A calculation method for the ultimate bending moment of steel box-LUHPC composite beams

Abstract

The present invention discloses a method for calculating the ultimate bending moment of a steel-box-LUHPC composite beam, comprising the following steps: clarifying the material properties of LUHPC, conducting a four-point bending loading test on the composite beam, determining the failure mode of the steel-box-LUHPC composite beam under bending, and judging the position of the neutral axis of the cross section when the steel-box-LUHPC composite beam reaches a bending state; based on the position of the plastic neutral axis, drawing a force diagram of the cross section of the steel-box-LUHPC composite beam, and establishing a formula for calculating the ultimate bending moment of the steel-box-LUHPC composite beam; and comparing and verifying the calculation results obtained from the formula for calculating the ultimate bending moment of the steel-box-LUHPC composite beam with the test results. This application proposes a method for determining the ultimate bending moment of a steel-box-LUHPC composite beam, providing a theoretical basis for the design and application of steel-box-LUHPC composite beam bridges, and providing technical support for promoting the application of LUHPC materials in bridge engineering.

Description

Technical Field

[0001] The present invention relates to the technical field of ultimate bending moment calculation of composite beams, and in particular to a method for calculating the ultimate bending moment of a steel box-LUHPC composite beam. Background Art

[0002] With the vigorous development of bridge construction, steel-concrete composite beams can give full play to the material properties and have good mechanical properties, and have been widely used in bridge engineering. In the design and construction process of steel-concrete composite beam bridges, the defects of ordinary concrete bridge decks, such as thicker and heavier self-weight and easy cracking of concrete in the negative bending moment area, have restricted its further development. Therefore, reducing the self-weight of composite bridges and proposing lightweight composite bridge structures are the development trends of steel-concrete composite bridges. Among them, high strengthening and lightweighting of concrete materials is an important research direction. Lightweight Ultra-high Performance Concrete (LUHPC) uses ceramic sand instead of quartz sand, and has high strength (compressive strength ≥100MPa, splitting tensile strength ≥10MPa), low self-weight (apparent density ≤2100kg / m 3 ) and other characteristics, LUHPC materials are applied to steel box-concrete composite bridge projects to form steel box-LUHPC composite beams, which can reduce the cross-sectional size, reduce the deadweight of the structure, improve the structural stress performance, and enhance the spanning capacity of the composite bridge. The application prospects are very broad.

[0003] Patent CN110990922A discloses a method for calculating the bending bearing capacity of a cross-section beam under negative bending moment. The method determines the position of the neutral axis of the cross-section when the composite beam with a new cross-section and a fully shear-resistant connection reaches the ultimate bearing capacity under negative bending moment. The method substitutes the position of the neutral axis into the corresponding formula to solve the ultimate bending bearing capacity. When the plastic neutral axis is inside the corrugated side plate, the cross-section stress distribution satisfies the formula fybdtd+α1fc(b-hr)β1(ha-td-tu)≥fpyAp+2fybutu+fysAs(1). The height x of the equivalent compression zone of concrete is calculated based on the balance of forces, fpyAp+2fybutu+fysAs=fybdtd+a1fc(b-hr)x(2a). The moment of the equivalent rectangular resultant force point of the concrete in the compression zone is taken to obtain the ultimate bending bearing capacity Mu of the shell beam.

[0004] However, the above-mentioned existing technology is a calculation method for shell beams, which is not applicable to steel box-LUHPC composite beams. In addition, the compressive strength of concrete specified in the Chinese standard for the calculation of the ultimate bending moment of steel-concrete composite beams does not exceed 80MPa. Therefore, the calculation of the ultimate bending moment of steel box-LUHPC composite beams can no longer meet the use conditions of the existing standard calculation formula. Summary of the Invention

[0005] The purpose of the present invention is to overcome the above technical deficiencies and propose a method for calculating the ultimate bending moment of a steel box-LUHPC composite beam. The method solves the technical problem that the calculation method of the shell beam in the prior art is not applicable to steel box-LUHPC composite beams, and the compressive strength of concrete specified in the Chinese standard for the ultimate bending moment calculation of steel-concrete composite beams does not exceed 80 MPa, so the ultimate bending moment calculation of steel box-LUHPC composite beams can no longer meet the use conditions of the existing standard calculation formula.

