Calculation method of flexural bearing capacity of corroded double reinforced concrete beams

Abstract

A method for calculating the bending bearing capacity of the cross section of a corroded double-reinforced concrete beam comprises the following steps: (1) measuring and calculating the basic parameters of the double-reinforced concrete beam before and after corrosion; (2) determining the bending failure mode of the cross section; (3) calculating the bending bearing capacity of the cross section of the corroded double-reinforced concrete beam under different failure modes. The method for calculating the bending bearing capacity of the cross section of a corroded double-reinforced concrete beam provided by the present invention is based on determining the stress state of the tensile and compressive steel bars in the beam during bending failure, and realizes the calculation of the bending bearing capacity of the cross section of the reinforced concrete beam when the tensile and compressive steel bars are corroded to any degree. The highest-order equation to be solved is a quadratic equation, which has the advantages of clear concepts and simple calculations, and is convenient for technicians in this field to quickly and accurately evaluate the bending bearing capacity of the cross section of corroded reinforced concrete components, providing strong support for the safety assessment of in-service reinforced concrete structures.

Description

Technical Field

[0001] The invention belongs to the technical field of civil engineering and construction, and relates to a method for calculating the bending bearing capacity of a normal section of a corroded double-reinforced concrete beam. Background Art

[0002] Under the long-term action of corrosive media in the environment, the steel bars in the concrete structure will corrode. The corrosion of steel bars leads to the degradation of the performance of the concrete structure, causing the premature failure of the concrete structure, and bringing a huge burden to the national economy and social development. Therefore, grasping the evolution law of concrete structure performance has attracted widespread attention from academic and engineering circles at home and abroad.

[0003] To this end, a large number of scholars at home and abroad have explored the bending performance of corroded reinforced concrete beams and proposed a calculation method for their cross-section bending bearing capacity. For example, Jiang Chao et al. (2020, 2021) invented a simplified calculation method for the cross-section bending bearing capacity of corroded single-reinforced concrete beams that can predict the failure mode in advance. This method has a clear concept and simple calculation, but it is only applicable to corroded single-reinforced reinforced concrete beams. However, in actual reinforced concrete structures, reinforced concrete beams usually use double-sided reinforcement, and both tensile and compressive steel bars may corrode. On the one hand, the corrosion of compressive steel bars can lead to a decrease in the yield stress and buckling stress of the compressive steel bars, and on the other hand, it can cause the concrete protective layer in the compression zone to peel off, thereby reducing the cross-section bending bearing capacity of the double-reinforced concrete beam. A practical calculation method for the cross-section bending bearing capacity of reinforced concrete beams that simultaneously considers the corrosion of compressive and tensile steel bars has yet to be developed. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention aims to provide a method for calculating the bending bearing capacity of the positive section of a corroded double-reinforced concrete beam, which can conveniently and accurately calculate the bending bearing capacity of the positive section of a corroded double-reinforced concrete beam under different failure modes.

[0005] The method for calculating the bending bearing capacity of the normal section of a corroded double-reinforced concrete beam provided by the present invention comprises the following steps:

[0006] (1) Measure and calculate the basic parameters of double reinforced concrete beams before and after corrosion:

[0007] The basic parameters of the double reinforced concrete beam before and after corrosion include the section width b, section height h, section effective height h0, thickness of concrete cover in the compression zone c', distance a' from the center line of the compression steel bar to the edge of the compression zone of the section s ; Maximum adjacent uncorroded stirrup spacing s; Concrete strength grade, concrete compressive strength f c , concrete tensile strength f t ; Types of deformed or rounded tensile and compressive reinforcements, average corrosion rate of tensile reinforcement η s , Average corrosion rate of compressive steel bars η's , Initial reinforcement area of ​​tensile steel bars A s0 , initial reinforcement area of ​​compressive steel bars A' s0 , initial diameter of compression steel bar d'0; elastic modulus of uncorroded tension steel bar E s0 , yield strength f y0 , Ultimate Strength f u0 , yield strain ε y0 , strengthening strain ε sh0 , ultimate strain ε u0 ; Elastic modulus of uncorroded compressive steel bar E' s0 , yield strength f' y0 , yield strain ε' y0 ; Calculate the limit I corrosion rate η syb 、Boundary II corrosion rate η shb And limit III corrosion rate η sub ; Calculate the boundary I relative to the height of the compression zone ξ yb , height of relative compression zone of boundary II ξ hb and the relative compression zone height ξ of boundary III ub .

[0008] (2) Determine the bending failure mode of the cross section of the corroded double reinforced concrete beam:

[0009] The bending failure modes of the corroded double reinforced concrete beam positive section include:

[0010] 1) If 0≤η s <η syb , then it is determined to be mode ①;

[0011] 2) If η syb ≤η s <η shb , then it is determined to be mode ②;

[0012] 3) If η shb ≤η s <η sub , then it is determined to be mode ③;

[0013] 4) If η sub ≤η s <1, it is judged as mode ④.

[0014] (3) Calculate the bending bearing capacity of the cross section of the corroded double reinforced concrete beam corresponding to different failure modes:

[0015] The flexural bearing capacity of the normal section of the corroded double-reinforced concrete beam includes: the flexural bearing capacity of the normal section of the corroded double-reinforced concrete beam corresponding to mode ①, mode ②, mode ③ and mode ④.

[0016] In step (1), the section width b, section height h, section effective height h0, thickness of concrete cover in compression zone c', distance a' from the center line of compression steel bar to the edge of compression zone of section s , the maximum adjacent uncorroded stirrup spacing s, concrete strength grade, concrete compressive strength f c , concrete tensile strength f t , the types of deformed or round tensile and compressive reinforcements, and the average corrosion rate of tensile reinforcement η s , Average corrosion rate of compressive steel bars η' s , Initial reinforcement area of ​​tensile steel bars A s0 , initial reinforcement area of ​​compressive steel bars A' s0 , initial diameter of the compressive reinforcement d'0, elastic modulus of the uncorroded tensile reinforcement E s0 , yield strength f y0 , Ultimate Strength f u0 , yield strain ε y0 , strengthening strain ε sh0 , ultimate strain ε u0 , elastic modulus of uncorroded compressive steel bar E' s0 , yield strength f' y0 , yield strain ε' y0 Parameters such as the above can be measured according to the method described in the Technical Standard for Field Testing of Concrete Structures GB / T 50784-2013; if the mechanical properties of uncorroded steel bars are inconvenient to obtain, the values ​​can be obtained by referring to the table of initial mechanical properties of commonly used steel bars, as shown in the following table.

