A method for analyzing shear lag effect of single-box three-cell section beam bridge

Abstract

The application discloses a kind of single-box three-chamber cross-section girder bridge shear lag effect analysis method, belong to bridge construction control technical field.The method includes the following steps: S1. with quadratic parabola function to build shear lag warping displacement function, select the coordinate at the location of half of box girder section, i.e. the wing plate longitudinal displacement function of single-box three-chamber thin-walled box girder considering shear lag effect is obtained;S2. calculate the normal strain and shear strain of upper and lower wing plate and web of thin-walled box girder;S3. calculate the strain energy of upper and lower wing plate and web of thin-walled box girder;S4. calculate the total potential energy of single-box three-chamber girder system;S5. according to the principle of minimum potential energy, simplification is carried out using the method of partial integration, and the control differential equation set and boundary conditions of single-box three-chamber thin-walled box girder considering shear lag effect are obtained.The application discloses a kind of single-box three-chamber cross-section girder bridge shear lag effect analysis method, and the prediction result of main girder stress and deformation is more in line with actual situation, improves the accuracy of single-box three-chamber cross-section girder bridge construction process, and higher safety.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of bridge construction control, and particularly relates to a method for analyzing shear lag effect of a single-box three-room section beam bridge. BACKGROUND

[0002] Under the action of symmetrical bending load, the longitudinal stress of the top and bottom plates of the thin-walled box girder is uniformly distributed along the transverse direction according to the elementary beam theory. However, in the actual situation, the shear deformation of the flange plate will lead to that the transverse distribution of the longitudinal stress of the section does not satisfy the plane section assumption. There is a certain gap between the normal stress at the junction of the web and the upper and lower flange plates and the normal stress in the plate, which is due to the fact that the shear flow gradually weakens in the process of transmission into the plate, and the longitudinal displacement of the flange plate far away from the web lags behind that of the web, leading to that the normal stress distribution of the flange plate is not uniform. This non-uniform phenomenon will be enhanced with the increase of the width of the flange plate. This phenomenon of transverse longitudinal stress transmission lag in the section is called "shear lag effect".

[0003] The existence of the shear lag effect will adversely affect the design of the box girder and the stability of the project. The instability and failure of the steel box girder occurred in the United Kingdom, Germany and other countries in the 1970s and 1980s are related to the influence of the shear lag effect of the box girder. In China, there is also the phenomenon of box girder segment fracture in the cantilever construction process of Ningbo Zhaobaoshan Bridge. The shear lag effect will cause excessive stress at the junction of the web and the flange plate or at the center line of the flange plate, which is very unfavorable to the integrity and stability of the structure, especially the safety during construction. Therefore, it is necessary to consider the influence of the shear lag effect in the design of the box girder.

[0004] The box section girder has light self-weight, good bending and torsional performance, and is widely used in modern long-span cable-stayed bridges. With the development of modern transportation, the requirement for the span of the main girder of the cable-stayed bridge is increasing, and the cross section form and material used are various. The shear lag effect of the main girder section is more significant due to the complex structure, which may have a great impact on the safety of the bridge structure. In the past research, the research on the shear lag effect is mostly concentrated on simply supported and continuous girder bridges. The axial force provided by the cables of the cable-stayed bridge and the multi-point elastic support will make the internal force distribution of the cable-stayed bridge different from that of the general girder bridge. The research on the cable-stayed bridge is mostly for single-box single-room, single-box double-room or Π-shaped girder cable-stayed bridges, and there is less research on the shear lag effect of the single-box three-room section girder bridge. SUMMARY

[0005] Therefore, the present application aims to provide a method for analyzing the shear lag effect of a single-box three-room section girder bridge. The present application aims to solve the problem that the existing analysis method cannot accurately analyze the shear lag effect of a single-box three-room section girder bridge, affecting the construction safety.

