CN114878354A - Method for determining bending strength of external prestressed concrete beam with internal FRP (fiber reinforced Plastic) ribs - Google Patents

Method for determining bending strength of external prestressed concrete beam with internal FRP (fiber reinforced Plastic) ribs Download PDF

Info

Publication number
CN114878354A
CN114878354A CN202210631329.2A CN202210631329A CN114878354A CN 114878354 A CN114878354 A CN 114878354A CN 202210631329 A CN202210631329 A CN 202210631329A CN 114878354 A CN114878354 A CN 114878354A
Authority
CN
China
Prior art keywords
prestressed
frp
external
prestressed concrete
reinforcement
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202210631329.2A
Other languages
Chinese (zh)
Other versions
CN114878354B (en
Inventor
楼铁炯
李张翔
胡涵
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Wuhan University of Technology WUT
Original Assignee
Wuhan University of Technology WUT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Wuhan University of Technology WUT filed Critical Wuhan University of Technology WUT
Priority to CN202210631329.2A priority Critical patent/CN114878354B/en
Publication of CN114878354A publication Critical patent/CN114878354A/en
Application granted granted Critical
Publication of CN114878354B publication Critical patent/CN114878354B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • G01N2203/02—Details not specific for a particular testing method
    • G01N2203/06—Indicating or recording means; Sensing means
    • G01N2203/067—Parameter measured for estimating the property
    • G01N2203/0676—Force, weight, load, energy, speed or acceleration
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Physics & Mathematics (AREA)
  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Analytical Chemistry (AREA)
  • Biochemistry (AREA)
  • General Health & Medical Sciences (AREA)
  • General Physics & Mathematics (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Rod-Shaped Construction Members (AREA)

Abstract

本申请公开了一种内配FRP筋体外预应力混凝土梁抗弯强度确定方法，包括：获取体外预应力混凝土梁和非预应力FRP筋的特征参数；根据体外预应力混凝土梁和非预应力FRP筋的特征参数，确定体外预应力混凝土梁内配置所述非预应力FRP筋，所构成的内配FRP筋体外预应力梁被破坏时的中性轴高度；根据中性轴高度确定所述内配FRP筋体外预应力混凝土梁的体内非预应力FRP筋和体外预应力筋的极限应力；根据体内非预应力FRP筋和体外预应力筋的极限应力确定所述内配FRP筋体外预应力混凝土梁的抗弯强度。本发明为内配FRP筋体外预应力混凝土梁的抗弯强度计算提供了有效的计算方法，具有计算简便、精度高、实用性强等特点。

Figure 202210631329

The present application discloses a method for determining the flexural strength of externally prestressed concrete beams with internal FRP reinforcement, including: acquiring characteristic parameters of externally prestressed concrete beams and non-prestressed FRP reinforcement; The non-prestressed FRP reinforcement is configured in the external prestressed concrete beam, and the neutral axis height of the external prestressed beam formed with the internal FRP reinforcement is damaged; the external prestressing of the internal FRP reinforcement is determined according to the neutral axis height. The ultimate stress of the internal non-prestressed FRP tendons and external prestressed tendons of the concrete beam; the flexural strength of the externally prestressed concrete beam with internal FRP tendons is determined according to the ultimate stress of the internal non-prestressed FRP tendons and external prestressed tendons. The invention provides an effective calculation method for calculating the flexural strength of external prestressed concrete beams with internal FRP reinforcement, and has the characteristics of simple calculation, high precision, strong practicability and the like.

