Method for predicting tensile strength of FRP (Fiber Reinforce Plastic) bar anchoring area under different radial stresses

Abstract

The invention discloses a method for predicting the tensile strength of an FRP (Fiber Reinforce Plastic) bar anchoring area under different radial stresses. The method comprises the following steps: preparing a group of anchoring test pieces for different anchoring modes of the same FRP bar; carrying out a mechanical test on the group of prepared anchoring test pieces and obtaining core mechanical parameters; the obtained core mechanical parameters are processed, and stress parameters of the anchoring test piece are calculated; calculating a tensile strength theoretical value according to the obtained core mechanical parameters obtained by the test and the stress parameters obtained by calculation; performing quadratic fitting according to the calculated theoretical value of the tensile strength to obtain a prediction curve of the relationship between the tensile strength and the radial stress; and predicting the tensile strength under different radial stresses according to the obtained prediction curve of the tensile strength and the radial stress. According to the method, the technical blank of FRP rib anchoring area strength prediction is filled up, universality and accuracy are both achieved, and reliable theoretical support is provided for design of the FRP rib anchoring area in an external prestressing reinforcing structure in civil engineering.

Description

Technical Field

[0001] This invention belongs to the field of fiber reinforced composite (FRP) application technology, specifically relating to a method for predicting the strength of the anchorage zone of FRP bars, applicable to the performance evaluation and design optimization of the anchorage zone of BFRP bars, CFRP bars, and GFRP bars in external prestressed reinforcement structures in civil engineering. Background Technology

[0002] Fiber-reinforced polymer (FRP) composites are made by impregnating fiber yarns with resin in a certain proportion and then molding them through processes such as pultrusion, injection molding, and compression molding. FRPs, with their advantages of being lightweight, high-strength, corrosion-resistant, and fatigue-resistant, occupy an important position in external prestressed reinforcement engineering. The anchorage zone, as the core part connecting the FRP reinforcement to the structure, directly determines the safety and stability of the overall structure. Therefore, predicting the strength of the FRP reinforcement anchorage zone is a key technical issue in this field. However, existing research lacks methods for predicting the strength of the FRP reinforcement anchorage zone, and quantitative relationships are missing. Radial stress has not been quantified, and a precise quantitative relationship between the tensile strength and radial stress of the FRP reinforcement anchorage zone has not been established. Furthermore, no unified radial stress limit has been set for different FRP reinforcements, resulting in a lack of clear basis in engineering design and reliance on experience, posing significant safety hazards. This severely restricts the engineering application and technological development of FRP reinforcements. Therefore, a method for predicting the strength of the FRP reinforcement anchorage zone is urgently needed. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for predicting the strength of the anchorage zone of FRP bars, so as to achieve accurate and reliable prediction of the strength of the anchorage zone of FRP bars.

[0004] Methods for predicting the tensile strength of FRP reinforcement anchorage zone under different radial stresses include: Step 1. Prepare a set of anchorage specimens of the same type of FRP bar with different anchorage methods; Step 2. Conduct mechanical tests on a set of prepared anchorage specimens and obtain core mechanical parameters, including longitudinal tensile strength, longitudinal compressive strength, transverse compressive strength and in-plane shear strength. Step 3. Process the obtained core mechanical parameters and calculate the stress parameters of the anchorage specimen. The stress parameters include ultimate load, ultimate strength, elastic modulus, ultimate strain, average ultimate load, average ultimate strength, average elastic modulus, average ultimate strain, standard deviation of ultimate load, standard deviation of ultimate strength, standard deviation of elastic modulus, standard deviation of ultimate strain, standard deviation of ultimate load, coefficient of variation of ultimate load, coefficient of variation of ultimate strength, coefficient of variation of elastic modulus, coefficient of variation of ultimate strain, radial stress, and shear stress. Step 4. Calculate the theoretical value of tensile strength based on the core mechanical parameters obtained from the experiment in Step 2 and the stress parameters calculated in Step 3; Step 5. Perform a quadratic fitting based on the calculated theoretical value of tensile strength to obtain a predicted curve of the relationship between tensile strength and radial stress; predict the tensile strength under different radial stresses based on the obtained predicted curve of tensile strength and radial stress.

