A prestressed CFRP reinforced RC simply supported beam bending design method

Abstract

This invention relates to the field of bridge reinforcement design technology, and in particular to a method for flexural design of prestressed CFRP-reinforced reinforced concrete (RC) simply supported beams. The method includes the following steps: determining whether the bridge can achieve improved flexural bearing capacity through prestressed CFRP reinforcement of the RC simply supported beams; if the conditions are met, then performing a load-bearing capacity calculation for the prestressed CFRP-reinforced RC simply supported beams, including: firstly, obtaining the initial tension strain limit range of the prestressed CFRP according to the principle of adequate reinforcement failure, and then calculating the load-bearing capacity requirement M of the reinforced RC simply supported beams. s The control tension strain and the number of CFRP reinforcement layers for prestressed CFRP-strengthened simply supported RC beams were determined. Finally, based on the initial tension strain limit range of prestressed CFRP, the initial control tension strain and the design reinforcement amount of CFRP were obtained. A method for determining the initial control tension stress of prestressed CFRP was proposed, and the relationship between the number of CFRP layers and the initial tension stress was established. Based on this, a bending design method for prestressed CFRP-strengthened RC beams was proposed.

Description

Technical Field

[0001] This invention relates to the field of bridge reinforcement design technology, and in particular to a prestressed CFRP reinforced RC simply supported beam bending design method. Background Technology

[0002] Non-prestressed carbon fiber reinforced composite material (CFRP) reinforcement technology has been widely used in the reinforcement of reinforced concrete bridges. However, engineering practice shows that this reinforcement technology cannot fully utilize the high strength performance of CFRP materials, cannot effectively inhibit the cracking and propagation of bridge cracks, and brittle glass failure is prone to occur at the CFRP-concrete interface.

[0003] Prestressed CFRP reinforcement technology can overcome the above-mentioned shortcomings. At present, there are various methods for determining the initial tension prestress of prestressed CFRP reinforcement technology. However, due to the lack of theoretical basis, it is still impossible to determine the initial control tension stress of prestressed CFRP, and to clarify the relationship between the initial control tension stress of prestressed CFRP and the amount of CFRP used. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method for designing the bending resistance of prestressed CFRP-strengthened simply supported reinforced concrete (RC) beams. This invention proposes a method for determining the initial control tension stress of prestressed CFRP, establishes the relationship between the number of CFRP layers and the initial tension stress, and, based on this, proposes a method for designing the bending resistance of prestressed CFRP-strengthened RC beams. To achieve the above objective, this invention is implemented through the following technical solution:

[0005] This invention provides a method for designing the bending resistance of prestressed CFRP-strengthened simply supported RC beams, comprising the following steps:

[0006] Determine whether a bridge can achieve the goal of improving its flexural bearing capacity by reinforcing a simply supported RC beam with prestressed CFRP.

[0007] If the conditions are met, the bearing capacity calculation of the prestressed CFRP-reinforced simply supported RC beam will be performed, including:

[0008] First, the initial tension strain limit range of prestressed CFRP is obtained according to the principle of appropriate reinforcement failure. Then, the bearing capacity requirement M of the simply supported RC beam after reinforcement is determined. s The control tension strain and the number of CFRP reinforcement layers for the prestressed CFRP-reinforced simply supported beam Rc were determined. Finally, based on the initial tension strain limit range of the prestressed CFRP, the initial control tension strain of the CFRP and the design reinforcement amount of the CFRP were obtained.

[0009] As a further implementation method, the bearing capacity M of the beam before reinforcement is calculated based on the on-site service conditions of the bridge. y and its maximum possible ultimate bearing capacity M after reinforcement kmaxBased on the loads acting on the bridge, calculations are performed on the bridge structure to determine the bearing capacity requirement M of a single beam. s To determine whether a bridge can be reinforced with prestressed CFRP to achieve its load-bearing capacity requirements using simply supported RC beams.

[0010] As a further implementation, if M y <M s <M kmax The load-bearing capacity requirement can be met by reinforcing the simply supported RC beam with prestressed CFRP.

[0011] As a further implementation, if M s <M y If M, then there is no need to reinforce the bridge to increase its load-bearing capacity to meet the bridge's load-bearing requirements; s ≥M kmax Therefore, simply reinforcing a RC simply supported beam with prestressed CFRP will not meet the bridge's load-bearing capacity requirements.

[0012] As a further implementation method, the prestressed CFRPRC simply supported beam must undergo adequate reinforcement failure during the process of determining the initial tension strain limit range of prestressed CFRP.

[0013] As a further implementation, the initial tension strain of prestressed CFRP should meet the tensile strength index of CFRP material.

[0014] As a further implementation, if the cutting width of the CFRP used for reinforcement is equal, the initial tensile strain limit range for different numbers of CFRP layers can be determined.

[0015] As a further implementation method, based on the load-bearing capacity requirements of the beam after reinforcement, the control tension strain of the prestressed CFRP reinforced RC simply supported beam is determined by preliminary calculation of the number of CFRP reinforcement layers.

[0016] As a further implementation method, a set of equations is established based on the force balance equation and the bending moment balance equation of the reinforced beam, and the initially proposed number of CFRP reinforcement layers is substituted into the set of equations for trial calculation.

[0017] As a further implementation method, based on the initial control tension strain of CFRP and the design reinforcement amount of CFRP, the prestressed CFRP-reinforced RC simply supported beam is checked to see if it meets the bearing capacity requirements of the bridge.

[0018] The beneficial effects of the present invention are as follows:

[0019] (1) This invention proposes a method for determining the initial control tension stress of prestressed CFRP for reinforced RC simply supported beams, and establishes the relationship between the number of CFRP layers and the initial tension stress. It can be used to simply and quickly determine the range of initial tension stress under reinforcement with different numbers of CFRP layers.

[0020] (2) Based on the theory of failure of reinforced beams and the bearing capacity requirements of reinforced beams, this invention proposes a design calculation method for prestressed CFRP bending reinforcement based on the number of CFRP layers and the initial tensile stress, which enriches the practice of bridge reinforcement design and improves the theoretical guidance for the design and construction of prestressed carbon fiber reinforced RC simply supported beams. Attached Figure Description

[0021] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0022] Figure 1 This is a flowchart of the bending design method for prestressed CFRP-reinforced simply supported RC beams in an embodiment of the present invention.

[0023] Figure 2 This is a distribution diagram of the failure modes of a prestressed CFRP-reinforced RC simply supported beam in an embodiment of the present invention.

[0024] Figure 3 This is a simplified diagram of the bending calculation of the normal section of the prestressed CFRP reinforced RC simply supported beam in an embodiment of the present invention.

[0025] Figure 4 This is a simplified diagram for calculating the bearing capacity of the normal section of a prestressed CFRP-reinforced simply supported RC beam in an embodiment of the present invention.

[0026] The diagram exaggerates the spacing or dimensions between parts to show their positions; the diagram is for illustrative purposes only. Detailed Implementation

[0027] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0028] Example

[0029] In a typical embodiment of the present invention, reference is made to Figure 1 As shown, a method for designing the bending resistance of a prestressed CFRP-reinforced simply supported RC beam includes:

[0030] I. Through analysis of research data, determine whether the bridge can achieve the goal of improving its bending bearing capacity by reinforcing the RC simply supported beam with prestressed CFRP.

[0031] Step 1: Survey and data analysis of prestressed CFRP bridges to be reinforced

[0032] By investigating the design data and the service status of bridges on site, the cross-sectional dimensions, concrete strength, reinforcement, and other information of the RC simply supported beam were clarified.

[0033] Step 2: Calculation of the bearing capacity of the simply supported RC beam before and after prestressed CFRP reinforcement

[0034] Calculation to determine the bearing capacity M of the simply supported RC beam before prestressed CFRP reinforcement. y and its maximum possible ultimate bearing capacity M after reinforcement kmax .

[0035] Bearing capacity M of simply supported RC beam before reinforcement y The calculation formulas are (1) and (2):

[0036]

[0037]

[0038] In the formula: α1 is a coefficient taken according to the "Code for Design of Concrete Structures", f c Here, b is the design value of the axial compressive strength of concrete, x is the width of the simply supported beam, h0 is the height of the compression zone of the section, and A is the effective height of the simply supported beam. s f is the cross-sectional area of ​​the longitudinal ordinary reinforcement in the tension zone. y This is the design value for the tensile strength of ordinary steel bars.

[0039] The maximum possible ultimate bearing capacity M of a simply supported RC beam after reinforcement kmax The calculation formula is (3):

[0040]

[0041] In the formula: β1 is a coefficient taken according to the "Code for Design of Concrete Structures", ε cu ε is the ultimate compressive strain of concrete in the normal cross section. y This represents the yield strain of the steel reinforcement.

[0042] Step 3: Determine the load-bearing capacity requirements after prestressed CFRP-reinforced simply supported RC beams

[0043] Based on the loads acting on the bridge, calculations are performed on the bridge structure to determine the bearing capacity requirement M of a single beam. s .

[0044] Step 4: Determine whether the bridge can be reinforced with prestressed CFRP to achieve its load-bearing capacity requirements using simply supported RC beams.

[0045] If M s <M y If M, then there is no need to reinforce the bridge to increase its load-bearing capacity to meet the bridge's load-bearing requirements; y <M s <M kmax Then, the bearing capacity requirement of the simply supported Rc beam can be met by strengthening it with prestressed CFRP; if M s ≥M kmax If the load-bearing capacity of a bridge cannot be met by simply reinforcing a prestressed CFRP-supported RC beam, other bridge reinforcement methods should be considered.

[0046] II. Bending Design Calculation of Prestressed CFRP-Reinforced Simply Supported RC Beam

[0047] Step 1: Determine the initial tensile strain limit range of prestressed CFRP

[0048] First, according to the requirement that prestressed CFRPRC simply supported beams must undergo adequate reinforcement failure, that is, its failure mode should be between boundary failure I (simultaneous occurrence of ultimate compressive strain in the concrete at the edge of the compression zone and yielding of the original tensile reinforcement) and boundary failure II (simultaneous occurrence of ultimate compressive strain in the concrete at the edge of the compression zone and ultimate tensile strain in the CFRP). Figure 2 As shown, and the force balance equations of the reinforced simply supported RC beam, as follows: Figure 3 As shown, the initial tension control strain of the prestressed CFRPRC simply supported beam satisfies formula (4).

[0049]

[0050] In the formula: h is the height of the simply supported beam, ε su The ultimate tensile strain of the reinforcing steel is taken according to the value specified in the "Code for Design of Concrete Structures", E cf Let n be the elastic modulus of the carbon fiber cloth, n be the number of carbon fiber cloth reinforcement layers, and b be the elastic modulus of the carbon fiber cloth. cf The width of the carbon fiber cloth is determined by the applicable width of the carbon fiber cloth tensioning equipment used, h. cf ε represents the thickness of the carbon fiber cloth. cf0 The initial tensile strain of the carbon fiber cloth is given.

[0051] Secondly, according to the principle that the initial tension strain of prestressed CFRP should meet the tensile strength index of CFRP material, that is, the initial tension strain of CFRP should be greater than 0 and less than the ultimate strain of CFRP, the initial tension control strain of prestressed CFRPRC simply supported beam should also meet the formula (5).

[0052]

[0053] Where: ε cu Let f be the ultimate compressive strain of the concrete cross section, taken according to the "Code for Design of Concrete Structures". α1 and β1 are coefficients taken according to the "Code for Design of Concrete Structures". c Here, b is the design value of the axial compressive strength of the concrete, h is the width of the simply supported beam, and f is the height of the simply supported beam. y A is the design value of the tensile strength of ordinary steel bars. s E represents the cross-sectional area of ​​the longitudinal ordinary reinforcement in the tension zone. cf ε is the elastic modulus of carbon fiber cloth. cf0 ε represents the initial tensile strain of the carbon fiber cloth. cfu The value represents the ultimate tensile strain of the carbon fiber cloth.

[0054] Finally, the initial tensile strain limit range of the prestressed CFRP is determined according to formulas (4) and (5). If the cut width of the CFRP used for reinforcement is equal, the initial tensile strain limit range for different numbers of CFRP layers can be determined according to formulas (4) and (5).

[0055] Step 2: Based on the load-bearing capacity requirement M of the simply supported RC beam after reinforcement. s Determine the controlling tensile strain (stress) and the number of CFRP reinforcement layers for prestressed CFRP-reinforced simply supported RC beams.

[0056] Based on the force balance equation and the bending moment balance equation of the reinforced RC simply supported beam, as follows: Figure 4 As shown, the cross-sectional strain relationship is established, and equation set (6) is set:

[0057]

[0058] Where: ε cf1 The strain of the carbon fiber cloth when the reinforced beam fails.

[0059] Based on the load-bearing capacity requirements of the beam after reinforcement, i.e. the load-bearing capacity of the prestressed CFRP reinforced RC simply supported beam, the number of CFRP reinforcement layers is initially estimated and substituted into the equation set (6) to determine the control tension strain (stress) of the prestressed CFRP reinforced RC simply supported beam.

[0060] Step 3: Determine the initial control tensile strain of CFRP and the amount of CFRP reinforcement required for design based on the initial tensile strain limit range of prestressed CFRP.

[0061] Based on the initial tensile strain limit ranges for different CFRP layer numbers calculated in step 1, the control tensile strain (stress) of the prestressed CFRP reinforced RC simply supported beam determined in step 2 is verified, and the initial control tensile strain of CFRP and the design reinforcement amount of CFRP are determined.

[0062] This embodiment proposes a method for determining the initial control tensile stress of prestressed CFRP, and establishes the relationship between the number of CFRP layers and the initial tensile stress. It can be used to simply and quickly determine the range of initial tensile stress under reinforcement with different numbers of CFRP layers.

[0063] Step 4: Based on the initial control tension strain of CFRP and the design reinforcement amount of CFRP, verify whether the prestressed CFRP reinforced RC simply supported beam meets the bearing capacity requirements of the bridge.

[0064] Based on the theory of failure of reinforced beams with appropriate reinforcement and the bearing capacity requirements of reinforced beams, this embodiment proposes a design calculation method for prestressed CFRP flexural reinforcement based on the number of CFRP layers and the initial tensile stress. This enriches the practice of bridge reinforcement design and provides theoretical guidance for the design and construction of prestressed carbon fiber reinforced RC simply supported beams.

[0065] Test case

[0066] The actual dimensions of the simply supported RC beam are 150mm × 250mm × 2000mm, with a calculated span of 1800mm. The concrete is C30. The main reinforcement and stirrups are HRB400, and the stirrups are HPB300. The bottom tension reinforcement is 2C12, the stirrups are 2C10, and the stirrups are A8@100.

[0067] The concrete cover thickness at the bottom of the simply supported beam is 40mm, and the clear spacing between the main reinforcement bars is 30mm.

[0068] I. Through analysis of research data, determine whether the bridge can achieve the goal of improving its bending bearing capacity by reinforcing the RC simply supported beam with prestressed CFRP.

[0069] Step 1: Survey and data analysis of prestressed CFRP bridges to be reinforced

[0070] Based on the design data and an investigation of the service conditions of existing bridges, the cross-sectional dimensions, concrete strength, and reinforcement details of the RC simply supported beam are as follows:

[0071]

[0072]

[0073] Step 2: Calculation of the bearing capacity of the simply supported RC beam before and after prestressed CFRP reinforcement

[0074] According to formulas (1) and (2), the bearing capacity M of the simply supported RC beam before reinforcement is... y for:

[0075]

[0076]

[0077] According to formula (3), the maximum possible ultimate bearing capacity M of the simply supported RC beam after reinforcement is... kmax for:

[0078]

[0079] Step 3: Determine the load-bearing capacity requirements of the prestressed CFRP-reinforced simply supported RC beam.

[0080] Due to the increased vehicle load, the bearing capacity of a single RC simply supported beam needs to be increased by 40%, that is:

[0081] M s =140%M y = 21.74 kN·m

[0082] Step 4: Determine whether the bridge can be reinforced with prestressed CFRP to achieve its load-bearing capacity requirements using simply supported RC beams.

[0083] Bearing capacity M of beam before reinforcement y and its maximum possible ultimate bearing capacity M after reinforcement kmax The load-bearing capacity requirement M of a single beam s The relationship is satisfied as follows:

[0084] M y <M s <M kmax

[0085] Therefore, the load-bearing capacity requirement of RC simply supported beams can be met by reinforcing them with prestressed CFRP.

[0086] II. Bending Design Calculation of Prestressed CFRP-Reinforced Simply Supported RC Beam

[0087] Step 1: Determine the initial tensile strain limit range of prestressed CFRP

[0088] Assuming the CFRP tensioning equipment used in this prestressed CFRP reinforcement has an applicable width of 50mm, then b cf The value is taken as 50mm; assuming the selected CFRP elongation is 1.6%, i.e., ε cfu =0.016.

[0089] According to formulas (4) and (5), the initial tension strain limit range of prestressed CFRP is determined as follows:

[0090] Number of carbon fiber fabric layers n Minimum limit value of initial tensile strain Initial tensile strain maximum limit value 1 0 0.0068 2 0 0.0096 3 0 0.0113 4 0 0.0125 5 0 0.0122 6 0 0.0097 7 0 0.0080 8 0 0.0066 9 0 0.0056 10 0 0.0047 11 0 0.0041 12 0 0.0035

[0091] Step 2: Based on the load-bearing capacity requirement M of the simply supported RC beam after reinforcement. s Determine the controlling tensile strain (stress) and the number of CFRP reinforcement layers for prestressed CFRP-reinforced simply supported RC beams.

[0092] ① The load-bearing capacity requirement M after reinforcing the simply supported RC beam s And the initial number of CFRP layers is n=1. Substituting this into equation (6), the initial tensile strain of the carbon fiber cloth is obtained as:

[0093] ε cf01 =0.0057 ε cf02 =0.4407

[0094] ②The load-bearing capacity requirement M after strengthening the simply supported RC beam s And the initial number of CFRP layers is n=2. Substituting this into equation system (6), the initial tensile strain of the carbon fiber cloth is obtained as:

[0095] ε cf01 =-0.0019 ε cf02 =0.2212

[0096] Step 3: Determine the initial control tensile strain of CFRP and the amount of CFRP reinforcement required for design based on the initial tensile strain limit range of prestressed CFRP.

[0097] The trial calculation results were verified based on the initial tensile strain limit ranges for different numbers of CFRP layers obtained in step 1.

[0098] ①The CFRP reinforcement layer is 1 layer, and the initial tensile strain is:

[0099] ε cf01 =0.0057=35.62%ε cfu ε cf02 =0.4407 (discarded)

[0100] ②The CFRP reinforcement consists of two layers, with an initial tensile strain of:

[0101] ε cf01 = -0.0019 (discarded) ε cf02 =0.2212 (discarded)

[0102] When the planned CFRP reinforcement amount is 2 layers, substituting into equation (6), the results obtained no longer meet the initial tension strain limit range of prestressed CFRP. Furthermore, in actual reinforcement, a smaller number of carbon fiber cloth layers can be selected under certain conditions to reduce the amount of construction while meeting the reinforcement requirements. Therefore, the selection of 1 layer reinforcement is stopped.

[0103] Therefore, a single beam needs to meet the load-bearing capacity requirement M s The initial control tensile strain of the CFRP is determined to be ε. cf0 =40%ε cfu =0.0064 < 0.0068, the CFRP design reinforcement amount is 1 layer.

[0104] Step 4: Based on the initial control tension strain of CFRP and the design reinforcement amount of CFRP, verify whether the prestressed CFRP reinforced RC simply supported beam meets the bearing capacity requirements of the bridge.

[0105] The initial control tensile strain of the CFRP is ε cf0 =40%ε cfu =0.0064, CFRP design reinforcement amount n=1, substituting into equation system (6), we get:

[0106] M u =22.28kN·m>M s = 21.74 kN·m

[0107] Therefore, the initial control tensile strain of the CFRP in the prestressed CFRP-reinforced simply supported RC beam is ε. cf0 =40%ε cfu =0.0064, the number of CFRP reinforcement layers n=1, which can meet the bearing capacity requirements after reinforcement.

[0108] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for designing the bending resistance of a prestressed CFRP-reinforced simply supported RC beam, characterized in that, Includes the following steps: Determine whether a bridge can achieve the goal of improving its flexural bearing capacity by reinforcing a simply supported RC beam with prestressed CFRP. If the conditions are met, the bearing capacity calculation of the prestressed CFRP-reinforced simply supported RC beam will be performed, including: First, the initial tension strain limit range of prestressed CFRP is obtained according to the principle of appropriate reinforcement failure. Then, the bearing capacity requirement of simply supported RC beams is determined. The control tension strain and the number of CFRP reinforcement layers for prestressed CFRP-reinforced simply supported RC beams are determined. Finally, based on the initial tension strain limit range of prestressed CFRP, the initial control tension strain of CFRP and the design reinforcement amount of CFRP are obtained. The aforementioned method for designing the bending resistance of a prestressed CFRP-reinforced simply supported RC beam involves determining the control tension strain of the prestressed CFRP-reinforced simply supported RC beam by initially estimating the number of CFRP reinforcement layers and conducting trial calculations based on the beam's load-bearing capacity requirements after reinforcement.

2. The method for designing the bending resistance of a prestressed CFRP-reinforced simply supported RC beam according to claim 1, characterized in that, The bearing capacity of the beam before reinforcement was calculated based on the on-site service conditions of the bridge. and its maximum possible ultimate bearing capacity after reinforcement Based on the loads acting on the bridge, calculations are performed on the bridge structure to determine the load-bearing capacity requirements of individual beams. To determine whether a bridge can be reinforced with prestressed CFRP to achieve its load-bearing capacity requirements using simply supported RC beams.

3. The method for designing the bending resistance of a prestressed CFRP-reinforced simply supported RC beam according to claim 2, characterized in that, like The load-bearing capacity requirement can be met by reinforcing the simply supported RC beam with prestressed CFRP.

4. The method for designing the bending resistance of a prestressed CFRP-reinforced simply supported RC beam according to claim 3, characterized in that, like If so, then it is not necessary to reinforce the bridge to increase its load-bearing capacity to meet the bridge's load-bearing requirements; if Therefore, simply reinforcing a RC simply supported beam with prestressed CFRP will not meet the bridge's load-bearing capacity requirements.

5. The method for designing the bending resistance of a prestressed CFRP-reinforced simply supported RC beam according to claim 1, characterized in that, During the process of determining the initial tension strain limit range of prestressed CFRP, the prestressed CFRPRC simply supported beam must undergo adequate reinforcement failure.

6. The method for designing the bending resistance of a prestressed CFRP-reinforced simply supported RC beam according to claim 5, characterized in that, The initial tension strain of prestressed CFRP should meet the tensile strength requirements of CFRP material.

7. The method for designing the bending resistance of a prestressed CFRP-reinforced simply supported RC beam according to claim 6, characterized in that, If the cutting width of the CFRP used for reinforcement is equal, the initial tensile strain limit range for different numbers of CFRP layers can be determined.

8. The method for designing the bending resistance of a prestressed CFRP-reinforced simply supported RC beam according to claim 1, characterized in that, Based on the force balance equation and the bending moment balance equation of the reinforced beam, a set of equations is established, and the initially proposed number of CFRP reinforcement layers is substituted into the set of equations for trial calculation.

9. The method for designing the bending resistance of a prestressed CFRP-reinforced simply supported RC beam according to claim 1, characterized in that, Based on the initial control tension strain of CFRP and the design reinforcement amount of CFRP, verify whether the prestressed CFRP-reinforced RC simply supported beam meets the bearing capacity requirements of the bridge.

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