Figure 202210631329

Description

Method for determining bending strength of external prestressed concrete beam with internal FRP (fiber reinforced Plastic) ribs
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 an internally-arranged FRP rib, electronic equipment and a computer-readable storage medium.
Background
The external prestress technology is widely applied to the construction of new projects and the reinforcement or the reconstruction of existing damaged structures. For the external prestressed concrete beam, a certain amount of bonding ribs are required to be arranged in the beam to limit the width and the spacing of overlarge cracks and avoid the occurrence of tie rod arch behaviors in the structure.
The traditional external non-bonding steel bar and the internal bonding steel bar are respectively prestressed steel bar and non-prestressed steel bar, the steel bar corrosion can cause structural damage, and the adoption of the corrosion-resistant FRP bar to replace the traditional steel bar is an effective method for solving the problem. The FRP is a linear elastic material, has no yield platform like a steel bar, and has an elastic modulus generally lower than that of a common steel bar. The use of FRP reinforcement instead of conventional (prestressed or non-prestressed) reinforcement thus presents new challenges to the buckling-resistant design of the externally prestressed concrete beam. At present, an effective calculation method for the bending strength of an in-vitro prestressed concrete beam internally provided with non-prestressed FRP ribs is lacked.
Therefore, it is necessary to provide a method for determining the bending strength of the in vitro prestressed concrete beam with the in vivo non-prestressed FRP bars, which calculates the bending strength of the in vitro prestressed concrete beam with the in vivo non-prestressed FRP bars and provides theoretical guidance for determining the bending strength of the in vitro prestressed concrete beam with the in vivo non-prestressed FRP bars.
Disclosure of Invention
In view of the above, it is necessary to provide a method, an apparatus, an electronic device and a computer readable storage device for determining the bending strength of an external prestressed concrete beam with an internal FRP bar, so as to solve the problem in the prior art that an effective calculation method for the bending strength of the external prestressed concrete beam with an internal non-prestressed FRP bar is lacking.
In order to solve the problems, the invention provides a method for determining the bending strength of an external prestressed concrete beam with an internally-arranged FRP reinforcement, which comprises the following steps:
acquiring characteristic parameters of an external prestressed concrete beam and a non-prestressed FRP rib;
determining the neutral axis height of the external prestressed concrete beam formed by the non-prestressed FRP ribs arranged in the external prestressed concrete beam and the internal FRP ribs when the external prestressed concrete beam is damaged according to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP ribs;
determining the limit stress of the in-vivo non-prestressed FRP tendon and the in-vitro prestressed tendon of the in-vivo FRP tendon and the in-vitro prestressed tendon of the in-vitro prestressed concrete beam according to the height of the neutral axis;
and determining 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.
Further, 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: and (4) information of the non-prestressed FRP rib material.
Further, determining the height of the neutral axis of the external prestressed concrete beam with the internal FRP tendon when the external prestressed concrete beam is damaged according to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP tendon, includes:
establishing a stress analysis model based on a finite element method;
carrying out a numerical test on the in-vitro prestressed concrete beam by using the stress analysis model to obtain a limit stress increment formula of the in-vitro prestressed tendon;
determining a neutral axis height calculation formula when the external prestressed concrete beam of the internal FRP tendon is damaged according to a limit stress increment formula of the external prestressed tendon, an external prestressed tendon limit stress calculation equation, an integrated tendon index calculation equation of the external prestressed concrete beam of the internal FRP tendon and a section balance condition;
and determining the height of the neutral axis when the external prestressed concrete beam with the internal FRP rib is damaged according to the calculation formula of the height of the neutral axis and the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib.
Further, the numerical test is performed on the external prestressed concrete beam by using the stress analysis model to obtain an ultimate stress increment formula of the external prestressed tendon, and the ultimate stress increment formula comprises the following steps:
dividing the external prestressed concrete beam into a plurality of stressed units;
obtaining a change curve of the ultimate stress increment of the external prestressed tendons along with the comprehensive reinforcement allocation index of the external prestressed concrete beam according to the action of the stressed unit on three-point load and mid-span single-point load;
and performing linear fitting on the change curve to obtain a limit stress increment formula of the in-vitro prestressed tendon.
Further, determining the limit stress of the in-vivo non-prestressed FRP tendon and the in-vitro prestressed tendon of the internally-matched FRP tendon and the in-vitro prestressed concrete beam according to the height of the neutral axis comprises the following steps:
determining the tensile ultimate stress of the in-vivo non-prestressed FRP rib according to the height of the neutral axis;
determining a comprehensive reinforcement index of the external prestressed concrete beam of the internal FRP reinforcement according to the tensile ultimate stress;
determining the ultimate stress increment of the external prestressed tendon according to the comprehensive reinforcement index;
and 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 external prestressed concrete beam with the internal FRP tendons.
Further, determining a comprehensive reinforcement allocation index of the internal FRP rib external prestressed concrete beam according to the tension limit stress, wherein the comprehensive reinforcement allocation index comprises the following steps:
when the tensile ultimate stress of the non-prestressed FRP rib is larger than the breaking strength of the non-prestressed FRP rib, taking the breaking strength of the non-prestressed FRP rib as the tensile ultimate stress;
and determining a comprehensive reinforcement allocation index of the external prestressed concrete beam of the internal FRP rib according to the tensile ultimate stress of the non-prestressed FRP rib.
Further, 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, comprising the following steps:
determining the compression limit stress of the in-vivo non-prestressed FRP rib according to the height of the neutral axis;
taking a moment for the internal FRP rib external prestressed concrete beam to obtain a nominal bending strength calculation equation of the internal FRP rib external prestressed concrete beam;
and determining the bending strength of the external prestressed concrete beam with the internal FRP tendon according to the ultimate stress of the external prestressed tendon, the tensile ultimate stress of the internal non-prestressed FRP tendon, the compressive ultimate stress and the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP tendon.
The invention also provides a device for predicting the bending strength of the external prestressed concrete beam with the internally-arranged FRP rib, which comprises:
the parameter acquisition module is used for acquiring the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib;
a neutral axis height calculation module, configured to determine, according to characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP bars, a neutral axis height at which the non-prestressed FRP bars are configured in the external prestressed concrete beam and the external prestressed FRP bars formed by the configuration of the non-prestressed FRP bars are damaged;
the ultimate stress calculation module is used for determining the ultimate stress of the in-vivo non-prestressed FRP tendon and the in-vitro prestressed tendon of the in-line FRP tendon and the in-vitro prestressed concrete beam according to the height of the neutral axis;
and the bending strength determining module is used for 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 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 internal FRP rib is realized according to any technical scheme.
The invention also provides a computer readable storage medium, which stores a computer program, and when the computer program is executed by a processor, the method for determining the bending strength of the external prestressed concrete beam with the internal FRP rib is realized according to any technical scheme.
Compared with the prior art, the invention has the beneficial effects that: firstly, acquiring characteristic parameters of an external prestressed concrete beam and a non-prestressed FRP rib; secondly, determining the height of a neutral axis when the external prestressed concrete beam with the internal FRP ribs is damaged according to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP ribs; thirdly, determining the limit stress of the in-vivo non-prestressed FRP ribs and the in-vitro prestressed ribs of the in-vivo FRP rib in-vitro prestressed concrete beam according to the height of the neutral axis; 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 the bending strength calculation of the external prestressed concrete beam with the internally-matched 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 internally-matched non-prestressed FRP ribs is lack of the bending strength calculation method in the prior art, has very high practical value, and can provide theoretical guidance for the bending strength calculation of the external prestressed concrete beam with the internally-matched non-prestressed FRP ribs.
