A method for analyzing torsional stress of a curved box girder with corrugated steel webs based on prestress effect

Abstract

The application relates to the technical field of highway and railway bridge design, and discloses a corrugated steel web curved box girder torsional stress analysis method based on prestress effect, which comprises the following steps: S1, determining the mechanical characteristics of the corrugated steel web box girder bridge; S2, performing equivalent load processing on the prestress effect and performing reasonable simplification; S3, establishing a constraint torsion differential equation of the corrugated steel web combined curved box girder to obtain the constraint torsional normal stress and the constraint torsional shear stress of the required section; S4, combining the curved beam boundary conditions, the torsional double moment and the torsional stress formula of the box girder under various load conditions, adopting the initial parameter method to superimpose the boundary conditions into the general solution form of the constraint torsion differential equation of the corrugated steel web combined curved box girder, extracting the calculation data of the torsional stress of the corrugated steel web combined curved box girder, and analyzing to obtain the torsional stress result of the corrugated steel web combined curved box girder. The corrugated steel web curved box girder bridge torsional performance based on the prestress effect is researched by adopting the application.

Description

Technical Field

[0001] This application relates to the field of highway and railway bridge design technology, specifically a method for analyzing torsional stress in corrugated steel web curved box girders based on prestressing effects. Background Technology

[0002] Traditional curved bridges and curved beam bridges mostly use prestressed concrete box girder structures. As the span increases, the thickness of the box girder web increases due to the need for prestressed steel strand arrangement. This leads to an increasing proportion of the web weight in the bridge span structure, which seriously affects the bridge's spanning capacity. Therefore, corrugated steel web composite box girder bridges have emerged.

[0003] Under eccentric loads, the box girder of this new type of bridge will undergo torsion. Excessive torsional deformation will make it difficult to guarantee the comfort and safety of vehicle travel. Furthermore, due to the torsional effect generated by the prestressed steel strands in curved bridges, excessive torsional effect will have a more detrimental impact on the bridge structure. Currently, research on the torsional performance of corrugated steel webs is still in its early stages, and most studies focus on single-cell, single-box straight box girder bridges with corrugated steel webs. Research on the torsional performance of curved box girder bridges with corrugated steel webs is scarce, especially research on the torsional performance of curved box girder bridges with corrugated steel webs based on prestressing effects, which is almost non-existent. Therefore, there is an urgent need for a torsional stress analysis technique for curved box girders with corrugated steel webs based on prestressing effects. Summary of the Invention

[0004] The purpose of this application is to provide a method for analyzing the torsional stress of corrugated steel web curved box girders based on the prestressing effect, so as to improve the calculation theory of corrugated steel web curved box girders.

[0005] To achieve the above objectives, this application discloses the following technical solution: This application discloses a method for torsional stress analysis of corrugated steel web curved box girders based on prestressing effect, the method comprising the following steps: S1. Clarify the mechanical characteristics of corrugated steel web box girder bridges; S2. Treat the prestressing effect as an equivalent load and simplify it appropriately; S3. Establish the constrained torsion differential equation for the corrugated steel web composite curved box girder, and obtain the constrained torsion normal stress and constrained torsion shear stress of the required section. S4. Combining the boundary conditions of the curved beam and the formulas for the torsional double moment and torsional stress of the box girder under various load conditions, the initial parameter method is used to superimpose them into the general solution form of the constrained torsional differential equation of the corrugated steel web composite curved box girder. The calculation data of the torsional stress of the corrugated steel web composite curved box girder are extracted, and the torsional stress results of the corrugated steel web composite curved box girder are obtained through analysis.

[0006] Preferably, in S1, the mechanical characteristics include the longitudinal elastic modulus of the corrugated steel web and the effective shear modulus of the corrugated steel web. The expression for the longitudinal elastic modulus is: in, The longitudinal elastic modulus of the corrugated steel web along the longitudinal direction of the bridge is given. For the thickness of the corrugated steel web along the longitudinal direction of the bridge, This refers to the wave height of the corrugated steel web along the longitudinal direction of the bridge. The shape factor of the corrugated steel web; The expression for the effective shear modulus of corrugated steel web is: in, The length of the straight section. This refers to the longitudinal dimension of the inclined slab segment in the bridge. The angle between the inclined plate segment and the straight plate segment. For effective shear modulus, This is the shear modulus of the corrugated steel web.