[0017] Initial mechanical properties parameters of common steel bars

[0018]

[0019] The limit I corrosion rate η described in step (1) syb and the relative height of the compression zone ξ yb , the calculation steps are as follows:

[0020] 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off. If η' s <η' s,sp , the concrete cover in the compression zone does not peel off; if η' s ≥η' s,sp , the concrete protective layer in the compression zone has peeled off. ,in is the edge compressive strain of concrete in the compression zone, ε' sc is the strain of corroded compressive reinforcement; where η' s,sp is the critical corrosion rate of concrete cover spalling in the compression zone;

[0021] 2) If η' s <η' s,sp :

[0022] a. Assume that the compressive reinforcement is in the yield stage when the beam is subjected to bending failure, that is, σ' sc =f' yc (η' s ), where σ' sc is the stress of corroded compressive steel bars, f' yc (η' s ) is the corrosion rate η' s Yield stress of corroded compressive reinforcement at 100°;

[0023] b. Let the concrete strain at the edge of the compression zone of the section , stress of corroded tensile reinforcement σ sc =f yc (η s ), strain of corroded tensile reinforcement ε sc =ε yc (η s ), ε cu is the ultimate compressive strain of concrete, and ε cu =0.0033, f yc (η s ) is the corrosion rate η s Yield stress of corroded tensile reinforcement, ε yc (η s ) is the corrosion rate η s Substituting the yield strain of the corroded tensile reinforcement into the deformation coordination equation and the normal section force balance equation, we can obtain the corrosion rate η of the tensile reinforcement. s The quadratic equation of , take 0 ≤ eta s The smaller solution in the range of ≤0.8 is taken as η s The temporary value η s * , if there is no solution within this range, take η s * =0;

[0024] c. Set the temporary value η s * Substituting into the deformation coordination equation, we can get the temporary value of relative compression zone height ξ * , the critical relative compression zone height ξ' corresponding to the yield strain of the compressive reinforcement yb Compare, if ξ * ≥ξ' yb , then assuming that the compressive reinforcement yields correctly, take η syb =η s * , yb =ξ * ; if ξ *<ξ' yb , then it is assumed that the compressive reinforcement is in the elastic stage and the yield error is Substituting into the deformation coordination equation, the strain ε' of the corroded compressive reinforcement related to the relative compressive zone height ξ can be obtained: sc (ξ), ε' sc Substituting (ξ) into the stress-strain relationship of the corroded steel bar, we can get σ' sc =E' sc ε' sc (ξ), where E' sc is the elastic modulus of corroded compressive reinforcement; update the stress expression of compressive reinforcement σ' sc =E' sc ε' sc (ξ), and then resubstituting it into the deformation coordination equation and the normal section force equilibrium equation, we can obtain the corrosion rate η of the tensile reinforcement. s The linear equation of one variable ( * ), take 0≤η s The smaller solution in the range of ≤0.8 is taken as η syb , if there is no solution within this range, take η syb =0, the obtained η syb Substituting into the deformation coordination equation, we can obtain ξ yb ;

[0025] If η' s ≥η' s,sp :

[0026] Let σ' sc =f' b (η' s ), σ sc =f yc (η s ), ε sc =ε yc (η s ), where f' b (η' s ) is the corrosion rate η' s Substituting the actual yield or buckling stress of the compressive reinforcement into the deformation coordination equation and the normal section force equilibrium equation, we can obtain the corrosion rate η of the tensile reinforcement. s The quadratic equation of , take 0≤eta s The smaller solution in the range of ≤0.8 is taken as η syb , if there is no solution within this range, take η syb =0, the obtained η syb Substituting into the deformation coordination equation, we can obtain ξ yb .

[0027] The limit II corrosion rate η described in step (1) shband the relative height of the compression zone ξ hb , the calculation steps are as follows:

[0028] 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off;

[0029] 2) If η' s <η' s,sp :

[0030] a. Assuming that the beam is subjected to bending failure in the normal section, σ' sc =f' yc (η' s );

[0031] b. Order σ sc =f yc (η s ), ε sc =ε shc (η s ), where ε shc (η s ) is the corrosion rate η s Substituting the tensile reinforcement strengthening strain into the deformation coordination equation and the normal section force balance equation, we can obtain the tensile reinforcement corrosion rate η s The quadratic equation of ( * ), take η syb ≤η s ≤η s,cr The smaller solution in the range is taken as η s The temporary value η s * , if there is no solution within this range, take η s * =η syb , where η s,cr is the critical corrosion rate at which the yield platform disappears. For accelerated corrosion, η of deformed steel bars and plain round steel bars is s,cr can be taken as 0.3 and 0.15 respectively. For natural corrosion, the η of deformed steel bars and plain round steel bars is s,cr can be taken as 0.2 and 0.1 respectively;

[0032] c. Set the temporary value η s * Substituting into the deformation coordination equation, we can get the temporary value of relative compression zone height ξ * , if ξ * ≥ξ' yb , take η shb =η s * , hb =ξ * ; if ξ* <ξ' yb , let σ' sc =E' sc ε' sc (ξ), and then resubstituting it into the deformation coordination equation and the normal section force equilibrium equation, we can obtain the corrosion rate η of the tensile reinforcement. s The quadratic equation of ( * ), take η syb ≤η s ≤η s,cr The smaller solution in the range is taken as η shb , if there is no solution within this range, take η shb =η syb , the obtained η shb Substituting into the deformation coordination equation, we can obtain ξ hb ;

[0033] If η' s ≥η' s,sp :

[0034] Let σ' sc =f' b (η' s ), σ sc =f yc (η s ), ε sc =ε shc (η s ), and then substitute the deformation coordination equation and the normal section force balance equation to obtain the corrosion rate η of the tensile reinforcement. s The quadratic equation of ( * ), take η syb ≤η s ≤η s,cr The smaller solution in the range is taken as η shb , if there is no solution within this range, take η shb =η syb , the obtained η shb Substituting into the deformation coordination equation, we can obtain ξ hb .

[0035] The limit III corrosion rate η described in step (1) sub and the relative height of the compression zone ξ ub , the calculation steps are as follows:

[0036] 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off;

[0037] 2) If η' s <η' s,sp :

[0038] a. Assuming that the beam is subjected to bending failure in the normal section, σ' sc =f' yc (η' s );

[0039] b. Order σ sc =f uc (η s ), ε sc =ε suc (η s ), where f uc (η s ) is the corrosion rate η s The ultimate stress of the tensile reinforcement at suc (η s ) is the corrosion rate η s Substituting the ultimate strain of the tensile reinforcement into the deformation coordination equation and the normal section force balance equation, we can obtain the corrosion rate η of the tensile reinforcement. s A quadratic equation of one variable, taking η shb ≤η s The smaller solution in the range of ≤0.8 is taken as η s The temporary value η s * , if there is no solution within this range, take η s * =0.8;

[0040] c. Set the temporary value η s * Substituting into the deformation coordination equation, we can get the temporary value of relative compression zone height ξ * , if ξ * ≥ξ' yb , take η sub =η s * , ub =ξ * ; if ξ * <ξ' yb , let σ' sc =E' sc ε' sc (ξ), and then resubstituting it into the deformation coordination equation and the normal section force equilibrium equation, we can obtain the corrosion rate η of the tensile reinforcement. s A quadratic equation of one variable, taking η shb ≤η s The smaller solution in the range of ≤0.8 is taken as η sub , if there is no solution within this range, take η sub =0.8, the obtained η sub Substituting into the deformation coordination equation, we can obtain ξ ub ;

[0041] If η' s ≥η' s,sp :

[0042] Let σ' sc =f' b (η' s ), ε sc =ε suc (η s ), and then substitute the deformation coordination equation and the normal section force balance equation to obtain the corrosion rate η of the tensile reinforcement. s The quadratic equation of one variable, η shb ≤η s The smaller solution in the range of ≤0.8 is taken as η sub , if there is no solution within this range, take η sub =0.8.

