Combination beam flexural capacity calculation method based on plasticity theory and use method

Abstract

The invention discloses a method for calculating the flexural capacity of a composite beam based on a plastic theory, and relates to the field of bridge design. The method aims at solving the problems that complex deformation of a plastic hinge area is not fully considered in a traditional elastic theory in calculation of the flexural capacity of the steel-concrete composite beam, deformation of a reinforcing material and deformation of concrete are not coordinated, the superimposed effect of deformation of a positive bending moment area and a negative bending moment area of a continuous beam is lacked, and calculation of stress increment and secondary effect of an external prestress CFRP rib is insufficient. An iterative computation method is proposed. According to the method, a plastic hinge area deformation coordination mechanism and a continuous beam deformation superposition model are coupled, refined analysis parameters for the first and second types of section steel beams are introduced, a rapid convergence iterative algorithm is constructed, the calculation precision of the bending bearing capacity of the external prestress CFRP rib reinforced composite beam is remarkably improved, meanwhile, the calculation process is simplified, and the calculation efficiency is improved. And high-precision and high-efficiency calculation is realized on the premise of ensuring the engineering applicability.

Description

Technical Field

[0001] The present invention relates to the field of bridge design, and in particular to a calculation method and a use method of the bending bearing capacity of a composite beam based on plasticity theory. Background Art

[0002] In the existing technology, there are some limitations in the calculation methods of the flexural bearing capacity of steel-concrete composite beams. The traditional calculation method is mainly based on elastic theory, which does not fully consider the complex deformation of the plastic hinge area of ​​the composite beam under the limit state, as well as the deformation incompatibility between the reinforcement material (such as prestressed steel strands or prestressed carbon fiber tendons) and the concrete, which leads to a deviation between the calculation results and the actual bearing capacity. In addition, when calculating the positive and negative bending moment zones of continuous beams, the existing technology lacks consideration of the superposition of deformations, making it difficult for the calculation accuracy to meet engineering requirements. At the same time, for new reinforcement materials such as external prestressed carbon fiber composite (CFRP) tendons, the existing calculation method fails to fully calculate their stress increments and secondary effects under the limit state, further affecting the accuracy of the calculation results. Summary of the Invention

[0003] The main purpose of the present invention is to provide a calculation method for the bending bearing capacity of composite beams based on plasticity theory, which can effectively solve the problems in the background technology.

[0004] To achieve the above object, the technical solution adopted by the present invention is:

[0005] A method for calculating the bending bearing capacity of a composite beam based on plasticity theory comprises the following steps:

[0006] S1: Introducing the initial external prestressed tendon ultimate stress:

[0007] f ps =f pe

[0008] where f ps is the ultimate stress of the external reinforcement; f pe For permanent prestressing;

[0009] S2: Calculate the relative compression zone height c using the composite beam based on the plasticity theory model:

[0010]

[0011] A r Cross-sectional area of ​​the steel bar, A p Cross-sectional area of ​​prestressed CFRP tendons, A s Cross-sectional area of ​​the steel beam, A c Cross-sectional area of ​​concrete, f ysrepresents the stress of the lower flange of the steel beam on the calculation section under the elastic state, taking the design value of the tensile strength of the steel beam, f yr Design value of tensile strength of upper reinforcement in concrete slab, t w Thickness of steel beam web, t fb Thickness of steel beam in compression zone, A fb Cross-sectional area of ​​the steel beam in the compression zone, h d Height of the web of the steel beam;

[0012] S3: Reference [4] calculated the bearing capacity of the steel-concrete composite beam section under plastic state, and combined with this model to derive the ultimate bearing capacity Mu of the reinforced composite beam:

[0013] M u =A c f ys (ha rp -y cb )+(A S -A c )f ys (h d -a rp -y tt ) (Formula 14)