[0007] Preferably, in S2, the equivalent load expression for the prestress acting on the curved box girder bridge section with corrugated steel web is: in, For the equivalent uniformly distributed force of prestress in the vertical direction of the curved beam, The equivalent uniformly distributed force of prestress in the radial direction of the curved beam is... This refers to the equivalent uniformly distributed force of prestress in the tangential direction of the curved beam. The equivalent uniformly distributed torque of prestress in the vertical direction of the curved beam is given by [the torque]. The equivalent uniformly distributed torque of the prestress in the radial direction of the curved beam is given by [the torque]. The equivalent uniformly distributed torque of prestress in the tangential direction of the curved beam is... The magnitude of the preload, Let be the radius of curvature of the curved beam. Let be the transverse coordinate of the prestressed steel strand. For the longitudinal coordinates of the prestressed steel strands, superscript... For the first derivative with respect to the arc length of the curved beam, the superscript is... This is the second derivative with respect to the arc length of the curved beam.

[0008] Preferably, in S2, the vertical coordinates of the prestressed steel strands are not considered. When the load changes longitudinally, the simplified equivalent load expression for the prestress acting on the cross section of a corrugated steel web curved box girder bridge is: At this point, the prestressed equivalent load is simplified to a radially distributed force and a uniformly distributed torque along the entire length of the bridge.

[0009] Preferably, S3 specifically includes: Obtaining the differential equation for torsional warping of a curved box girder Where m is the external torque intensity, , The total torsional angle of the cross section. The warping function of the cross section, with superscripts relative to the vertical coordinates. The derivative of the corrugated steel web, For concrete top and bottom slabs, , For concrete, the elastic modulus; for corrugated steel webs, For concrete top and bottom slabs, , For concrete shear modulus; for generalized sector moment of inertia Principal sector coordinates of closed section , For the sector coordinates of the closed section, It is twice the area of ​​the closed cross section. ds For a curved arc segment, in the case of a corrugated steel web, , For corrugated steel web thickness; for concrete top and bottom slabs, , Thickness of the concrete top and bottom slabs; free torsional moment of inertia ; The warping function can be obtained using deformation and equilibrium conditions. Total torsion angle The relationship between them yields a torsional differential equation expressed by the warp function. ; v The warpage factor is 1. Polar moment of inertia , The radius of curvature of the neutral layer. dA It is a small area on the cross section; Based on the equilibrium equation of the torque along the z-axis of the curved beam, and considering the equivalent load of the prestressing effect, we have: ,in ， The uniformly distributed torque generated by the curvature. For the uniformly distributed torque acting on the curved beam, The uniformly distributed torque along the z-axis generated by the prestressed equivalent load. The torque generated is the bending moment caused by the radially distributed force produced by the prestressed equivalent load. The uniformly distributed torque is caused by the radially distributed force generated by the prestressed equivalent load. definition Where k is the warp-torsional attenuation coefficient; Substituting into the torsional warping differential equation, we obtain the torsional differential equation considering the prestressed equivalent load as follows: ; Based on the fundamental assumptions of Ubbelohde's second warping theory, the formula for the constrained torsional normal stress of a thin-walled closed section is: Wherein, the constrained torsional bi-moment B is the total cross-sectional torsional bi-moment after considering the prestress effect, and the generalized sector moment of inertia For corrugated steel webs, For concrete top and bottom slabs, , The elastic modulus of concrete; principal sector coordinates of the closed section. , For the sector coordinates of the closed section, It is twice the area of ​​the closed cross section; The formula for constrained torsional shear stress in a thin-walled closed section is: ,in The bending torsional moment of the closed section. The converted sector static moment of the cross section; The shear stress of the corrugated steel plate is ,in, L The total torque after taking into account the prestress effect.

