CN114878354B - A method for determining the flexural strength of externally prestressed concrete beams with internal FRP bars - Google Patents

A method for determining the flexural strength of externally prestressed concrete beams with internal FRP bars Download PDF

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CN114878354B
CN114878354B CN202210631329.2A CN202210631329A CN114878354B CN 114878354 B CN114878354 B CN 114878354B CN 202210631329 A CN202210631329 A CN 202210631329A CN 114878354 B CN114878354 B CN 114878354B
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frp
concrete beam
external
external prestressed
prestressed concrete
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CN114878354A (en
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楼铁炯
李张翔
胡涵
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Wuhan University of Technology WUT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/20—Investigating strength properties of solid materials by application of mechanical stress by applying steady bending forces
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0001—Type of application of the stress
    • G01N2203/0003—Steady
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0014—Type of force applied
    • G01N2203/0023—Bending
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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Abstract

The application discloses a method for determining bending strength of an external prestressed concrete beam with built-in FRP ribs, which comprises the steps of obtaining characteristic parameters of the external prestressed concrete beam and the external prestressed FRP ribs, determining the neutral axis height of the external prestressed concrete beam with the external prestressed FRP ribs according to the characteristic parameters of the external prestressed concrete beam and the external prestressed FRP ribs when the external prestressed concrete beam with built-in FRP ribs is damaged, determining the limit stress of the internal non-prestressed FRP ribs and the external prestressed concrete beam with built-in FRP ribs according to the neutral axis height, and determining the bending strength of the external prestressed concrete beam with built-in FRP ribs according to the limit stress of the internal non-prestressed FRP ribs and the external prestressed concrete beam with built-in FRP ribs. The application provides an effective calculation method for calculating the bending strength of the external prestressed concrete beam with the FRP rib inside, and has the characteristics of simple calculation, high precision, strong practicability and the like.

Description

Method for determining bending strength of external prestressed concrete beam with FRP ribs inside
Technical Field
The invention relates to the technical field of concrete beam bending strength calculation, in particular to a method and a device for determining the bending strength of an external prestressed concrete beam with FRP ribs, electronic equipment and a computer readable storage medium.
Background
The external prestressing technology is widely applied to the construction of new construction and the reinforcement or reconstruction of the existing damaged structure. For an external prestressed concrete beam, a certain amount of bonding ribs are required to be arranged in the beam so as to limit the width and the interval of an oversized crack and avoid the tie bar arch behavior of the structure.
The traditional external unbonded tendons and the internal bonded tendons are respectively prestressed and non-prestressed tendons, and the corrosion of the tendons can cause structural damage, so that the adoption of corrosion-resistant FRP tendons instead of the traditional tendons is an effective method for solving the problem. FRP is a wire elastic material, has no yield platform like steel bars, and has an elastic modulus generally lower than that of common steel bars. Therefore, the FRP reinforcement can be used for replacing the traditional (prestressed or non-prestressed) reinforcement, and new challenges are brought to the bending-resistant design of the external prestressed concrete beam. At present, an effective calculation method for the bending strength of an external prestressed concrete beam internally provided with non-prestressed FRP ribs is lacking.
Therefore, it is needed to provide a method for determining the bending strength of an external prestressed concrete beam capable of predictably configuring internal non-prestressed FRP tendons, which calculates the bending strength of the external prestressed concrete beam with internal FRP tendons and provides theoretical guidance for determining the bending strength of the external prestressed concrete beam with internal FRP tendons.
Disclosure of Invention
In view of the foregoing, it is necessary to provide a method, a device, an electronic device and a computer readable storage device for determining the bending strength of an external prestressed concrete beam with built-in FRP tendons, so as to solve the problem that in the prior art, an effective calculation method is lacking in the bending strength of an external prestressed concrete beam with built-in non-prestressed FRP tendons.
In order to solve the problems, the invention provides a method for determining the bending strength of an external prestressed concrete beam with FRP ribs, which comprises the following steps:
acquiring characteristic parameters of an external prestressed concrete beam and a non-prestressed FRP rib;
According to characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP bars, determining the neutral axis height when the external prestressed concrete beam with the built-in FRP bars is damaged, wherein the non-prestressed FRP bars are configured in the external prestressed concrete beam;
Determining the limit stress of the in-vivo non-prestressed FRP tendon and the in-vitro prestressed tendon of the in-vitro prestressed concrete beam with the FRP tendon according to the neutral axis height;
And determining the bending strength of the external prestressed concrete beam of the internal FRP rib according to the limit stress of the internal non-prestressed FRP rib and the external prestressed rib.
Further, the characteristic parameters of the external prestressed concrete beam comprise structural information, section information, load information, external prestressed tendon material information and concrete material information;
The characteristic parameters of the non-prestressed FRP rib comprise non-prestressed FRP rib material information.
Further, according to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP tendon, determining the neutral axis height when the external prestressed concrete beam with the built-in FRP tendon is damaged comprises the following steps:
creating a stress analysis model based on a finite element method;
Carrying out a numerical test on the external prestressed concrete beam by using the stress analysis model to obtain a limit stress increment formula of the external prestressed tendon;
determining a neutral axis height calculation formula when the external prestressed concrete beam of the built-in FRP tendon is damaged according to a limit stress increment formula of the external prestressed tendon, a limit stress calculation formula of the external prestressed tendon, a comprehensive reinforcement index calculation formula of the external prestressed concrete beam of the built-in FRP tendon and a section balance condition;
and determining the neutral axis height when the external prestressed concrete beam with the built-in FRP ribs is damaged according to the neutral axis height calculation formula and the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP ribs.