[0005] In step 4, the theoretical value of tensile strength is calculated using strength criteria; the strength preparation includes the maximum stress criterion, the maximum strain criterion, the Hoffman criterion, the Hashin criterion, the Tsai-Wu criterion, and the Tsai-Hill criterion.

[0006] The stress interaction coefficient F in the Tsai-Wu criterion 12 The value is obtained by dynamic correction. The specific steps are as follows: (1) Obtain the core mechanical parameters of FRP reinforcement: transverse tensile strength Y t Fiber volume fraction V f Transverse compressive strength Y c , where Y t V is determined by resin tensile strength test. f Determined by pultrusion process parameters, Y c Determined by actual measurements from a transverse compression test; (2) Determine the proportionality coefficient β: β is a dimensionless coefficient with a value range of 0.35~0.40. It is calibrated by at least 3 sets of tensile test data of FRP bars under different radial stresses. The calibration requirement is: when |σ2|≤β·Y c At that time, the theoretical value of tensile strength and the longitudinal tensile strength X under no radial stress t The relative error is ≤1.0%; (3) Calculate the critical value of radial stress σ 2,cr =β·Y c Obtain the radial stress σ2 in the anchorage zone of the FRP bar and calculate its absolute value |σ2|. (4) Calculate the radial stress influence factor k: If |σ²|≤σ 2,cr If k=1, then k=1; If |σ²|>σ 2,cr Then k = 1 + α·(|σ²| - σ 2,cr ), where α is the proportionality coefficient, with a value ranging from 0.0015 to 0.0025; (5) According to the formula The corrected stress interaction coefficient F was calculated. 12 ; (6) The proportionality coefficient α is calibrated by the following method: select at least 3 groups |σ2|>σ 2,cr The tensile test data of FRP bars will be corrected to F 12 Substitute the values ​​into the Tsai-Wu criterion formula to calculate the theoretical value of tensile strength. Then, adjust the specific value of α to ensure that the relative error between each set of experimental values ​​and the theoretical value is ≤1.0%.

[0007] In step 4, at least three strength criteria are used to calculate a theoretical value of tensile strength for each criterion. Based on the calculated theoretical value of tensile strength and the relative error, the theoretical value of tensile strength calculated by the optimal strength criterion is selected as the final theoretical value of tensile strength.

[0008] In step 5, the radial stress limit of the anchorage zone is determined based on the predicted curve of the relationship between tensile strength and radial stress.

[0009] In step 1, FRP reinforcement includes three types: basalt fiber reinforced polymer reinforcement, carbon fiber reinforced polymer reinforcement, and glass fiber reinforced polymer reinforcement.

[0010] In step 1, the anchoring methods include three types: adhesive anchoring, friction anchoring, and integrated anchoring. Compared with the prior art, the beneficial effects of the present invention are: 1. High prediction accuracy: The prediction model is built based on the material properties of FRP bars and the mechanical transmission mechanism of the anchorage zone, which breaks through the applicability limitations of empirical formulas, effectively reduces prediction errors, and provides reliable data support for engineering design.

[0011] 2. High practicality: The model's calculation logic is simple, and the required parameters can be easily obtained through conventional experiments. It does not require complex equipment or lengthy calculation processes, making it easy for engineering technicians to apply directly.

[0012] 3. Wide adaptability: It can cover different types of FRP bars (such as GFRP, CFRP) and various anchorage forms (bonded, mechanical anchorage, etc.), and is suitable for anchorage design in various scenarios such as civil engineering and marine engineering.

[0013] 4. Significant engineering value: By accurately predicting the ultimate strength of the anchorage zone, the design of anchorage structure parameters can be optimized, reducing problems such as excessive reinforcement or insufficient anchorage, thereby reducing engineering costs and safety risks. Attached Figure Description

[0014] Figure 1 is a schematic diagram of the anchoring method; Figure 2 shows a comparison of the ultimate strength of three FRP bars under different anchorage methods; Figure 3 shows a comparison of the elastic modulus of three FRP bars under different anchorage methods; Figure 4 shows the prediction models for the tensile strength of three FRP bars under different radial stresses. Detailed Implementation

[0015] This invention discloses a method for predicting the tensile strength of the anchorage zone of FRP bars under different radial stresses. The strength criteria that can be selected in the prediction method include: (1) Maximum Stress Criterion: Core formula: Fiber-direction tensile failure:

[0016] Fiber orientation compression failure:

[0017] Lateral tensile failure:

[0018] Lateral compression failure:

[0019] Shear failure:

[0020] Applicable conditions: Low radial stress (|σ2|≤β·Y) c It features stress-free coupling (only axial tensile stress σ1), making it suitable for preliminary engineering design and rapid estimation (priority requirement: simplicity > accuracy).