Drawings
FIG. 1 is a schematic flow chart of an embodiment of a method for determining the bending strength of an external prestressed concrete beam with internally-arranged FRP ribs according to the present invention;
FIG. 2 is a schematic structural view of an embodiment of an externally prestressed concrete beam with internally arranged FRP ribs according to the present invention;
FIG. 3 is a schematic view of an embodiment of a stress analysis model of an external prestressed concrete beam with an internally-arranged FRP tendon provided by the invention;
FIG. 4 is a schematic diagram of variation of the ultimate stress increment of the external tendon with the comprehensive bar distribution index according to an embodiment of the present invention under different load types and internal non-prestressed tendon types;
FIG. 5 is a schematic diagram of an embodiment of a fitting curve of an ultimate stress increment of an in-vitro prestressed reinforcement and a comprehensive reinforcement index of an internally-arranged non-prestressed FRP reinforcement provided by the invention;
FIG. 6 is a schematic view of a calculation process of nominal bending strength of an in-vitro prestressed concrete beam with non-prestressed FRP ribs provided therein according to an embodiment of the present invention;
FIG. 7 is a comparison diagram of an embodiment of a predicted value and an actual value of an incremental model of the ultimate stress of the in-vitro prestressed tendons provided by the invention;
FIG. 8 is a comparison graph of a predicted value and an actual value of a nominal bending strength model of an external prestressed concrete beam with an internally-arranged FRP tendon provided by the invention;
fig. 9 is a schematic structural diagram of an embodiment of the device for determining the bending strength of the external prestressed concrete beam with the internal FRP reinforcements provided by the present invention;
fig. 10 is a block diagram of an embodiment of an electronic device provided in the present invention.
Detailed Description
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate preferred embodiments of the invention and together with the description, serve to explain the principles of the invention and not to limit the scope of the invention.
The invention provides a method and a device for determining the bending strength of an external prestressed concrete beam with an internally-arranged FRP rib, electronic equipment and a computer-readable storage medium, which are respectively explained in detail below.
The embodiment of the invention provides a method for determining the bending strength of an external prestressed concrete beam with an internally-arranged FRP rib, a flow schematic diagram of the method is shown in figure 1, and the method comprises the following steps:
s101, acquiring characteristic parameters of an external prestressed concrete beam and a non-prestressed FRP rib;
step S102, determining the neutral axis height of the external prestressed concrete beam with the built-in FRP rib when the external prestressed concrete beam is damaged, wherein the non-prestressed FRP rib is configured in the external prestressed concrete beam according to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib;
s103, determining the limit stress of the in-vivo non-prestressed FRP ribs and the in-vitro prestressed ribs of the in-line FRP rib and in-vitro prestressed concrete beam according to the height of the neutral axis;
and S104, determining the bending strength of the external prestressed concrete beam with the internal FRP ribs according to the limit stress of the internal non-prestressed FRP ribs and the external prestressed ribs.
Compared with the prior art, the method for determining the bending strength of the external prestressed concrete beam with the internal FRP ribs provided by the embodiment comprises the following steps of firstly, obtaining characteristic parameters of the external prestressed concrete beam and non-prestressed FRP ribs; secondly, determining the height of a neutral axis when the external prestressed concrete beam with the internal FRP ribs is damaged according to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP ribs; thirdly, determining the limit stress of the in-vivo non-prestressed FRP ribs and the in-vitro prestressed ribs of the in-vivo FRP rib in-vitro prestressed concrete beam according to the height of the neutral axis; 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 the bending strength calculation of the FRP rib external prestressed concrete beam, has the characteristics of simple and convenient 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 very high practical value, and can provide theoretical guidance for the bending strength calculation of the external prestressed concrete beam internally provided with the FRP rib.
For better understanding of the above technical solutions, the idea of the method for determining the bending strength of the external prestressed concrete beam with the internal non-prestressed FRP reinforcement described in this embodiment is described below with reference to fig. 2 to 6, taking the determination of the bending strength of the external prestressed concrete beam with the internal non-prestressed FRP reinforcement as an example.
In order to determine the bending strength of the external prestressed concrete beam internally provided with the FRP ribs, the key is to determine the ultimate stress of the external prestressed ribs. Because the external prestressed tendons are not coordinated with the strain of the surrounding concrete, the strain or stress of the external prestressed tendons depends on the integral deformation of the beam, and the conventional section deformation coordination condition is not applicable any more.
The ultimate stress of the external tendons is generally represented by the following formula:
σ pu ＝σ pe +Δσ p (1)
wherein σ pu Is the ultimate stress of the external prestressed tendon; sigma pe Is the effective prestress of the external prestressed tendon; delta sigma p Is the ultimate stress increment of the external prestressed tendon. Sigma pe Can be confirmed according to the material information of the external prestressed tendonDefinite, external prestressed rib ultimate stress increment delta sigma p 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 ultimate stress increment of the external prestressed tendon can be calculated by determining the relationship between the ultimate stress increment of the external prestressed tendon and the comprehensive reinforcing steel bar index.
In order to determine the relationship between the ultimate stress increment of the in-vitro prestressed tendon and the comprehensive reinforcing steel bar index, a stress analysis model is established based on a finite element method. As shown in fig. 2, an external prestressed concrete girder in which the type, area and load type of the internal non-prestressed tendons are varied is designed.
As shown in FIG. 2, the span length of the beam is 10m, two turning blocks are arranged at the three points, the effective height of the external prestressed tendon at the end part of the beam is 0.3m, and the effective height of the turning block is 0.5 m. The compressive strength of the concrete axle center is 60 MPa. The external prestressed tendons are CFRP tendons with the area of 10cm 2 The tensile strength was 1840MPa, the modulus of elasticity was 147GPa, and the initial prestress was 60% of the tensile strength. The area of the non-prestressed tendon under pressure is 3.6cm 2 The area of the tension non-prestressed tendon is variable: 3.6cm 2 -35.6cm 2 。
The non-prestressed ribs consider two typical FRP ribs of CFRP (tensile strength of 1840MPa and elastic modulus of 147GPa) and GFRP (tensile strength of 750MPa and elastic modulus of 40GPa), and also consider common steel bars (yield strength of 450MPa and elastic modulus of 200GPa) for comparative analysis.
Three typical load types are considered, as well as three-point load, uniform load and cross-center single-point load.
Numerical tests are carried out on the in-vitro 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, a 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 is divided into 10 concrete layers and 2 non-prestressed tendon layers (each layer represents tensile and compressive non-prestressed tendons).
FIG. 4 shows the in vitro prediction under different load typesThe ultimate stress increment of the stress tendon changes with the index of the comprehensive reinforcing steel bar. It can be seen from fig. 4 that the ultimate stress increment of the external prestressed tendon under the action of the three-point load and the uniformly distributed load is basically close to but significantly higher than that of the external prestressed tendon under the action of the mid-span single-point load. Ultimate stress increment delta sigma of external prestressed tendon of beam internally provided with non-prestressed FRP tendon (including CFRP/GFRP tendon) p Index q along with comprehensive reinforcement 0 The change trend of the pressure sensor is basically consistent. Since CFRP represents a high elastic modulus and GFRP represents a low elastic modulus in the FRP material category, it is possible to estimate Δ σ of an in-vitro prestressed concrete beam in which different types of non-prestressed FRP bars are fitted p -q 0 The responses are substantially the same.