Further, the numerical test is performed on the external prestressed concrete beam by using the stress analysis model to obtain a limit stress increment formula of the external prestressed tendon, which comprises the following steps:
Dividing the external prestressed concrete beam into a plurality of stress units;
Obtaining a change curve of the limit stress increment of the external prestressed reinforcement along with the comprehensive reinforcement index of the external prestressed concrete beam according to the action of the stress unit on the tri-division load and the mid-span single-point load;
And performing linear fitting on the change curve to obtain a limit stress increment formula of the external prestressed tendon.
Further, determining the limit stress of the in-vivo non-prestressed FRP tendon and the in-vitro prestressed tendon of the in-vivo non-prestressed FRP tendon and in-vitro prestressed concrete beam of the in-vivo-matched FRP tendon according to the neutral axis height comprises the following steps:
Determining the tension limit stress of the in-vivo non-prestress FRP rib according to the neutral axis height;
According to the tensile limit stress, determining the comprehensive reinforcement index of the external prestressed concrete beam with the FRP reinforcement arranged inside;
determining the limit stress increment of the external prestressed tendons according to the comprehensive reinforcement indexes;
and determining the limit stress of the external prestressed tendons according to the limit stress increment of the external prestressed tendons and the characteristic parameters of the external prestressed concrete beam internally provided with the FRP tendons.
Further, according to the tensile limit stress, determining a comprehensive reinforcement index of the external prestressed concrete beam with the FRP reinforcement, including:
when the tensile ultimate stress of the non-prestressed FRP rib is larger than the self-fracture strength, taking the self-fracture strength of the non-prestressed FRP rib as the tensile ultimate stress;
And determining the comprehensive reinforcement index of the external prestressed concrete beam with the FRP reinforcement according to the tensile limit stress of the non-prestressed FRP reinforcement.
Further, determining the bending strength of the external prestressed concrete beam of the internal FRP tendon according to the limit stress of the internal non-prestressed FRP tendon and the external prestressed tendon, comprising:
Determining the compressive limit stress of the in-vivo non-prestress FRP rib according to the neutral axis height;
Moment is taken from the external prestressed concrete beam with the FRP rib internally, and a nominal bending strength calculation equation of the external prestressed concrete beam with the FRP rib internally is obtained;
And determining the bending strength of the external prestressed concrete beam of the internal FRP rib according to the limiting stress of the external prestressed rib, the tensile limiting stress of the internal non-prestressed FRP rib, the compressive limiting stress, and the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib.
The invention also provides a bending strength prediction device of the external prestressed concrete beam internally provided with the FRP rib, which comprises the following components:
the parameter acquisition module is used for acquiring characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib;
the neutral axis height calculation module is used for determining the neutral axis height when the external prestressed concrete beam with the built-in FRP ribs is damaged according to the characteristic parameters of the external prestressed concrete beam and the external non-prestressed FRP ribs and the non-prestressed FRP ribs are configured in the external prestressed concrete beam;
The limit stress calculation module is used for determining limit stress of the internal non-prestressed FRP bars and the external prestressed bars of the external prestressed concrete beam internally matched with the FRP bars according to the neutral axis height;
The bending strength determining module is used for determining the bending strength of the external prestressed concrete beam with the FRP bars according to the limit stress of the internal non-prestressed FRP bars and the external prestressed bars.
The invention also provides electronic equipment, which comprises a processor and a memory, wherein the memory is stored with a computer program, and when the computer program is executed by the processor, the method for determining the bending strength of the external prestressed concrete beam with the FRP rib arranged inside is realized.
The invention also provides a computer readable storage medium, on which a computer program is stored, which when being executed by a processor, realizes the method for determining the bending strength of the external prestressed concrete beam with the FRP rib arranged inside according to any technical scheme.
Compared with the prior art, the method has the beneficial effects that firstly, characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib are obtained, secondly, the neutral axis height of the internal FRP rib external prestressed concrete beam when damaged is determined according to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib, thirdly, the limit stress of the internal non-prestressed FRP rib and the external prestressed rib of the internal FRP rib external prestressed concrete beam is determined according to the neutral axis height, and finally, the bending strength of the internal FRP rib external prestressed concrete beam is determined according to the limit stress of the internal non-prestressed FRP rib and the external prestressed rib. The method provides an effective calculation method for calculating the bending strength of the external prestressed concrete beam with the built-in FRP ribs, has the characteristics of simplicity and convenience in calculation, high precision, strong practicability and the like, solves the problem that the external prestressed concrete beam with the built-in non-prestressed FRP ribs lacks the bending strength calculation method in the prior art, has strong practical value, and can provide theoretical guidance for calculating the bending strength of the external prestressed concrete beam with the built-in non-prestressed FRP ribs.
