A method for calculating interface slip of prestressed GFRP-concrete-steel composite beam

Abstract

This invention relates to a method for calculating interface slip in prestressed GFRP-concrete-steel composite beams. The method includes establishing a calculation model of the composite beam, dividing the beam longitudinally into several segments and further subdividing them into micro-segments, establishing a load-slip relationship for shear connectors, establishing an equivalent stress model for the concrete with GFRP vertical ribs and determining the equivalent elastic modulus of the micro-segments, establishing a recursive relationship between the interface slip at both ends of the beam segment and the interface slip strain, establishing a cross-sectional strain distribution relationship based on the shared curvature condition of the composite slab and the steel beam, and establishing axial force balance equations, bending moment balance equations, and compatibility equations. These equations are then solved simultaneously with boundary conditions to obtain the interface slip distribution along the longitudinal direction of the composite beam and the shear force distribution of the shear connectors. This invention can consider the influence of the stiffness and arrangement of the GFRP vertical ribs and shear connectors on interface slip, and is applicable to the connection performance analysis and shear connector arrangement design of prestressed GFRP-concrete-steel composite beams.

Description

Technical Field

[0001] This invention relates to the field of computational analysis technology for composite structure bridges, specifically to a calculation method for interface slippage of prestressed GFRP-concrete-steel composite beams, and more particularly to a calculation method for interface slippage and shear force distribution of prestressed GFRP-concrete-steel composite beams considering the influence of GFRP vertical ribs, the stiffness of shear connectors, and the arrangement of shear connectors. Background Technology

[0002] With the increasing demands for bridge structural durability, glass fiber reinforced polymer (GFRP) has been increasingly used in bridge engineering due to its advantages such as good corrosion resistance and light weight. Combining GFRP with concrete and steel can form GFRP-concrete-steel composite beam bridges, which consist of GFRP-concrete composite slabs and steel beams.

[0003] In the transverse direction, the load is borne by the GFRP-concrete composite slab; in the longitudinal direction, the load is borne by the GFRP-concrete-steel composite beam. Under prestressed loads, slippage will occur at the interface between the GFRP-concrete composite slab and the steel beam, especially near the prestressing loading end, where interface slippage and shear forces borne by shear connectors are relatively large.

[0004] Therefore, accurately calculating the interface slip between the GFRP-concrete composite slab and the steel beam under prestressing, as well as the shear force distribution of the shear connectors, is of great significance for the design of shear connectors.

[0005] Existing interface slip analysis methods for steel-concrete composite beams are mostly designed for traditional composite beams with uniform cross-sectional properties and evenly spaced shear connectors. These methods struggle to account for the influence of GFRP ribs and the non-uniform arrangement of shear connectors. Currently, calculation methods for GFRP-concrete-steel composite beams primarily focus on bending deformation analysis, while methods for calculating interface slip under prestressing remain incomplete. Directly applying traditional slip analysis methods for steel-concrete composite beams may fail to adequately consider factors such as the non-uniform arrangement of GFRP plates and shear connectors, thus affecting the accuracy of interface slip and shear force calculations for shear connectors. This, in turn, negatively impacts structural safety evaluation and connector optimization design.

[0006] Therefore, there is an urgent need for a calculation method for the interface slippage and shear force distribution of prestressed GFRP-concrete-steel composite beams that takes into account the influence of GFRP vertical ribs, the stiffness of shear connectors, and the arrangement of shear connectors. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a calculation method for interface slippage in prestressed GFRP-concrete-steel composite beams to solve the aforementioned problems.

[0008] This invention provides the following technical solution: A method for calculating interface slip in prestressed GFRP-concrete-steel composite beams includes the following steps: A calculation model for a prestressed GFRP-concrete-steel composite beam is established. The prestressed GFRP-concrete-steel composite beam includes a GFRP-concrete composite slab, a steel beam, shear connectors, and prestressing tendons. The GFRP-concrete composite slab includes a GFRP base plate and concrete with GFRP vertical ribs. The prestressing tendons are located in the GFRP-concrete composite slab. The GFRP-concrete composite slab is connected to the steel beam through shear connectors. The composite beam is divided into several beam segments along its longitudinal direction, and each beam segment is further divided into several micro segments. Each micro segment corresponds to a GFRP rib plate influence zone or an equivalent element. Establish the load-slip relationship of the shear connector; An equivalent stress model was established for concrete with GFRP vertical ribs in a micro-segment; Establish arbitrary beam segments j The relationship between the slip at both ends of the interface and the slip strain; Based on the condition of co-curvature between GFRP-concrete composite slab and steel beam, the cross-sectional strain distribution relationship of each section is established, and the axial force balance equation, bending moment balance equation, and coordination equation composed of the difference in axial force at both ends of the beam segment and the shear force of the shear connector are established for each beam segment. Solve the equations of each beam segment simultaneously based on the boundary conditions to obtain the interface slip distribution of the composite beam along the longitudinal direction, and determine the shear force distribution borne by the shear connector based on the interface slip distribution.

