A method for predicting the flexural strength of a negative moment area of a steel-concrete composite bridge deck

Abstract

The application discloses a kind of steel-concrete composite bridge deck slab negative bending moment area bending strength prediction method, it is related to steel-concrete composite bridge deck slab bending strength prediction technical field. Including: setting basic assumption;Determine material constitutive relation;According to neutral axis position and steel plate yield range, divide 4 kinds of stress conditions;For each kind of working condition, establish section force balance equation and geometric deformation coordination equation, solve neutral axis position;The neutral axis position is substituted into section bending moment balance equation, and the ultimate bending capacity of negative bending moment area is calculated.The application considers the strain hardening characteristics of UHPC to divide 4 kinds of stress conditions, constructs section balance equation, and solves the bearing capacity based on accurate material constitutive and stress mechanism, to fill in the blank of specification calculation, give full play to UHPC material performance, adapt to different UHPC thickness and reinforcement design.

Description

Technical Field

[0001] This invention relates to the field of prediction technology for the bending strength of steel-concrete composite bridge decks, and more specifically to a method for predicting the bending strength of steel-concrete composite bridge decks in the negative bending moment zone. Background Technology

[0002] Steel-concrete composite bridge decks possess excellent mechanical properties and good construction performance, better meeting the design requirements of high toughness and long service life for bridges, and have a wide range of applications. However, steel-concrete composite bridge decks are currently in the initial application stage, especially flat steel plate composite bridge decks. Existing technologies do not specify the arrangement and structural requirements of new connectors such as perforated steel plates (PBLs) and steel stiffeners in flat steel plate composite bridge decks, making actual design reliant on experience and lacking clear safety margins. At the same time, fatigue defects frequently occur in bridge decks under heavy traffic, and there is a lack of fatigue research on flat steel plate composite bridge decks and a lack of reliable assessment methods.

[0003] Currently, some experimental and theoretical studies have been conducted on steel-concrete composite bridge decks both domestically and internationally. However, related research in China is still in its early stages. How to solve the bearing capacity based on accurate material constitutive and stress mechanisms, thereby filling the gaps in standard calculations, fully utilizing the performance of UHPC materials, and adapting to different UHPC thicknesses and reinforcement designs, is a problem that urgently needs to be solved by those skilled in the art.

[0004] Therefore, a method for predicting the flexural strength of steel-concrete composite bridge deck in the negative bending moment zone is proposed to address the difficulties in existing technologies. Summary of the Invention

[0005] In view of this, the present invention provides a method for predicting the flexural strength of steel-concrete composite bridge deck in the negative bending moment zone. By considering the strain hardening characteristics of UHPC, four stress conditions are divided and a section equilibrium equation is constructed. The bearing capacity is solved based on the accurate material constitutive model and stress mechanism, thereby filling the gap in the standard calculation, giving full play to the performance of UHPC material, and adapting to different UHPC thicknesses and reinforcement designs.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for predicting the flexural strength of a steel-concrete composite bridge deck in the negative bending moment zone includes the following steps: S1. Determine the cross-sectional geometry and stress conditions, considering the UHPC layer and the perforated stiffening steel plate, deducting the perforated area from the stress-bearing area; S2. Set basic assumptions, including the plane section assumption, no relative slip at the steel-concrete interface, concrete exiting tensile work after cracking, and UHPC maintaining tensile strain hardening characteristics; S3. Determine the constitutive relations of materials. Linear hardening constitutive models are used for steel plates and steel bars, compression constitutive models are used for concrete, and bilinear constitutive models of tension / compression considering strain hardening are used for UHPC. S4. Based on the position of the neutral axis and the yield range of the steel plate, four types of stress conditions are defined. S5. For each working condition, establish the cross-sectional force balance equation and the geometric deformation compatibility equation, and solve for the position of the neutral axis; S6. Substitute the neutral axis position into the section moment equilibrium equation to calculate the ultimate flexural capacity in the negative moment zone.

[0007] Optionally, the specific details of the linearly strengthened constitutive model for steel plates and reinforcing bars in S3 are as follows: The stress-strain relationship of reinforcing steel is expressed as follows: ; In the formula: This is the elastic modulus of the reinforcing steel, expressed in MPa. This represents the yield strength of the reinforcing steel, expressed in MPa. The yield strain of the steel reinforcement; This represents the ultimate stress of the reinforcing steel, expressed in MPa. This represents the ultimate strain of the reinforcing steel. For the stress of the reinforcing steel; For the strain of the reinforcing steel; The stress-strain relationship of a steel plate is expressed as follows: ; In the formula: This is the elastic modulus of the steel plate, expressed in MPa. This represents the yield strength of the steel plate, expressed in MPa. The yield strain of the steel plate; The ultimate strain of the steel plate; This represents the ultimate stress of the steel plate, expressed in MPa. For steel plate stress; For the strain of the steel plate.