[0014] where a rp is the distance from the combined force point of the steel bar and CFRP bar to the neutral axis, cb Indicates the distance from the centroid of the steel beam in the compression zone to the bottom of the steel beam, y ct The distance from the centroid of the steel beam in the compression zone to the plastic neutral axis, y tb The distance from the centroid of the steel beam in the tension zone to the plastic neutral, y tt The distance from the centroid of the steel beam in the tension zone to the top surface of the steel beam can be calculated by this model to obtain the relative compression zone height c and the ultimate bearing capacity M of the reinforced composite beam. u ;

[0015] S4: According to the elastic theory method, the bending moment value obtained by the theoretical model is M y =min{M yr , M ys};

[0016] S5: Use the M obtained in steps S3 and S4 u and M y Substitute the following formula:

[0017]

[0018] L s is the distance from the support to the loading point;

[0019] S6: Substitute the obtained x into the following formula to obtain L p The range of the plastic hinge region is obtained byp :

[0020] L p =L s -x+L a (Formula 9)

[0021] S7: L obtained by S6 p Δf is obtained as follows ps :

[0022]

[0023] where ε su is the ultimate compressive strain of steel, according to European standard EN1993-1-1:2005 [1] A more conservative ultimate compressive strain value can be used to ensure the safety of the structure, so ε su -0.014; l p is the effective length of CFRP reinforcement; E p is the elastic modulus of the CFRP reinforcement; d p is the distance from the prestressed tendons to the bottom of the beam; Δf ps It is the stress increment caused by external load after the external prestressed tendons are tensioned;

[0024] S8: The existing expression for the ultimate stress of external prestressed tendons is as follows:

[0025] f ps =f pe +Δf ps (Formula 1)

[0026] The Δf obtained by S7 ps Combined with the above formula, we can obtain:

[0027]

[0028] S9: Repeat the calculation process of the prestress increment in the above calculation. If the error with the previous calculation is less than 5%, the calculation is considered correct. Otherwise, recalculate;

[0029] S10: This article refers to AASHTO specifications [3] The initial ultimate stress value calculated by the increment of 105 MPa for the external prestressed tendons of ordinary concrete beams is also applicable to the calculation theory of this paper. One iteration of the order can meet the accuracy requirements.

[0030] The calculation steps are for Class 1 and Class 2 sections.

[0031] Preferably, the above calculation steps are for Class 1 and Class 2 sections; we make basic assumptions for the steel beam: after the composite beam is bent, the section (excluding the CFRP bars) satisfies the flat section assumption; the tensile strength after concrete cracking is not considered; the influence of slip deformation in the negative bending moment zone is not considered; the width-to-thickness ratio of the steel beam plate meets the requirements of Class 1 and Class 2 sections; the deformation of the steel support at the CFRP bar connection is not considered; and the secondary effect of the CFRP bars is not considered.

[0032] Preferably, Δf in S1 ps The detailed calculation is as follows:

[0033] The beam is simplified into two rigid components connected by a plastic hinge. The plastic hinge rotation angle θ is calculated using formula (2):

[0034] θ=φ u ·L p (Formula 2)

[0035] L p is the range of the plastic hinge area; θ is the angle of rotation of the plastic hinge, φ u is the curvature of the plastic zone, and the curvature φ u The deformation relationship is expressed by the following formula:

[0036]

[0037] where ε su is the ultimate compressive strain of steel, and ε is taken according to the European standard EN1993-1-1:2005[1] su = -0.014, c is the height of the compression zone at the limit state; the CFRP tendon elongation δ and strain ε at the limit state can be obtained from the deformation relationship p They can be expressed by the following formulas:

[0038] δ=(d p -c)·θ (Formula 4)

[0039]

[0040] l p is the effective length of the CFRP tendon. Combining (Formula 2) to (Formula 5), ​​the stress increment Δf on the CFRP tendon can be obtained. ps Its form can be expressed as:

[0041]

[0042] Preferably, the effective length l of the external reinforcement in formula 5 is p It can be expressed by the following formula:

[0043]

[0044] where N s It represents the number of plastic hinges formed when the component fails, and L0 is the length between the external prestressed tendon anchors.