[0010] Preferably, S4 specifically includes: Choose an arbitrary cross-section for the coordinate system, and let the angle of twist at the cross-section where z=0 be . 0, torque is The two torques are The torque is ; Find the general solution to the homogeneous equation of the torsional differential equation considering the prestressed equivalent load. The homogeneous equation has the following form: The general solution is as follows: ,in Let be the state vector of any cross section. To affect the function matrix or transformation matrix, Let be the initial state vector, and , , The superscript T is the transpose symbol for the matrix; Based on the particular solutions of the homogeneous constrained torsion differential equation under various load state vectors, the general solution of the non-homogeneous constrained torsion differential equation is obtained by superimposing the particular solutions under each load with the general solution of the homogeneous constrained torsion differential equation.

[0011] Preferably, when, in addition to the existence of an initial state vector, there is a concentrated load at a certain cross-section t, i.e., another set of vectors acting at z=t, the step of obtaining the general solution of the non-homogeneous constrained torsion differential equation by superimposing the particular solutions of each load under various load state vectors with the general solution of the homogeneous constrained torsion differential equation includes: When z ≤ t, we have ; When z > t, we have ; in, .

[0012] Preferably, when a uniformly distributed load exists on a certain section of the cross-section of the closed-loop corrugated steel web curved box girder, i.e., a uniformly distributed load acts on the section where a≤z≤b. When applied, the method of obtaining the general solution of the non-homogeneous constrained torsion differential equation by superimposing the particular solutions of the homogeneous constrained torsion differential equation under various load state vectors with the general solution of the homogeneous constrained torsion differential equation includes: When z ≤ a, we have ; When a < z ≤ c, we have ; When z > c, we have: .

[0013] Preferably, when a distributed force acts on the closed corrugated steel web curved box girder at a≤z≤c... Function, and when When it is a constant, .

[0014] Technical Effects: The torsional stress analysis method for corrugated steel web curved box girders based on prestressing effect proposed in this application treats the prestressing effect as an equivalent load, establishes the torsional differential equation using Ubbelohde's second warping theory, and solves it using the initial parameter method. This is a relatively practical calculation and analysis method that considers the prestressing effect. Furthermore, the torsional stress analysis of corrugated steel web composite curved box girder bridges under bending-torsional coupling based on prestressing effect is of positive significance for the application and promotion of this new bridge structure. It can also improve the torsional calculation theory of this type of bridge and provide a reference for the formulation of relevant code provisions. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of a corrugated steel web. Figure 2 Schematic diagram of prestress components and their coordinate relationships; Figure 3 This is a schematic diagram of the cross-section of a corrugated steel web curved box girder bridge. Figure 4 This is a schematic diagram of the shape of the corrugated steel web. Figure 5 A simplified cross-sectional diagram of a corrugated steel web curved box girder bridge; Figure 6 This is a diagram showing the arrangement of prestressed steel strands; Figure 7 The diagram shows the constrained torsional normal stress (MPa). Figure 8 The diagram shows the constrained torsional shear stress (MPa). Detailed Implementation

[0017] The technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0018] In this document, the term "comprising" is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0019] This embodiment provides a method for torsional stress analysis of corrugated steel web curved box girders based on prestressing effect, including the following steps: S1. Clarify the mechanical characteristics of corrugated steel web box girder bridges; S2. Treat the prestressing effect as an equivalent load and simplify it appropriately; S3. Considering the influence of bending-torsional coupling and shear deformation of curved box girders, based on the warping displacement theory and combined with the special characteristics of bending-torsional coupling of corrugated steel web curved beams and the prestress effect applied to them, the constrained torsion differential equation of corrugated steel web composite curved box girder is established, and the constrained torsion normal stress and constrained torsion shear stress of the required section are obtained. S4. Combining the boundary conditions of the curved beam, the formulas for the torsional double moment and torsional stress of the box girder under various load conditions are superimposed using the initial parameter method to obtain the general solution form of the constrained torsional differential equation of the corrugated steel web composite curved box girder. The calculation data of the torsional stress of the corrugated steel web composite curved box girder are extracted, and the torsional stress results of the corrugated steel web composite curved box girder are obtained through analysis.