[0008] Optionally, the specific details of using a compression constitutive model for concrete in S3 are as follows: The stress-strain relationship of concrete is expressed as follows: ; In the formula: This refers to the compressive stress in the concrete. This represents the compressive strain of the concrete. This represents the ultimate compressive stress in concrete. To achieve ultimate compressive stress in concrete Compressive strain at time; This represents the ultimate compressive strain of concrete.

[0009] Optionally, the specific details of the tensile / compression bilinear constitutive model considering strain hardening in UHPC in S3 are as follows: The expression for the uniaxial tensile stress-strain relationship of UHPC is as follows: ; In the formula: The initial crack strength of UHPC; The initial crack strain of UHPC; For UHPC strain; For UHPC strain; The strain is the strain when the tensile strength of the UHPC is 0.

[0010] Optionally, S4 classifies the load conditions into four types based on the neutral axis position and the yield range of the steel plate: Condition 1: The neutral shaft is in the stiffener hole, the steel plate above the stiffener partially yields, and the concrete above the section collapses. e 4= e cu , e 3< e so , e 4> e so ; Condition 2: The neutral shaft is in the stiffener hole, the steel plate above and below the stiffener partially yields, and the concrete above the section collapses. e 4= e cu , e 3< e so , e 4> e so , e 2< e so , e 1> e so ; Operating Condition 3: The neutral shaft is in the stiffening rib hole, and the steel plate below the stiffening rib yields. e 2= e so , e 1> e so ; Condition 4: The neutral shaft is in the steel plate below the stiffener, and the steel plate below the stiffener yields. e 2= e so , e 1> e so ; in, e 1 represents the strain at the lower edge of the steel plate below the stiffening rib; e 2 represents the strain at the upper edge of the steel plate below the stiffening rib; e 3 represents the strain at the lower edge of the steel plate above the stiffening rib; e 4 represents the strain at the upper edge of the steel plate above the stiffening rib and the strain at the upper edge of the concrete above the section.

[0011] Optionally, in S5, for each working condition, the section force balance equation and geometric deformation compatibility equation are established, and the specific details for solving the neutral axis position are as follows: Operating Condition 1: (a) Cross-section under force equilibrium: ; (b) Cross-sectional geometric relationships: ; (c) Stress-strain relationship: ; Combining conditions (a), (b), and (c), the neutral axis position x in load case 1 is obtained. Substituting this into the following formula yields the bending moment of the composite bridge deck section. : ; Operating Condition 2: (a) The cross-section is in force equilibrium: ; (b) Cross-sectional geometric relationships: ; (c) Stress-strain relationship: ; Combining conditions (a), (b), and (c), the neutral axis position x in load case 2 is obtained. Substituting this into the following formula yields the bending moment of the composite bridge deck section. : ; Operating Condition 3: (a) The cross-section is in force equilibrium: ; (b) Cross-sectional geometric relationships: ; (c) Stress-strain relationship: ; Combining conditions (a), (b), and (c), the neutral axis position x in working condition 3 is obtained. Substituting this into the following formula yields the bending moment of the composite bridge deck section. : ; Operating Condition 4: (a) Cross-section under force equilibrium ; (b) Cross-sectional geometric relationships ; (c) Stress-strain relationship ; Combining conditions (a), (b), and (c), the neutral axis position x in load case 4 is obtained. Substituting this into the following formula yields the bending moment of the composite bridge deck section. : ; Where x is the distance from the upper surface of the bridge deck to the neutral axis, in mm; co The distance from the top surface to the point where the concrete reaches its axial compressive strength is expressed in mm. s ( x () represents the concrete stress at different cross-sectional heights, in MPa; A s This refers to the total cross-sectional area of ​​the transverse reinforcement at the same height of the cross-section, in mm². 2 ; x uh The thickness of the UHPC layer is in mm.

[0012] Optionally, in S6, the neutral axis position is substituted into the section moment equilibrium equation to calculate the ultimate flexural capacity in the negative moment zone. Based on the obtained section bending moment , , , Substituting into the following calculation formula, the ultimate bearing capacity of the composite bridge deck during the test is obtained: ; In the formula: This represents the ultimate bearing capacity of the composite bridge deck in the negative bending moment zone, expressed in N. Bending moment of section , , , The unit is N·mm; This is the distance from the center of the support to the variable cross-section, in mm.

