Unified bearing capacity prediction method and system for box section bridge based on plate member discretization

Abstract

The present application relates to the technical field of bridge structure design, and particularly relates to a box section bridge unified bearing capacity prediction method and system based on plate piece discretization. The present application converts the bearing capacity failure problem at the section level into the bearing capacity failure problem at the arbitrary plate piece level by discretizing the box section into different plate pieces, converts the complex coupling bearing capacity problem at the section internal force level into the coupling bearing capacity problem at the plate piece stress level, further divides the plate pieces into layers and proposes interlayer stress balance equations, converts the plate piece bearing capacity failure problem into the upper and lower film layer bearing capacity failure problems of the plate pieces again, and proposes three possible failure modes of the upper and lower film layers under complex external loads and corresponding bearing capacity calculation methods, and finally applies the step-by-step failure loading method to the determination of the section failure state to obtain the ultimate bearing capacity of the box section.

Description

Technical Field

[0001] This invention relates to the field of bridge structure design technology, and in particular to a method and system for predicting the unified bearing capacity of box-section bridges based on discrete plate components. Background Technology

[0002] For box girder bridges, due to spatial effects, the structure is generally subjected to a complex combination of tension, compression, bending, shear, torsion, and frame effects, resulting in highly complex failure mechanisms. Currently, there is no universally accepted unified failure theory or method for calculating bearing capacity. This long-standing theoretical imperfection directly impacts the calculation of bearing capacity for box girder bridges under various combined loads. Consequently, to ensure structural safety, various amplification factors are often added to the bearing capacity calculation methods, leading to conservative bearing capacity design, wasted structural materials, and poor economic efficiency.

[0003] The main reason for the above problems is that many existing load-bearing capacity calculation theories are developed at the cross-sectional level of the structure, taking the internal forces of the cross-section as the object of load-bearing capacity calculation. Since it is difficult to study the coupling mechanism of the structure under different force combinations from the perspective of internal forces, for a long time these load-bearing capacity calculation theories have mostly separated the tension, compression, bending, shear and torsion parts, or even separated the longitudinal and transverse load-bearing capacities of box girder bridges. During the design, the envelope results of the load-bearing capacities corresponding to various individual forces are taken on a conservative basis, which is often too conservative.

[0004] Therefore, in the context of increasingly emphasizing the refinement, economy and low carbon of structural design, it is essential to establish a unified load-bearing theory and calculation method that can take into account the complex stress characteristics of box-section bridges, more clearly express the coupling mechanism of the cross section under different stress combinations, and realize the unification of the calculation method of the load-bearing capacity of box-section bridges. Summary of the Invention

[0005] To overcome the deficiency of the lack of a unified bearing capacity calculation method for box-section bridges in the existing technology, this invention proposes a unified bearing capacity prediction method for box-section bridges based on plate discretization. Based on different plates formed discretely within the section, accurate bearing capacity calculation and judgment are performed.

[0006] This invention proposes a unified bearing capacity prediction method for box-section bridges based on plate discretization, comprising the following steps:

[0007] S1. Set the load F of the box-section bridge, discretize the cross section of the box-section bridge into multiple plates, establish a finite element model of the box-section bridge discretized into plates under load, and calculate the load components borne by each plate.

[0008] S2. Divide the plate into an upper thin film layer, a middle layer and a lower thin film layer along the thickness direction, and construct the interlayer force balance equation of the plate under the ultimate state.

[0009] S3, the upper film layer and the lower film layer are collectively referred to as the film layer. The failure mode of the film layer under the ultimate state and the force balance equation of the film layer under the ultimate state are defined. The calculation formula of the ultimate bearing capacity under each failure mode is constructed by combining the interlayer force balance equation of the plate and the force balance equation of the film layer. The failure modes include under-reinforced failure mode, moderately reinforced failure mode and over-reinforced failure mode.

[0010] S4. Assuming the membrane layer is in the optimal reinforcement failure mode, calculate the ultimate bearing capacity τ of the membrane layer under the optimal reinforcement failure mode. xyu and principal tensile stress f 1u Determine whether f is satisfied. 1u >f cr f cr If the value is the standard value of the tensile strength of concrete, then calculate the ultimate bearing capacity τ' under the under-reinforced failure mode. xyu As the actual destructive bearing capacity τ xyu,act If yes, then proceed to step S6; if yes, then proceed to step S5.

[0011] S5. Obtain the principal compressive strength f corresponding to the oblique crushing of the membrane layer concrete under two-dimensional plane stress state. c2,max Calculate the principal compressive stress f of the concrete in the membrane layer under the appropriate reinforcement failure mode. c2,u ; Determine f c2,u ≤f c2,max Does this hold true? If so, calculate the ultimate bearing capacity τ under the appropriate reinforcement failure mode. xyu As the actual destructive bearing capacity τ xyu,act Then proceed to step S6; otherwise, calculate the ultimate bearing capacity τ″ under the over-reinforced failure mode. xyu As the actual destructive bearing capacity τ xyu,act Then proceed to step S6;

[0012] S6. Determine whether at least one of the upper and lower thin film layers satisfies τ. xy ≥τ xyu,act , τ xy If the load F is the horizontal shear stress of the membrane layer, then the load F is the predicted uniform bearing capacity of the box girder bridge; otherwise, the load F is updated to a larger value, and the load component borne by the plate is adjusted according to the proportional relationship before and after the load update, and then the process returns to step S2.