[0020] Furthermore, in S1, the mechanical characteristics of the corrugated steel web box girder bridge are the longitudinal elastic modulus of the corrugated steel web and the effective shear modulus of the corrugated steel web. The longitudinal elastic modulus of the corrugated steel web along the bridge longitudinal direction... Its thickness t, wave height h, and shape factor of the steel plate The relevant expression is as follows: (14) Furthermore, due to the corrugations in the web of the corrugated steel, its effective shear modulus is related to the shear modulus of the steel plate, and its expression is as follows: (15) in, The length of the straight section. This refers to the longitudinal dimension of the inclined slab segment in the bridge. The angle between the inclined plate segment and the straight plate segment. For effective shear modulus, Let be the shear modulus of the corrugated steel web, and b , d The meaning is evident. Figure 1 Marking.

[0021] Furthermore, in S2, the most significant stress characteristic of the corrugated steel web curved box girder bridge is bending-torsional coupling. Under the action of prestress, it will also produce bending-torsional coupling effect caused by prestress. Due to the spatial effect of the corrugated steel web curved box girder bridge, its stress is more complex than that of the corrugated steel web straight box girder bridge. Therefore, the prestress effect needs to be treated as an equivalent load and reasonably simplified.

[0022] The equivalent load expression for the prestress acting on the cross section of a curved box girder bridge with corrugated steel web is: (16) In the formula, W and Q are the equivalent uniformly distributed force and torque of the prestressing, the subscripts L, M, and N are the tangential, radial, and vertical directions of the curved beam, F is the magnitude of the prestressing force, R is the radius of curvature of the curved beam, and h and z are the transverse and vertical coordinates of the prestressed steel strands, respectively. For the equivalent uniformly distributed force of prestress in the vertical direction of the curved beam, The equivalent uniformly distributed force of prestress in the radial direction of the curved beam is... This refers to the equivalent uniformly distributed force of prestress in the tangential direction of the curved beam. The equivalent uniformly distributed torque of prestress in the vertical direction of the curved beam is given by [the torque]. The equivalent uniformly distributed torque of the prestress in the radial direction of the curved beam is given by [the torque]. The equivalent uniformly distributed torque of prestress in the tangential direction of the curved beam is... The magnitude of the preload, Let be the radius of curvature of the curved beam. Let be the transverse coordinate of the prestressed steel strand. Let be the longitudinal coordinates of the prestressed steel strands, and its corresponding prestress components and coordinate relationships be as follows: Figure 2 As shown. In addition, superscript For the first derivative with respect to the arc length of the curved beam, the superscript is... This is the second derivative with respect to the arc length of the curved beam.

[0023] Preferably, without considering the variation of the vertical coordinate z of the prestressed steel strand along the longitudinal direction, equation (16) simplifies to: (17) At this point, the prestressed equivalent load is simplified to a radially distributed force and a uniformly distributed torque along the entire length of the bridge.

[0024] Furthermore, in S3, the geometric physical equations of the unit volume are used. The differential equation for the torsional warping of a curved box girder can be derived as follows: (18) Where m is the external torque intensity. The total torsional angle of the cross section. The warping function of the cross section, with superscripts relative to the vertical coordinates. The derivative of the corrugated steel web, For concrete top and bottom slabs, , For concrete, the elastic modulus; for corrugated steel webs, For concrete top and bottom slabs, , For concrete shear modulus; for generalized sector moment of inertia Principal sector coordinates of closed section , For the sector coordinates of the closed section, It is twice the area of ​​the closed cross section. ds For a curved arc segment, in the case of a corrugated steel web, , For corrugated steel web thickness; for concrete top and bottom slabs, , Thickness of the concrete top and bottom slabs; free torsional moment of inertia ; The warping function can be obtained using deformation and equilibrium conditions. Total torsion angle The relationship between these factors yields a torsional differential equation expressed by the warp function: (19) in The warpage factor is 1. Polar moment of inertia , The radius of curvature of the neutral layer. dA Let be the infinitesimal area on the cross section.