[0013] As can be seen from the above technical solution, compared with the prior art, the present invention provides a method for predicting the flexural strength of steel-concrete composite bridge deck in the negative bending moment zone, which has the following beneficial effects: This invention divides the stress conditions into four types by considering the strain hardening characteristics of UHPC, constructs the cross-sectional equilibrium equation, and solves the bearing capacity based on the accurate material constitutive model and stress mechanism, thereby filling the gap in the standard calculation, giving full play to the performance of UHPC material, and adapting to different UHPC thicknesses and reinforcement designs. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0015] Figure 1 A flowchart of a method for predicting the flexural strength of a steel-concrete composite bridge deck in the negative bending moment zone provided by the present invention; Figure 2 A schematic diagram of the stress-strain curve of reinforcing steel provided for this invention; Figure 3 A schematic diagram of the stress-strain curve of the steel plate provided by the present invention; Figure 4 A schematic diagram of the concrete stress-strain curve provided by this invention; Figure 5 This is a schematic diagram of the stress-strain curve of UHPC provided by the present invention; Figure 6 This is a schematic diagram illustrating the calculation and classification of the flexural bearing capacity of the negative bending moment zone of the flat steel plate composite bridge deck provided by the present invention. Figure 7 This is a schematic diagram of the calculation for working condition 1 provided by the present invention; Figure 8 This is a schematic diagram of the calculation for working condition 2 provided by the present invention; Figure 9 This is a schematic diagram of the calculation for working condition 3 provided by the present invention; Figure 10 This is a schematic diagram of the calculation for working condition 4 provided by the present invention; Figure 11 A schematic diagram of the layout of the composite bridge deck test device in the negative bending moment zone provided by the present invention; Figure 12 A schematic diagram comparing the theoretical, experimental, and finite element values ​​of the ultimate load provided by this invention. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] See Figure 1 As shown, this invention discloses a method for predicting the flexural strength of a steel-concrete composite bridge deck in the negative bending moment zone, comprising the following steps: S1. Determine the cross-sectional geometry and stress conditions, considering the UHPC layer and the perforated stiffening steel plate, deducting the perforated area from the stress-bearing area; S2. Set basic assumptions, including the plane section assumption, no relative slip at the steel-concrete interface, concrete exiting tensile work after cracking, and UHPC maintaining tensile strain hardening characteristics; S3. Determine the constitutive relations of materials. Linear hardening constitutive models are used for steel plates and steel bars, compression constitutive models are used for concrete, and bilinear constitutive models of tension / compression considering strain hardening are used for UHPC. S4. Based on the position of the neutral axis and the yield range of the steel plate, four types of stress conditions are defined. S5. For each working condition, establish the cross-sectional force balance equation and the geometric deformation compatibility equation, and solve for the position of the neutral axis; S6. Substitute the neutral axis position into the section moment equilibrium equation to calculate the ultimate flexural capacity in the negative moment zone.

[0018] Furthermore, the specific details of the linear strengthening constitutive model used for steel plates and reinforcing bars in S3 are as follows: The stress-strain relationship of reinforcing steel is expressed as follows: ; In the formula: This is the elastic modulus of the reinforcing steel, expressed in MPa. This represents the yield strength of the reinforcing steel, expressed in MPa. The yield strain of the steel reinforcement; This represents the ultimate stress of the reinforcing steel, expressed in MPa. This represents the ultimate strain of the reinforcing steel. For the stress of the reinforcing steel; For the strain of the reinforcing steel; The stress-strain relationship of a steel plate is expressed as follows: ; In the formula: This is the elastic modulus of the steel plate, expressed in MPa. This represents the yield strength of the steel plate, expressed in MPa. The yield strain of the steel plate; The ultimate strain of the steel plate; This represents the ultimate stress of the steel plate, expressed in MPa. For steel plate stress; For the strain of the steel plate.

[0019] Furthermore, the specific details of using a compression constitutive model for concrete in S3 are as follows: The stress-strain relationship of concrete is expressed as follows: ; In the formula: This refers to the compressive stress in the concrete. This represents the compressive strain of the concrete. This represents the ultimate compressive stress in concrete. To achieve ultimate compressive stress in concrete Compressive strain at time; This represents the ultimate compressive strain of concrete.

[0020] Furthermore, the specific details of the tensile / compression bilinear constitutive model considering strain hardening adopted by UHPC in S3 are as follows: The expression for the uniaxial tensile stress-strain relationship of UHPC is as follows: ; In the formula: The initial crack strength of UHPC; The initial crack strain of UHPC; For UHPC strain; For UHPC strain; The strain is the strain when the tensile strength of the UHPC is 0.