[0043] The calculation steps of the bending bearing capacity of the normal section of the corroded double reinforced concrete beam corresponding to mode ① described in step (3) are as follows:

[0044] 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off;

[0045] 2) If η' s <η' s,sp :

[0046] a. Assuming that the beam is subjected to bending failure in the normal section, σ' sc =f' yc (η' s );

[0047] b. Order Substituting into the deformation coordination equation, we can get the strain ε of the corroded steel bar related to the relative compression zone height ξ sc (ξ);

[0048] c. The strain of the corroded steel bar ε sc Substituting (ξ) into the stress-strain relationship of the corroded steel bar, we can obtain the stress σ of the corroded steel bar related to the relative height ξ of the compression zone. sc =E sc ε sc (ξ);

[0049] d. The stress of corroded steel bar σ sc Substitute (ξ) into the normal section force balance equation to obtain a quadratic equation about ξ. Solve the quadratic equation and take 0.8≥ξ>ξ yb The larger solution in the range is taken as the temporary value of ξ * ;

[0050] ei) If ξ * ≥ξ'yb , let ξ=ξ * ii) If ξ * <ξ' yb , update σ' sc =E' sc ε' sc (ξ), substitute it into the normal section force balance equation, and obtain a quadratic equation about ξ. Solve the quadratic equation and take 0.8≥ξ>ξ yb The larger solution in the range is taken as the value of ξ;

[0051] f. Substitute ξ into the normal section bending moment equilibrium equation to calculate the normal section bending bearing capacity of the corroded double reinforced concrete beam corresponding to mode ①;

[0052] If η' s ≥η' s,sp :

[0053] Let σ' sc =f' b (η' s ), σ sc =E sc ε sc (ξ), substitute it into the normal section force balance equation, and obtain a quadratic equation about ξ. Solve the quadratic equation and take 0.8≥ξ>ξ yb The larger solution in the range is taken as the value of ξ, and ξ is substituted into the moment equilibrium equation of the positive section to calculate the bending bearing capacity of the positive section of the corroded double-reinforced concrete beam corresponding to mode ①.

[0054] The calculation steps of the bending bearing capacity of the normal section of the corroded double reinforced concrete beam corresponding to mode ② described in step (3) are as follows:

[0055] 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off;

[0056] 2) If η' s <η' s,sp :

[0057] a. Assuming that the beam is subjected to bending failure in the normal section, σ' sc =f' yc (η' s );

[0058] b. Let σ sc =f yc (η s ), and then substitute it into the normal section force balance equation to obtain a linear equation about ξ, which can directly calculate the relative compression zone height ξ;

[0059] ci) If ξ *≥ξ' yb , let ξ=ξ * ii) If ξ * <ξ' yb , update σ' sc =E' sc ε' sc (ξ), Substitute the deformation coordination equation and the normal section force balance equation to obtain a quadratic equation about ξ. Solve the quadratic equation and take ξ yb ≥ξ>ξ hb The larger solution in the range is taken as the value of ξ;

[0060] d. Substitute ξ into the normal section moment equilibrium equation to calculate the normal section bending bearing capacity of the corroded double reinforced concrete beam corresponding to mode ②;

[0061] If η' s ≥η' s,sp :

[0062] Let σ' sc =f' b (η' s ), σ sc =f yc (η s ), substitute it into the normal section force equilibrium equation, obtain a linear equation about ξ, solve the value of ξ, substitute ξ into the normal section bending moment equilibrium equation, and calculate the normal section bending bearing capacity of the corroded double reinforced concrete beam corresponding to mode ②.

[0063] The calculation steps of the bending bearing capacity of the normal section of the corroded double reinforced concrete beam corresponding to mode ③ described in step (3) are as follows:

[0064] 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off;

[0065] 2) If η' s <η' s,sp :

[0066] a. Assuming that the beam is subjected to bending failure in the normal section, σ' sc =f' yc (η' s );

[0067] b. Order Substituting into the deformation coordination equation, we can get the strain ε of the corroded steel bar related to the relative compression zone height ξ sc (ξ);

[0068] c. The strain of the corroded steel bar ε scSubstituting (ξ) into the stress-strain relationship of the corroded steel bar, we can obtain the stress σ of the corroded tensile steel bar related to the relative compressive zone height ξ. sc (ξ)=f yc (η s )+E shc (η s )(ε sc (ξ)-ε shc (η s ));

[0069] d. The stress of corroded steel bar σ sc Substitute (ξ) into the normal section force balance equation to obtain a quadratic equation about ξ. Solve the quadratic equation and take ξ hb ≥ξ>ξ ub The larger solution in the range is taken as the temporary value of ξ * ;

[0070] ei) If ξ * ≥ξ' yb , let ξ=ξ * ii) If ξ * <ξ' yb , update σ' sc =E' sc ε' sc (ξ), substitute it into the normal section force balance equation, and obtain a quadratic equation about ξ. Solve the quadratic equation and take ξ hb ≥ξ>ξ ub The larger solution in the range is taken as the value of ξ;

[0071] f. Substitute ξ into the normal section moment equilibrium equation to calculate the normal section bending bearing capacity of the corroded double reinforced concrete beam corresponding to mode ③;

[0072] If η' s ≥η' s,sp :

[0073] Let σ' sc =f' b (η' s ), σ sc (ξ)=f yc (η s )+E shc (η s )(ε sc (ξ)-ε shc (η s )), substitute into the normal section force balance equation, obtain the quadratic equation about ξ, solve the quadratic equation, and take ξ hb ≥ξ>ξ ubThe larger solution in the range is taken as the value of ξ; ξ is substituted into the positive section bending moment equilibrium equation to calculate the positive section bending bearing capacity of the corroded double reinforced concrete beam corresponding to mode ③.

[0074] The calculation steps of the bending bearing capacity of the normal section of the corroded double reinforced concrete beam corresponding to mode ④ described in step (3) are as follows:

[0075] 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off;

[0076] 2) If η' s <η' s,sp :

[0077] a. Calculate the bending bearing capacity M of the normal section determined by the tensile and compressive reinforcement couples u1 :

[0078] M u1 =min{f′ yc (η′ s )A′ s0 (1-η′ s )(h0-a′ s ),f uc (η s )A s0 (1-η s )(h0-a′ s )};

[0079] b. Calculate the bending bearing capacity M of the normal section determined by concrete u2 =0.292f t bh0 2 ;

[0080] If η' s ≥η' s,sp :

[0081] a. Calculate the bending bearing capacity M of the normal section determined by the tensile and compressive reinforcement couples u1 :

[0082] M u1 =min{f′ b (η′ s )A′ s0 (1-η′ s )(h0-a′ s ),f uc (η s )A s0 (1-η s )(h0-a′ s )};

[0083] b. Calculate the bending bearing capacity M of the normal section determined by concrete u2 =0.292f t b(h0-a' s ) 2 ;

[0084] 3) Calculation mode ④ corresponding to the cross-section bending bearing capacity of the corroded double reinforced concrete beam M u =max{M u1 , M u2}.

[0085] The corrosion rate η of the tensile reinforcement described in step (1) s The linear equation of one variable ( * ) and the quadratic equation ( * ), after the yield strain of the corroded tensile reinforcement and the strengthening strain coefficient (1-1.092η s ) / (1-η s ) is simplified to 1.