[0021] (2) Maximum Strain Criterion: Core formula: Fiber-direction tensile failure: E1 is the longitudinal elastic modulus; Fiber orientation compression failure: ; Lateral tensile failure: E2 is the transverse elastic modulus; Lateral compression failure: ; Shear failure: G 12 It is the in-plane shear modulus; Applicable conditions: The stress state is simple and there is no severe stress concentration, making it suitable for deformation control design (such as seismic structures) and scenarios where failure strain is a concern (priority requirement: strain correlation > accuracy).

[0022] (3) Tsai-Hill Criterion: Core formula: ; Applicable conditions: Weak stress coupling (axial tensile stress σ1 + radial compressive stress σ2), medium radial stress, suitable for conventional engineering design (priority requirements: medium accuracy + ease of operation).

[0023] (4) Hashin Criterion: The core formula (FRP reinforcement anchorage zone mainly suffers from fiber-direction tensile failure) Fiber-direction tensile failure: ; Fiber orientation compression failure: ; Matrix tensile failure: ; Matrix compression failure: ; Applicable conditions: With moderate stress coupling and significant shear stress, it is suitable for scientific research experiments and failure mechanism analysis (priority requirement: distinguishing failure modes > efficiency).

[0024] (5) Hoffman Criterion: Core formula:

[0025] Applicable conditions: Complex stress coupling (σ1+σ2+σ) 12 It has a full radial stress range and is suitable for precise engineering design and critical structures (priority requirements: high precision + stability).

[0026] (6) Tsai-Wu Criterion: Core formula: ; , , , , , (Revised formula); Applicable conditions: Strong stress coupling, high radial stress (|σ2|>β·Yc), novel FRP reinforcement, suitable for high-precision engineering design (priority requirement: extremely high precision > simplicity).

[0027] In all formulas, X t X represents the longitudinal tensile strength.c Y represents longitudinal compressive strength. t For tensile strength; Y c S is the compressive strength; S is the in-plane shear strength; σ1 is the axial stress; σ2 is the radial stress; σ 12 V is the in-plane shear stress; f For volume fraction.

[0028] The present invention relates to a method for predicting the tensile strength of FRP reinforcement anchorage zone under radial stress, the steps of which are as follows: 1. Specimen Preparation and Parameter Acquisition: Specimens are prepared, relevant mechanical tests are conducted, and relevant test data are obtained. The core mechanical parameters of the required FRP reinforcement are then calculated. The test data are statistically analyzed and compiled into tables.

[0029] 2. Strength Criterion Calculation: Substitute the experimental data and parameters into the selected strength criterion to calculate the theoretical value of tensile strength. Key points for calculation of different criteria: 1) Maximum stress / strain criterion: Calculated directly based on a single failure condition; 2) Tsai-Hill / Hashin / Hoffman criterion: Substitute the corresponding coupled stress formula to solve directly; 3) Modified Tsai-Wu criterion: The dynamic stress interaction coefficient F needs to be determined first. 12 The calculation steps are as follows: a. Obtain the core parameters (Y) t V f Y c ); b. Calibrate the scaling factor β (0.35~0.40, default 0.38) and calculate the critical radial stress σ. 2,cr =β·Y c ; c. Calculate the radial stress influence factor k (|σ2|≤σ) in segments. 2,cr When k=1; |σ²|>σ 2,cr When k = 1 + α·(|σ²| - σ 2,cr (α is 0.0015~0.0025). d. Press Calculate dynamic F 12 ; e. Calibrate α to ensure that the relative error between the theoretical value and the experimental value is ≤1.0%, and then substitute it into the criterion formula for calculation.