[0009] Preferably, for a micro-segment containing GFRP vertical ribs, the concrete region with GFRP vertical ribs within the micro-segment is equivalent to an equivalent concrete region, and the equivalent stress and equivalent strain of the micro-segment satisfy the following:

[0010] in, For the equivalent stress within the micro-segment, The elastic modulus of concrete. For equivalent strain within a micro-segment; For micro-segments without GFRP vertical ribs, calculations are performed as for ordinary concrete areas; Preferred load-slip relationship for shear connectors:

[0011] Where V is the shear force borne by the shear connector, and k is the stiffness of the shear connector. This refers to the amount of interface sliding. The shear connector is a stud shear connector, and its stiffness is... k Determine using the following formula:

[0012] in, d The diameter of the stud. For concrete compressive strength, This refers to the elastic modulus of concrete.

[0013] Preferably, the equivalent stress model for concrete with GFRP vertical ribs in the micro-segment adopts the following equivalent elastic modulus relationship:

[0014] in, For the equivalent elastic modulus of the micro-segment, The elastic modulus of concrete. Let be the elastic modulus of the GFRP base plate along the longitudinal direction of the composite beam. Let denoted as , and denoted as , where is the total thickness of the GFRP vertical ribs within the micro-segment, and ... The GFRP rib thickness correction factor satisfies ; The equivalent elastic modulus of concrete without GFRP vertical ribs in the micro-segment is taken as the concrete elastic modulus. E c .

[0015] Preferably, the mid-span section of the composite beam is used as the starting point for calculation, and each section is sequentially numbered along the direction from the mid-span section to the prestressing loading end. j The beam segment is composed of the first j Section and the first j +1 section defined, and the first j The interfacial slip strain within the beam segment varies linearly along the longitudinal direction of the composite beam, satisfying:

[0016] in, and The first j Section and the first j Interface slip at section +1 and The first j Section and the first j Slip strain at section +1 For the first j Beam segment length.

[0017] Preferably, any cross-sectionj The strain distribution relationship satisfies:

[0018] in, and The first j Equivalent concrete region strain at the top and bottom surfaces of the cross section For the first j Strain along the centerline of the GFRP base plate. and The first j Strain along the centerline of the upper flange and the centerline of the lower flange of the cross-section steel beam. For the first j The curvature of the cross section For concrete thickness, The thickness of the GFRP base plate is... This is the distance between the centerlines of the upper and lower flanges of the steel beam. For the first j Interfacial slip strain of the cross section.

[0019] Preferably, the first step is to calculate the strain distribution and linear elastic constitutive relation of each material. j The axial resultant force of each component of the cross section; when establishing the axial force balance equation and the bending moment balance equation, both the steel beam and the GFRP base plate adopt a linear elastic constitutive relationship.

[0020] Preferably, according to the first j The relationship between the difference in axial resultant force between the GFRP-concrete composite slabs at both ends of the beam segment and the shear force borne by the shear-resistant connectors within the beam segment is established using a compatibility equation. The boundary conditions include: the resultant force of the GFRP-concrete composite slab at the loading end is equal to the resultant force of the prestress at the loading end, and the interface slip at the mid-span section of the composite beam, which serves as the starting point for calculation, is zero.

[0021] Preferably, the analysis of each beam segment satisfies the following conditions: the resultant force of the prestressing tendons remains constant within each micro-segment; the stress in the GFRP-concrete composite slab within the micro-segment is expressed as equivalent stress; the interface slip strain within the beam segment varies linearly along the longitudinal direction; and the shear force borne by the shear connectors within the beam segment is uniformly distributed. j The slippage of each shear connector within the beam segment is taken as the first... j Interface slippage at section +1.

[0022] Preferably, the relative slippage between the GFRP base plate and the concrete is negligible, the composite beam is in the elastic working stage, and no vertical separation occurs between the steel beam and the GFRP-concrete composite slab.

