Method for calculating ultimate bending moment of steel box-LUHPC composite beam

Abstract

The invention discloses a method for calculating the ultimate bending moment of a steel box-LUHPC composite beam. The method comprises the following steps: determining the material performance of the LUHPC, carrying out a four-point bending loading test of the composite beam, determining the failure mode of the steel box-LUHPC composite beam under the bending action, and judging the position of a section neutral axis when the steel box-LUHPC composite beam is bent to a state; according to the position of the plastic neutral shaft, a section stress action diagram of the steel box-LUHPC composite beam is made, and a calculation formula of the ultimate bending moment of the steel box-LUHPC composite beam is established; and comparing and checking a calculation result obtained by the calculation formula of the ultimate bending moment of the steel box-LUHPC composite beam with a test result. The method suitable for determining the ultimate bending moment of the steel box-LUHPC composite beam is provided, a theoretical basis is provided for design and application of the steel box-LUHPC composite beam bridge, and technical support is provided for promoting application of LUHPC materials in bridge engineering.

Description

Technical Field

[0001] The invention relates to the technical field of ultimate bending moment calculation of composite beams, and in particular to an ultimate bending moment calculation method for 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 stress performance, 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 are thick, heavy, and concrete in the negative bending zone is easy to crack, which restricts its further development. Therefore, reducing the deadweight 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. It has high strength (compressive strength ≥ 100MPa, splitting tensile strength ≥ 10MPa), low deadweight (apparent density ≤ 2100kg / m 3 ) and other characteristics, the LUHPC material is applied to the steel box-concrete composite bridge project to form a steel box-LUHPC composite beam, 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 prospect is 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 the concrete is calculated based on the force balance, fpyAp+2fybutu+fysAs=fybdtd+a1fc(b-hr)x(2a). The moment is taken at the equivalent rectangular resultant force point of the concrete in the compression zone to obtain the ultimate bending bearing capacity Mu of the shell beam.

[0004] However, the above-mentioned prior art 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 calculation of the ultimate bending moment of steel-concrete composite beams in my country's standards does not exceed 80MPa, so 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, so as to solve the technical problem that the calculation method of the shell beam in the prior art is not applicable to the steel box-LUHPC composite beam, and the compressive strength of the concrete specified in the ultimate bending moment calculation of the steel-concrete composite beam in the Chinese standard does not exceed 80MPa, so the ultimate bending moment calculation of the steel box-LUHPC composite beam 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: The present invention provides a method for calculating the ultimate bending moment of a steel box-LUHPC composite beam, comprising the following steps: Step 1: Clarify the material properties of LUHPC, carry out four-point bending loading test of composite beams, determine the failure mode of steel box-LUHPC composite beams under bending, and judge the position of the neutral axis of the cross section when the steel box-LUHPC composite beams reach the bending state; Step 2: According to 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.

[0007] In some embodiments, the steps are specifically included: 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 in the steel box beam.

[0008] In some embodiments, when the cross-sectional stress distribution satisfies the formula: When , the plastic neutral axis is located inside the LUHPC bridge deck; In the formula, 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.

[0009] In some embodiments, when the cross-sectional stress distribution satisfies the formula: When , the plastic neutral axis is located inside the steel box girder; In the formula, 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.

[0010] 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 action diagrams of the steel box-LUHPC composite beam section are proposed; 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 action of the concrete in the tension zone and the force action of the longitudinal steel bars 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. Calculate the neutral axis distance from the surface of the LUHPC concrete slab according to the force balance equation x .

[0011] In some embodiments, when the plastic neutral axis is located in 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) In the formula, 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, given by x Calculation available; h cis the cross-sectional height of LUHPC concrete slab.

[0012] In some embodiments, the ultimate bending moment of the steel box-LUHPC composite beam can be obtained based on the section moment balance: M : When the plastic neutral axis is located inside the LUHPC bridge deck, M Satisfies formula (3): (3) When the plastic neutral axis is located inside the steel box girder, M Satisfies formula (4): (4) In the formula, 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 cross section of the tension zone 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 on the upper side of 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.

[0013] 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.

[0014] 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, carries out 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 made, 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 checked with the test results. In this application, the ultimate bending moment calculation formula of the steel box-LUHPC composite beam can be considered to be the ultimate bending moment calculation formula of the steel box-LUHPC composite beam under the bending state. The characteristics of HPC under compression and steel beam under tension are taken into account, and the tensile effect of LUHPC materials is taken into account to accurately determine the stress distribution characteristics of the mid-span section of the steel box-LUHPC composite beam. A determination method suitable for 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 in the LUHPC bridge deck and in 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 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, which has good practical engineering application value.

[0015] This application aims at the stress distribution characteristics of the cross-section of the steel box-LUHPC composite beam, transforms the stress distribution of the LUHPC concrete in the compression zone into a triangular distribution, and takes into account the tensile effect of the concrete in the tension zone and the force effect of the longitudinal steel bars in the concrete slab, and proposes a method for determining the ultimate bending moment of the steel box-LUHPC composite beam, which provides a theoretical basis for the design and application of the steel box-LUHPC composite beam bridge and provides technical support for promoting the application of LUHPC materials in bridge engineering.

