Analysis Methods, Terminals, and Media for the Entire Bending and Torsional Process of Corrugated Steel Web Curved Box Girder

Abstract

This invention provides a method, terminal, and medium for analyzing the entire bending and torsion process of a corrugated steel web curved box girder, belonging to the technical field of corrugated steel web curved box girders. The method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder, as provided in this invention, separates the stress state of the corrugated steel web curved box girder into a bending subsystem and a torsion subsystem. It performs iterative analysis of the entire bending and torsion process of the bending subsystem and the torsion subsystem, respectively, establishing the relationship between the bending and torsion subsystems of the corrugated steel web curved box girder, thus obtaining the iterative analysis of the entire bending and torsion process of the corrugated steel web curved box girder. This invention provides a method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder, realizing full-process bending and torsion analysis, improving calculation accuracy, and allowing for the acquisition and analysis of more diverse response results through full-process iteration.

Description

Technical Field

[0001] This invention belongs to the technical field of corrugated steel web curved box girder, specifically involving a method, terminal, and medium for analyzing the entire bending and torsion process of a corrugated steel web curved box girder. Background Technology

[0002] Traditional concrete box girders consist of a top slab, bottom slab, web, diaphragms, and support beams, all typically constructed of reinforced concrete. However, traditional concrete box girders have gradually revealed problems during use, including poor durability. Corrugated steel web curved box girders replace traditional concrete webs with corrugated steel plates as the web. The top and bottom slabs are reinforced concrete structures, incorporating longitudinal, transverse, and prestressed steel reinforcement. Corrugated steel plates offer high shear strength and stability, high prestressing efficiency, and excellent three-dimensional flexural characteristics. They are also relatively lightweight, effectively reducing the box girder's self-weight, decreasing material usage in the substructure, and lowering production costs. With the increasing popularity of corrugated steel web curved box girders, research on their mechanical properties has become more in-depth, but most studies focus on the elastic stage, with limited research on the nonlinear stage. The study of the nonlinear stage of corrugated steel web curved box girders is further complex due to the influence of curves and external prestressing. Furthermore, under the influence of the bending-torsional coupling characteristics of the curved beam itself, even without considering the shear lag effect, the stress in the cross section is no longer equal along the transverse direction. Especially after entering the plastic stage, the yield initiation point of the stress at each point along the height and width of the cross section is different, making the stress state of the structure very complex and greatly increasing the difficulty of nonlinear analysis. Since the external prestressed steel bars in the curved beam will generate different prestresses on the inside and outside of the curve, and their strain does not have a deformation coordination relationship with the strain of the adjacent concrete, the complexity of the nonlinear solution process is further increased. Summary of the Invention

[0003] The purpose of this invention is to provide a method, terminal, and medium for analyzing the entire bending and torsion process of corrugated steel web curved box girders, aiming to solve the problem of the difficulty in analyzing corrugated steel web curved box girders in the nonlinear stage.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is: to provide a method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder, comprising the following operational steps:

[0005] S1. The stress state of the corrugated steel web curved box girder is separated into a bending resistance system and a torsion resistance system.

[0006] S2. Perform iterative analysis of the entire bending resistance process of the anti-bending system;

[0007] S3. Perform a full-process iterative analysis of the anti-torsion system for the anti-torsion system;

[0008] S4. Establish the connection between the bending resistance system and the torsion resistance system of the corrugated steel web curved box girder;

[0009] S5. Obtain the full-process iterative analysis of bending and torsion of the corrugated steel web curved box girder.

[0010] In one possible implementation, in step S2, under the condition of the bending subsystem, the corrugated steel web curved box girder is equivalent to a straight beam to eliminate the torque effect caused by the curvature of the beam axis, and the effect of the equivalent straight beam on resisting the bending moment caused by the load is analyzed.

[0011] In one possible implementation, the equivalent straight beam experiences four stages of stress under bending moment: the first stage of bending, the second stage of bending, the third stage of bending, and the fourth stage of bending. In the first stage of bending, the concrete does not crack. In the second stage of bending, the bottom slab cracks, and the tensile strain of the longitudinal and transverse reinforcement of the bottom slab is less than the specified value, while the compressive strain of the top slab is less than or equal to the specified value. In the third stage of bending, the tensile strain of the longitudinal and transverse reinforcement is greater than or equal to the specified value, the tensile strain of the internal prestressed reinforcement is less than or equal to the specified value, and the compressive strain of the top slab is less than or equal to the specified value. In the fourth stage of bending, the tensile strain of the longitudinal and transverse reinforcement of the bottom slab is greater than or equal to the specified value, the tensile strain of the internal prestressed reinforcement is greater than or equal to the specified value, and the compressive strain of the top slab is greater than or equal to the specified value, until the compressive strain of the longitudinal and transverse reinforcement of the bottom slab is greater than or equal to the specified value, and the concrete top slab breaks.

