Corrugated steel web box girder ultimate state analysis method, terminal and storage medium

Abstract

The application provides a corrugated steel web box girder ultimate state analysis method, a terminal and a storage medium, and belongs to the technical field of electric digital data processing. The corrugated steel web box girder ultimate state analysis method provided by the application comprises the following steps: introducing three failure modes of the corrugated steel web box girder in the ultimate state, which are failure mode I (bending failure), failure mode II (torsional failure) and failure mode III (bending-torsional failure); respectively calculating the bending moment formula and the torsional moment formula under the three failure modes; unifying the bending moment formula and the torsional moment formula under the three failure modes to obtain a bending-torsional failure envelope; and determining the type of the failure mode generated under different conditions according to the obtained bending-torsional failure envelope. The corrugated steel web box girder ultimate state analysis method provided by the application is helpful to analyzing and obtaining the failure form of the corrugated steel web box girder under different conditions by drawing the bending-torsional failure envelope of the three failure modes.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electric digital data processing, and particularly relates to a corrugated steel web box girder limit state analysis method, a terminal and a storage medium. BACKGROUND

[0002] The traditional concrete box girder is composed of a top plate, a bottom plate, a web plate, a transverse plate, a support beam and the like, and the top plate, the bottom plate, the web plate, the transverse plate and the support beam are usually of a reinforced concrete structure. The traditional concrete box girder gradually exposes some problems in the use process. With the increase of the span, the self weight of the box girder rapidly increases, and therefore a stronger lower structure is needed to support, and the material consumption of the corresponding lower structure increases, and the overall cost rises. In addition, the concrete web plate is prone to cracks under the influence of the environment, affecting the durability in use. The corrugated steel web plate composite box girder uses a corrugated steel plate as the web plate of the box girder to replace the traditional concrete web plate, and the top plate and the bottom plate still adopt a reinforced concrete structure and are provided with longitudinal reinforcement, transverse reinforcement, prestressed reinforcement and the like. The corrugated steel plate has high shear strength and stability, and the weight is relatively light, which can effectively reduce the self weight of the box girder, reduce the material consumption of the lower structure and reduce the production cost. In the actual use process, compared with the traditional concrete box girder, the torsional stiffness and the distortion stiffness of the cross section of the corrugated steel web plate composite box girder are reduced, the buckling failure of the corrugated steel web plate is relatively sudden, and with the increase of the use time, the performance degradation occurs, affecting the service life. In order to improve the safety of the corrugated steel web plate composite box girder, it is necessary to analyze the failure mode of the corrugated steel web plate composite box girder, but the existing traditional concrete box girder cannot be applied to the failure mode analysis of the corrugated steel web plate composite box girder. SUMMARY

[0003] The application aims to provide a corrugated steel web box girder limit state analysis method, a terminal and a storage medium, and aims to solve the problem of failure mode analysis of the corrugated steel web plate composite box girder.

[0004] To achieve the above-mentioned purpose, the technical scheme adopted by the application is as follows: a corrugated steel web box girder limit state analysis method is provided, comprising the following steps:

[0005] S1, three failure modes under the limit state of the corrugated steel web box girder are introduced, which are failure mode I (bending failure), failure mode II (torsional failure) and failure mode III (bending-torsional failure);

[0006] S2, bending moment formulas and torsional moment formulas under the three failure modes are calculated respectively;

[0007] S3, the bending moment formulas and the torsional moment formulas under the three failure modes are unified to obtain a bending-torsional failure envelope diagram;

[0008] S4. According to the obtained bending-torsion failure envelope, the type of the failure mode generated under different conditions is determined.

[0009] In a possible implementation, in the calculation process, a cross section formed after the failure of the corrugated steel web box girder is defined as a torsional failure surface, a compression resultant force action point is selected on the torsional failure surface, the stress of the compression resultant force action point is analyzed, and a bending moment formula and a torsional moment formula at the compression resultant force action point are calculated.

[0010] In a possible implementation, under the failure mode I (bending failure), when the stress of the bottom plate steel bar reaches the tensile yield, the crack develops into the failure mode I (bending failure) rapidly, and the compression resultant force action point is on the top plate.

[0011] In a possible implementation, under the failure mode II (torsional failure), the tensile stress generated by the torsional moment offsets the compressive stress generated by the positive bending moment on the top plate, the longitudinal steel bar of the top plate reaches the yield strength earlier than the longitudinal steel bar of the bottom plate, the crack is formed on the top plate and expands to the corrugated steel webs on both sides, due to the yield of the longitudinal steel bar of the top plate, the oblique compression surface generates a plastic hinge rotating downward, the bottom plate concrete is compressed, and the failure mode II (torsional failure) is developed, and the compression resultant force action point is on the bottom plate.

[0012] In a possible implementation, under the failure mode III (bending-torsional failure), the main tensile stress direction generated by the torsional moment and the vertical shear force is consistent, the cracks are formed on the side walls of the top plate and the bottom plate and expand to the plate surfaces of the top plate and the bottom plate, the main tensile stress directions on the top plate and the bottom plate are opposite, the cracks on the side walls of the top plate and the bottom plate are inhibited, one of the side walls of the top plate and the bottom plate is in tension and the other is in compression, the failure mode III (bending-torsional failure) is developed, and the compression resultant force action point is on the corrugated steel web.