[0021] Furthermore, based on the position of the neutral axis and the yield range of the steel plate, S4 is divided into four stress conditions: Condition 1: The neutral shaft is in the stiffener hole, the steel plate above the stiffener partially yields, and the concrete above the section collapses. e 4= e cu , e 3< e so , e 4> e so ; Condition 2: The neutral shaft is in the stiffener hole, the steel plate above and below the stiffener partially yields, and the concrete above the section collapses. e 4= e cu , e 3< e so , e 4> eso , e 2< e so , e 1> e so ; Operating Condition 3: The neutral shaft is in the stiffening rib hole, and the steel plate below the stiffening rib yields. e 2= e so , e 1> e so ; Condition 4: The neutral shaft is in the steel plate below the stiffener, and the steel plate below the stiffener yields. e 2= e so , e 1> e so ; in, e 1 represents the strain at the lower edge of the steel plate below the stiffening rib; e 2 represents the strain at the upper edge of the steel plate below the stiffening rib; e 3 represents the strain at the lower edge of the steel plate above the stiffening rib; e 4 represents the strain at the upper edge of the steel plate above the stiffening rib and the strain at the upper edge of the concrete above the section.

[0022] Specifically, the description of the location of the stiffening steel plate in the stress condition and Figure 6 The same applies in the middle. Invert the cross-section and take the steel base plate as the uppermost part of the cross-section.

[0023] Furthermore, in S5, for each working condition, the section force balance equation and geometric deformation compatibility equation are established, and the specific details for solving the neutral axis position are as follows: Operating Condition 1: (a) Cross-section under force equilibrium: ; (b) Cross-sectional geometric relationships: ; (c) Stress-strain relationship: ; Combining conditions (a), (b), and (c), the neutral axis position x in load case 1 is obtained. Substituting this into the following formula yields the bending moment of the composite bridge deck section. : ; Operating Condition 2: (a) The cross-section is in force equilibrium: ; (b) Cross-sectional geometric relationships: ; (c) Stress-strain relationship: ; Combining conditions (a), (b), and (c), the neutral axis position x in working condition 2 is obtained. Substituting this into the following formula, the bending moment of the composite bridge deck section can be obtained. : ; Operating Condition 3: (a) The cross-section is in force equilibrium: ; (b) Cross-sectional geometric relationships: ; (c) Stress-strain relationship: ; Combining conditions (a), (b), and (c), the neutral axis position x in working condition 3 is obtained. Substituting this into the following formula yields the bending moment of the composite bridge deck section. : ; Operating Condition 4: (a) Cross-section under force equilibrium ; (b) Cross-sectional geometric relationships ; (c) Stress-strain relationship ; Combining conditions (a), (b), and (c), the neutral axis position x in load case 4 is obtained. Substituting this into the following formula yields the bending moment of the composite bridge deck section. : ; Where x is the distance from the upper surface of the bridge deck to the neutral axis, in mm; co The distance from the top surface to the point where the concrete reaches its axial compressive strength is expressed in mm. s ( x () represents the concrete stress at different cross-sectional heights, in MPa; A s This refers to the total cross-sectional area of ​​the transverse reinforcement at the same height of the cross-section, in mm². 2 ; x uh This represents the thickness of the UHPC layer, in mm.

[0024] Furthermore, in S6, the neutral axis position is substituted into the section moment equilibrium equation to calculate the ultimate flexural capacity in the negative moment zone. Based on the obtained section bending moment , , , Substituting into the following calculation formula, the ultimate bearing capacity of the composite bridge deck during the test is obtained: ; In the formula: This represents the ultimate bearing capacity of the composite bridge deck in the negative bending moment zone, expressed in N. Bending moment of section , , , The unit is N·mm; This is the distance from the center of the support to the variable cross-section, in mm.

[0025] In one specific embodiment, the following is included: (i) Determine the cross-sectional geometric properties and stress conditions. Compared with ordinary steel-concrete composite bridge decks, consider the UHPC layer and the perforated stiffening steel plate, deducting the perforated area from the stress-bearing. The composite bridge deck involved in this invention is a flat steel plate composite bridge deck. For example... Figure 6 to Figure 10 As shown, the cross-section of the composite bridge deck includes a steel base plate, a perforated stiffening plate (PBL), a concrete layer, and a UHPC layer along the height direction of the cross-section, and the transverse reinforcement is arranged along the width direction of the bridge deck; wherein, the perforated stiffening plate includes stiffening ribs and steel plates disposed at the ends of the stiffening ribs, the perforated stiffening plate is connected to the steel base plate, the concrete layer is located between the UHPC layer and the perforated stiffening plate, the UHPC layer is located on the upper surface side of the bridge deck, and the steel base plate is located on the lower surface side of the bridge deck; Figure 6 This is a schematic diagram illustrating the theoretical calculation classification of the flexural bearing capacity of the negative bending moment zone of a flat steel plate composite bridge deck. Figure 7 to Figure 10 These are schematic diagrams of theoretical calculation models for the composite bridge deck cross-section under four different stress conditions.