[0006] To achieve the above-mentioned purpose, the present application provides a method for analyzing the shear lag effect of a single-box three-room section girder bridge, which comprises the following steps:

[0007] S1. Establish the coordinate system of single-box three-room beam, construct the shear lag warping displacement function with quadratic parabolic function, select the coordinate at the position of half of the box girder section, and the wing plate longitudinal displacement function of single-box three-room thin-walled box girder considering shear lag effect is obtained as follows:

[0008]

[0009] In the formula, w(x) is the vertical deflection function of the box girder under the action of load obtained from the elementary beam theory, w'(x) is the first order inverse of the vertical deflection function obtained from the elementary beam theory, that is, the angle of rotation; u1(x, y, z) is the longitudinal displacement function of the top plate of the inner room at any coordinate position of the thin-walled box girder section considering shear lag effect; u2(x, y, z) is the longitudinal displacement function of the top plate of the outer room at any coordinate position of the thin-walled box girder section considering shear lag effect; u3(x, y, z) is the longitudinal displacement function of the bottom plate of the inner room at any coordinate position of the thin-walled box girder section considering shear lag effect; u4(x, y, z) is the longitudinal displacement function of the bottom plate of the outer room at any coordinate position of the thin-walled box girder section considering shear lag effect; u5(x, y, z) is the longitudinal displacement function of the middle web at any coordinate position of the thin-walled box girder section considering shear lag effect; u6(x, y, z) is the longitudinal displacement function of the side web at any coordinate position of the thin-walled box girder section considering shear lag effect. w1 w2 They are the shear lag longitudinal angle difference functions considering the different widths of the inner and outer room wing plates of the single-box three-room box girder, respectively; b1 is half of the width of the top plate of the inner room of the three-room box girder, b2 is half of the width of the top plate of the outer room of the three-room box girder, b3 is half of the width of the bottom plate of the inner room of the three-room box girder, and b4 is half of the width of the bottom plate of the outer room of the three-room box girder; Z1 is the height from the center of the three-room box girder section to the center of the top plate of the inner room, Z2 is the height from the center of the three-room box girder section to the center of the top plate of the outer room, Z3 is the height from the center of the three-room box girder section to the center of the bottom plate of the inner room, and Z4 is the height from the center of the three-room box girder section to the center of the bottom plate of the outer room.

[0010] S2. According to the shear lag warping displacement function constructed in step S1, the normal strain and shear strain of the upper and lower wing plates and webs of the thin-walled box girder are calculated.

[0011] S3. According to the normal strain and shear strain of the thin-walled box girder obtained in step S2, the strain energy of the upper and lower wing plates and webs of the thin-walled box girder is calculated.

[0012] S4. According to the strain energy of the upper and lower wing plates and webs of the thin-walled box girder obtained in step S3, the total potential energy of the single-box three-room beam system is calculated.

[0013] S5. According to the total potential energy of the single-box three-room beam system obtained in step S4, the control differential equation set and boundary conditions of the single-box three-room thin-walled box girder considering shear lag effect are obtained by simplifying the integral function by using the method of partial integration in accordance with the principle of minimum potential energy.​​

[0014] Furthermore, in step S2, the calculation expressions for the normal strain and shear strain of the upper and lower flanges and web of the thin-walled box girder are as follows:

[0015]

[0016] In the formula, ε1 and γ1 are the normal strain and shear strain of the upper flange of the inner chamber, respectively; ε2 and γ2 are the normal strain and shear strain of the upper flange of the outer chamber, respectively; ε3 and γ3 are the normal strain and shear strain of the lower flange of the inner chamber, respectively; ε4 and γ4 are the normal strain and shear strain of the lower flange of the outer chamber, respectively; ε w1 γ w1 These are the normal strain and shear strain of the web, respectively; ε w2 γ w2 These are the normal strain and shear strain of the side web, respectively.

[0017] Furthermore, in step S3, the calculation expressions for the strain energy of the upper and lower flanges and web of the thin-walled box girder are as follows:

[0018]

[0019]

[0020]

