A method for determining the flexural strength of an externally prestressed concrete beam with internal FRP tendons

Abstract

The present application discloses a method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars, including: obtaining the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars; determining the neutral axis height at the time of failure of the externally prestressed concrete beam with internal non-prestressed FRP bars formed by configuring the non-prestressed FRP bars in the externally prestressed concrete beam according to the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars; determining the ultimate stresses of the internal non-prestressed FRP bars and the external prestressing tendons in the externally prestressed concrete beam with internal FRP bars according to the neutral axis height; and determining the flexural strength of the externally prestressed concrete beam with internal FRP bars according to the ultimate stresses of the internal non-prestressed FRP bars and the external prestressing tendons. The present invention provides an effective calculation method for calculating the flexural strength of an externally prestressed concrete beam with internal FRP bars, and has the characteristics of simple calculation, high precision, strong practicability, etc.

Description

Technical Field

[0001] The present invention relates to the technical field of calculating the flexural strength of concrete beams, and particularly to a method, device, electronic device, and computer-readable storage medium for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars Background Art

[0002] The externally prestressed technology is widely applied to the construction of new projects and the strengthening or renovation of existing damaged structures. For an externally prestressed concrete beam, a certain amount of bonded bars need to be arranged in the beam to limit the excessive crack width and spacing and avoid the occurrence of a tied-arch behavior in the structure

[0003] The traditional externally unbonded bars and internally bonded bars are respectively prestressed and non-prestressed steel bars, and the corrosion of steel bars will cause damage to the structure. Using corrosion-resistant FRP bars to replace traditional steel bars is an effective method to solve this problem. FRP is a linear elastic material without a yield platform like steel bars, and its elastic modulus is generally lower than that of ordinary steel bars. Therefore, using FRP bars to replace traditional (prestressed or non-prestressed) steel bars will bring new challenges to the flexural design of externally prestressed concrete beams. At present, there is a lack of an effective calculation method for the flexural strength of externally prestressed concrete beams with internal non-prestressed FRP bars

[0004] Therefore, there is an urgent need to provide a method for determining the flexural strength of an externally prestressed concrete beam with internal non-prestressed FRP bars, calculate the flexural strength of an externally prestressed concrete beam with internal FRP bars, and provide a theoretical guidance for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars Summary of the Invention

[0005] In view of this, it is necessary to provide a method, device, electronic device, and computer-readable storage device for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars to solve the problem that there is a lack of an effective calculation method for the flexural strength of an externally prestressed concrete beam with internal non-prestressed FRP bars in the prior art

[0006] To solve the above problems, the present invention provides a method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars, including:

[0007] Obtaining the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars

[0008] Determining the neutral axis height at which the externally prestressed concrete beam with internal non-prestressed FRP bars is damaged according to the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars

[0009] Determine the ultimate stresses of the in - placed non - prestressed FRP bars and external prestressing tendons of the externally prestressed concrete beam with in - placed FRP bars according to the height of the neutral axis;

[0010] Determine the flexural strength of the externally prestressed concrete beam with in - placed FRP bars according to the ultimate stresses of the in - placed non - prestressed FRP bars and external prestressing tendons.

[0011] Furthermore, the characteristic parameters of the externally prestressed concrete beam include: structural information, cross - section information, load information, external prestressing tendon material information, and concrete material information;

[0012] The characteristic parameters of the non - prestressed FRP bars include: non - prestressed FRP bar material information.

[0013] Furthermore, according to the characteristic parameters of the externally prestressed concrete beam and non - prestressed FRP bars, determine the height of the neutral axis when the externally prestressed concrete beam with in - placed FRP bars is damaged, including:

[0014] Create a stress analysis model based on the finite element method;

[0015] Conduct numerical tests on the externally prestressed concrete beam using the stress analysis model to obtain the formula for the ultimate stress increment of the external prestressing tendons;

[0016] According to the formula for the ultimate stress increment of the external prestressing tendons, the calculation equation for the ultimate stress of the external prestressing tendons, the calculation equation for the comprehensive reinforcement index of the externally prestressed concrete beam with in - placed FRP bars, and the section equilibrium condition, determine the calculation formula for the height of the neutral axis when the externally prestressed concrete beam with in - placed FRP bars is damaged;

[0017] According to the calculation formula for the height of the neutral axis, and the characteristic parameters of the externally prestressed concrete beam and non - prestressed FRP bars, determine the height of the neutral axis when the externally prestressed concrete beam with in - placed FRP bars is damaged.

[0018] Furthermore, conduct numerical tests on the externally prestressed concrete beam using the stress analysis model to obtain the formula for the ultimate stress increment of the external prestressing tendons, including:

[0019] Divide the externally prestressed concrete beam into multiple force - bearing units;

[0020] According to the action of the force - bearing units under the three - point load and single - point load at the mid - span, obtain the curve of the change of the ultimate stress increment of the external prestressing tendons with the comprehensive reinforcement index of the externally prestressed concrete beam;

[0021] Perform linear fitting on the change curve to obtain the formula for the ultimate stress increment of the external prestressing tendons.

