Method for calculating load capacity of end debonding failure of prestressed CFRP plate
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY
- Filing Date
- 2026-05-25
- Publication Date
- 2026-07-24
Smart Images
Figure CN122263251B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of bridge reinforcement technology, and in particular to a method for calculating the bearing capacity of prestressed CFRP slabs in the event of end-peel failure. Background Technology
[0002] With the aging of my country's infrastructure becoming increasingly prominent, the maintenance and reinforcement of concrete bridges has become a key research focus in the engineering field. Carbon fiber reinforced polymer (CFRP) composites are widely used in the reinforcement of concrete structures due to their advantages such as lightweight, high strength, corrosion resistance, and convenient construction. In particular, prestressed CFRP reinforcement technology can significantly improve the structural bearing capacity and stiffness, and enhance service performance.
[0003] Currently, externally bonded prestressed CFRP reinforcement technology has been applied to some practical engineering projects, but its reliance on permanent anchors for prestressing anchorage leads to high construction costs and significant durability risks. To address this issue, end-mounted prestressed CFRP reinforcement technology (NEEE) has been proposed. This technology involves slotting and embedding CFRP plates within the concrete cover at the beam end, utilizing resin bonding materials to achieve prestress transfer and anchorage. It eliminates the need for additional anchors, significantly reducing economic costs and durability risks.
[0004] However, NEEE-reinforced beams are still prone to concrete cover stripping (CCS) failure under bending loads. This is a common brittle failure mode that significantly reduces the reinforcement effect and may even lead to premature structural failure. Current research on this type of failure mainly focuses on traditional external fiber-reinforced composite (FRP) reinforcement methods, and a calculation model for the peeling failure bearing capacity of beams reinforced with prestressed CFRP at the ends has not yet been developed.
[0005] In terms of numerical simulation, traditional methods such as concrete damage plasticity model, extended finite element method and cohesion model have certain limitations when simulating the peeling behavior of complex interfaces. For example, they are difficult to reflect the crack propagation path, require the failure path to be predefined, and have complicated parameter calibration, which limits their application in the analysis of plate end peeling behavior.
[0006] Therefore, in response to the peeling failure behavior of the end protective layer of the prestressed CFRP reinforced beam, it is urgent to establish a bearing capacity prediction model that can accurately reflect its failure mechanism, take into account the influence of prestress, and be applicable to this specific structural form, so as to guide engineering design and construction and promote the standardized application and popularization of this reinforcement technology. Summary of the Invention
[0007] To address the above problems, this invention provides a method for calculating the bearing capacity of prestressed CFRP slab end peel failure. Based on fracture phase field simulation and parameter analysis, a calculation model for the end peel bearing capacity of CFRP-reinforced beams and slabs considering the influence of prestress is established. Furthermore, a bending-shear correlation equation is introduced, which can accurately predict the peel failure bearing capacity under combined bending and shear action.
[0008] This invention provides a method for calculating the bearing capacity of prestressed CFRP slabs in the event of end-peel failure, comprising: S1, A finite element model of a prestressed CFRP-reinforced concrete beam with end fittings was established based on the fracture phase field method; S2, the peeling failure behavior of the protective layer at the plate end of the reinforced beam under different parameters is simulated by the finite element model, and the key parameters affecting the peeling failure bearing capacity are determined based on the simulation results; S3. Based on the key parameters, establish a load-bearing capacity calculation model for plate end peeling failure, including a bending peeling load-bearing capacity sub-model and a shear peeling load-bearing capacity sub-model. S4. Based on the bearing capacity calculation model, a bending-shear correlation equation is established to comprehensively evaluate the peeling bearing capacity of the plate end section under combined bending and shear action.
[0009] Furthermore, the key parameters include concrete strength, CFRP elastic modulus, adhesive elastic modulus, CFRP prestress level, CFRP slab-support spacing, concrete cover thickness, shear span ratio, stirrup spacing, and longitudinal reinforcement ratio.