[0006] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

[0007] The present invention provides a method for calculating the ultimate bending moment of a steel box-LUHPC composite beam, comprising the following steps:

[0008] Step 1: Clarify the material properties of LUHPC, conduct a four-point bending loading test on the composite beam, determine the failure mode of the steel box-LUHPC composite beam under bending, and determine the position of the neutral axis of the cross section when the steel box-LUHPC composite beam reaches the bending state;

[0009] Step 2: Based on the position of the plastic neutral axis, a force diagram of the steel box-LUHPC composite beam section is drawn, and a calculation formula for the ultimate bending moment of the steel box-LUHPC composite beam is established;

[0010] Step 3: Compare and verify the calculation results obtained from the ultimate bending moment calculation formula of the steel box-LUHPC composite beam with the test results.

[0011] In some embodiments, the specific steps include: experimentally determining the axial tensile strength, axial compressive strength and uniaxial compressive constitutive relationship of LUHPC, obtaining relevant parameters of the specimen, conducting a composite beam bending test, and determining the position of the plastic neutral axis of the cross section when the steel box-LUHPC composite beam reaches a bending state, wherein the plastic neutral axis is divided into two situations: the plastic neutral axis is located in the LUHPC bridge deck and the steel box beam.

[0012] In some embodiments, when the cross-sectional stress distribution satisfies the formula: When , the plastic neutral axis is located inside the LUHPC bridge deck;

[0013] Where, A c is the area of ​​LUHPC concrete slab; A r is the cross-sectional area of ​​the longitudinal reinforcement in the LUHPC concrete slab; A s is the cross-sectional area of ​​the steel box girder; f c is the axial compressive strength value of LUHPC material; f ryis the yield strength of the longitudinal reinforcement in the LUHPC concrete slab; f sy is the yield strength value of steel box girder steel.

[0014] In some embodiments, when the cross-sectional stress distribution satisfies the formula: When , the plastic neutral axis is located inside the steel box girder;

[0015] Where, A c is the area of ​​LUHPC concrete slab; A r is the cross-sectional area of ​​the longitudinal reinforcement in the LUHPC concrete slab; A s is the cross-sectional area of ​​the steel box girder; f c is the axial compressive strength value of LUHPC material; f ry is the yield strength of the longitudinal reinforcement in the LUHPC concrete slab; f sy is the yield strength value of steel box girder steel.

[0016] In some embodiments, for the two cases where the plastic neutral axis is located in the LUHPC bridge deck and in the steel box girder, corresponding force diagrams of the steel box-LUHPC composite beam section are proposed;

[0017] When the plastic neutral axis is located within the LUHPC bridge deck, the stress distribution of the LUHPC concrete in the compression zone is triangular, and the tensile effect of the concrete in the tension zone and the force of the longitudinal reinforcement in the concrete slab are taken into account. The steel box girder in the tension zone yields as a whole, and the stress distribution is rectangular. When the plastic neutral axis is located within the steel box girder, the stress distribution of the steel box girder in the compression zone is equivalent to a rectangular distribution with reference to existing specifications.

[0018] Calculate the neutral axis distance from the surface of the LUHPC concrete slab based on the force balance equation x .

[0019] In some embodiments, when the plastic neutral axis is located within the LUHPC bridge deck, formula (1) is satisfied:

[0020] (1)

[0021] When the plastic neutral axis is located inside the steel box girder, formula (2) is satisfied:

[0022] (2)

[0023] Where, b c is the cross-sectional width of the LUHPC concrete slab;x is the distance between the plastic neutral axis and the upper surface of the LUHPC concrete slab; f t is the tensile strength of LUHPC concrete; A sc is the cross-sectional area of ​​the steel box girder on the plastic neutral axis, x Calculation can be obtained; h c is the cross-sectional height of LUHPC concrete slab.