[0026] (II) Basic Assumptions

[0027] The following assumptions are made: (1) The strain of concrete, reinforcing steel and steel base plate varies linearly along the height of the cross section; (2) The steel reinforcement and concrete are well bonded during the bending process, and the steel base plate and concrete are well bonded. Relative slippage is not considered. Even under large deformation, the integrity of the component can still be maintained. (3) The influence of stiffening steel plates on the bending bearing capacity of composite bridge deck is considered. At the same time, in order to ensure structural safety, the contribution of the stiffening rib opening is not considered. (4) After the concrete cracks, it is no longer used. After the UHPC cracks, its strength decreases, but it can continue to participate in the stress.

[0028] (III) Stress-strain relationship of materials

[0029] The constitutive relations of materials were determined. A linear hardening constitutive model was used for steel plates and steel bars, a compression constitutive model was used for concrete, and a bilinear constitutive model of tension / compression considering strain hardening was used for UHPC. The constitutive models for the above materials are determined based on the stress characteristics of each material and combined with experimental and finite element analysis results: For steel plates and reinforcing bars, a linear hardening constitutive model is used, whose stress-strain relationship consists of an elastic segment and a linear hardening segment, reflecting the hardening stress characteristics of steel after yielding; for concrete, a compression constitutive model is used, where 0 ≤ ε c ≤ε co The stress in the segment increases approximately linearly with strain, at ε co <ε c ≤ε cu The segment maintains the ultimate compressive stress σ cu The model is used to reflect the stress characteristics of the concrete compression zone from the rising section to the peak plateau section; the UHPC adopts a tensile / compression bilinear constitutive model considering strain hardening to reflect the strain hardening characteristics of the UHPC after tensile cracking and the bilinear stress characteristics under compression. When calculating the ultimate flexural bearing capacity of the composite bridge deck in the negative bending moment zone, the composite bridge deck is in the ultimate stress state, i.e., the main tensile reinforcement and steel plate of the section yield or the concrete on the upper side of the section crushes (ε4=ε). cu In this ultimate state, the strain at the upper edge of the concrete in the compression zone has reached the ultimate compressive strain ε of the concrete. cu The concrete stress in the compression zone has approached and remained at the ultimate compressive stress σ. cu The contribution of the concrete in the compression zone to the cross-sectional bearing capacity mainly depends on the ultimate compressive stress σ. cu The linear simplification of the ascending segment in the concrete compression constitutive model has a limited impact on the resultant force and internal force arm in the compression zone, and does not affect the accuracy of the ultimate bearing capacity calculation results. The rationality of the above constitutive model and calculation method has been verified by experiments and finite element analysis. The ratio of theoretical calculation values ​​to experimental values ​​is 0.92 to 0.99, and the relative error between theoretical calculation values ​​and finite element simulation results is controlled within 10%, indicating that the method of the present invention can accurately predict the ultimate flexural bearing capacity of composite bridge decks in the negative bending moment zone while ensuring a certain safety margin.

[0030] The specific details of the linear strengthening constitutive model for steel plates and reinforcing bars are as follows: Figure 2 As shown, the stress-strain relationship expression for reinforcing bars is as follows: ; In the formula: This is the elastic modulus of the reinforcing steel, expressed in MPa. This represents the yield strength of the reinforcing steel, expressed in MPa. The yield strain of the steel reinforcement; This represents the ultimate stress of the reinforcing steel, expressed in MPa. This represents the ultimate strain of the reinforcing steel. For the stress of the reinforcing steel; For the strain of the reinforcing steel; like Figure 3 As shown, the stress-strain relationship expression for the steel plate is as follows: ; In the formula: This is the elastic modulus of the steel plate, expressed in MPa. This represents the yield strength of the steel plate, expressed in MPa. The yield strain of the steel plate; The ultimate strain of the steel plate; This represents the ultimate stress of the steel plate, expressed in MPa. For steel plate stress; For the strain of the steel plate.