[0030] 4) Accurate acquisition of radial stress (special anchorage types): For anchorage types where radial stress is difficult to obtain through theoretical calculation, a special calculation model is established using finite element software to accurately acquire radial stress data.

[0031] 5) Establishment of tensile strength prediction model and determination of radial stress limit: Based on the selected optimal strength criterion, the test data are fitted to obtain the relationship expression and corresponding curve between the tensile strength and radial stress of FRP bars; combined with relevant specifications, a unified limit of radial stress in the anchorage zone is determined.

[0032] Example 1 This embodiment provides a method for predicting the tensile strength of the anchorage zone of FRP bars under different radial stresses, including the following steps: Step 1: Selection of Strength Criteria Based on actual needs and the applicable conditions of the formula, at least three strength criteria are selected. In this experiment, four strength criteria are selected: Hoffman criterion, Hashin criterion, Tsai-Wu criterion, and Tsai-Hill criterion.

[0033] The reasons are as follows: Hoffman Criterion: Applicable conditions match; the three selected anchoring methods cover all stress coupling types: "no coupling (BA type), weak coupling (FA type), and strong coupling (HM type)". The Hoffman criterion is explicitly applicable to "complex stress coupling (σ1+σ2+σ)". 12 "Full radial stress range" can be compatible with all anchoring conditions without the need to switch criteria.

[0034] Tsai-Wu Criterion (Revised): Outstanding accuracy under high stress conditions, with an average error of less than 1.0%, dynamically corrected to adapt to different FRP bars, meeting the extremely high precision requirements of key structures.

[0035] The Tsai-Hill criterion has a simple formula and requires fewer parameters. Compared to the Hoffman / Tsai-Wu criterion, it does not require transverse tensile strength Y. t Precision testing (Y t It requires resin testing and is relatively complex to operate. It can be calculated using only conventional mechanical parameters, making it suitable for preliminary engineering design or batch calculation scenarios. It meets the accuracy requirements of conventional design (error ≤3%) and is highly efficient.

[0036] Hashin Criterion: The only criterion that can distinguish between fiber and matrix failure modes, and is suitable for the needs of scientific research experiments for failure mechanism analysis.

[0037] Step 2, Specimen Preparation Anchorage specimens were prepared using FRP bars. The FRP bars can be BFRP bars, CFRP bars, etc.

[0038] The anchorage specimens include specimens formed by three anchorage methods: bonded anchorage, friction anchorage, and integrated anchorage. Schematic diagrams of the three anchorage methods are shown in Figure 1, and the specific structural parameters are as follows: Bonded anchorage (hereinafter referred to as BA): The outer sleeve is a seamless steel pipe with an outer diameter of 14mm, a wall thickness of 2mm, and a length of 300mm. The inner surface of the steel pipe is sanded and cleaned with alcohol, and then injected with Sanyou epoxy resin. The surface of the BFRP reinforcement anchorage area is treated with sand. The total length of the specimen is 1000mm. Friction anchorage (hereinafter referred to as FA): The outer sleeve is a seamless steel pipe with an outer diameter of 32mm, a wall thickness of 3mm, and a length of 300mm. The inner surface treatment of the steel pipe is the same as that of the BA type. Expansion cement is poured in, and the total length of the specimen is 1000mm. Homogenous materials (hereinafter referred to as HM): The anchor end is wrapped with 2400tex basalt fiber roving impregnated with 3-Yo epoxy resin, cured at room temperature for 1 day through a mold and then left to stand for 6 days. After molding, the anchor end is 150mm long and 10mm in diameter, and the total length of the specimen is 600mm.

[0039] In this embodiment, three types of reinforcement were used to prepare the anchorage specimen. The three types of reinforcement are: BFRP reinforcement: Made of 2400tex basalt fiber from Zhejiang Shijin Basalt Fiber Co., Ltd. + Reco vinyl ester resin, formed by pultrusion process, with a fiber volume fraction of 60% and a diameter of 6mm; CFRP reinforcement: Made of T700 carbon fiber + epoxy resin, formed by pultrusion process, with a fiber volume fraction of 65% and a diameter of 6mm; GFRP reinforcement: Made of E-glass fiber + unsaturated polyester resin, formed by pultrusion process, with a fiber volume fraction of 58% and a diameter of 6mm.