[0086] In steps (1) and (3),

[0087] The calculation formula for the critical corrosion rate of the concrete protective layer peeling in the compression zone is:

[0088]

[0089] Among them, w cr is the critical rust expansion crack width of concrete cover peeling in the compression zone. For deformed steel bars, w cr =3.5mm, for round steel bars, w cr =2.5mm; d'0 is the initial diameter of the compression steel bar, c' is the thickness of the concrete cover in the compression zone;

[0090] The calculation formula of the stress-strain relationship of the corroded steel bar is:

[0091]

[0092] The calculation formula for the compressive yield stress of the corroded steel bar is:

[0093]

[0094] The calculation formula for the compressive buckling stress of the corroded steel bar is:

[0095]

[0096] Wherein, μ is the effective length coefficient, μ=1.0;

[0097] The calculation formula for the actual compressive yield or buckling stress of the corroded steel bar is:

[0098] f' b =min{f' yc , f b}

[0099] The calculation formula for the actual compressive yield or buckling strain of the corroded steel bar is:

[0100]

[0101] The calculation formula of the tensile elastic modulus of the corroded steel bar is:

[0102] E' sc =E' s0

[0103] The calculation formula for the tensile yield stress of the corroded steel bar is:

[0104]

[0105] The calculation formula of the tensile limit stress of the corroded steel bar is:

[0106]

[0107] The calculation formula for the tensile yield strain of the corroded steel bar is:

[0108]

[0109] The calculation formula for the tensile strengthening strain of the corroded steel bar is:

[0110]

[0111] The calculation formula for the ultimate tensile strain of the corroded steel bar is:

[0112]

[0113] The calculation formula of the tensile elastic modulus of the corroded steel bar is:

[0114] E sc =E s0

[0115] The calculation formula of the tensile strengthening modulus of the corroded steel bar is:

[0116]

[0117] The calculation formula of the normal section force balance equation is:

[0118] If η' s <η' s,sp :

[0119] α1f c bξh0+σ′ sc A′ s0 (1-η′ s )=σ sc A s0 (1-η s )

[0120] If η' s ≥η' s,sp :

[0121] α1f c bξ(h0-a′ s )+f′ b A′ s0 (1-η′ s )=σ sc A s0 (1-η s )

[0122] Among them, α1 is the equivalent rectangular coefficient. When the concrete strength grade is less than or equal to C50, α1 = 1.0;

[0123] The calculation formula of the normal section bending moment equilibrium equation is:

[0124] If η' s <η' s,sp :

[0125]

[0126] If η' s ≥η' s,sp :

[0127] M u =α1f c b(h0-a′ s ) 2 (ξ-0.5ξ 2 )+f′ b A′ s0 (1-η′ s )(h0-a′ s )

[0128] The deformation coordination equation calculation formula is:

[0129]

[0130] Where β1 is the equivalent rectangular coefficient. When the concrete strength grade is less than or equal to C50, β1 = 0.8; x n is the actual height of the compression zone;

[0131] The calculation formula for the tensile corroded steel bar strain related to the relative compression zone height ξ is:

[0132]

[0133] The calculation formula of the compressive corroded steel bar strain related to the relative compressive zone height ξ is:

[0134]

[0135] The calculation formula for the critical relative compression zone height corresponding to the yield strain of the compression steel bar is:

[0136]

[0137] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0138] By considering the degradation of the mechanical properties of steel bars caused by corrosion, three critical corrosion rates can be accurately calculated through cross-sectional analysis, based on which four failure modes can be distinguished, and the actual stress state of the tensile and compressive steel bars when the cross-sectional bending failure of the beam occurs can be determined, so that the cross-sectional bending failure mode of the corroded double-reinforced concrete beam under a known corrosion rate can be determined, and the cross-sectional bending bearing capacity of the corroded double-reinforced concrete beam under the corresponding mode can be calculated based on this. The method provided by the present invention involves solving a quadratic equation with the highest order, and has the advantages of clear concepts, simple calculations, and strong practicality, which facilitates technicians in this field to quickly and accurately evaluate the cross-sectional bending bearing capacity of corroded reinforced concrete components, and provides strong support for the safety assessment of in-service reinforced concrete structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0139] FIG. 1( a ) is a cross-sectional stress distribution diagram of a corroded double-reinforced concrete beam in the present invention before the concrete protective layer in the compression zone is peeled off.

[0140] FIG. 1( b ) is a diagram showing the equivalent stress distribution of the cross section of the corroded double-reinforced concrete beam before the concrete protective layer in the compression zone of the present invention is peeled off.

[0141] FIG. 1( c ) is a cross-sectional strain distribution diagram of the corroded double-reinforced concrete beam of the present invention before the concrete protective layer in the compression zone is peeled off.

[0142] FIG. 2( a ) is a diagram showing the stress distribution of the cross section of the corroded double-reinforced concrete beam after the concrete protective layer in the compression zone is peeled off.

[0143] FIG. 2( b ) is a diagram showing the equivalent stress distribution of the normal section of the corroded double-reinforced concrete beam after the concrete protective layer in the compression zone of the present invention is peeled off.

[0144] FIG. 2( c ) is a cross-sectional strain distribution diagram of the corroded double-reinforced concrete beam of the present invention after the concrete protective layer in the compression zone is peeled off. DETAILED DESCRIPTION

[0145] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0146] The present invention provides a method for calculating the bending bearing capacity of the normal section of a corroded double-reinforced concrete beam. To facilitate those skilled in the art to implement the present invention, the present invention is further described in detail with reference to embodiments.

[0147] Example:

[0148] A laboratory in Shanghai used the method of accelerated corrosion by electricity to obtain 6 double-reinforced concrete beam specimens with different degrees of corrosion (numbered L11, L12, L13, L21, L22, and L23). Calculate the bending bearing capacity of the normal section of these 6 corroded double-reinforced concrete beams.

[0149] (1) Measurement and calculation of basic parameters of double reinforced concrete beams before and after corrosion

[0150] 1) According to the method described in the Technical Standard for Field Testing of Concrete Structures GB / T 50784-2013, the cross-sections of the six double-reinforced concrete beams are all rectangular, and the cross-section width b, cross-section height h, cross-section effective height h0, thickness of concrete cover in the compression zone c', and distance a' from the center line of the compression steel bar to the edge of the cross-section compression zone are all measured. s , as shown in Table 1; the measured concrete compressive strength f c , concrete tensile strength f t , as shown in Table 1; the average corrosion rate of tensile steel bars was measured s , Average corrosion rate of compressive steel bars η' s , cross-section reinforcement information (based on which the initial tensile reinforcement area A can be calculated s0 and the initial compression reinforcement area A' s0 ), as shown in Table 1; the elastic modulus E of the uncorroded tensile steel bar was measured s0 , yield strength f y0 , Ultimate Strength f u0 , yield strain ε y0 , strengthening strain ε sh0 , ultimate strain ε u0 , elastic modulus of uncorroded compressive steel bar E' s0 , yield strength f' y0 , yield strain ε' y0 As shown in Table 2, the maximum spacing between adjacent unrusted stirrups is s = 150 mm.

[0151] Table 1 Related parameters of corroded double reinforced concrete beam specimens

[0152]

[0153] Table 2 Initial mechanical properties parameters of tensile reinforcement

[0154]

[0155] 2) Calculate the critical corrosion rate and critical relative compression zone height of each beam specimen

[0156] Beam L11:

[0157] a) Calculation of limit I corrosion rate η syb

[0158] Determine whether the concrete cover in the compression zone is peeling off: if the corrosion rate of the compression steel bar is 0, the concrete cover in the compression zone is not peeling off;

[0159] Calculate the critical relative compression zone height ξ' corresponding to the yield strain of the compressive reinforcement yb :

[0160]

[0161] make

[0162] Substituting into the deformation coordination equation, we can get

[0163]

[0164] Assume that when the beam is subjected to bending failure, the compressive reinforcement is in the yield stage, that is, σ' sc =f' yc (η' s ), substituting into the normal section force balance equation, we can obtain

[0165]

[0166] Arranged

[0167]

[0168] Solving for η s = -1.9018 or 0.9945. If there is no solution in the range of 0 to 0.8, it means that the limit I corrosion rate does not exist, and η is taken s * = 0. s * = 0 and substitute it into the deformation coordination equation to obtain the corresponding relative pressure zone height ξ * =0.5214.