[0022] Further, determining the ultimate stresses of the in - built non - prestressed FRP bars and the external prestressed tendons of the externally prestressed concrete beam with in - built FRP bars according to the neutral axis height includes:

[0023] Determining the tensile ultimate stress of the in - built non - prestressed FRP bars according to the neutral axis height;

[0024] Determining the comprehensive reinforcement index of the externally prestressed concrete beam with in - built FRP bars according to the tensile ultimate stress;

[0025] Determining the ultimate stress increment of the external prestressed tendons according to the comprehensive reinforcement index;

[0026] Determining the ultimate stress of the external prestressed tendons according to the ultimate stress increment of the external prestressed tendons and the characteristic parameters of the externally prestressed concrete beam with in - built FRP bars.

[0027] Further, determining the comprehensive reinforcement index of the externally prestressed concrete beam with in - built FRP bars according to the tensile ultimate stress includes:

[0028] When the tensile ultimate stress of the non - prestressed FRP bars is greater than its own fracture strength, taking the fracture strength of the non - prestressed FRP bars as the tensile ultimate stress;

[0029] Determining the comprehensive reinforcement index of the externally prestressed concrete beam with in - built FRP bars according to the tensile ultimate stress of the non - prestressed FRP bars.

[0030] Further, determining the flexural strength of the externally prestressed concrete beam with in - built FRP bars according to the ultimate stresses of the in - built non - prestressed FRP bars and the external prestressed tendons includes:

[0031] Determining the compressive ultimate stress of the in - built non - prestressed FRP bars according to the neutral axis height;

[0032] Taking moments for the externally prestressed concrete beam with in - built FRP bars to obtain the nominal flexural strength calculation equation of the externally prestressed concrete beam with in - built FRP bars;

[0033] Determining the flexural strength of the externally prestressed concrete beam with in - built FRP bars according to the ultimate stress of the external prestressed tendons, the tensile ultimate stress and compressive ultimate stress of the in - built non - prestressed FRP bars, and the characteristic parameters of the externally prestressed concrete beam and the non - prestressed FRP bars.

[0034] The present invention also provides a flexural strength prediction device for an externally prestressed concrete beam with in - built FRP bars, including:

[0035] A parameter acquisition module for acquiring the characteristic parameters of the externally prestressed concrete beam and the non - prestressed FRP bars;

[0036] A neutral axis height calculation module, configured to determine the neutral axis height when an externally prestressed concrete beam with non-prestressed FRP bars inside is damaged, according to the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars.

[0037] An ultimate stress calculation module, configured to determine the ultimate stresses of the non-prestressed FRP bars inside the body and the externally prestressed bars of the externally prestressed concrete beam with non-prestressed FRP bars inside, according to the neutral axis height.

[0038] A flexural strength determination module, configured to determine the flexural strength of the externally prestressed concrete beam with non-prestressed FRP bars inside, according to the ultimate stresses of the non-prestressed FRP bars inside the body and the externally prestressed bars.

[0039] The present invention also provides an electronic device, including a processor and a memory, where a computer program is stored on the memory, and when the computer program is executed by the processor, a method for determining the flexural strength of an externally prestressed concrete beam with non-prestressed FRP bars inside as described in any of the above technical solutions is implemented.

[0040] The present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, a method for determining the flexural strength of an externally prestressed concrete beam with non-prestressed FRP bars inside as described in any of the above technical solutions is implemented.

[0041] Compared with the prior art, the beneficial effects of the present invention include: First, obtaining the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars; Second, determining the neutral axis height when the externally prestressed concrete beam with non-prestressed FRP bars inside is damaged, according to the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars; Third, determining the ultimate stresses of the non-prestressed FRP bars inside the body and the externally prestressed bars of the externally prestressed concrete beam with non-prestressed FRP bars inside, according to the neutral axis height; Fourth, determining the flexural strength of the externally prestressed concrete beam with non-prestressed FRP bars inside, according to the ultimate stresses of the non-prestressed FRP bars inside the body and the externally prestressed bars. The present invention provides an effective calculation method for the flexural strength calculation of the externally prestressed concrete beam with non-prestressed FRP bars inside, and has the characteristics of simple calculation, high precision, strong practicability, etc., solves the problem in the prior art that there is a lack of a flexural strength calculation method for the externally prestressed concrete beam with non-prestressed FRP bars inside, has strong practical value, and can provide theoretical guidance for the flexural strength calculation of the externally prestressed concrete beam with non-prestressed FRP bars inside. Description of the Drawings

[0042] Figure 1Schematic flow chart of an embodiment of a method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars provided by the present invention;

[0043] Figure 2 Schematic structural diagram of an embodiment of an externally prestressed concrete beam with internal FRP bars provided by the present invention;

[0044] Figure 3 Schematic diagram of an embodiment of a stress analysis model of an externally prestressed concrete beam with internal FRP bars provided by the present invention;

[0045] Figure 4 Schematic diagram of the variation of the ultimate stress increment of external prestressing tendons with the comprehensive reinforcement index under different load types and internal non - prestressed tendon types provided by the present invention;

[0046] Figure 5 Schematic diagram of an embodiment of the fitting curve between the ultimate stress increment of external prestressing tendons with non - prestressed internal FRP bars and the comprehensive reinforcement index provided by the present invention;

