] The calculation results of the bending stiffness parameters of the flat steel plate are as follows:

[0206]

[0207] Step S2: Solve for the equivalent stiffness coefficient of the orthotropic corrugated steel plate in the global coordinate system;

[0208] Integral coefficient , , The calculation result is:

[0209]

[0210]

[0211]

[0212] stiffness coefficient The calculation result is:

[0213]

[0214]

[0215]

[0216]

[0217]

[0218]

[0219]

[0220]

[0221]

[0222]

[0223] Therefore, the equivalent stiffness coefficient of the corrugated steel plate is:

[0224] Equivalent tensile stiffness:

[0225]

[0226]

[0227]

[0228]

[0229] Equivalent bending stiffness:

[0230]

[0231]

[0232]

[0233]

[0234] Equivalent shear stiffness:

[0235]

[0236]

[0237] Step S3, solve for the equivalent flexural stiffness of the corrugated steel support structure:

[0238] stiffness coefficient , , , The coefficients have been obtained in step S1. and The calculation is performed using the following formula:

[0239]

[0240]

[0241] Example 2: The corrugated steel plate support structure has a pipe arch cross-section, and the integral term... , The result is:

[0242]

[0243] Therefore, the equivalent sectional bending stiffness of the corrugated steel plate support structure is:

[0244]

[0245] Step S4, solve for the equivalent section shear stiffness of the corrugated steel support structure:

[0246] stiffness coefficient , It has already been obtained in step S2.

[0247] Example 3: The corrugated steel plate support structure has a pipe arch cross-section, and the integral term... , The result is:

[0248] Therefore, the equivalent cross-sectional shear stiffness of the corrugated steel plate support structure is:

[0249] Equivalent section shear stiffness:

[0250]

[0251] Step S5: Equivalently model the corrugated steel support structure as a Timoshenko beam.

[0252] Steps S3 and S4 have yielded the equivalent section bending stiffness of the corrugated steel plate support structure. and equivalent section shear stiffness According to Timoshenko beam theory, the bending moment of a corrugated steel plate supported structure is equivalent to that of a Timoshenko beam. and shear force The expression is:

[0253]

[0254]

[0255] In the formula and These represent the vertical deformation and deflection angle of the Timoshenko beam under load.

[0256] Thus, the equivalent Timoshenko beam model of the corrugated steel plate support structure was completed using the above method.

[0257] To verify the accuracy of the calculation results, ABAQUS finite element software was used to perform a detailed simulation calculation on Example 3, employing methods such as... Figure 7 Simulation calculations were performed on the stress loading mode shown, and the equivalent flexural stiffness and equivalent shear stiffness of the corrugated steel plate support structure were calculated. The calculation results are as follows:

[0258]

[0259]

[0260] The ratio of the calculation results in this publication to the simulation calculation results is:

[0261] , ,

[0262] As can be seen, the ratios of the calculation results in Example 3 to the simulation results are all above 0.9, indicating a high degree of agreement and verifying the accuracy of the calculation method disclosed herein.

[0263] Example 4

[0264] One embodiment of this disclosure provides a Timoshenko beam model equivalent system for a corrugated steel plate support structure, including:

[0265] The parameter calculation module is used to obtain the equivalent corrugated steel plate support structure and calculate the stiffness coefficient of the corrugated steel plate in the local coordinate system.

[0266] The equivalent module treats the corrugated steel plate as an orthotropic plate, analyzes the stress behavior of the corrugated steel plate element and the corresponding element of the orthotropic plate, and calculates the equivalent stiffness coefficient of the corrugated steel plate based on the stiffness coefficient. Based on the equivalent stiffness coefficient, considering the influence of cross-sectional shape deformation on the bending stiffness coefficient and shear stiffness coefficient, the equivalent cross-sectional bending stiffness and equivalent cross-sectional shear stiffness of the corrugated steel plate support structure are calculated. Based on the equivalent cross-sectional bending stiffness and equivalent cross-sectional shear stiffness of the corrugated steel plate support structure, the Timoshenko beam equivalent model of the corrugated steel plate support structure is constructed based on the Timoshenko beam theory.

[0267] Example 5

[0268] One embodiment of this disclosure provides a computer program product, including a computer program that, when executed by a processor, implements the Timoshenko beam model equivalent method for a corrugated steel plate support structure.

[0269] Example 6

[0270] One embodiment of this disclosure provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the Timoshenko beam model equivalent method for a corrugated steel plate support structure.

[0271] Example 7

[0272] One embodiment of this disclosure provides an electronic device, including a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to execute the Timoshenko beam model equivalent method for implementing a corrugated steel plate support structure.

[0273] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0274] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0275] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A Timoshenko beam model equivalent method for corrugated steel plate support structures, characterized in that, include: Obtain the equivalent corrugated steel plate support structure; Calculate the stiffness coefficient of the corrugated steel plate in the local coordinate system; The corrugated steel plate is treated as an orthotropic plate. The stress behavior of the corrugated steel plate element and the stress behavior of the corresponding element of the orthotropic plate are analyzed. The equivalent stiffness coefficient of the corrugated steel plate is calculated based on the stiffness coefficient. Based on the equivalent stiffness coefficient, considering the influence of cross-sectional shape deformation on the bending stiffness coefficient and the shear stiffness coefficient, the equivalent cross-sectional bending stiffness and equivalent cross-sectional shear stiffness of the corrugated steel plate support structure are calculated. The equivalent section bending stiffness is: ； in, For equivalent section bending stiffness, This is the bending stiffness correction factor, and the factor is... ,coefficient , , , This is the equivalent tensile stiffness coefficient. , , This is the equivalent bending stiffness coefficient. , This is the integral term, determined based on the cross-sectional shape; The equivalent section shear stiffness is: ； in, For equivalent section shear stiffness, This is the shear stiffness correction factor. This is the equivalent tensile stiffness coefficient. This is the equivalent shear stiffness coefficient. , This is the integral term, determined based on the cross-sectional shape; Based on the equivalent section bending stiffness and equivalent section shear stiffness of the corrugated steel plate support structure, and based on the Timoshenko beam theory, expressions for the bending moment and shear force of the equivalent Timoshenko beam of the corrugated steel plate support structure are constructed, and the vertical deformation and deflection angle of the Timoshenko beam under load are calculated. The bending moment is: ； in, For bending moment, For equivalent section bending stiffness, The angle of deflection of the Timoshenko beam under load; The shear force is: ； in, For shear force, For equivalent section shear stiffness, and These represent the vertical deformation and deflection angle of the Timoshenko beam under load.