[0021] In the formula, E is the elastic modulus of the material; G represents the shear modulus of the material; U su U represents the strain energy of the upper flange of the box girder. sb U represents the strain energy of the lower flange of the box girder. w For the strain energy of the box girder web; U su1 U su2 These are the strain energies of the upper flange plates of the inner and outer chambers of the box girder, respectively; U sb3 U sb4 These are the strain energies of the lower flange plates of the inner and outer chambers of the box girder, respectively; U w1 U w2 These are the strain energies of the inner and outer webs of the box girder, respectively; I i (i = 1, 2, 3, 4) represent the moments of inertia of the upper and lower flanges of the box girder relative to the centroid of the section, where I1 = 2b1t1Z1 2 The moment of inertia of the upper flange of the box girder chamber relative to the centroid of the section; I2=2(2b2)t2Z2 2 I3 is the moment of inertia of the upper flange of the box girder relative to the centroid of the section; I3 = 2b3t3Z3 2 The moment of inertia of the lower flange of the box girder relative to the centroid of the section; I4=2(2b4)t4Z4 2 I is the moment of inertia of the lower flange of the box girder relative to the centroid of the section; w I is the moment of inertia of the box girder web relative to the centroid of the section;w1 I w2 t1 represents the moment of inertia of the inner and outer webs of the box girder relative to the centroid of the box girder section, t2 represents the thickness of the top slab of the inner chamber of the three-chamber box girder, t3 represents the thickness of the bottom slab of the inner chamber of the three-chamber box girder, and t4 represents the thickness of the bottom slab of the outer chamber of the three-chamber box girder.

[0022] Furthermore, in step S4, the calculation expression for the total potential energy of the single-box three-cell cross-section beam bridge system is as follows:

[0023]

[0024] In the formula, U is the deformation potential energy of the system; V is the load potential energy of the system; and M(x) is the bending moment load.

[0025] Furthermore, in step S5, the expressions for the governing differential equations and boundary conditions of the single-box three-cell thin-walled box girder considering the shear lag effect are as follows:

[0026] Governing differential equations:

[0027]

[0028] Boundary conditions:

[0029]

[0030] In the formula, I is the moment of inertia of the box girder section about the neutral axis. l represents the bridge span.

[0031] The beneficial effects of this invention are as follows:

[0032] This invention provides an analytical method for the shear lag effect of a single-box three-cell section beam bridge. Through cross-sectional analysis of the single-box three-cell thin-walled box girder, a reasonable shear lag warping displacement mode is proposed, and the governing differential equations and boundary conditions considering the shear lag effect are obtained. The analytical method of this invention is easy to operate and program, reduces manual calculations, can adapt to different displacement boundaries and load conditions, and can obtain deflection and stress functions considering the shear lag effect. The predicted results for the stress and deformation of the main beam are more consistent with reality, improving the accuracy of the construction process of single-box three-cell section beam bridges.

[0033] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating the analytical method for the shear lag effect of a single-box three-cell beam bridge according to the present invention.

[0035] Figure 2 This is a schematic diagram showing the cross-sectional dimensions of the single-box three-chamber box girder of the present invention;

[0036] Figure 3 This is a schematic diagram of the load of the present invention;

[0037] Figure 4 This is a schematic diagram of a simply supported beam subjected to a uniformly distributed load according to the present invention.

[0038] Figure 5 This is a schematic diagram of the box girder cross-sectional dimensions in Example 1. Detailed Implementation

[0039] To make the technical solutions, advantages, and objectives of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the protection scope of this application.

[0040] This invention relates to a beam element, primarily deriving and describing the formation of the element. Therefore, it is necessary to establish a coordinate system and define the element coordinate system, such as... Figure 2 As shown, the longitudinal direction (length direction) is the X direction, the transverse direction (width direction) is the Y direction, and the vertical direction (height direction) is the Z direction. The structural coordinate system may vary depending on the software and the user; this only involves finite element coordinate transformation and is not within the scope of this invention.

[0041] like Figure 1 As shown, this invention discloses an analysis method for the shear lag effect of a single-box three-cell cross-section beam bridge, specifically including the following steps:

[0042] Step S1: Establish the coordinate system of the single-box three-cell beam, and then construct the shear lag warping displacement function using a quadratic parabolic function. Select the coordinates at the halfway point of the box girder section to obtain the longitudinal displacement function of the flange of the single-box three-cell thin-walled box girder considering the shear lag effect, as shown below:

[0043] Interior ceiling

[0044] exterior roof slab

[0045] Interior floor

[0046] Outer floor plate

[0047] In the formula, u i (i=1,2,3,4) represents the longitudinal displacement function at any coordinate of the top and bottom plates of the thin-walled box girder section considering the shear lag effect; w(x) represents the vertical deflection function of the box girder under load, and w′(x) represents the first reciprocal of the vertical deflection function, i.e., the rotation angle; Let Z1, Z2, and Z4 be the longitudinal displacement function considering the shear lag effect, respectively, for a single-box three-cell box girder with different inner and outer wing plate widths. Z1 represents half the width of the inner wing plate top, Z2 half the width of the outer wing plate top, Z3 half the width of the inner wing plate bottom, and Z4 half the width of the outer wing plate bottom. Z1 is the height from the center of the three-cell box girder section to the center of the inner wing plate top, Z2 to the center of the outer wing plate top, Z3 to the center of the inner wing plate bottom, and Z4 to the center of the outer wing plate bottom. The first term in the square brackets on the right side of the above longitudinal displacement function expression is the longitudinal displacement function of the box girder section obtained from elementary beam theory, and the second term is the longitudinal displacement function considering the shear lag effect.

[0048] For the deformation of the box girder web, the longitudinal displacement is obtained based on the flange displacement function and the plane section assumption, as shown below:

[0049] Middle web u w1 =-zw′(x) (-Z1≤z≤Z3) (5)

[0050] Side web u w2 =-zw′(x) (-Z2≤z≤Z4) (6)

[0051] Step S2: According to the principle of minimum potential energy, among all displacements that satisfy the boundary conditions, there exists a set of displacements that make the total potential energy of the box girder structure stable under the action of external forces. At this time, the total potential energy of the box girder structure is minimized, that is, the first variation of the total potential energy of the system should be zero.

[0052] δΠ=δ(U+V)=0 (7)

[0053] Where: U—the deformation potential energy of the system;

[0054] V—The system's load potential energy.

[0055] Strain energy of the upper flange of the box girder:

[0056]

[0057] Strain energy of the lower flange of the box girder:

[0058]

[0059] Box girder web strain energy

[0060]

[0061] In the formula, U su1 U su2 These are the strain energies of the upper flange plates of the inner and outer chambers of the box girder, respectively; U sb3 U sb4 These are the strain energies of the lower flange plates of the inner and outer chambers of the box girder, respectively; U w1 U w2 These represent the strain energies of the inner and outer webs of the box girder, respectively; E is the elastic modulus of the material; G represents the shear modulus of the material; I w1 I w2 t1 represents the moment of inertia of the inner and outer webs of the box girder relative to the centroid of the box girder section, t2 represents the thickness of the top slab of the inner chamber of the three-chamber box girder, t3 represents the thickness of the bottom slab of the inner chamber of the three-chamber box girder, and t4 represents the thickness of the bottom slab of the outer chamber of the three-chamber box girder.

[0062] From equations (1)-(6) and the geometric equations of elasticity The expressions for the normal strain and shear strain of the thin-walled box girder can be obtained as follows:

[0063] Upper wing panel of the inner chamber:

[0064]

[0065] Upper wing of the outer chamber:

[0066]

[0067] Lower wing panel of the inner chamber:

[0068]

[0069] Lower wing of outer chamber:

[0070]

[0071] Center web: ε w1 =-zw″,γ w1 =0 (15)

[0072] Side web: ε w2 =-zw″,γ w2 =0 (16)

[0073] Step S3: Substituting equations (11)-(16) into equations (8)-(10), the strain energy of the upper and lower flanges and web of the box girder can be obtained:

[0074] Upper wing panel:

[0075]

[0076] Lower wing plate:

[0077]

[0078] Web:

[0079]

[0080] In the formula, I i (i = 1, 2, 3, 4) represents the moments of inertia (negligible) of the upper and lower flanges of the box girder relative to the centroid of the section, where I1 = 2b1t1Z1 2 The moment of inertia of the upper flange of the box girder chamber relative to the centroid of the section; I2=2(2b2)t2Z2 2 I3 is the moment of inertia of the upper flange of the box girder relative to the centroid of the section; I3 = 2b3t3Z3 2 The moment of inertia of the lower flange of the box girder relative to the centroid of the section; I4=2(2b4)t4Z4 2 I is the moment of inertia of the lower flange of the box girder relative to the centroid of the section; w Let be the moment of inertia of the web of the box girder relative to the centroid of the cross section.