[0023] The present invention has the following beneficial technical effects: This invention establishes an interface slip calculation method for prestressed GFRP-concrete-steel composite beams, and introduces the load-slip relationship of shear connectors into the cross-sectional analysis of composite beams, which can obtain the interface slip distribution between the GFRP-concrete composite slab and the steel beam along the beam length under prestressing. This invention improves the applicability and accuracy of interface slip calculation for GFRP-concrete-steel composite beams by treating the concrete region with GFRP vertical ribs as an equivalent concrete region with an equivalent elastic modulus, thus taking into account the influence of GFRP vertical ribs on the longitudinal stiffness of the composite slab. This invention adopts an analysis method that combines beam segments and micro-segments, which can take into account the influence of the number and stiffness of shear connectors in different beam segments on interface slippage and shear force of shear connectors. It is applicable to prestressed GFRP-concrete-steel composite beams with non-uniform arrangement of shear connectors. This invention can further determine the shear force distribution borne by the shear connector based on the calculated interface slip distribution, providing a calculation basis for the stress verification, layout optimization and safety evaluation of the shear connector under prestressing. This invention provides a clear calculation process and well-defined physical meanings for the parameters, under the conditions of effective bonding between the GFRP board and concrete, the composite beam being in an elastic working stage, and no vertical separation between the steel beam and the GFRP-concrete composite board, making it easy to apply in engineering design and numerical analysis. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the overall structure and longitudinal segmentation of the prestressed GFRP-concrete-steel composite beam of the present invention; Figure 2 This is a schematic diagram of the stress on any beam segment of the present invention; Figure 3 This is a schematic diagram of the cross-section and strain distribution of the composite beam of the present invention.

[0025] 10. GFRP-concrete-steel composite beam; 11. GFRP-concrete composite slab; 12. Steel beam; 13. Prestressed tendons; 14. Shear connectors; 111. GFRP base plate; 112. Concrete with GFRP vertical ribs; 21. GFRP vertical ribs; 31. Micro-segments j 32. Micro-segment j +1. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] A type of interface slippage in prestressed GFRP-concrete-steel composite beams, such as Figures 1-3 As shown, The prestressed GFRP-concrete-steel composite beam 10 includes a GFRP-concrete composite slab 11, a steel beam 12, a shear connector 14, and prestressing tendons 13; the GFRP-concrete composite slab 11 includes a GFRP base plate 111 and a concrete slab 112 with GFRP vertical ribs, the prestressing tendons 13 are located in the GFRP-concrete composite slab 11, and the GFRP-concrete composite slab 11 is connected to the steel beam 12 through the shear connector 14; The calculation method is applicable to the following conditions: there is effective bond between the GFRP base plate 111 and the concrete, the composite beam is in the elastic working stage, and there is no vertical separation between the steel beam 12 and the GFRP-concrete composite slab 11. During the calculation, the relative slippage between the GFRP base plate 111 and the concrete is ignored, and the GFRP-concrete composite slab 11 and the steel beam 12 are assumed to have the same cross-sectional curvature.

[0028] The method includes the following steps: (1) Establish a calculation model for the prestressed GFRP-concrete-steel composite beam 10.

[0029] (2) Divide the composite beam 10 longitudinally into several beam segments, and further divide each beam segment into several micro segments. Each micro segment corresponds to a GFRP rib plate influence zone or an equivalent element. (3) Establish the load-slip relationship of shear connector 14

[0030] Where V is the shear force borne by the shear connector 14. k The shear connector has a stiffness of 14. This refers to the amount of interface sliding. (4) An equivalent stress model is established for concrete 112 with GFRP vertical ribs in the micro-segment, and the following equivalent elastic modulus relationship is adopted:

[0031] in, For the equivalent elastic modulus of the micro-segment, The elastic modulus of concrete. Let be the elastic modulus of the GFRP base plate 111 along the longitudinal direction of the composite beam. The total thickness of the GFRP vertical rib 21 within the micro-segment is given. a The total length of the micro-segment This is the GFRP rib thickness correction factor; (5) Establish arbitrary beam segments jThe relationship between the slip at both ends of the interface and the slip strain is discussed, with the mid-span section of the composite beam serving as the starting point for calculation. Each section is sequentially numbered along the direction from the mid-span section to the prestressed loading end. j The beam segment is composed of the first j Section and the first j +1 section limit, and the first j The interfacial slip strain within the beam segment varies linearly along the longitudinal direction of the composite beam, satisfying:

[0032] in, and The first j Section and the first j Interface slip at section +1 and The first j Section and the first j Slip strain at section +1 For the first j Beam segment length; (6) Based on the co-curvature condition of GFRP-concrete composite slab 11 and steel beam 12, the cross-sectional strain distribution relationship of each section is established, and the axial force balance equation, bending moment balance equation and the coordination equation composed of the axial force difference at both ends of the beam segment and the shear force of the shear connector are established for each beam segment. (7) Solve the equations of each beam segment simultaneously according to the boundary conditions to obtain the interface slip distribution of the composite beam along the longitudinal direction, and determine the shear force distribution borne by the shear connector based on the interface slip distribution.

[0033] Shear connector 14 is a stud shear connector, and its stiffness k is determined by the following formula:

[0034] Where d is the diameter of the stud. This refers to the compressive strength of concrete.

[0035] The equivalent stress and equivalent strain of the micro-segment satisfy:

[0036] For the equivalent stress within the micro-segment, This represents the equivalent strain within the micro-segment.

[0037] When establishing the axial force equilibrium equation and bending moment equilibrium equation, both steel beam 12 and GFRP base plate 111 adopt linear elastic constitutive relations, wherein the stress and strain of steel beam 12 satisfy:

[0038] The stress and strain of the GFRP base plate 111 along the longitudinal direction of the composite beam satisfy the following:

[0039] in, For the stress of the steel beam, The elastic modulus of the steel beam. For the strain of the steel beam; The stress of the GFRP base plate along the longitudinal direction of the composite beam is... The strain of the GFRP base plate along the longitudinal direction of the composite beam is given. E f The elastic modulus of the GFRP base plate along the longitudinal direction of the composite beam is given.

[0040] GFRP rib thickness correction factor To correct the calculation deviation caused by equating the concrete 112 with GFRP vertical ribs to an equivalent concrete region, the total thickness of the GFRP vertical ribs 21 within the micro-segment is used when calculating the equivalent elastic modulus of the micro-segment. Revised to And the GFRP rib thickness correction factor satisfy GFRP rib thickness correction factor The preferred value is 0.5.

[0041] arbitrary cross section j The strain distribution relationship satisfies:

[0042] in, and The first j Equivalent concrete region strain at the top and bottom surfaces of the cross section For the first j Strain along the centerline of the GFRP base plate. and The first j Strain along the centerline of the upper flange and the centerline of the lower flange of the cross-section steel beam. For the first j The curvature of the cross section For concrete thickness, The thickness of the GFRP base plate is... This is the distance between the centerlines of the upper and lower flanges of the steel beam. For the first j Interfacial slip strain of the cross section.

[0043] The coordination equations satisfy:

[0044] in, and The first jThe resultant force of the prestressing tendons at both ends of the beam segment, and The first j The resultant force in the concrete regions with GFRP vertical ribs at both ends of the beam segment. and The first j The resultant force of the GFRP base plate at both ends of the beam segment For the first j Number of shear connectors within the beam segment.

[0045] The boundary conditions include at least the resultant force of the GFRP-concrete composite slab at the loading end being equal to the resultant force of the prestress at the loading end, and the interface slip at the mid-span section of the composite beam, which serves as the starting point for calculation, being zero.

[0046] When the GFRP-concrete composite slab 111 is not equipped with GFRP vertical ribs 21 at its ends, the equivalent elastic modulus of the corresponding micro-segment is taken as the elastic modulus of concrete. E c .

[0047] When the height of the GFRP vertical rib 21 is equal to the concrete thickness, the equivalent elastic modulus of the micro-segment is calculated according to the equivalent elastic modulus relationship; when the height of the GFRP vertical rib 21 is less than the concrete thickness, the equivalent elastic modulus of the micro-segment is still calculated according to the equivalent elastic modulus relationship, so as to make a conservative prediction of interface slip and shear force of shear connector.

[0048] The relative slippage between the GFRP base plate 111 and the concrete is negligible. The composite beam is in the elastic working stage, and there is no vertical separation between the steel beam 12 and the GFRP-concrete composite plate 11.

[0049] The analysis of each beam segment satisfies the following conditions: the resultant force of the prestressing tendons remains constant within each micro-segment; the stress of the GFRP-concrete composite slab 11 within the micro-segment is expressed as equivalent stress; the interface slip strain within the beam segment varies linearly along the longitudinal direction; and the shear force borne by the shear connector 14 within the beam segment is uniformly distributed. j The slippage of each shear connector 14 within the beam segment is taken as the first... j Interface slippage at section +1.

[0050] Example: I. Establishing a computational model A calculation model of the prestressed GFRP-concrete-steel composite beam 10 was established to determine the geometric parameters, material parameters, shear connector parameters 14, and prestressing parameters of the composite beam.

[0051] Geometric parameters include concrete thickness GFRP base plate thickness 111 h fDistance from the top surface of the composite beam to the centerline of the lower flange of steel beam 12 h The distance between the center lines of the upper and lower flanges of steel beam 12 GFRP-concrete composite slab 111 width b, steel beam 12 lower flange width b 1. The total width of the upper flange of steel beam 12 b 3. Thickness of the lower flange of steel beam 12 t 1. Thickness of the upper flange of steel beam 12 t 3. The total thickness of the web of steel beam 12 t 2. The distance e between the center of prestressing tendon 13 and the top surface of the composite beam; the thickness of GFRP vertical rib 21. a 1. The length of a micro-segment containing a GFRP vertical rib. a Length of composite beam and length of each beam segment .

[0052] Material parameters include the elastic modulus of concrete. E c , GFRP base plate along the longitudinal direction of the composite beam E f , elastic modulus of steel beam E s Concrete compressive strength f ck wait.

[0053] The 14 parameters for shear connectors include shear connector type, shear connector stiffness k, and shear connector diameter. The number of shear connectors and their arrangement along the longitudinal direction of the composite beam.

[0054] Prestressing parameters include the resultant force of prestressing tendons at each section. N j When prestress loss is ignored, the resultant force of the prestressing tendons at each section can be taken as the same value, which is the resultant force N of the prestressing tendons at the tensioning end section; when prestress loss is considered, the resultant force of the prestressing tendons at different sections can be determined based on the calculation results of prestress loss.

[0055] II. Dividing beam segments into micro-segments The composite beam is divided into several segments along its longitudinal direction. The mid-span section of the composite beam is used as the starting point for calculation, and each segment is sequentially numbered along the direction from the mid-span section to the prestressing loading end. j The beam segment is composed of the first j Section and the first j +1 section limit, its length is Z j .

[0056] Each beam segment is divided into several micro-segments. Each micro-segment corresponds to a GFRP vertical rib influence zone or an equivalent element. For a micro-segment containing GFRP vertical ribs 21, the concrete 112 region with GFRP vertical ribs within that micro-segment is equivalent to an equivalent concrete region; for micro-segments without GFRP vertical ribs 21, calculations are performed according to ordinary concrete regions.

[0057] By dividing the beam into segments and micro-segments as described above, the local stiffness variation caused by the GFRP vertical rib plate 21 along the longitudinal direction of the composite beam can be considered in the calculation, as can the variation in the number of shear connectors 14 in different beam segments.

[0058] III. Establishing the load-slip relationship of shear connection Establish the load-slip relationship for shear connections:

[0059] Where V is the shear force borne by the shear connector, and k is the stiffness of the shear connector. This represents the amount of interface slip between the GFRP-concrete composite slab 11 and the steel beam 12.

[0060] When the shear connector 14 is a stud shear connector, its stiffness k can be determined by the following formula:

[0061] Where d is the diameter of the stud. For concrete compressive strength, E c This refers to the elastic modulus of concrete.

[0062] IV. Establishing Constitutive Relations of Materials During the prestressing stage, the composite beam is in the elastic working stage, and the steel beam 12 and the GFRP base plate 111 adopt a linear elastic constitutive relationship.

[0063] The stress and strain of steel beam 12 satisfy:

[0064] The stress and strain of the GFRP base plate 111 along the longitudinal direction of the composite beam satisfy the following:

[0065] in, For the stress of the steel beam, The elastic modulus of the steel beam. For the strain of the steel beam; The stress of the GFRP base plate 111 along the longitudinal direction of the composite beam is... The strain of the GFRP base plate 11 along the longitudinal direction of the composite beam is given. E fThe elastic modulus of the GFRP base plate 111 along the longitudinal direction of the composite beam is given.

[0066] For the concrete region 112 with GFRP vertical ribs, the equivalent stress and equivalent strain are expressed, and their relationship satisfies:

[0067] in, For the equivalent stress within the micro-segment, For equivalent strain within a micro-segment, It is the equivalent elastic modulus of the micro-segment.

[0068] V. Determine the equivalent elastic modulus of the micro-segment An equivalent stress model is established for concrete segment 112 with GFRP vertical ribs in the micro-segment. The total length of the micro-segment is assumed to be... a The total thickness of the GFRP vertical rib 21 within the micro-segment is The GFRP rib thickness correction factor is Then the equivalent elastic modulus of the micro segment Calculate using the following formula:

[0069] GFRP rib thickness correction factor This is used to correct calculation errors that occur when equating the concrete 112 with GFRP vertical ribs to an equivalent concrete region. When calculating the equivalent elastic modulus of a micro-segment, the total thickness of the GFRP vertical ribs 21 within the micro-segment is used. Revised to GFRP rib thickness correction factor satisfy:

[0070] In this embodiment, .

[0071] When the GFRP-concrete composite slab 11 is not provided with GFRP vertical ribs 21 at its ends, the equivalent elastic modulus of the corresponding micro-segment is taken as the elastic modulus of concrete. E c .

[0072] When the height of the GFRP vertical rib 21 is equal to the concrete thickness, the equivalent elastic modulus of the micro-segment is calculated according to the above equivalent elastic modulus relationship; when the height of the GFRP vertical rib 21 is less than the concrete thickness, the equivalent elastic modulus of the micro-segment is still calculated according to the above equivalent elastic modulus relationship, so as to make a conservative prediction of interface slip and shear force of shear connector.

[0073] VI. Establish the recursive relationship between interface slip and interface slip strain For any i jFor each beam segment, a recursive relationship is established between the slip at both ends of the interface and the slip strain at the interface. j The beam segment is composed of the first j Section and the first j If the beam segment is limited by section +1, and the interface slip strain within this beam segment varies linearly along the longitudinal direction of the composite beam, then the following conditions must be met:

[0074] in, and The first j Section and the first j Interface slip at section +1 and The first j Section and the first j Slip strain at section +1 For the first j Beam segment length.

[0075] VII. Establishing the cross-sectional strain distribution relationship Based on the condition of shared curvature between GFRP-concrete composite slab 11 and steel beam 12, establish any... j The cross-sectional strain distribution relationship. The cross-sectional strain distribution relationship satisfies:

[0076] in, and The first j Equivalent concrete region strain at the top and bottom surfaces of the cross section For the first j Strain along the centerline of the GFRP base plate. and The first j Strain along the centerline of the upper flange and the centerline of the lower flange of the cross-section steel beam. For the first j The curvature of the cross section For concrete thickness, The thickness of the GFRP base plate is... This is the distance between the centerlines of the upper and lower flanges of the steel beam. For the first j Interfacial slip strain of the cross section.

[0077] 8. Calculate the resultant force of each component of the cross section. Based on the strain distribution and linear elastic constitutive relation of each material, calculate the first... j The resultant axial force of each component of the cross section.

[0078] No. j The resultant force in the equivalent region of concrete section 112 with GFRP vertical ribs can be calculated using the following formula:

[0079] No. j The resultant force of the GFRP base plate can be calculated using the following formula:

[0080] No. j The resultant forces of the upper flange, web, and lower flange of the steel beam are respectively denoted as: , and The resultant force of each part of the aforementioned steel beam 12 can be calculated by integration or equivalent strain based on the cross-sectional dimensions of the steel beam 12, the elastic modulus of the steel beam, and the strain at the corresponding positions.

[0081] 9. Establish the axial force equilibrium equation, bending moment equilibrium equation, and compatibility equation. For the first j Establish the axial force equilibrium equations for the cross section:

[0082] in, For the first j The resultant force of the prestressing tendons in the cross section.

[0083] At the same time, for the first j Establish the moment equilibrium equation for the cross section.

[0084]

[0085]

[0086] in, y These are the integral coordinates of the 12 sections of the steel beam along the height direction. y 2 are the integral coordinates along the height direction of the concrete 112 portion with GFRP vertical ribs.

[0087] According to the j The relationship between the difference in axial resultant force between the GFRP-concrete composite slabs at both ends of the beam segment and the shear force borne by the shear-resistant connectors within the beam segment is established using a compatibility equation:

[0088] in, and The first j The resultant force of the prestressing tendons at both ends of the beam segment, and The first j The resultant force in the concrete regions with GFRP vertical ribs at both ends of the beam segment. and The first jThe resultant force of the GFRP base plate at both ends of the beam segment For the first j Number of shear connectors within the beam segment.

[0089] 10. Apply boundary conditions and solve simultaneously. Boundary conditions are applied based on the stress characteristics of the composite beam. These boundary conditions must include at least the following: zero interface slip at the mid-span section of the composite beam and the resultant force of the GFRP-concrete composite slab at the loading end must be equal to the resultant force of the prestressing at the loading end. These conditions must be solved simultaneously.

[0090] The calculation starts at the mid-span section of the composite beam, and each section is numbered sequentially along the direction from the mid-span section to the prestressing loading end. The interface slip at the mid-span section of the composite beam satisfies:

[0091] The resultant force of the GFRP-concrete composite slab at the loading end satisfies:

[0092] in, This represents the interface slip at the mid-span section of the composite beam. The resultant force in the concrete region with GFRP vertical ribs at the loading end section is... N is the resultant force of the GFRP base plate at the loading end section, and N is the resultant force of the prestressing tendons at the loading end section.

[0093] By combining the recursive relationship between the interface slip and interface slip strain of each beam segment, the cross-sectional strain distribution relationship, the axial force balance equation of each cross-section, the bending moment balance equation, the coordination equation of each beam segment, and the above boundary conditions, a set of equations is formed for the equivalent concrete region strain, GFRP base plate strain, steel beam strain, cross-sectional curvature, interface slip strain, and interface slip amount of each cross-section.

[0094] By solving the equations, the equivalent concrete zone strain, GFRP base plate strain, steel beam strain, section curvature, interface slip strain, and interface slip amount of each section are obtained. Furthermore, the interface slip distribution between the GFRP-concrete composite slab and the steel beam along the direction from the mid-span section to the prestressed loading end is obtained.

[0095] XI. Determine the interface slip distribution and shear force distribution of shear connectors Based on the simultaneous solution results, the interface slip distribution between the GFRP-concrete composite slab and the steel beam along the longitudinal direction of the composite beam is obtained. Based on the load-slip relationship of the shear connector:

[0096] Calculate the shear force borne by shear connector 14 in each beam segment to obtain the shear force distribution of the shear connector. jThe slippage of each shear connector 14 within the beam segment can be taken as the first... j The interface slip at section +1 is used to calculate the shear force borne by a single shear connector 14 within the beam segment.

[0097] XII. Specific Calculation Examples In one embodiment, a calculation model is first established based on the structural dimensions, material parameters, resultant force of prestressed tendons, and arrangement parameters of shear connectors of the prestressed GFRP-concrete-steel composite beam. Then, the beam is divided into segments along the longitudinal direction of the composite beam from the mid-span section to the prestressing loading end, and each segment is further divided into several micro-segments based on the position of the GFRP vertical ribs. Next, the equivalent elastic modulus is determined based on whether the micro-segment contains GFRP vertical ribs, and the load-slip relationship, slip recursion relationship, cross-sectional strain distribution relationship, axial force equilibrium equation, bending moment equilibrium equation, and compatibility equation of the shear connectors are established. Finally, the boundary conditions of zero interface slip at the mid-span section of the composite beam and the resultant force of the GFRP-concrete composite slab at the loading end being equal to the resultant force of the prestressed tendons at the loading end are combined to solve the equations simultaneously, obtaining the interface slip distribution along the longitudinal direction of the composite beam, and further determining the shear force distribution borne by the shear connectors based on the load-slip relationship.

[0098] The embodiments described above are merely illustrative of specific implementations of the present invention, and while the descriptions are detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for calculating interface slip in a prestressed GFRP-concrete-steel composite beam, characterized in that, Includes the following steps: A calculation model for a prestressed GFRP-concrete-steel composite beam is established. The prestressed GFRP-concrete-steel composite beam includes a GFRP-concrete composite slab (11), a steel beam (12), a shear connector (14), and prestressing tendons (13). The GFRP-concrete composite slab (11) includes a GFRP base plate (111) and a concrete (112) with GFRP vertical ribs. The prestressing tendons (13) are located in the GFRP-concrete composite slab (11). The GFRP-concrete composite slab (11) is connected to the steel beam (12) through the shear connector (14). The composite beam is divided into several beam segments along its longitudinal direction, and each beam segment is further divided into several micro segments. Each micro segment corresponds to a GFRP rib plate influence zone or an equivalent element. Establish the load-slip relationship of the shear connector (14); An equivalent stress model was established for concrete (112) with GFRP vertical ribs in a micro-segment; Establish arbitrary beam segments j The relationship between the slip at both ends of the interface and the slip strain; Based on the co-curvature condition of GFRP-concrete composite slab (11) and steel beam (12), the cross-sectional strain distribution relationship of each section is established, and the axial force balance equation, bending moment balance equation and the coordination equation composed of the axial force difference at both ends of the beam section and the shear force of the shear connector (14) are established for each beam segment. Solve the equations of each beam segment simultaneously based on the boundary conditions to obtain the interface slip distribution of the composite beam along the longitudinal direction, and determine the shear force distribution borne by the shear connector (14) based on the interface slip distribution.

2. The method for calculating interface slip of a prestressed GFRP-concrete-steel composite beam according to claim 1, characterized in that, For a micro-segment containing GFRP vertical ribs (21), the concrete region containing GFRP vertical ribs (21) within the micro-segment is equivalent to an equivalent concrete region, and the equivalent stress and equivalent strain of the micro-segment satisfy: in, For the equivalent stress within the micro-segment, The elastic modulus of concrete. For equivalent strain within a micro-segment; For micro-segments without GFRP vertical ribs (21), calculations are performed as for ordinary concrete areas.

3. The method for calculating interface slip of a prestressed GFRP-concrete-steel composite beam according to claim 1, characterized in that, Load-slip relationship of shear connector (14): Where V is the shear force borne by the shear connector (14), and k is the stiffness of the shear connector (14). This refers to the amount of interface sliding. The shear connector (14) is a stud shear connector, and its stiffness is... k Determine using the following formula: in, d The diameter of the stud. For concrete compressive strength, This refers to the elastic modulus of concrete.

4. The method for calculating interface slippage of a prestressed GFRP-concrete-steel composite beam according to claim 1, characterized in that, The equivalent stress model of concrete (112) with GFRP vertical ribs in the micro-segment adopts the following equivalent elastic modulus relationship: in, For the equivalent elastic modulus of the micro-segment, The elastic modulus of concrete. The elastic modulus of the GFRP base plate (111) along the longitudinal direction of the composite beam is given by [missing information]. Let 'a' be the total thickness of the GFRP vertical rib (21) within the micro-segment, and 'a' be the total length of the micro-segment. The GFRP rib thickness correction factor satisfies ; The equivalent elastic modulus of concrete without GFRP vertical ribs in the micro-segment is taken as the concrete elastic modulus. E c .

5. The method for calculating interface slip of a prestressed GFRP-concrete-steel composite beam according to claim 1, characterized in that, Taking the mid-span section of the composite beam as the starting point for calculation, and sequentially numbering each section along the direction from the mid-span section to the prestressed loading end, the calculation begins with the section at mid-span. j The beam segment is composed of the first j Section and the first j +1 section defined, and the first j The interfacial slip strain within the beam segment varies linearly along the longitudinal direction of the composite beam, satisfying: in, and The first j Section and the first j Interface slip at section +1 and The first j Section and the first j Slip strain at section +1 For the first j Beam segment length.

6. The method for calculating interface slip of a prestressed GFRP-concrete-steel composite beam according to claim 1, characterized in that, arbitrary cross section j The strain distribution relationship satisfies: in, and The first j Equivalent concrete region strain at the top and bottom surfaces of the cross section For the first j Strain along the centerline of the GFRP base plate (111) section. and The first j The strain along the centerline of the upper flange and the strain along the centerline of the lower flange of the cross-section steel beam (12) For the first j The curvature of the cross section For concrete thickness, The thickness of the GFRP base plate (111) is... The distance between the centerlines of the upper and lower flanges of the steel beam (12) is... For the first j Interfacial slip strain of the cross section.

7. The method for calculating interface slip of a prestressed GFRP-concrete-steel composite beam according to claim 1, characterized in that, Based on the strain distribution and linear elastic constitutive relation of each material, calculate the first... j The axial resultant force of each component of the cross section; when establishing the axial force balance equation and the bending moment balance equation, the steel beam (12) and the GFRP base plate (111) both adopt linear elastic constitutive relations.

8. The method for calculating interface slippage of a prestressed GFRP-concrete-steel composite beam according to claim 7, characterized in that, According to the j The relationship between the difference in axial resultant force between the GFRP-concrete composite slabs at both ends of the beam segment and the shear force borne by the shear-resistant connectors within the beam segment is established using a compatibility equation. The boundary conditions include: the resultant force of the GFRP-concrete composite slab at the loading end is equal to the resultant force of the prestress at the loading end, and the interface slip at the mid-span section of the composite beam, which serves as the starting point for calculation, is zero.

9. The method for calculating interface slip of a prestressed GFRP-concrete-steel composite beam according to claim 8, characterized in that, The analysis of each beam segment satisfies the following conditions: the resultant force of the prestressing tendons in each micro-segment remains unchanged; the stress of the GFRP-concrete composite slab (11) in the micro-segment is expressed as equivalent stress; the interface slip strain in the beam segment varies linearly along the longitudinal direction; the shear force borne by the shear connector (14) in the beam segment is uniformly distributed; j The slippage of each shear connector (14) within the beam segment is taken as the first j Interface slippage at section +1.

10. The method for calculating interface slip of a prestressed GFRP-concrete-steel composite beam according to claim 1, characterized in that, The relative slip between the GFRP base plate (111) and the concrete is negligible. The composite beam is in the elastic working stage, and no vertical separation occurs between the steel beam (12) and the GFRP-concrete composite slab (11).

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