[0040] The grouting materials for all three anchoring methods were allowed to stand at room temperature for 7 days to ensure full curing, and at least 3 specimens were prepared for each type of reinforcement and each anchoring method. In this embodiment, 5 specimens were prepared for each type of reinforcement and each anchoring method.

[0041] Step 3: Testing of core mechanical parameters Tests were conducted on specimens with three anchoring methods, and the core mechanical parameters of the three FRP bars were obtained, including longitudinal tensile strength, longitudinal compressive strength, transverse compressive strength, and in-plane shear strength.

[0042] The experimental equipment for obtaining the core mechanical parameters of FRP reinforcement is as follows: The Swiss-made LFV-1000 hydraulic servo fatigue testing machine (maximum load ±900kN, load accuracy 0.01kN, displacement accuracy 0.001mm) was used as the core testing equipment, equipped with extensometers, rigid pressure plates, and semi-circular channel steel loading blocks, to conduct tensile tests, longitudinal compression tests, transverse compression tests, and in-plane shear tests. Tensile testing machine (LFV-1000 hydraulic servo fatigue testing machine): The integrated anchored specimen is installed in the upper and lower clamps of the testing machine. The extensometer gauge length is 50mm. The strain of the specimen is measured. The tensile rate of BA and FA groups is 10mm / min, and the tensile rate of HM-I and HM-II groups is 6mm / min. The extensometer is removed when the load reaches 60% of the estimated ultimate load. The data recording rate is once per second. Longitudinal compression testing device (LFV-1000 hydraulic servo fatigue testing machine): The specimen is fixed with a rigid pressure plate. The total length of the specimen is 50mm, and the length of the middle section after deducting the sleeve is 30mm. According to GB / T 1448-2005 standard, the loading rate is 2mm / min. Transverse compression testing device (LFV-1000 hydraulic servo fatigue testing machine): adopts a steel loading block with a semi-circular groove, the total length of the specimen is 100mm, the length of the compressed part is 50mm, according to IEEE Std. 1138-1994 standard, the loading rate is 200N / min; In-plane shear test apparatus (LFV-1000 hydraulic servo fatigue testing machine): adopts a short beam three-point bending structure, with a support spacing of 84mm, a total specimen length of 130mm, and loading points and supports being cylinders with diameters of 6mm and 3mm, respectively. The loading rate is 1mm / min according to ASTM D 2344 standard.

[0043] Step 4: Experimental Data Processing After the test is completed, based on the core mechanical parameters obtained from the test (including longitudinal compressive strength, transverse compressive strength and in-plane shear strength), the ultimate load, ultimate strength, elastic modulus, ultimate strain of each group of specimens, as well as the average value, standard deviation and coefficient of variation of each parameter are calculated.

[0044] The core mechanical parameters obtained from the tests were compiled into experimental data tables. The tensile test data for BFRP bars are shown in Table 1, the longitudinal compressive strength data in Table 2, the transverse compressive strength data in Table 3, and the in-plane shear strength data in Table 4; the corresponding test data for CFRP bars are shown in Tables 5-8; and the corresponding test data for GFRP bars are shown in Tables 9-12.

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052] According to the working conditions, four strength criteria are used: Hoffman criterion, Hashin criterion, Tsai-Wu criterion, and Tsai-Hill criterion. The relevant parameters are shown in Tables 13-16. The theoretical values ​​of the four strength criteria for three types of FRP bars are compared in Tables 17-19. The selected formulas have been mentioned before. The following are the methods for calculating the specific parameters.

[0053]

[0054] Note: Stress interaction term coefficients are dimensionless.

[0055]

[0056]

[0057] In the table, X c Y was measured experimentally. c From the formula Calculate (d is the specimen diameter, l is the length of the specimen compression zone, F) u (This is the ultimate load).

[0058] S is derived from the formula Calculate (d is the specimen diameter, F) u (This is the ultimate load).

[0059] X t From the formula We obtain f f and fr are the tensile strengths (measured values) of the fiber and resin, respectively, V f and V r These are the volume fractions of fiber and resin, respectively.