[0081] Step S4: As Figure 3 As shown, the load potential energy of the beam under bending is as follows:

[0082]

[0083] The total potential energy of the system is expressed as:

[0084]

[0085] Step S5: The variation of the total potential energy of the system can be obtained from equation (7), and the integrand is simplified by integration by parts, thus obtaining the set of governing differential equations and boundary conditions for the single-box three-cell thin-walled box girder considering shear lag effect:

[0086] Governing differential equations:

[0087]

[0088]

[0089]

[0090] Boundary conditions:

[0091]

[0092]

[0093] In the formula, I is the moment of inertia of the box girder section about the neutral axis. l represents the bridge span.

[0094] From equation (22), we can obtain:

[0095]

[0096] Taking the first derivative of equation (27) and substituting it into the equation, we have:

[0097]

[0098]

[0099] After rearranging equations (28) and (29), we obtain the following about The matrix equation is as follows:

[0100]

[0101] In the formula,

[0102] Further rearranging equation (30) yields:

[0103]

[0104] In the formula, [C] = [A] -1 [B],

[0105] Reduce the order of equation (31) by letting We obtain a first-order linear nonhomogeneous ordinary differential equation that can be solved directly:

[0106]

[0107] In the formula,

[0108] The solution to equation (32) consists of the general solution and a particular solution of the corresponding homogeneous differential equation. For a single-box three-cell thin-walled box girder, when b1≠b2, the quartic characteristic equation (N-λE)x=0 corresponding to matrix [N] is solved. It can be proved that the matrix has four eigenvalues ​​±λ1, ±λ2, and the corresponding eigenvector can be assumed to be α1=(α 11 α 21 λ1α 11 λ1α 21 ) T , α2=(α 11 α 21 -λ1α 11 -λ1α 21 ) T , α3=(α 12 α 22λ2α 12 λ2α 22 ) T , α4=(α 12 α 22 -λ2α 12 -λ2α 22 ) T .

[0109] matrix Substituting the corresponding eigenvectors into the characteristic equation and simplifying, we can obtain:

[0110]

[0111] Then the eigenvalues ​​of matrix [C] can be obtained as λ1. 2 ,λ2 2 The corresponding eigenvector is (α) 11 α 21 ) T , (α 12 α 22 ) T For equation (32), we only need to find the eigenvalues ​​and eigenvectors of matrix [C] to find the eigenvalues ​​and eigenvectors of matrix [N], and then obtain the general solution of its corresponding homogeneous differential equation. Taking the first two terms... This is the general solution of the equation. For equation (31), when M(x) is a cubic function of x, a particular solution to the system of equations can be obtained:

[0112]

[0113] When M(x) is an nth-degree function of x (0≤n≤2), the second term on the right-hand side of equation (34) is zero, and the particular solution of the system of equations is:

[0114] The solution to the system of equations (31) can then be obtained as follows:

[0115]

[0116]

[0117] In equation (35), the coefficient k i Determined by boundary conditions.

[0118] Example 1

[0119] Figure 4 The diagram shows a simply supported beam under a uniformly distributed load. The uniformly distributed load q acts symmetrically and uniformly along the longitudinal direction of the box girder on the top surface of the web. The length of the box girder is L. The bending moment and shear force of the simply supported beam under the uniformly distributed load are expressed as follows:

[0120]

[0121] From equation (34) and the expressions for bending moment and shear force of a simply supported beam, we can obtain the system of differential equations regarding... Special solution:

[0122]

[0123] Boundary conditions for simply supported beams:

[0124] w(0)=0,w(L)=0 (38)

[0125]

[0126] Substituting equations (37) and (38) into the equation, we can obtain the following expression for the coefficient k in the equation:

[0127]

[0128] Substituting equations (37) and (40) into the equation, we can obtain the following about the simply supported beam under uniformly distributed load: The expression is as follows:

[0129]

[0130] Taking the first derivative of the above equation, we get:

[0131]

[0132] Substituting equation (42) into equation (27), we obtain the vertical displacement function of a simply supported beam under uniformly distributed load, considering the shear lag effect:

[0133]

[0134] For a simply supported beam, with boundary conditions w(0) = 0 and w(L) = 0, the expressions for G1 and G2 can be obtained as follows:

[0135]

[0136] Depend on From the expression, we can obtain the expression for the longitudinal stress of the flange of the simply supported beam under uniformly distributed load, considering the shear lag effect, as follows:

[0137] Interior ceiling:

[0138]

[0139] exterior roof slab:

[0140]

[0141] Interior floor:

[0142]

[0143] Outer floor slab:

[0144]

[0145] Using the analytical method described above, the calculation formulas for the normal stress and deflection of the flange of the box girder section were derived. A MATLAB program was used to analyze the numerical examples, revealing the stress distribution law of the flange. Furthermore, a spatial finite element model of the box girder using plate and shell elements was established using the finite element software ANSYS to analyze the shear lag effect of the box girder section under external loads. The finite element plate and shell element selected was the SHELL181 element with four nodes, each containing three translational degrees of freedom and three rotational degrees of freedom. By comparing the stress distribution of the section at different longitudinal positions of the box girder, the shear lag effect distribution law of a single-box, three-cell thin-walled beam was obtained.

[0146] Now, a single-box, three-cell thin-walled box girder is selected, and its cross-section is as follows: Figure 5 As shown. The thickness of the inner chamber top and bottom slab of the box girder is b1=b3=4m, the thickness of the outer chamber top and bottom slab is b2=b4=2m, the thickness of both inner and outer chamber top and bottom slabs is t1=t2=t3=t4=0.02m, the thickness of the inner and outer chamber webs is tw1=tw2=0.02m, and the beam height is h=4m. The material elastic modulus is E=2.1×105MPa, and Poisson's ratio is μ=0.3. The beam span is L=50m. The shear lag of the simply supported box girder under (a) a concentrated load F=300kN at mid-span and (b) a uniformly distributed load q=20kN / m is analyzed.

[0147] During the calculation, the load is evenly divided into 4 parts and applied to the top surface of the web. The deflection and cross-sectional stress are obtained by analytical solution according to the present invention, and the results are compared with the finite element model data. See Table 1 and Table 2 for details.

[0148] Table 1. Stress values ​​(MPa) of the top plate at mid-span section of a simply supported beam under uniformly distributed load.

[0149]

[0150] Table 2. Stress values ​​(MPa) of the bottom plate at mid-span section of a simply supported beam under uniformly distributed load.

[0151]

[0152] The stress values ​​of the top and bottom plates at the mid-span section of a simply supported beam under uniformly distributed load showed a maximum relative error of 2.29% between the theoretical solution and the ANSYS finite element solution, occurring at the interface between the web and the bottom plate. Overall, the theoretical solution and the finite element solution showed little difference and good agreement, verifying the accuracy of the proposed method.

[0153] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the protection scope of the present invention.

Claims

1. A method for analyzing the shear lag effect of a single-box three-cell cross-section girder bridge, characterized by, The method comprises the following steps: S1. Establishing a coordinate system of the single-box three-room beam, constructing a shear lag warping displacement function with a quadratic parabolic function, selecting a coordinate at a position of one-half of a section of the box girder, and obtaining a wing plate longitudinal displacement function of the single-box three-room thin-walled box girder considering the shear lag effect, as shown below: wherein w(x) is the vertical deflection function of the box girder under load obtained from the elementary beam theory, w'(x) is the first derivative of the vertical deflection function obtained from the elementary beam theory, i.e. the rotation angle; u1(x, y, z) is the longitudinal displacement function of the top plate of the inner chamber at any coordinates when the shear lag effect is considered for the thin-walled box girder section; u2(x, y, z) is the longitudinal displacement function of the top plate of the outer chamber at any coordinates when the shear lag effect is considered for the thin-walled box girder section; u3(x, y, z) is the longitudinal displacement function of the bottom plate of the inner chamber at any coordinates when the shear lag effect is considered for the thin-walled box girder section; u4(x, y, z) is the longitudinal displacement function of the bottom plate of the outer chamber at any coordinates when the shear lag effect is considered for the thin-walled box girder section; u w1 is the longitudinal displacement function of the middle web at any coordinates when the shear lag effect is considered for the thin-walled box girder section; u w2 is the longitudinal displacement function of the side web at any coordinates when the shear lag effect is considered for the thin-walled box girder section; are the shear lag longitudinal rotation angle difference functions considering the different widths of the inner and outer chamber wing plates of the single-box three-chamber box girder, respectively; b1 is half the width of the top plate of the inner chamber of the three-chamber box girder, b2 is half the width of the top plate of the outer chamber of the three-chamber box girder, b3 is half the width of the bottom plate of the inner chamber of the three-chamber box girder, and b4 is half the width of the bottom plate of the outer chamber of the three-chamber box girder; Z1 is the height from the center of the three-chamber box girder section to the center of the top plate of the inner chamber, Z2 is the height from the center of the three-chamber box girder section to the center of the top plate of the outer chamber, Z3 is the height from the center of the three-chamber box girder section to the center of the bottom plate of the inner chamber, and Z4 is the height from the center of the three-chamber box girder section to the center of the bottom plate of the outer chamber. S2. Calculating normal strain and shear strain of the upper and lower wing plates and the web of the thin-walled box girder according to the shear lag warping displacement function constructed in step S1; S3. Calculating strain energy of the upper and lower wing plates and the web of the thin-walled box girder according to the normal strain and shear strain of the thin-walled box girder obtained in step S2; S4. Calculating total potential energy of the single-box three-room beam system according to the strain energy of the upper and lower wing plates and the web of the thin-walled box girder obtained in step S3; S5. According to the total potential energy of the single-box three-room beam system obtained in step S4, the control differential equation set and the boundary conditions of the single-box three-room thin-walled box girder considering the shear lag effect are obtained by simplifying the integral function by using the method of partial integration according to the principle of minimum potential energy.