[0010] The key parameters affecting the end-stripping failure bearing capacity of the plate were identified, making subsequent modeling and parameter analysis more targeted. These parameters cover material properties, geometry, and prestress level, comprehensively reflecting the stress characteristics of the reinforcement system and providing a foundation for optimized design and parameter sensitivity analysis.
[0011] Furthermore, a prestressing influence factor is introduced into the flexural peel bearing capacity sub-model, and the pretension force is equivalent to an additional bending moment to correct the flexural peel bearing capacity. The corrected expression for the flexural peel bearing capacity sub-model is as follows: ; ; ; ; ; ; in, This refers to the peeling moment without considering the effect of prestress. The end bending moment of the slab does not take into account the effect of prestress; The additional bending moment caused by CFRP prestress; This refers to the pretension force of the CFRP sheet; The height of the CFRP plate from the beam's neutral axis; and The coefficient is dimensionless. To reinforce the ultimate bending moment of the beam; The peeling moment is calculated to account for the effects of prestress. To reinforce the actual bending moment at the plate end section when the beam experiences end-stripping failure; Strengthen the flexural stiffness of cracked beams using FRP reinforcement; Cracking flexural stiffness of unreinforced FRP beams; E frp The elastic modulus of FRP; t frp The thickness of the FRP; E c This refers to the elastic modulus of concrete. d e The effective depth for reinforcing the beam.
[0012] Introducing a prestress influence factor into the flexural peel load capacity model, which equates pretension force to additional bending moment, corrects the shortcomings of traditional models that do not consider the influence of prestress. This makes the model more suitable for prestressed CFRP reinforced structures and improves the accuracy of flexural peel load capacity prediction.
[0013] Furthermore, the expression for the shear peel bearing capacity sub-model is as follows: ; ; in, Shearing force is the force required for peeling. Contribution of concrete to the shear capacity of flexurally reinforced beams; This refers to the longitudinal reinforcement ratio in the tension zone; This represents the compressive strength of the concrete column. b is the width of the reinforced beam; The effective depth for reinforcing the beam.
[0014] In the shear peel bearing capacity model, the existing model is modified based on experimental and simulation data, which better reflects the structural characteristics of the end-embedded prestressed CFRP reinforced beam, improves the accuracy and applicability of shear peel bearing capacity calculation, and avoids overly conservative design.
[0015] Furthermore, a bending-shear correlation equation is established using the circular correlation curve fitting method, expressed as: ; in, This refers to the actual shear force at the plate end section when the beam experiences end-stripping failure.
[0016] By using circular correlation curves to establish bending-shear correlation equations, the coupling effect of bending moment and shear force in plate end peeling failure can be reasonably reflected. This is suitable for bearing capacity assessment under complex stress conditions and improves the comprehensiveness and engineering applicability of the overall calculation model.
[0017] Furthermore, the finite element model is a quarter-symmetric model, and symmetric boundary conditions are applied on the symmetry plane.
[0018] By employing a quarter-symmetric model and applying symmetric boundary conditions, the size and computational cost of the finite element model are significantly reduced, while maintaining the accuracy of the mechanical response in key regions. This modeling strategy is suitable for large-scale parametric analysis and rapid evaluation, improving the computational efficiency and practicality of the method.
[0019] Furthermore, the concrete strength ranges from 25 MPa to 80 MPa, the CFRP elastic modulus ranges from 155 GPa to 400 GPa, the adhesive elastic modulus ranges from 2.0 GPa to 4.0 GPa, the CFRP prestress level ranges from 300 MPa to 1380 MPa, the concrete cover thickness ranges from 30 mm to 46 mm, the shear span ratio ranges from 1.6 to 3.6, the stirrup spacing ranges from 50 mm to 200 mm, and the longitudinal reinforcement ratio ranges from 0.60% to 1.77%.
[0020] Defining reasonable ranges for key parameters such as concrete strength, prestress level, and protective layer thickness provides clear guidance for engineering design and parameter research. These ranges, determined based on extensive numerical simulations and experimental data, help mitigate the risk of structural performance degradation or damage caused by unreasonable parameter values in practical applications.