[0045] Preferably, M in S4 y The detailed calculation process is as follows:

[0046] According to the elasticity theory method, the following formula is obtained:

[0047] The bending moment M of the upper reinforcement yielding under tension yr :

[0048]

[0049] The bottom steel beam compressive yield moment M ys :

[0050]

[0051] e0 is the distance from the CFRP reinforcement to the elastic neutral axis, y t is the distance from the upper reinforcement to the neutral point in the concrete slab; c A is the distance from the bottom of the steel beam to the elastic neutral axis; rt Indicates the area of ​​the upper reinforcement in the concrete slab; A rs Indicates the area of ​​the lower reinforcement in the concrete slab; f yt 、f yb 、f ys They represent the stress of the upper reinforcement, lower reinforcement and lower flange of the steel beam in the elastic state; when the upper reinforcement yields, f yt Take the design value of the tensile strength of the steel bar; for the yield of the lower steel beam f ys Take the design value of the tensile strength of the steel beam, I eff Indicates that when calculating the deflection of reinforced concrete components (M>M cr ) is used when the effective moment of inertia of the section is used, M represents the bending moment shown in the calculated section combination of the steel-concrete composite beam, and M cr It represents the cracking moment of the steel-concrete composite beam in the calculated section, N p represents the prestressing tendon tension, α2 is the conversion factor of the CFRP tendon cross section;

[0052] Yield bending of steel-concrete composite beam (elastic ultimate bearing capacity) M y =min{M yr , M ys That is, please note that the prestress value N in the above formula p It is recommended to take the initial prestressing force without considering the increment on the prestressing tendons during the elastic stage.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] The present invention takes into account the deformation of the plastic hinge area and the superposition of the deformation in the positive and negative bending moment areas of the continuous beam, thereby solving the problem of insufficient calculation accuracy in the prior art.

[0055] The present invention proposes an iterative calculation method, which can quickly converge, simplify the calculation process and improve calculation efficiency.

[0056] The present invention is applicable to steel beams of cross-section types 1 and 2, and further improves the pertinence and accuracy of the calculation.

[0057] Through the above technical solution, this patent can significantly improve the calculation accuracy of the bending bearing capacity of steel-concrete composite beams after external prestressed CFRP reinforcement, while simplifying the calculation process, and has high engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Calculation flow chart of the present invention;

[0059] Figure 2 This is a diagram of the deformation model of the plastic hinge theory of the present invention;

[0060] Figure 3 This is a curvature and bending moment relationship diagram of the present invention;

[0061] Figure 4 This is a diagram of the elastic theory calculation model of the steel-concrete composite beam of the present invention;

[0062] Figure 5 This is a diagram of the plasticity theory calculation model of the steel-concrete composite beam of the present invention; DETAILED DESCRIPTION

[0063] In order to make the technical means, creative features, objectives and effects achieved by the present invention easier to understand, the present invention is further described below in conjunction with specific implementation methods.

[0064] In the description of the present invention, it should be noted that the terms "upper," "lower," "inner," "outer," "front end," "rear end," "both ends," "one end," "the other end," and the like, indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limiting the present invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0065] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed," "provided with," "connected," etc., should be understood in a broad sense. For example, "connected" may refer to a fixed connection, a detachable connection, or an integral connection; it may refer to a mechanical connection or an electrical connection; it may refer to a direct connection or an indirect connection through an intermediate medium; it may refer to internal communication between two components. Those skilled in the art will be able to understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0066] Example

[0067] See also Figure 1-5 , the present invention provides a technical solution:

[0068] The present invention discloses a calculation method and application method of the bending bearing capacity of a composite beam based on plasticity theory. The specific implementation process is as follows:

[0069] In existing research and specifications, the ultimate stress of external prestressed tendons is usually expressed as

[0070] f ps =f pe +Δf ps (Formula 1)

[0071] where f ps is the ultimate stress of the external reinforcement; f pe is the permanent prestress (tension prestress minus prestress loss); Δf ps It is the stress increment caused by external load after the external prestressed tendons are tensioned.