Drawings
FIG. 1 is a schematic flow chart of an embodiment of a method for determining the flexural strength of an external prestressed concrete beam with FRP ribs arranged inside;
FIG. 2 is a schematic structural view of an embodiment of an external prestressed concrete beam with FRP ribs arranged inside;
FIG. 3 is a schematic diagram of an embodiment of a stress analysis model of an external prestressed concrete beam with FRP ribs arranged inside;
FIG. 4 is a schematic diagram showing the variation of the limit stress increment of the external tendon with the integrated tendon distribution index according to an embodiment of the present invention under different load types and in-vivo non-tendon types;
FIG. 5 is a schematic diagram of an embodiment of a fit curve of the limit stress increment of an external prestressed reinforcement and the comprehensive reinforcement index of an internal non-prestressed FRP reinforcement provided by the invention;
FIG. 6 is a schematic diagram of a calculation flow of an embodiment of nominal bending strength of an external prestressed concrete beam with an internal non-prestressed FRP tendon;
FIG. 7 is a graph showing the comparison of the predicted value and the actual value of the in-vitro tendon limit stress increment model according to an embodiment of the present invention;
FIG. 8 is a graph showing a comparison of a predicted value and an actual value of a nominal bending strength model of an external prestressed concrete beam with FRP ribs arranged inside according to an embodiment of the invention;
FIG. 9 is a schematic structural view of an embodiment of a device for determining the flexural strength of an external prestressed concrete beam with FRP ribs arranged inside;
fig. 10 is a block diagram of an embodiment of an electronic device according to the present invention.
Detailed Description
The following detailed description of preferred embodiments of the application is made in connection with the accompanying drawings, which form a part hereof, and together with the description of the embodiments of the application, are used to explain the principles of the application and are not intended to limit the scope of the application.
The invention provides a method and a device for determining the bending strength of an external prestressed concrete beam internally provided with FRP ribs, electronic equipment and a computer readable storage medium, and the method and the device are respectively described in detail below.
The embodiment of the invention provides a method for determining the bending strength of an external prestressed concrete beam with FRP ribs arranged inside, wherein a flow diagram is shown in figure 1, and the method comprises the following steps:
s101, obtaining characteristic parameters of an external prestressed concrete beam and a non-prestressed FRP rib;
Step S102, according to characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP bars, determining the neutral axis height when the external prestressed concrete beam with the built-in FRP bars is damaged, wherein the non-prestressed FRP bars are configured in the external prestressed concrete beam;
S103, determining the limit stress of the internal non-prestressed FRP tendon and the external prestressed tendon of the external prestressed concrete beam with the internal FRP tendon according to the height of the neutral axis;
and S104, determining the bending strength of the external prestressed concrete beam with the FRP bars according to the limit stress of the internal non-prestressed FRP bars and the external prestressed bars.
Compared with the prior art, the method for determining the bending strength of the external prestressed concrete beam with the built-in FRP ribs comprises the steps of firstly obtaining characteristic parameters of the external prestressed concrete beam and the external prestressed FRP ribs, secondly determining the neutral axis height of the external prestressed concrete beam with the built-in FRP ribs when the external prestressed concrete beam with the built-in FRP ribs is damaged according to the characteristic parameters of the external prestressed concrete beam with the external prestressed FRP ribs, thirdly determining the limit stress of the internal prestressed FRP ribs and the external prestressed concrete beam with the built-in FRP ribs according to the neutral axis height, and finally determining the bending strength of the external prestressed concrete beam with the built-in FRP ribs according to the limit stress of the internal non-prestressed FRP ribs and the external prestressed ribs. The method provides an effective calculation method for calculating the bending strength of the FRP rib external prestressed concrete beam, has the characteristics of simplicity and convenience in calculation, high precision, strong practicability and the like, solves the problem that the external prestressed concrete beam internally provided with the non-prestressed FRP rib lacks a bending strength calculation method in the prior art, has strong practical value, and can provide theoretical guidance for calculating the bending strength of the external prestressed concrete beam internally provided with the FRP rib.
In order to better understand the above technical solution, the following takes the determination of the bending strength of the external prestressed concrete beam with the internal non-prestressed FRP tendons as an example, and the concept of the method for determining the bending strength of the external prestressed concrete beam with the internal FRP tendons according to the method of this embodiment is described with reference to fig. 2 to 6.
In order to determine the bending strength of the external prestressed concrete beam with the FRP bars, the key point is to determine the limit stress of the external prestressed bars. Because the external prestressed tendons and the surrounding concrete are not in coordination with each other, the external prestressed tendons are in stress or strain depending on the integral deformation of the beam, and the conventional section deformation coordination condition is not applicable any more.
The ultimate stress of an external tendon is generally represented by the following formula:
σpu＝σpe+Δσp (1)
Wherein sigma pu is the limit stress of the external prestressed tendon, sigma pe is the effective prestress of the external prestressed tendon, and delta sigma p is the limit stress increment of the external prestressed tendon. Sigma pe can be determined according to the material information of the external prestress rib, and the limit stress increment delta sigma p of the external prestress rib is an unknown quantity and needs to be further calculated.
The comprehensive reinforcement index is one of the optimal parameters for calculating the stress increment of the external prestressed reinforcement. The limit stress increment of the external prestressed tendon can be calculated by determining the relation between the limit stress increment of the external prestressed tendon and the comprehensive reinforcement index.
In order to determine the relation between the limit stress increment of the external prestressed tendon and the comprehensive reinforcement index, a stress analysis model is created based on a finite element method. As shown in fig. 2, an external prestressed concrete beam with the type, the area and the load type of the internal non-prestressed tendons as variables is designed.