2. The method of claim 1, wherein the method is characterized by: In the step S2, the calculation expression of the normal strain and shear strain of the upper and lower wing plates and the web of the thin-walled box girder is as follows: wherein ε1, γ1 are the normal and shear strains of the upper inner panel; ε2, γ2 are the normal and shear strains of the upper outer panel; ε3, γ3 are the normal and shear strains of the lower inner panel; ε4, γ4 are the normal and shear strains of the lower outer panel; ε w1 , γ w1 are the normal and shear strains of the middle web; and ε w2 , γ w2 are the normal and shear strains of the side web.

3. The method of claim 2, wherein the method is characterized by: In the step S3, the calculation expression of the strain energy of the upper and lower wing plates and the web of the thin-walled box girder is as follows: where E is the modulus of elasticity of the material; G represents the shear modulus of the material; U su is the strain energy of the top flange of the box girder; U sb is the strain energy of the bottom flange of the box girder; U w is the strain energy of the web of the box girder; U su1 , U su2 are the strain energies of the top flanges of the inner and outer chambers of the box girder, respectively; U sb3 , U sb4 are the strain energies of the bottom flanges of the inner and outer chambers of the box girder, respectively; U w1 , U w2 are the strain energies of the webs of the inner and outer chambers of the box girder, respectively; I i represents the moment of inertia of the top and bottom flanges of the box girder with respect to the centroid of the cross section, i = 1, 2, 3, 4, where I1= 2b1t1Z1 2 is the moment of inertia of the top flange of the inner chamber of the box girder with respect to the centroid of the cross section; I2= 2(2b2)t2Z2 2 is the moment of inertia of the top flange of the outer chamber of the box girder with respect to the centroid of the cross section; I3= 2b3t3Z3 2 is the moment of inertia of the bottom flange of the inner chamber of the box girder with respect to the centroid of the cross section; I4= 2(2b4)t4Z4 2 is the moment of inertia of the bottom flange of the outer chamber of the box girder with respect to the centroid of the cross section; I w is the moment of inertia of the web of the box girder with respect to the centroid of the cross section; I w1 , I w2 are the moments of inertia of the webs of the inner and outer chambers of the box girder with respect to the centroid of the cross section of the box girder, respectively; t1 is the thickness of the top plate of the three-room box girder, t2 is the thickness of the top plate of the outer room of the three-room box girder, t3 is the thickness of the bottom plate of the inner room of the three-room box girder, t4 is the thickness of the bottom plate of the outer room of the three-room box girder, and l is the span of the bridge.

4. The method of claim 3, wherein the method is characterized by: In the step S4, the calculation expression of the total potential energy of the single-box three-room section beam bridge system is as follows: In the formula, U is the deformation potential energy of the system, V is the load potential energy of the system, and M(x) is the bending moment load.

5. The method of claim 4, wherein the method is characterized by: In the step S5, the expression of the control differential equation set and the boundary conditions of the single-box three-room thin-walled box girder considering the shear lag effect is as follows: Control differential equation: Boundary condition: In the formula, I is the moment of inertia of the box girder section about the neutral axis, l is the bridge span.

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