[0072] For the calculation of the increment of external prestressed tendons, Du et al. [2] For ordinary reinforced concrete beams with external prestressed unbonded reinforcement, a final failure model based on the plastic hinge deformation relationship was proposed. When the beam fails, it can be regarded as two rigid components connected by a plastic hinge, and the two components can rotate relative to each other around the plastic hinge. At this time, the deformation of the external reinforcement depends on the deformation caused by the rotation of the plastic hinge. When a steel-concrete composite beam fails in bending, a plastic hinge is formed in the mid-span compression zone, and the beam body can continue to rotate relative to each other around the mid-span plastic hinge. Therefore, referring to the theory of Du et al., the deformation model of the CFRP reinforcement composite beam at the time of failure of negative bending moment can be expressed as follows Figure 1 shown

[0073] Figure 1 Medium L p is the range of the plastic hinge area; d p is the distance from the prestressed tendons to the bottom of the beam; c is the height of the compression zone at the limit state; θ is the angle of rotation of the plastic hinge, which can be calculated from the curvature of the plastic zone φ u It can be expressed as:

[0074] θ=φ u ·L p (Formula 2)

[0075] The curvature φ u The deformation relationship is expressed by the following formula:

[0076]

[0077] where ε su is the ultimate compressive strain of steel, according to European standard EN1993-1-1:2005 [1] A more conservative ultimate compressive strain value can be used to ensure the safety of the structure, so ε su =-0.014. From the deformation relationship, we can get the CFRP reinforcement elongation δ and strain ε under the limit state. p They can be expressed by the following formulas respectively

[0078] δ=(d p -c)·θ (Formula 4)

[0079]

[0080] Where l p is the effective length of CFRP reinforcement, and the effective length of external reinforcement l p It can be expressed by the following formula:

[0081]

[0082] where N s It represents the number of plastic hinges formed when the component fails, and L0 is the length between the external prestressed tendon anchors.

[0083] The number of plastic hinges when a simply supported beam fails is one, and a continuous beam forms a plastic hinge at the maximum positive and negative bending moments. In a continuous beam, in addition to calculating the deformation of the external reinforcement at the negative bending moment position, the deformation of the positive bending moment at the mid-span must also be considered, and the calculated deformations are finally superimposed (the calculation method for positive bending moment is the same as that for negative bending moment. The value of the concrete compressive strain at the positive bending moment at the mid-span can be mainly based on relevant specifications and actual engineering experience, generally around -0.0033, so the concrete compressive strain can be calculated as -0.0033). By combining (Formula 1) to (Formula 4), the stress increment Δf on the CFRP reinforcement can be obtained ps Its form can be expressed as:

[0084]

[0085] Where E p is the elastic modulus of the CFRP reinforcement.

[0086] Therefore, the corresponding total stress fps It can be expressed as:

[0087]

[0088] For L p The calculation of the plastic region is relatively complex, and the calculation method is different for different loading methods. Previous researchers have given the theoretical relationship between the curvature and bending moment of the composite beam along the length of the beam, such as Figure 2 shown.

[0089] Figure 2 In, L s is the distance from the support to the loading point; L a is the distance between loading points; φ y is the curvature of the elastic zone; the length of the yellow shaded area is L p The length of the plastic region is the length of the composite beam within the limit state where the bending moment is greater than the yield moment M y In the section where the bending moment is greater than M y Less than the ultimate bending moment M u The distance of the segment.