[0025] Based on the equilibrium equation of the torque along the z-axis of the curved beam, and considering the equivalent load of the prestressing effect, we have: (20) The first term is the uniformly distributed torque generated by curvature; the second term is the uniformly distributed torque acting on the curved beam; the third term is the uniformly distributed torque along the z-axis generated by the prestressed equivalent load; the fourth term is the torque generated by the bending moment caused by the radially distributed force generated by the prestressed equivalent load; and the last term is the uniformly distributed torque caused by the radially distributed force generated by the prestressed equivalent load. Rearranging the above equation and letting... Substituting into the torsional warping differential equation, we obtain the torsional differential equation considering the prestressed equivalent load as follows: (twenty one) in k This is the warp and torsional attenuation coefficient.

[0026] Based on the fundamental assumptions of Ubbelohde's second warping theory, the formula for the constrained torsional normal stress of a thin-walled closed section is: (twenty two) Wherein, the constrained torsional bi-moment B should be the total cross-sectional torsional bi-moment after considering the prestress effect, and the generalized sector moment of inertia. For corrugated steel webs, For concrete top and bottom slabs, , The elastic modulus of concrete; principal sector coordinates of the closed section. , For the sector coordinates of the closed section, It is twice the area of ​​the closed cross section.

[0027] The formula for constrained torsional shear stress in a thin-walled closed section is: (twenty three) Among them, the converted static moment ,in The bending torsional moment of the closed section. Let be the equivalent sector static moment of the cross section. The above equation shows that the first term is the shear flow of free torsion, and its value is a constant; the second term represents the correction of the free torsion shear stress after the warping of the cross section is constrained.

[0028] Since the stress characteristics of this structure can be assumed to be that it is only subjected to free torsion and thus generates corresponding shear stress, the shear stress of the corrugated steel plate is: (twenty four) in To account for the total torque after considering the prestress effect; for corrugated steel webs, , For corrugated steel web thickness; for concrete top and bottom slabs, , The thickness of the concrete top and bottom slabs.

[0029] Specifically, S4 is: To solve the fourth-order differential equation (21), the initial parameter method is used. That is, the coordinate system is first chosen at an arbitrary cross-section, and the angle of twist at the cross-section at z=0 is set as... 0, with a torsion rate of β ’ 0, the dual torque is B0, and the torque is L0.

[0030] First, find the general solution to the homogeneous equation of equation (21). The homogeneous equation has the following form: (25) Its general solution is of the following form: (26) Where {Z(z)} is called the state vector of any cross section, [P(z)] is called the influence function matrix or transformation matrix, and {Z0} is called the initial state vector. Their specific expressions are as follows: ,{Z0}= , The superscript T is the transpose of the matrix. sh and ch This is the symbol for a hyperbolic function.

[0031] Equation (26) gives the general solution of the homogeneous constraint torsion differential equation. In order to further find the general solution of the non-homogeneous constraint torsion differential equation, it is only necessary to know its particular solution under various load state vectors. Then, the particular solution under each load and the general solution of the homogeneous constraint torsion differential equation are superimposed to obtain the general solution of the non-homogeneous constraint torsion differential equation, that is, the solution of equation (21).

[0032] The first case involves a concentrated load acting on a closed-loop corrugated steel web curved box girder. This means that in addition to the initial state vector, a concentrated load exists at a certain cross-section t, i.e., there is another set of vectors acting at z=t. Therefore, the following formula can be derived: When z ≤ t, we have ; When z > t, we have , In the formula, [P(zt)] can be obtained by simply replacing z with zt in [P(z)], while {Z t}= .