2. The Timoshenko beam model equivalent method for a corrugated steel plate support structure as described in claim 1, characterized in that, The process of obtaining the equivalent corrugated steel plate support structure and calculating the stiffness coefficient of the corrugated steel plate in the local coordinate system includes: The corrugated steel plate support structure is composed of a combination of arc segments and straight segments, with the dividing point being the tangent point between the straight segments and the arc segments, thus determining various parameters of the corrugated steel plate support structure. Based on various parameters, the stiffness coefficients of corrugated steel plates in the local coordinate system are determined using the basic formula of elasticity mechanics for flat steel plates. These coefficients include tensile stiffness coefficient, bending stiffness coefficient, and shear stiffness coefficient.

3. The Timoshenko beam model equivalent method for a corrugated steel plate support structure as described in claim 1, characterized in that, The process of treating corrugated steel plates as orthotropic plates, analyzing the stress behavior of corrugated steel plate elements and corresponding elements of orthotropic plates, and calculating the equivalent stiffness coefficient of the corrugated steel plate based on the stiffness coefficient includes: Treating the corrugated steel plate as an orthogonal irregular plate, a global coordinate system is defined, and the corrugation extension direction of the corrugated steel plate is... x The direction, perpendicular to the ripples, is y The direction of the corrugated steel sheet is outward. z direction; Based on the fundamental theory of elasticity, the constitutive equations of the corrugated steel plate in the global coordinate system are constructed. Take a corrugated steel plate element, compare its stress behavior with that of the corresponding element of the orthotropic plate, and use the principle of equivalent stress, the principle of equivalent strain energy and the law of conservation of energy to solve for the equivalent stiffness coefficient of the corrugated steel plate.

4. The Timoshenko beam model equivalent method for a corrugated steel plate support structure as described in claim 1, characterized in that, Based on the equivalent stiffness coefficient, considering the influence of cross-sectional shape deformation on the bending stiffness coefficient and shear stiffness coefficient, the equivalent cross-sectional bending stiffness and equivalent cross-sectional shear stiffness of the corrugated steel plate support structure are calculated, including: A micro-element of a set length is taken along the longitudinal direction of the corrugated steel plate support structure. A pair of equal and opposite bending moments are applied at the neutral axis positions at both ends of the micro-element. The uncorrected equivalent section bending stiffness coefficient of the corrugated steel plate support structure is calculated by using the basic theory of elasticity and the law of conservation of energy. Considering the influence of cross-sectional shape deformation on the bending stiffness coefficient, the uncorrected equivalent cross-sectional bending stiffness coefficient is corrected to obtain the corrected equivalent cross-sectional bending stiffness of the corrugated steel plate support structure.

5. The Timoshenko beam model equivalent method for a corrugated steel plate support structure as described in claim 4, characterized in that, A micro-element of a set length is taken along the longitudinal direction of the corrugated steel structure. A pair of equal and opposite shear forces are applied at the neutral axis positions at both ends of the micro-element. The uncorrected equivalent section shear stiffness of the corrugated steel plate support structure is calculated by using the basic theory of elasticity and the law of conservation of energy. Considering the influence of section shape deformation on the shear stiffness coefficient, the uncorrected equivalent section shear stiffness coefficient is corrected to obtain the corrected equivalent section shear stiffness of the corrugated steel plate support structure.

6. A Timoshenko beam model equivalent system for a corrugated steel plate support structure, employing the Timoshenko beam model equivalent method for a corrugated steel plate support structure as described in any one of claims 1-5, characterized in that, include: The parameter calculation module is used to obtain the equivalent corrugated steel plate support structure and calculate the stiffness coefficient of the corrugated steel plate in the local coordinate system. The equivalent module treats the corrugated steel plate as an orthotropic plate, analyzes the stress behavior of the corrugated steel plate element and the corresponding element of the orthotropic plate, and calculates the equivalent stiffness coefficient of the corrugated steel plate based on the stiffness coefficient. Based on the equivalent stiffness coefficient, considering the influence of cross-sectional shape deformation on the bending stiffness coefficient and shear stiffness coefficient, the equivalent cross-sectional bending stiffness and equivalent cross-sectional shear stiffness of the corrugated steel plate support structure are calculated. Based on the equivalent cross-sectional bending stiffness and equivalent cross-sectional shear stiffness of the corrugated steel plate support structure, the Timoshenko beam equivalent model of the corrugated steel plate support structure is constructed based on the Timoshenko beam theory.

7. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the Timoshenko beam model equivalent method for a corrugated steel plate support structure as described in any one of claims 1-5.

8. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the Timoshenko beam model equivalent method for a corrugated steel plate support structure as described in any one of claims 1-5.

9. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to perform the Timoshenko beam model equivalent method for implementing a corrugated steel plate support structure as described in any one of claims 1-5.

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