[0090] Assume that the length of the elastic zone along the length of the beam is x, and the corresponding bending moment is M. y , and because the bending moment value corresponding to the loading point is M u Therefore, the plastic hinge region can be expressed as:

[0091] L p =L s -x+L a (Formula 9)

[0092]

[0093] For the yield moment M y The theoretical model can be obtained according to the elasticity theory method. Figure 3 As shown in the figure, e0 is the distance from the CFRP reinforcement to the elastic neutral axis, y t is the distance from the upper reinforcement to the neutral point in the concrete slab; c A is the distance from the bottom of the steel beam to the elastic neutral axis; rt Indicates the area of ​​the upper reinforcement in the concrete slab; A rs Indicates the area of ​​the lower reinforcement in the concrete slab; f yt 、f yb 、f ys They represent the stress of the upper reinforcement, lower reinforcement and lower flange of the steel beam in the elastic state. yt Take the design value of the tensile strength of the steel bar; for the yield of the lower steel beam f ys Take the design value of the tensile strength of the steel beam.

[0094] The bending moment M of the upper reinforcement yielding under tension yr :

[0095]

[0096] The bottom steel beam compressive yield moment M ys :

[0097]

[0098] Among them I eff Indicates that when calculating the deflection of reinforced concrete components (M>M cr ) is used when the effective moment of inertia of the section is used, M represents the bending moment shown in the calculated section combination of the steel-concrete composite beam, and M cr It represents the cracking moment of the steel-concrete composite beam in the calculated section, N p represents the prestressed tendon tension, and α2 is the conversion coefficient of the CFRP tendon cross section.

[0099] In summary, the ultimate elastic bearing capacity M of the steel-concrete composite beam is y =min{M yr , M ys}. Please note that the prestress value N in the above formula p It is recommended to take the initial prestressing force without considering the increment on the prestressing tendons in the elastic stage, and then calculate the elastic ultimate bearing capacity, which is more convenient and the calculation result is more conservative, which meets the actual engineering needs.

[0100] At this time, the prestress value N p The value of should be the prestress of CFRP reinforcement in the ultimate state, that is, f ps Multiply by A p To calculate, A p is the cross-sectional area of ​​the prestressed CFRP tendon.

[0101] Calculation of ultimate bending bearing capacity:

[0102] Based on classical plasticity theory, we can establish a model for the ultimate bending bearing capacity of CFRP-reinforced composite beams in the negative bending moment zone. This model can be used to evaluate the ultimate bearing capacity of composite beams reinforced with CFRP bars when subjected to bending moment.

[0103] Figure 4 The force mode diagram of the composite beam based on plasticity theory, in the figure a rp is the distance from the combined force point of the steel bar and CFRP bar to the neutral axis; cb Indicates the distance from the centroid of the steel beam in the compression zone to the bottom surface of the steel beam; y ct The distance from the centroid of the steel beam in the compression zone to the plastic neutral axis; y tb Indicates the distance from the centroid of the steel beam in the tension zone to the plastic neutral; ytt Represents the distance from the centroid of the steel beam in the tension zone to the top surface of the steel beam; the relative compression zone height c of the reinforced composite beam can be calculated through this model, as shown in (Formula 13).

[0104]

[0105] Reference [4] calculated the bearing capacity of the steel-concrete composite beam section under plastic state, and combined with the model to obtain the ultimate bearing capacity Mu of the reinforced composite beam, which is expressed as (Formula 14)

[0106] M u =A c f ys (ha rp -y cb )+(A s -A c )f ys (h d -a rp -ytt) (Formula 14)

[0107] in

[0108] A r ——Cross-sectional area of ​​steel bar

[0109] A p ——Cross-sectional area of ​​prestressed CFRP tendons

[0110] A s ——Cross-sectional area of ​​steel beam

[0111] A c - cross-sectional area of ​​concrete

[0112] f ys ——Indicates the stress on the lower flange of the steel beam on the calculation section under the elastic state, and takes the design value of the tensile strength of the steel beam.