[0024] In some embodiments, the ultimate bending moment of the steel box-LUHPC composite beam can be obtained based on the section moment balance: M :

[0025] When the plastic neutral axis is located inside the LUHPC bridge deck, M Satisfying formula (3):

[0026] (3)

[0027] When the plastic neutral axis is located inside the steel box girder, M Satisfying formula (4):

[0028] (4)

[0029] Where, y 1 is the distance from the resultant force position in the compression zone of the LUHPC concrete slab to the plastic neutral axis; y 2 is the distance from the centroid of the longitudinal reinforcement section to the plastic neutral axis in the LUHPC concrete slab; y 3 is the distance from the centroid of the tensile zone section of the LUHPC concrete slab to the plastic neutral axis; y 4 is the distance from the centroid of the steel box girder section to the plastic neutral axis; A cc is the cross-sectional area of ​​the LUHPC concrete slab above the plastic neutral axis; A cs is the cross-sectional area of ​​the LUHPC concrete slab below the plastic neutral axis; A sc is the cross-sectional area of ​​the steel box girder on the upper side of the plastic neutral axis; A ss is the cross-sectional area of ​​the steel box girder below the plastic neutral axis; f co is the compressive strength of the lower edge of the LUHPC concrete slab.

[0030] In some embodiments, the connection between the steel box girder and the LUHPC concrete slab is reliable, the mid-span section conforms to the plane section assumption during bending, and the failure mode is characterized by tensile yielding of the steel box girder and crushing of the upper surface of the concrete slab.

[0031] Compared with the prior art, the method for calculating the ultimate bending moment of a steel box-LUHPC composite beam provided by the present invention clarifies the material properties of LUHPC, conducts a four-point bending loading test on the composite beam, determines the failure mode of the steel box-LUHPC composite beam under bending, and judges the position of the neutral axis of the cross section when the steel box-LUHPC composite beam reaches the bending state; according to the position of the plastic neutral axis, a force diagram of the cross section of the steel box-LUHPC composite beam is drawn, and a calculation formula for the ultimate bending moment of the steel box-LUHPC composite beam is established; the calculation results obtained by the calculation formula for the ultimate bending moment of the steel box-LUHPC composite beam are compared and verified with the test results. In this application, the ultimate bending moment calculation formula of the steel box-LUHPC composite beam under the bending state can be considered. By taking into account the compression characteristics of HPC and the tension characteristics of steel beams, and considering the tensile influence of LUHPC materials, the stress distribution characteristics of the mid-span section of the steel box-LUHPC composite beam are accurately determined. A method for determining the ultimate bending moment of the steel box-LUHPC composite beam is proposed, which can comprehensively consider the two neutral axis position distribution situations. For the two cases where the neutral axis is located inside the LUHPC bridge deck and inside the steel box beam, the ultimate bending moment of the steel box-LUHPC composite beam can be accurately determined. The ratios of the calculation results obtained using the ultimate bending moment calculation formula for the steel box-LUHPC composite beam to the experimental results are 0.998 and 0.983, respectively. The ultimate bending moment of the steel box-LUHPC composite beam can be calculated reasonably and accurately, which has good practical engineering application value.

[0032] This application focuses on the stress distribution characteristics of the steel box-LUHPC composite beam cross section, transforms the stress distribution of LUHPC concrete in the compression zone into a triangular distribution, and takes into account the tensile effect of concrete in the tension zone and the force of the longitudinal reinforcement in the concrete slab. A method for determining the ultimate bending moment of steel box-LUHPC composite beams is proposed, which provides a theoretical basis for the design and application of steel box-LUHPC composite beam bridges and offers technical support for promoting the application of LUHPC materials in bridge engineering.

[0033] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention and to implement it according to the contents of the description, the preferred embodiments of the present invention are described in detail below with reference to the accompanying drawings. The specific implementation methods of the present invention are given in detail by the following embodiments and the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Flowchart of a method for calculating the ultimate bending moment of a steel box-LUHPC composite beam in one embodiment of the present invention;

[0035] Figure 2 It is a schematic diagram of the force and strain response of the present invention when the plastic neutral axis is located in the LUHPC bridge deck;

[0036] Figure 3It is a schematic diagram of the force and strain response of the present invention when the plastic neutral axis is located in the steel box girder;

[0037] Figure 4 It is a longitudinal schematic diagram of the test piece in the present invention;

[0038] Figure 5 is a schematic cross-sectional view of the SLB-1 specimen of the present invention;

[0039] Figure 6 is a schematic transverse cross-sectional view of the SLB-2 specimen of the present invention;

[0040] Figure 7 is a top view of the test piece of the present invention;

[0041] Figure 8 It is a schematic diagram of the arrangement of the loading device of the present invention;

[0042] Figure 9 is a distribution diagram of strain gauges of the present invention;

[0043] Figure 10 is the load-mid-span deflection relationship curve of the SLB-1 specimen of the present invention;

[0044] Figure 11 This is the load-mid-span deflection relationship curve of the SLB-2 specimen of the present invention.

[0045] Description of reference numerals:

[0046] 1- Specimen, 2- Loading device, 3- Support, 4- Displacement meter. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0048] In order to solve the technical problem that the calculation method of the shell beam in the existing technology is not applicable to the steel box-LUHPC composite beam, and the compressive strength of concrete specified in the Chinese standard for the calculation of the ultimate bending moment of the steel-concrete composite beam does not exceed 80MPa, so the calculation of the ultimate bending moment of the steel box-LUHPC composite beam can no longer meet the use conditions of the calculation formula in the existing standard, the present invention provides a method for calculating the ultimate bending moment of the steel box-LUHPC composite beam. According to the stress distribution characteristics of the cross-section of the steel box-LUHPC composite beam, the stress distribution of the LUHPC concrete in the compression zone in the state is triangular, and the tensile effect of the concrete in the tension zone and the force effect of the longitudinal steel bars in the concrete slab are taken into account. A method for determining the ultimate bending moment of the steel box-LUHPC composite beam is proposed, which provides a theoretical basis for the design and application of steel box-LUHPC composite beam bridges and provides technical support for promoting the application of LUHPC materials in bridge engineering.

[0049] See also Figure 1 , Figure 1 Flowchart of a method for calculating the ultimate bending moment of a steel box-LUHPC composite beam in one embodiment of the present invention.

[0050] The present invention provides a method for calculating the ultimate bending moment of a steel box-LUHPC composite beam, comprising the following steps:

[0051] Step 1: Clarify the material properties of LUHPC, conduct a four-point bending loading test on the composite beam, determine the failure mode of the steel box-LUHPC composite beam under bending, and determine the position of the neutral axis of the cross section when the steel box-LUHPC composite beam reaches the bending state;

[0052] Step 2: Based on the position of the plastic neutral axis, a force diagram of the steel box-LUHPC composite beam section is drawn, and a calculation formula for the ultimate bending moment of the steel box-LUHPC composite beam is established;

[0053] Step 3: Compare and verify the calculation results obtained from the ultimate bending moment calculation formula of the steel box-LUHPC composite beam with the test results.

[0054] In this embodiment, the material properties of LUHPC are clarified, a four-point bending loading test of the composite beam is carried out, the failure mode of the steel box-LUHPC composite beam under bending is determined, and the position of the neutral axis of the cross section of the steel box-LUHPC composite beam when the steel box-LUHPC composite beam reaches the bending state is determined; according to the position of the plastic neutral axis, a force diagram of the cross section of the steel box-LUHPC composite beam is drawn, and a calculation formula for the ultimate bending moment of the steel box-LUHPC composite beam is established; the calculation results obtained by the calculation formula for the ultimate bending moment of the steel box-LUHPC composite beam are compared and verified with the test results. In this application, the characteristics of the LUHPC under compression and the steel beam under tension in the bending state of the steel box-LUHPC composite beam can be considered. Taking into account the tensile influence of LUHPC materials, the stress distribution characteristics of the mid-span section of the steel box-LUHPC composite beam are accurately determined, and a method for determining the ultimate bending moment of the steel box-LUHPC composite beam is proposed. The method can comprehensively consider the two neutral axis position distribution situations. For the two cases where the neutral axis is located inside the LUHPC bridge deck and inside the steel box beam, the ultimate bending moment of the steel box-LUHPC composite beam can be accurately determined. The ratios of the calculation results obtained using the ultimate bending moment calculation formula for the steel box-LUHPC composite beam and the test results are 0.998 and 0.983, respectively. The ultimate bending moment of the steel box-LUHPC composite beam can be calculated reasonably and accurately, and has good practical engineering application value.

[0055] In this example, see Figures 4 to 7 First, two steel box-LUHPC composite beam specimens were designed and manufactured, numbered SLB-1 and SLB-2. The length of both specimens was 4800mm and the board width was 1000mm. Among them, the steel box-LUHPC composite beam specimen includes a LUHPC concrete slab, a steel box girder and a bolt connector. The LUHPC concrete slab is fixedly installed on the upper side of the steel box girder through the bolt connector. Two layers of steel mesh are provided in the LUHPC concrete slab. The two layers of steel mesh are arranged at intervals from top to bottom in the LUHPC concrete slab. Each layer of the steel mesh includes multiple transverse steel bars and multiple longitudinal steel bars. The multiple transverse steel bars are arranged at intervals along the transverse direction, and the multiple longitudinal steel bars are arranged at intervals along the longitudinal direction. The multiple transverse steel bars and the multiple longitudinal steel bars are connected and fixed to each other. The steel box girder includes a bottom plate and two T-shaped steels. The two T-shaped steels are arranged on the bottom plate at intervals along the width direction. The bottom plate and the two T-shaped steels are fixedly connected. Two groups of bolt connectors are provided on the upper side of each T-shaped steel to connect with the LUHPC concrete slab.

[0056] Specifically, the specific dimensions of the SLB-1 specimen are: the length of the LUHPC concrete slab is 4800mm, the width is 1000mm, and the thickness is 160mm. The distance between the upper steel mesh and the upper side of the LUHPC concrete slab is 20mm, and the distance between the lower steel mesh and the lower side of the LUHPC concrete slab is 20mm. The distance between the steel bars at both ends of the multiple longitudinal steel bars and the side of the LUHPC concrete slab is 50mm, and the distance between two adjacent longitudinal steel bars is 100mm. The length of the bolt connector is 90mm and the diameter is 19mm. The thickness of the upper side plate of the T-steel is 14mm, the thickness of the side plate of the T-steel vertical plate is 10, the width of the bottom plate is 600mm, the thickness of the bottom plate is 10mm, and the height of the entire specimen is 484mm.

[0057] Specifically, the specific dimensions of the SLB-2 specimen are: the length of the LUHPC concrete slab is 4800mm, the width is 1000mm, and the thickness is 100mm. The distance between the upper steel mesh and the upper side of the LUHPC concrete slab is 20mm, and the distance between the lower steel mesh and the lower side of the LUHPC concrete slab is 20mm. The distance between the steel bars at both ends of the multiple longitudinal steel bars and the side of the LUHPC concrete slab is 50mm, and the distance between two adjacent longitudinal steel bars is 100mm. The length of the bolt connector is 70mm and the diameter is 19mm. The thickness of the upper side plate of the T-steel is 14mm, the thickness of the side plate of the T-steel vertical plate is 10, the width of the bottom plate is 700mm, the thickness of the bottom plate is 14mm, and the height of the entire specimen is 480mm.

[0058] In some embodiments, see Figures 2 to 3 , specifically including the following steps: experimentally determine the axial tensile strength, axial compressive strength and uniaxial compression constitutive relationship of LUHPC, obtain relevant parameters of the specimen, carry out composite beam bending tests, and determine the position of the plastic neutral axis of the cross-section when the steel box-LUHPC composite beam reaches the bending state. Among them, there are two cases: the plastic neutral axis is located in the LUHPC bridge deck and in the steel box beam.

[0059] In this embodiment, the position of the plastic neutral axis can be determined by calculation. The calculation method varies depending on the location of the plastic neutral axis. Two cases can be divided here: one is that the plastic neutral axis is located in the LUHPC concrete slab, and the other is that the plastic neutral axis is located in the steel box girder. For the two cases where the plastic neutral axis is located in the LUHPC bridge deck and the steel box girder, the ultimate bending moment of the steel box-LUHPC composite beam can be accurately determined.

[0060] In some embodiments, when the cross-sectional stress distribution satisfies the formula: When , the plastic neutral axis is located inside the LUHPC bridge deck;

[0061] Where,A c is the area of ​​LUHPC concrete slab; A r is the cross-sectional area of ​​the longitudinal reinforcement in the LUHPC concrete slab; A s is the cross-sectional area of ​​the steel box girder; f c is the axial compressive strength value of LUHPC material; f ry is the yield strength of the longitudinal reinforcement in the LUHPC concrete slab; f sy is the yield strength value of steel box girder steel.

[0062] In some embodiments, when the cross-sectional stress distribution satisfies the formula: When , the plastic neutral axis is located inside the steel box girder;

[0063] Where, A c is the area of ​​LUHPC concrete slab; A r is the cross-sectional area of ​​the longitudinal reinforcement in the LUHPC concrete slab; A s is the cross-sectional area of ​​the steel box girder; f c is the axial compressive strength value of LUHPC material; f ry is the yield strength of the longitudinal reinforcement in the LUHPC concrete slab; f sy is the yield strength value of steel box girder steel.

[0064] In some embodiments, for the two cases where the plastic neutral axis is located in the LUHPC bridge deck and in the steel box girder, corresponding force diagrams of the steel box-LUHPC composite beam section are proposed;

[0065] When the plastic neutral axis is located within the LUHPC bridge deck, the stress distribution of the LUHPC concrete in the compression zone is triangular, and the tensile effect of the concrete in the tension zone and the force of the longitudinal reinforcement in the concrete slab are taken into account. The steel box girder in the tension zone yields as a whole, and the stress distribution is rectangular. When the plastic neutral axis is located within the steel box girder, the stress distribution of the steel box girder in the compression zone is equivalent to a rectangular distribution with reference to existing specifications.

[0066] Calculate the neutral axis distance from the surface of the LUHPC concrete slab based on the force balance equation x .

[0067] In some embodiments, when the plastic neutral axis is located within the LUHPC bridge deck, formula (1) is satisfied:

[0068] (1)

[0069] When the plastic neutral axis is located inside the steel box girder, formula (2) is satisfied:

[0070] (2)

[0071] Where, b c is the cross-sectional width of the LUHPC concrete slab; x is the distance between the plastic neutral axis and the upper surface of the LUHPC concrete slab; f t is the tensile strength of LUHPC concrete; A sc is the cross-sectional area of ​​the steel box girder on the plastic neutral axis, x Calculation can be obtained; h c is the cross-sectional height of LUHPC concrete slab.

[0072] In some embodiments, the ultimate bending moment of the steel box-LUHPC composite beam can be obtained based on the section moment balance: M :

[0073] When the plastic neutral axis is located inside the LUHPC bridge deck, M Satisfying formula (3):

[0074] (3)

[0075] When the plastic neutral axis is located inside the steel box girder, M Satisfying formula (4):

[0076] (4)

[0077] Where, y 1 is the distance from the resultant force position in the compression zone of the LUHPC concrete slab to the plastic neutral axis; y 2 is the distance from the centroid of the longitudinal reinforcement section to the plastic neutral axis in the LUHPC concrete slab; y 3 is the distance from the centroid of the tensile zone section of the LUHPC concrete slab to the plastic neutral axis; y 4 is the distance from the centroid of the steel box girder section to the plastic neutral axis; A cc is the cross-sectional area of ​​the LUHPC concrete slab above the plastic neutral axis; A cs is the cross-sectional area of ​​the LUHPC concrete slab below the plastic neutral axis; A sc is the cross-sectional area of ​​the steel box girder on the upper side of the plastic neutral axis; Ass is the cross-sectional area of ​​the steel box girder below the plastic neutral axis; f co is the compressive strength of the lower edge of the LUHPC concrete slab.

[0078] In some embodiments, the connection between the steel box girder and the LUHPC concrete slab is reliable, the mid-span cross-section conforms to the flat cross-section assumption during bending, and the failure mode is characterized by tensile yielding of the steel box girder and crushing of the upper surface of the concrete slab. In the steel box-LUHPC composite beam, the stress distribution of the LUHPC concrete in the compression zone is triangular, accounting for the tensile effect of the concrete in the tension zone and the force of the longitudinal reinforcement in the concrete slab. The steel box girder in the tension zone yields as a whole, resulting in a rectangular stress distribution. When the neutral axis is located within the steel box girder, the stress distribution of the steel box girder in the compression zone is equivalent to a rectangular distribution, referring to existing specifications.

[0079] In this embodiment, the ratios of the calculation results obtained by using the calculation formula for the ultimate bending moment of the steel box-LUHPC composite beam to the test results are 0.998 and 0.983, respectively. This method can reasonably and accurately calculate the ultimate bending moment of the steel box-LUHPC composite beam and has good practical engineering application value.