[0013] In a possible implementation, the stress of the compression resultant force action point is analyzed, a local coordinate system is established at the compression resultant force action point, and the forces in the x axial direction, y axial direction, and z axial direction are analyzed under different failure modes. x The force in the axial direction includes the forces generated by the top plate, the bottom plate, the longitudinal steel bar, and the prestressed tendon. y The force in the axial direction includes the force generated by the transverse steel bar. z The force in the axial direction includes the vertical force of the corrugated steel web on the boundary of the torsional failure surface.

[0014] In a possible implementation, the bending-torsional failure envelope takes the ratio of the bending moment of the compression resultant force action point to the limit bending moment under pure bending as the x axial direction, and takes the ratio of the torsional moment of the compression resultant force action point to the limit torsional moment under pure torsion as the yThe shaft is used to draw the relationship formula of the bending moment and the torque in three damage modes into the same bending-torsion damage envelope diagram, and the damage curves in the three damage modes are obtained.

[0015] In a possible implementation manner, in the method, y In the axial direction, the damage mode represented by the lowermost damage curve occurs.

[0016] To achieve the above object, the technical scheme adopted by the present application is to provide a terminal comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the steps of any one of the above methods when executing the computer program.

[0017] To achieve the above object, the technical scheme adopted by the present application is to provide a computer readable storage medium, which stores a computer program, characterized in that the computer program is executed by a processor to implement the steps of any one of the above methods.

[0018] The wave-shaped steel web box girder limit state analysis method provided by the present application has the following beneficial effects:

[0019] Compared with the prior art, the parameters of the wave-shaped steel web box girder, such as the size and position of the top plate, the bottom plate, the web plate, the transverse plate, the support beam, the longitudinal steel bar, the transverse steel bar and the prestressed steel bar, are determined, a virtual model of the wave-shaped steel web box girder is established according to the parameters of the wave-shaped steel web box girder, the limit state of the wave-shaped steel web box girder is analyzed, three damage modes in the limit state of the wave-shaped steel web box girder are introduced, i.e., damage mode I (bending damage), damage mode II (torsion damage) and damage mode III (bending-torsion damage), the stress of the limit state of the wave-shaped steel web box girder in different damage modes is analyzed, the bending moment formula and the torsion formula of the compression resultant force action point on the wave-shaped steel web box girder in different damage modes are obtained, the bending moment formula and the torsion formula in the same damage mode are unified, the relationship formula between the bending moment and the torsion is obtained, the analytical curves are drawn through the relationship formula, the analytical curves related to the bending moment and the torsion in the three damage modes are drawn in the same graph, i.e., a bending-torsion damage envelope diagram is obtained, the type of the damage mode generated by the virtual model of the wave-shaped steel web box girder is determined according to the obtained bending-torsion damage envelope diagram, the damage mode analysis of the wave-shaped steel web box girder is performed through virtual analysis and calculation, the parameters of the wave-shaped steel web box girder are adjusted according to the analysis result, and the safety of the wave-shaped steel web box girder in the construction and use process is greatly improved, and the analysis cost is reduced. BRIEF DESCRIPTION OF DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows. Obviously, the drawings in the following description only constitute some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort.

[0021] Figure 1 A three-dimensional structural schematic diagram of a failure mode I (bending failure) of the limit state analysis method of the corrugated steel web box girder provided by the embodiments of the present application;

[0022] Figure 2 A plan view structural schematic diagram of the failure mode I (bending failure) of the limit state analysis method of the corrugated steel web box girder provided by the embodiments of the present application;

[0023] Figure 3 A side view structural schematic diagram of the failure mode I (bending failure) of the limit state analysis method of the corrugated steel web box girder provided by the embodiments of the present application;

[0024] Figure 4 A three-dimensional structural schematic diagram of a failure mode II (torsional failure) of the limit state analysis method of the corrugated steel web box girder provided by the embodiments of the present application;

[0025] Figure 5 A plan view structural schematic diagram of the failure mode II (torsional failure) of the limit state analysis method of the corrugated steel web box girder provided by the embodiments of the present application;

[0026] Figure 6 A side view structural schematic diagram of the failure mode II (torsional failure) of the limit state analysis method of the corrugated steel web box girder provided by the embodiments of the present application;

[0027] Figure 7 A three-dimensional structural schematic diagram of a failure mode III (bending-torsional failure) of the limit state analysis method of the corrugated steel web box girder provided by the embodiments of the present application;

[0028] Figure 8 A plan view structural schematic diagram of the failure mode III (bending-torsional failure) of the limit state analysis method of the corrugated steel web box girder provided by the embodiments of the present application;

[0029] Figure 9 A side view structural schematic diagram of the failure mode III (bending-torsional failure) of the limit state analysis method of the corrugated steel web box girder provided by the embodiments of the present application;

[0030] Figure 10 A bending-torsional failure envelope of the limit state analysis method of the corrugated steel web box girder provided by the embodiments of the present application Figure 1 ;

[0031] Figure 11 The bending-torsion failure envelope of the corrugated steel web box girder limit state analysis method provided by the embodiment of the present application Figure 2 ;

[0032] Figure 12 The bending-torsion failure envelope of the corrugated steel web box girder limit state analysis method provided by the embodiment of the present application Figure 3 .