As shown in FIG. 2, the beam span length is 10m, two steering blocks are arranged at the trisection points, the effective height of the external prestressed tendons at the end part of the beam is 0.3m, and the effective height of the steering blocks is 0.5m. The compressive strength of the concrete axle center is 60MPa. The external prestress rib is CFRP rib, the area is 10cm 2, the tensile strength is 1840MPa, the elastic modulus is 147GPa, and the initial prestress is 60% of the tensile strength. The area of the pressed non-prestressed tendons is 3.6cm 2, and the area of the pulled non-prestressed tendons is 3.6cm 2-35.6cm2.
The non-prestressed tendons consider two typical FRP tendons of CFRP (tensile strength of 1840MPa, elastic modulus of 147 GPa) and GFRP (tensile strength of 750MPa, elastic modulus of 40 GPa), and meanwhile consider common steel bars (yield strength of 450MPa, elastic modulus of 200 GPa) for comparative analysis.
Three typical load types are considered, and a three-point load, an even load and a mid-span single-point load are considered.
Numerical tests are carried out on the external FRP prestressed concrete beam by adopting a finite element method, and a stress analysis model based on finite elements is shown in figure 3. During modeling, the beam body is divided into 18 beam units, the external prestressed tendons are divided into 18 units corresponding to the beam units, and the cross section of the external prestressed tendons is divided into 10 concrete layers and 2 non-prestressed tendons layers (each layer represents a tensile and compression non-prestressed tendon).
Figure 4 shows the variation of the limit stress increment of the external prestressed tendons under the action of different load types along with the comprehensive reinforcement indexes. As can be seen from fig. 4, the limit stress increment of the external prestressed tendons under the action of the three-point load and the uniformly distributed load is basically similar to, but is significantly higher than that of the external prestressed tendons under the action of the mid-span single-point load. The limit stress increment delta sigma p of the external prestressed reinforcement of the beam internally provided with the non-prestressed FRP reinforcement (including CFRP/GFRP reinforcement) is basically consistent with the change trend of the comprehensive reinforcement index q 0. Because CFRP represents a high elastic modulus and GFRP represents a low elastic modulus in the FRP material types, it can be estimated that Δσ p-q0 responses of the external prestressed concrete beams in which different types of non-prestressed FRP tendons are built in are substantially the same.
As shown in fig. 5, the numerical data of the limit stress increment of the external prestressed reinforcement and the comprehensive reinforcement index delta sigma p-q0 of the internal non-prestressed FRP reinforcement under the action of the three-point load and the single-point concentrated load are respectively subjected to linear fitting, the type of the prestressed reinforcement is promoted to the general condition, and the following calculation formula of the limit stress increment of the external prestressed reinforcement is obtained:
Δσp＝(k1+k2q0)Ep (2)
The coefficient k 1、k2 has the values of trisection or uniform load, k 1＝4.26,k2 = -7.02, and single-point concentrated load, k 1＝2.3,k2 = -2.67.
Substituting the formula (2) into the formula (1) to obtain an in-vitro prestressed reinforcement limit stress calculation formula of the beam under the condition of internally matching the non-prestressed FRP reinforcement, wherein the in-vitro prestressed reinforcement limit stress calculation formula is as follows:
σpu＝σpe+(k1+k2q0)Ep (3)
Therefore, according to the analysis process, the corresponding relation between the limit stress increment of the external prestressed tendons and the comprehensive reinforcement index is determined.
When the non-prestressed FRP bars are built in, the non-prestressed FRP bars do not reach the breaking strength in normal conditions, so that the comprehensive reinforcement indexes of the external prestressed concrete beam with the built-in non-prestressed FRP bars can be expressed as follows:
Wherein A p is the area of the external prestressed tendon, sigma pe is the effective prestress of the external prestressed tendon, A f is the area of the tensile non-prestressed FRP tendon, sigma f is the tensile non-prestressed FRP tendon stress in a limit state, b is the section width, d p is the height of the external prestressed tendon before deformation, and f c is the compressive strength of the concrete axle center. For an in-vitro prestressed concrete beam internally provided with non-prestressed FRP ribs, the stress sigma f of the non-prestressed FRP ribs is unknown, so q 0 is also unknown. Therefore, the limit stress of the external prestressed tendons still cannot be determined, and the joint section balance equation is needed to solve.
The section balance equation of the external prestressed concrete beam with the non-prestressed FRP ribs is as follows:
0.85fcbβcu＝Apσpu+Afσf-A'fσ'f (5)
Wherein A p is the area of the external prestressed reinforcement, sigma pu is the limit stress of the external prestressed reinforcement, A f is the area of the tensile non-prestressed FRP reinforcement, sigma f is the stress of the tensile non-prestressed FRP reinforcement in a limit state, A 'f is the area of the pressed non-prestressed FRP reinforcement, sigma' f is the stress of the pressed non-prestressed FRP reinforcement in a limit state, f c is the compressive strength of the concrete axis, b is the width of the section, beta is the coefficient of a concrete stress block, and c u is the height of the neutral axis when the external prestressed concrete beam of the built-in FRP reinforcement is damaged.
According to the formula (5), the relation between the limit stress sigma pu of the external prestressed reinforcement, the tension non-prestressed FRP reinforcement stress sigma f in the limit state and the compression non-prestressed FRP reinforcement stress sigma' f in the limit state and the neutral axis height c u when the external prestressed reinforcement is damaged can be determined.
Under the condition of plane section assumption and strain coordination, the strain of the non-prestress FRP rib in the limit state is as follows:
Wherein epsilon f and epsilon 'f are respectively the tensile and compressive non-prestressed FRP rib strains, d f and d' f are respectively the effective heights of the tensile and compressive non-prestressed FRP ribs, c u is the neutral axis height when the external prestressed concrete beam of the internal FRP rib is damaged, epsilon fu is the FRP rib fracture strain, epsilon u is the concrete ultimate compressive strain, and the value is 0.003.
Therefore, the tensile and compressive non-prestress FRP tendon stresses (σ f and σ' f) in the limit state are respectively:
Wherein E f and E 'f are respectively the elastic modulus of the tensile and compressive non-prestressed FRP bars, f f is the breaking strength of the FRP bars, d f and d' f are respectively the effective heights of the tensile and compressive non-prestressed FRP bars, c u is the neutral axis height when the external prestressed concrete beam with the built-in FRP bars is broken, and ε u is the ultimate compressive strain of the concrete.
Substituting the formulas (3), (8), and (9) into the cross-sectional balance equation (5) can obtain:
Wherein the method comprises the steps of ,A＝0.85fcbβ;B＝AfEfεu(1+k2Epρp/fc)+A'fE'fεu-Ap(σpe+k1Ep+k2Epqp);C＝-AfEfεudf(1+k2Epρp/fc)-A'fE'fεud'f;
Ρ p is the tendon arrangement ratio, q p is the tendon arrangement index:
Therefore, according to the obtained characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib, the neutral axis height c u when the external prestressed concrete beam with the built-in FRP rib is damaged can be obtained through formulas (10), (11) and (12).
According to the formula (8) and the formula (9), the tensile and compressive non-prestress FRP rib stress (sigma f and sigma' f) in the limit state is calculated, and then the formula (4) is combined to calculate the external prestressed concrete beam comprehensive reinforcement index q 0 of the internal non-prestress FRP rib, so that the limit stress sigma pu of the external prestressed rib of the beam under the condition of the internal non-prestress FRP rib is calculated according to the formula (3).
Moment is taken from the resultant force of the concrete, and the nominal bending strength of the external prestressed concrete beam with the internal non-prestressed FRP rib can be calculated by the following formula:
Mn＝Apσpu(deff-βcu/2)+Afσf(df-βcu/2)-A'fσ'f(d'f-βcu/2) (13)
from the above analysis, c u、σf、σ′f、σpu in the formula has been successively found, and d eff is the effective height of the external tendon in the limit state, and can be calculated by the following formula:
deff＝dp[λ1-λ2(L/dp)-λ3(Sd/L)] (14)
The L is span length, S d is span inner steering block distance, and the coefficient lambda 1、λ2、λ3 is as follows, trisection or even distribution load, lambda 1＝1.25,λ2＝0.01,λ3 =0.38, single-point concentrated load, lambda 1＝1.14,λ2＝0.005,λ3 =0.19.
Therefore, the bending strength of the prestressed concrete beam outside the internally-matched FRP rib body can be determined through the calculation process. A complete flow chart of the above calculation idea is shown in fig. 6.
According to the above-mentioned calculation concept, the initial characteristic parameters need to be obtained, and in a preferred embodiment, in step S101, the characteristic parameters of the external prestressed concrete beam include structural information, section information, load information, external prestressed tendon material information, and concrete material information;
The characteristic parameters of the non-prestressed FRP rib comprise non-prestressed FRP rib material information.
As a specific embodiment, in the characteristic information of the external prestressed concrete girder,
The structure information includes inter-span length and inter-steering block spacing.
The section information comprises the external prestressed rib area, the section width and the external prestressed rib height of the external prestressed concrete beam before deformation.
The load information comprises three-point or even-distributed load coefficients and single-point concentrated load information.
The external prestressed tendon material information comprises effective prestress of the external prestressed tendon and elastic modulus of the external prestressed tendon.
The concrete material information comprises the compressive strength of the concrete axle center, the ultimate compressive strain of the concrete and the coefficient of a concrete stress block.
The information of the non-prestressed FRP rib material comprises the elastic modulus of the non-prestressed FRP rib in the tensile and compression bodies, the breaking strength of the non-prestressed FRP rib, the area of the tensile non-prestressed FRP rib, the effective height of the tensile non-prestressed FRP rib, the area of the compression non-prestressed FRP rib and the effective height of the compression non-prestressed FRP rib.
As a preferred embodiment, in step S102, determining the neutral axis height when the external prestressed concrete beam of the built-in FRP tendon is damaged according to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP tendon, includes:
creating a stress analysis model based on a finite element method;
Carrying out a numerical test on the external prestressed concrete beam by using the stress analysis model to obtain a limit stress increment formula of the external prestressed tendon;
Determining a neutral axis height calculation formula when the external prestressed concrete beam with the built-in FRP tendon is damaged according to a limit stress increment formula of the external prestressed tendon, an external prestressed tendon limit stress calculation formula, an external prestressed concrete beam comprehensive reinforcement index calculation formula and a section balance condition;
and determining the neutral axis height when the external prestressed concrete beam with the built-in FRP ribs is damaged according to the neutral axis height calculation formula and the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP ribs.