[0169] ξ * <ξ' yb , assuming that the compressive reinforcement yields incorrectly, the compressive reinforcement is in the elastic stage, that is

[0170]

[0171] Substituting into the normal section force balance equation, we can obtain

[0172]

[0173] Arranged

[0174]

[0175] Solving for η s = -1.8920 or 0.9946. If there is no solution in the range of 0 to 0.8, it means that the limit I corrosion rate does not exist, and η is taken syb = 0. syb = 0 and substitute it into the deformation coordination equation to obtain the corresponding relative pressure zone height ξ yb =0.5214.

[0176] (Note: If there is a solution in the range 0 to 0.8, take it as η syb ; If there are two solutions, take the smaller value as η syb )

[0177] b) Calculate the limit II corrosion rate η shb

[0178] Only consider 0<η s ≤η s,cr =0.3,

[0179] make

[0180] Substitute the deformation coordination equation to solve the relative height of the compression zone. Assuming that the compression reinforcement is in the yield stage when the beam is subjected to bending failure, that is, σ' sc =f' yc (η' s ), and then substitute it into the normal section force balance equation, we can get

[0181]

[0182] Arranged

[0183] 5.19656η s 2 -4.49118η s -0.04429 = 0

[0184] Solving the problem yields two roots -0.00975 and 0.8740. syb =0<η s <η s,cr = There is no solution within the range of 0.3, that is, take η s * =η syb = 0. s *= 0 and substitute it into the deformation coordination equation to obtain the corresponding relative pressure zone height ξ hb =0.1086.

[0185] ξ * <ξ' yb , assuming that the compressive reinforcement yields incorrectly, the compressive reinforcement is in the elastic stage, that is

[0186]

[0187] Substituting into the normal section force balance equation, we can obtain

[0188]

[0189] Arranged

[0190]

[0191] Solving for η s =0.5871 or 0.1419. syb =0<η s <η s,cr =0.3, take the smaller value, that is, η shb =0.1419. shb =0.1419 Substituting into the deformation coordination equation, we can get the corresponding relative compression zone height ξ hb =0.1740.

[0192] (Note: If in η syb ~η s,cr If there is no solution in the range, it means that for the double reinforced concrete beam with the initial reinforcement, the limit II does not exist, and η shb =η syb )

[0193] c) Calculate the limit III corrosion rate η sub

[0194] make

[0195] Substitute the deformation coordination equation to solve the relative height of the compression zone. Assuming that the compression reinforcement is in the yield stage when the beam is subjected to bending failure, that is, σ' sc =f' yc (η' s ), and then substitute it into the normal section force balance equation, we can get

[0196]

[0197] After sorting, we enter the j and k coefficients of each group and find the solution that satisfies each segment interval. There is no solution, which means that the boundary III does not exist at this time. Take η s * =0.8.s * = 0 and substitute it into the deformation coordination equation to obtain the corresponding relative pressure zone height ξ ub =0.0959.

[0198] ξ * <ξ' yb , assuming that the compressive reinforcement yields incorrectly, the compressive reinforcement is in the elastic stage, that is

[0199]

[0200] Substituting into the normal section force balance equation, we can obtain

[0201]

[0202] After sorting, we enter the j and k coefficients of each group and find the solution that satisfies each segment interval. There is no solution, which means that the boundary III does not exist at this time. Take η sub =0.8. sub = 0 and substitute it into the deformation coordination equation to obtain the corresponding relative pressure zone height ξ ub =0.0959.

[0203] (Note: If in the range η shb ~0.8 has no solution, which means that the limit III does not exist at this time, so take η sub =0.8)

[0204] The calculation steps of the limit corrosion rate and the corresponding relative compression zone height of beams L12, L13, L21, L22 and L23 are similar to those of beam L11. According to the above steps, the limit corrosion rate and the corresponding relative compression zone height of the six corroded double reinforced concrete beams are calculated, as shown in Table 3.

[0205] (2) Determination of the bending failure mode of the cross-section of the corroded double-reinforced concrete beam

[0206] The corrosion rate of the tensile reinforcement of beams L11, L12 and L21 is within the limit I corrosion rate η syb and limit II corrosion rate η shb The bending failure mode of the three corroded double reinforced concrete beams is determined to be mode ②; the corrosion rate of the tensile reinforcement of beams L13, L22 and L23 is within the limit II corrosion rate η shb and limit III corrosion rate η sub The bending failure mode of the three corroded double reinforced concrete beams is determined to be mode ③. Under the limit I, limit II and limit III states, the compressive steel bars are in the elastic stage, that is, when the tensile steel bars are in mode ② to mode ③, the compressive steel bars have not yielded. The failure modes of each beam are shown in Table 3.

[0207] Table 3 Limit corrosion rate and bending failure mode of normal section

[0208]

[0209] (3) Calculation of the bending bearing capacity of the normal section of the corroded double reinforced concrete beam

[0210] 1) Beam L11

[0211] The bending failure mode of the normal section of beam L11 is mode ②, and the calculation steps of its normal section bending bearing capacity are as follows:

[0212] According to the corrosion rate of compressive steel bars η' s =0, it is judged that the concrete cover in the compression zone has not peeled off;

[0213] According to the analysis in step (2), the compressive steel bar is in the elastic stage, that is, σ' sc =E' sc ε' sc (ξ), let Substituting the deformation coordination equation and the normal section force balance equation, we obtain the quadratic equation about ξ:

[0214]

[0215] Arranged

[0216] 39.14153ξ 2 -1.52436ξ-1=0

[0217] Solve for ξ=0.1805 or -0.1415, take ξ yb =0.5214≥ξ>ξ hb The larger solution in the range of =0.1740 is taken as the value of ξ, that is, ξ=0.1805.

[0218] Substitute ξ=0.1805 into the moment equilibrium equation of the normal section to calculate the normal section bending bearing capacity of the corroded double reinforced concrete beam corresponding to mode ②:

[0219]

[0220] 2) Beam L22

[0221] The bending failure mode of the normal section of beam L22 is mode ③, and the calculation steps of its normal section bending bearing capacity are as follows:

[0222] First, the yield stress, ultimate stress, hardening strain, ultimate strain and hardening modulus are obtained as follows:

[0223]

[0224]

[0225]

[0226] ε suc (η s )=0.182×(1-2.0011×0.1356)=0.1326

[0227]

[0228] make Substituting into the deformation coordination equation, we can get ε sc =0.0033×(0.8 / ξ-1), substituting into the stress-strain relationship of the corroded steel bar, we can get

[0229] σ sc =353.720+1424.7443×[0.0033×(0.8 / ξ-1)-0.0125556]

[0230] =331.1298+3.7613 / ξ

[0231] Substituting it into the normal section force balance equation, we can get the following equation about ξ:

[0232]

[0233] Arranged

[0234] 3904.3119ξ 2 +185.8473ξ-101.37685=0

[0235] Solving for ξ=0.1391 or -0.1867. Take ξ hb =0.1409≥ξ>ξ ub =0.0983 is taken as the larger solution, that is, ξ=0.1391. Substituting ξ=0.1391 into the normal section bending moment equilibrium equation, the normal section bending bearing capacity of beam L22 under mode ③ can be obtained:

[0236]

[0237] The calculation steps of the bending capacity of the cross-section of beams L12 and L21 are similar to those of beam L11, and the calculation steps of the bending capacity of the cross-section of beams L13 and L23 are similar to those of beam L22. According to the above steps, the bending capacity of the cross-section of the six corroded double-reinforced concrete beams is calculated, as shown in Table 4.