[0047] Figure 6 Schematic flow chart of the calculation process of the nominal flexural strength of an externally prestressed concrete beam with non - prestressed internal FRP bars provided by the present invention;

[0048] Figure 7 Comparison diagram of the predicted value and the actual value of the ultimate stress increment model of external prestressing tendons in an embodiment provided by the present invention;

[0049] Figure 8 Comparison diagram of the predicted value and the actual value of the nominal flexural strength model of an externally prestressed concrete beam with internal FRP bars in an embodiment provided by the present invention;

[0050] Figure 9 Schematic structural diagram of an embodiment of a device for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars provided by the present invention;

[0051] Figure 10 Schematic block diagram of an embodiment of an electronic device provided by the present invention. Detailed Embodiments

[0052] The following specifically describes the preferred embodiments of the present invention in conjunction with the accompanying drawings. The accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to explain the principles of the present invention, and are not used to limit the scope of the present invention.

[0053] The present invention provides a method, a device, an electronic device and a computer - readable storage medium for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars, which are described in detail below.

[0054] An embodiment of the present invention provides a method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars. The schematic flow diagram is as follows Figure 1 and includes:

[0055] Step S101: Obtain the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars.

[0056] Step S102: Determine the height of the neutral axis when the externally prestressed concrete beam with internal non-prestressed FRP bars is damaged, based on the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars.

[0057] Step S103: Determine the ultimate stresses of the internal non-prestressed FRP bars and the external prestressing tendons in the externally prestressed concrete beam with internal FRP bars, based on the height of the neutral axis.

[0058] Step S104: Determine the flexural strength of the externally prestressed concrete beam with internal FRP bars, based on the ultimate stresses of the internal non-prestressed FRP bars and the external prestressing tendons.

[0059] Compared with the prior art, the method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars provided in this embodiment first obtains the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars; secondly, determines the height of the neutral axis when the externally prestressed concrete beam with internal FRP bars is damaged, based on the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars; thirdly, determines the ultimate stresses of the internal non-prestressed FRP bars and the external prestressing tendons in the externally prestressed concrete beam with internal FRP bars, based on the height of the neutral axis; and finally, determines the flexural strength of the externally prestressed concrete beam with internal FRP bars, based on the ultimate stresses of the internal non-prestressed FRP bars and the external prestressing tendons. The present invention provides an effective calculation method for the flexural strength calculation of externally prestressed concrete beams with FRP bars, and has the characteristics of simple calculation, high accuracy, and strong practicability. It solves the problem in the prior art that there is a lack of a flexural strength calculation method for externally prestressed concrete beams with internal non-prestressed FRP bars, and has strong practical value, and can provide theoretical guidance for the flexural strength calculation of externally prestressed concrete beams with internal FRP bars.

[0060] To better understand the above technical solution, the following takes the determination of the flexural strength of an externally prestressed concrete beam with internal non-prestressed FRP bars as an example, and combines Figures 2 - 6 to illustrate the idea of the method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars described in this embodiment.

[0061] To determine the flexural strength of an externally prestressed concrete beam with internal FRP tendons, the key is to determine the ultimate stress of the external prestressing tendons. Since the strain of the external prestressing tendons is not coordinated with the surrounding concrete, the strain or stress of the external prestressing tendons depends on the overall deformation of the beam, and the conventional section deformation coordination conditions are no longer applicable.

[0062] The ultimate stress of the external prestressing tendons is generally expressed by the following formula:

[0063] σ pu = σ pe + Δσ p (1)

[0064] Where, σ pu is the ultimate stress of the external prestressing tendons; σ pe is the effective prestress of the external prestressing tendons; Δσ p is the increment of the ultimate stress of the external prestressing tendons. σ pe can be determined according to the material information of the external prestressing tendons, while the increment of the ultimate stress of the external prestressing tendons Δσ p is an unknown quantity and further calculations are required.

[0065] The comprehensive reinforcement index is one of the optimal parameters for calculating the stress increment of the external prestressing tendons. The increment of the ultimate stress of the external prestressing tendons can be calculated by determining the relationship between the increment of the ultimate stress of the external prestressing tendons and the comprehensive reinforcement index.

[0066] To determine the relationship between the increment of the ultimate stress of the external prestressing tendons and the comprehensive reinforcement index, a stress analysis model is created based on the finite element method. As Figure 2 shown, externally prestressed concrete beams are designed with the type, area of the internal non-prestressed tendons and the type of load as variables.

[0067] As Figure 2 shown, the beam span is 10 m, two deviators are set at the third points, the effective height of the external prestressing tendons at the beam ends is 0.3 m, and the effective height at the deviators is 0.5 m. The axial compressive strength of the concrete is 60 MPa. The external prestressing tendons are CFRP tendons with an area of 10 cm 2 , a tensile strength of 1840 MPa, an elastic modulus of 147 GPa, and the initial prestress is taken as 60% of the tensile strength. The area of the compressive non-prestressed tendons is 3.6 cm 2 , and the area of the tensile non-prestressed tendons is a variable: 3.6 cm 2 - 35.6 cm 2 .