[0031] like Figure 4 As shown, the specific content of the compression constitutive model for concrete is as follows: The stress-strain relationship expression for concrete is as follows: ; In the formula: This refers to the compressive stress in the concrete. This represents the compressive strain of the concrete. This represents the ultimate compressive stress in concrete. To achieve ultimate compressive stress in concrete Compressive strain at time; This represents the ultimate compressive strain of concrete.

[0032] like Figure 5 As shown, the specific content of the tensile / compression bilinear constitutive model of UHPC considering strain hardening is as follows: The expression for the uniaxial tensile stress-strain relationship of UHPC is as follows: ; In the formula: The initial crack strength of UHPC; The initial crack strain of UHPC; For UHPC strain; For UHPC strain; The strain is the strain when the tensile strength of the UHPC is 0.

[0033] (iv) Based on the position of the neutral axis and the yield range of the steel plate, four types of stress conditions are classified.

[0034] Based on experimental and finite element analysis results, the tensile portions of the main tensile reinforcement and stiffeners yielded at specimen failure. Therefore, in calculations, the yielding of the main tensile reinforcement and steel plate, or the crushing of the concrete on the upper side of the section, is used as the criterion for determining whether the composite bridge deck has reached its ultimate bearing capacity. According to the cross-sectional geometry and concrete location, the stress state of the composite bridge deck can be divided into... Figure 6 The following are some of the situations shown; Condition 1: The neutral shaft is in the stiffener hole, the steel plate above the stiffener partially yields, and the concrete above the section collapses. e 4= e cu , e 3< e so , e 4> e so ; Condition 2: The neutral shaft is in the stiffener hole, the steel plate above and below the stiffener partially yields, and the concrete above the section collapses. e 4= e cu , e 3< e so , e 4> e so , e 2< e so , e 1> e so ; Operating Condition 3: The neutral shaft is in the stiffening rib hole, and the steel plate below the stiffening rib yields. e 2= e so , e 1> e so ; Condition 4: The neutral shaft is in the steel plate below the stiffener, and the steel plate below the stiffener yields. e 2= e so , e 1> e so ; in, e 1 represents the strain at the lower edge of the steel plate below the stiffening rib; e 2 represents the strain at the upper edge of the steel plate below the stiffening rib; e 3 represents the strain at the lower edge of the steel plate above the stiffening rib; e 4 represents the strain at the upper edge of the steel plate above the stiffening rib and the strain at the upper edge of the concrete above the section.

[0035] (v) For each working condition, establish the cross-sectional force balance equation and the geometric deformation compatibility equation, and solve for the neutral axis position.

[0036] The theoretical calculation model for working condition 1 is as follows: Figure 7 As shown, the calculated bending moment of the section is... The theoretical calculation model for working condition 2 is as follows: Figure 8 As shown, the calculated bending moment of the section is... The theoretical calculation model for working condition 3 is as follows: Figure 9 As shown, the calculated bending moment of the section is... The theoretical calculation model for working condition 4 is as follows: Figure 10 As shown, the calculated bending moment of the section is... .

[0037] See Figure 7-Figure 10 , Figure 7-Figure 10 These are schematic diagrams of the theoretical calculation models of the composite bridge deck cross-sections for working conditions 1-4, respectively. The meanings of the labels in the figures are as follows: B represents the cross-sectional width of the composite bridge deck; t s t represents the thickness of the steel plate. b h1 represents the thickness of the stiffening rib; h1, h2, h3, and h4 represent the dimensions of each component of the cross-section along the height of the cross-section; x represents the distance from the upper surface of the bridge deck to the neutral axis; x c x represents the distance from the characteristic location of the concrete compression zone to the upper surface; UH x represents the thickness of the UHPC layer. s1 x s2 x1, x2, x4, and x5 represent the distances from the bottom and top rows of transverse reinforcing bars to the top surface, respectively; x1, x2, x4, and x5 represent the distances from each characteristic location of the section to the top surface, respectively; ε1 is the strain at the lower edge of the steel plate below the stiffener, ε2 is the strain at the upper edge of the steel plate below the stiffener, ε3 is the strain at the lower edge of the steel plate above the stiffener, ε4 ​​is the strain at the upper edge of the steel plate above the stiffener and the strain at the upper edge of the concrete above the section, and ε5 and ε6 represent the strains at other characteristic locations of the section, respectively; ε so ε is the yield strain of the steel plate. cu ε represents the ultimate compressive strain of concrete. s1 ε s2 These represent the strains of the bottom and top row of transverse reinforcing bars, respectively; ε uh1 ε uh2 σ1, σ2, σ3, σ4, and σ5 are the strains at the upper and lower edges of the UHPC layer, respectively; σ1, σ2, σ3, σ4, and σ5 are the stresses at the corresponding positions; σ6, σ7, σ8, σ9, σ1, σ2, σ3, σ4, and σ5 are the stresses at the corresponding positions; σ8, σ9, σ1so σ is the yield stress of the steel plate; cu σ represents the ultimate compressive stress in concrete. s1 σ s2 These represent the stresses of the bottom and top row of transverse reinforcing bars, respectively; σ uh1 σ uh2These represent the stresses at the upper and lower edges of the UHPC layer, respectively; As represents the total cross-sectional area of ​​the transverse reinforcement at the same height of the section.