[0238] Table 4 Test and calculated values ​​of bending bearing capacity

[0239]

[0240] It can be seen from Table 4 that the ratio of the calculated value of the bending bearing capacity to the test value isu,cal / M u,exp The average value is 1.0753, the sample standard deviation is 0.04106, and the coefficient of variation is 0.03818. This shows that the method for calculating the bending bearing capacity of the normal section of the corroded double-reinforced concrete beam provided by the present invention is highly accurate and practical.

[0241] The above-mentioned related explanations and descriptions of the embodiments are for the convenience of those skilled in the art to understand and apply the present invention. It is obvious that those familiar with the art can easily make various modifications to these contents and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above-mentioned related explanations and descriptions of the embodiments. Improvements and modifications made by those skilled in the art based on the disclosure of the present invention without departing from the scope of the present invention should be within the protection scope of the present invention.

Claims

1. A method for calculating the bending bearing capacity of the normal section of a corroded double reinforced concrete beam, characterized in that: Based on the determination of the stress state of the tensile and compressive steel bars in the beam during bending failure, the calculation of the bending bearing capacity of the cross section of the reinforced concrete beam with any degree of corrosion of the tensile and compressive steel bars is realized; including: measuring and calculating the basic parameters of the double-reinforced concrete beam before and after corrosion; determining the bending failure mode of the cross section; calculating the bending bearing capacity of the cross section of the corroded double-reinforced concrete beam under different failure modes; The method comprises the following steps: (1) Measure and calculate the basic parameters of double reinforced concrete beams before and after corrosion; The basic parameters of the double reinforced concrete beam before and after corrosion include the section width b, section height h, effective section height h0, thickness of concrete cover in the compression zone c', distance a' from the center line of the compression steel bar to the edge of the compression zone of the section s ; Maximum adjacent uncorroded stirrup spacing s; Concrete strength grade, concrete compressive strength f c , concrete tensile strength f t ; Types of deformed or rounded tensile and compressive reinforcements, average corrosion rate of tensile reinforcement η s , Average corrosion rate of compressive steel bars η' s , Initial reinforcement area of ​​tensile steel bars A s0 , initial reinforcement area of ​​compressive steel bars A' s0 , initial diameter of compression steel bar d'0; elastic modulus of uncorroded tension steel bar E s0 , yield strength f y0 , Ultimate Strength f u0 , yield strain ε y0 , strengthening strain ε sh0 , ultimate strain ε u0 ; Elastic modulus of uncorroded compressive steel bar E' s0 , yield strength f' y0 , yield strain ε' y0 ; Calculate the limit I corrosion rate η syb 、Boundary II corrosion rate η shb And limit III corrosion rate η sub ; Calculate the boundary I relative to the height of the compression zone ξ yb , height of relative compression zone of boundary II ξ hb and the relative compression zone height ξ of boundary III ub ; (2) Determine the bending failure mode of the normal section of the corroded double reinforced concrete beam; The bending failure modes of the corroded double reinforced concrete beam positive section include: Mode ①: 0≤η s <η syb ; Mode ②: η syb ≤η s <η shb ; Mode ③: η shb ≤η s <η sub ; Mode ④: η sub ≤η s <1; where η s is the average corrosion rate of the tensile longitudinal reinforcement, η syb is the limit I corrosion rate, η shb is the limit II corrosion rate, η sub is the limit III corrosion rate; (3) Calculate the bending bearing capacity of the cross-section of the corroded double-reinforced concrete beam corresponding to different failure modes; The bending bearing capacity of the normal section of the corroded double-reinforced concrete beam includes: the bending bearing capacity of the normal section of the corroded double-reinforced concrete beam corresponding to mode ①, mode ②, mode ③ and mode ④ respectively; The limit I corrosion rate η syb and the relative height of the compression zone ξ yb , the calculation steps are as follows: 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off. If η' s <η' s,sp , the concrete cover in the compression zone does not peel off; if η' s ≥η' s,sp , the concrete protective layer in the compression zone has peeled off. in is the edge compressive strain of concrete in the compression zone, ε' sc is the strain of corroded compressive reinforcement; where η' s,sp is the critical corrosion rate of concrete cover spalling in the compression zone; 2) If η' s <η' s,sp : a. Assume that the compressive reinforcement is in the yield stage when the beam is subjected to bending failure, that is, σ' sc =f' yc (η' s ), where σ' sc is the stress of corroded compressive steel bars, f' yc (η' s ) is the corrosion rate η' s Yield stress of corroded compressive reinforcement at 10000 rpm; b. Let the concrete strain at the edge of the compression zone of the section Corroded tensile steel bar stress σ sc =f yc (η s ), strain of corroded tensile reinforcement ε sc =ε yc (η s ), ε cu is the ultimate compressive strain of concrete, and ε cu =0.0033, f yc (η s ) is the corrosion rate η s Yield stress of corroded tensile reinforcement, ε yc (η s ) is the corrosion rate η s Substituting the yield strain of the corroded tensile reinforcement into the deformation coordination equation and the normal section force balance equation, we can obtain the corrosion rate η of the tensile reinforcement. s The quadratic equation of , take 0≤eta s The smaller solution in the range of ≤0.8 is taken as η s The temporary value η s * If there is no solution within this range, take η s * =0; c. Set the temporary value η s * Substituting into the deformation coordination equation, we can get the temporary value of relative compression zone height ξ * , the critical relative compression zone height ξ' corresponding to the yield strain of the compressive reinforcement yb Compare, if ξ * ≥ξ' yb , then assuming that the compressive reinforcement yields correctly, take η syb =η s * , yb =ξ * ; if ξ * <ξ' yb , then it is assumed that the compressive reinforcement yields incorrectly and is in the elastic stage. Substituting into the deformation coordination equation, the strain ε' of the corroded compressive reinforcement related to the relative compressive zone height ξ can be obtained: sc (ξ), ε' sc Substituting (ξ) into the stress-strain relationship of the corroded steel bar, we can get σ' sc =E' sc ε' sc (ξ), where E' sc is the elastic modulus of corroded compressive reinforcement; update the stress expression of compressive reinforcement σ' sc =E' sc ε' sc (ξ), and then resubstituting it into the deformation coordination equation and the normal section force equilibrium equation, we can obtain the corrosion rate η of the tensile reinforcement. s The linear equation of one variable ( * ), take 0≤η s The smaller solution in the range of ≤0.8 is taken as η syb If there is no solution within this range, take η syb =0, the obtained η syb Substituting into the deformation coordination equation, we can obtain ξ yb ; If η' s ≥η' s,sp : Let σ' sc =f' b (η' s ), σ sc =f yc (η s ), ε sc =ε yc (η s ), where f' b (η' s ) is the corrosion rate η' s Substituting the actual yield or buckling stress of the compressive reinforcement into the deformation coordination equation and the normal section force equilibrium equation, we can obtain the corrosion rate η of the tensile reinforcement. s The quadratic equation of , take 0≤eta s The smaller solution in the range of ≤0.8 is taken as η syb If there is no solution within this range, take η syb =0, the obtained η syb Substituting into the deformation coordination equation, we can obtain ξ yb； The limit II corrosion rate η shb and the relative height of the compression zone ξ hb , the calculation steps are as follows: 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off; 2) If η' s <η' s,sp : a. Assuming that the beam is subjected to bending failure in the normal section, σ' sc =f' yc (η' s ); b. Let ε c t =ε cu , σ sc =f yc (η s ), ε sc =ε shc (η s ), where ε shc (η s ) is the corrosion rate η s Substituting the tensile reinforcement strengthening strain into the deformation coordination equation and the normal section force balance equation, we can obtain the tensile reinforcement corrosion rate η s The quadratic equation of ( * ), take η syb ≤η s ≤η s,cr The smaller solution in the range is taken as η s The temporary value η s * If there is no solution within this range, take η s * =η syb , where η s,cr is the critical corrosion rate at which the yield platform disappears. For accelerated corrosion, η of deformed steel bars and plain round steel bars is s,cr can be taken as 0.3 and 0.15 respectively. For natural corrosion, the η of deformed steel bars and plain round steel bars is s,cr can be taken as 0.2 and 0.1 respectively; c. Set the temporary value η s * Substituting into the deformation coordination equation, we can get the temporary value of relative compression zone height ξ * , if ξ * ≥ξ' yb , take η shb =η s * , hb =ξ * ; if ξ * <ξ' yb , let σ' sc =E' sc ε' sc (ξ), and then resubstituting it into the deformation coordination equation and the normal section force equilibrium equation, we can obtain the corrosion rate η of the tensile reinforcement. s The quadratic equation of ( * ), take η syb ≤η s ≤η s,cr The smaller solution in the range is taken as η shb If there is no solution within this range, take η shb =η syb , the obtained η shb Substituting into the deformation coordination equation, we can obtain ξ hb ; If η' s ≥η' s,sp : Let σ' sc =f' b (η' s ), ε c t =ε cu , σ sc =f yc (η s ), ε sc =ε shc (η s ), and then substitute the deformation coordination equation and the normal section force balance equation to obtain the corrosion rate η of the tensile reinforcement. s The quadratic equation of ( * ), take η syb ≤η s ≤η s,cr The smaller solution in the range is taken as η shb If there is no solution within this range, take η shb =η syb , the obtained η shb Substituting into the deformation coordination equation, we can obtain ξ hb； The limit III corrosion rate η sub and the relative height of the compression zone ξ ub , the calculation steps are as follows: 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off; 2) If η' s <η' s,sp : a. Assuming that the beam is subjected to bending failure in the normal section, σ' sc =f' yc (η' s ); b. Let ε c t =ε cu , σ sc =f uc (η s ), ε sc =ε suc (η s ), where f uc (η s ) is the corrosion rate η s The ultimate stress of the tensile reinforcement at suc (η s ) is the corrosion rate η s Substituting the ultimate strain of the tensile reinforcement into the deformation coordination equation and the normal section force balance equation, we can obtain the corrosion rate η of the tensile reinforcement. s A quadratic equation of one variable, taking η shb ≤η s The smaller solution in the range of ≤0.8 is taken as η s The temporary value η s * If there is no solution within this range, take η s * =0.8; c. Set the temporary value η s * Substituting into the deformation coordination equation, we can get the temporary value of relative compression zone height ξ * , if ξ * ≥ξ' yb , take η sub =η s * , ub =ξ * ; if ξ * <ξ' yb , let σ' sc =E' sc ε' sc (ξ), and then resubstituting it into the deformation coordination equation and the normal section force equilibrium equation, we can obtain the corrosion rate η of the tensile reinforcement. s A quadratic equation of one variable, taking η shb ≤η s The smaller solution in the range of ≤0.8 is taken as η sub If there is no solution within this range, take η sub =0.8, the obtained η sub Substituting into the deformation coordination equation, we can obtain ξ ub ; If η' s ≥η' s,sp : Let σ' sc =f' b (η' s ), σ sc =f uc (η s ), ε sc =ε suc (η s ), and then substitute the deformation coordination equation and the normal section force balance equation to obtain the corrosion rate η of the tensile reinforcement. s The quadratic equation of one variable, η shb ≤η s The smaller solution in the range of ≤0.8 is taken as η sub If there is no solution within this range, take η sub =0.