[0068] Among them, the non-prestressed reinforcement considers two typical FRP reinforcements, CFRP (tensile strength of 1840 MPa and elastic modulus of 147 GPa) and GFRP (tensile strength of 750 MPa and elastic modulus of 40 GPa), and also considers ordinary steel bars (yield strength of 450 MPa and elastic modulus of 200 GPa) for comparative analysis.

[0069] Three typical load types are considered, namely the third-point load, the uniform load, and the single-point load at the mid-span.

[0070] The finite element method is used to conduct numerical tests on the above-mentioned external prestressed FRP concrete beams. The stress analysis model based on the finite element method is as Figure 3 shown. When modeling, the beam body is divided into 18 beam elements, the external prestressed reinforcement is divided into 18 elements corresponding to the beam elements, and the cross-section is divided into 10 concrete layers and 2 non-prestressed reinforcement layers (each layer represents the tensile and compressive non-prestressed reinforcements).

[0071] Figure 4 The variation of the ultimate stress increment of the external prestressed reinforcement with the comprehensive reinforcement index under different load types is given. From Figure 4 it can be seen that the ultimate stress increments of the external prestressed reinforcement under the third-point load and the uniform load are basically close, but significantly higher than the ultimate stress increment of the external prestressed reinforcement under the single-point load at the mid-span. The variation trend of the ultimate stress increment Δσ p of the external prestressed reinforcement in the beam with internal non-prestressed FRP reinforcements (including CFRP / GFRP reinforcements) is basically the same as that of the comprehensive reinforcement index q0. Since in the FRP material types, CFRP represents high elastic modulus and GFRP represents low elastic modulus, it can be inferred that the Δσ p -q0 responses of the external prestressed concrete beams with different types of internal non-prestressed FRP reinforcements are basically the same.

[0072] As Figure 5 shown, the numerical data of the ultimate stress increment of the external prestressed reinforcement with internal non-prestressed FRP reinforcements and the comprehensive reinforcement index Δσ p -q0 under the third-point load and the single-point concentrated load are linearly fitted respectively. By generalizing the prestressed reinforcement type to the general case, the following calculation formula for the ultimate stress increment of the external prestressed reinforcement is obtained:

[0073] Δσ p =(k1 + k2q0)E p (2)

[0074] Among them, the values of the coefficients k1 and k2 are as follows: for the third-point or uniform load, k1 = 4.26 and k2 = -7.02; for the single-point concentrated load, k1 = 2.3 and k2 = -2.67.

[0075] Substituting Equation (2) into Equation (1), the formula for calculating the ultimate stress of the external prestressing tendon in the beam with internal non-prestressed FRP bars is obtained as follows:

[0076] σ pu =σ pe +(k1 + k2q0)E p (3)

[0077] Therefore, according to the above analysis process, the corresponding relationship between the ultimate stress increment of the external prestressing tendon and the comprehensive reinforcement index is determined.

[0078] When internal non-prestressed FRP bars are used, generally the non-prestressed FRP bars are far from reaching their fracture strength. Therefore, the comprehensive reinforcement index of the external prestressed concrete beam with internal non-prestressed FRP bars can be expressed as:

[0079]

[0080] where A p is the area of the external prestressing tendon; σ pe is the effective prestress of the external prestressing tendon; A f is the area of the non-prestressed FRP bars in tension; σ f is the stress of the non-prestressed FRP bars in tension under the ultimate state; b is the section width; d p is the height of the external prestressing tendon before deformation; f c is the axial compressive strength of concrete. For the external prestressed concrete beam with internal non-prestressed FRP bars, the stress σ f of the non-prestressed FRP bars is an unknown quantity, so q0 is also an unknown quantity. Therefore, the ultimate stress of the external prestressing tendon still cannot be determined and needs to be solved by combining the section equilibrium equation.

[0081] The section equilibrium equation of the external prestressed concrete beam with internal non-prestressed FRP bars is:

[0082] 0.85f c bβc u =A p σ pu +A f σ f -A' f σ' f (5)

[0083] where A p is the area of the external prestressing tendon; σ pu is the ultimate stress of the external prestressing tendon, A f is the area of the non-prestressed FRP bars in tension; σ f is the stress of the non-prestressed FRP bars in tension under the ultimate state; A' fis the area of non - prestressed FRP bars under compression; σ' f is the stress of non - prestressed FRP bars under compression at the ultimate state; f c is the axial compressive strength of concrete; b is the cross - section width; β is the coefficient of concrete stress block; c u is the neutral axis height at the failure of the externally prestressed concrete beam with internal FRP bars.

[0084] According to Equation (5), the ultimate stress σ of the externally prestressed tendon pu , the stress σ of non - prestressed FRP bars in tension at the ultimate state f , the stress σ' of non - prestressed FRP bars under compression at the ultimate state f and the neutral axis height c at the failure u are related.

[0085] Based on the plane - section assumption and strain - compatibility conditions, the strains of non - prestressed FRP bars at the ultimate state are:

[0086]

[0087]

[0088] where, ε f and ε' f are the strains of non - prestressed FRP bars in tension and compression respectively; d f and d' f are the effective depths of non - prestressed FRP bars in tension and compression respectively; c u is the neutral axis height at the failure of the externally prestressed concrete beam with internal FRP bars; ε fu is the fracture strain of FRP bars; ε u is the ultimate compressive strain of concrete, and its value is 0.003.