[0038] (vi) Substitute the neutral axis position into the section moment equilibrium equation to calculate the ultimate flexural capacity in the negative moment zone.

[0039] Based on the obtained section bending moment , , , Substituting into the following calculation formula, the ultimate bearing capacity of the composite bridge deck during the test is obtained: ; In the formula: This represents the ultimate bearing capacity of the composite bridge deck in the negative bending moment zone, expressed in N. M Bending moment of section , , , The unit is N·mm; This is the distance from the center of the support to the variable cross-section, in mm.

[0040] The results show that the theoretical calculation values ​​are generally slightly smaller than the experimental values, with a ratio of 0.92 to 0.99. This indicates that the method of the present invention, while ensuring a certain safety margin, can well reflect the actual load-bearing capacity of the specimen, and has good representativeness and accuracy. The theoretical calculation values ​​are basically consistent with the finite element simulation results, with the relative error controlled within 10%, showing good agreement. The proposed theoretical method has good accuracy and applicability under different structural and material conditions. Table 1 and Figure 12 The results comparing the ultimate bearing capacity of the composite bridge deck in the negative bending moment zone obtained from experiments and finite element analysis with the theoretical calculations are presented.

[0041] Table 1. Comparison of theoretical and experimental / finite element simulation values ​​of ultimate load on composite bridge deck;

[0042] in, Figure 11 This is a schematic diagram of the layout of the composite bridge deck test device in the negative bending moment zone provided by the present invention. In the figure, L M The distance is from the center of the support to the variable cross section. HY-1~HY-4 and SY-1~SY-3 are the measuring point marks set during the test.

[0043] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0044] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the flexural strength of a steel-concrete composite bridge deck in the negative bending moment zone, characterized in that, Includes the following steps: S1. Determine the cross-sectional geometry and stress conditions, considering the UHPC layer and the perforated stiffening steel plate, deducting the perforated area from the stress-bearing area; S2. Set basic assumptions, including the plane section assumption, no relative slip at the steel-concrete interface, concrete exiting tensile work after cracking, and UHPC maintaining tensile strain hardening characteristics; S3. Determine the constitutive relations of materials. Linear hardening constitutive models are used for steel plates and steel bars, compression constitutive models are used for concrete, and bilinear constitutive models of tension / compression considering strain hardening are used for UHPC. S4. Based on the position of the neutral axis and the yield range of the steel plate, four types of stress conditions are defined. S5. For each working condition, establish the cross-sectional force balance equation and the geometric deformation compatibility equation, and solve for the position of the neutral axis; S6. Substitute the neutral axis position into the section moment equilibrium equation to calculate the ultimate flexural capacity in the negative moment zone.

2. The method for predicting the flexural strength of a steel-concrete composite bridge deck in the negative bending moment zone according to claim 1, characterized in that, The specific details of the linearly strengthened constitutive model for steel plates and reinforcing bars in S3 are as follows: The stress-strain relationship of reinforcing steel is expressed as follows: ； In the formula: This is the elastic modulus of the reinforcing steel, expressed in MPa. This represents the yield strength of the reinforcing steel, expressed in MPa. The yield strain of the steel reinforcement; This represents the ultimate stress of the reinforcing steel, expressed in MPa. This represents the ultimate strain of the reinforcing steel. For the stress of the reinforcing steel; For the strain of the reinforcing steel; The stress-strain relationship of a steel plate is expressed as follows: ； In the formula: This is the elastic modulus of the steel plate, expressed in MPa. This represents the yield strength of the steel plate, expressed in MPa. The yield strain of the steel plate; The ultimate strain of the steel plate; This represents the ultimate stress of the steel plate, expressed in MPa. For steel plate stress; For the strain of the steel plate.

3. The method for predicting the flexural strength of a steel-concrete composite bridge deck in the negative bending moment zone according to claim 1, characterized in that, The specific details of using a compression constitutive model for concrete in S3 are as follows: The stress-strain relationship of concrete is expressed as follows: ； In the formula: This refers to the compressive stress in the concrete. This represents the compressive strain of the concrete. This represents the ultimate compressive stress in concrete. To achieve ultimate compressive stress in concrete Compressive strain at time; This represents the ultimate compressive strain of concrete.