[0113] f yr ——Design value of tensile strength of upper reinforcement in concrete slab

[0114] t w ——Thickness of steel beam web

[0115] t fb ——Thickness of steel beam in compression zone

[0116] A fb ——Cross-sectional area of ​​the steel beam in the compression zone

[0117] h d ——Height of the web of the steel beam

[0118] It should be pointed out that for the entire calculation process, an initial CFRP reinforcement limit stress value f is required at the beginning. ps , put it into the above formula to calculate the relative compression zone height c and plastic hinge area range L p After that, the new CFRP reinforcement limit stress is calculated by referring to the formula here. This process is recorded as completing one iteration calculation. ps The value of f is usually pe As the initial f for the first iteration ps By repeating the calculation process of the prestress increment, if the error with the previous calculation is less than 5%, the calculation is considered correct. The whole process is as follows Figure 1 (a). For the accuracy required by the project, a specific initial f ps This article refers to the AASHTO specification. [3] The initial ultimate stress value given by the incremental calculation of the external prestressed tendons of ordinary concrete beams is as shown in (Formula 14).

[0119] The calculation process is simplified as follows Figure 1 (b) is shown. The calculation theory in this paper is also applicable, and one order iteration can meet the accuracy requirements.

[0120] f ps =f pe +105Mpa (Formula 15).

[0121] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the bending bearing capacity of a composite beam based on plasticity theory, characterized in that: The following steps are involved: S1: Introducing the initial external prestressed tendon ultimate stress: f ps =f pe (Formula 16) where f ps is the stress of the external tendon; f pe For permanent prestressing; S2: Calculate the relative compression zone height c using the composite beam based on the plasticity theory model: A r Cross-sectional area of ​​the steel bar, A p Cross-sectional area of ​​prestressed CFRP tendons, A s Cross-sectional area of ​​the steel beam, A c Cross-sectional area of ​​concrete, f ys represents the stress of the lower flange of the steel beam on the calculation section under the elastic state, taking the design value of the tensile strength of the steel beam, f yr Design value of tensile strength of upper reinforcement in concrete slab, t w Thickness of steel beam web, t fb Thickness of steel beam in compression zone, A fb Cross-sectional area of ​​the steel beam in the compression zone, h d Height of the web of the steel beam; S3: Reference [4] calculated the bearing capacity of the steel-concrete composite beam section under plastic state, and combined with this model to derive the ultimate bearing capacity Mu of the reinforced composite beam: M u (A c f ys (and rp -y cb )+(A S -A c )f ys (h d -a rp -y tt ) (Picture 14) where a rp is the distance from the combined force point of the steel bar and CFRP bar to the neutral axis, cb Indicates the distance from the centroid of the steel beam in the compression zone to the bottom of the steel beam, y ct The distance from the centroid of the steel beam in the compression zone to the plastic neutral axis, y tb The distance from the centroid of the steel beam in the tension zone to the plastic neutral, y tt The distance from the centroid of the steel beam in the tension zone to the top surface of the steel beam can be calculated by this model to obtain the relative compression zone height c and the ultimate bearing capacity M of the reinforced composite beam. u ; S4: According to the elastic theory method, the bending moment value obtained by the theoretical model is M y =min{M yr , M ys }; S5: Use the M obtained in steps S3 and S4 u and M y Substitute the following formula: L s is the distance from the support to the loading point; S6: Substitute the obtained x into the following formula to obtain L p The range of the plastic hinge region is obtained by p : L p =L s -x+L a (Formula 9) S7: L obtained by S6 p Δf is obtained as follows ps : where ε su is the ultimate compressive strain of steel, according to European standard EN1993-1-1:2005 [1] A more conservative ultimate compressive strain value can be used to ensure the safety of the structure, so ε su -0.014; l p is the effective length of CFRP reinforcement; E p is the elastic modulus of the CFRP reinforcement; d p is the distance from the prestressed tendons to the bottom of the beam; Δf ps It is the stress increment caused by external load after the external prestressed tendons are tensioned; S8: The existing expression for the ultimate stress of external prestressed tendons is as follows: f ps =f pe +Δf ps (Formula 1) The Δf obtained by S7 ps Combined with the above formula, we can obtain: S9: Repeat the calculation process of the prestress increment in the above calculation. If the error with the previous calculation is less than 5%, the calculation is considered correct. Otherwise, recalculate; S10: This article refers to AASHTO specifications [3] The initial ultimate stress value calculated by the increment of 105 MPa for the external prestressed tendons of ordinary concrete beams is also applicable to the calculation theory of this paper. One iteration of the order can meet the accuracy requirements. The calculation steps are for Class 1 and Class 2 sections.

