Method for calculating flexural capacity of hogging moment area of reinforced concrete composite beam reinforced based on UHPC (Ultra High Performance Concrete) thin layer

Abstract

The invention relates to a method for calculating the flexural capacity of a hogging moment area of a reinforced concrete composite beam based on a UHPC thin layer. The method comprises the steps that a test piece is prepared, measuring points are arranged, a load strain curve and a loading result graph of the test piece are obtained through a pressure loading test, and flexural performance characterization is determined. Determining an associated stress area of the composite beam according to the bending resistance characterization, presetting a first assumption condition, and performing derivation based on a strain expression, an internal force expression and a force balance equation to obtain a calculation expression of a cracking bending moment; presetting a second assumption condition, deducing and determining the position of a plastic neutral shaft, establishing a moment balance equation, and deducing according to the section strain expression, the internal force expression and the moment balance equation to obtain a calculation expression of the flexural capacity of the composite beam.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bridge engineering, and in particular to a method for calculating the flexural bearing capacity of a steel-concrete composite beam in the negative moment region based on UHPC thin layer reinforcement. BACKGROUND

[0002] In bridge engineering, steel-concrete composite beams are widely used as bridge structures due to their advantages of high efficiency, light weight, and convenient construction. However, during the stress process of the composite beam, especially in the negative moment region of the composite beam, cracks are prone to occur due to the weak tensile capacity of concrete and the invisible cracking, which changes the force transmission path and affects the overall stress performance and safety of the structure.

[0003] There is little research on the flexural performance of steel-concrete composite beams in the negative moment region in the prior art, and inaccurate analysis results of the flexural performance in the negative moment region will affect the load distribution of steel-concrete composite beams in actual engineering, and there is a problem of deviation of the uniform load assumption from the actual engineering, which leads to frequent local stress concentration in steel-concrete composite beams. Therefore, it is an urgent problem to be solved to accurately calculate the bearing capacity of steel-concrete composite beams by studying and analyzing the flexural performance of steel-concrete composite beams in the negative moment region. SUMMARY

[0004] The primary purpose of the present application is to solve at least one of the above problems and provide a method for calculating the flexural bearing capacity of a steel-concrete composite beam in the negative moment region based on UHPC thin layer reinforcement.

[0005] To achieve the purpose of the present application, the following technical solutions are adopted: A method for calculating the flexural bearing capacity of a steel-concrete composite beam in the negative moment region based on UHPC thin layer reinforcement is provided to achieve one of the purposes of the present application, comprising the following steps: Based on the steel-concrete composite beam formwork, test specimens are set up, and measurement points are arranged on the test specimens. Load-strain curves and loading result graphs of each test specimen are obtained through a pressure loading test. The flexural performance is determined according to the load-strain curves and the loading result graphs; The associated stress region of the crack formation process of the composite beam is determined according to the flexural performance. A first assumption condition for deriving the cracking moment calculation expression is preset. The expression of the composite beam cross-section strain is determined according to the crack formation process. The internal force expression and the force balance equation of the associated stress region are determined according to the first assumption condition. The strain expression, the internal force expression, and the force balance equation are used for derivation to obtain the calculation expression of the UHPC cracking moment and the calculation expression of the NC cracking moment; According to the influence of cracking stress hardening on the composite beam, a second assumption condition for deriving the bending resistance capacity calculation expression is preset, the position of the plastic neutral axis is determined based on the cross-section strain expression and the internal force expression, the moment balance equation is established according to different plastic neutral axis positions, and the bending resistance capacity calculation expression of the composite beam corresponding to different plastic neutral axis positions is derived based on the cross-section strain expression, the internal force expression and the moment balance equation.

[0006] In an optional embodiment, based on the steel-concrete composite beam formwork, test specimens are arranged, and specific measures are as follows: The test specimen reinforced by a UHPC thin layer is set as a target specimen, and the test specimen not reinforced by a UHPC thin layer is set as a control specimen; Linear variable differential transducers are arranged at the bottom of the beam length, the middle of the beam length, the support position and the beam end position of the test specimen, and the linear variable differential transducers are used to collect pressure loading test parameters and draw load-strain curves of the test specimen.

[0007] In an optional embodiment, the pressure loading test is as follows: The pressure loading test uses a press to apply loads in different stages, and the loads are transmitted to the test specimen through a distribution beam, and the pressure loading test includes the following stages: In the preloading stage, each test specimen is preloaded to a preset load; In the preliminary loading stage, after the preloaded load is zeroed, the load is applied from zero until the concrete layer of the test specimen cracks for the first time; In the ultimate loading stage, after the concrete layer cracks for the first time, the loading step and the loading rate are adjusted, and the monotonic loading is continued until the composite beam fails.

[0008] In an optional embodiment, the bending resistance performance characterization is as follows: According to the local instability of the steel beam and the tensile failure of the concrete indicated by the loading result graph and the load-strain curve, the bending resistance transfer relationship between the steel beam and the concrete is determined; According to the inhibitory effect of the interface anchorage on crack propagation indicated by the loading result graph and the load-strain curve, the bending resistance transfer relationship of the reinforcement to the interface shear deformation of the composite beam is determined; According to the inhibitory effect of the UHPC reinforcement on the crack propagation of the NC layer indicated by the loading result graph and the load-strain curve, the anti-cracking bearing bending resistance transfer relationship of the UHPC layer thickness to the composite beam is determined.

[0009] In an optional embodiment, the first assumption condition is as follows: The interface slip between the steel beam and the NC layer is minimum; and the interface slip between the UHPC layer and the NC layer is minimum. The strain distribution of the composite beam after the concrete cracks is calculated based on geometric relations; the influence of the transverse steel bars in the NC layer on the flexural capacity is ignored.

[0010] In an optional embodiment, an expression of the sectional strain of the composite beam is determined according to a crack formation process, an internal force expression and a force balance equation of the associated force region are determined according to a first assumption condition, and a calculation expression of the UHPC cracking moment is derived based on the strain expression, the internal force expression and the force balance equation, specifically as follows: For the UHPC layer cracking stage of the crack formation process, an expression of the strain corresponding to the target position of the UHPC layer section is proposed according to the fact that the tensile stress limit of the UHPC layer is close to the tensile strength of the UHPC layer. For the UHPC layer cracking stage of the crack formation process, the associated force region of the negative moment zone of the composite beam is determined to include the steel beam, the UHPC layer, the NC layer and the steel bars, and expressions of the internal forces of the steel beam, the UHPC layer, the NC layer and the steel bars and a force balance equation are proposed. The plastic neutral axis position corresponding to the UHPC layer cracking stage is derived by substituting the expressions of the internal forces into the strain expression, and the strain corresponding to the target position of each associated force region is calculated according to the plastic neutral axis position of the UHPC layer cracking stage. The internal forces of the associated force region and the distance between the internal forces of the associated force region and the plastic neutral axis position are calculated according to the strain corresponding to the target position of the force region of the UHPC layer cracking stage, the internal forces of the associated force region and the distance between the internal forces of the associated force region and the plastic neutral axis position are substituted into the force balance equation for derivation, and a calculation expression of the UHPC cracking moment of the UHPC layer cracking stage is obtained. The calculation expression of the UHPC cracking moment is expressed as:

[0011] In the formula, Mcr represents the UHPC cracking moment of the UHPC layer cracking stage, Msb represents the internal force of the steel beam of the composite beam at the UHPC layer cracking stage, Dsb represents the distance between the internal force of the steel beam of the composite beam at the UHPC layer cracking stage and the plastic neutral axis, Mnc represents the internal force of the NC layer of the composite beam at the UHPC layer cracking stage, Dnc represents the distance between the internal force of the NC layer of the composite beam at the UHPC layer cracking stage and the plastic neutral axis, Muh represents the internal force of the UHPC layer of the composite beam at the UHPC layer cracking stage, Duh represents the distance between the internal force of the UHPC layer of the composite beam at the UHPC layer cracking stage and the plastic neutral axis. an internal force of the steel bar representing the steel bar in the UHPC layer cracking stage of the composite beam, a distance between the internal force of the steel bar and the plastic neutral axis representing the steel bar in the UHPC layer cracking stage of the composite beam.

[0012] In an optional embodiment, an expression of a section strain of the composite beam is determined according to a crack formation process, an internal force expression and a force balance equation of an associated force area are determined according to a first assumption condition, and a calculation expression of the NC cracking moment is derived based on the strain expression, the internal force expression and the force balance equation, and specifically, the calculation expression of the NC cracking moment is derived by: For the NC layer cracking stage of the crack formation process, when the tensile stress limit of the NC layer is close to the tensile strength of the NC layer, a strain expression corresponding to a target position of the NC layer section is proposed; For the NC layer cracking stage, the internal force of the associated force area is calculated according to the strain expression corresponding to the target position of the NC layer section by substituting each internal force expression into the strain expression corresponding to the target position of the NC layer section, and the distance between the internal force of the associated force area and the plastic neutral axis position corresponding to the NC layer cracking stage is calculated according to the strain corresponding to the target position of the associated force area in the NC layer cracking stage; The internal force of the associated force area and the distance between the internal force of the associated force area and the plastic neutral axis position are substituted into the force balance equation to derive a calculation expression of the NC cracking moment in the NC layer cracking stage: The calculation expression of the NC cracking moment is represented as:

[0013] In the formula, an NC cracking moment of the composite beam in the NC layer cracking stage, an internal force of the steel beam representing the steel beam in the NC layer cracking stage of the composite beam, a distance between the internal force of the steel beam and the plastic neutral axis representing the steel beam in the NC layer cracking stage of the composite beam, an internal force of the UHPC layer representing the UHPC layer in the NC layer cracking stage of the composite beam, a distance between the internal force of the UHPC layer and the plastic neutral axis representing the UHPC layer in the NC layer cracking stage of the composite beam, an internal force of the NC layer representing the NC layer in the NC layer cracking stage of the composite beam, a distance between the internal force of the NC layer and the plastic neutral axis representing the NC layer in the NC layer cracking stage of the composite beam, an internal force of the steel bar representing the steel bar in the NC layer cracking stage of the composite beam.