[0033] The second scenario occurs when a uniformly distributed load exists on a certain section of the cross-section of a closed-loop corrugated steel web curved box girder, specifically at a ≤ z ≤ c, where a uniformly distributed load m acts. z Its function can be used to derive the following formula: When z ≤ a, we have When a < z ≤ c, we have: When z > c, we have: The third scenario involves a distributed force acting on the closed-loop corrugated steel web curved box girder at points a≤z≤c. Function, and when When m is a constant, the derived formula is the same as the formula for uniformly distributed torque; only the value of m needs to be changed. z Replace with That's all.

[0034] Based on the above introduction, the general solution of equation (21) can be obtained, that is, the general solution of the homogeneous constrained torsion differential equation is added to the solution under concentrated load, uniformly distributed torque and The equation obtained by superimposing particular solutions under load is denoted as the general solution of the non-homogeneous constrained torsional differential equation, which is the general solution of equation (21).

[0035] When solving the constrained torsion differential equation (21) using the initial parameter solution method, the initial state vector must be determined by the boundary conditions. The values ​​of the initial state vector for different boundary conditions are shown in Table 1 below: Table 1. Values ​​of the initial state vector under different boundary conditions. Substituting the initial state vectors corresponding to each boundary condition in Table 1 into the solution formulas for each load, we can obtain the bi-moment B and torque L under each load. Then, we can obtain the required constraint torsional normal stress and shear stress according to the corresponding constraint torsional normal stress and shear stress formulas.

[0036] S5.1, taking a simply supported curved beam with corrugated steel web as an example, its calculated span is 52.25 m, radius of curvature R = 250 m, corresponding central angle is 12°, and it is simply supported at both ends. The cross-section of the corrugated steel web curved box girder bridge is as follows. Figure 3 As shown. The box girder has a closed width b = 4950 mm, a closed height h = 2340 mm, and a corrugated steel plate thickness of 8 mm. Its dimensions are as follows. Figure 4 As shown. The eccentric load P = 550 kN, and the prestressing force is 2932 kN. Material properties: The top and bottom concrete slabs and transverse diaphragms are all C50, with an elastic modulus E... C =3.45×10⁴ MPa, Poisson's ratio v c =0.2; Elastic modulus E of steel plate S =2.1×10⁵ MPa, Poisson's ratio v s =0.3.

[0037] S5.2, according to the principle of equivalent cross-sectional area, for Figure 3 The cross-section is simplified to obtain the following: Figure 5 The simplified cross-section is shown. The top plate is 300 mm thick, the bottom plate is 260 mm thick, and the web height h = 2340 mm. The prestressed steel strands are arranged at the intersection of the bottom plate outline and the inner web as follows: Figure 6 As shown. According to equation (14), E is obtained. Z =233 MPa. The longitudinal elastic modulus of the corrugated steel plate is much smaller than that of the steel plate. Since the corrugated steel plate is relatively thin, the web can be neglected when calculating the geometric properties of the cross-section. Therefore, the centroid position y is given. 上 =0.769 m, y 下 =1.571 m, moment of inertia of section I y =22.514 m4, with the center of torsion A located 0.317 m below the centroid.

[0038] S5.3, Generalized sectoral moment of inertia Polar moment of inertia Free torsional moment of inertia Warping coefficient of closed cross section =0.297, the warping torsional attenuation coefficient of the closed section k=0.383. From the previous simplified prestressing treatment, the final equivalent prestressing load is a uniformly distributed torque along the z-axis. The constrained torsional normal stress is calculated using the mid-span section, and its bi-moment is obtained using the initial parameter method: The first term represents the two moments caused by the load; the second term represents the two moments caused by the prestressing effect; the third term represents the two moments caused by the uniformly distributed torsion due to curvature; the fourth term represents the two moments caused by the bending moment resulting from the radially distributed force generated by the equivalent prestressing load, and the last term represents the two moments caused by the uniformly distributed torque generated by the radially distributed force generated by the equivalent prestressing load. Finally, the constrained torsional normal stress is obtained as follows: Figure 7 As shown. The warping shear stress is calculated using a 1 / 4 section. The equivalent static moment can be obtained from the sector static moment, and then the warping shear stress at the 1 / 4 section can be calculated as follows. Figure 8 As shown.