As a preferred embodiment, the method for obtaining the limit stress increment formula of the external prestressed tendon comprises the following steps of:
Dividing the external prestressed concrete beam into a plurality of stress units;
Obtaining a change curve of the limit stress increment of the external prestressed reinforcement along with the comprehensive reinforcement index of the external prestressed concrete beam according to the action of the stress unit on the tri-division load and the mid-span single-point load;
And performing linear fitting on the change curve to obtain a limit stress increment formula of the external prestressed tendon.
As a preferred embodiment, in step S103, determining the limiting stress of the in-vivo non-prestressed FRP tendon and the in-vitro prestressed tendon of the in-vivo-matched FRP tendon-in-vitro prestressed concrete beam according to the neutral axis height includes:
Determining the tension limit stress of the in-vivo non-prestress FRP rib according to the neutral axis height;
According to the tensile limit stress, determining the comprehensive reinforcement index of the external prestressed concrete beam with the FRP reinforcement arranged inside;
determining the limit stress increment of the external prestressed tendons according to the comprehensive reinforcement indexes;
and determining the limit stress of the external prestressed tendons according to the limit stress increment of the external prestressed tendons and the characteristic parameters of the external prestressed concrete beam internally provided with the FRP tendons.
As a preferred embodiment, according to the tensile limit stress, determining the comprehensive reinforcement index of the external prestressed concrete beam with the internally-matched FRP reinforcement includes:
when the tensile ultimate stress of the non-prestressed FRP rib is larger than the self-fracture strength, taking the self-fracture strength of the non-prestressed FRP rib as the tensile ultimate stress;
And determining the comprehensive reinforcement index of the external prestressed concrete beam with the FRP reinforcement according to the tensile limit stress of the non-prestressed FRP reinforcement.
As a preferred embodiment, determining the bending strength of the external prestressed concrete beam of the internal FRP tendon according to the limit stress of the internal non-prestressed FRP tendon and the external prestressed tendon, includes:
Determining the compressive limit stress of the in-vivo non-prestress FRP rib according to the neutral axis height;
Moment is taken from the external prestressed concrete beam with the FRP rib internally, and a nominal bending strength calculation equation of the external prestressed concrete beam with the FRP rib internally is obtained;
And determining the bending strength of the external prestressed concrete beam of the internal FRP rib according to the limiting stress of the external prestressed rib, the tensile limiting stress of the internal non-prestressed FRP rib, the compressive limiting stress, and the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib.
In order to verify the effect of determining the bending strength of the external prestressed concrete beam with the FRP tendon matched inside in the technical scheme, as a specific embodiment, the model prediction values and the actual values of the external tendon limit stress increment and the nominal bending strength of the external prestressed concrete beam with the non-prestressed FRP tendon matched inside and outside in 45 different types and areas under the action of different load types are compared, as shown in fig. 7 and 8, fig. 7 shows the comparison of the calculated value and the actual value of the external prestressed tendon limit stress increment, and fig. 8 shows the comparison of the nominal bending strength and the actual value of the external prestressed concrete beam with the non-prestressed FRP tendon matched inside calculated by the method.
As can be seen from the graph, the result of the embodiment is better matched with the actual value, wherein the average deviation of the limit stress increment of the external prestressed tendons is 1.2%, the standard deviation is 7.1%, the average deviation of the nominal bending strength of the external prestressed concrete beam with the internal FRP tendons is-4.8%, and the standard deviation is 2.9%. The error range is acceptable in practical application, so that the method has good practicability and can provide theoretical guidance for calculating the bending strength of the external prestressed concrete beam with the FRP rib.
The embodiment of the invention also provides a device for determining the bending strength of the external prestressed concrete beam with the FRP rib internally, the structural block diagram of which is shown in figure 9, and the device 900 for determining the bending strength of the external prestressed concrete beam with the FRP rib internally comprises:
The parameter acquisition module 901 is used for acquiring characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib;
The neutral axis height calculation module 902 is configured to determine a neutral axis height when the external prestressed concrete beam with the built-in FRP tendons is damaged according to characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP tendons;
the limit stress calculation module 903 is configured to determine limit stress of the in-vivo non-prestressed FRP tendon and the in-vitro prestressed tendon of the in-vivo non-prestressed FRP tendon and the in-vitro prestressed concrete beam according to the neutral axis height;
The bending strength determining module 904 is configured to determine the bending strength of the external prestressed concrete beam with the internal FRP tendon according to the limit stress of the internal non-prestressed FRP tendon and the external prestressed tendon.
As shown in fig. 10, the present invention further provides an electronic device 1000, which may be a mobile terminal, a desktop computer, a notebook computer, a palm computer, a server, and other computing devices. The electronic device comprises a processor 1001, a memory 1002 and a display 1003.
The memory 1002 may be an internal storage unit of a computer device, such as a hard disk or memory of a computer device, in some embodiments. The memory 1002 may also be an external storage device of a computer device, such as a plug-in hard disk provided on a computer device, a smart memory card (SMART MEDIA CARD, SMC), a Secure Digital (SD) card, a flash memory card (FLASH CARD), or the like, in other embodiments. Further, the memory 1002 may also include both internal storage units and external storage devices of the computer device. The memory 1002 is used for storing application software installed on the computer device and various kinds of data, such as program codes for installing the computer device, and the like. The memory 1002 may also be used to temporarily store data that has been output or is to be output. In an embodiment, a memory 1002 stores a method program 1004 for determining the bending strength of an external prestressed concrete beam with built-in FRP tendons, where the method program 1004 for determining the bending strength of an external prestressed concrete beam with built-in FRP tendons can be executed by a processor 1001, so as to implement the method for determining the bending strength of an external prestressed concrete beam with built-in FRP tendons according to embodiments of the present invention.