8.

2. The method for calculating the bending bearing capacity of the normal section of a corroded double reinforced concrete beam according to claim 1 is characterized in that: The calculation steps of the bending bearing capacity of the normal section of the corroded double reinforced concrete beam corresponding to the above-mentioned mode ① are as follows: 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off; 2) If η' s <η' s,sp : a. Assuming that the beam is subjected to bending failure in the normal section, σ' sc =f' yc (η' s ); b. Let ε c t =ε cu Substituting into the deformation coordination equation, we can obtain the corroded steel bar strain ε related to the relative compression zone height ξ sc (ξ); c. The strain of the corroded steel bar ε sc Substituting (ξ) into the stress-strain relationship of the corroded steel bar, we can obtain the stress σ of the corroded steel bar related to the relative height ξ of the compression zone. sc =E sc ε sc (ξ); d. The stress of corroded steel bar σ sc Substitute (ξ) into the normal section force balance equation to obtain a quadratic equation about ξ. Solve the quadratic equation and take 0.8≥ξ>ξ yb The larger solution in the range is taken as the temporary value of ξ * ; ei) If ξ * ≥ξ' yb , let ξ=ξ * ii) If ξ * <ξ' yb , update σ' sc =E' sc ε' sc (ξ), substitute it into the normal section force balance equation, and obtain a quadratic equation about ξ. Solve the quadratic equation and take 0.8≥ξ>ξ yb The larger solution in the range is taken as the value of ξ; f. Substitute ξ into the normal section bending moment equilibrium equation to calculate the normal section bending bearing capacity of the corroded double reinforced concrete beam corresponding to mode ①; If η' s ≥η' s,sp : Let σ' sc =f' b (η' s ), Substitute into the normal section force balance equation to obtain a quadratic equation about ξ. Solve the quadratic equation and take 0.8≥ξ>ξ yb The larger solution in the range is taken as the value of ξ, and ξ is substituted into the moment equilibrium equation of the positive section to calculate the bending bearing capacity of the positive section of the corroded double-reinforced concrete beam corresponding to mode ①.

3. The method for calculating the bending bearing capacity of the normal section of a corroded double reinforced concrete beam according to claim 1 is characterized in that: The calculation steps of the bending bearing capacity of the positive section of the corroded double reinforced concrete beam corresponding to the mode ② are as follows: 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off; 2) If η' s <η' s,sp : a. Assuming that the beam is subjected to bending failure in the normal section, σ' sc =f' yc (η' s ); b. Let σ sc =f yc (η s ), and then substitute it into the normal section force balance equation to obtain a linear equation about ξ, which can directly calculate the relative compression zone height ξ; ci) If ξ * ≥ξ' yb , let ξ=ξ * ii) If ξ * <ξ' yb , update σ' sc =E' sc ε' sc (ξ), Substitute the deformation coordination equation and the normal section force balance equation to obtain a quadratic equation about ξ. Solve the quadratic equation and take ξ yb ≥ξ>ξ hb The larger solution in the range is taken as the value of ξ; d. Substitute ξ into the normal section moment equilibrium equation to calculate the normal section bending bearing capacity of the corroded double reinforced concrete beam corresponding to mode ②; If η' s ≥η' s,sp : Let σ' sc =f' b (η' s ), σ sc =f yc (η s ), substitute it into the normal section force equilibrium equation, obtain a linear equation about ξ, solve the value of ξ, substitute ξ into the normal section bending moment equilibrium equation, and calculate the normal section bending bearing capacity of the corroded double reinforced concrete beam corresponding to mode ②.