[0089] Therefore, the stresses (σ f and σ′ f ) of non - prestressed FRP bars in tension and compression at the ultimate state are respectively:

[0090]

[0091]

[0092] where, E f and E' f are the elastic moduli of non - prestressed FRP bars in tension and compression respectively; f f is the fracture strength of FRP bars; d f and d' f are the effective depths of non - prestressed FRP bars in tension and compression respectively; c u is the neutral axis height at the failure of the externally prestressed concrete beam with internal FRP bars; εu is the ultimate compressive strain of concrete.

[0093] Substituting Eqs. (3), (8), and (9) into the section equilibrium equation (5), we can obtain:

[0094]

[0095] where A = 0.85f c bβ; B = A f E f ε u (1 + k2E p ρ p / f c ) + A' f E' f ε u -A p (σ pe + k1E p + k2E p q p );C = -A f E f ε u d f (1 + k2E p ρ p / f c ) - A' f E' f ε u d' f ;

[0096] ρ p is the reinforcement ratio of the prestressing tendon, and q p is the reinforcement index of the prestressing tendon:

[0097]

[0098]

[0099] Therefore, according to the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars obtained, through Eqs. (10), (11), and (12), the neutral axis height c of the externally prestressed concrete beam with internal FRP bars at failure can be calculated. u .

[0100] According to Eqs. (8) and (9), the stresses of the tensile and compressive non-prestressed FRP bars (σ f and σ′ f ) under the ultimate state are obtained; then, combined with Eq. (4), the comprehensive reinforcement index q0 of the externally prestressed concrete beam with internal non-prestressed FRP bars can be calculated; thus, according to Eq. (3), the ultimate stress σ of the external prestressing tendon of the beam with internal non-prestressed FRP bars can be obtained.pu 。

[0101] Taking moments about the resultant force of concrete, the nominal flexural strength of an externally prestressed concrete beam with non-prestressed FRP bars can be calculated by the following formula:

[0102] M n =A p σ pu (d eff -βc u / 2)+A f σ f (d f -βc u / 2)-A' f σ' f (d' f -βc u / 2) (13)

[0103] Through the above analysis, c u 、σ f 、σ′ f 、σ pu in the formula have been successively obtained. d eff is the effective height of the external prestressing tendon in the ultimate state and can be calculated by the following formula:

[0104] d eff =d p [λ1-λ2(L / d p )-λ3(S d / L)] (14)

[0105] where L is the span length; S d is the spacing of the internal deviator blocks; the values of the coefficients λ1, λ2, and λ3 are as follows: for a three-point or uniformly distributed load, λ1 = 1.25, λ2 = 0.01, λ3 = 0.38; for a single-point concentrated load, λ1 = 1.14, λ2 = 0.005, λ3 = 0.19.

[0106] Therefore, the flexural strength of the externally prestressed concrete beam with internal FRP bars can be determined through the above calculation process. The complete flowchart of the above calculation idea is as Figure 6 shown.

[0107] According to the above calculation idea, the initial characteristic parameters need to be obtained. As a preferred embodiment, in step S101, the characteristic parameters of the externally prestressed concrete beam include: structural information, cross-sectional information, load information, external prestressing tendon material information, and concrete material information;

[0108] The characteristic parameters of the non-prestressed FRP bars include: non-prestressed FRP bar material information.

[0109] As a specific embodiment, among the characteristic information of the externally prestressed concrete beam,

[0110] The structural information includes: span length, spacing of internal turning blocks.

[0111] The sectional information includes: the area of the external prestressing tendons of the externally prestressed concrete beam, sectional width, height of the external prestressing tendons before deformation.

[0112] The load information includes: three-point or uniform load coefficient, single-point concentrated load information.

[0113] The material information of the external prestressing tendons includes: effective prestress of the external prestressing tendons, elastic modulus of the external prestressing tendons.

[0114] The concrete material information includes: axial compressive strength of concrete, ultimate compressive strain of concrete, concrete stress block coefficient.

[0115] The material information of the non-prestressed FRP bars includes: elastic modulus of the tensile and compressive internal non-prestressed FRP bars, fracture strength of the non-prestressed FRP bars, area of the tensile non-prestressed FRP bars, effective height of the tensile non-prestressed FRP bars, area of the compressive non-prestressed FRP bars, and effective height of the compressive non-prestressed FRP bars.

[0116] As a preferred embodiment, in step S102, according to the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars, determining the neutral axis height when the internally FRP-reinforced externally prestressed concrete beam is damaged includes:

[0117] Creating a stress analysis model based on the finite element method;

[0118] Performing a numerical test on the externally prestressed concrete beam using the stress analysis model to obtain the ultimate stress increment formula of the external prestressing tendons;

[0119] According to the ultimate stress increment formula of the external prestressing tendons, the ultimate stress calculation equation of the external prestressing tendons, the comprehensive reinforcement index calculation equation of the externally prestressed concrete beam, and the sectional equilibrium condition, determining the calculation formula for the neutral axis height when the internally FRP-reinforced externally prestressed concrete beam is damaged;

[0120] According to the neutral axis height calculation formula, the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars, determining the neutral axis height when the internally FRP-reinforced externally prestressed concrete beam is damaged.