[0080] In this example, see Figure 8 When conducting a loading test, the apparatus includes a specimen 1, a loading device 2, two supports 3, and a displacement meter 4. The two supports 3 are spaced apart along the length direction, and the specimen 1 is placed on the two supports 3. The loading device 2 is located between the two supports 3 and on the upper side of the specimen 1. The loading device 2 can apply a downward force to the specimen 1. Five displacement meters 4 are provided, two of which are located on the upper side of the specimen 1 and correspond to the abutment between the specimen 1 and the supports 3. The remaining three are located on the lower side of the specimen 1 and between the two supports 3. One of them is located in the middle of the specimen 1, and the other two correspond to the abutment between the loading device 2 and the specimen 1. The loading device 2 can apply a downward force to the specimen 1, and the displacement meter 4 can detect the displacement of the specimen 1.

[0081] In this example, see Figure 9 , and also includes multiple strain gauges, which are arranged on the outer side of the steel box-LUHPC composite beam (as shown by the triangle in the figure). The strain gauges can measure strain, thereby obtaining the strain value at each location of the steel box-LUHPC composite beam.

[0082] In order to better understand the present invention, the following Figures 1 to 11 The technical solution of the present invention is described in detail:

[0083] The experiment determines the axial tensile strength, axial compressive strength and uniaxial compression constitutive relationship of lightweight ultra-high performance concrete, carries out composite beam bending tests, and determines the position of the plastic neutral axis of the cross section when the steel box-LUHPC composite beam reaches the bending state. It is divided into the two cases where the plastic neutral axis is located in the LUHPC bridge deck and in the steel box beam. According to the two cases where the plastic neutral axis is located in the LUHPC bridge deck and in the steel box beam, the corresponding force diagram of the steel box-LUHPC composite beam cross section is proposed. When the plastic neutral axis is located in the LUHPC bridge deck, the stress distribution of the LUHPC concrete in the compression zone of the steel box-LUHPC composite beam is triangular, and the tensile effect of the concrete in the tension zone and the force effect of the longitudinal steel bars in the concrete slab are taken into account. The steel box beam in the tension zone yields as a whole, and the stress is rectangular. When the plastic neutral axis is located in the steel box beam, the stress distribution of the steel box beam in the compression zone is equivalent to a rectangular distribution with reference to the existing specifications, and the distance between the neutral axis and the upper surface of the LUHPC concrete slab is calculated according to the force balance equation. x， According to the section moment balance, the ultimate bending moment of the steel box-LUHPC composite beam can be obtained M。

[0084] In this application, the characteristics of LUHPC under compression and steel beam under tension in the bending state of the steel box-LUHPC composite beam can be considered, and the tensile effect of the LUHPC material can be taken into account to accurately determine the stress distribution characteristics of the mid-span section of the steel box-LUHPC composite beam. A method for determining the ultimate bending moment of the steel box-LUHPC composite beam is proposed, which can comprehensively consider the two neutral axis position distribution situations. For the two cases where the neutral axis is located inside the LUHPC bridge deck and inside the steel box beam, the ultimate bending moment of the steel box-LUHPC composite beam can be accurately determined. The ratios of the calculation results obtained by using the ultimate bending moment calculation formula of the steel box-LUHPC composite beam to the test results are 0.998 and 0.983, respectively. The ultimate bending moment of the steel box-LUHPC composite beam can be reasonably and accurately calculated, and it has good practical engineering application value.

[0085] This application focuses on the stress distribution characteristics of the steel box-LUHPC composite beam cross section, transforms the stress distribution of LUHPC concrete in the compression zone into a triangular distribution, and takes into account the tensile effect of concrete in the tension zone and the force of the longitudinal reinforcement in the concrete slab. A method for determining the ultimate bending moment of steel box-LUHPC composite beams is proposed, which provides a theoretical basis for the design and application of steel box-LUHPC composite beam bridges and offers technical support for promoting the application of LUHPC materials in bridge engineering.

[0086] The specific embodiments of the present invention described above do not limit the scope of protection of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the scope of protection of the claims of the present invention.