The processor 1001 may be a central processing unit (Central Processing Unit, CPU), microprocessor or other data processing chip in some embodiments, for running the program codes or processing data stored in the memory 1002, for example, executing a program for determining the bending strength of an external prestressed concrete beam with an FRP tendon built in.
The display 1003 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch, or the like in some embodiments. The display 1003 is used for displaying information at the computer device and for displaying a visual user interface. The components 1001-1003 of the computer device communicate with each other over a system bus.
The embodiment also provides a computer readable storage medium, on which a program of the method for determining the bending strength of the prestressed concrete beam outside the built-in FRP tendon is stored, and when the processor executes the program, the method for determining the bending strength of the prestressed concrete beam outside the built-in FRP tendon is realized.
According to the computer readable storage medium and the computing device provided by the above embodiments of the present invention, the method for determining the bending strength of the prestressed concrete beam outside the built-in FRP tendon according to the present invention may be specifically described, and has similar advantages as the method for determining the bending strength of the prestressed concrete beam outside the built-in FRP tendon according to the present invention, and will not be described herein.
The invention discloses a method, a device, electronic equipment and a computer readable storage medium for determining the bending strength of an external prestressed concrete beam internally provided with FRP ribs, wherein the method comprises the steps of firstly, obtaining characteristic parameters of the external prestressed concrete beam and non-prestressed FRP ribs; the method comprises the steps of firstly, determining the characteristic parameters of an external prestressed concrete beam and an external prestressed concrete beam, secondly, determining the neutral axis height of the internal FRP rib external prestressed concrete beam when the internal FRP rib external prestressed concrete beam is damaged according to the characteristic parameters of the external prestressed concrete beam and the external prestressed FRP rib, thirdly, determining the limit stress of the internal non-prestressed FRP rib and the external prestressed rib of the internal FRP rib external prestressed concrete beam according to the neutral axis height, and finally, determining the bending strength of the internal FRP rib external prestressed concrete beam according to the limit stress of the internal non-prestressed FRP rib and the external prestressed rib. The method provides an effective calculation method for calculating the bending strength of the external prestressed concrete beam with the built-in FRP ribs, has the characteristics of simplicity and convenience in calculation, high precision, strong practicability and the like, solves the problem that the external prestressed concrete beam with the built-in non-prestressed FRP ribs lacks the bending strength calculation method in the prior art, has strong practical value, and can provide theoretical guidance for calculating the bending strength of the external prestressed concrete beam with the built-in non-prestressed FRP ribs.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention.

Claims (8)

1. The method for determining the bending strength of the external prestressed concrete beam with the FRP ribs inside is characterized by comprising the following steps of:
acquiring characteristic parameters of an external prestressed concrete beam and a non-prestressed FRP rib;
According to characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP bars, determining the neutral axis height when the external prestressed concrete beam with the built-in FRP bars is damaged, wherein the non-prestressed FRP bars are configured in the external prestressed concrete beam;
Determining the limit stress of the in-vivo non-prestressed FRP tendon and the in-vitro prestressed tendon of the in-vitro prestressed concrete beam with the FRP tendon according to the neutral axis height;
determining the bending strength of the external prestressed concrete beam of the internal FRP rib according to the limit stress of the internal non-prestressed FRP rib and the external prestressed rib;
the method for determining the neutral axis height of the external prestressed concrete beam with the built-in FRP ribs when the external prestressed concrete beam is damaged is determined according to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP ribs, and specifically comprises the following steps:
creating a stress analysis model based on a finite element method;
Carrying out a numerical test on the external prestressed concrete beam by using the stress analysis model to obtain a limit stress increment formula of the external prestressed tendon;
Determining a neutral axis height calculation formula when the external prestressed concrete beam with the built-in FRP tendon is damaged according to a limit stress increment formula of the external prestressed tendon, an external prestressed tendon limit stress calculation formula, an external prestressed concrete beam comprehensive reinforcement index calculation formula and a section balance condition;
Determining the neutral axis height when the external prestressed concrete beam with the built-in FRP ribs is damaged according to the neutral axis height calculation formula and the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP ribs;
Determining the bending strength of the external prestressed concrete beam of the internal FRP rib according to the limit stress of the internal non-prestressed FRP rib and the external prestressed rib, wherein the method specifically comprises the following steps:
Determining the tension limit stress and the compression limit stress of the in-vivo non-prestress FRP rib according to the neutral axis height;
Moment is taken from the external prestressed concrete beam with the FRP rib internally, and a nominal bending strength calculation equation of the external prestressed concrete beam with the FRP rib internally is obtained;
and determining the bending strength of the external prestressed concrete beam of the internal FRP rib according to the ultimate stress of the external prestressed rib, the tensile ultimate stress of the internal non-prestressed FRP rib, the compressive ultimate stress, and the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib.
2. The method for determining the bending strength of the external prestressed concrete beam with the FRP tendon matched inside according to claim 1, wherein the characteristic parameters of the external prestressed concrete beam comprise structural information, section information, load information, external prestressed tendon material information and concrete material information;
The characteristic parameters of the non-prestressed FRP rib comprise non-prestressed FRP rib material information.