As shown in FIG. 5, the ultimate stress increment and the comprehensive reinforcement index delta sigma of the external prestressed reinforcement of the internal non-prestressed FRP reinforcement under the action of three-point load and single-point concentrated load p -q 0 Respectively carrying out linear fitting on the numerical data, and popularizing the type of the prestressed tendon to a common condition to obtain the following calculation formula of the ultimate stress increment of the external prestressed tendon:
Δσ p ＝(k 1 +k 2 q 0 )E p (2)
wherein the coefficient k 1 、k 2 The values are as follows: trisection point or even load, k 1 ＝4.26,k 2 -7.02; single point concentrated load, k 1 ＝2.3,k 2 ＝-2.67。
Substituting the formula (2) into the formula (1) to obtain the calculation formula of the ultimate stress of the external prestressed tendon of the beam under the condition of the internal non-prestressed FRP tendon, wherein the calculation formula comprises the following steps:
σ pu ＝σ pe +(k 1 +k 2 q 0 )E p (3)
therefore, according to the analysis process, the corresponding relation between the ultimate stress increment of the in-vitro prestressed tendon and the comprehensive reinforcement index is determined.
When the non-prestressed FRP rib is internally provided, the non-prestressed FRP rib usually does not reach the breaking strength, so the comprehensive reinforcing index of the external prestressed concrete beam internally provided with the non-prestressed FRP rib can be expressed as follows:
Figure BDA0003679987680000091
wherein A is p Is the area of the external prestressed tendon; sigma pe Is the effective prestress of the external prestressed tendon; a. the f Is the area of the tensioned non-prestressed FRP rib; sigma f The stress of the tensioned non-prestressed FRP rib under the limit state; b is the cross-sectional width; d is a radical of p The height of the external prestressed tendon before deformation; f. of c The compressive strength of the concrete axle center. For the external prestressed concrete beam internally provided with the non-prestressed FRP rib, the stress sigma of the non-prestressed FRP rib f Is an unknown quantity, so q 0 Also unknown. Therefore, the ultimate stress of the external prestressed tendon still cannot be determined, and the solution needs to be combined with a section balance equation.
The balance equation of the section of the external prestressed concrete beam internally provided with the non-prestressed FRP ribs is as follows:
0.85f c bβc u ＝A p σ pu +A f σ f -A' f σ' f (5)
wherein, A p Is the area of the external prestressed tendon; sigma pu Is the ultimate stress of the external prestressed tendon, A f Is the area of the tensioned non-prestressed FRP rib; sigma f The stress of the tensioned non-prestressed FRP rib under the limit state; a' f Is the area of the non-prestressed FRP rib under pressure; sigma' f The stress of the non-prestressed FRP rib is under the limit state; f. of c The axial compressive strength of the concrete; b is the cross-sectional width; beta is the concrete stress mass coefficient; c. C u The height of the neutral axis is the height of the external prestressed concrete beam with the internal FRP rib when the external prestressed concrete beam is damaged.
The ultimate stress sigma of the external prestressed tendon can be determined according to the formula (5) pu Stress sigma of tensile non-prestressed FRP rib in extreme state f And stress sigma 'of the pressed non-prestressed FRP rib in the extreme state' f And neutral axis height c when broken u The relationship (2) of (c).
Under the coordination condition of the assumption of a flat section and strain, the strain of the non-prestressed FRP rib under the limit state is as follows:
Figure BDA0003679987680000101
Figure BDA0003679987680000102
wherein epsilon f And epsilon' f Respectively strain of the tensile non-prestress FRP rib and the compressive non-prestress FRP rib; d f And d' f The effective heights of the tensioned and compressed non-prestressed FRP ribs are respectively; c. C u The height of a neutral axis is the height of the external prestressed concrete beam with the internal FRP rib when the external prestressed concrete beam is damaged; epsilon fu The FRP rib fracture strain is obtained; epsilon u The value of the ultimate compressive strain of the concrete is 0.003.
Therefore, the non-prestressed FRP rib stress (σ) in tension and compression in the limit state f And σ' f ) Respectively as follows:
Figure BDA0003679987680000103
Figure BDA0003679987680000104
wherein E is f And E' f The elastic modulus of the non-prestressed FRP rib is respectively under tension and compression; f. of f The breaking strength of the FRP rib is obtained; d f And d' f The effective heights of the tensioned and compressed non-prestressed FRP ribs are respectively; c. C u The height of a neutral axis is the height of the external prestressed concrete beam with the internal FRP rib when the external prestressed concrete beam is damaged; epsilon u Is the ultimate compressive strain of the concrete.
Substituting equations (3), (8), and (9) into the cross-sectional balance equation (5) can yield:
Figure BDA0003679987680000105
wherein A is 0.85f c bβ；B＝A f E f ε u (1+k 2 E p ρ p /f c )+A' f E' f ε u -A p (σ pe +k 1 E p +k 2 E p q p )；C＝-A f E f ε u d f (1+k 2 E p ρ p /f c )-A' f E' f ε u d' f ；
ρ p Is the tendon distribution ratio of the prestressed tendon, q p The steel bar distribution indexes of the prestressed steel bar are as follows:
Figure BDA0003679987680000111
Figure BDA0003679987680000112
therefore, according to the obtained characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib, the neutral axis height c of the external prestressed concrete beam with the internally-arranged FRP rib can be obtained through the formulas (10), (11) and (12) when the external prestressed concrete beam is damaged u 。
According to the formula (8) and the formula (9), the stress (sigma) of the tensile and compressive non-prestressed FRP rib in the limit state is obtained f And σ' f ) (ii) a And then the formula (4) is combined to calculate the comprehensive reinforcement index q of the external prestressed concrete beam with the internal non-prestressed FRP reinforcement 0 (ii) a Thus, the ultimate stress sigma of the external prestressed tendon of the beam under the condition of internally-arranged non-prestressed FRP tendon is obtained according to the formula (3) pu 。
And (3) taking a moment at the resultant force position of the concrete, wherein the nominal bending strength of the external prestressed concrete beam with the internal non-prestressed FRP rib can be calculated according to the following formula:
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)
through the above analysis, c in the formula u 、σ f 、σ′ f 、σ pu Successively found out d eff The effective height of the external prestressed tendon in the limit state can be calculated by the following formula:
d eff ＝d p [λ 1 -λ 2 (L/d p )-λ 3 (S d /L)] (14)
wherein L is span length; s d To span the inter-turning block spacing; coefficient lambda 1 、λ 2 、λ 3 The values are as follows: trisection point or even load, lambda 1 ＝1.25,λ 2 ＝0.01,λ 3 0.38; single point concentrated load, lambda 1 ＝1.14,λ 2 ＝0.005,λ 3 ＝0.19。
Therefore, the bending strength of the external prestressed concrete beam with the internally-arranged FRP ribs can be determined through the calculation process. The complete flow chart of the above computing concept is shown in fig. 6.
According to the above calculation idea, initial characteristic parameters need to be obtained, and as 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: and (4) information of the non-prestressed FRP rib material.
As a specific example, in the characteristic information of the external prestressed concrete girder,
the structure information includes: span length, span inner turning block spacing.
The section information includes: the external prestressed reinforcement area, the section width and the external prestressed reinforcement height before deformation of the external prestressed concrete beam.
The load information includes: trisection point or uniform load coefficient, 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 includes: the compressive strength of the concrete axis, the ultimate compressive strain of the concrete and the coefficient of the concrete stress block.
The information of the non-prestressed FRP rib material comprises the following steps: the elastic modulus of the non-prestressed FRP ribs in the tensioned and stressed bodies, the breaking strength of the non-prestressed FRP ribs, the area of the tensioned non-prestressed FRP ribs, the effective height of the tensioned non-prestressed FRP ribs, the area of the stressed non-prestressed FRP ribs and the effective height of the stressed non-prestressed FRP ribs.
As a preferred embodiment, in step S102, determining the neutral axis height of the external prestressed concrete beam with the internal FRP reinforcement when the external prestressed concrete beam is damaged according to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP reinforcement includes:
establishing a stress analysis model based on a finite element method;
carrying out a numerical test on the in-vitro prestressed concrete beam by using the stress analysis model to obtain a limit stress increment formula of the in-vitro prestressed tendon;
determining a neutral axis height calculation formula when the external prestressed concrete beam of the internal FRP tendon is damaged according to a limit stress increment formula of the external prestressed tendon, an external prestressed tendon limit stress calculation equation, an external prestressed concrete beam comprehensive reinforcement index calculation equation and a section balance condition;
and determining the height of the neutral axis when the external prestressed concrete beam with the internal FRP rib is damaged according to the calculation formula of the height of the neutral axis and the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP rib.