[0013] Preferably, in S1, the load component borne by the plate includes: axial force n along the x-direction. x Axial force n along the y direction y Bending moment m along the x-direction xBending moment m along the y direction y Torque m in the y-direction within a plane perpendicular to the x-direction xy Torque m in the x-direction within a plane perpendicular to the y-direction yx Vertical shear force v along the z-direction in a plane perpendicular to the x-direction xz Vertical shear force v along the z-direction in a plane perpendicular to the y-direction yz Horizontal shear force v along the y-direction in a plane perpendicular to the x-direction xy And the horizontal shear force v along the x-direction in a plane perpendicular to the y-direction. yx The x-direction is the longitudinal direction of the bridge; the y-direction is the transverse direction of the bridge.

[0014] Preferably, the formulas for calculating the ultimate bearing capacity of the thin film layer under various failure modes are as follows:

[0015] Under the optimal failure mode, when the horizontal shear stress τ of the thin film layer... xy During forward propagation:

[0016]

[0017] Under the optimal failure mode, when the horizontal shear stress in the thin film layer propagates in the negative direction:

[0018]

[0019] Let σ x σ is the normal stress along the x-direction of the thin film layer. y The normal stress of the thin film layer along the y-direction; k x The normal stress σ on the thin film layer x With horizontal shear stress τ xy The ratio of their interaction, σ x =k x τ xy ;k y The normal stress σ on the thin film layer y With horizontal shear stress τ xy The ratio of their interaction, σ y =k y τ xy ;ρ x ρ is the steel reinforcement ratio along the x-direction within the membrane layer. y f is the steel reinforcement ratio along the y-direction within the membrane layer. xd f is the yield strength of the steel reinforcement along the x-direction within the membrane layer. yd The yield strength of the steel reinforcement along the y-direction within the membrane layer;

[0020] Ultimate bearing capacity τ' of the thin film layer under the low-reinforcement failure mode xyu The calculation formula is:

[0021]

[0022] Among them, f' c This refers to the standard value of the axial compressive strength of concrete.

[0023] Ultimate bearing capacity τ″ of the membrane layer under over-reinforced failure mode xyu Solve by combining the following formulas:

[0024] ∑F x =0,ρ x f sxr cosθ=k x τ″ xyu cosθ+τ″ xyu sinθ (20)

[0025] ∑F y =0,ρ y f syr sin θ =k y τ″ xyu sinθ+τ″ xyu cosθ (21)

[0026] ∑F x =0,f c2,max sinθ+k x τ″ xyu sinθ=τ″ xyu cosθ+ρ x f sx sinθ (22)

[0027] ∑F y =0,f c2,max cosθ+k y τ″ xtu cosθ=τ″ xyu sinθ+ρ y f sy cosθ (23)

[0028]

[0029] Among them, F x ∑F represents the force exerted by the thin film layer along the x-axis. x F is the sum of all forces acting on the thin film layer along the x-axis. y ∑F represents the force exerted on the thin film layer along the y-axis. y f is the sum of all forces acting on the thin film layer along the y-axis. sxr f represents the steel reinforcement stress along the x-direction at the crack surface of the thin film layer. syr θ represents the steel reinforcement stress along the y-direction at the crack surface of the membrane layer; θ is the crack inclination angle within the membrane layer under the ultimate state; fsx The average stress of the steel reinforcement along the x-direction within the thin film layer, f sy f represents the average stress of the reinforcing steel along the y-direction within the thin film layer. c1 f is the average principal tensile stress of the concrete within the membrane layer. cr f is the standard value of tensile strength of concrete; c2,max This is the principal compressive strength corresponding to the oblique crushing of the thin-film concrete under two-dimensional plane stress.

[0030] Preferred, f c2,max The calculation formula is:

[0031]

[0032] Among them, E s This represents the elastic modulus of the steel reinforcement in the membrane layer.

[0033] Preferably, for the upper thin film layer, the following are available:

[0034]

[0035] For the lower thin film layer, we have:

[0036]

[0037] Where, n x,top n is the axial force along the x-direction of the upper thin film layer. x,bot n represents the axial force along the x-direction in the lower thin film layer. y,top n is the axial force along the y-direction of the upper thin film layer. y,bot v is the axial force along the y-direction in the lower thin film layer; xy,top v is the horizontal shear force along the y-direction in a plane perpendicular to the x-direction in the upper thin film layer. xy,bot The horizontal shear force along the y-direction in a plane perpendicular to the x-direction within the lower thin film layer; z top Z represents the thickness of the upper thin film layer. bot The thickness of the lower thin film layer;

[0038]

[0039]

[0040]

[0041]

[0042] In the formula, z d d1 is the lever arm between the upper and lower film layers; z is the plate thickness; d1 is the distance between the reinforcing mesh in the upper film layer and the plate surface; d2 is the distance between the reinforcing mesh in the lower film layer and the plate surface.

[0043] Preferably, in S5, f c2,u The calculation formula is:

[0044] f c2,u =τ xyu (tanθ u +cotθ u )-f c1 (15)

[0045] Where, τ xyu To determine the ultimate bearing capacity of the membrane layer under the appropriate reinforcement failure mode, θ u To determine the fracture angle of the thin film layer under the appropriate reinforcement failure mode, f c1 This represents the average principal tensile stress of the concrete within the membrane layer.

[0046] Preferred;

[0047] Under the optimal failure mode, when the horizontal shear stress τ of the thin film layer... xy During forward propagation:

[0048]

[0049] Under the optimal failure mode, when the horizontal shear stress in the thin film layer propagates in the negative direction:

[0050]

[0051] Among them, f xd f is the yield strength of the steel reinforcement along the x-direction within the membrane layer. yd The yield strength of the steel reinforcement along the y-direction within the membrane layer.

[0052] Preferably, in S4, f 1u The calculation formula is as follows:

[0053] Under the optimal failure mode, when the horizontal shear stress τ of the thin film layer... xy During forward propagation:

[0054]

[0055] Under the optimal failure mode, when the horizontal shear stress in the thin film layer propagates in the negative direction:

[0056]

[0057] Where, k x The normal stress σ on the thin film layer x With horizontal shear stress τ xy The ratio of their interaction, k y The normal stress σ on the thin film layer y With horizontal shear stress τ xy The proportion of influence between them.

[0058] This invention also proposes a unified bearing capacity prediction system for box-section bridges based on discrete plate components, including a memory containing a computer program. When the computer program is executed, it is used to implement the unified bearing capacity prediction method for box-section bridges based on discrete plate components.

[0059] Priority is also given to the inclusion of a processor connected to a memory, which executes the computer program to implement the unified bearing capacity prediction method for box-section bridges based on discrete plate components.

[0060] The advantages of this invention are:

[0061] (1) This invention provides a unified bearing capacity theory and calculation method for box-section bridges under complex combined forces such as tension, compression, bending, shear, torsion, and frame effect. By discretizing the box section into different plates, the bearing capacity failure problem of the section level is transformed into the bearing capacity failure problem of any plate level that makes up the section. The complex problem of coupled bearing capacity at the internal force level of the section is transformed into the coupled bearing capacity problem at the stress level of the plate. Furthermore, the plates are layered and the interlayer force balance equation is proposed. The bearing capacity failure problem of the plate is transformed again into the bearing capacity failure problem of the upper and lower membrane layers that make up the plate. Three possible failure modes of the upper and lower membrane layers under complex external loads and their corresponding bearing capacity calculation methods are proposed. Finally, the progressive failure loading method is applied to determine the failure state of the section to obtain the ultimate bearing capacity of the box section.

[0062] (2) This invention considers that box-section bridges are mostly thin-walled sections. Their unique thin-walled plate shell structure mechanical characteristics make it possible to discretize the section into different plates and use the forces of different plates to characterize the overall force of the section. Thus, the overall bearing capacity problem of the box section is transformed into the bearing capacity problem of different plates that make up the section, and a unified failure bearing capacity calculation method is formed for discrete plates under different force combinations, which can accurately calculate and judge the bearing capacity.

[0063] (3) This invention, by continuously increasing the loading ratio, i.e., the load F, until any discrete plate within the cross-section fails, can determine the bearing capacity of a box-section bridge under complex combined forces such as tension, compression, bending, shear, torsion, and frame effects, thus achieving a unified method for calculating bearing capacity. Furthermore, this invention adjusts the load components on the plates using proportional relationships, eliminating the need for repeated finite element modeling and improving computational efficiency.

[0064] (4) This invention is a unified load-bearing theory and calculation method for box-section bridges, which solves the problem that the traditional load-bearing capacity calculation method has long been incomplete in the face of complex combined forces such as tension, compression, bending, shear, torsion and frame effect, and realizes the unification of the load-bearing capacity calculation method.

[0065] (5) This invention starts from the perspective of the plates that make up the box section and analyzes the coupling failure mechanism of the box section bridge under different stress combinations from the stress level, which is something that traditional bearing capacity calculation methods cannot achieve from the internal force level.

[0066] (6) This invention promotes the innovation of design theory and deepens the understanding of the characteristics of box-section bridges. It has important theoretical value and economic and social benefits. It can significantly improve the precision of the load-bearing capacity design of box-section bridges, effectively reduce the waste of structural materials, and improve the economy of box-section bridges. Attached Figure Description

[0067] Figure 1 The flowchart shows the unified bearing capacity prediction method for box-section bridges based on plate discreteness proposed in this invention.

[0068] Figure 2 This is a schematic diagram showing the discretization of the box-section bridge into plate components according to the present invention; wherein (a) is a structural diagram of the box-section bridge, and (b) is a schematic diagram showing the discretization of the box-section bridge into plate components.

[0069] Figure 3 This is a schematic diagram showing all complete load components borne by any discrete plate component of the present invention.

[0070] Figure 4 This is a schematic diagram of the layering pattern and principle of the plate along the thickness direction of the present invention; wherein (a) is a perspective view of the plate, (b) is a discrete schematic diagram of the plate, and (c) is a schematic diagram of the plate in the thickness direction;

[0071] Figure 5 This is a schematic diagram of a reinforced concrete film layer unit subjected to two-dimensional plane stress according to the present invention;

[0072] Figure 6 This is a schematic diagram of the isolation body used when establishing the limit state force equilibrium equation of this invention, wherein (a) is the isolation body along the parallel crack surface, and (b) is the isolation body along the perpendicular crack surface.

[0073] In the diagram: 1-Top slab; 2-Web slab; 3-Bottom slab; 4-Upper membrane layer; 5-Middle layer; 6-Lower membrane layer; 7-Reinforcing mesh; 8-Concrete. Detailed Implementation

[0074] 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 embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0075] The structure of a box girder bridge is as follows Figure 2 As shown, it includes a top plate 1, a web plate 2, and a bottom plate 3.

[0076] like Figures 1-6 As shown in the figure, the unified bearing capacity prediction method for box-section bridges based on discrete plate components proposed in this embodiment includes the following steps:

[0077] S1. Set the load F for the box girder bridge, discretize the cross-section of the box girder bridge into multiple plates, establish a finite element model of the box girder bridge discretized into plates under load, and calculate the load components borne by each plate. The load components borne by the plates include: axial force n along the x-direction. x Axial force n along the y direction y Bending moment m along the x-direction x Bending moment m along the y direction y Torque m in the y-direction within a plane perpendicular to the x-direction xy Torque m in the x-direction within a plane perpendicular to the y-direction yx Vertical shear force v along the z-direction in a plane perpendicular to the x-direction xz Vertical shear force v along the z-direction in a plane perpendicular to the y-direction yz Horizontal shear force v along the y-direction in a plane perpendicular to the x-direction xy And the horizontal shear force v along the x-direction in a plane perpendicular to the y-direction. yx The x-direction is the longitudinal direction of the bridge; the y-direction is the transverse direction of the bridge.

[0078] S2. Divide the plate into upper thin film layer 4, middle layer 5 and lower thin film layer 6 along the thickness direction, and construct the interlayer force balance equation of the plate under the ultimate state.

[0079] In this embodiment, the limit state of the plate is assumed to satisfy the following internal force distribution assumptions 1a-4a:

[0080] 1a) Axial force n borne by the plate x axial force n y Horizontal shear force v xy and v yx They are evenly distributed to the upper thin film layer 4 and the lower thin film layer 6, respectively;

[0081] 2a) Bending moment m borne by the plate xBending moment m y Torque m xy Torque m yx The corresponding lever arms are evenly distributed to the upper thin film layer 4 and the lower thin film layer 6, respectively.

[0082] 3a) Vertical shear force v borne by the plate xz and vertical shear force v yz The entire load is borne by the middle layer 5;

[0083] 4a) Since the vertical shear force of bridge structures is generally very small, the bearing capacity of the middle layer 5 is not controlled by the design under the action of only vertical shear force, and it is assumed that the vertical shear force v xz v yz It has no effect on the stress on the upper thin film layer 4 and the lower thin film layer 6.

[0084] Based on the above distribution assumptions 1a-4a, in this embodiment, the interlayer force equilibrium equations of the plate under the limit state are as follows: (1)-(5):

[0085]

[0086]

[0087]

[0088] v xz,mid =v xz (4)

[0089] v yz,mid =v yz (5)

[0090] Where, n x,top n is the axial force along the x-direction of the upper thin film layer 4. x,bot n is the axial force along the x-direction in the lower thin film layer 6; y,top n is the axial force along the y-direction of the upper thin film layer 4. y,bot The axial force along the y-direction is the force in the lower thin film layer 6; v xy,top v is the horizontal shear force along the y-direction in the plane perpendicular to the x-direction in the upper thin film layer 4. xy,bot The horizontal shear force along the y-direction in the plane perpendicular to the x-direction in the lower thin film layer 6; v xz,mid The vertical shear force along the x-direction of the middle layer 5, v yz,mid The vertical shear force along the y-direction of the middle layer 5; z d It is the lever arm between the upper thin film layer 4 and the lower thin film layer 6. z represents the thickness of the sheet metal; top Z represents the thickness of the upper thin film layer 4. bot The thickness of the lower thin film layer 6; z top =2d1,zbot =2d2, where d1 is the thickness of the steel mesh 7 in the upper film layer 4 from the surface of the plate, and d2 is the thickness of the steel mesh 7 in the lower film layer 6 from the surface of the plate.

[0091] S3, upper thin film layer 4, and lower thin film layer 6 are collectively referred to as thin film layers. The failure mode of the thin film layer under the ultimate condition and the force balance equation of the thin film layer under the ultimate condition are defined. The calculation formula of the ultimate bearing capacity under each failure mode is constructed by combining the interlayer force balance equation of the plate and the force balance equation of the thin film layer.

[0092] The membrane layer is equivalent to a reinforced concrete slab consisting of concrete 8 and a steel mesh 7 embedded in the concrete. The steel mesh 7 specifically adopts bidirectional orthogonal reinforcement. In this step, the membrane layer is defined to satisfy the following assumptions 1b-4b in the ultimate state:

[0093] 1) The 10-cracks formed by the cracking of the thin film layer are diffusely and uniformly distributed;

[0094] 2) The dowel force of bidirectional orthogonal reinforcement is not considered;

[0095] 3) The principal tensile stress in the concrete between cracks is assumed to be half of the concrete's tensile strength;

[0096] 4) Consider the difference in tensile stress between the two-way orthogonal reinforcement at the crack surface and between cracks.

[0097] In this embodiment, the force balance equation of the thin film layer under the limit state is given by the following formulas (6)-(10).

[0098] First, take the isolation body along the parallel crack surface, such as... Figure 6 (a) The equilibrium equations along the x and y directions are established as follows:

[0099] ∑F x =0,ρ x f sxr cosθ=σ x cosθ+τ xy sinθ (6)

[0100] ∑F y =0,ρ y f syr sinθ=σ y sinθ+τ xy cosθ (7)

[0101] Among them, F x ∑F represents the force exerted by the thin film layer along the x-axis. x F is the sum of all forces acting on the thin film layer along the x-axis. y ∑F represents the force exerted on the thin film layer along the y-axis. yρ is the sum of all forces acting on the thin film layer along the y-axis; x ρ is the steel reinforcement ratio along the x-direction within the membrane layer. y f is the steel reinforcement ratio along the y-direction within the membrane layer. sxr f represents the steel reinforcement stress along the x-direction at the crack surface of the thin film layer. syr σ represents the reinforcing steel stress along the y-direction at the crack surface of the membrane layer; θ represents the crack inclination angle within the membrane layer under the ultimate state; σ x σ is the normal stress along the x-direction of the thin film layer. y τ represents the normal stress along the y-direction of the thin film layer. xy This represents the horizontal shear stress of the thin film layer along the xy direction.

[0102] Specifically, for the upper thin film layer 4, σ x σ y and τ xy The calculation formula is as follows:

[0103]

[0104] For the lower thin film layer 6, σ x σ y and τ xy The calculation formula is as follows:

[0105]

[0106] Secondly, take the isolation body along the vertical crack surface, such as... Figure 6 (b) The equilibrium equations along the x and y directions are established as follows:

[0107] ∑F x =0,f c2 sinθ+σ x sinθ=τ xy cosθ+ρ x f sx sinθ (8)

[0108] ∑F y =0,f c2 cosθ+σ y cosθ=τ xy sinθ+ρ y f sy cosθ (9)

[0109] Among them, f c2 f is the average principal compressive stress of the concrete within the membrane layer; sx The average stress of the steel reinforcement along the x-direction within the thin film layer, f sy This represents the average stress of the reinforcing steel along the y-direction within the thin film layer.

[0110] The relationship between the average tensile stress between cracks in the bidirectional orthogonal reinforcement mesh and the tensile stress at the crack surface is calculated as follows:

[0111]

[0112] Among them, f c1 f is the average principal tensile stress of the concrete within the membrane layer; sxr f represents the steel reinforcement stress along the x-direction at the crack surface of the thin film layer. syr f represents the steel reinforcement stress along the y-direction at the crack surface of the thin film layer. cr f' is the standard value of tensile strength of concrete. c This is the standard value for the axial compressive strength of concrete.

[0113] The failure modes of the thin film layer under extreme conditions defined in this step include the following three:

[0114] The first type is the under-reinforced failure mode, which is characterized by the concrete cracking first, followed by the rapid yielding and failure of the bidirectional orthogonal reinforcement in the steel mesh 7.

[0115] The second type is the appropriate reinforcement failure mode, which is characterized by the first yielding of the bidirectional orthogonal reinforcement in the steel mesh 7, followed by the gradual oblique crushing failure of the concrete.

[0116] The third type is the over-reinforced failure mode, which is characterized by the concrete first undergoing oblique crushing, while the bidirectional orthogonal reinforcements in the steel mesh 7 do not yield.

[0117] By combining the performance of each failure mode with the above formulas (6)-(10), the failure bearing capacity under each failure mode can be obtained.

[0118] Under the appropriate reinforcement failure mode, i.e., the yielding of the bidirectional orthogonal reinforcement in the membrane layer occurs before the oblique crushing of the concrete in the ultimate state, the equilibrium equations (6) to (7) are transformed as follows:

[0119] ρ x f xd cosθ=σ x cosθ+τ xy sinθ (6.1)

[0120] ρ y f yd sinθ=σ y sinθ+τ xy cosθ (7.1)

[0121] Among them, f xd f is the yield strength of the steel reinforcement along the x-direction within the membrane layer. yd The yield strength of the steel reinforcement along the y-direction within the membrane layer.

[0122] Under the optimal failure mode, the ultimate bearing capacity of the membrane layer is denoted as τ. xyu The angle of inclination of the fracture is denoted as θ. u , τ xyu The corresponding principal tensile stress is denoted as f. 1u ;

[0123] When the horizontal shear stress τ of the thin film layer xy During forward propagation:

[0124]

[0125]

[0126]

[0127] When the horizontal shear stress in the thin film layer propagates in the negative direction:

[0128]

[0129]

[0130]

[0131] Where, k x The normal stress σ on the thin film layer x With horizontal shear stress τ xy The ratio of their interaction, σ x =k x τ xy ;k y The normal stress σ on the thin film layer y With horizontal shear stress τ xy The ratio of their interaction, σ y =k y τ xy ;f xd f is the yield strength of the steel reinforcement along the x-direction within the membrane layer. yd The yield strength of the steel reinforcement along the y-direction within the membrane layer.

[0132] Let the ultimate bearing capacity of the thin film layer under the unreinforced failure mode be denoted as τ' xyu The calculation formula is as follows:

[0133]

[0134] Among them, f' c This is the standard value for the axial compressive strength of concrete.

[0135] Let the ultimate bearing capacity of the thin film layer under the over-reinforced failure mode be denoted as τ″. xyu ,τ″ xyu Solve by combining the following equations (20) to (24):

[0136] ∑F x =0,ρ x f sxr cosθ=k x τ″ xyu cosθ+τ″ xyu sinθ (20)

[0137] ∑F y =0,ρ y f syr sinθ=k y τ″ xyu sinθ+τ″ xyu cosθ (21)

[0138] ∑F x =0,f c2,max sinθ+k x τ″ xyu sinθ=τ″ xyu cosθ+ρ x f sx sinθ (22)

[0139] ∑F y =0,f c2,max cosθ+k y τ″ xyu cosθ=τ″ xyu sinθ+ρ y f sy cosθ (23)

[0140]

[0141] Among them, f c2,max f is the principal compressive strength corresponding to the oblique crushing of the membrane-layer concrete under two-dimensional plane stress. c2,max The derivation process is as follows:

[0142] f c2,max =βf' c (16)

[0143]

[0144] Where β is the concrete compressive softening coefficient, and is a function of the ultimate tensile strain ε1 of the membrane layer;

[0145] By assuming the bidirectional orthogonal reinforcement in the membrane layer as "equivalent virtual reinforcement" along the principal tensile strain direction of the concrete, the equivalent reinforcement ratio is ρ. x cos 4 θ+ρ y sin 4θ, combined with equilibrium equations (6) and (7), can be used to derive the formula for calculating the principal tensile strain ε1 of the membrane layer concrete:

[0146]

[0147] Among them, E s This represents the elastic modulus of the steel reinforcement in the membrane layer.

[0148] Combining formulas (16), (17), and (18), we can obtain:

[0149]

[0150] S4. Assuming the thin film layer is in a suitable failure mode, let Calculate the ultimate bearing capacity τ of the membrane layer under the appropriate reinforcement failure mode. xyu and principal tensile stress f 1u Determine whether f is satisfied. 1u >f cr No, indicating that the thin film layer exhibits an unreinforced failure mode; calculate the ultimate bearing capacity τ'. xyu As the actual destructive bearing capacity τ xyu,act Then proceed to step S6; if yes, it means that the thin film layer does not experience the low-stretcher failure mode, and proceed to step S5.

[0151] S5. Obtain the principal compressive strength f corresponding to the oblique crushing of the membrane layer concrete under two-dimensional plane stress state. c2,max Calculate the principal compressive stress f of the concrete in the membrane layer under the appropriate reinforcement failure mode. c2,u ; Determine f c2,u ≤f c2,max Does this condition hold true? If so, then the membrane layer is determined to be in the adequately reinforced failure mode, and the ultimate bearing capacity τ is calculated. xyu As the actual destructive bearing capacity τ xyu,act Then proceed to step S6; otherwise, determine that the membrane layer belongs to the over-reinforced failure mode and calculate the ultimate bearing capacity τ″. xyu As the actual destructive bearing capacity τ xyu,act Then proceed to step S6.

[0152] f c2,u =τ xyu (tanθ u +cotθ u )-f c1 (15)

[0153] S6. Determine if τ is satisfied. xy ≥τ xyu,actIf yes, it indicates that the plate has failed. The load F at this point is the predicted uniform bearing capacity of the box girder bridge, meaning that the box girder bridge may experience ultimate failure when the load reaches F. If no, the load F is updated to a larger value, and the load component n borne by the plate is adjusted according to the proportional relationship before and after the load update. x n y m x m y m xy m yx v x v y v xy and v yx Then return to step S2.

[0154] In a specific embodiment of the method proposed in this application, the load-bearing capacity calculation of a box girder bridge ultimately falls into the load-bearing capacity calculation of a reinforced concrete membrane layer of a plate. Therefore, by processing the reinforced concrete membrane and conducting tests on different reinforced concrete membrane load-bearing mechanisms, the test results of the corresponding membrane ultimate load-bearing capacity are obtained. These results are then compared with the membrane layer unit ultimate load-bearing capacity calculation method proposed in this application to verify the accuracy of the method proposed in this application. The following describes the load-bearing capacity calculation process using a reinforced concrete membrane layer S-31 subjected to pure shear loading as an example. The calculation parameters are shown in the table below:

[0155]

[0156] First, assuming that the membrane layer fails under adequate reinforcement, the bidirectional orthogonal reinforcement yields first in the ultimate state. The ultimate bearing capacity τ of the membrane layer under adequate reinforcement failure can be calculated according to formulas (11) and (12). xyu and the angle of the fracture θ u All values ​​are positive.

[0157]

[0158]

[0159] τ can then be calculated. xyu The corresponding principal tensile stress f 1u :

[0160] f 1u =τ xyu =16.18MPa

[0161] Assuming that the film layer experiences adequate reinforcement failure, the first step should be to perform a calculation for under-reinforced failure of the film layer:

[0162]

[0163] If the thin film layer does not experience under-reinforced failure, then further calculations for over-reinforced failure of the thin film layer are required:

[0164] The above τ xyu and θ u Substituting into formula (15), the principal compressive stress f of the concrete at the yield point of the bidirectional orthogonal reinforcement can be obtained. c2,u :

[0165]

[0166] The average principal tensile strain ε1 of the concrete at yield of the bidirectional orthogonal reinforcement is calculated using formula (18), and the elastic modulus of the reinforcement is taken as E. s =2e5MPa:

[0167]

[0168] Substituting into formula (17), the compressive softening coefficient β of concrete and the corresponding principal compressive strength f when bidirectional orthogonal reinforcement yields can be obtained. c2,max :

[0169]

[0170] f c2,max =βf' c =0.568 × 30.2 = 17.15 MPa

[0171] Compare f c2 with f c2,max Based on the size relationship, calculate the failure of the over-reinforced membrane layer:

[0172] f c2 =31.45MPa>f c2,max =17.15MPa

[0173] Therefore, the reinforced concrete membrane layer is actually an over-reinforced failure member, and its corresponding over-reinforced failure bearing capacity τ″ should be calculated. xyu Solving the system of equations (19) to (24) again yields:

[0174] τ″ xyu =8.33MPa; θ″ u =45°; f sx =194.7MPa; f sy =194.7MPa

[0175] That is, the true ultimate bearing capacity τ of the reinforced concrete membrane layer. xyu,act =8.33MPa, compared with the experimentally measured value τ test =8.34MPa is basically the same, which verifies the accuracy of the method proposed in this application.

[0176] Of course, those skilled in the art will recognize that the present invention is not limited to the details of the exemplary embodiments described above, but also includes the same or similar structures that can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0177] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

[0178] The technologies, shapes, and structures not described in detail in this invention are all known technologies.

Claims

1. A unified bearing capacity prediction method for box-section bridges based on plate discretization, characterized in that, Includes the following steps: S1. Set the load F of the box-section bridge, discretize the cross section of the box-section bridge into multiple plates, establish a finite element model of the box-section bridge discretized into plates under load, and calculate the load components borne by each plate. S2. Divide the plate into an upper thin film layer (4), a middle layer (5) and a lower thin film layer (6) along the thickness direction, and construct the interlayer force balance equation of the plate under the ultimate state. S3, the upper film layer (4) and the lower film layer (6) are collectively referred to as film layers. The failure mode of the film layer under the ultimate state and the force balance equation of the film layer under the ultimate state are defined. The calculation formula of the ultimate bearing capacity under each failure mode is constructed by combining the interlayer force balance equation of the plate and the force balance equation of the film layer. The failure modes include under-reinforced failure mode, moderately reinforced failure mode and over-reinforced failure mode. S4. Assuming the membrane layer is in the optimal reinforcement failure mode, calculate the ultimate bearing capacity τ of the membrane layer under the optimal reinforcement failure mode. xyu and principal tensile stress f 1u Determine whether f is satisfied. 1u >f cr f cr If the value is the standard value of the tensile strength of concrete, then calculate the ultimate bearing capacity τ′ under the under-reinforced failure mode. xyu As the actual destructive bearing capacity τ xyu，act If yes, then proceed to step S6; if yes, then proceed to step S5. S5. Obtain the principal compressive strength f corresponding to the oblique crushing of the membrane layer concrete under two-dimensional plane stress state. c2，max Calculate the principal compressive stress f of the concrete in the membrane layer under the appropriate reinforcement failure mode. c2，u ; Determine f c2，u ≤f c2，max Does this hold true? If so, calculate the ultimate bearing capacity τ under the appropriate reinforcement failure mode. xyu As the actual destructive bearing capacity τ xyu，act Then proceed to step S6; otherwise, calculate the ultimate bearing capacity τ″ under the over-reinforced failure mode. xyu As the actual destructive bearing capacity τ xyu，act Then proceed to step S6; S6. Determine whether there is at least one of the upper thin film layer (4) and the lower thin film layer (6) that satisfies τ. xy ≥τ xyu，act , τ xy If the load F is the horizontal shear stress of the membrane layer, then the load F is the predicted uniform bearing capacity of the box girder bridge; otherwise, the load F is updated to a larger value, and the load component borne by the plate is adjusted according to the proportional relationship before and after the load update, and then the process returns to step S2.

2. The method for predicting the unified bearing capacity of box-section bridges based on discrete plate components as described in claim 1, characterized in that, In S1, the load components borne by the plate include: axial force n along the x-direction. x Axial force n along the y direction y Bending moment m along the x-direction x Bending moment m along the y direction y Torque m in the y-direction within a plane perpendicular to the x-direction xy Torque m in the x-direction within a plane perpendicular to the y-direction yx Vertical shear force v along the z-direction in a plane perpendicular to the x-direction xz Vertical shear force v along the z-direction in a plane perpendicular to the y-direction yz Horizontal shear force v along the y-direction in a plane perpendicular to the x-direction xy And the horizontal shear force v along the x-direction in a plane perpendicular to the y-direction. yx The x-direction is the longitudinal direction of the bridge; the y-direction is the transverse direction of the bridge.

3. The method for predicting the unified bearing capacity of box-section bridges based on discrete plate components as described in claim 1, characterized in that, The formulas for calculating the ultimate bearing capacity of the thin film layer under various failure modes are as follows: Under the optimal failure mode, when the horizontal shear stress τ of the thin film layer... xy During forward propagation: Under the optimal failure mode, when the horizontal shear stress in the thin film layer propagates in the negative direction: Let σ x σ is the normal stress along the x-direction of the thin film layer. y The normal stress of the thin film layer along the y-direction; k x The normal stress σ on the thin film layer x With horizontal shear stress τ xy The ratio of their interaction, σ x =k x τ xy ;k y The normal stress σ on the thin film layer y With horizontal shear stress τ xy The ratio of their interaction, σ y =k y τ xy ;ρ x ρ is the steel reinforcement ratio along the x-direction within the membrane layer. y f is the steel reinforcement ratio along the y-direction within the membrane layer. xd f is the yield strength of the steel reinforcement along the x-direction within the membrane layer. yd The yield strength of the steel reinforcement along the y-direction within the membrane layer; Ultimate bearing capacity τ′ of the thin film layer under the low-reinforcement failure mode xyu The calculation formula is: Where, f′ c This refers to the standard value of the axial compressive strength of concrete. Ultimate bearing capacity τ″ of the membrane layer under over-reinforced failure mode xyu Solve by combining the following formulas: ∑F x =0,ρ x f sxr cosθ=k x the xyu cosθ+τ″ xyu sin (20) ∑F y =0,ρ y f syr sinθ=k y the xyu sinθ+τ″ xyu cosθ (21) ∑F x =0,f c2,max sinθ+k x the xyu sinθ=τ″ xyu cosθ+ρ x f sx sin (22) ∑F y =0,f c2,max cosθ+k y the xyu cosθ=τ″ xyu sinθ+ρ y f sy cosθ (23) f sxr =f sx +f c1 ,f syr =f sy +f c1 , Among them, F x ∑F represents the force exerted by the thin film layer along the x-axis. x F is the sum of all forces acting on the thin film layer along the x-axis. y ∑F represents the force exerted on the thin film layer along the y-axis. y f is the sum of all forces acting on the thin film layer along the y-axis. sxr f represents the steel reinforcement stress along the x-direction at the crack surface of the thin film layer. syr θ represents the steel reinforcement stress along the y-direction at the crack surface of the membrane layer; θ is the crack inclination angle within the membrane layer under the ultimate state; f sx The average stress of the steel reinforcement along the x-direction within the thin film layer, f sy f represents the average stress of the reinforcing steel along the y-direction within the thin film layer. c1 f is the average principal tensile stress of the concrete within the membrane layer. cr f is the standard value of tensile strength of concrete; c2,max This is the principal compressive strength corresponding to the oblique crushing of the thin-film concrete under two-dimensional plane stress.

4. The method for predicting the unified bearing capacity of box-section bridges based on discrete plate components as described in claim 3, characterized in that, f c2,max The calculation formula is: Among them, E s This represents the elastic modulus of the steel reinforcement in the membrane layer.

5. The method for predicting the unified bearing capacity of box-section bridges based on discrete plate components as described in claim 3, characterized in that, Regarding the upper thin film layer (4), we have: For the lower thin film layer (6), we have: Where, n x，top n is the axial force along the x-direction of the upper thin film layer (4). x，bot n is the axial force along the x-direction of the lower thin film layer (6); y,top n is the axial force along the y direction of the upper thin film layer (4). y，bot The axial force along the y-direction of the lower thin film layer (6); v xy,top v is the horizontal shear force along the y direction in the plane perpendicular to the x direction in the upper thin film layer (4). xy,bot The horizontal shear force along the y direction in the plane perpendicular to the x direction in the lower thin film layer (6); z top z is the thickness of the upper thin film layer (4). bot The thickness of the lower thin film layer (6); With top =2d1;z bot =2d2; In the formula, z d d1 is the lever arm between the upper film layer (4) and the lower film layer (6); z is the thickness of the plate; d1 is the thickness of the steel mesh (7) in the upper film layer (4) from the surface of the plate, and d2 is the thickness of the steel mesh (7) in the lower film layer (6) from the surface of the plate.

6. The method for predicting the unified bearing capacity of box-section bridges based on discrete plate components as described in claim 1, characterized in that, In S5, f c2,u The calculation formula is: f c2,u =t xyu (tanθ u +cotθ u )-f c1 (15) Where, τ xyu To determine the ultimate bearing capacity of the membrane layer under the appropriate reinforcement failure mode, θ u To determine the fracture angle of the thin film layer under the appropriate reinforcement failure mode, f c1 This represents the average principal tensile stress of the concrete within the membrane layer.

7. The method for predicting the unified bearing capacity of box-section bridges based on discrete plate components as described in claim 6, characterized in that... ； Under the optimal failure mode, when the horizontal shear stress τ of the thin film layer... xy During forward propagation: Under the optimal failure mode, when the horizontal shear stress in the thin film layer propagates in the negative direction: Among them, f xd f is the yield strength of the steel reinforcement along the x-direction within the membrane layer. yd The yield strength of the steel reinforcement along the y-direction within the membrane layer.

8. The method for predicting the unified bearing capacity of box-section bridges based on discrete plate components as described in claim 1, characterized in that, In S4, f 1u The calculation formula is as follows: Under the optimal failure mode, when the horizontal shear stress τ of the thin film layer... xy During forward propagation: Under the optimal failure mode, when the horizontal shear stress in the thin film layer propagates in the negative direction: Where, k x The normal stress σ on the thin film layer x With horizontal shear stress τ xy The ratio of their interaction, k y The normal stress σ on the thin film layer y With horizontal shear stress τ xy The proportion of influence between them.

9. A unified bearing capacity prediction system for box-section bridges based on plate discretization, characterized in that, It includes a memory storing a computer program, which, when executed, is used to implement the unified bearing capacity prediction method for box-section bridges based on plate discreteness as described in any one of claims 1-8.

10. The unified bearing capacity prediction system for box-section bridges based on discrete plate components as described in claim 9, characterized in that, It also includes a processor connected to a memory, the processor being used to execute the computer program to implement the unified bearing capacity prediction method for box-section bridges based on discrete plate components as described in any one of claims 1-8.

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