[0021] Furthermore, when establishing the finite element model, the transition structure at the junction of the surface-mounted section, the oblique-embedded section and the flat-embedded section of the CFRP board is simplified, and the arc-shaped transition is replaced with a folded transition.
[0022] When establishing the finite element model, the geometry of the CFRP plate at the turning point is reasonably simplified, which significantly reduces the modeling complexity and mesh generation difficulty, while ensuring the model accurately simulates the overall stress behavior and failure mode.
[0023] Compared with existing technologies, the beneficial effects of this invention are as follows: by applying the fracture phase field method to simulate the end-plate peeling behavior of prestressed CFRP reinforced beams, the limitations of traditional numerical methods, such as the need to pre-set the failure path and the difficulty in parameter calibration, when simulating peeling at complex interfaces, are overcome; by establishing a bending and shear peeling sub-model that considers the influence of prestress, and combining it with the bending-shear correlation equation, a comprehensive evaluation of the peeling bearing capacity under combined bending and shear stress is achieved, which significantly improves the prediction accuracy and engineering applicability, and provides a reliable basis for the design and safety assessment of this type of reinforced structure. Attached Figure Description
[0024] To more clearly illustrate the technical solutions in the embodiments of this drawing or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this drawing. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.
[0025] Figure 1 This is a flowchart of the method of the present invention; Figure 2 Diagram showing the reinforcement design and loading method for the reinforced beam; Figure 3 A schematic diagram of a quarter-strength reinforced beam model; Figure 4 A comparison of experimental and simulation results for reinforcing the peeling interface of the beam; Figure 5 A comparison chart of the phase field model prediction results and experimental results for reinforced beams; Figure 6 A comparison of experimental and simulated load-deflection curves based on NEEE-1 specimens; Figure 7 A comparison of experimental and simulated load-deflection curves based on NEEE-2 specimens; Figure 8 A comparison of experimental and simulated CFRP strain distributions based on NEEE-1 specimens; Figure 9 A comparison of experimental and simulated CFRP strain distributions based on NEEE-2 specimens; Figure 10 Diagram of concrete shear-crushing failure mode; Figure 11 Diagram of concrete crushing failure mode; Figure 12 Diagram of concrete shear failure mode; Figure 13 Correlation diagram of simulated ultimate bearing capacity of reinforced beam and influencing factors; Figure 14 The bending-shear correlation curve for plate end peeling failure; Figure 15 This is a verification diagram of the bearing capacity model for the peeling failure of the protective layer at the plate end. Detailed Implementation
[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described and illustrated below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. All other embodiments obtained by those skilled in the art based on the embodiments provided by this invention without inventive effort are within the scope of protection of this invention.
[0027] This invention provides a method for calculating the bearing capacity of prestressed CFRP slabs in the event of end-peel failure, such as... Figure 1 As shown, it specifically includes: S1. A finite element model of a prestressed CFRP-reinforced concrete beam with end fittings was established based on the fracture phase field method.
[0028] A finite element model of a flexurally reinforced concrete beam with end-mounted NEEE prestressed CFRP slabs was established using the fracture phase-field method. The reinforced beam dimensions are 3500mm × 160mm × 350mm (length × width × height), with a clear span of 3300mm. Two 16mm diameter HRB400 ribbed longitudinal bars are arranged on both the tension and compression sides, and 8mm diameter HRB400 stirrups are arranged at equal intervals every 100mm in the longitudinal direction (e.g., ...). Figure 2 As shown in Table 1, the specific structure and parameters of the NEEE prestressed CFRP reinforced beam are as follows.