[0014] In an optional embodiment, the second assumption condition is specifically: the interface slip between the steel beam and the NC layer is minimum; the interface slip between the UHPC layer and the NC layer is minimum; the shear lag effect of the concrete slab is ignored; the cross-sectional curvature of the concrete slab is the same as that of the steel beam; the influence of the transverse steel bars in the concrete slab on the flexural capacity is ignored; the strain distribution of the composite beam is calculated based on geometric relations; and the influence of the studs on the flexural capacity of the composite beam is ignored.

[0015] In an optional embodiment, the position of the plastic neutral axis is determined based on a cross-sectional strain expression and an internal force expression, a moment equilibrium equation is established according to different positions of the plastic neutral axis, and a calculation expression of the flexural capacity of the composite beam corresponding to different positions of the plastic neutral axis is derived based on the cross-sectional strain expression, the internal force expression and the moment equilibrium equation, including: For the composite beam in the stress hardening stage, a cross-sectional strain expression for solving the stress corresponding to the target position of the cross section is proposed, and the position of the plastic neutral axis and the cross-sectional bending curvature are solved based on the cross-sectional strain expression; When the plastic neutral axis is located in the concrete slab, a corresponding internal force expression and a first moment equilibrium equation are proposed according to the current stress-strain state analysis, the position of the plastic neutral axis and the cross-sectional bending curvature solved are substituted into the cross-sectional strain expression, and the cross-sectional stress of the composite beam at any position along the beam height and the stress distribution of each cross-sectional stress are determined; According to the cross-sectional stress and the stress distribution, the internal force of each stress region is calculated through the internal force expression, the distance between the internal force of each stress region and the plastic neutral axis is determined according to the position of the plastic neutral axis, the distance and the internal force size are substituted into the first moment equilibrium equation for derivation, and a first calculation expression of the flexural capacity of the UHPC thin layer reinforced steel-concrete composite beam when the plastic neutral axis is located in the concrete slab is obtained; The first calculation expression of the flexural capacity of the UHPC thin layer reinforced steel-concrete composite beam is expressed as:

[0016] In the formula, represents the flexural capacity of the composite beam in the stress hardening stage when the plastic neutral axis is located in the concrete slab, represents the internal force of the steel beam of the composite beam in the stress hardening stage, represents the distance between the internal force of the steel beam of the composite beam in the stress hardening stage and the plastic neutral axis located in the concrete slab, represents the internal force of the NC layer in compression in the stress hardening stage of the composite beam, represents the distance between the internal force of the NC layer in compression of the composite beam in the stress hardening stage and the plastic neutral axis located in the concrete slab, represents the internal force of the UHPC layer of the composite beam in the stress hardening stage, a distance between the internal force of the UHPC layer of the composite beam at the stress hardening stage and the plastic neutral axis located in the concrete slab, an internal force of the longitudinal reinforcement in the tension region of the composite beam at the stress hardening stage, a distance between the internal force of the longitudinal reinforcement in the tension region of the composite beam at the stress hardening stage and the plastic neutral axis located in the concrete slab.

[0017] In an optional embodiment, the plastic neutral axis position is determined based on the sectional strain expression and the internal force expression, the moment equilibrium equation is established according to different plastic neutral axis positions, and the calculation expression of the flexural capacity of the composite beam corresponding to different plastic neutral axis positions is obtained based on the sectional strain expression, the internal force expression and the moment equilibrium equation derivation, and further comprising: When the plastic neutral axis is located on the upper flange of the steel beam, the corresponding internal force expression and the second moment equilibrium equation are proposed according to the current stress-strain state analysis, the plastic neutral axis position and the sectional bending curvature obtained by solving are substituted into the sectional strain expression, and the sectional stress of the composite beam at any position along the beam height and the stress distribution of each sectional stress are determined; According to the sectional stress and the stress distribution, the internal force size of each stress region is calculated through the internal force expression, the distance between the internal force of each stress region and the plastic neutral axis is determined according to the plastic neutral axis position, the distance and the internal force size are substituted into the second moment equilibrium equation for derivation, and the second calculation expression of the flexural capacity of the UHPC thin layer reinforced steel-concrete composite beam when the plastic neutral axis is located on the upper flange of the steel beam is obtained; The second calculation expression of the flexural capacity of the UHPC thin layer reinforced steel-concrete composite beam is expressed as:

[0018] In the formula, the flexural capacity of the UHPC thin layer reinforced steel-concrete composite beam when the plastic neutral axis is located on the upper flange of the steel beam at the stress hardening stage of the composite beam, the internal force of the UHPC layer of the composite beam at the stress hardening stage, the internal force of the longitudinal reinforcement in the tension region corresponding to the plastic neutral axis located on the upper flange of the steel beam at the stress hardening stage of the composite beam, the internal force of the tension region on the upper flange of the steel beam at the stress hardening stage of the composite beam, the internal force of the compression region of the steel beam at the stress hardening stage, the distance between the internal force of the tension region on the upper flange of the steel beam at the stress hardening stage of the composite beam and the plastic neutral axis located on the upper flange of the steel beam, the distance between the internal force of the compression region of the steel beam at the stress hardening stage of the composite beam and the plastic neutral axis located on the upper flange of the steel beam, a distance between the internal force of the UHPC layer in the stress hardening stage of the composite beam and the plastic neutral axis located at the upper flange of the steel beam, a distance between the internal force of the longitudinal steel in the tension region and the plastic neutral axis located at the upper flange of the steel beam.

[0019] In another aspect, a device for calculating the flexural capacity of the negative moment region of a UHPC thin layer reinforced steel-concrete composite beam is provided for one of the purposes of the present application, comprising a central processing unit and a memory, wherein the central processing unit is configured to invoke a computer program stored in the memory to execute the steps of the method for calculating the flexural capacity of the negative moment region of a UHPC thin layer reinforced steel-concrete composite beam as described in the present application.

[0020] In another aspect, a computer readable storage medium is provided for one of the purposes of the present application, wherein the computer readable storage medium stores computer executable instructions for causing a computer to execute the method for calculating the flexural capacity of the negative moment region of a UHPC thin layer reinforced steel-concrete composite beam as described in any one of the first aspect of the present application.

[0021] The technical solution of the present application has multiple advantages, including but not limited to the following aspects: Firstly, based on the steel-concrete composite beam formwork, the present application sets up test specimens and sets up a control group, collects parameters in the process of pressure loading test through the arrangement of measuring points, analyzes the force transmission performance of the negative moment region of the UHPC thin layer reinforced steel-concrete composite beam according to the load strain curve of the test parameters and the result graph of the pressure loading test, determines the stress state and force transmission path of the negative moment region of the composite beam in the actual bearing process, and thus provides an analysis basis of the force transmission mechanism for the calculation of the bearing performance of the negative moment region of the composite beam, ensuring the accuracy of the subsequent bearing performance calculation results.

[0022] Secondly, the present application considers the cracking formation process of the composite beam under the action of negative moment, determines the stress region related to the cracking moment according to the analysis-determined performance of the bending resistance, sets up a first assumed condition for the influence of the cracking formation process on the composite beam in order to facilitate the derivation of the calculation of the cracking moment, respectively solves the corresponding section strain of the UHPC layer cracking stage and the NC layer cracking stage through the target section strain expression of the cracking formation process, calculates the internal force of the stress region according to the section strain, and finally calculates the cracking moment of the UHPC layer and the NC layer according to the distance between the internal force and the plastic neutral axis, which can express the bearing performance of the composite beam in the cracking formation process through the cracking moment, and can be used as a reference for the bearing performance evaluation in the design stage of the composite beam, thereby reducing the deviation of the load distribution of the steel-concrete composite beam from the actual engineering demand, and further improving the accuracy of the bearing performance evaluation of the steel-concrete composite beam.