[0060] Y tFor transverse tensile strength, due to limitations of existing equipment, the transverse tensile strength is set at 55 MPa for vinyl ester resin for BFRP, 75 MPa for epoxy resin for CFRP, and 55 MPa for unsaturated polyester resin for GFRP.

[0061] Radial stress σ2 and shear stress σ 12 calculate: (1) Homogeneous integrated anchoring (HM) To address the difficulty in calculating the radial stress on the surface of FRP reinforcement bars with integrated anchorage using theoretical methods, a three-dimensional geometric model was established using ANSYS finite element software. Material parameters were input, and corresponding experimental loads were applied to accurately obtain the radial stress.

[0062] radial stress Based on the finite element analysis results, the shear stress According to the formula Calculate (uniform shear stress distribution in the anchorage zone).

[0063] (2) Adhesive anchorage (BA) Radial stress =0, shear stress According to the formula calculate.

[0064] (3) Friction anchor (FA) Based on the expansion characteristics of expansive cement, the following formula is derived: Calculate radial stress It is 66 MPa.

[0065] In the formula, ε ce E represents the cement expansion rate, which is equal to 0.00132. ce The elastic modulus of cement is equal to 35 GPa; ν ce The Poisson's ratio for cement is 0.3.

[0066] The shear stress is calculated using the same method as the BA type.

[0067] Based on the above experimental data, we plotted the ultimate strength and elastic modulus of three FRP bars under different anchorage methods (Figure 2 - Figure 3) to intuitively reflect the performance differences of different materials under different anchorage methods.

[0068] Step 5: Calculation of target strength criterion (1) Calculation of conventional criteria: Substitute the core mechanical parameters obtained from the experiment and the stress parameters obtained from the calculation into the Tsai-Hill, Hashing, and Hoffman criteria to directly calculate the theoretical value of tensile strength.

[0069] (2) Calculation of the modified Tsai-Wu criterion: Obtain the core parameter Y t V f Y c ; Calibration proportionality coefficient β: β is a dimensionless coefficient with a value range of 0.35~0.40.

[0070] Calibration was performed using tensile test data of FRP bars under at least three sets of different radial stresses. The calibration requirement was: when |σ²| ≤ β·Y c At that time, the theoretical value of tensile strength and the longitudinal tensile strength X under no radial stress t The relative error is ≤1.0%; Specifically as follows: Based on the low-stress test data (BA type, FA type) of BFRP, CFRP, and GFRP bars in Tables 1, 5, and 9, it is required that when |σ²| ≤ β·Y c At that time, the theoretical value of tensile strength and the longitudinal tensile strength X under no radial stress t The relative error is ≤1.0%. When β<0.35, the error of CFRP reinforcement FA type working condition is >1.3% (exceeding the standard); when β>0.40, the low stress range of GFRP reinforcement is too large, resulting in insufficient samples of high stress working conditions. Therefore, 0.35~0.40 is locked as the effective range.

[0071] By iterating through the candidate values ​​within the interval, 0.38 can reduce the error of BFRP BA type to 0.57%, CFRP FA type to 1.0% (both meet the standards), and GFRP BA type to 1.17% (a slight deviation caused by objective fluctuations in test data, ≤0.2%, which is within the allowable range for engineering), resulting in the best adaptability.

[0072] The calibrated proportional coefficient β is taken as 0.38, and the critical radial stress σ is calculated. 2,cr , σ 2,cr =β·Y c ; Segmented calculation of radial stress influence factor k: |σ²|≤σ 2,cr When k=1; |σ2|>σ 2,cr When k = 1 + α·(|σ²| - σ 2,cr ), where α is 0.0015~0.0025; Calculate the dynamic stress interaction coefficient F 12 :

[0073] Calibrate the proportionality coefficient α: The proportionality coefficient α is calibrated by selecting at least 3 sets of |σ²|>σ. 2,cr The tensile test data of FRP bars will be corrected to F 12 Substitute the values ​​into the Tsai-Wu criterion formula to calculate the theoretical value of tensile strength. Then, adjust the specific value of α to ensure that the relative error between each set of experimental values ​​and the theoretical value is ≤1.0%.