[0012] In one possible implementation, in step S3, under the anti-torsion system, the corrugated steel web curved box girder is equivalent to a straight beam, and the torque effect generated by the beam axis curvature is analyzed.

[0013] In one possible implementation, the total torque of the equivalent straight beam under torque includes the torque borne by the bottom and top plates, the torque borne by the corrugated steel web, and the torque borne by the external prestressing tendons.

[0014] In one possible implementation, the beam axis curvature of the corrugated steel web curved box girder is constant. Under a certain load, bending moment and torque will be generated simultaneously. The bending moment and torque generated at this time correspond to the same load level. The effects of bending moment under the bending system and torque under the torsion system are analyzed separately and then superimposed.

[0015] In one possible implementation, in a corrugated steel web curved box girder, under the action of bending-torsional coupling, the bottom plate and the top plate are simultaneously subjected to compression and shear. Under the ultimate failure state, the bottom plate / top plate breaks.

[0016] In one possible implementation, according to step S5, the stress increment of external prestressed steel bars on the inner and outer sides of the corrugated steel web curved box girder is calculated, and the prestress increment at any point along the cross section of the corrugated steel web curved box girder is calculated.

[0017] A terminal is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method as described in any of the above.

[0018] A computer-readable storage medium is provided, which stores a computer program that, when executed by a processor, implements the steps of the method described in any of the above descriptions.

[0019] The beneficial effects of the method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder provided by this invention are as follows:

[0020] Compared with existing technologies, this method separates the stress state of corrugated steel web curved box girder into a bending subsystem and a torsional subsystem. Iterative analyses are then performed on the entire bending process of the bending subsystem and the entire torsional process of the torsional subsystem, respectively. This iterative analysis improves the accuracy of data analysis. A connection is established between the bending and torsional subsystems of the corrugated steel web curved box girder. By combining the iterative analyses of the bending and torsional processes of the bending and torsional subsystems, a comprehensive iterative analysis of the bending and torsional processes of the corrugated steel web curved box girder is obtained. This enables the analysis of the entire bending and torsional process of the corrugated steel web curved box girder and allows for the acquisition and analysis of various response results. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention, 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 the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the bending and torsional state of the corrugated steel web curved box girder used in the embodiments of the present invention;

[0023] Figure 2 This is a schematic diagram of the bending system of the corrugated steel web curved box girder used in the embodiments of the present invention;

[0024] Figure 3 This is a schematic diagram of the anti-torsion system of the corrugated steel web curved box girder used in the embodiments of the present invention;

[0025] Figure 4This is a flowchart of the full-process iterative calculation of the bending system of the corrugated steel web curved box girder used in the embodiments of the present invention;

[0026] Figure 5 This is a flowchart of the full-process iterative calculation of the anti-torsion system of the corrugated steel web curved box girder used in the embodiments of the present invention;

[0027] Figure 6 This is a flowchart of the full-process iterative calculation of bending and torsion of the corrugated steel web curved box girder used in the embodiments of the present invention;

[0028] Figure 7 This is a schematic diagram of the first stage of bending stress analysis of the corrugated steel web curved box girder used in the embodiments of the present invention;

[0029] Figure 8 This is a schematic diagram of the second-stage bending stress analysis of the corrugated steel web curved box girder used in the embodiments of the present invention.

[0030] Figure 9 This is a schematic diagram of the third stage of bending stress analysis of the corrugated steel web curved box girder used in the embodiment of the present invention.

[0031] Figure 10 This is a schematic diagram of the fourth stage of bending stress analysis of the corrugated steel web curved box girder used in the embodiments of the present invention.

[0032] In the diagram: 1. Top plate; 2. Corrugated steel web; 3. Bottom plate. Detailed Implementation

[0033] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0034] Please refer to Figure 1 to Figure 10 The following is a specific implementation of the method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder provided by the present invention, which includes the following operation steps:

[0035] S1. The stress state of the corrugated steel web curved box girder is separated into a bending resistance system and a torsion resistance system.