As a preferred embodiment, the method for obtaining the ultimate stress increment formula of the external prestressed reinforcement by performing a numerical test on the external prestressed concrete beam by using the stress analysis model includes:
dividing the external prestressed concrete beam into a plurality of stressed units;
obtaining a change curve of the ultimate stress increment of the external prestressed tendons along with the comprehensive reinforcement allocation index of the external prestressed concrete beam according to the action of the stressed unit on three-point load and mid-span single-point load;
and performing linear fitting on the change curve to obtain a limit stress increment formula of the in-vitro prestressed tendon.
As a preferred embodiment, in step S103, determining the limit stresses of the in-vivo non-prestressed FRP tendons and the in-vitro prestressed tendons of the internal FRP tendon and the in-vitro prestressed concrete beam according to the neutral axis height includes:
determining the tensile ultimate stress of the in-vivo non-prestressed FRP rib according to the height of the neutral axis;
determining a comprehensive reinforcement index of the external prestressed concrete beam of the internal FRP reinforcement according to the tensile ultimate stress;
determining the ultimate stress increment of the external prestressed tendon according to the comprehensive reinforcement index;
and 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 external prestressed concrete beam with the internal FRP tendons.
As a preferred embodiment, determining a comprehensive reinforcement allocation index of the external prestressed concrete beam with the internal reinforced FRP reinforcement according to the ultimate tension stress includes:
when the tensile ultimate stress of the non-prestressed FRP rib is larger than the breaking strength of the non-prestressed FRP rib, taking the breaking strength of the non-prestressed FRP rib as the tensile ultimate stress;
and determining a comprehensive reinforcement allocation index of the external prestressed concrete beam of the internal FRP rib according to the tensile ultimate stress of the non-prestressed FRP rib.
As a preferred embodiment, determining the bending strength of the internal FRP bar external prestressed concrete beam according to the ultimate stresses of the internal non-prestressed FRP bar and the external prestressed bar includes:
determining the compression limit stress of the in-vivo non-prestressed FRP rib according to the height of the neutral axis;
taking a moment for the internal FRP rib external prestressed concrete beam to obtain a nominal bending strength calculation equation of the internal FRP rib external prestressed concrete beam;
and determining the bending strength of the external prestressed concrete beam with the internal FRP tendon according to the ultimate stress of the external prestressed tendon, the tensile ultimate stress of the internal non-prestressed FRP tendon, the compressive ultimate stress and the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP tendon.
In order to verify the bending strength determining effect of the external prestressed concrete beam with the internally-arranged FRP ribs in the technical scheme, as a specific embodiment, the external rib limit stress increment and the model predicted value of the nominal bending strength of the external prestressed concrete beam with the internally-arranged non-prestressed FRP ribs of different types and areas under the action of 45 different load types are compared with actual values, as shown in fig. 7 and 8, and fig. 7 shows the comparison of the calculated value and the actual value of the external prestressed rib limit stress increment; fig. 8 shows the nominal bending strength of the in-line non-prestressed FRP tendon in-vitro prestressed concrete beam calculated by the above method compared with an actual value.
It can be seen from the figure that the result of this embodiment is well matched with the actual value, wherein the mean deviation of the ultimate stress increment of the external prestressed tendons is 1.2%, the standard deviation is 7.1%, the mean 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 the calculation of the bending strength of the external prestressed concrete beam with the internally-arranged FRP tendon.
The embodiment of the present invention further provides a device for determining the bending strength of an external prestressed concrete beam with an internal FRP tendon, a structural block diagram of which is shown in fig. 9, and the device 900 for determining the bending strength of an external prestressed concrete beam with an internal FRP tendon comprises:
a parameter obtaining module 901, configured to obtain characteristic parameters of an external prestressed concrete beam and a non-prestressed FRP bar;
a neutral axis height calculation module 902, configured to determine, according to characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP bars, a neutral axis height of the external prestressed concrete beam in which the non-prestressed FRP bars are configured and the internal-configuration FRP bars are formed when the external prestressed concrete beam is damaged;
the limit stress calculation module 903 is used for determining the limit stress of the in-vivo non-prestressed FRP tendon and the in-vitro prestressed tendon of the internal FRP tendon and the in-vitro prestressed concrete beam according to the height of the neutral axis;
and the bending strength determining module 904 is configured to determine the bending strength of the internal FRP bar external prestressed concrete beam according to the limit stresses of the internal non-prestressed FRP bar and the external prestressed bar.
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, a palm computer, a server, or other computing devices. The electronic device includes a processor 1001, a memory 1002, and a display 1003.
The memory 1002 may be an internal storage unit of the computer device, such as a hard disk or a memory of the computer device, in some embodiments. The memory 1002 may be an external storage device of a computer device in other embodiments, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), and the like provided on the computer device. Further, the memory 1002 may also include both internal and external storage units of the computer device. The memory 1002 is used for storing application software installed in the computer device and various data, such as program codes for installing the computer device. The memory 1002 may also be used to temporarily store data that has been output or is to be output. In an embodiment, the memory 1002 stores a program 1004 for determining the bending strength of the external prestressed concrete beam with the internal FRP tendon, and the program 1004 for determining the bending strength of the external prestressed concrete beam with the internal FRP tendon can be executed by the processor 1001, so as to implement a method for determining the bending strength of the external prestressed concrete beam with the internal FRP tendon according to various embodiments of the present invention.
The processor 1001 may be a Central Processing Unit (CPU), microprocessor or other data Processing chip in some embodiments, and is configured to run program codes stored in the memory 1002 or process data, such as executing a program for determining the bending strength of the external prestressed concrete beam with the internal FRP ribs.
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 panel, or the like in some embodiments. The display 1003 is used to display information at the computer device and to display a visual user interface. The components 1001 and 1003 of the computer device communicate with each other via the system bus.
The embodiment also provides a computer readable storage medium, which stores a program of the method for determining the bending strength of the external prestressed concrete beam with the internally-arranged FRP reinforcement, and when the processor executes the program, the method for determining the bending strength of the external prestressed concrete beam with the internally-arranged FRP reinforcement is realized.
According to the computer-readable storage medium and the computing device provided by the above embodiments of the present invention, the content specifically described for implementing the method for determining the bending strength of the internal FRP reinforcement external prestressed concrete beam according to the present invention can be referred to, and the method has similar beneficial effects to the method for determining the bending strength of the internal FRP reinforcement external prestressed concrete beam according to the present invention, and is not described herein again.
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 with an internal FRP (fiber reinforced Plastic) rib, which comprises the steps of firstly, obtaining characteristic parameters of the external prestressed concrete beam and a non-prestressed FRP rib; secondly, determining the height of a neutral axis when the external prestressed concrete beam with the internal FRP ribs is damaged according to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP ribs; thirdly, determining the limit stress of the in-vivo non-prestressed FRP ribs and the in-vitro prestressed ribs of the in-vivo FRP rib in-vitro prestressed concrete beam according to the height of the neutral axis; 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 the bending strength calculation of the external prestressed concrete beam with the internally-matched 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 internally-matched non-prestressed FRP ribs is lack of the bending strength calculation method in the prior art, has very high practical value, and can provide theoretical guidance for the bending strength calculation of the external prestressed concrete beam with the internally-matched non-prestressed FRP ribs.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (10)