[0033] In the figure: 1, top plate; 2, bottom plate; 3, corrugated steel web; 4, torsional failure surface; 5, longitudinal steel bars; 6, transverse steel bars; 7, prestressed steel bars. DETAILED DESCRIPTION

[0034] In order to make the technical problems to be solved by the present application, technical solutions and beneficial effects more clearly understood, the present application will be further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0035] Please refer to Figures 1 to 12 , a specific embodiment of a corrugated steel web box girder limit state analysis method provided by the present application will be described, including the following steps:

[0036] S1, introduce three failure modes under the limit state of the corrugated steel web box girder, which are failure mode I (bending failure), failure mode II (torsional failure) and failure mode III (bending-torsional failure);

[0037] S2, respectively calculate the bending moment formula and the torsional moment formula under the three failure modes;

[0038] S3, unify the bending moment formula and the torsional moment formula under the three failure modes to obtain a bending-torsional failure envelope;

[0039] S4, according to the obtained bending-torsional failure envelope, determine the type of failure mode produced under different conditions.

[0040] The application provides a wave-shaped steel web box girder ultimate state analysis method, which determines parameters of the wave-shaped steel web box girder, such as sizes and positions of a top plate 1, a bottom plate 2, a web plate and a transverse plate, a support beam, longitudinal steel bars 5, transverse steel bars 6 and prestressed steel bars 7, establishes a virtual model of the wave-shaped steel web box girder according to the parameters of the wave-shaped steel web box girder, analyzes the wave-shaped steel web box girder ultimate state, introduces three damage modes of the wave-shaped steel web box girder under the ultimate state according to a traditional concrete box girder, the three damage modes are damage mode I (bending damage), damage mode II (torsion damage) and damage mode III (bending-torsion damage), analyzes stress of the wave-shaped steel web box girder under different damage modes, obtains bending moment formulas and torsion formulas of a compression resultant force action point on the wave-shaped steel web box girder under different damage modes, unifies the bending moment formulas and the torsion formulas under the same damage mode, obtains a relationship between the bending moment and the torsion, draws an analytic curve through the relationship, draws the analytic curve related to the bending moment and the torsion under the three damage modes in the same graph, that is, obtains a bending-torsion damage envelope, determines the type of the damage mode of the virtual model of the wave-shaped steel web box girder according to the obtained bending-torsion damage envelope, analyzes the damage mode of the wave-shaped steel web box girder through virtual analysis calculation, adjusts the parameters of the wave-shaped steel web box girder according to the analysis result, greatly improves safety of the wave-shaped steel web box girder in the construction and use process, and reduces analysis cost.

[0041] Specifically, refer to Figures 1 to 12For the traditional concrete box girder, the limit state calculation method of the "oblique bending failure theory" is adopted, according to the different torsional bending ratios, there are three classical bending-torsional failure modes, respectively, bending failure, torsional failure and bending-torsional failure, under the bending failure, the compression zone under the action of the bending moment and the torsional moment occurs in the bottom plate 2 of the concrete box girder, under the torsional failure, the compression zone under the action of the bending moment and the torsional moment occurs in the top plate 1 of the concrete box girder, under the bending-torsional failure, the compression zone under the action of the bending moment and the torsional moment occurs in the side web of the concrete box girder, for the limit state analysis of the three bending-torsional failure modes of the concrete box girder, there are related analysis formulas, the corrugated steel web box girder replaces the web of the traditional concrete box girder with the corrugated steel plate, when the limit state analysis is carried out, the three bending-torsional failure modes of the concrete box girder are introduced into the limit state analysis of the corrugated steel web box girder, respectively, failure mode I (bending failure), failure mode II (torsional failure) and failure mode III (bending-torsional failure), the limit state of the corrugated steel web box girder under the three failure modes is analyzed respectively, the relationship between the bending moment and the torsional moment under the three failure modes is obtained, the relationship between the bending moment and the torsional moment is converted into an analytical curve, which is drawn in the plane coordinate system, the analytical curves related to the bending moment and the torsional moment of the same corrugated steel web box girder under the three failure modes are drawn in the same plane coordinate system, that is, the bending-torsional failure envelope is obtained, according to the obtained bending-torsional failure envelope, the type of the failure mode generated by the virtual model of the corrugated steel web box girder is determined, the failure mode analysis of the corrugated steel web box girder is carried out through virtual analysis calculation, and the parameters of the corrugated steel web box girder are adjusted according to the analysis result, which greatly improves the safety of the corrugated steel web box girder in the construction and use process, and reduces the analysis cost.