[0121] As a preferred embodiment, performing a numerical test on the externally prestressed concrete beam using the stress analysis model to obtain the ultimate stress increment formula of the external prestressing tendons includes:

[0122] Divide the externally prestressed concrete beam into multiple stress units;

[0123] According to the action of the stress units under the three - point load and the single - point load at the mid - span, obtain the variation curve of the ultimate stress increment of the external prestressing tendon with the comprehensive reinforcement index of the externally prestressed concrete beam;

[0124] Perform linear fitting on the variation curve to obtain the formula for the ultimate stress increment of the external prestressing tendon.

[0125] As a preferred embodiment, in step S103, determining the ultimate stresses of the internal non - prestressed FRP bars and the external prestressing tendons of the internally - FRP - reinforced externally prestressed concrete beam according to the neutral axis height includes:

[0126] Determine the tensile ultimate stress of the internal non - prestressed FRP bars according to the neutral axis height;

[0127] Determine the comprehensive reinforcement index of the internally - FRP - reinforced externally prestressed concrete beam according to the tensile ultimate stress;

[0128] Determine the ultimate stress increment of the external prestressing tendon according to the comprehensive reinforcement index;

[0129] Determine the ultimate stress of the external prestressing tendon according to the ultimate stress increment of the external prestressing tendon and the characteristic parameters of the internally - FRP - reinforced externally prestressed concrete beam.

[0130] As a preferred embodiment, determining the comprehensive reinforcement index of the internally - FRP - reinforced externally prestressed concrete beam according to the tensile ultimate stress includes:

[0131] When the tensile ultimate stress of the non - prestressed FRP bars is greater than its own fracture strength, take the fracture strength of the non - prestressed FRP bars itself as the tensile ultimate stress;

[0132] Determine the comprehensive reinforcement index of the internally - FRP - reinforced externally prestressed concrete beam according to the tensile ultimate stress of the non - prestressed FRP bars.

[0133] As a preferred embodiment, determining the flexural strength of the internally - FRP - reinforced externally prestressed concrete beam according to the ultimate stresses of the internal non - prestressed FRP bars and the external prestressing tendons includes:

[0134] Determine the compressive ultimate stress of the internal non - prestressed FRP bars according to the neutral axis height;

[0135] Take moments about the internally - FRP - reinforced externally prestressed concrete beam to obtain the nominal flexural strength calculation equation of the internally - FRP - reinforced externally prestressed concrete beam;

[0136] According to the ultimate stress of the external prestressing tendon, the ultimate tensile stress and the ultimate compressive stress of the internal non-prestressed FRP tendon, as well as the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP tendon, the flexural strength of the externally prestressed concrete beam with internal FRP tendons is determined.

[0137] In order to verify the determination effect of the flexural strength of the externally prestressed concrete beam with internal FRP tendons in the above technical solution, as a specific embodiment, the incremental limit stress of the external tendons and the comparison between the model predicted values and the actual values of the nominal flexural strength of the externally prestressed concrete beams with different types and areas of internal non-prestressed FRP tendons under 45 different load types are compared, as Figure 7 and Figure 8 shown, Figure 7 shows the comparison between the calculated value and the actual value of the incremental limit stress of the external prestressing tendon; Figure 8 shows the comparison between the nominal flexural strength of the externally prestressed concrete beam with internal non-prestressed FRP tendons calculated by the above method and the actual value.

[0138] It can be seen from the figure that the results of this embodiment are in good agreement with the actual values. Among them, the average deviation of the incremental limit stress of the external prestressing tendon is 1.2%, and the standard deviation is 7.1%. The average deviation of the nominal flexural strength of the externally prestressed concrete beam with internal FRP tendons is -4.8%, and the standard deviation is 2.9%. The error range is acceptable in practical applications, so it has good practicability and can provide theoretical guidance for the calculation of the flexural strength of the externally prestressed concrete beam with internal FRP tendons.

[0139] The embodiment of the present invention also provides a device for determining the flexural strength of an externally prestressed concrete beam with internal FRP tendons. The structural block diagram is as Figure 9 shown. The device 900 for determining the flexural strength of an externally prestressed concrete beam with internal FRP tendons includes:

[0140] A parameter acquisition module 901 for acquiring the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP tendon;

[0141] A neutral axis height calculation module 902 for determining the neutral axis height at the time of failure of the externally prestressed concrete beam with internal non-prestressed FRP tendons formed by configuring the non-prestressed FRP tendon in the externally prestressed concrete beam according to the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP tendon;

[0142] An ultimate stress calculation module 903 for determining the ultimate stresses of the internal non-prestressed FRP tendon and the external prestressing tendon of the externally prestressed concrete beam with internal FRP tendons according to the neutral axis height;

[0143] The flexural strength determination module 904 is configured to determine the flexural strength of the concrete beam with externally prestressed tendons and internally arranged FRP tendons according to the ultimate stresses of the internally non-prestressed FRP tendons and the externally prestressed tendons in the body.

[0144] As Figure 10 shown, for the above method for determining the flexural strength of a concrete beam with externally prestressed tendons and internally arranged FRP tendons, the present invention also correspondingly provides an electronic device 1000, which may be a computing device such as a mobile terminal, a desktop computer, a notebook, a palm computer, and a server. The electronic device includes a processor 1001, a memory 1002, and a display 1003.