2. The method for calculating the bending bearing capacity of a composite beam based on plasticity theory according to claim 1, characterized in that: The above calculation steps are for Class 1 and Class 2 sections; we make basic assumptions for the steel beam: after the composite beam is bent, the section (excluding the CFRP bars) satisfies the flat section assumption; the tensile strength after concrete cracking is not considered; the influence of slip deformation in the negative bending moment zone is not considered; the width-to-thickness ratio of the steel beam plate meets the requirements of Class 1 and Class 2 sections; the deformation of the steel support at the CFRP bar connection is not considered; and the secondary effect of the CFRP bars is not considered.

3. The method for calculating the bending bearing capacity of a composite beam based on plasticity theory according to claim 1, characterized in that: Δf in S1 ps The detailed calculation is as follows: The beam is simplified into two rigid components connected by a plastic hinge. The plastic hinge rotation angle θ is calculated using formula (2): θ=φ u ·L p (Formula 2) L p is the range of the plastic hinge region; θ is the angle of plastic hinge rotation, φ u is the curvature of the plastic zone, and the curvature φ u The deformation relationship is expressed by the following formula: where ε su is the ultimate compressive strain of steel, and ε is taken according to the European standard EN1993-1-1:2005[1] su = -0.014, c is the height of the compression zone at the limit state; the CFRP tendon elongation δ and strain ε at the limit state can be obtained from the deformation relationship p They can be expressed by the following formulas: δ = (d p - c)·θ (Equation 4) l p is the effective length of the CFRP tendon. Combining (Formula 2) to (Formula 5), ​​the stress increment Δf on the CFRP tendon can be obtained. ps Its form can be expressed as:

4. The method for calculating the bending bearing capacity of a composite beam based on plasticity theory according to claim 2, wherein: The effective length l of the external reinforcement in formula 5 p It can be expressed by the following formula: where N s It represents the number of plastic hinges formed when the component fails, and L0 is the length between the external prestressed tendon anchors.

5. The method for calculating the bending bearing capacity of a composite beam based on plasticity theory according to claim 1, characterized in that: S4 mid-M y The detailed calculation process is as follows: According to the elasticity theory method, the following formula is obtained: The bending moment M of the upper reinforcement yielding under tension yr : The bottom steel beam compressive yield moment M ys : e0 is the distance from the CFRP reinforcement to the elastic neutral axis, y t is the distance from the upper reinforcement to the neutral point in the concrete slab; c A is the distance from the bottom of the steel beam to the elastic neutral axis; rt Indicates the area of ​​the upper reinforcement in the concrete slab; A rs Indicates the area of ​​the lower reinforcement in the concrete slab; f yt 、f yb 、f ys They represent the stress of the upper reinforcement, lower reinforcement and lower flange of the steel beam in the elastic state; when the upper reinforcement yields, f yt Take the design value of the tensile strength of the steel bar; for the yield of the lower steel beam f ys Take the design value of the tensile strength of the steel beam, I eff Indicates that when calculating the deflection of reinforced concrete components (M>M cr ) is used when the effective moment of inertia of the section is used, M represents the bending moment shown in the calculated section combination of the steel-concrete composite beam, and M cr It represents the cracking moment of the steel-concrete composite beam in the calculated section, N p represents the prestressing tendon tension, α2 is the conversion factor of the CFRP tendon cross section; Yield bending of steel-concrete composite beam (elastic ultimate bearing capacity) M y =min{M yr , M ys That is, please note that the prestress value N in the above formula p It is recommended to take the initial prestressing force without considering the increment on the prestressing tendons during the elastic stage.

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