[0039] Finally, it should be noted that the above are merely preferred embodiments of this application and are not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for analyzing torsional stress in a corrugated steel web curved box girder based on prestressing effect, characterized in that, The method includes the following steps: S1. Clarify the mechanical characteristics of corrugated steel web box girder bridges; S2. Treat the prestressing effect as an equivalent load and simplify it appropriately; S3. Establish the constrained torsion differential equation for the corrugated steel web composite curved box girder, and obtain the constrained torsion normal stress and constrained torsion shear stress of the required section. S4. Combining the boundary conditions of the curved beam and the formulas for the torsional double moment and torsional stress of the box girder under various load conditions, the initial parameter method is used to superimpose them into the general solution form of the constrained torsional differential equation of the corrugated steel web composite curved box girder. The calculation data of the torsional stress of the corrugated steel web composite curved box girder are extracted, and the torsional stress results of the corrugated steel web composite curved box girder are obtained through analysis.

2. The method for analyzing torsional stress in a corrugated steel web curved box girder based on prestressing effect according to claim 1, characterized in that, In S1, the mechanical characteristics include the longitudinal elastic modulus of the corrugated steel web and the effective shear modulus of the corrugated steel web; The expression for the longitudinal elastic modulus is: in, The longitudinal elastic modulus of the corrugated steel web along the longitudinal direction of the bridge is given. For the thickness of the corrugated steel web along the longitudinal direction of the bridge, This refers to the wave height of the corrugated steel web along the longitudinal direction of the bridge. The shape factor of the corrugated steel web; The expression for the effective shear modulus of corrugated steel web is: in, The length of the straight section. This refers to the longitudinal dimension of the inclined slab segment in the bridge. The angle between the inclined plate segment and the straight plate segment. For effective shear modulus, This is the shear modulus of the corrugated steel web.

3. The method for analyzing torsional stress in a corrugated steel web curved box girder based on prestressing effect according to claim 1, characterized in that, In S2, the equivalent load expression for the prestress acting on the corrugated steel web curved box girder bridge section is: in, For the equivalent uniformly distributed force of prestress in the vertical direction of the curved beam, The equivalent uniformly distributed force of prestress in the radial direction of the curved beam is... This refers to the equivalent uniformly distributed force of prestress in the tangential direction of the curved beam. The equivalent uniformly distributed torque of prestress in the vertical direction of the curved beam is given by [the torque]. The equivalent uniformly distributed torque of the prestress in the radial direction of the curved beam is given by [the torque]. The equivalent uniformly distributed torque of prestress in the tangential direction of the curved beam is... The magnitude of the preload, Let be the radius of curvature of the curved beam. Let be the transverse coordinate of the prestressed steel strand. For the longitudinal coordinates of the prestressed steel strands, superscript... For the first derivative with respect to the arc length of the curved beam, the superscript is... This is the second derivative with respect to the arc length of the curved beam.

4. The method for analyzing torsional stress in a corrugated steel web curved box girder based on prestressing effect according to claim 3, characterized in that, In S2, when the vertical coordinates of the prestressed steel strands are not considered... When the load changes longitudinally, the simplified equivalent load expression for the prestress acting on the cross section of a corrugated steel web curved box girder bridge is: At this point, the prestressed equivalent load is simplified to a radially distributed force and a uniformly distributed torque along the entire length of the bridge.