[0145] The memory 1002 may be an internal storage unit of the computer device in some embodiments, such as the hard disk or memory of the computer device. The memory 1002 may also be an external storage device of the computer device in other embodiments, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) card, a Flash Card, etc. equipped on the computer device. Further, the memory 1002 may include both the internal storage unit and the external storage device of the computer device. The memory 1002 is used to store application software installed on the computer device and various types of data, such as program codes installed on the computer device. The memory 1002 may also be used to temporarily store data that has been output or will be output. In one embodiment, a program 1004 for determining the flexural strength of a concrete beam with externally prestressed tendons and internally arranged FRP tendons is stored on the memory 1002. The program 1004 for determining the flexural strength of a concrete beam with externally prestressed tendons and internally arranged FRP tendons can be executed by the processor 1001, so as to implement the method for determining the flexural strength of a concrete beam with externally prestressed tendons and internally arranged FRP tendons in various embodiments of the present invention.

[0146] The processor 1001 may be a central processing unit (CPU), a microprocessor, or other data processing chips in some embodiments, and is used to run the program codes stored in the memory 1002 or process data, such as executing a program for determining the flexural strength of a concrete beam with externally prestressed tendons and internally arranged FRP tendons.

[0147] The display 1003 may be an LED display, a liquid crystal display, a touch liquid crystal display, and an OLED (Organic Light-Emitting Diode) toucher, etc. in some embodiments. The display 1003 is used to display information on the computer device and to display a visual user interface. The components 1001 - 1003 of the computer device communicate with each other through a system bus.

[0148] This embodiment also provides a computer-readable storage medium, on which there is a program for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars. When the processor executes the program, it implements the method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars as described above.

[0149] According to the computer-readable storage medium and computing device provided in the above embodiments of the present invention, it can be implemented with reference to the content specifically described in implementing a method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars according to the present invention, and has beneficial effects similar to those of the method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars as described above, which will not be elaborated here.

[0150] A method, device, electronic device and computer-readable storage medium for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars disclosed by the present invention. First, obtain the characteristic parameters of the externally prestressed concrete beam and non-prestressed FRP bars; secondly, determine the neutral axis height when the externally prestressed concrete beam with internal FRP bars is damaged according to the characteristic parameters of the externally prestressed concrete beam and non-prestressed FRP bars; thirdly, determine the ultimate stresses of the internal non-prestressed FRP bars and external prestressing tendons of the externally prestressed concrete beam with internal FRP bars according to the neutral axis height; finally, determine the flexural strength of the externally prestressed concrete beam with internal FRP bars according to the ultimate stresses of the internal non-prestressed FRP bars and external prestressing tendons. The present invention provides an effective calculation method for calculating the flexural strength of an externally prestressed concrete beam with internal FRP bars, and has the characteristics of simple calculation, high precision, strong practicability, etc., solves the problem that there is a lack of a calculation method for the flexural strength of an externally prestressed concrete beam with internal non-prestressed FRP bars in the prior art, has strong practical value, and can provide theoretical guidance for calculating the flexural strength of an externally prestressed concrete beam with internal non-prestressed FRP bars.

[0151] As mentioned above, the above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars, characterized in that, Including: Obtaining the characteristic parameters of an externally prestressed concrete beam and non-prestressed FRP bars; According to the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars, determining the neutral axis height when the internally FRP-bar-reinforced externally prestressed concrete beam formed by configuring the non-prestressed FRP bars in the externally prestressed concrete beam is damaged; Determining the ultimate stresses of the internal non-prestressed FRP bars and the external prestressing tendons in the internally FRP-bar-reinforced externally prestressed concrete beam according to the neutral axis height; Determining the flexural strength of the internally FRP-bar-reinforced externally prestressed concrete beam according to the ultimate stresses of the internal non-prestressed FRP bars and the external prestressing tendons; Among them, according to the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars, determining the neutral axis height when the internally FRP-bar-reinforced externally prestressed concrete beam is damaged specifically includes: Creating a stress analysis model based on the finite element method; Performing a numerical test on the externally prestressed concrete beam using the stress analysis model to obtain the ultimate stress increment formula of the external prestressing tendons; According to the ultimate stress increment formula of the external prestressing tendons, the ultimate stress calculation equation of the external prestressing tendons, the comprehensive reinforcement index calculation equation of the externally prestressed concrete beam, and the section equilibrium condition, determining the calculation formula for the neutral axis height when the internally FRP-bar-reinforced externally prestressed concrete beam is damaged; Determining the neutral axis height when the internally FRP-bar-reinforced externally prestressed concrete beam is damaged according to the neutral axis height calculation formula and the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars; Determining the flexural strength of the internally FRP-bar-reinforced externally prestressed concrete beam according to the ultimate stresses of the internal non-prestressed FRP bars and the external prestressing tendons specifically includes: Determining the tensile ultimate stress and the compressive ultimate stress of the internal non-prestressed FRP bars according to the neutral axis height; Taking moments for the internally FRP-bar-reinforced externally prestressed concrete beam to obtain the nominal flexural strength calculation equation of the internally FRP-bar-reinforced externally prestressed concrete beam; Determining the flexural strength of the internally FRP-bar-reinforced externally prestressed concrete beam according to the ultimate stress of the external prestressing tendons, the tensile ultimate stress and the compressive ultimate stress of the internal non-prestressed FRP bars, and the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars.