3. The method for determining the flexural strength of an external prestressed concrete beam with an internally-arranged FRP tendon according to claim 1, wherein the numerical test is performed on the external prestressed concrete beam by using the stress analysis model to obtain a limit stress increment formula of the external prestressed tendon, comprising:
Dividing the external prestressed concrete beam into a plurality of stress units;
Obtaining a change curve of the limit stress increment of the external prestressed reinforcement along with the comprehensive reinforcement index of the external prestressed concrete beam according to the action of the stress unit on the tri-division load and the mid-span single-point load;
And performing linear fitting on the change curve to obtain a limit stress increment formula of the external prestressed tendon.
4. The method for determining the flexural strength of an internally-matched FRP tendon external prestressed concrete beam according to claim 1, wherein determining the limit stresses of the internal non-prestressed FRP tendon and the external prestressed tendon of the internally-matched FRP tendon external prestressed concrete beam according to the neutral axis height comprises:
Determining the tension limit stress of the in-vivo non-prestress FRP rib according to the neutral axis height;
According to the tensile limit stress, determining the comprehensive reinforcement index of the external prestressed concrete beam with the FRP reinforcement arranged inside;
determining the limit stress increment of the external prestressed tendons according to the comprehensive reinforcement indexes;
and determining the limit stress of the external prestressed tendons according to the limit stress increment of the external prestressed tendons and the characteristic parameters of the external prestressed concrete beam internally provided with the FRP tendons.
5. The method for determining the flexural strength of an internally-distributed FRP-reinforced external prestressed concrete beam according to claim 4, wherein determining the comprehensive reinforcement index of the internally-distributed FRP-reinforced external prestressed concrete beam according to the tensile ultimate stress comprises:
when the tensile ultimate stress of the non-prestressed FRP rib is larger than the self-fracture strength, taking the self-fracture strength of the non-prestressed FRP rib as the tensile ultimate stress;
And determining the comprehensive reinforcement index of the external prestressed concrete beam with the FRP reinforcement according to the tensile limit stress of the non-prestressed FRP reinforcement.
6. The utility model provides an external prestressed concrete roof beam bending strength determining means of interior FRP muscle that joins in marriage which characterized in that includes:
the parameter acquisition module is used for acquiring characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib;
the neutral axis height calculation module is used for determining the neutral axis height when the external prestressed concrete beam with the built-in FRP ribs is damaged according to the characteristic parameters of the external prestressed concrete beam and the external non-prestressed FRP ribs and the non-prestressed FRP ribs are configured in the external prestressed concrete beam;
The limit stress calculation module is used for determining limit stress of the internal non-prestressed FRP bars and the external prestressed bars of the external prestressed concrete beam internally matched with the FRP bars according to the neutral axis height;
The bending strength determining module is used for determining the bending strength of the external prestressed concrete beam with the FRP bars matched inside according to the limit stress of the internal non-prestressed FRP bars and the external prestressed bars;
the method for determining the neutral axis height of the external prestressed concrete beam with the built-in FRP ribs when the external prestressed concrete beam is damaged is determined according to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP ribs, and specifically comprises the following steps:
creating a stress analysis model based on a finite element method;
Carrying out a numerical test on the external prestressed concrete beam by using the stress analysis model to obtain a limit stress increment formula of the external prestressed tendon;
Determining a neutral axis height calculation formula when the external prestressed concrete beam with the built-in FRP tendon is damaged according to a limit stress increment formula of the external prestressed tendon, an external prestressed tendon limit stress calculation formula, an external prestressed concrete beam comprehensive reinforcement index calculation formula and a section balance condition;
Determining the neutral axis height when the external prestressed concrete beam with the built-in FRP ribs is damaged according to the neutral axis height calculation formula and the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP ribs;
Determining the bending strength of the external prestressed concrete beam of the internal FRP rib according to the limit stress of the internal non-prestressed FRP rib and the external prestressed rib, wherein the method specifically comprises the following steps:
Determining the tension limit stress and the compression limit stress of the in-vivo non-prestress FRP rib according to the neutral axis height;
Moment is taken from the external prestressed concrete beam with the FRP rib internally, and a nominal bending strength calculation equation of the external prestressed concrete beam with the FRP rib internally is obtained;
and determining the bending strength of the external prestressed concrete beam of the internal FRP rib according to the ultimate stress of the external prestressed rib, the tensile ultimate stress of the internal non-prestressed FRP rib, the compressive ultimate stress, and the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib.
7. An electronic device, comprising a processor and a memory, wherein the memory stores a computer program, and the computer program, when executed by the processor, implements the method for determining the flexural strength of an external prestressed concrete beam with an internal FRP tendon according to any one of claims 1 to 5.
8. A computer-readable storage medium, wherein a computer program is stored thereon, which when executed by a processor, implements the method for determining the flexural strength of an in-built FRP tendon out-of-body prestressed concrete beam according to any one of claims 1 to 5.
CN202210631329.2A 2022-06-06 2022-06-06 A method for determining the flexural strength of externally prestressed concrete beams with internal FRP bars Active CN114878354B (en)

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CN206487068U (en) * 2017-02-16 2017-09-12 沈阳建筑大学 Assembled FRP strengthens steel core concrete column

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FRP筋无粘结预应力混凝土结构极限强度分析;吴岩;刘海霞;李玉顺;杨光;盛可鉴;;黑龙江工程学院学报(自然科学版);20110930;25(03);22-37 *

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