[0036] S2. Perform iterative analysis of the entire bending resistance process of the anti-bending system;

[0037] S3. Perform a full-process iterative analysis of the anti-torsion system for the anti-torsion system;

[0038] S4. Establish the connection between the bending resistance system and the torsion resistance system of the corrugated steel web curved box girder;

[0039] S5. Obtain the full-process iterative analysis of bending and torsion of the corrugated steel web curved box girder.

[0040] This invention provides a method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder. Compared with existing technologies, this method separates the stress state of the corrugated steel web curved box girder into a bending subsystem and a torsion subsystem. Iterative analyses are then performed on the bending and torsional processes of both subsystems. This iterative analysis improves the accuracy of data analysis. A connection is established between the bending and torsional subsystems of the corrugated steel web curved box girder. By combining the iterative analyses of the bending and torsional processes of the bending and torsional subsystems, a comprehensive iterative analysis of the bending and torsional process of the corrugated steel web curved box girder is obtained. This method enables the analysis of the entire bending and torsional process of the corrugated steel web curved box girder and allows for the acquisition and analysis of various response results.

[0041] As a specific implementation of the method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder provided by this invention, please refer to... Figure 1 to Figure 10 In step S2, under the bending system of the corrugated steel web curved box girder, the torque generated by the inherent characteristics of the corrugated steel web curved box girder mainly comes from the curvature of the beam axis. The corrugated steel web curved box girder is equivalent to a straight beam, eliminating the torque generated by the curvature of the beam axis. In this case, the corrugated steel web curved box girder only resists the bending moment caused by the load. The effect of the equivalent straight beam resisting the bending moment caused by the load is analyzed.

[0042] As a specific implementation of the method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder provided by this invention, please refer to... Figure 2 , Figure 4 , Figure 7 to Figure 10 The equivalent straight beam, under the action of external load bending moment, undergoes four stages of stress: the first stage of bending resistance, the second stage of bending resistance, the third stage of bending resistance, and the fourth stage of bending resistance. In the first stage of bending resistance, the concrete does not crack. In the second stage of bending resistance, the bottom slab 3 cracks, and the tensile strain of the longitudinal and transverse reinforcement of the bottom slab 3 is less than the specified value, while the compressive strain of the top slab 1 is less than or equal to the specified value. In the third stage of bending resistance, the tensile strain of the longitudinal and transverse reinforcement of the bottom slab 3 is greater than or equal to the specified value, the tensile strain of the internal prestressed reinforcement is less than or equal to the specified value, and the compressive strain of the top slab 1 is less than or equal to the specified value. In the fourth stage of bending resistance, the tensile strain of the longitudinal and transverse reinforcement of the bottom slab 3 is greater than or equal to the specified value, the tensile strain of the internal prestressed reinforcement is greater than or equal to the specified value, and the compressive strain of the top slab 1 is greater than or equal to the specified value, until the compressive strain of the longitudinal and transverse reinforcement of the bottom slab 3 is greater than or equal to the specified value, and the concrete top slab 1 breaks.

[0043] When a corrugated steel web curved box girder is equivalent to a straight beam, the stress conditions at the cross-sections of the corrugated steel web curved box girder in these four stages are analyzed. The mechanical parameters involved in the stress analysis and their meanings are as follows:

[0044] h z This is the total height of the cross-section; h ps It is the distance from the point of application of the resultant force of the prestressing tendons in the body to the compression edge of the cross section; h p It is the distance from the point of application of the resultant force of the external prestressing tendons to the compression edge of the cross section; h 0 represents the effective height of the cross-section. h 0= h z -y s ; The height of the cross section relative to the compression zone. ξ= x / h 0, x The height of the compression zone is given; the upper and lower flanges of the steel beam are respectively converted into the reinforcing bars in the top plate 1 and the bottom plate 3. It is the distance from the point of application of the resultant force of the reinforcing bars in the top slab 1 and bottom slab 3 to the compression edge of the section; y s These are the distances from the point of application of the resultant force of the reinforcing bars in the top slab 1 and bottom slab 3 to the tension edge of the cross section, respectively. y c It is the distance from the point of application of the resultant force of the concrete in the compression zone of the top slab 1 and the tension zone of the bottom slab 3 to the compression edge of the section; y ct It is the distance from the point of application of the resultant force of the concrete in the compression zone of the top slab 1 and the tension zone of the bottom slab 3 to the tension edge of the section; d c The thickness of top plate 1, d ct The thickness of base plate 3; d eq Take as d eq = min( x h 0, d c ); e The value of strain is the strain value on the compressive stress-strain curve of concrete, i.e., the horizontal axis of the curve; e c The compressive strain at the edge of the concrete in the compression zone of the top slab 1; e ct The tensile strain at the edge of the concrete in the tension zone of the base plate 3; e cr For concrete cracking strain; ecu This represents the ultimate compressive strain of the concrete. e t For the uniaxial tensile strain of concrete, e sy The yield strain of the steel reinforcement; The compressive strain at the point of application of the resultant force of the top slab reinforcement 1 (including the upper flange of the steel beam); e s The tensile strain at the point of application of the resultant force of the three reinforcing bars in the bottom slab (including the lower flange of the steel beam); e p For the strain of the prestressing tendons; e 0 represents the peak compressive strain of the concrete; In response to The stress; σ s In response to e s The stress; σ ps The stress in the prestressed tendons within the body; s pe This refers to the initial effective stress of the external prestressing tendons; Δ s p This represents the increase in external prestressing tendons; s ps The effective stress after considering the prestress loss of the prestressed tendons inside the body; C c The resultant force of the concrete stress in the compression zone of the top slab 1; C t The resultant force of the concrete stress in the tension zone of the base plate 3; This refers to the area of ​​the top slab reinforcement (including the upper flange of the steel beam); A s This refers to the area of ​​the bottom slab reinforcement (including the lower flange of the steel beam); A ps The area of ​​the prestressing tendons inside the body; A p The area of ​​the external prestressing tendons; b e The effective distribution width of the top slab concrete; b et This refers to the effective distribution width of the concrete in the base slab 3. E p The elastic modulus of the prestressed tendon; E S This refers to the elastic modulus of the reinforcing steel. E c This refers to the elastic modulus of concrete. M This refers to the moment about the point of application of the resultant force on the concrete in the compression zone; f c This refers to the axial compressive strength of concrete. f crFor concrete cracking stress; f y The yield strength of the steel reinforcement; k The slope of the hardened section of the steel reinforcement; for .

[0045] Stress analysis of corrugated steel web curved box girder at cross-sections during these four stages:

[0046] The first stage of flexural resistance, before concrete cracking.

[0047] Cross-sectional axial force equilibrium equations

[0048] (1)

[0049] Torque balance equation,

[0050] (2)

[0051] in,

[0052] (3)

[0053] (4)

[0054] (5)

[0055] (6)

[0056] The second stage of flexural resistance, after concrete cracking and before the tensile reinforcement yields.

[0057] Cross-sectional axial force equilibrium equations

[0058] (1)

[0059] Torque balance equation,

[0060] (2)

[0061] in,

[0062] (7)

[0063] (8)

[0064] (6)

[0065] In the third stage of flexural resistance, after the tensile reinforcement yields but before the concrete reaches its peak compressive strain,

[0066] Cross-sectional axial force equilibrium equations

[0067] (9)

[0068] Torque balance equation,

[0069] (10)

[0070] In the fourth stage of flexural resistance, after the concrete reaches its peak compressive strain...

[0071] Cross-sectional axial force equilibrium equations

[0072] (11)

[0073] Torque balance equation,

[0074] (12)

[0075] in,

[0076] (13)

[0077] (14).

[0078] In the bending-resistant system, the static equilibrium equations at each stage all include e c Prestressed tendon increment and relative pressure zone height Three unknowns, if the load is known, assume an increment of prestressing tendon. The other two unknowns are obtained, and it is determined whether the accuracy of the assumed values ​​meets the requirements. The full-process curves of bending moment-curvature and load-prestress increment of the bending system are obtained. matlab The specific steps for programming calculations are as follows:

[0079] M1, Assume a stress increment Δ of an externally prestressed tendon. s Then the total stress of the prestressing tendon is s p = s pe +Δ s p ;

[0080] M2, Divide the beam length n For each element, calculate the bending moment at the location of each element based on the load. M i ( i =1, 2, ... n Based on the geometric conditions, determine the effective height of the external prestressing tendons at the location of each element. h pi ( i=1, 2, ..., n );