[0042] As a specific embodiment of the corrugated steel web box girder limit state analysis method provided by the present application, please refer to Figures 1 to 9 In the calculation process, the cross section formed after the failure of the corrugated steel web box girder is defined as the torsional failure surface 4, and the compression force action point is selected on the torsional failure surface 4, and the stress of the compression force action point is analyzed to obtain the bending moment formula and the torsional moment formula at the compression force action point.

[0043] Specifically, please refer to Figures 1 to 9 In the stress analysis process, the cross section formed after the failure of the corrugated steel web box girder is defined as the torsional failure surface 4, the torsional failure surface 4 is a virtual surface, it is assumed that the failure of the corrugated steel web box girder occurs at the torsional failure surface 4, the compression force action point is selected on the torsional failure surface 4, and the stress of the compression force action point in each direction is analyzed to obtain the bending moment formula and the torsional moment formula at the compression force action point, and the bending moment formula and the torsional moment formula are simplified and related to obtain the relationship between the bending moment and the torsional moment at the compression force action point.

[0044] As a specific embodiment of the wave-shaped steel web box girder limit state analysis method provided by the present application, please refer to Figures 1 to 9 , the force of the compression force action point is analyzed, a local coordinate system is established at the compression force action point, and the forces in different failure modes are analyzed x , the forces in the axial direction, y , the forces in the axial direction, and z , the forces in the axial direction, x , the forces in the axial direction include the forces generated by the top plate 1, the bottom plate 2, the longitudinal steel bars 5, and the prestressed steel bars 7, y , the forces in the axial direction include the forces generated by the transverse steel bars 6, z , the forces in the axial direction include the vertical forces of the wave-shaped steel webs 3 on the boundary of the torsional failure surface 4.

[0045] Specifically, please refer to Figures 1 to 9 , in the analysis of the compression force action point, a three-dimensional local coordinate system is established at the compression force action point, and the analysis of the forces in the axial direction, x , the forces in the axial direction, y , the forces in the axial direction, and z , the forces in the axial direction are carried out simultaneously in the analysis process, and the forces of the top plate 1, the bottom plate 2, the longitudinal steel bars 5, the prestressed steel bars 7, the transverse steel bars 6, and the wave-shaped steel webs 3 acting on the forces are analyzed.

[0046] As a specific embodiment of the wave-shaped steel web box girder limit state analysis method provided by the present application, please refer to Figures 1 to 3 , in the case of failure mode I (bending failure), when the torsion is small, cracks first appear in the bending tensile bottom plate 2, develop to both sides of the bottom plate 2, and spiral virtual cracks appear on both sides of the wave-shaped steel webs 3, when the bending moment is large, the top surface is under compression, no cracks appear, and a spiral crack appears between the top of the oblique crack on the side of the bottom plate 2 and the bottom of the oblique crack on the side of the top plate 1. A virtual boundary is connected along the direction of the spiral crack, the spiral crack of the bottom plate 2 and the extension of the virtual boundary on the two wave-shaped steel webs 3 form a torsional failure surface 4, when the steel stress of the bottom plate 2 reaches the tensile yield, the cracks develop rapidly and become failure mode I (bending failure), the compression failure surface appears on the top surface, and the compression force action point is on the top plate 1.

[0047] In the limit state, the compression force action point of the top plate 1 is located on the torsional failure surface 4, the force of the compression force action point is analyzed, and a local three-dimensional coordinate system is established at the compression force action point.

[0048] The compression force action point is analyzed along xThe axial force includes the force of longitudinal reinforcement 5 in the top slab 1, the force of longitudinal reinforcement 5 in the bottom slab 2, the force of prestressed reinforcement 7, and the force of the top slab 1 (concrete). The force of the bottom slab 2 is not considered because it is not in tension after cracking. The axial force at the compression point is the sum of the forces of the longitudinal reinforcement 5 in the top slab 1 and the bottom slab 2. y The axial force is the sum of the transverse forces of the transverse reinforcement 6 in the top slab 1 and the bottom slab 2. z The axial force is the sum of the vertical forces of the corrugated steel web 3 on the virtual boundary of the torsional failure surface 4.

[0049] The compression point of the top slab 1 is the point of action of the compression force. y The ultimate bending moment is obtained by calculating the bending moment about the axis of the compression point. M u ,

[0050] (1),

[0051] In the formula: h z H is the total height of the corrugated steel web box girder; h w h is the height of the corrugated steel web 3; h p h is the height from the prestressed reinforcement 7 of the bottom slab 2 to the upper end surface of the top slab 1; y′ s L is the distance from the position of the resultant force of the reinforcement in the top slab 1 to the compression edge of the section, y s L is the distance from the position of the resultant force of the reinforcement in the bottom slab 2 to the tension edge of the section; y c L is the distance from the position of the resultant force of the top slab 1 in the compression zone to the upper edge of the compression of the top slab 1; b L is the farthest distance between the outermost corrugated steel webs 3 on both sides; δ t L is the thickness of the top slab 1, δ b L is the thickness of the bottom slab 2, δ w L is the thickness of the corrugated steel web 3; the crack angles of the top slab 1, the bottom slab 2, the left corrugated steel web 3 face, and the right corrugated steel web 3 face are α t , α b , α l , α r ; A′ s L is the area of the reinforcement in the top slab 1 (including the upper flange of the steel beam), A sArea of the bottom plate 2 reinforcement (including the lower flange of the steel beam), A p Area of the prestressed reinforcement 7; f y Yield strength of the longitudinal reinforcement 5; σ pu Ultimate stress of the prestressed reinforcement 7; f w Yield strength of the corrugated steel web 3.