[0074] Specifically as follows: Based on the test data of the three types of FRP bars under high stress conditions (HM-II type) in Tables 1, 5, and 9, the relative error between the theoretical and measured values ​​for each group should be ≤1.0%. When α < 0.0015, the error of BFRP bar HM-II type is >1.2% (insufficient weakening); when α > 0.0025, the error of GFRP bar HM-II type is >1.5% (excessive weakening). Therefore, 0.0015~0.0025 is locked as the effective range.

[0075] By traversing the candidate values ​​within the interval, 0.0020 can reduce the error of CFRP HM-II type to 0.34%, BFRP HM-II type to 0.67%, and GFRP HM-II type to 0.35% (all ≤0.8%), achieving the optimal balance between accuracy and stability. The calibrated proportional coefficient α is set to 0.0020; F 12 Substitute the values ​​into the Tsai-Wu criterion formula to calculate the theoretical values.

[0076] Step 7: Establishment of tensile strength prediction model and determination of radial stress limit: Based on the comprehensive comparison of the four strength criteria in Tables 17-19, the Hoffman criterion demonstrates the best overall theoretical performance for the anchorage strength of the three types of FRP bars: an average relative error of 1.5% for BFRP bars, 1.0% for CFRP bars, and 1.65% for GFRP bars, with an overall average relative error of 1.38%. Furthermore, the relative errors of all test groups are less than 3%, meeting the accuracy requirements of the screening criteria. In contrast, other criteria show an overall average relative error of 2.23% for the Hashin criterion and 2.36% for the Tsai-Hill criterion. Although the Tsai-Wu criterion has an average relative error of only 0.5%, its applicability is limited due to instability in the fitting of stress interaction coefficients in some test groups (such as the BFRP bar HM-II group and the GFRP bar HM-II group). Therefore, the Hoffman criterion is determined to be the optimal strength criterion for the anchorage strength of FRP bars.

[0077] Based on the optimal Hoffman criterion, the tensile strength of the FRP reinforcement anchorage zone of different anchorage specimens was obtained according to the radial stress calculated in step 4, as shown in Tables 20-22.

[0078]

[0079] By fitting the experimental data of three types of FRP bars, the relationship between the tensile strength of the anchorage zone and the radial stress of the FRP bar was obtained: BFRP reinforcement is: CFRP reinforcement is as follows: GFRP reinforcement is as follows:

[0080] Based on Tables 20-22, the corresponding relationship curves are shown in Figure 4. It should be noted that when the radial stress is less than 50 MPa, the existence of extreme points will cause the predicted value to be slightly greater than the ideal tensile strength (the strength without radial stress). To address this limitation, the formula specifically emphasizes that when the radial stress is less than 50 MPa, σ1=f u In other words, the effect of radial stress on tensile strength is negligible. When the radial stress is greater than 50 MPa, the tensile strength decreases significantly with increasing radial stress. When the radial stress increases to 130 MPa (i.e., the transverse compressive strength of the BFRP bar), transverse compressive failure will occur in the anchorage zone. Based on the requirement of an anchorage efficiency coefficient greater than 90% in GB / T 14370 "Anchorages, Clamps and Connectors for Prestressed Tendons", the radial stress limit in the anchorage zone of BFRP bars is determined to be no more than 90 MPa. At this value, the tensile strength retention rate is not less than 90%, meeting the requirements for engineering applications. Similarly, the radial stress limit in the anchorage zone of CFRP bars is no more than 131 MPa, and the radial stress limit in the anchorage zone of GFRP bars is no more than 95 MPa.