1.一种内配FRP筋体外预应力混凝土梁抗弯强度确定方法，其特征在于，包括：1. a method for determining the flexural strength of external prestressed concrete beams with internal FRP reinforcement bars, is characterized in that, comprises: 获取体外预应力混凝土梁和非预应力FRP筋的特征参数；Obtain the characteristic parameters of externally prestressed concrete beams and non-prestressed FRP bars; 根据所述体外预应力混凝土梁和非预应力FRP筋的特征参数，确定所述体外预应力混凝土梁内配置所述非预应力FRP筋，所构成的内配FRP筋体外预应力混凝土梁被破坏时的中性轴高度；According to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP reinforcement, it is determined that the non-prestressed FRP reinforcement is configured in the externally prestressed concrete beam, and the external prestressed concrete beam formed with the internal FRP reinforcement is damaged. neutral axis height; 根据所述中性轴高度确定所述内配FRP筋体外预应力混凝土梁的体内非预应力FRP筋和体外预应力筋的极限应力；Determine the ultimate stress of the internal non-prestressed FRP reinforcement and the external prestressed reinforcement of the externally prestressed concrete beam with the internal FRP reinforcement according to the height of the neutral axis; 根据所述体内非预应力FRP筋和体外预应力筋的极限应力确定所述内配FRP筋体外预应力混凝土梁的抗弯强度。The flexural strength of the externally prestressed concrete beam with internal FRP reinforcement is determined according to the ultimate stress of the internal non-prestressed FRP reinforcement and the external prestressed reinforcement. 2.根据权利要求1所述的内配FRP筋体外预应力混凝土梁抗弯强度确定方法，其特征在于，所述体外预应力混凝土梁的特征参数包括：结构信息、截面信息、荷载信息、体外预应力筋材料信息、混凝土材料信息；2. The method for determining the flexural strength of externally prestressed concrete beams with internal FRP reinforcement according to claim 1, wherein the characteristic parameters of the externally prestressed concrete beams include: structural information, section information, load information, external prestressed Rebar material information, concrete material information; 所述非预应力FRP筋的特征参数包括：非预应力FRP筋材料信息。The characteristic parameters of the non-prestressed FRP rib include: material information of the non-prestressed FRP rib. 3.根据权利要求1所述的内配FRP筋体外预应力混凝土梁抗弯强度确定方法，其特征在于，根据所述体外预应力混凝土梁和非预应力FRP筋的特征参数，确定所述内配FRP筋体外预应力混凝土梁被破坏时的中性轴高度，包括：3. The method for determining the flexural strength of externally prestressed concrete beams with internal FRP reinforcement according to claim 1, characterized in that, according to the characteristic parameters of the external prestressed concrete beams and non-prestressed FRP reinforcement, it is determined that the external FRP reinforcement is externally equipped The neutral axis height of the prestressed concrete beam at failure, including: 基于有限元方法创建应力分析模型；Create a stress analysis model based on the finite element method; 利用所述应力分析模型对所述体外预应力混凝土梁进行数值试验，得到体外预应力筋的极限应力增量公式；Use the stress analysis model to carry out a numerical test on the externally prestressed concrete beam to obtain the ultimate stress increment formula of the externally prestressed tendon; 根据所述体外预应力筋的极限应力增量公式、体外预应力筋极限应力计算方程、体外预应力混凝土梁综合配筋指标计算方程和截面平衡条件，确定所述内配FRP筋体外预应力混凝土梁被破坏时的中性轴高度计算式；According to the ultimate stress increment formula of the external prestressed tendons, the calculation equation of the ultimate stress of external prestressed tendons, the calculation equation of the comprehensive reinforcement index of external prestressed concrete beams, and the section balance condition, determine the external prestressed concrete with internal FRP tendons The calculation formula of the height of the neutral axis when the beam is damaged; 根据所述中性轴高度计算式、所述体外预应力混凝土梁和非预应力FRP筋的特征参数，确定所述内配FRP筋体外预应力混凝土梁被破坏时的中性轴高度。According to the calculation formula of the neutral axis height, the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP reinforcement, the neutral axis height of the external prestressed concrete beam with internal FRP reinforcement is determined when it is damaged. 4.根据权利要求3所述的内配FRP筋体外预应力混凝土梁抗弯强度确定方法，其特征在于，利用所述应力分析模型对所述体外预应力混凝土梁进行数值试验，得到体外预应力筋的极限应力增量公式，包括：4. The method for determining the flexural strength of externally prestressed concrete beams with internal FRP reinforcement according to claim 3, characterized in that, using the stress analysis model to carry out a numerical test on the externally prestressed concrete beams to obtain the Ultimate stress increment formula, including: 将所述体外预应力混凝土梁划分为多个受力单元；dividing the external prestressed concrete beam into a plurality of stress units; 根据所述受力单元在三分点荷载和跨中单点荷载的作用，得到所述体外预应力筋极限应力增量随所述体外预应力混凝土梁综合配筋指标的变化曲线；According to the action of the load-bearing unit at the third point load and the single-point load in the mid-span, the change curve of the ultimate stress increment of the external prestressed reinforcement with the comprehensive reinforcement index of the external prestressed concrete beam is obtained; 对所述变化曲线进行线性拟合，得到体外预应力筋的极限应力增量公式。Linear fitting is performed on the change curve to obtain the ultimate stress increment formula of the external prestressed tendons. 5.根据权利要求1所述的内配FRP筋体外预应力混凝土梁抗弯强度确定方法，其特征在于，根据所述中性轴高度确定所述内配FRP筋体外预应力混凝土梁的体内非预应力FRP筋和体外预应力筋的极限应力，包括：5. The method for determining the flexural strength of an externally prestressed concrete beam with internal FRP reinforcement according to claim 1, wherein the non-prestressed body of the externally prestressed concrete beam with internal FRP reinforcement is determined according to the height of the neutral axis. Ultimate stress of FRP tendons and external prestressed tendons, including: 根据所述中性轴高度确定所述体内非预应力FRP筋的受拉极限应力；Determine the ultimate tensile stress of the non-prestressed FRP bars in the body according to the height of the neutral axis; 根据所述受拉极限应力，确定所述内配FRP筋体外预应力混凝土梁的综合配筋指标；According to the ultimate tensile stress, determine the comprehensive reinforcement index of the externally prestressed concrete beam with internal FRP reinforcement; 根据所述综合配筋指标，确定所述体外预应力筋的极限应力增量；According to the comprehensive reinforcement index, determining the ultimate stress increment of the external prestressed reinforcement; 根据体外预应力筋的极限应力增量和所述内配FRP筋体外预应力混凝土梁的特征参数，确定所述体外预应力筋的极限应力。