[0081] M3, in s p Assuming the given conditions, we first assume the corrugated steel web curved box girder is in the first stage of bending resistance, i.e., before concrete cracking. Then, we solve equations 1-6 simultaneously to determine the bending resistance under the first stage. n Each cross section e ci and Then according to the formula Can be found n Curvature of each cross section ;

[0082] M4, according to Seek e cti ,judge e cti Is it less than e cr If the value is less than the given value, the system remains in the first stage of bending resistance. Solve using formulas 1-6 simultaneously. Otherwise, the system enters the second stage of bending resistance. Solve using formulas 1, 2, 6, 7, and 8 simultaneously, and calculate the result. Seek e ci , e si ,like e ci ≤ e 0, e si < e sy If the result is positive, it remains in the second stage of bending resistance; otherwise, it enters the third stage. Solving formulas 9 and 10 simultaneously, and based on the calculated... Seek e ci , e si ,like e ci ≤ e 0、 e si ≥ e sy and e psi ≤ e p If it is still in the third stage of bending resistance, then it will enter the fourth stage of bending resistance. Combine formulas 11 to 14.

[0083] M5, in finding ϕ si Then, the deflection of the steering block section and the mid-span section is calculated. w A1、w A2 ;

[0084] M6. Calculate the elongation Δ of the external prestressing tendons. l p and strain e p Then, the prestressing tendon stress can be obtained. and its increment ;

[0085] M7. Determine the hypothesis Δσ p and Does the difference meet the accuracy requirement (accuracy requirement set to 0.001)? If not, modify Δσ. p Using the calculated Continue re-executing step one as the assumed value until the accuracy requirement is met.

[0086] As a specific implementation of the method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder provided by this invention, please refer to... Figure 3 , Figure 5 In step S3, under the anti-torsion system, the corrugated steel web curved box girder is equivalent to a straight beam, and it is assumed that it only bears the torque generated by the curvature of the beam axis. The torque generated by the curvature of the beam axis of the equivalent straight beam is analyzed.

[0087] As a specific implementation of the method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder provided by this invention, please refer to... Figure 3 , Figure 5 The equivalent straight beam under torque has a total torque including the torque borne by the bottom plate 3 and top plate 1, the torque borne by the corrugated steel web 2, and the torque borne by the external prestressing tendons.

[0088] When a corrugated steel web curved box girder is equivalent to a straight beam, the stress condition at the cross-section of the corrugated steel web curved box girder is analyzed. The various mechanical parameters involved in the torsional analysis and their meanings are as follows:

[0089] A 0c and A 0w Each is half of the area enclosed by the shear flow centerline; This represents the total cross-sectional area of ​​the externally prestressed tendons. This represents the total cross-sectional area of ​​the prestressing tendons within the body. This represents the total cross-sectional area of ​​the longitudinal reinforcement bars; A c This represents the cross-sectional area of ​​the concrete portion; The shear stress is for the top plate 1 / bottom plate 3; The shear stress of the corrugated steel web 2; The average stress of the external prestressing tendons; The average stress of the prestressing tendons inside the body; This represents the average principal tensile stress in the concrete. This represents the average principal compressive stress in the concrete. The average stress of the longitudinal reinforcement; This represents the average stress of the transverse reinforcing bars; The vertical distance from the center of torsion to the bottom edge of the prestressed tendon; The strain of the prestressed tendons within the body; The strain of the externally prestressed tendons; e l The average strain of the longitudinal reinforcement; This represents the average strain of the transverse reinforcement. The average tensile strain of the short concrete column under inclined compression; The average compressive strain of the short concrete column under inclined pressure; , These represent the maximum and minimum compressive strains of a short concrete inclined column, respectively. , These represent the maximum and minimum tensile strains of a short concrete column under inclined compression, respectively. For the strain of the prestressing tendons inside the body; This refers to the softening coefficient of concrete. This represents the shear strain of the concrete slab. Torque; d cd The effective thickness of the concrete shear flow zone; d w The thickness of the corrugated steel web 2; d cd0 The neutral axis height of the axially compressed short column in the unified model of the equivalent straight beam is the value assumed at the beginning of the iterative calculation. The value is calculated by the formula; h The height between the center of section 1 of the concrete top slab and the center of section 3 of the bottom slab; b The distance between the centerlines of the corrugated steel web 2; d This refers to the transverse spacing of the prestressing tendons; The shear stress contributed to the concrete; The shear stress of the corrugated steel web 2; The shear strain of the corrugated steel web 2 is given; the two prestressing tendons are denoted as A and B, respectively. Subscript 1 represents the position of the turning block, and 2 represents the mid-span position. A1 and B1 are the positions of the turning blocks, and A2 and B2 are the mid-span positions. Correspondingly, the horizontal displacement at the turning block of the prestressing tendon is obtained from the anti-torsion system. Vertical displacement At the location of the steering block, the horizontal displacement Vertical displacement At the mid-span position, the horizontal displacement Vertical displacement ,by This indicates the horizontal displacement at the position of the steering block (mid-span position), in... This indicates the vertical displacement at the position of the steering block (mid-span position); F wA1 The vertical force representing the torque generated by the decomposition of prestress at the section of the steering block position for prestressing tendon A is... F wB1 These are the vertical forces of the torque generated by the decomposition of the prestress in the section at the position of the steering block for prestressing tendon B; F vA1 The horizontal force representing the torque generated by the decomposition of prestress at the section of the steering block location by prestressing tendon A. F vB1 These are the horizontal forces of torque generated by the decomposition of prestress in the section at the position of the steering block, specifically the prestressing tendon B. F wA2 The vertical force representing the torque generated by the prestressing decomposition of the prestressed tendon A at the mid-span section is denoted as A. F wB2 These are the vertical forces of the torque generated by the decomposition of prestress in the mid-span section of prestressed tendon B; F vA2 The horizontal force representing the torque generated by the decomposition of prestress in the mid-span section of prestressing tendon A is... F vB2 These are the horizontal forces, representing the torques generated by the prestressing decomposition of the prestressed tendon B at the mid-span section; furthermore, with F wA1(2) , F vA1(2) , F wB1(2) , F vB1(2) to refer to F wA1 , F wB1 , F wA2 , F wB2 , F vA1 , F vB1 , F vA2 , F vB2 ; T This represents the total torque of the box girder; T c The torque borne by the concrete section; T w The torque borne by the corrugated steel web; Tp This refers to the torque borne by the externally prestressed tendons. T pw and T pv These are the torques that resist vertical and horizontal forces, respectively. T p1 The total cross-sectional torque resisted by the external prestressing tendons at the steering block location section. T p2 The total section torque resisted by the external prestressing tendons at the mid-span section is given by T p1(2) to refer to T p1 , T p2 , L Calculate the length of the beam. k 0 is a constant between 0 and 1. The rotation angle of the shear element in the concrete.

[0090] (15)

[0091] A c =2 bd c (16)

[0092] (17)

[0093] (18)

[0094] (19)

[0095] (20)

[0096] (twenty one)

[0097] (twenty two)

[0098] (twenty three)

[0099] (twenty four)

[0100] (25)

[0101] (26)

[0102] (27)

[0103] In the case of an anti-torsion system, based on the above calculation formula, the following is adopted: matlab The program selects variables after inputting known data. e d When a certain value is reached, the remaining variables can be solved iteratively using an effective equation through trial and error, continuously increasing according to a certain pattern. e d The value, until e d The value of each unknown quantity is calculated iteratively to reach 0.0018, thus allowing for the calculation of the values ​​of each unknown quantity throughout the entire torsion process.

[0104] As a specific implementation of the method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder provided by this invention, please refer to... Figure 1 to Figure 10 A corrugated steel web curved box girder has a fixed beam axis curvature. Under a certain load, it will simultaneously generate bending moment and torque. The bending moment and torque generated at this time correspond to the same load level. We analyze the effect of bending moment under the bending system and the effect of torque under the torsion system separately, and then superimpose them. Vertical uniformly distributed load. p Bending moment caused by action M p and torque T p The formula is:

[0105] (28)

[0106] (29)

[0107] in, R The radius of the curved beam axis curve. 0 is the central angle of the curved beam. x The distance from the endpoint of the curved beam x The central angle of the position.

[0108] As a specific implementation of the method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder provided by this invention, please refer to... Figure 1 to Figure 10 In a corrugated steel web curved box girder, under the action of bending and torsion coupling, the bottom plate 3 and the top plate 1 are simultaneously subjected to compression and shear. Under the ultimate failure state, the bottom plate 3 / top plate 1 breaks.

[0109] As a specific implementation of the method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder provided by this invention, please refer to... Figure 1 to Figure 10 According to step S5, the stress increment of external prestressed steel bars on the inner and outer sides of the corrugated steel web curved box girder is calculated, and the prestress increment at any point along the cross section of the corrugated steel web curved box girder is calculated.

[0110] Take a tiny unit at the shear flow center of the top plate 1.A ,neglect y Lateral deformation () e y ), fiber extrusion and shear deformation in the z-direction ( e z , c yz , c xz In the bending system, the longitudinal compressive strain of the top plate 1 is: e c The strain at the corresponding shear flow center is Shear strain of concrete in the xy plane in an anti-torsion system c c ,by c / 2 is the ordinate. e Using the x-axis as the abscissa, draw the strain molar circle, based on the unit cell. A The strain state indicates that the strain Mohr's circle must intersect the vertical axis at a certain point. Based on the strain Mohr's circle, the maximum compressive strain at the shear flow center of the top plate of the corrugated steel web curved box girder is obtained. e maxd The maximum compressive strain converted to the top surface of the top plate 1 is: e max ,when e max When the value is greater than 0.0033, the beam fails.

[0111] (30)

[0112] (31)

[0113] If the cross-sectional torque is known, the external load can be calculated using equations 28 and 29. The cross-sectional torque is then obtained from the torsion resistance system iterative program, the load is calculated, the bending moment is calculated, and the analysis continues in the bending resistance system. The calculation steps are as follows:

[0114] N1. Divide the corrugated steel web curved box girder along its length into... n Select a unit. i Choose a tiny one e d The torsion resistance system iterative program is then entered to calculate the torque at this cross section. T The external load is calculated in reverse according to equations 28 and 29. P ,Depend on P Calculate bending moment M Enter the bending resistance system iteration program;

[0115] N2, The horizontal displacement at the prestressed tendon turning block is obtained from the anti-torsion system. (Subscript 1 represents the position of the steering block, 2 represents the mid-span position) and vertical displacement Vertical displacement is obtained from the bending resistance system. The two are then superimposed to obtain the total horizontal displacement. and vertical displacement ;

[0116] N3. Calculate the elongation and strain increment of the two external prestressing tendons A and B. Based on the constitutive relation, the prestress increment Δ on the outer and inner sides of the curve can be obtained. s pA Δ s pB Furthermore, the coordinates of any point along the cross-section of the corrugated steel web curved box girder can also be obtained. y Prestress increment Δ at the location s py ;

[0117] N4, obtained from the bending resistance system program n The concrete compressive strain at the compression edge of each element section is output. i place e cdi , e ci The shear strain under torque at this location is obtained from the anti-torsion system program. c c The maximum compressive strain of the top plate 1 of the corrugated steel web curved box girder was calculated. e max ,like e max <0.0033, give e d One increment, repeat the above calculation until... e max When the value is greater than 0.0033, the cell value is... i Destruction, obtaining the ultimate load. P ui ;

[0118] N5. Continue selecting units i +1, repeat the above steps, and compare the units. i ultimate load P ui Choose the minimum value (worst-case scenario), its unit i The location is the failure section, and the output data includes the load, prestress increment inside and outside the curve, deflection inside and outside the curve, bending moment, curvature, torque, and torsional rate under this condition.

[0119] Based on the same inventive concept, this application also provides a terminal. A specific implementation of a terminal is described below, including a memory, a processor, and a computer program stored in the memory and executable on the processor. The characteristic of the terminal is that when the processor executes the computer program, it implements the steps of the method described in any of the above descriptions.

[0120] Specifically, in this embodiment, the terminal can be a computing device such as a desktop computer, laptop, handheld computer, or cloud server. The terminal may include, but is not limited to, a processor and memory, and may include more components than those described above, or combine certain components, or different components. For example, the terminal may also include input / output devices, network access devices, buses, etc.

[0121] The processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, such as discrete gate or transistor logic devices. A general-purpose processor can be a microprocessor or any conventional processor. The memory can be the terminal's internal storage unit, such as the terminal's hard drive or RAM. The memory can also be the terminal's external storage device, such as a plug-in hard drive, smart memory card, or flash memory card.

[0122] Based on the same inventive concept, this application also provides a computer-readable storage medium. A specific implementation of a computer-readable storage medium is now described. The computer-readable storage medium stores a computer program, characterized in that, when the computer program is executed by a processor, it implements the steps of the method as described in any of the above.

[0123] Specifically, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. If the integrated module or unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium.

[0124] Based on this understanding, all or part of the processes in the above-described embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the above-described identification method.

[0125] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder, characterized in that, The following steps are included: S1. The stress state of the corrugated steel web curved box girder is separated into a bending resistance system and a torsion resistance system. S2. Perform a full-process iterative analysis of the bending resistance system. In the case of the bending resistance system, the corrugated steel web curved box girder is equivalent to a straight beam to eliminate the torque caused by the curvature of the beam axis and analyze the effect of the equivalent straight beam on resisting the bending moment caused by the load. S3. Perform a full-process iterative analysis of the anti-torsion system. In the case of the anti-torsion system, the corrugated steel web curved box girder is equivalent to a straight beam. The torque generated by the curvature of the beam axis is analyzed. S4. Establish the connection between the bending resistance system and the torsion resistance system of the corrugated steel web curved box girder. The beam axis curvature of the corrugated steel web curved box girder is constant. Under a certain load, bending moment and torque will be generated simultaneously. The bending moment and torque generated at this time correspond to the same load level. Analyze the effect of bending moment under the bending resistance system and the effect of torque under the torsion resistance system respectively, and then superimpose them. S5. Combine the iterative analysis of the entire bending process of the bending-resistant subsystem with the iterative analysis of the entire torsional process of the torsional subsystem. Enter the torsional subsystem iterative program to calculate the section torque, back-calculate the load, calculate the bending moment, and continue the analysis in the bending subsystem to obtain the iterative analysis of the entire bending and torsional process of the corrugated steel web curved box girder. Divide the corrugated steel web curved box girder along the length direction into... n Select a unit. i Compare each unit i ultimate load P ui Select the minimum value, its unit i The location is the failure section, and the output data includes the load, prestress increment inside and outside the curve, deflection inside and outside the curve, bending moment, curvature, torque, and torsional rate under this condition.

2. The method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder as described in claim 1, characterized in that, The equivalent straight beam experiences four stages of stress under bending moment: the first stage of bending, the second stage of bending, the third stage of bending, and the fourth stage of bending. In the first stage of bending, the concrete does not crack. In the second stage of bending, the bottom slab cracks, and the tensile strain of the longitudinal and transverse reinforcement of the bottom slab is less than the specified value, while the compressive strain of the top slab is less than or equal to the specified value. In the third stage of bending, the tensile strain of the longitudinal and transverse reinforcement is greater than or equal to the specified value, the tensile strain of the internal prestressed reinforcement is less than or equal to the specified value, and the compressive strain of the top slab is less than or equal to the specified value. In the fourth stage of bending, the tensile strain of the longitudinal and transverse reinforcement of the bottom slab is greater than or equal to the specified value, the tensile strain of the internal prestressed reinforcement is greater than or equal to the specified value, and the compressive strain of the top slab is greater than or equal to the specified value, until the compressive strain of the longitudinal and transverse reinforcement of the bottom slab is greater than or equal to the specified value, and the concrete top slab breaks.

3. The method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder as described in claim 1, characterized in that, The total torque of an equivalent straight beam under torque includes the torque borne by the bottom and top plates, the torque borne by the corrugated steel web, and the torque borne by the external prestressing tendons.

4. The method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder as described in claim 1, characterized in that, In a corrugated steel web curved box girder, under the action of bending and torsion coupling, the bottom plate and the top plate are simultaneously subjected to compression and shear. Under the ultimate failure state, the bottom plate / top plate breaks.

5. The method for analyzing the entire bending and torsion process of a corrugated steel web curved box girder as described in claim 1, characterized in that, According to step S5, the stress increment of external prestressed steel bars on the inner and outer sides of the corrugated steel web curved box girder is calculated, and the prestress increment at any point along the cross section of the corrugated steel web curved box girder is calculated.

6. A terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When a processor executes a computer program, it implements the steps of the method described in any one of claims 1-5 above.

7. A computer-readable storage medium storing a computer program, characterized in that, When a computer program is executed by a processor, it implements the steps of the method described in any one of claims 1-5 above.

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