[0029] Table 1. Structure and Parameters of Reinforced Beams
[0030] To reduce computational costs, only one-quarter of the model is built, such as... Figure 3As shown, symmetrical boundary conditions are applied to the symmetry plane. Furthermore, to simulate the loading and support behavior of the beam, the vertical degrees of freedom at the bottom support are constrained, while a vertically downward displacement boundary condition is applied to the top support. The global size of the model is approximately 7 mm, and all elements are connected at common nodes. To reduce the difficulty and complexity of model mesh generation, three assumptions are made regarding the model: 1. Ignore the resin thickness fluctuation, that is, the resin thickness between the CFRP board and the concrete in the surface-mounted section is consistent; 2. At the junction of the surface-mount, oblique-embedded, and flat-embedded sections, CFRP uses a folded angle instead of an actual arc-shaped transition; 3. The resin adhesive does not crack, and the CFRP board-resin adhesive interface does not peel off, thus simplifying the bonding and slip relationship.
[0031] S2, the peeling failure behavior of the protective layer at the plate end of the reinforced beam is simulated under different parameters using the finite element model, and the key parameters affecting the peeling failure bearing capacity are determined based on the simulation results.
[0032] Comparing the phase field model prediction results and experimental results of NEEE prestressed CFRP-strengthened beams, Figure 4 (a) and 4(b) show two types of delamination interfaces that occur in the surface-mounted and end-mounted sections when the NEEE prestressed CFRP plate-strengthened beam fails. Their locations and stress behaviors are effectively simulated in the phase-field numerical model. Figure 4 (c)). Additionally, Figure 5 (a) and Figure 5 (b) The experimental and simulation results of crack distribution in NEEE-1 were compared. It can be seen that the model accurately captures the distribution of bending and shear cracks in the reinforced beam, especially the concrete cover peeling (CCS) failure behavior at the slab end, that is, the horizontal branches and intersecting cracks extending from the critical oblique crack at the slab end (or the flat-embedded-oblique-embedded junction in NEEE technology), which were also simulated well.
[0033] Table 2 compares the model analysis results and experimental results for the ultimate bearing capacity and deflection of the reinforced beam. The data in the table show that the deviation in ultimate bearing capacity is distributed within the range of 3.03%-3.45%, while the deviation in deflection is relatively larger, but the maximum deviation is only 16.11%. Considering that the test results for deflection fluctuate more, this error is acceptable. Therefore, overall, the model results and experimental results can be considered to be in good agreement. The load-deflection simulation curves of the reinforced beam based on NEEE-1 and NEEE-2 specimens are compared separately, as shown below. Figure 6 , 7As shown, the simulated curve has two inflection points, corresponding to the beam cracking and the steel reinforcement yielding states, respectively, which conforms to the typical stress characteristics of reinforced concrete beams. Furthermore, the slopes of each segment of the simulated curve are close to the experimental results, indicating that the phase-field numerical model can well reflect the stiffness degradation law of the strengthened beam. The ultimate bearing capacity and mid-span deflection extracted from the load-deflection curve are shown in Table 2. The deviation rates of the simulated ultimate bearing capacity values for the two beams are 3.45% and 3.03%, respectively, and the deviation rates of the simulated ultimate mid-span deflection values are 16.11% and 2.59%, respectively, showing good accuracy.
[0034] Table 2. Bending test and simulation results of NEEE prestressed CFRP plate reinforced concrete beams
[0035] The experimental and simulation results of the CFRP tensile strain distribution of the two specimens are as follows: Figure 8-9 As shown in the figure, the phase-field numerical model effectively simulates the distribution of tensile strain in CFRP and the strain magnitude at key sections. The simulated curve matches the experimental CFRP strain distribution well, and the maximum CFRP strain is almost identical. The simulation error should be attributed to experimental measurement errors. In summary, the failure modes, load-deflection curves, and basic laws of CFRP strain distribution in the experiments and simulations are compared. Therefore, the method proposed in this invention, which uses the fracture phase-field method to simulate the stress behavior of reinforced beams, is feasible and can effectively reproduce the CCS failure behavior of NEEE prestressed CFRP plate reinforced beams.