[0016] 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 implement it according to the contents of the specification, the preferred embodiments of the present invention are described in detail as follows with reference to the accompanying drawings. The specific implementation of the present invention is given in detail by the following embodiments and their accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of a method for calculating the ultimate bending moment of a steel box-LUHPC composite beam in one embodiment of the present invention; 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; Figure 3 It is a schematic diagram of the force and strain response of the plastic neutral axis located in the steel box girder of the present invention; Figure 4 It is a longitudinal schematic diagram of the test piece in the present invention; Figure 5 is a schematic cross-sectional view of the SLB-1 specimen of the present invention; Figure 6 is a schematic cross-sectional view of the SLB-2 specimen of the present invention; Figure 7 is a top view of the test piece of the present invention; Figure 8 It is a schematic diagram of the arrangement of the loading device of the present invention; Fig. 9 is the strain gauge distribution diagram of the present invention; Fig.10 is the load-mid-span deflection relationship curve of the SLB-1 specimen of the present invention; Fig.11 It is the load-mid-span deflection relationship curve of the SLB-2 specimen of the present invention.

[0018] Description of reference numerals: 1- specimen, 2- loading device, 3- support, 4- displacement meter. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with 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.

[0020] In order to solve the technical problem that the calculation method of the shell beam in the prior art is not applicable to the steel box-LUHPC composite beam, and the compressive strength of the concrete specified in the Chinese code 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 existing code calculation formula, 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 under the state is triangular distribution, 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, and 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 the steel box-LUHPC composite beam bridge and provides technical support for promoting the application of LUHPC materials in bridge engineering.

[0021] See also Figure 1 , Figure 1 The figure is a flow chart of a method for calculating the ultimate bending moment of a steel box-LUHPC composite beam in one embodiment of the present invention.

[0022] The present invention provides a method for calculating the ultimate bending moment of a steel box-LUHPC composite beam, comprising the following steps: Step 1: Clarify the material properties of LUHPC, carry out four-point bending loading test of composite beams, determine the failure mode of steel box-LUHPC composite beams under bending, and judge the position of the neutral axis of the cross section when the steel box-LUHPC composite beams reach the bending state; Step 2: According to 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.

[0023] 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 when the steel box-LUHPC composite beam reaches the bending state is judged; according to the position of the plastic neutral axis, a force diagram of the cross section of the steel box-LUHPC composite beam is made, 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 checked with the test results. In this application, the characteristics of LUHPC compression and steel beam tension under the bending state of the steel box-LUHPC composite beam can be considered. The tensile strength of LUHPC materials is taken into consideration, and 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 by 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.

[0024] In this example, see Figures 4 to 7First, two steel box-LUHPC composite beam specimens were designed and manufactured, numbered SLB-1 and SLB-2. The length of the two 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 beam and a bolt connector. The LUHPC concrete slab is fixedly installed on the upper side of the steel box beam through the bolt connector. Two layers of steel mesh are arranged in the LUHPC concrete slab from top to bottom. Each layer of the steel mesh includes a plurality of transverse steel bars and a plurality of longitudinal steel bars. The plurality of transverse steel bars are arranged at intervals along the transverse direction, and the plurality of longitudinal steel bars are arranged at intervals along the longitudinal direction. The plurality of transverse steel bars and the plurality of longitudinal steel bars are connected and fixed to each other. The steel box beam 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 the bolt connectors are arranged on the upper side of each T-shaped steel to connect with the LUHPC concrete slab.

[0025] 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.

[0026] 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.

[0027] 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 test, 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 which, it is divided into two cases: the plastic neutral axis is located in the LUHPC bridge deck and in the steel box beam.

[0028] In this embodiment, the position of the plastic neutral axis can be determined by calculation, and the calculation method is different when the plastic neutral axis is located at different positions. It can be divided into two cases, one of which 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 in the steel box girder, the ultimate bending moment of the steel box-LUHPC composite beam can be accurately determined.

[0029] In some embodiments, when the cross-sectional stress distribution satisfies the formula: When , the plastic neutral axis is located inside the LUHPC bridge deck; In the formula, 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.

[0030] In some embodiments, when the cross-sectional stress distribution satisfies the formula: When , the plastic neutral axis is located inside the steel box girder; In the formula, 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.

[0031] 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 action diagrams of the steel box-LUHPC composite beam section are proposed; 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 action of the concrete in the tension zone and the force action of the longitudinal steel bars 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. Calculate the neutral axis distance from the surface of the LUHPC concrete slab according to the force balance equation x .

[0032] In some embodiments, when the plastic neutral axis is located in 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) In the formula, 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, given by x Calculation available; h c is the cross-sectional height of LUHPC concrete slab.

[0033] In some embodiments, the ultimate bending moment of the steel box-LUHPC composite beam can be obtained based on the section moment balance: M : When the plastic neutral axis is located inside the LUHPC bridge deck, M Satisfies formula (3): (3) When the plastic neutral axis is located inside the steel box girder, M Satisfies formula (4): (4) In the formula, y 1 is the distance from the resultant force position in the compression zone of the LUHPC concrete slab to the plastic neutral axis; y2 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 cross section of the tension zone 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 on the upper side of 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.