4. The method for predicting the flexural strength of a steel-concrete composite bridge deck in the negative bending moment zone according to claim 1, characterized in that, The specific details of the tensile / compressive bilinear constitutive model for UHPC in S3, which considers strain hardening, are as follows: The expression for the uniaxial tensile stress-strain relationship of UHPC is as follows: ； In the formula: The initial crack strength of UHPC; The initial crack strain of UHPC; For UHPC strain; For UHPC strain; The strain is the strain when the tensile strength of the UHPC is 0.

5. The method for predicting the flexural strength of a steel-concrete composite bridge deck in the negative bending moment zone according to claim 1, characterized in that, Based on the position of the neutral axis and the yield range of the steel plate, S4 classifies the load into four types: Condition 1: The neutral shaft is in the stiffener hole, the steel plate above the stiffener partially yields, and the concrete above the section collapses. ε 4= ε cu , ε 3< ε so , ε 4> ε so ; Condition 2: The neutral shaft is in the stiffener hole, the steel plate above and below the stiffener partially yields, and the concrete above the section collapses. ε 4= ε cu , ε 3< ε so , ε 4> ε so , ε 2< ε so , ε 1> ε so ; Operating Condition 3: The neutral shaft is in the stiffening rib hole, and the steel plate below the stiffening rib yields. ε 2= ε so , ε 1> ε so ; Condition 4: The neutral shaft is in the steel plate below the stiffener, and the steel plate below the stiffener yields. ε 2= ε so , ε 1> ε so ; in, ε 1 represents the strain at the lower edge of the steel plate below the stiffening rib; ε 2 represents the strain at the upper edge of the steel plate below the stiffening rib; ε 3 represents the strain at the lower edge of the steel plate above the stiffening rib; ε 4 represents the strain at the upper edge of the steel plate above the stiffening rib and the strain at the upper edge of the concrete above the section.

6. The method for predicting the flexural strength of a steel-concrete composite bridge deck in the negative bending moment zone according to claim 1, characterized in that, In S5, for each working condition, the section force balance equation and geometric deformation compatibility equation are established, and the specific content for solving the neutral axis position is as follows: Operating Condition 1: (a) Cross-section under force equilibrium: ； (b) Cross-sectional geometric relationships: ； (c) Stress-strain relationship: ； Combining conditions (a), (b), and (c), the neutral axis position x in load case 1 is obtained. Substituting this into the following formula yields the bending moment of the composite bridge deck section. : ； Operating Condition 2: (a) The cross-section is in force equilibrium: ； (b) Cross-sectional geometric relationships: ； (c) Stress-strain relationship: ； Combining conditions (a), (b), and (c), the neutral axis position x in load case 2 is obtained. Substituting this into the following formula yields the bending moment of the composite bridge deck section. : ； Operating Condition 3: (a) The cross-section is in force equilibrium: ； (b) Cross-sectional geometric relationships: ； (c) Stress-strain relationship: ； Combining conditions (a), (b), and (c), the neutral axis position x in working condition 3 is obtained. Substituting this into the following formula yields the bending moment of the composite bridge deck section. : ； Operating Condition 4: (a) Cross-section under force equilibrium ； (b) Cross-sectional geometric relationships ； (c) Stress-strain relationship ； Combining conditions (a), (b), and (c), the neutral axis position x in load case 4 is obtained. Substituting this into the following formula yields the bending moment of the composite bridge deck section. : ； Where x is the distance from the upper surface of the bridge deck to the neutral axis, in mm; co The distance from the top surface to the point where the concrete reaches its axial compressive strength is expressed in mm. σ ( x () represents the concrete stress at different cross-sectional heights, in MPa; A s This refers to the total cross-sectional area of ​​the transverse reinforcement at the same height of the cross-section, in mm². 2 ; x uh The thickness of the UHPC layer is in mm.

7. A method for predicting the flexural strength of a steel-concrete composite bridge deck in the negative bending moment zone according to claim 1 or 6, characterized in that, In S6, the neutral axis position is substituted into the section moment equilibrium equation to calculate the ultimate flexural capacity in the negative moment zone. The specific details are as follows: Based on the obtained section bending moment , , , Substituting into the following calculation formula, the ultimate bearing capacity of the composite bridge deck during the test is obtained: ； In the formula: This represents the ultimate bearing capacity of the composite bridge deck in the negative bending moment zone, expressed in N. Bending moment of section , , , The unit is N·mm; This is the distance from the center of the support to the variable cross-section, in mm.

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