Claims

1. A method for calculating the ultimate bending moment of a steel box-LUHPC composite beam, characterized in that: It includes the following steps: Step 1: Clarify the material properties of LUHPC, conduct a four-point bending loading test on the composite beam, determine the failure mode of the steel box-LUHPC composite beam under bending, and determine the position of the plastic neutral axis of the cross section when the steel box-LUHPC composite beam reaches the ultimate bending state; Step 2: Based on the position of the plastic neutral axis, a force diagram of the steel box-LUHPC composite beam section is drawn, and a calculation formula for the ultimate bending moment of the steel box-LUHPC composite beam is established; Step 3: Compare and verify the calculation results obtained from the ultimate bending moment calculation formula of the steel box-LUHPC composite beam with the test results; Among them, when the cross-sectional stress distribution satisfies the formula: When , the plastic neutral axis is located inside the LUHPC bridge deck; when the cross-sectional stress distribution satisfies the formula: When , the plastic neutral axis is located inside the steel box girder; where, A c is the area of ​​LUHPC concrete slab; A r is the cross-sectional area of ​​the longitudinal reinforcement in the LUHPC concrete slab; A s is the cross-sectional area of ​​the steel box girder; f c is the axial compressive strength value of LUHPC material; f ry is the yield strength of the longitudinal reinforcement in the LUHPC concrete slab; f sy is the yield strength value of the steel box girder steel; When the plastic neutral axis is located in the LUHPC bridge deck, the stress distribution of the LUHPC concrete in the compression zone is triangular, and the tensile effect of the concrete in the tension zone and the force of the longitudinal reinforcement in the concrete slab are taken into account. The steel box girder in the tension zone yields as a whole and the stress is rectangular. When the plastic neutral axis is located in the steel box girder, the stress distribution of the steel box girder in the compression zone is equivalent to a rectangular distribution with reference to the existing specifications. The distance between the neutral axis and the upper surface of the LUHPC concrete slab is calculated according to the force balance equation. x； When the plastic neutral axis is located inside the LUHPC bridge deck, formula (1) is satisfied: （1） When the plastic neutral axis is located inside the steel box girder, formula (2) is satisfied: （2） Where, b c is the cross-sectional width of the LUHPC concrete slab; x is the distance between the plastic neutral axis and the upper surface of the LUHPC concrete slab; f t is the tensile strength of LUHPC concrete; A sc is the cross-sectional area of ​​the steel box girder on the plastic neutral axis, x Calculation can be obtained; h c is the cross-sectional height of the LUHPC concrete slab; According to the section moment balance, the ultimate bending moment of the steel box-LUHPC composite beam can be obtained M : When the plastic neutral axis is located inside the LUHPC bridge deck, M Satisfying formula (3): （3） When the plastic neutral axis is located inside the steel box girder, M Satisfying formula (4): （4） Where, y 1 is the distance from the resultant force position in the compression zone of the LUHPC concrete slab to the plastic neutral axis; y 2 is the distance from the centroid of the longitudinal reinforcement section to the plastic neutral axis in the LUHPC concrete slab; y 3 is the distance from the centroid of the tensile zone section of the LUHPC concrete slab to the plastic neutral axis; y 4 is the distance from the centroid of the steel box girder section to the plastic neutral axis; A cc is the cross-sectional area of ​​the LUHPC concrete slab above the plastic neutral axis; A cs is the cross-sectional area of ​​the LUHPC concrete slab below the plastic neutral axis; A sc is the cross-sectional area of ​​the steel box girder on the upper side of the plastic neutral axis; A ss is the cross-sectional area of ​​the steel box girder below the plastic neutral axis; f co is the compressive strength of the lower edge of the LUHPC concrete slab.

2. The method for calculating the ultimate bending moment of a steel box-LUHPC composite beam according to claim 1 is characterized in that: Step 1 specifically includes the following steps: experimentally determine the axial tensile strength, axial compressive strength and uniaxial compressive constitutive relationship of LUHPC, obtain relevant parameters of the specimen, carry out composite beam bending tests, and determine the position of the plastic neutral axis of the cross-section when the steel box-LUHPC composite beam reaches the ultimate bending state. Among them, there are two cases: the plastic neutral axis is located in the LUHPC bridge deck and in the steel box girder.

3. The method for calculating the ultimate bending moment of a steel box-LUHPC composite beam according to claim 1, characterized in that: The connection between the steel box girder and the LUHPC concrete slab is reliable. The mid-span section conforms to the flat section assumption during bending. The failure mode is characterized by tensile yielding of the steel box girder and crushing of the upper surface of the concrete slab.

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