4. The method for calculating the bending bearing capacity of the normal section of a corroded double reinforced concrete beam according to claim 1, characterized in that: The calculation steps of the bending bearing capacity of the normal section of the corroded double reinforced concrete beam corresponding to the mode ③ are as follows: 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off; 2) If η' s <η' s,sp : a. Assuming that the beam is subjected to bending failure in the normal section, σ' sc =f' yc (η' s ); b. Order Substituting into the deformation coordination equation, we can get the strain ε of the corroded steel bar related to the relative compression zone height ξ sc (ξ); c. The strain of the corroded steel bar ε sc Substituting (ξ) into the stress-strain relationship of the corroded steel bar, we can obtain the stress σ of the corroded tensile steel bar related to the relative compressive zone height ξ. sc (ξ)=f yc (η s )+E shc (η s )(ε sc (ξ)-ε shc (η s )); d. The stress of corroded steel bar σ sc Substitute (ξ) into the normal section force balance equation to obtain a quadratic equation about ξ. Solve the quadratic equation and take ξ hb ≥ξ>ξ ub The larger solution in the range is taken as the temporary value of ξ * ; ei) If ξ * ≥ξ' yb , let ξ=ξ * ii) If ξ * <ξ' yb , update σ' sc =E' sc ε' sc (ξ), substitute it into the normal section force balance equation, and obtain a quadratic equation about ξ. Solve the quadratic equation and take ξ hb ≥ξ>ξ ub The larger solution in the range is taken as the value of ξ; f. Substitute ξ into the normal section moment equilibrium equation to calculate the normal section bending bearing capacity of the corroded double reinforced concrete beam corresponding to mode ③; If η' s ≥η' s,sp : Let σ' sc =f' b (η' s ), ε c t =ε cu , σ sc (ξ)=f yc (η s )+E shc (η s )(ε sc (ξ)-ε shc (η s )), substitute into the normal section force balance equation, obtain the quadratic equation about ξ, solve the quadratic equation, and take ξ hb ≥ξ>ξ ub The larger solution in the range is taken as the value of ξ; ξ is substituted into the positive section bending moment equilibrium equation to calculate the positive section bending bearing capacity of the corroded double reinforced concrete beam corresponding to mode ③.

5. The method for calculating the bending bearing capacity of the normal section of a corroded double reinforced concrete beam according to claim 1, characterized in that: The calculation steps of the bending bearing capacity of the normal section of the corroded double reinforced concrete beam corresponding to the mode ④ are as follows: 1) According to the corrosion rate of compressive steel bars η' s Determine whether the concrete cover in the compression zone is peeling off; 2) If η' s <η' s,sp : a. Calculate the bending bearing capacity M of the normal section determined by the tensile and compressive reinforcement couples u1 : M u1 =min{f′ yc (or' s )A′ s0 (1-th′ s )(h0-a′ s ),f uc (or s )A s0 (1st) s )(h0-a′ s )}; b. Calculate the bending bearing capacity M of the normal section determined by concrete u2 =0.292f t bh0 2 ; If η' s ≥η' s,sp : a. Calculate the bending bearing capacity M of the normal section determined by the tensile and compressive reinforcement couples u1 : M u1 =min{f′ b (or' s )A′ s0 (1-th′ s )(h0-a′ s ),f uc (or s )A s0 (1st) s )(h0-a′ s )}; b. Calculate the bending bearing capacity M of the normal section determined by concrete u2 =0.292f t b(h0-a' s ) 2 ; 3) Calculation mode ④ corresponding to the cross-section bending bearing capacity of the corroded double reinforced concrete beam M u =max{M u1 , M u2 }.

6. The method for calculating the bending bearing capacity of the normal section of a corroded double reinforced concrete beam according to claim 1, characterized in that: The corrosion rate of tensile reinforcement η s The linear equation of one variable ( * ) and the quadratic equation ( * ), after the yield strain of the corroded tensile reinforcement and the strengthening strain coefficient (1-1.092η s ) / (1-η s ) is simplified to 1.

7. The method for calculating the bending bearing capacity of the normal section of a corroded double reinforced concrete beam according to any one of claims 1 to 5, characterized in that: The calculation formula for the critical corrosion rate of the concrete protective layer peeling in the compression zone is: Among them, w cr is the critical rust expansion crack width of concrete cover peeling in the compression zone. For deformed steel bars, w cr =3.5mm, for round steel bars, w cr =2.5mm; d'0 is the initial diameter of the compression steel bar, c' is the thickness of the concrete cover in the compression zone; The calculation formula of the stress-strain relationship of the corroded steel bar is: The calculation formula for the compressive yield stress of the corroded steel bar is: The calculation formula for the compressive buckling stress of the corroded steel bar is: Wherein, μ is the effective length coefficient, μ=1.0; The calculation formula for the actual compressive yield or buckling stress of the corroded steel bar is: f' b =min{f' yc ,f b } The calculation formula for the actual compressive yield or buckling strain of the corroded steel bar is: The calculation formula of elastic modulus of corroded compressive steel bar is: AND' sc =It's s0 The calculation formula for the tensile yield stress of the corroded steel bar is: The calculation formula of the tensile limit stress of the corroded steel bar is: The calculation formula for the tensile yield strain of the corroded steel bar is: The calculation formula for the tensile strengthening strain of the corroded steel bar is: The calculation formula for the ultimate tensile strain of the corroded steel bar is: The calculation formula of the tensile elastic modulus of the corroded steel bar is: AND sc =And s0 The calculation formula of the tensile strengthening modulus of the corroded steel bar is: The calculation formula of the normal section force balance equation is: If η' s <η' s,sp : a1f c bξh0+σ′ sc A′ s0 (1-th′ s )=s sc A s0 (1st) s ) If η' s ≥η' s,sp : a1f c bξ(h0-a′ s )+f′ b A′ s0 (1-th′ s )=s sc A s0 (1st) s ) Among them, α1 is the equivalent rectangular coefficient. When the concrete strength grade is less than or equal to C50, α1 = 1.0; The calculation formula of the normal section bending moment equilibrium equation is: If η' s <η' s,sp : If η' s ≥η' s,sp : M u =α1f c b(h0-a′ s ) 2 (ξ-0.5ξ 2 )+f′ b A′ s0 (1-th′ s )(h0-a′ s ) The deformation coordination equation calculation formula is: Where β1 is the equivalent rectangular coefficient. When the concrete strength grade is less than or equal to C50, β1 = 0.8; x n is the actual height of the compression zone; The calculation formula for the tensile corroded steel bar strain related to the relative compression zone height ξ is: The calculation formula of the compressive corroded steel bar strain related to the relative compressive zone height ξ is: The calculation formula for the critical relative compression zone height corresponding to the yield strain of the compression steel bar is:

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