Claims

1. A method for predicting the tensile strength of an anchorage zone of an FRP tendon under different radial stresses, characterized by, The method comprises the following steps: Step 1. Preparing a group of anchoring test pieces of the same FRP tendon with different anchoring modes; Step 2. Carrying out mechanical test on the prepared group of anchoring test pieces and obtaining core mechanical parameters, wherein the core mechanical parameters include longitudinal tensile strength, longitudinal compressive strength, transverse compressive strength and in-plane shear strength; Step 3. Processing the obtained core mechanical parameters and calculating stress parameters of the anchoring test pieces, wherein the stress parameters include ultimate load, ultimate strength, elastic modulus, ultimate strain, average value of the ultimate load, average value of the ultimate strength, average value of the elastic modulus, average value of the ultimate strain, standard deviation of the ultimate load, standard deviation of the ultimate strength, standard deviation of the elastic modulus, standard deviation of the ultimate strain, standard deviation of the ultimate load, coefficient of variation of the ultimate load, coefficient of variation of the ultimate strength, coefficient of variation of the elastic modulus, coefficient of variation of the ultimate strain, radial stress and shear stress; Step 4. Calculating tensile strength theoretical values according to the core mechanical parameters obtained in step 2 and the stress parameters calculated in step 3; Step 5. Carrying out one-dimensional quadratic fitting according to the calculated tensile strength theoretical values to obtain a prediction curve of the relationship between tensile strength and radial stress; According to the obtained prediction curve of the relationship between tensile strength and radial stress, the tensile strength under different radial stresses is predicted.

2. The method for predicting the tensile strength of the FRP tendon anchorage zone under different radial stresses according to claim 1, characterized in that, In step 4, the strength criterion is used to calculate the tensile strength theoretical values; the strength criterion includes maximum stress criterion, maximum strain criterion, Hoffman criterion, Hashin criterion, Tsai-Wu criterion and Tsai-Hill criterion.

3. The method for predicting the tensile strength of the FRP tendon anchorage zone under different radial stresses according to claim 2, characterized in that, The stress interaction coefficient in the Tsai-Wu criterion F 12 The dynamic correction value is adopted, and the specific value taking steps are as follows: (1) Obtain the core mechanical parameters of FRP bars: transverse tensile strength Y t , fiber volume fraction V f , transverse compressive strength Y c , wherein Y t determined by resin tensile strength test, V f determined by pultrusion process parameters, Y c determined by transverse compression test; (2) Determine the proportionality coefficient β: β is a dimensionless coefficient, the value range is 0.35~0.40, and is calibrated by at least 3 groups of FRP bar tensile test data under different radial stresses, and the calibration requirements are: when |σ2|≤β· Y c , the relative error between the tensile strength theoretical value and the longitudinal tensile strength without radial stress X t ≤1.0%; (3) Calculate the radial stress critical value σ 2,cr = β · Y c , get the radial stress σ2 of the FRP bar anchorage zone, and calculate its absolute value |σ2|; (4) calculating a radial stress influence factor k : if |σ2|≤σ 2,cr then k = 1; if |σ2| > σ 2,cr then k = 1 + a · (|σ2| - σ 2,cr ), where a is a proportional coefficient, and a value range is 0.0015~0.0025; (5) The corrected stress interaction coefficient is calculated according to the formula F 12 ;​ (6) The proportional coefficient a is calibrated by the following method: selecting at least 3 groups of FRP bar tensile test data with |σ2|>σ 2,cr , substituting the modified F 12 into the Tsai-Wu criterion formula to calculate the theoretical tensile strength value, and fitting and adjusting the specific value of a to make the relative error between each test value and the theoretical value ≤1.0%.

4. The method for predicting the tensile strength of the FRP tendon anchorage zone under different radial stresses according to claim 3, characterized in that, In step 4, at least three kinds of strength criterion are used to calculate a tensile strength theoretical value respectively, and the tensile strength theoretical value calculated by the optimal strength criterion is selected as the final tensile strength theoretical value according to the calculated tensile strength theoretical values and relative errors.

5. The method for predicting the tensile strength of the FRP tendon anchorage zone under different radial stresses according to claim 2, characterized in that, In step 5, the limit value of the radial stress of the anchoring area is determined according to the prediction curve of the relationship between tensile strength and radial stress.

6. The method for predicting the tensile strength of the FRP tendon anchorage zone under different radial stresses according to any one of claims 1 to 5, characterized in that, In step 1, the FRP tendon includes basalt fiber reinforced polymer tendon, carbon fiber reinforced polymer tendon and glass fiber reinforced polymer tendon.

7. The method for predicting the tensile strength of the FRP tendon anchorage zone under different radial stresses according to any one of claims 1 to 5, characterized in that, In step 1, the anchoring mode includes three anchoring modes of adhesive anchoring, frictional anchoring and homologous integrated anchoring.

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