5. The method for analyzing torsional stress in a corrugated steel web curved box girder based on prestressing effect according to claim 4, characterized in that, S3 specifically includes: Obtain the differential equation for torsional warping of a curved box girder. Where m is the external torque intensity, The total torsional angle of the cross section. The warping function of the cross section, with superscripts relative to the vertical coordinates. The derivative of the corrugated steel web, For concrete top and bottom slabs, , For concrete, the elastic modulus; for corrugated steel webs, For concrete top and bottom slabs, , For concrete shear modulus; for generalized sector moment of inertia Principal sector coordinates of closed section , For the sector coordinates of the closed section, It is twice the area of ​​the closed cross section. ds For a curved arc segment, in the case of a corrugated steel web, , For corrugated steel web thickness; for concrete top and bottom slabs, , Thickness of the concrete top and bottom slabs; free torsional moment of inertia . The warping function can be obtained using deformation and equilibrium conditions. Total torsion angle The relationship between them yields a torsional differential equation expressed by the warp function. ; v The warpage factor is 1. Polar moment of inertia , The radius of curvature of the neutral layer. dA Let be the infinitesimal area on the cross section. Based on the equilibrium equation of the torque along the z-axis of the curved beam, and considering the equivalent load of the prestressing effect, we have: ,in, The uniformly distributed torque generated by the curvature. For the uniformly distributed torque acting on the curved beam, The uniformly distributed torque along the z-axis generated by the prestressed equivalent load. The torque generated is the bending moment caused by the radially distributed force produced by the prestressed equivalent load. The uniformly distributed torque is caused by the radially distributed force generated by the prestressed equivalent load. definition ,in, k The warp and torsional attenuation coefficient; Substituting into the torsional warping differential equation, we obtain the torsional differential equation considering the prestressed equivalent load as follows: Based on the fundamental assumptions of Ubbelohde's second warping theory, the formula for the constrained torsional normal stress of a thin-walled closed section is: Wherein, the constrained torsional bi-moment B is the total cross-sectional torsional bi-moment after considering the prestress effect; The formula for constrained torsional shear stress in a thin-walled closed section is: ,in The bending torsional moment of the closed section. The converted sector static moment of the cross section; The shear stress of the corrugated steel plate is ,in, L The total torque after taking into account the prestress effect.

6. The method for analyzing torsional stress in a corrugated steel web curved box girder based on prestressing effect according to claim 5, characterized in that, S4 specifically includes: Choose an arbitrary cross-section for the coordinate system, and let the angle of twist at the cross-section where z=0 be . 0, torque is The two torques are The torque is ; Find the general solution to the homogeneous equation of the torsional differential equation considering the prestressed equivalent load. The homogeneous equation has the following form: The general solution is as follows: ,in Let the state vector be any cross section. To affect the function matrix or transformation matrix, Let be the initial state vector, and , , The superscript T is the transpose symbol for the matrix; Based on the particular solutions of the homogeneous constrained torsion differential equation under various load state vectors, the general solution of the non-homogeneous constrained torsion differential equation is obtained by superimposing the particular solutions under each load with the general solution of the homogeneous constrained torsion differential equation.

7. The method for analyzing torsional stress in a corrugated steel web curved box girder based on prestressing effect according to claim 6, characterized in that, When, in addition to the existence of an initial state vector, there is a concentrated load at a certain cross-section t, i.e., another set of vectors acting at z=t, the method of obtaining the general solution of the non-homogeneous constrained torsion differential equation by superimposing the particular solutions of the homogeneous constrained torsion differential equation under various load state vectors with the general solution of the homogeneous constrained torsion differential equation includes: When z ≤ t, we have ; When z > t, we have ; in, .

8. The method for analyzing torsional stress in a corrugated steel web curved box girder based on prestressing effect according to claim 7, characterized in that, When a uniformly distributed load exists on a certain section of the cross-section of a closed-corrugated steel web curved box girder... When applied, the method of obtaining the general solution of the non-homogeneous constrained torsion differential equation by superimposing the particular solutions of the homogeneous constrained torsion differential equation under various load state vectors with the general solution of the homogeneous constrained torsion differential equation includes: When z ≤ a, we have ; When a < z ≤ c, we have ； When z > c, we have: 。 9. The method for analyzing torsional stress in a corrugated steel web curved box girder based on prestressing effect according to claim 8, characterized in that, When a distributed force acts on a closed-corrugated steel web curved box girder at a≤z≤c, Function, and when When it is a constant, .

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