[0023] Finally, the present application considers the influence of stress hardening phenomenon of the composite beam after the UHPC cracking on the flexural capacity of the composite beam, in order to facilitate the derivation of the calculation of the flexural capacity of the composite beam, the second assumption condition of the influence of the stress hardening process on the composite beam is set, the influence of the different plastic neutral axis positions in the stress hardening stage on the calculation of the flexural capacity is considered, the plastic neutral axis positions in the stress hardening stage are divided into the concrete slab and the steel beam upper flange for the evaluation of the flexural capacity calculation expression, the plastic neutral axis position and the sectional bending curvature are obtained by solving the internal force expression of the composite beam in the stress hardening stage and the sectional strain expression corresponding to the target position of the section, the plastic neutral axis position and the sectional bending curvature are substituted into the strain expression corresponding to the target position of the section, the plastic strain corresponding to the arbitrary beam height position of the composite beam is solved, and the plastic strain corresponding to the beam height position is substituted into the internal force expression of the composite beam in the stress hardening stage, the internal force corresponding to each stress region is solved, and the internal force and moment balance equation of each stress region are derived, and then the first calculation expression of the flexural capacity of the composite beam corresponding to the plastic neutral axis located in the concrete slab is obtained, and the second calculation expression of the flexural capacity of the composite beam corresponding to the plastic neutral axis located in the steel beam upper flange is obtained, the flexural capacity expression of the composite beam in the stress hardening process can be used to evaluate the bearing capacity of the composite beam in the design stage, so as to reduce the deviation of the load distribution of the steel-concrete composite beam from the actual engineering demand, and to improve the accuracy of the bearing capacity evaluation of the steel-concrete composite beam. BRIEF DESCRIPTION OF DRAWINGS

[0024] The above and / or additional aspects and advantages of the present application will become apparent and more readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings, in which: Figure 1 A flow chart of an embodiment of the present application based on the UHPC thin layer reinforced steel-concrete composite beam negative moment zone flexural capacity calculation method; Figure 2 A structural schematic diagram of an exemplary UHPC thin layer reinforced steel-concrete composite beam in the present application; Figure 3 A sectional structural schematic diagram of an exemplary target specimen in the present application; Figure 4 A measurement point layout diagram of an exemplary specimen in the present application; Figure 5 A cracking test result diagram of an exemplary target specimen numbered SN-U0-SO-WO in the present application; Figure 6 A cracking test result diagram of an exemplary target specimen numbered SUN-U35-SO-WO in the present application; Figure 7A cracking test result graph for an example target test piece numbered SUN-U50-SO-WO in the present application; Figure 8 A cracking test result graph for a control test piece numbered SUN-U35-S450-WO in the present application; Figure 9 A cracking test result graph for an example target test piece numbered SUN-U35-S30O-WO in the present application; Figure 10 A cracking test result graph for an example target test piece numbered SUN-U35-S45O-W1 in the present application; Figure 11 A load-strain curve recorded by an LVDT in a pressure loading test of an example test piece in the present application; Figure 12 A stress-strain analysis graph of an example UHPC thin-layer reinforced steel-concrete composite beam under negative bending moment in the present application; Figure 13 A stress-strain analysis graph corresponding to the plastic neutral axis located in the concrete slab of an example UHPC thin-layer reinforced steel-concrete composite beam under negative bending moment in the present application; Figure 14 A stress-strain analysis graph corresponding to the plastic neutral axis located in the top flange of the steel beam of an example UHPC thin-layer reinforced steel-concrete composite beam under negative bending moment in the present application. DETAILED DESCRIPTION

[0025] The technical solution of the present application is applicable to the field of bridge engineering, and is particularly applicable to the design, detection and maintenance of highway bridges, railway bridges or other long-span steel-concrete composite beam structures. In this context, as shown in Figure 2 , the technical solution of the present application can be applied in a typical UHPC thin-layer reinforced steel-concrete composite beam.

[0026] In bridge engineering, steel-concrete composite beams are widely used as bridge structures due to their advantages of high efficiency, light weight and convenient construction. However, in the stress process of the composite beam, especially in the negative bending moment area of the composite beam, cracks are prone to occur due to the weak tensile capacity of concrete and invisible cracking, which changes the force transmission path and affects the overall stress performance and safety of the structure.

[0027] The analysis of the bending resistance performance of the steel-concrete composite beam in the negative bending moment zone in the prior art is less, and the analysis result of the bending resistance performance in the negative bending moment zone is inaccurate, which will affect the load distribution of the steel-concrete composite beam in the actual engineering, there is a problem that the assumption of uniform load deviates from the actual engineering, and the local stress concentration phenomenon of the steel-concrete composite beam occurs frequently, therefore, it is an urgent problem to be solved to analyze the bending resistance performance of the steel-concrete composite beam in the negative bending moment zone to accurately calculate the bearing capacity of the steel-concrete composite beam.

[0028] To solve the problem of inaccurate calculation of the bearing capacity of the steel-concrete composite beam caused by the insufficient analysis of the bending resistance performance of the steel-concrete composite beam in the negative bending moment zone, the technical scheme provided by the embodiments of the present application has the following general idea: Based on the steel-concrete composite beam template, the test specimen is set, the pressure loading test is designed, and the test data is collected through the sensor, the bending resistance performance of the UHPC thin layer reinforced steel-concrete composite beam is analyzed according to the test result graph and the test data, the force transmission path related to the overall stress performance of the composite beam structure under the action of the negative bending moment is determined, and then the theoretical basis of the force transmission mechanism for the calculation of the bearing capacity in the negative bending moment zone is provided; considering the cracking formation process of the composite beam under the action of the negative bending moment, the first assumption condition is used to deduce the cracking moment, and the UHPC layer cracking moment and the NC layer cracking moment are deduced by calculating the stress, internal force and plastic neutral axis position; considering the influence of the stress hardening phenomenon of the composite beam after the UHPC cracking on the bending resistance bearing capacity of the composite beam, the second assumption condition is used to deduce the bending resistance bearing capacity, and the calculation expression of the bending resistance bearing capacity of the UHPC thin layer reinforced steel-concrete composite beam corresponding to different plastic neutral axis positions is deduced by calculating the stress, internal force and plastic neutral axis position.

[0029] In order to better understand the above technical scheme, the above technical scheme will be described in detail in combination with the drawings of the specification and the specific embodiments.

[0030] The specific embodiments below can be combined with each other, and the same or similar concepts or processes will not be described again in some embodiments. The embodiments of the present application will be described below in combination with the drawings.

[0031] Referring to Figure 1 The present application discloses a method for calculating the bending resistance bearing capacity of the negative bending moment zone of the UHPC thin layer reinforced steel-concrete composite beam, which comprises the following steps: 110. Based on the steel-concrete composite beam template, the test specimen is set, the test specimen is arranged, the load strain curve and the loading result graph of each test specimen are obtained through the pressure loading test, and the bending resistance performance is determined according to the load strain curve and the loading result graph; As an example, please refer to Figure 3In the prior art, five UHPC thin layer reinforced steel-concrete composite beams are obtained by using UHPC thin layer to reinforce the steel-concrete composite beam, and one ordinary test specimen without UHPC thin layer reinforcement is designed as a control specimen, wherein the ordinary test specimen without UHPC thin layer reinforcement is numbered as SUN-U35-S450-W0. It can be understood that the steel-concrete composite beam is a composite structure combining the advantages of steel and concrete, which is connected by shear connectors (such as studs, channel steel, bent bars, etc.) to form a whole with the steel beam and the concrete slab (or concrete flange) to bear the load together. This structure is widely used in bridges, floor slabs, platforms and other engineering projects, and has high strength, high stiffness and good seismic performance. UHPC is a cement-based composite material with excellent performance, which is optimized in material composition and process to have excellent strength, durability and construction flexibility. UHPC has very high compressive strength and bending strength, which is usually two to three times that of traditional concrete, so it can bear larger load and deformation. The test specimen in the present application is not a new steel-concrete composite beam structure designed independently, but is set as a test specimen based on the existing steel-concrete composite beam structure, so as to study the bending resistance of the steel-concrete composite beam in the negative moment area, and to provide a method for calculating the bending resistance of the steel-concrete composite beam in the negative moment area.

[0032] Please refer to Figure 4 In specific implementation, a linear variable differential transducer (LVDT) numbered V1 is installed at the bottom of the midspan of the test specimen, a linear variable differential transducer numbered V2 is installed at the bottom of the 1 / 4 beam length of the test specimen, and a linear variable differential transducer numbered V3 is installed at the bottom of the 3 / 4 beam length of the test specimen, wherein the linear variable differential transducers numbered V1, V2 and V3 are used to record the vertical deflection of the test specimen. A linear variable differential transducer numbered H1 is installed at the support position of the 1 / 4 beam length of the test specimen, and a linear variable differential transducer numbered H2 is installed at the support position of the 3 / 4 beam length of the test specimen, wherein the linear variable differential transducers numbered H1 and H2 are used to measure the interface slip between the UHPC layer and the NC layer, and the NC layer represents the concrete layer. A linear variable differential transducer numbered H3 is installed at the beam end position of the test specimen, wherein the linear variable differential transducer numbered H3 is used to measure the interface slip between the concrete layer bridge deck and the steel beam.

[0033] In specific implementation, the pressure loading test uses a press to apply load, and the load is transmitted to the test specimen through a distribution beam. The pressure loading test includes: Preloading stage, preloading each test specimen to a preset load; Optionally, the size of the preset load is set to 50kN, which can eliminate the defects and errors that may exist in the test equipment and ensure the accuracy of the test results.

[0034] In the preliminary loading stage, the preloaded load is zeroed, and loading is started from zero until the concrete layer of the test specimen first cracks; Optionally, the preliminary loading stage adopts a monotonic loading method, and the constant loading rate is 0.2kN / s. Generally, the load at the first cracking of the concrete layer is 20%Peu, and Peu is the ultimate bearing capacity predicted by the finite element simulation.

[0035] In the ultimate loading stage, after the concrete layer first cracks, the loading step is adjusted to 5%Peu, the loading rate is adjusted to 0.5kN / s, and monotonic loading is continued until the composite beam fails.

[0036] Optionally, for each loading step, the load is maintained for 5 minutes to ensure that the deflection and cracks of the composite beam develop fully.

[0037] Optionally, fixed hinge supports and sliding hinge supports are respectively arranged at both ends of the test specimen beam, and the bottom of the support is treated with gypsum leveling to adjust the test specimen to ensure that the test beam is horizontal.

[0038] As an example, please refer to Figures 5 to 10 , according to Figures 5 to 10 the crack pattern exhibited by the six test specimens, the cracking mode of the concrete changes significantly with the test parameters, especially under the action of negative bending moment, the five test specimens reinforced with UHPC have a relatively wide main crack on the surface of the UHPC reinforcement layer, and shear failure occurs in the NC layer. However, the test specimen numbered SUN-U35-S450-W0, which is not reinforced with UHPC, has a large number of fine main cracks on the surface of the composite slab, and no shear failure occurs. The five steel-concrete test specimens reinforced with UHPC have multiple peeling cracks at the UHPC-NC interface on the side of the slab.

[0039] As an example, please refer to Figure 11 , wherein Figure 11 the load-strain curve is the load-strain curve of the lower flange of the test specimen I-shaped steel beam. According to the load-strain curve, the steel beam strain follows a linear strain distribution in the elastic stage, and enters the plastic stage after the steel flange yields. Among them, except for the test specimen (numbered SUN-U35-S450-W0) not reinforced with UHPC, the maximum strain measured by the other five target specimens is about-9000 , while the maximum strain measured by the control specimen numbered SUN-U35-S450-W0 is about-2900 , which are far beyond the yield strain of Q345C steel, indicating that the steel beam as a component of the composite beam has fully developed the material properties in the pressure loading test, and the test specimen of the pressure loading test is fully compressed, and the strain of the steel beam component of the composite beam is calculated based on the load-strain curve and the loading result of the pressure loading test. Figure 11 It can be seen that the interface shear reinforcement has little effect on the steel beam component of the composite beam, and the use of UHPC reinforcement and the configuration of anti-cracking steel wire mesh can effectively reduce the strain of the steel beam component of the composite beam, indicating that UHPC can delay the yield of the steel beam.

[0040] Specifically, according to the load-strain curve and the loading result of the pressure loading test, the load bending performance of the steel-concrete composite beam in the negative bending moment area includes four aspects. In the first aspect of the bending performance, the buckling of the steel beam upper flange indicates local instability of the steel beam, and the bottom crack of the concrete slab indicates that the bending tensile stress of the concrete is beyond the limit, indicating that the instability of the steel beam and the tensile failure of the concrete occur synchronously, and the synergy is fully developed. In the second aspect of the bending performance, the interface planting has a certain inhibitory effect on the crack propagation of the concrete bottom plate, because the interface shear reinforcement of the UHPC-NC interface can constrain the shear deformation of the UHPC and NC interface, reduce the interface slip, and thus reduce the stress concentration phenomenon at the interface. In the third aspect of the bending performance, UHPC reinforcement has an inhibitory effect on the crack propagation of the NC layer of the steel-concrete composite beam, and the greater the thickness of the UHPC, the better the inhibitory effect. In the fourth aspect of the bending performance, the configuration of the anti-cracking steel wire mesh can effectively delay the generation of cracks and block the crack propagation.

[0041] 210、According to the bending performance characterization, determine the associated stress area of the crack formation process of the composite beam, preset the first assumption condition of the derivation of the cracking moment calculation expression, determine the strain expression of the target section of the composite beam according to the crack formation process, determine the internal force expression and force balance equation of the associated stress area according to the assumption condition, and derive the calculation expression of the UHPC cracking moment of the composite beam in the UHPC layer cracking stage and the calculation expression of the NC cracking moment of the composite beam in the NC layer cracking stage based on the strain expression, the internal force expression and the force balance equation; In specific implementation, the first assumption condition includes: the interface slip between the steel beam and the NC layer is minimum; the interface slip between the UHPC layer and the NC layer is minimum; after the concrete cracks, the strain distribution of the composite beam is calculated based on the geometric relationship; the influence of the transverse steel bars in the NC layer on the bending resistance capacity is ignored.

[0042] It needs to be explained that due to the dominant role of longitudinal steel in the NC layer, the ultimate bearing capacity of the composite beam under the action of negative bending moment is not significant when the UHPC reinforcing layer is used. On the other hand, the UHPC reinforcing layer improves the crack resistance of the composite beam, and the UHPC-NC bridge deck will go through three stages in the crack formation process, among which the first stage is the stage before crack formation, the second stage is the UHPC layer cracking stage, and the third stage is the NC layer cracking stage. In order to evaluate the crack resistance of the composite beam, the crack formation process and the assumed conditions can be used as the basis for expression derivation, so as to consider the influence of the constraint of the UHPC reinforcing layer and the crack bridging effect of the steel fiber.

[0043] Specifically, please refer to Figure 12 , the use of UHPC thin layer to reinforce the steel-concrete composite beam can significantly improve the cracking moment of the composite beam. In order to accurately calculate the cracking moment of the steel-concrete composite beam reinforced by UHPC thin layer, based on the observed crack development law, the composite beam is analyzed elastically and plastically, and the calculation expression of the cracking moment of the UHPC reinforced steel-concrete composite beam considering the influence of steel fiber is derived, as shown in Figure 12 , the analysis diagram of the UHPC thin layer reinforced steel-concrete composite beam under the action of negative bending moment, Figure 12 It can be seen that the plastic neutral axis of the UHPC reinforcing layer before cracking is located in the upper flange of the steel beam. At the beginning of the crack formation process (i.e. the second stage of the crack formation of the UHPC-NC bridge deck), the UHPC layer will crack first. When the tensile stress limit in the UHPC layer approaches the tensile strength of the UHPC layer, the strain corresponding to the target position of the UHPC layer section can be determined. In specific implementation, the strain expression of the target position of the UHPC layer section in the UHPC layer cracking stage of the composite beam is:

[0044] In the formula, , the strain of the target position of the UHPC layer section in the UHPC layer cracking stage of the composite beam, , the distance between the target position and the plastic neutral axis, k represents the bending curvature of the section, , the distance between the vertex of the UHPC layer and the plastic neutral axis, , the elastic limit strain of the UHPC layer, wherein , can be expressed as , , the tensile strength of the UHPC layer, , the elastic modulus of the UHPC layer.

[0045] Specifically, based on the flexural performance characterization, the associated stress areas bearing the load in the negative bending moment zone of the composite beam can be determined, including the steel beam, the UHPC layer, the NC layer, and the reinforcing steel. Figure 12 The analysis diagram under negative bending moment can determine the internal force expressions of the steel beam, UHPC layer, NC layer and reinforcement, and then derive the force balance equation of the cracking stage of UHPC layer.

[0046] In practical implementation, the internal force expression of the steel beam during the cracking stage of the UHPC layer in the composite beam is as follows:

[0047] In the formula, This represents the internal forces in the steel beams of the composite beam during the cracking stage of the UHPC layer. This indicates the elastic modulus of steel. This represents the strain in the compression zone of the upper flange of the steel beam. This indicates the transverse width of the upper flange of the steel beam. This indicates the vertical thickness of the compression zone on the upper flange of the steel beam. This represents the strain in the tension zone of the upper flange of the steel beam. This indicates the vertical thickness of the tension zone of the upper flange of the steel beam. This represents the strain in the web of the steel beam. This indicates the transverse width of the web of the steel beam. This indicates the vertical thickness of the web of the steel beam. This represents the strain in the lower flange of the steel beam. This indicates the transverse width of the lower flange of the steel beam. This indicates the vertical thickness of the lower flange of the steel beam.

[0048] In practical implementation, the expression for the internal forces of the UHPC layer during the cracking stage of the composite beam is as follows:

[0049] In the formula, This represents the internal forces in the UHPC layer during the cracking stage of the composite beam. This represents the crack bridging coefficient of steel fiber reinforced plastic. Indicates the width of the concrete slab. Indicates the vertical thickness of the UHPC layer. This indicates the tensile strength of the UHPC layer.

[0050] Optionally, the expression for the crack bridging coefficient of steel fiber is:

[0051] In the formula, This represents the crack bridging coefficient of steel fiber reinforced plastic. This represents the plasticity parameter, which is typically set to 0.35. This indicates the volume ratio of steel fibers. Indicates the length of the steel fiber. This indicates the diameter of the steel fiber.

[0052] In practical implementation, the expression for the internal forces in the NC layer of the composite beam during the cracking stage of the UHPC layer is as follows:

[0053] In the formula, This represents the internal forces in the NC layer of the composite beam during the cracking stage of the UHPC layer. Indicates the width of the concrete slab. Indicates the vertical thickness of the NC layer. This represents the elastic modulus of the NC layer. Indicates the strain of the NC layer. This represents the tensile strain of the NC layer.

[0054] In practical implementation, the expression for the internal force of the reinforcement in the composite beam during the cracking stage of the UHPC layer is as follows:

[0055] In the formula, This represents the internal force of the reinforcement in the composite beam during the cracking stage of the UHPC layer. This indicates the elastic modulus of steel. Indicates the strain of the reinforcing steel. This indicates the total area of ​​the reinforcing steel bars.

[0056] In practical implementation, the force balance equation of the composite beam during the cracking stage of the UHPC layer is expressed as:

[0057] In the formula, This represents the internal forces in the steel beam of the composite beam during the cracking stage of the UHPC layer. This represents the internal forces in the NC layer of the composite beam during the cracking stage of the UHPC layer. This represents the internal forces in the UHPC layer during the cracking stage of the composite beam. This represents the internal force of the reinforcement in the composite beam during the cracking stage of the UHPC layer.

[0058] In practical implementation, the position of the plastic neutral axis is determined by deriving the internal force expression of the associated stress region. The distance between the internal force of each associated stress region and the plastic neutral axis is calculated based on the position of the plastic neutral axis. The distance between the internal force and the plastic neutral axis is substituted into the force balance equation of the UHPC layer cracking stage to obtain the calculation expression of the UHPC cracking moment of the composite beam in the UHPC layer cracking stage. Specifically, the calculation expression of the UHPC cracking moment of the composite beam at the UHPC cracking stage is expressed as:

[0059] In the formula, represents the UHPC cracking moment at the UHPC cracking stage, represents the internal force of the steel beam of the composite beam at the UHPC cracking stage, represents the distance between the internal force of the steel beam of the composite beam at the UHPC cracking stage and the plastic neutral axis, represents the internal force of the NC layer of the composite beam at the UHPC cracking stage, represents the distance between the internal force of the NC layer of the composite beam at the UHPC cracking stage and the plastic neutral axis, represents the internal force of the UHPC layer of the composite beam at the UHPC cracking stage, represents the distance between the internal force of the UHPC layer of the composite beam at the UHPC cracking stage and the plastic neutral axis, represents the internal force of the steel bar of the composite beam at the UHPC cracking stage, represents the distance between the internal force of the steel bar of the composite beam at the UHPC cracking stage and the plastic neutral axis.

[0060] Subsequently, after the crack formation process enters the second stage (i.e., the UHPC layer cracks), the position of the plastic neutral axis of the section moves to the web of the steel beam, and when the peak tensile stress of the NC layer approaches the tensile strength of the NC layer, the crack formation process is ready to enter the third stage (i.e., the NC layer first cracks), at this time, the strain corresponding to the target position of the section of the composite beam at the NC cracking stage is expressed as:

[0061] In the formula, represents the strain corresponding to the target section of the composite beam at the NC cracking stage, k represents the bending curvature of the section, represents the distance between the target position and the plastic neutral axis, represents the elastic limit strain of the NC layer, can be expressed as , wherein represents the tensile strength of the NC layer, represents the elastic modulus of the NC layer, represents the distance between the vertex of the UHPC layer and the plastic neutral axis, represents the vertical thickness of the UHPC layer.

[0062] Specifically, according to the stress distribution shown in Figure 11 , the internal force expression of each related force area at the NC cracking stage is proposed.

[0063] In a specific implementation, the internal force expression of the steel beam in the NC layer cracking stage of the composite beam is:

[0064] wherein, represents the internal force of the steel beam in the NC layer cracking stage of the composite beam, represents the elastic modulus of the steel material, represents the total strain of the steel beam, represents the transverse width of the upper flange of the steel beam, represents the total vertical thickness of the steel beam, represents the strain of the tensile region of the web of the steel beam, represents the transverse width of the web of the steel beam, represents the distance between the top of the web of the steel beam and the plastic neutral axis, represents the strain of the compressive region of the web of the steel beam, represents the transverse width of the web of the steel beam, represents the distance between the bottom of the web of the steel beam and the plastic neutral axis, represents the strain of the lower flange of the steel beam, represents the transverse width of the lower flange of the steel beam, represents the vertical thickness of the lower flange of the steel beam.

[0065] In a specific implementation, the internal force expression of the UHPC layer in the NC layer cracking stage of the composite beam is:

[0066] wherein, represents the internal force of the UHPC layer in the NC layer cracking stage of the composite beam, represents the steel fiber crack bridging coefficient, represents the width of the concrete slab, represents the vertical thickness of the UHPC layer, represents the tensile strength of the UHPC layer.

[0067] In a specific implementation, the internal force expression of the NC layer in the NC layer cracking stage of the composite beam is:

[0068] wherein, represents the internal force of the NC layer in the NC layer cracking stage of the composite beam, represents the tensile strength of the NC layer, represents the width of the concrete slab, represents the vertical thickness of the NC layer.

[0069] In a specific implementation, the internal force expression of the steel bar in the NC layer cracking stage of the composite beam is:

[0070] wherein, represents the internal force of the steel beam in the NC cracking stage of the composite beam, represents the elastic modulus of the steel material, represents the strain of the steel bar, represents the total area of the steel bar.

[0071] In the specific implementation, the force balance equation of the composite beam in the NC cracking stage is represented as:

[0072] wherein, represents the internal force of the steel beam in the NC cracking stage of the composite beam, represents the internal force of the UHPC layer in the NC cracking stage of the composite beam, represents the internal force of the NC layer in the NC cracking stage of the composite beam, represents the internal force of the steel bar in the NC cracking stage of the composite beam.

[0073] In the specific implementation, the position of the plastic neutral axis in the NC cracking stage is determined according to the internal force expression of each associated force area in the NC cracking stage of the composite beam, the distance between the internal force and the plastic neutral axis of each associated force area is calculated according to the position of the plastic neutral axis, the distance between the internal force and the plastic neutral axis is substituted into the force balance equation in the NC cracking stage to obtain the calculation expression of the NC cracking moment in the NC cracking stage of the composite beam; the NC cracking moment is the cracking moment corresponding to the first cracking of the NC layer.

[0074] Specifically, the calculation expression of the NC cracking moment in the NC cracking stage of the composite beam is represented as:

[0075] wherein, represents the NC cracking moment in the NC cracking stage of the composite beam, represents the internal force of the steel beam in the NC cracking stage of the composite beam, represents the distance between the internal force of the steel beam and the plastic neutral axis in the NC cracking stage of the composite beam, represents the internal force of the UHPC layer in the NC cracking stage of the composite beam, represents the distance between the internal force of the UHPC layer and the plastic neutral axis in the NC cracking stage of the composite beam, represents the internal force of the NC layer in the NC cracking stage of the composite beam, represents the distance between the internal force of the NC layer and the plastic neutral axis in the NC cracking stage of the composite beam, represents the internal force of the steel bar in the NC cracking stage of the composite beam.

[0076] 310、According to the second assumed condition of deriving the preset calculation expression of the flexural capacity based on the cracking stress hardening effect, the position of the plastic neutral axis is determined based on the sectional strain expression and the internal force expression, the moment equilibrium equation is established according to different positions of the plastic neutral axis, and the calculation expression of the flexural capacity of the composite beam corresponding to different positions of the plastic neutral axis is derived according to the sectional strain expression, the internal force expression and the moment equilibrium equation.

[0077] It should be noted that, since the UHPC still has stress hardening phenomenon after cracking, the influence of the UHPC layer on the flexural capacity of the composite beam after cracking is still considered when deriving the flexural capacity formula, and therefore the second assumed condition is set, and the following calculation process is used to solve the flexural capacity based on the second assumed condition: firstly, it is assumed that the failure of the composite beam is dominated by the steel beam, and the sectional curvature in the elastic stage is calculated accordingly; secondly, the sectional strain and stress distribution are derived according to the curvature equation; thirdly, the internal force of each stress region is calculated respectively through the principle of material mechanics; and finally, the moment equilibrium equation is established to solve the result of the flexural capacity.

[0078] In specific implementation, the second assumed condition includes: the interface slip between the steel beam and the NC layer is minimum; the interface slip between the UHPC layer and the NC layer is minimum; the shear lag effect of the concrete slab is ignored; the sectional curvatures of the concrete slab and the steel beam are the same; the influence of the transverse steel bars in the concrete slab on the flexural capacity is ignored; the strain distribution of the composite beam is calculated based on the geometric relationship; and the influence of the studs on the flexural capacity of the composite beam is ignored.

[0079] In specific implementation, the sectional strain expression corresponding to the target position of the section in the stress hardening stage of the composite beam is represented as:

[0080] In the formula, represents the sectional strain corresponding to the target position of the section in the stress hardening stage, k represents the sectional bending curvature, represents the distance between the target position and the plastic neutral axis, represents the ultimate strain of the UHPC layer, represents the distance between the vertex of the UHPC layer and the plastic neutral axis.

[0081] Please refer to Figure 13 , after the UHPC cracks, when the plastic neutral axis is located in the concrete slab, the stress and strain distribution is as shown in Figure 13 , according to the stress and strain distribution analysis, the internal force expression of each stress region of the composite beam and the first moment equilibrium equation corresponding to the plastic neutral axis located in the concrete slab in the stress hardening stage of the composite beam are proposed.

[0082] In the specific implementation, the internal force expression of the longitudinal reinforcement in the tensile zone of the composite beam in the stress hardening stage is:

[0083] In the formula, represents the internal force of the longitudinal reinforcement in the tensile zone of the composite beam in the stress hardening stage, represents the total area of the reinforcement, represents the tensile strength of the longitudinal reinforcement in the tensile zone.

[0084] In the specific implementation, the internal force expression of the UHPC layer of the composite beam in the stress hardening stage is:

[0085] In the formula, represents the internal force of the UHPC layer of the composite beam in the stress hardening stage, represents the crack bridging coefficient of the steel fiber, represents the width of the concrete slab, represents the vertical thickness of the UHPC layer, represents the tensile strength of the UHPC layer.

[0086] In the specific implementation, the internal force expression of the NC layer in the compressive zone of the composite beam in the stress hardening stage is:

[0087] In the formula, represents the internal force of the NC layer in the compressive zone of the composite beam in the stress hardening stage, represents the tensile strength of the NC layer, represents the width of the concrete slab, represents the total thickness of the concrete slab, wherein , represents the distance between the vertex of the UHPC layer and the plastic neutral axis.

[0088] In the specific implementation, the internal force expression of the top flange of the steel beam of the composite beam in the stress hardening stage is:

[0089] In the formula, represents the internal force of the top flange of the steel beam of the composite beam in the stress hardening stage, represents the elastic modulus of the steel material, represents the total strain of the steel beam, represents the transverse width of the top flange of the steel beam, represents the total vertical thickness of the steel beam.

[0090] In the specific implementation, the internal force expression of the web of the steel beam of the composite beam in the stress hardening stage is:

[0091] wherein, represents the internal force of the steel beam web of the composite beam in the stress hardening stage, represents the elastic modulus of the steel material, represents the strain of the steel beam web, represents the transverse width of the steel beam web, represents the vertical thickness of the steel beam web.

[0092] In a specific implementation, the internal force expression of the steel beam bottom flange of the composite beam in the stress hardening stage is:

[0093] wherein, represents the internal force of the steel beam bottom flange of the composite beam in the stress hardening stage, represents the elastic modulus of the steel material, represents the strain of the steel beam bottom flange, represents the transverse width of the steel beam bottom flange, represents the vertical thickness of the steel beam bottom flange.

[0094] In a specific implementation, the internal force expression of the steel beam of the composite beam in the stress hardening stage is:

[0095] wherein, represents the internal force of the steel beam of the composite beam in the stress hardening stage, represents the internal force of the steel beam top flange of the composite beam in the stress hardening stage, represents the internal force of the steel beam web of the composite beam in the stress hardening stage, represents the internal force of the steel beam bottom flange of the composite beam in the stress hardening stage.

[0096] In a specific implementation, the first moment equilibrium equation is represented as:

[0097] wherein, represents the internal force of the UHPC layer of the composite beam in the stress hardening stage, represents the internal force of the longitudinal steel in the tension zone of the composite beam in the stress hardening stage, represents the internal force of the NC layer in the compression zone of the composite beam in the stress hardening stage, represents the internal force of the steel beam of the composite beam in the stress hardening stage.

[0098] In specific implementation, the internal force expression of the composite beam in the stress hardening stage and the cross-section strain expression corresponding to the target position of the cross-section are solved to obtain the plastic neutral axis position and the cross-section bending curvature. The plastic neutral axis position and the cross-section bending curvature are substituted into the strain expression corresponding to the target position of the cross-section to solve the plastic strain corresponding to the arbitrary beam height position of the composite beam. The plastic strain corresponding to the beam height position is substituted into the internal force expression of the composite beam in the stress hardening stage to solve the internal force corresponding to each stress region. According to the internal force solved by each stress region and the first moment balance equation, the first calculation expression of the flexural capacity of the composite beam with the plastic neutral axis located in the concrete slab is obtained.

[0099] Specifically, the first calculation expression of the flexural capacity of the UHPC thin layer reinforced steel composite beam is expressed as:

[0100] In the formula, represents the flexural capacity of the composite beam in the stress hardening stage with the plastic neutral axis located in the concrete slab, represents the internal force of the steel beam of the composite beam in the stress hardening stage, represents the distance between the internal force of the steel beam of the composite beam in the stress hardening stage and the plastic neutral axis located in the concrete slab, the internal force of the NC layer compression zone of the composite beam in the stress hardening stage, represents the distance between the internal force of the NC layer compression zone of the composite beam in the stress hardening stage and the plastic neutral axis located in the concrete slab, the internal force of the UHPC layer of the composite beam in the stress hardening stage, represents the distance between the internal force of the UHPC layer of the composite beam in the stress hardening stage and the plastic neutral axis located in the concrete slab, represents the internal force of the longitudinal reinforcement of the tension zone of the composite beam in the stress hardening stage, represents the distance between the internal force of the longitudinal reinforcement of the tension zone of the composite beam in the stress hardening stage and the plastic neutral axis located in the concrete slab.

[0101] Please refer to Figure 14 , after the UHPC cracks, when the plastic neutral axis is located on the upper flange of the steel beam, the stress and strain distribution is as shown in Figure 14 According to the stress and strain distribution analysis, the internal force expression of each stress region of the composite beam and the second moment balance equation are proposed when the plastic neutral axis of the composite beam in the stress hardening stage is located on the upper flange of the steel beam.

[0102] In specific implementation, the second moment balance equation is expressed as:

[0103] In the formula, the internal force of the UHPC layer of the composite beam at the stress hardening stage, the internal force of the longitudinal reinforcement of the tensile region of the upper flange of the steel beam corresponding to the plastic neutral axis located at the upper flange of the steel beam at the stress hardening stage of the composite beam, the internal force of the tensile region of the upper flange of the steel beam at the stress hardening stage of the composite beam, the internal force of the compressive region of the steel beam at the stress hardening stage.

[0104] In an optional embodiment, the internal force expressions corresponding to the plastic neutral axis located at the upper flange of the steel beam and the plastic neutral axis located within the concrete slab at the stress hardening stage of the composite beam differ in that the internal force expression of the longitudinal reinforcement of the tensile region of the upper flange of the steel beam corresponding to the plastic neutral axis located at the upper flange of the steel beam at the stress hardening stage of the composite beam is:

[0105] wherein, represents the total area of the reinforcement, represents the tensile strength of the reinforcement.

[0106] In a specific implementation, the internal force expression of the tensile region of the upper flange of the steel beam at the stress hardening stage of the composite beam is:

[0107] wherein, represents the elastic modulus of the steel material, represents the strain of the tensile region of the upper flange of the steel beam, represents the lateral width of the upper flange of the steel beam, represents the vertical thickness of the tensile region of the upper flange of the steel beam.

[0108] In a specific implementation, the internal force expression of the compressive region of the steel beam at the stress hardening stage of the composite beam is:

[0109] wherein, represents the elastic modulus of the steel material, represents the strain of the compressive region of the upper flange of the steel beam, represents the lateral width of the upper flange of the steel beam, represents the vertical thickness of the compressive region of the upper flange of the steel beam, the internal force of the compressive region of the steel beam can be represented as wherein, represents the internal force of the web of the steel beam at the stress hardening stage of the composite beam, represents the internal force of the lower flange of the steel beam at the stress hardening stage of the composite beam.

[0110] In a specific implementation, the internal force expression of the combined beam in the stress hardening stage and the expression of the strain corresponding to the target position of the section are solved to obtain the plastic neutral axis position and the section bending curvature, the plastic neutral axis position and the section bending curvature are substituted into the expression of the strain corresponding to the target position of the section, the plastic strain corresponding to the beam height position is solved, the plastic strain corresponding to the beam height position is substituted into the internal force expression of the combined beam in the stress hardening stage, and the internal force corresponding to each stress region is solved. According to the internal force solved by each stress region and the second moment balance equation, the second calculation expression of the flexural capacity of the combined beam with the plastic neutral axis located in the concrete slab is obtained.

[0111] Specifically, the second calculation expression of the flexural capacity of the UHPC thin layer reinforced steel-concrete composite beam is expressed as:

[0112] In the formula, represents the flexural capacity of the UHPC thin layer reinforced steel-concrete composite beam when the plastic neutral axis of the combined beam is located on the upper flange of the steel beam in the stress hardening stage, represents the internal force of the UHPC layer of the combined beam in the stress hardening stage, represents the internal force of the longitudinal reinforcement of the tensile region corresponding to the plastic neutral axis located at the upper flange of the steel beam in the stress hardening stage of the combined beam, represents the internal force of the tensile region of the upper flange of the steel beam in the stress hardening stage of the combined beam, represents the internal force of the compressive region of the steel beam in the stress hardening stage, represents the distance between the internal force of the tensile region of the upper flange of the steel beam in the stress hardening stage of the combined beam and the plastic neutral axis located at the upper flange of the steel beam, represents the distance between the internal force of the compressive region of the steel beam in the stress hardening stage of the combined beam and the plastic neutral axis located at the upper flange of the steel beam, represents the distance between the internal force of the UHPC layer in the stress hardening stage of the combined beam and the plastic neutral axis located at the upper flange of the steel beam, represents the distance between the internal force of the longitudinal reinforcement of the tensile region and the plastic neutral axis located at the upper flange of the steel beam.

[0113] The unique technical advantages of the present application are that, first, based on the steel-concrete composite beam formwork, test specimens and control groups are set, parameters in the process of pressure loading test are collected through measurement point arrangement, the load strain curve of the test parameters and the result graph of the pressure loading test are used to analyze the load transfer of the flexural performance of the negative moment region of the UHPC thin layer reinforced steel-concrete composite beam, so as to determine the stress state and load transfer path of the negative moment region of the combined beam in the actual bearing process, thereby providing an analysis basis of the load transfer mechanism for the bearing performance calculation of the negative moment region of the combined beam, and ensuring the accuracy of the subsequent bearing performance calculation results.

[0114] Secondly, this application considers the crack formation process of composite beams under negative bending moment. Based on the flexural performance characterization determined by analysis, the stress region related to the cracking bending moment is identified. To facilitate the derivation of the cracking bending moment calculation, a first assumption is set regarding the impact of the crack formation process on the composite beam. Then, the cross-sectional strain corresponding to the cracking stages of the UHPC layer and the NC layer is solved using the target cross-sectional strain expression of the crack formation process. The internal forces in the stress region are calculated based on the cross-sectional strain. Finally, the cracking bending moments of the UHPC layer and the NC layer are calculated based on the distance between the internal forces and the plastic neutral axis. The cracking bending moment can express the load-bearing capacity of the composite beam during the crack formation process and can serve as a reference for load-bearing capacity assessment in the design stage of composite beams. This reduces the deviation between the load distribution of steel-concrete composite beams and actual engineering requirements, thereby improving the accuracy of load-bearing capacity assessment of steel-concrete composite beams.

[0115] Finally, this application considers the influence of stress hardening on the flexural capacity of the composite beam after cracking in the UHPC. To facilitate the derivation of the flexural capacity calculation, a second assumption is made regarding the influence of the stress hardening process on the composite beam. Simultaneously, the influence of different plastic neutral axis positions during the stress hardening stage on the flexural capacity calculation is considered. The plastic neutral axis position during the stress hardening stage is divided into those located within the concrete slab and those on the upper flange of the steel beam for flexural capacity calculation expression evaluation. By simultaneously establishing the internal force expression of the composite beam during the stress hardening stage and the cross-sectional strain expression corresponding to the target cross-section position, the plastic neutral axis position and cross-sectional curvature are obtained. Substituting the plastic neutral axis position and cross-sectional curvature into the expression for the strain corresponding to the target cross-section position, the plastic neutral axis position and cross-sectional curvature of the composite beam at any beam height are calculated. The plastic strain at the corresponding beam height is then substituted into the expression for the internal force of the composite beam during the stress hardening stage to obtain the internal forces corresponding to each stress region. Based on the internal force and moment balance equations obtained for each stress region, the first calculation expression for the flexural bearing capacity of the composite beam corresponding to the plastic neutral axis located within the concrete slab, and the second calculation expression for the flexural bearing capacity of the composite beam corresponding to the plastic neutral axis located at the upper flange of the steel beam are obtained. The flexural bearing capacity can express the bearing performance of the composite beam during the stress hardening process and can serve as a reference for the bearing performance evaluation in the design stage of composite beams. This can reduce the deviation between the load distribution of steel-concrete composite beams and actual engineering requirements, thereby improving the accuracy of the bearing performance evaluation of steel-concrete composite beams. It has high application prospects in the field of bridge engineering technology.

[0116] Another embodiment of the present application also provides a device for calculating flexural capacity of negative moment region of steel-concrete composite beam reinforced by UHPC thin layer, which comprises a processor, a computer readable storage medium, a memory and a network interface connected through a system bus. The computer readable nonvolatile storage medium of the device for calculating flexural capacity of negative moment region of steel-concrete composite beam reinforced by UHPC thin layer stores an operating system, a database and computer readable instructions. The database can store information sequences. When the computer readable instructions are executed by the processor, the processor can implement a method for calculating flexural capacity of negative moment region of steel-concrete composite beam reinforced by UHPC thin layer.

[0117] The processor of the device for calculating flexural capacity of negative moment region of steel-concrete composite beam reinforced by UHPC thin layer is used to provide computing and control capabilities to support the operation of the entire device for calculating flexural capacity of negative moment region of steel-concrete composite beam reinforced by UHPC thin layer. The memory of the device for calculating flexural capacity of negative moment region of steel-concrete composite beam reinforced by UHPC thin layer can store computer readable instructions, which can make the processor execute the method for calculating flexural capacity of negative moment region of steel-concrete composite beam reinforced by UHPC thin layer of the present application when executed by the processor. The network interface of the device for calculating flexural capacity of negative moment region of steel-concrete composite beam reinforced by UHPC thin layer is used to connect and communicate with a terminal.

[0118] The present application also provides a nonvolatile storage medium storing computer readable instructions, which are executed by one or more processors.

Claims

1. A method for calculating the flexural capacity of the negative moment region of a steel-concrete composite beam reinforced with thin layers of UHPC, characterized in that, The method comprises the following steps: Based on the steel-concrete composite beam template, test specimens are set, and measuring points are arranged on the test specimens. Load-strain curves and loading results of each test specimen are obtained through the pressure loading test. The bending resistance performance is determined according to the load-strain curves and the loading results. According to the bending resistance performance, the associated stress area of the crack formation process of the composite beam is determined. The first assumption condition for deriving the cracking moment calculation expression is preset. The expression of the cross-section strain of the composite beam is determined according to the crack formation process. The internal force expression and the force balance equation of the associated stress area are determined according to the first assumption condition. The calculation expression of the UHPC cracking moment and the calculation expression of the NC cracking moment are obtained by derivation based on the strain expression, the internal force expression and the force balance equation. According to the influence of the cracking stress hardening on the composite beam, the second assumption condition for deriving the bending resistance calculation expression is preset. The plastic neutral axis position is determined based on the cross-section strain expression and the internal force expression. The moment balance equation is established according to different plastic neutral axis positions. The bending resistance calculation expression of the composite beam corresponding to different plastic neutral axis positions is obtained by derivation based on the cross-section strain expression, the internal force expression and the moment balance equation.

2. The method for calculating the flexural capacity of the negative moment region of the steel-concrete composite beam reinforced by the UHPC thin layer according to claim 1, characterized in that, Based on the steel-concrete composite beam template, test specimens are set, and measuring points are arranged on the test specimens. Specifically: The UHPC thin layer reinforced steel-concrete composite beam test specimen is set as the target test specimen, and the steel-concrete composite beam test specimen without UHPC thin layer reinforcement is set as the control test specimen. Linear variable differential transducers are arranged at the bottom of the beam length, the bottom of the midspan, the support position and the beam end position of the test specimen. The linear variable differential transducers collect pressure loading test parameters and draw the load-strain curve of the test specimen. 3.The method for calculating the flexural capacity of the negative moment region of the steel-concrete composite beam based on the UHPC thin layer reinforcement according to claim 1, characterized in that, The pressure loading test, specifically: The pressure loading test uses a press to apply loads in different loading stages, and transmits the loads to the test specimen through a distribution beam. The pressure loading test includes the following stages: In the preloading stage, each test specimen is preloaded to a preset load. In the preliminary loading stage, after the preloading load is zeroed, the load is increased from zero until the concrete layer of the test specimen cracks for the first time. In the ultimate loading stage, after the concrete layer cracks for the first time, the loading step and the loading rate are adjusted, and the monotonic loading is continued until the composite beam fails.

4. The method for calculating the flexural capacity of the negative moment region of the steel-concrete composite beam reinforced by the UHPC thin layer according to claim 1, characterized in that, The bending resistance performance, specifically: According to the steel beam local instability and the concrete tensile failure indicated by the loading results and the load-strain curve, the bending resistance transmission relationship between the steel beam and the concrete is determined. According to the inhibitory effect of the interface anchorage on crack propagation indicated by the loading results and the load-strain curve, the bending resistance transmission relationship between the reinforcement and the interface shear deformation of the composite beam is determined. According to the inhibitory effect of the UHPC reinforcement on the crack propagation of the NC layer indicated by the loading results and the load-strain curve, the anti-cracking bending resistance transmission relationship between the thickness of the UHPC layer and the composite beam is determined.

5. The method for calculating the flexural capacity of the negative moment region of the steel-concrete composite beam reinforced by the UHPC thin layer according to claim 1, characterized in that, The first assumption condition, specifically: The interface slip between the steel beam and the NC layer is minimal; the interface slip between the UHPC layer and the NC layer is minimal. The strain distribution of the composite beam after the concrete cracking is calculated based on geometric relations; and the influence of the transverse steel bars in the NC layer on the flexural capacity is ignored.

6. The method for calculating the flexural capacity of the negative moment region of the steel-concrete composite beam reinforced by the UHPC thin layer according to claim 1, characterized in that, According to the crack formation process, the strain expression of the composite beam section is determined, the internal force expression and the force balance equation of the associated stress region are determined according to the first assumption condition, and the calculation expression of the UHPC cracking moment is obtained based on the strain expression, the internal force expression and the force balance equation, and the calculation expression of the UHPC cracking moment is specifically as follows: For the UHPC layer cracking stage of the crack formation process, according to the fact that the tensile stress limit of the UHPC layer is close to the tensile strength of the UHPC layer, the strain expression corresponding to the target position of the UHPC layer section is proposed; For the UHPC layer cracking stage of the crack formation process, the associated stress region of the negative bending moment zone of the composite beam is determined to include the steel beam, the UHPC layer, the NC layer and the steel bars, and the expression of the internal force of the steel beam, the internal force of the UHPC layer, the internal force of the NC layer, the internal force of the steel bars and the force balance equation is proposed; According to the expression of each internal force, the strain expression is substituted into the strain expression for deduction and calculation, and the plastic neutral axis position corresponding to the UHPC layer cracking stage is obtained, and the strain corresponding to the target position of each associated stress region in the UHPC layer cracking stage is calculated according to the plastic neutral axis position of the UHPC layer cracking stage; According to the strain corresponding to the target position of the stress region in the UHPC layer cracking stage, the internal force of the associated stress region is calculated, and the distance between the internal force of the associated stress region and the plastic neutral axis position in the UHPC layer cracking stage is calculated, and the internal force of the associated stress region and the distance between the internal force of the associated stress region and the plastic neutral axis position are substituted into the force balance equation for deduction, and the calculation expression of the UHPC cracking moment in the UHPC layer cracking stage is obtained: The calculation expression of the UHPC cracking moment is expressed as: wherein, Mcr,cr represents the UHPC cracking moment at the UHPC cracking stage of the composite beam, Mcr,cr represents the UHPC cracking moment at the UHPC cracking stage of the composite beam, Mcr,cr represents the UHPC cracking moment at the UHPC cracking stage of the composite beam, Mcr,cr represents the UHPC cracking moment at the UHPC cracking stage of the composite beam, Mcr,cr represents the UHPC cracking moment at the UHPC cracking stage of the composite beam, Mcr,cr represents the UHPC cracking moment at the UHPC cracking stage of the composite beam, Mcr,cr represents the UHPC cracking moment at the UHPC cracking stage of the composite beam, Mcr,cr represents the UHPC cracking moment at the UHPC cracking stage of the composite beam, Mcr,cr represents the UHPC cracking moment at the UHPC cracking stage of the composite beam, 7. The method for calculating the flexural capacity of the negative moment region of the steel-concrete composite beam reinforced by the UHPC thin layer according to claim 6, characterized in that, According to the crack formation process, the strain expression of the composite beam section is determined, the internal force expression and the force balance equation of the associated stress region are determined according to the first assumption condition, and the calculation expression of the UHPC cracking moment is obtained based on the strain expression, the internal force expression and the force balance equation, and the calculation expression of the UHPC cracking moment is specifically as follows: For the UHPC layer cracking stage of the crack formation process, according to the fact that the tensile stress limit of the UHPC layer is close to the tensile strength of the UHPC layer, the strain expression corresponding to the target position of the UHPC layer section is proposed; According to the expression of each internal force, the strain expression is substituted into the strain expression for deduction and calculation, and the plastic neutral axis position corresponding to the UHPC layer cracking stage is obtained, and the strain corresponding to the target position of each associated stress region in the UHPC layer cracking stage is calculated according to the plastic neutral axis position of the UHPC layer cracking stage; The calculation expression of the NC cracking moment in the NC layer cracking stage is obtained by substituting the internal force of the associated stress region and the distance between the internal force of the associated stress region and the plastic neutral axis position into the force balance equation: The calculation expression of the NC cracking moment is expressed as: wherein, MNC,crackrepresents the NC cracking moment of the composite beam at the NC cracking stage, Msteel,crackrepresents the internal force of the steel beam of the composite beam at the NC cracking stage, dsteel,crackrepresents the distance between the internal force of the steel beam and the plastic neutral axis of the composite beam at the NC cracking stage, MUHPC,crackrepresents the internal force of the UHPC layer of the composite beam at the NC cracking stage, dUHPC,crackrepresents the distance between the internal force of the UHPC layer and the plastic neutral axis of the composite beam at the NC cracking stage, MNC,crackrepresents the internal force of the NC layer of the composite beam at the NC cracking stage, dNC,crackrepresents the distance between the internal force of the NC layer and the plastic neutral axis of the composite beam at the NC cracking stage, Msteel,crackrepresents the internal force of the steel reinforcement of the composite beam at the NC cracking stage. 8.The method for calculating the flexural capacity of the negative moment region of the steel-concrete composite beam reinforced by the UHPC thin layer according to claim 1, wherein, The second assumption condition is specifically as follows: The interface slip between the steel beam and the NC layer is minimal; the interface slip between the UHPC layer and the NC layer is minimal; the shear lag effect of the concrete slab is ignored; the cross-sectional curvature of the concrete slab is the same as that of the steel beam; the influence of the transverse steel bars in the concrete slab on the flexural capacity is ignored; the strain distribution of the composite beam is calculated based on geometric relations; and the influence of the studs on the flexural capacity of the composite beam is ignored.

9. The method for calculating the flexural capacity of the negative moment region of the steel-concrete composite beam reinforced by the UHPC thin layer according to claim 1, characterized in that, The plastic neutral axis position is determined based on the sectional strain expression and the internal force expression, the moment balance equation is established according to different plastic neutral axis positions, and the calculation expression of the flexural capacity of the composite beam corresponding to different plastic neutral axis positions is obtained through deduction based on the sectional strain expression, the internal force expression and the moment balance equation, including: For the stress hardening stage of the composite beam, a sectional strain expression for solving the stress corresponding to the target position of the section is proposed, the plastic neutral axis position and the sectional bending curvature are solved according to the sectional strain expression; When the plastic neutral axis is located in the concrete slab, the corresponding internal force expression and the first moment balance equation are proposed according to the current stress-strain state analysis, the plastic neutral axis position and the sectional bending curvature solved are substituted into the sectional strain expression to determine the sectional stress of the composite beam at any position along the beam height and the stress distribution of each sectional stress; According to the sectional stress and the stress distribution, the internal force of each stress region is calculated through the internal force expression, the distance between the internal force of each stress region and the plastic neutral axis is determined according to the plastic neutral axis position, the distance and the internal force size are substituted into the first moment balance equation for deduction, and the first calculation expression of the flexural capacity of the UHPC thin layer reinforced steel-concrete composite beam when the plastic neutral axis is located in the concrete slab is obtained; The first calculation expression of the flexural capacity of the UHPC thin layer reinforced steel-concrete composite beam is expressed as: wherein, Mnc, plastic represents the flexural capacity of the composite beam in the plastic stage with the plastic neutral axis located in the concrete slab, Mnc, steel represents the internal force of the steel beam of the composite beam in the stress hardening stage, Mnc, plastic represents the distance between the internal force of the steel beam of the composite beam in the stress hardening stage and the plastic neutral axis located in the concrete slab, Mnc, nc represents the internal force of the NC layer compression zone of the composite beam in the stress hardening stage, Mnc, plastic represents the distance between the internal force of the NC layer compression zone of the composite beam in the stress hardening stage and the plastic neutral axis located in the concrete slab, Mnc, uhpc represents the internal force of the UHPC layer of the composite beam in the stress hardening stage, Mnc, plastic represents the distance between the internal force of the UHPC layer of the composite beam in the stress hardening stage and the plastic neutral axis located in the concrete slab, Mnc, tension represents the internal force of the tension zone longitudinal reinforcement of the composite beam in the stress hardening stage, Mnc, plastic represents the distance between the internal force of the tension zone longitudinal reinforcement of the composite beam in the stress hardening stage and the plastic neutral axis located in the concrete slab.

10. The method for calculating the flexural capacity of the negative moment region of a steel-concrete composite beam reinforced with UHPC thin layers according to claim 9, characterized in that, The plastic neutral axis position is determined based on the sectional strain expression and the internal force expression, the moment balance equation is established according to different plastic neutral axis positions, and the calculation expression of the flexural capacity of the composite beam corresponding to different plastic neutral axis positions is obtained through deduction based on the sectional strain expression, the internal force expression and the moment balance equation, including: When the plastic neutral axis is located on the top flange of the steel beam, the corresponding internal force expression and the second moment balance equation are proposed according to the current stress-strain state analysis, the plastic neutral axis position and the sectional bending curvature solved are substituted into the sectional strain expression to determine the sectional stress of the composite beam at any position along the beam height and the stress distribution of each sectional stress; According to the sectional stress and the stress distribution, the internal force of each stress region is calculated through the internal force expression, the distance between the internal force of each stress region and the plastic neutral axis is determined according to the plastic neutral axis position, the distance and the internal force size are substituted into the second moment balance equation for deduction, and the second calculation expression of the flexural capacity of the UHPC thin layer reinforced steel-concrete composite beam when the plastic neutral axis is located on the top flange of the steel beam is obtained; The second calculation expression of the flexural capacity of the UHPC thin layer reinforced steel-concrete composite beam is expressed as: wherein, represents the flexural capacity of the UHPC thin layer reinforced steel-concrete composite beam with the plastic neutral axis located at the top flange of the steel beam in the stress hardening stage, represents the internal force of the UHPC layer of the composite beam in the stress hardening stage, represents the internal force of the longitudinal tensile reinforcement corresponding to the tensile region of the composite beam in the stress hardening stage with the plastic neutral axis located at the top flange of the steel beam, represents the internal force of the tensile region of the top flange of the steel beam of the composite beam in the stress hardening stage, represents the internal force of the compressive region of the steel beam in the stress hardening stage, represents the distance between the internal force of the tensile region of the top flange of the steel beam of the composite beam in the stress hardening stage and the plastic neutral axis located at the top flange of the steel beam, represents the distance between the internal force of the compressive region of the steel beam of the composite beam in the stress hardening stage and the plastic neutral axis located at the top flange of the steel beam, represents the distance between the internal force of the UHPC layer of the composite beam in the stress hardening stage and the plastic neutral axis located at the top flange of the steel beam, represents the distance between the internal force of the longitudinal tensile reinforcement and the plastic neutral axis located at the top flange of the steel beam.

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