The ultimate stress of the external prestressed tendon is determined according to the ultimate stress increment of the external prestressed tendon and the characteristic parameters of the externally prestressed concrete beam with the internal FRP tendon. 6.根据权利要求5所述的内配FRP筋体外预应力混凝土梁抗弯强度确定方法，其特征在于，根据所述受拉极限应力，确定所述内配FRP筋体外预应力混凝土梁的综合配筋指标，包括：6. The method for determining the flexural strength of an externally prestressed concrete beam with internal FRP reinforcement according to claim 5, wherein, according to the ultimate tensile stress, the comprehensive reinforcement of the externally prestressed concrete beam with internal FRP reinforcement is determined. Metrics, including: 当所述非预应力FRP筋的受拉极限应力大于自身的断裂强度时，将所述非预应力FRP筋自身的断裂强度作为受拉极限应力；When the ultimate tensile stress of the non-prestressed FRP bar is greater than its own fracture strength, the fracture strength of the non-prestressed FRP bar itself is taken as the ultimate tensile stress; 根据所述非预应力FRP筋受拉极限应力，确定所述内配FRP筋体外预应力混凝土梁的综合配筋指标。According to the ultimate tensile stress of the non-prestressed FRP reinforcement, the comprehensive reinforcement index of the externally prestressed concrete beam with internal FRP reinforcement is determined. 7.根据权利要求1所述的内配FRP筋体外预应力混凝土梁抗弯强度确定方法，其特征在于，根据所述体内非预应力FRP筋和体外预应力筋的极限应力确定所述内配FRP筋体外预应力混凝土梁的抗弯强度，包括：7. The method for determining the flexural strength of externally prestressed concrete beams with internal FRP reinforcement according to claim 1, wherein the internal FRP reinforcement is determined according to the ultimate stress of the non-prestressed FRP reinforcement in the body and the external prestressed reinforcement Flexural strength of externally prestressed concrete beams, including: 根据所述中性轴高度确定所述体内非预应力FRP筋的受压极限应力；Determine the ultimate compressive stress of the non-prestressed FRP bars in the body according to the height of the neutral axis; 对内配FRP筋体外预应力混凝土梁取矩，得到内配FRP筋体外预应力混凝土梁的名义抗弯强度计算方程；Taking the moment of external prestressed concrete beam with internal FRP reinforcement, the calculation equation of nominal flexural strength of external prestressed concrete beam with internal FRP reinforcement is obtained; 根据所述体外预应力筋的极限应力、体内非预应力FRP筋受拉极限应力、受压极限应力以及体外预应力混凝土梁、非预应力FRP筋的特征参数，确定所述内配FRP筋体外预应力混凝土梁的抗弯强度。According to the ultimate stress of the external prestressed tendons, the ultimate tensile stress of the internal non-prestressed FRP tendons, the ultimate compression stress, and the characteristic parameters of external prestressed concrete beams and non-prestressed FRP tendons, determine the external Flexural strength of prestressed concrete beams. 8.根据权利要求1所述的内配FRP筋体外预应力混凝土梁抗弯强度确定装置，其特征在于，包括：8. The device for determining the flexural strength of an externally prestressed concrete beam with internal FRP reinforcement according to claim 1, characterized in that, comprising: 参数获取模块，用于获取体外预应力混凝土梁和非预应力FRP筋的特征参数；The parameter acquisition module is used to acquire the characteristic parameters of external prestressed concrete beams and non-prestressed FRP bars; 中性轴高度计算模块，用于根据所述体外预应力混凝土梁和非预应力FRP筋的特征参数，确定所述体外预应力混凝土梁内配置所述非预应力FRP筋，所构成的内配FRP筋体外预应力混凝土梁被破坏时的中性轴高度；The neutral axis height calculation module is used to determine, according to the characteristic parameters of the external prestressed concrete beam and the non-prestressed FRP reinforcement, to configure the non-prestressed FRP reinforcement in the external prestressed concrete beam, and the formed internal FRP reinforcement The height of the neutral axis when the external prestressed concrete beam is damaged; 极限应力计算模块，用于根据所述中性轴高度确定所述内配FRP筋体外预应力混凝土梁的体内非预应力FRP筋和体外预应力筋的极限应力；The ultimate stress calculation module is used to determine the ultimate stress of the non-prestressed FRP reinforcement in the body and the external prestressed reinforcement of the externally prestressed concrete beam with the internal FRP reinforcement according to the height of the neutral axis; 抗弯强度确定模块，用于根据所述体内非预应力FRP筋和体外预应力筋的极限应力确定所述内配FRP筋体外预应力混凝土梁的抗弯强度。The flexural strength determination module is configured to determine the flexural strength of the externally prestressed concrete beam with internal FRP reinforcement according to the ultimate stress of the internal non-prestressed FRP reinforcement and the external prestressed reinforcement. 9.一种电子设备，其特征在于，包括处理器以及存储器，所述存储器上存储有计算机程序，所述计算机程序被所述处理器执行时，实现如权利要求1-7任一所述的内配FRP筋体外预应力混凝土梁抗弯强度确定方法。9. An electronic device, comprising a processor and a memory, wherein a computer program is stored on the memory, and when the computer program is executed by the processor, the computer program according to any one of claims 1-7 is implemented. Method for determining the flexural strength of externally prestressed concrete beams with internal FRP reinforcement. 10.一种计算机可读存储介质，其特征在于，其上存储有计算机程序，所述计算机该程序被处理器执行时，实现如权利要求1-7任一所述的内配FRP筋体外预应力混凝土梁抗弯强度确定方法。10. A computer-readable storage medium, characterized in that, a computer program is stored thereon, and when the computer program is executed by the processor, it realizes the internal configuration of the FRP muscle and the external pre-conditioning as described in any one of claims 1-7. Method for determining the flexural strength of stressed concrete beams.
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)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210631329.2A CN114878354B (en) 2022-06-06 2022-06-06 A method for determining the flexural strength of externally prestressed concrete beams with internal FRP bars