[0052] The point of action of the compressive resultant force on the top plate 1 is opposite x The ultimate torque is obtained by calculating the torque about the axis of the T u ,

[0053] (2),

[0054] Where: A sv1 Area of the single-leg transverse reinforcement 6 of the bottom plate 2; f yv Yield strength of the transverse reinforcement 6; S Spacing of the transverse reinforcement 6 along the axis of the corrugated steel web box girder.

[0055] Assuming that the crack angles on each face of the corrugated steel web box girder are the same, i.e. α = α l = α r = α b ， Let A cor0 = bh w , A corⅠ = b(h z - y c - δ b / 2) , u cor0 = 2(h z + b) Substituting formulas 1 and 2, we get

[0056] (3),

[0057] (4),

[0058] According to formula 4, we get

[0059] (5),

[0060] Substitute equation 5 into equation 3, we get

[0061] (6),

[0062] In the formula, ζ Ⅰ The ratio of the axial force (longitudinal reinforcement 5 and prestressed reinforcement 7) and the effect of the corrugated steel web 3 is defined as the axial force effect ratio of the corrugated steel web 3,

[0063] (7),

[0064] In equation 6, it is assumed that in the limit case of only pure bending force, the torque T u =0, i.e. only bending moment effect, the limit bending moment capacity in the direction of pure bending is defined as z The limit bending moment capacity in the direction of pure bending is obtained as

[0065] (8),

[0066] In equation 6, it is assumed that in the limit case of only pure torsion force, the bending moment M u =0, i.e. only torsion effect, the limit torsion moment capacity in the direction of pure torsion is defined as x The limit torsion moment capacity in the direction of pure torsion is obtained as

[0067] (9),

[0068] Substitute equation 8 and equation 9 into equation 6, we get

[0069] (10).

[0070] As a specific embodiment of the corrugated steel web box girder limit state analysis method provided by the present application, please refer to Figures 4 to 6 In the case of failure mode II (torsional failure), when the torsion-bending ratio is large, the bending moment is small, and the longitudinal reinforcement 5 of the top plate 1 is significantly less than that of the bottom plate 2, the tensile stress generated by the torsion moment offsets the compressive stress generated by the positive bending moment in the top plate 1, the longitudinal reinforcement 5 of the top plate 1 reaches the yield strength earlier than the longitudinal reinforcement 5 of the bottom plate 2, cracks are formed in the top plate 1 and expand to the corrugated steel webs 3 on both sides, due to the yield of the longitudinal reinforcement 5 of the top plate 1, a plastic hinge is generated in the inclined compression surface, the bottom plate 2 concrete is compressed, and the failure mode II (torsional failure) is developed, and the compression force point is selected on the bottom plate 2.

[0071] ​​Under the limit state, the compression force action point of the bottom plate 2 is located on the twist failure surface 4, and the force analysis is performed on the compression force action point, and a local three-dimensional coordinate system is established at the compression force action point.

[0072] The force in the axial direction at the compression force action point includes the force of the longitudinal steel bars 5 in the top plate 1, the force of the longitudinal steel bars 5 in the bottom plate 2, the force of the prestressed steel bars 7, and the force of the bottom plate 2 (concrete). x The force in the axial direction at the compression force action point includes the force of the longitudinal steel bars 5 in the top plate 1, the force of the longitudinal steel bars 5 in the bottom plate 2, the force of the prestressed steel bars 7, and the force of the bottom plate 2 (concrete). y The force in the axial direction at the compression force action point includes the force of the longitudinal steel bars 5 in the top plate 1, the force of the longitudinal steel bars 5 in the bottom plate 2, the force of the prestressed steel bars 7, and the force of the bottom plate 2 (concrete). z The force in the axial direction at the compression force action point includes the force of the longitudinal steel bars 5 in the top plate 1, the force of the longitudinal steel bars 5 in the bottom plate 2, the force of the prestressed steel bars 7, and the force of the bottom plate 2 (concrete).

[0073] The bending moment of the compression force action point of the bottom plate 2 is calculated with respect to the y axis to obtain the limit bending moment M u ,

[0074] (11),

[0075] The torsion of the compression force action point of the bottom plate 2 is calculated with respect to the x axis to obtain the limit torsion T u ,

[0076] (12),

[0077] It is assumed that the crack angles on each surface of the corrugated steel web box girder are the same, and α = α l = α r = α t , A′ corⅠ = b(h z - y c - δ t / 2) , and by substituting formula 11 and formula 12, we obtain

[0078] (13),

[0079] (14),

[0080] Referring to the simplified calculation process of the failure mode I (bending failure), ζ ⅠIThe ratio of the axial force of the longitudinal reinforcement 5 and the prestressed reinforcement 7 to the action effect of the corrugated steel web 3 in the mode Ⅱ (torsional failure) is defined as

[0081] (15),

[0082] The limit bending moment in the direction of pure bending is defined as T u =0, i.e. only the bending moment acts, and is defined as z The limit bending moment in the direction of pure bending is defined as

[0083] (16),

[0084] The limit torsional moment in the direction of pure torsion is defined as M u =0, i.e. only the torsional moment acts, and is defined as x The limit torsional moment in the direction of pure torsion is defined as

[0085] (17),

[0086] According to the formulas 11 to 17, the same simplified derivation process as the simplified calculation process of the failure mode Ⅰ (bending failure) is used to obtain

[0087] (18).

[0088] As a specific embodiment of the corrugated steel web box girder limit state analysis method provided by the present application, please refer to Figures 7 to 9 In the case of the failure mode Ⅲ (bending-torsional failure), when the torsional-bending ratio is large and the thickness of the corrugated steel web 3 is thin, the cracks are formed in the side walls of the top plate 1 and the bottom plate 2, expand to the plate surfaces of the top plate 1 and the bottom plate 2, the direction of the principal tensile stress on the top plate 1 and the bottom plate 2 is opposite, the cracks in the side walls of the top plate 1 and the bottom plate 2 are suppressed or even compressed, one of the side walls of the top plate 1 and the bottom plate 2 is in tension and the other is in compression, and the failure mode Ⅲ (bending-torsional failure) is developed. The compression force point is selected on the corrugated steel web 3. At this time, the bending capacity around the y axis is easy to meet, but the bending moment around the z axis may exceed its capacity, and bending failure around the z axis occurs, so the bending moment balance around the z axis needs to be considered.

[0089] ​​Under the limit state, the compression force action point of the corrugated steel web 3 is located on the twist failure surface 4, and the force analysis is performed on the compression force action point, and a local three-dimensional coordinate system is established at the compression force action point.

[0090] The force in the x axial direction at the compression force action point includes the force of the longitudinal steel bars 5 in the top plate 1, the force of the longitudinal steel bars 5 in the bottom plate 2, the force of the prestressed steel bars 7, and the force of the top plate 1 (concrete) and the bottom plate 2 (concrete) on the compression side. The force in the y axial direction at the compression force action point is the sum of the transverse forces of the top plate 1 transverse steel bars 6 and the bottom plate 2 transverse steel bars 6. The force in the z axial direction at the compression force action point is the sum of the vertical forces of the corrugated steel web 3 on the virtual boundary of the failure surface.

[0091] The bending moment of the compression force action point of the corrugated steel web 3 is calculated with respect to the z axial direction to obtain the limit bending moment M zu (not considering the axial stiffness of the corrugated steel web 3), and the limit bending moment is obtained as

[0092] (19),

[0093] In the formula: A is the area of the single limb transverse steel bar 6 of the top plate 1.

[0094] The torsion moment of the compression force action point of the corrugated steel web 3 is calculated with respect to the x axial direction to obtain the limit torsion moment T u ,

[0095] (20),

[0096] It is assumed that the crack angles on each surface of the corrugated steel web box girder are the same ，α = α r = α b = α t , A corⅡ = b ( h z - δ b ), A′ corⅡ = b ( h z - δ t ), and by substituting formula 19 and formula 20, we obtain

[0097] (21),

[0098] (22),

[0099] Referring to the simplified calculation process of the failure mode I (bending failure), ζ Ⅲ The ratio of the axial force bar (longitudinal reinforcement 5 and prestressed tendon 7) to the wave-shaped steel web 3 under the failure mode III (bending-torsion failure) is defined as

[0100] (23),

[0101] The torsion moment is set to be 0 in the limit case of only pure bending force, i.e. only the bending moment acts, and the limit bending moment bearing capacity under the pure bending in the direction is defined as T u =0, i.e. only the bending moment acts, and the limit bending moment bearing capacity under the pure bending in the direction is defined as z =0, i.e. only the bending moment acts, and the limit bending moment bearing capacity under the pure bending in the direction is defined as

[0102] (24),

[0103] The bending moment is set to be 0 in the limit case of only pure torsion force, i.e. only the torsion moment acts, and the limit torsion moment bearing capacity under the pure torsion in the direction is defined as M u =0, i.e. only the bending moment acts, and the limit bending moment bearing capacity under the pure bending in the direction is defined as x =0, i.e. only the bending moment acts, and the limit bending moment bearing capacity under the pure bending in the direction is defined as

[0104] (25),

[0105] According to the formulas 19 to 25, the same simplified derivation process as the simplified calculation process of the failure mode I (bending failure) is adopted, z When the limit equilibrium formula of the wave-shaped steel web 3 under the pure bending in the direction is

[0106] (26).

[0107] As a specific embodiment of the wave-shaped steel web box girder limit state analysis method provided by the present application, please refer to Figures 1 to 12 The bending-torsion failure envelope is drawn in the same bending-torsion failure envelope by taking the ratio of the bending moment to the limit bending moment under the pure bending in the direction of the compressive resultant force acting point as the x axis, and taking the ratio of the torsion moment to the limit torsion moment under the pure torsion in the direction of the compressive resultant force acting point as the y axis, and the bending moment and the torsion moment under the three failure modes are drawn into the same bending-torsion failure envelope, respectively, to obtain the failure curves under the three failure modes. According to the positions of the three groups of failure curves, the type of failure is judged. In the y axis direction, the failure mode represented by the failure curve located at the lowermost position occurs. ​​

[0108] The formulas 10 for the failure mode I (bending failure), the formulas 18 for the failure mode II (torsional failure), and the formulas 26 for the failure mode III (bending-torsional failure) are unified, and the calculation is derived. The formulas 10, the formulas 18, and the formulas 26 all use M u 、 M u0 、 T u 、 T u0 to represent, wherein M u0 = , the ultimate bending moment capacity under pure bending, T u0 = , the ultimate torsional moment under pure torsion, and r , r is introduced as a constant value, r reflects the ratio of the action effect of the longitudinal reinforcement in the top plate 1 to the total longitudinal reinforcement of the bottom plate 2, is the product of the ratio of the action effect of the longitudinal reinforcement in the top plate to the total longitudinal reinforcement of the section and the ratio of the action effect of the transverse reinforcement and the corrugated steel web,

[0109] (27),

[0110] (28),

[0111] Correspondingly, the formulas 10 for the failure mode I (bending failure) are simplified as

[0112] (29),

[0113] Correspondingly, the formulas 18 for the failure mode II (torsional failure) are simplified as

[0114] (30),

[0115] Correspondingly, the formulas 26 for the failure mode III (bending-torsional failure) are simplified as

[0116] (31).

[0117] A rectangular coordinate system is established, and the failure curves under the three failure modes represented by the formulas 29 to 31 are drawn into the same bending-torsional failure envelope to show T u / T u0 as the longitudinal coordinate, M u / M u0For the abscissa, in the bending-torsion failure envelope, the failure curves of the three failure modes have a positional relationship, the failure curves of the three failure modes have intersection points in the bending-torsion failure envelope, the failure curve represents the limit case of the occurrence of this failure mode, therefore, when the cross section fails, at the same abscissa, the failure mode represented by the failure curve located below will occur first, three failure curves are solved together to obtain the intersection point coordinates, according to the relative position of the three curves, the bending-torsion failure envelope is divided into three cases:

[0118] Case 1, please refer to Figure 10 , , according to the intersection position of the failure curve, failure mode II (torsional failure) does not occur, failure mode III (bending-torsional failure) in T u / T u0 ≤1.0, formula 29 and formula 31 are solved together to obtain the intersection abscissa of the failure curves of failure mode I (bending failure) and failure mode III (bending-torsional failure) , then failure mode III (bending-torsional failure) occurs, failure mode I (bending failure) occurs.

[0119] Case 2, please refer to Figure 11 , , it can be seen that failure mode III (bending-torsional failure) in , formula 30 and formula 31 are solved together to obtain the intersection abscissa of the curves of failure mode II (torsional failure) and failure mode III (bending-torsional failure) ; formula 29 and formula 31 are solved together to obtain the intersection abscissa of the failure curves of failure mode I (bending failure) and failure mode III (bending-torsional failure) , then failure mode II (torsional failure) occurs, failure mode III (bending-torsional failure) occurs, failure mode I (bending failure) occurs.

[0120] Case 3, please refer to Figure 12 , : failure mode III (bending-torsional failure) in , formula 29 and formula 30 are solved together to obtain the intersection abscissa of the failure curves of failure mode I (bending failure) and failure mode II (torsional failure) , then failure mode II (torsional failure) occurs, failure mode I (bending failure) occurs.

[0121] Based on the same inventive concept, the embodiments of the present application also provide a terminal. Now a specific embodiment of a terminal is described, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the method according to any one of the above embodiments when executing the computer program.

[0122] Specifically, in the embodiments, the terminal can be a desktop computer, a notebook computer, a palm computer, a cloud server, and the like. The terminal can include, but is not limited to, a processor and a memory, and can include more components, or combine some components, or different components, for example, the terminal can also include an input / output device, a network access device, a bus, and the like.

[0123] The processor can be a central processing unit, and can also be other general-purpose processors, digital signal processors, application-specific integrated circuits, field programmable gate arrays, or other programmable logic devices discrete gate or transistor logic components, discrete hardware components, and the like. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor. The memory can be an internal storage unit of the terminal, for example, a hard disk or a memory of the terminal. The memory can also be an external storage device of the terminal, for example, a plug-in hard disk, a smart memory card, a flash memory card, and the like.

[0124] Based on the same inventive concept, the embodiments of the present application also provide a computer readable storage medium. Now a specific embodiment of a computer readable storage medium is described, and the computer readable storage medium stores a computer program, and the computer program is executed by a processor to implement the steps of the method according to any one of the above embodiments.

[0125] Specifically, each functional unit in each embodiment of the present application can be integrated in one processing unit, or each unit can exist physically, or two or more units can be integrated in one unit. The integrated unit can be realized in the form of hardware or in the form of a software functional unit. If the integrated module or unit is realized in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer readable storage medium.

[0126] Based on such understanding, the present application implements all or part of the processes in the above-mentioned embodiments, and can also be completed by a computer program instructing related hardware. The computer program can be stored in a computer readable storage medium, and when the computer program is executed by a processor, the steps of the above-mentioned identification method can be implemented.

[0127] The above merely preferred embodiments of the present application are not used to limit the present application, any modification, equivalent replacement and improvement etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for analyzing the limit state of a corrugated steel web box girder, characterized by, It comprises the following steps: S1, introducing three failure modes of corrugated steel web box girder under the limit state, which are failure mode I (bending failure), failure mode II (torsional failure) and failure mode III (bending-torsional failure); S2, calculating the bending moment formula and the torsional moment formula under the three failure modes respectively; S3, unifying the bending moment formula and the torsional moment formula under the same failure mode to obtain the relationship formula between the bending moment and the torsional moment, drawing the analytical curve through the relationship formula, drawing the analytical curve related to the bending moment and the torsional moment under the three failure modes in the same graph to obtain the bending-torsional failure envelope; S4, determining the type of failure mode generated under different conditions according to the obtained bending-torsional failure envelope.

2. A method of analyzing a corrugated steel web box girder in a limit state according to claim 1, characterized in that, In the calculation process, the cross section formed after the failure of the corrugated steel web box girder is defined as a twisted failure surface, and a compression force action point is selected on the twisted failure surface. The stress of the compression force action point is analyzed to calculate the bending moment formula and the torsional moment formula at the compression force action point.

3. A method of analyzing a corrugated steel web box girder according to claim 2, wherein Under the failure mode I (bending failure), the crack develops into the failure mode I (bending failure) when the stress of the bottom plate reinforcement reaches the tensile yield, and the compression force action point is on the top plate.

4. A method of analyzing a corrugated steel web box girder according to claim 2, wherein Under the failure mode II (torsional failure), the tensile stress generated by the torsional moment offsets the compressive stress generated by the positive bending moment on the top plate, the longitudinal reinforcement of the top plate reaches the yield strength earlier than the longitudinal reinforcement of the bottom plate, the crack is formed on the top plate and expands to the corrugated steel webs on both sides. Due to the yield of the longitudinal reinforcement of the top plate, a plastic hinge is generated on the inclined compression surface, the bottom plate concrete is compressed, and the failure mode II (torsional failure) is developed, and the compression force action point is on the bottom plate.

5. A method of analyzing a corrugated steel web box girder according to claim 2, wherein Under the failure mode III (bending-torsional failure), the principal tensile stress direction generated by the torsional moment and the vertical shear force is consistent, the cracks are formed on the side walls of the top plate and the bottom plate and expand to the plate surfaces of the top plate and the bottom plate. The principal tensile stress direction on the top plate and the bottom plate is opposite, the cracks on the side walls of the top plate and the bottom plate are inhibited, one of the side walls of the top plate and the bottom plate is in tension and the other is in compression, and the failure mode III (bending-torsional failure) is developed, and the compression force action point is on the corrugated steel web.

6. A method of analyzing a corrugated steel web box girder according to claim 2, wherein The force of the compression force action point is analyzed, a local coordinate system is established at the compression force action point, and the forces in the axial direction under different failure modes are analyzed x forces in the axial direction, y forces in the axial direction, and z forces in the axial direction, x The axial force includes the forces generated by the top plate, the bottom plate, the longitudinal steel bar and the prestressed tendon, y The axial force includes the force generated by the transverse steel bar, z The axial force includes the vertical force of the corrugated steel web on the boundary of the torsional failure surface.

7. A method of analyzing a box girder with corrugated steel webs according to claim 1, wherein The ratio of the bending moment of the point of action of the compressive resultant force to the ultimate bending moment under pure bending is taken as the bending-torsion failure envelope of the shaft x The ratio of the torsional moment of the point of action of the compressive resultant force to the ultimate torsional moment under pure torsion is taken as the torsional failure envelope of the shaft y The relationship expressions of the bending moment and the torsional moment under the three failure modes are respectively drawn into the same bending-torsion failure envelope of the shaft, and the failure curves under the three failure modes are obtained. According to the positions of the three groups of failure curves, the type of the failure occurring is determined.

8. A method of ultimate limit state analysis of a box girder with corrugated steel webs as defined in claim 7, characterized in that In y In the axial direction, the failure mode represented by the lowermost failure curve occurs.

9. A terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor executes the computer program to implement the steps of the method of any one of claims 1-8. 10.A computer readable storage medium, storing a computer program, the computer readable storage medium comprising instructions which, when executed by a processor, cause the processor to perform the method according to any one of claims 1 to 9. The computer program is executed by the processor to implement the steps of the method of any one of claims 1-8.

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