2. The method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars according to claim 1, characterized in that, The characteristic parameters of the externally prestressed concrete beam include: structural information, section information, load information, external prestressing tendon material information, concrete material information; The characteristic parameters of the non-prestressed FRP bars include: non-prestressed FRP bar material information.

3. The method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars according to claim 1, characterized in that, Performing a numerical test on the externally prestressed concrete beam using the stress analysis model to obtain the ultimate stress increment formula of the external prestressing tendons, including: Dividing the externally prestressed concrete beam into multiple stress units; According to the action of the stress units under the three-point load and the single-point load at the mid-span, obtaining the variation curve of the ultimate stress increment of the external prestressing tendons with the comprehensive reinforcement index of the externally prestressed concrete beam; Perform a linear fitting on the variation curve to obtain the formula for the ultimate stress increment of the external prestressing tendon.

4. The method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars according to claim 1, characterized in that, Determine the ultimate stresses of the internal non-prestressed FRP tendons and the external prestressing tendons of the externally prestressed concrete beam with internal FRP tendons according to the neutral axis height, including: Determine the tensile ultimate stress of the internal non-prestressed FRP tendons according to the neutral axis height; Determine the comprehensive reinforcement index of the externally prestressed concrete beam with internal FRP tendons according to the tensile ultimate stress; Determine the ultimate stress increment of the external prestressing tendons according to the comprehensive reinforcement index; Determine the ultimate stress of the external prestressing tendons according to the ultimate stress increment of the external prestressing tendons and the characteristic parameters of the externally prestressed concrete beam with internal FRP tendons.

5. The method for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars according to claim 4, characterized in that, Determine the comprehensive reinforcement index of the externally prestressed concrete beam with internal FRP tendons according to the tensile ultimate stress, including: When the tensile ultimate stress of the non-prestressed FRP tendons is greater than their own fracture strength, take the fracture strength of the non-prestressed FRP tendons themselves as the tensile ultimate stress; Determine the comprehensive reinforcement index of the externally prestressed concrete beam with internal FRP tendons according to the tensile ultimate stress of the non-prestressed FRP tendons.

6. An apparatus for determining the flexural strength of an externally prestressed concrete beam with internal FRP bars, characterized in that, Include: A parameter acquisition module for acquiring the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP tendons; A neutral axis height calculation module for determining the neutral axis height at the time of failure of the externally prestressed concrete beam with internal FRP tendons formed by configuring the non-prestressed FRP tendons in the externally prestressed concrete beam according to the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP tendons; An ultimate stress calculation module for determining the ultimate stresses of the internal non-prestressed FRP tendons and the external prestressing tendons of the externally prestressed concrete beam with internal FRP tendons according to the neutral axis height; A flexural strength determination module for determining the flexural strength of the externally prestressed concrete beam with internal FRP tendons according to the ultimate stresses of the internal non-prestressed FRP tendons and the external prestressing tendons; Among them, determining the neutral axis height at the time of failure of the externally prestressed concrete beam with internal FRP tendons according to the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP tendons specifically includes: Create a stress analysis model based on the finite element method; Perform a numerical test on the externally prestressed concrete beam using the stress analysis model to obtain the formula for the ultimate stress increment of the external prestressing tendon; Determine the calculation formula for the neutral axis height at the time of failure of the externally prestressed concrete beam with internal FRP tendons according to the formula for the ultimate stress increment of the external prestressing tendon, the calculation equation for the ultimate stress of the external prestressing tendon, the calculation equation for the comprehensive reinforcement index of the externally prestressed concrete beam, and the section equilibrium condition; Determine the neutral axis height at the time of failure of the externally prestressed concrete beam with internal FRP tendons according to the neutral axis height calculation formula and the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP tendons; Determine the flexural strength of the externally prestressed concrete beam with internal FRP tendons according to the ultimate stresses of the internal non-prestressed FRP tendons and the external prestressing tendons, specifically including: Determine the tensile ultimate stress and compressive ultimate stress of the non-prestressed FRP bars in the body according to the neutral axis height; Take moments for the externally prestressed concrete beam with internal FRP bars to obtain the nominal flexural strength calculation equation of the externally prestressed concrete beam with internal FRP bars; Determine the flexural strength of the externally prestressed concrete beam with internal FRP bars according to the ultimate stress of the externally prestressed tendons, the tensile ultimate stress and compressive ultimate stress of the non-prestressed FRP bars in the body, and the characteristic parameters of the externally prestressed concrete beam and the non-prestressed FRP bars.

7. An electronic device, characterized in that, It includes a processor and a memory, and a computer program is stored on the memory. When the computer program is executed by the processor, the method for determining the flexural strength of the externally prestressed concrete beam with internal FRP bars as described in any one of claims 1-5 is realized.

8. A computer-readable storage medium, characterized in that, A computer program is stored thereon. When the computer program is executed by a processor, the method for determining the flexural strength of the externally prestressed concrete beam with internal FRP bars as described in any one of claims 1-5 is realized.

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