[0036] The concrete cover peeling (CCS) failure mode of reinforced beams occurs under bending moment and shear force at the CFRP ends. Since the existing experimental dataset of NEEE reinforced beams exhibiting CCS failure is very limited and insufficient to support parametric analysis, this invention establishes a dataset based on 103 phase-field models of NEEE prestressed CFRP reinforced beams. This dataset is based on the material and geometric parameters of specimen NEEE-2 and is divided into 10 parameter series. Table 3 presents the parametric design schemes. Series 1–9 are studied individually for the influence of the following parameter variations: concrete cube compressive strength (… ), CFRP elastic modulus ( ), elastic modulus of adhesive ( ), CFRP prestress level ( ), CFRP plate-support spacing ( ), Concrete cover thickness ( ), shear span ratio ( ), stirrup spacing ( ) and longitudinal reinforcement ratio ( ); Series 10 studies , , and The effects of coupling changes.
[0037] It should be noted that in all models, the horizontal and diagonal embedding lengths (300 mm and 200 mm, respectively) within the NEEE segment remain constant. According to the modeling assumptions, the influence of these two parameters on CCS behavior is negligible. All models use a uniform CFRP strip geometry (30 mm wide × 3 mm thick), which is selected based on the NEEE empirical design criteria to optimize interfacial bonding performance. The variation range of the concrete cover thickness is intentionally extended beyond the conventional design range to enhance the discernibility of qualitative trend analysis. Table 3 shows the range of construction parameters used in the parametric analysis based on the phase-field model.
[0038]
[0039] Figure 13 (a) to Figure 13 (i) The simulation results of the ultimate bearing capacity of the phase field numerical models corresponding to series 1–9 in Table 3 are presented respectively. Figure 13 (a) to Figure 13 (i) The vertical axis represents the ultimate bearing capacity. Except when the CFRP plate-support spacing mm model ( Figure 13 (e) The model corresponding to the hollow square) experiences concrete crushing failure, shear span ratio The model ( Figure 13 (g) The model corresponding to the hollow circle) experiences concrete shear-crushing failure and stirrup spacing. mm model ( Figure 13 Except for the model corresponding to the forked circle in (h) that experiences shear failure, the other models ( Figure 13 (a) to Figure 13 (i) All models corresponding to the solid circles in the model experienced CCS failure. The concrete shear-crushing failure mode, concrete crushing failure mode, and concrete shear failure mode are as follows: Figure 10-12 As shown.
[0040] For variations in material parameters (Series 1–3), the bearing capacity of CCS ( In CFRP elastic modulus and the elastic modulus of adhesives It remains basically stable when changes occur, but varies with the compressive strength of the concrete cube. It increased slightly due to the improvement. However, when When the pressure increases from 25 MPa to 80 MPa The increase of only about 10% indicates that material properties have a limited impact on the load-bearing capacity of CCS in the NEEE system. In contrast, variations in geometric parameters (Series 4–9) have a significant impact on the load-bearing capacity of CCS: as the CFRP plate-support spacing increases... Increase Reduced by 17.6%; with the increase in concrete protective layer thickness Increase Decreased by 24.9%; with the shear span ratio Increase Reduced by 21.2%; with the increase in stirrup spacing Increase A decrease of 15.6%. Conversely, when the longitudinal reinforcement ratio... When it increases from 0.6% to 1.77%, The longitudinal reinforcement ratio increased by 60.1%, demonstrating a significant enhancement effect on the bearing capacity of the CCS. Furthermore, the analysis results indicate that the optimal range for CFRP prestress level is 600–800 MPa. When the prestress exceeds this range, under simulated loading conditions, stress concentration occurs at the ends of the CFRP slab. Instead, it decreases by about 15%. This is because in the 600-800MPa range, the upward reaction force generated by the prestress offsets part of the peeling stress generated by the external load, but above 800MPa, the huge initial shear stress reserve at the end makes the material more likely to reach the fracture threshold, resulting in a decrease in load-bearing capacity.
[0041] S3. Based on the key parameters, establish a load-bearing capacity calculation model for plate end peeling failure, including a bending peeling load-bearing capacity sub-model and a shear peeling load-bearing capacity sub-model.
[0042] The construction process of the flexural peel bearing capacity sub-model is as follows: Considering the characteristics of the end-embedded prestressed CFRP reinforced beam, the pretension force is equivalent to an additional bending moment acting on the reinforced beam to reflect its influence on the flexural peel bearing capacity. Finally, a calculation formula for the flexural peel bearing capacity considering the prestressing effect and applicable to end-embedded prestressed CFRP reinforced beams is obtained, and its expression is as follows: ; ; ; ; ; ; in, This refers to the peeling moment without considering the effect of prestress. The end bending moment of the slab does not take into account the effect of prestress; The additional bending moment caused by CFRP prestress; This refers to the pretension force of the CFRP sheet; The height of the CFRP plate from the beam's neutral axis; and The coefficient is dimensionless. To reinforce the ultimate bending moment of the beam; Strengthen the flexural stiffness of cracked beams using FRP reinforcement; Cracking flexural stiffness of unreinforced FRP beams; The peeling moment is calculated to account for the effects of prestress. To reinforce the actual bending moment at the plate end section when the beam experiences end-stripping failure; E frp The elastic modulus of FRP; t frp The thickness of the FRP; E c This refers to the elastic modulus of concrete. d e The effective depth for reinforcing the beam.
[0043] The construction process of the shear peel bearing capacity sub-model is as follows: Based on the fracture phase field method model of 103 end-embedded prestressed CFRP reinforced beams, the shear peel bearing capacity sub-model is constructed, and its expression is as follows: ; in, Shearing force is the force required for peeling. The contribution of concrete to the shear capacity of the flexurally strengthened beam, without considering the shear contribution of internal reinforcement, is calculated using the following formula: ; in, This refers to the longitudinal reinforcement ratio in the tension zone; The compressive strength of the concrete column is 0.79. , This refers to the standard value of the compressive strength of a concrete cube. b is the width of the reinforced beam; To increase the effective depth of the beam, ≥1.4.
[0044] S4. Based on the bearing capacity calculation model, a bending-shear correlation equation is established to comprehensively evaluate the peeling bearing capacity of the plate end section under combined bending and shear action.
[0045] Specifically, phase field model data from 103 end-embedded prestressed CFRP-reinforced beams were used, and dimensionless circular curves were fitted to them. Finally, circular interaction curves suitable for end-embedded prestressed CFRP-reinforced beams were obtained, such as... Figure 14 As shown, the experimental values and the theoretical fitting curves agree well, indicating that the model can accurately predict the plate end peeling failure of the reinforced beam. Its expression is as follows: ; in, To reinforce the actual bending moment at the plate end section when the beam experiences end-stripping failure; This refers to the actual shear force at the plate end section when the beam experiences end-stripping failure.
[0046] To verify the accuracy of the proposed model, test data of nine NEEE prestressed CFRP-reinforced beams that experienced CCS failure were collected and compiled (see Tables 4 and 5). Figure 14 The comparison results between the predicted values and experimental values of the model of this invention are given, and the correlation coefficient reaches [value missing]. With the exception of a few specimens, the prediction errors were all less than 10%, and most were controlled within 5%, indicating that the model has high prediction accuracy. Figure 15 Further comparative analysis was conducted with other models. The results show that the model of this invention has higher accuracy in predicting the CCS bearing capacity of NEEE-reinforced beams; its overall prediction performance is better than existing theoretical models established for external reinforcement technology.
[0047] In summary, the proposed modified model can effectively predict the prestressing effect of CFRP slabs and the structural characteristics of NEEE, providing a more reliable theoretical basis for the design of the bearing capacity of CCS beams reinforced with NEEE prestressed CFRP slabs.
[0048]
[0049]
[0050] It should be noted that the present invention is not limited to the above-described embodiments. The above embodiments are merely examples, and any embodiments that have the same structure and perform the same effects as the technical concept within the scope of the present invention are included within the scope of the present invention. Furthermore, various modifications that can be conceived by those skilled in the art to the embodiments, and other ways of constructing by combining some of the constituent elements of the embodiments, without departing from the spirit of the present invention, are also included within the scope of the present invention.
Claims
1. A method for calculating the bearing capacity of prestressed CFRP slabs under end-peel failure, characterized in that, include: S1, A finite element model of a prestressed CFRP-reinforced concrete beam with end fittings was established based on the fracture phase field method; S2, the peeling failure behavior of the protective layer at the plate end of the reinforced beam under different parameters is simulated by the finite element model, and the key parameters affecting the peeling failure bearing capacity are determined based on the simulation results; S3. Based on the key parameters, establish a load-bearing capacity calculation model for plate end peeling failure, including a bending peeling load-bearing capacity sub-model and a shear peeling load-bearing capacity sub-model. In the bending peel bearing capacity sub-model, a prestressing influence factor is introduced, and the pretension force is equivalent to an additional bending moment to correct the bending peel bearing capacity. The expression of the corrected bending peel bearing capacity sub-model is as follows: ； ； ； ； in, This refers to the peeling moment without considering the effect of prestress. The end bending moment of the slab does not take into account the effect of prestress; The additional bending moment caused by CFRP prestress; This refers to the pretension force of the CFRP sheet; The height of the CFRP plate from the beam's neutral axis; and The coefficient is dimensionless. To reinforce the ultimate bending moment of the beam; The peeling moment is calculated to account for the effects of prestress. To reinforce the actual bending moment at the plate end section when the beam experiences end-stripping failure; The formula for calculating the dimensionless coefficient is as follows: ； ； in, Strengthen the flexural stiffness of cracked beams using FRP reinforcement; Cracking flexural stiffness of unreinforced FRP beams; E frp The elastic modulus of FRP; t frp The thickness of the FRP; E c This refers to the elastic modulus of concrete. d e To reinforce the effective depth of the beam; The expression for the shear peel bearing capacity sub-model is: ； ； in, Shearing force is the force required for peeling. Contribution of concrete to the shear capacity of flexurally reinforced beams; This refers to the longitudinal reinforcement ratio in the tension zone; This refers to the compressive strength of the concrete column; b is the width of the reinforced beam; S4. Based on the bearing capacity calculation model, a bending-shear correlation equation is established to comprehensively evaluate the peeling bearing capacity of the plate end section under combined bending and shear action. The bending-shear correlation equation is established using the circular correlation curve fitting method, and its expression is as follows: ； in, This refers to the actual shear force at the plate end section when the beam experiences end-stripping failure.
2. The method for calculating the bearing capacity of prestressed CFRP slabs under end-peel failure as described in claim 1, characterized in that, The key parameters include concrete strength, CFRP elastic modulus, adhesive elastic modulus, CFRP prestress level, CFRP slab-support spacing, concrete cover thickness, shear span ratio, stirrup spacing, and longitudinal reinforcement ratio.
3. The method for calculating the bearing capacity of prestressed CFRP slabs under end-peel failure as described in claim 1, characterized in that, The finite element model is a quarter-symmetric model, and symmetric boundary conditions are applied on the symmetry plane.
4. The method for calculating the bearing capacity of prestressed CFRP slabs under end-peel failure as described in claim 2, characterized in that, The concrete strength ranges from 25 MPa to 80 MPa, the CFRP elastic modulus ranges from 155 GPa to 400 GPa, the adhesive elastic modulus ranges from 2.0 GPa to 4.0 GPa, the CFRP prestress level ranges from 300 MPa to 1380 MPa, the concrete cover thickness ranges from 30 mm to 46 mm, the shear span ratio ranges from 1.6 to 3.6, the stirrup spacing ranges from 50 mm to 200 mm, and the longitudinal reinforcement ratio ranges from 0.60% to 1.77%.
5. The method for calculating the bearing capacity of prestressed CFRP slabs under end-peel failure as described in claim 1, characterized in that, When establishing the finite element model, the transition structure of the CFRP board at the junction of the surface-mounted section, the oblique-embedded section and the flat-embedded section is simplified, and the arc-shaped transition is replaced with a beveled transition.