[0034] In some embodiments, the connection between the steel box girder and the LUHPC concrete slab is reliable, the mid-span section during bending conforms to the flat section assumption, and the failure mode is characterized by the steel box girder yielding in tension and the upper surface of the concrete slab crushing. In the state of the steel box-LUHPC composite beam, 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 effect of the longitudinal steel bars 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 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.

[0035] In this embodiment, the ratios of the calculation result obtained by using the calculation formula for the ultimate bending moment of the steel box-LUHPC composite beam to the test result 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.

[0036] In this example, see Figure 8 , when carrying out a loading test, it includes a specimen 1, a loading device 2, two supports 3 and a displacement meter 4. The two supports 3 are arranged at intervals along the length direction. 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. There are five displacement meters 4, 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.

[0037] In this example, see Fig. 9, and also includes a plurality of 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 the strain, thereby obtaining the strain value at each location of the steel box-LUHPC composite beam.

[0038] 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: The experiment determines the axial tensile strength, axial compressive strength and uniaxial compressive 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 plastic neutral axis 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 steel box-LUHPC composite beam is in the state, and the stress distribution of the LUHPC concrete in the compression zone is triangular distribution, and the tensile action of the concrete in the tension zone and the force action 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 distribution; 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 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。

[0039] In the present application, the characteristics of LUHPC under compression and steel beam under tension under the bending state of the steel box-LUHPC composite beam can be considered, and the tensile effect of the LUHPC material can be considered to accurately determine the stress distribution characteristics of the mid-span section of the steel box-LUHPC composite beam, and a determination method suitable for the ultimate bending moment of the steel box-LUHPC composite beam is proposed. The two neutral axis position distributions can be fully considered. For the two cases where the neutral axis is located in the LUHPC bridge deck and in 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 the ultimate bending moment calculation formula of the steel box-LUHPC composite beam to the test results are 0.998 and 0.983 respectively, which can reasonably and accurately calculate the ultimate bending moment of the steel box-LUHPC composite beam and has good practical engineering application value.

[0040] This application aims at the stress distribution characteristics of the cross-section of the steel box-LUHPC composite beam, transforms the stress distribution of the LUHPC concrete in the compression zone into a triangular distribution, and takes into account the tensile effect of the concrete in the tension zone and the force effect of the longitudinal steel bars in the concrete slab, and proposes a method for determining the ultimate bending moment of the steel box-LUHPC composite beam, which provides a theoretical basis for the design and application of the steel box-LUHPC composite beam bridge and provides technical support for promoting the application of LUHPC materials in bridge engineering.

[0041] The specific implementation of the present invention described above does not constitute a limitation on the protection scope 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 protection scope 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, carry out four-point bending loading test of composite beams, determine the failure mode of steel box-LUHPC composite beams under bending, and judge the position of the neutral axis of the cross section when the steel box-LUHPC composite beams reach the bending state; Step 2: According to 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.

2. The method for calculating the ultimate bending moment of a steel box-LUHPC composite beam according to claim 1 is characterized in that: The specific steps include: The experiment determined the axial tensile strength, axial compressive strength and uniaxial compressive constitutive relationship of LUHPC, obtained the relevant parameters of the specimen, carried out composite beam bending tests, and determined the position of the plastic neutral axis of the cross-section when the steel box-LUHPC composite beam reached the bending state. There are two cases where 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 2 is characterized in that: When the cross-sectional stress distribution satisfies the formula: When , the plastic neutral axis is located inside the LUHPC bridge deck; In the formula, 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.

4. The method for calculating the ultimate bending moment of a steel box-LUHPC composite beam according to claim 2 is characterized in that: When the cross-sectional stress distribution satisfies the formula: When , the plastic neutral axis is located inside the steel box girder; In the formula, 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.

5. The method for calculating the ultimate bending moment of a steel box-LUHPC composite beam according to claim 2 is characterized in that: According to the two cases where the plastic neutral axis is located in the LUHPC bridge deck and the steel box girder, the corresponding force diagrams of the steel box-LUHPC composite beam section are proposed. 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 action of the concrete in the tension zone and the force action of the longitudinal steel bars 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. Calculate the neutral axis distance from the surface of the LUHPC concrete slab according to the force balance equation x .

6. The method for calculating the ultimate bending moment of a steel box-LUHPC composite beam according to claim 5, characterized in that: 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） In the formula, 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, given by x Calculation available; h c is the cross-sectional height of LUHPC concrete slab.

7. The method for calculating the ultimate bending moment of a steel box-LUHPC composite beam according to claim 6 is characterized in that: 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 Satisfies formula (3): （3） When the plastic neutral axis is located inside the steel box girder, M Satisfies formula (4): （4） In the formula, 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 cross section of the tension zone 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 on the upper side of 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.

8. The method for calculating the ultimate bending moment of a steel box-LUHPC composite beam according to claim 1 is characterized in that: 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. 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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