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210631329.2A CN114878354B (en) 2022-06-06 2022-06-06 A method for determining the flexural strength of externally prestressed concrete beams with internal FRP bars

Publications (2)

Publication Number Publication Date
CN114878354A true CN114878354A (en) 2022-08-09
CN114878354B CN114878354B (en) 2025-06-17

Family

ID=82680158

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210631329.2A Active CN114878354B (en) 2022-06-06 2022-06-06 A method for determining the flexural strength of externally prestressed concrete beams with internal FRP bars

Country Status (1)

Country Link
CN (1) CN114878354B (en)

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN206487068U (en) * 2017-02-16 2017-09-12 沈阳建筑大学 Assembled FRP strengthens steel core concrete column
CN107742019A (en) * 2017-10-09 2018-02-27 重庆大学 A kind of simplified calculation method of FRP tendons beams of concrete mechanical property

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN206487068U (en) * 2017-02-16 2017-09-12 沈阳建筑大学 Assembled FRP strengthens steel core concrete column
CN107742019A (en) * 2017-10-09 2018-02-27 重庆大学 A kind of simplified calculation method of FRP tendons beams of concrete mechanical property

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
吴岩;刘海霞;李玉顺;杨光;盛可鉴;: "FRP筋无粘结预应力混凝土结构极限强度分析", 黑龙江工程学院学报(自然科学版), no. 03 *
吴岩;刘海霞;李玉顺;杨光;盛可鉴;: "FRP筋无粘结预应力混凝土结构极限强度分析", 黑龙江工程学院学报(自然科学版), vol. 25, no. 03, 30 September 2011 (2011-09-30), pages 22 - 37 *
郑振鹏;: "预应力纤维增强塑料筋混凝土桥梁抗弯承载力计算方法研究", 中外建筑, no. 04, 1 April 2010 (2010-04-01), pages 132 - 133 *

Also Published As

Publication number Publication date
CN114878354B (en) 2025-06-17

Similar Documents

Publication Publication Date Title
Piscesa et al. Three-dimensional finite element analysis of circular reinforced concrete column confined with FRP using plasticity model
CN111680435A (en) Fatigue life prediction method and prediction device for notched parts
Imjai et al. A practical method for determining shear crack induced deformation in FRP RC beams
Filatov et al. Research of the stress condition of the normal section of reinforced concrete elements using nonlinear deformation model
CN114861398A (en) Method for predicting macroscopic mechanical property of fiber reinforced composite material
CN109117573A (en) A kind of nonlinear numerical simulation method of consideration composite material parameter three dimensional anisotropic
CN118673751A (en) Method for analyzing external buckling and buckling of cylindrical shell of variable-rigidity composite material based on isogeometry
Wang et al. Effective flange width of steel–concrete composite beam with partial openings in concrete slab
CN114878354A (en) Method for determining bending strength of external prestressed concrete beam with internal FRP (fiber reinforced Plastic) ribs
Zhou et al. Evaluation of the shear behavior of RC beams strengthened with prestressing BFRP grids
Han et al. Residual strain analysis of non-prestressed reinforcement in PPC beams under fatigue loading
Lou et al. Numerical analysis of second-order effects of externally prestressed concrete beams
Nguyen et al. Analysis of composite beams in the hogging moment regions using a mixed finite element formulation
Wu et al. Flexural behavior of over-reinforced beam with ECC layer: Experimental and numerical simulation study
Zona et al. Probabilistic analysis for design assessment of continuous steel–concrete composite girders
CN120951542A (en) A method and system for predicting the mechanical properties of UHPC-NC interfaces considering size effects
Gribniak et al. Improving efficiency of inverse constitutive analysis of reinforced concrete flexural members
CN116384076A (en) A Modeling Method for Cross-Scale Equivalent Elastic Mechanical Properties of Fiber Reinforced Composite Materials
Aref et al. Analysis of hybrid FRP-concrete multi-cell bridge superstructure
Miàs et al. A simplified method to obtain time-dependent curvatures and deflections of concrete members reinforced with FRP bars
CN114756943B (en) A method, device, electronic device and medium for determining time-dependent displacement of a composite beam
CN120745243B (en) A Method for Long-Term Loss Analysis and Service Life Prediction of Prestress in Nuclear Power Plant Containment Structures
Alkhairo et al. The effect of cyclic loading on the nonlinear response of structural concrete members with arbitrary cross-sectional shapes
CN119849135B (en) Whole-process analysis method, terminal and medium for corrugated steel web curve box Liang Wanniu
Adam et al. Multi-scale modeling of crash & failure of reinforced plastics parts with digimat to ls-dyna interface

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant